National Curriculum Statement (NCS)
ISINDEBELE MATHEMATICS
Curriculum and Assessment
Policy Statement
Foundation Phase
Grade 1-3
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ISITATIMENDE SOMTHETHO-KAMBISO
WEKHARIKHYULAMU NOKUHLOLA
AMAGREYIDI 1-3
IIMBALO
CAPS
ISIGABA ESISISEKELO AMAGREYIDI 1-3
DISCLAIMER
In view of the stringent time requirements encountered by the Department of Basic Education to effect the necessary editorial changes and layout
to the Curriculum and Assessment Policy Statements and the supplementary policy documents, possible errors may occur in the said documents
placed on the official departmental websites.
There may also be vernacular inconsistencies in the language documents at Home-, First and Second Additional Language levels which have
been translated in the various African Languages. Please note that the content of the documents translated and versioned in the African Lan-
guages are correct as they are based on the English generic language documents at all three language levels to be implemented in all four school
phases.
If any editorial, layout or vernacular inconsistencies are detected, the user is kindly requested to bring this to the attention of the Department of
Basic Education.
E-mail: capslangcomments@dbe.gov.za or fax (012) 328 9828
Department of Basic Education
222 Struben Street
Private Bag X895
Pretoria 0001
South Africa
Tel: +27 12 357 3000
Fax: +27 12 323 0601
120 Plein Street Private Bag X9023
Cape Town 8000
South Africa
Tel: +27 21 465 1701
Fax: +27 21 461 8110
Website: http://www.education.gov.za
© 2011 Department of Basic Education
Isbn: 978-1-4315-0451-0
Design and Layout by: Ndabase Printing Solution
Printed by: Government Printing Works
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
FOREWORD by the minister
Our national curriculum is the culmination of our efforts over a period of seventeen
years to transform the curriculum bequeathed to us by apartheid. From the start of
democracy we have built our curriculum on the values that inspired our Constitution
(Act 108 of 1996). The Preamble to the Constitution states that the aims of the
Constitution are to:
• heal the divisions of the past and establish a society based on democratic
values, social justice and fundamental human rights;
• improve the quality of life of all citizens and free the potential of each person;
• lay the foundations for a democratic and open society in which government is
based on the will of the people and every citizen is equally protected by law;
and
• build a united and democratic South Africa able to take its rightful place as a sovereign state in the family of
nations.
Education and the curriculum have an important role to play in realising these aims.
In 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience
of implementation prompted a review in 2000. This led to the first curriculum revision: the Revised National Curriculum
Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).
Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National
Curriculum Statement (2002) and the National Curriculum Statement Grades 10-12 to produce this document.
From 2012 the two National Curriculum Statements, for Grades R-9 and Grades 10-12 respectively, are combined
in a single document and will simply be known as the National Curriculum Statement Grades R-12. The National
Curriculum Statement for Grades R-12 builds on the previous curriculum but also updates it and aims to provide
clearer specification of what is to be taught and learnt on a term-by-term basis.
The National Curriculum Statement Grades R-12 represents a policy statement for learning and teaching in South
African schools and comprises of the following:
(a) Curriculum and Assessment Policy Statements (CAPS) for all approved subjects listed in this document;
(b) National policy pertaining to the programme and promotion requirements of the National Curriculum Statement
Grades R-12; and
(c) National Protocol for Assessment Grades R-12.
MRS ANGIE MOTSHEKGA, MP
MINISTER OF BASIC EDUCATION
CAPS
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
OKUMUMETHWEKO
ISIGABA 1: ISINGENISO BEGODU NESENDLALELO............................................................................................. 3
1.1 Isendlalelo. ....................................................................................................................................................... 3
1.2 Umbono-mazombe........................................................................................................................................... 3
1.3 Iminqopho evamileko yekharikhyulamu yeSewula Afrika . ....................................................................... 4
1.4 Ukwabiwa kwesikhathi.................................................................................................................................... 6
1.4.1 IsiGaba esisiSekelo................................................................................................................................. 6
1.4.2 IsiGaba esiPhakathi................................................................................................................................. 6
1.4.3 IsiGaba esiPhakamileko.......................................................................................................................... 7
1.4.4 AmaGreyidi 10-12.................................................................................................................................... 7
ISIGABA 2: IHLATHULULO, IMINQOPHO, AMAKGHONO NOKUMUMETHWEKO................................................ 8
2.1 Isingeniso......................................................................................................................................................... 8
2.2 Ziyini iimbalo?.................................................................................................................................................. 8
2.3 Iinhloso Ezinqophileko ................................................................................................................................... 8
2.4 Amakghono Anqophileko. .............................................................................................................................. 8
2.5 Iminqopho yeengaba zokumumethweko....................................................................................................... 9
2.6 Ukwabiwa kwesikhathi sokumumethweko ngokweengaba....................................................................... 10
2.7 Iimbalo esiGabeni esisiSekelo:. ................................................................................................................... 11
2.7.1 Imihlahlandlela etjhukunyeziweko yokuphatha ikumba yokufundela..................................................... 11
2.7.2 Abafundi abaneenqabo ekufundeni iimbalo . ........................................................................................ 13
2.7.3 Iimbalo zehloko...................................................................................................................................... 13
2.8 IGreyidi R........................................................................................................................................................ 13
2.9 Iinsetjenziswa Eziphakanyisiweko: Itlasi leeMbalo lesiGaba EsisiSekelo............................................... 16
ISIGABA 3: UKUNQOPHISA NOKUHLATHULULA OKUMUMETHWEKO............................................................. 17
3.1 Isingeniso ...................................................................................................................................................... 17
3.2 Isenzo sokunqophisa iragelo phambili kilokho okumumethweko............................................................ 17
1. Iinomboro, ama-opharetjhini nobudlelwano................................................................................................. 18
2. Amaphetheni, amafanktjhini ne-aljibhra....................................................................................................... 24
3. Isikhala nobujamo (ijiyometrhi)..................................................................................................................... 25
4. Ukumeda...................................................................................................................................................... 28
5. Ukuphatha idatha......................................................................................................................................... 34
3.3 Ihlathululo Lokumumethweko . .................................................................................................................... 36
CAPS 1
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.4 Ukulandelanisa nokuhlela okuMumethweko............................................................................................... 36
3.4.1 Umbonomazombe we Greyidi yoku-1ngeThemu.......................................................................................................40
3.4.2 Umbonomazombe weGreyidi yesi-2 ngeThemu..................................................................................... 56
3.4.3 Umbonomazombe we Greyidi yesi- 3 ngeThemu................................................................................... 73
3.5 AMANOTHI WOKUTLHADLHULA NEMIHLAHLANDLELA YOKUFUNDISA . ............................................ 92
3.5.1 Ihlathululo Yokumumethweko eGreyidini yoku-1. ................................................................................... 93
3.5.2 Ihlathululo Yokumumethweko Egreyidini Yesi-2.................................................................................... 212
3.5.3 Ihlathululo Yokumumethweko eGreyidini yesi-3.................................................................................... 342
ISAGABA 4: UKUHLOLA. ...................................................................................................................................... 489
4.1 Isingeniso..................................................................................................................................................... 489
4.2 Ukuhlola okungakahleleki nanyana ukuhlola kwangamalanga ............................................................ 489
4.3 Ukuhlola okuhlelekileko.............................................................................................................................. 489
4.4 Ihlelo lokuhlola okuhlelekileko................................................................................................................... 490
4.5. Ukurekhoda nokubika. ................................................................................................................................ 491
4.6 Ukulinganisa ukuhlola................................................................................................................................. 491
4.7 Okuvamileko................................................................................................................................................. 491
4.8 Iimbonelo zamathaski wokuhlola zamagreyidi woku-1 ukuya ku-3........................................................ 492
2 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISIGABA 1: ISINGENISO BEGODU NESENDLALELO
1.1 Isendlalelo
IsiTatimende seKharikhyulamu yeliZweloke amaGreyidi R - 12 (TKZ) sendlala umthetho-kambiso wekharikhyulamu
nokuhlola emkhakheni wezefundo.
Ukuthuthukisa ukusetjenziswa kwaso, isiTatimende seKharikhyulamu yeliZweloke satjhugululwa, amatjhuguluko la
azokuthoma ukusetjenziswa ngenyanga kaTjhirhweni ngomnyaka we-2012. Kwenziwa umtlolo owodwa opheleleko
womThetho-kambiso weKharikhyulamu nokuHlola esifundweni ngasinye ukujamiselela iinTatimende zeemFundo,
imiHlahlandlela yamaHlelo wokuFunda kanye nemiHlahlandlela yokuHlola iimFundo emaGreyidi R - 12.
1.2 Umbonomazombe
(a) IsiTatimende seKharikhyulamu yeliZweloke samaGreyidi R - 12 (sangoTjhirhweni we-2012) sijamele
isitatimende somThetho-kambiso sokufunda nokufundisa eenkolweni zeSewula Afrika begodu simumethe
okulandelako:
(i) IinTatimende zomThetho-kambiso weKharikhyulamu nokuHlola zaleso naleso sifundo sesikolo
esiphasisweko
(ii) Umtlolo womThetho-kambiso, iNational policy pertaining to the programme and promotion requirements
of the National Curriculum Statement Grades R - 12; kanye no
(iii) Mtlolo womThetho-kambiso, iNational Protocol for Assessment Grades R - 12 (kaTjhirhweni 2012)
(b) IsiTatimende seKharikhyulamu yeliZweloke samaGreyidi R - 12 (sikaTjhirhweni 2011 sijamiselela iintatimende
zekharikhyulamu zelizweloke ezimbili zanje, ezibizwa
(i) IsiTatimende seKharikhyulamu esiBuyekeziweko amaGreyidi R - 9, Government Gazette No. 23406
yamhlana amalanga ama--31 kuMrhayili 2002, begodu ne-
(ii) IsiTatimende seKharikhyulamu seLizwe Loke amaGreyidi 10 - 12 Government Gazettes, No. 25545
yahlana amalanga asi- 6 October 2003 and No. 27594 yamhlana amalanga ali-17 kuMrhayili 2005.
(c) Iintatimende zekharikhyulamu yelizweloke eziseengatjaneni (a) no (b) ngehla, zimumethe imitlolo yemithetho-
kambiso elandelako esuswe beyajanyiselelwa siTatimende seKharikhyulamu yeliZweloke samaGreyidi 10 - 12
(kuTjhirhweni 2012) ngesikhathi seminyaka we-2012-2014.
(i) IinTatimende zeemFundo, imiHlahlandlela yamaHlelo wokuFundo begodu nemihlahlandlela yokuHlola
iimFundo emaGreyidi R-9 nemaGreyidi 10-12 ;
(ii) Umtlolo womthetho-kambiso, iNational Policy on assessment and qualifications for schools in the
General Education and Training Band, egadangiswe kuGovernment Notice No. 124 ku Government
Gazette No. 29626 yamhlana amalanga ali- 12 kuMhlolanja 2007;
(iii) Umtlolo womthetho-kambiso, iNational Senior Certificate: A qualification at Level 4 on the National
Qualifications Framework (NQF), egadangiswe kuGovernment Gazette No.27819 yamhlana amalanga
ama- 20 kuVelabahlinze 2005;
CAPS 3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
(iv) Umtlolo womthetho-kambiso, i-addendum to the policy document, the National Senior Certificate: A
qualification at Level 4 on the National Qualifications Framework (NQF), regarding learners with special
needs, owagadangiswa kuGovernment Gazette, No.29466 yamhlana amalanga ali-11 kuNobayeni
2006, ungeniswe emtlolweni womthetho-kambiso, iNational policy pertaining to the programme and
promotion requirements of the National Curriculum Statement emaGreyidini R - 12; begodu
(v) Umtlolo womthetho-kambiso, i-addendum to the policy document, the National Senior Certificate: A
qualification at Level 4 on the National Qualifications Framework (NQF), regarding the National Protocol
for Assessment (emaGreyidini R - 12), ogadangiswe kuGovernment Notice No.1267 kuGovernment
Gazette No. 29467 ymhlana amalanga ali-11 kuNobayeni 2006.
(d) Umtlolo womthetho-kambiso, iNational policy pertaining to the programme and promotion requirements of
the National Curriculum Statement Grades R - 12, begodu neengaba zesiTatimende somThetho-kambiso
weKharikhyulamu nokuHlola njengombana zifakwe ezahlukweni 2, 3 begodu 4 zomtlolo lo eziphathelene
nemigomo namazinga wesiTatimende seKharikhyulamu seLizwe Loke emaGreyidini R - 12. Ngakhoke,
ngokuya ngokwesection 6A ye South African Schools Act, 1996 (Act No. 84 of 1996,) yakha isendlalelo
sokobana uNgqongqotjhe weFundo esiSekelo abonelele isilinganiso samazinga nemiphumela kanye
nekambiso yokuhlola umsebenzi womntwana bona ibe khona eenkolweni zomphakathi nalezo ezizijameleko.
1.3 Iminqopho evamileko yekharikhyulamu yeSewula Afrika
(a) IsiTatimende seKharikhyulamu yeliZweloke samaGreyidi R - 12 sethula lokho okungathathwa njengelwazi,
amakghono namagugu okumele kufundwe eenkolweni zeSewula Afrika. Ikharikhyulamu le inqophe
ukuqinisekisa bonyana abantwana bazuza bebasebenzise ilwazi namakghono ngeendlela ezizwisekako
emaphilweni wabo. Ngalokho, ikharikhyulamu ithuthukisa umqondo wokubuthelela ilwazi ebujameni
obujayelekileko, ngesikhathi atjheja eembophweni zephasi.
(b) IsiTatimende seKharikhyulamu yeliZweloke amaGreyidi R - 12 sifeza iminqopho yoku:
• hlomisa abafundi, ngaphandle kokutjheja ibhoduluko lezokuhlalisana-nezomnotho, ubulili, ikghono
lezomzimba nofana lezengqondo, amakghono namagugu adingekako ukuzanelisa, begodu
nokuzibandakanya okuzwisisekako emphakathini njengabahlali benarha etjhaphulukileko;
• enza ifundo yamazinga aphezulu ifinyeleleke;
• enza kube lula bonyana abafundi basuke emazikweni wezefundo baye emisebenzini; begodu
• nikela abaqatjhi ngephrofayili eyaneleko yamakghono womfundi.
(c) IsiTatimende seKharikhyulamu yeliZweloke amaGreyidi R - 12 sisekelwe eenkambisweni ezilandelako:
• Ukutjhuguluka kwezokuhlalisana: ukuqinisekisa bonyana ukungalingani kwezefundo kwesikhathi
esidlulileko kwalungiswa nokuthi amathuba alinganako wezefundo anikelwe zoke iingaba zesintu.
• Ukufunda ngomdlandla nangelihlo elihlabako: ukukhuthaza indlela yokufunda ngelihlo elihlabako
nelinomdlandla, kunokobana kubanjwe izinto ngehloko ngaphandle kokuzizwisisa.
• Ilwazi namakghono asezingeni eliphakamileko: iimfuneko ezimbalwa zelwazi namakghono okufanele
zifunyanwe kileyo naleyogreyidi zibekiwe begodu zibekwe emazingeni aphakamileko, afunyanekako kizo
zoke iimfundo
4 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukuragela phambili: okumumethweko nobujamo baleyo naleyo greyidi kutjengisa ukuragela phambili
ukusukela kokulula ukuya kokubudisi.
• Amalungelo wobuntu, ukufaka koke, ubulungiswa bezebhoduluko nokuhlalisana: ukufaka imigomo
yobulungiswa kezokuhlalisana, kezebhoduluko begodu namalungelo wabantu njengombana
kuhlathululiwe kumThetho-sisekelo weSewula Afrika. IsiTatimende seKharikhyulamu yeliZweloke
amaGreyidi 10 – 12 sitjhetjha khulu izinto ezifana nokutlhaga, ukungafani, ukungalingani, ubuhlanga,
ilimi, iminyaka, abaphila nokukhubazeka begodu namanye amatshwayo.
• Ukukarekela amahlelo welwazi lendabuko: ukuthabela umlando onothileko wenarha namagugu wenarha
le njengezinto eziqakathekileko ukunothisa amagugu amumethwe emThethweni-sisekelo; begodu
• Ukuthembeka, ikhwalithi nekghono: ukunikela ifundo emadanisekako ngekhwalithi, ububanzi
nangokudepha kwefundo yakezinye iinarha.
(d) IsiTatimende seKharikhyulamu yeliZweloke amaGreyidi R–12 sinqophe ukukhiqiza abafundi abakwazi uku:
• bona nokurarulula imiraro nokuthatha iinqunto kusetjenziswa ukucabanga ngelihlo elibukhali
nelokuzitlamela ;
• sebenzisana ngepumelelo ngokuzijamela begodu nabanye njengamalunga wesiqhema ;
• hlela nokuziphatha begodu nokuphatha imisebenzi yabo ngokuziphendulela nangepumelelo ;
• buthelela, ukutsenga, ukuhlela bese bahlaziya ilwazi ngelihlo lokuhlaba ;
• khulumisana ngepumelelo basebenzisa amakghono wokubonwako/ wokubukelwako, wamatshwayo
begodu /nanyana welimi ngeendlela ezinengi
• sebenzisa isayensi nethekhnoloji ngepumelelo nangokucabangisisa begodu batjengise, ukuziphendulela
ebhodulukweni neempilweni zabanye; noku
• Tjengisa ukuzwisisa iphasi bonyana linamahlelo anetjhebiswano ngokuyelela bonyana ukurarulula imiraro
akwenzeki kukodwa ngeqadi.
(e) Ukuhlanganisa imihlobo ehlukahlukeneko yabafundi kufanele kube mgogodlha womkhandlu, wokuhlela
begodu nokufundisa kileso naleso sikolo. Lokhu kungenzeka kwaphela lokha abotitjhere boke banokuzwisisa
okuhluzekileko bokobana iinqabo zokufunda zingalemukwa bezilungiswe bunjani, begodu ukuhlanganisa
kungahlelelwa bunjani
Okuqakathekileko ngokuhlanganisa imihlobo ehlukahlukeneko yabafundi kuqinisekisa bonyana iinqabo
ziyabonwa bezitjhejwa ngiyo yoke imikhandlu efaneleko ehlangana nomphakathi wesikolo, okufaka hlangana
abotitjhere, iinQhema eziSekelako eziNzinze kumaDistrigi, iinQhema eziSekelako eziseZingeni leenHlangano,
ababelethi neenKolo eziKhethekileko njengeendawo zemiThombo. Ukulungisa iinqabo ngetlasini, abotitjhere
bafanele basebenzise amaqhinga amanengi wekharikhyulamu afana nalawo afakwe ku- Guidelines for
Inclusive Teaching and Learning (2010) yoMnyango weFundo Sisekelo
CAPS 5
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1.4 Ukwabiwa kwesikhathi
1.4.1 IsiGaba esisiSekelo
(a) Isikhathi sokufundisa esiGabeni-esisiSekelo sitjengisiwe ngenzasi:
IGREYIDI R AMAGREYIDI 1-2 IGREYIDI 3
ISIFUNDO
(AMA-IRI) (AMA-IRI) (AMA-IRI)
ILimi leKhaya 10 7/8 7/8
ILimi lokuThoma lokwEngeza 2/3 3/4
IimBalo 7 7 7
AmaKghono wePilo 6 6 7
• ILwazi lokuThoma (1) (1) (2)
• UbuKghwari bokuTlama (2) (2) (2)
• IsiFundo sokuziThabulula (2) (2) (2)
• UbuYena neHlalakuhle yomuntu qobo lakhe (1) (1) (1)
INANI 23 23 25
(b) Isikhathi sokufundisa samaGreyidi R, 1 no 2 ma-iri ama-23 begodu seGreyidi yesi-3 ma- iri ama-25.
(c) Ama-iri alitjhumi abelwe amalimi emaGreyidini R – 2 bese ama-iri ali-11eGreyidini yesi-3. ILimi leKhaya labelwe
ubunengi bama-iri abu-8 nobuncani bama-iri ali-7 begodu iLimi lokuThoma lokwEngeza labelwe ubuncani
bama-iri ama-2 nobukhulu bama-iri ama-3 emaGreyidini R-2. ILimi leKhaya eGreyidini yesi- 3 labelwe ubunengi
bama-iri- abu-8 nobuncani bama-iri ali-7 begodu iLimi lokuThoma lokwEngeza labelwe ubuncani bama-iri
ama-3 nobunengi bama-iri ama-4.
(d) Kumakghono wePilo iLwazi Lokuthoma labelwe i-iri li-1 emaGreyidini R-2 nama –iri ama-2 njengombana
kutjengiswe ngeembayaneni zeGreyidi yesi-3
1.4.2 IsiGaba esiPhakathi
(a) Isikhathi sokufundisa esiGabeni-esiPhakathi sitjengisiwe ngenzasi:
ISIFUNDO AMA-IRI
ILimi leKhaya 6
ILimi lokuThoma lokweNgeza 5
IimBalo 6
ISayensi Yemvelo neTheknoloji 3,5
ISayensi yokuHlalisana 3
AmaKghono wePilo 4
• UbuKghwari bokuTlama (1,5)
• IsiFundo sokuziThabulula (1)
• UbuYena nokuHlalisana komuntu qobo lakhe (1,5)
INANI 27,5
6 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1.4.3 IsiGaba esiPhakamileko
(a) Isikhathi sokufundisa esiGabeni-esiPhakakamileko sitjengisiwe ngenzasi:
ISIFUNDO AMA-IRI
ILimi leKhaya 5
ILimi lokuThoma lokwEngeza 4
IimBalo 4,5
ISayensi yeMvelo 3
ISayensi yokuHlalisana 3
ITheknoloji 2
ISayensi yezomNotho nokuPhatha 2
UkuziJayeza zePilo 2
UbuKghwari namaSiko 2
INANI 27,5
1.4.4 AmaGreyidi 10 - 12
(a) Isikhathi sokufundisa emaGreyidini 10-12 sitjengisiwe ngenzasi
Isikhathi esabiweko ngeveke
ISIFUNDO
(ama-iri)
I. ILimi leKhaya 4.5
II. ILimi LokuThoma lokweNgeza 4.5
III. IimBalo 4.5
IV. UkuziJayeza zePilo 2
V. Ubuncani bananyana ngiziphi iimfundo ezintathu ezikhethwe 12 (3x4ama-iri)
esiQhemeni B i-Anekstjha B, Amathebula B1-B8 yomtlolo womthetho-
kambiso, iNational policy pertaining to the programme and promotion
requirements of the National Curriculum Statement Grades R – 12,
enqotjhiswe esigabeni sama-28 somtlolo womthetho- kambiso
onikelweko..
INANI 27,5
Isikhathi esabiweko ngeveke singasetjenziselwa kwaphela ubuncani obufunwa ziimfundo zeenTatimende
zeKharikhyulamu yeliZweloke amaGreyidiR-12 (TKZ) njengombana ziveziwe ngehla, begodu angeze
zasetjenziselwa nanyana ngiziphi iimfundo zokungezelele ezingezelelwe erhelweni leemfundo. Lokha umfundi
nakafuna ukungezelela iimfundo, isikhathi esingezelelweko kufanele sabelwe ukufundisa iimfundo lezo.
CAPS 7
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISIGABA 2: IHLATHULULO, IMINQOPHO, AMAKGHONO
NOKUMUMETHWEKO
2.1 Isingeniso
Esahlukweni sesi 2, esiGabeni esisiSekelo isitatimende somgomo wekharikhyulamu yezweloke yokuhlola iimbalo
inikela abotitjhere ihlathululo yeembalo imigomo ethile, amakghono athile, iminqopho yokumumethweko, isisindo
sokumumethweko, iinsetjenziswa ezitjhukumeziweko zesifundo seembalo eemfundweni zesiGaba esisiSekelo,
imihlahlandlela ezitjhukumeziweko yokusekela abafundi abaneenqabo zokufunda iimbalo, iimbalo zehloko
nokuthuthukisa ukufundisa amakghono wolwazi lokubala lwangaphambili ngeGreyidini R.
2.2 Ziyini iimbalo?
Iimbalo lilimi elisebenzisa amasimboli/ amatshwayo/amaphawu nenotheyitjhini ukuhlathulula ubudlelwano
beenomboro, kweJiyomethri neenjamelo zegrafu. Kumisebenzi womuntu okufaka hlangana ukuqala, ukujamisela
nokuphenya amaphetheni nobudlelwana obuqakathekileko ezintweni ezithintekako/ ezibonakala ngamehlo
nesenzeko esiphathelene nokuhlalisana naphakathi kwamabumbeko weembalo ngokwazo. Kuyarhelebha
ukuthuthukisa ikambiso yokomkhumbulo engezelela ilojikhi nokucabanga ngokuhlaba, ngokunemba nokurarulula
imiraro ezakurholela ekuthatheni iinqunto.
2.3 Iinhloso Ezinqophileko
Ukufundisa nokufundwa kweembalo kuhlose ukuthuthukisa okulandelako emfundini:
• Ilemuko lelihlo lokuhlaba lokuthi ubudlelwano bembalo busetjenziswa njani epilweni ephathelene
nezokuhlalisana, ibhoduluko, itjhebiswano lamasiko nokomnotho;
• Ukuzithemba nekghono lokuqalana namtjhana ngibuphi ubujamo beembalo ngaphandle kokuliywa
kukwesaba iimbalo;
• Umoya werhuluphelo nethando leembalo;
• Ukuthokozela ubuhle nokukarisa kweembalo;
• Ukubona bonyana iimbalo ziyingcenye yemisetjenzana umuntu azitlamela yona;
• Umcabango ojulileko wokuzwisisa ukwenza umqondo weembalo ; no
• Ukuthola ilwazi elithile namakghono athlogekako woku:
-- Ukusebenzisa iimbalo eentweni ezithintekako, zokuhlalisana nemiraro yeembalo;
-- Ukufunda okuhlobana nokufundiswako ( isib.ezinye iimfundo) noku;
-- Ragela phambili nokufunda iimbalo.
2.4 Amakghono Anqophileko
Ukuthuthukisa amakghono weembalo aqakathekileko umfundi kufanele:
• athuthukisa ukusebenzisa ilimi lembalo ngefanelo;
• athuthukise ilwazi leenomboro, umqondo nomboro, nokubalisisa namakghono wokwenza;
• afunde ukulalela, ukukhuluma, ukucabanga, ikghono lokusebenza nokurarulula imiraro ngelojikhi
nokusebenzisa ilwazi leembalo alizuzileko;
• akufunda ukurhubhulula , ukuhlaziya, ukujamisela nokurhumutjha ilwazi;
• akufunda ukuveza nokurarulula imiraro; noku
• ukwakha ilemuko lokubaluleka kwendima edlalwa ziimbalo epilweni yamambala, okufaka hlangana
ukuthuthuka komfundi ngokwakhe.
8 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
2.5 Iminqopho yeengaba zokumumethweko
Esigabeni Esisisekelo, iimbalo zithatha iingaba ezihlanu zokumumethweko. Esinye nesinye isigaba sifaka isandla
ekutholeni amakghono anqophileko. Ithebula elingenzasi litjengisa umnqopho ovamileko walokho okumumethwe
esigabeni nomnqopho onqophileko walokho okumumethwe Esigabeni Esisisekelo.
Ithebula 2.1 Iminqopho yeengaba zokumumethweko esiGabeni esisiSekelo
ILWAZI LOKUMUMETHWEKO LEEMBALO
Isigaba Isigaba esivamileko Iminqopho Enqophileko yesigaba Esimumethweko
sokumumethweko sokumumethweko Esigabeni Esisisekelo
Ukuthuthukisa umqondo Irherho leenomboro ezithuthukiswa ekupheleni kweGreyidi yesi-
weenomboro okufaka hlangana: 3 lifaka hlangana iinomboro ezipheleleko okungasenani 1000
nama fraktjhini apheleleko.
• Ihlathululo yemihlobo
ehlukeneko yeenomboro; Esigabeni lesi, umqondonomboro womfundi uthuthukiswa
ngokusebenzisa izinto eziphathekako ngokubala izinto
• Ubudlelwana phakathi ezibuthelelweko, ukuhlukanisa nokubuthelela ubungako,
kweenomboro ngokubala ngokweqa ngeendlela ezihlukahlukeneko, ukurarulula
ezahlukahlukeneko; imiraro yobujamo obuthileko (igama) nokwakha nokwakha
• Ukuhlobana ngobukhulu nokuphula iinomboro.
kweenomboro • Ukubala kujayeza abafundi ukuthuthukisa umqondo nomboro,
ezihlukahlukeneko; iimbalo zehloko, isilinganiso, amakghono wokubala nokubona
amaphetheni.
• Ukujanyelwa
kweenomboro ngeendlela • Ukuthuthukisa komqondonomboro kurhelebha abafundi
Iinomboro, ama- ezahlukahlukeneko; noku ukufunda nngemikghwa/ ngemikhuba yeenomboro
Opharetjhini nokuthuthukisa iindlela ezingenza ukubala kubelula.
nobudlelwano • Umphumela wokusebenza • Ukurarulula imiraro ngobujamo /ngobunjalo kungenza abefundi
ngeenomboro. bakghone ukuveza imicabango ekungeyabo ngokukhuluma
nangokutlola ngemigwalo namngamatshwayo.
• Abefundi bakha ukuzwisisa umgomosiseko wokuhlanganisa,
ukukhupha, ukubuyabuyelela nokuhlukanisa.
• Abefundi bathuthukisa umqondo wefraktjhini ngokurarulula
imiraro efakahlangana ukwabelanakobungako kwezinto
eziphathekako ngokusebenzisa imigwalo. Imiraro kufanele
ifake hlangana iinsombululo ezineensalelo zeenomboro
ezipheleleko nofana amafraktjhini. Ukwabelana akukafaneli
kuthole ingcenye yokipheleleko kwaphela, kodwana
nokufunyana iingcenye zokubuthelelwa kwezinto. Esigabeni
lesi abafundi basengakabi nobukghoni bokufunda nofana
ukutlola amatshwayo wamafraktjheni.
I-Aljibra lilimi lokurhubhulula Esigabeni lesi, abafundi basebenza ngakho kokubili:
nokukhulumisana ngokunengi • Iphetheni yeenomboro (isib. ukubala ngokweqa) na
kweembalo begodu
• Maphetheni weJiyomethri (isib. iinthombe)
kunganabiselwa eenfundweni
zemisebenzi nobunye Abefundi kufanele basebenzise izinto eziphathekako, imigwalo
ubudlelwana obuphakathi namatshwayo webumbeko ukukopa, ukwandisa, ukuhlathulula
kwezinto ezitjhugulukako. nokutlhama amaphetheni.
Ingcenye ephakathi yesigaba Ukukopa amaphetheni kusiza abafundi bonyana babone ilojigi
sokumumethweko kungobana yokubana iphetheni yenziwe bunjani.
umfundi aphumelele amakghono Ukungezelela iphetheni kusiza umfundi ukuhlola bonyana
nokweza ngokusebenzisa bayizwisisile ilojijgi yephetheni.
AmaPhetheni, i-Aljibra. Begodu kunqophe eku:
amaFanktjhini ne- Ukuhlathulula iphetheni kusiza abafundi ukuthuthukisa
• Ekuhlathululeni amakghono welimi.
Aljibhra
amaphetheni nobudlelwana
ngokusebenzisa amatshwayo Ukunqophisa ephethinini yelojigi kwendlalela isiwekelo
wokuphandhusela, amagrafu sokuthuthukisa amakghono wokucabanga we-Aljibhra.
namathebula; noku Amaphetheni wenomboro asekela ukuthuthukisa
• Nokubona ukuhlaziya umqondonomboro nemizwa yokusebenza ukwakha iinomboro,
kokuvamileko umbalo nobudlelwano.
nokutjhugulukako Amaphetheni weJiyomethri ifaka hlangana nokulandelanisa
emaphethenini, nobudlelwano imida, amabumbeko nezinto begodu namaphetheni asephasini.
ukwenza bonyana umfundi Emaphethenini weJiyomethriki abafundi basebenzisa ilwazi labo
enze ibonelophambili lesikhala nebumbeko.
nokurarulula imiraro.
CAPS 9
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ILWAZI LOKUMUMETHWEKO LEEMBALO
Isigaba Isigaba esivamileko Iminqopho Enqophileko yesigaba Esimumethweko
sokumumethweko sokumumethweko Esigabeni Esisisekelo
Isifundo sesikhala Esigabeni lesi abafundi banqophe ezintweni ezinejamo
nobujamo kwenzangcono ezibusontathu (3-D), nobujamo obubusobubili (2-D), indawo
ukwizisisa nokuthanda/ nelayelo.
ukuthokozela kwamaphetheni,
• Abafundi bahlola izinto zobujamo ezibusontathu (3-D)
ngokunembako,
nobujamo obubusobubili (2-D) ngokuhlukanisa, ngemihlobo,
ngokuphumelelako nangobuhle
ngokuhlukanisa ngeengaba, ukuhlathulula nokuzitjho.
bebumbeko ngokwemvelo
nangendlela yokuphila/yesiko. • Abafundi bagwala ubujamo/amajamo bebakhe ngezinto.
Isikhala nobujamo Inqophe
(Jiyomethri) • Abafundi babona bebahlathulule amajamo/ubujamo bezinto
• matshwayo (ubunjalo) ezisemphakathini bazifanise nezinto nobujamo beembalo.
ubudlelwano
• Abafundi bahlathulula ubujamo bezinto, bonangokwabo
• ibandulo nelwazi, indawo/ nabanye ngokusebenzisa ilwazimagama elifaneleko.
ubujamo noku
• Abafundi balandela bebanikele nelayelo.
• tjhugulula ubujamo
obubusobubili nezinto
ezinobujamo ezibobusontathu.
Isilinganiso sinqophe • Esigabeni lesi umnqopho wesilinganiso wabafundi
ekukhethweni nekusetjenziswa uthuthukiswa ngokusebenza ngokwenza ngezinto
kwamayunithi afaneleko, eziphathekako ezihlukeneko namajamo, ukufunda
iinlinganisi/iimedo, amafomula ngamatshwayo/ngobunjalo bobude, umthamo, ubudisi, indawo
ngokwesinganiso kwezakhi nesikhathi.
zezehlakalo, ubujamo,
• Abafundi balinganisa amatshwayo wobujamo nezinto
izintonebhoduluko.
ngokusebenzisa ama unithi angakalungiselelwa lapho
Ihlobanisa ngokunqophileko
kufaneleko, okufana nezandla, amagadango isimumathi njll.
ngokwesayensi
Ukumeda nangobuthegnigi, nangomnotho • Abafundi bamadanisa ubungako obuhlukahlukeneko
wephasi ukuvumela umfundi: ngokusebenzisa amagama amadanisako afana nokuthi,
omude/omfitjhani, ebudisi khulu/elula njll.
• Ukwenza isilinganiso
esifaneleko; noku • Abafundi baziswa emayunithi avamileko afana namagremu,
khilogremu, mililitha, amalitha, amasentimitha, amamitha njll.
• Thlogomela ngokuzwakalako
kwesilinganiso nemiphumela. Imisebenzi ehlobana nesikhathi kufanele yakhiwe ngelemuko
lokobana ukuzwisisa kwabafundi ngokudlula kwesikhathi ku-
fanele kuthuthukiswe ngaphambi kokufundiswa kwesikhathi.
Ngesifundo sokuphatha Umnqopho wokufundisa nokufunda ngokuphathwa
imininingwana, umfundi kwemininingwana efundweni esisekelo esekuhlukanisa
uthuthukisa amakghono wo: ngeengaba izinto nemininingwana ngeendlela
ezihlukahlukeneko, kususelwa ebujameni obuhlukahlukeneko
• Buthelela
bezinto nofana imininingwana/idatha.
Ukuphatha idatha • Ukugqugquzela/
• Abafundi balindeleke bonyana barhumutjhe bebakhe
ukuhlanganisa ngeqhinga
isithombemgwalo negrafu yebha ekhambisana
• Ukubonisa/ukubukisa noku nokukhambelana ngakhunye ngakunye ngemininingwana
enikeliweko.
• Ukuhlaziya nokurhumutjha
idatha enikelweko.
2.6 Ukwabiwa kwesikhathi sokumumethweko ngokweengaba
Ukwabiwa kwesikhathi seembalo sokumumethweko ngokweengaba kusebenzela iinhloso eziqakathekileko
ezimbili: Okokuthoma ukwabiwa kwesikhathi kunikela ikhokhelo lobungako besikhathi esithlogekako ukufundisa
okumumethweko kileso naleso isigaba sokumumethweko ngokwaneleko; kwesibili isikhathi esabiweko sinikela
ikhokhelo lobungako kokumumethweko okusabalaliselwe ekuhlolweni. Ukwabiwa kwesikhathi kweengaba
zokumumethweko azifani Efundweni Esisekelo.
10 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ithebula 2.2 Ukwabiwa kwesikhathi kweengaba zokumumethweko esiGabeni esisisSekelo
Ukwabiwa kwesikhathi kweengaba zokumumethweko
Iingaba zokumumethweko: iGreyidi 1 iGreyidi 2 iGreyidi 3
Iinomboro,ama-Opharetjhini nobudlelwano* 65% 60% 58%
AmaPhetheni, amaFanktjhini ne-Aljibhra 10% 10% 10%
Isikhala nobujamo (Jiyomethri) 11% 13% 13%
Ukumeda 9% 12% 14%
Ukuphatha iDatha 5% 5% 5%
100% 100% 100%
*EmaGreyidini R – 3, kuqakathekile bona isigaba seenomboro, ama-Opheretjhini nobudlelwano kumnqopho oqakathekileko
weeMbalo. Abafundi badinga ukuphuma Efundweni Esisekelo banesiqiniseko seenomboro ngokuzizwa nokusetjenziswa
butjhelela. Ihloso kukobana abafundi bakghone bebazethembe ngeenomboro nokubalisisa. Ngalesi isizathu isikhathi
senotjhinali esabelwe Iinomboro, ama-Opharetjhini nobudlelwano singezelelwe. Umsebenzi omnengi wephetheni kufanele
unqophe kuphetheni yeenomboro, ukuhlanganisa ikghono leenomboro ebafundini ukuya phambili.
2.7 Iimbalo esiGabeni esisiSekelo:
Efundweni Esisekelo iimbalo zilingisa ngokwamanga ukuhlobana phakathi kwepilo yangaphambili-kwesikolo nepilo
engaphandle kwesikolo ngakesinye isandla, begodu ngakesinye isandla kube ziiMbalo ezisezingeni eliphezulu,
emaGreyidini alandelako. EmaGreyidini asesephasi abantwana kufanele kuvezwe epepeneneni ilemuko lakhe
leembalo elibanikela amathuba amanengi wokwenza, wokukhuluma newokurekhoda imicabango yeeMbalo
okungeyabo.
Ubungako besikhathi esiqithwa eembalweni yenza, iinqunto zamandla atjhayisanako ekuthuthukisweni umqondo
weeMbalo namaKghono. Imisetjenzana abantwana ababandekanywa kiyo kufanele kungabi ngeyokubalibazisa nje
kwaphela kodwana ifanele inqophe eeMbalweni njengombana kwethuliwe kwiKharikhyulamu.
2.7.1 Imihlahlandlela etjhukunyeziweko yokuphatha ikumba yokufundela.
Soke isikhathi esabiweko seembalo ngelanga kufanele sithathwe njengehlelo lesikhathi esisodwa. Ngesikhathi
seembalo okulandelako kufanele kwenziwe:
• Umsebenzi wetlasi loke
-- Iimbalo zehloko
-- Ukuhlanganisa imiqondo
-- Ukuphathwa kwetlasi (ukwabiwa kwemisetjenzana ngokuzijamela njll)
• Ukufundisa ngesiqhema esincani
-- Ukubala
-- Ukuthuthukisa umqondo wenomboro (ngokukhuluma nangemisetjenzana yokwenza)
-- Ukusombulula imiraro (ngokukhuluma nangemisetjenzana yokwenza)
-- Ukurhekhoda okutloliweko
-- Ukuthuthukisa iindlela zokubalisisa (ngokukhuluma nangemisetjenzana yokwenza)
-- Amaphetheni
-- Isikhala nobujamo
-- Ukumeda
-- Ukuphatha idatha
CAPS 11
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Umsebenzi wokuzijamela
Abafundi bayazilungiselela bebahlanganise ukuthuthukisa imiqondo emfumndweni zetlasi loke nekufundisweni
ngesiqhema esincani.
Imisetjenzana yetlasi loke: Umnqopho uzokuba kakhulukazi eembalweni zehloko, ukuhlanganisa imiqondo
nekwabeni kwemisetjenzana yokuzijamela okungasenani imizuzu ema-20 ngelanga ekuthomeni kwesifundo
seembalo. Ngalesosikhathi utitjhere uzokusebenzisa netlasi loke ukubona nokurekhoda (lokha kufaneleko)
ilanga losuku, zingaki enyangeni, inani labafundi abakhona nabangekho, nobujamo bezulu. Iimbalo zehloko
zifakahlangana iimbalo zehloko ezisungulako ezifana “nenomboro ezangemuva nangaphambili ko-8, okunengi/
nokuncani kuno-8 nga-2 yi: 4+2; 5+2; 6+2” njll. Ngaso leso sikhathi utitjhere angahlanganisa imiqondo engaba
budisana. Begodu kuqakathekile bona itlasi inikelwe imisetjenzana evamileko begodu nemisetjenzana
yokuzijamela abazenzela yona ngokwabo, ngalesosikhathi utitjhere uraga ngesigaba sesiqhema esincani.
Iimfundo eziqaliswe esiqhemeni esincani: Ngeziphumelelisako nange utitjhere athatha isiqhema sabantwana
esincani (8 ukuya 12) abasezingeni elilinganakobabe naye emadeni nofana ematafuleni wabo, ngasikhathi
leso itlasi loke libandakanywe emisetjenzaneni yokuzijamela. Utitjhere usebenza nabentwana ngokukhuluma
nangokwenza, ababandakanye emisetjenzaneni efana nokubala, ukulinganisa, ukuthuthukiswa komnqopho
weenomboro, imisetjenzana yokurarulula imiraro, nemisetjenzana ephathelene namaphetheni, isikhala
nobujamo, ukumeda nokuphatha idatha okufanele kuhlelwe ngokuqophelela.
Ukuze uqinisekise ukufunda umsebenzi otloliweko (incwadi yokusebenzela, isibonelo iphepha lokusebenzela,
amakarada wokusebenzela njll) kufuneka kube yingcenye yomsebenzi wesiqhema nakungakghoneka/
nakukghonakalako. Abafundi kufanele babe neentlabagelo zokutlola (incwadi yokusebenzela njll)
isentjenziselwe imisetjenzana yokurarulula imiraro. Isigaba sesiqhema kufanele bakhuthazwe “ukwenza,
ukukhuluma ukulingisa nokurekhoda” ukucabanga kwabo kweembalo.
Abotitjhere kufanele banakekele bangaqaleliphasi/banganyazi abafundi ababuthaka, kufanele nabo badoswe.
Kubalula ukumedanisa izinga lobudisi lomsebenzi wabafundi nangabe utitjhere usebenza ngezinga elipheze
lalingana, Okungenani iinqhema ezisemazingeni ahlangeneko zingasebenza ngcono nekwakhiwako, kumeda
kwenziwa amaphetheni nofana imisetjenzana yokuhlukanisa ngeengaba, nofana kwemidlalo.
Imisetjenzana yokuzijamela: Ngesikhathi utitjhere asebenza ngemfundo ezinqophiswe esiqhemeni esincani,
abafundi boke ngetlasini kufanele babandakanywe ngehloso yemisetjenzana ehlukahlukeneko yeembalo
enqotjhiswe ekuqiniseni nekuhlanganiseni iminqopho namakghono asele afundisiweko ngesikhathi
esinqotjhiswe esiqhemeni esincani. Imisetjenzana yokuzijamela kufanele ihlukaniswe ukwenzelela bonyana
inakekele iinqhema ezinamakghono ahlukeneko. Imisetjenzana yokuzijamela ifanele ifake hlangana:
-- Imisetjenzana yencwadi yokusebenzela
-- Amaphepha wokusebenzela ahlelwe ngokwemihlobo/amakarada wokusebenza wokubala, ukusebenzisa
iinomboro, imiraro elula esebujameni (imiraro yamagama) njll
-- Imidlalo yeembalo efana neLudo, amadomino, amaphazeli wejigso nama
-- AmaThaski afakahlangana nokwakha, ukuhlukanisa ngeengaba, ukuphethina nokumeda.
Isikhathi seembalo kufanele sinikele ukulekelela ebafundini abaneenqabo zokufunda, imisetjenzana
engezelelako yabakghonako, imisetjenzana yokuhlola njll.
Imisetjenzana yokuzijamela neyesiqhema esincani kufanele iqalwe (ngokwenza, nangokukhuluma) itshwaywe
bese iyaqalisiswa (ukurhekhoda okutloliweko) ngutitjhere njengengcenye yokuhlola okulungiselelweko
nengakalungiselelwa.
Ukulandela umkhondo wempendulo zabafundi (ngokukhuluma, ngokucocwako, ngokwenza, ngokurekhoda
okutloliweko) esimeni sokufunda nokufundisa evumela utitjhere ukwenza ukuhlola okuragela phambili,
ukulandelela iragelophambili nokuhlela ilekelelo ngokuya kwabafundi abaneenqabo zokufunda.
12 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
2.7.2 Abafundi abaneenqabo ekufundeni iimbalo
Kuqakathekile bonyana abafundi abahlangabezana neenqabo zokufunda iimbalo bonyana kuvezwe epepeneneni
ekufundeni okusekelwe ngemisetjhenzana yokufunda. Ukwenza kweemboniso kusetjhenziswa izinto ezibonakalako
ngokuhlanganyela nemisetjhenzana yokwenziwa kufanele isetjhenziswe ithutjana elide kunalabo abafundi
abakghonako ngombana ukutjhugulukela emisebenzini engabonakaliko ngokurhabako kungabanga ukutjhuragana
nokusalela. Abafundi labo bangadinga nofana banikelwe isikhathi esinengi soku:
• Qedelela imisebenzi yokuhlola namathaski
• Ukuthola amakghono wokucabanga (amaqhinga okungewabo)
Inani lemisetjhenzana okufanele iqedelelwe kufanele yehliswe ngaphandle kokuzwana ngokulisa okhunye iminqopho
namakghono lawo anqotjhiweko.
2.7.3 Iimbalo zehloko
Iimbalo zehloko zidlala indima eqakathekileko kukharikhulamu. Amabhondi weenomboro nethebula yokkubuyelela
okulindeleke bona abafundi bawazi nofana bawakhumbule ngokurhabako keliny nelinye igreyidi arhemisiwe.
Ngokungezelelweko, iimbalo zehloko zisetjhenziswa ngokubanzi ngokuhlola iinomboro eziphakamileko ezihlangana
kweenlinganiso ezimbili ngokubala ngokweqa nangokwenza imisetjenzana efuna ukuya phezulu naphasi elerini.
Isib. Utitjhere wegreyidi yesi 3 angahle abuze imibuzo elandelanako, “thoma nga 796 ungezelela nge 7, Iye ma 803.
Yenza lokhu kwehle nge 5 Iye ma 798. Ngezelela nge 10... ungezelela 2... ungezelele nga 90 ... yehlisa nga 5 ” njll.
Imisetjenzana leyo irhelebha abafundi ukwakha inambalayini yembalo zehloko.
Iimbalo zehloko ziboniswa khulu ekubaleni nesahluko somqondo wokuthuthukisa inomboro okuhlobanisa inhloko
zeenomboro namaPhetheni begodu kungenzeka ngesikhathi sokumeda nemisetjenzana yokuphatha kwedatha.
Nakwenziwa iimbalo zehloko, utitjhere angakateleli abafundi ukwenza iimbalo zokubalisisa abangakwazi ukuzenza-
iintlabagelo zokutlola nofana izinto zokubala kufanele zihlale njalo zikhona ukwenzelela abafundi abasazithlogako
2.8 IGreyidi R
Indlela yokufunda i-IiMbalo kufanele isekelwe emithethweni yokuhlanganisa ngokuzeleko nokufunda okusekelwe
ekudlaleni. Utitjhere kufanele asebenzele phambili, abemlamuli kunokuba mkghonakalisi. Umlamuli wenza
amathuba amanengi wokufunda anganakuqakatheka avela ngokuzenzakalelako ngezikhathi semisetjenzana
edzimelele emntwaneni efana nokudlala ngokutjhaphuluka ekhoneni lomkhumbulo olibhudango nofana endaweni
lapha kwakhiwa khona ngamabhlogo, emisetjenzaneni yokudlala ngehlabathi namanzi okufaka imisetjenzana
ekhokholwa ngutitjhere, enqophiswe emqondweni wokubala, ukuthuthukiswa komqondonomboro, isikhala nobujamo,
amaphetheni, isikhathi neminye imisetjenzana yokuthoma i-IiMbalo. Umbala ngokwawo awusiwo umqondo we-
IiMbalo, kodwana ungasetjenziselwa ukuthuthukisa umqondo we-IiMbalo ngemisetjenzana efana nokuhlela
ngemihlobo, ukuhlela ngeenqhema nokuhlukanisa ngeengaba.
Woke amahlangothi weGreyidi R, okufaka hlangana ibhoduluko letlasi nokujayela ukufundisa nokufunda, kufanele
kukhuthaze ukuthuthukisa umntwana ngokuzeleko. Ukuthuthuka okuhlanganisiweko nokuthoma ukwazi iimbalo
okufakahlangana nokuthuthukiswa kokusebenzisa umkhumbulo
(ukurarulula-umraro, ukucabanga nokucabangisisa okuhlelekileko), ukuthuthukisa kwelimi (ilimi le-IiMbalo)
nokubona kwanga uyezwa begodu nangokwemizwa nangokuhlalisana. Woke amahlangothi lawa angathuthukiswa
ngeendatjana, iingoma, imidunduzelo, imidlalo yemino neyamanzi, amathoyisi wokufunda afakahlangana umdlalo
webhodi, imisetjenzana yokwakha nokuhlola (ubudisi, isikhathi, ubungako, ukumeda njll). Ukudlala ngokuzakhela
engqondweni, ukudlala ngaphandle nemidlalo yekundleni yezemidlalo. Imidlalo eminengi ingafakahlangana ihlangothi
lenumeresi, isibonelo ukulinganisa ngesikhathi sokupheka nofana ukubala nakuthengwako.
Ngamanye amagama ukukghona ukuthoma ukubala nakuhlobana kwemiqondomagama weembalo kufanele
njengokufundisa okuhle kulandele imithetho yokufunda elandelako lapha abantwana badlula eengabeni eentathu
zokufunda:
CAPS 13
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Isigaba sekhinestethiki (ilemuko lemiqondo ngemizimba nangemizwa);
• Isigaba sokuphathekako (3-D), kusetjenziswe izinto ezihlukahlukeneko ezifana namabhlogo, iimvalo
zamabhodlela, iingojwana nezinyo izinto ezisemphakathini);
• Iphepha nepensela (iinjamiseleli ezisaphathekako kusetjenziswa imigwalo, amakarada amadanisako njll)
EGreyidini R ithebula lesikhathi libizwa ihlelo langamalanga (qala Umfanekiso woku-1) begodu ihlukaniswe
ngeengaba ezintathu eziqakathekileko zibizwa:
• Imisetjenzana ekhokhelwa ngutitjhere
• Imisetjenzana yangamalanga/evamileko
• Imisetjenzana esungulwa bantwana nofana ukudlala ngokutjhaphuluka.
Igandelelo kufanele libe sekusebenziseni amahlangothi welandelano lemilayelo ukukhuthaza ukuzuza kokuthoma
ukwazi inumeresi ngendlela esebujameni bokudlala nangokuzenzakalelako. Isibonelo, amathuba wokufunda
inumeresi ngokukhokhelwa ngutitjhere enziwa ngesikhathi sendulungu. Iindulungu zinganikelwa umnqopho
wokubala. Ekuseni ngesikhathi sokulotjhisana nalapha nakuqalwa abantwana abakhona nabangekho ingathathwa
njengethuba lokudlala ngeenomboro isibonelo, ukubala. Ezinye iindulungu ezifana nendulungu ye-IiMbalo, indulungu
yokuzwa inga uyabona, yokusikinyeka, yomvumo neyesayensi zinganikela umnqopho we-IiMbalo.
Imisetjenzana yobuciko bokuzithlamela ingagandelela i-IiMbalo isibonelo, ukusebenzisa amabumbeko weJiyomethri
ezifana nendulungu nesikwere ukwenza ikholaji nofana ukutlama ifreyimu yesithombe. Itjhadi lobujamo bezulu,
ikhalenda nendulungu yelanga lamabeletho zinikela ithuba lokuhlola umnqopho wokubala. Kulilwazi nokusungula
kwakatitjhere okungandise ikghono lokufunda.
• Umsebenzi wangamalanga lapha abantwana bazibandakanya khona efana nesikhathi sokudla, isikhathi
sokubuyelela ekhaya, nesokuya endlwaneni singanikelwa umnqopho oqaliswe ekubaleni. Boke abentwana
abembethe izambatho ezibomvu baye endlwaneni kokuthoma (umbala neenomborosikhundla) omunye
nomunye umntwana uthola isitja nembedlezwana (ukukhambelana kunye nakunye), uThandi ubawa
imbedlezwana enye godi, uSipho akasayifuni enye imbedlezwana. Utitjhere ubona asebenzise isikhathi leso
njengesikhathi sokufundisa ngamanye amagama utitjhere abemlamuli wokufundisa.
• Ngesikhathi sokudlala ngokutjhaphululaka utitjhere angathuthukisa iiMbalo ezisathomako ngokwakhiwa
okufaneleko kwendawo yokudlalela. Ukudlala okutjhaphulukileko kwangaphandle okufana nokukhwela
ifreyimu yesigodo nofana ukukhwela itsikiri kungathuthukisa ilwazimagama weembalo afana naphezulu/
phasi, masinya/buthaka, ngaphasi/ngaphezulu njll. Ukudlala ngehlabathi namanzi kungangezelela ukuzwisisa
kwemiqondo efana nobudisi nomthamo. Yoke imisetjenzana izokungezelela amakghono wokuzwa kwanga
uyabona enza, lokhu kuba yengcenye yokuphila njengendabuko okutholakala ngokuphumelela ekufundisweni
okuhleliweko kwelitheresi nenumeresi. Iimbonelo zamakghono ngilezi:
-- ukuthuthukisa ukuzwisisa ubujamo ebusesikhaleni isibonelo, ngemuva, ngaphambi kwe, ngaphasi kwe
nofana hlanu kwento (lokhu kungahlanganiswa nokujanyelwa kwedijithi); ne
-- ukunqophisa nelathelarithi (lokhu kungahlanganiswa nokubunjwa kwenomboro neledere, nokufunda
kusukela ngesinceleni ukuya ngesidleni)
Ukulungiselela okwendlalwe ngehla kutjengisa indlela ekhuthaza indlela yokurarulula umraro, ukucabanga
nokucabangisisa isikhathi sokufunda, utitjhere angakhuthaza abantwana bonyana batjengise ngeenquto
nebonelophambili lokungenzeka isibonelo, Njengokuthi isimumathi esisetjenziswe ngesikhathi sokudlala
ngokutjhaphuluka singathatha umthamo omnengi kunesinye.
Ngokwenza iintjhukumezo ezingarhelebha nokumema umntwana bonyana acabange ngezinye iindlela zokurarulula
imiraro. Utitjhere angakhuthaza abantwana ukucabanga ngokujulileko nangeendaba nangeenqunto abazithathako.
Ngaleyondlela kuzabe kungasi ngokweembalo kwaphela kodwana ukuthuthukisa okupheleleko ngelihlo elihlabako
okuvezwa Sitatimende soMthetho-kambiso weKharikhyulamu nokuHlola kulethwa ngokudlala.
14 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Umfanekiso woku-1: Ihlelo langamalanga le Greyidi R
(Kusuka ± 7:30 – 13:00)
UKUFIKA NOKUDLALA OKUTJHAPHULUKILEKO IiMbalo
• Imisetjenzana esuselwe
Ukulotjhisa Amalanga IiMbalo
kuma (IiMbalo).
Wamabeletho Iregistara AmaLimi
Iindaba AmaKghono WePilo • Iingoma nombhino
Imizuzu
e-36 • Imisetjenzana ebonakalako
IMISETJENZANA ERHOLWA NGUTITJHERE
• Imilolozelo yokubala
IiMbalo, AmaLimi, AmaKghono WePilo
• Imidlalo • Ukucocisana ngommongo
yokuzenzisa • Isitjengiso – mbono
• UMSEBENZI WOBUKGHWARI
• Ukulingisa sesayensi
umsetjenzana o-1 oqakathekileko
50 kanye nemi- 2 nofana emi-3 • Ukudlala • Ukudlala okutjhaphulukileko
imizuzu esekelako yangamalanga. ngokwakha • Imisebenzi yangamalanga
• ukudlala batjhaphulukile • Amabhblogo
• nokubutha ngetlasini • Kokufunda
AMALIMI
• Izinto zokudlala
IMISETJENZANA ERHOLWA
30 • Imidlalo • Imisetjenzana esuselwe
NGUTITJHERE
imizuzu ecabangisako kuma (ILimi Lekhaya).
IiMbalo, AmaLimi, AmaKghono WePilo.
• Iindatjana
• Amaphazela
10 Ukuya ngendlwaneni kwangamalanga • Umdlalo wesiteji
• Ihugwana
imizuzu IiMbalo, AmaLimi, AmaKghono WePilo • Iincwadi / iinthombe
yeencwadi
• Ukufundi iinthombe
• Ukucocisana ngeenthombe
• Imisetjenzana ebonakalako
• Ipostara yababelethi
20 IINQABULI:
imizuzu Amalimi, Iimbalo, AmaKghono WePilo • Ukudlala • Incwadi yomzali
ngamanzi • Iindaba
• Ukudlala • Iinkondlo / imilolozelo
ngesanda • Umbhino / iingomo /
Ukudlala utjhaphulukile • Ukulingisa imilolozelo
60 ngaphandlenokubutha
imizuzu • Iimbholo • Umtjhinin wokudlala
• Ukujinka amakhasede
• Izinto zokudlala • Ukucocisana ngommongo
ezinamavili • Imidlalo yemikhambo
• Izinto zokudlala yabantu
ezifundisako • Imisebenzi yangamalanga
10 • Ijungel jimu • Ukudlala okutjhaphulukileko
Ukuya ngendlwaneni kwangamalanga
imizuzu IiMbalo, AmaLimi, AmaKghono WePilo. • Amatayere
• Ukuthabulula
IMISETJENZANA ERHOLWA umzimba AMAKGHONO WEPILO
30 • Imidlalo
NGUTITJHERE
imizuzu • Imisetjenzana esuselwe
IiMbalo, AmaLimi, AmaKghono WePilo.
kuma (AmaKghono
WePilo).
30
INDATJANA ngamalanga • Imidlalo yemikhambo
imizuzu
yabantu
• Umvumo nombhino
ukuphumula / isikhathi sokuthula nesokukhamba • Iinkondlo nemilolozelo
• Ukucocisana ngommongo
• Amalanga wamabeletho
• Imisebenzi yangamalanga
• Ukudlala okutjhaphulukileko
CAPS 15
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuhlolwa eGreyidini R kufanele kube ngokungakalungiselelwa begodu abantwana akukafaneli babekwe ebujameni
bokutlola ukuhlola.
Kungalesi sizathu imisetjenzana yokuhlola ingakafakwa eSitatimende Somthetho-kambiso Wekharikhyulamu
nokuHlola eGreyidini R. Omunye nomunye umsebenzi wokuhlola ufanele uhlelwe ngokuqophelela ukuze ihlanganise
nemihlobobohlobo yamakghono.
EGreyidi R ukuhlolwa okunengi kwenziwa ngokubukela, lapho utitjhere arekhoda khona imphumela yokuhlolwa
ngokusebenzisa irherho lokuhlola. Ngokukhamba konyaka, isithombe esizeleko ngomntwana ngamunye siyakheka,
zizaliswe ngeentjhijilo nangobukghoni bakhe kwenza bonyana iintjhijilo ziqalelelwe, ubukghoni buthuthukiswe. Lokhu
kuvumela intjhijilo bonyana ziqalelelwe nobukghoni buthuthukiswe.
Ihlelo lokufunda elihlelelweko langekumbeni yokufunda ehlelwe ngokusekelweko afanele angenziwa, njengombana
angalekeleli ukukghonakala kweNumeresi emntwaneni weGreyidi R.
UGreyidi R akukafaneli kube yiGreyidi 1 eyehlisiweko. IGreyidi R unemikghwa yayo ehlukileko esekelwe ngokuthi
umntwana oseminyakeni leyo wenza njani umqondo ngephasi aphila kilo, nokuthi uzuza njani ilwazi, amakghono,
amagugu nendlela yokucabanga ebanikela amathuba weminyaka yokufunda okuhlelelweko.
2.9 Iinsetjenziswa Eziphakanyisiweko zetlasi yeeMbalo esiGabeni Esisisekelo.
• Iimbali
• Idayisi elikhulu
• Ifreyimu ekulu yokubala
• Itjhadi lobude
• Iphostara ekulu eneenomboro 1 – 100 nephostara yegridi yeenomboro 101 – 200 (itjhadi lenomboro ezi-
100)
• Amanambalayini ahlukahlukeneko (ajame rwe nathabaleleko)
• Isede yama karada flardi ( amakarada anabisako)
• Imali yokudlala — iinhlamvu zemali nemali yephepha.
• Ikhalenda yonyaka loyo
• Iwatjhi ekulu yamasiba yebodeni
• Isikala sokudzimelela
• Amabhlogo wokwakha
• Idaka lokubumba
• Amabhoksi ahlukahlukeneko ngobujamo nesayizi athethwe ekhaya
• Amabhodlelo weplastiki ahlukahlukeneko nezinye iimumathi zokuhlathulula nokumadanisa umthamo
• Iimbonelo ezihle zeendulungu (iimbholo), iphrizimu enguncamane (ibhoksi), ikhuyubhu, ikurwana, iphiramidi
namasilinda. Utitjhere angazenzela yena ngokwakhe lokhu.
• Iinkwere ezinengi zamaplastiki nofana amakhadibhoksi, aboncamane abahlukahlukeneko, iindulungu,
aboncantathu abahlukahlukeneko babe namasayizi ahlukahlukeneko boke.
• Imidlalo yeeMbalo isib. iLudo, iinyoka namaleri, amaphazela angenelanako, amaDomino, amaTangremu njll.
• Okuqakathekileko emaGreyidini R neyoku 1:
-- Iindawo lapho kudlalwa khona ngesanda namanzi
-- Iinsetjenziswa zokukhwela , zokudzimelela, zokujinka nokweqayeqa
-- Isitolo sokudlala nezinto okufanele zithengwe ngemali yokudlala
-- Imihlobohlobo yemidlalo efaneleko okufana nokuthi ‘kunani ngaphakathi kwesikwere’?
-- Amabhlogo.
16 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISIGABA 3: UKUNQOPHISA NOKUHLATHULULA OKUMUMETHWEKO
3.1 Isingeniso
Eemfundweni ezisesiGabeni seFundo ephasi, kuhlanu okumumethwe eendaweni ze-IiMbalo
• Iinomboro, ama-Opharetjhini noBudlelwano
• AmaPhetheni, amaFanktjhini ne-Aljibhra
• ISikhala nobuJamo (Jiyomethri)
• UkuMeda
• UkuPhatha iDatha
Esinye nesinye isigaba sokumumethweko siphulwa sibe ziinhlokwana zeeMbalo, isibonelo kuSikhala nobuJamo
Esigabeni Esisisekelo esinye seenhloko bujamo obubusobubili (2-D). ImiQondo namaKghono ayanqotjhiswa
ngaphakathi kwesinye nesinye isihloko. Esigabeni sesi-3 seSigaba Esisisekelo se-Mbalo, ISitatimende Somgomo
WeKharikhyulamu nokuHlola sinqophisa besihlathulule lokho okufunekako kokumumethwe ziiMbalo.
3.2 Isenzo sokunqophisa iragelo phambili kilokho okumumethweko.
Ithebula yehlathululo efitjhazana yesigaba esithile sokukhula itjengisa isenzo seragelo phambili yeminqopho
namakghono netuthuko kusukela eGreyidini R ukuya kweyesi-3. Ithebula yehlathululo efitjhazana yesigaba esithile
sokukhula kweGreyidi itjengisa ituthuko yemiqondo namakghono buvundla kiwo womane amathemu wonyaka.
Noma kunjalo, kezinye iinhloko imiqondo namakghono ayafana emagreyidini amabili nofana amathathu alandelanako.
Ukuhlathulula okumumethweko kuzakunikela umhlahlandlela wokobana iragelo phambili kufanele yenziwe bunjani
ebujamweni obunjalo. Isenzo sokunqophisa okumumethweko kufanele sifundwe ngokuhlanganyela nokuhlukanisa
ngeengaba kokumumethweko.
Umbonomazombe omfitjhazana wemininingwana Esigabeni Esisisekelo itjengisa iragelo phambili leengaba
ezimumethweko; Iinomboro, ama-Opharetjhini noBudlelwano, amaPhetheni, amaFanktjhini ne-Aljibhra, Isikhala
noBujamo (Jiyomethri), Ukumeda no kuPhatha iDatha buvundla emaGreyidini R – 3 njengoba zibekiwe ethebuleni
elingenzasi.
CAPS 17
UMBONOMAZOMBE WESIGABA ESISISEKELO
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANO
18
Iragelo phambili leenomboro, ukusebenza nobudlelwano.
• Iragelo phambili eliqakathekileko leenomboro,ukusebenza nobudlelwano elenzeka ngeendlela ezintathu:
-- Ihlelo leenomboro liyanyuka.
-- Ukwethulwa kwemihlobo ehlukeneko yeenomboro.
-- Ukutjhuguluka kwamaqhinga wokubala.
• Njengombana ihlelo leenomboro lokubala linyuka ukufika kugreyidi 3, abafundi kufanele bathome ukuba namaqhinga amanengi afaneleko wokubala.
• Imiraro yobujamo kufanele ibe nokuphenduleka ehlelweni leenomboro egreyidini kunye nekghono lokubala labafundi.
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
UKUTHUTHUKA KWEMIQONDO YEENOMBORO : Bala ngeenomboro ngokupheleleko
1.1 Ukubala izinto eziphathekako Ukubala izinto eziphathekako Ukubala izinto eziphathekako Ukubala izinto eziphathekako
Ukubala izinto Linganisa bewubale ngokuthembeka Linganisa bewubale ngokuthembeka Linganisa bewubale ngokuthembeka Linganisa bewubale ngokuthembeka
okungenani kufika ema-10 izinto okungenani kufika ema-50 izinto okungenani kufika ema 200 izinto okungenani kufika e-1000 izinto
zangamalanga zangamalanga. ngamalanga. zangamalanga.
Ukubala ngeenqhema Ukubala ngeenqhema Ukubala ngeenqhema kuyakhuthazwa
kuyakhuthazwa kuyakhuthazwa.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1.2 Ukubala uyephambili nemuva nga: Ukubala uyephambili nemuva nga: Ukubala uyephambili neemuva nga: Ukubala uyephambili neemuva nga:
Ukubala Ku-1 ukusuka kwenye nenye Ku-1 ukusuka kwenye nenye • Ku- 1 ukusuka nanyana ngiyiphi • Ku-1 ukusuka nanyana ngiyiphi
uyephambili inomboro kusukela keyo-1 ukufika inomboro hlangana no-1 ne-100 inomboro ehlangana ne-0 na 200 inomboro ehlangana ne-0 ne-1000
nemuva keye-10 • Li- 10 ukusuka nanyana ngiliphi • Li- 10 ukusuka nanyana ngiliphi
Ukubala uye phambili nga-
Sebenzisa imilolozelo yeenomboro ibuyelelo le- 10 hlangana ne-0 ne ibuyelelo le 10 hlangana ne- 0 ne
• Li-10 ukusukela kwenye nenye
kunye neengoma 200 1000
inomboro ebala ngali-10 ehlangana
no -1 ne-100 • Ku- 5 ukusuka nanyana ngaliphi • Ku- 5 ukusuka nanyana ngaliphi
ibuyelelo laka 5 hlangana ne- 0 ne ibuyelelo laka 5 hlangana ne- 0 ne
• Ku-5 ukusukele kwenye nenye
200 1000
inomboro ebala nga ku-5
ehlangana no -1 ne-100 • Ku- 2 ukusuka nanyana ngaliphi • Ku- 2 ukusuka nanyana ngaliphi
ibuyelelo laka 2 hlangana ne- 0 ne ibuyelelo laka 2 hlangana ne- 0 ne
• Ku-2 ukusukela kwenye nenye 200 1000
inomboro ebala nga- 2 ehlangana
no -1 ne-100 • Ku- 3 ukusuka nanyana ngaliphi • Ku- 3 ukusuka nanyana ngaliphi
ibuyelelo laka 3 hlangana ne- 0 na ibuyelelo laka 3 hlangana ne- 0 ne
200 1000
• Ku- 1 ukusuka nanyana ngaliphi • Ku- 1 ukusuka nanyana ngaliphi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ibuyelelo laka 1 hlangana ne- 0 ne ibuyelelo laka 1 hlangana ne- 0 ne
200 1000
• Ma 20, 25, 50,100 ukufika
okungenani e-1000.
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
UKUTHUTHUKA KWEMIQONDO YEENOMBORO: Ukujamisela iinomboro ngokupheleleko
1.3 Ukukhumbula, ukubona Ukukhumbula, ukubona Ukukhumbula, ukubona nokufunda Ukukhumbula, ukubona nokufunda
CAPS
nokufunda iinomboro nokufunda iinomboro iinomboro iinomboro
Amatshwayo
weenomboro • Khumbula, ubone begodu ufunde • Khumbula, ubone begodu ufunde • Khumbula, ubone , ukubona • Khumbula, ubone begodu ufunde
namabizo amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka nokufunda amatshwayo wenomboro amatshwayo wenomboro ukusuka
weenomboro ku-1 ukufika ku-10 ku-1 ukufika e-100 ukusuka e-0 ukufika e-200 e-0 ukufika e-1000.
• Khumbula, ubone begodu ufunde • Tlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro • Tlola amatshwayo wenomboro
amagama weenomboro ukusuka ukusuka ku-1 ukufika e-20 ukusuka e-0 ukufika e-200 ukusuka ku-1 ukufika e-1000
ku-1 ukufika ku-10
• Khumbula, ubone begodu ufunde • Khumbula, ubone begodu ufunde • Khumbula, ubone begodu ufunde
amagama weenomboro kusuka igama lenomboro ukusuka e-0 amagama weenomboro ukusuka
ku-1 ukufika e-10 ukufika e-100 ku-1 ukufika e-1000.
• Tlola amagama weenomboro • Ukutlola amagama weenomboro • Tlola amagama weenomboro
ukusuka ku-1 ukufika e-10 ukusuka e-0 ukufika e-100 ukusuka ku-1 ukufika e-1000
UKUTHUTHUKA KWEMIQONDO YEENOMBORO: Ukuhlathulula, ukumadanisa nokuhlela inomboro ngokupheleleko
1.4 Ukuhlathulula, ukumadanisa Ukuhlathulula, ukumadanisa,
nokuhlela ibuthelelo lezinto nokuhlela izinto ukufika e-20
Ukuhlathulula,
ukufika e-10
ukumadanisa • Ukuhlathulula nokumadanisa
nokuhlela • Ukuhlathulula iinomboro izinto ezibuthelelweko ukuya
inomboro ngokupheleleko ukufika e-10. ngobunengi, okungenani,
ngokupheleleko kufana.
• Ukumadanisa bonanyana,
ekudlwana, ekulu khulu • Ukuhlathulula nokumadanisa
engaphasi, elinganako izinto ezibuthelelweko ukusuka
epheze ilingane, engaphezulu kubunengi ukuya okulingeneko
ezimbadlwana kwe-10 ngiyiphi kunye nokusuka kokulingene
ekulu, encani, hlangana nezimbili uye kokunengi.
izinto ezibuthelelweko.
• Ukuhlela ngaphezu kwezimbili
zebuthelelo lezinto ukusuka
kencani ukuya kekulu ukufika e-10.
19
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
UKUTHUTHUKA KWEMIQONDO YEENOMBORO: Ukujamisela iinomboro ngokupheleleko
20
1.4 Ukuhlathulula, ukumadanisa and Ukuhlathulula, ukumadanisa and Ukuhlathulula, ukumadanisa
nokuhlela iinomboro ukufika e-20 nokuhlela iinomboro ukufika e- 99 nokuhlela iinomboro ukufika e-999.
Ukuhlathulula, • Ukuhlathulula nokumadanisa • Ukuhlathulula nokumadanisa • Ukuhlathulula nokumadanisa
ukumadanisa iinomboro ezipheleleko iinomboro ezipheleleko ukufika e-99 iinomboro ezipheleleko ukufika
nokuhlela ngokusebenzisa okuncani kuna, ngokusebenzisa okuncani kuna, e- 999 ngokusebenzisa okuncani
inomboro okukhulu kuna, okunengi kuna, okukhulu kuna, okunengi kuna, kuna, okukhulu kuna, okunengi
ngokupheleleko okungaphasi kuna, okulinganako. okungaphasi kuna, okulinganako. kuna, okungaphasi kuna,
• Ukuhlathulula bewuhlele iinomboro • Ukuhlathulula bewuhlele iinomboro okulinganako.
kusuka ngencani-khulu ukufika ezipheleleko ukufika e-99 kusuka • Ukuhlathulula bewuhlele iinomboro
kekulukulu nokusuka kekulukulu kencani-khulu ukufika kekulukulu ezipheleleko ukufika e-999 kusuka
kufika kencani-khulu nokusuka kekulukulu kufika kencani-khulu ukufika kekulukulu
kencani-khulu nokusuka kekulukulu kufika
kencani-khulu
Sebenzisa inomborosikhundla Sebenzisa inomborosikhundla
Sebenzisa inomborosikhundla Sebenzisa inomborosikhundla ukutjengisa ukulandelana, indawo
ukutjengisa ukulandelana, indawo ukutjengisa ukulandelana, indawo
ukutjengisa ukulandelana, indawo namkha ubujamo namkha ubujamo
namkha ubujamo namkha ubujamo
• Ukubeka izinto ngokulandelana • Ukusebenzisa , ukufunda nokutlola
Thoma ilemuko • Ukubeka izinto ngokulandelana iinomborosikhundla kufaka
kusukela keyokuthoma kusukela keyokuthoma ukufika
leenomborosikhundla Isib. keyamatjhumi amabili namkha hlangana nezirhunyeziweko (1st-
Yokuthoma, yesibili, yesithathu ukufika keyetjhumi namkha koku1, 2nd-kwesi2, 3rd- kwesi-3
keyokuthoma ukuya keyokugcina, keyokuthoma ukuya keyokugcina,
ukufika keyesithandathu Isib. Yokuthoma, yesibili, ukufika kokwama 31st)
neyokugcina. Isib. Yokuthoma, yesibili,
yesithathu........ yetjhumi yesithathu........Yamatjhumi amabili.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UKUTHUTHUKA KWEMIQONDO YEENOMBORO :Ubukhulu bedijithi
1.5 Thoma ukulemuka ubukhulu Thoma ukulemuka ubukhulu Ukulemuka ubukhulu bedijithi
bedijithi okungenani iinomboro bedijithi okungenani iinomboro okungenani iinomboro zamadijithi
Ubukhulu bedijithi zamadijithi ama-2 ukufika e-20 zamadijithi ama-2 ukufika e-99 ama-3 ukufika e-999
• Ukuphula iinomboro zamadijithi • Ukuphula iinomboro zamadijithi • Ukuphula iinomboro zamadijithi
ama-2 ukuya ngesibuyabuyelelo ama-2 ukuya ngesibuyabuyelelo ama-3 ukufika e-999 ukuya
se-10 nakunye/ namayunidi. se-10 nakunye/namayunidi. ngesibuyabuyelelo se-100,
ngesibuyabuyelelo se-10 nakunye/
namayunidi.
• Ukufanisa nokutjho ubukhulu benye • Ukufanisa nokutjho ubukhulu benye
nenye idijithi. nenye idijithi.
UKURARULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki Sebenzisa amathekhiniki
ukufika e-10. nawurarulula imiraro uhlathulule alandelako lokha urarulula imiraro alandelako lokha urarulula imiraro
Amaqhinga neensombululo: bekuhlathululwe iinsombululo bekuhlathululwe iinsombululo
wokurarulula • Iinsetjenziswa eziphathekako Isib. zemiraro: zemiraro:
imiraro Izinto zokubala. • Ama-apharethasi aphathekako
njengezinto zokubala • Imigwalo nofana amapharethasi • Ukwakha nokuphula kweenomboro
• Ileri yeenomboro ebonakalako. • Iinthombe zokugwala iimbalo aphathekako isib. Izinto zokubala • Ukubuyelela kabili nokuqunta
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
zendatjhana • Ukwakha nokuphula kweenomboro phakathi
• Ukuphula nokuphula iinomboro • Ukubuyelela kabili nokuqunta • Inambalayini
• Ukubuyelela nokuqunta phakathi phakathi
• Tlola ngamatjhumi.
• Iinambalayini • Inambalayini
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
1.7 Rarulula iimbalo zamagama (Indaba Rarulula iimbalo zamagama Ukusombulula imiraro yeembalo Ukusombulula imiraro yeembalo
CAPS Ukuhlanganisa zokuhlanganisa) ezisebujameni ezisebujameni bewuhlathulule zamagama ezisebujameni abe zamagama ezisebujameni abe
nokukhupha bewuhlathulule iinsombululo zakho iinsombululo zakho zemiraro, ahlathululo iinsombululo okungezakhe ahlathululo iinsombululo okungezakhe
zemiraro ezifaka ukuhlanganisa faka ukuhlanganisa, ukukhupha umraro ofakahlangana ukuhlanganisa umraro ofakahlangana ukuhlanganisa
nokukhupha ngempendulo ukufika nempendulo ukufika e-20. nokukhupha okuneempendulo nokukhupha okuneempendulo
e-10. ezifikelela e-99. ezifikelela e-999.
1.8 Rarulula iimbalo zamagama Ukusombulula imiraro yeembalo Ukusombulula imiraro yeembalo
Ukuhlanganisa ezisebujameni bewuhlathulule zamagama ezisebujameni zamagama ezisebujameni abe
okubuyelelweko iinsombululo zakho zemiraro, abe ahlathululo iinsombululo ahlathululo iinsombululo okungezakhe
kurholela faka ukuhlanganisa okubuyelelko okungezakhe, umraro ofakahlangana umraro ofakahlangana ukubuyelela
ekubuyabuyeleleni nempendulo ukufiika ku-20 ukuhlanganisa okubuyelelweko okuneempendulo ezifikelela e-100.
okukhokhela ekubuyeleleni
okunomphumelo ofikelela e-50.
1.9 Rarulula iimbalo zamagama Rarulula iimbalo zamagama Ukusombulula imiraro yeembalo Ukusombulula nokuhlathulula
Ukubuthelela ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule zamagama ezisebujameni iinsombululo zemiraro eyenzekako
nokwabelana iinsombululo zakho ufake iinsombululo zakho ufake abe ahlathululo iinsombululo efakahalangana ukwabelana
okurholela ukwabelana ngokulingana ukwabelana ngokulingana okungezakhe, umraro efakahlangana ngokulinganako nokuhlela
ekuhlukaniseni. nokubuthelela kwenomboro nokubuthelela kwenomboro ezizeleko ukwabelana ngokulinganako ngeenqhema ukufikela e-100
ezizeleko ukufika e-10 begodu ukufika e-20 begodu nangempendulo nangokuhlela ngeenqhema ukufikelela kumphumela ozokufakahlangana
nangempendulo ezifaka hlangana ezifaka hlangana okuseleko. e-50 kumphumela ozokufakahlangana neensalela.
okuseleko. neensalela.
1.10 Ukusombulula nokuhlathulula Ukusombulula nokuhlathulula
Ukwabelana iinsombululo zemiraro iinsombululo zemiraro
okurholela eyenzekako efakahlangana eyenzekako efakahlangana
emafraktjhinini ukwabelana ngokulinganako ukwabelana ngokulinganako
ekurholela eensombululweni ekurholela eensombululweni
ezifaka amafraktjhini ahlobanako ezifaka amafraktjhini ahlobanako
nangahlobaniko. nangahlobaniko.
1.11 Thoma ukulemuka amasende nemali • Khumbula bewufanise imali • Ukukhumbula nokufanisa imali • Ukukhumbula nokufanisa imali yoke
Imali yamaphepha yeSewula Afrika. eziinhlavu yeSewula Afrika: yeSewula Afrika eziinhlamvu 5c, yeSewula Afrika eziinhlamvu nemali
• (5c, 10c, 20, 50c, R1, R2; R5) 10c, 20c, 50c, R1, R2, R5, nemali emaphepha
kunye nemali emaphepha i-R10 emaphepha R10, R20, R50
• Ukurarulula imiraro yemali
ne R20 • Ukurarulula imiraro yemali efakahlangana amanani netjhentjhi
• Ukurarulula imiraro efaka efakahlangana inani netjhentjhi yamaranda namasende
hlangana amanani wemali kufikela emarandeni ama-R99
• Tjhugulula amarandi namasende
netjhentjii yama R20 namasende ama- 90c.
neyamasende ukufika ema-20c
21
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
UKUBALA OKUSEBUJAMENI OBUTJHAPHULUKILEKO
22
1.12 Sebenzisa amathekhiniki alandelayo Sebenzisa amaqhinga alandelako Sebenzisa amaqhinga alandelako
Amathekhiniki nawubalako lokhana nakubalwako. lokhana nakubalwako.
• Ama-apharethasi aphathekako • Imidwebo nofana amapharethasi • Ukwakha nokuphula kweenomboro
(iindlela njengezinto zokubala aphathekako isib. Izinto zokubala
namaqhinga) • Ukubuyelela kabili nokuqunta
• Gwala iinthombe • Ukwakha nokuphula kweenomboro phakathi
• Ukwakhabewuphadhle iinomboro • Ukubuyelela kabili nokuqunta • Inambalayini
• Ukubuyelela nkuqunta phakathi phakathi • Tlola ngamatjhumi.
• Iinamba layini • Inambalayini
1.13 Ukusombulula imiraro yokuhlanganisa • Ukuhlanganisa ukufika e-20 • Ukuhlanganisa ukufikela e-99 • Ukuhlanganisa ukufikela ku-999
nokukhupha etjhiwo ngomlomo • Ukukhupha ema-99 • Ukukhupha ema-999
Ukuhlanganisa • Ukukhupha ema- 20
ngeensombululo ukufika e-10.
nokukhupha • Sebenzisa amatshwayo afaneleko • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo
(+, –, =, ) afaneleko (+, –, =, ) afaneleko (+, –, =, )
• Ukuphrakthisa inambabhondi • Ukuphrakthisa inambabhondi • Ukuphrakthisa inambabhondi
ukufika e-10 ukufika e-20 ukufika e-30
1.14 • Hlanganisa inomboro efanako • Buyabuyelela iinomboro ukusuka • Buyabuyelela iinomboro ngeye 2, 3,
Ukuhlanganisa ngokubuyelela ukufika e-20 keyo-1 ukufika e-10 ngaku -2, 5, 3 4,5,10 ukuhlanganisa i-100.
okubuyelelweko neye- 4 ukwenza ama-50.
• Sebenzisa amatshwayo afaneleko • Ukusebenzisa amatshwayo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kurholela (+, =, ) • Ukusebenzisa amatshwayo afaneleko (x, )
ekubuyabuyeleleni afaneleko (+, x, =, )
1.15 • Hlukanisa iinomboro ukufika e-99
ngeye-2, 3, 4,5,10.
Ukuhlukanisa
• Ukusebenzisa amatshwayo
afaneleko (÷, =, )
1.16 Umqondo nomboro : Irherho 10 Umqondonomboro: Irherho Umqondonomboro: Umqondonomboro:
Umsetjenzana ngamunye uthoma ukufika e-20 Irherho ukufika e-99 Irherho ukufika e-1000
Iimbalo zehloko
ngeembalo zehloko: • Nikela inomboro ngaphambili • Ukurhemisa iinomboro • Ukurhemisa iinomboro
• Ukubala izinto zangamalanga namkha ngemuva kwenye ezikhethiweko ngokwesede ezikhethiweko ngokwesede
• Ukubala uyephambili nemuva inomboro. enikeliweko. enikeliweko.
• Iinomboro sikhundla • Hlela isede enikelweko • Ukumadanisa iinomboro ukufika • Ukuqanathisa iinomboro ukufika
yeenomboro ezikhethiweko e-99 bewutjho bonyana ngiyiphi e-1000 nokutjho bona ngiyiphi ekulu
• Wahla izandla amahlandlha
enengi nofana encani nga: 1, 2, 3, 4, namkha encani nga: 1, 2,3,4,5
amanengi/ambalwa • Madanisa iinomboro ukufika e-20
5, begodu nangali-10 begodu nangali 10.
• Ngimaphi amahlandlha wokuwahla bewutjho nokobana ngiyiphi keyo-1
amanengi khulu/ncani khulu/ nengi/ neye-2 ekulu namkha encani.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ncanyana
• Ngiyiphi inomboro eza ngaphambili/
ngemuva /hlangana
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
UKUBALA OKUSEBUJAMENI OBUTJHAPHULUKILEKO (KURAGELA PHAMBILI)
CAPS 1.16 Ukukhumbula msinyana: Ukukhumbula msinyana : Ukukhumbula msinyana :
• Ukukhumbula amaphuzu
Iimbalo zehloko • Ukukhumbula amaphuzu • Ukukhumbula amaphuzu wamambala ngokuhlanganisa
wamambala ngokuhlanganisa wamambala ngokuhlanganisa nokukhupha ukufika e-20
nokukhupha ukufika e-10 nokukhupha ukufika e-20 • Hlanganisa nofana ukhuphe
• Hlanganisa nofana ukhuphe iimbuyabuyeleli ze-10 ukusukela e-0
iimbuyabuyeleli ze-10 ukusukela e-0 ukuya e-100
ukuya e-100 • Ukubuyelela kwamambala kwe:
-- Ithebula 2 wokubuyabuyelela
aneempendulo ukufika e-20
-- 10 amathebula wokubuyabuyelela
aneempendulo ukufika e-100
• Amaphuzu weenomboro
wokuhlukanisa:
-- ukufika e-20 ezihlukaniseka ngo
ku 2
-- ukufika e-100 ezihlukaniseka nge-
10
Amaqhinga wokubala Amaqhinga wokubala Amaqhinga wokubala
Ukusebenzisa amaqhinga wokubala
Ukusebenzisa amaqhinga wokubala Ukusebenzisa amaqhinga wokubala alandelako:
ukuhlanganisa nokukhupha ukuhlanganisa nokukhupha • Beka inomboro ekulu maqangi
ngekghono elifaneleko: ngekghono elifaneleko: ukuze ubale uyephambili nofana
• Beka inomboro ekulu maqangi • Beka inomboro ekulu maqangi ubale uye emuva
ukuze ubale uyephambili nofana ukuze ubale uyephambili nofana • Inambalayini.
ubale uye emuva ubale uye emuva • Ukubuyelela nokuhlukanisa
• Inambalayini. • Inambalayini. • Ukwakha nokuphula
• Ukusebenzisa ubudlelwana
• Ukubuyelela nokuhlukanisa • Ukubuyelela nokuhlukanisa
obuphakathi okuhlanganisa
• Ukwakha nokuphula • Ukwakha nokuphula nokukhupha.
• Ukusebenzisa ubudlelwana • Ukusebenzisa ubudlelwana
obuphakathi okuhlanganisa hlangana bokubuyelela
nokukhupha. nokuhlukanisa.
1.17 • Sebenzisa bewutjho amafraktjhini • Sebenzisa bewutjho amafraktjhini
wohlavu olulodwa ajayelekileko wohlavu olulodwa nalayo angena
Amafraktjhini. okufakahlangana neengcezu, hlavu olulodwa ajayelekileko
amakota, isithathu begodu nesihlanu okufakahlangana neengcezu,
njll amakota, isithathu begodu nesihlanu
njll
• Ukubona amafraktjhini ebujameni • Ukubona amafraktjhini ebujameni
obuyidayagremu obuyidayagremu
• Tlola amafraktjhini njengecezu • Thoma ukulemuka bona iinquntu
elilodwa, iinthathu ezimbili ezimbili namkha iinthathu ezintathu
zenza yinye epheleleko nokuthi
isiquntu esisodwa namakota amabili
23 ziyalingana.
• Tlola amafraktjhini njengesiquntu
esisodwa, iinthathu ezimbili
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UMBONOMAZOMBE WESIGABA ESISISEKELO
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
24
Iragelo phambili lamaPhetheni, amaFanktjhini ne-Aljibhra.
• KumaPhetheni, amaFanktjhini ne-Aljibhra abafundi banikelwa amathuba wokuthi :
-- Baqedelele bebangezelele amaphetheni ajanyiselwe ngeendlela ezihlukeneko.
-- Bafanise bebahlathulule amaphetheni.
• Ukuhlathulula amaphetheni kuleka isisekelo kubafundi besigaba esiphakathi ukuthi bahlathulule imithetho yamaphetheni. Kwamva lokhu kuba ngendlela ehlelekileko emsebenzini
we-aljibra esigabeni esiphakathi.
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
2.1 Ukukopa nokungezelela. Ukukopa, ungezelele Ukukopa, ungezelele Ukukopa, ungezelele
Ukukopa nokungezelela bewuhlathulule bewuhlathulule bewuhlathulule
Amaphetheni
weJiyomethri amaphetheni alula Ukukopa, ungezelele bewuhlathulule Ukukopa, ungezelele nokuhlathulula Ukukopa, ungezelele nokuhlathulula
ngokusebenzisa izinto ngamagama ngamagama ngamagama
ezibonakalako kunye nemigwalo • Amaphetheni alula enziwe ngezinto • Amaphetheni arareneko eyenziwe • Amaphetheni arareneko eyenziwe
(Isib. ngokusebenzisa imibala ezibonakalako ngezinto eziphathekako ngezinto eziphathekako
nobujamo)
• Amaphetheni alula enziwe • Amaphetheni arareneko enziwa • Amaphetheni arareneko enziwa
ngemigwalo yemida, ubujamo ngokugwala imida, ubujamo nofana ngokugwala imida, ubujamo nofana
nofana izinto. izinto. izinto.
Yenza bewuhlathulule amaphetheni Yenza bewuhlathulule amaphetheni Yenza bewuhlathulule amaphetheni
ISIGABA ESISISEKELO AMAGREYIDI 1-3
wakho okungewakhe wakho
Yenza amaphetheni weJiyomethri • Ngezinto eziphathekako • Ngezinto ezibonakalako
• Ngezinto ezibonakalako • Ngokugwala imida, ubujamo nofana • Ngokugwala imida, ubujamo nofana
• Ngokugwala imida, ubujamo nofana izinto izinto
izinto
Amaphetheni asizombelezileko Amaphetheni asizombelezileko Amaphetheni asizombelezileko
Ukukhomba, ukuhlathulula Ukukhomba, ukuhlathulula Ukukhomba, ukuhlathulula
ngamagama nokukopa amaphetheni ngamagama nokukopa amaphetheni ngamagama nokukopa amaphetheni
weJiyomethri weJiyomethri weJiyomethri
• Ngokwemvelo • Ngokwemvelo • Ngokwemvelo
• Kusukela epilweni yangamalanga • Kusukela epilweni yangamalanga • Kusukela epilweni yangamalanga
yesimodeni, yesimodeni, yesimodeni,
• Asuka kwilifa lamasiko wethu • Asuka kwilifa lamasiko wethu • Asuka kwilifa lamasiko wethu
2.2 Ukukopa, ukungezelela Ukukopa, ukwandisa Ukukopa, ukwandisa
nokuhlathulula nokuhlathulula. nokuhlathulula.
Amaphetheni
weenomboro. Ukukopa, ungezelele bewuhlathulule Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ukulandelanisa kwenomboro elula iinomboro ezilula ezilamanako ukufika iinomboro ezilula ezilamanako ukufika
ukufika e-100. okungenani e-200. okungenani e-999
Ukutlama nokuhlathulula Ukutlama nokuhlathulula Ukutlama nokuhlathulula
amaphetheni okungewakhe amaphetheni okungewakhe amaphetheni okungewakhe
UMBONOMAZOMBE WESIGABA ESISISEKELO
3. ISIKHALA NOBUJAMO (IJIYOMETRHI)
Iragelo phambili lesikhala nobujamo.
CAPS
Iragelo phambili eliqakathekileko lesikhala nobujamo liphumelele ngoku :
• Nqophisa emikghweni emitjha nematshwayeni wobujamo nezinto egreyidini enye nenye begodu;
• Tjhida ekufundeni ilimi lobujamo nokumadanisa imibono ehlukeneko entweni eyodwa ekufundeni nekulandeleni iinkombatjhuba ezisemebheni engakahleleki.
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
3.1 Ilimi lobujamo Ilimi lobujamo Ilimi lobujamo
Ubujamo, Hlathulula ubujamo bento Hlathulula ubujamo bento Hlathulula ubujamo bento
ukujayeza nokuhlobana kwenye nenye isib. nokuhlobana kwenye nenye isib. nokuhlobana kwenye nenye isib.
nokubukela phezu-kwe, phambi-kwe, ngemuva- phezu-kwe, phambi-kwe, ngemuva- phezu-kwe, phambi-kwe, ngemuva-
kwe, ngesinceleni, ngesidleni, kwe, ngesinceleni, ngesidleni, phezulu, kwe, ngesinceleni, ngesidleni, phezulu,
phezulu, phasi, hlanu-kwe. phasi, hlanu-kwe. phasi, hlanu-kwe.
Ubujamo nokubukela Ubujamo nokubukela Ubujamo nokubukela
• Ukukhumbula nokumadanisa • Ukukhumbula nokumadanisa • Ukukhumbula nokumadanisa
imibono ehlukeneko yezinto imibono ehlukeneko yezinto imibono ehlukeneko yezinto
ezifanako zangamalanga. ezifanako zangamalanga. ezifanako zangamalanga
• Yitjho into esetjenziswa ngamalanga
lokha nawutjengiswa ihlangothi layo
elingakajayeleki
• Funda, hlathulula begodu ugwale
amamebhe angasisemthethweni,
nofana ukubona ingaphezulu
lebuthelelo lezinto.
• Thola izinto emimebheni
Ubujamo nekombatjhuba Ubujamo nekombatjhuba Ubujamo nekombatjhuba Ubujamo nekombatjhuba
• Ukulandela ikombatjhuba • Ukulandela ikombatjhuba Landela iinlayelo ukukhambakhamba • Landela iinlayelo ukwenzela
yokukhambakhamba ngetlasini yokukhambakhamba ngeklasini ngetlasini. ukukhambakhamba ngetlasini,
begodu nesikolweni.
• Ukulandela umlayezo ubeka into
ngokuhlobana kwenye nenye isib. • Nikela iinlayelo ukwenzela
beka ipensela ngemuva kwebhoksi. ukukhambakhamba.
• Landela iinlayeelo kusuka kwenye
indawo ukuya kwenye emebheni
ongasingowomthetho.
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
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3.2 Irherho lezinto Irherho lezinto Irherho lezinto Irherho lezinto
26
Izinto Ukubona nokutjho izinto Ukubona nokutjho izinto Ukubona nokutjho izinto Ukubona nokutjho izinto
ezibobusontathu ezibobusontathu (3-D) ezingetlasini ezibobusontathu (3-D) ezingetlasini ezibobusontathu (3-D) ezingetlasini ezibobusontathu (3-D) ezingetlasini
neenthombeni neenthombeni neenthombeni neenthombeni
(3-D)
• Ubujamo bebhola • Ubujamo bebhola (indulungu) • Ubujamo bebhola (indulungu) • Ubujamo bebhola (indulungu)
• Ubujamo bebhoksi • Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhoksi (iphrizimu)
• Isilinda • Isilinda
• Amaphiramidi.
• Amakhowuni.
Amatshwayo wezinto Amatshwayo wezinto Amatshwayo wezinto Amatshwayo wezinto
Hlathulula, hlukanisa ngemihlobo, Hlathulula, hlukanisa ngemihlobo, Hlathulula, hlukanisa ngemihlobo, Ukuhlathulula, ukubeka ngeengaba
umadanise izinto ezibusontathu umadanise izinto ezibusontathu (3-D) umadanise izinto ezibusontathu (3-D) nokumadanisa izinto ezibobusontathu
(3-D) ngokuya: ngokuya: ngokuya: (3-D) ngokuya nga:
• ngobukhulu • ngobukhulu • Ngobukhulu / isayizi • Mabumbeko abobusobubili (2-
D) lawo enza ubuso bezinto
• ngombala • ngombala • ngezinto ezigedekako
ezibobusontathu (3-D)
• ngezinto ezigedekako • ngezinto ezigedekako • ngezinto ezitjhelelako
• Mabala aparaleleko nofana ajikako.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• ngezinto ezitjhelelako • ngezinto ezitjhelelako
Imisebenzi enqotjhiweko Imisebenzi enqotjhiweko Imisebenzi enqotjhiweko Imisebenzi enqotjhiweko.
• Ukusebenzisa izinto ze 3-D • Ukuyelela nokwakha izinto ze 3-D • Ukuyelela nokwakha izinto ze 3-D • Ukuyelela nokwakha izinto ze 3-D
ezifana namabhlogo wokwakha, ngokusebenzisa iinsetjenziswa ngokusebenzisa iinsetjenziswa ngokusebenzisa iinsetjenziswa
izinto ezibuyelelweko njll. eziphathekako ezifana amabhlogo eziphathekako ezifana eziphathekako ezifana
Ukwakha / ukutlama izinto .Isib wokwakha, izinto ezibuyelelweko, namabumbeko we 2-D asikiweko, namabumbeko we 2-D asikiweko,
umbhotjhongo, amabhlorho njll. iinsetjenziswa zokwakha. amabhlogo wokwakha, izinto idaka, iingojwana zamazinyo,
ezibuyelelweko, iinsetjenziswa amathunjana wokusela, nezinye
zokwakha, nezinye izinto izinto zeJiyomethri ezi 3-D.
zeJiyomethri ezi 3-D.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
3.3 Ukukhumbula, ukubona Iirhemo lamajamo Ubujamo obuhlukeneko. Ubujamo obuhlukeneko.
begodu nokutjho ubujamo
CAPS Ubujamo Yazi bewutjho ubujamo obubusobubili Yazi bewutjho ubujamo obubusobubili Yazi bewutjho ubujamo obubusobubili
obubuso bubili obungetlasini
obubusobubili (2-D) (2-D) (2-D)
begodu neenthombeni, okufaka
(2-D)
hlangana: • indulungu • Indulungu • Indulungu
a) Amatshwayo wabafundi. • uncantathu • Uncantathu • Uncantathu
b) Igama letlasi • isikwere • Isikwere • Isikwere
• Uncamane • Uncamane
Amatshwayo wamajamo Amatshwayo wamajamo Amatshwayo wamajamo
Ukuhlathulula, ukuhlukanisa Ukuhlathulula, ukuhlukanisa Ukuhlathulula, ukuhlukanisa
ngemihlobo, nokumadanisa amajamo ngemihlobo nokumadanisa amajamo ngemihlobo nokumadanisa amajamo
abobusobubili (2-D) ngokuya ngo/nga: abobusobubili (2-D) ngokuya ngo /nge/ abobusobubili (2-D) ngokuya nge/nga:
nga:
• bukhulu • jamo
• bukhulu
• mbala • amahlangothi athwi/anqophileko
• jamo
• amahlangothi athwi/anqophileko • amahlangothi andulungu/arondo
• amahlangothi athwi/anqophileko
• amahlangothi andulungu/arondo
• amahlangothi andulungu/arondo
Gwala amajamo
• Iindulungu
• Aboncantathu
• Iinkwere
• Aboncamane
3.4 Isimethri Isimethri Isimethri Isimethri
Isimethri • Yazi isimethri ngowakho • Yazi isimethri ngowakho umzimba. • Yazi bewuthale umuda wesimethri • Yazi bewuthale umuda wesimethri
umzimba. kumajamo abobusobubili (2-D) kumajamo abobusobubili (2-D)
• Yazi bewuthale umuda wesimethri
weJiyomethri nalawo angasiwo weJiyomethri
kumajamo abobusobubili (2-D)
weJiyomethri.
weJiyomethri nalawo angasiwo • nalawo angasiwo weJiyomethri.
weJiyomethri.
• Ukukhetha umuda wesimethri
ngokubhinca iphepha nokuveza
isiboniso.
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4. UKUMEDA
28
Iragelo phambili lokuMeda
• Iragelo phambili lokumeda ukweqela kamanye amagreyidi kuphumelele ngokungenisa lokhu :
-- Iindlela ezitja zokumeda;
-- Amathulusi amatjha wokumeda,ukuthoma ngamathulusi angakahleleki ukuya kunsetjenziswa zeemedo ezihlelekileko zegreyidi 2 neye 3;
-- Amayunidi amatjha wokumeda, khulukhulu kugreyidi ye 2 neye 3.
• Ukubala nokurarulula imiraro yokumeda kufanele kuveze ilemuko lemisebenzi yeenomboro esele yenziwe.
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
4.1 Ukudlula kwesikhathi Ukudlula kwesikhathi
Isikhathi Kukhuluma ngokudlula kwesikhathi Kukhuluma ngokudlula kwesikhathi
• Khuluma ngezinto ezenzeka • Hlela izehlakalo eziqhelekileko
emini nezinto ezenzeka ebusuku. ezisuke epilweni yabo.
• Abafundi balandelanisa • Ukumadanisa ubude besikhathi
izehlakalo ezenzeke emini. kusetjenziswa ilimi isib.iskhathi
eside, isikhathi esifitjhani,
• Ukuhlela izehlakalo ezenzeka
masinyana, kabuthaka.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
njalo emaphilweni wabo.
• Ukulandelanisa izehlakalo
kusetjenziswa ilimu elifaka nokuthi
izolo, namhlanje, kusasa
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
4.1 Ukutjho isikhathi Ukutjho isikhathi Ukutjho isikhathi
CAPS Isikhathi • Ukuhlathulula nangabe kwenzeka • Funda amalanga ekhalendeni.
into kusetjenziswa ilimi isib.
• Ukubeka ekhalendeni amalanga
Ekuseni, ngemuva kwedina,
wamabeletho, imigidingo yekolo,
ebusuku, ekuseni khlu, ngemuva
amalanga wamaholideyi, izehlakalo
kwesikhathi.
zomlando, izehlakalo zesikolo.
• Ukutjho nokulandelanisa amalanga • Ukutjho nokulandelanisa amalanga
• Ukutjho isikhathi sama iri ali-12
weveke, neenyanga zonyaka. weveke ne Iinyanga zonyaka.
-- ngama-iri,
• Ukubeka amalanga wamabeletho • Ukubeka ekhalendeni amalanga
ekhalendeni wamabeletho, imigidingo yekolo, -- isigamu se-iri
amalanga wamaholideyi, izehlakalo
-- ikota ye-iri
zomlando, izehlakalo zesikolo.
-- ngamaminithi
• Ukutjho isikhathi ngama-iri ali-
12, isigamu se-iri nekota ye-iri asewatjhini ye-analogo newatjhi yedijithi
esisewatjhini ye-analogo. nezinye iintlhabagelo zamadijithi
ezitjengisa isikhathi: isib. Umaliledinini.
Bala ubude besikhathi nokudlula Bala ubude besikhathi nokudlula
kwesikhathi kwesikhathi
• Sebenzisa amakhalenda ukubala • Sebenzisa amakhalenda ukubala
nokuhlathulula ubude besikhathi nokuhlathulula ubude besikhathi
ukuya nga: ukuya nga:
-- malanga -- malanga
-- mveke. -- mveke
-- nyanga.
• Ukutjhugululwa hlangana namalanga
nemveke
• Ukutjhugululwa hlangana kwemveke
nenyanga
• Sebenzisa iwatjhi ukubala ubude • Sebenzisa amawatjhi ukubala ubude
besikhathi ukuya: besikhathi ukuya:
-- ngama-iri -- ngama-iri
-- nge siquntu se-iri. -- Iinquntu ze-iri.
-- Amakota we-iri.
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4.2 Ukumeda okungakahleleki Ukumeda okungakahleleki Ukumeda okungakahleleki Ukumeda okungakahleleki
30 • Ukumadanisa nokuhlela ubude, • Ukumadanisa nokuhlela ubude,
Ubude
ukuphakama nofana ububanzi ukuphakama nofana ububanzi
bezinto ezimbili nofana ezinengi bezinto ezimbili nofana ezinengi
ngokuzibeka enye eqadi kwenye. ngokuzibeka enye eqadi kwenye.
Ukusebenzisa ilimu ukukhuluma Ukusebenzisa ilimu ukukhuluma
nokufanisa Isib.ubude, nokufanisa Isib.ubude, ubufitjhani,
ubufitjhani, omude nobubanzi. omude nobubanzi.
• Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela ukumadanisa, ukuhlela ukumadanisa, ukuhlela nokurekhoda
bewurekhode ubude usebenzise bewurekhode ubude usebenzise ubude ngokusebenzisa iimedo
iimedo ezisezingeni elingakahleleki iimedo ezisezingeni elingakahleleki ezisezingeni elingakahleleki Isib.
isib. Ubude besandla, igadango, isib. Ubude besandla, igadango, Izandla, igadango, ubude bepensela,
ubude bepensela, izinto zokubala. ubude bepensela, izinto zokubala. izinto zokubala.
• Hlathulula ubude bezinto ngokubala • Hlathulula ubude bezinto ngokubala • Hlathulula ubude bezinto ngokubala
nokutjho ubude kumayunidi nokutjho ubude kumayunidi nokutjho bona mangaki amayunidi
angakahleleki. angakahleleki. wobude angakahleleki abekakhona.
Ukwethula ukumeda okuhlelekileko. Ukwethula ukumeda okuhlelekileko.
• Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela nokurekhoda ukumadanisa, ukuhlela nokurekhoda
ubude ngokusebenzisa amamitha ubude ngokusebenzisa amamitha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
(kungaba iingodo zamamitha (kungaba iingodo zamamitha namkha
namkha iintambo zobude iintambo zobude bamamithara)
bamamithara) njenge yunidi yobude njenge yunidi yobude obusezingeni.
obusezingeni. • Ukulinganisa nokumeda ubude
ngamasentimitha ngokusebenzisa
irula.
(Ukutjhugululwa hlangana namamitha
namasentimitha akufuneki).
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
4.3 Ukulinganisa okungakahleleki Ukulinganisa okungakahleleki Ukulinganisa okungakahleleki kulinganisa okungakahleleki
CAPS Ubungako/ • Ukumadanisa nokuhlela • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, ukumadanisa,
ubudisi ubudisi bezinto ezimbili namkha ukumadanisa, ukuhlela, ukumadanisa, ukuhlela, ukuhlela, bekurekhodwe ubudisi,
ngaphezulu ngokuzizwa bekurekhodwe ubudisi, bekurekhodwe ubudisi, kusetjenziswa kusetjenziswa isikala sokudzimelela
namkha ngokusebenzisa isikala kusetjenziswa isikala sokudzimelela isikala sokudzimelela nesilinganiso nesilinganiso esingakahleleki isib.
esimedako. nesilinganiso esingakahleleki isib. esingakahleleki isib. amabhlogo,iintina amabhlogo,iintina
Amabhlogo, iintina njll.
• Hlathulula ubudisi bezinto ngokubala • Hlathulula ubudisi bezinto ngokubala
• Hlathulula ubudisi bezinto nokutjho ubudisi bamayunidi nokutjho ubudisi bamayunidi
ngokubala nokutjho ubudisi angakahleleki. angakahleleki.
bamayunidi angakahleleki.
• Ukusebenzisa ilimi ukukhuluma • Ukusebenzisa ilimi ukukhuluma
• Ukusebenzisa ilimi ukukhuluma • Ukusebenzisa ilimi ukukhuluma ngokumadanisa isib. ngokumadanisa isib.elula,ebudisi,elula-
nokumadanisa Isib. Umkhanyo, ngokumadanisa isib.elula, ebudisi, elula,ebudisi,elula-khulu,ebudisi-khulu khulu,ebudisi-khulu
budisi, lula, budisi khulu. elula-khulu, ebudisi-khulu.
Ukwethula ukulinganisa Ukwethula ukulinganisa
okuhlelekileko okuhlelekileko
• Ukumadanisa, ukuhlela • Ukumadanisa, ukuhlela nokurekhoda
nokurekhoda ubudisi beempakana ubudisi beempakana zezinto
zezinto zerhwebo lezo ubudisi bazo zerhwebo lezo ubudisi bazo bubalwe
bubalwekwaphela ngamakiligremu ngamakhilogremu Isib.
Isib. Amakhilogremu ama-2 wereyisi
-- Amakhilogremu ama-2 wereyisi
nekilogremu e-1 yeflowuru.
nekhilogremu e-1 yeflowuru.
-- Ngamagremu Isib amagremu ama-
500 wetshwayi.
• Balinganise ubudisi babo • Balinganise ubudisi babo
ngamakhilogremu ngokusebenzisa ngamakhilogremu ngokusebenzisa
isikala sangendlini yokuhlambela. isikala sangendlini yokuhlambela.
(Ukutjhugululwa hlangana namagremu
namakhilogremu akufuneki)
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4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Ukumeda okungakahlelelwa Ukumeda okungakahlelelwa
32
Umthamo/ • Ukumadanisa nokuhlela • Ukumadanisa nokuhlela
Ivolumu ubungako okusamanzi ubungako okusamanzi (umthamo)
(umthamo) okuseemumathini okuseemumathini ezimbili
ezimbili ezibekwe enye eduze ezibekwe enye eduze kwenye.
kwenye. Abafundi bazokuhlola Abafundi bazokuhlola ngokuthela
ngokuthela esimumathini esimumathini sesithathu
sesithathu nakunesidingo. nakunesidingo.
• Ukumadanisa nokuhlela • Ukumadanisa nokuhlela
ubungako balokho okusamanzi ubungako balokho okusamanzi
okungaphathwa ziimumathi okungaphathwa ziimumathi ezimbili
ezimbili nazizalisiweko. nazizalisiweko.
(umthamo)
• Sebenzisa ilimi ukukhuluma • Sebenzisa ilimi ukukhuluma
ngokufana Isib okunengi,okunca ngokufana Isib okunengi, okuncani,
ni,okuzeleko,okunganalitho okuzeleko, okunganalitho.
• Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela ukumadanisa, ukuhlela ukumadanisa, ukuhlela bewurekhode
nokurekhoda umthamo bewurekhode umthamo umthamo ongeemumathini (Isib.
weemumathi ngokusebenzisa weemumathi (Isib. ubunengi ubunengi isimumathi esikghona
iimedo ezingakahleleki. Isib isimumathi esikghona ukuphatha ukuphatha nasizalisiweko)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Isigobho nekomitjhi nasizalisiweko) ngokusebenzisa ngokusebenzisa izinto zokumeda
izinto zokumeda ezingakahleleki isib. ezingakahleleki isib. Iingobho
Iingobho neenkomitji. neenkomitji.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
4.4 • Ukuhlathulula umthamo • Ukuhlathulula umthamo • Ukuhlathulula umthamo wesimumathi
wesimumathi ngokubala nookutjho wesimumathi ngokubala nookutjho ngokubala nookutjho bonyana
CAPS Umthamo/
bonyana mayunithi amangaki bonyana mayunithi amangaki mayunithi amangaki angakahleleki
Ivolumu
angakahleleki angazalisa angakahleleki angazalisa isimumathi angazalisa isimumathi isib. Ibhodlelo
isimumathi isib. Ibhodlelo isib. Ibhodlelo linomthamo linomthamo weenkomitji ezine.
linomthamo weenkomitji ezine. weenkomitji ezine.
Ukwethula ukumeda okuhlelekileko. Ukwethula ukumeda okuhlelekileko.
• Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela nokurekhoda ukumadanisa, ukuhlela nokurekhoda
ubungako bezinto ngokumeda ubungako bezinto ngokumeda
ngamalitha. ngamalitha, isiquntu selitha nekota
yamalitha
• Ukumadanisa, ukuhlela • Ukumadanisa, ukuhlela nokurekhoda
nokurekhoda ubungako ubungako beempakana zezinto
beempakana zezinto zerhwebo lezo zerhwebo lezo ubungako bazo
ubungako bazo bubalwe ngamalitha bubhalwe ngamalitha isib. Ibisi
Isib ibisi lamalitha ama-2, isiselo lamalitha ama-2, isiselo selitha
selitha e-1, ipende yamalitha ama-5. e-1, ipende yamalitha ama-5
nofana kutlolwe ngamamililitha
isib. Ibisi elimamililitha ama-500,
isiselo esimamililitha ama -340, i-oli
emamililtha ama -750.
• Ukwazi bona ubungako bekomitji
elingeneko bumamililitha ama-250.
• Ukwazi bona ubungako betelebhula
elingeneko bumamililitha ama-5
(Ukutjhugululwa hlangana namamililitha
namalitha akufuneki).
4.5 Ipherimitha
Ipherimitha Ukurhubhulula ubude obuzombelezako
nobungako bezinto ezi-2-D nezi 3-D
bendawo ngokusebenzisa ukumadanisa
okunqophileko namayunidi
angakahleleki.
Ubungako bendawo
Ukurhubhulula ngobungako bendawo
33 ngokusebenzisa ukuthayela.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UMBONOMAZOMBE WESIGABA ESISISEKELO
5. UKUPHATHA IDATHA
34
Iragelo phambili lokuphatha iDatha.
• Iragelo phambili lokuphatha idatha ukweqela kamanye amagreyidi kuphumelele ngoku:
-- Ukutjhida ekusebenzeni ngezinto ukuya ekusebenzeni ngedatha, kanye
-- Ngokusebenza ngeendlela ezitja zokwethulwa kwedatha.
• Abafundi kufanele basebenze ngomzombe wedatha opheleleko okungenani kanye ngonyaka-lokhu kufaka ukubuthelela nokuhlelwa kwedatha, ukujamisela idatha, ukuhlaziya idatha,
ukurhumutjha idatha nokubika idatha.
• Amanye wamaphuzu wokuphatha idatha angasetjenziswa nemisebenzi ehlukeneko.
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
5.1 Ukubuthelela nokuhlela izinto Ukubuthelela nokuhlela izinto
ngemihlobo ngemihlobo
Ukubuthelela
nokuhlela izinto Ukubuthelela nokuhlela izinto Ukubuthelela nokuhlela izinto
ngemihlobo ezibonakalako ngemihlobo ezibonakalako ngemihlobo
5.2 Ukujamiselela ibuthelelo lezinto Ukujamiselela ibuthelelo lezinto
elihlelekileko elihlelekileko
Ukujamiselela
ibuthelelo lezinto Ukugwala iinthombe zezinto Ukugwala iinthombe zezinto
ISIGABA ESISISEKELO AMAGREYIDI 1-3
elihlelekileko ezibuthelelweko. ezibuthelelweko
5.3 Coca bewubike ngokuhlelwa Coca bewubike ngokuhlelwa
kwezinto ezibuthelelweko kwezinto ezibuthelelweko
Coca bewubike
Phendula imibuzo ngokuthi: • Nikela iinzathu ngokuthi
ngokuhlelwa
kwezinto • Okubuthelelweko kwahlelwa okubuthelelweko kuhlelwe bunjani.
ezibuthelelweko ngemihlobohlobo bunjani?
• Phendula imibuzo ngokuthi:
(umkhiqizo)
-- Ukuhlelwa ngemihlobo kwenziwa
• Imigwalo yebuthelelo.
bunjani ( indlela yekambiso)
-- Okubuthelelweko kwahlelwa
ngemihlobohlobo kunjani?
(umkhiqizo)
• Hlathulula okubuthelelweko
nemigwalo ngemihlobo
• Hlathululo bona okubuthelelweko
kuhlelwe bunjani
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO IGREYIDI R IGREYIDI 1 IGREYIDI 2 IGREYIDI 3
5.4 Ukubuthelela nokuhlela idatha Ukubuthelela nokuhlela idatha Ukubuthelela nokuhlela idatha
CAPS Ukubuthelela • Buthelela idatha yetlasi nofana • Buthelela idatha yetlasi nofana • Buthelela idatha yetlasi nofana
nokuhlela idatha yesikolo ukuphendula imibuzo yesikolo ukuphendula imibuzo yesikolo ukuphendula imibuzo
ebuzwa ngutitjhere ebuzwa ngutitjhere ebuzwa ngutitjhere
• Ukuhlela idatha enikelwe ngutitjhere
namkha incwadi yomsebenzi/
incwadi yokufunda
• Hlela idatha ukuya nge:
-- Amarhelo
-- Amathali
-- Amathebula
5.5 Ukujamiselela idatha Ukujamiselela idatha Ukujamiselela idatha
Ukujamiselela • Ukujamiselela idatha negrafu • Ukujamiselela idatha negrafu • Ukujamiselela idatha kuma
idatha yeenthombe. yeenthombe.
-- Iphikthografi (Umkhawulo
• Umkhawulo weenthombe • Umkhawulo weenthombe weenthombe zegrafu ngokunye
zegrafu ngokunye nokunye zegrafu ngokunye nokunye nokunye ngokukhambelana)
ngokukhambelana. ngokukhambelana.
-- Ibhagrafu
5.6 Hlaziya bewurhumutjhe idatha Hlaziya bewurhumutjhe idatha Hlaziya bewurhumutjhe idatha
Ukuhlaziya • Ukuphendula imibuzo ngedatha • Ukuphendula imibuzo ngedatha Ukuphendula imibuzo ngedatha
bebarhumutjhe yeemkhawulo esegrafini yeemkhawulo esegrafini ethulwe :
idatha yeenthombe ngakunye nakunye yeenthombe ngakunye nakunye
• Iphikthografi (Umkhawulo
ngokukhambelanako. ngokukhambelanako
weenthombe zegrafu ngokunye
nokunye ngokukhambelana)
• Ibhagrafi
35
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.3 Ihlathululo Lokumumethweko
Kilesi isigaba sokumumethweko okuhlathululako, utitjhere unikelwe loku:
• Umbonomazombe wegreyidi R-3
• Iintjhukumezo zeenhloko ngokulandelanako ngokuya ngamathemu; ingasi woke amahlangothi wezinye
iinhloko zoke owafundiswa kiwo woke amthemu. Amanye amahlangothi wezinye iinhloko afuna ukufundiswa
ngaphambili kwamanye amahlangothi wezinye iinhloko.
• Ibelo elitjhukunyeziweko leenhloko ngonyaka, njengombana okhunye okumumethweko kudinga isikhathi
esinengi kunesinye, ngokunjalo ezinye zeenhloko zidinga isikhathi esinengi kunezinye.
• Amanothi atlhadlhulako nomhlahlandlela wokufundisa aneembonelo nakufaneleko.
Esinye nesinye isigaba sokumumethweko siphulwe saba ziinhloko. Zoke iingaba zokumumethweko kufanele
zifundiswe kuwo woke amathemu. Ukulandelaniswa kweenhloko ngokwamathemu kunikela umqondo wokuthi iinhloko
zingasabalaliswa bezibuyekezwe unyaka woke. Akukakateleleki ukufundisa zoke iinhloko zeSikhala nobujamo,
ukumeda nokuphatha iDatha ngawowoke amathemu, kodwana, zoke iinhloko kufanele zifundiswe phakathi konyaka.
Esahlukweni 2 (ipharagrafu 2.6) ukulinganiswa kwesigaba sokumumethweko sinikeliwe. Nange lokhu kuhlanganiswa
nama-iri anikelweko ngomnyaka umuntu angabalisisa isikhathi esinikelweko kwesinye nesinye isigaba
sokumumethweko.
Abotitjhere bangakhetha ukulandelanisa (ukuhlela) nokubeka igadango okumumethweko ngokuhlukileko kunalokho
okuphakanyisiweko kilesi isahluko. Abotitjhere bangatjhugulula inani lesikhathi esinikelweko esihlokweni kancani,
kodwana kufanele kutjhejwe ukuthathwa kokuhlobana kwama –iri wokulinda nesikhathi esibekiweko sesigaba,
sokumumethweko eembalweni nofana esiGabeni esisiSekelo.
• EGreyidini -R iMathamethiksi ibunjwe ngendlela omhlobo weembalo ezivumbukako. Ngakho-ke kufanele
bona kuyelelwe bonyana akukafaneli kuphulwe kube isikhathi sezifundo. Utitjhe we greyidi R ufanele alukelele
iimbalo emisetjenzaneni yabafundi yangamalanga. Nanyana isikhathi sokufundisa iimbalo kufanele sibekelwe
lapho utitjhere azokunqopha emisebenzini yokufundisa iimbalo kwaphela, nakungasinjalo abafundi angeke
balemuke nofana bathuthukise iminqopho namakgono weembalo.
• Isikhathi samagreyidi 1-3 sabiwe ngale indlela
-- Ama-iri alikhomba kufanele asetjenziselwe iimbalo ngeveke (10x4 yamathemu x7yama-iri=280 yama-
iri ngonyaka).
-- Zoke iimfundo zeembalo kufanele zibe li-iri nemizuzu ema 24 ngelanga emagreyidini 1-3.
-- Lokhu kutjho ukuthi kunamathemu amane wemveeke ezi-10 ezinamalanga amahlanu (ngomvulo ukuya
kulosihlanu) weemfundo ngeveke.
-- Thatha iveke ukujayeza nokuhlanganisa njalo ekuthomeni kenye nenye ithemu, njengombana abantwana
abancani bakhohlwa okumumethweko okunengi ngesikhathi sokuphumula begodu balahlekelwa naligido
lokufunda. Nikela iveke eyodwa njalo ekupheleni kwethemu uhlanganise imiqondo. Lokhu kunikela
8x4x5=160 yeemfundo.
3.4 Ukulandelanisa nokuhlela okuMumethweko
Amathebula alandelayo anikelwe igreyidi negreyidi ku R-3.
• Ukubeka igadango leenhloko lonyaka woke (kutjengisa ukusabalaliswa kweenhloko ngamathemu woke,
bebuphakamise inani lesikhathi okufanelesicithwe kesinye nesinye isihloko sesinye nesinye isgamu
sokumumethweko).
• Ukulandelanisa iinhloko konyaka woke (kutjengisa bonyana iinhloko zahlukaniswe bunjani ngamathemu
nokuragela phambili kokumumethweko namakghono ngokuya ngamathemu).
• Amanothi wokuhlathulula ngokuya ngesihloko-amathebula lawo anikela ihlathululo lokumumethweko
nomhlahlandlela wokufundiswako yesinye nesinye isihloko njengombana zilandelisiweko emathemini woke.
36 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuhlela Isifundo – Ukunikela Isihloko Sethemu
Inomboro sihloko esiqakatheke khulu Eembalweni zeSigabeni Esisisekelo. Esikhathini esiningi kwenye nenye iveke,
ithemu, nonyaka inqophe eeNomborweni, Ukusebenza Nobudlelwana. Ngokulingeneko, iimfundo eentathu nofana
ngaphezulu zeeMbalo kufanele zinqophe eeNomborweni, UkusebenzaNobudlelwana kwenye neneye iveke. Isikhath
esiseleko sihlukaniselwa iingaba zokumumethweko ezinye.
Isikhala noBujamo nokuMeda zifuna isikhathi esinengi kunokuPhatha iDatha namaPhetheni, amaFanktjhini ne-
Aljibhra. Ithebula elingenzasi linikela isitjengiso sokobana ziimfundo ezingaki okufanele zinikelwe esinye nesinye
isigaba sokumumethweko nesihloko kwenye nenye igreyidi kuma Phetheni, amaFanktjhini ne-Aljibhra, Isikhala
noBujamo, Ukumeda nokuphatha iDatha:
• Ukwabela iGreyidi R iingaba zokumumethweko neenhloko eemfundweni
Njenge Greyidi R, Iimbalo zithatha ubujamo beMbalo Ezisathomako ngalokho ke isikhathi esilandelako
esiphakanyisiweko sinikela zombili izehlakalo zeeMbalo ezinqophileko nemisetjenzana ehlangeneko engakahlelelwa.
Lokhu kwenzelwe ukuqinisekisa ukufundiswa ngokuzeleko kwakho koke okumumethweko okukhona. Imisetjenzana
yeeMbalo Ezivumbukako kungaba kubala inani lama puleyiti neembhigiri okufanele bazikhuphele ukufaka
isibuyisamathe sabo, imidlalo yokubala edlalwa ngaphandle imidlalo yangendlini efana nama Domino namaphazili
wejikhsara, njll. Utitjhere kufanele ahlele kuhle yoke imisetjenzana ngokuya ngokweendingo zabantwana bakhe
neensetjenziswa ezikhona ngetlasini lakhe.
Isikhala noBujamo yingcenye eqakathekileko yokuthuthukisa i-IiMbalo yomfundi omncani begodu kufanele
busatjalaliswe iveke yoke, ngezehlakalo ezithize ezinqophileko ngaphasi kokukhokhelwa ngutitjhere, abafundi
banikelwe amathuba amanengi wokwakha, ukudlala umdlalo wesanda namanzi.
Ukumeda kufanele kufakwe hlangana emisetjenzaneni yokubala, isib. Ukufunisela/ ukulinganisa nokubala lokha
kumedwa ibanga ngezandla, iinyawo namagadango.
Irejistara yokubakhona netjhadi lobi ujamo bezulu zinikela amathuba aneleko wokusebenza ngokuPhatha iDatha.
Ithebula 3.1 Isikhathi esinikelweko ngokuya ngokumumethweko ngeveke
Iingaba zokumumethweko Iinhloko Isikhathi Esiphakanyisiweko
Iinomboro, Ukubala
ama-Opharetjhini Ukukhumbula Inomboro
noBudlelwano Ukubona nokurhumutjha iinomboro ezipheleleko imizuzu eli-120
Inomboro oyibona ngamehlo wengcondo
Ukurarulula imiraro
Amaphetheni, Ukukopulula, ukulula nokutlama amaphetheni wakhe.
imizuzu ema-80
amaFanktjhini ne-Aljibhra
Isikhala noBujamo Ukukhumbula, nokutjho iinthombe/ibumbeko ezinobujamo
(Jiyomethri) obubusobubili (2-D)
Amabumbeko weJiyomethri.
Ukwakha izinto ezinobujamo abobusontathu (3-D) imizuzu ema-80
usebenzise imatheriyali ephathekako
Ubudlelwana bendawo
Iinkombatjhuba
Ukumeda Isikhathi
Ubude
imizuzu ema- 80
Imasi / ubungakho/ ubunengi
Umthamo
Ukuphatha iDatha Ukubuthelela, ukuhlela ngamananeko, ukugwala, ukufunda
imizuzu ema-60
nokujamisela idatha.
Imizuzu ema - 420
INANI
(ama iri ali-7 ngeveke)
CAPS 37
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Isabelo seGreyidi yoku-1 sokumumethweko neenhloko zeemfundo emaGreyidini woku-1ukuya kwe-3
Ngokulingeneko iimfundo ezintathu (o.u hlangana kwama-iri ama-4 nama-iri ama-4½) ngeveke zisetjenziselwa iiNomboro,
ama-Opharetjhini noBudlelwano emagreyidini woku -1, wesi-2 nawesi-3. Iimfundo ezimbili eziseleko (o.u hlangana
kwama-iri ama-2½ nama-iri ama-3) zihlukaniswa hlangana neenhloko zokhunye okumumethwekonukuya ngendlela
ekuphakanyiswe ngayo ngenzasi.
Ithebula 3.2 Inani leemfundo eliphakanyisiweko ngokuya ngokumumethweko nangeThemu yeGreyidi yoku-1
Inani leemfundo
Iingaba zokumumethweko Iinhloko IThemu IThemu IThemu IThemu
Inani
yoku-1 yesi-2 yesi-3 yesi-4
Iinomboro, ama- Iinhloko zoke zeenomboro, ama-
Opharetjhini Opharetjhini noBudlelwano 22 30 28 25 105
Nobudlelwano
Amaphetheni weenomboro 3 3 3 3 12
Amaphetheni,
amaFanktjhini ne-Aljibhra 1 1 1 1 4
Amaphetheni weJiyomethri
Isikhala noBujamo Amajamo abusobubili (2-D) 3 3 6
(Jiyomethri)
Izinto ezibusontathu (3-D) 3 2 1 6
Ubujamo, ukujayeza nokubukela 2 1 3
Isimethri 1 1 2
Ukumeda Isikhathi 2 2
Ubude 2 2 4
Ubudisi 2 2 4
Umthamo/iVolumu 1 2 1 4
Ukuphatha iDatha Ukubuthelela, ukuhlela ngemihlobo,
2 1 3
ukujamisela nokurhumutjha izinto.
Umzombe wedatha opheleleko 3 3
Iingaba zomzombe wedatha 2 2
Inani leemfundo 40 40 40 40 160
38 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ithebula 3.3 Inani leemfundo eziphakanyisiweko ngokuya ngeGreyidi yesi- 2
Inani leemfundo
Iingaba zokumumethweko Iinhloko IThemu IThemu IThemu IThemu
Inani
yoku-1 yesi-2 yesi-3 yesi-4
Iinomboro, ama- Iinhloko zoke zeenomboro, ama-
24 25 24 26 99
Opharetjhini Nobudlelwano Opharetjhini noBudlelwano
Amaphetheni, amaFanktjhini Amaphetheni weenomboro 3 3 3 3 12
ne-Aljibhra Amaphetheni weJiyomethri 1 1 1 1 4
Isikhala noBujamo ubujamo obubusobubili (2-D) 3 3 6
(Jiyomethri)
Izinto ezibobusontathu
3 2 1 6
(3-D)
Ubujamo, ukujayeza nokubukela 2 1 3
Isimethri 1 1 2
Isikhathi 3 1 3 1 8
Ubude 3 1 4
Ukumeda
Ubudisi 3 1 4
Umthamo/iVolumu 3 1 4
Umzombe wedatha opheleleko 3 3 6
Ukuphatha idatha
Iingaba zomzombe wedatha 1 1 2
Inani leemfundo 40 40 40 40 160
Ithebula 3.4 Inani leemfundo eziphakanyisiweko ngokuya ngeGreyidi yesi- 3
Inani leemfundo
Iingaba zokumumethweko Iinhloko IThemu IThemu IThemu IThemu
Inani
yoku -1 yesi-2 yesi-3 yesi-4
Iinomboro, ama- Iinhloko zoke zeenomboro, ama-
26 22 19 27 94
Opharetjhini Nobudlelwano Opharetjhini noBudlelwano
Amaphetheni, amaFanktjhini Amaphetheni weenomboro 3 3 3 3 12
ne-Aljibhra Amaphetheni weJiyomethri 1 1 1 1 4
Isikhala ubujamo obubusobubili (2-D) 2 2 4
noBujamo(Jiyomethri)
Izinto ezibusontathu
3 3 1 7
(3-D)
Ubujamo, ukujayeza nokubukela 2 3 5
Isimethri 2 1 3
Isikhathi 3 2 3 2 10
Ubude 2 2 4
Ubudisi 2 1 3
Ukumeda
Umthamo/iVolumu 2 1 3
iPherimitha 1 1
Ubungako bendawo 2 2
Umzombe wedatha opheleleko 3 3 6
Ukuphatha idatha
Iingaba zomzombe wedatha 1 1 2
Inani leemfundo 40 40 40 40 160
CAPS 39
3.4.1 Umbonomazombe we Greyidi yoku-1ngeThemu
40 UMBONOMAZOMBE WEGREYIDI 1
1.IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDOWENOMBORO: Ukubala ngenomboro ezipheleleko
1.1 Ukubala izinto ngokuthembekako Ukubala izinto ngokuthembekako Ukubala izinto ngokuthembekako Ukubala izinto ngokuthembekako
kufika e -10. kufika ema- 20 kufika ema -40 kufika ema -50
Ukubala ngezinto
Ukunikela ngokuthembekako Nikela ngokuthembekako isilinganiso Nikela ngokuthembekako isilinganiso Nikela ngokuthembekako isilinganiso
isilinganiso senomboro yezinto senomboro yezinto ezingahlolwa senomboro yezinto esingahlolwa senomboro yezinto esingahlolwa
ezingahlolwa ngokuzibala ngokubala. ngokubala. ngokubala.
Kukhuthazwa ukubala ngeenqhema Kukhuthazwa ukubala ngeenqhema. Kukhuthazwa ukubala ngeenqhema
1.2 Ukubala uye phambili nemuva Ukubala uye phambili nemuva Ukubala uye phambili nemuva Ukubala uye phambili nemuva
nga: nga: nga: nga:
Ukubala uye phambili
nemuva • Kunye ukusuka kinanyana ngiyiphi • Kunye ukusuka kwenye nenye • Kunye ukusuka kwenye nenye • Kunye ukusuka kwenye nenye
inomboro hlangana no-1 ukuya inomboro hlangana ne-0 na- 50 inomboro ehlangana ne-0 na-80 inomboro hlangana ne-0 ne-100
ema -20 Ukubala uye phambili nga: Ukubala uye phambili nga: Ukubala uye phambili nga:
• Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye
isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ne-0 na-50 ne-0 na -80 ne-0 ne-100
• Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-5 isibuyabuyelelo saka ku-5 isibuyabuyelelo saka ku-5
hlangana ne-0 na-50 hlangana ne-0 na-80 hlangana ne-0 ne-100
• Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2
hlangana ne -0 na-20 hlangana ne -0 na-80 hlangana ne -0 ne-100
UKUTHUTHUKISWA KOMQONDO WENOMBORO: Ukujamiselela iinomboro ezipheleleko
1.3 Ukukhumbula, ukufanisa Ukukhumbula, ukufanisa Ukukhumbula, ukufanisa Ukukhumbula, ukufanisa
nokufunda iinomboro nokufunda iinomboro nokufunda iinomboro nokufunda iinomboro
Amatswayo
weenomboro • Khumbula, ufanise begodi ufunde • Khumbula, ufanise begodu ufunde • Khumbula, ufanise begodu ufunde • Khumbula, ufanise begodi ufunde
namagama amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka
weenomboro ku-1 ukuya ku-20 ku-1 ukufika ku-50 ku-1 ukufika ku-80 ku-1 kuya ku-100.
• Tlola amatshwayo wenomboro • Tlola amatshwayo wenomboro • Tlola amatshwayo wenomboro • Tlola amatshwayo wenomboro
ukusuka ku-1 ukuya ku-5 ukusuka ku-1 ukufika ku-10 ukusuka ku-1 ukufika ku-20 ukusuka ku-1 ukuya ku-20
• Khumbula,ufanise begodu ufunde • Khumbula, ufanise begodu ufunde • Khumbula, ufanise begodu ufunde • Khumbula, ufanise begodu ufunde
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
amagama wenomboro ukusuka amagama weenomboro ukusuka amagama weenomboro ukusuka amagama wenomboro ukusuka
ku-1 ukuya ku-5 ku-1 ukufika ku-10. ku-1 ukufika ku-10. ku-1 ukuya ku -10.
• Tlola amagama wenomboro • Tlola amagama weenomboro • Tlola amagama wenomboro • Tlola amagama wenomboro
ukusuka ku-1 ukuya ku-5 ukusuka ku-1 ukufika ku-10. ukusuka ku-1 ukufika ku-10 ukusuka ku-1 ukufika ku-10
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDO WENOMBORO: Ukuhlathulula, ukumadanisa nokuhlela iinomboro
1.4 Ukuhlathulula, ukumadanisa Ukuhlathulula, ukumadanisa Ukuhlathulula, ukumadanisa Ukuhlathulula, ukumadanisa
CAPS
begodu nokuhlela izinto ukufikela begodu nokuhlela izinto ukufikela begodu nokuhlela izinto ukufikela begodu nokuhlela izinto ukufikela
Ukuhlathulula,
ku-5 e-10 ku -15 ku -20
ukumadanisa begodu
nokuhlela iinomboro • Ukumadanisa izinto • Ukumadanisa izinto • Ukumadanisa izinto • Ukumadanisa izinto
ezibuthelelweko kuya ngobunengi ezibuthelelweko kuya ngobunengi ezibuthelelweko kuya ngobunengi ezibuthelelweko kuya ngobunengi
ezimbalwa; ngobunengi khulu, ezimbalwa; ngobunengi khulu, ezimbalwa; ngobunengi khulu, ezimbalwa; ngobunengi khulu,
ncanikhulu; nengi -kuna, ncani- ncanikhulu; nengi -kuna, ncani- ncanikhulu; nengi -kuna, ncani- ncanikhulu; nengi -kuna, ncani-
kuna; lingana na, ngobunengi, kuna; lingana na, ngobunengi, kuna; lingana na, ngobunengi, kuna; lingana na, ngobunengi,
obufana, okuhlukileko. obufana, okuhlukileko. obufana, okuhlukileko. obufana, okuhlukileko.
• Hlela izinto ezibuthelelweko
• Hlela izinto ezibuthelelweko • Hlela izinto ezibuthelelweko • Hlela izinto ezibuthelelweko
kusuka kezinengi khulu kuya
kusuka kezinengi khulu kuya kusuka kezinengi khulu kuya kusuka kezinengi khulu kuya
kezincanikhulu nokusuka
kezincanikhulu nokusuka kezincanikhulu nokusuka kezincanikhulu nokusuka
kezincanikhulu ukuya
kezincanikhulu ukuya kezincanikhulu ukuya kezincanikhulu ukuya
kezikulukhulu
kezikulukhulu kezikulukhulu kezikulukhulu
Hlathulula, umadanise, uhlele
Hlathulula, umadanise, uhlele Hlathulula, umadanise, uhlele Hlathulula, umadanise, uhlele neenomboro ukufika ku-20
neenomboro ukufika ku-5 neenomboro ukufika ku-10 neenomboro ukufika ku-15
• Hlathulula, umadanise iinomboro
• Hlathulula, umadanise iinomboro • Hlathulula, umadanise iinomboro • Hlathulula, umadanise iinomboro ezipheleleko ngokuya ngobuncani-
ezipheleleko ngokuya ngobuncani- ezipheleleko ngokuya ngobuncani- ezipheleleko ngokuya ngobuncani- kuna, ngobukhulu-kuna,
kuna, ngobukhulu-kuna, kuna, ngobukhulu-kuna, kuna, ngobukhulu-kuna, ngobunengi-kuna, ngaphasi kuna
ngobunengi-kuna, ngaphasi kuna ngobunengi-kuna, ngaphasi kuna ngobunengi-kuna, ngaphasi kuna nangokulingana
nangokulingana nangokulingana nangokulingana • Hlathulula bewuhlele neenomboro
• Hlathulula bewuhlele neenomboro • Hlathulula bewuhlele neenomboro • Hlathulula bewuhlele neenomboro -- Ukusuka ngencani-khulu ukufika
kekulukulu nokusuka kekulukulu
-- Ukusuka ngencani-khulu ukufika -- Ukusuka ngencani-khulu ukufika -- Ukusuka ngencani-khulu ukufika
kufika kencanikhulu
kekulukulu nokusuka kekulukulu kekulukulu nokusuka kekulukulu kekulukulu nokusuka kekulukulu
kufika kencanikhulu kufika kencanikhulu kufika kencanikhulu -- Ngaphambi, ngemuva, phakathi
nofana nahlangana
-- Sebenzisa inambalayini ka: 1 - 5 -- Ngaphambi, ngemuva, phakathi -- Ngaphambi, ngemuva, phakathi
-- Sebenzisa inambalayini ka:0 -
nofana nahlangana nofana nahlangana
20
-- Sebenzisa inambalayini ka:0 - -- Sebenzisa inambalayini ka:0 - Sebenzisa iinomborosikhundla
10 15 ukukhombisa ukuhlela, indawo
nofana ubujamo benomboro.
• Beka izinto ngokwerhemo
kusuka kweyokuthoma ukufika
kweyesumi, nofana kweyokuthoma
kufika kweyokuphela. Isib.
Yokuthoma, yesibili, yesithathu......
yesumi, kweyokuphela.
41
• Iinomborosikhundla zerherho
lokuthoma kufika etjhumini
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDO WENOMBORO: Ubukhulu bedijithi
42
1.5 Khumbula ubukhulu bedijithi Khumbula ubukhulu bedijithi i-11
beenomboro i-11 ukufika e-15 ukufika e-19.
Ubukhulu bedijithi
• Phulalaza inomboro zamadijithi • Phulalaza inomboro zamadijithi
amabili ngesumi nangayinye/imivo amabili ngesumi nangayinye/imivo
isib.12 li 10 na 2 isib.18 li 10 na 8
SOMBULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako
nawurarulula imiraro uhlathulule nawurarulula imiraro uhlathulule nawurarulula imiraro uhlathulule nawurarulula imiraro uhlathulule
Amathekhiniki
neensombululo: neensombululo: neensombululo: neensombululo:
wokurarulula imiraro
• Ama-apharethasi aphathekako • Ama-apharethasi aphathekako • Ama-apharethasi aphathekako • Ama-apharethasi aphathekako
isib. izinto zokubala isib. izinto zokubala isib. izinto zokubala isib. izinto zokubala
• Iinthombe ezisetjenziselwa • Iinthombe zokugwala iimbalo • Iinthombe zokugwala iimbalo • Iinthombe zokugwala iimbalo
ukwenza iindatjhana zeembalo. zendatjhana zendatjhana zendatjhana
• Amanambalayini ezisekelwe • Ukwakha nokuphula iinomboro • Ukwakha nokuphula iinomboro • Ukwakha nokuphula iinomboro
ma- apharethasi aphathekako
• Ukubuyelela nokuqunta phakathi • Ukubuyelela nokuqunta phakathi • Ukubuyelela nokuqunta phakathi
njengemincanyana yokubala
• Amanambalayini ezisekelwe • Amanambalayini ezisekelwe • Amanambalayini ezisekelwe
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ma- apharethasi aphathekako ma- apharethasi aphathekako ma- apharethasi aphathekako
njengemincanyana yokubala njengemincanyana yokubala njengemincanyana yokubala
1.7 Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama
ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
Ukuhlanganisa
iinsombululo zakho zemiraro iinsombululo zakho zemiraro iinsombululo zakho zemiraro iinsombululo zakho zemiraro
nokukhupha
ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha
nempendulo ukufika ku-5 nempendulo ukufika e-10. nempendulo ukufika e-15. nempendulo ukufika e-20.
1.8 Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama
ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
Ukuhlanganisa
iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro,
ngokubuyelela
ukuhlanganisa okubuyelelweko ukuhlanganisa okubuyelelweko ezifaka ukuhlanganisa okubuyelel-
okurholela
nempendulo ukufika e-10. nempendulo ukufika e-15. weko nempendulo ukufika e-20
ekubuyabuyeleleni
1.9 Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama
ezisebujameni bewuhlathulule esebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
Ukubuthelela
iinsombululo zakho ufake iinsombululo zakho zemiraro iinsombululo zakho ufake iinsombululo zakho ufake
ngeenqhema
ukwabelana ngokulingana okufaka hlangana ukwabelana ukwabelana ngokulingana ukwabelana ngokulingana
nokwabelana
nokubuthelela ngeenqhema ngokulingana nokubuthelela nokubuthelela ngeenqhema nokubuthelela ngeenqhema
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
okurholela
kweenomboro ezipheleleko ukufika ngeenqhema kweenomboro kweenomboro ezipheleleko ukufika kweenomboro ezipheleleko ukufika
ekuhlukaniselaneni
ku-5 kanye nempendulo ezingahle ezipheleleko ukufika ema-10 e-15 kanye nempendulo ezingahle e-20 kanye nempendulo ezingahle
zifaka iinsalela kanye nempendulo ezingahle zifaka zifaka iinsalela zifaka iinsalela
iinsalela
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
1.11 • Khumbula bewufanise imali • Khumbula bewufanise imali • Khumbula bewufanise imali
eziinhlavu zeSowula Afrika : eziinhlavu zeSowula Afrika : eziinhlavu zeSowula Afrika:
CAPS Imali
• 5c, 10c, 20c, 50c, R1, R2; R5 • 5c, 10c, 20c, 50c, R1, R2; R5 -- 5c, 10c, 20, 50c, R1, R2;R5
Imali yamaphepha ama R10
• Sombulula imiraro efaka hlangana • Sombulula imiraro efaka hlangana
nama R20
amanani wemali netjhentjii ye R10 amanani wemali netjhentjii ye R20
neyamasende ukufika ku-20c neyamasende ukufika ku-20c • Sombulula imiraro yemali efaka
hlangana amanani wemali
netjhentjil yama R20 namasende
ukufika ku-20c
UKUBALA OKUSEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Sebenzisa amathekhiniki alandelayo Sebenzisa amathekhiniki alandelayo Sebenzisa amathekhiniki alandelayo Sebenzisa amathekhiniki alandelayo
nawubalisisako nawubalisisako nawubalisisako nawubalisisako
Amathekhiniki
• Ama-apharethasi aphathekako • Ama-apharethasi aphathekako • Ama-apharethasi aphathekako • Ama-apharethasi aphathekako
(Iindlela namaqhinga)
njengezinto zokubala njengezinto zokubala njengezinto zokubala njengezinto zokubala
• Gwala iinthombe • Gwala iinthombe • Gwala iinthombe • Gwala iinthombe
• Amanambalayini ezisekelwe • Ukwakha bewuphadhle iinomboro • Ukwakha bewuphadhle iinomboro • Ukwakha bewuphadhle iinomboro
ama-apharethasi aphathekako
• Ukubuyelela nokuhafula phakathi • Ukubuyelela nokuhafula phakathi • Ukubuyelela nokuhafula phakathi
njengemincamo yokubala
• Amanambalayini ezisekelwe • Amanambalayini ezisekelwe • Amanambalayini ezisekelwe
ama-apharethasi aphathekako ama-apharethasi aphathekako ama-apharethasi aphathekako
njengemincamo yokubala njengemincamo yokubala njengemincamo yokubala
1.13 Irherho leenomboro: 1 - 5 Irherho leenomboro: 1 - 10 Irherho leenomboro: 1 - 15 Irherho leenomboro: 1 - 20
Ukuhlanganisa • Ukuhlanganisa kufika ku- 5 • Hlanganisa ukufika ku-10 • Hlanganisa ukufika ku-15 • Hlanganisa ukufika ku-20
nokukhupha
• Ukukhupha kusuka ku-5 • Khupha ukufika ku- 10 • Khupha e- 15 • Khupha ema- 20
• Ngokwenza bhala iinamba bhondi • Sebenzisa amatshwayo afaneleko • Sebenzisa amatshwayo afaneleko • Sebenzisa amatshwayo afaneleko
kufikela ku- 5 (+, –, =, ) (+, –, =, ) (+, –, =, )
• Ukuzijayeza inambabhondi kufika • Ukuzijayeza inambabhondi kufika • Ukuzijayeza inambabhondi kufika
ku-7 ku-9 ku-10
1.14 • Hlanganisa ngokubuyelela • Hlanganisa ngokubuyelela • Hlanganisa ngokubuyelela
(o.k.inomboro efanako) kufika (o.k.inomboro efanako) kufika (o.k.inomboro efanako) kufika
Ukuhlanganisa
ku-10 ku-15 ku-20
ngokubuyelela
okurholela • Sebenzisa amatshwayo afaneleko • Sebenzisa amatshwayo afaneleko • Sebenzisa amatshwayo afaneleko
(+, –, =, ) (+, –, =, ) (+, –, =, )
ekubuyabuyeleleni
43
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
1.16 Umqondonomboro: Irherho Umqondonomboro: Irherho Umqondonomboro: Irherho Umqondonomboro: Irherho
44 leenomboro kufika ku- 5 leenomboro kufika ku- 10 leenomboro kufika ku-15 leenomboro kufika ku- 20
Iimbalo zehloko
• Hlela isethi yeenomboro • Hlela isethi yeenomboro • Hlela isethi yeenomboro • Hlela isethi yeenomboro
ezikhethiweko ozinikelweko ezikhethiweko ozinikelweko ezikhethiweko ozinikelweko ezikhethiweko ozinikelweko
• Madanisa iinomboro kufika ku-5, • Madanisa iinomboro ukufikela • Madanisa iinomboro ukufikela • Madanisa iinomboro ukufikela
utjho bonyana ngiyiphi enengi e-10 bewutjho bonyana ngiyiphi e-15 bewutjho bonyana ngiyiphi e-20 bewutjho bonyana ngiyiphi
nga-1 nofana encani nga-2. enengi nga-1 nephasi nga-2 enengi nga-1 nephasi nga-2 enengi nga-1 nephasi nga-2
Ukukhumbula msinyana: Ukukhumbula msinyana:
• Inomboribhondi ukufika ku-5 • Inombori bhondi ukufika ku-10
• Khumbula amaphuzu wamambala • Khumbula amaphuzu wamambala
wokuhlanganisa nokukhupha wokuhlanganisa nokukhupha
kufika ku-5 kufika ku-10
Amaqhinga wokubalisisa Amaqhinga wokubalisisa
Sebenzisa amaqhinga wokubala Sebenzisa amaqhinga wokubala
nawu hlanganisako nokukhupha nawu hlanganisako nokukhupha
ngokuphumelela: ngokuphumelela:
• Beka inomboro ekulu ekuthomeni • Beka inomboro ekulu ekuthomeni
ukuze ukwazi ukubala uye ukuze ukwazi ukubala uye
ISIGABA ESISISEKELO AMAGREYIDI 1-3
phambili nemuva. phambili nemuva.
• Amanambalayini • Amanambalayini
• Ukubuyelela nokuhafula phakathi • Ukubuyelela nokuhafula phakathi
• Ukwakha nokuphula • Ukwakha nokuphula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Imihlobo yemiraro yeGreyidi yuku-1
Iimbonelo lezi zemiraro ziqakathekile kufanele utitjhere azethule ngokuzibuyelela njalo etlasini lakhe. Nangabe
utitjhere usebenza ngesiqhema esincani, kufanele aveze umraro ngokukhuluma. Nangabe abafundi bayakwazi uku-
funda utitjhere angabanikela umraro otloliweko, nokho utitjhere kusafanele aveze umraro ngokukhuluma.
Imiraro esebujameni ingafakwa emaphepheni wabantwana wokusebenzela nokho ifanele ibe mifitjhani,inqophe,
bekube ngejayelekileko nofana ngevamileko begodu utitjhere ufanele aqinisekise bonyana boke abafundi bayayiz-
wisisa.
Ukubuthelela ngeenqhema
Ukubuthelela ngeenqhema , ukulahla isalela
UZimkhona uthengisa amahabhula ngemigodla, ufaka amahabhula ngamathathu emgodleni. Unamahabhula ali-
14. Wenza imigodla emigodla emingaki yamahabhula nakakhamba ngamathathu?enamahabhula ngamathathu
emgodleni.
Ukubuthelela ngeenqhema, ukungenisa isalela ependulweni
UKosabo ufuna ukuyokupha ugogo wakhe amaqanda ali-15. ngemabhoksini afaka -6 yamaqanda, uzokudinga
amabhoksi amangaki ukufaka woke amaqanda anawo?
Ukwabelana
Ukwabelana, ukulahla isalela
Hlukanisa amaswidi ayi-14, hlukanisela abangani abathathu amaswidi ngokulinganako.
Ukuhlanganisa ngokubuyelela
Iintsikiri ezi-4 zinamavilo amangaki?
Ukuhlanganisa nokukhupha
Kunemihlobo emithathu yemiraro esisekelo yokuhlanganisa nokukhupha, omunye nomunye umraro ungabuzwa
ngendlela ehlukileko imihlobo esisekelo ngile:
Itjhuguluko
UNoluthando beka namahabhula ama-5. USilo wamupha amahabhula a-8. Mangaki amahabhula anawo
uNoluthando sewawoke?
UNoluthando bekanamahabhula ali-13, wapha uSilo amahabhula ama-5.UNoluthando usele namahabhula
amangaki?
Ukuhlanganisa
UNosisi unabomabula abahlanu abahlaza kotjani , nababunane abahlaza kwesibhakabhaka. Bangaki abomabula
anabo sebaboke?
CAPS 45
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukumadanisa
UNombuso unamabhanana ali-13. UThemba unamahlanu, uNombuso unabhanana amanengi kangangani kunoka
Themba?
Ukubuza omunye nomunye umraro ngendlela ehlukileko
Imiraro ifanele ibuzwe ngendlela ehlukileko. Isib. Yomibili imiraro le miraro etjhugulukileko, kodwana okungaziwako
kusendaweni ezihlukeneko.
UNoluthando bekanamahabhula. USilo wamupha abu-8 ngaphezulu. Kwanjesi sele anamahabhula ali-13.
UNoluthando bekanamahaghula amangaki ekuthomeni?
UNoluthando bekanamahabhula amahlanu. USilo umupha amanye amahabhula. UNoluthando sele anamahabhula
ali-13. Mangaki amahabhula awaphiwe ngu Silo?
Ubujamo bemiraro noBudlelwana bemisebenzi ehlukileko
UNino uthengisa amahotdog nge R4 ngayinye.Yenza ithebula elizomsiza ukuthola inani le- oda ekulu.
Inomboro yama Hotdogo 1 2 3 4 5 6 7
Inani ngama R 4 8
Sebenzisa ithebula lokuthola inani lama hotdogi alikhomba.
Lemihlobo yemiraro engehla inikelelwe ukurhola abotitjhere.Abafundi abangathweswa umthwalo ngemihlobo
yamagama. Yelela bonyana abafundi ngasikhathi basebenzisa iindlela ezihlukileko ukusombulula umraro
okungahle kungabi ngilokho utitjhere ebekakulindele.
46 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI 1
2. AMAPHETHENI,AMAFANKTJHINI NE-ALJIBHRA
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
2.1 Ukukopa bewungezelele Ukukopa , ungezelele Ukukopa , ungezelele Amaphatheni asemaqadi nathi
bewuhlathulule bewuhlathulule
Amaphetheni Ukukopa bewungezelele ukukhomba, uhlathulula ngamagama
wejiyomethri amaphetheni alula ngokusebenzisa: Ukukopa, ungezelele bewuhlathulule Ukukopa , ungezelele bewukope amaphetheni wejiyomtri
ngamagama bewuhlathulule ngamagama
• Izinto ezithintekako • Ngokwemvelo
• Amaphetheni alula enziwe • Amaphetheni alula enziwe
• Imigwalo (isib. sebenzisa imibala • Kusukela epilweni yangamalanga
ngezinto ezithintekako ngezinto ezithintekako
namajamo) yesimodeni,
• Amaphetheni alula enziwe • Amaphetheni alula enziwe
• Asuka kwilifa lamasiko wethu
ngemigwalo yemida, ubujamo ngemigwalo yemida, ubujamo
nafana izinto. nafana izinto.
Tlama begodu uhlathulule Tlama begodu uhlathulule Tlama begodu uhlathulule
amaphetheni wakho amaphetheni wakho amaphetheni wakho
• Yenza amaphetheni weJiyomethri • Yenza amaphetheni weJiyomethri • Yenza amaphetheni weJiyomethri
-- Ngezinto ezithintekako -- Ngezinto ezithintekako -- Ngezinto ezithintekako
-- Ngokugwala imida, amajamo -- Ngokugwala imida, amajamo -- Ngokugwala imida, amajamo
nofana izinto nofana izinto nofana izinto
• Hlathulula amaphetheni wakho • Hlathulula amaphetheni wakho • Hlathulula amaphetheni wakho
Imisebenzi yokulandelanisa
ephakanyisiweko
Thoma ukukopa bewungezelele
amaphetheni usebenzise izinto
ezithintekako angabe abafundi
sebayajayela ukusebenzisa
amakrayoni nempensela, thoma
ukukopa ungezelele amaphetheni
ngokugwala.
47
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela Ukukopa, ukungezelela Ukukopa, ukungezelela
48 nokuhlathulula nokuhlathulula nokuhlathulula nokuhlathulula
Amaphetheni
weenomboro Ukukopa, ungezelele bewuhlathulule Ukukopa, ungezelele bewuhlathulule Ukukopa, ungezelele bewuhlathulule Ukukopa, ungezelele bewuhlathulule
iinomboro ezilula ngokuzilandelanisa iinomboro ezilula ngokuzilandelanisa iinomboro ezilula ngokuzilandelanisa iinomboro ezilula ngokuzilandelanisa
kufika okungasenani ku-20. kufika okungasenani ku -50 kufika okungasenani ku -80 kufika okungasenani ku -100.
Ukulandelanisa ukhombise ukubala Ukulandelanisa ukhombise ukubala Ukulandelanisa ukhombise ukubala Ukulandelanisa ukhombise ukubala
uye phambli nasemuva nga: uye phambli nasemuva nga: uye phambli nasemuva nga: uye phambli nasemuva nga:
• Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye
inomboro hlangana ne-0 na-20 inomboro hlangana ne-0 na-50 inomboro hlangana ne-0 na-80 inomboro hlangana ne-0 ne-100
Ukubala uye phambili nga: Ukubala uye phambili nga: Ukubala uye phambili nga:
• Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye
isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana
ne-0 na-50 ne-0 na-80 ne-0 ne-100
• Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-5 isibuyabuyelelo saka ku-5 isibuyabuyelelo saka ku-5
hlangana ne-0 na-50 hlangana ne-0 na-80 hlangana ne-0 ne-100
• Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-2 isibuyabuyelelo saka ku-2 isibuyabuyelelo saka ku-2
hlangana ne -0 na-50 hlangana ne -0 na-80 hlangana ne -0 ne-100
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Yakha bewuhlathulule Yakha bewuhlathulule Yakha bewuhlathulule
amaphetheni wakho amaphetheni wakho amaphetheni wakho
• Yakha bewuhlathulule • Yakha bewuhlathulule amphetheni • Yakha bewuhlathulule
amaphetheni wakho wakho amaphetheni wakho
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI YOKU-1
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.1 Ilimi lobujamo Ilimi lobujamo
Ubujamo, Hlathulula ubujamo bento Hlathulula ubujamo bezinto
ukuzijayeza nokuhlobana kwenye nenye isib. nokuhlobana kwenye nenye isib.
nokubukela phezu-kwe, phambi-kwe, ngemuva- phezu-kwe, phambi-kwe, ngemuva
kwe, ngesinceleni, ngesidleni, -kwe, ngesinceleni, ngesidleni,
phezulu, phasi, hlanu-kwe. phezulu, phasi, hlanu-kwe.
Ubujamo nekombatjhuba Ubujamo nekombatjhuba
• Ukulandela ikombatjhuba • Ukulandela ikombatjhuba
yokukhambakhamba ngeklasini yokukhambakhamba ngeklasini
• Ukulandela umlayezo ubeka into • Ukulandela umlayezo ubeka into
ngokuhlobana kwenye nenye ngokuhlobana kwenye nenye
isib.beka ipensela ngaphakathi isib.beka ipensela ngaphakathi
kwebhoks. kwebhoks.
Isitjhukumiso esinqophileko Isitjhukumiso esinqophileko
sokulandelanisa umsebenzi sokulandelanisa umsebenzi
weThemu yoku-1 weThemu yesi-4
• Ilimi lobujamo lifanele lithulwe • Ukusebenza ngobujamo nelayelo
ngendlela ezokufaka abafundi kungaletha ndawonye ngokutlola
ngokwenza kokusikinya umzimba nangokurekhoda njengokugwala,
ukukhrayona nofana ukumadanisa
• Lokhu kungaletha ndawonye
imidwebo ngamagama
ngokutlola nangokurekhoda
njengokugwala, ukukhrayona • Elinye nelinye ilimi lobujamo lifanele
nofana ukumadanisa imidwebo lithulwe ngendlela ezokufaka
ngamagama. abafundi ngokwenza kokusikinya
umzimba
• Sebenzisa ilimi lobujamo
elifundweko nawulandela ilayelo/ • Ilayelo/ikombatjhuba yokwenza
iinkombatjhuba. kufanele iphrakthiswe ngokusikinya
umzimba lapho abafundi bazisikinya
• Ilayelo/indlela yokwenza kufanele
khona ngokukhupha izinto
iphrakthiswe ngokusikinya umzimba
njengokutjho komlayezo.
lapho abafundi bazisikinya khona
ngokukhupha izinto njengokutjho Ubujamo nokubona
komlayezo.
• Metjhisa imibono ehlukeneko
yezinto zangamalanga ezifanako.
49
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.2 Irherho lezinto Irherho lezinto Irherho lezinto
50 Ukubona nokutjho izinto
Izinto ezibusontathu (3-D)ezingetlasini Ukubona nokutjho izinto Ukubona nokutjho izinto
ezibusontathu neenthombeni ezibusontathu (3-D)ezingetlasini ezibusontathu (3-D) ezingetlasini
• Ubujamo bebhola (indulungu) neenthombeni neenthombeni
(3-D)
• Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhola (indulungu) • Ubujamo bebhola (indulungu)
Amatshwayo wezinto
• Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhoksi (iphrizimu)
Hlathulula, hlukanisa ngemihlobo,
umadanise izinto ezibusontathu Amatshwayo wezinto Amatshwayo wezinto
(3-D) ngokuya ngo:
Hlathulula, hlukanisa ngemihlobo, Hlathulula, hlukanisa ngemihlobo,
• bukhulu
umadanise izinto ezibusontathu umadanise izinto ezibusontathu (3-
• nangombala D) ngokuya:
Imisetjhenzana enqophako (3-D) ngokuya:
Ukubukela nokwakha izinto • ngobukhulu
• ngobukhulu
ezibusontathu (3-D) usebenzise • ngombala
amametheriyeli aphathekako njenge: • ngombala
amabhlogo wokwakha, imitheriyeli • ngezinto ezigedekako
esebenzileko ibuye isetjhenziswe, • ngezinto ezigedekako
izinto zokusebenza. • ngezinto ezitjhelelako
• ngezinto ezitjhelelako
Isitjhukumiso esinqophileko
nokulandelisana umsetjhenzana
weThemu yoku-1
• Ngesikhathi esitjhaphulukileko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kudlalwa ngezinto ezihlukeneko
ezibusontathu (3-D). Kwakhiwa
izinto ozithandako ngokusebenzisa Isitjhukumiso esinqophileko
Isitjhukumiso esinqophileko
amabhlogo, izinto zokusebenza nokulandelisana weThemu yesi-4
zokwakha nofana amamethiriyali nokulandelisana umsetjhenzana
asebenzile abuyelelwe weThemu yesi-3
asetjenziswa. Lokhu kungenziwa
ngesikhathi sokuzijamela. • Sebenza ngembholo nangezinto
• Kopa imifaniso yezinto ozinikelwe ezinobujamo obufana nobembholo,
ngutitjhere, lokhu kungenziwa nangamabhoksi, nangezinto
ngesikhathi sokuzijamela. ezinobujamo bephrizimu
• Madanisa ubukhulu bezinto kancamane nofana amakhyubhi.
ezifanako isib.itjho bonyana ngiyiphi Qalisisa bonyana ngiziphi izinto
ibholo ekulu. ezigedekako, ezitjhelelako,
• Khuluma ngemibala yezinto ezingapakelana.
bewuhlukanise izinto lezo
nangemibala yazo. • Fanisa bewuhlathulule izinto
• Fanisa bewuhlathulule izinto eziyiJiyomethri nezinto
eziyiJiyomethri nezinto zangamalanga ngokutjho bonyana
zangamalanga ngokutjho bonyana ubujamo bazo bunjengebholo
ubujamo bazo bunjengebholo
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
nofana njengebhoksi.
nofana njengebhoksi.
• Umsebenzi uyahlanganiswa • Umsebenzi uyahlanganiswa • Umsebenzi uyahlanganiswa
ngokutlola imisetjhenzana ngokutlola imisetjhenzana ngokutlola imisetjhenzana
ehleliweko. ehleliweko. ehleliweko.
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.3 Irherho lamajamo Irherho lamajamo
Ukubona nokutjho ubujamo
CAPS Ubujamo obubusobubili (2-D) Ukubona nokutjho ubujamo
obubusobubili • iindulungu obubusobubili (2-D)
(2-D) • aboncantathu • iindulungu
• iinkwere
• aboncantathu
Amatswhayo wamajamo
Ukuhlathulula, ukuhlukanisa • iinkwere
ngemihlobo nokumadanisa amajamo
obubusobubili (2-D) ngokuya: Amatswhayo wamajamo
• ngobukhulu Ukuhlathulula, ukuhlukanisa
• ngombala ngemihlobo nokumadanisa amajamo
• ngamahlangothi anqophileko obubusobubili (2-D) ngokuya:
• ngamahlangothi arondo
Iminqopho etjhukumeziweko • ngobukhulu
nokulandelanisa imisetjenzana • ngombala
yeThemu yesi-2
• Thoma ngokudlala • ngamahlangothi anqophileko
ngokutjhaphulukileko
ngemihlobohlobo yamajamo • ngamahlangothi arondo
okufaka hlangana ukwenza
iinthombe ngamajamo weJiyomethri Iminqopho etjhukumeziweko
asikiweyo. nokulandelanisa imisetjenzana
• Lokhu kungenziwa ngesikhathi yeThemu yesi-4
sokuzijamela nangesikhathi
sesifundo samakgono wepilo. • Ukusebenza ngendulungu
• Ukukopa isithombe esenziwe neenkwere zobukhulu
ngamajamo weJiyomethri. obuhlukahlukeneko naboncantathu
Lokhu kungenziwa ngesikhathi abanejamo elihlukaneko.Zihlele
sokuzijamela. ngokuya ngokuthi zinamahlangothi
• Madanisa ubukhulu bezinto anqophileko nofana ayindulunga.
ezifanako isib. Hlela iinkwere
kusukela kesincani ukuya kesikhulu • Ukuhlela nokubeka ngeenqhema
bewusebenzisa ilimi lobukhulu ngokuya ngokuthi mhlawumbe
ukuhlathulula ubujamo. ziboncantathu, iinkwere nofana
• Ukukhuluma ngemibala yamajamo indulungu.
bese uwahlela ngokuya ngemibala.
• Ukusebenza ngendulungu • Umsebenzi uhlanganiswa
neenkwere zobukhulu ngemisebenzi etloliweko.
obuhlukahlukeneko naboncantathu
abanejamo elihlukaneko.Zihlele
ngokuya ngokuthi zinamahlangothi
anqophileko nofana ayindulunga.
• Ukuhlela nokubeka ngeenqhema
ngokuya ngokuthi mhlawumbe
ziboncantathu, iinkwere nofana
51 indulungu.
• Umsebenzi uhlanganiswa
ngemisebenzi etloliweko.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.4 Isimethri Isimethri
52
Isimethri • Ukubona isimethri emizimbeni yabo. • Ukubona nokugwala umuda
wesimethri ebujameni
• Ukubona nokugwala umuda
babobusobubili (2-D) nasebujameni
wesimethri ebujameni
obuyijomthriki nobungasiyo
babobusobubili (2-D) nasebujameni
iJiyomethriki.
obuyijomthriki nobungasiyo
iJiyomethriki.
Iminqopho etjhukumeziweko
yemisetjenzana yeThemu yesi-3
Iminqopho etjhukumeziweko
• Qala imida yesimethri ezintweni yemisetjenzana yeThemu yesi-4
eziphathekako neenthombe.
• Imisetjenzana etlolwako ifanele
• Imisetjenzana etlolwako akukafaneli ifakehlangana iimbonelo lapho
bonyana igwalwe ngakenye umuda wesimethri awusiwo umuda
ingcenye kwaphela nokho ojame rwe kwaphela.
kufakwe hlangana neembolnelo
lapho abafundi bagwala emudeni
wesimethri.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI 1
4. UKUMEDA
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.1 Ukudlula kwesikhathi Isikhathi kusetjenzwa ngaso Isikhathi kusetjenzwa ngaso Isikhathi kusetjenzwa ngaso
Kukhulunywa ngokudlula kwesikhathi ngokuragela phambili ngesikhathi ngokuragela phambili ngesikhathi ngokuragela phambili ngesikhathi
Isikhathi
sokufundisa itlasi loke. sokufundisa itlasi loke. sokufundisa itlasi loke.
• Hlela izehlakalo eziqhelekileko
ezisuke epilweni yabo.
• Ukumadanisa ubude besikhathi
kusetjenziswa ilimi isib.iskhathi
eside, isikhathi esifitjhani,
masinyana, kabuthaka.
• Ukulandelanisa izehlakalo
kusetjenziswa iLimi elifaka nokuthi
izolo, namhlanje, kusasa.
Ukutjela ngesikhathi
• Ukuhlathulula nangabe kwenzeka
into kusetjenziswa iLimi isib.
Ekuseni, ngemuva kwedina,
ebusuku, ekuseni khlu, ngemuva
kwesikhathi.
• Ukutjho nokulandelanisa amalanga
weveke, neenyanga zonyaka.
• Ukubeka amalanga wamabeletho.
4.2 Ukumeda okungakahleleki Ukumeda okungakahleleki
Ubude • Ukumadanisa nokuhlela ubude,
ukuphakama nofana ububanzi
bezinto ezimbili nofana ezinengi
ngokuzibeka enye eqadi kwenye.
• Ukusebenzisa iLimi ukukhuluma
ngokufanisa isib.ubude, ubufitjhani,
ububanzi. •
• Ukulinganisa, ukumeda, Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela ukumadanisa, ukuhlela
bewurekhode ubude usebenzise nokurekhoda ubude kusetjenziswa
iimedo ezingakahlelwa isib. iimedo ezingakahlelelwa isib.
Ubude besandla, igadango, ubude Ubude besandla, amagadango,
bepensela, izinto zokubala, njll. ubude bepensela, izinto zokubala
njll.
53
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.3 Ukumeda okungakahleleki Ukumeda okungakahleleki
54
Ubudisi / • Ukulinganisa, isilinganiso, • Ukulinganisa, ukumeda,
ubungako ukumadanisa, ukuhlela, ukumadanisa, ukuhlela,
bekurekhodwe ubudisi, bekurekhodwe ubudisi,
kusetjenziswa isikala sokudzimelela kusetjenziswa isikala sokudzimelela
nesilinganiso esingakahleleki isib. nesilinganiso esingakahleleki isib.
Amabhlogo, iintina njll. Amabhlogo, iintina njll.
• Ukusebenzisa iLimi ukukhuluma • Ukusebenzisa iLimi ukukhuluma
ngokumadanisa isib.elula, ebudisi, ngokumadanisa isib.elula, ebudisi,
elula-khulu, ebudisi-khulu. elula-khulu, ebudisi-khulu.
4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Ukumeda okungakahleleki
Umthamo / • Ukumadanisa nokuhlela ubungako • Ukumadanisa nokuhlela ubungako
Ivolumu beketjezi/okusamanzi (umthamo) beketjezi/okusamanzi (umthamo)
okuseemumathini ezimbili okuseemumathini
ezibekwe esinye eduze nesinye.
• Ukusebenzisa iLimi ukukhuluma
Abafundi bazokuhlela ngokuhlela
ngokumadanisa isib.enengi
esimumathini sesithathu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kune, encani kune, encani, izele,
edududu.
• Ukulinganisa, ukumeda,
• Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela
ukumadanisa, ukuhlela
nokurekhoda umthamo
nokurekhoda umthamo
okusesimumathini ngokusebenzisa
okusesimumathini ngokusebenzisa
iimedo ezingakahleleki isib.
iimedo ezingakahleleki isib.
Iingobho namakomitji.
Iingobho namakomitji.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI 1
5. UKUPHATHA IDATHA
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
5.1 Ukubuthelela nokuhlela izinto Ukubuthelela nokuhlela izinto
ezithintekayo ngamalanga ezithintekayo ngamalanga
Ukubuthelela
nokuhlela Ukugwala iinthombe zezinto Ukugwala iinthombe zezinto
ngemihlobo ezihleleke ngemihlobo. ezihleleke ngemihlobo.
izinto
• Nikela iinzathu ngokuthi • Nikela iinzathu ngokuthi
5.2 okubuthelelweko kuhlelwe bunjani. okubuthelelweko kuhlelwe bunjani.
Ukujamiselela Phendula imibuzo ngokuthi: Phendula imibuzo ngokuthi:
okuhlelwe
-- Ukuhlelwa ngemihlobo kwenziwa -- Ukuhlelwa ngemihlobo kwenziwa
ngemihlobo
bunjani ( indlela yekambiso) bunjani ( indlela yekambiso)
ukubuthelela
kwezinto -- Okubuthelelweko kwahlelwa -- Okubuthelelweko kwahlelwa
ngemihlobo kunjani? (umkhiqizo) ngemihlobo kunjani? (umkhiqizo)
5.3
• Hlathulula okubuthelelwe • Hlathulula okubuthelelwe
Coca bewubike
ngemihlobo ngemihlobo
ngokuhlelwa
kwezinto
ezibuthelelweko
5.4 Okuphakanyisiweko:
Ukubuthelela Umzombe wedatha opheleleko
nokuhlela idatha ngokwenza igrafu yesithombe setlasi.
5.5 • Buthelela bewuhlele idatha
Ukujamiselela -- ngetlasi nofana ngesikolo
idatha
-- ukuphendulwa kwemibuzo
5.6 ebuzwa ngutitjhere
• Ukuhlaziya idatha ebuya
Ukuhlaziya • Ukujamiselela idatha ngegrafini
ekujanyiselelweni elinikelweko.
bewurhumutjhe yeenthombe.
idatha • Okuphakanyisiweko: okungasenani
• Ukuphendula imibuzo ngedatha
iingrafu zeenthombe ezimbili.
engegrafini yeenthombe.
55
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.4.2 Umbonomazombe weGreyidi yesi-2 ngeThemu
56 UMBONOMAZOMBE WEGREYIDI YESI-2
1.IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDO NOMBORO: Ukubala ngeenomboro ezipheleleko
1.1 • Ukubala okungasenani ukufikela • Bala okungasenani ukufikela • Bala okungasenani ukufikela • Bala okungasenani ukufikela
ku yezinto ngamalanga ku yezinto ngamalanga ku yezinto ngamalanga ku yezinto ngamalanga
Ukubala izinto
ngokuthembekako. ngokuthembekako ngokuthembekako ngokuthembekako
• Ukunikela isilinganiso senomboro • Ukunikela isilinganiso senomboro • Ukunikela isilinganiso senomboro • Ukunikela isilinganiso senomboro
yezinto ezingahlolwa ngokuzibala. yezinto ezingahlolwa ngokuzibala. yezinto ezingahlolwa ngokuzibala. yezinto ezingahlolwa ngokuzibala.
• Amaqhinga wokuhlela izinto • Amaqhinga wokuhlela izinto • Amaqhinga wokuhlela izinto • Amaqhinga wokuhlela izinto
ngokweenqhema kuyakhuthazwa. ngokweenqhema kuyakhuthazwa. ngokweenqhema kuyakhuthazwa. ngokweenqhema kuyakhuthazwa.
1.2 Bala uye phambili nasemuva nga: Bala uye phambili nemuva nga: Bala uye phambili nemuva nga: Ukubala uye phambili nemuva
nga:
Ukubala uye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye
phambili inomboro hlangana ne-0 ne-100 inomboro hlangana ne-0 ne-150 inomboro hlangana ne-0 ne-180 • Ku-1 ukusuka kwenye nenye
nemuva inomboro hlangana ne-0 na-200
• Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye
isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana • Li-10 ukusuka kesinye nesinye
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ne-0 ne-100 ne-0 ne-150 ne-0 ne-180 isibuyabuyelelo se-10 hlangana
ne-0 na -200
• Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana • Ku-5 ukusuka kesinye nesinye
ne-0 ne-100 ne-0 ne-150 ne-0 ne-180 isibuyabuyelelo saka ku-5 hlangana
ne-0 na-200
• Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 • Ku-2 ukusuka kesinye nesinye
hlangana ne -0 ne-100 hlangana ne-0 ne-150 hlangana ne-0 ne-180 isibuyabuyelelo saka ku- 2
hlangana ne -0 na-200
• Ku-3 ukusuka kesinye nesinye • Ku-3 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-3 hlangana isibuyabuyelelo saka ku-3 hlangana • Ku-3 ukusuka kesinye nesinye
ne -0 na-99 ne -0 na-180 isibuyabuyelelo saka ku-3 hlangana
ne -0 na-200
• Ku-4 ukusuka kesinye nesinye • Ku-4 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-4 hlangana isibuyabuyelelo saka ku-4 hlangana • Ku-4 ukusuka kesinye nesinye
ne -0 na-100 ne -0 na-180 isibuyabuyelelo saka ku-4 hlangana
ne -0 na-200
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDO NOMBORO : Jamiselela iinomboro ezipheleleko
CAPS 1.3 Ukufanisa, ukubona nokufunda Ukufanisa, ukubona nokufunda Ukufanisa, ukubona nokufunda Ukufanisa, ukubona nokufunda
iinomboro iinomboro iinomboro iinomboro
Amatshwayo
wenomboro • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda
namagama amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka
weenomboro kweli 0 ukuya e-100 kweli 0 ukuya e-150 kweli 0 ukuya e-180 kweli 0 ukuya e-200
• Ukutlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro
ukusuka kweli 0 ukuya e-100 ukusuka kweli 0 ukuya e-150 ukusuka kweli 0 ukuya e-180 ukusuka kweli 0 ukuya e-200
• Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda
igama lenomboro ukusuka kweli 0 igama lenomboro ukusuka kweli 0 igama lenomboro ukusuka kweli 0 igama lenomboro ukusuka kweli 0
ukuya ema-25 ukuya ema-50 ukuya ema-75 ukuya ema-100
• Ukutlola amagama weenomboro • Ukutlola amagama weenomboro • Ukutlola amagama weenomboro • Ukutlola amagama weenomboro
ukusuka kweli 0 ukuya ema-25 ukusuka kweli 0 ukuya ema-50 ukusuka kweli 0 ukuya ema-75 ukusuka kweli 0 ukuya ema-100
UKUTHUTHUKISWA KOMQONDO NOMBORO : Ukuhlathulula, ukumadanisa nokuhlela iinomboro ezipheleleko
1.4 Ukuhlathulula, ukumadanisa and Ukuhlathulula, ukumadanisa and Ukuhlathulula, ukumadanisa and Ukuhlathulula, ukumadanisa and
nokuhlela iinomboro ukufika ku 25 nokuhlela iinomboro ukufika ku 50 nokuhlela iinomboro ukufika ku 75 nokuhlela iinomboro ukufika ku 99
Ukuhlathulula,
ukumadanisa • Ukumadanisa iinomboro • Ukumadanisa iinomboro • Ukumadanisa iinomboro • Ukumadanisa iinomboro
nokuhlela ezipheleleko ngokusebenzisa ezipheleleko ngokusebenzisa ezipheleleko ngokusebenzisa ezipheleleko ngokusebenzisa
iinomboro ukuncani kuna, ukukhulu kuna, ukuncani kuna, ukukhulu kuna, ukuncani kuna, ukukhulu kuna, ukuncani kuna, ukukhulu kuna,
kunengi kuna, kungaphasi kuna kunengi kuna, kungaphasi kuna kunengi kuna, kungaphasi kuna kunengi kuna, kungaphasi kuna
nokuthi kuyalingana. nokuthi kuyalingana. nokuthi kuyalingana. nokuthi kuyalingana.
• Ukulandelanisa iinomboro • Ukulandelanisa iinomboro
• Ukulandelanisa iinomboro • Ukulandelanisa iinomboro ezipheleleko kusukela kencani ezipheleleko kusukela kencani
ezipheleleko kusukela kencani ezipheleleko kusukela kencani ukuya kekulukazi nokusuka ukuya kekulukazi nokusuka
ukuya kekulu khulu nokusuka ukuya kekulukazi nokusuka kwekulukazi ukuya kwencani khulu. kwekulukazi ukuya kwencani khulu.
kwekulu khulu ukuya kwencani kwekulukazi ukuya kwencani khulu.
khulu. Ukusebenzisa iinomborosikhundla Ukusebenzisa iinomborosikhundla
ukutjengisa ukuhleleka, indawo ukutjengisa ukuhleleka, indawo
nofana ubujamo nofana ubujamo
• Tjamisa izinto zirheme kusukela • Tjamisa izinto zirheme kusukela
keyokuthoma ukuya keyamatjhumi keyokuthoma ukuya keyamatjhumi
amabili nofana yokuthoma ukuya amabili nofana yokuthoma ukuya
keyokugcina isib. Kokuthoma, keyokugcina isib. Kokuthoma,
keyesibili, keyesithathu...... keyesibili, keyesithathu......
keyetjhumi keyetjhumi
Ukuthuthukiswa komqondonomboro : Ubukhulu bedijithi
1.5 Ukubona ubukhulu bedijithi Ukubona ubukhulu bedijithi Ukubona ubukhulu bedijithi Ukubona ubukhulu bedijithi
yeenomboro phakathi kwe-11 na-25 yeenomboro phakathi kwe-11 na-50 yeenomboro phakathi kwe-11 na-75 yeenomboro phakathi kwe-11 na-99
Ubukhulu
bedijithi • Ukuhlahlela iinomboro ezinamadijithi • Ukuhlahlela iinomboro ezinamadijithi • Ukuhlahlela iinomboro ezinamadijithi • Ukuhlahlela iinomboro ezinamadijithi
amabili zibe kubuyabuyelela amabili zibe kubuyabuyelela amabili zibe kubuyabuyelela amabili zibe kubuyabuyelela
kwamatjhumi nemivo/ngakunye. kwamatjhumi nemivo/ngakunye. kwamatjhumi nemivo/ngakunye. kwamatjhumi nemivo/ngakunye.
57 • Ukufanisa nokutjho ubukhulu • Ukufanisa nokutjho ubukhulu • Ukufanisa nokutjho ubukhulu • Ukufanisa nokutjho ubukhulu
bedijithi enye nenye. bedijithi enye nenye. bedijithi enye nenye. bedijithi enye nenye.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKURARULULA IMIRARO ESEBUJAMENI
58
1.6 Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako Sebenzisa amathekhiniki alandelako
lokha urarulula imiraro bekuhlathululwe lokha urarulula imiraro bekuhlathululwe lokha urarulula imiraro bekuhlathululwe lokha urarulula imiraro bekuhlathululwe
Amathekhiniki iinsombululo zemiraro: iinsombululo zemiraro: iinsombululo zemiraro: iinsombululo zemiraro:
wokurarulula
• Imigwalo nofana ama-apharethasi • Imigwalo nofana amapharethasi • Imigwalo nofana amapharethasi • Imigwalo nofana amapharethasi
imiraro
aphathekako isib. Izinto zokubala aphathekako isib. Izinto zokubala aphathekako isib. Izinto zokubala aphathekako isib. Izinto zokubala
• Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro
• Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro
• Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula
phakathi phakathi • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula
• Inambalayini esekelwe ngama- • Inambalayini esekelwe ngama- phakathi phakathi
apharathasi aphathekako apharathasi aphathekako • Inambalayini • Inambalayini
1.7 Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama
ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
Ukuhlanganisa
iinsombululo zakho zemiraro iinsombululo zakho zemiraro iinsombululo zakho zemiraro iinsombululo zakho zemiraro
nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha
nempendulo ukufika e-20. nempendulo ukufika e-50. nempendulo ukufika e-75. nempendulo ukufika e-99.
1.8 Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama
ukuhlanganisa ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
ngokubuyelela iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka
okurholela ukuhlanganisa okubuyelelweko ukuhlanganisa okubuyelelweko ukuhlanganisa okubuyelelweko ukuhlanganisa okubuyelelweko
ekubuyabuyele- okukhokhela ekubuyabuyeleleni okukhokhela ekubuyabuyeleleni okukhokhela ekubuyabuyeleleni okukhokhela ekubuyabuyeleleni
ISIGABA ESISISEKELO AMAGREYIDI 1-3
leni okunempendulo ufikela e-20. okunempendulo ufikela e-30. okunempendulo ufikela e-40. okunempendulo ufikela e-50.
1.9 Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama
ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
Ukubuthelela iinsombululo zakho ufake ukwabelana iinsombululo zakho ufake ukwabelana iinsombululo zakho ufake ukwabelana iinsombululo zakho ufake ukwabelana
nokwaba okur- ngokulingana nokubuthelela ngokulingana nokubuthelela ngokulingana nokubuthelela ngokulingana nokubuthelela
holela ekwahlu- ngeenqhema kweenomboro ngeenqhema kweenomboro ngeenqhema kweenomboro ngeenqhema kweenomboro
kaniselaneni ezipheleleko ukufika e-20 kanye ezipheleleko ukufika e-30 kanye ezipheleleko ukufika e-40 kanye ezipheleleko ukufika e-50 kanye
nempendulo ezingahle zifaka iinsalela nempendulo ezingahle zifaka iinsalela nempendulo ezingahle zifaka iinsalela nempendulo ezingahle zifaka iinsalela
1.10 Ukurarulula bewuhlathulule Ukurarulula bewuhlathulule Ukurarulula bewuhlathulule
iinsombululo zemiraro ezisebujameni iinsombululo zemiraro ezisebujameni iinsombululo zemiraro ezisebujameni
Ukwabelana
efaka hlangana ukwabelana efaka hlangana ukwabelana efaka hlangana ukwabelana
okurholela ngokulingana erholela empendulweni ngokulingana erholela empendulweni ngokulingana erholela empendulweni
emafraktjhinini zamafraktjhini wohlavu olulodwa .isib. zamafraktjhini wohlavu olulodwa .isib. zamafraktjhini wohlavu olulodwa .isib.
1 1 1 1 1 1 1 1 1 1 1 1
2 , 4 , 3 , 5 njll. 2 , 4 , 3 , 5 njll. 2 , 4 , 3 , 5 njll.
1.11 Ukukhumbula nokufanisa imali Ukukhumbula nokufanisa imali Ukukhumbula nokufanisa imali Ukukhumbula nokufanisa imali
yeSewula Afrika eziinhlamvu 5c, yeSewula Afrika eziinhlamvu 5c, yeSewula Afrika eziinhlamvu 5c, yeSewula Afrika eziinhlamvu 5c,
Imali 10c, 20c, 50c, R1, R2, R5, nemali 10c, 20c, 50c, R1, R2, R5, nemali 10c, 20c, 50c, R1, R2, R5, nemali 10c, 20c, 50c, R1, R2, R5, nemali
yamaphepha R10, R20, R50 yamaphepha R10, R20, R50 yamaphepha R10, R20, R50 yamaphepha R10, R20, R50
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Ukurarulula imiraro yemali efaka Ukurarulula imiraro yemali efaka Ukurarulula imiraro yemali efaka Ukurarulula imiraro yemali efaka
hlangana inani netjhentjhi hlangana inani netjhentjhi hlangana inani netjhentjhi hlangana inani netjhentjhi
ngamasende kufikela emasendeni ngamasende kufikela emasendeni ngamasende kufikela emasendeni ngamasende kufikela emasendeni
ama 50c namaranda ama- R20 ama 50c namaranda ama- R50 ama 75c namaranda ama- R75 ama 99c namaranda ama-R99
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUBALA OBUSEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki
CAPS
alandelako nakubalisiswako: alandelako nakubalisiswako: alandelako nakubalisiswako: alandelako nakubalisiswako:
Amathekhiniki
• Imigwalo nofana amapharethasi • Imigwalo nofana amapharethasi • Imigwalo nofana amapharethasi • Imigwalo nofana amapharethasi
(irherho namano)
aphathekako isib. Izinto zokubala aphathekako isib. Izinto zokubala aphathekako isib. Izinto zokubala aphathekako isib. Izinto zokubala
• Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro
• Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula
phakathi phakathi phakathi phakathi
• Inambalayini esekelwe ngama- • Inambalayini esekelwe ngama- • Inambalayini • Inambalayini
apharathasi aphathekako apharathasi aphathekako
1.13 • Ukuhlanganisa ukufikela ku-20 • Ukuhlanganisa ukufikela ku-50 • Ukuhlanganisa ukufikela ku-75 • Ukuhlanganisa ukufikela ku-99
Ukuhlanganisa • Ukukhupha ku-20 • Ukukhupha ku-50 • Ukukhupha ku-75 • Ukukhupha ku-99
nokukhupha
• Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo
afaneleko (+, –, =, ) afaneleko (+, –, =, ) afaneleko (+, –, =, ) afaneleko (+, –, =, )
• Ukulungiselela iinomboro bhodi • Ukulungiselela iinomboro bhodi • Ukulungiselela iinomboro bhodi • Ukulungiselela iinomboro bhodi
ukufika e 10 ukufika e 15 ukufika e 20 ukufika e 20
1.14 • Ukuhlanganisa inomboro efanako • Buyabuyelela iinomboro ukufika ku • Buyabuyelela iinomboro ukufika ku • Buyabuyelela iinomboro ukufika ku
ngokubuyelela ukufika ku-20 10 ngaku -2 nesi 5 10 ngaku -2, 5 nesi 4 10 ngaku -2, 5 nesi 4
ukuhlanganisa
ngokubuyelela • Buyabuyelela iinomboro ukufika ku • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo
okurholela 10 ngaku -2 ngokufaneleko (+, –, =, ) ngokufaneleko (+, –, =, ) ngokufaneleko (+, –, =, )
ekubuyabuyele-
• Ukusebenzisa amatshwayo
leni
ngokufaneleko (+, –, =, )
59
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
1.16 Umqondonomboro: Ezihlangana Umqondonomboro: E4zihlangana Umqondonomboro: Ezihlangana Umqondonomboro: Ezihlangana
60 na-25 na-50 na-75 na-99
Imbalo zehloko
• Ukurhemisa iinomboro ezikhethiweko • Ukurhemisa iinomboro ezikhethiweko • Ukurhemisa iinomboro ezikhethiweko • Ukurhemisa iinomboro ezikhethiweko
ngokwesede enikeliweko. ngokwesede enikeliweko. ngokwesede enikeliweko. ngokwesede enikeliweko.
• Ukuqanathisa iinomboro ukufika ku- • Ukuqanathisa iinomboro ukufika ku- • Ukuqanathisa iinomboro ukufika ku- • Ukuqanathisa iinomboro ukufika ku-
25 bewutjho bonyana ngiyiphi 50 bewutjho bonyana ngiyiphi: 75 bewutjho bonyana ngiyiphi: 99 bewutjho bonyana ngiyiphi:
-- enengi nga-1 nofana encani nga-1, -- enengi nga-1 nofana encani nga-1 -- enengi nga-1 nofana encani nga-1 -- enengi nga-1 nofana encani nga-1
-- enengi nga-2 nofana encani nga-2, -- enengi nga-2 nofana encani nga-2 -- enengi nga-2 nofana encani nga-2 -- enengi nga-2 nofana encani nga-2
-- enengi nge-10 nofana encani -- enengi nga-3 nofana encani nga-3 -- enengi nga-3 nofana encani nga-3 -- enengi nga-3 nofana encani nga-3
nge-10. -- enengi nga-4 nofana encani nga-4 -- enengi nga-4 nofana encani nga-4 -- enengi nga-4 nofana encani nga-4
-- enengi nga-5 nofana encani nga-5 -- enengi nga-5 nofana encani nga-5 -- enengi nga-5 nofana encani nga-5
-- enengi nge-10 nofana encani -- enengi nge-10 nofana encani -- enengi nge-10 nofana encani
nge-10 nge-10 nge-10
Ukukhumbula masinyana: Ukukhumbula masinyana: Ukukhumbula masinyana: Ukukhumbula masinyana:
• Ukukhumbula amaphuzu • Ukukhumbula amaphuzu • Ukukhumbula amaphuzu • Ukukhumbula amaphuzu
wamambala ngokuhlanganisa wamambala ngokuhlanganisa wamambala ngokuhlanganisa wamambala ngokuhlanganisa
nokukhupha ukufika e-10 nokukhupha ukufika e-10 nokukhupha ukufika e-15 nokukhupha ukufika e- 20
• Hlanganisa nofana ukhuphe • Hlanganisa nofana ukhuphe
iimbuyabuyeleli ze-10 ukusukela e-0 iimbuyabuyeleli ze-10 ukusukela e-0
ukuya ema-50 ukuya e-100
Amaqhinga wokubalisa Amaqhinga wokubalisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Amaqhinga wokubalisa Amaqhinga wokubalisa
Ukusebenzisa amaqhinga wokubalisa Ukusebenzisa amaqhinga wokubalisa
ukuhlanganisa nokukhupha ngekghono ukuhlanganisa nokukhupha ngekghono Ukusebenzisa amaqhinga wokubalisa Ukusebenzisa amaqhinga wokubalisa
elifaneleko: elifaneleko: ukuhlanganisa nokukhupha ngekghono ukuhlanganisa nokukhupha ngekghono
elifaneleko: elifaneleko:
• Beka inomboro ekulu maqangi ukuze • Beka inomboro ekulu maqangi ukuze
ubale uye phambili nofana ubale uye ubale uye phambili nofana ubale uye • Beka inomboro ekulu maqangi ukuze • Beka inomboro ekulu maqangi ukuze
emuva emuva ubale uye phambili nofana ubale uye ubale uye phambili nofana ubale uye
emuva emuva
• Inambalayini yehloko • Inambalayini yehloko
• Inambalayini yehloko • Inambalayini yehloko
• Ukubuyelela nokuhlukanisa • Ukubuyelela nokuhlukanisa
• Ukubuyelela nokuhlukanisa • Ukubuyelela nokuhlukanisa
• Ukwakha nokuphula • Ukwakha nokuphula
• Ukwakha nokuphula • Ukwakha nokuphula
• Ukusebenzisa ubudlelwana • Ukusebenzisa ubudlelwana
obuphakathi kokuhlanganisa obuphakathi kokuhlanganisa • Ukusebenzisa ubudlelwana • Ukusebenzisa ubudlelwana
nokukhupha. nokukhupha. obuphakathi kokuhlanganisa obuphakathi kokuhlanganisa
nokukhupha. nokukhupha.
1.17 • Sebenzisa bewutjho amafraktjhini • Sebenzisa bewutjho amafraktjhini • Sebenzisa bewutjho amafraktjhini
okufaka hlangana neengcezu, okufaka hlangana neengcezu, okufaka hlangana neengcezu,
Amafraktjhini amakota, isithathu begodu amakota, isithathu begodu amakota, isithathu begodu
nesihlanu njll nesihlanu njll nesihlanu njll
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukubona amafraktjhini ebujameni • Ukubona amafraktjhini ebujameni • Ukubona amafraktjhini ebujameni
obuyidayagremu obuyidayagremu obuyidayagremu
• Tlola amafraktjhini njengecezu • Tlola amafraktjhini njengecezu • Tlola amafraktjhini njengecezu
elilodwa, iinthathu ezimbili elilodwa, iinthathu ezimbili elilodwa, iinthathu ezimbili
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Imihlobo yemiraro yeGreyidi yesi-2
Lezi ziimbonelo zemihlobo yemiraro ekufanele utitjhere azethule ngokuzibuyelela njalo etlasini lakhe. Nangabe
utitjhere usebenza ngesiqhema esincani, kufanele aveze umraro ngokukhuluma. Nangabe abafundi bayakwazi
ukufunda, utitjhere angabanikela umraro otloliweko, nokho utitjhere kusafanele aveze umraro ngokukhuluma.
Imiraro esebujameni ingafakwa emaphepheni wabantwana wokusebenzela, nokho ifanele ibe mifitjhani, inqophe
bekube ngejayelekileko/ngevamileko, begodu utitjhere ufanele aqinisekise bonyana boke abafundi bayayizwisisa.
Ukubuthelela
Ukubuthelela, ukulahla isalela
UThoko uthengisa amahabhula ngemigodla eli-10 ngamunye. UThoko uthengisa amahabhula ngemigodla, ufaka
ali-10 ngemgodleni ngamunye. Unamahabhula ama-81. Wenze imigodla emingaki yamahabhula?
Ukubuthelela, ukungenisa isalela ephendulweni
Umlimi unamaqanda ama-47, ufaka amaqanda asithandathu ngebhoksini ngalinye, udinga amabhoksi amangaki
ukufaka woke amaqanda anawo?
Ukwabelana
Ukwabelana, ukulahla isalela.
Hlukanisa amaswidi ama-54, hlukanisela abangani abalikhomba amaswidi ngokulinganako.
Ukwabelana okurholela emafraktjhinini
Hlukanisa amatjhokolethi ali-11, wabele abangani abane ngokulinganako kungabi nesalela.
Amafraktjhini webuthelelo
Ugogo unikela uZizi ama-orentji ali-12, uZizi wenza ijuzi nge 1/3 ye-orentji. Usebenzise ama-orentji amangaki?
Imihlobo le yemiraro kufanele inikelwe abafundi ngemuva kokuba sele bararulule imiraro engaba mine nofana
mihlanu, ekhokhela emihlobeni yamafraktjhini bebazi namabizo weengcezu zamafraktjhini.
Ukuhlanganisa amafraktjhini
Umbanduli webhola yezandla unikela ingceny ye orentji komunye nomunye umdlali. Abadlali bebhola yezandla bali-
14. Umbanduli uthloga ama-orentji amangaki?
Imihlobo le yemiraro kufanele inikelwe abafundi ngemuva kokuba sele bararulule imiraro engaba mine nofana
mihlanu, ekhokhela emihlobeni yamafraktjhini bebazi namabizo weengcezu zamafraktjhini.
Ukuhlanganisa okubuyelelweko
Imilelenjana/iinsikiri ezi-20 zinavilo amangaki?
Linganisa
UThami ukhamba amabhlogo asithandathu ngelanga. Ukhamba amabhlogo amangaki ngeveke?
Amagridi
Umma utjala amareyi alikhomba wekhabitjhi, ireyi ngalinye linamakhabitjhi abunane, mangaki amakhabitjhi sele
awoke?
Ukuhlanganisa nokukhupha
CAPS 61
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Kunemihlobo emithathu yemiraro esisekelo yokuhlanganisa nokukhupha, omunye nomunye umraro ungabuzwa
ngendlela ehlukileko. Imihlobo esisekelo ngile:
Itjhuguluko
UNoluthando bekanamaswidi ama-25. USilo wamupha amaswidi ali-18. UNoluthando sele anamaswidi amangaki
sewawoke?
UNoluthando bekanaswidi ama-53. Wanikela uSilo amaswidi ama-32. UNoluthando usele namaseidi amangaki?
Ukuhlanganisa
Itlasi legrayidi 2 linaboncantathu aba-37 abahlaza kotjhani na-19 ahlaza kwesibhakabhaka. Bangaki aboncantathu
nasele baboke?
Baneendulungu ezi-63, ezi-27 zihlaza kotjhani zoke ezinye zibomvu. Zingaki iindulungu ezihlaza okwesibhakabhaka?
Ukumadanisa
UNosisi unamabhanana ali13. UThemba unahlanu. UNosisi unamabhanana amanengi kangangani kunonaka
Themba?
Ukubuza omunye nomunye umraro ngendlela ehlukileko.
Imiraro kufanele ibuzwe ngendlela ehlukileko. Isib. Yomibili imiraro le miraro etjhugulukileko, kodwana “ ukungaziwako”
kusendaweni ezihlukeneko.
UNoluthando bekanamswidi. USilo wamupha amaswidi ama-18 kwanjesi sele anamaswidi ama-43. UNoluthando
bekanamaswidi amangaki ekuthomeni?
UNoluthando bekanamahabhula ama-25. USilo umupha amanye amahabhula. UNoluthando sele anamahabhula
ama-43. Mangaki amahabhula awaphiwe nguSilo?
Ubujamo bemiraro noBudlelwana bemisebenzi ehlukileko.
ULina uthengisa amahotdog nge R4 ngalinye. Yenza ithebula elizomsiza ukuthola inani le-oda ekulu.
Ubunengi bama hotdogo 1 2 3 4 5 6 7 8 9 10
Inani ngama R 4 8
Sebenzisa ithebula elingehla ukuthola inani lamahotdog alikhomba namahotdog ali-15.
USibongile uhlala nabantwana. Ubiza ama R20 imali yokukhwela, bese ubiza R5 nge-iri ukuhlala nomntwana.
Qedelela ithebula elilandelako.
Sedick
Inani lama-iri 1 2 3 4 5 10
Inani lama R 25 30
Yelela bonyana umraro waka Sibongile nomraro wakaLina isetjenzwe ngendlela ezihlukileko.
Imihlobo yemiraro engehla inikelelwe abotitjhere. Abafundi abangathweswa umthwalo ngemihlobo yamagama. Yelela
bonyana abafundi ngasikhathi basebenzisa iindlela ezihlukileko ukusombulula umraro okungahle kungabi ngilokho
utitjhere ebekakulindeleko. Isib. Umraro wokuhlukanisa ungasombululwa ngokukhupha okubuyabuyelelweko,
ukuhlanganisa nofana ukubuyabuyelela. Iindlela zabafundi zizokutjhuguluka ngokukhamba konyaka njengombana
ukuzwisisa kwabo nokujayela umhlobo womraro, nangokuthuthuka kweenomboromqondo yabo.
62 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI YESI - 2
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
2.1 Ukukopa, ukwandisa Ukukopa, ukwandisa Ukukopa, ukwandisa Amaphetheni aseqadi kwethu
nokuhlathulula nokuhlathulula nokuhlathulula
Amaphetheni Ukukhomba, ukuhlathulula
weJiyomethri Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula ngamagama nokukopa amaphetheni
ngamagama ngamagama ngamagama weJiyomethri
• Amaphetheni enziwe ngezinto • Amaphetheni eyenziwe ngezinto • Amaphetheni eyenziwe ngezinto • Ngokwemvelo
eziphathekako eziphathekako eziphathekako
• Kusukela epilweni yangamalanga
• Amaphetheni enziwa ngokugwala • Amaphetheni enziwa ngokugwala • Amaphetheni enziwa ngokugwala yesimodeni,
imida, ubujamo nofana izinto. imida, ubujamo nofana izinto. imida, ubujamo nofana izinto.
• Asuka kwilifa lamasiko wethu
Imilandelande yamaphetheni: Imilandelande yamaphetheni: Imilandelande yamaphetheni:
Amaphetheni alula lapho amajamo, Amaphetheni alula lapho amajamo, Amaphetheni lapho inomboro nofana
nofana ibuthelelo lamajamo nofana ibuthelelo lamajamo ubukhulu bobujamo kesinye nesinye
ibuyelelwa ngendlela efana patsi. ibuyelelwa ngendlela efana patsi. isigaba buyatjhuguluka ngendlela
yokubonela phambili: o.u. njalonjalo
Amaphetheni lapho inomboro
amaphetheni ayangezeleleka
nofana isayizi yobujamo esigabeni
ngasinye itjhuguluka ngendlela
enebonelo phambili o.u amaphetheni
angezeleleka njalo njalo.
Ukutlama nokuhlathulula iphetheni
Ukutlama nokuhlathulula iphetheni
Ukutlama nokuhlathulula iphetheni okungewakhe
okungewakhe
okungewakhe
• Ukutlhama iphetheni yeJiyomethri
• Ukutlhama iphetheni yeJiyomethri
• Ukutlhama iphetheni yeJiyomethri okungewakhe
okungewakhe
okungewakhe
-- Ngezinto eziphathekako
-- Ngezinto eziphathekako
-- Ngezinto eziphathekako
-- Ngokugwala imida, amajamo
-- Ngokugwala imida, amajamo
-- Ngokugwala imida, amajamo nofana izinto
nofana izinto
nofana izinto
• Ukuhlathulula iphetheni
• Ukuhlathulula iphetheni
• Ukuhlathulula iphetheni okungewakhe
okungewakhe
okungewakhe
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
2.2 Ukukopa, ukwandisa Ukukopa, ukwandisa Ukukopa, ukwandisa Ukukopa, ukwandisa
64 nokuhlathulula nokuhlathulula nokuhlathulula nokuhlathulula
Amaphetheni
weenomboro Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula
ukulandelana kweenomboro ukulandelana kweenomboro ukulandelana kweenomboro ukulandelana kweenomboro
okungenani ukufika e- 100. okungenani ukufika e- 150. okungenani ukufika e- 180. okungenani ukufika e- 200.
• Ukulandelana kufanele kutjhengise • Ukulandelana kufanele kutjhengise • Ukulandelana kufanele kutjhengise • Ukulandelana kufanele kutjhengise
ukubala uye phambili nemuva nga: ukubala uye phambili nemuva nga: ukubala uye phambili nemuva nga: ukubala uye phambili nemuva nga:
• Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye
inomboro hlangana ne-0 ne-100 inomboro hlangana ne-0 ne-150 inomboro hlangana ne-0 ne-180 inomboro hlangana ne-0 na-200
• Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye
isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana
ne-0 ne-100 ne-0 ne-150 ne-0 ne-180 ne-0 na-200
• Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana
ne-0 ne-100 ne-0 ne-150 ne-0 ne-180 ne-0 na-200
• Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2
hlangana ne -0 ne-100 hlangana ne -0 ne-1 hlangana ne -0 ne- hlangana ne-0 na-200
• Ku-3 ukusuka kesinye nesinye • Ku-3 ukusuka kesinye nesinye • Ku-3 ukusuka kesinye nesinye
ISIGABA ESISISEKELO AMAGREYIDI 1-3
isibuyabuyelelo saka ku-3 hlangana isibuyabuyelelo saka ku-3 hlangana isibuyabuyelelo saka ku-3 hlangana
ne -0 ne-1 ne -0 ne- ne-0 na-200
• Ku- 4 ukusuka kesinye nesinye • Ku- 4 ukusuka kesinye nesinye • Ku- 4 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-4 hlangana isibuyabuyelelo saka ku-4 hlangana isibuyabuyelelo saka ku-4 hlangana
ne -0 ne-1 ne -0 ne- ne-0 na-
Ukuzitlamela iphetheni yakhe Ukuzitlamela iphetheni yakhe
yeenomboro yeenomboro
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI YESI-2
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.1 Ilimi lobujamo Ubujamo nokubukela
Ubujamo, • Ukuhlathulula ubujamo bento • Madanisa imibono ehlukaneko
ukuzijayeza yinye ngokuhlobane nenye isib. yezinto ezifanako zamalanga woke.
nokubukela ngaphezulu, ngaphambi kwe,
ngemuva, esinceleni, ngesindleni,
phezulu, phasi, eqadi kwe
Ubujamo nekombatjhuba Ubujamo nekombatjhuba
• Landela ilayelo ukukhambakhamba • Landela ilayelo ukukhambakhamba
ngetlasini ngetlasini
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.2 Izinto ezihlukahlukeneko Izinto ezihlukahlukeneko Izinto ezihlukahlukeneko
66 Ukubona nokutjho izinto ezi abobusontathu
Izinto Ukubona nokutjho izinto ezi Ukubona nokutjho izinto ezi
(3-D) ezingetlasini neenthombeni
ezibusontathu abobusontathu (3-D) ezingetlasini abobusontathu (3-D) ezingetlasini
• Ubujamo bebhola (indulungu) neenthombeni
(3-D) neenthombeni
• Ubujamo bebhoksi (iphrizimu)
• Ubujamo bebhola (indulungu) • Ubujamo bebhola (indulungu)
Amatshwayo wezinto
Ukuhlathulula, ukubeka ngeengaba • Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhoksi (iphrizimu)
nokumadanisa izinto ezi abobusontathu (3-D)
ngokuya ngo: • Isilinda
• Isilinda
• ngobukhulu Amatshwayo wezinto
Amatshwayo wezinto
• ngezinto ezigedekako Ukuhlathulula, ukubeka ngeengaba
• ngezinto ezitjhelelelako nokumadanisa izinto ezi Ukuhlathulula, ukubeka ngeengaba
Imisetjenzana enqotjhiweko abobusontathu (3-D) ngokuya: nokumadanisa izinto ezi
• Ukuqala nokwakha izinto ezibusontathu (3- abobusontathu (3-D) ngokuya:
• ngobukhulu
D) ezinikelweko ngokusebenzisa imethiriyeli • ngobukhulu
ephathekako ezifana sika ubujamo (2- • ngezinto ezigedekako
D), amabhlogo wokwakha, ukubuyelela • ngezinto ezigedekako
iberegise into esetjenzisiweko, ipahla • ngezinto ezitjhelelelako
esetjenzisa emsebenzini yokwakha, nezinye • ngezinto ezitjhelelelako
izinto ezibusontathu (3-D) zeJiyomethri ne
Umnqopho otjhukumeziweko
nemisetjenzana yokulandelanisa Umnqopho otjhukumeziweko
eseThemeni yoku-1
nemisetjenzana yokulandelanisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukukopa umfuziselo wento enikelwe Umnqopho otjhukumeziweko
eseThemeni yesi-3
ngutitjhere. Ukufuzisela nofana ukwakha eseThemeni yesi-4
kungenziwa kusetjenziswa amabhlogo Ukusebenza nge:
wokwakha, ukubuyelela usebenzise izinto
ezakhe zasetjenziswa ipahla esetjenziswa • Iimbholo nezinto ezibumbeke
emsebenzini, nezinye izinto zeJiyomethri njengeembholo
ezibusontathu (3-D), ukusika ubujamo
obubusobubili (2-D). Lokhu kungenziwa • Amasilinda nezinto ezibumbeke
ngesikhathi sokusebenza ngokuzijamela njengesilinda
• Ukumadanisa nokuhlathulula ubukhulu • Amabhoksi amihlobohlobo nezinye
bezinto ezifanako isib. Gandelela amabhoksi izinto ezibumbeke njengoncamane
kusukela kelikhulu ukuya kelincani.
oyiphrizimu nofana ikhyubhu.
• Iminqopho etjhukumeziweko
nokulandelanisa imisetjenzana yeThemu Rhubhulula bonyana ngiziphi izinto
yoku-1. Ukusebenza nge: ezigedekako, ngiziphi ezitjhelelako
• Iimbholo nezinto ezibumbeke njengeembholo begodu ngiziphi ezingagandelelwa.
Amabhoksi amihlobohlobo nezinye izinto Ukubona nokuhlathulula iJiyomethrik
ezibumbeke njengoncamane oyiphrizimu
nofana ikhyubhu. nezinto zangamalanga ngokutjho
Ukubona nokuhlathulula iJiyomethrik nezinto bonyana zijame njengebholo, zijjame
zangamalanga ngokutjho bonyana zijame jengebhoksi, ijame njengesilinda.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
njengebholo, zijjame njengebhoksi, ijame Imisebenzi ihlanganiswa
njengesilinda. • Imisebenzi ihlanganiswa
ngemisebenzana etloliweko ngemisebenzana etloliweko
Imisebenzi ihlanganiswa ngemisebenzana
etloliweko
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.3 Amajamo ahlukahlukeneko Amajamo ahlukahlukeneko
CAPS Amajamo Ukubona nokutjho ubujamo obubusobubili Ukubona nokutjho ubujamo
abobusobubili (2-D) abobusobubili (2-D)
(2-D) • Indulungu
• Indulungu
• Uncantathu
• Isikwere • Uncantathu
• Uncamane • Isikwere
Ubujamo bebumbeko
• Uncamane
Ukuhlathulula, ukuhlela nokumadanisa
amajamo abusobubili (2-D): Ubujamo bebumbeko
• Ubukhulu Ukuhlathulula, ukuhlela
• Umbala nokumadanisa amajamo
• ibumbeko abusobubili(2-D) kuya :
• amahlangothi anqophileko • ngobukhulu
• amahlangothi arondo
• ngombala
Iminqopho etjhukumeziweko
nokulandelanisa imisetjenzana yeThemu • ngebumbeko
yoku-1.
• ngamahlangothi anqophileko
• ukudlala ngokutjhaphuluka ngemihlobohlobo
yamajamo okufaka hlangana iinthombe • ngamahlangothi arondo
ezisikwe ezinobujamo beJiyomethriki. Lokhu
kungenziwa ngesikhathi sokuzijamela. Iminqopho etjhukumeziweko
nokulandelanisa imisetjenzana
• Ukukopa iinthombe ezenziwe ngamajamo
weJiyomethriki. Lokhu kungenziwa yeThemu yesi-4
ngesikhathi sokuzijamela. • Ukuhlela amajamo ngokuya
• Ukumadanisa ubukhulu bamajamo afanako. ngokuthi anamahlangothi
Isib.ukuhlela aboncamane ukusuka kencani anqophileko nofana ayindulungu.
ukuya kekulu ube usebenzise ilimi lobukhulu Ukusebenza ngeendulungu
ukuhlathulula ubujamo. neenkwere zobukhulu
• Ukukhuluma ngemibala yamajomo bese obuhlukahlukeneko, aboncantathu
kuhlelwa amajamo ngokuya kombala. naboncamane ababumbeke
• Ukuhlela amajamo ngokuya ngokuthi ngendlela ezihlukeneko.
anamahlangothi anqophileko nofana
ayindulungu. Ukusebenza ngeendulungu • Abafundi bahlela, babeke
neenkwere zobukhulu obuhlukahlukeneko, ngeenqhema ubujamo ngokuya
naboncantathu naboncamane ngendlela ngokuthi ziboncantathu, iinkwere,
ezihlukeneko. aboncamane nofana indulungu.
• Ukuhlela nokubeka ngesiqhema amajamo • Umsebenzi uhlanganiswa
ngokuya ngokuthi ziboncantathu, iinkwere, ngemisetjenzana etloliweko
aboncamane, nofana ziindulungu.
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• Umsebenzi uhlanganiswa ngemisetjenzana
etloliweko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.4 Isimethri Isimethri
68
Isimethri Ukubona nokugwala umuda Ukubona nokugwala umuda
wesimethri ebujameni obubusobubili wesimethri ebujameni obubusobubili
(2-D) obusebujameni obuyiJiyomethri (2-D) obusebujameni obuyiJiyomethri
nobungasiyo iJiyomethri. nobungasiyo iJiyomethri.
Iminqopho etjhukumeziweko Iminqopho etjhukumeziweko
yemisetjenzana yeThemu yesi-2 yemisetjenzana yeThemu yesi-4
• Imida yesimethri ezintweni • Imida yesimethri ezintweni
eziphathekako neenthombeni. eziphathekako neenthombeni.
• Imisetjenzana etlolwako ifanele • Imisetjenzana etlolwako ifanele
ifake hlangana iimbonelo lapho ifakehlangana iimbonelo lapho
umuda wesimethri awusiwo umuda umuda wesimethri ungasiwo umuda
ojame rwe kwaphela. ojame rwe kwaphela.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI YESI-2
4. UKUMEDA
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.1 Ukutjho isikhathi Ukutjho isikhathi Ukutjho isikhathi Ukutjho isikhathi
Isikhathi • Ukutjho nokulandelanisa amalanga • Ukutjho isikhathi ngama-iri ali-12 • Ukutjho nokulandelanisa amalanga
weveke. usebenzise ama-iri, nesigamu se-iri weveke.
esisewatjhini ye-analogo. • Ukutjho nokulandelanisa iinyanga
• Ukutjho nokulandelanisa iinyanga zonyaka.
zonyaka.
• Ukubeka ekhalendeni amalanga
• Ukubeka ekhalendeni amalanga wamabeletho, imigidingo yekolo,
wamabeletho, imigidingo yekolo, amalanga wamaholideyi, izehlakalo
amalanga wamaholideyi, izehlakalo zomlando, izehlakalo zesikolo.
zomlando, izehlakalo zesikolo. • Ukutjho isikhathi ngama-iri ali-12
• Ukutjho ama-iri ali-12 ngama-iri, usebenzise ama-iri, nesigamu se-iri
• Ukutjho isikhathi ngama-iri ali-12 nesigamu se-iri esisewatjhini ye- esisewatjhini ye-analogo.
usebenzise ama-iri, nesigamu se-iri analogo.
esisewatjhini ye-analogo. Balisisa ubude besikhathi
Balisisa ubude besikhathi
nokudlulisa isikhathi
Balilsisa ubude besikhathi Balisisa ubude besikhathi nokudlulisa isikhathi
nokudlulisa isikhathi nokudlulisa isikhathi • Sebenzisa iwatjhi ukubalisisa ubude • Sebenzisa iwatjhi ukubalisisa ubude
besikhathi ngama-iri nofana isigamu besikhathi ngama-iri nofana isigamu
• Sebenzisa iwatjhi ukubalisisa ubude • Sebenzisa iwatjhi ukubalisisa ubude se-iri.
besikhathi ngama-iri nofana isigamu se-iri.
besikhathi ngama-iri nofana isigamu
se-iri. se-iri. • Sebenzisa amakhalenda ukubala
nokuhlathulula ubude besikhathi
ngamalanga nofana ngemveke.
4.2 Ukulinganisa okungakahleleki
ubude • Linganisa, meda, madanisa,
hlela bewurekhode ubude
kusetjhenziswa izinto zokumeda
ezingakalinganiswa isib. Ubude
besandla, igadango, ubude
bepensela, izinto zokubala njll.
• Ukuhlathulula ubude bezinto
ngokuzibala nokutjho ubude
ngendlela engakalinganiswa.
• Ukusebenzisa ilimi ukukhuluma
ngokumadanisa isib. Edenyana,
efitjhazana, ede, ebanzi
Ukwazisa iimedo ezihlelekileko Ukwazisa iimedo ezihlelekileko
• Linganisa, meda, madanisa, hlela • Linganisa, meda, madanisa,
bewurekhode ubude kusetjhenziswa hlela bewurekhode ubude
amamitha (nofana iingojwana kusetjhenziswa amamitha (nofana
69 ezibubude bemitha nofana intambo iingojwana ezibubude bemitha
enobude bemitha) njengeemedo nofana indambo enobude bemitha)
ezihlelelweko zobude. njengemedo elihlelelweko lobude.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.3 Ukulinganisa okungakahleleki
70
Ubudisi • Linganisa, meda, madanisa,
hlela bewurekhode ubudisi
kusetjhenziswa isikala
sokudzimelela nezinto zokumeda
ezingakalinganiswa isib.
Amabhlogo, iintina njll.
• Ukuhlathulula ubudisi bezinto
ngokuzibala noutjho amayunithi
ngendlela engakalinganiswa.
• Ukusebenzisa ilimi ukukhuluma
ngokumadanisa isib. Lula, kubudisi,
kulula khulu, kubudisi khulu
Ukwazisa ukulinganisa Ukwazisa ukulinganisa
okuhlelekileko okuhlelekileko
• Ukumadanisa, ukuhlela Amathaski atloliweko ukuhlanganisa
nokurekhoda ubudisa bezinto okulandelako okufaka hlangana
ezipakwe ngokwerhwebo okubonisa nokufunda kweenthombe ze:
ubudisi butjhiwe ngamakhilogremu
isib. Amakhilogremu ama-2 wereyisi • Imikhiqizo enobudisi obutloliweko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nekhilogremu -1 yeflowuru kizo
• Lapho kunesikala sangendlini • Isikala sangendlwaneni
yokuhlambela, abafundi yokuhlambela esinenalidi ekhombe
bangazilinganisa ubudisi babo ilayini yegradiyetjhini
ngamakhilogremu kusetjenziswa
isikala. Kulindeleke bonyana
abafundi bafunde kwaphela
inomboro eseduzana
nekombabudisi. Bahlathulula
ubudisi babo njengokuthi pheze/
citjhe/eduze ne/ khulu kancani
kuna/ khulu nofana ngaphasi
nofana ilingana patsi (nenomboro
yamakhilogremu) bafunda esikaleni.
• Lapho kunesikala sokudzimelela
esinenquntu ezitlolwe ngamagremu
abentwana bangalinganisa ubudisi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.4 Ukulinganisa okungakahleleki
CAPS Umthamo/ • Linganisa, meda, madanisa,
iVolumu hlela bewurekhode umthamo
ongeemumathini (o.u. ubunengi
isimumathi esikghona ukubuthatha
nasizalisiweko) ngokusebenzisa
izinto zokumeda ezingakahleleki
isib. Iingobho neenkomitji.
• Ukuhlathulula umthamo
wesimumathi ngokubala nookutjho
bonyana mayunithi amangaki
angakahleleki angazalisa
isimumathi isib. Ibhodlelo
linomthamo weenkomitji ezine.
Ukwazisa ukulinganisa Ukwazisa ukulinganisa
okuhlelekileko okuhlelekileko
• Ukulinganisa, ukumeda, Amathaski atloliweko ukuhlanganisa
ukumadanisa, ukuhlela okulandelako okufaka hlangana
bewurekhode umthamo nokufunda kweenthombe ze:
wezinto ngokumeda ngamalitha • Imikhiqizo enemithamo etloliweko
kusetjenziswa: kizo ukuze kulandelaniswe
-- Amabhodlelo anomthamo ngokuhlela.
ongamalitha • Iinthombe zeenjege lapho umthamo
-- Ijege yokumeda enemida upheze walingana ilitha eli-1
enenkombamthamo wamalitha nofana amalitha ama-2 enomuda
wegradetjhini
• Ukumadanisa, ukuhlela
nokurekhoda umthamo wezinto • Ukufunda ngokutjhideza
ezipakwe ngokwerhwebo ukubonisa enomborweni enomuda
umthamo obutjhiwo ngamalitha wegradetjhini ngokuhlathulula
isib. Amalitha ama-2 webisi, ilitha umthamo yazo njengokuthi
yi-1 yesiselo esimakhaza, amalitha pheze, eduzana, enengi kuna,
ama-5 wepende elinganapatsi nenomboro
(yamalitha)
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
UMBONOMAZOMBE WEGREYIDI 2
5. UKUPHATHA IDATHA
72
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
5.4 Eziphakamisiweko: Eziphakamisiweko:
Ukubuthelela Hlanganisa umzombe wegrafu Yenza igrafu yeenthombe
bewuhlele idatha yeenthombe yetlasi ngakunye eyodwa enakunye nakunye
nakunye okukhambelanako. kokukhambisanako ngedatha
5.5 oyinikelweko ingaba isithombe nofana
• Buthelela idatha ngetlasi nofana
Ukujamiselela ithebula.
ngesikolo ukuphendula imibuzo
idatha ebuzwe ngutitjhere. • Buthelela idatha ngetlasi nofana
ngesikolo ukuphendula imibuzo
• Jamisela idatha egrafini
ebuzwe ngutitjhere.
yeenthombe ngakunye nakunye
okukhambelanako. • Jamisela idatha egrafini
yeenthombe ngakunye nakunye
okukhambelanako.
5.6 • Phendula imibuzo ngedatha Ukuhlaziya idatha esijamiselelweni Ukuhlaziya idatha esijamiselelweni
esegrafini yeenthombe ngakunye esinikelweko esinikelweko
Ukuhlaziya
bewurhumutjha nakunye okukhambelanako Eziphakamisiweko Eziphakamisiweko
idatha
Okungasenani igrafu Okungasenani igrafu
eyodwa enakunye nakunye eyodwa enakunye nakunye
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kokukhambisanako kokukhambisanako
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
3.4.3 Umbonomazombe we Greyidi yesi- 3 ngeThemu
UMBONOMAZOMBE WEGREYIDI YESI- 3
CAPS 1.IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDO NOMBORO: Ukubala ngenomboro eziphelelko
1.1 Buthelela okungasenani ama- Buthelela okungasenani ama- Buthelela okungasenani ama- Buthelela okungasenani
yezinto ukulinganisa nokubala yezinto ukulinganisa nokubala yezinto ukulinganisa nokubala
Ukubala izinto i- yezinto ukulinganisa nokubala
ngokuthembekako. ngokuthembekako. ngokuthembekako.
ngokuthembekako.
Ukunikela isilinganiso senomboro Ukunikela isilinganiso senomboro Ukunikela isilinganiso senomboro
Ukunikela isilinganiso senomboro
yezinto ezingahlolwa ngokuzibala. yezinto ezingahlolwa ngokuzibala. yezinto ezingahlolwa ngokuzibala.
yezinto ezingahlolwa ngokuzibala.
Amaqhinga wokuhlela izinto Amaqhinga wokuhlela izinto Amaqhinga wokuhlela izinto
Amaqhinga wokuhlela izinto
ngokweenqhema kuyakhuthazwa. ngokweenqhema kuyakhuthazwa. ngokweenqhema kuyakhuthazwa.
ngokweenqhema kuyakhuthazwa.
1.2 Ukubala uye phambili nemuva nga: Ukubala uye phambili nemuva nga: Ukubala uye phambili nemuva nga: Ukubala uye phambili nemuva nga:
Ukubala uye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye nenye
phambili inomboro hlangana ne-0 na-200. inomboro hlangana ne-0 na-500. inomboro hlangana ne-0 na-700. inomboro hlangana ne-0 ne-1000.
nasemuva
• Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye • Li-10 ukusuka kesinye nesinye
isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana isibuyabuyelelo se-10 hlangana
ne-0 na-200. ne-0 na-500. ne-0 na-700. ne-0 ne-1000.
• Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye • Ku-5 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana isibuyabuyelelo saka ku-5 hlangana
ne-0 na-200. ne-0 na-500. ne-0 na-700. ne-0 ne-1000.
• Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye • Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2 isibuyabuyelelo saka ku- 2
hlangana ne-0 na-200. hlangana ne-0 na-500. hlangana ne-0 na-700. hlangana ne-0 ne-1000.
• Ku-3 ukusuka kesinye nesinye • Ku-3 ukusuka kesinye nesinye • Ku-3 ukusuka kesinye nesinye • Ku-3 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-3 hlangana isibuyabuyelelo saka ku-3 hlangana isibuyabuyelelo saka ku-3 hlangana isibuyabuyelelo saka ku-3 hlangana
ne -0 na-200. ne -0 na-500. ne -0 na-700. ne -0 ne-1000
• Ku-4 ukusuka kesinye nesinye • Ku-4 ukusuka kesinye nesinye • Ku-4 ukusuka kesinye nesinye • Ku-4 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-4 hlangana isibuyabuyelelo saka ku-4 hlangana isibuyabuyelelo saka ku-4 hlangana isibuyabuyelelo saka ku-4 hlangana
ne-0 na-200. ne-0 na-500. ne-0 na-700. ne -0 ne-1000
• Ma-100 okungasenani ukufika • Ma-50, 100 okungasenani ukufika • Ma-20, 25, 50, 100 okungasenani • Ma-20, 25, 50, 100 okungasenani
e-1000. e-1000. ukufika e-1000. ukufika e-1000.
73
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUTHUTHUKISWA KOMQONDONOMBORO : Jamiselela iinomboro ezipheleleko
74
1.3 Ukufanisa, ukubona nokufunda Ukufanisa, ukubona nokufunda Ukufanisa, ukubona nokufunda Ukufanisa, ukubona nokufunda
iinomboro iinomboro iinomboro iinomboro
Amatshwayo
namagama • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda
amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka amatshwayo wenomboro ukusuka
wenomboro
kweli ukuya e-500 kweli ukuya e-1000 kweli ukuya e-1000 kweli ukuya e-1000
• Ukutlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro • Ukutlola amatshwayo wenomboro
ukusuka kweli ukuya e-500 ukusuka kweli ukuya e-1000 ukusuka kweli ukuya e-1000 ukusuka kweli ukuya e-1000
• Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda • Ukufanisa, ukubona nokufunda
igama lenomboro ukusuka kweli igama lenomboro ukusuka kweli igama lenomboro ukusuka kweli igama lenomboro ukusuka kweli
ukuya ema-250 ukuya ema-250 ukuya ema-500 ukuya ema-1000
• Ukutlola amagama weenomboro • Ukutlola amagama weenomboro • Ukutlola amagama weenomboro • Ukutlola amagama weenomboro
ukusuka kweli ukuya ema-100 ukusuka kweli ukuya ema-250 ukusuka kweli ukuya ema-500 ukusuka kweli ukuya ema-1000
UKUTHUTHUKISWA KOMQONDONOMORO: Ukuhlathulula, ukumadanisa and nokuhlela iinomboro ezipheleleko
1.4 Ukukhumbula, ukumadanisa and Ukukhumbula, ukumadanisa and Ukukhumbula, ukumadanisa and Ukukhumbula, ukumadanisa and
nokuhlela iinomboro ukufika ku 99 nokuhlela iinomboro ukufika ku 500 nokuhlela iinomboro ukufika ku 700 nokuhlela iinomboro ukufika ku
Ukuhlathulula, • Ukumadanisa iinomboro 1000
ukumadanisa • Ukumadanisa iinomboro • Ukumadanisa iinomboro
ezipheleleko ngokusebenzisa ezipheleleko ngokusebenzisa ezipheleleko ngokusebenzisa • Ukumadanisa iinomboro
nokuhlela kuncani kuna, kukhulu kuna,
kuncani kuna, kukhulu kuna, kuncani kuna, kukhulu kuna, ezipheleleko ngokusebenzisa
iinomboro kunengi kuna, kungaphasi kuna kunengi kuna, kungaphasi kuna kunengi kuna, kungaphasi kuna kuncani kuna, kukhulu kuna,
ezipheleleko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokuthi kuyalingana. nokuthi kuyalingana. nokuthi kuyalingana. kunengi kuna, kungaphasi kuna
• Ukulandelanisa iinomboro nokuthi kuyalingana.
• Ukulandelanisa iinomboro • Ukulandelanisa iinomboro ezipheleleko kusukela kencani ukuya
ezipheleleko kusukela kencani ezipheleleko kusukela kencani kekulu khulu nokusuka kwekulu khulu • Ukulandelanisa iinomboro
ukuya kekulu khulu nokusuka ukuya kekulu khulu nokusuka ukuya kwencani khulu. ezipheleleko kusukela kencani
kwekulu khulu ukuya kwencani kwekulu khulu ukuya kwencani • Ukusebenzisa iinomborosikhundla ukuya kekulu khulu nokusuka
khulu. khulu. ukutjengisa ukuhleleka, indawo kwekulu khulu ukuya kwencani
nofana ubujamo khulu.
• Ukusebenzisa, ukufunda nokutlola
iinomboro sikhundla okufaka
hlangana inhlobo elirhunyeziweko
ukufikela ku-31
UKUTHUTHUKISWA KOMQONDONOMORO: Ubukhulu bedijithi
1.5 Ukukhumbula ubukhulu bedijithi Ukukhumbula ubukhulu bedijithi Ukukhumbula ubukhulu bedijithi Ukukhumbula ubukhulu bedijithi
yeenomboro kufika e-99 yeenomboro kufika e-500 yeenomboro kufika e-700 yeenomboro kufika e-999
Ubukhulu
• Ukwazi bonyana idijithi nedijithi • Ukwazi bonyana idijithi nedijithi • Ukwazi bonyana idijithi nedijithi • Ukwazi bonyana idijithi nedijithi
bedijithi lijamele ini. lijamele ini. lijamele ini. lijamele ini.
• Ukuhlahlela iinomboro • Ukuhlahlela iinomboro • Ukuhlahlela iinomboro • Ukuhlahlela iinomboro
ezinamadijithi amabili zibe ezinamadijithi amathathu zibe ezinamadijithi amathathu zibe ezinamadijithi amathathu zibe
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
kubuyabuyelela kwamatjhumi kubuyabuyelela kwamatjhumi kubuyabuyelela kwamatjhumi kubuyabuyelela kwamatjhumi
nemivo/ngakunye. nemivo/ngakunye. nemivo/ngakunye. nemivo/ngakunye.
• Ukufanisa nokutjho ubukhulu • Ukufanisa nokutjho ubukhulu • Ukufanisa nokutjho ubukhulu • Ukufanisa nokutjho ubukhulu
bedijithi enye nenye. bedijithi enye nenye. bedijithi enye nenye. bedijithi enye nenye.
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKURARULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Sebenzisa amathekhiniki Sebenzisa amathekhiniki
CAPS
Amathekhiniki alandelako lokha urarulula imiraro alandelako lokha urarulula imiraro alandelako lokha urarulula imiraro alandelako lokha urarulula imiraro
wokurarulula bekuhlathululwe iinsombululo bekuhlathululwe iinsombululo bekuhlathululwe iinsombululo bekuhlathululwe iinsombululo
zemiraro: zemiraro: zemiraro: zemiraro:
imiraro
• Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro
• Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula
phakathi phakathi phakathi phakathi
• Inambalayini • Inambalayini • Inambalayini • Inambalayini
• Tjhideza eduze kwetjhumi • Tjhideza eduze kwetjhumi • Tjhideza eduze kwetjhumi
Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama
1.7 ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
iinsombululo zakho zemiraro iinsombululo zakho zemiraro iinsombululo zakho zemiraro iinsombululo zakho zemiraro
Ukuhlanganisa ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha ezifaka ukuhlanganisa nokukhupha
nokukhupha nempendulo ukufika e-99. nempendulo ukufika e-400. nempendulo ukufika e-800. nempendulo ukufika e-999.
1.8 Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama Rarulula imiraro yamagama
ukuhlanganisa ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
ngokubuyelela iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka iinsombululo zakho zemiraro, ezifaka
okurholela ukubuyabuyelela okunempendulo ukubuyabuyelela okunempendulo ukubuyabuyelela okunempendulo ukubuyabuyelela okunempendulo
ekubuyabuyeleleni ufikela e-50. ufikela e-75. ufikela e-75. ufikela e-100.
1.9 Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama Ukurarulula imiraro yamagama
Ukubuthelela ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule ezisebujameni bewuhlathulule
nokwabelana iinsombululo zakho ufake ukwabelana iinsombululo zakho ufake ukwabelana iinsombululo zakho ufake ukwabelana iinsombululo zakho ufake ukwabelana
ngokulingana nokubuthelela ngokulingana nokubuthelela ngokulingana nokubuthelela ngokulingana nokubuthelela
okurholela ek-
ngeenqhema kweenomboro ngeenqhema kweenomboro ngeenqhema kweenomboro ngeenqhema kweenomboro
wahlukanisela- ezipheleleko ukufika e-50 kanye ezipheleleko ukufika e-75 kanye ezipheleleko ukufika e-75 kanye ezipheleleko ukufika e-100 kanye
neni nempendulo ezingahle zifaka nempendulo ezingahle zifaka nempendulo ezingahle zifaka nempendulo ezingahle zifaka
iinsalela. iinsalela. iinsalela. iinsalela.
1.10 Ukurarulula bewuhlathulule Ukurarulula bewuhlathulule Ukurarulula bewuhlathulule Ukurarulula bewuhlathulule
Ukwabelana iinsombululo zemiraro ephathekako iinsombululo zemiraro ephathekako iinsombululo zemiraro ephathekako iinsombululo zemiraro ephathekako
okurholela efaka hlangana ukwabelana efaka hlangana ukwabelana efaka hlangana ukwabelana efaka hlangana ukwabelana
ngokulingana erholela empendulweni ngokulingana erholela empendulweni ngokulingana erholela empendulweni ngokulingana erholela empendulweni
emafraktjhinini
zamafraktjhini wohlavu olulodwa zamafraktjhini wohlavu olulodwa zamafraktjhini wohlavu olulodwa zamafraktjhini wohlavu olulodwa
nalayo angenahlavu eyodwa. isib. njll. nalayo angenahlavu eyodwa. isib. njll. nalayo angenahlavu eyodwa. isib. njll. nalayo angenahlavu eyodwa. isib. njll.
1.11 • Ukukhumbula nokufanisa imali • Ukukhumbula nokufanisa imali • Ukukhumbula nokufanisa imali • Ukukhumbula nokufanisa imali
Imali yeSewula Afrika eziinhlamvu yeSewula Afrika eziinhlamvu yeSewula Afrika eziinhlamvu yeSewula Afrika eziinhlamvu
nemali yamaphepha nemali yamaphepha nemali yamaphepha nemali yamaphepha
• Ukurarulula imiraro yemali efaka • Ukurarulula imiraro yemali efaka • Ukurarulula imiraro yemali efaka • Ukurarulula imiraro yemali efaka
hlangana inani netjhentjhi hlangana inani netjhentjhi hlangana inani netjhentjhi hlangana inani netjhentjhi
75 ngamasende namaranda. ngamasende namaranda. ngamasende namaranda. ngamasende namaranda.
• Tjhugulula imali yamaranda • Tjhugulula imali yamaranda
namasende. namasende.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
UKUBALA OBUSEBUJAMENI OBUTJHAPHULUKILEKO
76
1.12 Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki
Amathekhiniki alandelako nakubalisiswako: alandelako nakubalisiswako : alandelako nakubalisiswako : alandelako nakubalisiswako :
(iindlela nofana • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro • Ukwakha nokuphula kweenomboro
amaqhinga) • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula • Ukubuyelela kabili nokuhafula
phakathi phakathi phakathi phakathi
• Inambalayini • Inambalayini • Inambalayini • Inambalayini
• Tjhideza eduze kwetjhumi • Tjhideza eduze kwetjhumi • Tjhideza eduze kwetjhumi
1.13 • Ukuhlanganisa ukufikela ku-99 • Ukuhlanganisa ukufikela ema-400 • Ukuhlanganisa ukufikela ema-800 • Ukuhlanganisa ukufikela ema-800
Ukuhlanganisa • Ukukhupha ku-99 • Ukukhupha ema-400 • Ukukhupha ema-800 • Ukukhupha ema-800
nokukhupha • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo
afaneleko (+, –, =, ) afaneleko (+, –, =, ) afaneleko (+, –, =, ) afaneleko (+, –, =, )
• Ukulungiselela iinomboro bhodi • Ukulungiselela iinomboro bhodi • Ukulungiselela iinomboro bhodi • Ukulungiselela iinomboro bhodi
ukufika e 20 ukufika e 30 ukufika e 30 ukufika e 30
1.14 • Buyelela iinomboro kusuka ku-1 • Buyelela i-2, 3, 4, 5, 10 kufika e-50 • Buyelela i-2, 3, 4, 5, 10 kufika e-100 • Buyelela i-2, 3, 4, 5, 10 kufika e-100
Ukuhlanganisa kufika e-10 nge 2, 5, 3, 4 • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo
ngokubuyelela • Ukusebenzisa amatshwayo ngokufaneleko (x, =, ) ngokufaneleko (x, =, ) ngokufaneleko (x, =, )
okurholela ngokufaneleko (x, =, )
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ekubuyabuyele-
leni
1.15 • Hlukanisa iinomboro kufika e-50 • Hlukanisa iinomboro kufika e-50 • Hlukanisa iinomboro kufika e-99 • Hlukanisa iinomboro kufika e-99
Ukuhlukanisa nga 2, 5, 10 nga 2, 4, 5, 10 nga 2, 3, 4, 5, 10 nga 2, 3, 4, 5, 10
• Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo • Ukusebenzisa amatshwayo
ngokufaneleko (÷, =, ) ngokufaneleko (÷, =, ) ngokufaneleko (÷, =, ) ngokufaneleko (÷, =, )
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
1.16 Umqondonomboro: Iinombiri Umqondonomboro: Iinombiri Umqondonomboro: Iinombiri Umqondonomboro: Iinombiri
ezihlangana na 200 ezihlangana na 500 ezihlangana na 750 ezihlangana ne 999
CAPS Imbalo zehloko
• Ukurhemisa iinomboro • Ukurhemisa iinomboro • Ukurhemisa iinomboro • Ukurhemisa iinomboro
ezikhethiweko ngokwesede ezikhethiweko ngokwesede ezikhethiweko ngokwesede ezikhethiweko ngokwesede
enikeliweko. enikeliweko. enikeliweko. enikeliweko.
• Ukuqanathisa iinomboro ukufika ku- • Ukuqanathisa iinomboro ukufika ku- • Ukuqanathisa iinomboro ukufika ku- • Ukuqanathisa iinomboro ukufika ku-
200 bewutjho bonyana ngiyiphi: 500 bewutjho bonyana ngiyiphi: 750 bewutjho bonyana ngiyiphi: 999 bewutjho bonyana ngiyiphi:
-- enengi nga-1 nofana encani nga-1 -- enengi nga-1 nofana encani nga-1 -- enengi nga-1 nofana encani nga-1 -- enengi nga-1 nofana encani nga-1
-- enengi nga-2 nofana encani nga-2 -- enengi nga-2 nofana encani nga-2 -- enengi nga-2 nofana encani nga-2 -- enengi nga-2 nofana encani nga-2
-- enengi nga-3 nofana encani nga-3 -- enengi nga-3 nofana encani nga-3 -- enengi nga-3 nofana encani nga-3 -- enengi nga-3 nofana encani nga-3
-- enengi nga-4 nofana encani nga-4 -- enengi nga-4 nofana encani nga-4 -- enengi nga-4 nofana encani nga-4 -- enengi nga-4 nofana encani nga-4
-- enengi nga-5 nofana encani nga-5 -- enengi nga-5 nofana encani nga-5 -- enengi nga-5 nofana encani nga-5 -- enengi nga-5 nofana encani nga-5
-- enengi nge-10 nofana encani nge- -- enengi nge-10 nofana encani nge- -- enengi nge-10 nofana encani nge- -- enengi nge-10 nofana encani nge-
10 10 10 10
Ukukhumbula masinyana: Ukukhumbula masinyana: Ukukhumbula masinyana: Ukukhumbula masinyana:
• Ukukhumbula amaphuzu • Ukukhumbula amaphuzu • Ukukhumbula amaphuzu • Ukukhumbula amaphuzu
wamambala ngokuhlanganisa wamambala ngokuhlanganisa wamambala ngokuhlanganisa wamambala ngokuhlanganisa
nokukhupha ukufika e- 20. nokukhupha ukufika e- 20 nokukhupha ukufika e- 20 nokukhupha ukufika e- 20
• Hlanganisa nofana ukhuphe • Hlanganisa nofana ukhuphe • Hlanganisa nofana ukhuphe • Hlanganisa nofana ukhuphe
iimbuyabuyeleli ze-10 ukusukela e-0 iimbuyabuyeleli ze-10 ukusukela e-0 iimbuyabuyeleli ze-10 ukusukela e-0 iimbuyabuyeleli ze-10 ukusukela e-0
ukuya e-100. ukuya e-100. ukuya e-100. ukuya e-100
• Ukubuyabuyelela nokuhlukanisa
amaphuzu wamambala wa:
-- Wamathebula wangakubili
ukufikela ku-2x10
-- Wamathebula wangalitjhumi
ukufikela e-10x10
Amaqhinga wokubalisa Amaqhinga wokubalisa Amaqhinga wokubalisa Amaqhinga wokubalisa
Ukusebenzisa amaqhinga wokubalisa Ukusebenzisa amaqhinga wokubalisa Ukusebenzisa amaqhinga wokubalisa Ukusebenzisa amaqhinga wokubalisa
ukuhlanganisa nokukhupha ukuhlanganisa nokukhupha ukuhlanganisa nokukhupha ukuhlanganisa nokukhupha
ngekghono elifaneleko: ngekghono elifaneleko: ngekghono elifaneleko: ngekghono elifaneleko:
• Beka inomboro ekulu maqangi • Beka inomboro ekulu maqangi • Beka inomboro ekulu maqangi • Beka inomboro ekulu maqangi
ukuze ubale uye phambili nofana ukuze ubale uye phambili nofana ukuze ubale uye phambili nofana ukuze ubale uye phambili nofana
ubale uye emuva ubale uye emuva ubale uye emuva ubale uye emuva
• Inambalayini yehloko • Inambalayini yehloko • Inambalayini yehloko • Inambalayini yehloko
• Ukubuyelela nokuhlukanisa • Ukubuyelela nokuhlukanisa • Ukubuyelela nokuhlukanisa • Ukubuyelela nokuhlukanisa
• Ukwakha nokuphula • Ukwakha nokuphula • Ukwakha nokuphula • Ukwakha nokuphula
• Ukusebenzisa ubudlelwana • Ukusebenzisa ubudlelwana • Ukusebenzisa ubudlelwana • Ukusebenzisa ubudlelwana
obuphakathi kokuhlanganisa obuphakathi kokuhlanganisa obuphakathi kokuhlanganisa obuphakathi kokuhlanganisa
nokukhupha. nokukhupha. nokukhupha. nokukhupha.
77
Ukusebenzisa ubudlelwano phakathi Ukusebenzisa ubudlelwano phakathi
kokubuyabuyelela nokuhlukanisa kokubuyabuyelela nokuhlukanisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
1.17 • Sebenzisa bewutjho amafraktjhini • Sebenzisa bewutjho amafraktjhini • Sebenzisa bewutjho amafraktjhini • Sebenzisa bewutjho amafraktjhini
78 Amafraktjhini okufaka hlangana namahafu, okufaka hlangana neengcezu, okufaka hlangana neengcezu, okufaka hlangana neengcezu,
amakota, kwesithathu, kobunane amakota, kwesithathu, kobunane amakota, kwesithathu, kobunane amakota, kwesithathu, kobunane
nokwesihlanu njll nokwesihlanu njll nokwesihlanu njll nokwesihlanu njll
• Ukubona amafraktjhini ebujameni • Ukubona amafraktjhini ebujameni • Ukubona amafraktjhini ebujameni • Ukubona amafraktjhini ebujameni
obuyidayagremu obuyidayagremu obuyidayagremu obuyidayagremu
• Tlola amafraktjhini njengehafu yi-1 , • Tlola amafraktjhini njenge hafu yi-1 , • Ukuthoma ukubona iincezu ezimbili • Ukuthoma ukubona iincezu ezimbili
ku-1 kokuthathu ku-1kokuthathu nofana iintathu ezintathu zenza nofana iintathu ezintathu zenza
okukodwa okuzeleko godu ucezu okukodwa okuzeleko godu ucezu
namakotara amabili ziyalingana. namakotara amabili ziyalingana.
• Tlola amafraktjhini njenge hafu yi-1, • Tlola amafraktjhini njenge hafu yi-1,
ku-2-kokuthathu. ku-2-kokuthathu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Imihlobo yemiraro yeGreyidi yesi-3
Lezi ziimbonelo zemihlobo yemiraro ekufanele utitjhere azethule ngokuzibuyelela njalo etlasini lakhe. Nangabe
utitjhere usebenza ngesiqhema esincani, kufanele aveze umraro ngokukhuluma. Nangabe abafundi bayakwazi
ukufunda, utitjhere angabanikela umraro otloliweko, nokho utitjhere kusafanele aveze umraro ngokukhuluma.
Imiraro esebujameni ingafakwa emaphepheni wabantwana wokusebenzela, nokho ifanele ibe mifitjhani, inqophe
bekube ngejayelekileko/ngevamileko, begodu utitjhere ufanele aqinisekise bonyana boke abafundi bayayizwisisa.
Ukubuthelela
Ukubuthelela, ukulahla isalela
Umbhagi uthengisa amarolo woburotho ngamaphakethi athwala -12. Unamarolo woburotho anga- 118. Maphakethe
amangaki angawenza ngemphakethi ezithwele -12 ngayinye?
Ukubuthelela, ukungenisa isalela ephendulweni
Umlimi unamaqanda ama-227. Ngemabhoksini ufaka 6 yamaqanda, uzodinga amabhoksi amangaki ukufaka
amaqanda woke?
Ukwabelana
Ukwabelana, ukulahla isalela.
Abangani abahlanu bahlukaniselana ibhoksi lamaswidi ama-84, bonyana boke bathole amaswidi ngokulinganako.
Umngani ngamunye uzokuthola ngaki yamaswidi?
Ukwabelana okurholela emafraktjhinini
Hlukanisa amatjhokolethi ali-15, wabele abangani abasithandathu ngokulinganako kungabi nesalela.
Amafraktjhini nebuthelelo
Ugogo unikela uZizi R12. UZizi ufuna ukonga isithathu semali. Yimalini afanele bonyana ayonge?
Imihlobo le yemiraro kufanele inikelwe abafundi ngemuva kokuba sele bararulule imiraro engaba mine nofana
mihlanu, ekhokhela emihlobeni yamafraktjhini bebazi namabizo weengcezu zamafraktjhini.
Ukuhlanganisa amafraktjhini
Umbanduli webhola yezandla unikela ingcenye ye-orentji komunye nomunye umdlali. Abadlali bebhola yezandla
bali-14. Umbanduli uthloga ama-orentji amangaki?
Imihlobo le yemiraro kufanele inikelwe abafundi ngemuva kokuba sele bararulule imiraro engaba mine nofana
mihlanu, ekhokhela emihlobeni yamafraktjhini bebazi namabizo weengcezu zamafraktjhini.
Ukwabelana ngokulinganako
UPeter mncancani kunoRhulani. Lokha uPeter nakadla isineyi sinye soburotho, uRhulani udinga zimbili iineyi
zoburotho. Lokha uPeter adla mbili yeeneyi, uRhulani uthloga iineyi ezine zoburotho. Ngemuva kwamalanga badle
iineyi ezi-12. UPeter udle iineyi ezingaki noRhulani wadla zingaki?
CAPS 79
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UMandla noSizwe benza umsetjenzana bobabili. UMandla usebenza ama-iri amathathu, USizwe yena usebenza i-iri
yinye. Babhadelwe R60. Kufanele bayabelane njani imali?
Ukuhlanganisa okubuyelelweko
Iinkoloyi ezi-36 zinamavili amangaki?
Linganisa
UThami wonga 35c njalo ngeveke. Uzokonga malini eemvekeni ezi-8?
Amagridi
Umnumzane Khumalo utjala amareyi a-20 wenhlahla zama-orentji. Kunenhlahla ezi-12 ereyini ngayinye. Zingaki
inhlahla sezizoke?
Ukuhlanganisa nokukhupha
Kunemihlobo emithathu yemiraro esisekelo yokuhlanganisa nokukhupha, omunye nomunye umraro ungabuzwa
ngendlela ehlukileko. Imihlobo esisekelo ngile:
Itjhuguluko
UNoluthando ubuthelele iintikara ezi-234. UGugu wamnikela iintikara ezi-80 ngaphezulu. Sekaneentikara ezingaki
kwanjesi?
Kunabakhweli aba-500 ngesitimeleni kwathi aba-176 behla. Kunabakhweli abangaki abasele ngesitimeleni?
Ukuhlanganisa
UNosisi ubuthelela izinto ezakhe zasebenza ulungiselela iphrojekthi yesikolo. Ubuthelele amabhodlela weplasitiki
ayi-124 namaketukana a-268. Ubuthelele izinto ezingaki?
Isitolo sinamaphakethi wamatjhipsi a-368; ama-82 ngawe Chippos amanye ngaweZiksnacks. Maphakhethe
amangaki wamaZiksnacks alapho?
Ukumadanisa
Abentwana begreyidi 2 babuthelele R446, kwathi abentwana begreyidi 3 babuthelela R729. Abentwana begreyidi 3
babuthelele malini ukudlula begreyidi 2?
Ukubuza omunye nomunye umraro ngendlela ehlukileko.
Imiraro kufanele ibuzwe ngendlela ehlukileko. Isib. Yomibili imiraro le miraro etjhugulukileko, kodwana “ ukungaziwako”
kusendaweni ezihlukeneko.
Isitolo besinamaphakethe wepuphu, kwa odwa amanye ayi-55. Manjesi sekunamaphakethe wepuphu ali-170.
Bekunanaphakethe wepuphu amangaki ekuthomeni?
Isitolo besinamaphakethe wetjhukela ama-500. Ngemuva kokuthengisa amanye amaphakethe, basala nama-324
wamaphakethe wetjhukela aseleko. Bathengise amaphakethe amangaki?
80 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ubujamo bemiraro noBudlelwana bemisebenzi ehlukileko.
ULina uthengisa amahotdog nge R4 ngalinye. Yenza ithebula elizomsiza ukuthola inani le-oda ekulu.
Inani lama hotdogi 1 2 3 4 5 10 20
Inani ngama R 4 8
Sebenzisa ithebula elingehla ukuthola inani lamahotdog alikhomba namahotdog ali-15.
USibongile uhlala nabantwana. Ubiza ama R20 imali yokukhwela, bese ubiza R5 nge-iri ukuhlala nomntwana.
Qedelela ithebula elilandelako.
Inani lama -iri 1 2 3 4 5 10
Inani ngama R 25 30
Yelela bonyana umraro waka Sibongile nomraro wakaLina isetjenzwe ngendlela ezihlukileko.
Imihlobo yemiraro engehla inikelelweukuhlahla / ukukhokhela abotitjhere. Abafundi abangathweswa umthwalo
ngemihlobo yamagama. Yelela bonyana abafundi ngasikhathi basebenzisa iindlela ezihlukileko ukusombulula umraro
okungahle kungabi ngilokho utitjhere ebekakulindeleko. Isib. Umraro wokuhlukanisa ungasonjululwa ngokukhupha
okubuyabuyelelweko, ukuhlanganisa nofana ukubuyabuyelela. Iindlela zabafundi zizokutjhuguluka ngokukhamba
konyaka njengombana ukuzwisisa kwabo nokuzijayeza imihlobo yemiraro ehlukahlukeneko, nangokuthuthuka
kweenomboromqondo yabo
CAPS 81
UMBONOMAZOMBE WEGREYIDI YESI-3
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
82
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
2.1 Ukukopa, ukwandisa Ukukopa, ukwandisa Ukukopa, ukwandisa Amaphetheni akhona koke
Amaphetheni nokuhlathulula nokuhlathulula nokuhlathulula Ukubona, ukuhlathulula ngamagama
weJiyomethri Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula Ukukopa, ukwandisa nokuhlathulula godu ukope amaphetheni
ngamagama ngamagama ngamagama weJiyomethri.
• Amaphetheni enziwe ngezinto • Amaphetheni enziwe ngezinto • Amaphetheni enziwe ngezinto • Ngokwemvelo
eziphathekako eziphathekako eziphathekako • Ngepilo yesimodeni
• Amaphetheni enziwa ngokugwala • Amaphetheni enziwa ngokugwala • Amaphetheni enziwa ngokugwala • Okususelwe kumagugu wesitjhaba
imida, ubujamo nofana izinto. imida, ubujamo nofana izinto. imida, ubujamo nofana izinto.
Amaphetheni ahlukahlukeneko: Amaphetheni ahlukahlukeneko : Amaphetheni ahlukahlukeneko :
• Amaphetheni alula lapho amajamo, • Amaphetheni alula lapho amajamo, • Amaphetheni alula lapho inani
nofana ibuthelelo lobujamo nofana ibuthelelo lobujamo lamajamo kesinye nesinye isigaba
libuyelelwa ngendlela efana patsi. libuyelelwa ngendlela efana patsi. litjhuguluka ngendlela yokubonela
• Amaphetheni lapho inomboro phambili: o.u. amaphetheni
nofana ubukhulu bobujamo kesinye ayangezeleleka njalonjalo.
nesinye isigaba buyatjhuguluka
ngendlela yokubonela phambili:
o.u. njalonjalo amaphetheni
ayangezeleleka
Ukutlhama nokuhlathulula Ukutlhama nokuhlathulula
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukutlhama nokuhlathulula iphetheni okungewakhe
iphetheni okungewakhe iphetheni okungewakhe
• Ukutlhama iphetheni yeJiyomethri • Ukutlhama iphetheni yeJiyomethri
• Ukutlhama iphetheni yeJiyomethri okungewakhe
okungewakhe okungewakhe
-- Ngezinto eziphathekako -- Ngezinto eziphathekako
-- Ngezinto eziphathekako
-- Ngokugwala imida, ubujamo -- Ngokugwala imida, ubujamo
-- Ngokugwala imida, ubujamo nofana izinto
nofana izinto nofana izinto
• Ukuhlathulula iphetheni • Ukuhlathulula iphetheni
• Ukuhlathulula iphetheni okungewakhe
okungewakhe okungewakhe
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela Ukukopa, ukungezelela Ukukopa, ukungezelela
Amaphetheni nokuhlathulula: nokuhlathulula: nokuhlathulula: nokuhlathulula :
weenomboro Ukukopa, ukungezelela nokuhlathulula Ukukopa, ukungezelela nokuhlathulula Ukukopa, ukungezelela nokuhlathulula Ukukopa, ukungezelela nokuhlathulula
ukulandelana kweenomboro ukulandelana kweenomboro ukulandelana kweenomboro ukulandelana kweenomboro
okungenani ukufika e-200. okungenani ukufika e-500. okungenani ukufika e-750. okungenani ukufika e-1000.
Ukulandelana kufanele kutjhengise Ukulandelana kufanele kutjhengise Ukulandelana kufanele kutjhengise Ukulandelana kufanele kutjhengise
ukubala uye phambili nemuva nga: ukubala uye phambili nemuva nga: ukubala uye phambili nemuva nga: ukubala uye phambili nemuva nga:
• amakhefu anqotjhisiweko eGreyidini • amakhefu anqotjhisiweko eGreyidini • amakhefu anqotjhisiweko eGreyidini • amakhefu anqotjhisiweko eGreyidini
yesi-2 ngamarherho weenomboro yesi-2 ngamarherho weenomboro yesi-2 ngamarherho weenomboro yesi-2 ngamarherho weenomboro
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
angezelelweko. angezelelweko. angezelelweko angezelelweko.
• ngama -100 ukuya okungasenani • Ngama 50, 100, ukuya • ngama -20, 25, 50, 100, ukuya • ngama -20, 25, 50, 100, ukuya
ema-500. okungasenani e-1000. okungasenani e-1000 okungasenani e-1000.
UMBONOMAZOMBE WEGREYIDI YESI-3
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.1 Ubujamo nokubukela Ubujamo nokubukela
Ubujamo, • Madanisa imibono ehlukeneko • Ukufunda, ukurhumutjha nokugwala
ukuzijayeza yezinto ezifanako zangamalanga amamebhe angakahleleki, nofana
nokubukela woke. ukubona ilingaphezulu lezinto
• Itjho into oyibona ngamalanga ezibuthelweleko.
woke nakuvezwa ihlangothi • Thola izinto emimebheni.
elingakajayeleki. Ubujamo nekombatjhuba
Ubujamo nekombatjhuba • Ukulandela ilayelo kusuka
• Landela ikombatjhuba endaweni eyodwa kuya kwenye
ukukhambakhamba ngetlasini emamebheni angakahleleki
nasesikoleni.
• Ukunikela ilayelo
ukukhambakhamba ngetlasini
nasesikoleni
83
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.2 Amajamo ahlukahlukeneko Amajamo ahlukahlukeneko Amajamo ahlukahlukeneko
84 Ukukhumbula nokutjho izinto ezi Ukukhumbula nokutjho izinto ezi Ukukhumbula nokutjho izinto ezi
Izinto abobusontathu (3-D)ezingetlasini
abobusontathu (3-D)ezingetlasini abobusontathu (3-D)ezingetlasini
ezibusontathu neenthombeni neenthombeni neenthombeni
(3-D) • Ubujamo bebhola (indulungu) • Ubujamo bebhola (indulungu) • Ubujamo bebhola (indulungu)
• Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhoksi (iphrizimu) • Ubujamo bebhoksi (iphrizimu)
• Amasilinda • Amasilinda • Amasilinda
• Amaphiramidi
• Amaphiramidi
• Iinkurwana
• Iinkurwana
Amatshwayo wezinto
Amatshwayo wezinto Amatshwayo wezinto
Ukuhlathulula, ukubeka ngeengaba
Ukuhlathulula, ukubeka ngeengaba Ukuhlathulula, ukubeka ngeengaba nokumadanisa izinto ezi abobusontathu
nokumadanisa izinto ezi abobusontathu nokumadanisa izinto ezi abobusontathu (3-D) ngokuya nge:
(3-D) ngokuya nge: (3-D) ngokuya nge: • ngokuya ngamajamo labobusobubili (2-
• ngokuya ngamajamo labobusobubili (2- • ngokuya ngamajamo labobusobubili (2- D) elenza ubuso bezinto zabobusontathu
D) elenza ubuso bezinto zabobusontathu D) elenza ubuso bezinto zabobusontathu (3-D)
(3-D) (3-D) • iindawo esipara nofana ilingaphandle
• iindawo esipara nofana ilingaphandle • iindawo esipara nofana ilingaphandle eligobeneko
eligobeneko eligobeneko
• Umnqopho otjhukumeziweko Imisetjenzana enqophiweko
eseThemeni 2 Tjheja bewakhe izinto ze abobusontathu
Imisetjenzana enqophiweko (3-D) ezinikelweko ngokusebenzisa
Tjheja bewakhe izinto ze abobusontathu amamathiriyeli aphathekako afana
(3-D) ezinikelweko ngokusebenzisa naikiweko akhitjhwa amajamo we
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amamathiriyeli aphathekako afana abobusobubili
naikiweko akhitjhwa amajamo we (2-D), umdaka/ibumba, isibangulimazinyo,
abobusobubili iphayiphi lokusela nezinye izinto eziyi
(2-D), umdaka/ibumba, isibangulimazinyo, abobusontathu (3-D) zeJiyomethriki. Umnqopho otjhukumeziweko
iphayiphi lokusela nezinye izinto eziyi Umnqopho otjhukumeziweko nokulandelanisa kwemisetjenzana
abobusontathu (3-D) zeJiyomethriki. nokulandelanisa kwemisetjenzana eseThemeni yesi-4
Umnqopho otjhukumeziweko eThemeni yesi-3
nokulandelanisa kwemisetjenzana Ukusebenza ngendulungu, iphrizimu,
eThemeni yesi-2 isilinda, iphiramidi nesikurwana.
Ukusebenza ngendulungu, iphrizimu, Ukunqopha emihlotjeni yelingaphezulu
isilinda, iphiramidi nesikurwana. yenye nenye umhlobo wento.
Ukunqopha emihlotjeni yelingaphezulu Ukuhlukanisa ilingaphezulu ngokuya
yenye nenye umhlobo wento. ngokuthi ligobene nofana lithabalele.
Ukuhlukanisa ilingaphezulu ngokuya Khuluma ngephasi elithabaleleko phezu
ngokuthi ligobene nofana lithabalele. kwe phrizimu, namasilinda bewuwa
Sebenzisa amakhadibhodi aziinkwere hlathulule ngokuya ngokuthi azindulungu,
asikiweko ukwena ibhoksi. Khuluma iinkwere, uncamane nofana uncantathu.
ngelingaphezulu ellithabalele phezulu Ukutjho nokubeka ngesiqhema izinto
kwamaphrizimu, namasilinda be zeJiyomethriki ezingehla. Ukusebenzisa
uwahlathulule ngokuthi azindulungu, iingojwana zokuthlorholoja amazinyo,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
iinkwere nofana uncamane. amaphayephi wokusela nofana amaphepha
Umsebenzi uhlanganiswa ngemisetjenzana
Umsebenzi uhlanganiswa ngemisetjenzana aphuthelweko ukwenza iphiramidi.
etloliweko
etloliweko Umsebenzi uhlanganiswa ngemisetjenzana
etloliweko
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
3.3 Ukubahlanga kobujamo Ukubahlanga kobujamo
CAPS Amajamo Ukubona nokutjho ubujamo Ukubona nokutjho ubujamo
abobusobubili obubusobubili (2-D) obubusobubili (2-D)
(2-D) • Indulungu • Indulungu
• Uncantathu • Uncantathu
• Isikwere • Isikwere
• Uncamane • Uncamane
Ubujamo bebumbeko Ubujamo bebumbeko
Ukuhlathulula, ukuhlela Ukuhlathulula, ukuhlela
nokumadanisa ubujamo nokumadanisa ubujamo
obubusobubili(2-D): obubusobubili(2-D):
• ibumbeko • ibumbeko
• amahlangothi anqophileko • amahlangothi anqophileko
• amahlangothi arondo • amahlangothi arondo
Iminqopho etjhukumeziweko Iminqopho etjhukumeziweko
nokulandelanisa imisetjenzana nokulandelanisa imisetjenzana
yeThemu yoku-1 yeThemu yesi-3
Itjho bewubuthelele amajamo. Itjho bewubuthelele amajamo.
Ukunqophisa emihlotjeni Ukunqophisa emihlotjeni
yamahlangothi kilelo nalelo ijamo. yamahlangothi kilelo nalelo ijamo.
Hlukanisa ubujamo ngokukhuluma Hlukanisa ubujamo ngokukhuluma
ngokuthi amahlangothi wawo ngokuthi amahlangothi wawo
ayindulungu nofana anqophile. ayindulungu nofana anqophile.
Gwala indulungu, iinkwere, Gwala indulungu, iinkwere,
aboncamane noncantathu. aboncamane noncantathu.
Umsebenzi uhlanganiswa Umsebenzi uhlanganiswa
ngemisetjenzana etloliweko. ngemisetjenzana etloliweko.
3.4 Isimethri Isimethri
Isimethri Jamisa umuda wesimethri ngokufoya Ukukhumbula nokugwala imida
amaphepha nokubonisa yesimethri kibo bubusobubili (2-D)
Umnqopho otjhukumeziweko bobujamo beJiyomethri nobujamo
eseThemeni yesi-2 okungasibo beJiyomethri
Imisebenzi yokufoya amaphepha Iminqopho ephakanyisiweko
eyakha ukuzwisisa isimethri kufaka: yeThemu yesi- 4
• imisebenzi lapho ipende emanzi Imisetjuenzana etlolwako kufanele
ebekwa ekhasini ngaphambi ifake iimbonelo lapho
kokulifoya • Umuda awusimumuda otjhingaphasi
• imisetjhenzana lapho iphepha ngasosoke isikhathi.
85 lisikwa lidatjulwe emudeni • Kunimida yesimethri edlula
obhinciweko. kowodwa ebujamweni nofana
entweni
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UMBONOMAZOMBE WEGREYIDI 3
4. UKUMEDA
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IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.1 Ukutjho isikhathi Ukutjho isikhathi ukufunda amalanga ekhalendeni ukufunda amalanga ekhalendeni
Isikhathi ukufunda amalanga ekhalendeni ukufunda amalanga ekhalendeni • Ukubeka ekhalendeni amalanga • Ukubeka ekhalendeni amalanga
• Ukubeka ekhalendeni amalanga • Ukubeka ekhalendeni amalanga wamabeletho, imigidingo yekolo, wamabeletho, imigidingo yekolo,
wamabeletho, imigidingo yekolo, wamabeletho, imigidingo yekolo, amalanga wamaholideyi, izehlakalo amalanga wamaholideyi, izehlakalo
amalanga wamaholideyi, izehlakalo amalanga wamaholideyi, izehlakalo zomlando, izehlakalo zesikolo. zomlando, izehlakalo zesikolo.
zomlando, izehlakalo zesikolo. zomlando, izehlakalo zesikolo. • Ukutjho isikhathi ngama-iri ali-12 • Ukutjho isikhathi ngama-iri ali-12
• Ukutjho isikhathi ngama-iri ali-12 • Ukutjho isikhathi ngama-iri ali-12 usebenzise usebenzise
usebenzise usebenzise -- ama-iri -- ama-iri
-- ama-iri -- ama-iri -- nesigamu se-iri -- nesigamu se-iri
-- nesigamu se-iri -- nesigamu se-iri -- nekota ye-iri -- nekota ye-iri
-- nekota ye-iri -- nekota ye-iri -- nemizuzu -- nemizuzu
-- nemizuzu -- nemizuzu ewatjhini ye-analogo neyedijithali ewatjhini ye-analogo neyedijithali
ewatjhini ye-analogo neyedijithali ewatjhini ye-analogo neyedijithali nezinye iinsetjenziswa zedijithali nezinye iinsetjenziswa zedijithali
nezinye iinsetjenziswa zedijithali nezinye iinsetjenziswa zedijithali ezitjhengisa isikhathi.isib umaliledinini/ ezitjhengisa isikhathi.isib umaliledinini/
ezitjhengisa isikhathi.isib umaliledinini/ ezitjhengisa isikhathi.isib umaliledinini/ ufunjathwako. ufunjathwako.
ufunjathwako. ufunjathwako. Balilsisa ubude besikhathi Balilsisa ubude besikhathi
Balilsisa ubude besikhathi nokudlulisa isikhathi nokudlulisa isikhathi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokudlulisa isikhathi Sebenzisa ikhalendara ukubala Sebenzisa ikhalendara ukubala
Sebenzisa ikhalendara ukubala nokuhlathulula ubude besikhathi nokuhlathulula ubude besikhathi
nokuhlathulula ubude besikhathi ngamalanga, ngemveke ngamalanga, ngemveke
ngamalanga, ngemveke nangenyanga. nangenyanga.
nangenyanga. Okufaka hlangana: Okufaka hlangana:
• Sebenzisa iwatjhi ukubalisisa ubude • UTjhuguluka hlangana namalanga • UTjhuguluka hlangana namalanga
besikhathi ngama-iri nofana isigamu nemveke nemveke
se-iri. • UTjhuguluka hlangana iimveke • UTjhuguluka hlangana iimveke
nenyanga nenyanga
Sebenzisa iwatjhi ukubalisisa ubude Sebenzisa iwatjhi ukubalisisa ubude
besikhathi ngama-iri nofana isigamu besikhathi ngama-iri nofana isigamu
se-iri nekota. se-iri nekota.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.2 Ukulinganisa okungakahlelelwa Ukwazisa iimedo ezihlelelweko
CAPS Ubude • Linganisa, meda, madanisa, • Linganisa, meda, madanisa,
hlela bewurekhode ubude hlela bewurekhode ubude
kusetjhenziswa izinto zokumeda kusetjhenziswa amamitha (nofana
ezingakalinganiswa isib. Ubude iingojwana ezibubude bemitha
besandla, igadango, ubude nofana indambo enobude bemitha)
bepensela, izinto zokubala njll. njengemedo elihlelelweko lobude.
• Ukuhlathulula ubude bezinto
ngokuzibala noutjho ubude
ngendlela engakalinganiswa.
• Ukusebenzisa ilimi ukukhuluma
ngokumadanisa isib. edenyana,
efitjhazana, ede, ebanzi
Ukwazisa iimedo ezihlelelweko
• Linganisa, meda, madanisa, • Linganisa, mmeda bewurekhode
hlela bewurekhode ubude ngamasenthimitha usebenzise irula.
kusetjhenziswa amamitha (nofana
iingojwana ezibubude bemitha
nofana indambo enobude bemitha)
njengemedo elihlelelweko lobude.
• Linganisa, meda bewurekhode
ngamasentimitha usebenzise irula.
Akungabinokutjhugululwa phakathi
kwamamitha namasenthimitha
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.3 Ukulinganisa okungakahlelelwa
88 Ubudisi/ • Linganisa, meda, madanisa,
Ubungako hlela bewurekhode ubudisi
kusetjhenziswa isikala
sokudzimelela nezinto zokumeda
ezingakalinganiswa isib.
Amabhlogo, iintina njll.
• Ukusebenzisa ilimi ukukhuluma
ngokumadanisa isib. lula, kubudisi,
kulula khulu, kubudisi khulu
Ukwazisa ukulinganisa
Ukwazisa ukulinganisa okuhlelekileko
okuhlelekileko
Amathaski atloliweko ukuhlanganisa
• Ukumadanisa, ukuhlela okulandelako okufaka hlangana
nokurekhoda ubudisa bezinto nokufunda kweenthombe ze:
ezipakwe ngokwerhwebo okubonisa
• Imikhiqizo enobudisi obutloliweko
ubudisi butjhiwe ngamakhilogremu
kizo
isib. Amakhilogremu ama-2 wereyisi
nekhilogremu yi-1 yeflowuru. • Isikala sangendlwaneni
yokuhlambela esinenalidi ekhombe
• Lapho kunesikala sangendlini
ilayini yegradiyetjhini
yokuhlambela, abafundi
bangazilinganisa ubudisi babo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngamakhilogremu kusetjenziswa
isikala. Kulindeleke bonyana
abafundi bafunde kwaphela
inomboro eseduzana
nekombabudisi Bahlathulula
ubudisi babo njengokuthi pheze/
citjhe/eduze ne/ khulu kancani
kuna/ khulu nofana ngaphasi
nofana ilingana patsi (nenomboro
yamakhilogremu) bafunda esikaleni.
• Lapho okuneenkala zokumeda
ezineencenye zobungako
ezimeregweko ngamagremu,
abafundi bangameda ubungako
nofana izinto ezihlukeneko.
(alikho itjhuguluko elihlangana
namagremu namakhilogremu
elifunekako)
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.4 Ukulinganisa okungakahlelelwa Ukwazisa ukulinganisa
CAPS Umthamo/ • Linganisa, meda, madanisa, okuhlelekileko
Ivolumu hlela bewurekhode umthamo Amathaski atloliweko ukuhlanganisa
ongeemumathini (o.u. ubunengi okulandelako okufaka hlangana
isimumathi esikghona ukubuthatha nokufunda kweenthombe ze:
nasizalisiweko) ngokusebenzisa
• Imikhiqizo enemithamo etloliweko
izinto zokumeda ezingakahleleki
kizo ukuze kulandelaniswe
isib. Iingobho neenkomitji.
ngokuhlela.
• Ukuhlathulula umthamo
wesimumathi ngokubala nookutjho • Iinthombe zeenjege lapho umthamo
bonyana mayunithi amangaki upheze walingana ilitha eli-1
angakahleleki angazalisa nofana amalitha ama-2 enomuda
isimumathi isib. Ibhodlelo wegradetjhini (gradation line)
linomthamo weenkomitji ezine. • Ukufunda ngokutjhideza
Ukwazisa iimedo ezihlelekileko enomborweni enomude
• Ukulinganisa, ukumeda, wegradetjhini (gradation line)
ukumadanisa, ukuhlela ngokuhlathulula umthamo yazo
bewurekhode umthamo njengokuthi pheze, eduzana,
wezinto ngokumeda ngamalitha enenganakuna, elinganapatsi
kusetjenziswa: nenomboro (yamalitha)
-- Amabhodlelo anomthamo Akukafaneli bona kube khona
ongamalitha nofana imumathi ukutjhugulula amamililitha abe malitha
ezinomthamo otlolwe nofana amalitha abe mamililitha
ngamamililitha isib. iketukana
-- Ijege yokumeda enemida
enenkombamthamo wamalitha,
isiquntu samalitha namakota
wamalitha
-- Ijege yokumeda enemida
enenkombamthamo wamamililitha
-- Iinkomitji nentelebhula ezitjengisa
umthamo wazo.
• Ukumadanisa, ukuhlela
nokurekhoda umthamo wezinto
ezipakwe ngokwerhwebo ukubonisa
umthamo obutjhiwo ngamalitha
isib. Amalitha ama-2 webisi, 1 ilitha
yesiselo esimakhaza, amalitha
ama-5 wepende
• Yazi bonyana ikopi ehlelekileko iyi-
250 yamamililitha
• Yazi bonya itelebhula ehlelekileko
89 i-5 sama milimitha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
4.5 Ipherimitha
90 Ipherimitha Phenya ibanga mazombe ebujameni
obubusobubili
(2-D) neentweni eziyi abobusontathu
(3-D) usebenzise ukumadanisa
okunqophileko nofana amayunithi
angakahleleki
4.6 Ubungako bendawo:
Ubungako Phenya ubungako bendawo
bendawo usebenzise amathayela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UMBONOMAZOMBE WEGREYIDI 3
5. UKUPHATHA IDATHA
CAPS IINHLOKO ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4
5.4 Okuphakayisiweko: Okuziphakanyisiweko:
Ukubuthelela Umzombe wedatha opheleleko Ukuhlela kabutjha kwedatha
bewuhlele idatha ukuwenza ibha grafu. enikelweko. Ngokwerherho, ngethali,
Buthelela idatha ngetlasi nofana nofana ngebha grafu.
5.5
ngesikolo ukuphendula imibuzo Jamiselela idatha kwi bha grafu.
Ukujamiselela ebuzwe ngutitjhere.
idatha Phendula imibuzo ngedatha ngebha
Ukusebenzisa amathali ukurekhoda grafu.
5.6 idatha emahlelweni anikelweko. Ukuhlaziya idatha esijamiselelweni Ukuhlaziya idatha esijamiselelweni
Ukuhlaziya Jamisela idatha e: esinikelweko esinikelweko
bewurhumutjha • Amathebula Okuphakanyisiweko: Okuphakanyisiweko:
idatha • Okungasenani igrafu eyodwa • ungasenani igrafu eyodwa
• Ibha grafu
yeenthombe ena 1 naku 1 enakunye nakunye
Ukukhuluma nge nokuphendula
okukhambisanako kokukhambisanako
imibuzo ngedatha esemathebuleni
naku bha grafu. • Okungasenani ibha grafu yinye • Okungasenani ibha grafu yinye
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.5 AMANOTHI WOKUTLHADLHULA NEMIHLAHLANDLELA YOKUFUNDISA
Ithebula engenzasi inikela utitjhere lokhu:
• iingaba zokumumethweko begodu neenhloko kenye nenye igreyidi ne themu;
• imiqondo namakghono atjhukunyisiweko anqotjhiweko ngethemu;
• amanothi wokutlhadlhula nemihlahlandlela yokufundisa; begodu
• ubude besikhathi esinikelwe isihloko ngasinye eemfundweni ezabelwe i iri li-1 namaminithi ama24.
92 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
3.5.1 Ihlathululo Yokumumethweko eGreyidini yoku-1
IGREYIDI YOKU-1 ITHEMU YOKU-1
CAPS 1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
NgeThemu yokuthoma, isikhathi sisetjenziselwa ukuthuthukisa imiqondo nomboro yangaphambili. Ukuthuthukisa amakghono wangaphambili aphathelene namaphetheni, isikhala
nobujamo, ukumeda begodu nedatha zakha isisekelo samakghono wokufunda ngokujayelekileko namakghono wenomboro ngokunqophileko.
Ukumetjha
Ukumetjha kurholela ekuzwisiseni umqondo wakunye nakunye okukhambelanako, okusisekelo sokumadanisa inani lezinto ezisesiqhemeni ngakelinye ihlangothi.
Lokha umfundi akghona ukubona “okufanako”, kuyakghoneka bona umetjhe amasede amabili. Ukufana yinto yokuthoma yokonga. Ukonga likghono eliqakathekileko lokumeda,
inomboro nesikhala nejamo.
Ukuhlela ngemihlobo
Lokha ubeka ngamananeko, abafundi bafuna okufanako nokuhlukileko. Abafundi bathuthukisa godu ikghono lokuhlathulula nokubona. Ukuhlathulula kutjho bonyana abafundi
bangakhumbula bebatjho izinto ezibazombelezileko. Ukubona kutjho bonyana abafundi bangayidobha into lokha naba nikelwe ihlathululo. Abafundi babona malungana nokuthize
okuphawulekako. Abafundi bahlela izinto ngokuya ngesayizi, umbala, ijamo, ubude, ubudisi, nomthamo. Ukuhlela kwenziwa :
ngezinto zangamalanga zekuphatheni idatha;
amajamo nezinto zejiyomethri ebujamweni nesikhaleni; begodu
nokuphawulekako ezintweni ezimedwako.
Ukumadanisa
Lokha abafundi bamadanisa izinto banqophisa emehlukweni ohlangana nezinto. Abafundi banganqophisa ngo:
• bukhulu nofana ngobuncani;
• budisi nofana ngokulula;
• bude nofana ngobufitjhani;
• kumakhaza nofana okutjhisako;
• kunganalitho nofana okuzeleko;
• bunengi nofana ngobuncani; na
• kuthoma, kokugqina nofana okuphakathi.
Ukufunda ukumadanisa sifundo sokunqophisa ku:
• misetjenzana yokuthoma yokumeda;
• misetjenzana yokuthoma yobujamo nesikhala (okufaka hlangana umsebenzi wobujamo/wendawo); begodu
• nemisetjenzana yokuthoma yamaphetheni.
Emisebenzini yeenomboro, abafundi bametjha izinto eziseenqhemeni ezihlukahlukeneko. Bafunda ukubona iinqhema ezinenani elinganako lezinto ngakizo, nokuhlukanisa iinqhema
ezingaba nezinto ezinengi nofana ezimbalwa kunezinye iinqhema.
Ukuhlela
Ukuhlela kusisekelo serherho leenomboro. Ukubeka nokubala izinto ngokuhlelekileko kusiza abafundi abancani ukwenza isiqinisekiso sokobana babala into kanye kuphela. Ukubeka
izinto ngokuhlelekileko nakubalwako kwenza isendlalelo sokuzwisisa bonyana iinomboro ungazihlela bunjani.
Imisebenzi yokuthoma yamaphetheni efaka hlangana amajamo nofana izinto isiza ukunqophisa ukulalelisisa komfundi lokha nakuhlelwako. Ngokuya kwesikhathi, abafundi
basebenzisa ikghono leli lokha nabasebenza ngamaphetheni weenomboro.
Ukulinganisa okunqophako ngaphandle kokubala
Ukulinganisa okunqophako ngaphandle kokubala kulemuka msinyana inani lezinto ebuthelelweni ngaphandle kokuzibala.
93
Ukulinganisa okunqophako ngaphandle kokubala kusiza abafundi ukubona amabuthelelo amancani njengeyunithi eyodwa. Lokhu kunikela abafundi isisekelo esiqinileko sokusebenza
ngeenomboro.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
94 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Ukubala kusiza abafundi ukuthuthukisa ilemuko lesayizi leenomboro nokwenza isendlalelo
Ukubala ngokuthembeka ukufika ngokuthembeka ukufika sokubala ngeenomboro ezipheleleko . NgeThemu yokuthoma, abafundi bathuthukiusa
izinto ema 50. ema 10. amakghono alandelako:
Nikela ukulinganisa Nikela ukulinganisa • Ukubala koke
okuzwakalako kwenani okuzwakalako kwenani • Ukubala uragele phambili
lezinto ezingahlolwa lezinto ezingahlolwa
• Umthetho wenani leenomboro
ngokubalwa. ngokubalwa.
• Ukusebenza ngamatheksti atloliweko
Ukubala eThemini yoku-1 kunqotjhiswe ekuthuthukiseni ikghono lomfundi lokubala.
Ukuthuthukisa ikghono lokubala kubavumela bona ba:
• bale izinto ezibuthelelweko nalezo ezingakabuthelelwa;
• ukubala baye phambili nemuva;
• ukubala izenzeko/imisikinyeko;
• ukubala kulandelane enambalayinini;
• ukuthuthukisa ikghono lokulemuka isayizi yeenomboro ngokuzihlela nokuzimadanisa;
noku
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Linganisa nokwenza ibonelo phambili.
Ukubala izinto
Ngaphambi kokobana abafundi babale izinto, batlhoga ithuba lokobana bazijayeze ukubala
ngehloko/ngokukhulunywako. Abafundi kufanele babe nerherho elikhulunywako /lehloko
lamagama weenomboro ngokuhlelekileko: kunye, kubilib, kuthathu, ukufika ema 20.
Khuthaza abafundi ukutjho imilolozelo yeenomboro begodu badlale nemidlalo ezoqinisekisa
ukubala ngehloko. Ikghono leli lokubala ngehloko nofana ukubala okungakahleleki
kuqakathekile ukuthuthukisa ilwazi lamagama weenomboro begodu nekghono legido/
iphetheni eseenomborweni.
Abafundi bazabala inomboro yento ngayinye begodu bametjhisa amagama weenomboro
namasede wezinto. Lokhu kufaka hlangana bonyananta nokutjhidisa into nokutjho igama
lenomboro.
Kuqakathekile bona abafundi bazi bonyana igama lenomboro yokugcina ekhulunyiweko
lijamele into yokugcina ebaliweko esiqhemeni. Kufanele bazi begodu bazwisise bona
inomboro yegama etjengiswe ekugcineni itjho inani lesede nofana ikhadinali yesede.
Akusingiboboke abafundi abakghona ukubala ngehloko begodu batjho amagama
weenomboro ngokulandelana abangenza umqondo ozwakalako ngokubala kwabo.
Kungenzeka beqe ezinye iinomboro begodu batjho bonyana kunezinto zokubala ezine
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
lokha nakunezinto zokubala ezihlanu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.1 Ukubala izinto Ukubala izinto Kuqakathekile bona abafundi babale inani elifanako lezinto ezingafaniko.
Ukubala ngokuthembeka ukufika ngokuthembeka ukufika Isibonelo:
izinto ema 50. ema 10.
• Ukubala izinto zokubala ezisithandathu
Nikela ukulinganisa Nikela ukulinganisa
• Ngilethela amapensela asithandathu
okuzwakalako kwenani okuzwakalako kwenani
lezinto ezingahlolwa lezinto ezingahlolwa • Bala iinkunubhe ezisithandathu
ngokubalwa. ngokubalwa. Ukongiwa / ukutlhogonyelwa
Abafundi bazathoma ukulemuka lokha nababala inani lezinto bona, inomboro
ayithikanyezwa yisayizi nofana ubujamo. Omunye angabuza: zingaki iinkwekwezi
ezikaradeni ngalinye?
Ubujamo nofana ukuhleleka kweenkwekwezi kuhlukile, kodwana inani leenkwekwezi
ekaradeni ngalinye lilingana patsi.
Kuqakathekile bona lokha sibala izinto eziphathekako, abafundi babone inani elincani
lezinto ngaphandle kokubala.
Isibonelo , ukubona
• kuhlanu , njengenani lemino esandleni sinye
• izinto zokubala ezintathu, zihleleke ngananyana ngiyiphi indlela
• kunye ukufika kusithandathu, ngokuhleleka kwamaqatjhazi edayisini
Lokhu singakubiza godu ngokuthi kulinganisa okunqophako ngaphandle kokubala.
Ngakho ke:
Isisekelo somqondonomboro siyathuthuka ngokubala izinto eziphathekako. Abafundi
bafunda:
• Ukuhlobanisa inomboro magama nebuthelelo lezinto;
• Ukwakha isithombe ngqondo sokobana inomboro itjho bonyanani o.u. yikulu kangangani;
nokuthi
• Igama lenomboro yento ebalwe kokugcina lijamele inani lezinto esiqhemeni.
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ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
96 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Iinlayelo nemibuzo yokusekela ukubala izinto
Ukubala ngokuthembeka ukufika ngokuthembeka ukufika • Bala iingojwana zokubala ezili 10. Zihlele zibe semudeni.
izinto ema 50. ema 10.
• Buyelela uhlele iingojwana begodu ubale. Inani lisalingana na?
Nikela ukulinganisa Nikela ukulinganisa
• Bala iimvala zamabhodlhelo la ngaphandle kokuzithinta.
okuzwakalako kwenani okuzwakalako kwenani
lezinto ezingahlolwa lezinto ezingahlolwa • Inani liyalingana na?
ngokubalwa. ngokubalwa. • Uqabanga bona kunamakhrayoni amangaki lapha?
• Manengi nofana mancani kunalokhu obewukucabanga?
• Wazinjani bonyana unenani lelo?
• Wazinjani bonyana ubale elinye nelinye ikhrayoni?
• Ungayihlola njani ipendulo yakho?
Ukudlulela emathekstini atloliweko
Abafundi kufanele banikelwe amathuba wokubala iimboniso zezinto. Isibonelo:
Kungaki lokhu?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ragela phambili ubale
Lokha abafundi sebakghona ukubala zoke izinto bathome ku-kunye, kufanele babale baye
phambili kusukela ebuthelelweni asele banalo. Isibonelo:
Bawa abafundi bona babale bakhuphe izinto ezilikhomba, bese kusukela ezintweni
ezilikhomba lezo, ababale bakhuphe ezinye godu ezintathu kufika lapho baba nezinto ezi-10.
Ukubala uragele phambili liqhinga eliphumelelisako lokubala kunokubala koke begodu
abafundi bazakiusebenzisa ukubala baragele phambili lokha nababalisisako.
Iinsetjenziswa:
Kuyasiza ukwakha ibuthelelo lezinto ezihlukeneko ezingasetjenziswa bafundi njengezinto
zokubala.
Isibonelo:
• Iinthoro zomlilo
• Iingojwana ze-ayisikhrimu
• Iintanga zeperegisi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Amabhontjisi
• Iimvalo zamabhodlelo
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ukubala uye phambili ngakunye
Ukubala uye nemuva ngakunye nemuva ngakunye Ukubala ngehloko nofana ukubala uphimisele (ukubala okungakahleleki) kuligadango
phambili ukusuka kwenye nenye ukusuka kwenye nenye eliqakathekileko lokubongelela amagama weenomboro ngokuhlelekileko. Lokha abafundi
nemuva inomboro hlangana ne-0 inomboro hlangana ne-0 bakghona ukwenza lokhu, akutjho bonyana banelwazi lesayizi yeenomboro abayitjhoko.
ne-100 na-20
Ethemini yoku-1 kulindeleke bona abafundi babale kwaphela baye phambili nemuva nga
Ukubala uye phambili kunye ukufikela ema-20.
nga:
Ukubala uye phambili nemuva kungenziwa netlasi loke. Yenza isiqinisekiso sokobana
• Li-10 ukusuka abafundi abarhuweleli nje kuphela ngaphandle kokuzwisisa. Eenqhemeni okunqotjhwe
kesinye nesinye kizo nemberegweni wokuzijamela imisetjenzana elandelako ingenziwa ukwenza umqondo
isibuyabuyelelo se-10 ozwakalako ekubaleni:
hlangana ne-0 ne-100
Thoma ku-kubili ubale ukufika ku-bunane
• Ku-5 ukusuka
Bala ukusuka ku-kune ukufika e-10
kesinye nesinye
isibuyabuyelelo saka Bala ukusuka ku-kubili ukufika ku-bunane. Ubale iinomboro ezingaki?
ku-5 hlangana ne-0 Bala ukufika etjhumini
ne-100 Ekuthomeni abafundi bazakuthoma babale ukufika etjhumini begodu baphrakthise
• Ku-2 ukusuka amagama weenomboro ngokulandelana.
kesinye nesinye Abafundi banga thitjhelekaka ukubala ngehloko ngakho ke kufanele babale ngeendlela
isibuyabuyelelo saka ezahlukahlukeneko, nakungasinjalo, bazamane barhuwelele. Ukubala okungakahleleki
ku-2 hlangana ne-0 kufanele kusekelwe ngokufunda amatshwayo weenomboro begodu nokubala izinto.
ne-100
Abafundi kufanele banikelwe imifanekiso ebonakalako yeenomboro ngokulandelana kwazo.
Imifanekiso ebonakalako elandelako ingasetjenziswa:
• Imincamo yokubala
• I-Abhakhasi
• Inambalayini
Ekuthomeni, inamba layini ayibe nazozoke iinomboro, bese kuba yinambalayini ekhamba
iba neenkhala lapho ezinye iinomboro zingekho, ingasetjenziswa. Lokhu kutjho bonyana
abafundi kufanele bazazi iinomboro ngokulandelana kwazo ukuzaliselela iinkhala.
Ukubala uye emuva
Ukubala uye emuva likghono elibudisi ebafundini begodu ukuzijayeza njalo kuyatlhogeka.
Thoma ukubala uye emuva kusukela enomborweni lokha abafundi nasele bayijayele
inomboro u- 2, bese wakhela phezu kwayo lokha unqophise enomborweni enye nenye
engaphezulu.
97
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
98 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ukubala ukufika ema-20
Ukubala uye nemuva ngakunye nemuva ngakunye Ukubala ukudlula etjhumini kungafuna bona abafundi batjho ukulandelana kokubala
phambili ukusuka kwenye nenye ukusuka kwenye nenye balandele/ngemuva kwakatitjhere. Kuqakathekile ukukhuthaza abafundi bona bathome
nemuva inomboro hlangana ne-0 inomboro hlangana ne-0 ukubala ukusukela kunoma ngiyiphi inomboro. Ukuthoma ku-8 kunzima khulu kunokuthoma
ne-100 na-20 ku-1. Abafundi bazakusebenzisa ikghono leli lokha nababala baragela phambili
Ukubala uye phambili ngokuhlanganisa/ekuhlanganiseni.
nga: Iinsetjenziswa
• Li-10 ukusuka • Imincamo yokubala ukufika ema-20
kesinye nesinye
• I-Abhakhasi
isibuyabuyelelo se-10
hlangana ne-0 ne-100 • Amagridi weenomboro ayasiza ukuthuthukisa ikghono labafundi lokufunda ilwazi
ethebuleni. Ngoba abafundi babala kufikela etjhumini, igridi kufanele ikhombise ilwazi
• Ku-5 ukusuka
elilandelako kuphela:
kesinye nesinye
isibuyabuyelelo saka 1 2 3 4 5 6 7 8 9 10
ku-5 hlangana ne-0
ne-100 11 12 13 14 15 16 17 18 19 20
• Ku-2 ukusuka • Inambalayini etjengisa iinomboro ezifika ema- 20
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kesinye nesinye
isibuyabuyelelo saka
ku-2 hlangana ne-0
ne-100
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.3 Ukubona, ukukhumbula Ukubona, ukukhumbula Ukufunda nokutlola amatshwayo namagama weenomboro
Amat- nokufunda iinomboro nokufunda iinomboro Abafundi bafanele bafunde bona bangakwenza bunjani lokhu:
shwayo • Ukubona, • Ukubona, • Ukutlola amatshwayo namagama weenomboro
namagama ukukhumbula ukukhumbula
• Ukufunda amatshwayo weenomboro
weenom- nokufunda nokufunda
boro amatshwayo amatshwayo • Ukutjho iinomboro
weenomboro ukusuka weenomboro ukusuka Ukufunda nokutlola amatshwayo namagama weenomboro kufuze kukhambisane
ku-1 ukufika e-100 ku-1 ukufika e-20 nemisetjenzana yokubala. Abafundi kufanele banikelwe amathuba wokumetjhisa
• Ukutlola amatshwayo • Ukutlola amatshwayo amatshwayo namagama weenomboro nebuthelelo lezinto abazibalako. Ngalendlela,
weenomboro ukusuka weenomboro ukusuka abafundi bamadanisa itshwayo lenomboro, igama lenomboro, isijamiselo senomboro
ku-1 ukufika ema-20 ku-1 ukufika ku-5 nehlathululo yenomboro.
• Ukubona, • Ukubona, Imisetjenzana yaphambili eminye
ukukhumbula ukukhumbula Ukuzijayeza ukutlola
nokufunda amagama nokufunda amagama Abafundi bangazijayeza ukutlola amatshwayo wenomboro ngeendlela ezihlukahlukeneko:
weenomboro ukusuka weenomboro ukusuka
• Ngokugadangisa phezu kweenamba
ku-1 ukufika e-10 ku-1 ukufika ku-5
• Ukwenza ‘ukuhlanganisa amaqathjaza’ imisetjenzana ngengaphandle lamatshwayo
• Ukutlola amagama • Ukutlola amagama
weenomboro
weenomboro ukusuka weenomboro ukusuka
ku-1 ukufika e-10 ku-1 ukufika ku-5 • Ngokutlola esandeni
• Tlola etjhokbhodini nofana esamendeni
• Ngokupenda
• Ngokukorotjha iinomboro ngokusebenzisa iwulu. Umsebenzi lo usiza khulukhulu
ekugandeleleni lapho kuthonywa khona lokha kutlolwa iinombor.
• Ngokugadangisa iinomboro ezikulu, ezisikwe ephepheni lokurhuhla nofana ematjhileni.
Ukufunda iinomboro
Lokhu kungenziwa ngoku:
• Ukukhomba iinomboro enambalayinini nofana egridini yeenomboro
• Ukufunda amakarada weenomboro
Ukumetjhisa amatshwayo weenomboro nebuthelelo lezinto
Lokhu kungenziwa ngoku :
• Metjhisa inani lezinto neenomboro
• Ukubala ibuthelelo lezinto nokukhetha ikarada leenomboro elifaneleko lenani lezinto lezo.
• Ukubala izinto eziseenthombeni begodu nokutlola itshwayo lenomboro.
99
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
100 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.4 Hlathulula , madanisa Hlathulula, madanisa Ukumadanisa nokuhlela iinomboro kusiza abafundi ukukhaliphisa umqondo wabo
begodu uhlele izinto begodu uhlele izinto wokuhlobana kwama sayizi weenomboro. Izaba siza ukuthuthukisa umqondo wokobana
Hlathulula,
ezifika ema-20 ezifika kwezi-5. inomboro yikulu nofana yincani kangangani kunezinye iinomboro. Lokha abafundi
madanisa • Hlathulula begodu
begodu • Hlathulula begodu banomqondo omuhle wokuhlobana kwamasayizi weenomboro, kuzakuba lula kibo
uhlele ibuthelelo lezinto uhlele ibuthelelo lezinto ukulemuka amatshwayo asisekelo. Emabangeni asiSekelo lokhu sikubiza bona
uhlele mayelana nokuthi
mayelana ezinengi , yinumerosithi.
iinomboro zinengi, lidlanzana,
ezincani, ezilinganako
ezidlulako, ezincani, Amakghono wokubala aqakathekile ekumadaniseni nokuhlela iinomboro. Ukuhlela
• Hlathulula begodu nengi kuna, ncani iinomboro kufaka hlangana:
uhlele ibuthelelo lezinto kuna, kuyalingana,
kusukela kwezinengi • Ukufunda ngamakhadinal namba asitjela ngobungako/ngenani lenomboro
zinengi okulinganako,
ukuya kwezincani umehluko • Ukusebenzisa, ukufunda nokutlola amagama namatshwayo weenomboro
nakusuka kwezincani • Hlathulula begodu • Ilimi lokumadanisa iinomboro
ukuya kwezinengi uhlele ibuthelelo lezinto Ukumadanisa inomboro yezinto
• Hlathulula, madanisa kusukela kwezinengi
begodu uhlele ukuya kwezincani Lokhu kwenziwa khulu khulu ngokusebenzisa kunye-nakunye-okukhambelanako. Abafundi
iinomboro kufika ema- nakusuka kwezincani babala ibuthelelo lezinto begodu bamadanise amagama weenomboro yinye-nayinye-nezinto
20 ukuya kwezinengi. lezo. Ukumadanisa ibuthelelo lezinto kudzimelele elemukweni lomfundi lokubala.
• Hlathulula begodu • Yenza Izinto Kuqakathekile ukunqophisa emqondweni wokuthi ‘ kunengi na kuncani’ lokha umadanisa
umadanise iinomboro ezihlukahlukeneko amanani.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
eziphelelekomayelana ezihlanu
• Hlathulula, madanisa Lokha umadanisa izinto, ilimi lokumadanisa liyathuthuka.
nokuthi yincani kuna,
yikulu kuna nokuthi begoduuhlele Isibonelo: Okunengi ngange, inomboro elinganako ne, lingana ne, kunengi kuna, kuncani
idlula nga, ingaphasi iinomboro kufika ku-5 kuna, kulidlanzana kuna
nga, ilingana na • Hlathulula begodu Ukuhlela ibuthelelo lezinto
• Hlathulula begodu umadanise iinomboro
eziphelelekokufika ku 5 Kusukela ekubaleni nekumadaniseni amasede amabili wezinto , abafundi bavumbulula
uhlele iinomboro
usebenzise ilimi isib. begodu bafunde ngobudlelwana obubili obuqakathekileko:
kusuka kwencani khulu
ukuya kwekulu khulu • Mayelana nokuthi, • Amabuthelelo amabili ayalingana lokha nakabelana igama lenomboro elifanako, nanoma
nakusuka kwekulu kuncani kuna, kukhulu amabuthelelo kungenzeka angakahleleki ngokufanako.
khulu ukuya kwencani kuna ,kudlula nga,
kuncani nga • Ukubala iinomboro kujamele ukulandelana kweenomboro ezilandelanako ezanda
khulu ngayinye ngasosoke isikhathi .isib ukuhlanu uza ngemuva kwaka kune, kungakho
• Hlathulula begodu
uhlele: ibuthelelo lezinto ezihlanu linengi ngakunye kunebuthelelo lezinto ezine nofana ibuthelelo
-- iinomboro kusukela lezinto ezine lincani ngakunye kunebuthelelo lezinto ezihlanu
kwencani khulu Ukuhlela nokumadanisa iinomboro
ukuya kwekulu khulu
nakusuka kwekulu Lokha abafundi bahlela iinomboro, bangahle basebenzise isikhala esikhona hlangana
khuluv ukuya neenomboro ukuthola bona ngiyiphi inomboro ekulu. Isibonelo, bazakuthi u-5 mkhulu kuno-
kwencani klhulu 2 ngombanyana u-5 uza ngemuva kuka ku-2. Abafundi bafanele bahlobanise ukubalwa
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
-- ngokusebenzisa kweezinto begodu bamadanise ibuthelelo yezinto ezilithoba nesiqhema sezinto ezimbili.
ilimi isib ngaphambi, Egreyidini 2 no 3 abafundi bazabe bahlela bebamadanise iinomboro ngokuhlathulula inani/
ngemuva phakathi/ ubungako bamadijithi. Abafundi bafanele bahlele iinomboro ngokusebenzisa imifanekiso
hlangana ehlukahlukeneko.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.4 Hlathulula , madanisa Hlathulula, madanisa Abafundi bangahlela iinomboro ngokusebenzisa inambalayini.
begodu uhlele izinto begodu uhlele izinto Isibonelo:
Hlathulula,
ezifika ema-20 ezifika kwezi-5.
madanisa • Hlathulula begodu • Thatha inomboro yesi-3 uyibeke enambalayinini
begodu • Hlathulula begodu
uhlele ibuthelelo lezinto uhlele ibuthelelo lezinto • Khetha inomboro ngemuva kwaka ku 4 uyibeke endaweni yayo efaneleko enambalayinini
uhlele mayelana nokuthi
mayelana ezinengi , • Khetha inomboro phakathi kuka ku-3 no ku-5 uyibeke endaweni yayo efaneleko
iinomboro zinengi, lidlanzana,
ezincani, ezilinganako enambalayinini
ezidlulako, ezincani,
• Hlathulula begodu nengi kuna, ncani • Khetha inomboro ngaphambi kwaka ku-2 uyibeke endaweni yayo efaneleko
uhlele ibuthelelo lezinto kuna, kuyalingana, enambalayinini
kusukela kwezinengi zinengi okulinganako,
ukuya kwezincani • Khetha inomboro ngaphambi kwaka ku-3 uyibeke endaweni yayo efaneleko
umehluko enambalayinini
nakusuka kwezincani • Hlathulula begodu
ukuya kwezinengi uhlele ibuthelelo lezinto Amakarada weenomboro
• Hlathulula, madanisa kusukela kwezinengi Isibonelo: Abafundi bangapaka amakarada ngokulandelana kwawo.
begodu uhlele ukuya kwezincani
iinomboro kufika ema- nakusuka kwezincani
20 ukuya kwezinengi.
• Hlathulula begodu • Yenza Izinto 1 2 3 4 5
umadanise iinomboro ezihlukahlukeneko
eziphelelekomayelana ezihlanu
nokuthi yincani kuna, • Hlathulula, madanisa Ukudlulela emathekstini atloliweko
yikulu kuna nokuthi begoduuhlele iinomboro Abafundi bangahlanganisa ilwazi labo ngokuqedelela imisebenzi eencwadini zabo
idlula nga, ingaphasi kufika ku-5 zokusebenzela. Lokhu kungenziwa ngesikhathi sokusebenza ngokuzijamela.
nga, ilingana na • Hlathulula begodu
umadanise iinomboro Ubukhadinali nobu-odinali
• Hlathulula begodu
uhlele iinomboro eziphelelekokufika ku 5 Ubukhadinali kutjho inani loke lesede nofana lebuthelelo. Ubu-odinali kutjho indawo /
kusuka kwencani khulu usebenzise ilimi isib. ubujamo lapho into ikhona hlangana nesede yezinto. Kufanele kwenziwe ukuhlobana
ukuya kwekulu khulu • Mayelana nokuthi, phakathi kweenomboro zekhadinali neenomboro ze-odinali. Abafundi bazakubona lokhu
nakusuka kwekulu kuncani kuna, kukhulu lokha nababala isiqhema sezinto begodu bazi bonyana lokha bathinte into yesihlanu,
khulu ukuya kwencani kuna ,kudlula nga, bazabe sebabale izinto ezihlanu ngesikhathi leso. Iinomborosikhundla kusetjenzwa ngazo
khulu kuncani nga
kwaphela eThemini yesi-4.
• Hlathulula begodu
uhlele:
-- iinomboro kusukela
kwencani khulu
ukuya kwekulu khulu
nakusuka kwekulu
khuluv ukuya
kwencani klhulu
-- ngokusebenzisa
101 ilimi isib ngaphambi,
ngemuva phakathi/
hlangana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
102 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
UKURARULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki NgeThemu le, abafundi bazakuthoma ukurarulula imiraro yamagama basebenzisa
Amathek- alandelako lokha alandelako lokha amathekhiniki alandelako ukurarulula imiraro leyo:
hiniki wok- nawurarulula imiraro nawurarulula imiraro • Iinsetjenziswa eziphathekako
urarulula begodu uhlathulule begodu uhlathulule
• Imigwalo
imiraro iinsombululo zemiraro: iinsombululo zemiraro:
• Amanambalayini
• Iinsetjenziswa • Iinsetjenziswa
eziphathekako isib. eziphathekako isib. Imigwalo neensetjenziswa eziphathekako
iimbali iimbali Abafundi bazakugwala iinthombe bebasebenzise neensetjenziswa eziphathekako
• Iinthombe zokugwala • Iinthombe zokugwala ukurarulula imiraro. Ekupheleni kweThemu abafundi banga gwala iinthombe eziphethe
isamba sendatjana isamba sendatjana iinomboro ukuhlathulula umbalo neensombululo. Kuqakathekile bona iinthombe nofana
imigwalo ephethe iinomboro ezihlathulula umbalo nesisombululo nge:
• Ukwakha nokuphula • Amanambalayini
iinomboro esekelwe • Amamaraga wobunye
• Ukubuyelela kabili ziinsetjenziswa • Iinomboro
nokuhafula eziphathekako isib. Amanambalayini
Imincamo yokubala
• Amanambalayini Ukusebenzisa Amanambalayini ukwenzela ukubasiza ukubalisisa kuzakunikela abafundi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
indlela yokurekhoda ukucabanga kwabo nokwenza ilandelela yalokho. Begodu ivumela
abafundi bona babe barekhode isiboniso abangasisebenzisa ukuhlathulula bona
bawurarulule njani umraro.
NgeThemu le, abafundi bazakuvezelwa Amanambalayini begodu bazathoma
ukuwasebenzisa njengeqhinga lokubalisisa.
Ekuthomeni, lokha kusetjenzwa ngamanambalayini intambo yemincamo ingabekwa ngehla
nofana ngaphasi kwenambalayini ukusiza abafundi ukubala.
Ngaphambi kokobana abafundi basebenzise inambalayini njengeqhinga lokubalisisa,
bafanele bayisebenzisele uku:
• Bala baye phambili nemuva
• Ukufunda amatshwayo weenomboro
• Ukutlola amatshwayo weenomboro
• Ukubeka /jamisa iinomboro enambalayinini
• Ukuhlela nokumadanisa iinomboro
Lokha usebenzisa inambalayini njengesiboniso sokubalisisa, umqondo wo ‘ukweqa’
ungafundwa ngokusebenzisa imino nofana ngokugwala umuda ngaphandle nangokweqa
kwamambala kusuka kwenye inomboro ukuya kwenye. Imisetjenzana yehlobo leli isiza
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
abafundi ukubona lapho iinomboro zikhambelana khona. Kufanele bakwazi bonyana:
“ukusuka ku-3 ukuya ku-5 kuzakuthatha imeqo emi-2”. Abafundi kufanele banikelwe amathuba
wokwenza ibonelo phambili lokuthi mimeqo emingaki khesithi kusuka ku-2 ukuya ku-5.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Isibonelo sokobana abafundi bangayisebenzisa njani inambalayini ethemini :
Amathek- alandelako lokha alandelako lokha Kunabesana abathathu nabantazana ababili abenza isifundo sobukghwari esingezelelweko
hiniki wok- nawurarulula imiraro nawurarulula imiraro esikolweni. Bangaki abafundi abangetlasini yobukghwari?
urarulula begodu uhlathulule begodu uhlathulule
Abafundi bangasebenzisa inambalayini ngendlela elandelako ukufinyelela ependulweni.
imiraro iinsombululo zemiraro: iinsombululo zemiraro:
• Iinsetjenziswa • Iinsetjenziswa
eziphathekako isib. eziphathekako isib.
iimbali iimbali
• Iinthombe zokugwala • Iinthombe zokugwala
0 1 2 3 4 5 6 7 8 9
isamba sendatjana isamba sendatjana
• Ukwakha nokuphula • Amanambalayini
iinomboro esekelwe Qala amanothi angenzasi ngaphasi kwe ‘iindlela nofana amaqhinga’ ukuveza inambalayini.
• Ukubuyelela kabili ziinsetjenziswa
Tjheja bona esikhathini esinengi abafundi bararulula imiraro ngendlela utitjhere
nokuhafula eziphathekako isib.
angakalindeli ngayo.
Imincamo yokubala
• Amanambalayini Isibonelo, ukurarulula umraro ongehla, abafundi bangakhetha ukuthoma ukubala ngenani
labantazana aba-2, bese bahlanganise noku-3. Iindlela yabafundi izakutjhuguluka
ngokukhamba konyaka lokha ukuzwisisa kwabo nokuzijayeza imihlobo yemiraro khula
begodu nomqondo nomboro wabo uthuthuka.
103
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
104 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Iimbalo zamagama zivame ukusetjenziswa njengesingeniso eembalweni (ama-oparetjhini).
Ukuh- yamagama yamagama Abafundi bathoma ngokurarulula imiraro ngokusebenzisa iinsetjenziswa eziphathekako;
langanisa ezisebujameni ezisebujameni lokhu kuthuthukisa:
nokukhupha bewuhlathulule bewuhlathulule • Ukugwala iinthombe;
iinsombululo zakho iinsombululo zakho
• Ukugwala iinthombe nokutlola iinomboro ukuhlathulula iimbalo (ama-opharetjhini) noku;
zemiraro ezifaka zemiraro ezifaka
ukuhlanganisa ukuhlanganisa • Ukusebenzisa iinomboro kuphela.
nokukhupha nempendulo nokukhupha nempendulo Isibonelo:
ukufika e-20. ukufika e-20. Kunabantwana abahlanu emjinkweni. Abathathu basehlangothini elilodwa. Bangaki
abangakelinye ihlangothi?
Ethemini yokuthoma abafundi bangarekhoda imiraro yamagama ngendlela elandelako.
Amaqhinga wokubalisisa
Ukusebenzisa ukubala koke ukwenzeka ukurarulula umraro womjinko
1,2,3,4,5
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1, 2, 3
ehlangothini
leli Kuna-2 ngakileli
ihlangothi
Lapha, abafundi babala isiqhema ngasinye nebuthelelo loke, ngakho ke, babala
okungasenani kathathu.
Ukusebenzisa ukubala uragele phambili ukurarulula umraro oyaphasi naphezulu (see-saw)
Abafundi babala baragele phambili ukusuka kukuthathu bebafike kukuhlanu. Leli liqhinga
elisiza khulu lokha umuntu nakalisebenzisako.
“Ngiyazi bona kunabantwana abathathu begodu umntwana oyedwa wenze babe bane,
begodu omunye umntwana oyedwa wenze babe bahlanu abantwana. Kunabantwana
ababili ngakwelinye ihlangothi”.
Ukuhlanganisa nokukhupha usebenzisa ama-apharathasi
Abafundi basebenzisa ama-apharathasi aphathekako ngendlela ethize ukufinyelela
ependulweni. Abafundi basebenzisa iinsetjenziswa ukwakha umqondo ozwakalako
wokuhlanganisa nokukhupha basebenzisa izinto abangazithinta, bazibambe begodu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
bajikajike nazo. Bonyana abafundi bazisebenzisa njani iinsetjenziswa, kuzakukhethwa
kbonyana isisbalo samagama sijame/sakhiwe bunjani.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Ukurekhoda imifanekiso yokuhlanganisa nokukhupha
Ukuh- yamagama yamagama • Ukurekhoda usebenzisa ama-apharathasi aphathekako
langanisa ezisebujameni ezisebujameni
Abafundi bangasebenzisa iinsetjenziswa eziphathekako ukbala koke nokubala baragele
nokukhupha bewuhlathulule bewuhlathulule
phambili. Nanyana kunjalo, abafundi bangasebenzisa amaqhinga la lokha nabagwala
iinsombululo zakho iinsombululo zakho
iinthombe ukutjengisa ukucabanga kwabo, amaqhinga wabo wokubalisisa begodu
zemiraro ezifaka zemiraro ezifaka
nomphumela.
ukuhlanganisa ukuhlanganisa
nokukhupha nempendulo nokukhupha nempendulo • Ukurekhoda iinthombe kwaphela
ukufika e-20. ukufika e-20. Isibonelo:
Ukurekhoda eenthombeni neenomborweni
Ukwenzela bona abafundi basebenzise iinomboro neenthombe ukuhlathulula ukucabanga
kwabo, kufanele ba:
• Kghone ukukhumbula iinomboro 1-5
• Bale izinto ezihlanu begodu bazi bonyana u ku 5 ujamele zoke izinto ezibaliweko.
• Tlole iinomboro
• Hlele begodu bamadanise iinomboro
Imihlobo yemiraro yokuhlanganisa neyokukhupha
Kunemihlobo okungasenani emithathu yemiraro esisekelo yokuhlanganisa nokukhupha
begodu omunye nomunye umhlobo ungabekwa ngeendlela ezahlukahlukeneko. Imihlobo
esisekelo ngile:
Itjhuguluko
UNoluthando beka namahabhula amabili. USilo wamupha amanye amhabhula amathathu.
Sekanamahabhula amangaki nje uNoluthando?
UNoluthando beka namahabhula amahlanu. Wapha uSilo amahabhula amane.
Sekanamahabhula amangaki nje uNoluthando?
Hlanganisa
UNosesi unamamabula ababili ahlaza kotjani nababili ahlaza kwesibhakabhaka.
Unamamabula amangaki sewawoke uNosesi?
105 UNosesi unamamabula amane. Amathathu ahlaza begodu aseleko ahlaza
kwesibhakabhaka. UNosesi unamamabula amangaki ahlaza kwesibhakabhaka?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
106 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Ukumadanisa
Ukuh- yamagama yamagama UNosesi unamabhanana amahlanu. UThemba unebhanana elilodwa. Amabhanana ka
langanisa ezisebujameni ezisebujameni Nosesi adlula wakaThemba ngamabhanana amangaki?
nokukhupha bewuhlathulule bewuhlathulule
Iinsetjenziswa:
iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka Abafundi bangasebenzisa izinto zokubala ezitjhaphulukileko, ukubasiza ukubona
ukuhlanganisa ukuhlanganisa bona kwenzekani lokha umuntu ahlanganisa amanani ndawonye nofana lokha umuntu
nokukhupha nempendulo nokukhupha nempendulo nakawahlukanisako.
ukufika e-20. ukufika e-20. Izinto zokubala ezitjhaphulukileko zisiza abafundi ukubona bona kwenzekani lokhana
babala koke.
Iimbonelo zezizinto zokubala ezitjhaphulukileko ngilezi:
• Izinto zokubala
• Iingojwana zokubala
• Iimvalo zamabhodlhelo
• Iintanga zeperegisi
• Amatje
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Amakhyubhu weyunifiksi
• Ukusebenza ngerherho leenomboro ukusuka ku-1 kuya ku-5, abafundi bangasebenzisa
imino yabo njengezizinto zokubala ezitjhaphulukileko.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.9 Ukurarulula Ukurarulula EGreyidini yoku-1 umqondo wokuhlukanisa uthulwe ngokunikela abafundi imiraro
Ukubuthele- nokuhlathulula nokuhlathulula ephathekako efaka hlangana ukwabelana nokubuthelela. Itshwayo lokuhlukanisa livezwa
la nok- iinsombululo zemiraro iinsombululo zemiraro kwaphela lokha abafundi sele baseGreyidini yesi- 3.
wabelana ephathekako okufaka ephathekako okufaka Ngaphasi lapha ziimbonelo zemihlobo yemiraro yamagama ezingenziwa.
okurholela hlangana ukwabelana hlangana ukwabelana
Ukubuthelela
ekuhlu- ngokulinganako ngokulinganako
nokubuthelela nokubuthelela Ukubuthelela, ulahle isalela
kaniseni
ngeenomboro ezibanzi ngeenomboro ezibanzi USphenge uthengisa amaskwatjhi ngemigodlana efaka amaskwatjhi amabili umgodlana
ukufika ema 20 begodu ukufika ku 5 begodu ngamunye. Usele namaskwatjhi amahlanu. Migodlana emingaki efaka amaskwatjhi amabili
nangeempendulo nangeempendulo umgodlana ngamunye, angayenza?
ezingahle zifake ezingafaka hlangana Ukubuthelela, ukufaka hlangana, isalela ependulweni
hlangana nesalela. isalela.
Kunamahabhula amane. Migodlana emingaki yamahabhula amabili athatha engazaliswa
ngawo?
Ukwabelana
Ukwabelana , kulahlwe isalela
Yabela abangani abathathu amaswidi amahlanu ukwenzela bona boke bathole inani
elilinganako lamaswidi.
Ukurekhoda imifanekiso ukwenzela ukubuthelela nokwabelana
Lokha sitjengisa ukwabelana kwemiraro yamagama, abafundi “bazakwabelana” into yinye
ngesikhathi esisodwa.
Abafundi beGreyidi yoku-1 balindeleke babelane into eyodwa ngesikhathi begodu
kuzokutjengiswa ekurekhodeni kwabo.
Lokha unyaka uragela phambili abafundi bazakghona ukurekhoda basebenzisa iinthombe
neenomboro ukubonisa inomboro eyabelweko.
107
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
108 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
UKUBALA OBUSEBUJAMWENI OBUTJHAPHULUKILEKO
Zinengi iindlela zokucabanga ngokuhlela ukubala kokufunda nokufundisa. Enye indlela ngeyokucabanga ngerherho leenomboro. Irherho leenomboro abafundi
abasebenza ngaphakathi kwalo lizakutjho bona ngimaphi ama-apharathasi wasebenzisako nokuthi bazazirekhoda bunjani iinsombululo zabo.
Ngakho-ke, enye indlela yokucabanga ngokubala esiGabeni esisiSekelo kujamisela ukubala. Lokhu kwenziwa ngoku:
• Sebenzisa ama-apharathasi aphathekako;
• Ukugwala iinthombe;
• Ukusebenzisa iinthombe namatshwayo;
• Ukusebenzisa iinomboro nabotjhobi; nofana
• Ukusebenzisa imitjho yeenomboro.
Abafundi basuka ekusebenziseni ama-apharathasi aphathekako ukuya ekusebenzeni ngezinto ezingaphathekiko ematshwayeni weenomboro nemitjhweni
yeenomboro. Ukubalisisa kuwela ngaphakathi komqondo wobujamo bokurarulula imiraro. Abafundi bathuthukisa amakghono wokurarulula imiraro ukwenzela
ukusebenza ngeenomboro. Abafundi bafanele benze ukubala obusebujameni obutjhaphulukileko. ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.12 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Ethemini yokuthoma abafundi bazakurarulula imiraro yeenomboro basebenzisa
Amathekh- alandelako nawenza: alandelako nawu ama-apharathasi aphathekako. Kuqakathekile bona abafundi basebenzise imihlobo
iniki • Ama-apharathasi urarulula imiraro begodu ehlukahlukeneko yama-apharathasi akhethiwe ngokuyelela ukuthuthukisa imiqondo
aphathekako isib. uhlathulule iinsombululo efundisiweko.
(iindlela
Izinto zokubala zemiraro: Lokha abafundi baba nokuzithemba ngokusebenzisa ama-apharathasi, ukutjengisa
nofana
amaqhinga) • Ukugwala iinthombe • Ama-apharathasi ukucabanga kwabo, bangarekhoda ukubala kwabo ngokugwala. Kufanele ulindele
aphathekako isib. bona imigwalo yabo itjengise ama-apharathasi aphathekako. Kungahle kube khona
• Ukwakha nokuphula
Izinto zokubala abanye abafundi abazakuthi zisuka nje batjengise ukubala kwabo ngokugwala begodu
iinomboro
• Iinthombe zokugwala bangasebenzisi iinsetjenziswa eziphathekako.
• Ukubuyelela
umphumela Amanambalayini asekelwe ma-apharathasi aphathekako
nokuhafula
wendatjana Lokha usebenzisa amanambalayini njengamathekhiniki ukwenzela ukubala, kuthlogeka
• Amanambalayini
• Amanambalayini bona abafundi bathome ngokusebenzisa lokhu:
asekelwe ma- • Amanye ama-apharathasi wokubala asemideni’ isib imincamo yokubala, iinomboro
apharathasi ezilandelanako;
aphathekako isib.
• Inambalayini yokubala uye phambili nemuva; ne
Imincamo yokubala
• Nambalayini ukwenzela ukubeka kuhle nokuhlela iinomboro.
Inambalayini ehleleke kuhle kufanele isetjenziswe (begodu ibe ngelungileko) lokha abafundi
nabahlanganisa begodu nabakhuphako. Inambalayini ehleleke kuhle kufanele itjengise
zoke iinomboro ezikiyo.
• Ukwethula ukuhlanganisa ngokusebenzisa inamba layini
a) Utitjhere ubeka inambalayini ethoma ngeli- ukuya e- ebhodini. Utjengisa abafundi
bona bangawurarulula njani umraro usebenzisa inambalayini. Ubeka isithombe
somqasana eli-.
Isibonelo: Umqasana weqa ukusuka eli- uye kusi- begodu usuke lapho weqe imeqo
emibili godu. Mimeqo emingaki nasele iphelele?
b) Abafundi basebenzisa imino yabo ukweqa enambalayinini esemadeskeni wabo,
lokha utitjhere abanikela imitjho yeenomboro neempendulo ezifika e-10,
Isibonelo: 1 + 2 =3.
109
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
110 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 Irherho leenomboro : 1 Irherho leenomboro : 1 -5 EThemini yoku-1 abafundi bazwisisa ukuhlanganisa njengokuhlanganisa iinqhema
Ukuh- -20 • Hlanganisa kufika ku 5 begodu nanjengokubala uragele phambili. Basebenzisa ukuzwisisa kwabo kokuthi
langanisa • Hlanganisa ukufika ukuhlanganisa kungenziwa nanganoma ngiyiphi indlela ukukhetha bona ubala njani.
• Khupha kusuka ku 5
nokukhupha ema-20 Basebenzisa intambo yemincamo, bagwala iinthombe nofana inambalayini ukwenzela
• Zijayeza ukulumbana ukubala njengokuthi 3 + 2 nofana 1 + 4 ngokubala uragele phambili. Bayaziphula iinomboro
• Khupha ukusuka ema / ukuhlangana ukwenzela ukuhlanganisa.
20 kweenomboro kufika
EThemini yoku-1 abafundi barhumutjha ukukhupha njengoku ‘thatha ususe’. Bajamisela
• Sebenzisa umbalo/ ku-5
u ‘thatha ususe’ ngokusebenzisa izinto nokugwala iinthombe nangemitjho yeenomboro.
itshwayo elifaneleko
Bayakhumbula bona inani lezinto eziseleko ziyipendulo yokubala. Babuye barekhode
• ( £) Ukuhlanganisa nokukhupha ngokusebenzisa:
• Zijayeza ukulumbana • ama-apharathasi aphathekako;
/ ukuhlangana
• Iinthombe nofana imigwalo; nofana
kweenomboro kufika
e 10 • Iinthombe neenomboro.
Ukusebenza ngerherho leenomboro 1 – 5
Lokha abafundi basebenza nofana babalisisa ngaphakathi kwerherho leli leenomboro
bangakha ukuzwisisa kwabo kokuhlanganisa nokukhupha ngendlela elandelako:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Sebenzisa ama-apharathasi aphathekako ukujamisela iinomboro nokubala
• Ukurekhoda ukubala kwabo basebenzisa iinthombe nofana iimfaniso
• Ukurekhoda ukubala kwabo ngokusebenzisa ukuhlanganisa iinthombe neenomboro
Ukwakha nokuphula iinomboro
Ukuhlanganisa nokukhupha eGreyidini yoku-1 kunqotjhiswe ekwenzeni bona abafundi
bacabange ngeenomboro njengento evela kwezinye iinomboro. Esikhathini esinengi
abafundi bazibandakanya emsebenzini owodwa owenziwe waba ziinkhawu-khawu.
Imisetjenzana le, inqotjhiswe enomborweni eyodwa. Isibonelo , lokha abafundi basebenza
ngenomboro u-4 abafundi bazaku:
• phula u-4 ngeendlela ezahlukahlukeneko;
• tjho nofana bafundele iinqetjhana lezo phezulu; nofana
• gwala nofana bazitlole phasi.
1
4
3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.13 Irherho leenomboro : 1 Irherho leenomboro : 1 -5 Abafundi bangasebenzisa namakarada weenomboro ukutjengisa iingcenye zeenimboro.
Ukuh- -20 • Hlanganisa kufika ku 5 Ngakho ke , ukutjengisa u 4, amanye wamakarada alandelako angasetjenziswa:
langanisa • Hlanganisa ukufika • Khupha kusuka ku 5
nokukhupha ema-20
• Zijayeza ukulumbana 1 3
• Khupha ukusuka ema / ukuhlangana
20 kweenomboro kufika
• Sebenzisa umbalo/ ku-5
itshwayo elifaneleko 2 2
• ( £)
• Zijayeza ukulumbana Imiqondo le ingasekelwa ngokurekhoda eencwadini zomsebenzi wangetlasini ngesikhathi
/ ukuhlangana sokusebenza ngokuzijamela
kweenomboro kufika
4
e 10
1 3
Lokhana bakhuphako, abafundi bavame ukuzibandakanya eembalweni zeendatjana
ezithuthukisa ukukhupha njengo ‘thatha ukhuphe’ nofana ‘bala ukhuphe’. Abafundi kufanele
benze imisetjenzana yeengcenye ezitjhiyiweko. Imisetjenzana le, isekela ukuzwisisa
ukukhupha begodu ifuna kube nencenye efihlekileko nofana engaziwako.
Isibonelo :
Ngina Ngifisa ngathana ngina-5
Itshwayo alithulwa kileThemu le. Abafundi kufanele bavezelwe iindlela ezinengi zokutlola
imitjho ezakubasiza lokha nakwethula itshwayo ngeThemu yesi-2.
Isibonelo soku-1
Example
1
Isibonelo sesi-2
Example
2
kwenza
make
3
ana
nd
make
ana
nd
kwenza 2
111
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
112 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 Irherho leenomboro : 1 Irherho leenomboro : 1 -5 Ukulumbana kweenomboro
Ukuh- -20 • Hlanganisa kufika ku 5 NgeThemu le, abafundi bazijayeza ukulumbana kweenomboro ukufika ku-5. Lokhu
langanisa • Hlanganisa ukufika • Khupha kusuka ku 5 kungathulwa ngokusebenzisa iinthombe nemitjho yeenomboro ngokusebenzisa iimfaniso
nokukhupha ema-20 ezihlukahlukeneko
• Zijayeza ukulumbana
• Khupha ukusuka ema Ukuhlanganisa
/ ukuhlangana
20 kweenomboro kufika Isibonelo:
• Sebenzisa umbalo/ ku-5 Ukwenza u-5 nofana ukuthola abangani aba-5 usebenzise iinthombe neenomboro
itshwayo elifaneleko Faka umbala ngeenkwereni ukwenza uku-5
• ( £) Isibonelo:
• Zijayeza ukulumbana
/ ukuhlangana
kweenomboro kufika ________ na __________ kwenza 5
e 10
________ na __________ kwenza 5
ISIGABA ESISISEKELO AMAGREYIDI 1-3
________ na __________ kwenza 5
________ na __________ kwenza 5
Ilimi loku hlanganisa nokukhupha
Abafundi kufanele bazijayeze ilimi lokuhlanganisa nokukhupha.
Ukuhlanganisa :
hlanganisa, ukuhlanganisa, begodu, ukwandisa nga, hlanganisa, sekukoke, kwenza, inani
Ukukhupha:
Khupha, thatha ususe, khupha, umehluko, phakathi, ncani kuna, ncitjhiswe nga.
Ethemini yesi-2 abafundi bazaku “tjhugulula” ilimi lokuhlanganisa nokukhupha benze
amatshwayo.
Abafundi kufanele bakghone ukulandela iinlayelo ezifana nalezi ezilandelako:
• Yenza kudlule ngaku 3
• Yandisa nga 1
• Khupha ku 3
• Yenza kube kuncani nga 1
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Kunengi ngaku 3 na 2
• 4 khupha 2
• 3 ncani nga-1
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
CAPS
ama -24)
1.16 Umqondonomboro : irherho 20 Umqondonomboro : Isikhathi seembalo zehloko zithuthukisa ebafundini:
Iimbalo • Ukuhlela amasede weenomboro irherho 5 • umqondonomboro;
zehloko ezikhethekiloeko onikelwe zona • Ukuhlela amasede • ilimi leemBalo ;
• Ukumadanisa iinomboro kufika weenomboro
• Amakghono wokucabanga; nama
e 100 begodu batjho bonyana ezikhethekiloeko
onikelwe zona • kghono wokulalela.
ngiyiphi ekulul nofana encani
• Ukumadanisa Ngesikhathi seembalo zehloko abafundi kufanele banikelwe ithuba lokuhlathulula
• Ukwazi bonyana ngiyiphi
iinomboro kufika e iindlela zabo zokwenza. Iimbalo zehloko zakha ilemuko leenomboro (ukuba
inomboro enengi nga 1 nofana
10 begodu batjho no ‘muzwa’ weenomboro) begodu zithoma ukufundisa abafundi indlela elula
encani nga 1 eenomborweni
bonyana ngiyiphi yokusebenza ngeenomboro. Inomboro u ku-5 akusese yinomboro nje kwaphela.
onokelwe zona
ekulul nofana encani Isibonelo, enomborweni uku-5, abafundi kufanele bazi bona:
• Ukwazi bonyana ngiyiphi
inomboro ekulu ngaku 2 nofana • Ukwazi bonyana • Uza ngemuva kuka ku-4;
encani nga 2 kunenomboro ngiyiphi inomboro • Uza ngaphambi kuka-6;
onikelwe yona enengi nga 1 nofana
• Ingakhambisana nezinto ezi-5 ;
encani nga 1
• Ukwazi bona ngiyiphi inomboro • Bangatlola itshwayo; begodu
ekulu nga li 10 nofana encani nga • Ukwazi bonyana
ngiyiphi inomboro • Bangatlola igama lenomboro.
li10 kunenomboro onikelwe yona
ekulu ngaku 2 nofana Umqondonomboro
Ukukhumbula masinyana :
encani ngaku 2 Iimbonelo zemibuzo nemisetjenzana engabuzwa begodu yenziwe:
• Ukuhlangana kweenomboro
kufika e 10 • Abafundi bajama emudeni bese uyababuza: ngubani osekuthomeni, wesibili,
wesithathu nofana wokugcina?
• Ukukhumbula amaphuzu
wokuhlanganisa nokukhupha • Ngiyiphi encani, 3 nofana 5?
kufika e 10 • Ngikuphi okunengi, 2 nofana 4?
Amaqhinga weembalo zehloko • Ngipha inomboro ephakathi kuka 1 no 3,
Sebenzisa amaqhinga wokubala • Ngipha inomboro ephakathi kuka 2 no 5. Yinye kuphela inomboro lapho?
Ukuhlanganisa nokukhupha • Beka amakarada weenomboro ngokulandelana ukusuka kwencani khulu
ngekghono: ukuya kwekulu khulu inomboro.
• Beka inomboro ekulu ekuthomeni Imibuzo engabuzwa ngokubala:
ukwenzela ukuragela phambili
nokubala nofana ukubala uye • Thoma ngaku-3 begodu ubale uye phambili ngakunye ukufika e-10.
emuva
• Inambalayini
• Ukubuyelela kabili nokuhafula
• Ukwakha nokuphula
113
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YOKU-1
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
114 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.1 Ukukopa ,ungezelele Ukukopa Ukukopa iphetheni kusiza abafundi ukubona ilojikhi yokuthi iphetheni yenziwe njani.
Amapheth- bewuhlathulule Nokungezelele Ukungezelela iphetheni kusiza abafundi ukubona bonyana bayizwisisile ilojikhi yephetheni.
eni weJi- Ukukopa, ungezelele Ukukopa bewungezelele Abafundi bangakopa begodu bangezelele amaphetheni enziwe ngezinto eziphathekako
yomethri bewuhlathulule amaphetheni alula nangaphambi kokuberegisa ikhrayoni nofana ipensela ukuthoma ukukopa nokungezelela
ngamagama usebenzisa amaphetheni ngokugwala.
• Amaphetheni alula • Izinto eziphathekako Amaphetheni angenziwa ngezinto zangamalanga ezijayelekile ezitholakala ngetlasini,
enziwe ngezinto • Imigwalo (isib. njengezinto zokubala, iinthoro zomlilo, amabhoksana womlilo, iimbumbeko zeJiyomethri,
eziphathekako Ukusebenzisa imibala imincamo, itolitji yekoteni, amabhoksi, amabholo, amakhrayoni, amapensela njll. Abafundi
• Amaphetheni alula nobujamo) bangenza izinto ngebumba nofana ihlama yokudlala izinto lezi zingaberegiswa ukwenzwa
enziwe ngemigwalo amaphetheni.
yemida, ubujamo Egreyidi yoku-1 abantwana banganqopha emaphethenini lapho iimbumbeko nofana izinto
nafana izinto. (iinqema zembumbeko nofana zezinto) zibuyabuyelelwe ngendlela efana poro.
Tlama begodu Isibonelo 1:
uhlathulule Emaphethenini amanye ubukhulu bezinto eenqhemeni buyatjhintjhana, kodwana iinqhema
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amaphetheni wakho
zibuyabuyelelwa ngendlela ezifana patsi.
Tlama amaphetheni
weJiyomethri
• Ngezinto Isibonelo 2:
eziphathekako
Amaphetheni angenziwa ngokusebenzisa into eyodwa kodwana imibala itjhuguluke
• Ngokugwala imida, ngendlela eqhelileko.
ubujamo nofana izinto
Amaphetheni
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni Isibonelo 3:
weJiyomethri Kwamaphethenini amanye izinto ezihlukahlukeneko zisetjenzisiwe ukwenza iinqhema,
• Wemvelo, kodwana iinqhema zezinto zibuyabuyelelwa ngendlela efana patsi
• Kusukela epilweni
yangamalanga
yesimodeni,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Kusukela kezamagugu
nendabuko yethu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
2.1 Ukukopa ,ungezelele Ukukopa Ukusiza abafundi begreyidi yoku 1 ukubona bonyana iinqhema zibuyelelwe njani, Isifundo -1
Amapheth- bewuhlathulule Nokungezelele kuqakathekile ukubeka isiqhema ngasinye embhampirini ezihlukeneko nofana uyibonise
eni weJi- Ukukopa, ungezelele Ukukopa bewungezelele ebhlogweni lekhasi.
yomethri bewuhlathulule amaphetheni alula Isibonelo 4:
ngamagama usebenzisa Amaphetheni angenziwa ngokubuyelela iinqhema zezinto. Iinqhema zingenziwa ngezinto
• Amaphetheni alula • Izinto eziphathekako ezifanako ezibekwe ebujameni obuhlukeneko.
enziwe ngezinto • Imigwalo (isib. Ukwenza amaphetheni kuyingcenye eqakathekileko emfundweni eziphasi, begodu
eziphathekako Ukusebenzisa imibala kwenzeka elimini, emaKghonweni wePilo nembalweni.
• Amaphetheni alula nobujamo) Isibonelo ukwenza amaphetheni kuyingcenye yomvumo, imidunduzelo, ukugida nokunye
enziwe ngemigwalo okunengi okuyimihlobo yobugwari obubonakalo. Kunamathuba wokujayeza abafundi
yemida, ubujamo amakghono abonakalako wamaphetheni aberegiswa embalweni lokha nabefunda
nafana izinto. amakghono wepilo – khulukhulu ukuthungelela imincamo nofana ukugwala amaphetheni.
Tlama begodu
uhlathulule
amaphetheni wakho
Tlama amaphetheni
weJiyomethri
• Ngezinto
eziphathekako
• Ngokugwala imida,
ubujamo nofana izinto
Amaphetheni
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni
weJiyomethri
• Wemvelo,
• Kusukela epilweni
yangamalanga
yesimodeni,
• Kusukela kezamagugu
nendabuko yethu.
115
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
116 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela EsiGabeni esisiSekelo, amaphetheni wenomboro akha imiqondo nomboro yabafundi. Iimfundo ezi-3
Amaphe- nokuhlathulula nokuhlathulula Amaphetheni wenomboro ahlanganiswe nama-opharetjhini kwenomboro noBudlelwana.
theni Ukukopa, ukungezelele Ukukopa, ukungezelele Ukulandelanisa iinomboro kungahlanganiswa nokubala. Ukulandelanisa iinomboro
weenom- bewuhlathulule bewuhlathulule kuhlanganisa begodu kuthuthukisa amakghono wabafundi wokubala. Njengombana
boro Ukulandelanisa Ukulandelanisa amakghono wabafundi wokubala atjhughuluka begodu athuthuka, ngesizathu salokho
kwenomboro elula kwenomboro elula nokulandelanisa kwenomboro kuyatjhughuluka.
ukufika ku-100. ukufika ku-20. Lokha abafundi babala ngehloko bangatjengiswa ukulandelana kweenomboro okutlolwe
Tlama begodu Ukulandelanisa kufanele phasi ngendlela ezihlukahlukeneko. Isib.
uhlathulule kubonise ukubalela
amaphetheni wakho ukuya phambili nemuva:
Yenza bewuhlathulule • nga-1 kusuka kwenye
amaphetheni nenye inomboro
weenomboro hlangana ne-0 na-20 ISIGABA ESISISEKELO AMAGREYIDI 1-3
Abafundi bangazalisela iinomboro ezitjhiyiweko ebanikelwe zona ngananoma ngiyiphi
indlela yokulandelanisa engaphezulu.
Khumbula, godu bonyana abafundi batlola iinomboro ukufika ku-5. Abafundi bangazaliselela
iinomboro ezitjhiyiweko ngehloko bebasebenzise amakarada weenomboro ukuqedelela
ukulandelana. Qala amanothi wokuhlathulula, wokumadanisa nokulandelanisa.
Isibonelo 1: Umkhondo weenomboro/igridi yenomboro
1 2 4 5 6 8
Isibonelo 2: Ukulandelanisa iinomboro
Ekupheleni kweThemu, irherho leenomboro likhuphuka beliyofika ema-20. Abafundi
bangasebenzisa ukulandelana kweenomboro kusika 1 – 20 nofana ingcenye yokulandelana
Isibonelo 3: Inambalayini
1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 18 20
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YOKU- 1 ITHEMU YOKU- 1
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.1 Ilimi lobujamo Ilimi lobujamo Ilimi lobujamo Iimfundo ezi-2
Ubujamo, Hlathulula ubujamo bento Hlathulula ubujamo bento Ilimi lobujamo kufanele lethulwe ngemisetjenzana ephathekako ebandakanya abafundi
ukuzijayeza eyodwa ehlobene nenye, eyodwa ehlobene nenye, ngokusikinyeka komzimba okufaka hlangana iingoma nemidunduzelo ngemisikinyeko
nokubukela isib.phezu kwe-, phambi isib.phezu kwe-, phambi nangemidlalo enamagama womsikinyeko. Lokhu kungenziwa ngesikhathi sokufundisa
kwe- ,emuva kwe-, kwe- ,emuva kwe-, ngetlasini loke nofana ngesikhathi esinqophileko sokufundisa isiqhema. Kuphakanyiswe
ngesinceleni, esidleni, ngesinceleni, esidleni, bonyana uthathe iimfundo ezimbili emisetjenzaneni yobujamo ngeThemini yoku-1, kodwana
phezulu, phasi, hlanu phezulu, phasi, hlanu ragela phambili uthule begodu uzijayeze amagama wobujamo weengcenyana zetlasi
kwe-. kwe-. loke, isiqhema esinqotjhiweko nesikhathi sokusebenza esitjhaphulukileko. Ilimi lobujamo
Ubujamo nokubukela Ubujamo lingajayezwa ngesikhathi seemfundo zeLimi namaKghono wePilo.
Madanisa imibono neenkombatjhuba Kuqakathekile ukuthula amagama wobujamo ngamapara ngesikhathi esisodwa isib. phasi
ehlukahlukeneko • Sebenzisa ilimi naphezulu; ngaphakathi nangaphandle.
yezinto ezifanako lobujamo olifunde Amagama wobujamo aqakathekile afaka hlangana:
zangamalanga. lokha nawulandela • Esinceleni, esidleni;
Ubujamo iinkombatjhuba.
• Phambili/ emuva;
neenkombatjhuba • Landela
• Ngemuva, ngaphambi kwe-;
• Landela iinkombatjhuba
ukukhambakhamba • Phezu kwe-/ ngaphasi;
iinkombatjhuba
ukukhambakhamba ngetlasini • Phakathi/ ngaphandle;
ngetlasini • Landela iinlayelo • Ngaphasi/ ngaphezu;
• Landela iinlayelo ukubeka into • Ngaphasi/ ngaphezulu;
ukubeka into eyodwa ngokuya
• Eduze/ kude;
eyodwa ehlobene ngobudlelwane
nenye isib. faka • Hlangana
nenye, isib. faka
ipensela ngaphakathi ipensela ngaphakathi Ilimi lobujamo lingahlanganiswa ngokurekhoda okutlolwako njengokugwala, ukufaka
kwebhoksi. kwebhoksi. umbala nofana ukumadanisa imigwalo ngamagama.
Ubujamo neenkombatjhuba
Abafundi bangathoma ngokufunda elinye ilimi lobujamo begodu basebenzise ilwazi leli
ukulandela:
• Iinyalelo ukukhomba nofana ukubeka izinto ezinoBudlelwana nezinye isib. “beka
amakhrayoni eqadi kwezinto zokubala”, “beka amakarada weenomboro phezu
kwamakhabhodi”.
• Iinkombatjhuba zokuzikhambela ngokwabo etlasini isib. “iza phambili”, jama eqadi
117 kwesitulo sakho”, “yeqa phezu komgqomu weenzibi” njll.
Ukufundisa abafundi ukulandela iinkombatjhuba kufanele kwenziwe ngemisetjenzana
ephathekako lapho abafundi bazikhambela ngokwabo nofana izinto ngokuya ngeenyalelo.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
118 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.2 Irherho lezinto Irherho lezinto Umsebenzi omnengi wezinto ezibusobuntathu (3-D) eGreyidini yoku-1 kufanele wenziwe
Izinto ezibu- Ukubona nokutjho izinto Ukubona nokutjho izinto ngezinto eziphathekako / ezithintekako. Iphasi silibona ngamahlangothi amathathu, ngakho
sobuntathu ezi 3-D ezingetlasini ezi 3-D ezingetlasini ke ukuthoma ngezinto eziphathekako kusiza abafundi bona bakhele phezu kwelwazi/
(3-D) begodu neenthombeni begodu neenthombeni kwelemuko abeza nalo esikolweni.
• Ubujamo bebholo • Ubujamo bebholo Abafundi abanengi abancani bayatlhaga ukuhlathulula izinto zejiyomethri ezibusobuntathu
(iindulungu) (iindulungu) (3-D) kusuka eenthombeni. Ukusebenza ngezinto eziphathekako kusiza abafundi bona
barhumutjhe iinthombe zobujamo beJiyomethri ngokukhamba kwesikhathi. Lokha
• Ubujamo bebhoksi • Ubujamo bebhoksi
nawuphethe into yamambala ephathekako, ungayijikajikisa uyiqale mahlangothi woke.
(amaphrizimu) (amaphrizimu)
Ungakghona ukubona ukuthi iqaleka injani ukusuka ngemuva nangaphasi.
Amatshwayo wezinto Amatshwayo wezinto Lokha nawuphethe isithombe kwaphela, kufanele ubone ngelihlo lemgqondo iingcenye
Ukuhlathulula, ukuhlela Ukuhlathulula, ezingabonakaliko emgwalweni lowo. Lokhu akusilula njalo ebafundini abancani. Lokha
nokumadanisa izinto ezi ukuhlela ngeengaba abafundi banikelwe ihlathululo yento kuphela ngaphandle kokuthi bayibone nofana
3-D ngokuya ngo: nokumadanisa izinto ezi bayiphathe, kuba budisi khulu ukuzwisisa ubujamo bento ngokupheleleko
• bukhulu 3-D ngokuya ngo: Ukwakha ngezinto ezi 3-D
• mbala • bukhulu Abafundi bathoma ngomdlalo otjhaphulukileko ngezinto ezihlukahlukeneko ezi 3D begodu
• izinto ezigedekako • mbala bazakhele izinto ezikhethwe ngibo basebenzisa amabhlogo wokwakha nofana izinto
Imisetjenzana zokwakha nofana izinto ezisetjenziswe zabuyelelwa godu. Lokhu kungenziwa ngesikhathi
• izinto ezitjhelelako
ISIGABA ESISISEKELO AMAGREYIDI 1-3
enqotjhiweko sokusebenza ngokuzijamela.
Imisetjenzana
Tjheja begodu wakhe Ungasebenzisa izinto ezisetjenziswe zabuyelelwa godu (njengamabhoksi weenthoro
enqotjhiweko
izinto ezibusontathu zomlilo) nofana amabhlogo wokwakha nofana ezinye izinto zokwakha ukwenza umfanekiso
Tjheja begodu nofana umakhiwo isib. umbhotjhongo, irobothi, isitimela, iteksi, inqaba njll. Abafundi
3-D ezinikelweko
wakhe izinto ezi bangenza ikhophi yomfanekiso. Lokhu kungenziwa ngesikhathi sokuzijamela, kodwana
ngokusebenzisa
3-D ezinikelweko kuqakathekile bonyana bacocisane nabafundi ngokobana kubayini imihlobo ethile
amamathiriyelii
ngokusebenzisa yezinto isetjenziswa ukwenza imifanekiso. Lokhu kusiza ukunqophisa abafundi ezintweni
aphathekako afana
amamathiriyelii eziphawulekako ebumbekweni lejiyomethri. Isibonelo, lokha umbhotjhongo nawakhiwa
namabhlogo wokwakha,
aphathekako afana ngamabhoksi nofana ngamabhlogo, ungabuza abafundi bonyana “ningakghona ukwakha
izinto ezibuyelelwa
namabhlogo wokwakha, umbhotjhongo nisebenzisa amabholo wodwana?” kufanele bahlathulule ipendulo yabo.
zisetjenziswe godu
izinto ezibuyelelwa Ukukhumbula nokutjho iimbholo (iindulungu) namabhoksi (amaphrizimu)
nezinto zokwakha
zisetjenziswe godu,
Abafundi bafanisa begodu bahlathulule ubujamo beembholo (iindulungu) nobujamo
nezinto zokwakha
bamabhoksi (amaphrizimu)
Abafundi kufanele bahlathulule izinto zangamalanga ngokutjho bonyana zinobujamo
bebholo nofana bebhoksi, isib. isitina lesi sijame njengebhoksi nofana ilamune leli lijame
njengebholo.
Kuqakathekile bonyana abafundi babone begodu basebenze ngeembonelo zezinto
ezinengana ezinobujamo obufana neembholo nezifana namabhoksi.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Abafundi kufanele banikelwe ihlelo lezinto ezisabundulunga bonyana basebenze ngazo
isib. iimbholo zobukhulu obuhlukakhlukeneko, iimabula, amalamune njll. Abafundi kufanele
banikelwe godu ihlelo lezinto ezinobujamo obufana nephrisimu ukusebenza ngazo isib.
amabhlogo, iintina, namabhoksi wobukhulu obungalinganiko.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
3.2 Irherho lezinto Irherho lezinto Abafundi bangathola begodu bahlukanise izinto zobujamo obufana nebholo (indulungu), Iimfundo ezi-3
Izinto ezibu- Ukubona nokutjho izinto Ukubona nokutjho izinto nofana ubujamo obufana nebhoksi (amaphrizimu) lokha nabanikelwa ibuthelelo lezinto.
sobuntathu ezi 3-D ezingetlasini ezi 3-D ezingetlasini Abafundi bangathola, babonise begodu batjho izinto ezinobujamo obufana namabhoksi
(3-D) begodu neenthombeni begodu neenthombeni (amaphrizimu) ngetlasini. Abafundi bangalayelwa bonyana benze ubujamo beembholo
nofana bamabhoksi ngebumba nofana ngehlama yokudlala.
• Ubujamo bebholo • Ubujamo bebholo
(iindulungu) (iindulungu) Ukumadanisa nokuhlathulula izinto ze3-D: ubukhulu
Abafundi bamadanisa ubukhulu bezinto ezifanako
• Ubujamo bebhoksi • Ubujamo bebhoksi
(amaphrizimu) (amaphrizimu) Isibonelo:
• hlela amabholo ngokuya ngobukhulu
Amatshwayo wezinto Amatshwayo wezinto
• sebenzisa ilimi lobukhulu ukumadanisa izinto “ibhoksi likhudlwana kunebholo, ngombana
Ukuhlathulula, ukuhlela Ukuhlathulula,
ngingafaka ibholo phakathi kwebhoksi.
nokumadanisa izinto ezi ukuhlela ngeengaba
3-D ngokuya ngo: nokumadanisa izinto ezi Ukuhlathulula izinto za (3-D)
3-D ngokuya ngo: Abafundi bakhuluma ngemibala yezinto begodu bazihlukanise ngokuya ngombala.
• bukhulu
• bukhulu Ukubona nokutjho izinto nemibala yazo, nokumadanisa ubukhulu bezinto kungajayezwa
• mbala
ngesikhathi sokusebenza ngamaphetheni
• izinto ezigedekako • mbala
Imisebenzi etlolwako
• izinto ezitjhelelako Imisetjenzana
Nanyana imisebenzi eminengi yezinto za3-D yenziwa ngokwenza, umsebenzi
enqotjhiweko
Imisetjenzana ungahlanganiswa ngemisebenzi etlolwako
enqotjhiweko Tjheja begodu wakhe ILimi
izinto ezibusontathu
Tjheja begodu Kuqakathekile ukuthuthukisa ikghono labafundi lokukhuluma ngezinto za3-D
3-D ezinikelweko
wakhe izinto ezi • ILimi lobukhulu: khulu, khudlwana, khulu khulu, ncani, ncanyana, ncani khulu
ngokusebenzisa
3-D ezinikelweko • Imibala
amamathiriyelii
ngokusebenzisa
aphathekako afana • ILimi lezinto ngokwazo: amabhoksi, iimbholo (abafundi abakalindeleki ukwazi
amamathiriyelii
namabhlogo wokwakha, amaThemu la: indulungu namaphrisimu)
aphathekako afana
izinto ezibuyelelwa • ILimi lobujamo ukuhlathulula umakhiwo
namabhlogo wokwakha,
zisetjenziswe godu Isibonelo
izinto ezibuyelelwa
nezinto zokwakha
zisetjenziswe godu, • Phezu kwe, ngaphasi
nezinto zokwakha • Ngemuva, ngaphambili
• Eqadi kwe, magega na
• Ngaphasi, ngaphezu
• Eduze, hlangana
• Ngaphakathi, ngaphandle
ILimi lobukhulu nombala lingathuthukisa elimini nofana ngesikhathi sesifundo samaKghono
wePilo begodu sisetjenziswe nofana sijayezwe esikhathini sokufunda iimbalo. Ilimi
119 lobujamo lingathuthukiswa elimini nofana esikhathini sokufunda amaKghono wePilo begodu
nangesikhathi lapho abafundi banqophe khulu khulu ebujameni. Kungasetjenziswa nofana
kujayezwe lokha abafundi nabasebenza ngezinto za3-D
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YOKU-1
4. UKUMEDA
120 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.1 Ukudlula kwesikhathi Ukudlula kwesikhathi Abafundi bafanele bafunde ukukhuluma ngoku: Iimfundo ezi-2
Isikhathi Khuluma ngokudlula Khuluma ngokudlula • Landelanisa izehlakalo begodu
kwesikhathi kwesikhathi • nobude besikhathi
• Ukuhlela izehlakalo • Ukuhlela izehlakalo Inengi lemisebenzi lenzeka ngamalanga ngesikhathi sokufundiswa kwetlasi nofana
eziqhelekileko ezisuke eziqhelekileko ezisuke ngesikhathi esinqophileko sokufundisa isiqhema
epilweni yabo epilweni yabo
Abafundi bakhuluma begodu baphendule imibuzo lokha izinto nazenzeka, basebenzisa ilimi
• Ukumadanisa • Ukumadanisa elinjenga: ekuseni, ngemva kwamadina, ebusuku, ngaphambi nangemva kwesikhathi
ubude besikhathi ubude besikhathi
Ukukhamba kwesikhathi
kusetjenziswe ilimi kusetjenziswe ilimi
isib. eside, esifitjhani, isib. eside, esifitjhani, Abafundi balandelanisa izehlakalo basebenzisa ilimi elinjenga: izolo, namuhla, kusasa.
kabuthaka. kabuthaka. Abafundi bamadanisa ubude besikhathi basebenzisa ilimi elinjenga: edenyana nofana
• Ukulandelanisa • Ukulandelanisa efitjhazana begodu emsinyazana nofana ebuthaka khulu.
izehlakalo izehlakalo Abafundi bakhuluma ngokuhlela izehlakalo zamaphilo wabo. Bahlela godu nokulandelana
ngokusebenzisa ilimi ngokusebenzisa ilimi kweenthombe njenga:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
elifaka njengokuthi elifaka njengokuthi • amagadango wokwenza imbhedlezwana nofana ikopi yetiye;
izolo, namhlanje, izolo, namhlanje,
• iinthombe ezitjengisa umtwana okhula abe mumuntu omkhulu
kusasa. kusasa.
• umzombe wepilo yeembandana isib. Iqanda ukuya ekukhwini, nofana iqanda ukuya
Ukutjho isikhathi Ukutjho isikhathi
esirhwarhweni nofana iqanda ukuya eviyaviyaneni; begodu
• Ukuhlathulula • Ukuhlathulula
• Izehlakalo eziqhelileko zangelanga (ukuvuka, ukuba sesikoleni, ukudlala, ukudla isidlo
nakwenzeka into nakwenzeka into
santambama, ukulala).
ngokusebenzisa ilimi ngokusebenzisa ilimi
isib. ekuseni,ngemuva isib. ekuseni,ngemuva Ukutjho isikhathi
kwedina, ebusuku, kwedina, ebusuku, • Abafundi bafunda amalanga weveke ngeengoma nangemidunduzelo. Lokhu kwenziwa
ekuseni khulu, ekuseni khulu, ngamalanga.
ngemuva kwesikhathi. ngemuva kwesikhathi. • Amalanga wamabeletho abekwa ekhalendeni ngelanga elifaneleko.
• Ukutjho begodu • Ukutjho begodu • Abafundi bafunda izinyanga zomnyaka ngengoma nangemidunduzelo.
nokulandelanisa nokulandelanisa
amalanga weveke. amalanga weveke.
• Ukutjho begodu • Ukutjho begodu
nokulandelanisa nokulandelanisa
iinyanga zonyaka. iinyanga zonyaka.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukubeka amalanga • Ukubeka amalanga
wamabeletho wamabeletho
ekhalendeni. ekhalendeni
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
4.2 Ukulinganisa Ukulinganisa Zoke iimedo zeGreyidi yoku-1 azikahleleki. Akukho ukumeda okuhlelekileko kobude
Ubude okungakahleleki okungakahleleki emayunithini ahlelekileko enziweko.
• Ukumadanisa • Ukumadanisa Kuphakanyiswe bonyana iimfundo zeembalo zinqotjhiswe emathemini amabili emnyakeni
nokuhlela ubude, nokuhlela ubude, munye (iThemu yoku-1 neyesi-3). Umnqopho eThemini yoku-1 ungaba sekumadaniseni
ukuphakama nofana ukuphakama nofana okunqotjhiweko begodu ngeThemu yesi-3 abafundi bangasebenza namayunithi wokumeda
ububanzi bezinto ububanzi bezinto angakahleleki. Abafundi bangabuya bazijayeze begodu bahlanganise imiqondo le
ezimbili nofana ezimbili nofana ngesikhathi sokusebenza sokuzijamela ngonyaka woke.
ezinengi ngokuzibeka ezinengi ngokuzibeka Ukumadanisa okunqophileko kobude bezinto ezithintekako ukuthuthukisa ukuzwisisa
enye eqadi kwenye. enye eqadi kwenye. ubude belimi lokukhuluma ngakho.
• Ukusebenzisa • Ukusebenzisa Abafundi bathoma ngokucabanga nokukhuluma ngobude ngokumadanisa izinto ezimbili
ilimi ukukhuluma ilimi ukukhuluma (nofana imigwalo yezinto ezimbili) ngomehluko obonakala khulu wobude.
ngokumadanisa, isib. ngokumadanisa, isib.
Isibonelo
ubude, ubufitjhani, ubude, ubufitjhani,
ububanzi. ububanzi. • Isiquntu eside nesincani sentambo
• Ukulinganisa, • Umuthi omude nomfitjhani,
ukumeda, • Umlambo obanzi nomatsikani
ukumadanisa, ukuhlela Abafundi bangenza nofana bagwale iimbonelo njengoku:
begodu nokurekhoda
• Sebenzisa ibumba nofana ihlama yokudlalisa ukwenza inyoka ede nefitjhani
ubude usebenzise
iimedo ezingakahleleki • Sebenzisa amabhlogo ukwenza umbhotjhongo omude nomncani/omfitjhani
isib. izandla, igadango, • Gwala utitjhere omude nomfitjhani
ubude bepensela, Lokha abafundi nabakhulumma ngobude ngokuya ngokungafani, ungabathulela elimini
izinto zokubala, njll. elitjha lokumadanisa isibonelo, “ngenze isitimela eside kodwana uSihle wenze esidanyana”.
• Ukuhlathulula ubude Ukumadanisa ubude ngokubeka izinto emaqadi kwezinye
bezinto ngokubala
nangokutjho ubude Lokha abafundi nabangakhuluma ngobude obudluleleko (ubude, ubufitjhani njll), begodu
ngamayunithi umadanise ubude bezinto ezihluke ngokubonakalako ngokurhedlula, bangaragela phambili
angakahleleki. eembonelweni ezingabonakali lulae nawuzirhedlulako kokuthoma begodu zifuna ukubekwa
enye hlanu kwenye ukwenzelela ukuzimadanisa. isibonelo,
• Thola bonyana ngibaphi abantwana abade ngokubajamisa bafulathelene
• Ukubeka amakhrayoni amabili elinye kelinye begodu banqophise ingaphasi lamakhrayoni
ukuthola bonyana ngiliphi elifitjhani khulu
Abafundi bafanele banikelwe ithuba lokumadanisa iimbonelo ezimbili zemihlobohlobo
eminengi njengeengodo, amapensela, amathunjana wokusela isiselo esimakhaza, ubude
bentambo, iribhoni, imitletlana yephepha njll. Imigwalo yezinto ezimbili ingamadaniswa
godu lokha nazingabekwa eqadi kenye nenye begodu zinqophise phezulu nofana phasi.
121
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
122 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.2 Ukulinganisa Ukulinganisa Abafundi bangaragela phambili ukumadanisa nokuhlela izinto ezintathu nofana ezinengi. Iimfundo ezi-2
Ubude okungakahleleki okungakahleleki Lokhu kwaziwa njengeserayetjhini. Iimbonelo zifaka hlangana:
• Ukumadanisa • Ukumadanisa • Iinqhema zabafundi ezijame zafulathelana ngamapara/ngababili bonyana bangazibeka
nokuhlela ubude, nokuhlela ubude, bona emdeni ukusuka komfitjhani ukuya komude; begodu
ukuphakama nofana ukuphakama nofana • Ukurhemisa iinqhema zezinto zangantathu nofana ezinengi ukusukela komude
ububanzi bezinto ububanzi bezinto khulu ukuya kwefitjhani khulu nofan ebanzi khulu ukuya kwematsikana khulu. Izinto
ezimbili nofana ezimbili nofana ezifanelekileko zifaka hlangana amapensela, amakhrayoni, amabhodlela, iingodo, ubude
ezinengi ngokuzibeka ezinengi ngokuzibeka bentambo nofana iribhoni, imitletlana yephepha nofana imethiriyeli, amanyathelo njll.
enye eqadi kwenye. enye eqadi kwenye.
Abafundi bathuthukisa umqondo wobude nelimi lokuhlathulula ubude ngesikhathi sinye.
• Ukusebenzisa • Ukusebenzisa
Njengombana lokhu kungasatlhogi iinomboro, bungenziwa ekuthomeni kweThemu yoku-1
ilimi ukukhuluma ilimi ukukhuluma
ngaphambi kobana abafundi bahlanganise inomboro yabo yokwenza umqondo ukufikela
ngokumadanisa, isib. ngokumadanisa, isib.
enomborweni yesi-5.
ubude, ubufitjhani, ubude, ubufitjhani,
ububanzi. ububanzi. Nanyana ukumeda kulikghono lokwenza, abafundi bafanele benze godu imisebenzi
yokutlola, engafaka hlangana ukugwala nokufaka umbala, kokubili bonyana bazijayeze
• Ukulinganisa,
ukusebenzisa amakhrayoni nofana amapensela begodu bonyana bazijayeze ukurekhoda
ukumeda,
lokha nabamedako.
ukumadanisa, ukuhlela
begodu nokurekhoda
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ubude usebenzise
iimedo ezingakahleleki
isib. izandla, igadango,
ubude bepensela,
izinto zokubala, njll.
• Ukuhlathulula ubude
bezinto ngokubala
nangokutjho ubude
ngamayunithi
angakahleleki.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
4.3 Ukumeda Ukumeda Koke ukumeda eGreyidini yoku-1 akukahleleki. Akukho ukumedwa okuhlelekileko
Ubungako/ okungakahleleki okungakahleleki kobungako ngokusebenzisa amayunithi ahlelekileko nofana iinsetjenziswa.
Ubudisi • Ukulinganisa, • Ukulinganisa, Kuphakanyiswe bonyana iimfundo zeembalo zinqotjhiswe ebudisini okungasenani
ukumeda, ukumeda, emathemini amabili wonyaka (iThemu yoku- 1 neyesi-4). Umnqopho eThemini yoku-
ukumadanisa, ukumadanisa, 1kungaba kumadanisa okunqophileko begodu eThemini yesi-4 abafundi bangasebenza
ukuhlela, begodu ukuhlela, begodu ngamayunithi angakahleleki wokumeda. Abafundi bangazijayeza begodu bahlanganise
nokurekhoda ubudisi, nokurekhoda ubudisi, imiqondo le ngesikhathi somsebenzi wokuzijamela umnyaka woke.
ngokusebenzisa ngokusebenzisa Ukumadanisa okunqophileko kobudisi bezinto ezithintekako
iimedo ezingakahleleki iimedo ezingakahleleki
• Ukuthuthukisa ukuzwisisa kobudisi nelimi lokukhuluma ngakho.
begodu nesikala begodu nesikala
sokudzimelela isib. sokudzimelela isib. Abafundi bathoma ukucabanga nokukhuluma ngobungako ngokumadanisa izinto ezidisi
amabhulogo, iintina amabhulogo, iintina nezilula. Baphakamisa into elula khulu begodu balinge ukuphakamisa into ebudisi khulu.
njll. njll. Lokhu kungahlanganiswa ngokuveza imigwalo emadanisa izinto ezibudisi khulu nalezo
ezilula khulu. Lokha abafundi nabangakhuluma ngobungako ukuya ngokungafani, ubudisi
• Ukusebenzisa • Ukusebenzisa
nobulula, abafundi bangamadanisa izinto ezimbili begodu batjho bonyana ngiyiphi ebudisi
ilimi ukukhuluma ilimi ukukhuluma
khulu begodu ngiyiphi elula khulu. Lokhu kungenziwa ngokuphatha into esandleni ngasinye
ngokumadanisa isib. ngokumadanisa isib.
nokumadanisa bonyana ngiyiphi ebudisi khulu nelula khulu.
lula, budisi, lula-khulu, lula, budisi, lula-khulu,
budisi-khulu. budisi-khulu. • Abafundi bafanele barekhode woke umsebenzi nanyana ngemigwalo nofana imisebenzi
ekhambelanako.
• Ukuhlathulula ubude
bezinto ngokubala • Ukumadanisa ubudisi kusetjenzisa isikala sokudzimelela isikhali zokudzimelela
nangokutjho ubude esithengwako singasetjenziswa. Lokha nawungenasikala sokudzimelela esithengwako,
ngamayunithi ungasenza ngokunamathisela ipara yakunye okulandelako ihangere yembaji: Ikopi
angakahleleki. yeyogathi, ingaphasi elisikiweko lebhodlela lamalitha ama-2 nofana ingaphasi elisikiweko
lelitha yi-1 yebisi nofana ibhoksi lejusi (iimumathi ezifanako zilengiswa emahlangothini
womabili wehangere).
• Abafundi bangathoma ngokubeka izinto ezilinganako emahlangothini womabili
wesidzimeleli, ukubona bonyana isisekelo sehangere yembaji sidzimelele lokha izinto lezi
ezimbili zinobudisi obulinganako.
• Abafundi bamadanisa izinto ngokubeka into yinye ehlangothini ngalinye lesidzimeleli,
ukubona bonyana ngiyiphi ebudisi khulu nofana elula khulu.
• Abafundi bangamadanisa izinto ngokubeka izinto ezinengana ehlangothini linye
nofana womabili wesidzimeleli ukubona bonyana zizinto ezingaki ngayinye ezinobudisi
obulingana nenye isib, amakhrayoni ama-5 anobudisi obulingana nesikere si-1.
• Lokhu kungandiselelwa kuserayitjhini , lapho abafundi bahlola khona ubudisi
obukhambelanako bezinto ezikhamba ngazibili baze bakghone ukulandelanisa izinto
ezintathu nofana ezinengi ukusuka kelula khulu ukuya kwebudisi khulu nofana ukusuka
123 kwebudisi khulu ukuya kwelula khulu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
124 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.3 Ukumeda Ukumeda Izinto ezikhethwako zifanele zifake hlangana izinto ezikulu ezilula nezinto ezincani Iimfundo ezi-2
Ubungako/ okungakahleleki okungakahleleki ezibudisi isib. Ipakana yetswayi enamagremu ama-250 amadaniswa nebhoksi lamasiriyeli
• Ukulinganisa, • Ukulinganisa, lamagremu ama-400. Lokhu kusiza abafundi bonyana bazwisise ukusuka ekuthomeni
Ubudisi
ukumeda, ukumeda, bonyana ubudisi buhlobana kuphela nobukhulu lokha nakukalwa izinto ezifanako.
ukumadanisa, ukumadanisa, Abafundi bathuthukisa umqondo wobudisi nelimi lokuhlathulula ubudisi ngesikhathi sinye.
ukuhlela, begodu ukuhlela, begodu Njengombana lokhu kungasatlhogi iinomboro, bungenziwa ekuthomeni kweThemu yoku-
nokurekhoda ubudisi, nokurekhoda ubudisi, 1 ngaphambi kokubana abafundi bahlanganise inomboro zabo zokwenza umqondo
ngokusebenzisa ngokusebenzisa wenomboro ne-opharetjhini ukufikela enomborweni yesi-5.
iimedo ezingakahleleki iimedo ezingakahleleki
Ukurhekhoda
begodu nesikala begodu nesikala
sokudzimelela isib. sokudzimelela isib. Nanyana ukumeda kulikghono lokwenza, abafundi bafanele benze godu imisebenzi
amabhulogo, iintina amabhulogo, iintina yokutlola, engafaka hlangana ukugwala nokufaka umbala, kokubili bonyana bazijayeze
njll. njll. ukusebenzisa amakhrayoni nofana amapensela begodu bonyana bazijayeze ukurekhoda
lokha nabamedako.
• Ukusebenzisa • Ukusebenzisa
ilimi ukukhuluma ilimi ukukhuluma
ngokumadanisa isib. ngokumadanisa isib.
lula, budisi, lula-khulu, lula, budisi, lula-khulu,
budisi-khulu. budisi-khulu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukuhlathulula ubude
bezinto ngokubala
nangokutjho ubude
ngamayunithi
angakahleleki.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
4.4 Ukumeda Ukumeda Uyini umthamo? Iyini ivolumu? Umthamo linani elingaphathwa yinto (inani loke lesikhala Isifundo esi-1
Umthamo/ okungakahleleki okungakahleleki esingaphakathi kwabo). IVolumu linani lesikhala esithathwa yinto. Ibhodlela lingaba
Ivolumu • Ukumadanisa • Ukumadanisa nomthamo wamakopi amane azeleko,kodwana ngesikhathi esithileko ingaba nekopi linye
nokuhlela ubungako nokuhlela ubungako lokumanzana ngaphakathi.Abafundi eGreyidini yoku-1 abakalindeleki ukwazi umehluko
obusamanzi (umthamo) okusamanzi hlangana nomthamo nevolumu.
obuseemumathini (umthamo) okuse Koke ukumeda eGreyidini yoku-1 akukahleleki. Akukho ukumedwa okuhlelekileko
ezimbili ezibekwe
mumathini ezimbili komthamo/kwevolumu ngokusebenzisa amayunithi ahlelekileko.
esinye hlanu kesinye.
Abafundi bahlola ezibekwe esinye eduze Kuphakanyisiwe bonyana iimfundo zeembalo zinqotjhiswe emthameni/evolumini
ngokuthi bathele nesinye. Abafundi emathemini amathathu wonyaka (iThemu yoku- 1, yesi-2 neyesi-4). Umnqopho
esimumathini sesithathu bahlola ngokuthi eThemini yoku-1 kungaba sekuthuthukiseni ilimi ukukhuluma nokumadanisa amavolumu
nakutlhogekako. bathele esimumathini adluleleko, iThemu yesi-2 ingaba sekumadaniseni okunqophileko. IThemu yesi-3 abafundi
• Ukumadanisa sesithathu bangasebenza amayunithi wokulinganisa angakahleleki. Abafundi bangazijayeza begodu
nokuhlela ubungako nakutlhogekako. bahlanganise imiqondo le ngesikhathi sokusebenza ngokuzijamela umnyaka woke.
beketjezi/okusamanzi • Ukusebenzisa Ukumadanisa okunqophileko kwamavolumu eemumathini
okungathathwa ilimi ukukhuluma
ziimumathi ezimbili Ukuthuthukisa ukuzwisisa kobudisi nelimi lokukhuluma ngakho.Abafundi bangathoma
ngokumadanisa isib.
nazizeleko ukucabanga nokukhuluma ngevolumu ngokumadanisa bonyana kungangani
enengi kune, encani
• ( umthamo) okuseemumathini ezimbili ezifanako(nofana imigwalo yeemumathi ezimbili ezifanako)
kune, encani, izele,
• Ukusebenzisa banqophisa :
edududu.
ilimi ukukhuluma • Okuzeleko nokudududu.
ngokumadanisa isib. • Okunengi kuna/okuncani kuna.
enengi kune, encani
kune, encani, izele, • Okufana na.
edududu. Abafundi bangazalisa begodu bathulule iimumathi basebenzisa amanzi nofana isanda njll.
• Ukulinganisa, Njengombana lokhu kungasatlhogi iinomboro, bungenziwa ekuthomeni kweThemu yoku-1
ukumeda, ukumadanisa ngaphambi kobana abafundi bahlanganise umqondo wenomboro ne-opharetjhini ukufikela
ukuhlela begodu enomborweni yesi-5.
nokurekhoda umthamo
Ukurhekhoda
ongeemumathini
ngokusebenzisa Nanyana ukumeda kulikghono lokwenza, abafundi baufanele benze godu imisebenzi
izinto zokumeda yokutlola, engafaka hlangana ukugwala nokufaka umbala, ukuze bazijayeze
ezingakahleleki isib. • ukusebenzisa amakhrayoni nofana amapensela begodu
Iingobho neenkomitji.
• barekhode lokha nabamedako.
• Ukuhlathulula umthamo
wesimumathi ngokubala
nokutjho bonyana
kuthathwa amayunithi
amangaki angakahleleki
ukuzalisa isimumathi.
125 isib.ibhodlela
linomthamo wamakopi
amane.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YOKU-1
5. UKUPHATHA IDATHA
126 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
Ukusebenza ngebuthelelo lezinto
5.1 Ukubuthelela nokuhlela Ukubuthelela nokuhlela Ukuhlela ngemihlobo, Ukujamiselela nokuhlathulula ibuthelelo elihlelekileko, kumakghono Iinfundo ezi-2
Ukubuthele- izinto ngemihlobo izinto ngemihlobo aqakathekileko wabafundi wokuthuthuka emazingeni asisekelo (qala amanothi
la nokuhlela Ukubuthelela nokuhlela Ukubuthelela nokuhlela wamakghono wangaphambili welwazi leenomboro ekuthomeni kwamanothi wehlathululo)
ngemihlobo ngemihlobo izinto ngemihlobo izinto Lendlela yekambiso ithuthukisa amakghono wabafundi abazowasebenzisa nabenza
izinto eziphathekako eziphathekako umzombe wokuphatha idatha.
zangamalanga zangamalanga Abafundi banganikelwa ibuthelelo lezinto begodu babawiwe bonyana bazihlele. Isibonelo,
Ukujamiselela nikela abafundi iinqhema ezifanako zezinto zokubala begodu ubawe abafundi bazihlele
5.2 Ukujamiselela ibuthelelo lezinto ngeenqhema ngokuya ngemibala, banikele ibuthelelo lezinto ezihlukeneko zokubala
Uku- ibuthelelo lezinto elihlelekileko njengekunubhana yokubopha uburotho, indumba yeperegisi, iinthoro zomlilo, imvalo
jamiselela ezihlelekileko zamabhodlelo begodu ubawe abafundi bazihlele ngeenqhema.
Ukugwala isithombe
ibuthelelo Ukugwala isithombe sezinto ezibuthelelweko Abafundi bese bagwala iinthombe zeenqhema abazenzileko. Ngalendlela abafundi
lezinto eli- sezinto ezibuthelelweko barekhoda lokho abakwenzileko. Baphendula imibuzo ngeenqhema.
hlelekileko Coca bewubike
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngokuhlelwa kwezinto Isibonelo
5.3 Coca bewubike ezibuthelelweko “Uzenze njani iinqhema zezinto zokubala? Ngenze iinqhema zemibala.”
Ukucoca be- ngokuhlelwa kwezinto • Nikela ngesizathu “Ngisiphi isiqhema sombala wezinto zokubala ezinengi”? Isiqhema sami esinengi sombala
godu ubike ezibuthelelweko lobonyana ibuthelelo besibomvu.”
ngebuthele- • Nikela iinzathu lihlelwe bunjani
“Bewunemibala emingaki yezinto zokubala ehlukahlukeneko?” Benginemibala emihlanu
lo lezinto zokobana ibuthelelo • Phendula imibuzo nge: ehlukahlukeneko.”
ezihleliweko lihlelwe bunjani -- ukuhlukanisa
• Phendula imibuzo ngemihlobo
Abafundi bangazitholela indlela yabo yebuthelelo. Isibonelo, abafundi bangabuthelela
bonyana: kwenziwe njani
amabhlari etatawini lesikolo, nofana beze neemumathi zokudla emakhaya.
-- ukuhlela kwenziwe (indlela yekambiso)
bunjani (indlela -- ihlukaniso
yekambiso) ngemihlobo libukeka
-- ibuthelelo bunjani (umkhiqizo)
elihlelekileko liqaleka • Coca ngebuthelelo
bunjani (umkhiqizo) nemigwalo
• Coca ngebuthelelo • Hlathulula bonyana
nemigwalo ibuthelelo lihleleke
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Hlathulula bonyana bunjani
ibuthelelo lihleleke
bunjani
IGREYIDI YOKU-I ITHEMU YESI-2
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
CAPS UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
UKUTHUTHUKA KWEMIQONDO YEENOMBORO : Bala ngeenomboro ngokupheleleko
1.1 Ukubala izinto Ukubala izinto Ngikuphi okuhlukileko kuneThemi yoku-1
Ukubala ngokuthembeka ukufika ngokuthembeka ukufika Ethemini yesi-2 ubala, irherho lenomboro liyangezeleleka. Kusesenomnqopho
izinto e-50. ema-20 ekuzwisiseni ukuba inomboro yamaswaphela itjho inani lezinto ngesedeni. Abafundi
• Nikela isilinganiso • Nikela isilinganiso babala izinto ezinengi begodu ethemini yesi-2 kufanele bafunde bonyana bajamisa
esizwakalako senani esizwakalako senani bunjani izinto lokha nababalako ukuze lokha nabahlola ukubala kwabo ihlelwelo
lezinto ezingahlolwa lezinto ezingahlolwa libarhelebhe ukubala bulula.
ngokuzibala. ngokuzibala. Isibonelo:
• Ukubala ngeenqhema Izinto zokubala ezingakabuthelelwa Izinto zokubala ezihlelwe
kuyakhuthazwa. ngeenqhema ngeenqhema
NgeThemu le abafundi baragela phambili ukungezelela amakghono wabo wokubala
nokuzijayeza:
• ukubala koke;
• ukubala uragele phambili
• ikambisolawulo lekhadinali yeenomboro; and begodu
• ukusebenza ngamatheksti atloliweko
NgeThemu lesibili abafundi bathoma uku:
• Bala izinto abangakghoni ukuzithinta nofana ukuzibamba.
Isibonelo :
Sibuza abafundi:
Ziingaba ezingaki ezikhona erhalasini lefesdiri
• Bala izehlakalo
127
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
128 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Isibonelo:
Ukubala ngokuthembeka ukufika ngokuthembeka ukufika Wahla amahlandla ali-15
izinto e-50. ema-20
Phakamisa imino ebu-8
• Nikela isilinganiso • Nikela isilinganiso
Isilinganiso
esizwakalako senani esizwakalako senani
lezinto ezingahlolwa lezinto ezingahlolwa Ukulinganisa inani lezinto esiqhemeni kuthuthukisa amakghono aqakathekileko
ngokuzibala. ngokuzibala. wokubonela phambili. Isiza abafundi ukubona bonyana ukubonela phambili
kuyakholakala. Lokhu kuqakathekile lokha nabenza iimbalo: bangazihlola bona
• Ukubala ngeenqhema
ukuqinisekisa bonyana iimpendulo zabo ngezikholwekako.
kuyakhuthazwa.
Kulisizo ebafundini ukubala iintjengiso zezinto ezibuthelelweko nalezo
ezingakabuthelelwa. Linga ukuhlukanisa izinto ezibuthelelweko nalezo
ezingakabuthelelwa ngokubawa abafundi bona balinganise bonyana ngiziphi
ezinezinto ezinengi. Bangalinganisa inomboro yezinto esithombeni ngasinye.
Bangatlola iinomborwezi phaasi. Bangabala ke. Kufanele bamadanise ukulinganisa
nokubala kwabo. Tjela abafundi bona bakhulume ngokuthi babale bunjani. Zama
ukuthola bona abanye abafundi babale ngeenqhema.
Ukulinganisa ngokunqophileko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Abafundi bangezelela ikghono labo lokukhumbula ibuthelelo elincani lezinto
Ukubala ngeenqhema
Ukusiza abafundi ukubala ngamakhefu waku-2, 5 begodu ne-10 kufuneka bona
babuthelele ngeenqhema zangaku-2, 5 nali -10. Amakarada weenomboro kufanele
aboniswe kilelo nalelo buthelelo ukubonisa inani lezinto ezibaliweko. Ukubala
ngeenqhema kuzokulungiselela abafundi ukuzwisisa ukubala ngokubuyelela
esigabeni esimaphakathi.
Iinsetjenziswa:
Itjhejo kufanele linikelwe emihlotjeni yama-apharathasi osetjenzisiweko
• Iinsetjenziswa ezihlelekileko, njengentambo yemincamo yokubala
• I-Abhakhasi yokujayeza ukubala ngeenqhema zanga-10
• Ukwenza iinyandazanga-2, iinyanda zanga-5 netjhumi begodu uzibale zoke.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko kuneThemu yoku-1?
Ukubala uye nemuva nga: nemuva nga: Ethemini ye-2, abafundi kwanje babala bafike ema-50 ngakunye.
phambili • Kunye ukusuka kwenye • Kunye ukusuka kwenye Babala godu ngamakhefu we-10, 5 naku-2
nemuva nenye inomboro hlangana nenye inomboro hlangana
Ukubala weqa ngomlomo
ne-0 ne-100 ne-0 na-50
Ukubala ngokweqa ngelinye ibizo lokubala ngeenqhema. Kuyasiza ukuthuthukisa
Ukubala uye phambili nga: Ukubala uye phambili nga:
ilemuko lamaphetheni weenomboro. Ukubala ngokweqa kugcugcuzela abafundi
• Li-10 ukusuka kesinye • Li-10 ukusuka kesinye ukubala nokucabanga ngeenqhema, okwenza bona babe nekghono elinengi. Lokhu
nesinye isibuyabuyelelo nesinye isibuyabuyelelo kusiza godu ukuthuthukisa amakghono wabo wokulinganisa.
se-10 hlangana ne-0 ne- se-10 hlangana ne-0 na-
Ukubala ngeenqhema kubenza baLimike ubudlelwano hlangana neenomboro
100 50
ezingalandelani kuhle. Ibeka isisekelo sephetheni yeenomboro nokubuyabuyelela.
• Ku-5 ukusuka kesinye • Ku-5 ukusuka kesinye
Imisebenzi eya phambili
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-5 hlangana ne-0 saka ku-5 hlangana ne-0 Nazi ezinye iimphakamiso zeendlela ezihlukeneko zokwenza ukubala ngokweqa:
ne-100 na-50 • Thoma ngokubala iinomboro ezilandelana kuhle kodwana ugandelele yesibili
• Ku-2 ukusuka kesinye • Ku-2 ukusuka kesinye ngaso soke isikhathi. Isibonelo abafundi bangawahla izandla, batjho leyo naleyo
nesinye isibuyabuyelelo nesinye isibuyabuyelelo nomboro yesibili phezudlwana. Begodu bawa abafundi bona babale kodwana
saka ku-2 hlangana ne-0 saka ku-2 hlangana ne-0 batjho leyo naleyo nomboro yesibili ngeenhlokweni zabo. Lokhu kungangezelelwa
ne-100 na-20 ebafundini bona batjho kuphela inomboro yesithathu, yesine nofana yesihlanu.
• Ungahlukanisa itlasi ngeenqhema, begodu isiqhema ngasinye singadlhegana
ukutjho inomboro elandelako. Nangabe, isibonelo, uhlukanisa itlasi ngeenqhema
ezihlanu, isiqhema ngasinye kufanele sibale leyo naleyo nomboro yesihlanu.
• Bawa abafundi benze iphetheni ephathekako njengokuthintana ngeenhloko
ekubaleni kokuthoma, baphambanise imikhono bathinte amahlombe wabo
ekubaleni kwesibili, babethe iinyonga lokha barhuwelela enye nenye inomboro
yesithathu.
• Isikhathi sokubetha nofana sokuwahlela umbhino kungasetjenziswa
ngokuhlanganyela nokubala ngokweqa.
Ukubala izinto kungathuthukisa ikghono lokubala ngokukhuluma.
Ngetlasini, imisetjenzana yokubala esikhathini esinengi ithuthukisa amakghono
ahlukahlukeneko Ukubala ngokweqa kuvezwa ngcono ngokwenza lokha
nawubuthelela izinto.
Imisebenzi eya phambili
Igridi yeenomboro
Bawa abafundi batjengise iinomboro abazibonako lokha nababala ngaku-2, 5, 10.
129 Buza bona khuyini abakubonako ngeenomboro lezo. Hlukanisa iinomboro lezo
abafundi abathoma ngazo.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
130 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ukuya emathekstini atlolwako
Ukubala uye nemuva nga: nemuva nga: • Amanambalayini – Abafundi bangatjengisa ukubala ngokweqa kwabo basebenzisa
phambili • Kunye ukusuka kwenye • Kunye ukusuka kwenye inambalayini.
nemuva nenye inomboro hlangana nenye inomboro hlangana • Ukulandelana kweenomboro – Ukuya ekugcineni kweThemu abafundi
ne-0 ne-100 ne-0 na-50 bangakghona ukuqedelela ukulandelana kweenomboro okulula (qala amanothi
Ukubala uye phambili nga: Ukubala uye phambili nga: wamaphetheni weenomboro)
• Li-10 ukusuka kesinye • Li-10 ukusuka kesinye Iimbonelo:
nesinye isibuyabuyelelo nesinye isibuyabuyelelo 2, 4, 6, 8, –
se-10 hlangana ne-0 ne- se-10 hlangana ne-0 na-
100 50 5, 10, 15, 20, –
• Ku-5 ukusuka kesinye • Ku-5 ukusuka kesinye 10, 20, 30, 40, –
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-5 hlangana ne-0 saka ku-5 hlangana ne-0
ne-100 na-50
• Ku-2 ukusuka kesinye • Ku-2 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
saka ku-2 hlangana ne-0 saka ku-2 hlangana ne-0
ne-100 na-20
1.3 Ukulemuka, ukubona Ukulemuka, ukubona Ngikuphi okuhlukileko kuneThemu yoku-1?
Amat- nokufunda amatshwayo nokufunda amatshwayo Ethemini le-2, irhelo leenomboro lokwazi, ukufunda nokutlola amatshwayo
shwayo weenomboro weenomboro wenomboro begodu nokungezelela amagama. Ukubala enambalayini begodu
namabizo • Khumbula, ufanise begodu • Khumbula, ufanise begodu namagridi weenomboro kunikela abafundi ijayelo ekufaniseni, ekukhumbuleni,
weenom- ufunde amatshwayo ufunde amatshwayo ekutjhweni nasekufundeni amatshwayo weenomboro.
boro wenomboro ukusuka ku-1 wenomboro ukusuka ku-1 Nikela abafundi ngokuzijayeza okuya phambili ngokunqopha itjhejo lamatshwayo
ukufika ku-100. ukufika ku-50. weenomboro ebhodulukweni nangomtlolo ogadangiswako.
• Tlola amatshwayo • Tlola amatshwayo Isibonelo:
wenomboro ukusuka ku-1 wenomboro ukusuka ku-1
• Ukuqala eenomborweni zamakhasi begodu, neencwadini
ukufika ku-20 ukufika e-10
• Ukukhomba amalanga wamabeletho ekhalendeni
• Khumbula, ufanise • Khumbula, ufanise
begodu ufunde amagama begodu ufunde amagama Imisebenzi eya phambili
weenomboro ukusuka weenomboro ukusuka • Utitjhere unikela imiyalelo ukufumana inomboro, begodu abafundi basebenzisa
ku-1 ukufika ku-10. ku-1 ukufika ku-10. amakarada wefladi aneenomboro ukukhomba iimpendulo
• Tlola amagama • Tlola amagama -- Thola inomboro eza nje ngaphambi kwe-12
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
weenomboro ukusuka weenomboro ukusuka -- Thola inomboro emuva nje kwe-12
ku-1 ukufika ku-10. ku-1 kufika ku-10.
-- Inomboro edlula i-11 ngaku-3
-- Inomboro engaphasi kwe-14 nga-1
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.4 Hlathulula, umadanise, Hlathulula, umadanise, Ngikuphi okuhlukileko kuneThemini yoku-1?
Ukuhlathu- uhlele izinto kufika ku-20 uhlele izinto ukufika e-10 Ethemini ye-2, abafundi baragela phambili uku:
lula, uku- • Ukuhlathulula • Ukuhlathulula • hlela nokumadanisa izinto;
madanisa nokumadanisa izinto nokumadanisa izinto • hlela nokumadanisa iinomboro; begodu
nokuhlela ezibuthelelweko ngokuya ezibuthelelweko ukuya
• sebenzisa ilimi lokuhlela nokumadanisa.
iinomboro ngobunengi, ngambalwa, ngobunengi, ngambalwa,
okunengi khulu, okuncani okunengi khulu, okuncani NgeThemu le abafundi baragela phambili ngokuhlela nokumadanisa izinto.
khulu, okunengi kuno, khulu, okunengi kuno, NgeThemu le abafundi bangathoma ukwakha ubudlelwano hlangana kweenomboro
okuncani kuna, kufana na, okuncani kuna, kufana na, ngokunqophisa kweyodwa begodu nakwezimbili ezingezelelweko, kweyodwa
okulinganako ngobunengi okulinganako ngobunengi begodu nakwezimbili ezingaphasi.
obulingana na, okuhlukileko. obulingana na, okuhlukileko. • Lokha nabamadanisa amasede kufanele bakghone ukuhlathulula lokhu ngokutjho
bonyana, “ Nginezinto zokubala ezinengi ngambili kunezakhe” nofana “ Unezidlula
• Ukuhlathulula nokuhlela • Ukuhlathulula nokuhlela
zami ngayinye”
izinto ezibuthelelwako izinto ezibuthelelweko
• Lokha nawumadanisa iinomboro kufanele bakwazi ukutjho bonyana “okunengi
ukusuka kwenengi ukuya ukusuka kubunengi ukuya
ngakunye kokune kuhlanu”
kencani begodu nokusuka okulingeneko kunye
kencani uye kokunengi. nokusuka kokulingene uye Ukwakha ilemuko lomqondo “wokudlula ngakunye kuna”
Hlathulula, ukumadanisa kokunengi. Umqondo wokunengi kuna nokuncani kuna kukuthoma kokuhlanganisa nokukhupha
begodu uhlele iinomboro Hlathulula, uqathanise, uhlele okungakahleleki. Ivumela abafundi bonyana bazwisise ubukhulu benomboro begodu
kufika ku-20 neenomboro kufika e-10 nehlelo leenomboro.
• Hlathulula, uqathanise • Hlathulula, uqathanise • Layela abafundi bonyana babeke into yokubala yi-1 ngesikhaleni sokuthoma
iinmboro ezipheleleko iinmboro ezipheleleko esingenalitho sekarada labo lefreyimu engaku -5”. Tjela abafundi bona babeke
ngokuya ngobuncani- ngokuya ngobuncani- enye godu into yokubala eqadi kweyokuthoma.
kuna, ngobukhulu – kuna, ngobukhulu –
kuna nobunengi-kuna kuna nobunengi-kuna
nangokulingana nangokulingana Buza:
• Hlathulula bewuhlele • Hlathulula bewuhlele Unazingaki njenganje?
neenomboro ukusuka neenomboro kusuka
Kunengi kangangani okukodwa ngakunye?
ngencani-khulu ukufika ngencani-khulu ukufika
kekulukulu nokusuka kekulukulu nokusuka • Layela abafundi bonyana babeke yi-1 godu into yokubala ekaradeni yabo
kekulukulu ukufika kencani kekulukulu kufika yefreyimu engaku-5
khulu kencanikhulu
--phambili, emuva, phakathi/ --Ngaphambili, ngemuva,
ngaphakathi/hlangana Buza:
--hlangana
--Usebenzisa inambalayini Unazingaki njenganje?
--Usebenzisa inambalayini
kusuka e-0 ukufika e-20 kusuka e-0 ukufika e-10 Kunengi kangangani okukodwa ngakubili?
• Hlathulula umadanise • Hlathulula umadanise • Layela abafundi bonyana babeke yi-1 godu into yokubala ekaradeni yabo
131 usebenzisa ilimi isib. usebenzisa ilimi isib. yefreyimu engaku-5
Ngaphambili, ngemuva, Ngaphambili, ngemuva,
ngaphakathi/hlangana ngaphakathi/hlangana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
132 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.4 Hlathulula, umadanise, Hlathulula, umadanise, Buza:
Ukuhlathu- uhlele izinto kufika ku-20 uhlele izinto ukufika e-10 Unazingaki njenganje?
lula, uku- • Ukuhlathulula • Ukuhlathulula Kunengi kangangani okukodwa
madanisa nokumadanisa izinto nokumadanisa izinto Ngakuthathu?
nokuhlela ezibuthelelweko ngokuya ezibuthelelweko ukuya
Zingaki izinto zokubala ozidingako ukwenza isihlanu?
iinomboro ngobunengi, ngambalwa, ngobunengi, ngambalwa,
okunengi khulu, okuncani okunengi khulu, okuncani Buza bonyana “ungangitjelani ngenomboro ye-4?(kuncani koku-5 nga-1)
khulu, okunengi kuno, khulu, okunengi kuno, Ungangitjelani ngenomboro ye-2? (kuncani koku-5 ngaku-3)
okuncani kuna, kufana na, okuncani kuna, kufana na, Ukuhlela iinomboro
okulinganako ngobunengi okulinganako ngobunengi Abafundi kufanele bahlele iinomboro basebenzisa imihlobohlobo yemifanekiso.
obulingana na, okuhlukileko. obulingana na, okuhlukileko. • Ukubeka imifanekiso ngeenqhema
• Ukuhlathulula nokuhlela • Ukuhlathulula nokuhlela Abafundi bamadanisa isiqhema sezinto ezi-9 esiqhemeni sezinto ezi-2
izinto ezibuthelelwako izinto ezibuthelelweko
• Imifanekiso yemida
ukusuka kwenengi ukuya ukusuka kubunengi ukuya
kencani begodu nokusuka okulingeneko kunye Lokha abafundi nabahlela iinomboro bangasebenzisa ibanga elihlangana
kencani uye kokunengi. nokusuka kokulingene uye neenomboro ukwazi bonyana ngiyiphi inomboro ekulu. Isibonelo, bazakutjho bona
Hlathulula, ukumadanisa kokunengi. i-9 likhulu kune-2 ngombana i-9 liza ngemuva kwe-2.
begodu uhlele iinomboro Hlathulula, uqathanise, uhlele Ukuhlelwa kweenomboro kungenziwa kanengi ngesikhathi sokuzijamela.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kufika ku-20 neenomboro kufika e-10 Imisebenzi eya phambili
• Hlathulula, uqathanise • Hlathulula, uqathanise Ukuhlela iinomboro
iinmboro ezipheleleko iinmboro ezipheleleko Abafundi bahlela amakarada weenomboro ukusukela kwe-1 ukuya kwezi-13
ngokuya ngobuncani- ngokuya ngobuncani- ukusuka kwencani khulu ukuya kwekulu khulu.
kuna, ngobukhulu – kuna, ngobukhulu – Abafundi bajikisa amakarada weenomboro zabo bawaqalisa phasi. Bakhetha
kuna nobunengi-kuna kuna nobunengi-kuna nanyana ngimaphi amakarada a-4, bawahlela ngobuncani khulu ukuya ngobukhulu
nangokulingana nangokulingana khulu babawe umkhozi bona ahlole bonyana ulungile. Nabakghona ukwazi
• Hlathulula bewuhlele • Hlathulula bewuhlele amakarada a-4 ngokupheleleko banga khetha ikarada lesihlanu. Bawabeka ngehlelo
neenomboro ukusuka neenomboro kusuka elilungileko begodu bakope iinomboro ukusukela kwencani khulu ukuya kwekulu
ngencani-khulu ukufika ngencani-khulu ukufika khulu.
kekulukulu nokusuka kekulukulu nokusuka Amathaski atloliweko
kekulukulu ukufika kencani kekulukulu kufika Abafundi kufanele bahlanganise ukuzwisisa kwabo ngokuqedelela amathaski
khulu kencanikhulu atloliweko
--phambili, emuva, phakathi/ --Ngaphambili, ngemuva, Iimbonelo
--hlangana ngaphakathi/hlangana
Ngokuphela kweThemu bafele bakwazi ukuqedelela umhlobo ofanako wemitjho.
--Usebenzisa inambalayini --Usebenzisa inambalayini Okudlula oku-3 nga-1 ku__________
kusuka e-0 ukufika e-20 kusuka e-0 ukufika e-10
Okudlula oku-4 nga-1 ku ___________
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Hlathulula umadanise • Hlathulula umadanise Okuncani nga-1 koku-2 ku ______
usebenzisa ilimi isib. usebenzisa ilimi isib.
Udlula oku-4 nga-1________
Ngaphambili, ngemuva, Ngaphambili, ngemuva,
ngaphakathi/hlangana ______ kuncani koku-3 nga-1
ngaphakathi/hlangana
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Ngikuphi okuhlukileko kuneThemu yoku-1?
Amathek- alandelako nawurarulula alandelako nawurarulula NgeThemu le abafundi baziswa ngokubuyelela kabili nangokuhafula phakathi. Qala
hiniki wok- imiraro begodu uhlathulule imiraro uhlathulule amanothi ngaphasi kwesigaba sokubala.
urarulula neensombululo zemiraro: neensombululo: Ekupheleni kweThemu le abafundi bathoma ukurarulula imiraro yamagama
imiraro • Ama-apharethasi • Ama-apharethasi basebenzisa amathekniki alandelako:
aphathekako njengezinto aphathekako njengezinto • Imigwalo nama-apharathasi aphathekako
zokubala zokubala • Ukwakha nokuphula iinomboro
• Iinthombe zokugwala • Iinthombe zokugwala • Ukubuyelela nokuhafula phakathi
indatjhana zeembalo iimbalo zendatjhana • Amanambalayini
• Ukwakha nokuphula • Ukwakha nokuphula Imigwalo nofana ama-apharathasi aphathekako
iinomboro iinomboro Abafundi baragela phambili ukugwala iinthombe begodu basebenzisa ama-
• Ukubuyelela nokuhafula • Ukubuyelela nokuhafula apharathasi aphathekako ukurarulula imiraro. Kuqakathekile bonyana iinthombe
phakathi phakathi nofana imigwalo zineenomboro begodu nemitjho yeenomboro.
• Amanambalayini • Amanambalayini esekelwe Ukwakha nokuphula
ngeesetjenziswa Le ngenye yamathekhiniki aqakathekileko Esigabeni Esisisekelo. Ukusebenzisa
eziphathekako isib. ikhekhiniki le izovumela abafundi bonyana bahlukane (ukuphula) babuye
Ukubala imincamo. bahlanganise iinomboro ukwenza ukubala kube lula.
Isibonelo
6 + 4 ➝ 5 + 1 + 4➝ 5 + 5 ➝ 10
Ithekhiniki le iyasetjenziswa godu njalonjalo esigabeni esiphakathi.
Ukubuyabuyelelela kabili nokuhafula phakathi
Ithekhiniki le inelwazi lwamambala begodu ifuna umqondo nomboro onamandla.
Abafundi abakghona ukukhetha lokhu njengethekhiniki bamajadu kwamambala
emaqhingeni wokuphumelelisa abawasebenzisako.
NgeThemu le abafundi bathoma Ukubuyelela kabili iinomboro ngombana babala
ukufika e-10. Ngaphambi kokusebenzisa Ukubuyelela kabili nokuhafula phakathi
njengeqhinga lokuphumelelisa ukubala umqondo kufanele ufundiswe.
EGreyidini ye-2 abafundi banikelelwa ngomutjho wenomboro begodu babuzwa:
“singasebenzisa bunjani Ukubuyelela kabili okuseduze ukukhupha ipendulo ya 5
+ 6=£?” Abafundi bayalemuka bonyana uku-5 nesi-6 kutjhidelene. Iisetjenziswa
eziphathekako ziyasetjenziswa ukubonisa bonyana: “Ngizokubuyelela uku-5
okuziinqhema ezimbili zakuhlanu. Ngihlanganise ukuhlanu kabili ngithole i-10
begodu nginayi-1 eseleko okufanele ngiyihlanganise. Ipendulo yi-11. Basebenzisa
ilimi labo nofana imigwalo, abafundi bangasebenzisa iqhinga. Egreyidi ye-3 abafundi
bazokghona ukusebenzisa amaqhinga nakabala ngeenomboro ezinamadijithi
133 amathathu.
NgeThemu le abafundi bazosebenzisa Ukubuyelela kabili nokuhafula phakathi
ngalendlela:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
134 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Ukubuyabuyelela kabili:
Amathek- alandelako nawurarulula alandelako nawurarulula • Imilelenjana emibili enamavili amathathu, inamavili amangaki?
hiniki wok- imiraro begodu uhlathulule imiraro uhlathulule • UBatjeleni noNowa banamamabula a-4 ngamunye. Mamabula amangaki abanawo
urarulula neensombululo zemiraro: neensombululo: selawoke?
imiraro • Ama-apharethasi • Ama-apharethasi Abafundi bangagwala iinthombe basebenzise ama-apharathasi aphathekako
aphathekako njengezinto aphathekako njengezinto ukubonisa bonyana inomboro ibuyabuyelelwe kabili.
zokubala zokubala Ukuhafula phakathi:
• Ethemini ye-2 abafundi bazijayeza ukuhafula phakathi bonyana bakghone
• Iinthombe zokugwala • Iinthombe zokugwala
ukuyisebenzisa njengeqhinga ngeThemu ye-3.
indatjhana zeembalo iimbalo zendatjhana
• Ukubuyelela kabili nokuhafula phakathi kufanele kujayezwe ebujameni
• Ukwakha nokuphula • Ukwakha nokuphula obutjhaphulukileko.
iinomboro iinomboro Amanambalayini
• Ukubuyelela nokuhafula • Ukubuyelela nokuhafula Ukusebenzisa amanambalayini ukusiza ukubala kuzovumela abafundi uku:
phakathi phakathi • Rekhoda ukucabanga kwabo;
• Amanambalayini • Amanambalayini esekelwe • Landela umkhondo wemicabango yabo; begodu
ngeesetjenziswa • Babe nesithombe sokurekhoda abangasisebenzisa ukuhlathulula bonyana
eziphathekako isib. bawurarulule bunjani umraro.
Abafundi bebasebenzisa Amanambalayini ukusuka ethemini yoku-1. Njengobana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukubala imincamo.
abafundi baragela phambili ebangeni elisisiSekelo kufanele bagqugquzelwe
ukusebenzisa amanambalayini ngendlela enelwazi elidluleleko.
Ethemini yoku-1, abafundi babale baya phambili ngakunye. Lokhu kuboniswa
enambalayinini ngokweqa ngakunye.
Isibonelo soku-1:
Kunabesana aba-5 nabentazana aba-4 abenza iimfundo ezingezelelweko
zobukghwari esikoleni. Bangaki abafundi abasetlasini yobukghwari?
Ethemini ye-2 abafundi bangaragela phambili ngokubala baya phambili ngakunye,
kodwana bangakhuthazwa ukusebenzisa inambalayini ukubonisa ukubala uye
phambili ngeenqhema.
Isibonelo sesi-2
Abafundi bangahlukanisa uku-4 ngeenqhema ezi-2. Inambalayini izobonisa imeqo
ngaku-2 ukusuka ku-5.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Ngikuphi okuhlukileko kuneThemu yoku-1?
Ukuh- yamagama ezisebujameni yamagama ezisebujameni NgeThemu le abafundi bazijayeza ukwenza imiraro yamagama begodu basebenzela
langanisa bewuhlathulule iinsombululo bewuhlathulule iinsombululo ukuzithemba nabasebenzisa amanye amaqhinga nabararulula imiraro. Umnqopho
nokukhupha zakho zemiraro ezifaka zakho zemiraro ezifaka ngeThemu le kufanele ube sekurekhodeni. Abafundi kufanele batlole phasi
ukuhlanganisa nokukhupha ukuhlanganisa nokukhupha imitjho yeenomboro njengerekhodi elitloliweko lemiraro ukuya kwemi-5. Abafundi
nempendulo ukufika e-20. nempendulo ukufika e-10. bazokuragela phambili ngokusebenzisa iisetjenziswa eziphathekako nokugwala
ukujamela iimbalo zabo ukusukela koku-5 ukuya e-10.
Qala amanothi weThemu yoku-1 wemihlobo yemiraro engenziwa ngeThemu le.
135
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
136 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.8 Rarulula imiraro Rarulula imiraro Ngezelela irherho lenomboro lifike e-10 ngeThemu le livumela bonyana abafundi
Ukuhlanga- yamagama ezisebujameni yamagama ezisebujameni bathome ngokuhlanganisa okubuyelelweko. Ukubala ufike e-10 kuvumela
nisa bewuhlathulule iinsombululo bewuhlathulule iinsombululo ukurekhoda.
ngokubu- zakho zemiraro, zakho zemiraro, Isibonelo:
yelela ezifaka ukuhlanganisa ezifaka ukuhlanganisa
• 1+1+1
okurholela okubuyelelweko okurholela okubuyelelweko okurholela
ekubuya- ekubuyabuyeleleni ekubuyabuyeleleni • 2+2+2+2
buyeleleni nempendulo ukufika e-20 nempendulo ukufika e-10 • 3+3+3
IThemu yoku-1 yakha umqondo begodu nokuzwisisa ukuhlanganisa begodu
abafundi kufanele bakghone ukuhlanganisa iinqhema ezilinganako.
NgeThemu le abafundi bazosebenza ngemiraro yamagama evumela umfanekios
wokuhlanganisa okubuyelelweko. Ukuhlanganisa okubuyelelwako kuvamise
ukuthulwa ebafundini njengeenqhema zeenomboro ezilinganako. Ekuthomeni
abafundi bangathulwa eenqhemeni ezilinganako zangamalanga.
Imiraro ebandakanya ukuhlanganisa okubuyelelweko
• Iinqhema zanga -2: izandla, iinyawo, amakowusu, amadlhavu, amanyathelo,
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amehlo, iindlebe, amavilo womlelenjana
• Iinqhema zanga -3: amavilo womlelenjane amathathu, umphetho waboncantathu
• Iinqhema zanga -4: amavilo wekoloyi, imilenze yeentulo
• Iinqhema zanga - : imino, iinzwani
Ilimi lokuhlanganisa okubuyelelweko liqakathekile. Abafundi kufabele banikelwe
amathuba wokuhlathulula ngomlomo lokhu abakubonako.
Ukurekhoda imifanekiso yokuhlanganisa okubuyelelweko
• Ukusebenzisa ama-apharethasi aphathekako.
• Abafundi bazokubonisa iimbalo zabo basebenzisa ama-apharethasi
abuthelelweko.
• Ngeethombe kwaphela.
• Abafundi bazokugwala iinthombe ukubonisa bona bazibuthelele bunjani
ukwenzela ukuzihlanganisa.
• Ukurekhoda iinthombe neenomboro.
• Iinthombe zizobonisa imigwalo esekelwa ziinomboro.
• Ukuya ematheksthini atlolwako.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.11 • Ukukhumbula nokufanisa • Ukukhumbula nokufanisa Ukufundisa abafundi ngemali, uhlathulula imiqondo elandelako:
Imali imali yeSewula Afrika imali yeSewula Afrika • iyini imali
-- iinhlamvu 5c, 10c, 20c, iinhlamvu 5c, 10c, 20c,
• kungani imali iqakathekille
50c, 50c, R1,
• indlela imali esetjenziswaa ngayo ngamalanga
-- imali yamaphepha R10, • Ukurarulula imiraro
yemali efaka hlangana • indlela abafundi ababala ngayo imali
ne-R20,
inani netjhentjhi kufikela Abafundi bafunda ngemali ngaphambi kobana beze esikoleni. Abanye abafundi
• Ukurarulula imiraro yemali
emarandeni ali-R10 bangaba nomqondo wokubaluleka kwemali begodu bakghone ukubona nokutjho
efaka hlangana inani
ukufikela emasendeni iinhlamvu nemali yamaphepha.
netjhentjhi ngamasende
ama-20c NgeThemu le abafundi bafanele bafunde imiqondo esisekelo yokusebenzisa imali
kufikela emasendeni ama
50c namaranda ama- R20 ngaphakathi kobujamo obenzekako njengokwenza umdlalo wesitolo.
• Letha iinhlamvu zeSewula Afrika begodu na-R20 ne-R10 esikoleni. Abafundi
bathinta imiphetho yeenhlamvu begodu bacocisane bonyana ihluka bunjani.
Bacocisana ngamatshwayo aseenhlamvini nasemalini yamaphepha.
• Abafundi babeka iinhlamvu ngaphasi kwesiquntu sephepha begodu basebenzise
isitlabagelo esithambileko sokutlola ukuhlikihla phezu kwazo isib. Amapensela
wemibala nofana amaphastelsi. Basika amakhophi, bawanamathisele encwadini
zabo begodu batjho iinhlamvu.
• Bagandangisa begodu basike imifanekiso eminengi yeenhlamvu zama -5c, 10c
nama 20c. Banamathelisa iinhlamvu zoke ezingenza ama -20c ne-10c isib. 20c =
10c ne-5c ne-5c
• 20c = 5c ne-5c ne-5c ne-5c
• Isamba ukufika ema-20c – iinhlamvu zodwa
-- Abafundi sele bakwazi ukubala ngaku -5 nangama-10c begodu basebenzisa
ilwazi ukuthola isamba.
-- Utitjhere unikela umfundi ngamunye iphepha lamakhophi leenhlamvu zemali
e-5c, 10c nama- 20c.
o Ubatjela bona ngiziphi iinhlavu abafanele bazikhuphe, isib. Iinhlamvu zemali
ezintathu zama-5c.
o Babala ngaku-5 nofana 10c benze ukuhlanganisa okubuyelelwako,
5c+5c+5c.
-- Utitjhere ubawa abafundi bonyana bakhuphe ama-20c basebenzisa iinhlamvu
zemali ezihlukahlukeneko. Kufanele babone bonyana ngamunye ukhupha
iinhlavu zemali ezima-5c amabili nehlamvu yinye yama-10c.
137 -- Abafundi bazalisa amaphepha wokusebenzela lapho babonisa khona bonyana
ngiziphi iinhlavu zemali ezenza isamba samasende ama-20c
Isibonelo: 20c = 10c + 10c nofana 5c+ 5c + 5c + 5c= 20c nofana 5c+5c + 10c =20c
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
138 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.11 • Ukukhumbula nokufanisa • Ukukhumbula nokufanisa • Nikela itjhentjhi usebenzise iinhlamvu zodwa
Imali imali yeSewula Afrika imali yeSewula Afrika -- Utitjhere wenza ukukhupha kweenhlamvu nabafundi isib. Bakhupha iinhlavu
-- iinhlamvu 5c, 10c, 20c, iinhlamvu 5c, 10c, 20c, zemali ezima-5c ukwenza ama-20c.
50c, 50c, R1,
-- Utitjhere uyabuza: “Nawubhadela umamukelimali ama-15c, yimalini eseleko?
-- imali yamaphepha R10, • Ukurarulula imiraro Abafundi ababa nobudisi bokusebenzisa iinhlavu zemali kuphela basebenzisa
ne-R20, yemali efaka hlangana izinto zokubala ukubasekela.
inani netjhentjhi kufikela
• Ukurarulula imiraro yemali -- Abafundi bazalisa amaphepha wokusebenzela lapho basebenzela khona
emarandeni ali-R10
efaka hlangana inani itjhentjhi yezinto abazithenge ngama-20c nofana ngaphasi
ukufikela emasendeni
netjhentjhi ngamasende Isibonelo:
ama-20c
kufikela emasendeni ama
-- 10c - 5c = 5c
50c namaranda ama- R20
-- 20c - 10c =10c - amatjhumi apheleleko
-- 20 -5c – 5c - 5c = 5c -ukukhupha okubuyelelweko
UKUBALA OBUSEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki Ngikuphi okuhlukileko kuneThemu yoku-1?
alandelako nakubalisiswako: alandelako nakubalisiswako:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Amathekh- EThemini ye-2, abafundi bathoma ukubala ukufika e-10. Ukusebenza ngaphakathi
iniki • Ama-apharethasi • Ama-apharethasi kwerherho lenomboro kutjho bonyana ithekhiniki yokubala ingathuthukiswa begodu
(iindlela aphathekako isib. Izinto aphathekako isib. Izinto ijayezwe.
nofana zokubala zokubala Amaqhinga la ayajayezwa nasesigabeni somraro wenomboro.
amaqhinga) • gwala iinthombe • ukwakha nokuphula Ukwakha nokuphula iinomboro
• ukwakha nokuphula iinomboro
Imisetjenzana yokwakha nokuphula ithuthukisela phambili ilemuko labafundi
iinomboro • ukubuyelela kabili lobukhulu obuhlobeneko beenomboro. Imisetjenzana le ibeka isisekelo sama-
• ukubuyabuyelela kabili nokuhafula opharetjhini. Ukuhlukanisa (ukuhlukanisa) nokubuya uhlanganise iinomboro
nokuhafula • Amanambalayini kungasiza ukwenza iimbalo zibe lula. Ukujayeza njalo emsebenzini onje kukhuthaza
• amanambalayini asekelwe ngama- abafundi bona bayisebenzise njengeqhinga leembalo.
apharethasi aphathekako Ukubuyebuyelela nokuhafula
isib. Ukubala imincamo.
Ngaphambi kokubana usebenzise Ukubuyelela nokuhafula phakathi njengeqhinga
lokubala lifuneka bona lithonywe ngokuzwisiseka begodu lijayezwe.
• Ukusebenzisa ama-apharethasi aphathekako.
Lokhu kungenziwa ngelayelo elinqophileko.Tjela begodu bonisa abafundi bonyana
kuneengojwana ezihlanu zokubala begodu uzokghona ukubuyabuyelela inani lelo
ngokundlala ezinye godu iingojwana zokubala ezihlanu.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukuya emathekstini atlolwako usebenzisa iinthombe.
• Abafundi banganikelwa imifanekiso yokubuyabuyelela kabili begodu
bangakghona ukujamela iinthombe ngeenthombeni
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.12 Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki • Ukusebenzisa iinomboro
Amathekh- alandelako nakubalisiswako: alandelako nakubalisiswako: Abafundi bangathoma ngokuzalisa imitjho enjenge:
iniki • Ama-apharethasi • Ama-apharethasi Uku -1 okubuyabuyelelwe kabili ngu.........................
(iindlela aphathekako isib. Izinto aphathekako isib. Izinto
Uku -2 okubuyabuyelelwe kabili ngu........................
nofana zokubala zokubala
Uku -3 okubuyabuyelelwe kabili ngu.........................
amaqhinga) • gwala iinthombe • ukwakha nokuphula
iinomboro Uku -4 okubuyabuyelelwe kabili ngu..........................
• ukwakha nokuphula
iinomboro • ukubuyelela kabili Amanambalayini asekelwe ma-apharethasi aphathekako.
• ukubuyabuyelela kabili nokuhafula Lokha nawusebenzisa amanambalayini njengethekhiniki ukuze ubale, abafundi
nokuhafula • Amanambalayini bafuneka bathome ngokusebenzisa.
• amanambalayini asekelwe ngama- • Amanye ama-apharethasi womuda isib. Ukubala imincamo, ukulandela imikhondo
apharethasi aphathekako yeenomboro;
isib. Ukubala imincamo. • Inambalayini ukubala uye phambili begodu nemuva; begodu
• Inambalayini ukuze abeke ebujameni nokuhlela iinomboro.
Inambalayini ehlelekileko ifanele isetjenziswe (begodu ifanele khulu) lokha abafundi
nabenza ukuhlanganisa nokukhupha. Inambalayini ehlelekileko ifanele ibonise zoke
iinomboro ezikiyo.
139
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
140 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.13 Irherho leenomboro: 1 -20 Irherho leenomboro: 1 -10 Ngikuphi okuhlukileko kuneThemu yoku-1?
Ukuh- • Hlanganisa ukufika ema- • Hlanganisa ukufika e-10 Ethemini le-2, irherho leenomboro ingezeleleke ukusuka ku-5 ukuya e-10.
langanisa 20 • Khupha e-10 NgeThemu le abafundi bazokuthoma ukuzwisisa:
nokukhupha • Khupha ukusuka ema-20 • Ihlelo elihlanakelekako lokuhlanganisa; begodu
• Sebenzisa amatshwayo
• Sebenzisa amatshwayo afaneleko (+, –, =, ) • Ubudlelwano phakathi kokuhlanganisa nokukhupha
afaneleko (+, –, =, ) • Ukujayela ukulumbana Ngaphambi kokobana abafundi bathulelwe amatshwayo wokuhlanganisa begodu
• Ukujayela ukulumbana kweenomboro ukuya ku-7 nokukhupha, abafundi kufanele babe nelemuko elaneleko loku:
kweenomboro ukuya e-10 • bala koke;
• bala uye phambili ukusuka enomborweni ekulu;
• sebenzisa nokuzwisisa ilimi lokuhlanganisa nokukhupha; begodu
• hlela nokumadanisa iinomboro.
Ethemini le, abafundi baragela phambili ukwakha ukuzwisisa kwabo kokuhlanganisa
nokukhupha.
Ukuhlangisa nokukhupha kusesenoBudlelwana obukhulu ekubaleni. Umqondo
wokunengi nga -1 nofana okuncani ngaku-2 kusetjenziswa ngombana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kukhambelana nenomboro elandelako ekubaleni okulandelanako.
NgeThemu le abafundi bazosebenzisa amatshwayo ukutlola ukulandelana
kweenomborongokubuyelela nangokuzithemba. Iragelo phambili ekusebenziseni
amatshwayo kufanele kusetjenzwe ngakho ngokuyelela. Kuqakathekile bonyana
abafundi bazwisise amahlathululo ahlukeneko akhambisana namatshwayo. Abafundi
kufanele bakghone ukuzwisisa nokusebenzisa amagama njengokuhlanganisa, koke,
koke kwenza, khupha, umehluko hlangana nokukhupha ngaphambi kokwethula
amatshwayo.
Abafundi kufanele bathome ngokwazi ukuphendula imibuzo enjenga-3 naku-2;
khupha oku-3 e-5, ngaphambi kokusebenzisa itshwayo.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.13 Irherho leenomboro: 1 -20 Irherho leenomboro: 1 -10 Ukurekhoda imifanekiso
Ukuh- • Hlanganisa ukufika ema- • Hlanganisa ukufika e-10 Ukubala ufike e-10 kutjho bonyana abafundi basazokurekhoda iimbalo zabo
langanisa 20 • Khupha e-10 basebenzisa:
nokukhupha • Khupha ukusuka ema-20 • imigwalo nofana iinsetjenziswa eziphathekako;
• Sebenzisa amatshwayo
• Sebenzisa amatshwayo afaneleko (+, –, =, ) • iinthombe neenomboro; nofana
afaneleko (+, –, =, ) • Ukujayela ukulumbana • Iinomboro zodwa.
• Ukujayela ukulumbana kweenomboro ukuya ku-7 Ukuya ekupheleni kweThemu, ngaphakathi kwerherho leenomboro yoku-1 ukuya
kweenomboro ukuya e-10 ku-5, abafundi kufanele bazithembe nabasebenzisa iinomboro zodwa begodu
bangagwali iinthombe ukujamela iimbalo zabo.
Amaqhinga wokubala nawenza ukuhlanganisa nokukhupha
Ukuhlanganisa ngokubala koke
Abafundi bazokuthoma ku-1 bafike ku-5 begodu baragele phambili ngokubala
ukufika ku-7
Ukuhlanganisa ngokubala uye phambili
5
Abafundi bazokubala baya phambili ukusuka ku-5 ukuya ku-7
Ithekhiniki le inekghono khulu kunokubala uye phambili ngakunye. Abafundi
bazosebenzisa ithekhiniki le kanengi khulu lokha irherho leenomboro lingezeleleka.
6
Bala uye phambili usuka enomborweni ekulu.
Abafundi babala baya phambili ukusuka enomborweni ekulu, esi-6, begodu babale
baye phambili ukufika-8.
Ukukhupha ngokukhupha
7–3=
7- 3 = 4
Lokha nabarekhoda ukukhupha abafundi bangakhansela imifanekiso ukutjengisa
141 ukukhupha.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
142 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.13 Irherho leenomboro: 1 -20 Irherho leenomboro: 1 -10 Ukukhupha ngokubala uye phambili
Ukuh- • Hlanganisa ukufika ema- • Hlanganisa ukufika e-10
langanisa 20 • Khupha e-10
nokukhupha • Khupha ukusuka ema-20 • Sebenzisa amatshwayo
• Sebenzisa amatshwayo afaneleko (+, –, =, )
6-2=
afaneleko (+, –, =, ) • Ukujayela ukulumbana
• Ukujayela ukulumbana kweenomboro ukuya ku-7 Abafundi bangabala baye phambili ukusuka e-2 ukuya esi-6. Bafanele bazi bonyana
kweenomboro ukuya e-10 babale iinomboro zingaki ukusuka kwe-2 ukuya esi-6.
Ukukhupha ngokubalela emuva
8-2=
Abafundi bangathoma enomborweni ekudlwana, ebu-8, begodu babalele babuyele
ISIGABA ESISISEKELO AMAGREYIDI 1-3
emuva ngamagadango ama-2 ukuya kwasi-6.
Ukwakha nokuphula iinomboro
Lokhu kungenziwa ngeendlela ezihlukahlukeneko
7=4+3
7=4+3
Ukulumbana kweenomboro
NgeThemu le abafundi bazijayeza ukulumbana kweenomboro ukufika ku-7.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Lokhu kungakhonjiswa ngeenthombe begodu nemitjho yeenomboro basebenzise
imifanekiso ehlukahlukeneko.
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.13 Irherho leenomboro: 1 -20 Irherho leenomboro: 1 -10 Ukuhlanganisa
Ukuh- • Hlanganisa ukufika ema- • Hlanganisa ukufika e-10 Iimbonelo:
langanisa 20 • Khupha e-10 Ukwenza isi-6 nofana ukuthola abangane aba-6 usebenzisa iinthombe begodu
nokukhupha • Khupha ukusuka ema-20 neenomboro
• Sebenzisa amatshwayo
• Sebenzisa amatshwayo afaneleko (+, –, =, )
afaneleko (+, –, =, ) • Ukujayela ukulumbana
• Ukujayela ukulumbana kweenomboro ukuya ku-7
kweenomboro ukuya e-10 Isibonelo soku-1
na kwenza
Isibonelo sesi-2
na kwenza
Isibonelo sesi-3
na kwenza
Ukwenza isi-6 ngokusebenzisa iinthombe neenomboro
Faka umbala ukubonisa isi-6 ngeendlela ezihlikeneko
__________ na________ kwenza isi- 6
Ukusebenzisa iinomboro zodwa
Madanisa iinomboro ezikhamba ngambili ukwenza isi-6
1 2
3 4
5 5
4 3
143
2 1
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
144 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1 namaminithi
ama -24)
1.13 Irherho leenomboro: 1 -20 Irherho leenomboro: 1 -10 Okuhlanakelekako
Ukuh- • Hlanganisa ukufika ema- • Hlanganisa ukufika e-10 NgeThemu le abafundi bathoma ukukhumbula umukghwa wokuhlanekezela
langanisa 20 • Khupha e-10 ukuhlanganisa ngaphandle kokwazi, iThemu.
nokukhupha • Khupha ukusuka ema-20 Isibonelo:
• Sebenzisa amatshwayo
• Sebenzisa amatshwayo afaneleko (+, –, =, ) Bala aboncantathu
afaneleko (+, –, =, ) • Ukujayela ukulumbana
• Ukujayela ukulumbana kweenomboro ukuya ku-7
kweenomboro ukuya e-10
6+2=
2+6=
Ukutlola okuhlobene nokuhlanganisa nokukhupha iinomboro zemitjho – ukuzwisisa
ubudlelwano hlangana kokuhlanganisa nokukhupha
NgeThemu le abafundi bafunda kobana bangatlola umutjho weenomboro
ISIGABA ESISISEKELO AMAGREYIDI 1-3
wokukhupha bawutlolela umutjho wenomboro wokuhlanganisa.
Isibonelo
4+2=6 en 6 – 2 = 4
2+4=6 en 6 – 4 = 2
Itshwayo lokulingana
Itshwayo lokulingana akukafaneli bona lithulwe msinyazana.
Kungasiza ukusebenzisa amatshwayo ngendlela enetjhuguluko elaneleko begodu
kunikela abafundi itjhuba esikhundleni setshwayo lokubala.
Isibonelo
Kukoke kwenza
4 en 2 ➝ 6
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YOKU-1
CAPS namaminithi
ama -24)
1.13 Irherho leenomboro: 1 -20 Irherho leenomboro: 1 -10 Ukusebenzisa inambalayini
Ukuh- • Hlanganisa ukufika ema- • Hlanganisa ukufika e-10 Thula ukukhupha ukufikela e-10 enambalayinini.
langanisa 20 • Khupha e-10 Utitjhere usebenzisa inambalayini ukukhupha iinomboro ezifika e-10 isib. 5 – 2 =
nokukhupha • Khupha ukusuka ema-20 Isibonelo: Umqasana weqela enomborweni yesi-5, bese ubuyela emuva ngokweqa
• Sebenzisa amatshwayo
• Sebenzisa amatshwayo afaneleko (+, –, =, ) iinomboro ezi- 2 begodu ujama enomborweni yesi-3.
afaneleko (+, –, =, ) • Ukujayela ukulumbana Ngakho-ke 5 – 2 = 3
• Ukujayela ukulumbana kweenomboro ukuya ku-7
kweenomboro ukuya e-10
Amathaski atloliweko
Abafundi bafanele banikelwe imihlobohlobo yemifanekiso ukusekela ukuzwisisa
ukuhlanganisa nokukhupha.
• Bala uye phambili
• Hlanganisa ngokubala ukusuka enomborweni ekulu; nofana
• Khupha ngokufaka isiphambano esivundlako phezu kweenthombe.
Umqondo wokubuyelela kabili
Irherho leenomboro abafundi abasebenza ngalo libavumela bonyana bathome
ukubuyelela kabili. Lokhu kungathulwa ngeendlela ezinengi begodu kungenziwa
lokha abafundi nababala izinto.
Isibonelo: Abafundi bangenza iinqhema zezinto zokubala zanga - 2, izinto zokubala
zanga - 4, izinto zokubala ezi-6 nezinto zokubala ezi -8 nezinto zokubala ezi-10.
Imitjho yeenomboro kufanele ikhambisane nemifanekiso.
Uku -1 obuyelelwe kabili Uku -1 obuyelelwe kabili Uku -1 obuyelelwe kabili
ngu…………............ ngu…………............ ngu…………............
145
Uku -1 obuyelelwe kabili Uku -1 obuyelelwe kabili
ngu…………............ ngu…………............
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
146 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.14 • Hlanganisa • Hlanganisa Ngikuphi okuhlukileko kuneThemu yoku-1?
Ukuh- ngokubuyelela ngokubuyelela Ethemini ye-2, abafundi bathoma ukwenza ukuhlanganisa okubuyelelweko ukufika e-10.
langanisa (o.u.inomboro efanako) (o.k.inomboro efanako) Lokha abafundi nabanomqondo omuhle kwamambala wenomboro yoku-1 ukufika keye- 5,
okubuyele- kufika ku-20 kufika e-10 ukuhlanganisa okubuyelelweko kuzokwenza ingqondo kibo.
lweko • Sebenzisa • Sebenzisa Ukuhlanganisa okubuyelelweko kufanele kuthulelwe abafundi njengeenqhema zeenomboro
kurholela amatshwayo afaneleko amatshwayo afaneleko ezilinganako.
ekubuy- (+, =, ) (+, =, )
Ukusebenza ngeenqhema zezinto kuqakathekile ekuzwisiseni ukubuyabuyelela. Abafundi
abuyeleleni
bafanele bakghone uku :
• enza iinqhema zezinto ezilinganako;
• hlathulula ihlelo; begodu
• bala inani loke lezinto.
Ekuthomeni abafundi bazobala ngakunye kodwana lokha nabatjhelelako ekubaleni
ngokweqa bafanele babale izinto ezihlelwe ngakubili, ngakuhlanu nofana ngalitjhumi.
Abafundi bamele bavezelwe epepeneneni imifanekiso eminengi ehlukahlukeneko ezisekela
ukuzwisisa kokuhlanganisa okubuyebuyelelweko.
Kungaba lisizo ukwethulela abafundi ngeenthombeni zeenqhema ezilinganako
ISIGABA ESISISEKELO AMAGREYIDI 1-3
zangamalanga, isibonelo:
Iinqhema zanga-2 – izandla, iinyawo, amakowusu, amadlhavu, iinyathelo, iindlebe, amavili
wemlelenjani.
Iinqhema zanga-3 - amavili wemlelenjani enamavili amathathu, umkhawulo wakancantathu.
Isibonelo:
Mangaki amavili nasele awoke?
Mingaki imino. Zalisa inomboro yemitjho engenzasi.
+ + = 15
Ukurekhoda imifanekiso yokuhlanganisa okubuyebuyelelweko.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Umnqopho la usekuthuthukiseni ilimi ukusekela ukuzwisisa ukubuyabuyelela. Abafundi
bazorekhoda ukuzwisisa kwabo ngokusebenzisa iinthombe. Abafundi kufanele banikelwe
iinthombe zezinto ezisesiqhemeni begodu bagwale isiyingilizi magega nazo ukubonisa
iinqhema zezinto.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.14 • Hlanganisa • Hlanganisa
Ukuh- ngokubuyelela ngokubuyelela
langanisa (o.u.inomboro efanako) (o.k.inomboro efanako)
okubuyele- kufika ku-20 kufika e-10
lweko • Sebenzisa • Sebenzisa
kurholela amatshwayo afaneleko amatshwayo afaneleko Ilimi elingasetjenziswa ngelithi kuna – 2 okunok kwaku-3nofana iinqhema ezi-2
ekubuy- (+, =, ) (+, =, ) zangaku-3. Lokha abafundi nabanokuzithemba ekuhlathululeni iinjamiseleli zeenthombe
abuyeleleni ngokusebenzisa ilimi bangahlathulula imitjho yeenomboro.
Umutjho wenomboro: 3 + 3 = 6
1.16 Umqondonomboro: Irherho Lemiqondo Ngikuphi okuhlukileko kuneThemu yoku-1?
Iimbalo hlangana na-20 Leenomboro 10 Ethemini ye-2, irherho leenomboro liyakhula ukusuka ku-5 ukufika e-10
zehloko • Hlela isede enikelweko • Hlela isede enikelweko
leenomboro Iimbonelo zemibuzo nemisetjenzana engabuzwa begodu nengenziwa:
yeenomboro
ezikhethiweko Thoma ngo-3 ubale uye phambili ngakunye ukufika e-10
• Madanisa iinomboro ezikhethiweko
Ngiyiphi encani ku -8 nofana ku-5?
ukufika ema- • Madanisa iinomboro
20 begodu utjho ukufika ema- Ngiyiphi enengi ku-8 nofana ku-4?
nokobana ngiyiphi 10 begodu utjho Kuyini okuncani ngaku-2 kune-9?
ekulu nofana encani nokobana ngiyiphi Kuyini oknengi ngaku-2 kuna -3?
nga-1 begodu nanga-2. ekulu nofana encani
Ukukhumbula Nginikela inomboro ehlangana kwa- 1 noku-3
nga-1 begodu nanga-2.
msinyazana Nginikela inomboro ehlangana kwe-6 begodu ne-10. Kunenomboro yinye kwaphela?
• Ukulumbana
kweenomboro ukufika Beka amakarada weenomboro la ukusuka enomborweni encani ukufika kwekulu.
e-10.
• Khumbula amaphuzu
wokuhlanganisa
nokuhlukanisa ukufika
e-10
Amaqhinga wokubala
Ukusebenzisa
amaqhinga wokubala
ukuhlanganisa
nokukhupha ngefanelo.
• Beka inomboro ekulu
maqangi ukuze ubale
uye phambili nofana
emuva
• Inambalayini.
147 • Ukubuyelela
nokuqunta phakathi
• Ukwakha nokuphula
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YESI-2
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
148 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.1 Ukukopa, ukungezelele Ukukopa, ukungezelela Ukukopa iphetheni kusiza abafundi ukubona ilojikhi yokobana iphetheni yenziwe bunjani.
Amapheth- begodu nokuhlathulula nokuhlathulula. Ukungezelela iphetheni kusiza abafundi ukuhlola bonyana bayizwisisile ilojikhi yephetheni.
eni weJi- Ukukopa, ukungezelela Ukukopa, ukungezelela Ukuhlathulula iphetheni kusiza abafundi ukuthuthukisa amakghono wabo welimi
yomethri begodu nokuhlathulula begodu bewuhlathulule nokukhuluma. Kuyokusiza ukubona bonyana abafundi bahlathulula njani amaphethini
ngamagama ngamagama
Egreyidini yoku-1 abafundi banganqopha emaphethinini wezinto nofana eenqhemeni
• Amaphetheni alula • Amaphetheni alula zezinto ezibuyelwe ngendlela efanako patsi/poro.
enziwe ngezinto enziwe ngezinto
eziphathekako eziphathekako Ethemini yesi-2 abafundi abanengi bayazigedla nabasebenzisa ikhrayoni nofana ipensela
nabagwalako. Abafundi bangaragela phambili ngokukopa nangokungezelela amaphetheni
• Amaphetheni alula • Amaphetheni alula enziwe ngeenthombe esikhundleni sezinto. Kufanele banqophise ekuhlathululeni
enziwe ngemigwalo enziwe ngemigwalo
amaphetheni. Akusilula ngasosoke isikhathi ukuhlathulula iphetheni. Ungabasiza ukufunda
yemida, amajamo yemida, amajamo
bonyana bakhulume njani, ngani ngokubuza imibuzo efana nelandelako:
nofana izinto. nofana izinto.
“Majamo anjani awabona ephetheneni le?”
Tlama amaphetheni Tlama amaphetheni
wakho. namamaphetheni wakho “Anemibala efanako?”
ISIGABA ESISISEKELO AMAGREYIDI 1-3
weJiyometri Tlama amaphetheni “Ubona ijamo linye nofana manengi ephetheneni?”
• Ngezinto weJiyometri “Ingabe zoke izinto ziqale endaweni yinye na?”
eziphathekako • Ngezinto “Kunenani elifanako lezinto esiqhemeni ngasinye?”
• Ngokugwala imida, eziphathekako “Zizinto ezingaki ezisesiqhemeni ngasinye?”
ubujamo nofana izinto • Ngokugwala imida, “ingabe amajamo woke anobungako obulinganako?” njll
Amaphetheni amajamo nofana izinto
asizombelezileko Ethemini yesi - 2 eminye yeminqopho ingaba sekusebenziseni amajamo weJiyometri
wa-3-D abafundi abawafunde eThemini yoku-1. Abafundi bangenza amajamo abo 2-D
Ukubona, ukuhlathulula
ngokusika iphepha nofana ikarada, nofana bangawagwala. Bangenza amaphetheni
ngamagama nokukopa
ngamajamo wamabhoksi begodu nangamajamo weembholo abazenze ngebumba nofana
amaphetheni
ngehlama yokudlala.
weJiyomethri
Amaphetheni angenziwa ngokusebenzisa ijamo elilodwa kodwana umbala wezinto
• Ngokwemvelo,
utjhuguluke ngendlela eqhelekileko isib.
• Kusukela epilweni
yangamalanga
yesimodeni,
• Kusukela kezamagugu
nendabuko yethu. Kuqakathekile eGreyidini yoku-1 ukusiza abafundi babone bonyana ngisiphi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
isiqhema esibuyelelwako, ngokubeka isiqhema ngasinye eencetjhaneni zephepha
ezahlukahlukeneko nofana kubonisa ngaphakathi kwebhlogo ngekhasini.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
2.1 Ukukopa, ukungezelele Ukukopa, ukungezelela Amaphetheni angenziwa ngeenqhema ezifanako ezibuyelelwako, lapho isiqhema ngasinye Isifundo-1
Amapheth- begodu nokuhlathulula nokuhlathulula. sinomhlobo munye wento kodwana indawo yezinto eenqhemeni iyatjhughuluka. Iinqhema
eni weJi- Ukukopa, ukungezelela Ukukopa, ukungezelela ezifanako poro ziyabuyelelwa isib.
yomethri begodu nokuhlathulula begodu bewuhlathulule
ngamagama ngamagama
• Amaphetheni alula • Amaphetheni alula
enziwe ngezinto enziwe ngezinto
eziphathekako eziphathekako
• Amaphetheni alula • Amaphetheni alula
enziwe ngemigwalo enziwe ngemigwalo
yemida, amajamo yemida, amajamo
nofana izinto. nofana izinto.
Tlama amaphetheni Tlama amaphetheni
wakho. namamaphetheni wakho Emaphethenini amanye izinto ezahlukeneko ziyasetjenziswa ukwenza isiqhema, kodwana
weJiyometri Tlama amaphetheni iinqhema zezinto ziyabuyelelwa ngendlela efanako isib.poro
• Ngezinto weJiyometri
eziphathekako • Ngezinto
• Ngokugwala imida, eziphathekako
ubujamo nofana izinto • Ngokugwala imida,
Amaphetheni amajamo nofana izinto
asizombelezileko Emaphethenini amanye ubukhulu bezinto eenqhemeni buyatjhuguluka, kodwana iinqhema
ziyabuyelelwa ngendlela efanako patsi/poro.
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni
weJiyomethri
• Ngokwemvelo,
• Kusukela epilweni Abafundi bangenza amaphetheni ngokuthungelela imincamo. Ukwenza amaphetheni
yangamalanga kungenziwa godu eemfundweni zamaKghono wePilo.
yesimodeni,
• Kusukela kezamagugu
nendabuko yethu.
149
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
150 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.2 Ukukopa, ukungezelela Ukulandelanisa kufanele Ukulamanisa iinnomboro kungahlanganiswa nokubala. Lokha amakghono wabafundi
Amaphe- begodu nokuhlathulula kubonise ukubala ukuya wokubala atjhugulukako godu athuthukako, imihlobo yokulamanisa iinomboro abafundi
theni Ukukopa, ukungezelela phambili nemuva abasebenza ngayo ingathuthuka.
weenom- begodu nokuhlathulula • Nga-1 ukusuka Ukulandelanisa kufanele kubonise ukubala uye phambili nemuva ngabo:
boro. Ukulandelaniswa kunanyana ngiyiphi • Kunye ukusuka kwenye nenye inomboro hlangana neyoku -1 ukufika ku- 50
kwenomboro elula inomboro hlangana na
• Litjhumi ukusukela kwenye nenye inomboro ebala ngali-10 ehlangana ne -0 na-50
ukufika ku-100. -1 nama-50
• Kuhlanu ukusukele kwenye nenye inomboro ebala ngaku-5 ehlangana ne -0 na-50
Tlama amaphetheni Ukubala uye phambili
nga: • Kubili ukusukela kwenye nenye inomboro ebala nga- 2 ehlangana ne - 0 na- 20
wakho
• Nga-10 ukusuka Lokha abafundi babala ngomlomo bangatjengiswa ukulandelanisa iinomboro ezitlolwe
Tlama amaphetheni
kwenye nenye phasi ngezindlela ezingafaniko.
wakho weenomboro
eyisibuyabuyeleli se-10 Bangakhomba inomboro ebaliweko
hlangana ne-0 na-50 Isibonelo :
• Ngaku-5 ukusuka
kwenye nenye 1 2 3 4 5 6 7 8 9 10
inomboro 11 12 13 14 15 16 17 18 19 20
esibuyabuyeleli saka
Abafundi bangazalisa iinomboro ezingekho ezivezwe nanoma ngawuphi umhlobo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ku-5 hlangana ne-0
na-50 wokulandelanisa ongehla.
• Ku-2 ukusuka kwenye Khumbula bonyana abafundi batlola iinomboro ngamatshwayo ukufika e-10. Abafundi
nenye inomboro bangazalisa iinomboro ezingekho ekulandelaneni kweenomboro ukudlula e-10 nangabe:
esibuyabuyeleli saka • yenziwa ngomlomo
ku-2 hlangana ne-0 • amakarada weenomboro anikelwe bonyana afakwe eenkhaleni; nofana
na-20
• irhelo lamatshwayo weenomboro linikelwe. Abafundi bangagwala umuda ukusuka
Tlama amaphetheni enomborweni ekhethiweko ukuya endaweni efaneleko.
wakho
Ezinye iimbonelo zinikelwe ngenzasi:
• Tlama amaphetheni
Inambalayini eneenomboro ezinye ezitjhiyiweko
wakho weenomboro
30
31
32
34
36
38
40
41
43
46
47
48
50
Ukulandelanisa okubonisa ukubala uye phambili nemuva ngakunye eneenomboro ezinye
ezitjhiyiweko.
Abafundi bamadanisa iinomboro erhelweni elinikelweko. Bagwala umuda ukubonisa lapho
inomboro ekhethiweko kufanele ifakwe khona.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
40, 41, 42, __, 44; __, __, 47, ___, 49, 50.
50, 49, 48, __, __, 45, 44, ___, ____, 41, 40
Zitlolwe ngokulandelana uye phambili ngembuyeleli ezitjhiwo ngehla ezinezinye iinomboro
ezitjhiyiweko.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
2.2 Ukukopa, ukungezelela Ukulandelanisa kufanele Inambalayini etjengisa iinkhala okufanele abafundi bazizalise Iimfundo ezi-3
Amaphe- begodu nokuhlathulula kubonise ukubala ukuya
phambili nemuva
theni Ukukopa, ukungezelela 0
2
4
6
8
weenom- begodu nokuhlathulula • Nga-1 ukusuka Igridi yenomboro efake nofana etjhiye ukubala okulandelanako
boro. Ukulandelaniswa kunanyana ngiyiphi
kwenomboro elula inomboro hlangana na 1 3 5 7 9
ukufika ku-100. -1 nama-50
11 13 15 17 19
Tlama amaphetheni Ukubala uye phambili
wakho nga:
Tlama amaphetheni • Nga-10 ukusuka
wakho weenomboro kwenye nenye Abafundi bafaka umbala nofana bagubuzese iinomboro lokha nababala ngokweqa.
eyisibuyabuyeleli se-10 Ekupheleni kweThemu, irherho leenomboro likhuphukela ema-50. Abafundi bangasebenza
hlangana ne-0 na-50 ngokulandelanisa inomboro ezipheleleko ukusuka 1 ku– 50 nofana iingcenye
• Ngaku-5 ukusuka zokulandelanisa.
kwenye nenye
inomboro
esibuyabuyeleli saka
ku-5 hlangana ne-0
na-50
• Ku-2 ukusuka kwenye
nenye inomboro
esibuyabuyeleli saka
ku-2 hlangana ne-0
na-20
Tlama amaphetheni
wakho
• Tlama amaphetheni
wakho weenomboro
151
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU- 1 ITHEMU YESI- 2
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
152 UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
IIMFUNEKO ZOKUPHELA KONYAKA IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
YOKU-1 namaminithi
ama -24)
3.1 Ilimi lobujamo Ilimi lobujamo elithuthukiswe eThemini loku-1 lifanele lijayezwe njalonjalo Iimfundo ezi-2
Ubujamo, Hlathulula Ubujamo bento eyodwa ngesikhathi sokufundisa itlasi loke begodu kunqotjhwe esikhathini
ukuzijayeza ehlobene nenye, isib.phezu sokufundisa ngeenqhema ethemini yoke, zinikele isikhathi esifitjhani
nokubukela kwe, phambi kwe- ,emuva kwe-, sokuzijayeza ilimi njalo njalo.
ngesinceleni, esidleni, phezulu, phasi, Ukusebenza ngelimi lobujamo kungahlanganiswa ngokutlola irekhodi
hlanu kwe-. njengokugwala, ukufaka umbala nofana ukumadanisa imigwalo
Ubujamo nokubukela namagama. Lokhu kungenziwa ngesikhathi sukuzijamela.
Madanisa imibono ehlukahlukeneko Amanye amalimi wobujamo angajayezwa abafundi nabasebenza
yezinto ezifanako zangamalanga. ngobujamo babobusobubili 2-D.
Ubujamo neenkombatjhuba
Landela iinkombatjhuba
ukukhambakhamba ngetlasini
Landela iinlayelo ukubeka into eyodwa
ehlobene nenye, isib. Ukubeka ipensela
ngaphakathi kwebhoksi.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.2 Ukubona nokutjho izinto ezibusontathu Abafundi bangaragela phambili bakhe izinto ngematheriyali ebuyelelwe
Izinto ezi- 3-D ezingetlasini begodu neenthombeni yasetjenziswa godu nofana amabhlogo wokwakha nofana amakhidi
busontathu • Ubujamo bebholo (indulungu) wokwakha ngesikhathi sokuzijamela
(3-D) • Ubujamo bebhoksi (iphrizimu)
Amatshwayo wezinto
Ukuhlathulula, ukuhlela ngeengaba
nokumadanisa izinto ezibusontathu 3-D
ngokuya ngo:
• bungako
• mbala
• izinto ezigedekako
• izinto ezitjhelelako
Imisetjenzana enqophiweko
Tjheja begodu wakhe izinto
ezibusontathu 3-D ezinikelweko
ngokusebenzisa amamathiriyelii
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
aphathekako afana namabhulogo
wokwakha, ukubuyelela usebenzise
godu imatheriyali namakhidi wokwakha
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
3.3 Irherho yobujamo Irherho yobujamo Imisebenzi eminengi isebenzaa ngamajamo eGreyididi yoku-1 yenziwa ngokuzijayeza izinto
Amajamo Ukubona nokutjho Ukubona nokutjho eziphathekako. Yoke imisebenzi ifanele ihlanganiswe ngokutlola imisebenzi.
abobusobu- ubujamo obubusobubili ubujamo obubusobubili Abafundi bathoma ngomdlala otjhaphululekileko onamajamo ahlukahlukeneko, okufaka
bili (2-D) ( 2-D) ( 2-D) hlangana ukwenza iinthombe ngenquntu ezisikiweko zamajamo weJiyomethri. Lokhu
• Iindulungu • Iindulungu kungenziwa ngesikhathi sokuzijamela. Lokhu kungabuye kwenziwe ngesikhathi sesifundo
samaKghono wePilo.
• Aboncantathu • Aboncantathu
Abafundi bakopa iinthombe ezenziwe ngamajamo weJiyomethri. Iinthombe lezi
• Iinkwere • Iinkwere
zingatholakala eencwadini zokufundisa nofana kutitjhera. Lokhu kwenza abafundi
Amatshwayo Amatshwayo babone iindulungu begodu neenkwere zobungako obuhlukahlukeneko, iinkwere begodu
wamajamo wamajamo naboncantathu abasebujameni obuhlukahlukeneko begodu naboncantathu abanobujamo
Ukuhlathulula, ukuhlela Ukuhlathulula, ukuhlela obuhlukahlukeneko. Lokhu kungenziwa ngesikhathi sokuzijamela. Lokhu kungabuye
nokumadanisa ubujamo nokumadanisa ubujamo kwenziwe ngesikhathi sesifundo samaKghono wePilo.
obubusobubili (2-D ): obubusobubili (2-D ): Ukumadanisa nokuhlathulula izinto ezibobusombili (2-D): isayizi
• ubukhulu • ubukhulu Abafundi bamadanisa isayizi yezinto ezifana patsi ngobujamo Isib.
• umbala • umbala • Ukuhlela iindulungu ukusuka kencani ukuya kwekulu
• ibumbeko • ibumbeko • ukubeka zoke iinkwere ndawonye nofana ukubeka ezinesayizi efanako ndawonye
• amahlangothi • amahlangothi Sebenzisa ilimi lesayizi ukumadanisa amajamo ahlukahlukeneko, isib. “Ngagwala
anqophileko anqophileko uncantathu ngaphakathi kwesikwere, ngakho-ke uncantathu mncani kunesikwere”.
• amahlangothi • amahlangothi arondo Ukuhlathulula amajamo wabobusombili (2-D) : umbala
ayindulungu
Abafundi bakhuluma ngemibala yamabumbeko begodu bahlela amabumbeko ngokuya
ngemibala.
Ukubona nokutjho amagama wezinto begodu nemibala yazo, kanye nokumadanisa isayizi
yezinto kungajayezwa ngesikhathi sokusebenza ngamaphetheni
Ukulemuka nokutjho iindulungu, aboncantathu begodu neenkwere
Abafundi bafanele basebenze ngeendulungu nangeenkwere zamasayizi ahlukahlukeneko,
begodu nangaboncantathu abanobujamo obuhlukileko.
Kuqakathekile bonyana abafundi bangaboni isibonelo sobujamo obubodwa kwaphela.
Amasede wamabumbeko athengiswako amanengi anikela isibonelo esisodwa
saboncantathu.Abafundi bafanele bbakghone ukuwabona
• Aboncantathu abanamabumbeko ahlukahlukeneko begodu babekwa endaweni
ezihlukahlekeneko. Laba ngabanye baboncantathu:
153
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
154 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.3 Irherho yobujamo Irherho yobujamo • Iinkwere zamasayizi ahlukahlukeneko zibekwe ngeendlela ezihlukahlukeneko Iimfundo ezi-3
Amajamo Ukubona nokutjho Ukubona nokutjho
abobusobu- ubujamo obubusobubili ubujamo obubusobubili
bili (2-D) ( 2-D) ( 2-D)
• Iindulungu • Iindulungu
• Iindulungu zamasayizi ahlukahlukeneko. Lezi ngezinye zeendulungu.
• Aboncantathu • Aboncantathu
• Iinkwere • Iinkwere
Amatshwayo Amatshwayo
wamajamo wamajamo
Ukuhlathulula, ukuhlela Ukuhlathulula, ukuhlela Kuqakathekile bonyana abafundi basebenze ngeemfaniso zamakhadibhodi asikiweko
nokumadanisa ubujamo nokumadanisa ubujamo wamajamo. Lokhu kwenza abafundi babone abancantathu abahlukahlukeneko begodu
obubusobubili (2-D ): obubusobubili (2-D ): neenkwere ezibekwe eendaweni ezihlukahlukeneko.
• ubukhulu • ubukhulu Abafundi bahlela ngemihlobo amabumbeko ngokuya ngokuthi zinamahlangothi anqophileko
• umbala • umbala nofana ayindulungu.
• ibumbeko • ibumbeko Abafundi bahlela ngemihlobo begodu babeka amajamo ngeenqhema ngokuya ngokuthi
• amahlangothi • amahlangothi aboncantathu, aziinkwere, nofana azindulungu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
anqophileko anqophileko Umsebenzi uhlanganiswa ngokutlola imisebenzi. Imisebanzi le ifaka hlangana ukufa
• amahlangothi • amahlangothi arondo umbala, ukumadanisa amagama namabumbeko, njll
ayindulungu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YOKU-1 ITHEMU YESI-2
4. UKUMEDA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.1 Ukudlula kwesikhathi Abafundi bafanele bafunde bonyana kukhulunywa njani :
Isikhathi Khuluma ngokudlula • ngokulandelanisa izehlakalo
kwesikhathi • nangobude besikhathi
• Ukuhlela izehlakalo Abafundi baragela phambili nokuhlanganisa iindlela yokukhuluma ngesikhathi ngamalanga
eziqhelekileko ezisuke ngesikhathi sokufundisa setlasi loke nofana ngesikhathi sokunqopha sokufundisa
epilweni yabo ngesiqhema.
• Ukumadanisa Abafundi bakhuluma begodu baphendula imibuzo ephathelene nokuthi izinto zenzeka nini,
ubude besikhathi ngokusebenzisa ilimi elinjengokuthi ekuseni, ngemuva kwedina, ebusuku, ekuseni khulu,
kusetjenziswe ilimi isib. ngemuva kwesikhathi.
iskhathi eside, isikhathi
Abafundi balandelanisa izehlakalo ngokusebenzisa ilimi elinjengokuthi izolo, namhlanje,
esifitjhani, kabuthaka.
kusasa; amalanga weveke begodu neenyanga zonyaka
• Ukulandelanisa
Abafundi bamadanisa ubude besikhathi ngokusebenzisa ilimi elinjengokuthi isikhathi eside
izehlakalo
nofana isikhathi esifitjhani begodu msinyana nofana buthaka.
ngokusebenzisa ilimi
elifaka njengokuthi Abafundi bakhuluma ngokuhlela izehlakalo zepilo yabo. Bahlela ukulandelana
izolo, namhlanje, kweenthombe ezinjenga
kusasa. • amagadango wokwenza iimbedlezwana nofana ikopi letiye;
Ukutjho isikhathi • iinthombe ezitjengisa ukukhula komntwana aze abe mumuntu okhulileko;
• Ukuhlathulula • umzombelezo wepilo yeembandana, isib. Iqanda liba yikukhu, nofana iqanda liba
nakwenzeka into sirhwerhwe nofana iqanda liba iviyaviyani;begodu
ngokusebenzisa ilimi • izehlakalo eziqhelileko zelanga ( ukuvuka, ukuba sesikolweni, ukudlala, ukudla
isib. ekuseni,ngemuva kwamadina, ukulala).
kwedina, ebusuku,
Ragela phambili ukubeka amalanga wamabeletho ekhalendeni umnyaka woke
ekuseni khulu,
ngemuva kwesikhathi.
• Ukwazi amalanga
weveke, neenyanga
zonyaka.
• Ukwazi iinyanga
zonyaka
• Ukubeka amalanga
awamabeletho
ekhalendeni
155
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
156 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.2 Ukulinganisa Zoke iimedo zeGreyidi yoku-1 azikahleleki. Akukho ukumeda okuhlelekileko kobude
Ubude okungakahleleki emayunithini asezingeni enziweko.
• Ukumadanisa EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
nokuhlela ubude,
• ekumadaniseni okunqophileko kobude bezinto ngokubeka into hlanu kwenye;
ukuphakama nofana
ububanzi bezinto • ukuhlela nokumadanisa ubude nofana ukuphakama nofana ububanzi bezinto ezintathu
ezimbili nofana nofana ezinengi, ngokubeka izinto ngazimbili enye hlanu kwenye, bekufike lapho zoke
ezinengi ngokuzibeka izinto zilandelaniswe khona godu
enye eqadi kwenye. • Ukuthuthukisa ilimi lokukhuluma ngemahluko ngobude, ukuphakama, nobubanzi, njll
• Ukusebenzisa
Ngesikhathi sokusebenza ngokuzijamela ethemini yoke, abafundi bangazijayeza begodu
ilimi ukukhuluma
ngokumadanisa, isib. bahlanganise ukuhlela nokumadanisa ubude nofana ukuphakama nofana ububanzi bezinto
ubude, ubufitjhani, ezintathu nofana ezinengi, ngokubeka izinto ngazimbili ezinye hlanu kwezinye, bekufike
ububanzi. lapho zoke izinto zilandelaniswe khona.
• Ukulinganisa, Woke umsebenzi ufanele urekhodwe.
ukumeda,
ukumadanisa, ukuhlela
begodu urekhode
ubudeusebenzise
ISIGABA ESISISEKELO AMAGREYIDI 1-3
iimedo
ezingasisezingeni isib.
Izandla, igadango,
ubude bepensela,
izinto zokubala, njll.
4.3 Ukumeda Zoke iimedo zeGreyidi yoku-1 azikahleleki. Akukho ukumeda okuhlelekileko bobungako
Ubungako/ okungakahleleki emayunithini ahlelekileko enziweko.
ubudisi • Ukulinganisa, EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
ukumeda,
• ekumadaniseni okunqophileko kobungako bezinto ; begodu
ukumadanisa,
ukuhlela, • ukuhlela nokumadanisa ubungako bezinto ezintathu nofana ezinengi ngokubeka izinto
bekurekhodwe ubudisi, ngazimbili ezihlaleleneko, bekufike lapho zoke izinto zilandelaniswe khona godu
ngokusebenzisa iimedo • Ukuthuthukisa ilimi lokukhuluma ngokuhlukahluka bobungako
ezingasisezingeni
begodu nesikala Ngesikhathi sokusebenza ngokuzijamela ethemini yoke, abafundi bangazijayeza
sokudzimelela isib. begodu bahlanganise ukuhlela nokumadanisa ubungako bezinto ezintathu nofana
Amabhulogo, iintina ezinengi, ngokubeka izinto ngazimbili ezinye hlanu kwezinye, bekufike lapho zoke izinto
njll. zilandelaniswe khona. Woke umsebenzi ufanele urekhodwe.
• Ukusebenzisa
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ilimi ukukhuluma
ngokumadanisa isib.
lula, budisi, lula-khulu,
budisi-khulu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
4.4 Ukumeda Ukumeda Zoke iimedo eGreyidini yoku-1 azikahleleki. Asikho isimedo esihlelekileko zobungako Iinfundo ezi- 2
Umthamo/ okungakahleleki okungakahleleki emayunithini ahlelekileko enziweko.
Ivolumu • Ukumadanisa • Ukumadanisa Umnqopho ophakanyisweko weThemi yoku-1 bewukuthuthukisa ilimi lokukhuluma
nokuhlela ubungako nokuhlela ubungako ngomthamo odluleleko begodu nokumadaniswako.
obusamanzi okusamanzi iminqopho yethemu yesi-2 ungaba sekumadaniseni okuhlelekileko
(umthamo) (umthamo) okuse
iminqopho yethemu yesi-4 ungaphathelana nabafundi basebenza ngamayunithi wokumeda
obuseemumathini mumathini ezimbili
angakahleleki. Abafundi bangazijayeza begodu bahlanganise imiqondo lengesikhathi
ezimbili ezibekwe ezibekwe esinye eduze
sokusebenza ngokuzijamela okwenzeka umnyaka woke.
esinye eduze nesinye. Abafundi
kesinye. Abafundi bahlola ngokuthi Ukumadanisa okuhlelekileko wemithamo ongeemumathini
bahlola ngokuthi bathele esimumathini • Ukuthuthukisa ukuzwisisa komthamo begodu nelimi lokukhuluma ngawo.
bathele esimumathini sesithathu Abafundi bathoma ukucabanga begodu bakhulume ngomthamo ngokumadanisa bonyana
sesithathu nakutlhogekako. kungangani okungaphakathi kweemumathi ezimbili ezifana patsi (nofana imigwalo
nakutlhogekako. • Ukumadanisa yeemumathi ezimbili azifana patsi. Kunqotjhwe kokulandelako:
• Ukumadanisa nokuhlela ubungako -- zele begodu dududu
nokuhlela ubungako beketjezi/okusamanzi
-- nengi kuna/ncani kuna
beketjezi/okusamanzi okungathathwa
okungathathwa ziimumathi ezimbili -- fana na
ziimumathi ezimbili nazizeleko (umthamo) Abafundi bangazalisa begodu bathulule iimumathi ngokuthi ba:
nazizeleko (umthamo) • Ukusebenzisa • Madanisa amavolumu amabili nofana amanengi, iimumathi eziqaleka zihlukile ngokuthela
• Ukusebenzisa ilimi ukukhuluma esimumathini sesithathu.
ilimi ukukhuluma ngokumadanisa isib. Lokha abafundi nabakghona ukukhuluma ngamavolumu adluleleko (angenalitho begodu
ngokumadanisa isib. enengi kune, encani nazeleko, njll) begodu bamadanisa amavolumu (ahlukileko ngokuwaqala nje akude)
enengi kune, encani kune, encani, izele, eemumathini ezimbili ezifanako. Nqopha khulu khulu eemumathini ezibanzi nezincani
kune, encani, izele, edududu. ngobubanzi, isib.
edududu. • Ukulinganisa • zalisa ibhodlelo lamalitha ama-2 begodu nebhodlelo elinama-500ml alingane;
• Ukulinganisa, nokumeda;
begodu nokumeda; Ukumadanisa • Buza abafundi bonyana ngisiphi isimumathi sebhodlelo esinengi.
Ukumadanisa nokuhlela Abafundi bangahlola ngokuthi bathele iketjezi esimumathini sesithathu begodu nokumerega
nokuhlela bewurekhode umthamo ukuphakama kwalo.
bewurekhode ongeemumathini Abafundi abasese batjha kanengi abatjheji bonyana isimumathi sibanzi kangangani
umthamo ngokusebenzisa nababeka umbono ngevolumu; baqala kwaphela bonyana isimumathi sizaliswe kangangani
ongeemumathini izinto zokumeda Abafundi bafanele banikelwe ilemuko elinengi nakumadaniswa amavolumu eemumathini
ngokusebenzisa ezingakahleleki isib. ezinobubanzi obuhlukahlukeneko.
izinto zokumeda Iingobho neenkomitji.
ezingakahleleki isib. Ukurekhoda
Iingobho neenkomitji. Abafundi bafanele barekhode woke umsebenzi.
157
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YESI-2
5. UKUPHATHA IDATHA
158 UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO: AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YESI-2
ama -24)
UKUSEBENZA NGEBUTHELELO LEZINTO
5.1 Ukubuthelela nokuhlela Ukubuthelela nokuhlela Qala amanothi weThemu yoku-1 Isifundo -1
Ukubuthelela izinto izinto Ethemini ye-2 abafundi baragela phambili ngokusebenza ngokubuthelela ngendlela
nokuhlela Ukubuthelela nokuhlela Ukubuthelela nokuhlela efanako, kodwana bahlahlwa/bakhokhelwa kancani.
ngeengaba ngeengaba izinto ngeengaba izinto Lokha abafundi nasele bakhokhelwe ekambisweni yokuhlela ngeengaba begodu
kwezinto eziphathekako eziphathekako nokujamisela ibuthelelo, ngesikhathi sokunqophisa iinqhema, bangazijayeza wona
zangamalanga zangamalanga ngesikhathi sokuzijamela.
5.2 Ukujamiselela ibuthelelo Lokha abafundi sebejayele ukuphendula imibuzo ngebuthelelo labo, ungababawa
lezinto elihlelekileko Ukujamiselela ibuthelelo bonyana bahlathulule ibuthelelo labo, ngaphandle kokubakhokela ngemibuzo
Ukujamiselela lezinto elihlelekileko enqophileko.
ibuthelelo Ukugwala isithombe
lezinto sezinto ezihleleke Ukugwala isithombe sezinto
elihlelekileko ngemihlobo ezibuthelelweko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukucoca nokubika
5.3 Ukucoca nokubika ngokuhlelwa kwezinto
Ukucoca ngokuhlelwa kwezinto ezibuthelelweko
nokubika ezibuthelelweko
• Nikela iinzathu zokobana
ngokuhlelwa • Nikela iinzathu zokobana ibuthelelo lihlelwe bunjani
kwezinto ezi- ibuthelelo lihlelwe bunjani
• Phendula imibuzo ngo:
buthelelweko • Phendula imibuzo nge:
-- ukuhleleka ngemihlobo
-- ukuhleleka ngemihlobo kwenziwe bunjani
kwenziwe bunjani (indlela yekambiso)
(indlela yekambiso)
-- Ukuhlelela ngemihlobo
-- Ukuhlelela ngemihlobo kwebuthelelo kuqaleka
kwebuthelelo kuqaleka bunjani (umkhiqizo)
bunjani (umkhiqizo)
• Hlathulula ibuthelelo
• Hlathulula ibuthelelo begodu nemigwalo
begodu nemigwalo
• Hlathulula bonyana
• Hlathulula bonyana ibuthelelo lihleleke
ibuthelelo lihleleke bunjani
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
bunjani
Kuphakanyiswa bonyana ukusebenza ngomzombelezo wokuphathwa kwedatha kumnqopho weThemu ye-3 neye 4.
IGREYIDI YOKU-1 ITHEMU YESI-3
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
UKUTHUTHUKISA UMQONDONOMBORO: Bala ngeenomboro ezipheleleko
1.1 Ukubala izinto Ukubala izinto Khuyini okuhlukileko kuneThemini yesi-2
Ukubala ngokuthembeka ukufika ngokuthembeka ukufika Ethemini yesi-3, abafundi bandisa irherho lokubala. Kusese nomnqopho wokuzwisisa
izinto ema-50 ema-40 umthetho wekhadinali. Ngesikhathi seThemu le, abafundi bafanele bafunde ukubeka
Nikela ukulinganisa Nikela ukulinganisa izinto ngokuhleleka ngerherho nababalako ukuze nabahlola ukubala kwabo, ihlelo libasize
okuzwakalako kwenani okuzwakalako kwenani ukubala lula khulu.Isib, izinto zokubala zingabekwa ngamareyi.
lezinto ezingahlolwa lezinto ezingahlolwa
ngokubala ngokubalwa
NgeThemu le abafundi baragela phambili ngokwandisa amakghono wabo wokubala
nokuzijayeza:
• Ukubala zoke
• Ukubala okuragela phambili
• Umthetho weenomboro zekhadinali, begodu noku
• Sebenza ngamatheksti atloliweko
Ukulinganisa okunqophe patsi
Abafundi baragela phambili ngokuzijayeza ukubona ibuthelelo elincani lezinto
Ukubala ngeenqhema
Ukuze silekelele abafundi ukubala ngamakhefu wangakubili, ngakuhlanu begodu nanga-10,
bafanele babuthelele izinto ngazimbili, ngazihlanu begodu nangetjhumi ukuze babale
ibuthelelo lezinto. Amakarada weenomboro afanele akhangiswe kelinye nelinye ibuthelelo
ukutjengisa inani lezinto ezibaliweko.Ukubala ngeenqhema kuzokubalungiselela abafundi
bonyana bazwisise ukubuyabuyelela
Iinsetjenziswa:
Ukuyelela ngokutjheja kufanele kunikelwe imihlobo yeensetjenziswa ezisetjenziswako
• Ama-apharethasi ahlelekileko njengentambo enemincamo yokubala, ingasetjenziswa.
• I –abhakhasi ingasetjenziselwa ukuzijayeza ukubala ngeenqhema zangalitjhumi.
• Bangenza iinyanda zanga-2, iinyanda zanga-5 begodu nangalitjhumi ngeenthoro zomlilo
159 nofana iingojwana zokubala begodu babale koke.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
BESIKHATHI
IMIQONDO NAMAKGHONO : IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO
160 IIMFUNEKO ZOKUPHELA KONYAKA IMINQOPHO YETHEMU YESI-3 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
namaminithi ama
-24)
1.2 Ukubala uye phambili nemuva nga: Ukubala uye phambili nemuva Khuyini okuhlukileko kuneThemu yoku-1?
Ukubala uye • Ku-1 ukusuka kwenye nenye nga- EThemini yesi-3, abafundi sebabala ukufika ku-80
phambili inomboro hlangana ne-0 ne-100 • Ku-1 ukusuka kwenye nenye Baragela phambili nokubala ngeembuyabuyelelo za-2, 5
nemuva Ukubala uye phambili nga: inomboro hlangana ne-0 na-80 begodu ne-10
• Li-10 ukusuka kesinye nesinye Ukubala uye phambili nga: Imisetjenzana engezelelweko
isibuyabuyelelo se-10 hlangana ne-0 • Li-10 ukusuka kesinye nesinye Imisetjenzana yetlasi loke
ne-100 isibuyabuyelelo se-10 hlangana
Ukubala uye phambili nemuva ukufika ku-80
• Ku-5 ukusuka kesinye nesinye ne-0 na-80
• Abafundi babala baye phambili nemuva
isibuyabuyelelo saka ku-5 hlangana • Ku-5 ukusuka kesinye nesinye
ne-0 ne-100 isibuyabuyelelo saka ku-5 • Utitjhere ukhomba iinomboro egridini yeenomboro
hlangana ne-0 na-80 njengombana abafundi babala bebafike ku-70.
• Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-2 hlangana • Ku-2 ukusuka kesinye nesinye • Abafundi babala ngakuhlanu ukusuka ku-25 ukuya ukufika
ne-0 ne-100 isibuyabuyelelo saka ku-2 ku-60.
hlangana ne-0 na-80 • Abafundi babala ngamatjhumi ukuya phambili ukusukela
ku-0 ukufika ku-80
Ukubala ngokweqa kusetjenziswa abo-5,nabo-10 ukufika
ku-80
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Abafundi babala nga-10 ukufika ku-50 ngesikhathi
utitjhere akhomba itjhadini leenomboro
• Utitjhere ukhomba iimbuyeleli zaka -5 etjhadini le-100
abafundi bona babale.
• Abafundi babala baye phambili begodu nemuva ngabo-10
Ngokusetjenziswa itjhadi le-100, abafundi bafanele
baphendule emiyelelweni yemihlobo efanako:
• Bala uye phambili ngamatjhumi ukusuka ema-20
• Bala uye umva ngakunye ukusukela ema-56.
• 80, 70, 60: batjho iinomboro ezintathu ezilandelako
kusetjenziswa itjhadi le-100.
Umsebenzi wokuzijamela
Amakghono wokubala ngokweqa kudingeka bonyana
asetjenziswe emisetjenzaneni etloliweko. Isibonelo:
Abafundi bakhambisa amehlo:
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Baqedelela ukulandelana kweenomboro ezilula; begodu
• Bazalisa iinomboro ezitjhiyiweko emkhondweni
weenomboro begodu nenambalayini, nitlola iinomboro
ezimbili ezilandelako 66, 65, 64,-----,-----,
UBUDE
BESIKHATHI
IMIQONDO NAMAKGHONO : IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO
IIMFUNEKO ZOKUPHELA KONYAKA IMINQOPHO YETHEMU YESI-3 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
namaminithi ama
CAPS
-24)
1.3 Ukwazi nokufunda iinomboro Ukwazi nokufunda iinomboro Ngikuphi okuhlukileko kuneThemini yesi-2?
Amatshwayo • Ukwazi nokufunda amatshwayo • Ukwazi nokufunda amatshwayo Ethemini yesi-3, irherho leenomboro likhuphukele ema-80.
weenomboro wenomboro kusukela ku- 0 ukufika wenomboro 0-80 Kwanjesi kulindeleke bonyana abafundi batlole amatshwayo
namagama ku-100 • Ukutlola amatshwayo weenomboro ukufika ema-20. Kudingeka bonyana bakghone
weenomboro • Ukutlola amatshwayo weenomboro weenomboro 0-80 ukwenza lokho ngombana babala ukufika ema-20 begodu
ukusukela ku -0 ukufika ku-100 kutlolwa imitjho yeenomboro. Abafundi baragela phambili
• Ukwazi nokufunda amabizo
nokuzijayeza ukufunda nokutlola amagama weenomboro
• Ukwazi nokufunda amabizo weenomboro 1-10
zabo. Bafanele bakghone ukumadanisa itshwayo negama
wenomboro kusuka ku- 1ukufika-10 • Tlola amabizo wenomboro 1-10 lenomboro. Imisetjenzana yencwadi yokusebenzela nokutlola
• Ukutlola amabizo wenomboro ngetlasini-incwadi yokusebenzela ingenziwa ngesikhathi
• Kusukela ku-1ukufika ku-10 sokuzijamela.
Isibonelo somsebenzi wokutlola:
Madanisa amagama nezinto
Kunye
Kubili
Kuthathu
Kune
Kuhlanu
Sithandathu
Likhomba
Bunane
Litjhumi
Okulindeleke ebafundini?
• Bangakghona ukufunda amatshwayo weenomboro
ukufika e-50
• Bakghona ukutlola amatshwayo weenomboro ukufika
e-20
• Bakghona ukufunda amagama weenomboro ukufika e-10
• Bakghona ukutlola amagama weenomboro ukufika e-10
161
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
BESIKHATHI
IMIQONDO NAMAKGHONO : IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO
162 IIMFUNEKO ZOKUPHELA KONYAKA IMINQOPHO YETHEMU YESI-3 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
namaminithi ama
-24)
1.4 Ukuhlela nokumadanisa, Izinto Ukuhlela nokumadanisa izinto Ngikuphi okuhlukileko eThemini 2?
Ukuhlathulula, • Madanisa ibuthelelo lezinto ngokuya ezi-15 Ethemini 3,abafundi baragela phambili ngoku:
ngobunengi, ngambalwa, ngokunengi • Madanisa ibuthelelo lezinto
ukumadanisa, • ngokuhlela nokumadanisa izinto
khulu,ngokuncani khulu, okunengi ngokuya ngobunengi,ngokunca
nokuhlela kuna, okuncani kuna, okulinganako, ni,ngokunengi khulu,ngokuncani • ngokuhlela nokumadanisa iinomboro; noku
iinomboro ngokunengi, okulingana na, kuna,ngokulingana • sebenzisa ilimi lokuhlela nokumadanisa.
okuhlukileko na,okungafaniko
Imisetjenzana iragela phambili
• Ukuhlela ibuthelelo lezinto kusukela • Ukuhlela ibuthelelo lezinto
kokukhulu khulu kuya kokuncani kusukela kezinengi khulu ukuya Utitjhere utjho inomboro isib. 12
khulu nakokuncani khulu ukuya kezincani khulu begodu nezincani Utitjhere ubuza imibuzo: ikuphi inomboro le phezulu
kokukhulu khulu khulu ukuya kezikhulu khulu kwenambalayini?
• Izinto ezihlukahlukenekoukufikela • Ukuhlela izinto kufikela e-15 Ngiyiphi inomboro eza ngemuva kwenomboro u-12
e-100 Ukuhlela nokumadanisa iinom- Ngiyiphi inomboro eza ngaphambili kwenomboro u -12?
Ukuhlela nokumadanisa iinomboro boro
• Ukuhlela iinomboro • Ukuhlela iinomboro Ngiyiphi inomboro eza ngemuva kwenomboro 12?
-- Kusukela kencani khulu ukuya -- Kusukela kencani khulu ukuya 12 munengi nga-1 kune------
kekulu khulu nakusukela kekhulu kekulu khulu nakusukela 12 mncani nga 1 kune------
khulu kuya kencani khulu. kekhulu khulu kuya kencani
ISIGABA ESISISEKELO AMAGREYIDI 1-3
-- Ngaphambili,ngemuva,phakathi/ khulu.
hlangana -- Ngaphambili,ngemuva,phakathi/
-- Ukusebenzisa inambalayini 0-100 -- hlangana
• Ukumadanisa iinomboro -- Ukusebenzisa inambalayini
ezipheleleko ngokuya ngobunani 0-80
kuna, okukhulu kuna, engaphasi • Ukumadanisa iinomboro
kuna, ilingana na ezipheleleko ngokuya ngobunani
• Kunye –nakhunye kuna,okukhulu kuna, engaphasi
kokukhambelanako kuna,ilingana na
• Izinto ezihlukahlukenekoukufikela • Kunye –nakhunye
e-100 kokukhambelanako
Sebenzisa inomborosikhundla • Izinto ezihlukahlukenekoukufikela
ukutjengisa ukulandelana ,indawo e-15
namkha ubujamo Sebenzisa inomborosikhundla
• Beka izinto emudeni ngokulandelana ukutjengisa ukulandelana ,indawo
kusukela keyokuthoma ukufika namkha ubujamo
keyamatjhumi namkha keyokuthoma • Beka izinto emudeni kusukela
ukuya keyokugcina, Isib. Yokuthoma, keyokuthoma ukuya keyesitjhumi
yesibili, yesithathu..yetjhumi nofana keyokuthoma ukuya
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
yamaswaphela(iinomboro zeodinali) keyokugcina isib.kokuthoma,
Amahlangothi womraro weenom- kwesibili,kwesithathu ...
boro zekhadinali ngerherho lokusuka keyetjhumi, yokugcina (iinomboro
ekuthomeni ukuya etjhumini ezima odinali)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.5 Thoma ukulemuka Ukubona Ngikuphi okuhlukileko kune Themu yesi-2?
Ubukhulu ubukhulu bedijithi ubungako bedijithi NgeThemu leli abafundi bathoma ukuphula iinomboro zibe matjhumi nangakunye /
bedijithi okungenani iinomboro bokungasenani amayunithi kusetjenziswa:
zamadijithi ama-2 iinomboro zamadijithi • Ukubuthelela izinto zibe matjhumi; begodi.
ukufika kama-20 ama-2 ukuya ku-15 • Nehlobo lokutlola u-14=10 no 4
• Ukuphula iinomboro • Hlukanisa iinomboro Ukuzwisisa kobukhulu bedijithi buthuthukiswa kusukela esigabeni esisisekelo nesiphakathi.
zamadijithi amabili izinamadijithi amabili eGreyidini 1 abafundi bathoma ukucabanga ngeenqhema zezinto ezibekwe ngamatjhumi
ukuya ngamatjhumi ngamatjhumi nofana njenge unithi.Bathoma ukudlula ekuboneni itjhumi njengezinto ezilitjhumi
nangakunye ukufika nangakunye ukuya ezihlukeneko, njenga nje sebabona u-10 njengeyunithi elilodwa nofana njenga-1 yetjhumi.
ema-20 isib. 12 li-10 e-15 isib.u-12 li-10 Ukuthoma ukwizisisa ubukhulu bedijithi ethemini le,abafundi bafanele ba:
naku-2 naku-2 • bazi amagama weenomboro bebabale ngokulandelanisa ngokuzithemba okungasenani
ukufika ema-20
• ukutlola nokufunda amatshwayo weenomboro
• ukwenza ukuhlanganisa nokukhupha okulula
• ukubala izinto ngokwenza ngokubuthelela:na
• ngokukghona ukujamiselela iinqhema/okubuthelelweko
Ukuphula iinomboro zibe matjhumi nangakunye/nangamayunithi
Umnqopho eGreyidini 1 kukwenza ibuthelelo lamatjhumi nangokuhlukeneko okunga kunye.
Ngaphambili kokuphula iinomboro zibe matjhumi nangakhunye, abafundi kufanele bathole
ithuba elaneleko lokuzijayeza ukuphula iinomboro ngeendlela ezihlukeneko ngeThemu
yoku-1 no 2.Lokho kufanele kwenzeke ngehlobo lokwenza nangokutlola.
Ukusebenzisa iinsetjenziswa eziphathekako
Iimbonelo eziphathekako ziqakathekile ekwakheni umqondonomboro
wabafundo,ukujamiselela iinomboro nomthetho wobukhulu bedijithi.Nakubalwa
ngamatjhumi nangokubeka ngeenqhema zetjhumi,abafundi bazokuthoma ukuzwisisa
bonyana iimbuyabuyeleli ze-10 zinikela ibhrorho nakubalwako isib.26,27,28,29,30,31.
Bafanele bathome ukulemuka bonyana igama netshwayo 10 kujamele iyunithi elilodwa.
Ukusebenza ngezinto eziphathekako ngokuzibeka ngeenqhema ukubumba itjhumi
langakunye bebazwisise bonyana i-10 libuthelelo linye lezinto ezilitjhumi ezikhamba
ngakhunye.
Ukutjengisa abafundi ibuthelelo langokwetjhumi bese ubatjele bonyana i-14 litjhumi –li-1
naku-4 okuhlukeneko, kuzokwakha umqondo wokobana i-14 lilitjhumi eli-1 na -4 yezinto
ezihlukeneko.
Ukubuthelela izinto ezihlukeneko kwenza ibuthelelo lokwetjhumi kube nokuzwisiseka khulu.
Ukusebenzisa i-abhakhasi,abafundi kufanele batjengise:
Itjhumi linye
163 Itjhumi linye nokukodwa oku-2;
Itjhumi linye noku-3 okungakodwa begodi
Itjhumi linye naku-4 okungakodwa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
164 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.5 Thoma ukulemuka Ukubona Lindela abafundi bonyana babale ngakunye ukwenza ibuthelelo langa litjhumi .Kabanengi
Ubukhulu ubukhulu bedijithi ubungako bedijithi kuzokuba ngiyoyodwa indlela ukutjho inomboro nofana ukutjho bonyana zingakhi lapho.
bedijithi okungenani iinomboro bokungasenani Abafundi bangenza iinyanda zangalitjhumi nezihlukeneko ngakunye ukutjengisa bonyana
zamadijithi ama-2 iinomboro zamadijithi i-11 angaphulwa ngokuba yinyanda yinye yetjhumi nokukodwa okuhlukeneko.
ukufika kama-20 ama-2 ukuya ku-15
• Ukuphula iinomboro • Hlukanisa iinomboro
zamadijithi amabili izinamadijithi amabili
ukuya ngamatjhumi ngamatjhumi
nangakunye ukufika nangakunye ukuya
ema-20 isib. 12 li-10 e-15 isib.u-12 li-10
naku-2 naku-2 Ukungenelanisa amakhyubhu kungapakwa ukwenza umbhotjhongo nofana ikholomu ye-10
Amakarada wobukhulu bedijithi angasetjenziswa ukutjhengiswa amatjhumi nangakunye.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukudlulela ethekisini etloliweko
Ukujamiselela ngeenthombe ngebuthelelo lamatjhumi nangakunye.
Abafundi bangajanyiselelwa ngeenthombe ezivumela ibuthelelo lamatjhumi nangakunye
okuseleko.
Isibonelo.
Ekupheleni kweThemu abafundi bafanele bakghone ukutlola:
13 = 1 itjhumi naku 3 okukodwa okuhlukeneko
13 = 10 noku 3
Iinsetjenziswa ezitjhukunyeziweko
Izinto ezingabuthelelwa:
• Iingojwana zokubala
• Izinto zokubala ezingathungelelwa
• Iingojwana zomlilo
• Iingojwana ze ayisikhrimu
• Amakhyubhu angenelanako
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Imincamo yokubala
• I-abhakhasi
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Ngikuphi okuhlukileko kuneThemu yesi-2
Amathek- alandelako nawurarulula alandelako nawurarulula Amakghono wokubala aragela phambili nokujayezwa.
hiniki wok- imiraro uhlathulule imiraro bewuhlathulule
neensombululo zemiraro: iinsombululo zemiraro Ukubuyelela kabili nokuhlukanisa phakathi kungasetjenziswa njengethekhniki yokubalisisa
urarulula ngeThemu leli. Nanyana kunjalo, abafundi bafanele baragele phambili nokuzijayeza
imiraro • Ama-apharethasi • Ama-apharethasi
aphathekako isib. izinto aphathekako isib. ukubuyelela kabili nokuhlukanisa phakathi imiraro yamagama nojameni obutjhaphukileko.
zokubala Izinto zokubala Ekupheleni kweThemu le abafundi bathoma ukurarulula imiraro yamagama basebenzise
• Iinthombe zokugwala • Iinthombe zokugwala amathekhiniki alandelako:
iimbalo zendatjhana isamba sendatjana • Ukugwala nofana ama-Apharethasi aphathekako
• Ukwakha nokuphula • Ukukwakha nokuphula • Ukwakha nokuphula iinomboro
iinomboro iinomboro
• Ukubuyelela kabili nokuhlukanisa phakathi
• Ukubuyelela • Ukubuyelela
nokuhafula phakathi nokuhlukanisa • Amanambalayini
• Amanambalayini phakathi Qala amanothi eThemini yesi-2.
• Inambalayini
esekelwe ngezinto
eziphathekako
1.7 Rarulula imiraro Rarulula imiraro
Ukuh- yamagama yamagama
langanisa ezisebujameni ezisebujameni
bewuhlathulule bewuhlathulule
nokukhupha iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka
ukuhlanganisa ukuhlanganisa
nokukhupha nempendulo nokukhupha nempendulo
ukufika e-20. ukufika e-15.
1.8 Rarulula imiraro Rarulula imiraro Qala iThemu yesi-2 iimbonelo zemiraro kodwana sebenza ngeenomboro ukufika e-15.
Ukuh- yamagama esebujameni yamagama esebujameni
langanisa begodu uhlathulule bewuhlathulule
iinsombululo zakho iinsombululo zakho
okubuyele-
zemiraro, ezifaka zemiraro, ezifaka
lweko ukuhlanganisa ukuhlanganisa
kurholela okubuyelelweko okubuyelelweko
ekubuy- okurholela okurholela
abuyeleleni ekubuyabuyeleleni ekubuyabuyeleleni
nempendulo ukufika e-20 nempendulo ukufika e-15
165
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
166 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.9 Ukurarulula Ukurarulula Bona iThemu yoku-1 iimbonelo zemiraro kodwana sebenza ngeenomboro ukufika e-15.
Ukubuthele- imiraro yamagama imiraro yamagama
la nok- ezisebujameni ezisebujameni
bewuhlathulule bewuhlathulule
wabelana
iinsombululo zakho iinsombululo zakho
okurholela ufake ukwabelana ufake ukwabelana
ekuhlu- ngokulingana ngokulingana
kaniseni nokubuthelela nokubuthelela
ngeenqema ngeenqema
kweenomboro kweenomboro
ezipheleleko ukufika ezipheleleko ukufika
e-20 kanye nempendulo e-15 kanye nempendulo
ezingahle zifaka iinsalela ezingahle zifaka iinsalela
1.11 • Khumbula bewufanise • Khumbula bewubone Isamba – amaranda kwaphela
Imali imali eziihlavu iinhlavu zemali Abafundi basebenza nga R1, R2, R5, R10 ne R20 imali yamaphepha. Abafundi
zeSewula Afrika : yeSewula Afrika 5c, bahlanganisa isamba ukufika ema-R20 ngokwenza basebenzisa ukudlala ngemali.
-- Iinhlavu (5c, 10c, 20, 10c, 20c, 50c, R1, R2,
Isibonelo:
50c, R1, R2; R5) R5
ISIGABA ESISISEKELO AMAGREYIDI 1-3
R5 + R10 = R15
-- nemali emaphepha • Sombulula imiraro
yemali okufaka R10 + R10 + R10 =R30 – ukuhlanganisa ngokubuyelela
iR10 ne R20
hlangana isamba R5 +R2 + R8 = R15 – ukuzaliselela ukufika e- 10
• Sombulula imiraro
nethjentjhi ukuya ku Itjhentjhi: amaranda kwaphela
efaka hlangana
R20 nangamasende
amanani wemali Abafundi basebenza nge R1, R2, R5, R10 ne R20 imali yephepha. Benza ukukhupha
ukuya ku20c
netjhentjii yama R20 ngokusebenzisa imali yamaphepha.
neyamasende ukufika Abafundi baqedelela amaphepha wokusebenzela lokha nabasebenzisa itjhentjhi yezinto
ku-20c abazithenge R20 nofana ngaphasi
Isibonelo:
R10 – R8 =R2
R15 – R5 =R10
UKUBALA OKUSEJAMENI OBUTJHAPHULUKILEKO
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.12 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Abafundi balindeleke bonyana bararulule ukubalisisa okusebujameni obutjhaphulukileko
Amathekh- alandelayo nawubalako alandelayo nawenza ngokusebenzisa amathekhiniki alandelako:
iniki (iindle- • Ama-apharethasi iimbalo • Ukwakha nokuphula iinomboro
la namkha aphathekako • Ama-apharethasi • Ukubuyelela kabili nokuhlephula phakathi
amaqhinga) njengezinto zokubala aphathekako
• Amanambalayini
• Gwala iinthombe • Ukwakha bewuphadhle
Qala amanothi weThemu yesi-2
• Ukwakha bewuphadhle iinomboro
iinomboro • Ukubuyelela
• Ukubuyelela nokuhafula phakathi
nokuhafula phakathi • Iinamba layini
• Amanambalayini esekelwe ngamas
apharethasi
aphathekako isib.
ukubala umncamo
167
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
168 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 Irherho leenomboro: Irherho leenomboro: Ngikuphi okuhlukileko kuneThemu yesi-3?
Ukuh- 0 - 20 0 - 15 EThemini 2, ukubalisisa kwerherho leenomboro selandisiwe ukusuka e-10 ukuya -15
langanisa • Hlanganisa ukufika • Hlanganisa ukufika Ukuze usebenze ngamatshwayo wokuhlanganisa nowokukhupha, abafundi kufanele babe
nokukhupha ku-20 ku-15 nelemuko elaneleko loku:
• Khupha ukufika ku- 20 • Khupha ukusuka ku- • Ukusebenzisa nokuzwisisa ilimi lokuhlanganisa nelokukhupha
• Sebenzisa 15
• Ukubala koke
amatshwayo afaneleko • Sebenzisa
• Ukubala uye phambili kusuka enomborweni ekulu
(+, –, =, ) amatshwayo afaneleko
(+, –, =, ) • Ukuhlela nokumadanisa iinomboro
• Ukuphrakhthisa
ukulumbana • Ukuphrakhthisa Amaqhinga wokubalisa nakwenziwa ukuhlanganisa nokukhupha
kwenomboro ukufika ukulumbana NgeThemu le abafundi bazokuragela phambili nokusebenzisa amaqhinga alandelako:
e-10 kwenomboro ukufika • Ukwenza ukuhlanganisa ngokubala koke
e-9
• Ukwenza ukuhlanganisa ngokubala uye phambili
• Ukubala uye phambili ukusuka enomborweni ekulu
• Ukwenza ukukhupha ngokukhupha okhunye
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukukhupha ngokubala aye emuva
NgeThemu le abafundi bozoku:
Ukutjhugulula inomboro yetjhumi begodu akhuphe nofana kuhlanganiswe yinye.
Iqhinga leli lingafundiswa ngerherho eliphasi leenomboro belisetjenziswe eenomborweni
eziphezulu.
Isibonelo:
9+6=
Abafundi bangathi kibo: “Ngizokukhupha yinye ku-6 begodu ngihlanganise ne-9 ukwenza
i-10.”
Bese 9 + 6 angatlolwa nje 10 + 5 = 15
Isibonelo :
8+5=
Abafundi bangathi kibo “ngizokukhupha 2 koku -5 begodu ngihlanganise koku-8 ukwenza
i-10”.
Bese 8 + 5 angatlolwa banjesi 10 + 3 = 13
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 Irherho leenomboro: Irherho leenomboro: Nakufundwa iqhinga leli, abafundi basebenzisa iinsetjenziswa eziphathekako ukuzwisisa
Ukuh- 0 - 20 0 - 15 iqhinga.
langanisa • Hlanganisa ukufika • Hlanganisa ukufika Isibonelo: buthelela izinja ukuze zenze i- 10
nokukhupha ku-20 ku-15
• Khupha ukufika ku- 20 • Khupha ukusuka ku-
• Sebenzisa 15
amatshwayo afaneleko • Sebenzisa
(+, –, =, ) amatshwayo afaneleko
• Ukuphrakhthisa (+, –, =, )
ukulumbana • Ukuphrakhthisa
kwenomboro ukufika ukulumbana
e-10 kwenomboro ukufika 9+4
e-9
10 + 3
9 + 4 = 10 + 3 = 13
Ukuphula inomboro ibe yingcenye encani ukwenza ukubalisisa kube lula
Abafundi bazophula inomboro ibe ziingcenye ezihlukeneko. Bazokuphula inomboro ibe
ziingcenye ezilawulekako ebafundini.
• Ukusebenzisa abotjhobi neenomboro ukutjengisa ukucabanga
8+6=
8+2+4
8 + 2 → 10 + 4 = 14
8+7=
8+2+5
8 + 2 → 10 + 5 = 15
15 – 9 =
169 15 – (5+4)
15 – 5 → 10 – 4 = 6
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
170 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 Irherho leenomboro: Irherho leenomboro: Ukusebenzisa ilwazi elidlulileko njengethekhniki
Ukuh- 0 - 20 0 - 15 Amathekhiniki atjengiswe ngenzasi avumela abafundi bonyana bahlele ukubala nomqondo
langanisa • Hlanganisa ukufika • Hlanganisa ukufika weenomboro. Ukuzijayeza amathekhiniki angenzasi kuzokhuthaza abafundi bonyana
nokukhupha ku-20 ku-15 bakghone ukutjengisa ubudlelwano obuphakathi kweenomboro nokufundisa abafundi
bonyana bangakwazi ukusenzisa iwazi labo ukuze babalisise.
• Khupha ukufika ku- 20 • Khupha ukusuka ku-
15 Ukubeka inomboro ekulu ekuthomeni ukuze akghone ukubala aye phambili nofana
• Sebenzisa uye emuva.
amatshwayo afaneleko • Sebenzisa
4 + 12 =
(+, –, =, ) amatshwayo afaneleko
(+, –, =, ) Hlela kabutjha u- 4 + 12 njenge 12 + 4 bese ubala uye phambili 4 kusuka ku12.
• Ukuphrakhthisa
ukulumbana • Ukuphrakhthisa Ukubona ukubuyelela kabili okuseduzane
kwenomboro ukufika ukulumbana 7+6
e-10 kwenomboro ukufika Abafundi bangahlathulula bona isibalo singatlolwa bunjesi 6 + 6 -1 (ukubuyelela kabili bese
e-9 uhlanganise na- 1) nofana 7 + 7 - 1 (buyelela kabili i-7 bese ukhupha 1).
Abafundi bangahle barekhode amaqhinga wabo ngokusebenzisa abotjhobi
6 + 6 ➝ 12 + 1 = 13
Ukusebenzisa ilwazi eliphikisako lobudlelwano obuphakathi kokuhlanganisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokukhupha
15 – 9 =
Abafundi bayazi bonyana isibalo sengabuye sitlolwe njengokuhlanginisa. “Ngiyazi bonyana
9 + = 15.”
Abafundi bangahle basebenzise ukubala uye phambili ukuze bakwazi ukubalisisa.
Ukulumbana kweenomboro
Ukuze uzijayeze ukulumbana kweenomboro abafundi bafanele banikelwe imisetjenzana
ehlukahlukeneko okufanele bayenze. Lokhu kwenziwa ngesikhathi sokuzijamela.
Inambalayini nayo ingasetjenziswa ukuze bazijayeze ukulumbanisa ukufika e-9
Umqondo wokubuyelela kabili
Abafundi kufanele batlole imitjho yeenomboro ngeThemu le:
1 + 1 = 2 – 1 =
2 + 2 = 4 – 2 =
3 + 3 = 6 – 3 =
4 + 4 = 8 – 4 =
Abafundi kufanele bakghone ukuphendula imibuzo elandelako:
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukubuyelela kabili 3
• Bayini abobuthathu ababili?
• Ngigeda isithandathu ngokubuyelela kabili. Ayini amaphuzu wami?
• Mangaki amakowusu asempareni ezi-5 zamakowusu?
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-3 YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
1.14 • Hlanganisa ngokubuyelela • Hlanganisa ngokubuyelela Ngikuphi okuhlukileko ethemeni 2?
Ukuh- (o.k.inomboro efanako kufika) (o.k.inomboro efanako kufika) Ethemeni 3, abafundi baragela phambili nokuthuthukisa ilimi loku
langanisa ku-20 e-15 kokuhlanganisa okubuyelelako. Isibonelo
okubuyele- • Sebenzisa amatshwayo • Sebenzisa amatshwayo • Kuna -2 ubunengi babo 3
lweko afaneleko ( +, =, ) afaneleko ( +, =, ) • Iinqhema ezi-4 zabo- 2
kurholela Abafundi baragela phambili nokutlola imitjho yeenomboro ukujamisela
ekubuy- kweenthombe. Ukubala ngokweqa kufanele kuragele phambili ukulekelela
abuyeleleni abafundi ukubala izinto ezibuthelelweko eziseenthombeni. Nangabe iinthombe
nofana izinto zibuthelelwe ngazimbili, abafundi bafanele babale ngazimbili
ingasi ngakuny ukuthola inani lezinto.
1.16 Umnqopho wenomboro: Umnqopho Ngikuphi okuhlukile ethemeni yesi-2?
Iimbalo ze- irherho 20 wenomboro:irherho 15 Ethemeni 2, irherho leenomboro lingezelelwe kusuka e-10 ukufika e-15
hloko • Hlela isethi enikelweko • Hlela isethi leenomboro Iimbonelo zemibuzo nemisetjenzana okungabuzwa begodu kewnziwe:
leenomboro ezikhethiweko ezikhethiweko olinikelweko • Thoma ku-3 bese ubale uye phambili ngokunye bewufike e-10
• Madanisa iinomboro ema-20 • Madanisa iinomboro bewutjho • Abafundi bajama umjeje begodu babuze: Ngubani wokuthoma, wesibili,
bewutjho bonyana ngiyiphi bonyana ngiyiphi enengi wesithathu nofana wokugcina?
enengi nofana encani nofana encani
• Ngiyiphi engaphasi nge-14 nofana 8?
• Ukwazi bonyana ngiyiphi • Ukwazi bonyana ngiyiphi
inomboro enokunengi nga-1 inomboro enengi nga-1 nofana • Ngiyiphi ekulu li-8 nofana yi-4?
nofana ngencani nga-1 encani nga-1 • Ngiyiphi engaphasi ngaku-2 kune-13?
• Ukwazi bonyana ngiyiphi • Ukwazi bonyana ngiyiphi • Ngiyiphi ekulu nga-2 kune -8
inomboro ekulu nga-2 nofana inomboro enengi nga-2nofana • Nginikela inomboro ehlangana kuka-1 na-3
ngokuncani nga-2 encani nga-2 • Nginikela inomboro ehlangana kwe-10 ne-14. Ingabe inomboro yinye
• Ukuwazi bonyana ngiyiphi • Ukukhumbula msinyana: kwaphela?
inomboro enokunengi nga-10 • Ukulumbana kwenomboro • Beka amakarada weenomboro ngehlelo elisuka kencani khulu ukuya kekulu
nofana incani nga-10 ukufika e-5 khulu.
• Ukukhumbula msinyana: • Ukukhumbula amaphuzu Ukukhumbula msinyana
• Ukulumbana kwenomboro wokuhlanganisa Ngitjengisa inomboro enginga yihlanganisa ukuze ngenze oku-5 (ukutlola
ukufika ke-10 nowokukhupha e-5 phasi nofana kusetjenziswe ubukhulu bedijithi nofana amakarada weflaridi)
• Ukukhumbula amaphuzu Amaqhinga wokubala • 1
wokuhlanganisa Ukusebenzisa amaqhinga • 2
nowokukhupha e-10 wokubala ukuhlanganisa • 3
Amaqhinga wokubala nokukhupha ngekghono • 4
Ukusebenzisa amaqhinga elifaneleko:
Ngitjengise inomboro eseleko____ nange kususwa ku-5(ukutlola phasi
wokubala ukuhlanganisa • Beka inomboro ekulu maqangi nofana ukusebenzisa ubukhulu bedijithi nofana amakarada weflaridi)
nokukhupha ngekghono ukuze ubale uye phambili
elifaneleko: nofana ubale uye emuva • 1
• Beka inomboro ekulu maqangi • Inambalayini. • 2
ukuze ubale uye phambili • Ukubuyelela kabili nokuhafula • 3
nofana ubale uye emuva • 4
• phakathi
171 • Inambalayini. 1 + 2 = 3 uyini u- 2 + 1? Ipendulo iyafana?
• Ukwakha nokuphula
• Ukubuyelela kabili nokuhafula 3 + 1 = 4 uyini u 1 + 3? Ingabe ipendulo iyafana?
phakathi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
172 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.16 Umnqopho Umnqopho Amaqhinga wokubala :
wenomboro: irherho wenomboro:irherho 15
Iimbalo 20 Ukusebenzisa amaqhinga wokubalisisa ekuhlanganiseni nekukhupheni ngokuphumelelako.
zehloko • Hlela isethi
• Hlela isethi enikelweko leenomboro Hlanganisa okulandelako ngokubeka inomboro ekulu kokuthoma bese ubala uye phambili :
leenomboro ezikhethiweko 1+2
ezikhethiweko olinikelweko
2+3
• Madanisa iinomboro • Madanisa iinomboro
ema-20 bewutjho bewutjho bonyana 1+4
bonyana ngiyiphi ngiyiphi enengi nofana Buyelela kabili u-1
enengi nofana encani encani
• Ukwazi bonyana • Ukwazi bonyana Bayini abo-2 ababili?
ngiyiphi inomboro ngiyiphi inomboro Kuyini ukuhlukana phakathi kwa-4
enokunengi nga-1 enengi nga-1 nofana
nofana ngencani nga-1 encani nga-1 Ngokusebenzisa inambalayini
• Ukwazi bonyana • Ukwazi bonyana Mumeqo emingaki ukusuka ku-3 ukuya ku 5?
ngiyiphi inomboro ngiyiphi inomboro Mimeqo emingaki wokeqa ubuyela emuva kusuka ku-5 ukuya ku-2?
ekulu nga-2 nofana enengi nga-2nofana
ngokuncani nga-2 encani nga-2
• Ukuwazi bonyana • Ukukhumbula
ngiyiphi inomboro msinyana:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
enokunengi nga-10 • Ukulumbana
nofana incani nga-10 kwenomboro ukufika
• Ukukhumbula e-5
msinyana: • Ukukhumbula
• Ukulumbana amaphuzu
kwenomboro ukufika wokuhlanganisa
ke-10 nowokukhupha e-5
• Ukukhumbula Amaqhinga wokubala
amaphuzu Ukusebenzisa
wokuhlanganisa amaqhinga wokubala
nowokukhupha e-10 ukuhlanganisa
Amaqhinga wokubala nokukhupha ngekghono
Ukusebenzisa elifaneleko:
amaqhinga wokubala • Beka inomboro ekulu
ukuhlanganisa maqangi ukuze ubale
nokukhupha ngekghono uye phambili nofana
elifaneleko: ubale uye emuva
• Beka inomboro ekulu • Inambalayini.
maqangi ukuze ubale • Ukubuyelela kabili
uye phambili nofana nokuhafula
ubale uye emuva
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• phakathi
• Inambalayini.
• Ukwakha nokuphula
• Ukubuyelela kabili
nokuhafula phakathi
IGREYIDI YOKU-1 ITHEMU YESI-3
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
CAPS UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
2.1 Ukukopa, ungezele Ukukopa, ungezele Egreyidi yoku-1 abafundi banganqhopha emaphethinini lapho amalunga abuyelelwe Isifundo 1
Amapheth- bewuhlathulule bewuhlathulule ngendlela ejayelekileko.
eni weji- Ukukopa, ungezelele Ukukopa, ungezelele
yomethri bewuhlathulule ngamagama bewuhlathulule ngamagama
• Amaphetheni alula enziwe Amaphetheni alula enziwe Qala amanothi weThemu yesi-2.
ngezinto ezibonakalako ngezinto ezibonakalako
• Amaphetheni alula enziwe • Amaphetheni alula enziwe
ngemigwalo yemida, ngemigwalo yemida,
ubujamo nafana izinto. ubujamo nafana izinto.
Tlama begodu uhlathulule • Tlama begodu uhlathulule
amaphetheni wakho amaphetheni wakho
Tlama amaphetheni Tlama amaphetheni
weJiyomethri wakho:
• Ngezinto ezibonakalako Ngezinto ezibonakalako
• Ngokugwala imida, • Ngokugwala imida,
ubujamo nofana izinto ubujamo nofana izinto
Tlama begodu uhlathulule
amaphetheni wakho
Tlama amaphetheni wakho:
• Ngezinto ezibonakalako
• Ngokugwala imida,
ubujamo nofana izinto
Amaphetheni
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni weJiyomethri
• Ngokwemvelo,
• Kusukela epilweni
yangamalanga
yesimodeni,
173 • Kusukela kezamagugu
nendabuko yethu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
174 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela Ukulandelana kweenomboro kungahlanganiswa nokubala. Lokha amakghono Iimfundo- 3
Amaphe- nokuhlathulula nokuhlathulula wabafundi wokubala atjhugulukako godu athuthukako, imihlobo yokulandelana
theni Ukukopa, ukungezelele Ukubala uye phambili kweenomboro abafundi ababerega ngayo ingathuthuka.
weenom- bewuhlathulule nemuva nga: Ukulandelanisa kufanele kubonise ukubala uye phambili nemuva ngabo:
boro Ukulandelanisa kwenomboro • Ku-1 ukusuka kwenye • Ku-1 kusuka kwenye nenye inomboro hlangana ne-1 kuya 80
elula ukufika ku-100. nenye inomboro hlangana • Li-10 kusukela kwenye nenye inomboro ebala ngali-10 ehlangana ne -0 na 80
Tlama begodu uhlathulule ne-0 na-80
• Ku-5 kusukele kwenye nenye inomboro ebala nga ku-5 ehlangana ne - 0 na 80
amaphetheni wakho • Ukubala uye phambili
• Ku-2 kusukela kwenye nenye inomboro ebala nga- 2 ehlangana ne - 0 na- 80
Yenza bewuhlathulule nga:
Lokha abafundi babala ngomlomo bangatjengiswa ukulandelanisa iinomboro
amaphetheni weenomboro • Li-10 ukusuka kesinye
ezitlolwe phasi ngezindlela ezingafaniko.
nesinye isibuyabuyelelo
se-10 hlangana ne-0 Bangakhomba inomboro ebaliweko.
na-80 Isibonelo 1: Sebenzisa itjhadi yeenomboro
• Ku-5 ukusuka kesinye 1 2 3 4 5 6 7 8 9 10
nesinye isibuyabuyelelo
saka ku-5 hlangana ne-0 11 12 13 14 15 16 17 18 19 20
na-80
21 22 23 24 25 26 27 28 29 30
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ku-2 ukusuka kesinye
nesinye isibuyabuyelelo 31 32 33 34 35 36 37 38 39 40
saka ku-2 hlangana ne-0
na-80 Isibonelo 2: Ukusebenzisa inambalayini ukukhomba iphetheni
Ukubala nge- 10 kusuka e-50 kuya -80.
Abafundi bafunda iinomboro kuya -80, kodwana batlola iinomboro kusuka -1 kuya
-15. Amaphetheni weenomboro ngaphezu kwe 15 angenziwa nge:
• Faka umbala emaphethenini weenomboro esegridini yeenomboro;
• Zungeleza iphethenini yeenomboro ezisegridini yeenomboro nofana
enambalayinini;
• Sebenzisa amakarada weenomboro ukupaka ukulandelana kweenomboro;
• Ukusebenzisa amakarada weenomboro ukubonisa iinomboro ezitjhiyiweko
ngendlela etloliweko yokulandelanisa
• Ukusebenzisa irhelo lamatshwayo weenomboro elinikelweko ukugwala umuda
ukusukela eenomborweni ezilungileko kuya endaweni ekufanele iyivale.
Abefundi banganikelwa iinomboro ezitlolwe ngokulandelana neenomboro
ezitjhiyiweko. Mabanikelwe irhelo leenomboro ezingahle zisetjenziswe,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
abangakhetha ipendulo elungileko. Abafundi bangazalisa iinomboro ezingekho
ezivezwe nanoma ngawuphi umhlobo wokulandelanisa ongehla, godu bazalise
iinomboro ezitjhiyiweko eenomborweni ezitlolwe ngokulandelana. isib. 2, 12, 22,
___, 42, 52, 62.
IGrEYIdI YOKU-1 IThemu YESI-3
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
CAPS UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
3.1 Ilimi lobujamo Ilimi lobujamo elithuthukiswe eThemini loku-1 lifanele lijayezwe njalonjalo
Ubujamo, Hlathulula ubujamo ngesikhathi sokufundisa itlasi loke begodu kunqotjhiswe esikhathini sokufundisa
ukuzijayeza bento eyodwa ehlobene ngesiqhema ethemini yoke, zinikele isikhathi esifitjhani sokuzijayeza ilimi njalo njalo.
nokubukela nenye, isib.phezu kwa-, Amanye amalimi wobujamo angajayezwa abafundi nabasebenza ngezinto zobujamo
phambi kwa- ,emve kwa, obubobusontathu (3-D).
ngesinceleni, esidleni, Ukusebenza ngendawo begodu nangekombatjhuba kungahlanganiswa ngokutlola
phezulu, phasi, hlanu kwa-. irekhodi njengokugwala, ukufaka umbala nofana ukumadanisa imigwala namagama.
Ubujamo nokubukela Lokhu kungenziwa ngesikhathi sokuzijamela.
Madanisa imibono
ehlukahlukeneko yezinto
ezifanako zangamalanga
woke.
Ubujamo
neenkombatjhuba
Landela iinkombatjhuba
ukukhambakhamba
ngetlasini
Landela iinlayelo ukubeka
into eyodwa ehlobene
nenye, isib. Ukubeka
ipensela ngaphakathi
kwebhoksi.
175
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
176 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
3.2 Izinto ezihlukahlukeneko Izinto ezihlukahlukeneko Ukunqopha ematshwayeni wezinto ezibusontathu 3D Iimfundo ezi- 2
Izinto ezibu- Ukubona nokutjho izinto Ukubona nokutjho izinto Abafundi basebenza ngeembholo begodu ngezinto ezinesibumbeko
sontathu ezibusontathu 3-D ezibusontathu 3-D esifana neembholo, begodu nezinye izinto ezinesibumbeko esifana
(3-D) ezingetlasini begodu ezingetlasini begodu nerekhthengelaamaphrizimu nofana amakhyubsi. Abafundi bangenza into
neenthombeni neenthombeni yokutjhelela nofana ngokuphatha ngokujayelekileko ngokubeka ibhoksi ngakelinye
• Ubujamo bebhola • Ubujamo bebhola ihlangothi lencwadi ekulu. Abafundi barhubhulula bonyana ngiziphi izinto
(indulungu) (indulungu) ezigedekako, nezitjheleleko
• Ubujamo bebhoksi • Ubujamo bebhoksi
(iphrizimu) (iphrizimu)
Amatshwayo wezinto Amatshwayo wezinto
Ukuhlathulula, ukubeka Ukuhlathulula, ukubeka
ngeengaba nokumadanisa ngeengaba nokumadanisa Abafundi bangarhubhulula godu bonyana bangakhgona ukupakelanisa nofana
izinto ezibusontathu 3-D izinto ezibusontathu 3-D benze imibhotjhongo ngokusebenzisa iimbholo zodwa nofana amabhoksi wodwa
ngokuya: ngokuya : Ngesikhathi sokuzijamela abafundi bangakghona ukuragela phambili ngoku:
• ngobukhulu • ngobukhulu • hlela izinto ngokuya ngobungako;
• ngombala • ngombala • hlela izinto ngokuya ngobungako;
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• ngezinto ezigedekako • ngezinto ezigedekako • ukwakha ngezinto; begodu
• ngezinto ezitjhelelako • ngezinto ezitjhelelako • ukwenza iimbholo nofana amabhoksi ngomdaka nofana ngahlama yokudlala.
Imisetjenzana Ukukhumbula nokutjho iimbholo (iindulungu) begodu namabhoksi
enqophiweko
( amaphrizimu)
Tjheja begodu wakhe
Abafundi baragela phambili ngokubona begodu bahlathulule izinto zeJiyomethri
izinto ezibusontathu
nezangamalanga ngokutjho bonyana zinesibumbeko esifana nebholo nofana
3-D ezinikelweko
ibhoksi, isib. Isitina lesi sinobujamo obufana bebhoksi nofana ilamuna leli linobujamo
ngokusebenzisa
obufana nebholo.
amamathiriyelii aphathekako
afana namabhulogo Imisebenzi etlolwako
wokwakha, ukubuyelela Umsebenzi owenziwako ngezinto za 3D ufanele uhlanganiswe ngokutlola
usebenzise godu imatheriyali imisebenzi.
namakhidi wokwakha
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3
CAPS namaminithi
ama -24)
3.3 Imihlobohlobo yobujamo Akukanqotjhiswa emajamweni wabobusobubili (2-D) eThemini yesi-3. Kodwana,
Amajamo Ukubona nokutjho ubujamo abafundi bangaragela phambili benze iinthombe ngokusika amajamo wabosombili
abobusobu- obubusobubili (2-D) nofana batlola imisebenzi ngesikhathi sokusebenza ngokuzijamela eeMbalweni
bili nofana kemaKghono wePilo.
• Iindulungu
(2-D) • Aboncantathu
• Iinkwere
Ubujamo bebumbeko
Ukuhlathulula, ukuhlela
nokumadanisa ubujamo
obubusobubili (2-D ):
• Ubukhulu
• Umbala
• ibumbeko
• amahlangothi anqophileko
• amahlangothi arondo
3.4 Isimethri Isimethri Abafundi bafanele baqale imida yamasimethri ezintweni eziphathekako Isifundo-1
Isimethri Ukukhumbula isimethri Ukukhumbula isimethri neenthonjeni.
emzimbeni wakhe emzimbeni wakhe Imisebenzi etlolwako ifanele ingabi ngileyo yokutlola kwaphela, kodwana ifanele
• Ukukhumbula nokugwala • Ukukhumbula nokugwala ifake iimbonelo lapho abafundi bagwala khona umuda wesimethri emahlangothini
umuda wesimethri umuda wesimethri woke wamajamo weJiyomethri, abantantathu, begodu namajamo angasiwo
emajamweni wejiyimethri emajamweni wejiyimethri weJiyomethri, isib. Ukugwala umuntu.
wabobusobubili wabobusobubili
• (2-D) begodu • (2-D) begodu
nemajamweni nemajamweni
angasiwo weJiyomethri angasiwo weJiyomethri
wabobusobubili (2-D) wabobusobubili (2-D)
177
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YESI-3
4. UKUMEDA
178 UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI -3 namaminithi
ama -24)
4.1 Ukudlula kwesikhathi Abafundi bafanele bafunde bonyana kukhulunywa njani :
Isikhathi Kukhulunywa ngokudlula • ngokulandelanisa izehlakalo begodu
kwesikhathi • nangobude besikhathi
• Hlela izehlakalo Abafundi baragela phambili ukuhlanganisa iindlela zokukhuluma ngesikhathi
eziqhelekileko ezisuke ngamalanga ngesikhathi sokufundisa itlasi loke nofana ngesikhathi sokufundisa
epilweni yabo isiqhema esinqotjhiweko.
• Ukumadanisa ubude Abafundi bakhuluma bebaphendule imibuzo ephathelene nokuthi izinto zenzeka nini,
besikhathi ngokusebenzisa ngokusebenzisa ilimi njengokuthi ekuseni, ngemuva kwamadina, ebusuku, ekuseni
ilimi isib.isikhathi eside, khulu, emuva kwesikhathi.
isikhathi esifitjhani,
Abafundi balandelanisa izehlakalo ngokusebenzisa ilimi njengokuthi izolo,
msinyana, kabuthaka.
namhlanje, kusasa; amalanga weveke begodu neenyanga zonyaka.
• Ukulandelanisa izehlakalo
Abafundi bamadanisa ubude besikhathi ngokusebenzisa ilimi njengokuthi isikhathi
ngokusebenzisa
eside nofana isikhathi esifitjhani begodu msinyana nofana buthaka.
ilimi elinjekuthi izolo,
ISIGABA ESISISEKELO AMAGREYIDI 1-3
namhlanje, kusasa. Abafundi bakhuluma ngokuhlela izehlakalo zepilo yabo. :Bahlela godu ukulandelana
kweenthombe njengokuthi
Ukutjho isikhathi
• amagadango wokwenza iimbedlezwana nofana ikopi letiye;
• Ukuhlathulula nangabe
kwenzeka into • iinthombe ezitjengisa ukukhula kwesana belibe mumuntu okhulileko;
ngokusebenzisa ilimi • umzombelezo wepilo yeembandana, isib. Iqanda liba yikukhu, nofana iqanda liba
isib. ekuseni,ngemuva sirhwerhwe nofana iqanda liba iviyaviyani;begodu
kwedina, ebusuku, • izehlakalo eziqhelileko zelanga ( ukuvuka, ukuba sesikolweni, ukudlala, ukudla
ekuseni khulu, ngemuva kwamadina, ukulala).
kwesikhathi.
Ragela phambili ukubeka amalanga wamabeletho ekhalendeni umnyaka woke
• Ukwazi amalanga weveke,
• Ukwazi iinyanga zonyaka.
• Ukubeka amalanga
wamabeletho ekhalendeni
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA YESI -3 namaminithi
ama -24)
4.2 Ukulinganisa Ukulinganisa Khuyini ukumeda okuhlukileko eThemini yesi-3?
Ubude okungakahleleki okungakahleleki Zoke iimedo egreyidini yoku-1 azikahleleki. Akukafaneli bonyana kwenziwe ukumeda
• Ukumadanisa nokuhlela • Ukulinganisa, ukumeda, okuhlelekileko bobungako kusetjenziswa imivosimedo ejayelekileko.
ubude, ukuphakama ukumadanisa, ukuhlela EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
nofana ububanzi bezinto begodu urekhode • ekumadaniseni okunqophileko kobungako bezinto ngokuzibeka enye hlanu
ezimbili nofana ezinengi ubudeusebenzise iimedo kwenye
ngokuzibeka enye eqadi ezingasisezingeni • ukuhlela nokumadanisa ubungako nofana ukuphakama nofana ububanzi bezinto
kwenye. isib. Ubude besandla, ezintathu nofana ezinengi ngokubeka izinto ngazimbili enye hlanu kwenye,
• Ukusebenzisa igadango, ubude bekufike lapho zoke izinto zilandelaniswe khona; begodu
ilimi ukukhuluma bepensela, izinto • Ukuthuthukisa ilimi lokukhuluma ngemahluko yobungako, ukuphakama nofana
ngokumadanisa, isib. zokubala, njll. ububanzi, njll
ubude, ubufitjhani, Ngesikhathi sokusebenza ngokuzijamela ethemini yoke, abafundi bangazijayeza
ububanzi. begodu bahlanganise ukuhlela nokumadanisa ubude nofana ukuphakama nofana
• Ukulinganisa, ukumeda, ububanzi bezinto ezintathu nofana ezinengi, ngokubeka izinto ngazimbili ezinye
ukumadanisa, ukuhlela hlanu kwezinye, bekufike lapho zoke izinto zilandelaniswe khona. Woke umsebenzi
begodu urekhode ubude ufanele urekhodwe.
usebenzise iimedo EThemini yesi-3 abafundi banganqopha ekwenzeni ukumeda okungakahleleki
ezingasisezingeni ngokusebenzisa ubungako bamayunithi obungakahleleki.
isib. Ubude besandla, Ukumeda okungakahleleki kobude ngokusebenzisa amayunithi wobude
igadango, ubude angakahleleki.
bepensela, izinto Abafundi bangafunda woke amakambisolawulo begodu nokuprakthisa ukumeda
zokubala, njll. ngokusebenzisa amayunithi angasi sezingeni. Ukumeda okungakahleleki
bamayunithi kufanele kungathathwa njengokunyazekako kunokumeda ngamayunithi
asezingeni.
Ukumeda ubude bamayunithi angasisezingeni kufaka ukubala bonyana mangaki
amayunithi akhethiweko afanako ngobude njengezinto ezimedwako.Isibonelo,
ubude bedeski bububude bezandla ezi-8.
Abafundi bafanele bemede imihlobo eminengi yezinto ngokusebenzisa imihlobo
yezinto njengamayunithiangakahleleki
Zintathu iindlela zokusebenzisa amayunithi angakahleleki
• Ukubeka ngereyi entweni emedwako izinto ezimedako zobude obulinganako,
njengamabhoksana womlilo, iimvadlwana zamabhodlela ezinobujamo obufana
patsi nofana izinto zokubala, amapensela amatjha, njll. Isibonelo, ukumeda
ububanzi bedeski, amapensela amatjha angabekwa ngokulandelana ukusuka
ekuthomeni ukufika ekugcineni uvundle itafula. Lapha kuqakathekile bonyana
• Zoke izinto zinobude obulinganako. Angekhe utjho bonyana incwadi yakho
inobubanzi beemuvalo zamabhodlelo webisi ali-12 nangabe iimvalo zamabhodlelo
179 zinobukhulu obungalinganiko, isib. Iimvalo zamabhodlelo webisi ezimalitha ama-2,
iimvalo zamabhodlelo wenamaneyidi weplastiki, iimvalo zamabhodlelo wesimbi,
njll; begodu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
180 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI -3 namaminithi
ama -24)
4.2 Ukulinganisa Ukulinganisa • Akunankhala ezitjhiywa hlangana nezinto : zifanele zipakelwe ngokulandelana Iimfundo zesi-2
Ubude okungakahleleki okungakahleleki ukuze zithintane
• Ukumadanisa nokuhlela • Ukulinganisa, ukumeda, • Sebenzisa izinto ezimbili ezifana patsi njengamayunithi angasi sezingeni. Beka
ubude, ukuphakama ukumadanisa, ukuhlela yinye hlanu kwenye, bese ukhambisa yokuthoma uyise kelinye ihlangothi lesibili.
nofana ububanzi bezinto begodu urekhode Lokhu kwenziwa nakumedwa ngobude besandla, ubude benyawo nofana
ezimbili nofana ezinengi ubudeusebenzise iimedo amagadango
ngokuzibeka enye eqadi ezingasisezingeni • Ukusebenzisa into eyodwa kwaphela njengesimedo esingasisezingeni begodu
kwenye. isib. Ubude besandla, ngokuyigeda nofana ukumerega lapho iphelela khona ngaphambi kokuyigeda.
• Ukusebenzisa igadango, ubude
Abafundi bafanele bafundiswe ukutjho iyunithi, isib. Incwadi inobubanzi beemuvalo
ilimi ukukhuluma bepensela, izinto
zebhodlelo ezi-12, ikumba yokufundela inobude obumagadango ama-38.
ngokumadanisa, isib. zokubala, njll.
Lokha abafundi nasele bamede ngananyana ngiyiphi iyunithi amahlandla ambala,
ubude, ubufitjhani,
bafanele balinganise bonyana ingaba nobude obungangani beyunithi into efanele
ububanzi.
imedwe
• Ukulinganisa, ukumeda,
Abafundi bafanele bafundiswe bonyana ukuze nimadanise ubude, ukuphakama
ukumadanisa, ukuhlela
nanyana ububanzi iyunithi efana patsi ifanele isetjenziswe. Isib.nangabe ububanzi
begodu urekhode ubude
bomnyango omedweko bububude besandla obu-20 begodu ububanzi bedeski
usebenzise iimedo
bububude bamapensela a-8, angekhe utjho bonyana umnyango ubanzi kunedeski.
ezingasisezingeni
ISIGABA ESISISEKELO AMAGREYIDI 1-3
isib. Ubude besandla, Abafundi bafanele bamede ngamayunithi angakahleleki ahlukahlukeneko, ukuze
igadango, ubude bakghone
bepensela, izinto • ukuthoma ukuzwisisa bonyana lokha iyunithi nayiyincani , izokusetjenziswa
zokubala, njll. amahlandla amanengana ,isib. ububanzi bekumba yokufundela bungaba
magadango ama-20 kodwana kube bubude beenyawo obuma-48.
• Thoma ukusebenzisa amayunithi afanele lokho abakumedako, isib. Ukumeda
ububanzi bekumba yokufundela ngeemuvalo zamabhodlelo kukumorosa isikhathi.
Ukurekhoda iimedo
Nanyana ukumeda kulikghono lokuzijayeza ukwenza, abafundi bafanele barekhode
iimedo zabo ngaso soke isikhathi.
Ukumeda ubude njengobujamo bokurarulula imiraro begodu nokubala
Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi
bangararulula imiraro esebenzisa ubujamo bobude beemedo ezingakahleleki, isib.
Ibhoksi lesibha sephuphu sokuvasa linokuphakama kweenthoro zomlili ezi-8. Ibhoksi
lesiriyeli linokuphakama kweenthoro zomlilo ezi-13. Liphakame kangangani ibhoksi
lamasiriyeli kunebhoksi lesibha sepuphu sokuvasa?
Yelela irherho leenomboro ezifaneleko zeThemu, nemihlobo ehlukahlukeneko
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
yeenkinga zeThemu
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA YESI -3 namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Zoke iimedo egreyidini yoku-1 azikahleleki. Akukafaneli bonyana kwenziwe ukumeda
Ubungako/ • Ukulinganisa, ukumeda, okuhlelekileko bobungako kusetjenziswa imivosimedo ejayelekileko.
ukumadanisa, ukuhlela, EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
ubudisi
bekurekhodwe ubungako, • ekumadaniseni okunqophileko kobungako bezinto ;
ngokusetjenzisa iimedo • ukuhlela nokumadanisa ubungako bezinto ezintathu nofana ezinengi ngokubeka
ezingakahleleki begodu izinto ngazimbili zidzimelele, bekufike lapho zoke izinto zilandelaniswe khona;
nesikala sokudzimelela begodu
isib. Amabhulogo, iintina
njll. • Ukuthuthukisa ilimi lokukhuluma ngemahluko yobungako
• Ukusebenzisa Ngesikhathi sokusebenza ngokuzijamela ethemini yoke, abafundi bangazijayeza
ilimi ukukhuluma begodu bahlanganise ukuhlela nokumadanisa ubungako bezinto ezintathu nofana
ngokumadanisa isib. ezinengi, ngokubeka izinto ngazimbili zidzimelele, bezifike lapho zoke izinto
elula, ebudisi, elula-khulu, zilandelaniswe khona.
ebudisi-khulu. Woke umsebenzi ufanele urekhodwe.
181
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
182 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI -3 namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Zoke iimedo egreyidini yoku-1 azikahleleki Akukafaneli bonyana kwenziwe ukumeda
Umthamo/ • Ukumadanisa okuhlelekileko bobungako kusetjenziswa imivosimedo ejayelekileko.
Ivolumu nokuhlela ubungako Ukufikela nje phakathi konyaka umnqopho womthamo/ ivolumu bekuku
okusamanzi (umthamo) • thuthukisa ilimi ngokukhuluma ngomthamo/ ngevolumu;
okuseemumathini
ezimbili ezibekwe esinye • ukumadanisa amavolumu eemumathini ezimbili ezifanako; and
eduze nesinye. Abafundi • ukumadanisa amavolumu eemumathini ezinobubanzi obuhlukahlukeneko,
bahlola ngokuthi bathele ngokuthela esimumathini sesithathu.
esimumathini sesithathu
nakutlhogekako. Qala amanothi weThemu yesi-2
• Ukumadanisa Abafundi bangazijayeza begodu bahlanganise imiqondo le ngesikhathi sokusebenza
nokuhlela ubungako ngayedwana.
beketjezi/okusamanzi
okungathathwa ziimumathi
ezimbili nazizeleko
• (umthamo)
• Ukusebenzisa
ilimi ukukhuluma
ngokumadanisa isib.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
enengi kune, encani kune,
encani, izele, edududu.
• Ukulinganisa nokumeda;
Ukumadanisa nokuhlela
bewurekhode umthamo
ongeemumathini
ngokusebenzisa izinto
zokumeda ezingakahleleki
isib. Iingobho neenkomitji.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YOKU-1 ITHEMU YESI-3
5. UKUPHATHA IDATHA
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
CAPS
NAMAKGHONO NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO : IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YETHEMU YESI -3 namaminithi
ama -24)
UKUSEBENZA NGEBUTHELELO LEZINTO
5.1 Ukubuthelela nokuhlela Ukuhlukanisa
Ukubuthelela izinto ngemihlobo ngemihlobo
nokuhlukanisa Ukubuthelela nokuhlela Ukuhlukanisa
ngemihlobo izinto ngemihlobo ngemihlobo
kwezinto eziphathekako ibuthelelo lwezinto
ngamalanga akusese munqopho
onqophileko
5.2 Ukujamiselela ibuthelelo engcenyeni yesibili
Ukujamiselela lezinto elihlelekileko yonyaka.
ibuthelelo lezinto Ukugwala isithombe Kodwana, inganikelwa
elihlelekileko sezinto ezihleleke njengemisetjhenzana
ngemihlobo engakavami
ngesikhathi
5.3 Coca bewubike sokusebenza
ngokuhlelwa kwezinto ngokuzijamela.
Coca bewubike
ngokuhlelwa ezibuthelelweko Umnqopho
kwezinto • Nikela ngesizathu ophakamisiweko
ezibuthelelweko lobonyana ibuthelelo ethemini –3 umzombe
lihlelwe bunjani wokuphatha idatha:
bona okulandelako.
• Phendula imibuzo ngo:
-- kuhlukanisa
ngemihlobo
kwenziwe njani
(indlela yekambiso)
-- hlukaniso ngemihlobo
libukeka bunjani
(umkhiqizo)
• Coca ngebuthelelo
nemigwalo
• Hlathulula bonyana
ibuthelelo lihleleke
183 bunjani
Ukusebenza ngedatha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
184 : IIMFUNEKO : IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YETHEMU YESI -3 namaminithi
ama -24)
5.4 Ukubuthelela nokuhlela Ukubuthelela Umnqopho ophakamisiweko: Umzombe opheleleko wokuphatha idatha Isifundo 3
Ukubuthelela idatha nokuhlela idatha Emzombeni wokuphatha idatha
nokuhlela idatha • Buthelela idatha Buthelela idatha • Abefundi babuthelela ilwazi ukuphendula imibuzo. Eemfundweni ezisisekelo
yetlasi nofana yesikolo yetlasi nofana yesikolo nasemabangeni aphakathi umbuzo lo ujwayeleke ukunikelwa ngutitjhere nofana incwadi
ukuphendula imibuzo ukuphendula imibuzo yokufundisa.
ebuzwa ngutitjhere ebuzwa ngutitjhere • Abefundi bahlukanisa ngemihlobo bebajamisele ilwazi ngezindlela ezenza kubelula
ukuhlaziya. Umhlobo wokujamisela lowo abefundi begreyidi -1 bazijayeza yona igrafu
Jamiselela idatha
yeentombe; godu
5.5 Ukujamiselela idatha • Ukujamiselela idatha • Abefundi bahlaziya ilwazi egrafini yeenthombe ngokuphendula imibuzo ebuzwe
Ukujamiselela Ukujamiselela idatha gegrafi yeenthombe. ngutitjhere.
idatha gegrafi yeenthombe. Igrafu yeenthombe yeklasi
Ukuhlaziya Egreyidini yo-1 kuqakathekile ukuthoma, UkuPhatha iDatha ngokwenza igrafu yesithombe
bewurhumutjhe seklasi.
5.6 Ukuhlaziya Ukusebenzisana njengetlasini, kusiza abefundi ukuzibandakanya kizozoke iingaba
idatha
Ukuhlaziya bewurhumutjhe idatha zekambiso ngaphandle kokulahlekelwa mininingwana yananyana ngiliphi izinga.
• Ukuphendula
bewurhumutjhe Ukuphendula imibuzo • Ukwenza igrafu kuvumela utitjhere bonyana ukunqophisa abafundi ngamahlangothi
imibuzo ngedatha
idatha ngedatha esegrafini abalulekileko wokuphathwa kwedatha begodu nangalokho abadinga ukukwazi
esegrafini
yeenthombe ngokuqakatheka kwesimo segrafu yeenthombe
yeenthombe
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Igrafu ilebulwa kuphi godu bunjani (isihloko segrafu)
• Iingaba zilebulwa kuphi godu bunjani
• Igrafu yeentombe ithloga ukuba nento ehlathulula bonyana isithombe ngasinye
simayelana nani.
• Iinthombe nofana iinkhala zenthombe zithloga ukuba bukhulu obufanako.
• Zibekwa bunjani iinthombe ngokulinganako emareyini.
• Ifundwa bunjani igrafu
Ukusebenza emzombeni wedatha epheleleko kungathatha iinfundo ezimbalwa.
Buthelela, uhlele bewujamiselele idatha
Abotitjhere abasesigabeni kufanele bakhethe iinhloko ezahlukeneko ezenzelwe
ukubuthelela idatha nokuhlaziya egreyidini ngayinye.
Abotitjhere abasesigabeni kufanele baqinisekise bonyana iinhloko ezahlukeneko
zikhethelwe ukubuthelela idatha nokuhlaziya egreyidini ngayinye. Iinbonelo ezifaneleko
ezifaka hlangana ukuhlela kabutjha itjhadi lobujamo bezulu beenyanga ezidlulileko ukwakha
igrafu yeenthombe nofana igrafu yelanga lamabeletho labafundi.
Hlaziya idatha
Abafundi baphendula imibuzo njenge:
“Ngumhlobo muphi wobujamo bezulu bebubunengi khulu enyangeni le?”
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
“Ngumhlobo muphi wobujamo bezulu bebubuncani khulu enyangeni le?”
“Sibe namalanga amangaki anelanga ukudla amalanga anamafu?”
Ukusebenza emzombeni wedatha epheleleko kungathatha iinfundo ezimbalwa.
IGREYIDI YOKU-1 ITHEMU YESI- 4
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
CAPS UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU yesi-4 YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
UKUTHUTHUKISA UMQONDO NOMBORO : Ukubala ngeenomboro ezibanzi
1.1 Ukubala iinomboro Ukubala izinto ngokuthembeka Yini umehluko kuneThemini yesi 3?
Ukubala ngokuthembeka kufika ema 50 kufika ema 50 ETheminin ye 4, abafundi bangezelela irherho lokubala. Kusese nomqopho
izinto Nikela ukulinganisa Nikela ukulinganisa wokuzwisisa umthetho wekhadinalithi. NgeThemu le, abafundi kufanele
okuzwakalako kwenani lezinto okuzwakalako kwenani lezinto bafunde bona bangazibeka njani izinto ngerherho lokha nababalako
ezingahlolwa ngokubala ezingahlolwa ngokubala. ukwenzela bona bahlole ukubala kwabo, ihlelo leli lisiza abafundi ukubala lula
khulu. Isibonelo: Iimbali zingabekwa zibe mareyi.
NgeThemu le, abafundi baragela phambili nokulula amakghono wabo
wokubala begodu bazijayeza:
• Ukubala kokel;
• Ukubala baragele phambili;
• Umthetho weenomboro wekhadinalithi; noku
• Sebenza ngemitlolo etloliweko.
Abafundi kufanele benze ubudlelwano phakathi kokubala kwe – odinali ne
khadinali. Lokhu kuba yipumelelo lokha nabalemukako bona ukulisa ukubala
lokha ufika entweni yama 50, kutjho bonyana bazabe sebabale 50 yezinto.
Sikhatheso, sebayazi gadesi bona indlela umuntu abala ngayo izinto,
ayithikamezi ukubala.
Ukubala ngeenqhema
Ukusiza abafundi bona babale ngamakhefu wakubili, hlanu na li 10, kufanele
babuthelele izinto nga zi 2, 5 na li 10. Ikarada lenomboro kufanele libekwe
kwelinye nelinye ibuthelelo ukutjengisa inani lezinto ezibaliweko. Ukubala
ngeenqhema kuzakulungisa abafundi bona bazwisise ukubuyabuyelela noku
balisisa. Ekupheleni kweThemu abafundi kufanele bakghone ukukhumbula
ibuthelelo ngokuhlukanisa inomboro phakathi. Isibonelo : “ngiyazi bonyana
ngu li 10 ngoba ngibeke u ku 4 ngakelinye ihlanbothi no si 6 ngakwelinye”.
Iinsetjenziswa :
Kufanele bona kutjhejwe begodu kuthlogonyelwe ihlobo leensetjenziswa
eziberegiswako.
• Iinsetjenziswa ezisasakhiwo, njengentambo yemincamo yokubala,
ingasetjenziswa.
• I-abhakhasi ingasetjenziswa ukubala ngeenqhema ezingalitjhumi.
• Abafundi bangenza iinyanda zaku 2, iinyanda zaku 5 neenyanda zali
185 tjhumi beseke babala koke
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
186 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
1.2 Ukubala uye phambili nemuva Ukubala uye phambili Yini umehluko kuneThemini yesi 1?
Ukubala uye nga: nemuva nga: EThemini ye 4, abafundi babala ngamakhefu wali 10, 5 naku 2 kufika e 100.
phambili • Ku-1 ukusuka kwenye nenye • Ku-1 ukusuka kwenye Ukubala bngamakhefu kuba likghono eliqakathekileko elizakusetjenziswa
nemuva inomboro hlangana ne-0 ne-100 nenye inomboro bafundi eGreyidini yesi 2 neyesi 3 begodu izasiza abafundi lokha nabenza
Ukubala uye phambili nga: hlangana ne-0 ne-100 ukubalisisa kwabo.
• Li-10 ukusuka kesinye nesinye Ukubala uye phambili Ekupheleni kweThemu abafundi kufanele bakwazi uku:
isibuyabuyelelo se-10 hlangana nga: Bala nehloko begodu baphendule imibuzo imibuzo efana nokuthi :
ne-0 ne-100 • Li-10 ukusuka • Thoma ema 52, bala uye phambili ngakunye kufika ema 72.
• Ku-5 ukusuka kesinye nesinye kesinye nesinye
• Thoma ema 88 begodu ubale uye emuva ngakunye kufika ema 70.
isibuyabuyelelo saka ku-5 isibuyabuyelelo se-10
hlangana ne-0 ne-100 • Thoma ema 38 begodu ubale ngakubili kufika ema 50.
hlangana ne-0 ne-100
• Ku-5 ukusuka • Thoma ema 45 begodu ubale ngakuhlanu kufika e 100.
• Ku-2 ukusuka kesinye nesinye
isibuyabuyelelo saka ku-2 kesinye nesinye • Thoma e 10 begodu ubale nga litjhumi kifika e 100.
hlangana ne-0 ne-100 isibuyabuyelelo saka Abafundi kufanele bakgone ukusebenzisa amakghono wabo wokubala
ku-5 hlangana ne-0 emisebenzini etloliweko. isibonelo:
ne-100
• Kopulula begodu ukhulise ukulandelana okulula kweenomboro ukufika
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ku-2 ukusuka okungasenani kwezili 100. Bona isigaba samaphetheni weenomboro
kesinye nesinye
isibuyabuyelelo saka
ku-2 hlangana ne-0
ne-100
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.3 Ukwazi nokufunda iinomboro Ukwazi nokufunda Yini umehluko kuneThemini yesi 3?
Amatswayo • Ukwazi nokufunda amatshwayo iinomboro ETheminin ye 4, irherho leenomboro lingezeleleka lifike e 100. Ukutlola
weenom- weenomboro 0 kuya e 100 • Ukwazi nokufunda amatshwayo namagama weenomboro kuyaqinisekiswa ethemini le. Alikho
boro • Ukutlola amatshwayo amatshwayo ilwazi elitjha elifundwako. Kuqakathekile ukutjheja bona ukulinganisa nokubala
namagama weenomboro 0 kuya ema 20 weenomboro 0 kuya kudzimelele khulu ekusebenziseni amagama weenomboro. Abafundi kuthlogeka
weenom- e 100 bona basebenzise, batjho bebatlole amagama weenomboro ngeendlela ezinengi
• Ukwazi nokufunda amatshwayo
boro • Ukutlola amatshwayo ngokungakghoneka ngakho.
weenomboro 1 kuya e 10
weenomboro 0 kuya Ekupheleni kweThemu, kufanele bakghone ukwenza imihlobo elandelako
• Ukutlola amagama weenomboro
ema 20 yemisetjenzana:
1 kuya e 10.
• Ukwazi nokufunda Ukumetjhisa amatshwayo weenomboro, amagama weenomboro nofana
amatshwayo iinthombe zezinto
weenomboro 1 kuya Ikarada leli lithi si 6 Liyini leli ikarada?
e 10
• Ukutlola amagama 6 11
weenomboro 1 kuya
e 10. Metjhisa amagama nezinto
Kunye
Kubili ã ã ã
Kuthathu ì
Kune ëëëëë
Kuhlanu
Sithandathu õõ
Likhomba ðððððð
Bunane ø ø ø ø
Lithoba ööööööö
187
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
188 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
1.4 Hlela begodu umadanise izinto Ngokuhlela nokumadanisa izinto neenomboro, abafundi bafunde bonyana:
ezifika ema 20. • Ihlangothi lomraro lenomboro yekhadinali lisetjenziselwa ukuhlathulula
Ukuhlathu- • Madanisa ibuthelelo lezinto
lula, uku- inomboro esedeni.
mayelana nokuthi zinengi,
madanisa mbadlwana, ezinengi, ncani Yini umehluko kuneThemini yesi 3?
nokuhlela khulu; dluleleko kuna,ncani kuna; Abafundi bavezelwa eenimborweni ezima -odinali.
iinomboro okufanako na, nje okunengi Ekupheleni kweThemu nonyaka abafundi kufanele bakghone ukusebenzisa ilimi
nganga, hlukileko lokuhlela nokumadanisa ngeendlela ezilandelako:
• Hlela ibuthelelo lezinto kusukela • Kokuthoma, kwesibili, kwesithathu, kwesine, kwesihlanu,
kwezinengi ukuya kwezincani
khulu nakusuka kwezincani khulu kwesithandathu…………..
ukuya kwezinengi. • Kungaki …………
• Izinto ezihlukahlukenekoezifika • Kunengi ngange, inomboro efanako ne…
ema 20 • Kulingana na, nengi kuna, gaphasi kuna, lidlanzana kuna, khulu kuna, ncani
Ukuhlela nokumadanisa kuna, khulu kuna…………
iinomboro
• Hlela iinomboro : • Hlela , kokuthoma, kokugcina, ngaphambie, emuva kwe, duze na, phakathi
-- Kusuka kwencani khulu ukuya kwe
kwekulu khulu nakusuka • Iinomboro
kwekulu khulu ukuya kwencani • Kokuthoma, kwesibili, kwesithathu, kwesine, kwesihlanu,
khulu kwesithandathu…………..
ISIGABA ESISISEKELO AMAGREYIDI 1-3
-- Ngaphambi , ngemuva,
phakathi, /hlangana • Kungaki …………
-- Ngokusebenzisa inamba layini • Kunengi ngange, inomboro efanako ne…
ye 0 kufika ema 20 • Kulingana na, nengi kuna, gaphasi kuna, lidlanzana kuna, khulu kuna, ncani
• Madanisa iinomboro ezipheleleko kuna, khulu kuna…………
mayelana nencani kuna, ekulu • Hlela , kokuthoma, kokugcina, ngaphambie, emuva kwe, duze na, phakathi
kuna, enengi kuna, ncani kuna,
kulingana na kwe
• Kunye nakunye
okukhambelanako
• Irherho leenomboro kufika ema • Faka umbala osarulani endulungwini yesihlanu.
20 • Faka umbala obomvu endulungwini yokuthoma.
Sebenzisa iinomboro ezima –
odinali ukubonisa ukuhleleka , • Faka umbala ohlaza sasibhakabhaka endulungwini yobunane.
indawo nofana ubujamo Abafundi kufanele baphendule imibuzo efana nokuthi
• Hlela izinto ngomuda / ngelayini • Ngubani wokuthoma ereyini?
kusuka kweyokuthoma • Ngubani wesibili emudeni?
ukuya kweyetjhumi nofana • UMthunzi unamapensela wamakhrayoni ama 5 . UKali unamapensela
kweyokuthoma ukuya
kweyokugcina isib yokuthoma, wamakhrayoni abu 8.
yesibili, yesithathu … yetjhumi, • Ngubani onamapensela wamakhrayoni alidlanzana?
yokugcina. (iinomboro ezima • Nginikela inomboro phakathi kwe 15 ne 17?
-odinali)
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Tlola phasi iinomboro ezihlanga ku 4 ne 10
Ihlangothi lemiraro yeenomboro • 1, 2, 3, 4, _, _, _, _, _, 10
ezima- odinali zerherho elithoma
kweyokuthoma ukuya kweyetjhumi. • Zalisa iinomboro ezingekho
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.4 Hlela begodu umadanise izinto Ngaphambili Iinomboro Emuva
ezifika ema 20.
Ukuhlathu- • Madanisa ibuthelelo lezinto 17
lula, uku- mayelana nokuthi zinengi,
madanisa mbadlwana, ezinengi, ncani 12
nokuhlela khulu; dluleleko kuna,ncani kuna; 14
iinomboro okufanako na, nje okunengi
nganga, hlukileko 9
• Hlela ibuthelelo lezinto kusukela
kwezinengi ukuya kwezincani 6
khulu nakusuka kwezincani khulu Tlola iinomboro lezi ngokulandelana kusuka kekulu khulu ukya kencani khulu.
ukuya kwezinengi.
• Izinto ezihlukahlukenekoezifika Tlola iinomboro lezi ngokulandelana kusuka kencani khulu ukuya kekulu khulu .
ema 20 Tlola iinomboro lezi kusuka kencani khulu ukuya kekulu khulu.
Ukuhlela nokumadanisa Kopulula begodu uqedelele ngokusebenzisa amagama athi muncani no
iinomboro munengi:
• Hlela iinomboro :
-- Kusuka kwencani khulu ukuya • Ama-35 _______ kunama-38
kwekulu khulu nakusuka • Ama-79 __________kunama-65
kwekulu khulu ukuya kwencani
khulu Ukwazi bona inomboro engaphambili yincani ngayinye nokuthi inomboro
-- Ngaphambi , ngemuva, engemuva yikulu ngakunye.
phakathi, /hlangana Abafundi kufanele baphendule imibuzo efana nokuthi :
-- Ngokusebenzisa inamba layini
ye 0 kufika ema 20 • Ngiyiphi inomboro eza ngaphambi kwe-17?
• Madanisa iinomboro ezipheleleko • Ngiyiphi inomboro eza ngemuva kwama-82?
mayelana nencani kuna, ekulu
kuna, enengi kuna, ncani kuna, • Zalisa ngeenomboro ezingekho enambalayini.
kulingana na
• Kunye nakunye 85
86
87
88
89
90
91
92
93
94
95
okukhambelanako
• Irherho leenomboro kufika ema Beka amakarada weenomboro alandelako ngokuhlelekileko:
20 • Ngiziphi iinomboro ezitholakala phakathi kwama-25 nama-30?
Sebenzisa iinomboro ezima –
odinali ukubonisa ukuhleleka , • Nginikela inomboro edlula ama-76 nga-1?
indawo nofana ubujamo • Nginikela inomboro edlula ama-76 ngaku-2?
• Hlela izinto ngomuda / ngelayini
kusuka kweyokuthoma • Ngiyiphi inomboro encani ngaku-1 kuna- 45?
ukuya kweyetjhumi nofana • Ngiyiphi inomboro encani ngaku-2 kuna-39?
kweyokuthoma ukuya
kweyokugcina isib yokuthoma,
yesibili, yesithathu … yetjhumi,
yokugcina. (iinomboro ezima
-odinali)
Ihlangothi lemiraro yeenomboro
189 ezima- odinali zerherho elithoma
kweyokuthoma ukuya kweyetjhumi.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
190 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
1.5 Ukukhumbula ubukhulu bedijithi Yini umehluko kuneThemini yesi-3?
Ubukhulu beenomboro zamadijithi amabili NgeThemu le, abafundi baragela phambili nokwakha bebathuthukise umqondo
bedijithi okungasenani kufika ema 20 wobukhulu badijithi.
• Hlukanisa iinomboro zamadijithi EThemini yesi 4,abafundi basebenza ngerherho leenomboro ezikudlwana
amabili uzenze amatjhumi nama begodu baragele phambili noku:
yunithi isib. Uli- 12 uba li-10
• Bala begodu ubeke ngeenqhema ukwenzela ukwakha isiqhema samatjhumi
naku-2
nabo kunye abazijameleko;
• Tlola i18 = 1 itjhumi nabo kunye ababu 8 abazijameleko; noku
• Bese urekhoda uli 14 = 10 naku 4.
Abafundi kufanele baragele phambili nokusebenzisa iinsetjenziswa
eziphathekako ngokwenza iinqhema ukwenzela ukwakha amatjhumi begodu
nemivo ukuthuthukisa ukuzwisisa bonyana i- 10 lisiqhema sinye setjhumi sabo
kunye abazijameleko.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ngokusebenzisa i-abhakhasi, abafundi kufanele bakwazi ukutjengisa :
• Itjhumi linye;
• Itjhumi linye nabo kunye aba-5;
• Itjhumi linye nabo kunye abasi-6; njll
Ungalindela bona abafundi baragele phambili nokubala ngakunye ukwenza
iinqhema zabo litjhumi. Ebafundini abanengi, kuzakuba ngiyoyodwa indlela elula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) yokutjho inomboro nofana yokutjho bona zingaki.
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.5 Ukukhumbula ubukhulu bedijithi Amakarada wobukhulu bedijithi/amakarada wamaFladi
Ubukhulu beenomboro zamadijithi amabili Amakarada wobukhulu bedijithi kufanele asetjenziswe ethemini le ukutjengisa
bedijithi okungasenani kufika ema 20 bona iinomboro zakhiwa bunjani. Amakarada wobukhulu bedijithi angatjengiswa
• Hlukanisa iinomboro zamadijithi kanyekanye nenyanda nofana nesiqhema sezinto.
amabili uzenze amatjhumi nama Iinsetjenziswa
yunithi isib. Uli- 12 uba li-10
Izinto ezingabuthelelwa ndawonye:
naku-2
• Iingojwana zokubala
• Izinto zokubala ezingathungelelwa ndawonye
• Iingojwana zomlilo
• Iingojwana ze - ayisikhrimu
• Amakhuyubhu angenelanako
• Amakarada wobukhulu bedijithi
• Imali yokudlala
Kuyasiza ukuba neenqhema ezihlala zilungile zamatjhumi ezibekwe bafundi
ngeenqhema bazibulunga ngeemumathini.
1.6 Sebenzisa amathekhiniki Yini umehluko kuneThemini yesi 3?
Amathek- alandelako lokha nirarulula imiraro Ekupheleni kweThemu le, abafundi bathoma ukurarulula imiraro yamagama
hiniki wok- noku hlathulula iinsombululo basebenzisa amathekhiniki alandelako:
urarulula zemiraro:
• Ukugwala nofana iinsetjenziswa eziphathekako
imiraro • Iinsetjenziswa eziphathekako isib.
• Ukwakha nofana ukuphula iinomboro
Iimbali
• Ukubuyelela kabili noku hafula
• Iinthombe zokugwala umphumela
wendatjana Amanambalayini
• Ukwakha nokuphula iinomboro Qala amanothi weThemu yesi-2.
• Ukubuyelela kabili noku hafula
• Amanambalayini
191
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
192 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
1.7 Rarulula imiraro yamagama Ekupheleni kweThemu abafundi kufanele bakghone ukwenza/ ukurarulula
Ukuh- ezisebujameni bewuhlathulule imiraro efana nale engenzasi.
langanisa iinsombululo zakho zemiraro ezifaka Itjhuguluko
nokukhupha ukuhlanganisa nokukhupha
UNoluthando beka namahabhula ama-5. USilo wamupha amanye amahabhula
nempendulo ukufika e-20.
abu-8. Sekanamahabhula amangaki nje uNoluthando?
UNoluthando beka namahabhula ali-13. Wapha uSilo amahabhula ama-5.
Sekanamahabhula amangaki nje uNoluthando?
Hlanganisa
UNosesi unabomabula aba-5 abahlaza nababu-8 abahlaza kwesibhakabhaka.
Unabomabula abangaki sebaboke uNosesi?
UNosesi unabomabula abali-13. Aba-5 bahlaza okotjhani kuthi abaseleko
babe hlaza kwesibhakabhaka. UNosesi unabomabula abangaki abahlaza
kwesibhakabhaka?
Ukumadanisa
UNosesi unamabhanana ali-13. UThemba unamabhanana ama-5. Amabhanana
ka Nosesi adlula wakaThemba ngamabhanana amangaki?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1.8 Rarulula imiraro yamagama Ekupheleni kweThemu abafundi kufanele bakghone ukwenza/ ukurarulula
Ukuh- ezisebujameni bewuhlathulule imiraro efana nale engenzasi.
langanisa iinsombululo zakho zemiraro, Ukuhlanganisa okubuyelelako
okubuyele- ezifaka ukuhlanganisa
Iintsikiri ezi-4 zinama vili amangaki?
lwako okubuyelelweko okurholela
ekubuyabuyeleleni nempendulo Isilinganisa
okurholela
ekubuy- ukufika e-20 UThami usela iinkomitji ezi-2 zebisi ngamalanga. Ziinkomitji ezingaki zebisi
abuyeleleni aziselako ngeveke?
Amagridi
Umnu Khumalo utjala amareyi ama-3 wekhabitjhi. Kuneentjalo ezi-5 ereyini
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) ngalinye. Zingaki iintjalo zekhabitjhi azitjalileko sezizoke?
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.9 Ukurarulula imiraro yamagama Ekupheleni kweThemu abafundi kufanele bakghone ukwenza/ ukurarulula
Ukubuthele- ezisebujameni bewuhlathulule imiraro efana nale engenzas
la nok- iinsombululo zakho ufake Ukubuthelela ngeenqhema
wabelana ukwabelana ngokulingana
Ukubuthelela , ulahle isalela
okurholela nokubuthelela ngeenqema
kweenomboro ezipheleleko ukufika • UStela uthengisa amhabhula ngemigodla efaka 3 amhabhula emgodleni
ekuhlu-
e-20 kanye nempendulo ezingahle ngamunye. Unamhabhula ali 14. Angenza imigodla emingaki efaka ama- apula
kaniseni
zifaka iinsalela ama 3?
Ukubuthelela , ufake hlangana isalela ependulweni
• UBeni ufuna ukuyokunikela ugogo wakhe amaqanda ali 15. Uthloga
amabhoksi amangaki wokufaka amaqanda asi 6 ukupaka woke amaqanda?
Ukwabelana
Ukwabelana , ulahle isalela
• Ukwabelana abangani aba 3 amaswidi ali 14 ukwenzela bona boke bathole
inani elilinganako lamaswidi.
Ukwabelana , okurholela emafraktjhinini
• Ukwabela abangani aba 3 amatjhokoledi ama 4 ukwenzela bona boke bathole
iinqetjhana ezilinganako zetjhokoledi kungabi khona okusalelako. (Abafundi
akuthlogeki bonabatjho ingcenye yefratjhini eyodwa kokuthathu. Bangamane
bahlathulule ifraktjhini leyo ngobulula ngokuthi “isiqetjhana”okutjho bonyana
Amafraktjhini wokubuthelela).
1.11 Ukukhumbula nokubona iinhlamvu Ekupheleni kweThemu abafundi kufanele bakghone ukwenza/ ukurarulula
Imali zemali ye Sewula Afrika: 5c, 10c, imiraro efana nale engenzas
20c, 50c, R1, R2, R5, nemali UJobha uthenge ubrotho ngamaranda ali R8. Wabubhadela ngetjhumi lama R10
yamaphepha, R10 ne R20. efasi. Uzakuthola malini itjhentji?
Ukurarulula imiraro yemali efaka Unina laka Rosi wathenga isikhafu ngamaranda ali R17. Ubhadale ngama 2
hlangana amanani netjhentji kufika amaranda alitjhumi afasi. Wathola malini itjhentji?
ema R20 nangamasende ukufika
Ilanga lamabeletho laka Judi belingo Sondarha. Udadwabo umuphe amaranda
emasendeni 20c
ama R5, umnakwabo wamupa amaranda ama R2 umzawakhe wamupha
amaranda ali R10 . Uthole malini nasele iyoke?
193
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
194 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
UKUBALA
1.12 Ukusebenzisa amathekhiniki Yini umehluko kuneThemini yesi 3?
Amathekniki alandelako lokha kwenziwa Abafundi balindeleke bararulule ukubalisisa ebujamweni obutjhaphulukileko
(iindlela umsebenzi wokubalisisa: ngokusebenzisa amathekhiniki alandelako:
namaqh- • Ukugwala nofana iinsetjenziswa • Ukugwala nofana iinsetjenziswa eziphathekako
inga) eziphathekako isib. iimbali
-- Imigwalo yabafundi kufanele ithome ukuqaleka ngokuhlelekileko begodu
• Ukwakha nokuphula iinomboro kufanele bakwazi ukuhlathulula ukubalisisa kwabo okuddzimelele
• Ukubuyelela kabili nokuhafula emigwalweni yabo.
• Amanambalayini • Ukwakha nofana ukuphula iinomboro
• Ukubuyelela kabili noku hafula
• Amanambalayini.
Qala amanothi weThemu yesi-2.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.13 • Ngezelela ngama ema 20 Ukuhlanganisa nokukhupha ngerherho leenomboro elihlangana kwe 0 - 20
Ukuh- • Khupha ema 20 kutjho bonyana abafundi bazaku:
langanisa • Sebenzisa itshwayo elifaneleko • Thoma ukuthuthukisa umqondo wobukhulu bedijithi ematjhumini nakibo kunye;
nokukhupha (+, –, =, ) • Ragele phambili babale ngeenqhema; begodu
• Ukuzijayeza ukulumbana • Thome ukubona bonyana ukubala uragele phambili ngabo kunye akusiliqhinga
kweenomboro kufika e 10 eliphumelelisako.
Abafundi bazakuragela phambili noku:
• bala izinto;
• khumbula, ukufunda nokutlola amagama weenomboro; noku
• madanisa noku hlela iinomboro.
Ukwenzela kobana basebenze ngamatshwayo wokuhlanganisa nokukhupha,
abafundi kufanele babe nelwazi elaneleko loku:
• ukubala koke;
• ukubala baragele phambili kusuka enomborweni ekulu;
• ukusebenzisa nokuzwisisa ilimi lokuhlanganisa noku khupha ; noku
• ukuhlela nokumadanisa iinomboro.
Abafundi baragela phambili nokwakha ukuzwisisa kokuhlanganisa noku khupha.
Ekupheleni konyaka abafundi kufanele ba:
• ukusebenzisa ilwazi magama eliphathelene nokuhlanganisa nokukhupha
namatshwayo wokuhlathulula nokurekhoda imitjho yeenomboro
yokiuhlanganisa nokukhupha;
• ukusebenzisa umsebenzi ophathekako nongakahleleki womthetho
womsebenzi otlolwako wokutlola umsebenzi wokuhlanganisa nokukhupha;
• ukurarulula imiraro yokubala yokuhlanganisa nokukhupha begodu
bangarekhoda iimpendulo zabo ngokusebenzisa imitjho yeenomboro;
• ukuzwisisa bona ukukhupha kuhlanganisa okupherhukileko, kandi ngakelinye
ihlangothi ukuhlanganisa nacho kukhupha okupherhukileko begodu kufanele
basebenzise lokhu ukwenzela ukufinyelela eempendulweni nekurekhodeni
ukubalisisa.
195
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
196 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
1.13 • Ngezelela ngama ema 20 Ukuzwisisa Ukuhlanganisa nokukhupha abafundi kufanele bakghone uku:
Ukuh- • Khupha ema 20 • ukwazi nokusebenzisa iphuzu lokuthi ukuhlela ukuhlanganisa akutjho litho;
langanisa • Sebenzisa itshwayo elifaneleko • sebenzisa amatshwayo + , - ne = ;
nokukhupha (+, –, =, ) • ukwazi bonyana lijamele inomboro engaziwako;
• Ukuzijayeza ukulumbana • ukuzwisisa ukukhupha njengoku ‘thatha utjhidise’ nokuthi ‘ukliuthola umehluko
kweenomboro kufika e 10 phakathi kwe ’;no
• kutjho nokutlola amaphuzu akhambelanako ephuzwini lokuhlanganisa
onikelwe lona nofana ngendlela ephikisako isib.
8 + 6 = 14 kutjho bonyana 14 – 6 = 8.
Ukurekhoda iimfaniso zokuhlanganisa nokukhupha:
Lokha abanye abafundi basafuna ukurekhoda nokubala ngabo ku 1, bathloga
ukurhelejwa bona ukuthoma ukurekhoda nokubala ngeenqhema.
Kufanele bakghone uku:
Gwala iinthombe nokusebenzisa iinomboro, khulu khulu ukubonisa iinqhema.
Ukuphula inomboro ibe ziinqetjhana ukwenza ukubala kube lula
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Abafundi bazakuphula inomboro ibe ziinqetjhana ezahluka hlukeneko.
Bazakuphula inomboro ibe ziinqetjhana ezibambekako kibo. Kokuthoma,
abafundi bazahlephula u likhomba ab bokn. Nokho, lokha amaphuzu
wenomboro kufika e 10 azwisiseka begodu abafundi bakghona ukusebenza
ngeenomboroezingeni eliphezulu, bangamuhlephula u-likhomba abe ziinqetjhana
ezihluka hlukeneko.
Ukusebenzisa ubutjhobi neenomboro ukutjengisa ukucabanga
11 + 7 =
11 + 4 + 3
11 + 4 ➝ 15 + 3 = 18
11 + 7 =
11 + 5 + 2
11 + 5 ➝ 16 + 2 = 18
17 – 9 =
17 – (7 + 2)
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
17 – 7 ➝ 10 – 2 = 8
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.13 • Ngezelela ngama 20 Ukulumbana kweenomboro
Ukuh- • Khupha ema 20 Ukwenzela ukuzijayeza ukulumbana kweenomboro, abafundi kufanele banikelwe
langanisa • Sebenzisa itshwayo elifaneleko imisetjenzana ehlukahlukeneko bona bayenze. Lokhu kwenziwa kuhlekuhle
nokukhupha ngesikhathi sokusebenza ngokuzijamela.
(+, –, =, )
Inamba layini nayo ingasetjenziswa ukuzijayeza ukulumbana kweenomboro
• Ukuzijayeza ukulumbana kufika e 10.
kweenomboro kufika e 10
Ukusebenzisa ilwazi elidlulileko namathekhiniki
Amathekhiniki aboniswe ngaphasi avumela abafundi bona bahlele kuhle ukubala
kwabo nomqodo weemboro. Ukzijayeza amthekiniki angahaskuz gcugcuzela
abafundi bona batjengise ubudlelwano phakathi kweenomboro nokufundisa
abafundi bona kokwakho bangasebenzisa ilwazi labo ukusiza ukubalisisa.
Beka inomboro ekulu ekuthomeni ukwenzela ukubala uragele phambili
nofana ukubalauye emuva.
4 + 12 =
Buyelela uhlele 4 + 12 as 12 + 4 bese uyabala uragele phambili kusuka e-12.
Bala uragele phambili ukusuka enomborweni ekulu
Abafundi kufanele bakghone ukubala baragele phambili ukusukela enomborweni
ekulu. Lokhu liqhinga elisiza khulu kunokubala ngabo kunye ukufika ku-14 bese
ubala ungezelele ngakuhlanu.
14 + 5 =
Abafundi babala ukusuka e-14, bese 15, 16, 17, 18, 19.
Ukubona okuseduze nokubuyelelwe kabili
8+7
Umfundi angahlathulula bonyana umphumela ungatlolwa njenge 8 + 8 -1
(ukubuyelela kabili u bu 8 uhlanganise naku 1) nofana 7 + 7 + 1 (ukubuyelela
kabili u li 7 uhlanganise naku 1).
Abafundi bangarekhoda amaqhinga wabo ngokusebenzisa abotjhobi :
8 + 8 16 + 1 = 17
Tjhugulula inomboro ibe litjhumi bese ukhupha nofana uhlanganisa ngabokunye
Iqhinga leli lingafundiswa ngerherho leenomboro ezincani begodu lisetjenziswe
eenomborweni ezikudlwana.
9+6=
Abafundi bangazitjela bonyana : “Ngizakuthatha kunye ku-6 begodu
ngikuhlanganise ne-9 ukwenzela ukuthola i-10.”
U li 9 + 6 angatlolwa njengo 10 + 5 = 15
197
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
198 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
yesi-4
ama -24)
1.13 • Ngezelela ngama ema 20 8+5=
Ukuh- • Khupha ema 20 Abafundi bangazitjela bonyana : “Ngizakukhupha kubili ku-5 begodu
langanisa • Sebenzisa itshwayo elifaneleko ngikuhlanganise no-8 ukwenzela ukuthola i-10.”
nokukhupha (+, –, =, ) U- 8 + 5 angatlolwa njengo 10 + 3 = 13
• Ukuzijayeza ukulumbana Sebenzisa ilwazi lobudlelwano obuphikisanako bokuhlanganisa
kweenomboro kufika e 10 nokukhupha
15 – 9 =
Umfundi uyazi bona umphumela ungatlolwa njengesibalo sokuhlanganisa:
“Ngiyazi bona u- 9 + = 15.”
Umfundi angasebenzisa ukubala aragele phambili ukwenza ukubalisisa.
Amanambalayini
Kufanele bagkhone ukusebenzisa amanambalayini ukusekela ukubalisisa
kwabo. Isibonelo:
13 + 6 =
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1.14 • Hlanganisa inomboro efanako Yini umehluko kuneThemini yesi-3?
Ukuh- ngokubuyelela ema 20 EThemini yesi 4, abafundi baragela phambili nokuthuthukisa ilimi lokuhlanganisa
langanisa • Sebenzisa itshwayo elifaneleko okubuyelelako. Isibonelo:
okubuyele- ( +, =, ) • Abo-3 aba-2
lwako
• Iinqhema ezi 4 zabo ku 2
okurholela
ekubuy- Abafundi baragela phambili nokutlola imitjho yeenomboro ukwenzela iinjamiselo
abuyeleleni eziphathekako. Ukubala ngokweqa kufanele kuragele phambili kurhelebhe
abafundi ukubala izinto ezibuthelelwe ngeenthombe. Lokha iinthombe nofana
izinto zibuthelelwe ngazimbili, bese abafundi kufanele babale ngakubili
bangasabali ngakunye ukuthola inani lezinto.
Ekupheleni kweThemu abafundi kufanele bakghone uku:
• Ukuzwisisa ukuhlanganisa okubuyelelako njengokwenza iinqhema
ezilinganako;
• ukujamisela ukuhlanganisa okubuyelelako ngokusebenzisa izinto
eziphathekako nemigwalo;
• ukurekhoda imitjho yeenomboro ekhambelanako emsebenzini owenziwako
nofana imigwalo; no
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• ukusebenzisa inamba layini ukufika ependulweniuse number lines to arrive at
an answer.
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
yesi-4
ama -24)
1.16 Umqondonomboro : Irherho 20 Yini umehluko kuneThemini yesi 3?
Iimbalo • Yitjho inomboro engaphambi EThemini yesi 4, irherho leenomboro liyanda kusuka e-15 ukuya ema-20.
zehloko nengemuva kwenomboro Iimbonelo zemibuzo nemisetjenzana engabuzwa nengenziwa:
• Thoma ku-3 ubale uye phambili ngabo kunye kufika e-10.
onikelwe yona. Hlela isede
• Abafundi bajama umuda babuze: ngubani osekuthomeni, wesibili, wesithathu
yeenomboro ezikhethekileko nofana wokugcina?
onikelwe zona. • Ngiyiphi encani i-14 nofana bu- 8?
• Madanisa iinomboro kufika ema • Ngiyiphi enengi u bu-8 nofana u-4?
20 begodu utjho bonyana ngiyiphi • Yini encani ngaku-2 kune-13?
enengi nofana encani. • Yini enengi ngaku-2 kuno-8?
• Nikela inomboro ephakathi kuka-1 no-3.
• Ukwazi bonyana ngiyiphi • Nginikela inomboro ephakathi kwe-10 ne-14. Yinye kuphela inomboro leyo?
inomboro enengi ngaku 1 nofana • Beka amakarada weenomboro la ngokulandelana ukusuka kwelinenomboro
encani ngaku 1enomborweni. encani ukuya kwelinenomboro ekulu.
• Ukwazi bonyana ngiyiphi Ukukhumbula msinyana
inomboro enengi ngaku 2 nofana Ngitjengisa inomboro engingayihlanganisa ukwenza i-10 ( ukutlola phasi nofana
encani ngaku 2 enomborweni. ukusebenzisa ubukhulu bedijithi nofana amaflardi karada)
• 1
Ukukhumbula masinyana: • 2
• Amaphuzu wokuhlanganisa • 3
nawokukhupha kufika e 10 • 4
Amaqhinga wokubalisisa Ngitjengisa inomboro etjhiyekileko lokha ….suswe e 10 (ukutlola phasi nofana
ukusebenzisa ubukhulu bedijithi nofana amaflardi karada)
Ukusebenzisa amaqhinga wokubala • 1
ukuhlanganisa noku khupha • 2
ngokuphumelela: • 3
• Beka inomboro ekulu mantanzi • 4
ukwenzela ukubalela phezu • 6 + 4 = 10 kuyini uku- 4 + 6? Ipendulo iyafana na?
• 5 + 2 = 7 kuyini uku- 2 + 5? Ipendulo iyafana na?
kwayo nofana ukubala uye
Amaqhinga wokubalisisa:
emuva. Sebenzisa amaqhinga wokubalisisa Ukuhlanganisa nokukhupha ngekghono.
• Inanambalayini • Hlanganisa okulandelako ngokubeka inomboro ekulu mantanzi nokubala
• Ukubuyelela kabili noku hafula uragele phambili:
1+9
• Ukwakha nokuphula iinomboro 2+6
1+4
• Buyelela kabili u-1
Yini abo-2 ababili?
Iyini ihafu yaka ku-4?
• Ukusebenzisa inambalayini.
Mimeqo emingaki ukusuka ku-3 ukufika ku-5?
199 Mimeqo emingaki ebuyela emuva ukusuka ku-5 ukufika-2?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YESI-4
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
200 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA yesi-4 namaminithi
ama -24)
2.1 Ukukopa, ungezelele Amaphetheni Abafundi bazokusebenza ngamaphetheni ukusukela kewemvelo, kusukela epilweni 1 lsifundo
Amapheth- bewuhlathulule asizombelezileko yangamalanga yesimodeni nakezamagugu yendawo yethu ukusukela egreyidini 1 kufikela
eni weJi- Ukukopa,ungezelele Ukubona,ukuhlathulula kugreyidi 6. Lokhu kutjho bonyana akumelanga uchithe isikhathi esinengi esihlokweni lesi.
yomethri bewuhlathulule ngamagama nokukopa Kufanele begodu ukhethe imisetjenzana namaphetheni afanele nakhambelana igreyidi leyo
ngamagama amaphetheni naleyo.
• Amaphetheni alula weJiyomethri EGreyidini yoku-1 abafundi bangahlikihla amaphetheni ngaphakathi.
enziwe ngezinto • Ngokwemvelo Iimbonelo nofana iintjengiso ezisebenzisekako maphetheni wamakari wemithi, ibhasi
ezibonakalako • Kusukela epilweni lemuthi, isoli yamanyathelo, amaphetheni wamatayere, isivalo samadreyini, emapheyivinini
• Amaphetheni alula yangamalanga njll.
enziwe ngemigwalo yesimodeni Umhlobo omunye wamaphetheni abafundi abangawuqala ngewesimethri, isib. amakari
yemida, ubujamo • Kusukela kezamagugu amanengi wemithi ayi-simethri
nafana izinto. nendawo yethu Abafundi bangaqala amaphetheni endradeni ( wensimbi, zamaplanga, nofana ivayibrakrit);
Yenza amaphetheni Yenza amaphetheni Umsebenzi weentina namathayilesi wefluru;
wakho weJiyomethri wakho weJiyomethri Iizambatho namatjhila
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngezinto eziphathekako • ngezinto amabhorodo, iinkopi neempiringi;
• ngokugwala imida, eziphathekako,
ibholo leenyawo;
ubujamo nofana izinto ngokugwala imida
ubujamo nofana iinlwane ezifana neenkomo, iviyaviyani lebusuku, namaviyaviyani wemini, iduba, idlulamithi,
Amaphetheni
bezinto iziingwe, iinyoni, iingogwana;
asizombelezileko
amathuthumbo namakari weemithi;
Ukubona, ukuhlathulula
ngamagama nokukopa imisebenzi yemincamo yesindu neyesimanje; begodu
amaphetheni neempoto zomdaka zesindu nofana iimantji ezilukiwe.
weJiyomethri Kuneendlela ezihlukileko zokuhlathulula amaphetheni esiwabonako asizombelezileko.
• ngokwemvelo, Amanengi amaphetheni asizombelezileko enziwe ngemida, ubujamo nofana ngezinto.
• kusukela epilweni Amajamo nofana izinto akuthlogeki bonyana zihlotjaniswe nabobusobubili nabobusontathu
yangamalanga beJiyomethri okusetjenziswa ngabo eGreyidini yoku-1. Abafundi bangaqalaqala begodu
yesimodeni, bebahlathulule bonyana
• kusukela kezamagugu • Kuyini ukubuyelela isib. amathosi, imida, nabonyana ngibuphi ubujamo; and
nendabuko yethu. • Kubuyelelwa njani isib.gwala imida iphambane omunye phezu komunye (njengase
fadugwini), ngabe woke ayalingana ngobukhulu na?, ngabe arhatjheke ngokulinganako
na?, ngabe woke amajamo ayalingana ngobukhulu na?,anemibala efanako na?, nofana
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
aqale ndawonye na?, isib. Nangabe usika ilamune phakathi ngokuphambanako woke
amalunga amatsikana phakathi begodu abanzi ngemaqadi.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA yesi-4 namaminithi
CAPS
ama -24)
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela Ukulandelana kweenomboro kungahlotjaniswa ngokubala. Lokho amakgono wabafundi Iinfundo ezi-3
Amaphe- nokuhlathulula nokuhlathulula wokubala akhula begodu atjhuguluka, iinhlobo zokulandelana kweenomboro zomsebenzi
theni Ukukopa, ungezelele Ukukopa, ungezelele wabafundi zingakhula.
weenom- bewuhlathulule bewuhlathulule Ukulandelana kufanele kutjengise ukubala uye phambili nemuva nga:
boro ukulandelanisa ukulandelanisa • ku-1 ukusukela kwenye nenye inomboro hlangana no-1 ne-100
kweenomboro ezilula kweenomboro ezilula
• li-10 ukusukela nanoma ngisiphi isibuyeleli se-10 hlangana ne-0 ne-100
ukufika e-100. ukufika e-100.
• ku-5 ukusukela nanoma ngisiphi isibuyeleli sika-5 hlangana ne-0 ne-100
Ukutlama amaphetheni Ukulandelana kufanele
okungewakhe kutjengise: • ku-2 ukusukela nanoma ngisiphi isibuyeleli sika-2 hlangana ne-0 ne-100
Tlama amaphetheni • Li-10 ukusuka Abafundi bangakhomba iinomboro enambalayinini, egridini yeenomboro, nofana
okungowakho kesinye nesinye ngokubhala ngokulandelana lokha babalakonokutlola ngokulandelana lokha nebabalako.
weenomboro. isibuyabuyelelo se-10 Abafundi bangavala (ngemmbali) nofana bafake umbala, nofana bazungelezele iinomboro
hlangana ne-0 ne-100 enambalayinini, eGridini yenomboro, nofana ukulandelana kokutloliweko lokha abalako.
• Ku-5 ukusuka Abafundi bangazalisa iinomboro ezitjhiyiweko nazitlolwako enambalayinini, nofana
kesinye nesinye emagreyidini ukuzijayeza ukubala. Khumbula bonyana abafundi babhala ukufika e-20.
isibuyabuyelelo saka Qala amanothi weThemu yesi-3 bonyana abafundi bangasebenza njani ngokulandelana
ku-5 hlangana ne-0 kweenomboro ngaphezulu kwa-20.
ne-100
• Ku-2 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-2 hlangana ne-0
ne-100
201
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YESI-4
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
202
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA yesi-4 namaminithi
ama -24)
3.1 Ilimi lobujamo Ilimi lobujamo Ubujamo neenkombatjhuba lsifundo esi-1
Ubujamo, Hlathulula ubujamo Hlathulula ubujamo Qala amanothi weThemu yoku-1.
ukuzijayeza bento yinye nokuhlobana bento yinye nokuhlobana Nanyana ngibuphi ubujamo beLimi kufanele bethulwe ngokwenza imisetjenzana efaka
nokubukela kwenye kenye isb. kwenye kenye isib. hlangana abafundi bonyana benze imsikinyeko. Lokho kungenziwa ngesikhathi sokufundisa
ngaphezulu, ngaphambi- ngaphezulu-kwe, itlasi loke nofana ngesikhathi somnqopho wokufundisa iinqhema.
kwe, ngemuva, ngaphambi-kwe,
Iinkombatjhuba kufanele zifundwe ngokwenza imisetjenzana ephathekako efaka hlangana
ngesinceleni, ngesidleni, ngemuva, ngesinceleni,
ukusikinya imizimba yabo nofana izinto ngokulandela iinyalelo. Lokhu kungenziwa
phezulu, phasi, hlanu- ngesidleni, phezulu,
ngesikhathi sokufundisa itlasi loke nofana ngesikhathi somnqopho sokufundisa isiqhema.
kwe. phasi, hlanu-kwe.
Umsebenzi wobujamo neenlayelo unganzinziswa ngamarekhodi atloliweko afana
Ubujamo Ubujamo
nemigwalo okufaka umbala nofana ukumadanisa imigwalo namagama. Lokhu kungenziwa
neenkombatjhuba neenkombatjhuba
ngesikathi sokuzijamela.
• Landela inkombatjhuba • Landela inkombatjhuba
Ubujamo nokubukela
zokukhambakhambe zokukhambakhambe
uzombeleze uzombeleze Abafundi besigaba esisiSekelo bafanele bazwisise bonyana izinto ziqaleka ngokuhlukeneko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngekumbeni ngekumbeni lokha umuntu aziqale ngehlangothi elingafaniko. Abafundi bangathatha lula bonyana
yokufundela. yokufundela. izinto ezifana neenkoloyi zibonakala zizincani lokha zivela kude. Njengombana abafundi
basebenza khulu ngeencwadi nangokutjengisa eencwadini zabo kufanele bonyana bazisise
• Landela iinlayelo • Landela iinlayelo
bonyana kungani into esebujameni obungaphambili buveza isithombe esikhulu kunaleso
ukubeka izinto ukubeka izinto
esisebujameni obungemuva.
ngokuhlobana kwenye nokuhlobana kwenye
kenye isib. Faka kenye isib. Faka Ngesikhathi somnqopho weenqhema zabafundi, abafundi bangatjengisa ngokubeka
ipensela ngaphakathi ipensela ngaphakathi izandlha zabo phambi kwabo, ukuvimbela ukubukela izinto ezibonakala zizikulu nazikude.
kwebhoksi. kwebhoksi. Abafundi besigaba esisiSekelo kufanele banikelwe imisetjenzana ehlukileko abangayenza
Ubujamo nemibono Ubujamo nemibono ukumadanisa ukubukela okuhlukeneko (ukubukela ngaphezulu, ngemaqadi, ngaphambili)
bezinto ezihlukeneko zangamalanga. Lokhu kuzakugcina kusiza abafundi bonyana
Madanisa imibono Madanisa imibono
bakgone ukuhlathulula imigwalo yeJiyomethri eyenziwe ebujameni obuhlukeneko.
ehlukeneko yezinto ehlukeneko yezinto
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) zangamalanga efifanako. zangamalanga efifanako.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA yesi-4 namaminithi
ama -24)
3.2 Irherho lezinto Irherho lezinto Ukusebenza ngezinto ezibusontathu (3-D) kunganzinziswa ngemisetjenzana etlolwako. 1 lsifundo
Izinto ezibu- Ukukhumbula nokutjho Ukukhumbula nokutjho
sontathu amagama wezinto izinto ezibusontathu
(3-D) ezibusontathu (3-D) ngeTlasini yokufundela
ngeTlasini nofana neenthombeni.
ngekumbeni yokufundela • Ubujamo bebholo
neenthombeni (iindulungu)
• Ubujamo bebholo • Ubujamo bebhoksi
• Ubujamo bebhoksi (iphrizimu)
Amatshwayo wezinto Amatshwayo wezinto
Hlathulula, hlukanisa, Hlathulula,hlukanisa
umadanise izinto ngemihlobo umadanise
ezibusontathu ngokuya: izinto ezinguSobantu
• ngobukhulu ngokuya ngo:
• ngokombala • bukhulu
• ngezinto ezigedekako • ngokombala
• ngezinto ezitjhelelako • izinto ezigedekako
Imisetjenzana • izinto ezitjhelelako
enqophikweko
Ukubona nokwakha
izinto ezinikelweko
ezibusontathu
ngokusebenzisa izinto
eziphathekako ezifana
namabhlogo wokwakha,
amamatheriyali
ebuyelelwe asetjenziswa
godu, ikhidi yokwakha.
203
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
204 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA yesi-4 namaminithi
ama -24)
3.3 Amajamo Irherho lamajamo Qala amanothi weThemu yesi-2 limfundo ezi-3
Amajamo ahlukahlukeneko Ukukhumbula nokutjho Abafundi basebenza ngezindingilizi nenkwere ezihlukahlukeneko naboncantathu
abobusobu- Bona bewutjho amagama abobusobubili abahlukeneko ngamasayizi. Bazihlela ngokubumbeka kwazo njengokuthi zindulungu
bili (2-D) wezinto ezikhombisa • indulungu nofana ezinqophileko nofana ezinamahlangothi arondo.
ubusobubili (2-D) Abafundi bahlela ngeengaba bebabuthelele ubujamo ngokuya bonyana boncantathu,
• uncantathu
• indulungu iinkwere nendulungu.
• isikwere
• unqanthathu Umsebenzi unzinziswa ngokutlolwa kwemisetjenzana.
• isikwere
Amatshwayo
Amatshwayo wobujamo
wobujamo bezinto
Ukuhlathulula,
Hlathulula,hlukanisa, ukuhlukanisa
umadanise ubujamo ngemihlobo,
ezibusobubili ngokuya: ukumadanisa ubujamo
• ngobukhulu babobusobubili ngokuya:
• ngombala • ngobukhulu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• ngezinto ezigedekako • ngombala
• ngezinto ezitjhelelako • ngamahlangothi
anqophileko
• ngamahlangothi
arondo
3.4 Isimethri Isimethri Abafundi kufanele baqale imida yesimethri ezintweni eziphathekako nasenthombeni lsifundo si-1
Isimethri • Ukubona ubujamo • Ukubona nokugwala Imisetjenzana etlolwako
besimethri emizimbeni imida ye Simethri • ayingathathwa kuphela ehafini enye kodwana
yabo ebujameni
• ayifake hlangana iimbonelo lapho abafundi bagwala imida yesimethri. Imida yesimethri
• Ukubona nokugwala obubusobubili
akukameli bonyana ijame poro njalo kodwana ingaba imida ethabaleleko.
umuda weSimethri • (2-D) yeJiyomethri
ebujameni namabumbeko
obubusobubili angasiwo weJiyomethri
beJiyomethri
namajamo
angasiwoweiJiyomethri
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YOKU-1 ITHEMU YESI-4
4. UKUMEDA
CAPS UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4 namaminithi
ama -24)
4.1 Ukudlula kwesikhathi Ukudlula kwesikhathi Abafundi bafanele bafunde bonyana kukhulunywa njani : Iimfundo ezi-2
Isikhathi Khuluma ngokudlula Khuluma ngokudlula • ngokulandelanisa izehlakalo begodu
kwesikhathi kwesikhathi • nangobude besikhathi
• Hlela izehlakalo • Hlela izehlakalo Abafundi baragela phambili ukuhlanganisa iindlela zokukhuluma ngesikhathi
eziqhelekileko zepilo yabo eziqhelekileko zepilo yabo ngamalanga ngesikhathi sokufundisa itlasi loke nofana ngesikhathi sokufundisa
• Ukumadanisa ubude • Ukumadanisa ubude ngesiqhema.
besikhathi ngokusebenzisa besikhathi ngokusebenzisa Abafundi bakhuluma begodu baphendula imibuzo ephathelene nokuthi izinto
ilimi isib.isikhathi eside, ilimi isib.isikhathi eside, zenzeka nini, basebenzise ilimi elinjengokuthi ekuseni, ngemuva kwedina, ebusuku,
isikhathi esifitjhani, isikhathi esifitjhani, ekuseni khulu, ngemuva kwesikhathi.
msinyana, kabuthaka. msinyana, kabuthaka.
Abafundi balandelanisa izehlakalo kusetjenziswa ilimi elifana nokuthi izolo,
• Ukulandelanisa izehlakalo • Ukulandelanisa izehlakalo namhlanje, kusasa; amalanga weveke begodu neenyanga zonyaka
ngokusebenzisa ilimi ngokusebenzisa ilimi
elifaka njengokuthi izolo, elifaka njengokuthi izolo,
namhlanje, kusasa. namhlanje, kusasa. Abafundi bamadanisa ubude besikhathi kusetjenziswa ilimi elifana nokuthi isikhathi
eside nofana isikhathi esifitjhani begodu msinyana nofana buthaka.
Ukutjho isikhathi Ukutjho isikhathi
Abafundi bakhuluma ngokuhlela izehlakalo ezisuke eempilweni zabo. Bahlela
• Ukuhlathulula nakwenzeka • Ukuhlathulula nakwenzeka
ukulandelana kweenthombe ezinjenga
into kusetjenziswa ilimi into kusetjenziswa ilimi
isib. Ekuseni, ngemuva isib. Ekuseni, ngemuva • magadango wokwenza iimbedlezwana nofana ikopi letiye;
kwedina, ebusuku, kwedina, ebusuku, • iinthombe ezitjengisa ukukhula komntwana aze abe mumuntu okhulileko;
ekuseni khulu, ngemuva ekuseni khulu, ngemuva • umzombelezo wepilo yeembandana, isib. Iqanda liba yikukhu, nofana iqanda liba
kwesikhathi. kwesikhathi. sirhwerhwe nofana iqanda liba iviyaviyani;begodu
• Ukwazi amalanga weveke, • Ukwazi amalanga weveke, • izehlakalo eziqhelileko zelanga ( ukuvuka, ukuba sesikolweni, ukudlala, ukudla
• Ukwazi iinyanga zonyaka • Ukwazi iinyanga zonyaka kwamadina, ukulala).
• Ukubeka amalanga • Ukubeka amalanga Ragela phambili ukubeka amalanga wamabeletho ekhalendeni unyaka woke
wamabeletho ekhalendeni wamabeletho ekhalendeni
205
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
206 YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4 namaminithi
ama -24)
4.2 Ukulinganisa Zoke iimedo egreyidini yoku-
Ubude okungakahleleki 1 azikahleleki. Akunamedo
• Ukumadanisa nokuhlela ezihlelekileko zobude
ubude, ukuphakama ezinamayunithini asezingeni
nofana ububanzi bezinto enziwako.
ezimbili nofana ezinengi
ngokuzibeka enye eqadi Ngesikhathi sokusebenza
kwenye. ngokuzijamela kiyo
• Ukusebenzisa yoke iThemu, abafundi
ilimi ukukhuluma bangazijayeza begodu
ngokumadanisa, isib. bahlanganise ukumeda
mude, fitjhani, mude khulu, ubude, ububanzi,
banzi. nokuphakama ngamayunithi
• Ukulinganisa, ukumeda, angakahleleki.
ukumadanisa, ukuhlela Woke umsebenzi ufanele
begodu urekhode urekhodwe. Qala amanothi
ubudeusebenzise iimedo weThemu yesi-3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ezingasisezingeni isib.
Izandla, igadango,
ubude bepensela, izinto
zokubala, njll.
4.3 Ukumeda okungakahleleki Ukumeda okungakahleleki Zoke iimedo eGreyidini yoku-1 azikahleleki. Akukafaneli bonyana kwenziwe
Ubungako • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, ukumeda okuhlelekileko bobungako kusetjenziswa amayunithi ahlelekileko.
/Ubudisi ukumadanisa, ukuhlela, ukumadanisa, ukuhlela, Khuyini okuhlukileko eThemini yesi-4?
bekurekhodwe ubungako, bekurekhodwe ubungako, EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
ngokusetjenzisa iimedo ngokusetjenzisa iimedo
• ekumadaniseni okunqophileko kobungako bezinto;
ezingakahleleki begodu ezingakahleleki begodu
nesikala sokudzimelela nesikala sokudzimelela • ukuhlela nokumadanisa ubungako bezinto ezintathu nofana ezinengi,ngokubeka
isib. Amabhulogo, iintina isib. Amabhulogo, iintina izinto ngazimbili enye hlanu kwenye, bekufike lapho zoke izinto zilandelaniswe
njll. njll. khona; begodu
• Ukusebenzisa • Ukusebenzisa • Ukuthuthukisa ilimi lokukhuluma ngomahluko wobungakol
ilimi ukukhuluma ilimi ukukhuluma EThemini yesi-4 abafundi banganqopha ekwenzeni ukumeda okungakahleleki
ngokumadanisa isib. ngokumadanisa isib. ngokusebenzisa ubungako bamayunithi obungakahleleki.
elula, ebudisi, elula-khulu, elula, ebudisi, elula-khulu,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ebudisi-khulu. ebudisi-khulu.
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4
CAPS namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Ukumeda okungakahleleki Ukumeda ubungako obungakahleleki ngokusebenzisa amayunithi Iimfundo ezi- 2
Ubungako • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, angakahleleki.
/Ubudisi ukumadanisa, ukuhlela, ukumadanisa, ukuhlela, Abafundi bangafunda zoke iinkambisolawulo begodu nekambiso yokumeda
bekurekhodwe ubungako, bekurekhodwe ubungako, ngokusebenzisa amayunithi angakahleleki. Ukumeda ngamayunithi angakahleleki
ngokusetjenzisa iimedo ngokusetjenzisa iimedo kufanele kungathathwa njengokunyazekako kunokumeda ngamayunithi ahlelekileko.
ezingakahleleki begodu ezingakahleleki begodu Ukumeda ubude ngamayunithi angasisezingeni kufaka ukubala bonyana mangaki
nesikala sokudzimelela nesikala sokudzimelela amayunithi akhethiweko afanako ngobude njengezinto ezimedwako.Isibonelo, irula
isib. Amabhulogo, iintina isib. Amabhulogo, iintina inobungako obufanako nebamabhulogo ali-9.
njll. njll.
Abafundi bafanele bamede imihlobohlobo yezinto basebenzise Izinto
• Ukusebenzisa • Ukusebenzisa ezihlukahlukenekoezinamayunithi angakahleleki.
ilimi ukukhuluma ilimi ukukhuluma
Abafundi bafanele bafundiswe ngeenkhathi zoke ukutjho iyunithi nabanikela
ngokumadanisa isib. ngokumadanisa isib.
ubungako, isib. Incwadi inobungako obufanako bamamabula ama-34.
elula, ebudisi, elula-khulu, elula, ebudisi, elula-khulu,
ebudisi-khulu. ebudisi-khulu. Lokha abafundi nasele bamede nanganyana ngiyiphi iyunithi amahlandla ambala,
bafanele balinganise bonyana ingaba ubungako obungangani beyunithi into efanele
imedwe. Ukulinganisa ngaphambi kokumeda kuqakathekile, kodwana kungenziwa
kwaphela lokha abafundi nabenze ukumeda ngeyunithi leyo.
Abafundi bafanele bafundiswe bonyana ukuze nimadanise ubungako bezinto
ezihlukahlukeneko, iyunithi efana patsi ifanele isetjenziswe. Isib. nangabe irula
inobungako obumabhlogo ama-20 begodu isikere sinobungako obulingana
namamabula ama-20, umuntu angekhe atjho bonyana zinobungako obulinganako
nofana obungalinganiko, nofana ngikuphi okubudisi.
Ukurekhoda iimedo
Nanyana ukumeda kulikghono lokuzijayeza ngokwenza. Abafundi bafanele
barekhode iimedo zabo ngaso soke isikhathi.
Ukumeda ubungako njengobujamo bokurarulula imiraro neembalo
Ngesikhathi esibekelwe Iinomboro, ama-Opharetjhini noBudlelwana, abafundi
bangararulula imiraro esebenzisa ubujamo bobungako besimedo ezingakahleleki,
isib. Idasta inobungako bamamabula ali-11. Ibhoksi lamakhrayoni linobungako
bamamabula a-8. Zizokuba nobungako bamamabula amangaki nasele zizoke?
Yelela irherho leenomboro ezifanele iThemu, nanyana imihlobo ehlukahlukeneko
yemiraro efanele iThemu.
207
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
208 YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4 namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Zoke iimedo eGreyidini yoku-1 azikahleleki. Akukafaneli bonyana kwenziwe
Umthamo/ • Ukumadanisa nokuhlela • Ukulinganisa nokumeda; ukumeda okuhlelekileko bobungako kusetjenziswa amayunithi angakahleleki.
Ivolumu ubungako beketjezi/ Ukumadanisa nokuhlela Khuyini okuhlukileko eThemini yesi-4?
okusamanzi (umthamo) umthamo weemumathini EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
obuseemumathini ngokusebenzisa iimeda
• ekuthuthuseni ilimi lokukhuluma ngemehluko yamavolumu;
ezimbili ezibekwe esinye ezingakahleleki isib.
eduze nesinye. Abafundi Iingobho neenkomitji. • ekumadaniseni amavolumu weemumathi ezimbili ezifanako
bahlola ngokuthi bathele • ekumadaniseni amavolumu eemumathini ezimbili ezingafani
esimumathini sesithathu EThemini yesi-4 abafundi banganqopha ekwenzeni ukumeda okungakahleleki
nakutlhogekako. ngokusebenzisa ubungako bamayunithi obungakahleleki.
• Ukumadanisa nokuhlela Uyini umthamo? Iyini ivolumu?
ubungako obusamanzi
Ibhodlelo lingaba nomthamo wamakopi amane, kodwana ngekhe lazaliswa swi,
obungathathwa ziimumathi
isibonelo, lingamumatha ivolumu yekopi elilodwa lamanzi ngesikhathi esithileko.
ezimbili nazizeleko
(umthamo) Umthamo ubungakho bento engamumathwa simumathi, Ivolumu bungako besikhala
esithathwa simumathi (soke isikhala esingaphakathi kwento).
• Ukusebenzisa
ilimi ukukhuluma Ivolumu bungako besikhala esithathwa simumathi.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngokumadanisa isib. Kesinye isikhathi abafundi bazokumeda bonyana kungangani okusamanzi
enengi kune, encani kune, okungesimumathini. Lokhu kumeda ivolumu yento engesimumathini.
encani,izele, idududu. Kesinye isikhathi abafundi bazokumeda bonyana isimumathi singamumatha
• Ukulinganisa nokumeda; kangangani nasizeleko swi.
Ukumadanisa nokuhlela Ukumeda ubude obungakahleleki ngokusebenzisa amayunithi wobude
umthamo weemumathini angakahleleki
ngokusebenzisa iimeda
ezingakahleleki isib. Abafundi bangafunda zoke iinkambisolawulo neenkambiso zokumeda
Iingobho neenkomitji. ngokusebenzisa amayunithi angakahleleki. Ukumeda ngamayunithi angakahleleki
kufanele bonyana zingaqaleka kwanga azikaqakatheki kunokumeda ngamayunuthi
ahlelekileko.
Abafundi bafanele bathole ithuba lokumeda ivolumu/umthamo ngokusebenzisa izinto
ezihlukahlukeneko njengamayunithi ahlelekileko, isib. Amakopi (kodwana ingasi
amakopi wokumeda), iingobho, (kodwana ingasi amathispuni wokumeda), iimvalo
zamabhodlelo njengeemvalo zamabhodlelo webisi wamalitha ama-2, Amabhlegana
amancani, amabhodlelo amancani, njll. Ukumeda ivolumu/umthamo ngamayunithi
angakahleleki kufaka ukubala bonyana kukangaki lapho umuntu azalisa begodu
athela khona eyunithini ekhethiweko bekufike lapho umuntu afinyelela khona
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ebungakweni nofana evolumini efunekako.
Abafundi bafanele bafundiswe ngaso soke isikhathi ukutjho iyunithi, isib.
Kuneegobho ezi-48 ezipheleleko zamanzi ngebhodlelweni nofana kunamanzi
angaphasi kwekopi ngebhodlelweni.
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4
CAPS namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Lokha abafundi nasele bameda nanyana ngiyiphi iyunithi amahlandla ambalwa,
Umthamo/ • Ukumadanisa nokuhlela • Ukulinganisa nokumeda; bafanele balinganise umthamo/ivolumu ngokusebenzisa iyunithi leyo. Ukulinganisa
Ivolumu ubungako beketjezi/ Ukumadanisa nokuhlela ngaphambi kokumeda kuqakathekile, kodwana kungenziwa kwaphela lokha
okusamanzi (umthamo) umthamo weemumathini abafundi nabameda ngeyunithi leyo.
obuseemumathini ngokusebenzisa iimeda Abafundi bafanele bafundiswe bonyana ukuze bamadanise amavolumu nofana
ezimbili ezibekwe esinye ezingakahleleki isib. imithamo, iyunithi efana patsi ifanele isetjenziswe. Isib.nangabe irhalasi Limimatha
eduze nesinye. Abafundi Iingobho neenkomitji. amathispuni ama-20 wamanzi begodu ikopi Limimatha iingobho zamanzi ezi-10,
bahlola ngokuthi bathele umuntu angekhe atjho bonyana irhalasi Limimatha amanzi amanengi.
esimumathini sesithathu Abafundi bafanele bamede ngamayunithi angakahleleki ahlukahlukeneko, ukuze
nakutlhogekako. bakghone
• Ukumadanisa nokuhlela • ukuthoma ukuzwisisa bonyana iyunithi nayiyincani , izokusetjenziswa amahlandla
ubungako obusamanzi amanengana, isib. ivolumu engebhodlelweni ingaba ziingobho ezi-20 kodwana
obungathathwa ziimumathi lilingane nekopi li-1; begodu.
ezimbili nazizeleko
• ukuthoma ukusebenzisa amayunithi afanele lokho abakumedako, isib. Ukumeda
(umthamo)
amalitha amabili wamabhodlelo azeleko ngethispuni kukumotjha isikhathi.
• Ukusebenzisa
Ukurekhoda iimedo
ilimi ukukhuluma
ngokumadanisa isib. Nanyana ukumeda kulikghono lokuzijayeza ukwenza, abafundi bafanele ukurekhoda
enengi kune, encani kune, iimedo zabo ngaso soke isikhathi.
encani,izele, idududu. Ukumeda umthamo njengobujamo bokurarulula imiraro neembalo
• Ukulinganisa nokumeda; Ngesikhathi esibekelwe Iinomboro, ama-Opharetjhini noBudlelwana, abafundi
Ukumadanisa nokuhlela bangararulula imiraro esebenzisa ubujamo bobungako / ivolumu besimedo
umthamo weemumathini ezingakahleleki, isibonelo, uGogo usebenzisa amakopi amabili webisi ukwenza
ngokusebenzisa iimeda iphudinghi. Nakabuyelela iresiphi kabili, uzokusebenzisa ibisi elingangani?
ezingakahleleki isib. Yelela irhelo leenomboro elifanako leThemu leyo, begodu nemihlobo yemiraro
Iingobho neenkomitji. ehlukahlukeneko.
209
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1 ITHEMU YESI-4
5. UKUPHATHA IDATHA
210
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO : NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
IIMFUNEKO ZOKUPHELA IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4 namaminithi
ama -24)
Ukusebenza ngebuthelelo lezinto
5.1 Ukubuthelela nokuhlela Ukuhlela ngemihlobo ibuthelelo lezinto akusese munqopho onqophileko engcenyeni
Ukubuthelela izinto ngemihlobo yesibili yonyaka.
nokuhlukanisa Ukubuthelela nokuhlela Kodwana, inganikelwa njengemisetjhenzana engakavami ngesikhathi sokusebenza
ngemihlobo izinto ngemihlobo ngokuzijamela.
kwezinto eziphathekako
ngamalanga
Umnqopho ophakamisiweko eThemini–4 kusekufundeni nasekuhlaziyeni igrafu
5.2 Ukujamiselela yeenthombe.
Ukujamise- ibuthelelo lezinto
lela ibuthelelo elihlelekileko
lezinto elihlele- Ukugwala isithombe
kileko sezinto ezihleleke
ngemihlobo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
5.3 Coca bewubike
Coca bewubike ngokuhlelwa kwezinto
ngokuhlelwa ezibuthelelweko
kwezinto ezi- • Nikela ngesizathu
buthelelweko lobonyana ibuthelelo
lihlelwe bunjani
• Phendula imibuzo nge:
-- ukuhlukanisa
ngemihlobo
kwenziwe njani
(indlela yekambiso)
-- ihlukaniso
ngemihlobo libukeka
bunjani (umkhiqizo)
• Coca ngebuthelelo
nemigwalo
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Hlathulula bonyana
ibuthelelo lihleleke
bunjani
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO : NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS IIMFUNEKO ZOKUPHELA IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA yesi-4 namaminithi
ama -24)
UKUSEBENZA NGEDATHA
5.4 Ukubuthelela nokuhlela
Ukubuthelela idatha
nokuhlela Buthelela idatha
idatha yetlasi nofana yesikolo
ukuphendula imibuzo
ebuzwa ngutitjhere
5.5 Jamiselela idatha
Ukujamiselela Ukujamiselela idatha
idatha gegrafi yeenthombe.
5.6 Hlaziya bewurhumutjhe Hlaziya idatha Lokha abafundi balemuka umzombe wedatha epheleleko (okuphakamisiweko Iimfundo ezi-2
Ukuhlaziya idatha kusuka ebujamelweni eThemini-3), banganqophisa ekuhlaziyeni iinjamiselelo abanikelwe zona.
bewurhumutjhe Ukuphendula imibuzo obunikelweko Kuphakanyisiwe bonyana eThemini–4 abafundi bahlaziye (ngokuphendula imibuzo)
idatha ngedatha esegrafini okungenani amagrafu ama–2 weenthombe.
yeenthombe
211
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.5.2 ITLHADLHULO YOKUMUMETHWEKO EGREYIDINI YESI-2
212 IGREYIDI YESI-2 ITHEMU YOKU- 1
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
UKUTHUTHUKISA INOMBORO MNQONDO: Bala ngeenomboro ezipheleleko
1.1 Ukubala izinto Ukubala izinto Qala amanothi weGreyidi yoku-1, iThemu yesi-3 neye-4
Ukubala eziphathekako eziphathekako EThemini yoku- 1 yeGreyidi 2 kuhlanganiswe umsebenzi owenziwe ngeThemu ye-4
izinto Linganisa begodu ubale Bala ngokuthembeka yeGreyidi yoku-1
ngokuthembeka izinto izinto zangamalanga Ukubala ngeenqhema
zangamalanga ukuya ukuya okungasenani
Umnqopho weThemu le usekubaleni uye phambili ngeenqhema.
okungaseneni ema-200. i-100
Lekelela abafundi ukubala iinomboro yezinto ngokubagqugquzela bonyana babeke izinto
Amaqhinga Nikela isilinganiso
ngeenqhema zangakubili, ngakuhlanu nangalitjhumi.
wokubuthelela senomboro yezinto
ayakhuthazwa. ngokuzwakalako Amakarada weenomboro kufanele kutjengiswe kelinye nelinye ibuthelelo ukutjengisa
inomboro yezinto ezibaliweko. Ukubala ngeenqhema kuzokulungiselela abafundi bonyana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ezingahlolwa ngokubala
bazwisise ukubuyabuyelela.
Abafundi kufanele banikelwe ithuba lokubona bonyana isiqhema se-100 singenziwa
ngeendlela ezihlukneko. isibonelo
• I-10 leenqhema zamatjhumi;
• I-100 lezinto ezikhamba ngayinye nofana
• Iinqhema ezi-2 zama-50.
Ukubala uye phambili
Abafundi basadinga ilemuko lokunikelwa ibuthelelo lezinto bese babala baye phambili
ukusuka lapho.
Iinsetjenziswa:
Ukuyelela ngokutjheja kufanele kunikelwe imihlobo yeensetjenziswa ezisetjenziswako
• Iinsetjenziswa ezihlelekileko, ezifana imilandelande yemincamo yokubala,
zingasetjenziswa.
• I –abhakhasi ingasetjenziselwa ukulungiselela ukubala ngeenqhema zangokulitjhumi.
• Bangenza iinyanda zanga-2, iinyanda zanga-5 nangalitjhumi ngeenthoro zomlilo nofana
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
iingojwana zokubala bese zibalwa sezizoke.
• Imali yokudlalisa
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Abafundi nasele babone ama-apharathasi wokubala angakahleleki nofana ezingakabekwa
Ukubala eziphathekako eziphathekako ngeenqhema, bagqugquzele bonyana babeke izinto ngeenqhema nebabalako.
izinto Linganisa begodu ubale Bala ngokuthembeka Abafundi kudingeka benze ukuhlangana phakathi kwama odinali namakhadinali
ngokuthembeka izinto izinto zangamalanga nebabalako. Lokhu kuphumelela lokha abafundi babona bonyana nawujamisa ukubala uye
zangamalanga ukuya ukuya okungasenani phambili afike entweni ya-50. Ekupheleni kweThemu abafundi bafanele bakghone uku:
okungaseneni ema-200. i-100 • bala izinto abangazithinta nofana baziphathe;
Amaqhinga Nikela isilinganiso • bala izinto zokubala ngeenqhema zangakuhlanu nangalitjhumi; begodu
wokubuthelela senomboro yezinto
• hlela kabutjha izinto zokubala begodu abuyelele azibale. Abafundi bafanele bakghone
ayakhuthazwa. ngokuzwakalako
ukuphendula imibuzo.”Usese nenani lezinto zokubala ezilinganako?”
ezingahlolwa ngokubala
Imisetjenzana iragela phambili
Abafundi kufanele bakghone ukuphendula imihlobo yeenlayelo nemibuzo elandelako:
• Nazi izinto zokubala ezili-100. Zibale ngokuzibuthelela ngeenqhema ezimatjhumi. Manjesi
zihlole ngokuzibala ngakunye. Ngaphambi kokubana uthome, uqabanga bonyana isamba
sisazokufana?
• Ukubala zoke izinto zokubala ezi-100, uzokunyula ukubala ngeenqhema zama-20 nofana
ngama-25? Kungani?
• Thatha isiqunto bonyana kungaba ngiyiphi indlela engcono yokubala iimpensela
ezibuthelelweko.
• Lapha kune zinto zokubala ezi-80. Nasingazibala ngazimbili nofana ngamatjhumi, isamba
sezinto zokubala zisazokulingana.
• Bala izinto zokubala ezima-46 ngokuzibeka ngeenqhema zangazimbili.
213
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
214 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili IThemu yoku- 1 yeGreyidi yesi- 2 umsebenzi ohlanganisiweko owenziwe ngeThemu yesi-4
Ukubala uye nemuva nga: nemuva nga: eGreyidini yoku- 1.
phambili • Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye Ukubala ngokweqa kuzokuhlala kulikghono eliqakathekileko elizokulekelela abafundi
nemuva nenye inomboro nenye inomboro nebabalako. Ukwenza umlolozelo ngeenomboro ngokulandelana kusese likghono
hlangana ne-0 na-200 hlangana ne-0 na-100 eliqakathekileko elithlogekako. Ukubala kufanele kuragele phambili ukwenza ingcenye
• Li-10 ukusuka • Li-10 ukusuka yepilo yangamalanga yomfundi nangokunjalo nangemidunduzelo iingoma neendatjana
kesinye nesinye kesinye nesinye kufanele kube yingcenye yelemuko lokubala.
isibuyabuyelelo se-10 isibuyabuyelelo se-10 EGreyidini yoku-1 abafundi bathuthukise iminqopho elandelako ephathelene nokubala:
hlangana ne-0 na -200 hlangana ne-0 na -100 • Umnqopho wokonga
• Ku-5 ukusuka • Ku-5 ukusuka • Umthetho wekhadinali – ukutjho ibuthelelo
kesinye nesinye kesinye nesinye
• Ukulinganisa patsi
isibuyabuyelelo saka isibuyabuyelelo saka
ku-5 hlangana ne-0 ku-5 hlangana ne-0 • Ukumadanisa kunye-nakunye okukhambelanako
na-200 na-100 Ukubala ngokweqa
• Ku-2 ukusuka • Ku-2 ukusuka Ukubala ngokweqa kungelinye igama elitjho ukubala ngeenqhema kuyasiza ukuthuthukisa
kesinye nesinye kesinye nesinye ilemuko lamaphetheni weenomboro. Ukubala ngokweqa kugqugquzela abafundi ukubala
isibuyabuyelelo saka isibuyabuyelelo saka nokucabanga ngeenqhema, okubenza babe nekghono. Lokho nacho kubasiza bonyana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ku- 2 hlangana ne -0 ku- 2 hlangana ne-0 bathuthukise amakghono wabo wokulinganisa.
na-200 na-100. Ukubala ngeenqhema kubenza balemuke ubudlelwano obuphakathi kweenomboro
• Ku-3 ukusuka ezingalandelani kuhle. Iba sisandlalelo sephetheni yeenomboro nokubuyabuyelela
kesinye nesinye Abafundi kufanele baragele phambili nokusekelwa ngemifanekiso ukulekelela ukubala
isibuyabuyelelo saka ngokweqa:
ku-3 hlangana ne -0
Isibonelo
na-200
• Ku-4 ukusuka 2 4 6 8 10
kesinye nesinye 12 14 16 18 20
isibuyabuyelelo saka 22 24 26 8 30
ku-4 hlangana ne -0 32 34 36 38 40
na-200 42 44 46 48 50
52 54 56 58 60
62 64 66 68 70
72 74 76 78 80
82 84 86 88 90
92 94 96 98 100
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Imisetjenzana iragela phambili :
Ukubala uye nemuva nga: nemuva nga: Ukubala uye phambili nemuva ukufika e-100 kusetjhenziswa itjhadi le-100 elikhulu:
phambili • Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye (5-7 yemizuzu ngelanga). Thoma ukubala NETLASI LOKE, jama kenye yeenoboro isib.
nemuva nenye inomboro nenye inomboro 24. Abafundi bayadlhegana ngokubala baragele phambili kusukela enomborweni leyo
hlangana ne-0 na-200 hlangana ne-0 na-100 bakwenze ngeenqhema/ ngababili/ ngamunye ngamunye njengokulayelwa ngutitjhere,
• Li-10 ukusuka • Li-10 ukusuka kutlolwe inomboro lapho bagcina khona.
kesinye nesinye kesinye nesinye Buza imibuzo efana nokuthi ngiyiphi iphetheni oyibonako? Igcina kuphi iphetheni
isibuyabuyelelo se-10 isibuyabuyelelo se-10 yokuthoma (isibonelo: iphetheni yokubala ngaku 2: 2; 4; 6; 8; 10)
hlangana ne-0 na -200 hlangana ne-0 na -100 Ekhupheleni kweThemu abafundi bafanele bakghone uku:
• Ku-5 ukusuka • Ku-5 ukusuka Bala ngomlomo baphimisele bebaphendule imibuzo efana nokuthi:
kesinye nesinye kesinye nesinye
• Thoma ema-52, bala uye phambili ngakunye ukufika ema-75
isibuyabuyelelo saka isibuyabuyelelo saka
ku-5 hlangana ne-0 ku-5 hlangana ne-0 • Thoma ema-88 ubale uye emuva ngakunye ukufika ema-70
na-200 na-100 • Thoma ema-38 ubale ngakubili ukufika ema-50
• Ku-2 ukusuka • Ku-2 ukusuka • Thoma ema-45 ubale ngakuhlanu ukufika e-100
kesinye nesinye kesinye nesinye • Thoma e-10 ubale ngalitjhumi ukufika e-100
isibuyabuyelelo saka isibuyabuyelelo saka
Abafundi bafanele ukusebenzisa amakghono wabo wokubala emisetjenzaneni etloliweko.
ku- 2 hlangana ne -0 ku- 2 hlangana ne-0
Isibonelo, emisetjenzaneni yokuzijamela, bangaqedelela ukulandelana kweenomboro:
na-200 na-100.
Abafundi bakopa bebandise ukulandelana kweenomboro okuhlukeneko.
• Ku-3 ukusuka
kesinye nesinye Isibonelo
isibuyabuyelelo saka 76; 75; 74; __; 72; __; __; __; 68 (ubuyele emuva ngakunye)
ku-3 hlangana ne -0 27; 28; 29; __; __; 32; __ ( uye phambili ngakunye).
na-200
8; 10; __; 14, __ (ngakubili nofana inomboro-lingana)
• Ku-4 ukusuka
kesinye nesinye 5; 10, 15, 20; 25; ___ (ngakuhlanu)
isibuyabuyelelo saka 90; __; 70 60; __ (ukubala ubuyele emuva ngalitjhumi).
ku-4 hlangana ne -0 10, 20, 30, 40, ___, 60, 70, ___ (ukubala ubuyele emuva ngalitjhumi).
na-200
215
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
216 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.3 Ukukhumbula, ukubona Ukukhumbula, ukubona NgeThemu le abafundi baragela phambili ngoku:
Amat- nokufunda iinomboro nokufunda iinomboro • funda nokutlola amatshwayo wenomboro ukufika e-100, begodu
shwayo • Ukukhumbula, • Ukukhumbula, • funda nokutlola amagama wenomboro ukufika ema-25
weenom- ukubona nokufunda ukubona nokufunda
Ekupheleni kweThemu abafundi kufanele bakghone uku:
boro amatshwayo amatshway
namagama weenomboro wenomboro ukusukela • tlola itshwayo lenomboro legama lenomboro ethuliweko:
weenom- ukusukela e-0 ukufika e-0 ukufika e-100 • Itjhumi nekhomba
boro kuma-200 • Ukutlola amatshwayo Amatjhumi amabili nantathu
• Ukutlola amatshwayo weenomboro ukusuka
weenomboro ukusuka e-0 ukufika e-100 66 Amatjhumi alithoba nanye
e-0 ukufika ma-200 • Ukwazi nokufunda 8 Amatjhumi amahlanu nantathu
• Ukwazi nokufunda amabizo wenomboro
amabizo wenomboro kusuka e-0 ukufika 172 Amatjhumi amane
ukusuka e-0 ukufika ema-25 109 Amatjhumi amathathu nobunane
e-100 • Utlola amagama
• Utlola amagama wenomboro kusukela 91 Ikhulu namatjhumi alikhomba nambili
wenomboro ukusukela e-0 ukufika ema- 25
ISIGABA ESISISEKELO AMAGREYIDI 1-3
40 Amatjhumi asithandathu nathandathu
e-0 ukufika e-100
53 Bunane
38 Ikhulu nethoba
Fundela phezulu iinomboro ezisekaradeni ngalinye:
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.4 Ukumadanisa Ukumadanisa Irherho leenomboro lokuhlela nokumadanisa limetjha irherho leenomboro lokubala. Lokhu
Ukuhlathu- nokuhlela iinomboro nokuhlela iinomboro kutjho bonyana ukuze ubale ufike ema-99, umqondo weenomboro wabafundi kufanele
lula, uku- kufika ema- 99 kufika ema- 25 uthuthukise kuhle ukuze afike esisombululweni. Lokha abafundi bangahlela bamadanise
madanisa, • Ukuhlela iinomboro • Ukuhlela iinomboro ngokuzithemba ngaphezulu kwemfuneko lokho kungangezelea inomboro nokuzwisisa
nokuhlela ezipheleleko. Ukufika ezipheleleko. Kusukela amatswayo wembalo
iinomboro ema-99 kusukela kencani khulu kufikela Abafundi kufanele baragele phambili nokusebenzisa ilimi lokuhlela nokumadanisa:
kencani khulu ukuya kekulu khulu begodu • Wokuthoma, wesibili, wesithathu, wesine, wesihlanu, wesithandathu........
kwekulu khulu begodu kusukela kekulu khulu
• Zingaki..........
nakusukela kekulu kuya kencani khulu
khulu ukuya kwencani • Ngokunengi ngange, inomboro elinga na............
• Ukumadanisa
khulu iinomboro • Ilingana na, okunengi kuna, engaphasi kune, ezimbalwa kune, okukhulu kuna, okuncani
• Ukumadanisa ngokusebenzisa kuna ...banzi kuna…
iinomboro ezipheleleko ngokunengi khulu, • Kokuthoma, kokugcina, ngaphambili, ngemuva, okulandelako, hlangana na....
kufika ema- 99 ngokuncani khulu, Ngokuhlela nokumadanisa izinto neenomboro abafundi bafunda bonyana:
usebenzise okuncani okunengi kuna,
• ubujamo benomboro eyikhadinali busetjhenziswe ukuhlathulula inomboro ese-setheni;
kuna, okukhulu kuna, okuncani kuna,
okunengi kuna, okulinganako. • ubujamo benomboro eyi-odinali itjho inomboro ehlobana nendawo yayo esethini.
okuncani kuna, Isibonelo faka umbala osarulana esekeleni yesithathu
Sebenzisa
okulingana na. iinomborosikhundla Imisetjhenzana eragela phambili
Sebenzisa ukutjengisa ukuhlela, • Iinomboro eziyi odinali: Coca ngomahluko ophakathi kwamagama ‘kunye’ noko’kuthoma’;
iinomborosikhundla iindawo nofana ‘kubili’ no ‘kwesibili’ njll. Ukubuza imibuzo efana nokuthi: ungawasebenzisa nini amagama
ukutjengisa ukuhlela, ubujamo ‘kuthathu nokwesithathu?’ singatlola u-kokuthoma, kwesibili, kwesithathu ngendlela
iindawo nofana Beka izinto emudeni erhunyeziweko?
ubujamo ngokulandelana ukusuka • Hlukanisa abafundi babe ziinqhema ezintathu ukuya kezine ngokulinganako. Omunye
Beka izinto emudeni kweyokuthoma ukuya nomunye umfundi uthola ikarada lapho azokutlola khona igama lakhe. Abafundi
ngokulandelana ukusuka kweyetjhumi nofana bazokubeka amakarada wamagama ngokulandelana kwama alfabethi. Utitjhere
kweyokuthoma ukuya keyokuthoma ukuya nabafundi bangathoma babuze imibuzo, Isib. ngubani wesine esiqhemeni senu?
kweyetjhumi nofana keyokugcina, Isib.
keyokuthoma ukuya Yokuthoma, yesibili,
keyokugcina, Isib. yesithathu ... keyetjhumi.
Yokuthoma, yesibili,
yesithathu.... ematjhumini
amabili.
217
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
218 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.5 Ukulemuka ubukhulu Thoma ukulemuka Kuyini okuhlukileko kune Greyidi yoku-1?
Ubukhulu bedijithi okungenani ubukhulu bedijithi EThemeni yoku-1, abafundi basebenza ngerherho leenomboro eziphezulu bebaragele
bedijithi iinomboro zamadijithi okungenani iinomboro phambili noku:
ama-2 ukufika ema-99 zamadijithi ama-2 • bala begodu benze iinqhema zatjhumi nezitjhaphulukileko zangakunye; begodu
• Ukwazi bonyana idijithi ukufika ema-25
• tlola i-18 = 1 itjhumi nemivo e-8
ngayinye ijameleni • Ukwazi bonyana idijithi
13 = 10 na 3.
• Ukuphula iinomboro ngayinye ijameleni
NgeThemu le abafundi bafanele baragele phambili ukuzibandakanya emalemukweni
zamadijithi amabili • Ukuphula iinomboro
amanengi ukuthoma itjhumi libesilinganiso begodu libe liyunithi. Itjhumi liyitjhumi elilodwa
ukufika e-99 zibe zamadijithi amabili eLimimethe imivo elitjhumi. Amagama ajayelekileko ‘itjhumi nokukodwa’ (ama-24 ku-2
ziimbuyeleli zetjhumi zibe ziimbuyeleli yeenqhema nofana ku-2 yamatjhumi na-4 yokukodwa) kufanele asetjenziswe njalonjalo
nemivo (TM) zetjhumi nemivo (TM) ukuthoma ilimi elitshwaya ukuphula nokwakha.
• Bona bewutjho • Bona bewutjho Ukusebenza ngama-apharethasi aphathekako
ubukhulu bedijithi ubukhulu bedijithi
• Ukubala ngeengojwana/iinthoro zomlilo
ngayinye ngayinye
Ukubala iingojwana nofana iinthoro zomlilo zingabuthelelwa ukutjengisa iinyanda
zangalitjhumi nezingakahlangani ezingazinye.
Isibonelo:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukutjengisa 12 Ukutjengisa 18 Ukutjengisa 25
• I-Abhakhasi
Abafundi bafanele baragele phambili nokusebenzisa ama-apharathasi aphathekako
ngokubuthelela benze itjhumi lokukodwa nokuzwisisa bonyana i-10 lisiqhema sinye lezinto
ezilitjhumi ezingakunye. Ngokusebenzisa i-abhakhasi, abafundi bafanele bakghone
ukutjengisa:
• Itjhumi linye;
• Itjhumi linye nemivo e-5;
• Itjhumi linye nemivo e-6;
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Itjhumi linye nemivo e-7;
• Itjhumi linye nemivo e-8; begodu
• Itjhumi linye nemivo e-9
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.5 Ukulemuka ubukhulu Thoma ukulemuka • Amabhlogo weDienes
Ubukhulu bedijithi okungenani ubukhulu bedijithi Ngethemeni le iinsetjenziswa zokufundisa ubukhulu bedijithi bungakhuliswa. Amabhlogo
bedijithi iinomboro zamadijithi okungenani iinomboro wesisekelo se-10
ama-2 ukufika ema-99 zamadijithi ama-2
(kuyincenye yamabhlogo weDienes) angathulwa ukuthuthukisa umqondo wesumi
• Ukwazi bonyana idijithi ukufika ema-25
njengelinye elipheleleko begodu bonyana:
ngayinye ijameleni • Ukwazi bonyana idijithi
-- abokunye abali-10 benza itjhumi li-1;
• Ukuphula iinomboro ngayinye ijameleni
-- abokunye abama-20 benza amatjhumi ama-2; begodu
zamadijithi amabili • Ukuphula iinomboro
ukufika e-99 zibe zamadijithi amabili -- abokunye abali-16 benza itjhumi eli-1 nnemivo esi-6
ziimbuyeleli zetjhumi zibe ziimbuyeleli Nanyana abafundi basadinga ukubala nokubuthelela ngalitjhumi, bangatjengisa i-18
nemivo (TM) zetjhumi nemivo (TM) ngokubeka isitina sinye sangalitjhumi ndawonye abeke iintinyana ezibunane ezihlukeneko
• Bona bewutjho • Bona bewutjho ukutjengisa inomboro.
ubukhulu bedijithi ubukhulu bedijithi Abafundi bafanele begodu babuthelele ukutjengisa ama-20
ngayinye ngayinye Ukujamisela okulinganako
NgeThemu leli umnqopho kubonisa ukujamiselela okulinganako lwenomboro efanako.
Amatjhumi amabili kufanele ahlathululwe njengamatjhumi ama-2 (kusetjenziswa iinyanda
nofana iinqhema zezinto)
Nofana inqhema ezi-2 zamatjhumi. Kuqakathekile bonyana utjhengise abafundi bonyana
ama-20 wezinto ezikhamba ngayinye, isiqhema sinye esinetjhumi begodu neenqhema
ezimbili zakalitjhumi. Abafundi bafanele banikelwe ithuba lokuhlathulula amalungiselelo,
batjho bonyana ngokuphi okuhlukileko nokuthi ngikuphi okufanako.
• Amakarada wobukhulu bedijithi/ amakarada wamafladi
Amakarada wobukhulu beditjhithi angaziswa abe asetjenziswe ngeThemu leli ukutjengisa
bonyana iinomboro ziyakhiwa. Amakarada wobukhulu bedijithi angatjengiswa akhambisane
neenyanda nofana iinqhema zezinto.
• Ubungakho bedijithi
Abafundi bafanele bathome batjho bonyana idijithi ngalinye lijamele ini? Buza abafundi:
-- uli-7 ujamele liphi idigithi enomborweni ama-27?
-- uku-2 ujamele yiphi idijithi enomborweni ama-29?
Abafundi bafanele basebenzise amakarada wobungako bedijithi ukuqinisekisa iintatimende
zabo.
• Ukudlulela emathekistini atloliweko
Ngesikhathi sokuzijamela abafundi bafanele babandakanywe emisetjenzaneni etlolwako
eyakhako nehlanganisako:
219
-- Umqondo weenqhema zangalitjhumi nalezo ezihlukeneko zangakunye/imivo; begodu
-- Nobukhulu bedijithi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
220 IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.5 Ukulemuka ubukhulu Thoma ukulemuka Isibonelo:
Ubukhulu bedijithi okungenani ubukhulu bedijithi Faka umbala emincameni eli-12
bedijithi iinomboro zamadijithi okungenani iinomboro
ama-2 ukufika ema-99 zamadijithi ama-2
• Ukwazi bonyana idijithi ukufika ema-25 Faka umbala emincameni eli-16
ngayinye ijameleni • Ukwazi bonyana idijithi
• Ukuphula iinomboro ngayinye ijameleni
zamadijithi amabili • Ukuphula iinomboro Zaliselela ngenomboro engekho (lokhu kungenziwa nofana kuhlathululwe ngokusebenzisa
ukufika e-99 zibe zamadijithi amabili ama-apharathasi aphathekako
ziimbuyeleli zetjhumi zibe ziimbuyeleli i-18 = netjhumi li-1 nemivo ebu ____
nemivo (TM) zetjhumi nemivo (TM) ama-23 = namatjhumi ama_____ nemivo emi-3
• Bona bewutjho • Bona bewutjho Iinsetjenziswa eziphakanyisiweko
ubukhulu bedijithi ubukhulu bedijithi
ngayinye ngayinye Izinto ezingabuthelelwa:
• Iingojwana zokubala
• Izinto zokubala ezingathungelelwa
• Iinthoro zomlilo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Iingojwana ze-ayisikhrimu
• Amakhyubsi angenelanako
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Abafundi balindeleke bonyana basombulule imiraro yamagama ngokusebenzisa
Amathek- alandelako nawurarulula alandelako nawurarulula amathekhiniki alandelako:
hiniki wok- imiraro uhlathulule imiraro uhlathulule • Ukwakha nokuphula iinomboro
neensombululo zemiraro: neensombululo zemiraro: • Ukubuyelela kabili nokuquntula phakathi
urarulula
• Amanambalayini
imiraro • Imigwalonofana • Imigwalo nofana Imigwalo nofana ama-apharathasi aphathekako
ama-apharathasi ama-apharathasi Abafundi bazokuragela phambili nokugwala iinthombe begodu basebenzise ama-
aphathekako isib. izinto aphathekako isib. izinto apharathasi aphathekako ukusombulula imiraro. Kuqakathekile bonyana iinthombe nofana
zokubala zokubala imigwalo kumumethe iinomboro begodu nemitjho yeenomboro.
• Ukwakha nokuphula • Ukwakha nokuphula Ukwakha nokuphula
iinomboro iinomboro Le ngenye yamathekhiniki aqakatheke khulu esigabeni sisekelo. Ukusebenzisa ithekhniki le
kuvumela abafundi ukuhlukanisa nokuhlanganisa iinomboro ukulekelela ukwenza ukubalisa
• Ukubuyelela • Ukubuyelela kube lula. Bazokusebenzisa ithekhniki le ngobubanzi nesigabeni esiphakathi.
nokuhafula phakathi nokuhafula phakathi Ukubuyelela kabili nokuhafula phakathi
• Amanambalayini • Amanambalayini Ithekhniki le inelwazi lezinto zephasi begodu ifuna umqondo weenomboro eqinileko.
Abafundi abakghona ukukhetha ithekhniki le batjhuguluka lula emaqhingeni
abawasebenzisako. Isibonelo:
Umraro wamagama: ngelinye ilanga ekliniki abantwana abali-17 bahlatjwa injekhtjheni
yomgomani. Ngelanga elilandelako abanye abali-16 nabo bahlatjwa injekhtjheni
yomgomani. Abafundi abangaki abahlatjwe injekhtjheni nesele baboke?
Umraro kufanele usombululwe ngokusebenzisa ukubuyelela kabili. Umfundi angahle athi
buyelela kabili i-16 hlanganisa nanye nofana kubuyelele kabili i-17 ukhuphe yinye.
Amanambalayini
Ukusebenzisa inambalayini ngokulandelana kungavumela abafundi ukurhekhoda
ukucabanga kwabo nokulandelela umtlala wayo. Begodu ivumela abafundi bonyana babe
nomfanekiso wokurhekoda abangawusebenzisa ukuhlathulula bonyana bawusombulule
bunjani umraro.
Abafundi bathome ukusebenza ngenambalayini eGreyidini yo-1. Kwanje sekufanele
bakghone ukwakha inambalayini enganalitho lapho bazokufaka khona inomboro yokuthoma
begodu bakhetha bonyana bangasuka bunjani enomborweni enye ayekenye.
NgeThemu le kuzokuba neraagelo phambili esakhiweni senambalayini.
Isibonelo sokusebenzisa inambalayini ukurekhoda amathekhiniki wokubala:
UZonke unamathoyi asi-6, uZanele unamanengi nga-6 kunoZonke. UZanele unamathoyi
amanengi ngamangakhi? Abafundi bazokwakha inambalayini elandelako ukubasiza
bonyana bafike bunjani
ependulweni.
221 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Abafundi bangaphula i-6 ibe ziinqhema ezimbili. Inambalayini izokutjengisa imeqo yanga-2
kusuka esi-6.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
222 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Isibonelo:
Amathek- alandelako nawurarulula alandelako nawurarulula
hiniki wok- imiraro uhlathulule imiraro uhlathulule
urarulula neensombululo zemiraro: neensombululo zemiraro:
imiraro • Imigwalonofana • Imigwalo nofana
ama-apharathasi ama-apharathasi Abafundi nasele bazithemba ngokubala baye phambili kusukela enomborweni enikelweko.
Inambalayini ithome esi-6. Ngendlela inambalayini le yakhiwe ngayo imetjha umqondo
aphathekako isib. izinto aphathekako isib. izinto
wokubala uye phambili. Kubalulekile bonyana abafundi babone Amanambalayini ezithoma
zokubala zokubala eenomborweni ezihlukeneko nawuyisebenzisela ukubala uye phambili nofana ukuhlela
• Ukwakha nokuphula • Ukwakha nokuphula iinomboro. Omunye angaphula isi-6 sibe zinqhema za-2 begodu uhlanganise uye phambii
iinomboro iinomboro ukusuka esi-6.
• Ukubuyelela • Ukubuyelela Isibonelo:
nokuhafula phakathi nokuhafula phakathi
• Amanambalayini • Amanambalayini
U-12 angahafulwa begodu imeqo emi-3 yanga ku-2 iyarekhodwa.
Isibonelo:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Abafundi bafanele banikelwe amathuba amanengi wokutjho bonyana inomboro
ingatholakala bunjani nawusebenzisa inambalayini.
Omunye angabuza: mimeqo enjani ehlukeneko esingayenza ukufika ku-15? Ukuze weqe
ukuya eenomborweni abafundi bafanele bazi amabhondi ka-15 nofana bafanele bakwazi
ukusenzisa inambalayini ukuze bathole ipendulo. Kuqakathekile bonyana abafundi
bakhulume ngokuthi kufanele ube mude kangangani umeqo loyo. Ukuzijayeza imihlobo
le yemisebenzi ulungiselela abafundi bonyana bakwazi ukusebenza ngomuda onganazo
iinomboro.
Nawusebenza ngenambalayini, abanye abafundi badinga ukubamba intambo enemincamo
ibe ngaphezulu nofana ngaphasi kwenambalayini ukubasiza bonyana babale.
Vumela abafundi bonyana bakhethe amathekhiniki abazizwa batjhaphulukileko
nabawasebenzisako. Ngokunjalo, nangabe abafundi basebenzisa amathekhiniki layo
abazizwa banganakghono kiwo, badinga bonyana balulekwe bonyana basebenzise leyo
abayikghonako. Abafundi bazijayeza amaqhinga layo. Akutlogeki bonyana babe butjhelela
ekuwasebenziseni.
Yelela bonyana abafundi kanengi basebenzisa iindlela ezihlukeneko zokusombulula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
umraro okungenzeka bonyana akusikho obekulindelwe ngutitjhere. Isibonelo, umraro
wokuhlukanisa ungasombululwa ngokukhipha okubuyelelwe kabili. Iindlela zokwenza
zabafundi kuzokutjhugulula ngokukhamba konyaka njengombana ukuzwisa nokujayela
imihlobo yemiraro isiya ngokukhula begodu nomqondonomboro wabo uthuthuka
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Ngikuphi okuhlukileko kuneGreyidini yoku-1?
Ukuh- yamagama yamagama NgeThemu leli abafundi bazijayeza ukwenza imiraro yamagama bebasebenzela ukuba
langanisa ezisebujameni ezisebujameni babantu abazithembako ekusebenziseni amathekhiniki alandelako nabasombulula imiraro:
bewuhlathulule bewuhlathulule • Ukugwala nofana ama-apharathasi aphathekako
nokukhupha
iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka • Ukwakha nokuphula
ukuhlanganisa ukuhlanganisa
• Ukubuyelela kabili nokuhafula
nokukhupha nempendulo nokukhupha nempendulo
ukufika e-99. ukufika e-20. • Amanambalayini
Ethemini leli, nikela abafundi irhelebho elinengi emizameni yabo yokurekhoda
nokujamiselela ukubala kwabo. Abafundi bafanele batlole phasi ukulandelana
kweenomboro njengerekhodi lokusombulula imiraro. Kuqakathekile ukuqala bonyana
ngibaphi abafundi abatlagako ukutlola umutjho wenomboro ukuthola umraro othile.
Ihlobo lomraro 1: Itjhentjhi
Hlanganyela Hlukanisa
Umphumela UMoeketsi unamaswidi asi-6, Kunaswidi ali-15. UMoeketsie
awaziwa uMahlodi umnikela amanye amane udla asi- 6. Kusele mangaki
ngaphezulu. UMoeketsi unamaswidi wakaMahlodi?
amangaki nasele awoke?
Itjhentjhi UMoeketsi unamaswidi asi-6, utloga Moeketsi unamaswidi ali-15.
ayaziwa amaswidi amangaki ngaphezu kwala UMahlodi udla ambadlwana. Kusele
ukuze abe namaswidi ali-15? ali-9. UMahlodi udle amaswidi
amangaki?
Ukuthoma UMoeketsi unamaswidi UMoeketsi udle amaswidi. Unikela
akwaziwa ambadlwana. UMahlodi umnikela ali- uMahlodi asi-6 kwanjesi usele
9 ngaphezulu. UMoeketsi uthome namaswidi abu-8. Uthome
anamaswidi amangaki? anamaswidi amangaki?
Ihlobo lomraro 2: Ukumadanisa
Hlanganyela Hlukanisa
Umphumela UMoeketsi unamaswidi asi-6. UMahlodi unamaswidi -15.
awaziwa
Itjhentjhi UMahlodi unamaswidi ali-9. UMahlodi unamaswidi asi-
ayaziwa UMahlodi unamaswidi amanengi 6. Unamaswidi ali-9 angaphasi
ngamgaki kuno Moeketsi? kunowaka Moeketsi. UMahlodi
unamaswidi amangaki?
223 Ukuthoma UMahlodi unamaswidi -15. UMahlodi unamaswidi a 16.
akwaziwa Unamaswidi amanengi nga-9 kuno UMoeketsi unamaswidi angaphasi
Moeketsi. UMoeketsi unamaswidi nga-9 kuno Mahlodi. UMahlodi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amangaki? unamaswidi amangaki?
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
224 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Ihlobo lomraro 3: Ukulinganisa `
Ukuh- yamagama yamagama
Hlanganyela okuhlukanisiweko
langanisa ezisebujameni ezisebujameni
Umphumela UMahlodi unamaswidi ali-15. UMahlodi unamaswidi ali-16.
bewuhlathulule bewuhlathulule
nokukhupha awaziwa UMoeketsi unamaswidi asi-6. UMoeketsi unamaswidi asi-6.
iinsombululo zakho iinsombululo zakho Kudingeka amaswidi amangaki Kufanele uMoeketsi adle amaswidi
zemiraro ezifaka zemiraro ezifaka okufanele uMoeketsi awathole ukuze amangaki ukuze abe namaswidi
ukuhlanganisa ukuhlanganisa abe nalingana newaka Mahlodi? alingana newaka Moeketsi?
nokukhupha nempendulo nokukhupha nempendulo Itjhentjhi UMoeketsi unamaswidi asi-6. UMoeketsi unamaswidi asi-
ukufika e-99. ukufika e-20. ayaziwa Nakangathenga amanye ali -9 6. Nangabe uMahlodi angadla
uzokuba namswidi alingana newaka amaswidi ali-9 azokulingana
Mahlodi. UMahlodi unamaswidi namaswidi kaMoeketsi. UMoeketsi
amangaki? unamaswidi amangaki?
Ukuthoma UMahlodi unamaswidi ali-15. Nange UMahlodi unamaswidi ali-16.
akwaziwa Moeketsi angathenga amanye Nangakhe adle amaswidi ali-9
amaswidi asi-9 angaba namaswidi angaba namaswidi alingana newaka
alingana newaka Mahlodi. Moeketsi. UMoeketsi unamaswidi
UMoeketsi unamaswidi amangaki? amangaki?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
1.8 Rarulula imiraro Rarulula imiraro Ukubuyabuyelela
Ukuh- yamagama yamagama Isendlalelo sokuzwisisa ukubuyabuyelela eGreyidini le kungeenqhema. Ukwenza iinqhema
langanisa ezisebujameni ezisebujameni kungasiza abafundi ebujameni bokujamiselela ukubuyabuyelela.
okubuyele- bewuhlathulule bewuhlathulule
Kuneengaba ezintathu eziqakathekileko zobujamo bemiraro obufaka hlangana
lweko iinsombululo zakho iinsombululo zakho
ukubuyabuyelela kweenomboro ezipheleleko :
kurholela zemiraro, ezifaka zemiraro, ezifaka
ukuhlanganisa ukuhlanganisa • Iinqhema ezilinganako (isib. Amathebula kathathu, elinye nelinye linabantwana
ekubuy-
okubuyelelweko okubuyelelweko abathatho) layo ajanyiselelwe njengamasthi abuyelelweko.
abuyeleleni
okurholela okurholela • Ukubuyabuyelela kokumadanisa (isib. inani labendazana libuyabuyelela kathathu
ekubuyabuyeleleni ekubuyabuyeleleni ukudlula labesana)
okunempendulo ufikela okunempendulo ufikela • Ukurhemisa aboncamane (isib. Amareyi amane wabantwana abane): okujanyiselelwe
e-50. e-20. njengamareyi namakholomu.
Obunye nobunye ubujamo bungafaniswa neendlela ethile yokubuza umbuzo (bona
iumhlobo wokusombulula imiraro eseGreyidini yesi-2 wesahluko sesi-2)
Ubujamo bemiraro bokubuyabuyelela kufaka hlangana iinomboro ezintathu ezilandelanako
ebedlelwaneni beembalo:
• Ubunengi bezinto esedini ngayinye
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ubunengi bamasethi
• Isamba
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.8 Rarulula imiraro Rarulula imiraro Iimbonelo zemiraro ezingenziwa ngeThemu le
Ukuh- yamagama yamagama Kulindelekile bonyana ngesikhathi kurarululwa imiraro elandelako, abafundi
langanisa ezisebujameni ezisebujameni bazokusebenzisa iinthombe, imigwalo nofana ama-apharathasi aphathekako ukulekelela
okubuyele- bewuhlathulule bewuhlathulule ukubala. Nangabe abafundi bagwala iinthombe ezibalekelela ukubala, imigwalo ifanele
lweko iinsombululo zakho iinsombululo zakho itjengise isimo sokubuthelela. Abafundi bafanele bagqugquzelwe ukutlola imitjho
kurholela zemiraro, ezifaka zemiraro, ezifaka yeenomboro yayoyoke imiraro yamagama. Lindela abafundi bonyana basebenzise
ekubuy- ukuhlanganisa ukuhlanganisa ukuhlanganisa okubuyelelwe kabili komutjho weenomboro ukubonisa isisombululo.
abuyeleleni okubuyelelweko okubuyelelweko
Iimbonelo zemiraro ezingenziwa:
okurholela okurholela
ekubuyabuyeleleni ekubuyabuyeleleni Ukuhlanganisa okubuyelelwako
okunempendulo ufikela okunempendulo ufikela • Imilelenjana emine inamavili amangaki?
e-50. e-20. • Abafundi abali-7 banamehlo amangaki? Abafundi bangahle basombulule umraro
ngendlela elandelako:
Iinthombe nofana imigwalo kufanele zitjengise ukuhlela abantu/ izinto ngeenqhema
Abafundi kufanele bagqugquzelwe ukubala ngaku-2 ukuze bathole ipendulo. Bafanele godu
bagqugquzelwe bonyana bajamiselele ukubala kwabo ngemitjho yeenomboro.
2
+
2
+
2
+
2
+
2
+
2
+
2
=
14
Isilinganiso
UThami usela iinkomitji zebisi ezi-3 ngamalanga. Usela iinkomitji ezingaki zebisi ngeveke?
AmaGridi nofana ukurhemisa
UMnumzana uKhumalo utjale amareyi ama-3 wekhabitjhi. Kuneetjalo zekhabitjhi ezi-5
ereyini. Kuneentjalo ezingaki zamakhabitjhi nasele zizoke?
• Isivande somrorho sinamareyi ama-5 weentjalo elinye nelinye ireyi lineentjalo
ezilinganako. Nange kunesamba seentjalo esi-15, ziintjalo ezingaki ezisereyini ngayinye?
• Isivande semirorho sineentjalo ezi-18 ezitjalwe ereyini. Kuneentjalo ezi-6 ereyini
ngayinye. Mangaki amareyi akhona sewawoke?
225
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
226 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.9 Ukurarulula Ukurarulula Njengekubuyabuyeleni, isisekelo sokuzwisisa ukuhlukanisa eGreyidini leli, kukwaba
Ukubuthele- imiraro yamagama imiraro yamagama ngokulingana nokubuthelela ngeenqhema.
la nok- ezisebujameni ezisebujameni • Ukubuthelela (isib. kunabantwana abalitjhumi nambili, etafuleni ngayinye kunabantwana
wabelana bewuhlathulule bewuhlathulule abane, kunamatafula amangaki?)
okurholela iinsombululo zakho iinsombululo zakho
• Ukwabelana (isib. Abantwana abalitjhumi nambili abangematafuleni amane,
ekuhlu- ufake ukwabelana ufake ukwabelana
kunabantwana abangaki etafuleni ngayinye? )
kaniseni ngokulingana ngokulingana
nokubuthelela nokubuthelela Abanye abafundi bafika esikolweni bakghona ukwenza imiraro yokubuthelela nokwabelana
ngeenqema ngeenqema ngokusebenzisa ama-apharathasi aphathekako.Ubujamo bemiraro yokubuyabuyelela
kweenomboro kweenomboro nokuhlukanisa ifaka hlangana iinomboro ezintathu ezilandelanako ezisebudlelwaneni
ezipheleleko ukufika ezipheleleko ukufika obuseembalweni:
e-50 kanye nempendulo e-20 kanye nempendulo • Ubunengi bezinto obusesedini ngayinye
ezingahle zifaka iinsalela ezingahle zifaka iinsalela • Ubunengi bamasedini
• Isamba
Iimbonelo zemiraro ezingenziwa ngeThemu leli.
Ukwabelana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ngineempensela ezi-12 okufanele nginabele zona nobathathu ngokulinganako,
ziimpensela ezingaki ezizokutholwa ngomunye nomunye wenu?
• Kuneenkoloyi zokudlala ezi-18, ningazabelana ngokulingana phakathi kwenu nobabili?
• Kunamapremu ali-16 nabantwana aba-8 babele ngokulingana, umntwana ngamunye
uzokuthola amapremu amangaki?
• UPopana unamathuthumbo ama-20 uwafaka ngemavasini ama-2. Kungene
amathuthumbo amangaki evasini?
• UTomi ubhaga amakhekhe a-8. Unamasimathisi ali-40. Angafaka amasimathisi
amangaki ekhekheni ngalinye?
Ukubuthelela
• Ungenza iinkoloyi ezingaki nange unamavili abu-8? Iinthuthu zona zingaba zingaki?
• Kunamahabhula ali-18 ngebhoksini kungazaliswa imigodla emingaki enamahabhula ama-
3 engazaliswa?
• Umbhagi ubhaga amatjhatjhatjha ama-30. Ufaka amatjhatjhatjha asi-6 ngebhoksini elinye
nelinye, uzokuzalisa amabhoksi amangaki?
• Kunabantwana aba-16 ngendlini. Singenza iinqhema ezingaki ezinamalunga amane?
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Ukurhemisa
UMongezi upaka izinto zokubala ezi-20 emareyi ali-10. Kunezinto zokubala ezingaki ereyini
nghalinye?
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.11 • Khumbula begodu • Khumbula begodu Ngikuphi okuhlukileko kuneGreyidini yoku-1?
Imali ubone imali eziinhlavu ubone imali eziinhlavu NgeThemu le abafundi bazijayeza ukubona imali nokuphula imali ibe ziingcenye ezincani.
zeSewula Afrika : (5c, zeSewula Afrika : (5c,
Iimboniso zemiraro ezingenziwa ngeThemu leli
10c, 20, 50c, R1, R2; 10c, 20, 50c, R1, R2;
R5) kunye nemali R5) kunye nemali • Ukuhlukanisela abantwana abane ama-50c ngokulinganako. Hlathulula bonyana
yemaphepha (R10, yemaphepha (R10, ungakwenza bunjani?
R20, R50). R20, R50). • Itjhapisi eyodwa Ibiza i-10c. UBusi usebenzisa ama-50c. Ungathenga amatjhapisi
• Sombulula imiraro • Sombulula imiraro amangaki?
efaka hlangana efaka hlangana • UThenji ubhadelela ama-R5 ukukhwela iteksi nakaya esikolweni, ubhadele ngemali
amanani wemali amanani wemali yephepha ema-R20. Uzokubuyelwa yimalini itjhentjhi? Uzokusalelwa yimalini nasele
netjhentjii yama R99 netjhentjii emasende abuyela ekhaya ngeteksi?
neyamasende ukufika ukufika e-50c nofana • IFizipopo Ibiza R2-50, UPalesa ufuna ukuthenga amafizipopo a-4, unemali engange ama
e-90c amaranda ukufikela –R8, 00. Ngabe unemali eyaneleko yokuthenga amafizipopo? Nangabe ayikaneli, udinga
e-R20 imali engangani uPalesa?
227
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
228 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.12 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Ngikuphi okuhlukileko kuneGreyidini yoku-1?
Amathekh- alandelako nawubalako alandelayo nawubalako Abafundi balindeleke bonyana basombulule imiraro yokubala esebujameni
iniki • Imigwalo nofana • Imigwalo nofana obutjhaphulukileko kusetjenziswa amathekhiniki alandelako:
(iindlela ama-apharethasi ama-apharethasi • Imigwalo nofana ama-apharathasi aphathekako
namaqh- aphathekako aphathekako • Ukukwakha nokuphula iinomboro
inga) njengezinto zokubala njengezinto zokubala
• Ukubuyelela kabili nokuhafula phakathi
• Ukwakha bewuphadhle • Ukwakha bewuphadhle
• Amanambalayini
iinomboro iinomboro
Imigwalo namkha ama-apharathasi aphathekako
• Ukubuyelela • Ukubuyelela
nokuhafula phakathi nokuhafula phakathi Abafundi bazokuragela phambili nokugwala iinthombe begodu basebenzise ama-
apharathasi ukusombulula imiraro. Kuqakathekile bonyana iinthombe nofana imigwalo
• Iinamba layini • Iinamba layini
emumethe iinomboro begodu nemitjho yeenomboro.
Ukwakha nokuphula
Le ngenye yamathekkhniki aqakathekileko esigabeni esisekelo (abafundi bazokusebenzisa
ukusabalalisa njalonjalo esigabeni esiphakathi). Ukusebenzisa ithekhniki le kuvumela
abafundi ukusabalalisa nokubuyisela iinomboro okulekelela ukubala kubelula.
NgeThemu leli abafundi bazoku:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Phula iinomboro kusetjenzisa ubukhulu bedijithi
• Phula iinomboro kusetjenzisa isibuyabuyelelo se-10 noku
• Phula iinomboro zikhambe ngazimbili isib. Ukukhamba ngakubili okwenza ama-20
Ukubuyelela kabili nokuhafula phakathi
Abafundi baragela phambili nokusebenzisa ukubuyelela kabili nokuhlukanisa phakathi
njengeqhinga lokubala.
Amanambalayini
Qala amanothi ukubona iimbonelo zokwenza inambalayini okusesigabeni esiphathelene
nokusombulula imiraro.
• Ukuhlanganisa nokukhupha
Abafundi bafanele bakhe inambalayini okungeyabo begodu baphule iinomboro ngendlela
yeengcenye eziphathekako.
Isibonelo:
8 + 12
Inambalayini ifanele ithome ku-8 begodu abafundi batlama :
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
-- Imeqo emi 2 yesi 6
-- Imeqo emi 4 yaka- 3
-- Imeqo emi 3 yaka 4
-- Umeqo owodwa we-10 bese kube nemeqo waka-2
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.12 Sebenzisa amathekhiniki Sebenzisa amathekhiniki • Ukubuyelela
Amathekh- alandelako nawubalako alandelayo nawubalako Amanambalayini kufanele ziragele phambili nokusetjenziswa ukulekelela ukuhlanganisa
iniki • Imigwalo nofana • Imigwalo nofana ngokubuyelela. Umeqo olinganako urekhodwa enambalayini nemitjho elekelelako nayo
(iindlela ama-apharethasi ama-apharethasi ingarekhodwa ngokunjalo.
namaqh- aphathekako aphathekako Isibonelo:
inga) njengezinto zokubala njengezinto zokubala
5 + 5 + 5 + 5 + 5 = 25
• Ukwakha bewuphadhle • Ukwakha bewuphadhle
Iimeqo emi-5 yaku-5 yenza ama-25
iinomboro iinomboro
Iinqhema ezi-5 zaku-5 = 25
• Ukubuyelela • Ukubuyelela
nokuhafula phakathi nokuhafula phakathi 5 x 5 = 25
• Iinamba layini • Iinamba layini Ukubuyabuyelela okunikelweko, abafundi bafanele bakghone ukuhlathulula bonyana imeqo
ingenziwaa njani enambalayinini.
Vumela abafundi bonyana bakhethe amathekhiniki abazizwa batjhaphukile khulu. Nanyana
kunjalo nangabe abafundi basebenzisa amathekhniki lawo abanganakghono badinga
ukukhokhelwa bonyana basebenzise lawo abanekghono lokuwenza. Yelela bonyana
abafundi kanengi bangahle basombulule umraro ngendlela utitjhere agade angakayilindeli.
Isibonelo umraro wokuhlukanisa ungasombululwa ngokukhupha okubuyelelwe nofana
ukubuyabuyelela. Iindlela abafundi zizokutjhuguluka ngokukhamba konyaka njengombana
ukuzwisisa nokujayela umhlobo womraro ukhula, begodu njengembana umqondonomboro
uthuthuka.
229
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
230 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukusuka • Hlanganisa ukufika Ngikuphi okuhlukileko kuneGreyidini yoku-1?
Ukuh- ema-99 ema-20 Kunomnqopho omkhulu ngokuthuthukisa amaqhinga wokubalisisa nofana amathekhiniki
langanisa • Khupha ukufika ema- • Khupha ukusuka ema- ngeThemu leli. Ukuphula iinomboro ukuze ubale kuba ithekhniki ebalulekileko abafundi
nokukhupha 99 20 abangawajayela.
• Sebenzisa • Sebenzisa NgeThemu le iminqopho iba se:
amatshwayo afaneleko amatshwayo afaneleko Kusebenziseni imisetjenzana yokwakha nokuphula iinomboro ezokulekelela ukuzwisisa
( +, -, =, ) ( +, -, =, ) ukuhlanganisa nokukhupha
• Ukuzijayeza/ • Ukuzijayeza/ Abafundi bazijayeza ukuhlanganisa nokukhupha ukufika ema-20. Kuphakathi kwerherho
Ukuphrakhthisa Ukuphrakhthisa leenomboro lezi bonyana abafundi bazokuthoma ukuthuthukisa umqondo wetjhumi
ukulumbana ukulumbana neyunithi.
kwenomboro ukufika kwenomboro ukufika
Ukubala ngeenqhema kuhlala kubalulekile begodu abafundi bafanele bathome
e-10 e-10
ukubona bonyana ukubala uye phambili ngabo kunye ngokulula akusilo iqhinga elilula.
Kungaphakathi kwaleli irherho leenomboro lapho abafundi bafanele bacabange khulu
ngamaqhinga lawo abawasebenzisa ukukhetha iindlela amaqhinga afaneleko wokubala
kulekelela abafundi bonyana babe babali abanekghono.
Ukuze kubalwe phakathi kwerherho leenomboro kusuka kuli-0 kufika ema-20 ilemuko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
labafundi lifanele lifake hlangana:
• Ukubala izinto;
• Ukukhumbula, ukufunda nokutlola iinomboro;
• Ukumadanisa nokuhlela iinomboro;
• Ukukwa nokuphula iinomboro;
• Ukuzijayeza ukuhlanganisa nokukhupha ukufika ema-20
• Ukubuyelela kabili nokuhafula phakathi noku
• Ukutjho ngehloko amaphuzu weenomboro
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukusuka • Hlanganisa ukufika Amathekhiniki wokubala angenziwa wokubala nokukhupha
Ukuh- ema-99 ema-20 Amathekhiniki atjengiswe ngenzasi avumela abafundi ukwenza ngokomthetho ukubala
langanisa • Khupha ukufika ema- • Khupha ukusuka ema- nomqondo wenomboro. Ukujayeza amathekhiniki angenzasi azokugqugquzela abafundi
nokukhupha 99 20 ukubonisa ngobudlelwana obuhlangana neenomboro begodu ifundisa abafundi bonyana
• Sebenzisa • Sebenzisa bangasebenzisa bebenze ngokwelwazi labo ukuze babale.
amatshwayo afaneleko amatshwayo afaneleko Beka inomboro ekulu maqangi ukuze babale bayephambili nofana emuva.
( +, -, =, ) ( +, -, =, )
4 + 12 =
• Ukuzijayeza/ • Ukuzijayeza/
Ukuphrakhthisa Ukuphrakhthisa Hlela kabutjha 4 + 12 njengo 12 + 4 and babala on from 12.
ukulumbana ukulumbana Ukubona okuseduze nokubuyelela kabili
kwenomboro ukufika kwenomboro ukufika
8+7
e-10 e-10
Abafundi bangahlathulula bonyana isibalo singatlolwa bunjesi 8 + 8 -1 (buyelela kabili u 8
khupha u- 1) nofana 7 + 7 + 1 (buyelela kabili 7 hlanganisa no-1).
Abafundi bangahle barekhode amaqhinga wabo basebenzisa abotjhobi
8 + 8 ➝ 16 + 1 = 15
Tjhugulula inomboro iye etjhumini bese ukhiphe nofana uhlanganise kunye
Iqhinga leli lingafundiswa ngerherho leenomboro eziphasi bese isetjenziswa eenomborweni
eziphezulu.
9+6=
Abafundi bangathi ngokwabo “ngizokukhupha kunye koku-6 bese ngiyihlanganise koku-9
ukwenza i-10.”
Ngakho ke 9 + 6 angatlolwa bunjesi 10 + 5 = 15.
8+5=
Abafundi bangathi ngokwabo “ngizokukhupha okubili koku- 5 bese ngihlanganise no-8
ukwenza i-10.”
Ngakho-ke 8 + 5 angatlolwa bunje 10 + 3 = 13.
231
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
232 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukusuka • Hlanganisa ukufika Ukuphula inomboro ibe ziingcezu ezincani ukwenza ukubala kubelula
Ukuh- ema-99 ema-20 Abafundi bazokuphula inomboro zibe ziingcezu ezihlukeneko lezo eziphathekako kibo
langanisa • Khupha ukufika ema- • Khupha ukusuka ema- Ukubala uye phambili ngokuphula inomboro yinye
nokukhupha 99 20
11 + 7 =
• Sebenzisa • Sebenzisa
amatshwayo afaneleko amatshwayo afaneleko 11 + 4 + 3
( +, -, =, ) ( +, -, =, ) 11 + 4 ➝ 15 + 3 = 18
• Ukuzijayeza/ • Ukuzijayeza/
Ukuphrakhthisa Ukuphrakhthisa
ukulumbana ukulumbana 11 + 7 =
kwenomboro ukufika kwenomboro ukufika 11 + 5 + 2
e-10 e-10
11 + 5 ➝ 16 + 2 = 18
17 – 9 =
17 – (7 + 2)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
17 – 7 ➝ 10 – 2 = 8
12 + 7 =
10 + 2 + 7
7+2 ➝ 9 + 10 = 19
Ukusebenzisa ilwazi lobudlelwano lokupherhuka hlangana nokuhlanganisa
nokukhupha
15 – 9 =
Abafundi bayazi bonyana isibalo singabuyelelwa sitlolwe njengesibalo sokuhlanganisa:
“ngiyazi bonyana i-9 + = 15.”
Umfundi angahle asebenzise ukubala uye phambili ukuze ukwazi ukubala.
Ukulumbana kweenomboro
Ukuze kujayezwe iukulumbana kweenomboro imisetjenzana ehlukahlukeneko kufanele
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
inikelwe abafundi. Lokhu kwenziwa ngesikhathi sokuzijamela. Inambalayini nayo
ingasetjenziswa ukuzijayeza ibhondi ye-10.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.14 • Hlanganisa • Hlanganisa Ngikuphi okuhlukileko eGreyidini yoku-1?
Ukuh- ngokubuyelela ngokubuyelela Abafundi bazokutjhugulukela kusuka ekuhlanganiseni okubuyelelwako ukuya
langanisa o.u.inomboro efanako o.u.inomboro efanako ekubuyabuyeleni. Bazothoma ukuzwisisa umqondo ophathelene nokubuyabuyelela.
okubuyele- kufika ema-50 ukufika ema-20 Bazokubandakanywa emisetjenzaneni ebavumela bonyana babone ubudlelwana
lweko • Buyabuyelela • Buyabuyelela beenomboro:
okurholela iinomboro kusuka ku-1 iinomboro ukusuka • Inani lezinto esesethini/isiqhema
ekubuy- ukufika e-10 nga 1, 2, kweyoku-1 kufika e-10, • Inani lamasethi nofana iinqhema
abuyeleleni 5, 3 begodu nge-4 nga-2 • Isamba
• Sebenzisa • Sebenzisa Abafundi bafika eGreyidini ye-2 bazwisisa ukuhlanganisa okubuyelelwe:
amatshwayo afaneleko amatshwayo afaneleko Ekupheleni kweThemu bafanele bakghone uku:
( +, -, =, ) ( +, -, =, ) • hlobanisa ukubala ngokweqa nokuhlanganisa okubuyelelwe ukuzwisisa ukubuyabuyelela;
• sebenzisa, ufunde begodu utlole itshwayo lokubuyabuyelela;
• tlola umutjho weenomboro wokubuyabuyelela; noku
• buyelela iinomboro kusuka kweyoku- 1 kufika e-10 nga- 2.
Nakwenziwa imiraro yokusombulula yamagama, abafundi ngokulindelekileko okunengi
bazokusebenzisa ukuhlanganisa okubuyelelwe, ngaphandle kwaleyo imiraro yamagama
enokurhemisa imifanekiso. Kusebujameni obutjhaphukileko bonyana eminye imifanekiso
yokubuyabuyelela ingasetjenziswa.
Ukurhemisa
Njengombana abafundi bathola ilemuko ngemihlobohlobo ehlukeneko yeembalo
zamagama zokubuyabuyelela, ukuhlela iinqhema ngokurhemisa kunganikela isakhiwo
sokutjengisa ukukhulumisana kweendabuko kokubuyabuyelela
Isib. 2 x 4 ifana nokuthi 4 x 2
¥ ¥
¥ ¥
¥ ¥
¥ ¥
4+4=8
¥ ¥ ¥ ¥
¥ ¥ ¥ ¥
2+2+2+2=8
Ukusebenzisa ukurhemisa kuvumela u:
• kwakha nokuphula iinomboro
233 • ukuhlanganisa ekubuyabuyelela begodo nokuhlanganisa okubuyelelweko
• ukucabanga ngokubuyabuyelela njengokurhemisa begodu
• kundlalela isisekelo somthetho wokuhlanekela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
234 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.14 • Hlanganisa • Hlanganisa Nqophisa itjhejo labafundi eenomborweni ezisemareyini nenani leezinto zokubala
Ukuh- ngokubuyelela ngokubuyelela emareyini.
langanisa o.u.inomboro efanako o.u.inomboro efanako ¥ ¥
okubuyele- kufika ema-50 ukufika ema-20
lweko • Buyabuyelela • Buyabuyelela ¥ ¥
okurholela iinomboro kusuka ku-1 iinomboro ukusuka
ekubuy- ukufika e-10 nga 1, 2, kweyoku-1 kufika e-10,
¥ ¥
abuyeleleni 5, 3 begodu nge-4 nga-2 ¥ ¥
• Sebenzisa • Sebenzisa 4+4=8
amatshwayo afaneleko amatshwayo afaneleko Kunamareyi ama-4 wanga- 2, okwenza abe -8 nasele awoke.
( +, -, =, ) ( +, -, =, )
Abafundi kufanele godu barekhode ngendlela elandelako:
¥ ¥ ¥ ¥
¥ ¥ ¥ ¥
2+2+2+2=8
Kunamareyi ama-2 wanga- 4. Okwenza abe -8 nasele awoke.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Igama elithi “buyabuyelela” lingethulwa: uku-4 ubuyabuyelela ka-2 kwenza ubu-8.
Lokha abefundi sebanelemuko elaneleko, itshwayo lokubuyabuyelela lingethulwa
ndawonye nelimi elilandelako elithuthukisiweko:
kuneenqhema e-4 zika-2
abo-2 aba-4
2+2+2+2=8
Iinqhema ezi-4 zika-2 nofana uku-4 ubuyabuyelelwa ka-2 kulingana no-8
Nanyana itshwayo sele lithuliweko, amagama, iinthombe begodu nemifanekiso
ebuyabuyelelweko ukulekelela ukuzwisisa itshwayo kuhlala kubalulekile.
Imifanekiso yokuzwisisa ukubuyabuyelela:
• Amakhyubsi weyunifikisi angasetjenziswa begodu angapakwa amakholomu ama-4
wamakhyubsi begodu lelinye nelinye ikholomu kungaba namakhyubsi ama-2. Lokhu
kuvumela abafundi bonyana “kunamawobhu amane ewobhini ngalinye kunezinto ezi-2.
Ivumela bonyana barekhode 2 +2 + 2 + 2 begodu iinqhema ezi- 4 zika-2 ngu 4 x 2.
• Inambalayini ingasetjenziswa ukutjengisa ukuhlanganisa okubuyelelwe nofana iinqhema
zeenomboro. Lokhu kuhlanganiswa khulu nokubala kokweqa.
Abafundi bafanele bakghone ukurekhoda okulandelako:
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Isiqhema si-1 sika- 2 ngu-2 nofana buyabuyelela u-1 ngaku-2 ngu-2 nofana 1 x 2 = 2
Iinqhema ezi-2 zika-2 ngu- 4 nofana buyabuyelela u-2 ngaku-2 ngu- 4 nofana 2 x 2 = 4
Iinqhema ezi-3 zika-2 ngu- 6 nofana buyabuyelela u-3 ngaku- 2 ngu 6 nofana 3 x 2 = 6
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.16 Umnqopho wenom- Umnqopho wenom- Ngikuphi okuhlukileko eGreyidini yoku-1?
Iimbalo boro: irherho 99 boro: irherho 25 IThemu le inqophe eku:
zehloko • Hlela isethi enikelweko • Hlela isethi enikelweko Ihlelo leembalo zehloko kufanele zithuthukiswe ngokuhleleke ngokuyelela unyaka woke.
leenomboro leenomboro
Abafundi abakafaneli ukubawiwa ukubala okungakhethiko ngamalanga. Njengombana
ezikhethiweko ezikhethiweko
abafundi baqeda iinhloko bebathuthukise amaqhinga wokubalisisa engcenyeni yesifundo
• Madanisa iinomboro • Madanisa iinomboro ihlangothi lomraro lalokhu kungahlanganiswa nehlelo lembalo zehloko:
ema-99 bewutjho ema-99 bewutjho
bonyana ngiyiphi bonyana ngiyiphi Amaqhinga namakghono athuthukiswa ngesifundweni esiqakathekileko, bese siyajayezwa,
enengi nofana encani enengi nofana encani ngezinye iinkhathi ngerhelo leenomboro ezincani; ehlelweni lembalo zehloko.
nga-1, 2, 3, 4, 5 ne-10 nga-1, 2 ne-10 Ungahlalisa irherho leenomboro phasi ngeThemu yoku-1 bese lingezelelwe phakathi
• Ukukhumbula • Ukukhumbula nonyaka. Ekuthomeni konyaka, irherho leenomboro namaqhinga wokubala angasekelwa
masinyana: masinyana: ekuthuthukisweni eGreyidini yoku-1.
• Ukukhumbula • Ukukhumbula Umqondonomboro:
amaphuzu amaphuzu
Imihlobo yeembonelo zemibuzo engabuzwa:
wokuhlanganisa wokuhlanganisa
nowokukhupha kufika nowokukhupha kufika Amagama weenomboro namatshwayo
e- 20 e-10 Phakamisa ikarada nofana tlola igama lenomboro. Khetha umfundi bonyana atlole
• Hlanganisa nofana Amaqhinga wembalo iinomboro ezimadanako.
ukhuphe imbuyeleli zehloko Okunengi nofana okuncani
ze-10 Ukusebenzisa
Khuyini lokhu
Amaqhinga wokubala amaqhinga wokubala
Ukusebenzisa ukuhlanganisa • Kuncani ku-15 nga-1
amaqhinga wokubala nokukhupha ngekghono • Kunengi ku-9 nga-1
ukuhlanganisa elifaneleko:
• Okunengi e-15 nga-10
nokukhupha ngekghono • Beka inomboro ekulu
elifaneleko: maqangi ukuze ubale • Okuncani e-16 nga-10
• Beka inomboro ekulu uye phambili nofana Ngiliphi iledere lesi-5 lama Alfabethi?
maqangi ukuze ubale ubale uye emuva Ngiyiphi inyanga yonyaka yesi-9?
uye phambili nofana • Inambalayini.
Ukuhlela nokumadanisa
ubale uye emuva • Ukubuyelela kabili
nokuhafula phakathi Ngikuphi okunengi: 12 nofana 21
• Inambalayini.
• Ukubuyelela kabili • Ukwakha nokuphula Nginikela inomboro ehlangana kwe-17 ne-19
nokuhafula phakathi • Sebenzisa Amaqiniso ngokuhlanganisa nokukhupha:
• Ukwakha nokuphhula ubudlelwano phakathi • Ukwazi ngehliziyo koke ukuhlanganisa nokukhupha kwenomboro kokulumbana
• Sebenzisa kokuhlanganisa kweenomboro ze-10
ubudlelwano phakathi nokukhupha + = 10
kokuhlanganisa +=8
nokukhupha
235
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
236 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.16 Amaqhinga wokubala Amaqhinga wembalo Amaqiniso wokuhlanganisa nokukhupha nazozoke iinomboro ukufika okufaka hlangana
Iimbalo • Ukusebenzisa zehloko ne-10
zehloko amaqhinga wokubala Ukusebenzisa 1 + 9 = 10 9 + 1 = 10
ukuhlanganisa amaqhinga wokubala 2 + 8 = 10 8 + 2 = 10
nokukhupha ukuhlanganisa
ngekghono elifaneleko: nokukhupha ngekghono 8–4=4 8–4=4
• Beka inomboro ekulu elifaneleko: 8–5=3 8–3=5
maqangi ukuze ubale • Beka inomboro ekulu Ukukhumbula masinyana ukuhlanganisa okubuyelelwa kabili ukufika e-10. Lokhu kufanele
uye phambili nofana maqangi ukuze ubale kufake hlangana amaqiniso nokukhipha okukhambisanako.
ubale uye emuva uye phambili nofana • 1+1=2
• Inambalayini. ubale uye emuva • 2+2=4
• Ukubuyelela kabili • Inambalayini. • 3+3=6
nokuhafula phakathi • Ukubuyelela kabili • 4+4=8
• Ukwakha nokuphhula nokuhafula phakathi
• 5 + 5 = 10
• Sebenzisa • Ukwakha nokuphula
Ngitjengisa inomboro engingayihlanganisa .........ukwenza i-10.
ubudlelwano phakathi • Sebenzisa
kokuhlanganisa ubudlelwano phakathi ( Tlola phasi nofana usebenzise ubukhulu bedijithi nofana amakarada weFlardi)
nokukhupha kokuhlanganisa • 8
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokukhupha • 2
• 9
• 5
• 3
Ngitjengise inomboro etjhiyiweko lokha...............ekitjhwe e-10.
(Tlola phasi nofana usebenzise ubukhulu bedijithi nofana amakarada weFlardi)
• 5
• 3
• 6
• 1
• 7
Ezinye iimbalo zehloko zingenziwa ngaphandle kwama-apharathasi, nokho kanengi
kuqakathekile ukwenza imbalo zehloko ngama-apharathasi begodu wenze amarekhodi
walokho okwenziweko.
Ama-apharathasi aphakanyisiweko
• Inambalayini (ehlelekileko begodu engenalitho)
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• iGridi yenomboro
• amakarada wobukhulu bedijithi (amakarada weFladi)
• imincamo yokubala
IGREYIDI YESI-2 ITHEMU YOKU-1
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.1 Ukukopa, ungezelele Ukukopa, ungezelele Ukukopa iphetheni kusiza abafundi ukubona ilojikhi yokuthi iphetheni yenzwe njani. Isifundo esi-1
Amapheth- nokuhlathulula nokuhlathulula Ukungezelela iphetheni kusiza abafundi ukubona bonyana bayizwisisile ilojikhi yephetheni.
eni weJi- Ukukopa ,ungezelele Ukukopa ,ungezelele Ukuhlathulula iphetheni kusiza abafundi ukuthuthukisa amakghono welimi nokukhuluma.
yomethri nokuhlathulula nokuhlathulula Kuyosiza wena ukubona bonyana abafundi bahlathulula njani amaphethini
ngamagama ngamagama Kuvame ukuba lula ebafundini ukukhuluma ngephetheni ngemuva kokuyenza. Abafundi
• Amaphetheni alula • Amaphetheni alula bathloga bonyana babandulwe bonyana bafune ini begodu bayihlathulule njani iphetheni.
enziwe ngezinto enziwe ngezinto Ungabafanisela ngokubabuza imibuzo enjenge.
eziphathekako eziphathekako “Ubona ubujamo obunjani ephetheneni le?”
• Amaphetheni alula • Amaphetheni alula “Zinemibala efanako?”
enziwe ngemigwalo enziwe ngemigwalo
“Ubona ubujamo bunye nofana ubujamo obunengi ephetheneni?”
yemida, ubujamo yemida, ubujamo
nafana izinto. nafana izinto. “Ingabe zoke izinto ziqale endaweni yinye?”
Tlama begodu Tlama begodu “Kunenomboro ezifanako zezinto esiqhemeni ngasinye?”
uhlathulule uhlathulule “Zizinto ezingaki esiqhemeni ngasinye?”
amaphetheni wakho amaphetheni wakho “Ingabe ubujamo boke buyalingana?” njll
Yenza amaphetheni Yenza amaphetheni Faka ubujamo obungubusobubili beJiyomethri begodu nobujamo bezinto ezibusobantathu
weJiyomethri weJiyomethri beJiyomethri lokho abafundi abakufundile. Abafundi bangenza ubujamo bakabusobubili
• Ngezinto • Ngezinto ngokuqunta amaphepha nofana amakarada, nofana bangazigwala. Bangenza amaphetheni
eziphathekako eziphathekako ngobujamo bebhoksi, ubujamo bebholo nesilinda abazenze ngebumba nofana ngehlama
• Ngokugwala imida, • Ngokugwala imida, yokudlala.
amajamo nofana izinto amajamo nofana izinto Amaphetheni angenziwa ngokusebenzisa ubujamo obubodwa kodwana umbala wezinto
Amaphetheni utjhuguluke ngendlela ejayelekileko.
asizombelezileko Isibonelo :
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni
weJiyomethri Amaphetheni angenziwa ngeenqhema ezifanako ezibuyelelweko, lapho isiqhema ngasinye
• Ngokwemvelo, sinomhlobo munye wento, kodwana indawo yezinto eenqhemeni iyatjhughuluka. Iinqhema
ezifanako ziyabuyelelwa isib.
• Kusukela epilweni
yangamalanga
yesimodeni,
237 • Kusukela kezamagugu
nendabuko yethu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
238 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.1 Ukukopa, ungezelele Ukukopa, ungezelele Isibonelo : Isifundo esi-1
Amapheth- nokuhlathulula nokuhlathulula
eni weJi- Ukukopa ,ungezelele Ukukopa ,ungezelele
yomethri nokuhlathulula nokuhlathulula
ngamagama ngamagama
• Amaphetheni alula • Amaphetheni alula
enziwe ngezinto enziwe ngezinto
eziphathekako eziphathekako
• Amaphetheni alula • Amaphetheni alula
enziwe ngemigwalo enziwe ngemigwalo
yemida, ubujamo yemida, ubujamo
nafana izinto. nafana izinto. Emaphethenini amanye izinto ezahlukeneko ziyasetjenziswa ukwenza iinqhema, kodwana
Tlama begodu Tlama begodu iinqhema zezinto ziyabuyelelwa ngendlela efana patsi.
uhlathulule uhlathulule Isibonelo :
amaphetheni wakho amaphetheni wakho
Yenza amaphetheni Yenza amaphetheni
ISIGABA ESISISEKELO AMAGREYIDI 1-3
weJiyomethri weJiyomethri
• Ngezinto • Ngezinto
eziphathekako eziphathekako Emaphethenini amanye ubukhulu bezinto eenqhemeni buyatjhuguluka, kodwana iinqhema
• Ngokugwala imida, • Ngokugwala imida, ziyabuyelelwa ngendlela efanako.
amajamo nofana izinto amajamo nofana izinto
Amaphetheni
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni
Abafundi bangenza amaphetheni ngokuthungelela imincamo. Ukwenza amaphetheni
weJiyomethri
kungenziwa eemfundweni zamakghono wepilo.
• Ngokwemvelo,
• Kusukela epilweni
yangamalanga
yesimodeni,
• Kusukela kezamagugu
nendabuko yethu.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela Ukulandelana kweenomboro kungahlahlotjaniswa begodu kusekele ukubala. Lokha Iimfundo ezi- 3
Amaphe- nokuhlathulula nokuhlathulula amakghono wabafundi atjhuguluka begodu athuthuka, imihlobo yokulandelana
theni Ukukopa, ukungezelele Ukukopa, ukungezelele kweenomboro abafundi abasebenza ngakho kungathuthuka.
weenom- nokuhlathulula nokuhlathulula Ukulandelanisa kufanele kubonise ukubala uye phambili nemuva nga:
boro ukulandelanisa ukulandelanisa • ku-1 ukusuka kwenye nenye inomboro hlangana no-1 ne-100
kwenomboro elula kweenomboro okulula
• li-10 ukusukela kwenye nenye inomboro ebala ngali-10 ehlangana no-1 ne- 100
ukufika e-200 ukufika e-100
• Ku-5 ukusukele kwenye nenye inomboro ebala nga ku-5 ehlangana no–1 ne- 100
Tlama begodu Ukulandelana kufanele
kubonise ukubala uye • Ku-2 ukusukela kwenye nenye inomboro ebala nga-2 ehlangana no–1 ne-100
uhlathulule
amaphetheni wakho phambili nemuva nga: Egreyidini ye-2 abefundi babala baye phambili nga-10, 5 kanye na 2 kokuthoma.
Tlama begodu • Ku-1 ukusuka kwenye Abafundi bangakhomba iinomboro lokha nababalako. Kuqakathekile bonyana unikele
uhlathulule amaphetheni nenye inomboro abafundi ukulandelana kweenomboro okujamiselelweni okuhlukeneko. isib
weenomboro hlangana ne-0 ne-100 • Ukulandelanisa kweenomboro okutloliweko 100; 99; 98; 97; 96; ...
• Li-10 ukusuka • Amanambalayini
kesinye nesinye
• Igridi yeenomboro
isibuyabuyelelo se-10
hlangana ne-0 ne-100 • Iketani yeenomboro
• Ku-5 ukusuka Abafundi bangagubuzesa, bafake umbala, nofana bazungelezele iinomboro lokha
kesinye nesinye nababalako.
isibuyabuyelelo saka Abafundi bangazalisela iinomboro ezitjhiyiweko enambalayinini, egridini yeenomboro,
ku-5 hlangana ne-0 ekulandelaneni kweenomboro ezitloliweko begodu emaketanini weenomboro. Isib.
ne-100
• Ku-2 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-2 hlangana ne-0
ne-100
Ekupheleni kweThemu, abafundi babala umsebenzi ngokulandelanisa ukusuka nokufika
e-100
239
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YOKU-1
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
240
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.2 Izinto Izinto Ngikuphi okuhlukileko eThemini yoku- 1? Iimfundo ezi-3
Izinto ezibu- ezihlukahlukeneko ezihlukahlukeneko • Amasilinda matjha eGreyidini yesi-2 kodwana angavezwa eThemini yesi- 3.
sontathu Ukukhumbula nokutjho Ukukhumbula nokutjho EThemini yoku-1, abafundi banga buyekeza begodu banzinzise abakwenze eGreyidini
abobusontathu (3-D) abobusontathu (3-D)
(3-D ) yoku-1. Abafundi bangaqalana namasilinda eThemini yesi-3.
abakhona ngetlasini abakhona ngetlasini
neenthombeni neenthombeni Umsebenzi omnengi wezinto ezibusontathu (3-D) eGreyidini yesi-2 kufanele wenziwe
• Ubujamo beembholo, • Ubujamo beembholo, ngezinto eziphathekako / ezithintekako. Iphasi silibona ngamahlangothi amathathu, ngakho
(indulungu) (indulungu) ke ukuthoma ngezinto eziphathekako kusiza abafundi bona bakhele phezu kwelwazi/
• Ubujamo bebhoksi • Ubujamo bebhoksi kwelemuko abeza nalo esikoloweni.
(amaphrizimu) (amaphrizimu) Abafundi abanengi abancani bayatlhaga ukuhlathulula izinto zejiyomethri ezibusontathu
• Isilinda Amatshwayo wezinto (3-D) kusuka eenthombeni. Ukusebenza ngezinto eziphathekako kusiza abafundi bona
barhumutjhe iinthombe zobujamo beJiyomethri ngokukhamba kwesikhathi. Lokha
Amatshwayo wezinto Hlathulula, ubeke
ngamananeko nawuphethe into yamambala ephathekako, ungayijikajikisa uyiqale mahlangothi woke.
Hlathulula, ubeke Ungakghona ukubona bonyana iqaleka injani kusuka ngemuva nangaphasi.
ngamananeko begodu umadanise
ISIGABA ESISISEKELO AMAGREYIDI 1-3
begodu umadanise izinto ezinobujamo Lokha nawuphethe isithombe kwaphela, kufanele ubone ngelihlo lemgqondo iingcenye
izinto ezinobujamo babobusontathu ezingabonakaliko emgwalweni lowo. Lokhu akusilula njalo ebafundini abancani. Lokha
babobusontathu (3-D) (3-D) ngokucala abafundi banikelwe ihlathululo yento kuphela ngaphandle kokuthi bayibone nofana
ngokucala okulandelako: okulandelako: bayiphathe, kuba nzima khulu ukuzwisisa ubujamo bento ngokupheleleko.
• isayizi • isayizi Ukwakha ngezinto ezibusontathu ( 3-D)
• izinto ezigedekako • izinto ezigedekako Abafundi bakopulula isifaniso sento ethile obanikela yona wena njengotitjhere isib.
• izinto ezitjhelelako • izinto ezitjhelelako Umbhotjhongo, irobodo, isitimela, iteksi, indlu yekosi (ikhasele) njll. Iimfaniso nofana
Imisebenzi Imisebenzi izakhiwo zingenziwa ngokusebenzisa amabhlogo wokwakha, imatheriyali engabuye
okunqotjhiswe kiyo okunqotjhiswe kiyo isetjenziswe godu, amakhithi wokwakha nezinye izinto ezibusontathu
Tjheja begodu wakhe Tjheja begodu wakhe (3-D) zejiyomethri, nokusika izinto ezinobujamo babobusobubili (2-D).
izinto ezibusontathu izinto ezibusontathu Lokhu kungenziwa ngesikhathi sokusebenza ngokuzijamela. Kuqakathekile bona abafundi
(3-D) ngokusebenzisa (3-D) ngokusebenzisa bakhulume ngemifanekiso abayenzileko. Isibonelo, lookha kwakhiwe umbhotjhongo
umatheriyali umatheriyali ngamabhoksi nofana ngamabhlogo, ungabuza abafundi bonyana, “umjbhotjhongo
ophathekako nokusika ophathekako nokusika ungawakha ngeembholo kuphela na?” kufanele bahlathulule ipendulo yabo.
izinto ezinobujamo izinto ezinobujamo
obubusobubili obubusobubili Ukumadanisa nokuhlathulula izinto ezibusontathu ( 3-D): isayizi
(2-D), amabhlogo (2-D), amabhlogo Abafundi bamadanisa isayizi yezinto ezifanako isib.
wokwakha, umetheriyali wokwakha, umetheriyali • Ukuhlela iimbholo ngamasayizi wawo ;noku
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
obuyelelwa usetjenziswe, obuyelelwa usetjenziswe, • Sebenzisa ilimi lesayizi ukmadanisa izinto: “Ibhoksi likhulu kunebholo, ngoba ngingafaka
ikhithi yokwakha, nezinye ikhithi yokwakha, nezinye
ibholo ngaphakathi kwebhoksi.”
izinto ezibusontathu (3- izinto ezibusontathu
D) zejiyomethri (3-D) zejiyomethri.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.2 Izinto Izinto Ukuhlathulula izinto ezinobujamo obubusontathu (3-D): umbala
Izinto ezibu- ezihlukahlukeneko ezihlukahlukeneko Abafundi bakhuluma ngemibala yezinto begodu bahlele ngeengaba izinto ngokuya
sontathu Ukukhumbula nokutjho Ukukhumbula nokutjho ngemibala yazo.
(3-D ) abobusontathu (3-D) abobusontathu (3-D) Ukubona nokutjho izinto nemibala yazo, nokumadanisa amasayizi wezinto
abakhona ngetlasini abakhona ngetlasini kungaphrakthiswa ngesikhathi sokusebenza ngamaphetheni.
neenthombeni neenthombeni
Izinto ezibusontathu (3-D) eGreyidini yesi- 2
• Ubujamo beembholo, • Ubujamo beembholo,
Abafundi basebenza nge/nga:
(indulungu) (indulungu)
• iimbholo nezinto ezinobujamo obufana neembholo; na
• Ubujamo bebhoksi • Ubujamo bebhoksi
(amaphrizimu) (amaphrizimu) • mabhoksi ahlukahlukeneko nezinye izinto ezinobujamo obufana namaphrizimu,
aboncamane nofana amakhuyubhu. Abafundi bayaphenya bona ngiziphi izinto
• Isilinda Amatshwayo wezinto
ezigedekako, ngiziphi ezitjhelelako.
Amatshwayo wezinto Hlathulula, ubeke
Ukunqophisa ezintweni ezinamatshwayo abusontathu ( 3-D)
Hlathulula, ubeke ngamananeko
begodu umadanise Abafundi bangenza umtjhelelo nofana indawo eyehlelako ngokubeka ibhoksi ngaphasi
ngamananeko
izinto ezinobujamo kwehlangothi elithize lencwadi ekulu. Bangathoma ke benze isitjengiso–mbono ukwenzela
begodu umadanise
babobusontathu ukubona bonyana izinto ziyatjhelela nofana ziyagedeka na.
izinto ezinobujamo
babobusontathu (3-D) (3-D) ngokucala Lokhu kuliragelo phambili lalokho abakwenze eGreyidini yoku-1, kodwana ngalesisikhathi
ngokucala okulandelako: okulandelako: amasilinda nawo afakiwe.
• isayizi • isayizi
• izinto ezigedekako • izinto ezigedekako
• izinto ezitjhelelako • izinto ezitjhelelako
Imisebenzi Imisebenzi
okunqotjhiswe kiyo okunqotjhiswe kiyo Abafundi nabo banga phenya bona bangapakelanisa izinto nofana imibhotjhongo
Tjheja begodu wakhe Tjheja begodu wakhe basebenzisa amabholo kuphela nofana amabhoksi kuphela.
izinto ezibusontathu izinto ezibusontathu Ukukhumbula nokutjho iimbholo (iindulungu) namabhoksi (amaphrizimu)
(3-D) ngokusebenzisa (3-D) ngokusebenzisa Abafundi kufanele banikelwe imihlobohlobo yezinto okufanele baberege ngazo :
umatheriyali umatheriyali • amabumbeko afana neendulungu ,isib iimbholo zamasayizi angalinganiko nofana
ophathekako nokusika ophathekako nokusika abomabula, amalamune njll.; nama
izinto ezinobujamo izinto ezinobujamo
• phrizimu afana neendulungu, okufana namabhlogo, iintina, amabhoksi wamasayizi
obubusobubili obubusobubili
ahlukahlukeneko, isib. Amabhoksi womlilo, amabhoksi wamasiriyeli, amabhoksi wetiye,
(2-D), amabhlogo (2-D), amabhlogo amabhoksi wesibha samazinyo.
wokwakha, umetheriyali wokwakha, umetheriyali
Abafundi bangathola izinto ezibumbeke njengebholo (iindulungu), nofana ebumbeke njenge
obuyelelwa usetjenziswe, obuyelelwa usetjenziswe,
bhoksi (amaphrizimu) lokha nabanikelwe ibuthelelo lezinto. Abafundi bangathola nofana
ikhithi yokwakha, nezinye ikhithi yokwakha, nezinye
batjengise izinto ezibumbeke njengamabhoksi (amaphrizimu) ngetlasini. Isib. isitina lesi
241 izinto ezibusontathu (3- izinto ezibusontathu
sibumbeke njengebhoksi nofana ilamune leli libumbeke njenge bholo.
D) zejiyomethri (3-D) zejiyomethri.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
242 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.2 Izinto Izinto Ngesikhathi sokufunda ngokuzijamela, abafundi bangaragela phambili ngoku: Iimfundo ezi-3
Izinto ezibu- ezihlukahlukeneko ezihlukahlukeneko • hlela izinto ngama sayizi;
sontathu Ukukhumbula nokutjho Ukukhumbula nokutjho • hlela izinto ngemibala;
(3-D ) abobusontathu (3-D) abobusontathu (3-D)
• ukwakha ngezinto; no
abakhona ngetlasini abakhona ngetlasini
neenthombeni neenthombeni • kwenza iimbholo nobujamo bebhoksi (amaphrizimu) ngedaka nofana ihlamayokudlala.
• Ubujamo beembholo, • Ubujamo beembholo, Imisebenzi etlolwako
(indulungu) (indulungu) Nanoma umsebenzi omnengi wamabumbeko wezinto ezibusontathu
• Ubujamo bebhoksi • Ubujamo bebhoksi (3-D) zenziwa ngokwenza, umsebenzi kufanele uhlanganiswe ngomsebenzi ngokutlolwako.
(amaphrizimu) (amaphrizimu) Ilimi
• Isilinda Amatshwayo wezinto Kuqakathekile ukuthuthukisa ikghono lomfundi lokukhuluma ngamabumbeko
Amatshwayo wezinto Hlathulula, ubeke abobusontathu (3-D).
Hlathulula, ubeke ngamananeko • Ilimi lesayizi: kukhulu , kukhudlwana, kukhulu khulu, kuncani, kuncazana , kuncani khulu
ngamananeko begodu umadanise
• Imibala
begodu umadanise izinto ezinobujamo
babobusontathu • Ilimi lezinto ngokwazo: Amabhoksi, iimbholo (akukalindeleki bona abafundi bazi igama
izinto ezinobujamo
elithi indulungu)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
babobusontathu (3-D) (3-D) ngokucala
ngokucala okulandelako: okulandelako: • Ilimi lobujamo ukuhlathulula ukwakha isib. phezulu kwe, ngaphasi, ngemuva;
ngaphambili; qadi kwe, malungana ne, ngaphasi, ngehla, eduze, hlangana, ngaphakathi,
• isayizi • isayizi
ngaphandle.
• izinto ezigedekako • izinto ezigedekako
Ilimi lesayizi nombala lingathuthukiswa ngesikhathi seemfundo zeLimini nofana
• izinto ezitjhelelako • izinto ezitjhelelako Emakghonweni wePilo, begodu zisetjenziswe nofana ziphrakthiswe ngesikhathi
Imisebenzi Imisebenzi seemfundo zeeMbalo. Ilimi lobujamo lingathuthukiswa ngesikhathi sesifundo seLimini
okunqotjhiswe kiyo okunqotjhiswe kiyo nofana Emakghonweni wePilo begodu ngesikhathi abafundi banqophene ngqo nobujamo.
Tjheja begodu wakhe Tjheja begodu wakhe Lingasetjenziswa nofana lijayezwe lokha abafundi basebenza ngamabumbeko anobujamo
izinto ezibusontathu izinto ezibusontathu obubusontathu (3-D).
(3-D) ngokusebenzisa (3-D) ngokusebenzisa
umatheriyali umatheriyali
ophathekako nokusika ophathekako nokusika
izinto ezinobujamo izinto ezinobujamo
obubusobubili obubusobubili
(2-D), amabhlogo (2-D), amabhlogo
wokwakha, umetheriyali wokwakha, umetheriyali
obuyelelwa usetjenziswe, obuyelelwa usetjenziswe,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ikhithi yokwakha, nezinye ikhithi yokwakha, nezinye
izinto ezibusontathu (3- izinto ezibusontathu
D) zejiyomethri (3-D) zejiyomethri.
IGREYIDI YESI-2 ITHEMU YOKU-1
4. UKUMEDA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi EGreyidini yoku-1 abafundi bakhulume ngokulandelako:
Isikhathi • Ukwazi amalanga • Ukwazi amalanga • landelanisa izehlakalo; begodu
weveke weveke • nobude besikhathi
• Ukwazi iinyanga • Ukwazi iinyanga Bafunde ngamalanga weveke begodu naweenyanga zonyaka begodu basebenzisa lokhu
zonyaka zonyaka nawamanye amalimi ukukhuluma ngokulandelanisa izehlakalo zepilo yabo. Bakhuluma
• Ukubeka amalanga • Ukubeka amalanga ngokuthi izinto zithatha isikhathi esingangani, ngokusebenzisa ilimi njengokuthi isikhathi
wamabeletho, wamabeletho, eside nofana isikhathi esifitjhani begodu msinyana, buthaka.
amafestivali wezekolo, amafestivali wezekolo, Abafundi bahlela ukulandelana kweenthombe njenga:
amaholideyi amaholideyi
• amagadango wokwenza iimbedlezwana nofana ikopi letiye;
womphakathi, womphakathi,
iminyanya iminyanya • iinthombe ezitjengisa ukukhula kwesana lize libe mumuntu omdala;
wezomlando, wezomlando, • umzombelezo wepilo yeembandana, isib. Iqanda liba yikukhu, nofana iqanda liba
izehlakalo zesikolo izehlakalo zesikolo sirhwerhwe nofana iqanda liba iviyaviyani;begodu
ezisekhalendeni. ezisekhalendeni. • izehlakalo eziqhelileko zelanga (ukuvuka, ukuba sesikolweni, ukudlala, ukudla ukudla
• Ukutjho isikhathi • Ukutjho isikhathi sama- kwantambama, ukulala).
sama-iri ali-12 ngama- iri ali-12 ngama-iri Babeka amalanga wamabeletho umnyaka woke.
iri,ngesiquntu se-iri ngamawatjhi we-
EGreyidini yesi-2 abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi
begodu nangekota analogo
begodu nangokulandelanisa isikhathi. Ngesikhathi sokufundisa itlasi loke nesikhathi
ye-iri
sokufundisa ngeenqhema ezinqotjhiweko, abafundi baragela phambili ukukhuluma
Ukubala ubude ngamalanga weveke, ngeenyanga zonyaka begodu nangelanga lamhlokho, nangamalanga
besikhathi nokudlula adlulileko begodu nangamalanga asezako. Abafundi bajayela amakhalenda ngokuragela
kwesikhathi phambili ngokubeka:
Ukusebenzisa • amalanga wamabeletho;
amakhalenda ukubala
• amafestivali wezekolo,
nokuhlathulula ubude
besikhathi ngamalanga • iminyanya wezomlando,
nofana ngeemveke. • izehlakalo zesikolo;
Ukusebenzisa amawatjhi • amaholideyi womphakathi, ezisekhalendeni.
ukubala ubude besikhathi Ngesikhathi sokusebenza ngokuzijamela abafundi baragela phambili nokulandelanisa
ngama-iri, ngesiquntu izehlakalo zepilo yabo begodu balandelanisa iinthombe zezehlakalo ngefanelo.
se-iri nofana ngekotara
yama-iri.
243
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
244 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Ngikuphi okuhlukileko egreyidini yoku-1? Iimfundo ezi-2
Isikhathi • Ukwazi amalanga • Ukwazi amalanga Umnqopho wegreyidi yesi-2 usitjela ngesikhathi, khulukhulu ngokufunda iwatjhi. EThemini
weveke weveke yoku-1 abafundi banqophisa ukulalelisisa kwabo ekukhulumeni ngesikhathi ngama-
• Ukwazi iinyanga • Ukwazi iinyanga awa, ngokusebenzisa iwatjhi ye-analogo kodwana, abafundi bafanele batjho isikhathi
zonyaka zonyaka sezehlakalo esiqhelileko selanga esenzeka njalo. Isibonelo, abafundi bangabawiwa
bonyana batjho bonyana isikolo singena sikhathi bani, isikhathi sokudla sinini begodu
• Ukubeka amalanga • Ukubeka amalanga
isikolo siphuma nini, nofana batjhintja nini ukusuka kesinye isifundo ukuya kwesinye.
wamabeletho, wamabeletho,
Khetha iinkhathi lapho iwatjhi itjengisa isikhathi poro. Kuqakathekile bonyana kube newatjhi
amafestivali wezekolo, amafestivali wezekolo,
esebenzako ibekwe ngetlasini, ukuze abafundi baqale kiyo. Abafundi bangenza iimfaniso
amaholideyi amaholideyi
zamawatjhi. Ungababawa bonyana bakutjengise iinkhathi ezihlukileko begodu ufake
womphakathi, womphakathi,
neembalo, isib. Ngitjengise i-iri le-10 ehloko. Ngitjengise bonyana kuzokuba sikhathi bani
iminyanya iminyanya
ngemuva kwama-iri ama-2 ngemuva kwe-10.
wezomlando, wezomlando,
izehlakalo zesikolo izehlakalo zesikolo
ezisekhalendeni. ezisekhalendeni.
• Ukutjho isikhathi • Ukutjho isikhathi sama-
sama-iri ali-12 ngama- iri ali-12 ngama-iri
iri,ngesiquntu se-iri ngamawatjhi we-
ISIGABA ESISISEKELO AMAGREYIDI 1-3
begodu nangekota analogo
ye-iri
Ukubala ubude
besikhathi nokudlula
kwesikhathi
Ukusebenzisa
amakhalenda ukubala
nokuhlathulula ubude
besikhathi ngamalanga
nofana ngeemveke.
Ukusebenzisa amawatjhi
ukubala ubude besikhathi
ngama-iri, ngesiquntu
se-iri nofana ngekotara
yama-iri.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.2 Ukumeda Ukumeda Ngikuphi okuhlukileko egreyidini yoku-1? Iimfundo ezi-3
Ubude okungakahleleki okungakahleleki Egreyidini yoku-1 abafundi banqopha eku:
• Ukulinganisa, • Ukulinganisa, • bekeni izinto enye hlanu kwenye ukumadanisa ubude, ukuphakama nobubanzi; begodu
ukumeda, ukumeda, • Medeni okuhlelekileko ngeemivosimedo ezijayelekileko
ukumadanisa, ukuhlela ukumadanisa, ukuhlela Ethemini yoku-1 yegreyidi yesi-2 abafundi bafanele baragele phambili banqophe ekumedeni
begodu urekhode begodu urekhode okungakahleleki ngokusebenzisa amaminithi angakahleleki, kodwana bangabethulela
ubudeusebenzise ubudeusebenzise amamitha njengeyunithi yokumeda.
iimedo ezingakahleleki iimedo ezingakahleleki Ukumeda ubungakho obungakahleleki ngokusebenzisa amayunithi angakahleleki.
isib. Ubude besandla, isib. Ubude besandla, Abafundi bangafunda zoke iinkambisolawulo begodu nekambiso yokumeda
amagadango, ubude amagadango, ubude ngokusebenzisa amayunithi angakahleleki. Ukumeda ngamayunithi angakahleleki kufanele
bepensela, izinto bepensela, izinto kungathathwa njengokunyazekako kunokumeda ngamayunithi ahlelekileko.
zokubala, njll. zokubala, njll. Ukumeda ubude ngamayunithi angakahleleki kufana ukubala bonyana mangaki amayunithi
akhethiweko anobude obulinganako njengento emedweko. Isibonelo ubude bedeski
• Ukuhlathulula ubude • Ukuhlathulula ubude
bububude besandla esi-8.
bezinto ngokubala bezinto ngokubala
Abafundi bafanele bamede izinto ezihlukahlukeneko ngokusebenzisa izinto
begodu nokutjho begodu nokutjho ezihlukahlukeneko njengamayunithi angakahleleki.
bonyana anobude bonyana anobude
Kuneendlela ezintathu zokusebenzisa amayunithi angakahleleki: ubude, ubude begodu
obungangani obungangani nobanzi
amayunithi amayunithi
• Ukubeka ngereyi buvundla into emedwako, izinto ezinengi zobude obulinganako,
angakahleleki angakahleleki njengamabhoksana womlilo, iimvadlwana zamabhodlela ezinobujamo obufana patsi
• Ukusebenzisa • Ukusebenzisa nofana izinto zokubala, amapensela amatjha, njll. Isibonelo, ukumeda ububanzi
ilimi ukukhuluma ilimi ukukhuluma bedeski, amapensela amatjha angabekwa ngokulandelana ukusuka ekuthomeni ukufika
ngokumadanisa, isib. ngokumadanisa, isib. ekugcineni avundle itafula.
ubude, ubufitjhani, ubude, ubufitjhani, Lapha kuqakathekile bonyana
mude khulu, banzi mude khulu, banzi -- zoke izinto zinobude obulinganako. Angekhe utjho bonyana incwadi yakho inobubanzi
khulu. khulu. beemuvalo zamabhodlelo webisi ali-12 nangabe iimvalo zamabhodlelo zinobukhulu
Ukwethula ukumeda Ukwethula ukumeda obungalinganiko, isib. Iimvalo zamabhodlelo webisi ezimalitha ama-2, iimvalo
zamabhodlelo wenamaneyidi weplastiki, iimvalo zamabhodlelo wesimbi, njll; begodu
okuhlelekileko okuhlelekileko
-- Akunaankhala ezitjhiywa hlangana nezinto : zifanele zipakelwe ngokulandelana ukuze
• Ukulinganisa, • Ukulinganisa, zithintane
ukumeda, ukumeda, • Sebenzisa izinto ezimbili ezifana patsi njengamayunithi angakahleleki. Beka yinye hlanu
ukumadanisa, ukuhlela ukumadanisa, ukuhlela kwenye, bese ukhambisa yokuthoma uyise kelinye ihlangothi lesibili. Lokhu kwenziwa
begodu nokurekhoda begodu nokurekhoda nakumedwa ngobude besandla, ubude benyawo nofana amagadango
ubudengokusebenzisa ubudengokusebenzisa • Ukusebenzisa into eyodwa kwaphela njengesimedo esingasisezingeni begodu
amamitha (iintonga amamitha ngokuyigeda nofana ukumerega lapho iphelela khona ngaphambi kokuyitjhelelisa.
emamitha (iintongamamitha Abafundi bafanele bafundiswe ukutjho iyunithi, isib. Incwadi inobubanzi beemuvalo
nofana intambo nofana intambo zebhodlelo ezi-12, ikumba yokufundela inobude obumagadango ama-38.
enobude bemitha) enobude bemitha) Lokha abafundi nasele bamede ngananyana ngiyiphi iyunithi amahlandla ambala,
245 njengomuvosimedo njengomuvosimedo bafanele balinganise bonyana ingaba nobude obungangani beyunithi into efanele imedwe.
ojayelekileko. ojayelekileko. Ukulinganisa ngaphambi kokumeda kuqakathekile, kodwana kungenziwa kwaphela lokha
abafundi nabenze ukumeda ngeyunithi leyo.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
246 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.2 Ukumeda Ukumeda Abafundi bafanele bafundiswe bonyana ukuze nimadanise ubude, ukuphakama nanyana
Ubude okungakahleleki okungakahleleki ububanzi iyunithi efana patsi ifanele isetjenziswe. Isib.nangabe ububanzi bomnyango
• Ukulinganisa, • Ukulinganisa, omedweko bububude besandla obu-20 begodu ububanzi bedeski bububude bamapensela
a-8, angekhe utjho bonyana umnyango ubanzi kunedeski.
ukumeda, ukumeda,
ukumadanisa, ukuhlela ukumadanisa, ukuhlela Abafundi bafanele bamede ngamayunithi angakahleleki ahlukahlukeneko, ukuze bakghone
begodu urekhode begodu urekhode • ukuthoma ukuzwisisa bonyana lokha iyunithi nayiyincani , izokusetjenziswa amahlandla
ubudeusebenzise ubudeusebenzise amanengana ,isib. ububanzi bekumba yokufundela bungaba magadango ama-20
iimedo ezingakahleleki iimedo ezingakahleleki kodwana kube bubude beenyawo obuma-48.
isib. Ubude besandla, isib. Ubude besandla, • Thoma ukusebenzisa amayunithi afanele lokho abakumedako, isib. Ukumeda ububanzi
amagadango, ubude amagadango, ubude bekumba yokufundela ngeemuvalo zamabhodlelo kukumorosa isikhathi.
bepensela, izinto bepensela, izinto Ukwethula ukumeda okuhlelekileko
zokubala, njll. zokubala, njll. Isikhathi esinengi esisetjenziswa esifundweni sokumeda eGreyidini yesi-2 sifanele sibe
kumeda okungakahleleki. Nanyana kunjalo abantwana banganikelwa ithuba lokuthuthukisa
• Ukuhlathulula ubude • Ukuhlathulula ubude
ukucabanga bonyana imitha ingangani. Lokho kwenzeka kuhle lokha abafundi nabameda
bezinto ngokubala bezinto ngokubala ngesisetjenziswa esiyimitha yinye ngobude( njengerula yemitha, isigodo esiquntwe saba
begodu nokutjho begodu nokutjho yimitha yinye ngobude nofana iinquntu zentambo enobude bemitha yinye). Ukubona
bonyana anobude bonyana anobude ubude bemitha kusiza abafundi ukwenza umfanekiso wokobana imitha yide kangangani.
obungangani obungangani Kuyakghonakala ukumeda amamitha ngevili lethrandlela , kodwana ubude bemitha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amayunithi amayunithi abubonakali lula.
angakahleleki angakahleleki Abafundi bangathoma ngokuthola izinto ezinobude bemitha yi-1 poro. Kuqakathekile
• Ukusebenzisa • Ukusebenzisa ukuba nezinto eningaqala kizo ngamalanga njengeemadaniso, isib.ububanzi bomnyango
ilimi ukukhuluma ilimi ukukhuluma nokuphakama kwefesidere buyimitha yi-1 ubude. Lokhu kusiza abafundi basebenziseubude
ngokumadanisa, isib. ngokumadanisa, isib. lobu nofana ububanzi abakghona ukububona ukulinganisa ubude bezinye izinto
ubude, ubufitjhani, ubude, ubufitjhani, abazimedako.
mude khulu, banzi mude khulu, banzi Lokha abafundi nasele banelemuko lokumeda ngamamitha, bafanele balinganise
khulu. khulu. ngaphambi kokunye nokunye ukumeda .
Abafundi bangathola izinto ezingaba zide nofana zifitjhani kunemitha li-1. Ekugcineni
Ukwethula ukumeda Ukwethula ukumeda
bangakumeda ubude obuhlukahlukeneko nofana amabanga ngamamitha.
okuhlelekileko okuhlelekileko
Ukurekhoda iimedo
• Ukulinganisa, • Ukulinganisa, Nanyana ukumeda kulikghono lokuzijayeza ukwenza, abafundi bafanele barekhode iimedo
ukumeda, ukumeda, zabo ngaso soke isikhathi
ukumadanisa, ukuhlela ukumadanisa, ukuhlela Ukumeda ubude njengobujamo bokurarulula imiraro neembalo
begodu nokurekhoda begodu nokurekhoda
Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana,abafundi bangararulula
ubudengokusebenzisa ubudengokusebenzisa
imiraro esebenzisa
amamitha (iintonga amamitha
ubujamo bobude besimedo ezingakahleleki, isibonelo, ideski likaLebo libubude besandla
emamitha (iintongamamitha
obu-11. Ideski likathitjhera libubude besandla obu-19. Linobude obungangani itafula
nofana intambo nofana intambo likathitjhera?
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
enobude bemitha) enobude bemitha)
Ukumeda amamitha ngobude
njengomuvosimedo njengomuvosimedo
ojayelekileko. ojayelekileko. Yelela irhelo leenomboro elifanako leThemu leyo, begodu nemihlobo yemiraro
ehlukahlukeneko
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.3 Ukumeda Egreyidini yoku-1 kuphakanyiswe bonyana abafundi banqophe ekusebenzeni ngokumeda
Ubungako/ okungakahleleki ukudzimelela uku-:
ubudisi • Ukulinganisa, • madanisa ubungako bezinto bunqopha;
ukumeda, • hlela nokumadanisa ubungako bezinto ezintathu nofana ezinengi, ngokubeka izinto
ukumadanisa, ngazimbili esikaleni sokudzimelela, bezilandelaniswe zoke izinto; begodu
ukuhlela,
• Thola ubungako bezinto ngokusebenzisa amayunithi angakahleleki wobungako
bekurekhodwe
ubungako, Abafundi banqopha godu ekuthuthukiseni ilimi lokukhuluma ngobungako
ngokusetjenzisa Ngesikhathi sokusebenza ngesikhathi sokuzijamela abafundi bangazijayeza ukulinganisa,
iimedo ezingakahleleki ukumeda, ukumadanisa, ukuhlela begodu barekhoda ubungako ngokusebenzisa
begodu nesikala isidzimelelo begodu namayunithi wobungako obungakatheleki.
sokudzimelela isib. Ukumeda ubungako njengobujamo bokurarulula imiraro neembalo
Amabhulogo, iintina
Ukuraralula imiraro neembalo kungaragela phambili ngokusebenzisa ubujamo bobungako
njll.
obunikelwe ekumedeni okungakahleleki.
• Ukusebenzisa
Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi bangararulula
ilimi ukukhuluma
imiraro esebenzisa ubujamo bobungako besimedo ezingakahleleki, isib. Idasta inobungako
ngokumadanisa isib.
bamamabula ali-11. Ibhoksi lamakhrayoni linobungako bamamabula a-8 Zizokuba
elula, ebudisi, elula-
nobungako bamamabula amangaki nasele zizoke?
khulu, ebudisi-khulu.
Yelela irherho leenomboro ezifanele iThemu, nanyana imihlobo ehlukahlukeneko yemiraro
Ukwethula ukumeda
efanele iThemu.
okuhlelekileko
• Ukumadanisa, ukuhlela
nokurekhoda ubungako
bezinto ezipakelwe
ukuthengiswa
ezinobungako
obutjengiswe
ngamakhilogremu, isib.
amakhilogremu ama-2
wereyisi nekhiligremu
li-1 leflowuru
• Ukumeda ubungako
babo ngokusebenzisa
isikala sokumeda
sangendlini
yokuhlambela
247
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
248 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
4.4 Ukumeda Egreyidini yoku-1 kuphakanyiswe bonyana abafundi banqophe
Umthamo/ okungakahleleki • ekuthuthuseni ilimi lokukhuluma ngemehluko yamavolumu;
Ivolumu • Ukulinganisa • ekumadaniseni amavolumu weemumathi ezimbili ezifanako
nokumeda;
Ukumadanisa • ekumadaniseni amavolumu weemumathini ezimbili ezingafaniko, khulukhulu iimumathi
nokuhlela ezibanzi khulu begodu nezimatsikana khulu
(isib. umthamo • ekumedeni amavolumu nemithamo ngeensetjenziswa begodu namayunithi angakahleleki.
ongamumathwa
simumathii nasizeleko) Uyini umthamo? Iyini ivolumu?
ngokusebenzisa Ibhodlelo lingaba nomthamo wamakopi amane, kodwana ngekhe lizale swi, isibonelo,
iimedo ezingakahleleki ingamumatha ivolumu yekopi elilodwa lamanzi ngasikhathi.
isib. Iingobho Umthamo ubungako bento engamumathwa simumathi, Ivolumu bungako besikhala
namakopi.
esithathwa simumathi (soke isikhala esingaphakathi kwento).
• Ukuhlathulula
umthamo besimumathi Ivolumu bungako besikhala esithathwa simumathi.
ngokubala Kesinye isikhathi abafundi bazokumeda bonyana lingangani iketjezi ( nofana isanda nofana
nokutjho bonyana ezinye izinto) elingesimumathini. Lokhu kumeda ivolumu yento engesimumathini.
mangaki amayunihi Kesinye isikhathi abafundi bazokumeda bonyana isimumathi singamumatha kangangani
angakahleleki
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nasizeleko swi.
angazalisa isimumathi,
isib. Ibhodlelo Ngesikhathi sokusebenza ngokuzijamela abafundi bangajayela ukulinganisa, ukumeda,
linobungako bamakopi ukumadanisa
amane Ukupheka nokubhaga kubujamo obuqakathekileko lapho abafundi bangazijayeza ukumeda
Ukwethulwa kokumeda umthamo.
okuhlelekileko Ukumeda umthamo njengobujamo bokurarulula imiraro neembalo
• Ukulinganisa,
Ngesikhathi esibekelwe Iinomboro, amaFankhtjhini noBudlelwana, abafundi bangararulula
ukumeda;
ukumadanisa imiraro esebenzisa ubujamo bobungako / ivolumu besimedo ezingakahleleki, isibonelo,
nokuhlela nokurekhoda uGogo usebenzisa amakopi amabili wetiye ukwenza ipudinghi. Nakawabuyelela kabili,
umthamo wezino uzokusebenzisa ibisi elingangani? Zizokuba nobungako bamamabula amangaki nasele
ngokumeda amalitha. zizoke?
• Ukumadanisa, ukuhlela Yelela irhelo leenomboro elifanako leThemu leyo, begodu nemihlobo yemiraro
nokurekhoda umthamo ehlukahlukeneko.
wezinto ezipakelwe
ukuthengiswa,
ubungako bazo
butlolwa ngamalitha,
isib. Amalitha ama-
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
2 webisi, ilitha li-1
lesiselo esimakhaza,
amalitha ama-5
wepende
IGREYIDI YESI- 2 ITHEMU YOKU- 1
5. UKUPHATHA IDATHA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
5.4 Ukubuthelela nokuhlela Ukubuthelela nokuhlela Ngikuphi okuhlukileko eGreyidini -1? Iimfundo ezi-3
Ukubuthelela idatha idatha • Abafundi abasasebenzi ngeembuthelelo zezinto
nokuhlela idatha Buthelela idatha Buthelela idatha • Abafundi baragela phambili ngokusebenza ngegrafu yeenthombe-kobabili kwakha
yetlasi nofana yesikolo yetlasi nofana yesikolo umzombe wedatha begodu kuhlaziye igrafu yeenthombe abanikelwe yona.
ukuphendula imibuzo ukuphendula imibuzo
Ukuphathwa mazombe okupheleleko kwedatha
ebuzwa ngutitjhere ebuzwa ngutitjhere
Ukuphathwa mazombe kwedatha
5.5 Ukujamiselela idatha • Abafundi babuthelela ilwazi ukuphendula imibuzo. Esigabeni esisisekelo nesiphakathi
Ukujamiselela Jamiselela idatha yegrafu Ukujamiselela idatha
umbuzo lo ujwayeleke ukunikelwa ngutitjhere nofana incwadi yokufundisa;
idatha yeenthombe Jamiselela idatha yegrafu
• Abefundi bahlukanisa ngemihlobo bebajamisele ilwazi ngezindlela ezenza kubelula
yeenthombe
ukuhlaziya. Umhlobo wokujamisela lowo abefundi begreyidi -2 bazijayeza yona igrafu
yeentombe; godu
5.6 Ukuhlaziya
Ukuhlaziya • Abefundi bahlaziya ilwazi egrafini yeenthombe ngokuphendula imibuzo ebuzwe
Ukuhlaziya bewurhumutjhe idatha
bewurhumutjhe idatha ngutitjhere.
bewurhumutjhe Ukuphendula imibuzo
Ukuphendula imibuzo Igrafu yeenthombe yetlasi
idatha ngedatha esegrafini
ngedatha esegrafini
yeenthombe Kuphakanyisiwe bonyana abefundi begreyidini 2 basebenze mazombe ngokuphathwa
yeenthombe
Kwedatha epheleleko ngokwenza igrafu yesithombe seklasi okungenani kabili onyakeni
(kanye ethemini yoku-1 begodu kanye ethemini ye-3).
Ukusebenzisana njengetlasini, kusiza abefundi ukuzibandakanya kizozoke iingaba
zekambiso ngaphandle kokulahlekelwa mininingwana yananyana ngiliphi izinga. Isib.
Ukugwala iinthombe zoke. Ukwenza igrafu kukuvumela bonyana unqophise abafundi
ngamahlangothi abalulekileko wokuphathwa kwedatha begodu nangalokho abadinga
ukukwazi ngokuqakatheka kwesimo segrafu yeenthombe
Izimo zegrafu yeenthombe ekufanele abafundi bayifundiswe:
• Igrafu ilebulwa kuphi godu bunjani (isihloko segrafu)
• Iingaba zilebulwa kuphi godu bunjani
• Igrafu yeentombe ithloga ukuba nento ehlathulula bonyana isithombe ngasinye
simayelana nani.
• Iinthombe nofana iinkhala zenthombe zithloga ukuba bukhulu obufanako.
• Zibekwa bunjani iinthombe ngokulinganako emareyini.
• Ifundwa bunjani igrafu
249
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
250 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
Abafundi kufanele bazi bona kuqakathekile bonyana bathome ngokufunda isihloko
segrafu, ukuze bazi bonyana igrafu ikhuluma ngani. Bafanele bafunde godu iinhloko
ezibuthabalala nezijame rwe. Abafundi akukakateleleki bonyana bazi amagama
aphathelene netheknoloji asetjenzisiwe ukuhlathulula iingcenye zegrafu, kwaphela
kufanele bafunde ngaphasi nangehlangothini ukubona bonyana igrafu iphathelene
nani. Sivamise ukufunda ukusukela ngesinceleni kuya ngesidleni, kodwana lokha
abafundi bafunda amagrafu kufanele bafunde kusukela esinceleni kuya ngesidleni
begodu kusuka phasi kuya phezulu. Lokhu kufanele kuhlathululelwe abafundi. Badinga
ukuzijayeza amakghono la.
Ukukhetha isihloko begodu ubuze imibuzo yokubuthelela idatha
Egreyidini ye-2 kufanele ubuze imibuzo isib. “Ngiliphi ihlelo lakamabonwakude
elithandwa yitlasi lethu?” Abotitjhere abasesigabeni kufanele baqinisekise bonyana
iinhloko ezahlukeneko zikhethelwe ukubuthelela idatha nokuhlaziya egreyidini
ngayinye. Iihloko ezilingeneko zifaka hlangana umdlalo othandwako, isiselo
esimakhaza esithandwako, imibala ethandwako, iinkathi ezidlulile ezithandwako,
ukudla okuthandwako, ihlelo likamabonwakude elithandwako njll.
Ukuhlela iingaba zokubuthelela ilwazi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Nikela abafundi irherho leengaba ukukhetha kizo.
Ukujamisela kwedata
Umfundi ngamunye uthola isiquntu sephepha esilinganako ukugwala impendulo zabo.
Imigwalo ihlelwe ngamareyi ukwenza igrafu yeenthombe. Iinhloko zingezelelwe
emahlangothini nasegrafini.
Ukuhlaziya nokuhlathulula kwedatha
Abafundi baphendula imibuzo ababuzwe yona ngegrafu yeenthombe. Isib.
“Ngiliphi ihlelo likamabonwakude elinedumo khulu ngetlasini yethu?”
“Ngiliphi ihlelo elithandwa idlanzana labafundi ngetlasini?”
“Abafundi abanengi bathanda.......nofana ...............?
“Bangaki abanye abafundi abakhetha ....... kune ........?
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YESI-2 ITHEMU YESI-2
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.1 Ukubala izinto Bala okungasenani Ngikuphi okuhlukileko eThemini yoku-1?
Ukubala eziphathekako ukufikela ku yezinto Ethemini lesi-2 irherho leenomboro likhulile begodu abafundi kwanje babala izinto ezili-150.
izinto Linganisa begodu ubale ngamalanga Ngombana le yinomboro ekulu yezinto ukuyibala, umnqopho kufanele ube sekubaleni
okungasenani ukufikela ngokuthembekako ngeenqhema. Leli likghono abafundi bebazijayeza lona ukusukela egreyidini yoku-1 begodu
ku yezinto ngamalanga Ukunikela isilinganiso iyasetjenziswa erherhweni leenomboro ezikulu.
ngokuthembekako. senomboro yezinto Kuqakathekile bonyana ngokuphela kweThemu abafundi babone ibuthelelo lezinto ezili-150
Iqhinga lokubuthelela ezingahlolwa begodu bangaphamisa indlela enekghono khulu ukuyibala.
liyakhuthazwa ngokuzibala.
Ukubala izinto ethemini le kusekela:
• ikghono lokubala elitlhogekako ekuzwisiseni ubukhulu bedijithi;
• ukubala ngehloko
• ukutjho amagama weenomboro
• ukukhumbula amatshwayo weenomboro; begodu
• Ikghono lokubala elitlhogekako ekubaleni.
Iisetjenziswa
Kufanele kuyelelwe khulu iisetjenziswa ezisetjenziswako.
• Iinsetjenziswa ezihlelekile, njengemincamo yokubala
• I-abhakhasi ukujayeza ukubala ngeenqhema zangalitjhumi
• Iinyanda zanga-2, iiynanda zanga-5 nalitjhumi zibalwe zoke.
• Amabhlogo weDienes, khulukhulu lawo akhamba ngetjhumi.
• Imali yokudlalisa
251
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
252 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko eThemini yoku-1?
Ukubala uye nemuva nga: nemuva nga: Ethemini yesi-2 irherho leenomboro lokbala lingezelelekile begodu abafundi bathoma
phambili • Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye ukubala ngakuthathu nangakune kokuthoma. Lokhu kungathulwanlokha nakubalwa izinto
nemuva nenye inomboro nenye inomboro eziphathekako, ukubala entambeni yemincamo yokubala, ukusebenzisaigridi yekhulu
hlangana ne-0 na-200 hlangana ne-0 na-150 nenambalayini.
• Li-10 ukusuka • Li-10 ukusuka • Ekupheleni kweThemu abafundi bakghona ukuphendula imibuzo enjenge:
kesinye nesinye kesinye nesinye • Thoma e-132, bala uye phambili ngakunye ukufika e-150
isibuyabuyelelo se-10 isibuyabuyelelo se-10
• Thoma e-120 begodu ubale uye emuva ngakunye ukufika e-98
hlangana ne-0 na -200 hlangana ne-0 na -150
• Thoma ema-60 begodu ubale uye phambili ngakubili ukufika e-100
• Ku-5 ukusuka • Ku-5 ukusuka
kesinye nesinye kesinye nesinye • Thoma e-100 begodu ubale uye phambili ngakubili ukufika e-138
isibuyabuyelelo saka isibuyabuyelelo saka • Thoma ko-3 begodu ubale uye phambili ngakuthathu ukufika e-30
ku-5 hlangana ne-0 ku-5 hlangana ne-0 • Thoma ema-60 begodu ubale uye phambili ngakuthathu ukufika e-42
na-200 na-150.
• Thoma ku-4 begodu ubale uye phambili ngakune ukufika e-40
• Ku-2 ukusuka • Ku-2 ukusuka
• Thoma ema-84 ubale uye emuva ngakune ukufika e-68
kesinye nesinye kesinye nesinye
isibuyabuyelelo saka isibuyabuyelelo saka • Thoma ema-45 begodu ubale uye phambili ngakuhlanu ukufika e-100
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ku- 2 hlangana ne -0 ku- 2 hlangana ne -0 • Thoma ukubala e-100 begodu ubale uye emuva ngalitjhumi ukufika e-10
na-200 na-150. Abafundi kufanele babale baye emuva ukusuka kokhunye nokhunye ukubuyelelwa
• Ku-3 ukusuka • Ku-3 ukusuka abakunikelweko.
kesinye nesinye kesinye nesinye
isibuyabuyelelo saka isibuyabuyelelo saka
ku-3 hlangana ne -0 ku-3 hlangana ne -0
na-200 na-99.
• Ku-4 ukusuka • Ku-4 ukusuka
kesinye nesinye kesinye nesinye
isibuyabuyelelo saka isibuyabuyelelo saka
ku-4 hlangana ne -0 ku-4 hlangana ne -0
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) na-200 na-100.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.3 Ukukhumbula, ukubona Ukukhumbula, ukubona Ngikuphi okuhlukileko eThemini yoku-1?
Amat- nokufunda iinomboro nokufunda iinomboro Abafundi baragela phambili ngokufunda nokutlola amatshwayo weenomboro
shwayo • Ukukhumbulaukubona • Ukukhumbula, nokutjho amagama weenomboro ukungezeza irherho leenomboro.abafundi bazabe
weenom- nokufunda ukubona nokufunda bakhumbula, bafunda begodu batlola amatshwayo weenomboro ukudlula ikhulu batlole
boro amatshwayo amatshwayo namagamaweenomboro ukufika -50.
namagama wenomboro ukusuka wenomboro ukusuka Iyelelo kufanele lithathwe lokha nawukhuluma ngeenomboro zamadijithi amathathu,
weenom- eli 0 ukuya e-200 kweli 0 ukuya e-150 isibonelo, kufanele uthi “amakhulu amathathu namatjhumi amabili nantathu” kunokuthi “
boro • Ukutlola amatshwayo • Ukutlola amatshwayo kunye, kubili, kuthathu”.
wenomboro ukusuka wenomboro ukusuka Lokha nawutlola iinomboro zamadijithi amathathu hlangana kwe-100 ne-110, idijithi
eli-0 ukuya ema-200 kweli 0 ukuya e-150 ebujameni betjhumi lili-0. Abafundi abanye bathola kubudisi ukutlola iinomboro lezi
• Ukufanisa, ukubona • Ukufanisa, ukubona ngamatshwayo lokha nabanikelwa amatshwayo ngamagama. Isibonelo, ukutlola i-102
nokufunda igama nokufunda igama kungaba budisi kwabanye abafundi. Bangatlola i-1002. Amakarada wobukhulu bedijithi
lenomboro ukusuka eli lenomboro ukusuka eli alisizo khulukhulu ukusiza abafundi ukuzwisisa bonyana angajamela bunjani iinomboro
0 ukuya e-100 0 ukuya ema-50 kuhle. Abafundi bafanele ukunikelwa godu ukujayeza okwaneleko ukutlola iinomboro lezi.
• Ukutlola amagama • Ukutlola amagama Iimbonelo zokurekhoda okutloliweko:
weenomboro ukusuka weenomboro ukusuka • Tlola amatshwayo weenomboro.
eli 0 ukuya e-100. eli 0 ukuya ema-50
Ikhulu namatjhumi amathathu nakhunye
Ikhulu namatjhumi amane nekhomba
• Madanisa amagama weenomboro ematshwayeni weenomboro
• Zalisa umutjho weenomboro
• Zalisa amanambalayini neendlela zeenomboro
253
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
254 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.4 Ukuhlathulula, Ukuhlathulula, Ngikuphi okuhlukileko eThemini yoku-1?
Ukuhlathu- ukumadanisa nokuhlela ukumadanisa nokuhlela NgeThemu le abafundi baragela phambili ukuhlela nokumadanisa iinomboro.
lula, uku- iinomboro ukufika iinomboro ukufika
Inambalayini iihlala njalo imfanekiso oqakathekile olisizo khulukhulu ekuhloleni bonyana
madanisa ema-99 ema-50
inomboro ikuphi ekuhlobaneni nezinye iinomboro. Umfanekiso wenambalayini uzakusekela
nokuhlele • Ukuhlathulula abafundi emaqhingeni wabo wengqondo wokubala.
iinomboro nokumadanisa
Imisetjenzana yokuzijamela yokuzijamela
iinomboro ezipheleleko
ngokusebenzisa Zijayeza ukutlola kunye ukufika etjhumini
ukuncani kuna, Rekhoda okulandelako ngeencwadini zomsebenzi:
ukukhulu kuna, • Ngiyiphi inomboro eza ngaphambi kwa-46
kunengi kuna,
• ngiyiphi inomboro eza ngemuva kwa-48?
kungaphasi kuna
nokuthi kuyalingana. • Ngiyiphi inomboro ehlangana kwa-45 nama-47
• Ukuhlathulula • Sebeznisa umuda wenomboro begodu uzalise iinomboro ezitjhiyiweko.
nokulandelanisa • Tlola ku-1 okudlula iinomboro lezi:
iinomboro ezipheleleko -- ku-1 okudlula ama-23 ma ___
kusukela kencani
-- ku -1okudlula ama-29 ma___
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ukuya kekulukazi
nokusuka kwekulukazi -- ku -1okudlula ama-42 ma ___
ukuya kwencani khulu. • Tlola ku-1 okungaphasi kweenomboro lezi:
Sebenzisa -- ku -1 okungaphasi kwama-20 ma ___
iinomborosikhundla -- ku -1 okungaphasi kwama-31ma ___
ukubonisa ukuhlela,
indawo nofana -- ku -1 okungaphasi kwama -42 ma ___
ubujamo • Tlola kali-10 okudlula iinomboro lezi:
Beka izinto -- kali-10 okudlula ama-20 ma ____
emudeni ukusuka -- kali -10 okudlula ama 30 ma ___
kweyokuthoma ukufikela
• Tlola kali-10 okungaphasi kweenomboro lezi
kweyetjhuminahlanu
nofana yokuthoma -- kali – 10 okungaphasi kwama -50 ma ___
ukufika kweyokugcina -- kali – 10 okungaphasi kwama – 40 ma ___
isib. Kokuthoma, • Tlola iinomborongerhelo ukusuka kwekulukhulu ukuya kwencani khulu. 130, 133, 123,
kwesibili, kwesithathu...... 143, 103, 113)
kwetjhumi. • Zalisa umutjho:
-- ama -24 a __________ kunama-24
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
-- ama-36 a _____ ne-19
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.5 Khumbula ubukhulu Khumbula ubukhulu Ngikuphi okuhlukileko eThemini yoku-1?
Ubukhulu bedijithi beenomoro bedijithi beenomoro NgeThemu le irherho leenomboro ingezelelekile ukusuka ema-25 ukuya ema-50. Abafundi
bedijithi zamadijithi amabili zamadijithi amabili basebenzisa ilwazi labo lemiqondo yobukhulu bedijithi erherhweni leenomboro ezikulu.
ukufika ema-99 ukufika ema-50 NgeThemu le abafundi baragela phambili ngoku:
• khumbula bonyan • khumbula bonyan • bala begodu ubonise itjhumi nakunye ngeendlela ezihlukeneko;
idijithi ngayinye ijamele idijithi ngayinye ijamele • bala insetjenziswa ezibuthelelwe mantanzi/ ezithome ngokujanyiswa;
ini ini • sebenzisa amakarada wobukhulu bedijithi ukubonisa iinomboro ezibuthelelweko zabalwa
• Hlanganisa iinomboro • Hlanganisa iinomboro • Bonisa ukuhlela okuhlukahlukenenko kweenomboro, isibonelo, ama-35
zamadijithi amanbili zamadijithi amanbili angaboniswa njengama-35 yabokunye abatkjhaphulukileko, amatjhumi a-3 na-5
ngokubuyabuyelela ngokubuyabuyelela yabokunye abatjhaphulukileko godu neeqhema ezi-2 zamatjhumi ne-15 yabokunye
kwangalitjhumi kwangalitjhumi abatjhaphulukileko; begodu
nangakunye. nangakunye. • Yitjho ubungako bedijithi ngalinye
• Fanisa begodu utjho • Fanisa begodu utjho • Umsebenzi ongehla uvame ukwenziwa ziinqhema okunqotjwe kizo begodu ngesikhathi
ubungako bedijithi ubungako bedijithi sokufunda ngokuzijamela abafundi bnagarekhoda okulandeko
ngayinye. ngayinye. 48 = 4 iinqhema zangalitjhumi nabokunye abatjhaphulukileko ababu-8
48 = 40 na 8
Lokhu kusekelwa kusebenzisa amakarada amaflardi nofana amakarada wobukhulu bedijithi
Ubungako bedijithi
Abafundi kufanele bathome ukutjho bona idijithi ngalinye lijamele ini. Buza abafundi:
• Uli-7 ujamelel yiphi inomboro ema-27?
• U-4 ujamele yiphi inomboro ema-49?
Abafundi kufanele basebenzise amakarada wobukhulu bedijithi ukufakazela iintatimende zabo
255
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
256 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
UKURARULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Abafundi balindeleke bona bararulule imiraro yamagama basebenzise amathekhiniki
Amathekh- alandelako lokha alandelako lokha alandelako:
iniki wok- urarulula imiraro urarulula imiraro • Imigwalo nofana iinsetjenziswa eziphathekako isib, iimbali
bekuhlathululwe bekuhlathululwe
urarulula • Ukwakha nokuphula iinomboro
iinsombululo zemiraro: iinsombululo zemiraro:
imiraro • Ukubuyelela kabili nokuhafula phakathi
• Imgwalo nofana • Imgwalo nofana
iinsetjenziswa iinsetjenziswa • Amanambalayini
eziphathekako isib, eziphathekako isib, ukugwala nofana iinsetjenziswa eziphathekako
iimbali iimbali Abafundi bazaragela phambili nokugwala iinthombe begodu basebenzise iinsetjenziswa
• Ukwakha nokuphula • Ukwakha nokuphula eziphathekako ukurarulula imiraro. Ukugwala izinto ngayinye ukufikela ema-30 nofana
iinomboro iinomboro nema-50 akwanelisi begodu kufanele kungakhuzwa, bakhuthaze bona bafake hlangan
• Ukubuyabuyelel kabili • Ukubuyelela kabili amatshwayo weenomboro ekurekhodeni kwabo, okufaka hlangana iinjamiso zeenthombe.
nokuhafula phakathi nokuhafula phakathi Abafundi bangakhuthazwa godu bona batlole imitjho yeenpmboro.
• Amanambalayini • Amanambalayini Qala amanothi weThemu yoku-1
1.7 Rarulula imiraro Rarulula imiraro Ngikuphi okuhlukileko eThemini yoku-1?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuh- yamagama yamagama NgeThemu le abafundi kufuze baragele phambili nokwenza iimbalo zemitjho begodu
langanisa ezisebujameni ezisebujameni basebenzele ukusebenzisa amathekhiniki alandelako lokha nabararulula imiraro:
nokukhupha bewuhlathulule bewuhlathulule
• Imgwalo nofana iinsetjenziswa eziphathekako isib, iimbali
iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka • Ukwakha nokuphula iinomboro
ukuhlanganisa ukuhlanganisa • Ukubuyelela kabili nokuhafula phakathi
nokukhupha nempendulo nokukhupha nempendulo • Amanambalayini
ukufika e-99. ukufika e-50.
Umnqopho ngeThemu le ihlala ikurekhoda. Abafundi kufuze kobana batlole phasi imitjho
yeenomboro njengerekhodi elitloliweko emrarweni osombululiweko. Kuqakathekile ukuqala
bonyana ngibaphi abafundi abahlulekako ukutlola imitjho yeenomboro ukuqalana nomraro
othile. Lokha abafundi nabanbawa bona ubabonise bonyana ijanyelwa bunjani imiraro
nemitjho yeenomboro emuva kokuyirarulula, sikhathi esihle sokubabonisa Iimbonelo
zemiraro okufanele zenziwe ngeThemu le, qala amanothi weThemu yesi-2.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.8 Rarulula imiraro Rarulula imiraro Ngikuphi okuhlukileko eThemini yoku-1?
Ukuh- yamagama yamagama Irherho leenomboro leThemu le lingezeleleke lafika ema-30.
langanisa ezisebujameni ezisebujameni
Abafundi kufuze bagcugcuzelwe ukutlola imitjho yeenomboro. Umuntu angalindela
okurholela bewuhlathulule bewuhlathulule
abafundi bonayana basebenzise ukuhlanganisa okubuyelelweko kwemitjho yeenomboro
ekubuy- iinsombululo zakho iinsombululo zakho
ukubonisa isisombululo. NgeThemu le abafundi kufanele batlole imitjho yeenomboro
abuyeleleni zemiraro, ezifaka zemiraro, ezifaka
ebuyabuyelelwako yesisombululo sabo. Bebagade bathulwe etshwayeni lokubuyabuyelela
ukuhlanganisa ukuhlanganisa
ethemini yoku-1 begodu kufanele basebenzise ilemuko leli lokha nabararulula imiraro
okubuyelelweko okubuyelelweko
yokubuyabuyelela yeenomboro. Ukuhlanganisa okubuyelelweko nomhlobo wemiraro
okurholela okurholela
yegridi/yerhemo kufanele kubonise ukubuyabuyelela kwemitjho yeenomboro. Kusazokuba
ekubuyabuyeleleni ekubuyabuyeleleni
nabafundi abazobanokuzethemba okukhulu ekurekhodeni iinsombululo zabo basebenzisa
okunempendulo ufikela okunempendulo ufikela
ukuhlanganisa okubuyelelwe kungasi ukubuyabuyelela.
e-50. e-30.
Iimbonelo zemiraro engenziwa ngeThemu
Uukuhlanganisa okubuyelelweko
• Inamavilo amangaki imilelenjana eli-8?
• Banamehlo amangaki abantwana abali-9?
Isilinganiso
UThami usela amarhalasi wamanzi asi-6 qobe ngamalanga. Usela amarhalasi mngaki
ngeveke?
Amagridi/ Ukurhemisa
UMnu. Khumalo utjala amareyi asi-6 weentjalo zekhabitjhi. Kuneentjalo ezihlanu ereyini
.Kuneentjalo zekhabitjhi ezingaki sezizoke?
257
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
258 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.9 Ukurarulula Ukurarulula Iimbonelo zemiraro engenziwa ngeThemu
Ukubuthele- imiraro yamagama imiraro yamagama NgeThemu le yumela abafundi ukusebenzisa imigwalo neensetjenziswa eziphathekako
la nok- ezisebujameni ezisebujameni ukubonisa iinsombululo zabo. Imitjho yeenomboro kufanele isetjenziswe. Umfundi
wabelana bewuhlathulule bewuhlathulule angasebenzisa ukukhupha okubuyelelweko ukubonisa bonyana bafike bunjani
okurholela iinsombululo zakho iinsombululo zakho ependulweni.
ekuhlu- ufake ukwabelana ufake ukwabelana Irhemo/ Igridi
kaniseni ngokulingana ngokulingana UMongezi upakela izinto zokubala ezima-20 ngamareyi ali-10.
nokubuthelela nokubuthelela
Ukubuthelela
ngeenqema ngeenqema
kweenomboro kweenomboro Ukubuthelela, ukulahla okuseleko
ezipheleleko ukufika ezipheleleko ukufika Stella sells apples in bags of 6 apples each. She has 40 apples. How many bags of 6
e-99 kanye nempendulo e-50 kanye nempendulo apples each can she make up? UStella uthengisa ama-abhula ngeenkhwama zangesi-6
ezingahle zifaka iinsalela ezingahle zifaka iinsalela. ngalinye. Unama-abhula ama-40. Angenza iinkhwanyana zama-abhula ali-6 ngasinye
amangaki?
Ukubuthelela, ukufaka okuseleko ngependulweni
UBen ufuna ukusela ugogo wakhe amaqanda ama-35. Mabhoksi amangaki wamaqanda
angathatha amaqanda asi-6 ibhoksi ngalinye azowafuna ukupakela woke amaqanda?
Ukwabelana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukwabelana, ukulahla okuseleko
• Hlukanisa amaswidi ama-45 hlangana nabangane ukuze boke bathole inani lamaswidi
elilinganako.
• USue banoGreg benza umsetjenzana bobabili. USue usebenza ama-iri ama-3 uGreg
usebenza i-iri yi-1. Babhadalwa amaranda ama-R40. Kufuze bayihlukaniselane bunjani
imali le?
1.10 Ukurarulula Ukurarulula Ngikuphi okuhlukileko eThemini yoku-1?
Ukwabelana nokuhlathulula nokuhlathulula Enye yeminqopho yokuthoma ekuthuthukeni kwamafraktjhini kufanele kube ukusiza
okurholela iinsombululo zemiraro iinsombululo zemiraro abafundi bonyana bakhe umbono weengcenye zamafraktjhini yokuzeleko – iingcenye
emafra- ezisebujameni efaka ezisebujameni efaka ezitholakala lokha okuzeleko nofana iyunithi nayihlukaniswe ngeengcenye zobukhulu
khtjhinini hlangana ukwabelana hlangana ukwabelana obulinganako nofana ngokwabelana okulingeneko
ngokulingana erholela ngokulingana erholela Abafundi baqaleka bazwisisa umqondo wokuhlukanisa ubungako eengcenyeni ezimbili
empendulweni empendulweni nofana ezinengi ukuhlukaniswa ngokulinganako phakathi kwabangane. Bagcina
zamafraktjhini wohlavu zamafraktjhini wohlavu sebahlanganisa phakathi komqondo wokwabelana ngokulingana neengcenyana
olulodwa Isib. njll. olulodwa Isib. njll. zamafraktjhini. Ukwabelana imisetjenzana ziindawo ezihle zokuthoma umqondo
wamafraktjhini. Ikharikhulamu yethu ithule godu umqondo wokwabelana okurholela
eeengcenyaneni zamafraktjhini.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Ukwabelana imisetjenzana kububzwa ngokujayelekileko ngendlela yemiraro yemitjho elula.
Ekuthomeni lokha abafundi nabenza imisetjenzana yokwabelana (ukuhlukanisa) bathola
bona ukuhlukanisa nofana ukwabelana kutjhiya iinqunjwana zokuseleko. Babelana godu
iinqunjwana zokuseleko. Ilimi lamafraktjhini lingathulwa ngomlomo.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.10 Ukurarulula Ukurarulula Bese umuntu angatlola amagama wamafraktjhini, isib. Isiquntu sinye, ikotara yinye,
Ukwabelana nokuhlathulula nokuhlathulula ingcenye yinye yobuthathu. Lokha nawutlola ngeengcenye ezinengi zamafraktjhini isib.
okurholela iinsombululo zemiraro iinsombululo zemiraro Iinquntu ezi-3, amakotara ama-3, tlola lokhu njengedijithi nangegama. Itshwayo loku-3
ezisebujameni efaka ezisebujameni efaka ngaphezu koku-2 nofana oku-3 ngaphezu kwa-4 ayitjho litho begodu kungcono khulu
emafra-
hlangana ukwabelana hlangana ukwabelana bonyana itshwayo leli litjhiywe esigabeni esiphakathi.
khtjhinini
ngokulingana erholela ngokulingana erholela Ukwabelana
empendulweni empendulweni Eembonelweni ezingenzasi ubujamo bokwabelana ngokulinganako enensalela ezingabelwa
zamafraktjhini wohlavu zamafraktjhini wohlavu isetjenzisiwe.
olulodwa Isib. njll. olulodwa Isib. njll. Abantwana ababili babelana amakuke wetjhokoledi ama-5 ukuze omunye nomunye
athole inani elifanako. Umntwana ngamunye angathola mangaki? Abafundi bazokunikela
umntwana ngamunye ama-2 bese banqunta phakathi ikuke eliseleko
Iinsalela
Kuqakathekile bona abafundi bagwale iimpendulo zabo. Ekuthomeni lisa abafundi
bahlathulule ngamagama wabo “ingcenye” abayiphulileko. Lindela lokho lokha abafundi
nabaqunta ingcenye eseleko. Iingcenye lezo zingaba bukhulu obungalinganiko. Lokhu
ngeze kwathelela indlela abahlathulula ngayo ikambiso yokwabelana. Lokha abafundi
nabangabelana kuhle, amagama wamafraktjhini anganikelwa eengcenyeni.
Ukusuka ekwabelaneni imiraro ngeensombululo ezinensalelo zeensombululo ezinenomboro
ezipheleleko neengcenye zamafraktjhini, kutjho bonyana abafundi bavezwe epepeneneni
wezingaqhezu neenomboro ezihlangene. Abafundi akukalindeleki bonyana bazi begodu
basebenzise itheminoloji. Isibonelo: ingcenye ezi-2 nesiquntu kungatlolwa ngokuhlelekile
njengo-2½, eyinomboro ehlangeneko.
Ukwabelana amathaski nelimi lamafraktjhini
Ukucocisana ngemiphumela yabafundi sikhathi esihle sokuthula ilwazi leengcenye
zamafraktjhini. Lokha ikuke letjhokoledi naliphulwe ngenquntu ezilinganako, itjho bona,
“lokhu sikubiza ngeengcezu ezine”. Ikuke loke liquntwe iingcenye ezine. Iingcenye zoke
zinobujamo obufanako. Abafundi kufanele balemuke amahlangothi wamabili weengcenye
259 zamafraktjhini:
• Inani leengcenye; begodu
• Ukulingana kweengcenye.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
260 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.10 Ukurarulula Ukurarulula Ukwabelana imisetjenzana kusiza abafundi ukuthuthukisa imiqondo elandelako:
Ukwabelana nokuhlathulula nokuhlathulula • Lokha nasihlukanisa okuthileko ngeengcenye ezi -2 ezilinganako, sizibiza ngeenquntu/
okurholela iinsombululo zemiraro iinsombululo zemiraro ngamahafu
emafra- ezisebujameni efaka ezisebujameni efaka • Lokha nasihlukanisa okuthileko ngeengcenye ezi-3 ezilinganako, sizibiza ngokwesithathu
khtjhinini hlangana ukwabelana hlangana ukwabelana • Lokha nasihlukanisa okuthileko ngeengcenye ezi-4 ezilinganako, sizibiza iinkotara
ngokulingana erholela ngokulingana erholela
• Lokha nasihlukanisa okuthileko ngeengcenye ezi-5 ezilinganako, sizibiza ngobuhlanu.
empendulweni empendulweni
zamafraktjhini wohlavu zamafraktjhini wohlavu Umnqopho wamafraktjhini wemiraro yamagama ethemini le uvumela abafundi bonyana ba:
1 1 1 1 1 1 1 1
• abela ubuthelele izinto ezilinganako;
olulodwa Isib. 2 , 4 , 3 , 5 njll. olulodwa Isib. 2 , 4 , 3 , 5 njll. • itjho iingcenye zamafraktjhini;
• thola amafraktjhini wezinto ezipheleleko; begodu
• bona bonyana ifraktjhini yingcenye yokuzele.
Iimbonelo zemiraro ezilungele iThemu yesi-2
• UMompi, uSizwe noGugu kufanele babelane iliqa elisasitina letjhokoledi ngokulinganako.
Umntwana ngamunye kufanele athole itjhokoledi engangani? Gwala isithombe ukubonisa
ipendulwakho.
• UMandla, uBusi, uZitha noThembi babelana amaqa asasitina ama-5. Bangawabelana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
bunjani ngokulinganako? Gwala isithombe ukubonisa ipendulwakho.
• UNomfundo noKarabo babelana iswidi linye le-liquorice. UNomfundo uthi munye
namunye kufanele athole isiquntu. Uqinisile? Gwala isithombe ukubonisa ipendulo yakho.
Kuqakathekile bonyana lokha abafundi nabagwala iiinsombululo zabo bakghona
ukuhlathulula bona babelene bunjani. Ekuthomeni sebenzisa ilwazi labafundi
elingakahleleki ukuhlathulula iingcenye zamafraktjhini. Lokha nabanokuzithemba begodu
bazwisisa imiqondo “wokuzeleko nokuncanyana”, igama lefraktjhini lingathulwa. Bese
umuntu angatlola amagama wamafraktjhini, isib. Isiquntu sinye, ikotara yinye, ingcenye
yinye yangakuthathu. Itshwayo lefraktjhini alikathulwa, lokha itshwayo la-1 ngaphezu
kwaku-2 ayitjho litho begodu kungcono khulu bonyana itshwayo leli litjhiyelwe amagreyidi ezako.
1.11 • Ukukhumbula • Ukukhumbula Ngikuphi okuhlukileko eThemini yoku-1?
Imali nokubona imali nokubona imali NgeThemu le abafundi bazijayeza ukukhumbula imali nokuphula imali ngeengcenyana ezincani.
yeSewula Afrika yeSewula Afrika
Iimbonelo zemiraro ezingenziwa ngeThemu le
eziinhlamvu (5c, 10c, eziinhlamvu (5c, 10c,
20c, 50c, R1, R2, R5), 20c, 50c, R1, R2, R5), • Ungakghona ukwaba amasende ama-50c ngokulinganako hlangana kwabantwana laba
nemali yamaphepha nemali yamaphepha abane? Hlathulula bona bunjani?
(R10, R20, R50) (R10, R20, R50) • UJoe usebenzisa amasende ama-50c ukuthenga amaswidi wetjhingamu. Uthenge
• Ukurarulula imiraro • Ukurarulula imiraro amaswidi wetjhungamu amangaki?
yemali efaka hlangana yemali efaka hlangana • UThenje ubhadele amaranda R5 ukukhwela itaxi ekuseni ukuya esikoleni. Ubhadela
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
inani netjhentjhi inani netjhentjhi ngemali yephepha ema-R20. Uthola itjhentjhi yamalini? Uzabe anamalini eseleko
ngamasende kufikela ngamasende kufikela nakabuyela ekhaya?
emarandeni ama R99 emasendeni ama 50c • Itekhsi kaZurina ibiza amaranda a-R5, 50. Uthola itjhentjhi yamalini ngemarandeni ali-R10?
namasende ama- 90c namaranda ama- R50 UMia usebenzise amaranda ama-R38. Begade amaranda ama-R50. Yimalini anayo eseleko?
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
UKUBALA OKUSEBUJAMWENI OBUTJHAPHULUKILEKO
1.12 Ukusebenzisa Ukusebenzisa Ngikuphi okuhlukileko eThemini yoku-1?
Amathekh- amathekhiniki alandelako amathekhiniki alandelako Abafundi balindeleke bonyana bararulule iimbalo zobujamo obutjhaphulukileko usebenzisa
iniki nakubalisiswako: nakubalisiswako: amaqhinga alandelako:
(iindlela • Imgwalo nofana • Imgwalo nofana • Ukwakha nokuphula iinomboro
namaqh- iinsetjenziswa iinsetjenziswa • Ukubuyelela kabili nokuhafula phakathi
inga) eziphathekako isib, eziphathekako isib, • Amanambalayini
iimbali iimbali
Imigwalo nofana iinsetjenziswa eziphathekako
• Ukwakha nokuphula • Ukwakha nokuphula Abafundi baragela phambili ngokugwala iinthombe basebenzisa iisetjenziswa
iinomboro iinomboro eziphathekako ukurarulula imiraro. Kuqakathekile bonyana iinthombe nofana imigwalo ibe
• Ukubuyelel a kabili • Ukubuyelel a kabili neenomboro begodu nemitjho yeenomboro.
nokuhafula phakathi nokuhafula phakathi Ukwakha nokuphula
• Amanambalayini • Amanambalayini Le ngenye yamaqhinga aqakathekileko esigabeni esisisekelo (isetjenziswa kanenginengi
esigabeni esiphakathi)usebenzisa iqhinga leli kuvumela abafundi ukuhlukana (hlukanisa)
nokuhlanganisa iinomboro ukusiza ukwenza iimbalo lula.
Kuqakathekile bonyana abafundi basebenzise ilwazi abalaziko nabaphula iinomboro isib.
• ukuphula usebenzisa ubukhulu bedijithi;
• ukuphula usebenzisa ukubuyelela ngali-10; begodu
• ukuphula wenze amapara weenomboro isib. Amapara wangama-20 ziyaziwa alo ama-20
angaphulwa ngeendlela ezihlukeneko.
Ukubuyelela kabili nokuhafula phakathi
Abafundi bavame ukuthola ukubuyelela kabili kulula; kodwana, kuqakathekile ukufundisa
abafundi ukusebenzisa ilwazi labo ngokubuyelela kabili:
• Sebenzisa ukukhumbula kokubuyelela kabili ukubona eduze kokubuyelela kabili
Ukubuyelela kabili Ukubuyelela kabili okuseduze
12 + 12 12 + 13
25 + 25 25 + 24
• Sebenzisa iqhinga lokubuyelela kabili begodu uncephezele umehluko, isib. 13 = 14 =
ukubuyelela kabili i-13 naku-1
Iqhinga leli ngelinelwazi tle begodu lifuna inomboro mizwa enamandla. Abafundi abakghona
ukukhetha itheknini le bamajadu khulu emaqhingeni abawasebenzisako.
Isibonelo:
Ngelanga linye ekliniki abanatwana abama-24 banikelwa iinjektjheni zomgomane.
Ngelanga elilandelako abantwana abama-25 bafakwa iinjektjheni. Bantwana abangaki
261 abafakwa iijektjhini sele baboke.
Umraro ungararululwa ngokusebenzisa ukubuyelela kabili. Umfundi angatjho bonyana
ukubueyela kabili ngama -24 naku-1 nofana ukubuyelela kabili ngama-25 ukhuphe ku-1.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
262 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.12 Ukusebenzisa Ukusebenzisa Amanambalayini
Amathekh- amathekhiniki alandelako amathekhiniki alandelako Ukusebenzisa amanambalayini ukuze ukubasiza nababalako kuzanikela abafundi indlela
iniki nakubalisiswako: nakubalisiswako: yokurekhoda ukucabanga kwabo nokulandela umkhondo wayo. Ivumela abafundi godu
(iindlela • Imgwalo nofana • Imgwalo nofana ukuba nerekhodi lomfanekiso abangayisebenzisa ukuhlathulula bonyana bawurarulule
namaqh- iinsetjenziswa iinsetjenziswa bunjani umraro.
inga) eziphathekako isib, eziphathekako isib, Abafundi bebasebenzisa amanambalayini ukusuka egreyidini yoku-1. Njenganje kufanele
iimbali iimbali bakwazi ukwakha amanambalayi angenalitho lapho abazokubeka inomboro ethomako
• Ukwakha nokuphula • Ukwakha nokuphula begodu akhethe bonyana usuka bunjani kwenye aye kwenye.
iinomboro iinomboro Isibonelo sendlela umfundi angasebenzisa inamabalayini:
• Ukubuyelel a kabili • Ukubuyelel a kabili • Ukuhlanganisa nokukhupha
nokuhafula phakathi nokuhafula phakathi
Abafundi kufanele bonyana bakhe amanambalayini wabo begodu baphule iinomboro
• Amanambalayini • Amanambalayini ngeengcenyana ezilawulekako.
Isibonelo:
45 + 27
ISIGABA ESISISEKELO AMAGREYIDI 1-3
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
• Ukubuyabuyelela
Amanambalayini kufanele aragele phambili nokusetjenziswa ukusekela ukuhlanganisa
okubuyelelwe. Ukweqa okulingeneko kurekhodwa enambalayinini begodu imitjho esekelako
nayo ingarekhodwa.
Isibonelo:
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
8 + 8 + 8 = 24
ukweqa ka-3 kwango-8 kwenza ama-24
iinqhema ezi-3 zango-8 = 24
3x 8 = 24
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Ekubuyabuyeleni okunikelweko abafundi kufanele bakghone ukuhlathulula bonyana imeqo
ingenziwa enambalayinini.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Ngikuphi okuhlukileko eThemini yoku-1?
Ukuh- ukufikela ku-99 ukufikela ku-50 Abafundi egreyidini yesi-2 bazoragela phambili ukusebenzisa iinsetjenziswa eziphathekako
langanisa • Ukukhupha ku-99 • Ukukhupha ku-50 neminye imifanekiso ukusiza ukuhloma inomboro mizwa nokubala. Ukusetjenziswa
nokukhupha • Ukusebenzisa • Ukusebenzisa kwemifanekiso le kuzakuba ngokungabonakaliko ukuya nokuya kwesikhathi.ngokuphela
amatshwayo afaneleko amatshwayo afaneleko konyaka egreyidini yesi-2 abafundi kufanele ukube babala ukufikela eenomborweni
( +, -, =, ) ( +, -, =, ) yamadijithi amathathu ngaphandle kokusetjenziswa kweensetjenziswa eziphathekako.
Abafundi begreyidi yesi-2 baragela phambili uksebenzisa nokutjhega amaqhinga
• Ukuzijayeza iinomboro • Ukuzijayeza
wabo wokubala. Bathloga ukusekelwa ekwenzeni isiqiniseko sokobana ukurekhoda
ebhodini ukufika e 20 ukulumbana
kwabo kungerherho. Ukuze ifundwe ngibo nabanye. Begreyidi yesi-2 bazokusebenzisa
kweenomboro ukufika
ukurekhoda kwemihlobo eminengi bazakuba nokuzethemba okukhulu ekusebenziseni
e -15
iinomboro begodu namatshwayo njengendlela yokurekhoda.
Abafundi kufanele bakghone “ukucabanga” ngemibuzo ababuzwe yona begodu baqale
erherhweni leenomboro lomraro ukuthatha isinqumo ngeqhinga elihle khulu. Ngokurarulula
imiraro abafundi bathoma ukuthuthukisa amaqhinga wabo wokubala begodu neendlela
zabo zokurekhoda. Egreyidini yesi-2 bazokutjhega lokho. NgeThemu le kufanele babe
nokuzithemba ekufundeni iindlea zabo zokurekhoda begodu bahlathulula bonyana bafike
bunjani ependulweni
Abafundi kufanele bakghone ukwenza okulandelako ngokuhlanganisa nangokukhupha:
Nanyana abafundi basebenzisa iinsetjenziswa eziphathekako nemifanekiso ukusekela
ukubala kwabo nakuza ekusebenzeni ngeenomboro, kufanele bakghone ukubala ngeleveli
engaphathekiko.
Ngethemini abafundi kufuneka baragele phambili ngemibuzo yokubala ngokubuyelela kabili
ngeendlela ezihlukeneko ukuze bakghone ukusebenzisa ukubuyelela kabili okuseduze
njengeqhinga lokubala.
Isibonelo:
Buyelela kabili ama-20. Tlola lokhu njengokuhlanganisa imitjho yeenomboro
kopa uzalise:
• 12 + 12 =
• 15 + = 30
• 16 + = 32
• 17 + 17 =
• 36 = 18 +
• 38 = + 19
263
Iindlela ezingabakhona zokubonisa ukubala ngokuhlanganisa nangokukhupha.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
264 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa ukuphula inomboro ibe ziinqunjwana ezincani ukwenza ukubala kube lula
Ukuh- ukufikela ku-99 ukufikela ku-50 ukusebenzisa ilwazi lobukhulu bedijithi ukuphula iinomboro ngalitjhumi nangakunye
langanisa • Ukukhupha ku-99 • Ukukhupha ku-50 Ukuhlanganisa iinomboro zamadijithi amabili ngokuphula innomboror zombili
nokukhupha • Ukusebenzisa • Ukusebenzisa 23 + 36 =
amatshwayo afaneleko amatshwayo afaneleko
23 + 36 = (20 + 3) + (30 + 6)
( +, -, =, ) ( +, -, =, )
= (20 + 30) + (3 + 6)
• Ukuzijayeza iinomboro • Ukuzijayeza
ebhodini ukufika e 20 ukulumbana = 50 + 9
kweenomboro ukufika = 59
e -15 Ukuhlanganisa ngokuphula inomboro yinye
Ukuhlanganisa iinomboro zamadijithi amabili ngokuphula inomboro yinye
23 + 36 =
23 + (30 + 6)
23 + 30 ➝ 53 + 6 = 59
Abafundi bangaphula inomboro ngeendlea ezihlukeneko ezilawulekako. Lokhu kutjho
ISIGABA ESISISEKELO AMAGREYIDI 1-3
bonyana bazokwenza ngeendlela ezihlukeneko:
23 + 36 =
23 + (10 + 10 + 10 + 6)
23 + 10 ➝ 33 + 10 ➝ 43 + 10 ➝ 53 + 6 = 59
Ukukhupha
ukuphula iinomboro zombili
47 – 26 =
47 – 26 = (40 + 7) – (20 + 6)
= (40 – 20) + (7 – 6)
= 20 + 1
= 21
42 – 26 =
42 – 26
(30 + 12) – (20 + 6)
30 – 20 = 10
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
12 – 6 = 6
10 + 6 = 16
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa • Ukukhupha ngokuphula inomboro
Ukuh- ukufikela ku-99 ukufikela ku-50 47 – 26 =
langanisa • Ukukhupha ku-99 • Ukukhupha ku-50 47 – (20 + 6)
nokukhupha • Ukusebenzisa • Ukusebenzisa 47 – 20 = 27
amatshwayo afaneleko amatshwayo afaneleko
( +, -, =, ) ( +, -, =, ) 27 – 6 = 21
• Ukuzijayeza iinomboro • Ukuzijayeza 42 – 26 =
ebhodini ukufika e 20 ukulumbana (30 + 12) – 26
kweenomboro ukufika 30 – 26 = 4
e -15
12 + 4 = 16
lindela bonyana abanye abafundi banga phula inomboro ngeendlela ezihlukeneko ukwenza
bulula izinto bonyana babale:
47 – 26 =
47 – (10 + 10 + 6)
47 – 10 ➝ 37 – 10 ➝ 27 – 6 = 21
Ukusebenzisa ilwazi langaphambili njengamathekniki
Amathekniki aboniswa ngenzasi avumela abafundi bonyana bahlele kuhle ukubala kwabo
nemizwa yeenomboro. Ukujayeza amathekniki angenzasi kuzokuthaza abafundi bonyana
batjengise ubudlelwano hlangana kweenomboro nokufundisa abafundi bonyana bakghone
ukusebenzisa nokutjengisa ilwazi labo ukubasiza ukubala.
Bala uye phambili nemuva
48 – 39 =
Ukubala uye phezulu ngakunye ukusuka ema-39 liqhinga elifaneleko ngombana iinomboro
zitjhidelene.
Ukulemuka ukubuyelela kabili okuseduze
24 + 25 uhlathulula bonyana kubuyelwe kabili ngama-24 naku-1 nofana kubuyelelwe kabili
ngama-25 naku-1.
24 + 24 + 1
Abafundi bangarekhoda amaqhinga wabo basebenzisa amasungulo
24 + (20 + 4) + 1
24 + 20 ➝ 44 + 4 ➝ 48 + 1 = 49
265
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
266 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Ukusebenzisa ukuqunta kabili/ukuhafula ukuphula inomboro
Ukuh- ukufikela ku-99 ukufikela ku-50 29 + 12
langanisa • Ukukhupha ku-99 • Ukukhupha ku-50 29 + (6 + 6)
nokukhupha • Ukusebenzisa • Ukusebenzisa 29 + 6 ➝ 35 + 6 = 41
amatshwayo afaneleko amatshwayo afaneleko
( +, -, =, ) ( +, -, =, ) Tjhugulela inomboro ekubuyabuyeleni kwalitjhumi begodu ukhuphe nofana
uhlanganise
• Ukuzijayeza iinomboro • Ukuzijayeza
ebhodini ukufika e 20 ukulumbana Bala uye phezulu nofana phasi enomborweni eseduze ne-10
kweenomboro ukufika 28 + 19 =
e -15 La abafundi kufuze bazitjele bonyana banamandla wokuthetha amabili. Tjhugulula ama-28
nofana i-19 ebuyelelweni eliseduza langali-10. Bazazikhethela.
Isibalo singatlolwa bunje: 28 + 19 = 28 + 20 - 1
28 + 20 ➝ 48 - 1 = 47
Abanye abafundi bangaphula ama-20 ngeenqhema ezi-2 zangali-10 ukubala kuhle.
Kusiza abafundi ukuba nokuzithemba okukhulu eembalweni nofana ngokuzijamela
eembalweni, nabanamaqhinga
ISIGABA ESISISEKELO AMAGREYIDI 1-3
-- ukuhlola iinsombululo zabo; begodu
-- Ukuhlulela ukuzwakala kweensombululo zabo.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Ngikuphi okuhlukileko eThemini yesi-12
Ukuh- iinomboro ku-1ukufika iinomboro ukufika ku Ngethemini yesibili abafundi batjheje ukujayeza ukuzwisisa ukubuyabuyelela.
langanisa e- 10 ngaku – 1, 2,5,3 10 ngaku -2 nesi 5 Ukubuyabuyelela ku-1 ukufike e-10 ngaku-5 kuthulwa. Ukwethula ukubuyabuyelela
okubuyele- na-4 • Ukusebenzisa ngaku-5, qala amanothi wokubuyabuyelela ngaku-2 ethemini yoku-1.
lweko • Ukusebenzisa amatshwayo afaneleko Ekupheleni kweThemu abafundi bafanele bakghone ukurekhoda okulandelako:
okurholela amatshwayo afaneleko ( +, -, =, )
Isiqhema si-1 saku-5 ku-5 nofana ku-1 ukubuyabuyelele ngaku-5 ku-5 nofana 1 × 5 = 5
ekubuy- ( +, -, =, )
abuyeleleni Iinqhema ezi-2 zaku-2 ku-4 nofana ku-2 ukubuyabuyelele ngaku-2 ku-4 nofana 2 × 2 = 4
Iinqhema ezi-3 zaku-2 si-6 nofana ku-3 ukubuyabuyelele ngaku-2 si-6 nofana 3 × 2 = 6
Umnqopho awukho ekufundeni ngehloko kodwana ekwakheni umqondo wokubuyabuyelela.
Abafundi bafunda ukufunda begodu bazwisisa imitjho yeenomboro yokubuyabuyelela.
Imifanekiso yokubuyabuyelela ukubuyabuyelela kufanele kunikelwe begodu nokurekhoda
okunengi kwenziwe encwadini yomsebenzi.
Iimbonelo zomsebenzi otloliweko
Ukurekhoda emathebuleni:
Inani labantwana 1 2 3 4 5 6 7 8 9
Inani lemilenze
Amatjhadi naneko
1
2
3
4
× !
5
Lokha nawusebenza ngeenomboro zamaphetheni, ukubuyabuyelela kungahlanganiswa
nokubala okweqako, ngokuphenya amaphetheni wokubuyabuyelela egreyidini yenomboro.
Isibonelo: Abafundi bangarekhoda abobili nabohlanu egreyidini yenomboro. Bangakhuluma
ngokuthi ngiziphi iinomboro ezenzeka ngemathebuleni wokubuyelela kabili neyokubuyelela
kahlanu.
267
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
268 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.16 Umqondonomboro: Umqondonomboro: Umqondonomboro:
Iimbalo Irherho lama-99 Irherho lama-20 Amaqhinga wokubala, umqondonomboro, ilwazi namaphuzu weenomboro aziwako
zehloko • Ukurhemisa iinomboro • Ukurhemisa iinomboro ayathuthukiswa ngokurarulula imiraro nokubala. Lezi zijayeza ngesikhathi seembalo
ezikhethiweko ezikhethiweko zehloko. Lokhu kusiza abafundi bonyana babajayele begodu bakghone ukuzisebenzisa
ngokwesede ngokwesede ngobulula lokha nababala begodu nabararulula imiraro ngebujameni.
enikeliweko. enikeliweko.
Isibonelo semibuzo engabuzwa:
• Madanisa iinomboro • Madanisa iinomboro
ukufika ema-99 utjho ukufika e-100 utjho Amagama weenomboro namatshwayo
bonyana ngiyiphi e-1, bonyana ngiyiphi e-1, Phakamisa ikarada nofana utlole phasi igama lenomboro. Khetha umfundi ukutlola
2, 3, 4, 5 nakunengi 2, 3, 4, 5 nakunengi inyumerali emadanako.
nofana ngakuncani nofana ngakuncani
nge-10 nge-10 Okunengi nofana okuncani
Ukukhumbula: Ukukhumbula: Khuyini oku?
• Amaphuzu khumbula ukuhlanganisa • okuncani nga-1 ema -50
wokuhlukanisa nokukhupha amaphuzu • okunengi nga-1 ema -39
nokukhupha ukufika ukufika e-10
• okuncani ngaku-3 kunama -27
ema-20 Amaqhinga wokubala
• okunengi ngali-10 kunama -20
• hlanganisa nofana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukusebenzisa
ukhuphe ukubuyelela amaqhinga wokubalisa Ngiyiphi iledere yesi-5 ye-alfabhethi?
kali-10 ukusuka e-0 ukuhlanganisa Ngiyiphi inyanga ye-9 enyakeni?
ukufika 100 nokukhupha ngekghono Ngaphambi nofana ngemuva
Amaqhinga wokubala elifaneleko:
Ngiyiphi inomboro eza ngaphambi kwama-37?
Ukusebenzisa • Beka inomboro ekulu
amaqhinga wokubalisa maqangi ukuze ubale Ngiyiphi inomboro eza ngemuva kwama-39?
ukuhlanganisa uye phambili nofana Ukuhlela nokumadanisa
nokukhupha ngekghono ubale uye emuva
Ngiyiphi enengi: ama-21 nofana ama-41?
elifaneleko: • Inambalayini
• Beka inomboro ekulu Nginikela inomboro hlangana kwama-37 nama-39.
• Ukubuyelela kabili
ekuthomeni ukuze nokuhafula phakathi Amaphuzu wokuhlanganisa nokukhupha:
ubale uye phambili Qala amanothi weThemu yoku-1
nofana ubale uye • Ukwakha nokuphula
emuva • Sebenzisa
• Inambalayini ubudlelwano hlangana
kokuhlanganisa
• Ukubuyelela kabili nokukhupha
nokuhafula phakathi
• Ukwakha nokuphula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Sebenzisa
ubudlelwano hlangana
kokuhlanganisa
nokukhupha
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.16 Umqondonomboro: Umqondonomboro: Amaqhinga wokubala
Iimbalo Irherho lama-99 Irherho lama-20 Sebenzisa amaqhinga wokubala okuhlanganisa nokukhupha ngokuphumelela.
zehloko • Ukurhemisa iinomboro • Ukurhemisa iinomboro Hlanganisa iinomboro ezimbalwa ngokusebenzisa amaqhinga anjengo:
ezikhethiweko ezikhethiweko
ngokwesede ngokwesede • Qala iimpara zeenomboro ezingenza i-10 uzisebenzise mantanzi
enikeliweko. enikeliweko. 2+7+8
• Madanisa iinomboro • Madanisa iinomboro 2 + 8 benza i- 10 hlanganisa ne-7
ukufika ema-99 utjho ukufika e-100 utjho
bonyana ngiyiphi e-1, bonyana ngiyiphi e-1, Beka inomboro ekulu ekuthomeni ukuze ubale uye phambili nofana bala uye emuva.
2, 3, 4, 5 nakunengi 2, 3, 4, 5 nakunengi • Thoma ngenomboro ekulu khulu
nofana ngakuncani nofana ngakuncani 3+6
nge-10 nge-10
Yitjho godu umutjho wenomboro: 6 + 3 begodu ubale uye phambili ngesi-9
Ukukhumbula: Ukukhumbula:
• Sebenzisa ukubuyelela kabili njengeqhinga lokubala ngehloko
• Amaphuzu khumbula ukuhlanganisa
wokuhlukanisa nokukhupha amaphuzu Bona ukubuyelela kabili okuseduze.
nokukhupha ukufika ukufika e-10 Isibonelo:
ema-20 Amaqhinga wokubala 5 + 4 = 9 hlathulula bonyana ukubuyelela kabili kwanga-4 naku-1 nofana ukubuyelela kabili
• hlanganisa nofana Ukusebenzisa kwanga-5 ukhupha ku-1
ukhuphe ukubuyelela amaqhinga wokubalisa
kali-10 ukusuka e-0 Khumbula bonyana lokha iinomboro ezimbili zitjhidelene ngobukhulu kulula ukuthola
ukuhlanganisa
ukufika 100 umehluko ngokubala uye phezulu kunokubala uye emuva.
nokukhupha ngekghono
Amaqhinga wokubala elifaneleko: 8 – 6 = 2 begodu hlathulula bonyana ukubala uye phezulu ukusuka esi-6 ukuya e-8
Ukusebenzisa • Beka inomboro ekulu kukunikela oku-2
amaqhinga wokubalisa maqangi ukuze ubale Ezinye iimbalo zehloko zingenziwa ngaphandle kweensetjenziswa, kodwana kuyasiza
ukuhlanganisa uye phambili nofana ukwenza i imbalo zehloko ngeensetjenziswa.
nokukhupha ngekghono ubale uye emuva
Iinsetjenziswa eziphakamisiweko
elifaneleko: • Inambalayini
• Beka inomboro ekulu • Inambalayini (ehlelekileko nenganalitho)
• Ukubuyelela kabili
ekuthomeni ukuze nokuhafula phakathi • Igridi yenomboro
ubale uye phambili • amakarada wobukhulu beenomboro (amakarada wamaflardi)
nofana ubale uye • Ukwakha nokuphula
emuva • Sebenzisa • Ukubala imincamo
• Inambalayini ubudlelwano hlangana
kokuhlanganisa
• Ukubuyelela kabili nokukhupha
nokuhafula phakathi
• Ukwakha nokuphula
• Sebenzisa
269 ubudlelwano hlangana
kokuhlanganisa
nokukhupha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
270 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.17 • Sebenzisa begodu • Sebenzisa bewutjho IThemu le inqophise:
Amafra- utjho amafrakhtjhini amafraktjhini okufaka Ethemini le abafundi bathulwa emafraktjhinini. Abafundi bazothulwa emafraktjhinini ngokwabelana imiraro
khtjhini okufaka hlangana hlangana amahafu, yamagama nemisetjenzana
iinquntu,/amahafu amakota, isithathu
Nokho ke, umnqopho weengcenye zamafraktjhini uqakathekile bonyana kufanele ithuthukiswe ukuya phambili
amakotara, iingcenye begodu nesihlanu
usebenzisa imisetjenzana efakiweko.
ezintathu neengcenye • Ukubona amafraktjhini
ezihlanu • Ukwenza ubujamo besiquntu nekotara ngokubhinca nokuqunta.
ebujameni
• Ukubona obuyidayagremu Abafundi bangabhinca iphepha ngesiquntu batjhoingcenye ngayinye. Kuqakathekile bonyana bazwisie
amafrakhtjhini bonyana lokha nawenza iingcenye ezifanako ngokhunye, ubiza iingcenye ngayinye isiquntu/ihafu.
• Tlola amafraktjhini
ngendlela Bangabuyelela godu babhince isiquntu/ihafu sephepha. Okuqakathekile la ngukubhinca iphepha ngeendlela
njenge siquntu si-1
yedayagremu ezihlukeneko ukufumana isiquntu/ ihafu esihlukileko
ubu-2 kobu-3
• Ukutlola amafrakhtjhini
njengesiquntu si-
1, iingcenye ezi-2
zobuthathu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nofana
or
Ngaso soke isikhathi bawa abafundi ukubikezela bonyana ziiinquntu ezingaki abazozithola begodu
ukubavumela bonyana baphuthulule iphepha bahlole. Ukumadanisa iingcenye ezimbili ezingafaniko nofana
ubujamo obubili obungafaniko bamakotara kungarholela eenkulumeni ezikarisako zobujamo nobukhulu.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.17 • Sebenzisa begodu • Sebenzisa bewutjho Ungabuza abafundi:
Amafra- utjho amafrakhtjhini amafraktjhini okufaka Ngingabiza ubujamo lobu obubili ngegama elifanako lenomboro, isiquntu esisodwa?
khtjhini okufaka hlangana hlangana amahafu,
iinquntu,/amahafu amakota, isithathu
amakotara, iingcenye begodu nesihlanu
ezintathu neengcenye • Ukubona amafraktjhini
ezihlanu ebujameni
• Ukubona obuyidayagremu
Ngitjengisa bonyana ngingabiza ubujamo lobu obubili ngegama lenomboro ikotara yinye.
amafrakhtjhini • Tlola amafraktjhini
ngendlela njenge siquntu si-1
yedayagremu ubu-2 kobu-3
• Ukutlola amafrakhtjhini
njengesiquntu si- Abafundi kufanele batjho ingcenye ngayinye begodu lokhu kungenziwa ngokutlola amafrakthjini. Isibonelo:
1, iingcenye ezi-2
zobuthathu
ikotara yinye
• isiquntu sinye Ukuhlanganisa ukwenza okupheleleko
Abafundi abasebenzise amafraktjhini weendulungu nofana basike iindulungu emaphepheni ukuthola bonyana
isiquntu nekotara kungahlanganiswa bunjani ukwenza okupheleleko godu.
• Ukufaka umbala emafraktjhinini
Imisetjenzana le ikhuthaza:
• ukwazi bonyana amafraktjhini aziingcenye ezifanako;
• ukubona iingcenye zamafrakthjini; nokutjho iingcenye zamafraktjhini.
Ukutlola amagama wamafraktjhini
Abafundi asibathuli ekutloleni amatshwayo wamafraktjhini. Abafundi bafunda ukulebula iingcenye
zamafraktjhini ngokutlola isiquntu?ihafu sinye nofana ikotara yinye.
271
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI- 2 ITHEMU YESI- 2
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
272
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
2.1 Kopa ,ungezelele Kopa ,ungezelele Egreyidini yoku-1 neyesi -2,eThemini yoku-1, kuphakamisiwe bonyana abafundi Isifundo esi-1
Amapheth- bewuhlathulule bewuhlathulule basebenzise amaphetheni anamalunga (ubujamo, imida nofana izinto) aphindwe
eni weJi- Kopa ,ungezelele Kopa ,ungezelele ngendlela elinganako. Ethemini ye-2 yegreyidi ye-2 abafundi bangathoma ukusebenza
yomethri bewuhlathulule bewuhlathulule ngamaphetheni lapho ubukhulu bamajamo nofana inomboro zamajamo zitjhuguluka
ngamagama ngamagama ngendlela yokubonela phambili.
• Amaphetheni alula • Amaphetheni alula Amaphetheni ambadlwana aneenqhema zobujamo ezifana khulu nofana izinto
enziwe ngezinto enziwe ngezinto ezibuyelelweko, lapho ubukhulu bobujamo eengcenyeni ngayinye itjhuguluka ngendlela
eziphathekako eziphathekako ejayelekileko yokubonela phambili. Isib. Ubujamo bubabuncani
• Amaphetheni alula • Amaphetheni alula
enziwe ngemigwalo enziwe ngemigwalo
yemida,ubujamo yemida,ubujamo
nafana izinto . nafana izinto .
Tlama begodu Tlama begodu Amanye amaphetheni enziwa ngomhlobo owodwa wobujamo, kodwana isibonelo ngasinye
uhlathulule uhlathulule
ISIGABA ESISISEKELO AMAGREYIDI 1-3
sobujamo siyanda nofana siyaphunguka ngobukhulu
amaphetheni wakho amaphetheni wakho
Isibonelo:
tlama amaphetheni tlama amaphetheni
weJiyomethri weJiyomethri
• Ngezinto • Ngezinto
eziphathekako eziphathekako
• Ngokugwala imida, • Ngokugwala imida, Amanye amaphetheni ambadlwana enziwa ngeenqhema lapho amajamo afanako wezinto
ubujamo nofana izinto ubujamo nofana izinto avelako, kodwana inomboro yomhlobo yobujamo obuthile nofana into iyanda nofana
Amaphetheni iyaphunguka ngendlela ejayelekileko isib
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
Ukukopa iphetheni kusiza abafundi ukubona ilojikhi yokuthi iphetheni yenzwe njani.
amaphetheni
weJiyomethri Ukungezelela iphetheni kusiza abafundi ukubona bonyana bayizwisisile ilojikhi yephetheni.
• Ngokwemvelo, Ukuhlathulula amaphetheni kusiza abafundi ukuthuthukisa amakghono welimi
nowokukhuluma. Isiza nawe ukubona bonyana abafundi bayihlathulule njani iphetheni.
• Kusukela epilweni
Kuvamile ukubalula bonyana abafundi bakhulume ngephetheni ngemuva kokuyenza.
yangamalanga
Ngalesisikhathi abafundi kufanele bakwazi ukuhlathulula amaphetheni ngaphandle kosizo
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
yesimodeni,
lwemibuzo ekhokhelako. Ragela phambili ngomnqopho wokuthuthukisa ilimi abalitlhogako
• kusukela kezamagugu ukuhlathulula amaphetheni.
nendabuko yethu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelela Qala amanothi eThemini 1, kodwana wandise irherho leenomboro ukuya e-150 Iimfundo ezi-3
Amaphe- nokuhlathulula nokuhlathulula
theni Ukukopa, ukungezelela Ukukopa, ukungezelela
weenom- nokuhlathulula nokuhlathulula
boro ukulandelanisa ukulandelanisa
kweenomboro ezilula kweenomboro ezilula
ukufika ku-200 ukufika ku-150.
Tlama begodu Ukulandelanisa kufanele
uhlathulule kubonise ukubalela
amaphetheni wakho ukuya phambili nemuva
nga:
Tlama begodu
uhlathulule amaphetheni • Ku-1 ukusuka kwenye
weenomboro nenye inomboro
hlangana ne-0 ne-150
• Li-10 ukusuka
kesinye nesinye
isibuyabuyelelo se-10
hlangana ne-0 ne-150
• Ku-5 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-5 hlangana ne-0
ne-150
• Ku-2 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku- 2 hlangana ne -0
ne-150
• Ku-3 naku-4 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-3 hlangana ne -0
ne-150
273
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI-2
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
274
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
3.1 Ilimi lobujamo Ilimi lobujamo Umnqopho ophakanyisiweko weThemu 2: ubujamo belimi endaweni, ukulandela Iimfundo ezi-2
Ubujamo, Ukuhlathulula Ukuhlathulula ikombatjhuba
ukuzijayeza ubujamo bento yinye ubujamo bento yinye Umnqopho ethemini ye-2 ungaba sendaweni nasekuzijayezeni. NgeThemu yesi-3 abafundi
nokubukela ngokuhlobane nenye isib. ngokuhlobane nenye isib. bangasebenza ngemibono. Thoma ngokuhlola lokha abafundi abakwaziko begodu
ngaphezulu, ngaphambi ngaphezulu, ngaphambi ukhumbule indawo nokuzijayeza.
kwe, ngemuva, kwe, ngemuva, Ngikuphi okuhlukileko kuneThemu yoku-1?
esinceleni, ngesindleni, esinceleni, ngesindleni,
Egreyidini ye-2, abafundi bahlanganisa umsebenzi abawenze ngendawo, ukujayela
phezulu, phasi, eqadi phezulu, phasi, eqadi
nemibono egreyidini yo-1.
kwe kwe
Ubujamo belimi endaweni
Ubujamo nokubukela Indawo nekombatjhuba
Ubujamo belimi endaweni kufanele kuthulwe begodu bujayezwe ngemisetjenzana
Madanisa imibono Landela ilayelo
eyenzekako ebandakanya abafundi emisikinyekweni ephathekako, kubalwa iingoma
ehlukeneko yezinto ukukhambakhamba
nemidunduzelo enemisikinyeko begodu nemidlalo enamagama anomsikinyeko. Lokhu
zangamalanga ezifanako ngetlasini
kungenziwa ngesikhathi sokufundisa itlasi loke nofana ngesikhathi sokufundisa isiqhema
Indawo nekombatjhuba .
ISIGABA ESISISEKELO AMAGREYIDI 1-3
esinqotjhiweko. Kuphakanyiswe bona usebensize iinfundo ezimbili zemisetjenzana
Landela ilayelo yobujamo ethemini ye-2, kodwana ragela phambili ukuthula nokujayeza amagama
ukukhambakhamba wobujamo engcenyeni ezifitjhani zetlasi loke, isiqhema esinqotjhiweko nesikhathi
ngetlasini somsebenzi sokuzijamela. Ubujamo belimi endaweniingajayeza ngesikhathi sesifundo
seLimi namaKghono Wepilo.
Ubujamo belimi endaweni bungahlanganiswa ngokurekhodwa okutloliweko njengokufaka
umbala nofana ukumadanisa imigwalo ngamgama, ukugwala into nofana ubujamo
nabatjhelwe ukuhlobana kobujamo nezinye izinto nofana ubujamo, ukufaka umbala nofana
ukumadanisa imigwalo ngamagama.
Indawo nekombatjhuba
Ukufundisa abafundi ukulandela ikombandlela kufanele kwenziwe ngemisetjenzana
eyenzekako lapho abafundi bazikhambela bona balandela imiyalelo. Egreyidini
ye-2 abafundi banganikelwa nofana ngomlomo nofana ikombatjhuba etloliweko
ukukhambakhamba ngetlasini, isib. “yiza phambili etlasini”; ‘jama eqadi kwesitulo”; “yeqa
ngaphezu komgqomu weenzibi”.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
3.2 Imihlobohlobo Akunamnqopho onqophileko womsebenzi ophakanyisiweko weThemu ye-2. Kodwana,
Izinto ezi- yamajamo umsebenzi wobujamo-3-D ungahlanganiswa ngemisebenzi etlolwako. Abafundi
busontathu Ukukhumbula bangaragela phambili ukwakha izinto zobujamo be 3-D ngemathiriyali ebuyelelwe
(3-D) nokutjho izinto ezi yasetjenziswa godu nofana amakhidi wokwakha ngesikhathi sokusebenza ngokuzijamela.
3-D ezingetlasini
neenthombeni
• Ubujamo bebhola
(indulungu)
• Ubujamo bebhoksi
(iphrizimu)
• Amasilinda
Amatshwayo wezinto
Hlathulula, uhlele
ngamananeko
umadanise ubujamo be
3-D ngokuya nga:
• Bukhulu
• Izinto ezigedekako
• Izinto ezitjhelelelako
Imisetjenzana
enqotjhiweko
Ukuqala nokwakha izinto
ze 3-D ezinikelweko
ngokusebenzisa
imethiriyeli ephathekako
ezifana namajamo
wabo 2-D asikiweko ,
amabhlogo wokwakha,
ukubuyelela iberegise
into esetjenzisiweko,
ipahla esetjenziswa
emsebenzini wokwakha,
nezinye izinto
zeJiyomethri ne 3-D.
275
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
276 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
3.3 Amajamo Amajamo Ngikuphi okutjha ngegreyidini ysie-2
Amajamo ahlukahlukeneko ahlukahlukeneko • aboncantathu
abobusobu- Ukubona nokutjho Ukubona nokutjho Umsebenzi omnengi wobujamo egreyidini ye-2 wenziwa ngokwenza ngezinto
bili (2-D) amajamo be 2-D amajamo be 2-D eziphathekako. Woke umsebenzi kufanele uhlanganiswe ngemisebenzi etloliweko.
• Indulungu • Indulungu Abafundi bathoma ngomdlalo otjhaphulukileko ngobujamo obuhlukahlukeneko kubalwa
• Uncantathu • Uncantathu nokwenza iinthombe ngojamo obusikelwe futhi bejeyomethri. Lokhu kungenziwa
• Isikwere • Isikwere ngesikhathi sokuzijamela. Lokhu kungenziwa godu ngesifundo samaKghono Wepilo.
• Uncamane • Uncamane Abafundi bakhopha iinthombe ezenziwe ngobujamo bejeyomethri. Iinthombe lezi
zinganikelwa botitjhere nofana incwadi yokufunisa. Lokhu kusiza abafundi bona bakghone
Amatshwayo Amatshwayo
ukufanisa.
wamajamo wamajamo
• iindulungu neenkwere zobukhulu obuhlukeneko;
Hlathulula, uhlele Hlathulula, uhlele
ngemihlobo begodu ngemihlobo begodu • iinkwere, aboncamane naboncantathu ebujameni obuhlukeneko
umadanise amajamo umadanise amajamo • Aboncamane naboncantathu bobujamo obuhlukeneko. Lokhu kungenziwa ngesikhathi
abobusobubili (2-D) abobusobubili (2-D) sokuzijamela. Lokhu kungenziwa godu ngesifundo samaKghono Wepilo.
ngokuqala lokhu: ngokuqala lokhu:
• Ubukhulu • Ubukhulu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Umbala • Umbala
• ubujamo • ubujamo
• amahlangothi • amahlangothi
anqophileko anqophileko
• amahlangothi • amahlangothi
aziindulungu aziindulungu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
3.3 Amajamo Amajamo Ukumadanisa nokuhlathulula amajamo we-2-D: ubukhulu Iimfundo ezi-3
Amajamo ahlukahlukeneko ahlukahlukeneko Abafundi bamadanisa ubukhulu bobujamo obufanako isib.
abobusobu- Ukubona nokutjho Ukubona nokutjho • hlela iindulungu ukusukela kwencani khulu ukuya kwekulu khulu,
bili (2-D) amajamo be 2-D amajamo be 2-D
• beka zoke iinkwere nofana ubukhulu obufanako endaweni yinye,
• Indulungu • Indulungu
Sebenzisa ilimi lobukhulu ukumadanisa ubujamo obuhlukeneko isib. “ngigwale uncamane
• Uncantathu • Uncantathu ngaphakathi kwesikwere, ngakho-ke uncantathu mncani kunesikwere.
• Isikwere • Isikwere Ukuhlathulula amajamo we-(2-D): umbala
• Uncamane • Uncamane Abafundi bakhuluma ngemibala yobujamo begodu bahlela ubujamo ngokuya ngombala.
Amatshwayo Amatshwayo Ukufanisa nokutjho izinto nemibala yazo, begodu nokumadanisa ubukhulu bezinto,
wamajamo wamajamo kungajayezwa ngesikhathi sokusebenza ngamaphetheni.
Hlathulula, uhlele Hlathulula, uhlele Ukukhumbula nokutjho iindulungu, aboncantathu, iinkwere naboncane.
ngemihlobo begodu ngemihlobo begodu
Abafundi kufanele basebenze ngeendulungu nangeenkwere zobukhulu obuhlukeneko
umadanise amajamo umadanise amajamo
nangaboncantathu bobujamo obuhlukeneko.
abobusobubili (2-D) abobusobubili (2-D)
ngokuqala lokhu: ngokuqala lokhu: Kuqakathekile bona abafundi bangaboni isibonelo sinye sobujamo ngabunye. Amasede
wobujamo amaninginwokurhweba anikela isibonelo sinye saboncantathu. Abafundi
• Ubukhulu • Ubukhulu
kufanele bakghone ukukhumbula.
• Umbala • Umbala
-- Aboncantathu anamajamo ahlukahlukeneko begodu abekwa ngeendlela ezingafaniko.
• ubujamo • ubujamo Lezi ngezinye zeembonelo zaboncantathu
• amahlangothi • amahlangothi
anqophileko anqophileko
• amahlangothi • amahlangothi
aziindulungu aziindulungu
-- Iinkwere zobukhulu obuhlukeneko, zabekwa ngeendlela ezihlukeneko. Lezi ngezinye
zeembonelo zeenkwere:
-- Aboncamane bamajamo ahlukeneko, abekwe ngeendlela ezihlukeneko. Lezi ngezinye
zeembonelo zaboncamane
277
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
278 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
3.3 Amajamo Amajamo -- Iiindulungu zobujamo obuhlukeneko. Lezi ngezinye zeembonelo zeendulungu: Iimfundo ezi-3
Amajamo ahlukahlukeneko ahlukahlukeneko
abobusobu- Ukubona nokutjho Ukubona nokutjho
bili (2-D) amajamo be 2-D amajamo be 2-D
• Indulungu • Indulungu
• Uncantathu • Uncantathu
• Isikwere • Isikwere Kuqakathekile bona abafundi basebenze ngomfuziselo wamakhadibhodi asikiweko
• Uncamane • Uncamane wobujamo.lokhu kuvumela abafundi bonyana babone aboncantathu abahlukeneko,
iinkwere ezihlukeneko naboncamane abahlukeneko babekwe ngeendlela ezihlukeneko.
Amatshwayo Amatshwayo
wamajamo wamajamo Abafundi bahlela ubujamo ngokuya ngokuthi bunamahlangothi anqophileko nofana
ayindulunga.
Hlathulula, uhlele Hlathulula, uhlele
ngemihlobo begodu ngemihlobo begodu Abafundi bahlela begodu babuthelele nobujamo ukuya ngokuthi aboncamane, iinkwere,
umadanise amajamo umadanise amajamo nofana iindulungu.
abobusobubili (2-D) abobusobubili (2-D) Umsebenzi uhlanganiswa ngemisebenzi etlolwako. Imisebenzi le ingafaka ukufaka umbala,
ngokuqala lokhu: ngokuqala lokhu: ukumadanisa amagama ngobujamo njll.
• Ubukhulu • Ubukhulu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Umbala • Umbala
• ubujamo • ubujamo
• amahlangothi • amahlangothi
anqophileko anqophileko
• amahlangothi • amahlangothi
aziindulungu aziindulungu
3.4 Isimethri Isimethri Abafundi kufanele baqale imida yesimethri ngezinto eziphathekako nangeenthombe. Isifundo esi-1
Isimethri Ukukhumbula Ukukhumbula Iimisebenzi etlolwako
nokugwala umuda nokugwala umuda -- AKUKAFANELI bonyana ibe” gwala esinye isiquntu”;
wesimethri ebujameni wesimethri ebujameni
-- Kufanele ifake iimbonelo lapho abafundi bagwala khona ngemudeni wesimethri.
be 2-D obusebujameni be 2-D obusebujameni
Umuda wesimethri akukafaneli bonyana soke isikhathi ube umuda oya phezulu, isib.
obuyiJiyomethniki obuyiJiyomethniki
Esithombeni senyoka umuda wesimethri kufanele ube ngothabalele;
nobungasiyo nobungasiyo
iJiyomethniki. iJiyomethniki. -- Ungafaka iimbonelo ezingaphezu komuda munye wesimethri.
. Nangabe abafundi abanasiqiniseko sokuthi isithombe nofana ubujamo bunomuda
wesimethri, bangalinga ngokubhinca isiquntu sephepha phakathi babone bonyana
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
iinquntu lezo ezimbili zimadana patsi. Nazimadanako, bese umuda obhinciweko mumuda
wesimethri.
IGREYIDI YESI-2 ITHEMU YESI-2
4. UKUMEDA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi begodu Isifundo esi-1
Isikhathi • Ukwazi amalanga • Ukwazi amalanga nangokulandelana kwesikhathi.
weveke weveke Ngesikhathi sokufundisa itlasi loke nangesikhathi sokunqophisa esiqhemeni, abafundi
• Ukwazi inyanga • Ukwazi inyanga baragela phambili ngokukhuluma ngamalanga weveke neenyanga zonyaka begodu
zonyaka zonyaka nelanga lamhlokho, begodu namalanga adlulileko nalawo asezako. Abafundi bajayela
amakhalenda ngokuragela phambili babeka:
• Ukubeka ekhalendeni • Ukubeka ekhalendeni
amalanga amalanga • amalanga wamabeletho;
wamabeletho, wamabeletho, • imigidingo yekolo;
imigidingo imigidingo • izehlakalo zomlando;
yekolo, amalanga yekolo, amalanga
• izehlakalo zesikolo; begodu
wamaholideyi, wamaholideyi,
izehlakalo zomlando, izehlakalo zomlando, • amalanga wamaholideyi ekhalendeni
izehlakalo zesikolo izehlakalo zesikolo Ngesikhathi sokusebenza ngokuzijamela abafundi baragela phambili ngokulandelanisa
ekhalendeni ekhalendeni izehlakalo zamaphilo wabo wangemihla begodu balandelanise izehlakalo zeenthombe.
• Ukutjho isikhathi • Ukutjho isikhathi Abafundi babuya basebenze ngemisebenzi ehlobene nokutjho isikhathi ngama-iri.
ngama-iri ali-12, ngama-iri ali-12 Ngikuphi okuhlukileko kuneThemu yoku-1?
isiquntu se-iri nekotara usebenzise ama- Umnqopho ethemini yesi-2 ukubatjela isikhathi ngama-iri nangesiquntu se-iri usebenzisa
ye-iri. iri, nesigamu se-iri iwatjhi ye-analogo. Lokhu kungaba mnqopho wesifundo. Kufanele kufake ukukhuluma
Ukubalisisa ubude esisewatjhini ye- ngokusebenzisa abo a.m nabo p.m nesikhathi sama-iri ali-12. Ukutjho isikhathi, kufanele
besikhathi nokudlula analogo. kujayezwe ngethemini ngesisekelo esiragela phambili. Isibonelo, abafundi bangabawa
kwesikhathi Ukubalisisa ubude bonyana batjho isikhathi sokuthoma kwesikolo, ngesikhathi sokudla nangesikhathi sekhaya,
Sebenzisa besikhathi nokudlula nofana nabaphuma kwesinye isifundo baya kwesinye. Ukukhetha isikhathi lokhja iwatjhi
amakhalenda ukubalisisa kwesikhathi nayibonisa isikhathi esinqophe poro nofana isiquntu se-iri. Kuqakathekile bonyana kubekwe
nokuhlathulula ubude Sebenzisa iwatjhi iwatjhi ekulu ngetlasini, ukuze abafundi bangqala kuyo. Abafundi bangenza imifuziselo
besikhathi ngamalanga ukubalisisa ubude yamawatjhi. Ungababawa bonyana babonise iinkhathi ezihlukeneko ufake neembalo isib.
nofana ngeenveke. besikhathi ngama-iri “Ngibonisa i-iri le-10.” “Ngibonisa bonyana kuzabe kusikhathi bani ngemuva kwesiquntu
nofana isigamu se-iri. se-iri.”
Sebenzisa iwatjhi
ukubalisisa ubude
besikhathi ngama-iri
nofana isigamu se-iri.
279
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
280 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
4.2 Ukulinganisa Ngethemini yoku-1 bekuphakanyiswe bonyana abafundi banqophise ekulinganiseni, ekumedeni nasekurekhodeni ubude, ububanzi
Ubude okungakahleleki nobude ngamayunithi angakahleleki kodwana yenza godu isilinganiso, ukumeda, ukumadanisa nokurekhoda iimedo ngamamitha.
• Linganisa, meda, Zombili iindlela lezi zokumeda ubude zingazijayeza ngesikhathi sokusebenza esizijameleko iThemu yoke. Umsebenzi woke kufanele
madanisa, hlela urekhodwe.
bewurekhode ubude Ngesikhathi esabelwe Iinomboro, ama-Opharetjhini noBudlelwana abafundi bangararulula imiraro esebenzisa ubujamo obu:
kusetjhenziswa
• nobude besimedo esingakahleleki begodu
izinto zokumeda
ezingakalinganiswa • Ukumeda ubude ngamamitha.
isib. Ubude besandla, Tlhogomela irherho leenomboro elilungele iThemu, begodu nemiraro ehlukahlukeneko elungele iThemu.
igadango, ubude
bepensela, izinto
zokubala njll.
• Ukuhlathulula ubude
bezinto ngokubala
nokutjho bonyana
mayunithi amangaki
amadeangakahleleki
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukusebenzisa
ilimi ukukhuluma
ngokumadanisa isib.
Edenyana, efitjhazana,
ede, ebanzi
Ukwazisa /ukwethula
iimedo ezihlelelweko
Linganisa, meda,
madanisa, hlela
bewurekhode ubude
kusetjhenziswa
amamitha (nofana
iingojwana ezibubude
bemitha nofana
indambo enobude
bemitha) njengemedo
elihlelelweko lobude.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
4.3 Ukulinganisa Ukulinganisa Ngikuphi okuhlukileko eGreyidini yesi-2?
Imasi/ okungakahlelelwa okungakahlelelwa EGreyidini yoku-1 bekuphakanyiswe bonyana abafundi banqophise ekusebenzeni
Ubudisi • Linganisa, meda, • Linganisa, meda, nesimedo sokudzimelela uku
madanisa, hlela madanisa, hlela • ukumadanida ngokunqophileko ubungako bezinto;
bewurekhode ubudisi bewurekhode ubudisi
kusetjhenziswa kusetjhenziswa • ukuhlela nokumadanisa ubungako bezinto ezi-3 nofana ezingaphezulu, ngokubeka
isikala sokudzimelela isikala sokudzimelela amapara wezinto esidzimeleleni, bekufike lapho zoke izinto zilandelana kuhle khona.
nezinto zokumeda nezinto zokumeda • thola ubungako bezinto usebenzisa amayunithi angakahleleki wobudisi
ezingakalinganiswa ezingakalinganiswa isib. Abafundi banqopha godu ekuthuthukiseni ilimi ukukhuluma ngobudisi
isib. Amabhlogo, iintina Amabhlogo, iintina njll.
njll. Abafundi kufanele bathome ngokuhlanganisa abakwaziko ngokusebenzisa isidzimelelo
• Ukusebenzisa namayunithi angakahleleki ukumeda ubudisi. Bangaveza epepeneneni ubudisi
• Ukusebenzisa ilimi ukukhuluma ngamakhilogremu.
ilimi ukukhuluma ngokumadanisa isib.
ngokumadanisa isib. Lula, kubudisi, kulula Isimedo esingakahleleki sobudisi usebenzisa isidzimelelo namayunithi angakahleleki
Lula, kubudisi, kulula khulu, kubudisi khulu Abafundi bangafunda ngeemedo neenkambiso lawulo nangokuzijayeza koke asebenzisa
khulu, kubudisi khulu Ukwazisa/ ukwethula amayunithi angakahleleki.Ukumeda ngamayunithi angakahleleki akukafaneli bona
Ukwazisa/ukwethula ukulinganisa ithatheleke phasi kunokumeda ngamayunithi ahlelekile.
ukulinganisa okuhlelekileko Iindimelelo zobudisi zerhwebo zingasetjenziswa. Nawunganasidzimelelo serhwebo,
okuhlelekileko • Ukumadanisa, ukuhlela ungasenza ngokuhlanganisa ipara yakhunye okulandelako ehangereni: ikopi leyogadi,
• Ukumadanisa, ukuhlela nokurekhoda ubudisa ingaphasi lebhodlela eliquntiweko, nengaphasi lebhodlela eliquntiweko lelith yebisi nofana
nokurekhoda ubudisa bezinto ezipakwe ibhoksi leenselo ezimakhaza (iimumathi ezifanako zihlanganiswe ngemahlangothini
bezinto ezipakwe ngokwerhwebo womabili wehangere).
ngokwerhwebo okubonisa Ukumeda ubudisi ngamayunithi angakahleleki kufaka ukubala bonyana mangaki amayunithi
okubonisa ubudisi butjhiwe akhethiweko anobudisi obufana nezinto ezimediweko. Isibonelo irula inobudisi obufanako
ubudisi butjhiwe ngamakhilogremu isib. namabhlogo ali-9.
ngamakhilogremu isib. Amakhilogremu ama-2
Amakhilogremu ama-2 wereyisi nekhilogremu Abafundi kufanele bamede izinto ezihlukeneko basebenzisa izinto ezihlukeneko
wereyisi nekhilogremu -1 yeflowuru njengamayunithi angakahleleki.
-1 yeflowuru • Lapho kunesikala Abafundi kufanele bafundiswe ukutjho iyunithi lokha nabanikela ubudisi isib. Incwadi le
• Bameda ubungako sangendlini inobudisi obufanako namamabula ama-34.
babo basebenzisa yokuhlambela, Lokha abafundi nabamede ngenye nenye iyunithi iinkhathi ezimbalwa, kufanele balinganise
isikali sangendlini abafundi bonyana ngiyiphi ezoba nobudisi obufana naleyo emedwako. Ukulinganisa ngaphambi
yokuhlambela. bangazilinganisa kokumeda kuqakathekile, kodwana kungenziwa kuphela lokha abafundi nabamedile
ubudisi babo ngaleyo yunithi.
ngamakhilogremu
Abafundi kufanele bafundiswe bonyana ukuze bamadanise ubudisi bezinto ezihlukeneko
kusetjenziswa
iyunithi efanako kufanele isetjenziswe. Isibonelo nangabe irula inobudisi bamabhlogo
isikala. Kulindeleke
ama-20 begodu iskere sinobudisi bamamabula ama-20, ngeze watjho bonyana zinobudisi
bonyana abafundi
bafunde kwaphela obufanako nofana obungafaniko, nofana ngikuphi okubudisi khulu.
281 inomboro eseduzana Ukurekhoda iimedo
nekombabudisi Nanyana ukumeda kuyikghono lokwenziwako abafundi kufanele barekhode iimedo zabo
ngaso soke isikhathi.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
282 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
4.3 Ukulinganisa Ukulinganisa Ukusebenza ngamakhilogremu Iimfundo ezi-3
Imasi/ okungakahlelelwa okungakahlelelwa Abafundi bangathoma ukungeniswa emakhilogremini ngokusebenza izinto ezithengiswako
• Linganisa, meda, • Linganisa, meda, ezithengiswa ngamakhilogremu, lapha amakhilogremu azobe atlolwe khona esimumathini.
Ubudisi
madanisa, hlela madanisa, hlela Isibonelo abafundi bangamadanisa ubudisi bamapakana wezinto ezihlukeneko (njegereyisi,
bewurekhode ubudisi bewurekhode ubudisi iswigiri, ipuphu, iflowuru nofana isibha sokuvasa) ezithengiswa ngenani lekhilogremu-1.
kusetjhenziswa kusetjhenziswa Bangazibeka phezu kwesidzimelelo ukubona bonyana nanyana ubungako bempakana
isikala sokudzimelela isikala sokudzimelela bungahluka, zinobudisi obupheze bufane.
nezinto zokumeda nezinto zokumeda Abafundi banganikelwa imihlobohlobo yeempakana zezinto ezihlukeneko ukuzilandelanisa
ezingakalinganiswa ezingakalinganiswa isib. nokusuka kwebudisi khulu ukuya kwelula khulu, lapho balandelanisa ngokuya ngobudisi
isib. Amabhlogo, iintina Amabhlogo, iintina njll. obubhalwe empakaneni isib. Ireyisi ye-2kg, iswigiri ye1-kg, ipuphu ye-5kg, nestampa se-10kg.
njll. Ukufunda isikali sangendlini yokuhlambela
• Ukusebenzisa Lokha isikali sangendlini yokuhlambela nasikhona abafundi bangasisebenzisa ukufunda
• Ukusebenzisa ilimi ukukhuluma ubudisi babo.
ilimi ukukhuluma ngokumadanisa isib. Kunemihlobo emibili yobudisi bamamithara: kwedijithi ne-analogo.
ngokumadanisa isib. Lula, kubudisi, kulula Iinkali zedijithali zilula ukufundwa ngombana ubudisi butlolwe ngeenomboro. Nawunesikali
Lula, kubudisi, kulula khulu, kubudisi khulu sedijithali sangendlini yokuhlambela hlola bonyana sitjho ubungako ngamakhilogremu
khulu, kubudisi khulu Ukwazisa/ ukwethula kuphela. Ezinye iinkali ungazitjintja godu ukubonisa amakhilogremu apheleleko.
Ukwazisa/ukwethula ukulinganisa Nawungakghoni ukuhlela bonyana ibonise amakhilogremu apheleleko, fundisa abafundi
ukulinganisa okuhlelekileko ukulisa iingcenye zamakhilogremu kwanje.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
okuhlelekileko • Ukumadanisa, ukuhlela Iinkali ezinengi zangendlini yokuhlambela zinenomboro i-10kg inomboriwe, ngomuda
• Ukumadanisa, ukuhlela nokurekhoda ubudisa omude okhomba ubujamo ba-5kg. Imida yekhilogremu eli-1 ayikavami ukuboniswa lokhu
nokurekhoda ubudisa bezinto ezipakwe kuyafana ngendlela imida neenomboro ziraga ngakhona eruleni.
bezinto ezipakwe ngokwerhwebo Abafundi abathome ngokubala ukubona bonyana kuneenkhala ezili-10 ngaphambi
ngokwerhwebo okubonisa kwemaraga ye10kg, ukuze isikhala ngasinye sijamele ikhilogremu yi-1, umuda omude
okubonisa ubudisi butjhiwe ujamele amakhilogremu ama-5kg.
ubudisi butjhiwe ngamakhilogremu isib. Abafundi bangafunda iimedo zeenkali zamambala zangendlini yokuhlambela begodu
ngamakhilogremu isib. Amakhilogremu ama-2 neenthombe zeenkali zangendlini yokuhlambela. Kulula ukufunda ubungako besithombe
Amakhilogremu ama-2 wereyisi nekhilogremu sesikali sangendlini yokuhlambela kunasesikalini samambala.
wereyisi nekhilogremu -1 yeflowuru Ukurekhoda iimedo
-1 yeflowuru • Lapho kunesikala Nanyana ukumeda kuyikghono lokwenziwako abafundi kufanele barekhode iimedo zabo
• Bameda ubungako sangendlini ngaso soke isikhathi.
babo basebenzisa yokuhlambela, Ukumeda ubungako njengobujamo bokurarulula imiraro nokubalisia
isikali sangendlini abafundi Ngesikhathi esabelwe Iinomboro, ama-Opharetjhini noBudlelwana abafundi bagararulula
yokuhlambela. bangazilinganisa imiraro esebenzisa ubujamo obu:
ubudisi babo iimedo zobude ezingakahleleki;
ngamakhilogremu Isibonelo: Idastara inobudisi bamamabula ali-11. Ibhoksi lamakhrayoni linobudisi
kusetjenziswa bamamabula abu-8. Zizoke zizokwenza ubudisi bamamabula amangaki?
isikala. Kulindeleke • ukumeda ubungako ngamakhilogremu
bonyana abafundi Isibonelo: UPuleka uthenge ipuphu yamakhilogremu ali-12kg, amakhilogremu ama-
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
bafunde kwaphela 5kg wetjhukela begodu namakhilogremu ama-2kg wereyisi. Izinto azithengileko zikala
inomboro eseduzana kangangani nazizoke.
nekombabudisi Yelela irherho leenomboro elilungele iThemu, begodu nemihlobohlobo yemiraro elungele
iThemu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
4.4 Ukulinganisa Ukulandela imilayelo yokupheka, ukufaka nokubhaga, bujamo obuqakathekile lapho
Umthamo / okungakahlelelwa abafundi bajayeza khona ukumeda. Khetha imilayelo yokupheka lapho iintlabagelo
Ivolumu • Linganisa, meda, zinikelwa ngeenkopi, amathispuni nofana amayunithi angakahleleki.
madanisa, hlela Ukufika nje lonyaka kuphakanyiswe bonyana abafundi banqophe uku:
bewurekhode
umthamo • thuthukisa ilimi lokukhuluma ngamavolumu ahlukeneko.
ongeemumathini (o.u. • madanisa amavolumu ngemumathini ezimbili ezifanako,
ubunengi isimumathi • madanisa amavolumu weemumathi ezimbili ezihlukeneko khulukhulu ezivulekileko
esikghona ukubuthatha nezivalekile.
nasizalisiweko)
ngokusebenzisa • meda amavolomu nomthamo ngensetjenziswa ezingakahleleki namayunithi
izinto zokumeda Ngesikhathi sokusebenza esizijameleko abafundi bangalinganisa, bamede, bamadanise,
ezingakahleleki isib. bahlele begodu barekhode amavolomu nemithamo ngeensetjenziswa ezingakahleleki
Iingobho neenkomitji. namayunithi womthamo angakahleleki.
• Ukuhlathulula Ukupheka nokubhaga kuqakathekile ebujameni lapho abafundi bangazijayeza ukumeda
umthamo wesimumathi
umthamo. Khetha imilayelo yokupheka lapho iimedo zinikelwa ngeenkopi, amathispuni
ngokubala
begodu namanye amayunithi angakahleleki.
nookutjho bonyana
mayunithi amangaki Ukumeda umthamo njengobujamo bokurarulula imiraro nokubalisisa
angakahleleki Ngesikhathi esabelwe Iinomboro, ama-Opharetjhini noBudlelwana abafundi bangararulula
angazalisa imiraro esebenzisa ubujamo bokumeda obungakahleleki bomthamo/volomu isib. Ugogo
isimumathi isib. usebenzisa iinkopi zebisi ezi-2 ukwenza iphudinghi. Nakabuyelela iimedo kabili ukwenza
Ibhodlelo linomthamo
iphudinghi, uzofuna ibisi elingangani?
weenkomitji ezine.
Ukwazisa ukulinganisa Yelela irherho leenomboro ezihlukahlukeneko elilungele iThemu, begodu nemihlobo
okuhlelekileko ehlukeneko yemiraro.
• Ukulinganisa,
ukumeda,
ukumadanisa,
ukuhlela bewurekhode
umthamo wezinto
ngokumeda ngamalitha
• Ukumadanisa, ukuhlela
nokurekhoda umthamo
wezinto ezipakwe
ngokwerhwebo
ukubonisa umthamo
obutjhiwo ngamalitha
isib. Amalitha ama-2
283 webisi, 1 ilitha yesiselo
esimakhaza, amalitha
ama-5 wepende
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI- 2 ITHEMU YESI- 2
5. UKUPHATHA IDATHA
284
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
5.4 Ukubuthelela nokuhlela
Ukubuthelela idatha
nokuhlela idatha • Buthelela idatha
yetlasi nofana yesikolo
ukuphendula imibuzo
ibuzwe ngutitjhere
• Hlela idatha
ngamathali
5.5 Ukujamiselela idatha
Ukujamiselela • Jamiselela idatha
idatha yegrafu yeenthombe
5.6 Ukuhlaziya Hlaziya idatha kusuka Abafundi kufanele babenelemuko mazombe lokuphatha idatha eThemini yo-1, Isifundo si-1
bewurhumutjhe idatha ekujamiselelweni banganqopha ekuhlaziyeni ijamiselelo abanikelwe lona.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuhlaziya
bewurhumutjhe • Phendula imibuzo obunikelweko Kuphakamisiwe bonyana eThemini ye-2 abafundi bahlaziye (ngokuphendula imibuzo)
idatha ngedatha esegrafini okungenani igrafu yinye yeenthombe.
yeenthombe. Abafundi baphendula imibuzo leyo oyibuzako ngegrafu yesithombe isib.
“Ngiliphi ihlelo likamabonwakude elidumileko khulu ngetlasini yethu?”
“Ngiliphi ihlelo elithandwa idlanzana labafundi ngetlasini?”
“Abafundi abanengi bathanda.......nofana ...............?
“Bangaki abanye abafundi abakhetha ....... kune ........?
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YESI-2 ITHEMU YESI-3
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Ngikuphi okuhlukileko eThemini yesi-2?
Ukubala eziphathekako eziphathekako NgeThemu yesi-2 irherho leenomboro selandisiwe begodu abafundi kwanjesi babala izinto
izinto • Linganisa bewubale • Linganisa bewubale ezi-180.
ngokuthembeka ngokuthembeka Ukubala izinto ngeThemu leli kuragela phambili nokulekelela:
ukufika ema-200 ukufika ema-180
• amakghono wokubala atlhogekako ukuze uzwisise ubukhulu bedijithi
ngamalanga. ngamalanga.
• ukubala okungakahlelwa
• Amaqhinga • Nikela ukulinganisa
wokubuthelela ngokuzwakalako • ukutjho amagama weenomboro
ayakhuthazwa. izinto ezingahlolwa • ukubona amatshwayo weenomboro,
ngokubala • amakghono wokubala atlogekako wokubala
Umnqopho usese sekubaleni ngesiqhema kusetjenziswa imihlobohlobo yama-apharathasi
angakahleleki nofana ama-apharathasi ahlelelwe ngaphambili. Kulisizo ukusebenzisa
amanye wama-apharathasi nakwenziwa ubukhulu bedijithi.
Isibonelo: Abafundi bangasebenzisa isisekelo samabhlogo alitjhumi ukubala ngamatjhumi
abe atjengise iinqhema zangali-10.
Imibuzo elisizo engabuzwa abafundi nababala izinto ngile:
• Wazi bunjani bonyana uyibalile inomboro leyo?
• Ungayihlola bunjani ipendulo yakho?
285
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
286 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko kune Themu yesi-2?
nemuva nga: nemuva nga:
Ukubala uye Irherho leenomboro ngeThemu yesi-3 iyakhula kusuka e-150 ukuya 180
• Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye
phambili nenye inomboro nenye inomboro Nowenza ukubala okungakahlelwa nofana ukubala ngomlomo kuqakathekile bonyana
nemuva hlangana ne-0 na-200 hlangana ne-0 ne-180 kunqophiswe, abafundi eenomborweni abazibalako.
• Li-10 ukusuka kesinye • Li-10 ukusuka kesinye Isibonelo: Lokha nasibala ngakubili ukusuka e-120 ukufika e-140 sizokuyibala inomboro
nesinye isibuyabuyelelo nesinye isibuyabuyelelo i-121 na? Kungani singayibali?
se-10 hlangana ne-0 se-10 hlangana ne-0
na-200 ne-180 Kusaqakathekile bonyana inambalayini negridi yeenomboro ye-100 kusetjenziswe ukubona
• Ku-5 ukusuka kesinye • Ku-5 ukusuka kesinye bonyana amagama abawasebenzisako ahlangana nesakhiwo nehlelo leenomboro.
nesinye isibuyabuyelelo nesinye isibuyabuyelelo Qala amanothi weThemu yesi- 2.
saka ku-5 hlangana ne- saka ku-5 hlangana
0 na-200 ne-0 ne-180
• Ku-2 ukusuka kesinye • Ku-2 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku- 2 hlangana ne- saka ku- 2 hlangana ne-
0 na-200 0 ne-180
• Ku-3 ukusuka kesinye • Ku-3 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-3 hlangana ne- saka ku-3 hlangana
ISIGABA ESISISEKELO AMAGREYIDI 1-3
0 na-200 ne-0 ne-180
• Ku- 4 ukusuka kesinye • Ku- 4 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-4 hlangana saka ku-4 hlangana ne-
ne-0 na- 0 ne-180
UKUJAMISELELA IINOMBORO EZIPHELELEKO
1.3 Ukukhumbula, ukubona Ukukhumbula, ukubona Ngikuphi okuhlukileko kune Themu yesi-2?
nokufunda iinomboro nokufunda iinomboro
Amat- Irherho leenomboro lo:
• Ukwazi nokufunda nokufunda iinomboro
shwayo amatshwayo • Ukwazi nokufunda Ukwazi, ukufunda nokutlola amatshwayo weenomboro ziyakhula ukuya e-180 begodu
weenom- wenomboro kusukela amatshwayo Ukwazi, ukufunda nokutlola ukufika e-75.
boro ku- 0 ukufika ku-200 wenomboro kusukela
namagama • Ukutlola amatshwayo ku- 0 ukufika ku-180
weenom- weenomboro • Ukutlola amatshwayo Abafundi kufanele bakghone ukubona iinomboro bebathome ukuhlathulula umahluko
boro ukusukela ku -0 ukufika weenomboro ngamagama okungewabo.
ku-200 ukusukela ku -0 ukufika Isibonelo: bafanele baqale amakarada weenomboro alandelako begodu bakghone nokutjho
• Ukwazi nokufunda ku 180
umehluko phakathi kwananyana ngiziphi izinto ezimbili.
amabizo wenomboro • Ukwazi nokufunda
kusuka e-0 ukufika-100 amabizo wenomboro
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
16 11 16 13 16
• Ukutlola amabizo kusuka e-0 ukufika-75
wenomboro kusukela • Ukutlola amabizo
e- 0 ukufika ku-100 wenomboro kusukela Qala amanothi weThemu yesi-2
e- 0 ukufika ku-75
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
CAPS
ama -24)
1.4 Ukuhlela Ukuhlela Ngikuphi okuhlukileko kuneThemu yesi-2?
Ukuhlathu- nokumadanisa nokumadanisa Ethemeni leli abafundi bahlela bebamadanise ukufika e-75
lula, uku- iinomboro kufika e- 99 iinomboro kufika
Kuze kube nje abafundi bebasoloku bamadanisa begodu bahlela iinomboro ukuze
madanisa, • Ukuhlela iinomboro iinomboro kufika e- 75
kuthuthukiswe umuzwa wobukhulu beenomboro ngobudlelwana bazo. Imibuzo ephathelene
nokuhlela ezipheleleko. Kusukela • Ukuhlela iinomboro neenomboro kufanele ikhethwe ngokuyelela ukulekelela abafundi bonyana bathuthukise
iinomboro kencani khulu kufikela ezipheleleko. Kusukela amakghono wokucabanga asezingeni eliphezulu ngobujamo benomboro. Abafundi badinga
kekulu khulu begodu kencani khulu kufikela ukuphoselwa iselele ngemihlobo yemibuzo ebuzwako.
kusukela kekulu khulu kekulu khulu begodu
Begodu lekelela abafundi ukuthuthukanisa ilimi lokuhlathulula ukucabanga kwabo.
kuya kencani khulu kusukela kekulu khulu
kuya kencani khulu Iimbonelo zemibuzo ingafaka hlangana :
• Ukumadanisa
iinomboro kufika e- • Ukumadanisa • Nginikela inomboro ephakathi kwa-50 na-60. Ingabe inomboro leyo iseduzane kwa-50
99 ngokusebenzisa iinomboro kufika e- nofana ama-60? Hlathulula ipendulo yakho ngokusebenzisa inambalayini.
ngokunengi khulu, 99 ngokusebenzisa • Abafundi bafanele bafundiswe bonyana bangacabanga bunjani ngokuhlela iinomboro.
ngokuncani khulu, ngokunengi khulu, Abafundi bahlathulule bonyana kungani i-15 lincani kunama-50. Iinhlathululo
okunengi kuna, ngokuncani khulu, zingalekelelwa ngokusebenzisa ama-apharathasi aphathekako. Ekupheleni kweThemu
okuncani kuna, okunengi kuna, bafanele, isibonelo:
okulinganako. okuncani kuna, Bazi bonyana ngiziphi iinomboro ezincani kunama-50, ezinengi kuna-50, begodu
Sebenzisa okulinganako.
• Bakwazi ukutjengisa ubujamo bazo iinomboro ema-30, 40, njll, ngokusebenzisa igridi
iinomborosikhundla Ukusebenzisa yeenomboro
ukutjengisa iinomboro eziodinali
• Kunokubanyana njalo unikele abafundi imitjho yeenomboro kobana bayiqedelele,
ukulandelana ,indawo ukutjengisa
ngesinye isikhathi babawe bonyana bazenzele yabo imitjho yeenomboro, ukubonisa
namkha ubujamo ukuhlela,indawo nofana
ukuhlobana kobukhulu beenomboro.
Beka izinto emudeni indawo
Isibonelo:
ngokulandelana kusukela Beka izinto emudeni
keyokuthoma ukufika kusukela keyokuthoma Ukwenza imitjho elandelako ibe liqiniso:
keyamatjhumi namkha ukuya keyesitjhumi • nengi kuna nga-1
keyokuthoma ukuya nofana keyokuthoma • ncani kuna nga-1
keyokugcina, Isib. ukuya keyokugcina
Yokuthoma, yesibili, isib.kokuthoma, • nengi kuna nge-10
yesithathu, ematjhumini kwesibili, kwesithathu ... • ncani kuna nge-10
amabili keyetjhumi. Qala amanothi weThemu yesi-2
287
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
288 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.5 Thoma ukulemuka Thoma ukulemuka Ngikuphi okuhlukileko kune Themu yesi-2?
Ubukhulu ubukhulu bedijithi ubukhulu bedijithi NgeThemu leli abafundi baragela phambili nokuthuthukisa ukuzwisisa kwabo imiqondo
bedijithi okungenani iinomboro okungenani iinomboro yobukhulu bedijithi ukufika e-75.
zamadijithi ama-2 zamadijithi ama-2
NgeThemu leli abafundi baragela phambili uku:
ukufika ema-99 ukufika ema-75
• babala bebabuthelele ukutjengisa amatjhumi nangakunye ngeendlela ezihlukenekkko;
• Ukwazi bonyana idijithi • Ukwazi bonyana idijithi
ngayinye ijameleni ngayinye ijameleni • Babala ama-apharathasi abuthelelwe ngaphambili/ukuhlelwa okungaphambili;
• Ukuphula iinomboro • Ukuphula iinomboro • Ukusebenzisa amakarada wobukhulu bedijithi ukubonisa inani elibuthelelweko
zamadijithi amabili zamadijithi amabili bezabalwa, begodu
ukufika e-99 ukuya ukuya ngamatjhumi • Tjengisa ukuhlela okuhlukeneko beenomboro. Isibonelo ama-35 ezikhamba ngakunye,
ngamatjhumi nangakunye amatjhumi a-3 nokuhlukeneko oku-5 begodu neenqhema ezimbili zamatjhumi begodu
nangakunye • Bona bewutjho ne-15 yokukhamba ngakhunye.
• Bona bewutjho ubukhulu bedijithi Umsebenzi ongehla esikhathini esinengi wenziwa eenqhemeni ezinqophiweko begodu
ubukhulu bedijithi ngayinye ngesikhathi sokuzijamela abafundi bakghone ukurekhoda okulandelako:
ngayinye 68 = iinqhema ezi-6 zetjhumi nemivo -8
68 = ama-60 na 8
Lokhu kungasekelwa ngokusebenzisa amafladi karada nofana amakarada wobukhulu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
bedijithi.
Abafundi bafanele baphendule imibuzo neenlayelo ezifana no:
• Ngiyiphi inomboro efana nama-50 ne-7?
• Ngitjengisa ama-75 ngokusebenzisa amakarada wobukhulu bedijithi.
• Ngitjengisa ama-75 ku-abhakhasi
• Ngitjengisa ama-75 ngokusenzisa ibhlogo le-base ten
• Ngitjengisa ama-75 ngokusebenzisa amakhyubhu we unifix
• Ngitjengisa ama-75 ngokusebenzisa imincamo esentanjeni
• Bala iingojwana zomlilo ezima-70 ngokusebenzisa iinyanda za-10, uthole iinyanda za-10
ezingaki
Ukurekhoda ngencwadini yokusebenzela iragela phambili ngesikhathi sokuzijamela.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
CAPS
ama -24)
UKURARULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Abafundi balindeleke bonyana basombulule imiraro yamagama ngokusebenzisa
Amathek- alandelako nawurarulula alandelako nawurarulula amathekhiniki:
hiniki wok- imiraro uhlathulule imiraro uhlathulule • Imigwalo nofana ama-apharathasi aphathekako isib. Izinto zokubala
urarulula neensombululo zemiraro: neensombululo zemiraro:
• Ukwakha nokuphula iinomboro
imiraro • Ama-apharethasi • Ama-apharethasi
• Ukubuyelela kabili nokuhlukanisa phakathi
aphathekako isib. izinto aphathekako isib. izinto
zokubala zokubala • inambalayini
• Ukwakha nokuphula • Ukwakha nokuphula Qala amanothi weThemu yesi-2
iinomboro iinomboro
• Ukubuyelela • Ukubuyelela
nokuhafula phakathi nokuhafula phakathi
• Amanambalayini • Amanambalayini
1.7 Rarulula imiraro Rarulula imiraro Ngikuphi okuhlukileko eThemini yesi-2?
Ukuh- yamagama yamagama Abafundi baragela phambili ngokusebenza ngemihlobo ehlukeneko yemiraro yamagama
langanisa, ezisebujameni ezisebujameni okulinganiswe esahlukweni 2 kodwana irherho leenomboro likhuliselwe e-75
bewuhlathulule bewuhlathulule
nokukhupha Qala amanothi weThemu yesi-2
iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka
ukuhlanganisa ukuhlanganisa
nokukhupha nempendulo nokukhupha nempendulo
ukufika e-99. ukufika e-75.
1.8 Rarulula imiraro Rarulula imiraro Ngikuphi okuhlukileko eThemini yesi-2?
Ukuh- yamagama yamagama Abafundi baragela phambili ngokusebenza ngemihlobo ehlukeneko yemiraro yamagama
langanisa ezisebujameni ezisebujameni okulinganiswe esahlukweni 2 kodwana irherho leenomboro likhuliselwe e -40
okubuyele- bewuhlathulule bewuhlathulule
Qala amanothi weThemu yesi-2
lweko iinsombululo zakho iinsombululo zakho
kurholela zemiraro, ezifaka zemiraro, ezifaka
ekubuy- ukuhlanganisa ukuhlanganisa
abuyeleleni okubuyelelweko okubuyelelweko
okurholela okurholela
ekubuyabuyeleleni ekubuyabuyeleleni
okunempendulo ufikela okunempendulo ufikela
e-50 e-40
289
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
290 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.9 Ukurarulula Ukurarulula NgeThemu leli abafundi baragela phambili nokusebenzisa imigwalo nama-apharathasi
Ukubuthele- imiraro yamagama imiraro yamagama aphathekako ukubonisa iinsombuluso zabo. Imitjho yeenomboro ifanele isetjenziswe
la nok- ezisebujameni ezisebujameni abafundi bazokusebenzisa ukukhupha okubuyelelwe ukubonisa bonyana bafike bunjani
wabelana bewuhlathulule bewuhlathulule empendulweni.
okurholela iinsombululo zakho iinsombululo zakho Qala amanothi weThemu yesi-2
ekuhlu- ufake ukwabelana ufake ukwabelana
kaniseni ngokulingana ngokulingana
nokubuthelela nokubuthelela
ngeenqhema ngeenqhema
kweenomboro kweenomboro
ezipheleleko ukufika ezipheleleko ukufika
e-50 kanye nempendulo e-40 kanye nempendulo
ezingahle zifaka iinsalela ezingahle zifaka iinsalela
1.10 Ukurarulula Ukurarulula Umnqopho wemiraro yamafrakhtjhini wamagama ethemeni leli iragela phambili nokuvumela
Ukwabelana bewuhlathulule bewuhlathulule abafundi uku:
okurholela iinsombululo zemiraro iinsombululo zemiraro • kwaba nokubuthelela izinto ngokulinganako;
emafrak- ezisebujameni efaka ezisebujameni efaka
• kutjho amagama weengcezu zamafrakhtjhini;
ISIGABA ESISISEKELO AMAGREYIDI 1-3
tjhinini hlangana ukwabelana hlangana ukwabelana
ngokulingana erholela ngokulingana erholela • ukubona bonyana ifrakhtjhini liyingcenye yokupheleleko,
empendulweni empendulweni • kutlola amafrakhtjhini njengengcenye yokuthathu; begodu
zamafraktjhini wohlavu zamafraktjhini wohlavu • ukuthola iingcenye zezinto ezipheleleko;
1 1 1
olulodwa Isib. 12 , 14 , 15 njll olulodwa Isib. 2 , 4 , 5 njll. NgeThemu leli abafundi batjho okuthathu nokuhlanu. Kuqakathekile bonyana abafundi
bavezelwe epepeneneni amafrakhtjhini ngaphandle kwengcenye eyodwa nekota eyodwa.
Iimbonelo zemiraro engenziwa ngeThemu leli:
• Abangani abali-7 babelana zamaswidi ngokulinganako, Gwala isithombe ubonise
ipendulo yakho, madanisa ipendulo yakho, naleyo yomngani wakho.
• Abangani ababunani babelana iingojwana zamaswidi ezi-9 ngokulinganako. Gwala UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : iinthombe ukubonisa
AMANYE ipendulo yakho.
AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA
IINHLOKO (eemfundweni
: IIMFUNEKO IMINQOPHO YETHEMU Qala amanothi weThemu yesi-2 YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.11 • Khumbula bewufanise • Khumbula bewufanise Iimbonelo zemiraro ezingenziwa:
Imali imali eziinhlavu imali eziinhlavu • Abafundi aba-35 notitjhere 0-1 baya evakatjhweni lesikolo esiqiwini seembandana.
zeSewula Afrika : (5c, zeSewula Afrika : (5c, Isikolo sibhadela R1.20 umfundi ngamunye yokungena esiqiwini seembandanda. Yimalini
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
10c, 20, 50c, R1, R2; 10c, 20, 50c, R1, R2; okufanele ibhadalwe?
R5) kunye nemali R5) kunye nemali
• UMahewu uthengela umndeni wakhe amapani amabili woburotho ngamalanga. Ipani
yemaphepha (R10, yemaphepha (R10,
eyodwa yoburotho Ibiza R4, 99. Usebenzisa yimalini ngamalanga ama-5?
R20, R50). R20, R50).
Qala amanothi weThemu yesi-2
• Sombulula imiraro efaka • Sombulula imiraro efaka
hlangana amanani hlangana amanani
wemali netjhentjii yama wemali netjhentjii yama
R99 neyamasende R75 neyamasende
ukufika e-90c ukufika e-75c
R99 neyamasende R75 neyamasende
ukufika e-90c ukufika e-75c
UKUBALA OKUSEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Abafundi balindeleke ukusombulula ukubala ebujameni obutjhaphulukileko ngokusebenzisa
Amathekh- alandelayo nawubalako alandelayo nawubalako amathekhiniki alandelako:
iniki • Ama-apharethasi • Ama-apharethasi • Ukwakha bewuphadhle iinomboro
(iindlela aphathekako aphathekako • Ukubuyelela nokuhafula phakathi
CAPS namaqh- njengezinto zokubala njengezinto zokubala
• Amanambalayini
inga) • Ukwakha bewuphadhle • Ukwakha bewuphadhle
Qala amanothi weThemu yesi-2
iinomboro iinomboro
• Ukubuyelela • Ukubuyelela
nokuhafula phakathi nokuhafula phakathi
• Amanambalayini • Amanambalayini
291
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
292 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Qala amanothi weThemu yesi-2
Ukuh- e-99 e-75 Abafundi baragela phambili nokuphula iinomboro begodu babe nokuzethemba emaqhingeni
langanisa • Khupha ukufika e- 99 • Khupha ukufika e- 75 wokurekhoda.
nokukhupha • Sebenzisa • Sebenzisa Iindlela ezingakatjenziswa ukutjengisa ukubala ngokuhlanganisa nokukhupha:
amatshwayo afaneleko amatshwayo afaneleko Ukuphula inomboro ibe ziingcenye ezincani ukwenza ukubala kubelula.
• Ukuphrakhthisa • Ukuphrakhthisa Ukusebenzisa ilwazi lobukhulu bedijithi ukuphula iinomboro zibe matjhumi
ukulumbana ukulumbana namayunithi/ngakunye
kwenomboro ukufika kwenomboro ukufika Ukuhlanganisa iinomboro ezinamadijithi amabili ngokuphula iinomboro zombili
e-20 e-20
33 + 36 =
33 + 36 = (30 + 3) + (30 + 6)
= (30 + 30) + (3 + 6)
= 60 + 9
= 69
Ukuhlanganisa ngokuphula inomboro yinye
33 + 36 =
ISIGABA ESISISEKELO AMAGREYIDI 1-3
33 + (30 + 6)
33 + 30 ➝ 63 + 6 = 69
Abafundi bangahle baphule inomboro ngendlela ephathekako. Lokhu kutjho bonyana
bazokwenza ngeendlela ezihlukeneko.
33 + 36 =
33 + (10 + 10 + 10 + 6)
33 + 10 ➝ 43 + 10 ➝ 53 + 10 ➝ 63 + 6 = 69
Ukukhupha
Ukukhupha iinomboro zombili
75 – 54 =
75 – 54 = (70 + 7) – (50 + 4)
= (70 – 50) + (7 – 4)
= 20 + 3
= 23
Ukukhupha ngokuphula inomboro yinye
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
75 – 54 =
75 – (50 + 4)
75 – 50 ➝ 27 – 4 = 23
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
CAPS
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Lindela bonyana abafundi bangahle baphule iinomboro ngeendlela ezihlukeneko ukwenza
Ukuh- e-99 e-75 lula:
langanisa • Khupha ukufika e- 99 • Khupha ukufika e- 75 75- 54 =
nokukhupha • Sebenzisa • Sebenzisa 75- (20 + 20 + 10 + 6)
amatshwayo afaneleko amatshwayo afaneleko 75- 20 ➝ 57 – 20 ➝ 37- 10 ➝ 27- 4 = 23
• Ukuphrakhthisa • Ukuphrakhthisa Ukusebenzisa ukuhlukanisa phakathi ukuphula inomboro
ukulumbana ukulumbana 59 + 12
kwenomboro ukufika kwenomboro ukufika 59 + (6 + 6)
e-20 e-20
59 + 6 ➝ 65 + 6 = 71
Ukusebenzisa ilwazi elidlulileko njengethekhniki
Amathekhiniki atjengiswe ngenzasi kuvumela abafundi bonyana benze ngokomthetho
ukubala kwabo nomqondonomboro. Ukuzijayeza amathekhiniki angenzasi
azakugqugquzela abafundi ukubona ubudlelwana obuphakathi kweenomboro begodu
kufundisa abafundi bonyana basebenzise ulwazi labo ukubasiza bonyana babale.
Ukubala uye phambili nemuva:
68 – 59 = →
Ukubala uye phambili ngakunye ukusuka ema-59 kuliqhinga elifaneleko ngombana
iinomboro ziseduzana kwenye nenye.
Ukubona ukubuyelela kabili okuseduze
34 + 35 hlathulula bonyana kubuyelela kabili ama-34 uhlanganise na-1 nofana buyelela
kabili ama-35 ukhiphe 1.
34 + 34 + 1
Abafundi bangahle barekhode amaqhinga wabo ngokusebenzisa abonotjhobi.
34 + (30 + 4) + 1
34 + 30 ➝ 64 + 4 ➝ 68 + 1 = 69
Ukutjhugulula inomboro ibe sibuyabuyelelo setjhumi begodu ukhuphe nofana
uhlanganise okukodwa.
Ukubala uye phambili nofana uye phasi ekutjhidezeni e-10
58 + 19 =
Lapha abafundi bafanele bathi kibo ngokwabo babenemandla wokuzikhethela amabili.
Ukutjhugulula ama-58 nofana i-19 ekutjhideleni okuseduze kwesibuyabuyelelo ze-10.
banokuzikhethela
Isibalo singatlolwa ngalendlela le 58 + 19 = 58 + 20 - 1
58 + 20 ➝ 78 – 1 = 77
293 Abanye babafundi bangaphula ama-20 kube ziinqhema ezi-2 ze -10 ukubala
ngokunembako.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
294 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Ngikuphi okuhlukileko kune Themu yesi-2?
Ukuh- iinomboro kusuka ku-1 iinomboro kusuka ku-1 NgeThemu leli abafundi bahlala bazijayeza ukuzwisisa kwabo kokubuyabuyelela kwegreyidi
langanisa kufika e-10 ngo 1, 2, 5, kufika e-10 ngo 2, 5, kokuthoma.
okubuyele- 3 begodu nge-4 begodu nge-4
Baragela phambili noku:
lweko • Sebenzisa • Sebenzisa
• Rekhoda ngendlela elandelako:
kurholela amatshwayo afaneleko amatshwayo afaneleko
ekubuy- ( +, -, =, ) ( +, -, =, ) Isiqhema esi- 1 saku-2 zi -2 nofana 1 buyelela 2 ngu 2 nofana 1 x 2 = 2
abuyeleleni Iinqhema ezi-2 zaku-2 zi-4 nofana 2 buyelela 2 ngu 4 nofana 2 x 2 = 4
Iinqhema ezi-3 zaku-2 zi-6 nofana 3 buyelela 2 ngu 6 nofana 3 x 2 = 6
NgeThemu leli abafundi bathoma ngokubuyelela nga-4, ngokubuyelela nga-2 ne kuragela
phambili nokuzijayeza
Imifanekiso ebuyabuyelelweko iragela phambili nokurhekhoda okunengi kufanele
kwenziwe emisetjenzaneni yetlasini. Ukuzwisisa kungenziwa ngokuhlanganiswa
encwadini zokusebenzela. Inambalayini, itjhadi naneko namathebula zingasethenziswa
ukwakha ukuzwisisa kombalo. Abafundi bafanele banikelwe imitjho yeenomboro bonyana
bayiqedelele efana na:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
6x2=
5x7=
4x6=
Abafundi bafanele basebenzise igridi yokubuyabuyelela ukuthola iimpendulo. Lokhu
kuzobasiza bonyana bafunde begodu bazwisise ithebula bazi ngokupheleleko amaphuzu
wamambala wokubuyabuyelela.
× 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
4 4 8 12 14 20 24 28 32 26 40
5 5 10 15 20 25 30 35 40 45 50
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
CAPS
ama -24)
1.16 Umnqopho Umnqopho Iimbonelo zemibuzo engabuzwa:
Iimbalo wenomboro: irherho wenomboro: irherho Umqondo wenomboro:
zehloko 99 75
Amagama weenomboro namatshwayo
• Hlela isethi enikelweko • Hlela isethi enikelweko
leenomboro leenomboro Ukuphakisa ikarada nofana ukutlola igama lenomboro. Khetha umfundi bonyana atlole
ezikhethiweko ezikhethiweko inumerali elimetjhako.
• Madanisa iinomboro • Madanisa iinomboro Okunengi nofana okuncani
ema-99 bewutjho ema- 75 bewutjho khuyini
bonyana ngiyiphi bonyana ngiyiphi
enengi nofana encani enengi nofana encani • Okuncani e-45 nga-1
nga-1, 2, 3, 4, 5 ne-10 nga-1, 2, 3, 4, 5 ne-10 • Okunengi e-69 nga-1
Ukukhumbula Ukukhumbula • Okuncani ku-36 nga-5
masinyana: masinyana:
• Okunengi e-30 nga-10
• Ukukhumbula • Ukukhumbula
amaphuzu amaphuzu Ngiliphi iledere lesi-5 lama alfabethi?
wokuhlanganisa wokuhlanganisa Ngiyiphi inyanga ye-9 yonyaka?
nowokukhupha kufika nowokukhupha kufika
e- 20 e- 15 Ukuhlela nokumadanisa
• Hlanganisa nofana • Hlanganisa nofana Ngiyiphi enokunengi: 21 nofana 171?
ukhuphe imbuyeleli ukhuphe imbuyeleli Nginikela inomboro ehlangana ne-154 ne 159.
ze-10 kusuka e-0 kuya ze-10 kusuka e-0 kuya Amaphuzu aliqiniso ngokuhlanganisa nokukhupha:
e-100 e-50
• Ukwazi ngenhliziyo koke ukuhlanganisa nokukhupha iinomboro zebhodi ukufika e-20
Amaqhinga wokubala Amaqhinga wokubala
Ukusebenzisa Ukusebenzisa + = 20
amaqhinga wokubala amaqhinga wokubala + = 16
ukuhlanganisa ukuhlanganisa 18 = -
nokukhupha ngekghono nokukhupha ngekghono
elifaneleko: elifaneleko: Amaphuzu aliqiniso ngokuhlanganisa nokukhupha kufika e-15
• Beka inomboro ekulu • Beka inomboro ekulu Isibonelo
maqangi ukuze ubale maqangi ukuze ubale 1 + 14 = 15 14 + 1 = 15
uye phambili nofana uye phambili nofana
ubale uye emuva ubale uye emuva 2 + 13 = 12 13 + 2 = 15
• Inambalayini. • Inambalayini. 3 + 12 = 15 3 + 12 = 15
• Ukubuyelela kabili • Ukubuyelela kabili 15 – 4 = 11 15 – 11 = 4
nokuhafulaphakathi nokuhafulaphakathi 15 – 5 = 10 15 – 10 = 5
• Ukwakha nokuphhula • Ukwakha nokuphhula 15 – 6 = 9 15 – 9 = 6
• Sebenzisa • Sebenzisa
ubudlelwano phakathi ubudlelwano phakathi
295 kokuhlanganisa kokuhlanganisa
nokukhupha nokukhupha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
296 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.16 Umnqopho Umnqopho Ukukhumbula ngokurhabako ukuhlanganisa ukubuyelela kabili ukufika -15.
Iimbalo wenomboro: irherho wenomboro: irherho • 1+1=2
zehloko 99 75
• 2+2=4
• Hlela isethi enikelweko • Hlela isethi enikelweko
leenomboro leenomboro • 3+3=6
ezikhethiweko ezikhethiweko • 4+4=8
• Madanisa iinomboro • Madanisa iinomboro • 5 + 5 = 10
ema-99 bewutjho ema- 75 bewutjho
bonyana ngiyiphi bonyana ngiyiphi • 6 + 6 = 12
enengi nofana encani enengi nofana encani 7 + 7 + 14
nga-1, 2, 3, 4, 5 ne-10 nga-1, 2, 3, 4, 5 ne-10
Ngitjengisa inomboro okufanele uyihlanganise nalezi ezilandelako ukwenza i-15 (ngokutlola
Ukukhumbula Ukukhumbula nofana kusetjenziswe ubukhulu bedijithi namkha amakarada wefladi)
masinyana: masinyana:
• 8
• Ukukhumbula • Ukukhumbula
amaphuzu amaphuzu • 2
wokuhlanganisa wokuhlanganisa • 9
nowokukhupha kufika nowokukhupha kufika Ngitjengise inomboro ezokusala nange u_________akhitjhwa e-15 (ngokutlola nofana
e- 20 e- 15
kusetjenziswe ubukhulu bedijithi namkha amakarada wefladi)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Hlanganisa nofana • Hlanganisa nofana
ukhuphe imbuyeleli ukhuphe imbuyeleli • 5
ze-10 kusuka e-0 kuya ze-10 kusuka e-0 kuya • 13
e-100 e-50 • 0
Amaqhinga wokubala Amaqhinga wokubala Amaqhinga wokubala:
Ukusebenzisa Ukusebenzisa
Qala amanothi weThemu yesi-2
amaqhinga wokubala amaqhinga wokubala
ukuhlanganisa ukuhlanganisa
nokukhupha ngekghono nokukhupha ngekghono
elifaneleko: elifaneleko:
• Beka inomboro ekulu • Beka inomboro ekulu
maqangi ukuze ubale maqangi ukuze ubale
uye phambili nofana uye phambili nofana
ubale uye emuva ubale uye emuva
• Inambalayini. • Inambalayini.
• Ukubuyelela kabili • Ukubuyelela kabili
nokuhafulaphakathi nokuhafulaphakathi
• Ukwakha nokuphhula • Ukwakha nokuphhula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Sebenzisa • Sebenzisa
ubudlelwano phakathi ubudlelwano phakathi
kokuhlanganisa kokuhlanganisa
nokukhupha nokukhupha
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
CAPS
ama -24)
1.17 • Sebenzisa begodu • Sebenzisa begodu Ngikuphi okuhlukileko kune Themu yesi -2?
Amafrak- utjho amafraktjhini utjho amafraktjhini NgeThemu leli ukutjheja kwabafundi kunqotjhiswe ekubeni amagama wamafraktjhini
tjhini afaka hlangana afaka hlangana ahlanganiswa bunjani nenomboro yeengcenye ezilinganako zalokho okuzeleko
amahafu, ikotara, amahafu, ikotara, zihlukaniswe ngayo. Imihlobohlobo ehlukeneko yamadayagremu ingasetjenziswa ukwakha
kobunani, kobuthathu, kobunani, kobuthathu, ukuzwisisa okuya phambili.
kwesithandathu, kwesithandathu,
Isibonelo:
kwesihlanu kwesihlanu
• Ukukhumbula • Ukukhumbula
amafraktjhini amafraktjhini
asebujameni asebujameni
bedayagremu bedayagremu
• Tlola amafraktjhini • Tlola amafraktjhini Imihlobo yemibuzo elandelako ingabuzwa:
njenge ingcenye njenge ingcenye Kuneengcezu ezilinganako ezingaki?
eyodwa, izingcezu eyodwa, izingcezu
Siyibizani ingcezu elilodwa?
ezimbili zobuthathu ezimbili zobuthathu
Kuneengcezu ezilinganako ezingaki?
Siyibizani ingcezu elilodwa?
Kuneengcezu ezilinganako ezingaki?
Siyibizani ingcezu eyodwa?
Imihlobo le yemisetjenzana igqugquzela:
• Ukwazi bonyana amafraktjhini ayiingcenye ezilinganako;
• Ukubona iingcenye zamafrakhtjhini; begodu
• Ukutjho iingcenye zamafraktjhini
Ukutlola
Abafundi abaziswa ukutlola amatshwayo wamafraktjhini. Abafundi bafunda bonyana
bangalebula bunjani iingcenye zamafrakhtjhini njenge kota yi-1, isihlanu si-1.
297
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI-3
298
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
2.1 Ukukopa , ungezelele Ukukopa , ungezelele Ragela phambili unikele abafundi irherho elifanako lamaphetheni eThemini yesi-2. Qala Isifundo esi-1
Amapheth- bewuhlathulule bewuhlathulule amanothi weThemu yesi-2
eni weJi- Ukukopa ,ungezelele Ukukopa ,ungezelele Vumela abafundi bathome ngokukopa, bangezelele ekugcineni bahlathulule amaphetheni.
yomethri bewuhlathulule bewuhlathulule Ngalesisikhathi kufanele bazi ukuhlathulula amaphetheni ngaphandle kosizo lwemibuzo
ngamagama ngamagama ebakhokhelako. Ragela phambili unqophise ekuthuthukiseni ilimi abalithlogako
• Amaphetheni alula • Amaphetheni alula ukuhlathulula amaphetheni
enziwe ngezinto enziwe ngezinto
eziphathekako eziphathekako
• Amaphetheni alula • Amaphetheni alula
enziwe ngemigwalo enziwe ngemigwalo
yemida, ubujamo yemida, ubujamo
nafana izinto. nafana izinto.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Tlama amaphetheni Tlama amaphetheni
wakho wakho
Yenza amaphetheni Yenza amaphetheni
weJiyomethri weJiyomethri
• Ngezinto • Ngezinto
eziphathekako eziphathekako
• Ngokugwala imida, • Ngokugwala imida,
ubujamo nofana izinto ubujamo nofana izinto
Amaphetheni
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheni
weJiyomethri
• Ngokwemvelo,
• Kusukela epilweni
yangamalanga
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
yesimodeni,
• Kusukela kezamagugu
nendabuko yethu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
namaminithi
CAPS ZOKUPHELA KONYAKA YESI-3
ama -24)
2.2 Ukukopa, ukungezelela Ukukopa, ukungezelele Qala amanothi weThemu yoku-1, kodwana ungezelele irherho leenomboro kuya e-180 Iimfundo ezi-3
Amaphe- nokuhlathulula nokuhlathulula
theni Ukukopa, ukungezelele Ukukopa, ukungezelele
weenom- nokuhlathulula nokuhlathulula
boro ukulandelanisa ukulandelanisa
kwenomboro elula kwenomboro elula
ukufika e-180
ukufika ku-200
ukulandelanisa kufanele
Tlama begodu kutjengise
uhlathulule
amaphetheni wakho Ukubala uye phambili
nemuva nga:
Yenza bewuhlathulule
• Ku-1 ukusuka kwenye
amaphetheni nenye inomboro
weenomboro hlangana ne-0 ne-180
• Li-10 ukusuka
kesinye nesinye
isibuyabuyelelo se-10
hlangana ne-0 ne-180
• Ku-5 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-5 hlangana ne-0
ne-180
• Ku-2 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku- 2 hlangana ne -0
ne-180
• Ku-3 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-3 hlangana ne -0
ne-180
• Ku-4 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-4 hlangana ne -0
ne-180
299 Tlama amaphetheni
wakho
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI- 3
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
300 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
3.1 Ilimi lobujamo Ubujamo nokubukela Iminqopho etjhukunyisiweko yeThemu yesi-3:Ubujamo nokubukela Isifundo esi-1
Ubujamo, Hlathulula ubujamo • Ukumadanisa Ngikuphi okuhlukileko eGreyidini yoku-1?
ukuzijayeza bento eyodwa lokha ukuqaleka EGreyidini yesi-2 abafundi bazijayeza begodu banzinzise lokho abafunde ngakho
nokubukela nawuyimadanisa nenye okungafaniko kwento okukumadanisa ukuqaleka okungafaniko kwento eyodwa ngamalanga.
isib. Phezu kwe, phambi eyodwa ngamalanga.
Ubujamo nokubukela
kwe, emuva kwe, Ubujamo
ngesinceleni, ngesidleni, Anbafundi Esigabeni Esisissekelo kufanele bazwisise bonyana izinto ziqaleka
neenkombatjhuba
phezulu, phasi, eqadi zingafanilokha nawuziqalako kusukela emahlangothini ahlukahlukeneko. Abafundi bangahle
• Landela iinlayelo bathathe sakudlala bonyana izinto ezifana neemodoro ziqaleka zizincani lokha zikude.
kwe.
ukukhamba khamba Njengoba abafundi basebenza khulu ngeencwadi neemboniso eencwadini, kufanele
Ubujamo nokubukela ngetlasini. bazwisise bonyana kubangelwa yini bonyana into etjengiswa ngaphambili iqaleka iyikulu
Ukumadanisa ukuqaleka kunento engemuva. Ngesikhathi sokunqophana nesiqhemaabafundi bangenza umsebenzi
okungafaniko kwento wokulinga ngokubeka izandla zabo phambi kwabo, ukusitha ukuqaleka kwezinto ezikuluto
eyodwa ngamalanga. ezikudanyana.
Ubujamo EGreyidini yesi-2 abafundi kufanele banikelwe imisetjenzana lapho bazakumadanisa khona
ISIGABA ESISISEKELO AMAGREYIDI 1-3
neenkombatjhuba ukuqaleka okungafaniko (ukubona ungaphezulu, ukubona useqadi, ukubona ungaphambili)
Landela iinlayelo yezinto ezihlukahlukeneko zangamalanga.
ukukhamba khamba Ekugcineni lokhu kuzakusiza abafundi bona barhumutjhe imigwalo yezinto zeJiyomethri
ngetlasini. ezenziwe ngendlela ezihlukahlukeneko.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
namaminithi
CAPS ZOKUPHELA KONYAKA YESI-3
ama -24)
3.2 Izinto Izinto Ngikuphi okutjha eThemini yesi 3:
Izinto ezi- ezihlukahlukeneko ezihlukahlukeneko Amasilinda nawo ayafakwa ezintweni okusetjenzwa ngazo.
busontathu Ukukhumbula nokutjho Ukukhumbula nokutjho Amabumbeko abobusontathu (3-D) eGreyidini 2
(3-D) izinto ezibusontathu izinto ezibusontathu
Abafundi basebenza nge
( 3-D) ngetlasini (3-D) ngetlasini
neenthombeni neenthombeni • iimbholo nezinto ezibumbeke njengeembholo;
• Ubujamo bebholo, • Ubujamo bebholo, • amasilinda nezinto ezibumbeke njengama silinda; na
(iindulungu) (iindulungu) • mabhoksi ahlukahlukeneko nezinye izinto ezibumbeke p0hrizimu aboncamanenofana
• Ubujamo bebhoksi • Ubujamo bebhoksi amakhiyubhu.
(amaphrizimu) (amaphrizimu) Ukunqophisa ematshwayweni wezinto ezibusontathu( 3-D): Ezigedekako
• amasilinda • amasilinda nezitjhelelako
Amatshwayo wezinto Amatshwayo wezinto Lokhu liragelo phambili lalokhu abakwenze eGreyidini 1 neThemini 1, kodwana njenga nje,
amasilinda nawo afakiwe.
Ukuhlathulula, ukuhlela Ukuhlathulula, ukuhlela
ngeengaba noku ngeengaba noku
madanisa ( 3-D) izinto madanisa
ngokuqala okulandelako: ( 3-D) izinto ngokuqala
• isayizi okulandelako:
• izinto ezigedekako • isayizi Abafundi bangafunisisa ukiuthi bangakghona na ukupakelanisanofana imibhotjhongo
• izinto ezitjhelelako • izinto ezigedekako basebenzise amabholo kuphela, nofana amabhoksi kuphela amasilinda kuphela.
Imisetjenzana • izinto ezitjhelelako.
enqotjhiweko
Tjheja begodu wakhe
ubujamo babobusontathu
(3-D) onikelwe bona
usebenzise izinto
eziphathekako okufana
nokusika ubujamo
obubusobubili (2-D),
amabhlogo wokwakha,
izinto ezingabuye
zisetjenziswe
godu, amakhithi
wokwakha, ezinye
izinto ezinobujamo
obubusontathu (3-D)
301 zeJiyomethri.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
302 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
3.2 Izinto Izinto Ukukhumbula nokutjho iimbholo (iindulungu) namabhoksi (amaphrizimu) Iimfundo ezi-2
Izinto ezi- ezihlukahlukeneko ezihlukahlukeneko namasilinda
busontathu Ukukhumbula nokutjho Ukukhumbula nokutjho Abafundi baragela phambili nokutjho, ukuhlela ngeengaba nokubuthelela izinto,
(3-D) izinto ezibusontathu izinto ezibusontathu kodwana njenganje amasilinda akhona nawo. Abafundi kufanele banikelwe Izinto
( 3-D) ngetlasini (3-D) ngetlasini ezihlukahlukenekookufanele basebenze ngazo ezinobujamo obufana nalokhu:
neenthombeni neenthombeni • iindulungu ,isib iimbholo zamasayizi angalinganiko nofana abomabula, amalamune njll.;
• Ubujamo bebholo, • Ubujamo bebholo, • amaphrizimu isib amabhlogo , amabhoksi wamasayizi ahlukahlukeneko, isib. Amabhoksi
(iindulungu) (iindulungu) womlilo, amabhoksi wamasiriyeli, amabhoksi wetiye, amabhoksi wesibha samazinyo.
• Ubujamo bebhoksi • Ubujamo bebhoksi Nama
(amaphrizimu) (amaphrizimu) • silinda okufaka hlangana woke amade namatsikana isib. Iinquntwana zamaphayiphu
• amasilinda • amasilinda anobujamo bamasilinda, ingaphakathi kwe khadi bhoksi wamathawula agedwako, nofana
Amatshwayo wezinto Amatshwayo wezinto ingaphakathi lephepha langendlini yangasese, namasinda amafitjhani, navulekileko isib
amabhloegana wephoritjhi yamanyathelo, amabhlegana wesineyifu, njll.
Ukuhlathulula, ukuhlela Ukuhlathulula, ukuhlela
ngeengaba noku ngeengaba noku Abafundi bangathola izinto ezibumbeke njenge bholo (iindulungu), nofana okubumbeke
madanisa ( 3-D) izinto madanisa njenge bhoksi (amaphrizimu) nofanaokubumbeke njengamasilinda lokha nawu
ngokuqala okulandelako: nikelwe ibuthelelo lezinto. Abafundi bangathola nofana batjengise izintro ezibumbeke
( 3-D) izinto ngokuqala
njengamabhoksi (amaphrizimu) ngetlasini isib “ibhlegana lekofi leli libumbeke njenge
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• isayizi okulandelako:
silinda”.
• izinto ezigedekako • isayizi
Ngesikhathi sokufunda ngokuzijamela abafundi bangaragela phambili no
• izinto ezitjhelelako • izinto ezigedekako
• kwacha ngezinto ;no
Imisetjenzana • izinto ezitjhelelako.
• kwenza iimbholo , amasilinda namabumbeko wamabhoksi (amaphrizimu) ngedaka
enqotjhiweko
nofana ihlama yokudlala.
Tjheja begodu wakhe
Imisetjenzana etlolwako
ubujamo babobusontathu
(3-D) onikelwe bona Nanyana umsebenzi omnengi wezinto ezibusontathu (3-D) yenziwa ngokwenza, umsebenzi
usebenzise izinto kufanele unzinziswe ngomsebenzi otlolwako.
eziphathekako okufana Ilimi
nokusika ubujamo Ukuragela phambili nokuthuthukisa ikghono labafundi loku khuluma ngezinto ezibusontathu
obubusobubili (2-D), (3-D) Qala amanothi weThemu yoku-1
amabhlogo wokwakha,
izinto ezingabuye
zisetjenziswe
godu, amakhithi
wokwakha, ezinye
izinto ezinobujamo
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
obubusontathu (3-D)
zeJiyomethri.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
namaminithi
CAPS ZOKUPHELA KONYAKA YESI-3
ama -24)
3.3 Izinto Awukho umnqopho onqophileko wamajamo abobusobubili ( 2-D) etjhukunyisiweko
Amajamo ezihlukahlukeneko eThemini yesi 2. Nanyana kunjalo, umsebenzi wamajamo abobusobubili ( 2-D)
abobusobu- Ukukhumbula nokutjho unganzinziswa ngomsebenzi otlolwako ngesikhathi sokusebenza ngokuzijamela.
bili amajamo abobusobubili Abafundi bangaragela phambili nokwenza iinrhombe ngamabumbeko abobusobubili
(2-D) weJiyomethri ngesikhathi sokusebenza ngokuzijamela nangesikhathi sobuKghwari
(2-D) ( 2-D)
namaSiko.
• iindulungu
• aboncantathu
• iinkwere
• aboncamane
amatshwayo
wamajamo
Hlathulula , hlela
ngemihlobo begodu
umadanise izinto
ezinobujamo
babobusobubili (2-D)
ngokuqala lokhu:
• isayizi
• umbala
• ubjamo
• amahlangoth/ amaqadi
anqophileko
• amahlangothi /amaqadi
/aziindulungu
303
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI-3
4. UKUMEDA
304
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi begodu
Isikhathi • Ukutjho begodu • Ukutjho begodu nangokulandelanisa isikhathi.
ulandelanise ulandelanise Ngesikhathi sokufundisa itlasi loke nesikhathi sokufundisa ngeenqhema ezinqotjhiweko,
amalanga weveke amalanga weveke abafundi baragela phambili ngokukhuluma ngamalanga weveke, ngeenyanga zonyaka
• Ukutjho begodu • Ukutjho begodu begodu nangelanga lamhlokho, nangamalanga adlulileko begodu nangamalanga asezako.
ulandelanise iinyanga ulandelanise iinyanga Abafundi bajayela amakhalenda ngokuragela phambili ngokubeka:
zonyaka zonyaka • amalanga wamabeletho;
• Ukubeka amalanga • Ukubeka amalanga • amafestivali wezekolo,
wamabeletho, wamabeletho, • iminyanya wezomlando,
amafestivali wezekolo, amafestivali wezekolo,
• izehlakalo zesikolo;
amaholideyi amaholideyi
womphakathi, womphakathi, • amaholideyi womphakathi, ezisekhalendeni.
iminyanya iminyanya Ngesikhathi sokusebenza ngokuzijamela abafundi baragela phambili nokulandelanisa
wezomlando, wezomlando, izehlakalo zepilo yabo begodu balandelanisa iinthombe zezehlakalo ngefanelo.Abafundi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
izehlakalo zesikolo izehlakalo zesikolo basebenza godu ngemisebenzi ehlobene nama-iri begodu nesinquntu sama-iri
ezisekhalendeni. ezisekhalendeni. Ngikuphi okuhlukileko eGreyidini yesi-2?
• Ukutjho isikhathi • Ukutjho isikhathi • Ukutjho isikhathi ngama-iri, ngeenquntu zama-iri nangamakotara wama-iri
ukufika e-irini le-12 sama-iri ali-12 ngama-
iminqopho yethemu yesi-3 usitjela ngesikhathi ngama-iri nangesiquntu sama-iri begodu
ngama-iri, ngesiquntu iri,ngesiquntu se-iri
nangamakotara wama-iri ngokusebenzisa iwatjhi ye-analogo.Lokhu kuzokuba mnqopho
• se-iri begodu begodu nangekota
weemfundo ezimbili.
nangekota ye-iri ye-iri
Ukutjho isikhathi kufanele kujayezwe njalo ngeThemu.
Ukubala ubude Ukubala ubude
besikhathi nokudlula Isibonelo, abafundi bangabawiwa batjho bonyana isikolo singena sikhathi bani, isikhathi
besikhathi nokudlula
kwesikhathi sokudla sinini begodu isikolo siphuma nini, nofana batjhintja nini ukusuka kesinye isifundo
kwesikhathi
nabaya kesinye. Khetha iinkhathi lapho iwatjhi itjengisa isikhathi poro. Kufanelekile bonyana
• Ukusebenzisa • Ukusebenzisa
kube newatjhi esebenzako ebekwa ngetlasini, ukuze abafundi baqale kiyo. Abafundi
amakhalenda ukubala amakhalenda ukubala
bangenza iimfaniso zamawatjhi. Ungababawa bonyana bakutjengise iinkhathi ezihlukileko,
nokuhlathulula ubude nokuhlathulula ubude
isib. Ngitjengisa i-iri le-10 ehloko. Ngitjengise bonyana bekusikhathi bani ngaphambi
besikhathi ngamalanga besikhathi ngamalanga
kwekotara ye-iri.
nofana ngeemveke. nofana ngeemveke.
• Ukusebenzisa • Ukusebenzisa
amawatjhi ukubala amawatjhi ukubala
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ubude besikhathi ubude besikhathi
ngama-iri, ngesiquntu ngama-iri, ngesiquntu
se-iri nofana ngekotara se-iri nofana ngekotara
yama-iri. yama-iri.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi bafanele babale basebenzisa iwatjhi, isib. Batjengisa bonyana isikhathi sithi ma-iri Iimfundo ezi-3
Isikhathi • Ukutjho begodu • Ukutjho begodu ama-12 emini; babawe bonyana kuzabe kusikhathi bani ema-irini ama-3 ezako.Bakhambisa
ulandelanise ulandelanise izandla eemfanisweni zamawatjhi ( nofana baqala iwatjhi yangetlasini, nofana esithombeni
amalanga weveke amalanga weveke sewatjhi ukubala ipendulo yabo Abafundi abakalindeleki bonyana babale ubude
• Ukutjho begodu • Ukutjho begodu Besikhathi ngama-awara nofana isiquntu se-awa ngaphandle kokufunyana ubuso bewatjhi
ulandelanise iinyanga ulandelanise iinyanga • Sebenzisa amakhalenda ukubala nokuhlathulula ubude besikhathi ngamalanga nofana
zonyaka zonyaka ngeemveke
• Ukubeka amalanga • Ukubeka amalanga Abafundi banqopha ekufundeni ngamakhalenda. Bafunda ukuthola nokunikela amalanga
wamabeletho, wamabeletho, anqophileko.
amafestivali wezekolo, amafestivali wezekolo, Abafundi babala ubude besikhathi ngamalanga nofana iimveke, ngesikhathi baqala
amaholideyi amaholideyi ikhalenda.
womphakathi, womphakathi,
Abafundi abakalindekeki bonyana batjhugulule hlangana kweemveke namalanga.
iminyanya iminyanya
wezomlando, wezomlando, Abafundi abakalindeleki bonyana benze iimbalo ezifaka ukubala isikhathi hlangana
izehlakalo zesikolo izehlakalo zesikolo namalanga nangabe abakwazi ukufunyana amakhalenda
ezisekhalendeni. ezisekhalendeni.
• Ukutjho isikhathi • Ukutjho isikhathi
ukufika e-irini le-12 sama-iri ali-12 ngama-
ngama-iri, ngesiquntu iri,ngesiquntu se-iri
• se-iri begodu begodu nangekota
nangekota ye-iri ye-iri
Ukubala ubude Ukubala ubude
besikhathi nokudlula besikhathi nokudlula
kwesikhathi kwesikhathi
• Ukusebenzisa • Ukusebenzisa
amakhalenda ukubala amakhalenda ukubala
nokuhlathulula ubude nokuhlathulula ubude
besikhathi ngamalanga besikhathi ngamalanga
nofana ngeemveke. nofana ngeemveke.
• Ukusebenzisa • Ukusebenzisa
amawatjhi ukubala amawatjhi ukubala
ubude besikhathi ubude besikhathi
ngama-iri, ngesiquntu ngama-iri, ngesiquntu
se-iri nofana ngekotara se-iri nofana ngekotara
yama-iri. yama-iri.
305
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
306 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
4.2 Ukumeda EThemini yokuthoma kuphakanyiswe bonyana abafundi banqophe ekulinganiseni,
Ubude okungakahleleki ekumedeni, ekumadaniseni nekurekhodeni ubude, ubungako, ububanzi ngamayunithi
• Ukulinganisa, ahlelekileko kodwana benze ukulinganisa, ukumeda, akumadanisa nokurekhoda iimedo
ukumeda, ngamamitha.
ukumadanisa, ukuhlela Yomibili imihlobo yokumeda ubude ingajayezwa ngesikhathi sokusebenza ngokuzijamela
begodu urekhode ethemini yoke. Yoke imisebenzi ifanele ukurekhodwa.
ubudeusebenzise Ukumeda ubube njengobujamo bokurarulula imiraro nokubala
iimedo ezingakahleleki
Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi bangararulula
isib. Ubude besandla,
imiraro esebenzisa ubujamo
amagadango,ubude
bamapensela, izinto • bobude besimedo esingakahleleki, isib. Kumagadango ama-27 ukuya e-ofisini.
zokubala, njll. Kumagadango ama-36 ukuya ehegeni yesikolo. Kukude kangangani ukuya ehegeni
yesikolo.
• Ukuhlathulula ubude
bezinto ngokubala • Ukumeda ubude ngamamitha
begodu nokutjho Yelela irherho leenomboro ezifanele iThemu, nanyana imihlobo ehlukahlukeneko yemiraro
bonyana zinobude efaneleko yeThemu.
obungangani
ISIGABA ESISISEKELO AMAGREYIDI 1-3
bamayunithi
angakahleleki
• Ukusebenzisa
ilimi ukukhuluma
ngokumadanisa, isib.
ubude, ubufitjhani,
mude khulu, banzi
khulu.
Ukwethula ukumeda
okuhlelekileko
Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela
begodu urekhode
ubudengokusebenzisa
amamitha (iintonga
ezimamitha
nofana iintambo
ezinobude bemitha)
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
njengomuvosimedo
ojayelekileko.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
4.3 Ukumeda okungakahl- Abafundi bangaragela phambili ukuzijayeza ukulinganisa, ukumeda, ukumadanisa
Ubungako/ eleki nokurekhoda ubingako kusetjenziswa iimedo ezihlelekileko begodu nokumeda
• Ukulinganisa, ukum- ukudzimelela ngesikhathi sokusebenza ngokuzijamela.
Ubudisi
eda, ukumadanisa, Ukumeda umthamo njengobujamo bokurarulula imiraro nokubala
ukuhlela, bekurek- Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi bangararulula
hodwe ubungako, imiraro esebenzisa ubujamo
ngokusetjenzisa iimedo
• bobungako bokumeda okungakahleleki,
ezingakahleleki be-
godu nesikala sokud- • Ukumeda ubungako ngamakhilogremu
zimelela isib. Amabhu- Yelela irherho leenomboro ezihlukahlukeneko ezifanele iThemu, nanyana imihlobo
logo, iintina njll. ehlukahlukeneko yemiraro efaneleko yeThemu.
• Ukusebenzisa ilimi
ukukhuluma ngoku-
madanisa isib.elula,
ebudisi, elula-khulu,
ebudisi-khulu.
Ukwethula ukumeda
okuhlelekileko
• Ukumadanisa, uku-
hlela nokurekhoda
ubungako bezinto
ezipakelwe ukutheng-
iswae-zinobungako
obutjengiswe nga-
makhilogremu, isib.
amakhilogremu ama-2
wereyisi nekhiligremu
li-1 leflowuru
• Ukumeda ubungako
babo ngokusebenzisa
isikala sokumeda san-
gendlini yokuhlambela
307
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
308 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
4.4 Ukumeda Ukumeda Zoke iimedo egreyidini yoku-1 azikahleleki. Akukafaneli bonyana kwenziwe ukumeda
Umthamo/ okungakahleleki okungakahleleki okuhlelekileko bobungako kusetjenziswa imivosimedo ejayelekileko.
Ivolumu • Ukulinganisa • Ukulinganisa Ngikuphi okuhlukileko eThemini yesi-4?
nokumeda; nokumeda;
Ukumadanisa Ukumadanisa EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe
nokuhlela Isib. nokuhlela Isib. • ekuthuthuseni ilimi lokukhuluma ngemehluko yamavolumu;
Umthamo Umthamo • ekumadaniseni amavolumu weemumathi ezimbili ezifanako
ongamumathwa ongamumathwa
simumathii nasizeleko simumathii nasizeleko • ekumadaniseni amavolumu eemumathini ezimbili ezingafani
ngokusebenzisa ngokusebenzisa EThemini yesi-4 abafundi banganqopha ekwenzeni ukumeda okungakahleleki
iimedo ezingakahleleki iimedo ezingakahleleki ngokusebenzisa ubungako bamayunithi obungakahleleki.
isib. Iingobho isib. Iingobho
namakopi. namakopi. Uyini umthamo? Iyini ivolumu?
• Ukuhlathulula • Ukuhlathulula Ibhodlelo lingaba nomthamo wamakopi amane, kodwana ngekhelazaliswaswi, isibonelo,
umthamo besimumathi umthamo besimumathi ingamumatha nevolumu yekopi elilodwa lamanzi ngesikhathi esithileko.
ngokubala ngokubala umthamo ubungakobento engamumathwa simumathi, Ivolumu bungako besikhala
nokutjho bonyana nokutjho bonyana esithathwa simumathi(soke isikhala esingaphakathi kwento).
mangaki amayunihi mangaki amayunihi
angakahleleki angakahleleki Ivolumu bungako besikhala esithathwa simumathi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
angazalisa isimumathi, angazalisa isimumathi, Kesinye isikhathi abafundi bazokumeda bonyana lingangani iketjezi elingesimumathini.
isib. Ibhodlelo isib. Ibhodlelo Lokhu kumeda ivolumu yento engesimumathini.
linobungako bamakopi linobungako bamakopi
Kesinye isikhathi abafundi bazokumeda bonyana isimumathi singamumatha kangangani
amane amane
nasizeleko swi.
Ukwethulwa kokumeda Ukwethulwa kokumeda
okuhlelekileko okuhlelekileko Ukumeda ubude obungakahleleki ngokusebenzisa amayunithi wobude angakahleleki
• Ukulinganisa, • Ukulinganisa, Abafundi bangafunda zoke iinkambisolawulo neenkambiso zokumeda ngokusebenzisa
ukumeda; ukumeda; amayunithi angakahleleki. Ukumeda ngamayunithi angakahleleki kufanele bonyana
ukumadanisa ukumadanisa zingaqaleka kwanga azikaqakatheki kunokumeda ngamayunuthi ahlelekileko.
nokuhlela nokurekhoda nokuhlela nokurekhoda Abafundi bafanele bathole ithuba lokumeda ivolumu/ umthamo ngokusebenzisa izinto
umthamo wezinto umthamo wezinto
ezihlukahlukeneko njengamayunithi ahlelekileko, isib. Amakopi (kodwana ingasi amakopi
ngokumeda amalitha. ngokumeda amalitha.
wokumeda), iingobho,( kodwana ingasi amathispuni wokumeda),iimvalo zamabhodlelo
• Ukumadanisa, ukuhlela • Ukumadanisa, ukuhlela njengeemuvalo zamabhodlelo webisi wamalitha ama-2, Amabhlegana amancani,
nokurekhoda umthamo nokurekhoda umthamo
amabhodlelo amancani ,njll.
wezinto ezipakelwe wezinto ezipakelwe
ukuthengiswa, ukuthengiswa, Ukumeda ivolumu/umthamo ngamayunithi angakahleleki kufana ukubala bonyana
ubungako bazo ubungako bazo kukangaki lapho umuntu azalisa begodu athela khona eyunithini ekhethiweko bekufike
butlolwa ngamalitha, butlolwa ngamalitha, lapho umuntu afinyelela khona ebungakweni nofana evolumini efunekako.
isib. Amalitha ama- isib. Amalitha ama-
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
2 webisi, ilitha li-1 2 webisi, ilitha li-1
lesiselo esimakhaza, lesiselo esimakhaza,
amalitha ama-5 amalitha ama-5
wepende wepende
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
4.4 Ukumeda Ukumeda Abafundi bafanele bafundiswe ngaso soke isikhathi ukutjho iyunithi, isib. Kuneengobho Iimfundo ezi-3
Umthamo/ okungakahleleki okungakahleleki ezi-48 ezipheleleko zamanzi ngebhodlelweni nofana kunamanzi angaphasi kwekopi
Ivolumu • Ukulinganisa • Ukulinganisa ngebhodlelweni.
nokumeda; nokumeda; Lokha abafundi nasele bameda nanyana ngiyiphi iyunithi amahlandla ambalwa,bafanele
Ukumadanisa Ukumadanisa balinganise umthamo/ ivolumu ngokusebenzisa iyunithi leyo.
nokuhlela Isib. nokuhlela Isib.
Umthamo Umthamo Ukulinganisa ngaphambi kokumeda kuqakathekile, kodwana kungenziwa kwaphela lokha
ongamumathwa ongamumathwa abafundi nabameda ngeyunithi leyo.
simumathii nasizeleko simumathii nasizeleko Abafundi bafanele bafundiswe bonyana ukuze bamadanise amavolumu nofana imithamo,
ngokusebenzisa ngokusebenzisa iyunithi efana patsi ifanele isetjenziswe. Isib.nangabe irhalasi Limimatha amathispuni
iimedo ezingakahleleki iimedo ezingakahleleki ama-20 wamanzi begodu ikopi Limimatha iingobho zamanzi ezi-10, umuntu angekhe atjho
isib. Iingobho isib. Iingobho bonyana irhalasi Limimatha amanzi amanengi.
namakopi. namakopi.
Abafundi bafanele bamede ngamayunithi angakahleleki ahlukahlukeneko, ukuze bakghone
• Ukuhlathulula • Ukuhlathulula
umthamo besimumathi umthamo besimumathi • ukuthoma ukuzwisisa bonyana iyunithi nayiyincani , izokusetjenziswa amahlandla
ngokubala ngokubala amanengana ,isib. ivolumu engebhodlelweni ingaba ziingobho ezi-20 kodwana lilingane
nokutjho bonyana nokutjho bonyana nekopi li-1; begodu.
mangaki amayunihi mangaki amayunihi • ukuthoma ukusebenzisa amayunithi afanele lokho abakumedako, isib. Ukumeda amalitha
angakahleleki angakahleleki amabili wamabhodlelo azeleko ngethispuni kukumotjha isikhathi.
angazalisa isimumathi, angazalisa isimumathi,
isib. Ibhodlelo isib. Ibhodlelo Ukurekhoda iimedo
linobungako bamakopi linobungako bamakopi Nanyana ukumeda kulikghono lokuzijayeza ukwenza, abafundi bafanele ukurekhoda
amane amane iimedo zabo ngaso soke isikhathi,okufaka hlangana koke ukumeda okungakahleleki
Ukwethulwa kokumeda Ukwethulwa kokumeda nokulhelekileko.
okuhlelekileko okuhlelekileko Ukumeda umthamo njengobujamo bokurarulula imiraro neembalo
• Ukulinganisa, • Ukulinganisa, Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana,abafundi bangararulula
ukumeda; ukumeda;
imiraro esebenzisa
ukumadanisa ukumadanisa
nokuhlela nokurekhoda nokuhlela nokurekhoda • ubujamo bobungako / ivolumu besimedo ezingakahleleki, isibonelo, uGogo usebenzisa
umthamo wezinto umthamo wezinto amakopi amabili wetiye ukwenza ipudinghi. Nakawabuyelela kabili , uzokusebenzisa ibisi
ngokumeda amalitha. ngokumeda amalitha. elingangani?
• Ukumadanisa, ukuhlela • Ukumadanisa, ukuhlela • Amaliotha
nokurekhoda umthamo nokurekhoda umthamo
Yelela irhelo leenomboro elifanako leThemu leyo, begodu nemihlobo yemiraro
wezinto ezipakelwe wezinto ezipakelwe
ukuthengiswa, ukuthengiswa, ehlukahlukeneko.
ubungako bazo ubungako bazo
butlolwa ngamalitha, butlolwa ngamalitha,
isib. Amalitha ama- isib. Amalitha ama-
2 webisi, ilitha li-1 2 webisi, ilitha li-1
309 lesiselo esimakhaza, lesiselo esimakhaza,
amalitha ama-5 amalitha ama-5
wepende wepende
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI-3
5. UKUPHATHA IDATHA
310
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
5.4 Buthelela begodu Buthelela begodu Hlela idatha Iimfundo ezi-3
Ukubuthelela uhlele idatha uhlele idatha Bekutjhukunyiswe bona abafundi basebenze ngawowoke umzombe wedatha ngeThemu
nokuhlela • Buthelela idatha • Buthelela idatha yoku-1. Kutjhukunyiswe bona ngeThemu yesi-3, abafundi bazenzele amagrafu
idatha ngetlasi nofana ngetlasi nofana weenthombe umfundi ngamunye ngokusebenzisa idatha abnokelwe yona ngeenthombe
isikolo ukwenzela isikolo ukwenzela nofana ngamathebula.
ukuphendula imibuzo ukuphendula imibuzo Jamisela idatha
ebuzwa ngutitjhere. ebuzwa ngutitjhere.
Njengoba abafundi bazabe bagwala zoke iinthombe ezise / ezenza igrafu yeenthombe,
• Hlela idatha kuqakathekile ukukhetha iinhloko ezineengaba okulula bona abafundi bazigwale isib.
ngamathali Imihlobo yeenselo abazithandako, njengoba kulula ukugwala ibhlegana ukujamisela
5.5 Ukujamisela idatha Ukujamisela idatha isiseloesimakhaza esinye nesinye; iinthelo nazo kulula ukuzigwala, ngakho ke isithelo
esithadwako naso singagwalwa. Ukugwala iinthombe ukutjengisa imidlalo abayithandako,
Ukujamisela • Jamisela idatha • Jamisela idatha
amahlelo wakamabonakude abawathandako njll. Kungahle kube nzima khulu ebafundini
idatha ngegrafu yeenthombe ngegrafu yeenthombe
abanengi bamaGreyidi we-2.
5.6 Ukuhlaziya begodu Kulula ebafundini ukugwala amagrafu lokha nabanikelwe amaphepha anamabhlogo.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
urhumutjhe idatha Ukuhlaziya begodu Khumbuza abafundi ngobujamo obuqakathekileko begrafu yeenthombe (bona iThemu
Ukuhlaziya
urhumutjhe idatha yoku-1).
begodu • Phendula imibuzo
urhumutjhe ngedatha ethulwe nge: • Phendula imibuzo Hlaziya begodu urhumutjhe idatha
idatha ngedatha yegrafu
Abafundi kufanele baphendule imibuzo obabuza yona ngamagrafu weenthombe: Bona
yeenthombe.
iThemu 1 ukuthola ihlobo lemibuzo efaneleko.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YESI-2 ITHEMU YESI- 4
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Ngikuphi okuhlukileko kune Themu yesi-3?
Ukubala eziphathekako eziphathekako NgeThemu le abafundi babala izinto ezima-200. Ekupheleni kweThemu le abafundi babe
izinto Linganisa begodu ubale Linganisa begodu ubale sebabone, bakghwatha/bathinta bebatjhidisa izinto ezima-200. Bafanele babe nomuzwa
ngokuthembeka izinto ngokuthembeka izinto “wobunengi’ obuma-200. Ragela phambili nomnqopho wokubuthelela izinto.
zangamalanga zangamalanga Ekupheleni kweThemu bafanele bakghone ukuphendula imihlobo yemibuzo neenlayelo
ukuya okungaseneni ukuya okungaseneni ezilandelako:
ema-200. ema-200. • Ukubala izinto zokubala ngeenqhema zangakuhlanu, nangalitjhumi. Buyelela uhlele
Amaqhinga Amaqhinga begodu ubale. Usese nezinto zokubala ezilinganako?
wokubuthelela wokubuthelela • Nazi izinto zokubala ezima-200. Zibale ngokuzibuthelela ngeenqhema zangalitjhumi.
ayakhuthazwa. ayakhuthazwa. Ukubala izinto zokubala ezi-200 sezizoke, ungakhetha ukuzibala ngeenqhema zama-20
nofana ngama 25? Kungebanga lani?
• Thatha isiqunto bonyana ngiyiphi indlela engabalula ukubala ibuthelelo lamapensela.
• Nazi izinto zokubala ezima-80. Nange singabala ngaku-2 nofana ngali-10, izinto zokubala
zizokuhlala zinesamba esilinganako na?
• Bala izinto zokubala ezima-46 ngokuzibeka ngeenqhema ezingaku -2. Ingabe kumasinya
ukubala ngakubili kunokubala ngakunye na?
• Ziinqhema ezingaki zangali-10 ozibalileko lokha ubala izinto zokubala ezili-120?
311
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
312 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko kuneThemu yesi- 3?
Ukubala uye nemuva nga: nemuva nga: NgeThemu le abafundi babala ukuya phambili nemuva ukufika ema-200. Ngokuya
phambili • Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye ekupheleni kweThemu abafundi bafanele baqinise ukubala kwabo, ngokuhlanganisa
nemuva nenye inomboro nenye inomboro ukubala ngokweqa ethebuleni yokubuyabuyelela. Abafundi bafanele bahlathulule lokho
hlangana ne-0 na-200 hlangana ne-0 na-200 abakutjhejileko ethebuleni lokubala ngokubuyabuyelela bebakghone ukubona lokhu
• Li-10 ukusuka • Li-10 ukusuka nabenza ukubala ngokweqa. Bafanele bathome ngokusebenzisa ikghono lokubonela
kesinye nesinye kesinye nesinye phambili iinomboro ezizokubalwa.
isibuyabuyelelo se-10 isibuyabuyelelo se-10 Isibonelo:
hlangana ne-0 na -200 hlangana ne-0 na -200 Buza abafundi: Lokha nasibala ngakubili, sizoyisebenzisa inomboro ama-20? Ingabe
• Ku-5 ukusuka • Ku-5 ukusuka inomboro ama-20 ikhona na ethebuleni lakaku-2?
kesinye nesinye kesinye nesinye Ekupheleni kweThemu abafundi bafanele bakghone ukuphendula imihlobo yemibuzo
isibuyabuyelelo saka isibuyabuyelelo saka neenlayelo ezifana nokuthi:
ku-5 hlangana ne-0 ku-5 hlangana ne-0
• Bala ngamatjhumi ukusuka e-170 ukuya ema-200
na-200 na-200
• Bala uye emuva ngamatjhumi ukusuka e-180 ukuya e-140
• Ku-2 ukusuka • Ku-2 ukusuka
kesinye nesinye kesinye nesinye • Bala ngakuhlanu ukusuka e-115 ukuya e-145
isibuyabuyelelo saka isibuyabuyelelo saka • Bala uye emuva ngakuhlanu ukusuka e-135 ukuya e-110
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ku- 2 hlangana ne -0 ku- 2 hlangana ne -0 • Bala ngakuthathu ukusuka ema-66 ukuya e-81
na-200 na-200
• Bala uye emuva ngakuthathu ukusuka e-190 ukuya e-169
• Ku-3 ukusuka • Ku-3 ukusuka
• Bala ngakune ukusuka e-120 ukuya e-140
kesinye nesinye kesinye nesinye
isibuyabuyelelo saka isibuyabuyelelo saka • Bala uye emuva ngakune ukusuka e-180 ukuya e-160
ku-3 hlangana ne -0 ku-3 hlangana ne -0 Abafundi bangasebenzisa igridi yenomboro, inambalayini, umkhondo wenomboro,
na-200 na-200 i-abhakhasi begodu nemincamo yokusekela ukubala.
• Ku-4 ukusuka • Ku-4 ukusuka
kesinye nesinye kesinye nesinye
isibuyabuyelelo saka isibuyabuyelelo saka
ku-4 hlangana ne -0 ku-4 hlangana ne -0
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) na-200 na-200
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.3 Ukukhumbula, ukubona Ngikuphi okuhlukileko kuneThemu yesi- 3?
Amat- nokufunda iinomboro NgeThemu le abafundi kwanjesi babona, bafunde begodu nokutlola amatshwayo
shwayo • Ukwazi nokufunda weenomboro ukufika ema-200. Ilwazi lamatshwayo weenomboro ukuqinisekisa lokha
weenom- amatshwayo nakubalwa ngokuya phambili nokuya emuva.
boro wenomboro ukusukela Ekupheleni kweThemu abafundi bafanele bakghone ukuphendula imihlobo yemibuzo
namagama e-0 ukufika ema-200 nofana iinlayelo:
weenom- • Ukutlola amatshwayo Ukutlola itshwayo lenomboro:
boro weenomboro ukusuka
Amatjhumi amabili nantathu
e-0 ukufika ema-200
Amatjhumi amahlanu nekhomba
• Ukwazi nokufunda
amabizo wenomboro Amatjhumi alithoba nakubili
ukusuka e-0 ukufika Ikhulu nethoba
e-100 utlola amabizo Ikhulu netjhumi nanye
wenomboro ukusukela
Ikhulu namatjhumi amabili nekhomba
eli-0 ukufika e-100
Madanisa amatshwayo negama lenomboro
66 Amatjhumi alithoba nanye
8 Amatjhumi amahlanu nantathu
172 Amatjhumi amane
109 Amatjhumi amathathu nobunane
91 Ikhulu namatjhumi alikhomba nambili
40 Amatjhumi asithandathu nathandathu
53 Bunane
38 Ikhulu nethoba
umi
Amatjh u
m a th ath
a
Itjhumi
nesithandathu
Itjhumi
nethoba
i
Amatjhum
alikhomba
313 Ukufundela phezulu iinomboro kelinye nelinye ikarada:
198 67
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
314 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.4 Ukuhlela nokumadanisa Ngikuphi okuhlukileko kuneThemu yesi-3?
Ukuhlathu- iinomboro 4kufika ema- Irherho leenomboro lingezelelwe ukufika ema-99.
lula, 99 Ekupheleni kweThemu abafundi kufanele bakghone :
• Ukuhlela iinomboro Ukusebenzisa, ukufunda nokutlola.
ukumadani-
ezipheleleko ukufika Kokuthoma, kwesibili, kwesithathu, kwesine, kwesihlanu, kwesithandathu.................begodu
sa,
ema-99. Ukusukela neenrhunyezo: 1-thoma-, 2- bili, 3-thathu-, 4-ne,
nokuhlela Ukusebenzisa, ukufunda nokutlola ilimi lokuhlela nokumadanisa okulandelako
kencani khulu ukuya
iinomboro • Zingaki............
kwekulu khulu begodu
nakusukela kekulu • Okunengi kangange, inomboro efana na
khulu ukuya kwencani • Ilingana na, okunengi kuna, okuncani kuna, okumbadlwana kuna, okukhulu khulu kuna,
khulu okuyimbijana kuna, ekulu kuna
• Ukumadanisa • Enengi, ncani khulu, mbijana, okukhulu khulu
iinomboro • Hlela, kokuthoma,kokugcina, ngaphambi, ngemuva, okulandelako, hlangana, okuphakathi
ezipheleleko ukufika hlangana
ema-99 usebenzise Sebenzisa itshwayo = ukujamiselela ukulingana
okuncani kuna, Abafundi bafanele bakghone ukuphendula imibuzo efana nokuthi:
okukhulu kuna, Ngubani osebujameni besibili emjejeni?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
okunengi kuna, Ngiyiphi ipensela efitjhani khulu?
okuncani kuna, Hlela iinomboro ukufika okungasenani e-100 begodu uzibeke enambalayinini nofana
okulingana na. usebenzise igridi yesikwere.
Sebenzisa Zaliselela iinomboro ezitjhiyiweko engcenyeni zegridi ye-100
iinomborosikhundla
100
87
ukutjengisa ukuhlela,
iindawo nofana Tlola bonyana iinomboro lezi zizokuya kuphi: 88, 90, 92...
ubujamo Beka izinto Zaliselela ngenomboro etjhiyiweko:
emudeni ngokulandelana
115 117
ukusuka kweyokuthoma
ukuya kweyetjhumi 139 141
nofana keyokuthoma
ukuya keyokugcina, Isib. 187 185
Yokuthoma, yesibili, Phendula imibuzo elandelako ngokukhuluma:
yesithathu, ematjhumini Ngiziphi iinomboro ezihlangana kwama-82 nama- 87?
amabili Ngiziphi iinomboro ezihlangana kwama -45 nama 50?
Ngiziphi iinomboro ezihlangana kwama -69 nama 75?
Tlola iinomboro ngokuzihlela kusukela kwekulu khulu ukuya kwencani khulu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
127, 132, 165, 111, 189, 173, 156
Tlola iinomboro ngokuzihlela kusukela kwencani khulu ukuya kwekulu khulu
89, 62, 56, 72, 45, 39, 17
Tjengisa, funda begodu utlole inomborosikhundla.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
UBUKHULU BEDIJITHI
1.5 Ukulemuka ubukhulu Ekupheleni kweThemu abafundi bafanele bakghone uku:
Ubukhulu bedijithi okungenani • Zwisisa nokusebenzisa ilwazimagama lobukhulu bedijithi:
bedijithi iinomboro zamadijithi
Ukusebenzisa, ukufunda nokuthoma ukutlola:
amabili ukufika ema-99
Ngakunye nofana imivo, amatjhumi, idijithi, inomboro yedijithi elilodwa, inomboro
• Ukulemuka bonyana
yamadijithi amabili, ubukhulu bedijithi......
idijithi ngayinye
lijamele ini • Ukuhlukanisa phakathi iinomboro ezinamadijithi amabili ngesibuyabuyelelo setjhumi
nemivo
• Ukuphula iinomboro
zamadijithi amabili Tlola inomboro:
ukufika ema-99 zibe Amatjhumi asi-6 nemivo emi-3 ___________
ziiimbuyeleli zetjhumi Amatjhumi ama-2 nemivo emi -5____________
nemivo(TM)
Amatjhumi ali-12 nemivo ebu -8 ___________
• Bona bewutjho
Amatjhumi lia-18 nemivo emi-4 ___________
ubungako bedijithi
ngalinye • Ukusebenzisa ama-apharathasi:
Tjengisa amatjhumi ama-4 nemivo emi-5 ngokusebenzisa i-abhakhasi.
Tjengisa amatjhumi ali-7 nemivo esi-6 ngokusebenzisa i-abhakhasi
Yitjho bonyana idijithi bu-8 ema -28 lijamele ini? Begodu noku-2?
Yitjho bonyana ngiyiphi inomboro elingana nofana efana na:
-- Amatjhumi asi-6
-- Amatjhumi alithoba nemivo emithathu
-- Amatjhumi amahlanu nemivo elithoba
Ngiyiphi inomboro okufanele ingene ngebhoksini ngalinye?
34 = +4
78 = 70 +
Iinsetjenziswa
Izinto ezingabuthelelwa:
• Iingojwana zokubala
• Izinto zokubala ezingathungwa
• Iinthoro zomlilo
• Iingojwana ze-ayisikhrimu
315 • Amakhyubsi angenelelanako
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
316 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
UKURARULULA IMIRARO ESEBUJAMENI
1.6 Sebenzisa amathekhiniki Abafundi balindeke bonyana basombulule imiraro yamagama ngokusebenzisa
alandelako lokha amathekhiniki alandelako:
Amathek-
hiniki wok- nawurarulula imiraro • Ukwakha nofana ukuphula iinomboro
urarulula begodu uhlathulule • Ukubuyelela kabili nokuhafula phakathi
imiraro iinsombululo zemiraro:
• Amanambalayini
• Imigwalo nofana
Qala amanothi weThemu yoku-1 neyesi- 2 ukwenzela:
ama- aparethasi
aphathekako isib. izinto • Imigwalo nofana ama- aparethasi aphathekako
zokubala • Ukwakha nokuphula
• Ukwakha nokuphula • Ukubuyelela kabili nokuhafula phakathi
iinomboro Amanambalayini
• Ukubuyelela kabili Ukusebenzisa amanambalayini ukuze abarhelebhe ukubala, azakuvumela abafundi
nokuhafula phakathi bonyana barekhode ukucabanga kwabo begodu balandelele umkhondo wokucabanga
• Amanambalayini kwabo. Avumela abafundi bonyana babe nomfanekiso abangawusebenzisa ukuhlathulula
bonyana bawusombulule bunjani umraro.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Abafundi bebasebenzisa amanambalayini kusukela eGreyidini yoku-1. Ethemini yesi-
4 bafanele bakghone ukukwakha amanambalayini anganalitho lapho bazafaka khona
inomboro yokuthoma bese babone bonyana basuka bunjani enomborweni yinye ukuya
kwenye.
Isibonelo bonisa bonyana abafundi bangayisebenzisa bunjani inambalayini:
Abantwana abama-23 bathatha ikhambo lesikolo namhlanje. Kusele abantwana abama-63
esikolweni. Bekuna abantwana abangaki kwasekuthomeni?
+10
+10
+3
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
Vumela abafundi bonyana bakhethe ithekhiniki abazizwa batjhaphulukile ngayo. Nanyana
kunjalo lokha abafundi basebenzisa amathekhiniki lawa angabasiziko kufanele bonyana
bakhokhelwe ekusebenziseni azabasiza. Yelela bonyana abafundi esikhathi esinengi
basebenzise indlela ezihlukeneko zokusombulula imiraro okungahle kungabi ngilezo
ebezilindelwe ngutitjhere.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Isibonelo, umraro wokuhlukanisa ungasonjululwa ngokubuyelela ukukhupha, ukuhlanganisa
nofana ukubuyabuyelela. Iindlela zabafundi zizokutjhuguluka ngokukhamba njengombana
ilemuko nokujayela imihlobo yemiraro ikhula, begodu njengombana umqondo nomboro
wabo uthuthuka.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.7 Rarulula imiraro Iimbonelo zemiraro okufanele abafundi bakghone ukuyisombulula ekupheleni kweThemu.
Ukuh- yamagama Ukuhlanganisa nokukhupha
langanisa ezisebujameni
Kunemihlobo okungasenani emithathu esisekelo yemiraro yokuhlanganisa nokukhupha
bewuhlathulule
nokukhupha begodu omunye nomunye umhlobo ungabuzwa ngeendlela ezahlukahlukeneko.
iinsombululo zakho
zemiraro ezifaka Imihlobo esisekelo ngile:
ukuhlanganisa Itjhentjhi
nokukhupha nempendulo
• UNoluthando bekanamaswidi ama-25.USilo umuphe amaswidi ali-18. Sekanamaswidi
ukufika e-99.
amangaki njenganje?
• UNoluthando bekanamaswidi ama-53. Wanikela uSilo amaswidi ama-32. Sekanamaswidi
amangaki njenganje?
Hlanganisa
• Itlasi leGreyidi yesi- 2 linaboncantathu abahlaza satjani abama-37 begodu naboncantathu
abahlaza sasibhakabhaka abali-19. Bangaki aboncantathu abanabo?
• Baneendulungu ezima-63; ezima-27 zihlaza satjani begodu ezinye zihlaza
sasibhakabhaka. Baneendulungu ezingaki ezihlaza sasibhakabhaka abanazo?
Ukumadanisa
UNosisi unamabhanana ali-13. UThemba unamabhanana a-5. UNosisi unamabhanana
amanengi ngamangaki kunoThemba?
Ukubeka omunye nomuye umraro ngendlela ezihlukileko.
Imiraro ifanele ibekwe ngeendlela ezihlukeneko. Isibonelo, yomibili imiraro ngeyetjhentjhi
nokho “okungaziwa” kusendaweni ezahlukahlukeneko zemiraro.
• UNoluthando unamaswidi. USilo umupha amanye amaswidi ama-18. Kwanje sele
anamaswidi ama-43. UNoluthando bekanamaswidi amangaki ekuthomeni?
• UNoluthando bekanamahabhula ama-25. USilo wamupha amanye amahabhula. Kwanje
sele amahabhula ama- 43.USilo umuphe amahabhula amangaki?
317
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
318 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.8 Rarulula imiraro Iimbonelo zemiraro okufanele abafundi bakwazi ukuyisombulula ekupheleni
Ukuh- yamagama kweThemu.
langanisa ezisebujameni Ukuhlanganisa okubuyelelweko
okubuyele- bewuhlathulule
• Imilelenjana ema-20 inamavilo amangaki?
lweko iinsombululo zakho
zemiraro, ezifaka Isilinganiso
okurholela
ekubuy- ukuhlanganisa • UThami ukhamba amabhlogo asi-6 ngelanga. Mabhlogo amangaki awakhambako
abuyeleleni okubuyelelweko ngeveke?
okurholela Amagridi
ekubuyabuyeleleni
• UMnu. Khumalo utjala amareyi ali-7 wekhabitjhi. Kunamakhabitjhi ebu-8 ereyini. Mangaki
okunempendulo ufikela
amakhabitjhi sele awoke?
e-50.
1.9 Ukurarulula Iimbonelo zemiraro okufanele abafundi bakghone ukuyisombulula ekupheleni kweThemu.
Ukubuthele- imiraro yamagama Ukubuthelela
la nok- ezisebujameni
Ukubuthelela,ukulahla isalela
wabelana bewuhlathulule
iinsombululo zakho • UStella uthengisa amahabhula ngeenkhwanyana ezifaka amahabhula ali-10 sisinye.
okurholela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ufake ukwabelana Unamahabhula ama-80. Angenza iinkhwanyana ezifaka amahabhula ali-10 ezingaki?
ekuhlu-
kaniseni ngokulingana Ukubuthelela okufaka hlangana isalela ependulweni
nokubuthelela • Umlimi unamaqanda ama-47. Mabhoksi wamaqanda amangaki athatha amaqanda asi-6
ngeenqema lilinye azowatlhoga ukupaka woke amaqanda?
kweenomboro
Ukwabelana
ezipheleleko ukufika
e-50 kanye nempendulo Ukwabelana , ukulahla isalela
ezingahle zifaka iinsalela • Yabela abangani abali-7 amaswidi ama-54 ukuze boke bathole inani elilinganako
lamaswidi.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.10 Ukurarulula Umnqopho wemiraro yamagama wamafraktjhini weThemu le uragela phambili ukuvumela
bewuhlathulule abafundi :
Ukwabelana
okurholela iinsombululo zemiraro • Ukwaba begodu babuthelele ngokweenqhema izinto ngokulinganako;
emafrak- ezisebujameni efaka • ukutjho iingcenye zamafraktjhini;
tjhinini hlangana ukwabelana • Ukuthola amafraktjhini wezinto ezipheleleko;
ngokulingana erholela • Ukulemuka bonyana ifraktjhini yingcenye yokupheleleko;
empendulweni • Ukutlola ifraktjhini njengakunye kokuthathu
zamafraktjhini wohlavu
1 1 1 1 Ethemini le abafundi batjho amafratjhini amanengi. Kubalulekile bonyana abafundi
olulodwa isib. 2 , 4 , 3 , 5 njll bavezelwe epepeneneni amafraktjhini ngaphandle kwehafu yinye nekotara yinye.
Iimbonelo zemiraro engenziwa:
Ukwabelana, okurholela emafraktjhinini
• Yabela abangani aba-3 iintina ezili-7 zetjhokoledi ukuze boke bathole inani elilinganako
kungasali litho.
• Abangani abane babelana amapanekuku ama-3 ngokulinganako. Munye uzothola
mangaki?
Ekupheleni kweThemu abafundi bafanele bazi imiqondo elandelako:
Lokha nawuhlukanisa into phakathi:
• Iingcenye ezimbili ezilinganako, kubizwa ukuhafula; ingcenye yinye ibizwa ihafu.
• Iingcenye ezintathu ezilinganako, yinye ibizwa kunye kokuthathu;
• Iingcenye ezine ezilinganako, yinye ibizwa ikota;
• Iingcenye ezihlanu ezilinganako, yinye ibizwa kunye kokuhlanu;
• Iingcenye ezisithupha ezilinganako, yinye ibizwa kunye kwesithandathu;
• Iimbonelo zemiraro abafundi abafanele bayenze ekupheleni kweThemu.
Ukwabelana, okurholela emafraktjhinini
Yabela abangani aba-4 iintina eziyi-11 zetjhokoledi ukuze boke bathole inani elilinganako
ukuze kungasali litho.
Ifraktjhini lebuthelelo
Ugogo unikela uKiki amalamune ali-12. UKiki wenza ijuzi ngakunye kokuthathu
ngamalamune. Usebenzise amalume amangaki?
Imihlobo le yemiraro kufanele ibuzwe kwaphela lokha abafundi sele bararulule imiraro
emine namkha emihlanu yokwabelana, erholela emihlobeni yamafraktjhini begodu bazi
amagama weengcenye zamafraktjhini.
Ukubeka amafraktjhini ndawonye
Umbanduli webholo yezandla unikela umdlali ngamunye ihafu yelamune. Kunabadlali aba-
14. Uthloga amalumune amangaki?
319 Imihlobo le yemiraro kufanele ibuzwe kwaphela lokha abafundi sele bararulule imiraro
emine namkha emihlanu yokwabelana, erholela emihlobeni yamafraktjhini begodu bazi
amagama weengcenye zamafraktjhini.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
320 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.11 • Ukulemuka nokubona Iimbonelo zemiraro okufanele abafundi bakghone ukuyisombulula ekupheleni kweThemu.
Imali iinhlavu zemali Ubujamo bemiraro enoBudlelwana obusebenzako obuhlukeneko
zeSewula Afrika : (5c,
UHeila uthengisa amahotdogo ngama R4 ngayinye. Yenza ithebula lokumsiza athole inani
10c, 20, 50c, R1, R2;
yama-oda amanengi.
R5) kunye nemali
yemaphepha (R10,
Inani lama hotdogi
R20, R50).
• Sombulula imiraro Inani ngamaranda R
yemali efaka hlangana
amanani netjhentji
ngamasende ukufika Sebenzisa ithebula ukuthola inani lama hotdogo ali-7 nali-15.
ema-99c nofana USkhumbuzo ubhadelisa ama-R20 imali yokukhamba, abhadelise ama-R5 nge-iri
ngamaranda ukufika
ema-R99 ukuthlogomela umntwana. Mzalisele ithebula leli.
Inomboro yama-iri 1 2 3 4 5 10
Inani ngamaranda R 25 30
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Yelela bonyana umraro ka Heila noka Skhumbuzo usetjenzwa ngokuhlukileko.
UKUBALA OKUSEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Sebenzisa amathekhiniki Sebenzisa amathekhiniki Abafundi balindeke bonyana bararulule iimbalo ezisebujameni obutjhaphulukileko
Amathekh- alandelako nawubalako alandelako nawubalako ngokusebenzisa amathekhiniki alandelako:
iniki • Imigwalo nofana • Imigwalo nofana • Ukwakha nokuphula iinomboro
(iindlela ama-apharethasi ama-apharethasi • Ukubuyelela kabili nokuhafula phakathi
namaqh- aphathekako aphathekako
• Amanambalayini
inga) njengezinto zokubala njengezinto zokubala
Qala amanothi weThemu yoku-1 neyesi-2
• Ukwakha nokuphula • Ukwakha nokuphula
iinomboro iinomboro
• Ukubuyelela kabili • Ukubuyelela kabili
nokuhafula phakathi nokuhafula phakathi
• Amanambalayini • Amanambalayini
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika NgeThemu le abafundi baragela phambili ngokuphula iinomboro ukuze babale.
Ukuh- ema-99 e-99 Iindlela ezinokwenzeka ukubonisa iimbalo zokuhlanganisa nokukhupha
langanisa • Khupha ukusuka ema- • Khupha ukufika e- 99 Ukuphula inomboro ibe zingcezu ezincane ukwenzela ukubalisisa kube lula
nokukhupha 99 • Sebenzisa Ukusebenzisa ilwazi lobukhulu bedijithi, ukuphula iinomboro zibe matjhumi nemivo
• Sebenzisa amatshwayo afaneleko
amatshwayo afaneleko ( +, -, =, ) Hlanganisa amadijithi amabili ngokuphula iinomboro zombili
( +, -, =, ) • Ukuphrakhthisa 43 + 36 =
• Ukuphrakhthisa ukulumbana 43 + 36 = (40 + 3) + (30 + 6)
ukulumbana kweenomboro ukufika = (40 + 30) + (3 + 6)
kweenomboro ukufika ema-20
= 70 + 9
ema-20
= 79
Hlanganisa ngokuphula inomboro yinye
43 + 36 =
43 + (30 + 6)
43 + 30 → 73 + 6 = 79
Abafundi bangahle baphule inomboro ngezindlela abazikghonako. Lokhu kutjho bonyana
bazozenza ngeendlela ezahlukeneko.
43 + 36 =
43 + (10 + 10 + 10 + 6)
43 + 10 → 53 + 10 → 63 + 10 → 73 + 6 = 79
Ukukhupha
Ukuphula iinomboro zombili
87 – 56 =
87 – 56 = (80 + 7) - (50 + 6)
= (80 - 50) + (7 - 6)
= 30 + 1
= 31
321
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
322 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika • Ukukhupha ngophula inomboro yinye
Ukuh- ema-99 e-99 87 - 56 =
langanisa • Khupha ukusuka ema- • Khupha ukufika e- 99 87 - (50 + 6)
nokukhupha 99 • Sebenzisa 87 - 50 → 37 - 6 = 31
• Sebenzisa amatshwayo afaneleko Lindela bonyana abanye abafundi bangahle baphule inomboro ngendlela ezihlukileko
amatshwayo afaneleko ( +, -, =, ) ukwenzela bonyana babale lula:
( +, -, =, ) • Ukuphrakhthisa 87 - 56 =
• Ukuphrakhthisa ukulumbana 87 - (20 + 20 + 10 + 6)
ukulumbana kweenomboro ukufika
kweenomboro ukufika ema-20 87 - 20 → 67 - 20 → 47 - 10 = 37 - 6 = 31
ema-20 Ukusebenzisa ihafu ukuphula inomboro
69 + 12
69 + (6 + 6)
69 + 6 → 75 + 6 = 81
Ukubala uye phambili nemuva:
78 - 69 =
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukubala uye phambili ngakunye ukusuka ema-69 kuliqhinga elifaneleko ngombana
iinomboro ziseduzana kwenye nenye.
Ukubona ukubuyelela kabili okuseduze
34 + 35 hlathulula bonyana kubuyelela kabili ama-34 uhlanganise na-1 nofana buyelela
kabili ama-35 ukhuphe ku-1.
34 + 34 + 1
Abafundi bangahle barekhode amaqhinga wabo ngokusebenzisa abonotjhobi.
34 + (30 + 4) + 1
34 + 30 → 64 + 4 → 68 + 1 = 69
Ukutjhugulula inomboro ibe sibuyabuyelelo setjhumi begodu ukhuphe nofana
uhlanganise imivo.
Ukubala uye phambili nofana uye phasi ekutjhideleni eduze ne-10
58 + 19 =
Lapha abafundi bafanele batjho kibo ngokwabo bonyana banamathuba amabili
wokuzikhethela. Ukutjhugulula ama-58 nofana i-19 ekutjhideleni eduze kwesibuyabuyelelo
ze-10. Banokuzikhethela
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Isibalo singatlolwa ngendlela le: 58 + 19 = 58 + 20 - 1
58 + 20 → 78 - 1 = 77
Abanye abafundi bangaphula ama-20 ngeenqhema ezi-2 ze -10 ukubala ngokunembako.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Ekupheleni konyaka abafundi bafanele bakghone:
Ukuh- ema-99 e-99 Ukusebenzisa nokuzwisisa ilimi lokuhlanganisa
langanisa • Khupha ukusuka ema- • Khupha ukufika e- 99 Ukuzwisisa bonyana ukuhlanganisa ilize kutjhiya inomboro ingakatjhuguluki
nokukhupha 99 • Sebenzisa 75 + 0 = 75 0 + 75 = 75
• Sebenzisa amatshwayo afaneleko
amatshwayo afaneleko ( +, -, =, ) 75 = 75 + 0 75 = 0 + 75
( +, -, =, ) • Ukuphrakhthisa Ukuphendula imibuzo etloliweko ebekwe ngeendlela ezahlukahlukeneko:
• Ukuphrakhthisa ukulumbana • ukuhlanganisa ndawonye ama-43 ne-9
ukulumbana kweenomboro ukufika • ngezelela itjhumi ema-67
kweenomboro ukufika ema-20
• 11 hlanganisa nama-83
ema-20
• 80 = 62 + 8 +
• Ngiyiphi inomboro edlula ama-60 ngama-30
• Thola isamba sama-56 neli-14
• Hlanganisa itjhumi nambili namatjhumi alikhomba nahlanu
• Ngiyiphi inomboro edlula ama-83 ngetjhumi?
• Ngiyiphi inomboro ongayihlanganisa nama-45 ukuthola ama-78?
• Amatjhumi amane uhlanganise namatjhumi ama-3
• Amatjhumi ali-12 uhlanganise nemivo ebu-8
• 45 + 10 = 45 + 20 = 45 + 30 =
Ukwazi bonyana
Ukwazi bonyana ¨ lijamele inomboro engaziwako.
42 + 44 =
5 + 7 + = 80
57 + = 95
+ 15 = 81
Ngesizo lama-apharathasi: hlanganisa iinomboro ezintathu ndawonye
26 + + = 72
Khetha iinomboro ezintathu kulezi:15, 19, 22, 25
Zihlanganise zoke.
Mihlobo emingaki ehlukahlukeneko yamanani ongayenza?
323
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
324 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Baphendula imibuzo etloliweko begodu hlathulula bonyana bafike njani
Ukuh- ema-99 e-99 eempendulweni zabo:
langanisa • Khupha ukusuka ema- • Khupha ukufika e- 99 • Hlanganisa - 6, 12 ne -14.
nokukhupha 99 • Sebenzisa • Yini inani le- 10, 5 ne-19.
• Sebenzisa amatshwayo afaneleko Ukuzwisisa ukukhupha ekupheleni konyaka.
amatshwayo afaneleko ( +, -, =, ) Ekupheleni konyaka abafundi bafanele bakghone:
( +, -, =, ) • Ukuphrakhthisa Ukuzwisisa begodu basebenzise ilwazimagama lokukhupha:
• Ukuphrakhthisa ukulumbana Khupha, khupha, kusele mangaki, yincani kangangani............kune......, umehluko hlangana,
ukulumbana kweenomboro ukufika yikulu kangangani ......kune......, kufuneka kwenziwe okunengi kangangani .........begodu
kweenomboro ukufika ema-20 ufunde bewutlole itshwayo lokukhupha (-)
ema-20 Ragela phambili ngokuthuthukisa ukuzwisisisa ukukhupha njengoku:
• khupha
• thola umehluko hlangana
Ukuzwisisa bonyana nawukhupha ilize kutjhiya inomboro ingakatjintji:
92 – 0 = 92 92 = 92 – 0
Ukuphendula imibuzo etloliweko ebekwe ngeendlela ezahlukahlukeneko:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ama-37 khupha ku-3
• Khupha ama- 40 ema-80
• Ama-62 khupha ama- 42
• Khupha ama-45 ema-90
• Ngimuphi umehluko okhona hlangana nama-38 nama-57?
• Lincani kangangani i-17 kunama-49
• Ngiyiphi inomboro ongayikhupha ema-56 ukuthola ama -22?
• Ngiyiphi inomboro ongayikhupha -56 ukuthola ama– 32?
• Ngiyiphi inomboro ongayikhupha ama-56 ukuthola ama– 42?
• Thola iinomboro ezikhamba ngazimbili ezinomehluko we-10
Yazi bonyana sijamele inomboro engaziwako.
57 – 34 =
80 – 30 =
62 - = 48
98 – 42 =
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
87 - = 75
13 – 6 = 15 -
- 18 = 24
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Ukuthoma ukuzwisisa bonyana:
Ukuh- ema-99 e-99 25 – 10 kuhlukile ku 10 – 25
langanisa • Khupha ukusuka ema- • Khupha ukufika e- 99 Ukusebenzisa ubudlelwana obuphakathi kokuhlanganisa nokukhupha
nokukhupha 99 • Sebenzisa Yitjho bewutlole ukukhambelana kwamaphuzu wokukhupha ekuhlanganiseni amaphuzu
• Sebenzisa amatshwayo afaneleko anikelweko begodu uwahlanekezele. Isibonelo:
amatshwayo afaneleko ( +, -, =, )
( +, -, =, ) 73 + 17 =90 kutjho bonyana 90 – 17 = 73
• Ukuphrakhthisa
• Ukuphrakhthisa ukulumbana 17 + 73 = 90 kutjho bonyana 90 – 73 = 17
ukulumbana kweenomboro ukufika 42 – 18 = 24 kutjho bonyana 24 + 18 = 42
kweenomboro ukufika ema-20 42 – 24 = 18 kutjho bonyana 18 + 24 = 42
ema-20
Ngaphandle kokusebenzisa ama-apharathasi phendula okulandelako:
Nawazi bonyana 62 + 29 = 91.
Ayini ama-:
29 + 62
91 – 29
91 – 62
Nawazi bonyana 66 – 50 = 16
Ayini ama- :
66 – 16
50 + 16
16 + 50
Tlola bewuphendule okulandelako:
57 - 34 = 23 + 23 = 57 - 23 = 34 34 + 23 =
12 + 46 = 58 12 + = 58 58 - = 12 - 46 = 12
Tlola imihlobo emine yemitjho yeenomboro ehlukeneko usebenzise iinomboro ezi-3.
Isibonelo: 20, 30 and 50
20 + 30 = 50
30 + 20 = 50
50 – 30 = 20
50 - 20 = 30
325
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
326 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Ngikuphi okuhlukileko eThemeni yesi-4?
Ukuh- iinomboro ukusuka iinomboro ukusuka ku- NgeThemu le abafundi bazabe babuyababuyelela ngakuthathu kokuthoma. Qala amanothi
langanisa ku-1 ukufika e-10 ngo 1ukufika e-10 ngo 1, 2, asethemini yoku-1 ukwazisa umqondo omutjha.
okubuyele- 1, 2, 5, 3, 4 ukufika 5, 3, 4 ukufika ema-50
Ekupheleni kweThemu abafundi bafanele bakghone:
lweko ema-50 • Sebenzisa
Ukusebenzisa ilimi lokubuyabuyelela ebujameni obuphathekako:
kurholela • Sebenzisa amatshwayo afaneleko
ekubuy- amatshwayo afaneleko (+, x, =, ) Buyelela kabili, buyabuyelela, buyabuyelela nga,okubuyabuyelelo nga, isibuyabuyeleli
abuyeleleni (+, x, =, ) sa, okunengi kwa, iinqhema za....., ukubuyabuyelela njenga (ubukhulu, ubude,
ububanzi....), kabili, buyelela kathathu ngobunengi obungange, bafunde bebatlole itshwayo
lokubuyabuyelela (x)
Sebenzisa ilimi leli ukwenza iimbalo zokubuyabuyelela
Ukuzwisisa ukubuyabuyelela njengokuhlanganisa okubuyelelweko
6 esihlanganiswe ndawonye ka-3 zilingana na:
6 + 6 + 6 = 18
6 ngokubuyelelwa ka-3 = 18
ukubuyabuyelela isi- 6 ngaku-3 = 18
ISIGABA ESISISEKELO AMAGREYIDI 1-3
6 x 3 = 18
3 x 6 = 18
Ukuzwisisa ukubuyabuyelela njengokuhlathulula ukurhemisa into.
¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ 5 x 3 =15
¥ ¥ ¥ ¥ ¥ ¥
3 x 5 = 15
Ukuphendula imibuzo efana na:
Abokuhlanu abane
Ukubuyelela kabili isi-6
6 sibuyabuyelelwa ka-5
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Izinto zokubala ezintathu ereyini. Kunamareyi amane. Kunezinto zokubala ezingangani
Ukuh- iinomboro ukusuka iinomboro ukusuka ku- sezizoke?
langanisa ku-1 ukufika e-10 ngo 1ukufika e-10 ngo 1, 2, 2 kubuyabuyelelwa ngaku-4
okubuyele- 1, 2, 5, 3, 4 ukufika 5, 3, 4 ukufika ema-50
8 bubuyabuyelelwa ka-2
lweko ema-50 • Sebenzisa
Ukulemuka ukusetjenziswa kwesibambelindawo ukujamela inomboro engaziwako.
kurholela • Sebenzisa amatshwayo afaneleko
ekubuy- amatshwayo afaneleko (+, x, =, ) Iinqhema ezi-3 za-2 zi-6 nofana ku-3 kubuyabuyelela ka- 2 yisi- 6 nofana 3 x 2 =
abuyeleleni (+, x, =, ) Iinqhema ezi-4 za-3 zi-12 nofana 4 kubuyabuyelela ka- 3 yi- 12 nofana 4 x 3 =
Iinqhema ezi-6 za-3 zi-18 nofana 6 kubuyabuyelela ka- 3 yi- 18 nofana 6 x = 18
7 + = 14
Iinqhema ezi-2 za-7=
2 + + + + + + = 14
x 7 = 14
1x2=
2x2=
3x2=
1x5=
2x5=
3x5=
327
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
328 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.16 Umnqondo Iimbonelo zemibuzo engabuzwa:
Iimbalo wenomboro: irherho Umqondo nomboro:
zehloko ukufika ema-99
• Hlela isethi Amagama weenomboro namatshwayo
yeenomboro Phakamisa ikarada nofana utlole igama lenomboro. Khetha umfundi uzokutlola inomboro
ezikhethiweko ekhambelanako.
onikelwe yona
Okunengi nofana okuncani
• Madanisa iinomboro
ukufika ema-99 Kuyini o-
bewutjho bonyana • Kuncani ngaku-1 ema-70
ngiyiphi enengi nofana
encani nga-1, 2, 3, 4, • Kunengi ngaku-1 kunama-80
5 ne-10 • Kuncani ngaku-3 kunama-51
Ukukhumbula • Kuncani ngaku-4 kunama-67
masinyana:
• Ukukhumbula • Kuncani ngaku-5 kunama-85
amaphuzu • Kunengi ngali-10 kunama-90
wokuhlanganisa • Kuncani ngali- 10 kunama-80
newokukhupha ukufika
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ema- 20 Ngiliphi iledere lesi-5 lama alfabethini
• Hlanganisa nofana Ngiyiphi inyanga yobu-9 yomnyaka?
ukhuphe iimbuyeleli
Ukuhlela nokumadanisa
ze-10 ukusuka eli-0
ukuya e-100 Ngikuphi okunengi: 21 nofana 171?
Amaqhinga Nginikela inomboro ehlangana kwe- 154 ne-159.
ngengqondo
Ukusebenzisa Amaphuzu wokuhlanganisa nokukhupha:
amaqhinga wokubala • Ukwazi ngehliziyo ukulumbana kweenomboro ngokuhlanganisa nokukhupha ukuya ema-
ukuhlanganisa 20.
nokukhupha ngekghono + r = 20
elifaneleko:
• Beka inomboro ekulu + r = 16
maqangi ukwenzela
19 = - r
ukubalela uye phambili
nofana emuva Ukuhlanganisa nokukhupha amaphuzu wazo zoke iinomboro ukufika nokufaka hlangana
• Sebenzisa ama-20.
ubudlelwano phakathi 1 + 11 = 12 11 + 1 = 12
kokuhlanganisa
2 + 10 = 12 10 + 2 = 12
nokukhupha
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Inambalayini. 3 + 9 = 12 9 + 3 = 12
• Ukubuyelela kabili 18 – 4 = 14 18 – 14 = 4
nokuhafula 18 – 5 = 13 18 – 13 = 5
• Ukwakha nokuphula
18 – 6 = 12 18 – 12 = 6
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.16 Umnqondo Ngokurhabako khumbula ukuhlanganisa okubuyelelwa kabili ukufika-20. Lokhu kufanele
Iimbalo wenomboro: irherho kufake hlangana amaphuzu wokukhupha akhambelanako.
zehloko ukufika ema-99 • 1+1=2
• Hlela isethi
yeenomboro • 2+2=4
ezikhethiweko • 3+3=6
onikelwe yona • 4+4=8
• Madanisa iinomboro
• 5 + 5 = 10
ukufika ema-99
bewutjho bonyana • 6 + 6 = 12
ngiyiphi enengi nofana • 7 + 7 = 14
encani nga-1, 2, 3, 4, • 8 + 8 = 16
5 ne-10
Ukukhumbula • 9 + 9 = 18
masinyana: • 10 + 10 = 20
• Ukukhumbula Ngitjengise inomboro ongayihlanganisa ukwenza ama-20 (ukutlola phasi nofana
amaphuzu usebenzise isijameli sikhundla nofana amakarada wamaFladi)
wokuhlanganisa
newokukhupha ukufika • 8
ema- 20 • 2
• Hlanganisa nofana • 9
ukhuphe iimbuyeleli
• 15
ze-10 ukusuka eli-0
ukuya e-100 • 3
Amaqhinga Ngitjengisa inomboro esalako lokha ..... suswa ema -20 (ukutlola phasi nofana
ngengqondo ukusebenzisa isijameli sikhundla nofana amakarada wamaFladi)
Ukusebenzisa
• 5
amaqhinga wokubala
ukuhlanganisa • 18
nokukhupha ngekghono • 0
elifaneleko: • 14
• Beka inomboro ekulu
maqangi ukwenzela • 7
ukubalela uye phambili Amaqhinga wokubala:
nofana emuva Qala amanothi weThemu yesi- 2
• Sebenzisa
ubudlelwano phakathi
kokuhlanganisa
nokukhupha
• Inambalayini.
• Ukubuyelela kabili
329 nokuhafula
• Ukwakha nokuphula
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
330 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.17 • Sebenzisa begodu • Sebenzisa begodu Ngikuphi okuhlukileko ethemini yesi-4?
Amafrak- utjho amafraktjhini utjho amafraktjhini NgeThemu yesi- 3 ukulalelisisa kwabafunda bekunqotjhiswe ekubeni amagama
tjhini ukufaka hlangana ukufaka hlangana wamafraktjhini ahlanganiswe neenomboro zeengcenye ezilinganako lapho okuzeleko
amahafu,amakota, amahafu,amakota, kuhlukanisweko. Imihlobohlobo yamadayagramu asetjenziswa ukwakha ukuzwisisa
kunye kokuthathu, kunye kokuthathu, okuragela phambili.
kunye kokuhlanu kunye kokuhlanu
Abafundi baragela phambili nokutjho amafraktjhini emadagramini ngeThemu le, begodu
• Ukulemuka • Ukulemuka batjho iingcenye zamafraktjhini nabenza iimbalo zamagama. Iingcenye zamafraktjhini
amafraktjhini amafraktjhini eziboniweko zitlolwa njengehafu yi-1, ku- 1 kokuthathu, ikota yi-1.
asebujameni asebujameni
Umnqopho ngeThemu le ufanele ube kokuzeleko. Abafundi bafanele bakghone:
bedayagramu bedayagramu
Ukuqedelele imitjho:
• Ukutlola amafraktjhini • Ukutlola amafraktjhini
njengehafu eyodwa, njengehafu yi-1 Amahafu amabili alingana na _________okuzeleko
okubili kokuthathu kokuthathu Okuthathu kokuthathu kulingana na ________okuzeleko
Amakota amane alingana na _________okuzeleko
NgeThemu le abafundi bazokuthola amafraktjhini wesiqhema sezinto.
Isibonelo:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukusebenzisa izinto zokubala ezirhemisiweko abafundi bazokuthola:
Ihafu yi-1 yezinto zokubala ezibu-8
¥ ¥
¥ ¥
¥ ¥
¥ ¥
Abafundi bangahlukanisa izinto zokubala ezibu-8 ngeenqhema ezi-2 zangaku-4
¥ ¥
¥ ¥
¥ ¥
¥ ¥
Vumela abafundi basebenzise ama-apharathasi aphathekako ukwenza lokhu begodu
bahlele izinto zokubala ngokuzirhemisa.
Ekupheleni kweThemu le abafundi bafanele bakwazi ukuthola:
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Ihafu yi-1 yezinto ezibuthelelweko;
Ikota yi-1 yezinto ezibuthelelweko;
Kunye kokuthathu bezinto ezibuthelelweko; na
Kunye kokuhlanu bezinto ezibuthelelweko.
IGREYIDI YESI-2 ITHEMU YESI-4
2.AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
2.1 Ukukopa ,ungezelele Amaphetheni Abafundi bazokusebenza ngamaphetheni ukusukela kewemvelo, wepilweni yangamalanga
Amapheth- bewuhlathulule asizombelezileko yesimodeni, naselifeni lamasiko wethu ukusukela kugreyidi yoku-1ukufika kugreyidi yesi- 6.
eni weJi- Ukukopa, ungezelele Ukubona, ukuhlathulula Lokhu kutjho bonyana akukafaneli uthathe isikhathi esinengi kilesihloko. Kufanele bonyana
yomethri bewuhlathulule ngamagama nokukopa ukhethe imisetjenzana namaphetheni alungele leyo naleyo greyidi.
ngamagama amaphetheni Enye yemihlobo yamaphetheni abafundi abangayifuna yisimethri, isib: ubunengi
• Amaphetheni alula weJiyomethri bamakari nobuso beembandana bunobujamo besimethri. Zinjalo neenunwana ezinengi
enziwe ngezinto • Ngokwemvelo, nazibukelwako ukusukela ngaphezulu namaphetheni weenyoni ezinengi nazibukelwako
ezibonakalako; begodu ukusuka ngaphasi:
• Kusukela epilweni
• Amaphetheni alula yangamalanga Abafundi bangaqala amaphetheni ase:
enziwe ngemigwalo yesimodeni, • Mafensini (weendrada,weengodo nofana wevayibrakhrithi);
yemida,ubujamo • Kusukela elifeni • msebenzini weentina nasemathayilisini wefluru;
nofana izinto lamasiko wethu. • ephahleni;
Tlama bewuhlathulule
• zambathweni nasematjhileni;
amaphetheni
okungawakho • mabhorodweni,enkopini nasemapiringhini;
Ukwakha amaphetheni • embholweni ezirarhwako;
okungewakho • embandaneni njengeenkomo,amaviyaviyani webusuku newemini,iduba,
wejiyomethri idlulamithi,iingwenya,iinyoni,
• Ngezinto • iinunwana;
ezibonakalako • mathuthumbeni nasemakarini;
• Ngokugwala imida, • maphepheni abekwa emabodeni weepakana ezigwaliweko aneenthombe atholakala
ubujamo nofana izinto emikhukhwini nasezindlini ezingakahleleki.
Amaphetheni • imincamo yamasiko neyesimodeni; nase
asizombelezileko
• mpotweni zamasiko zomdaka nofana iimantjana ezilukiweko.
Ukubona, ukuhlathulula
Abafundi bangawahlathulula njani amaphetheni abawabonako abazombelezileko?
ngamagama nokukopa
amaphetheniwe Kunendlela ezihlukeneko zokuhlathulula amaphetheni esiwabonako asizombelezileko,
Jiyomethri Amaphetheni amanengi esiwabonako enziwe ngemida, ngobujamo nangezinto.Ubujamo
nofana izinto azikuthlogi ukuhlanganiswa nobujamo beJiyomethri obububuso bubili (2-D)
• Ngokwemvelo
nezinto ezibubuso buthathu (3-D) okusetjenzwe ngazo egreyidini yesi-2. Into okukuphela
• Kusukela epilweni kwayo eqalwe bafundi yi:
yangamalanga
• Lokho okubuyelelwako isib. Amaqatjhazi, imida, omunye nomunye umhlobo wobujamo
yesimodeni,
331 begodu nokuthi
• kusukela kezamagugu
• Zibuyelelwe njani.
nendabuko yethu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
332 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
2.1 Ukukopa ,ungezelele Amaphetheni Isibonelo : lsifundo esi-1
Amapheth- bewuhlathulule asizombelezileko -- Imida enqophileko evundlako (njengemida yetjhila loku hlanza iinkotlelo / ifadugu),
eni weJi- Ukukopa, ungezelele Ukubona, ukuhlathulula imida ekhamba magega nomqoqo wetjhila nofana buvundla erhembeni , imida
yomethri bewuhlathulule ngamagama nokukopa ekhuphuka nemilenze yamabhrugu,
ngamagama amaphetheni -- Imida egobeneko njengaleyo esiyithola lokha nasisika i- eyiye buvundla
• Amaphetheni alula weJiyomethri
-- Imida engalinganiko njengeyemino egadangisiweko njengaleyo yamadube nemida
enziwe ngezinto • Ngokwemvelo, etshwabeneko endhlovini, kubhejane nasebantwini abadala
ezibonakalako; begodu • Kusukela epilweni -- Imida ephenyezelako ongayithola lokha usika
• Amaphetheni alula yangamalanga
-- ikhabitjhi buvundla nofana ngileyo ongayithola eenajaneni zesanda
enziwe ngemigwalo yesimodeni,
yemida,ubujamo -- Amachatjhaza alinganako, amachatjhaza arhatjhwe ngokulingana
• Kusukela elifeni
nofana izinto lamasiko wethu. -- Ubujamo obulinganako isb.iphetheni yeentina ebodeni nofana epheyivini
Tlama bewuhlathulule -- Ubujamo bemibala efanako
amaphetheni -- Amaphetheni enziwa ngobujamo obufanako obuqale endaweni ezihlukeneko, isib.
okungawakho aboncantathu abaqale phezulu nofana phasi emisebenzini yemincamo yamasiko,
Ukwakha amaphetheni iintina zokupheyiva eziqale eendaweni ezihlukeneko
okungewakho -- Amaphetheni enziwe ngobujamo obuhlukeneko njengalawo weendlulamithi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
wejiyomethri
• Ngezinto
ezibonakalako
• Ngokugwala imida,
ubujamo nofana izinto
Amaphetheni
asizombelezileko
Ukubona, ukuhlathulula
ngamagama nokukopa
amaphetheniwe
Jiyomethri
• Ngokwemvelo
• Kusukela epilweni
yangamalanga
yesimodeni,
• kusukela kezamagugu
nendabuko yethu.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
2.2 Ukukopa, ungezelele Ukukopa, ungezelele Qala amanothi weThemu yoku-1, kodwana ngezelela irherho leenomboro ukufika kuma- limfundo ezi-3
Amaphe- bewuhlathulule bewuhlathulule 200
theni Ukukopa, ungezelele Ukukopa, ungezelele
weenom- bewuhlathulule bewuhlathulule
boro ukulandelana ukulandelana
kweenomboro ezilula kweenomboro ezilula
ukufika okungasenani ukufika okungasenani
ema-200. ema- 200.
Tlama amaphetheni Ukulandelana
angawakho kweenomboro kufanele
Tlama amaphetheni kutjengise ukubala uye
angawakho. phambili nemuva nga:
• Ku-1 ukusuka kwenye
nenye inomboro
hlangana ne-0 na-200
• Li-10 ukusuka
kesinye nesinye
isibuyabuyelelo se-10
hlangana ne-0 na -200
• Ku-5 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-5 hlangana ne-0
na-200
• Ku-2 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku- 2 hlangana ne -0
na-200
• Ku-3 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-3 hlangana ne -0
na-200
• Ku-4 ukusuka
kesinye nesinye
333 isibuyabuyelelo saka
ku-4 hlangana ne -0
na-200
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI-4
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
334 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
3.2 Izinto Izinto Umqopho ophakanyisiweko weThemu yesi- 4 Isifundo esi-1
Izinto ezi- ezihlukahlukeneko ezihlukahlukeneko Umsebenzi uhlanganiswa ndawonye ngokwenza imisetjenzana etlolwako.
busontathu Ukulemuka nokutjho Ukulemuka nokutjho
(3-D) izinto ezibusontathu izinto ezibusontathu
(3-D) ngetlasini (3-D) ngetlasini
neenthombeni neenthombeni
• Ubujamo bebholo,
• Ubujamo bebholo,
(iindulungu)
(iindulungu)
• Ubujamo bebhoksi
(amaphrizimu) • Ubujamo bebhoksi
(amaphrizimu)
• amasilinda
• amasilinda
Amatshwayo wezinto
Ukuhlathulula, Amatshwayo wezinto
ukuhlela ngeengaba Ukuhlathulula,
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokumadanisa Izinto ukuhlela ngeengaba
ezibusontathu (3-D) nokumadanisa Izinto
ngokuqala okulandelako: ezibusontathu (3-D)
• ubukhulu ngokuqala okulandelako:
• izinto ezigedekako • ubukhulu
• izinto ezitjhelelako • izinto ezigedekako
Imisetjenzana • izinto ezitjhelelako
enqotjhiweko
Tjheja begodu wakhe
izinto ezibusontathu
• (3-D) onikelwe zona
usebenzise izinto
eziphathekako okufana
nokusika ubujamo
obubusobubili (2-D),
amabhlogo wokwakha,
izinto ezingabuye
zisetjenziswe
godu, amakhithi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
wokwakha ,ezinye
izinto zeJiyomethri
ezibobusontath (3-D).
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
3.3 Irherho lamajamo Irherho lamajamo Qala amanothi weThemu yesi-2. Iimfundo ezi-3
Ubujamo Ukulemuka nokutjho Ukulemuka nokutjho EThemini le ungazijayeza, ubuyekeze begodu uhlanganise ndawonye umsebenzi
obubusobu- amajamo abobusobubili amajamo abobusobubili wamajamo abobusobubili (2-D). Kunqotjhiswe ekulemukeni nokutjho iindulungu, iinkwere,
bili (2-D) (2-D) (2-D) aboncamane, naboncantathu begodu kukhulunywe ngokuthi amahlangothi wabo anqophile
• iindulungu • iindulungu nofana aziindulungu na. Yenza imisebenzi ehlukileko kunaleyo eseThemini yesi- 2,
kodwana nqophisa kumatshwayo wamajamo nama bizo wamajamo.
• aboncantathu • aboncantathu
• iinkwere • iinkwere
• aboncamane • aboncamane
Amatshwayo wamajamo Amatshwayo wamajamo
Hlathulula , hlela Hlathulula , hlela
ngemihlobo begodu ngemihlobo begodu
umadanise amajamo umadanise amajamo
abobusobubili (2-D) abobusobubili (2-D)
ngokuqala lokhu: ngokuqala lokhu:
• ubukhulu • ubukhulu
• umbala • umbala
• ubujamo • ubujamo
• amahlangothi/ amaqadi • amahlangothi/ amaqadi
anqophileko anqophileko
• amahlangothi /amaqadi • amahlangothi /amaqadi
aziindulungu aziindulungu
3.4 Isimethri Isimethri Qala amanothi we Themu yesi-2. Isifundo esi-1
Isimethri Ukukhumbula Ukukhumbula
nokugwala umuda nokugwala umuda
wesimethri ebujameni wesimethri ebujameni
beJiyomethri beJiyomethri
nalobo obungasi nalobo obungasi
ngobeJiyomethri ngobeJiyomethri
bamajamo wobusobubili bamajamo wobusobubili
( 2-D) ( 2-D)
335
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-2 ITHEMU YESI-4
4. UKUMEDA
336 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi begodu Isifundo esi-1
Isikhathi • Ukutjho begodu • Ukutjho isikhathi nangokulandelanisa isikhathi.
ulandelanise ukufika e-irini le-12 Ngesikhathi sokufundisa itlasi loke nesikhathi sokufundisa ngeenqhema ezinqotjhiweko,
amalanga weveke ngama-iri, ngesiquntu abafundi baragela phambili ngokukhuluma ngamalanga weveke, ngeenyanga zonyaka
• Ukutjho begodu se-iri begodu begodu nangelanga lamhlokho, nangamalanga adlulileko begodu nangamalanga asezako.
ulandelanise iinyanga nangekota ye-iri Abafundi bajayela amakhalenda ngokuragela phambili ngokubeka:
zonyaka Ukubala ubude • amalanga wamabeletho;
• Ukubeka amalanga nokudlula kwesikhathi • amafestivali wezekolo,
wamabeletho, • Ukusebenzisa • iminyanya yezomlando,
amafestivali wezekolo, amawatjhi ukubala
• izehlakalo zesikolo;
amaholideyi ubude besikhathi
womphakathi, ngama-iri, ngesiquntu • amaholideyi womphakathi, ezisekhalendeni.
iminyanya se-iri nofana ngekota Ukutjho isikhathi ngama-iri, isiquntu se-iri begodu nangekota ye-iri
wezomlando, yama-iri. Ukutjho isikhathi ngama-iri, ngeenquntu zama-iri nangamakotara wama-iri
ISIGABA ESISISEKELO AMAGREYIDI 1-3
izehlakalo zesikolo
Qala amanothi weThemu yesi-3
ezisekhalendeni.
• Ukutjho isikhathi
ukufika e-irini le-12
ngama-iri, ngesiquntu
• se-iri begodu
nangekota ye-iri
Ukubala ubude
besikhathi nokudlula
kwesikhathi
• Ukusebenzisa
amakhalenda ukubala
nokuhlathulula ubude
besikhathi ngamalanga
nofana ngeemveke.
• Ukusebenzisa
amawatjhi ukubala
ubude besikhathi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ngama-iri, ngesiquntu
se-iri nofana ngekotara
yama-iri.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
4.2 Ukumeda Ukulinganisa, ukumeda, Ngikuphi okuhlukileko eThemini yoku-1? Isifundo esi-1
Ubude okungakahleleki ukumadanisa, ukuhlela EThemini yoku-1 kuphakanyiswe bonyana abafundi banqophe ekulinganiseni, ekumedeni,
• Ukulinganisa, nokurekhoda ubude ekumadaniseni nekurekhodeni ubude, ububanzi, ukuphakama ngamayunithi angakahleleki
ukumeda, ngokusebenzisa kodwana abafundi bathoma godu ukumeda ngamamitha.
ukumadanisa, amamitha
EThemini yesi-4 umnqopho ungaba sekulinganiseni, ekumedeni, ekumadaniseni
ukuhlela, begodu (iintongamamitha nofana
nekurekhodeni ubude, ukuphakama, ububanzi
kurekhodwe ubungako, iintambo ezinobude
bemitha) njengeyunithi ngamamitha
ngokusebenzisa
iimedo ezingakahleleki, ehlelekileko yobude. Qala amanothi weThemu yoku-1. Ukuhlanganisa kungaba ngendlela yemisebenzi
isib. Ubude besandla, etlolwako.
amagadango, ubude
bamapensela, izinto
zokubala, njll.
• Ukuhlathulula ubude
bezinto ngokubala
begodu nokutjho
bonyana zibubude
bamayunithi angangani
angakahleleki.
• Ukusebenzisa
ilimi ukukhuluma
ngokumadanisa isib.
ede khulu, efitjhani
khulu, mude khulu,
banzi khulu.
Ukwethula ukumeda
okuhlelekileko
• Ukulinganisa,
ukumeda,
ukumadanisa, ukuhlela
nokurekhoda ubude
ngokusebenzisa
amamitha
(iintongamamitha
nofana iintambo
ezinobude bemitha)
njengeyunithi
337 ehlelekileko yobude.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
338 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
4.3 Ukumeda Ethemini yesi-2 abafundi Isifundo esi-1
Ubungako/ okungakahleleki -- bameda ubungako obungakahleleki ngokusebenzisa isikala sokudzimelela;
Ubudisi • Ukulinganisa, -- bahlela imikhiqizo ngokuya ngobungako obutlolwe ephaketheni; begodu
ukumeda,
-- bafunda iinkala zangendlini yokuhlambela ( iinkala zombili zamambala begodu
ukumadanisa,
neenthombe)
ukuhlela,
bekurekhodwe Qala amanothi aseThemini yesi-2
ubungako, EThemini yesi-4 abafundi bafanele bahlanganise amakghono wabo wokufunda iinkala
ngokusetjenzisa zangendlini yokuhlambela begodu neenthombe zeenkala zangendlini yokuhlambela
iimedo ezingakahleleki ezinekhilogremu eseduzana ezeleko. Ukuhlanganisa lokhu, kungaba ngendlela
begodu nesikala yemisetjenzana etlolwako.
sokudzimelela isib.
Amabhlogo, iintina njll.
• Ukusebenzisa
ilimi ukukhuluma
ngokumadanisa isib.
elula,ebudisi, elula
khulu, ebudisi-khulu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukwethula ukumeda Ukwethula ukumeda
okuhlelekileko okuhlelekileko
• Ukumadanisa, ukuhlela Abafundi batlola
nokurekhoda ubungako amathaski ukuhlanganisa
bezinto ezipakelwe okulandelako, ukufaka
ukuthengiswa hlangana ukufunda
ezinobungako iinthombe ze:
obutjengiswe • mikhiqizo ezinobudisi
ngamakhilogramu, isib. obutlolwe kizo
amakhilogramu ama-2
wereyisi nekhilogramu • iinthombe zobudisi
li-1 leflowuru eziseenkala
zangendlini
• Ukumeda ubungako yokuhlambela lapho
babo ngokusebenzisa inalidi ikhomba
isikala sokumeda ikhilogremu ezeleko.
sangendlini
yokuhlambela
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
4.4 Ukumeda Ukwethulwa kokumeda Ngesikhathi sokusebenza ngokuzijamela abafundi bafanele baragele phambili: Isifundo si-1
Umthamo/ okungakahleleki okuhlelekileko -- Ukulinganisa nokumeda, ukumadanisa, ukuhlela begodu nokurekhoda ubungako
Ivolumu • Ukulinganisa Abafundi benza beemumathi nofana ivolumu eseemumathini ngokusebenzisa iimedo ezingakahleleki.
nokumeda;
amathaski atlolwako Amaresibhi alandeleko, okufaka hlangana ukubhaga, abujamo obulisizo lapho abafundi
Ukumadanisa
nokuhlela ukuhlanganisa bangazijayeza ukumeda. Khetha amaresibhi lapho iintlabagelo zinikelwa ngamakopi,
(isib. umthamo okulandelako, ukufaka amathispuni nofana amayunithi ahlelekileko;
ongamumathwa hlangana ukufunda -- Ukumadanisa begodu nokuhlela umthamo wamabhodlelo ahlukahlukeneko begodu
simumathi iinthombe izinto ezithengwa ngesitolo lapho ivolumu litlolwe emaphaketheni.
nasizeleko) nofana • Zemikhiqizo -- Ukusebenzisa amabhodlela welitha li-1 nofana amajege welitha li-1 ukulinganisa
ivolomu emumathini enobungako
ngokusebenzisa nokumeda, ukumadanisa ukuhlela begodu nokurekhoda umthamo weemumathi nofana
obutlolwe kizo ukuze ivolumu eliseemumathini zamalitha.
iimedo ezingakahleleki zilandeleniswe kuhle
isib. Iingobho Qala amanothi weThemu yesi- 3
namakopi. • Iinthombe zeenjege
Abafundi bafanele banikelwe amathaski atlolwako ukuze bahlanganise okulandelako,
• Ukuhlathulula lapho ivolumu iseduze
okufaka hlangana ukufunda iinthombe:
umthamo wesimumathi nenomboro elilitha eli-1
ngokubala nokutjho nofana amalitha ama-2 Zemikhiqizo enobungako obutlolwe kizo ukuze zilandeleniswe kuhle; begodu
bonyana mangaki womuda wegradatjhini. • Iinthombe zeenjege lapho ivolumu iseduze nenomboro emeregiweko elilitha eli-1 nofana
amayunithi amalitha ama-2 womuda onenomboro ezihlelekileko (umuda wegradetjhini).
Kulindeleke bonyana
angakahleleki
angazalisa isimumathi, abafundi bafunde • Kulindeleke bonyana abafundi bafunde kwaphela inomboro eseduze nomuda
isib. Ibhodlelo kwaphela kufikela onenomboro ehlelekileko.
linobungako bamakopi emudeni wegradetjhini Bahlathulula ivolumu njengokuthi pheze /eduze kwe/okudlula lokho kancani/ khulu nofana
ama-4 oseduzana. ncani/ nofana inomboro poro (yelitha) bafunda ejegeni
Ukwethulwa kokumeda Bahlathulula ivolumu
okuhlelekileko njengokuthi pheze,
• Ukulinganisa, eduze /okunengana/
ukumeda; pheze kube/ nofana
ukumadanisa ukuhlela
inomboro poro (yelitha)
nokurekhoda umthamo
wezinto ngokumeda bafunda ejegeni
ngamalitha.
• Ukumadanisa, ukuhlela
nokurekhoda umthamo
wezinto ezipakelwe
ukuthengiswa,
ubungako bazo
butlolwa ngamalitha,
isib. Amalitha ama-
2 webisi, ilitha li-1
339 lesiselo esimakhaza,
amalitha ama-5
wepende
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
340 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
4.4 Ukumeda Ukwethulwa kokumeda Ukumeda umthamo njengobujamo bokurarulula imiraro neembalo
Umthamo/ okungakahleleki okuhlelekileko Ngesikhathi esibekelwe Iinomboro, ama-Opheretjhini noBudlelwana, abafundi
Ivolumu • Ukulinganisa Abafundi benza bangararulula imiraro esebenzisa ubujamo
nokumeda;
amathaski atlolwako Ukumeda okungakahleleki komthamo / ivolumu, isib. UGogo usebenzisa amakopi amabili
Ukumadanisa
nokuhlela ukuhlanganisa webisi ukwenza ipudinghi. Nakabuyelela iresibhi kabili uzokudinga ibisi elingangani?
(isib. umthamo okulandelako, ukufaka
bamalitha
ongamumathwa hlangana ukufunda
simumathi iinthombe Yelela irherho leenomboro ezifanele iThemu, nanyana imihlobo ehlukahlukeneko yemiraro.
nasizeleko) nofana • Zemikhiqizo
ivolomu emumathini enobungako
ngokusebenzisa obutlolwe kizo ukuze
iimedo ezingakahleleki zilandeleniswe kuhle
isib. Iingobho
namakopi. • Iinthombe zeenjege
• Ukuhlathulula lapho ivolumu iseduze
umthamo wesimumathi nenomboro elilitha eli-1
ngokubala nokutjho nofana amalitha ama-2
bonyana mangaki womuda wegradatjhini.
amayunithi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Kulindeleke bonyana
angakahleleki
angazalisa isimumathi, abafundi bafunde
isib. Ibhodlelo kwaphela kufikela
linobungako bamakopi emudeni wegradetjhini
ama-4 oseduzana.
Ukwethulwa kokumeda Bahlathulula ivolumu
okuhlelekileko njengokuthi pheze,
• Ukulinganisa, eduze /okunengana/
ukumeda; pheze kube/ nofana
ukumadanisa ukuhlela
inomboro poro (yelitha)
nokurekhoda umthamo
wezinto ngokumeda bafunda ejegeni
ngamalitha.
• Ukumadanisa, ukuhlela
nokurekhoda umthamo
wezinto ezipakelwe
ukuthengiswa,
ubungako bazo
butlolwa ngamalitha,
isib. Amalitha ama-
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
2 webisi, ilitha li-1
lesiselo esimakhaza,
amalitha ama-5
wepende
IGREYIDI YESI-2 ITHEMU YESI-4
5. UKUPHATHA IDATHA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
5.4 Ukubuthelela begodu
Ukubuthelela nokuhlela idatha
begodu • Buthelela idatha
nokuhlele ngetlasi nofana
idatha isikolo ukwenzela
ukuphendula imibuzo
ebuzwa ngutitjhere.
• Hlela idatha
ngamathali
5.5 Jamisela idatha
Jamisela Jamisela idatha ngegrafu
idatha yeenthombe
5.6 Hlaziya begodu Hlaziya begodu Hlaziya begodu urhumutjhe idatha enikelweko. Isifundo si-1
Hlaziya urhumutjhe idatha urhumutjhe idatha Ngalesisikhathi sonyaka, abafundi kufanele bona sebawajayele amagrafu weenthombe.
begodu Phendula imibuzo Hlaziya idatha esuselwe Kuphakanyiswe bonyana eThemini yesi-4 abafundi banqopha ekuhlaziyeni idatha. Nikela
urhumutjhe ngedatha yegrafu eenjamelini ezinikelweko. abafundi idatha bonyana bahlaziye okungasenani igrafu yi-1yeenthombe.
idatha yeenthombe. Abafundi kufanele baphendule imibuzo obabuza yona ngegrafu nethebula:
Qala iThemu yoku-1 ukuthola imibuzo efaneleko ongayibuza.
341
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3.5.3 Itlhadlhulo lokumumethweko eGreyidini yesi-3
342 IGREYIDI YESI-3 ITHEMU YOKU- 1
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
Abafundi beGreyidi yesi 3 bazokuhlanganisa koke abakufunde eGreyidini yesi 2 begodu basebenzise amakghono lawo ukusebenza ngeenomboro ezihlangana kwe- nama
Abafundi abaseGreyidini yesi -3, njenganje bazo:
• Funda bebatlole iinomboro ematshwayweni nemagameni ukufika e-
• Baragela phambili nokubona bebabeke iinomboro;
• Basebenzisa ilwazi labo lobukhulu bedijithi ukuthola amakhulu, amatjhumi nemivo bebahlathulule nobudlelwana bazo;
• Hlukanisa iinomboro zamadijithi amathathu, bazokusebenzisa ilwazi labo lobukhulo bedijithi ukumadanisa nokuhlela iinomboro begodu bafanele banikele iizathu zalokho
abazikhethele khona;
• Ragela phambili nokubala baye phambili nemva, kwanjesi ngamakhefu wangama nange kwanjesi bazokuthoma ukubona ubudlelwana obuphakathi kokubala ngaku - nanga ku ;
• Kwazi ukubala izinto ezinengi ezibuthelelweko ngokuzibeka ngeenqhema. Njenganje, babala ngokuhlelekileko, ngokunembako bebakwazi ukunikela indlela yokuhlola umphumela;
• Hlanganisa nokukhupha iinomboro ngehloko ukufika ema- ;
• Sombulula imihlobo ehlukahlukeneko yemiraro begodu bazokufunda indlela yokuhlela iimpendulo zabo ezitloliweko ngendlela ehlelekileko;
• Khetha itshwayo elifaneleko lokha basenza ukusombulula umraro osebujamweni;
• Rekhoda ukubala kwabo ngokusebenzisa amatshwayo wokuhlanganisa (+), ukukhupha (-) ukulingana (=). Bangahlathulula iimpendulo zabo bebahlathulule iindlela zabo zokwenza;
• Sebenza ngeendlela ezisemthethweni zokurekhoda ukubala ngokuhlanganisa nangokukhupha; isibonelo bazokuphula inomboro yinye nofana zimbili ukuhlanganisa nokukhupha;
begodu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Kghona ukukhetha emilandelaneni yamaqhinga wokusombulula umraro. Isibonelo ukukhupha: abafundi bazokwazi ukukhupha ngokubala uye phambili nofan emva.
• Ikharikhyulami ilindele bonyana abafundi beGreyidi yesi-3 basebenzisa ama-apharathasi aphathekako ngokuphasi khulu ukujamisela ukuhlanganisa nokukhupha. Ekupheleni
konyaka abafundi kufanele bonyana bakghone ukuhlanganisa nokukhupha kusetjenziswa iindlela yepensela nephepha.
• Abafundi abangena eGreyidini yesi- 3 bafanele bakghone ukuzwisisa ubungako beenomboro nokuphula iinomboro ukuze bakwazi ukubala. Abafundi sebathoma ukuzwisisa ama-
njengemivo ema- begodu nanjengamatjhumi ali- nemivo ebu- . Umfundi akasatlhogi ama-apharathasi aphathekako ukusiza ukuzwisisa lokhu. EGreyidini 3 abafundi bazokuragela
phambili nokutlhoga amathuba wokuzijayeza ukuphula iinomboro ukwenzela ukuzwisisa ubungako beenomboro begodu nokusebenzisa ilwazi leli ukwenzela ukuphula iinomboro
nakuhlanganiswako nalokha kukhutjhwa.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.1 Ukubala izinto • Buthelela okungenani EGreyidini yesi-3 abafundi baragela phambili nokubala izintozangamalanga. Irherho
Ukubala eziphathekako izinto ezi-200 lenomboro lizokukhula kufika e-1000 ekupheleni konyaka. Lokhu kutjho bonyana ukutjheja
izinto Linganisa begodu ukulinganisa nokubala ngokuyelela kufanele kunikelwe imihlobo yama-apharathasi asetjenzisiweko:
ubale izinto ngokuthembeka • Amabhlogo weDienes
ngokuthembeka ukufika • Nikela ukulinganisa • Amakarada wobukhulu bedijithi
e-1000. Amaqhinga okuzwakalako kwenani
NgeThemu yokuthoma abafundi bazijayeza bebahlanganise izinto zokubala kufika ema-
wokubuthelela lezinto ezingahlolwa
200. Umnqopho usekubutheleleni izinto. Abafundi bafanele babe nomuzwa oqinileko
ayakhuthazwa. ngokubala
ozokubangcono, urhelebhe khulu begodu kube msinyana ukubala ngeenqhema
zangamatjhumi, ngamatjhumi amabili, ngamatjhumi amahlanu nangamakhulu kunokubala
ngakunye.
Bathoma ukubala ngamakhulu, ukuya phamblili nemva ngeThemu yokuthoma. Ukusekela
ukubala okungakahlelwa, abafundi bangahlela izinto ngeenqhema zama-100.
Isibonelo:
Esinye nesinye isiqhema sibonisa ikhulu.
Elke groep toon een honderd aan.
343
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
344 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.1 Ukubala izinto • Buthelela okungenani NgeThemu le begodu nonyaka woke abafundi bafanele balemukiswe bonyana ukubala `
Ukubala eziphathekako izinto ezi-200 izinto kuzabasiza njani ekubaleni.
izinto Linganisa begodu ukulinganisa nokubala Isibonelo:
ubale izinto ngokuthembeka
Ukubala izinto ngokuzihlukanisa zibe ziinqhema zangamatjhumi, ngama-20, ngama-50
ngokuthembeka ukufika • Nikela ukulinganisa nofana nangamakhulu kuzakuvumela abafundi bona bakwazi ukuphula iinomboro lokha
e-1000. Amaqhinga okuzwakalako kwenani nabahlanganisako nofana bakhupha. Ukuhlanganisa ama- 362 + 527, abafundi bangaphula
wokubuthelela lezinto ezingahlolwa iinomboro zibe ziingcezu zobukhulu bedijithi o.u
ayakhuthazwa. ngokubala
362 + 527 = (300 + 60 + 2) + (500 + 20 + 7).
Abafundi bangabala amakhulu woke ngombana bakwenzile lokhu nababala izinto
ezibuthelelwe gamakhulu. Abafundi gadesi babala amatjhumi (bakwenzile lokho kusukela
eGreyidini yoku-1) bese kuba mimivo. Abafundi bafanele bazwisise bonyana kungani
bacitha isikhathi sabo ngokubala izinto. Ukuhlangana/hlobana kufanele kwenziwe kabanzi.
NgeThemu le abafundi bangajamisela iinomboro ngokusebenzisa amabhlogo weDienes
nofana amabhlogo anesisikelo setjhumi.
Abafundi bawasebenzisile ama-apharathasi la eGreyidini yesi-2.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Abafundi bafanele bakghone ukuqedelela isitatimende esilandelako:
Inani lamabhlogo anesisekelo setjhumi yi__________
Abafundi bangasebenzisa amakarada wobukhulu bedijithi ukubonisa ubukhulu belinye
nelinye idijithi.
Umnqopho wemihlobo yemisebenzi le, asikho ukubala izinto kwaphela: Ngesikhathi leso
abafundi ba:
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukuzwisisa inanil edijithi
• Ukuphula nokwakha iinomboro, begodu
• Nokufunda amatshwayo weenomboro
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko eGreyidini yesi-2?
Ukubala uye nemuva nga: nemuva nga: Abafundi babala ngama- 100 kokuthoma. Benza lokhu kufika ema-500. Abafundi batlhoga
phambili • makhefu anqotjhiswe • makhefu anqotjhiswe isekelo lama apharathasi wamabhlogo anesisekelo setjhumi okufana ne :
nemuva eGreyidini yesi-2 eGreyidini yesi-2 • Imincamo yokubala
ngerherho leenomboro ngerherho leenomboro
• Amabhlogo we Dienes
eliphakamako kusukela eliphakamako.
kunanyana ngiyiphi • Amanambalayini
• ngama 100 ukufikela
inomboro okungasenani ema- • Igridi yeenomboro
• ngama- 20, 25, 500. Ukubala ngokweqa kufanele kuhlobaniswe nethebula yokubuyabuyelela. Ukubala ngaku -4
50,100 ukufikela kuzakusiza abafundi lokha ba:
okungasenani e-1 000 • Ukune mu-1 ngu-4
• Abokune aba-2 bu-8
• Abokune aba-3 li-12
Ukubala ngokweqa godu kusekela ukuziwisisa ukubuyabuyelela begodu kuzokusiza
abafundi nabaqedelela ukulandelana kweenomboro.
1.3 Ukubona, ukukhumbula Ukubona, ukukhumbula Ngikuphi okuhlukileko eGreyidini yesi-2?
Amat- nokufunda iinomboro nokufunda iinomboro NgeThemu le abafundi bayabona, bafunde bebatlole amatshwayo weenomboro ukufika
shwayo • Ukubona, • Ukubona, ema-500. Bafunda amagama weenomboro ukufika ema-250 bebatlole amagama
weenom- ukukhumbula ukukhumbula weenomboro ukufika e-100
boro nokufunda nokufunda Ukufunda nokutlola amatshwayo weenomboro kuyajayezwa naku:
namagama amatshwayo amatshwayo
weenom- • kubalwa izinto
wenomboro ukusuka wenomboro ukusuka
boro eli- 0 ukufika e-1000 eli- 0 ukufika ema-500 • kubalwa ukuya phambili nemuva
• Ukutlola amatshwayo • Ukutlola amatshwayo • kuqedelelwa ukulandelana kweenomboro; begodu
weenomboro ukusuka weenomboro ukusuka • kuhlelwa begodu kumadaniswa iinomboro
eli -0 ukufika e-1000 eli -0 ukufika ema- Kufanele kuyelelwe ukutjhiwo kweenomboro ngefanelo; umuntu ufanele “athi 323
• Ukubona, • Ukubona, njengokuthi makhulu amathathu namatjhumi amabili nantathu”, INGASI njenge “323”
ukukhumbula ukukhumbula Nakutlolwa iinomboro ezinamadijithi amathathu, iinomboro eziphakathi kwe-100 ne 110;
nokufunda amabizo nokufunda amabizo 200 nama 210; 300 nama 310; 400 nama 410, idijithi elisebujameni bamatjhumi lilize.
wenomboro ukusuka wenomboro ukusuka Abanye abafundi bathola ubudisi bokutlola iinomboro lezi ngamatshwayolokha nabanikelwe
eli-0 ukufika e-1000 eli-0 ukufika ema-250 inomboro ngamagama.
• Ukutlola amabizo • Ukutlola amabizo Isibonelo: Kungahle kube budisi kabanye abafundi ukutlola ‘amakhulu amathathu nakune’
wenomboro ukusuka wenomboro ukusuka ngamatshwayo. Bangahle batlole 3004. Amakarada wobukhulu bedijithi aqakathekile
eli- 0 ukufika e-1000 eli- 0 ukufika e khulukhulu ukusiza abafundi bazwisise bonyana bangajamiselela bunjani iinomboro lezi
345 ngefanelo. Abafundi kufanele godu banikelwe isikhathi esinengi sokuzijayeza ukutlola
iinomboro lezi.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
346 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.4 Hlathulula, madanisa, Ukuhlathulula, Ngikuphi okuhlukileko eGreyidini yesi- 2?
Hlathulula, begodu uhlele ukumadanisa NgeThemu le abafundi bahlanganisa ukuhlela nokumadanisa iinomboro ukufika ema-99
madanisa, iinomboro kufika ema- • nokuhlela iinomboro begodu kufanele bakghone ukunikela iinzathu zokobana kubayini enye inomboro iyikulu
begodu 999 ukufika ema- 99 kunenye. Vumela abafundi bonyana basebenzise inambalayini, umkhondo wenomboro,
uhlele Ukuhlathulula • Ukuhlathulula amagridi weenomboro nofana ilwazi labo lokuphula iinomboro ngamatjhumi nangemivo
iinomboro nokumadanisa nokumadanisa ukutjhengisa ukuzwisisa kwabo. Lokha nabahlela iinomboro abafundi bafanele bakwazi
• iinomboro ezipheleleko iinomboro ezipheleleko ukutjho bonyana kubayini inomboro iyikulu kunenye ngokusebenzisa ubungako bedijithi
ukufika ema- 999, ukufika ema- 99, ukuzihlathulula bona ngokwabo.
ngokusebenzisa ngokusebenzisa Isibonelo:
okuncani kuna, okuncani kuna, Ama - mancani kunama - ngombana:
okukhulu kuna, okukhulu kuna,
Ngiyazi bonyana ne, begodu ne. Begodu ziinyanda ezintathu zangalitjhumi begodu ama-
okunengi kuna, okunengi kuna,
ziinyanda ezihlanu zangalitjhumi. Kuneenyanda ezinengi zamatjhumi ema-50 kunema -30.
okuncani kuna begodu okuncani kuna begodu
kulingana na. kulingana na. Ukusebenza ngeenomborosikhundla, ikhalenda ibalulekile ngombana ivumela umfundi
bonyana akhulume ngelanga lama-23 nofana ilanga lama-31 lenyanga.
• Ukuhlathulula • Ukuhlathulula
nokuhlela iinomboro nokuhlela iinomboro Abafundi bafanele bazijayeze ukufunda nokutlola indlela erhunyeziweko.
ezipheleleko ukufika ezipheleleko kufika
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ema- 999, ukusuka ema- 99, kusukela
kencani khulu ukufika kencani khulu kufikela
kekulu khulu begodu kekulu khulu begodu
ukusuka kekulu khulu nakusukela kekulu
ukuya kencani khulu khulu ukuya kencani
Sebenzisa iinomboro khulu
sikhundla ukutjengisa Sebenzisa
ukuhlela, indawo iinomborosikhundla
namkha ubujamo ukutjengisa
Sebenzisa, ukulandelana, indawo
ufunde bewutlole namkha ubujamo
iinomborosikhundla, Sebenzisa,
okufaka hlangana indlela ufunde bewutlole
erhunyeziweko kufikela iinomborosikhundla,
ema-31 okufaka hlangana indlela
erhunyeziweko ukufika
ema-31
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.5 Ukukhumbula Ukukhumbula Ngikuphi okuhlukileko eGreyidini yesi-2?
Ubukhulu ubukhulu bedijithi ubukhulu bedijithi IThemu le imayelana nokuhlanganisa ukuzwisisa ubukhulu bedijithi obufundwe eGreyidini
bedijithi eenomborweni eenomborweni 2. Abafundi baragela phambili nokwenza imihlobo efanako yemisetjenzana efana
ezinamadijithi ezinamadijithi neyeGreyidini yesi-2 ngeThemu yesi-4:
amathathu ukufika amathathu ukufika Ukuzwisisa nokusebenzisa ilwazi magama lobukhulu bedijithi:
ema-999 ema-99 Ukusebenzisa, ukufunda nokuthoma ukutlola:
• Ukukhumbula bonyana • Ukukhumbula bonyana Abokunye nofana imivo, amatjhumi, idijithi, inomboro enedijithi elilodwa, inomboro
idijithi ngalinye lijamele idijithi ngalinye enamadijithi amabili.........ubukhulu bedijithi........
ini. lijameleni.
Ukuphula iinomboro ezinamadijithi amabili zibe ziimbuyabuyeleli zamatjhumi
• Ukuphula iinomboro • Ukuphula iinomboro nangakunye.
zamadijithi amathathu zamadijithi amabili Abafundi bakghona ukuphula iinomboro nga:
ukufika e-999 zibe ukufika ema-99 zibe
Ubungako bamatjhumi nobungako bemivo isib. 73 = 70 + 3 (amakarada wobukhulu bedijithi
zimbuyabuyeleli ze- zimbuyabuyeleli
angabalisizo ukwenza lokhu)
100, iimbuyabuyeleli zetjhumi nangakunye.
zamatjhumi Imbuyabuyelelo zamatjhumi nemivo isib. 73 = 7 yamatjhumi + 3 yemivo
• Ukubona bewutjho
nangakunye. Ukwakha iinomboro ezinamadijithi amabili ukusuka eengcenyeni zobukhulu bedijithi
ubukhulu bedijithi
lazo.
• Ukubona bewutjho ngayinye.
ubukhulu bedijithi Isibonelo
ngayinye. Tlola inomboro:
a) Amatjhumi asi-6 nemivo emi-3 _____________
b) Amatjhumi ama-2 nemivo emi-5 _____________
c) Amatjhumi ali-12 nemivo ebu-8 ____________
d) Amatjhumi ali-18 nemivo emi-4 _____________
Ukusebenzisa ama-apharathasi ukutjengisa ukuhlukaniswa kweenomboro:
• I-Abhakhasi
a) Tjengis amatjhumi ama-4 nemivo emi-5 ngokusebenzisa i-abhakhasi
b) Tjengisa amatjhumi ama-47nemivo esi-6 ngokusebenzisa i-abhakhasi
Amakarada wobukhulu bedijithi
347
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
348 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.5 Ukukhumbula Ukukhumbula • Abafundi basebenzisa amakarada wobukhulu bedijithi ukubonisa iingcenye zenomboro.
Ubukhulu ubukhulu bedijithi ubukhulu bedijithi Isibonelo:
bedijithi eenomborweni eenomborweni
ezinamadijithi ezinamadijithi Imihlobo yemibuzo elandelako ingabuzwa:
amathathu ukufika amathathu ukufika -- Tjengisa bonyana idijithi bu-8 ema-28 lijamele ini? Begodu no ku-2 ujamele ini?
ema-999 ema-99
-- Tjengisa bonyana ngiyiphi inomboro elingana nofana efana na:
• Ukukhumbula bonyana • Ukukhumbula bonyana
a) Amatjhumi asi-6
idijithi ngalinye lijamele idijithi ngalinye
ini. lijameleni. b) Amatjhumi alithoba nemivo emithathu.
• Ukuphula iinomboro • Ukuphula iinomboro c) Amatjhumi amahlanu nemivo elithoba.
zamadijithi amathathu zamadijithi amabili
ukufika e-999 zibe ukufika ema-99 zibe
zimbuyabuyeleli ze- zimbuyabuyeleli
100, iimbuyabuyeleli zetjhumi nangakunye.
zamatjhumi • Ukubona bewutjho
nangakunye. ubukhulu bedijithi
• Ukubona bewutjho ngayinye.
ubukhulu bedijithi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngayinye.
UKURARULULA IMIRARO ESEBUJAMENI OBUTHIZE
1.6 Sebenzisa amathekiniki Sebenzisa amathekhniki Ngikuphi okuhlukileko eGreyidini yesi-2?
Amathekini- alandelako ukurarulula alandelako ukurarulula Abafundi balindeleke bona bararulule imiraro yamagama ngokusebenzisa amathekiniki
ki wokuraru- imiraro nokuhlathulula imiraro. alandelako:
lula imiraro iinsombululo zemiraro: • Ukwakha nokuphula • Ukwakha nofana ukuphula iinomboro
• Ukwakha nokuphula iinomboro • Ukubuyelela kabili nokuhafula phakathi
iinomboro • Ukubuyelela kabili • Amanambalayini
• Ukubuyelela kabili nokuhafula phakathi Ukugwala izinto ngayinye kufike ema-99 akusiwo umbono omuhle begodu kufanele
nokuhafula phakathi • Amanambalayini ungakhuthazwa. Khuthaza ukungeniswa kwamatshwayo weenomboro ekurekhodeni
• Amanambalayini kwabo, okufaka hlangana iinjamiselo zeenthombe. Abafundi begodu bangakhuthazwa
• Ukutjhideza eduze bonyana batlole imitjho yeenomboro.
ngamatjhumi Vumela abafundi bonyan bakhethe ithekniki leyo abazigedlileko ngayo. Irherho leenomboro
nomhlobo womraro kuzakutjhobonyana ngiyiphi ithekniki ezokusetjenziswa. Nanyana
kunjalo, lokha abafundi basebenzisa amathekiniki anagabarhelebhiko, kufanele balulekwe
bonyana basebenzise iindlela zokwenza ezizabasiza.
Ukwakha nokuphula
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Le ngenye yamathekiniki aqakatheke khulu Esigabeni Esisisekelo. Ukusebenzisa ithekniki
le kuvumela abafundi ukuhlukanisa (ukuphula) nokuhlanganisa iinomboro ukusiza ukwenza
ukubala kubelula. Bazabe basebenzisa ithekniki le ngobunengi Esigabeni Esiphakathi
nakhona.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.6 Sebenzisa amathekiniki Sebenzisa amathekhniki Ukubuyelela kabili nokuhafula phakathi
Amathekini- alandelako ukurarulula alandelako ukurarulula Ithekniki le isezingeni eliphezulu begodu ithloga umqondo weenomboro onamandla.
ki wokuraru- imiraro nokuhlathulula imiraro. Abafundi abakghonako ukukhetha ithekniki le batjhaphulukile emaqhingeni
lula imiraro iinsombululo zemiraro: • Ukwakha nokuphula abawasebenzisako. Ukwazi ukubuyelela kabili, kuzokuvumela abafundi ukusebenzisa
• Ukwakha nokuphula iinomboro amaqhinga wokuseduze nokubuyelela kabili.
iinomboro • Ukubuyelela kabili Isibonelo:
• Ukubuyelela kabili nokuhafula phakathi Umraro wamagama: Ngelinye ilanga etlinigi bahlaba abantwana abama -45 umjovo
nokuhafula phakathi • Amanambalayini womkhuhlani. Ngelanga elilandelako bajova abantwana abama-46. Bantwana abangaki
• Amanambalayini abajovwako nasele baboke?
• Ukutjhideza eduze Umraro ungasombululwa ngokusebenzisa ukubuyelela kabili. Umfundi angahle athi
ngamatjhumi nowubuyelela kabili ama-45 bese uhlanganisa naku-1 nofana ukubuyelela ama-46 kabili
bese ukhuphe1.
Amanambalayini
Ukusebenzisa amanambalayini ukwenzela ukubasiza ukubala azakunikela abafundi indlela
yokurekhoda ukucabanga kwabo begodu balandelele umkhondo wokucabanga kwabo.
Begodu kuvumela abafundi bonyana babe nomfanekiso wokurekhoda abangawusebenzisa
ukuhlathulula bonyana bawusombulule bunjani umraro.
Abafundi bebasebenzisa amanambalayini kusukela eGreyidini yoku-1. Abafundi bafanele
bakghone ukwakha amanambalayini anganalitho lapho bafaka khona inomboro yokuthoma,
bese bathole bonyana bangasuka bunjani enomborweni yinye ukuya kwenye.
Isibonelo sokobana abafundi bangayisebenzisa bunjani inambalayini:
Abantwana abama-23 bathatha ikhambo lesikolo namhlanjesi. Kusele abantwana
abama-63 esikolweni. Bekunabantwana abangaki kwasekuthomeni?
+10
+10
+3
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
1.7 Rarulula imiraro Rarulula imiraro Iimbonelo zemiraro engenziwa ethemini le.
Ukuh- yamagama yamagama Ethemini leli abafundi bahlanganisa umsebenzi owenziwa eGreyidini yesi-2. Qala amanothi
langanisa ezisebujameni ezisebujameni wemihlobo yensombululo zemiraro eziseGreyidini yesi-2, Isahluko sesi-2.
bewuhlathulule bewuhlathulule
nokukhupha iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka
349 ukuhlanganisa ukuhlanganisa
nokukhupha nempendulo nokukhupha nempendulo
ukufika e-999. ukufika e-99.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
350 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.8 Rarulula imiraro Rarulula imiraro Iimbonelo zemiraro engenziwa ethemini le.
Ukuh- yamagama yamagama • Umakhi uthloga bonyana abeke amareyi asi-6 weentina zokupheyiva, kube neentina
langanisa ezisebujameni ezisebujameni ezibu-8 kelinye nelinye ireyi. Uzokuthloga iintina ezingaki?
okubuyele- bewuhlathulule bewuhlathulule
• UMarilina unemigodla emi-4 yamaswidi. Umgodla ngamunye uphethe amaswidi asi-6.
lweko iinsombululo zakho iinsombululo zakho
Kunamaswidi amangaki nasele awoke?
kurholela zemiraro, ezifaka zemiraro, ezifaka
ukubuyabuyelela ukubuyabuyelela • Umma ufuna ukubhaga amakhekhe ali-12. Lokha ikhekhe elilodwa lifuna amaqanda ama-
ekubuy-
okunempendulo ufikela okunempendulo ufikela 2, umma kufanele athenge amaqanda amangaki?
abuyeleleni
e-100. e-50. • Lokha umfundi ngamunye afunda iincwadi ezi-3 ngoVelabahlinze, ziincwadi ezingaki
ezingafundwa litlasi labantwana abama-20?
Umhlobo womraro : Ukurhemisa
• Isivande semirorho sinamareyi ali-12 weentjalo. Ireyi ngalinye lineentjalo ezili-7.
Kuneentjalo ezingaki esivandeni?
• Isivande semirorho sinamareyi ali-12 weentjalo. Elinye nelinye ireyi lineentjalo
ezilinganako. Lokha kuneentjalo ezima-48 sezizoke, kuneentjalo ezingaki ereyini
ngalinye?
• Isivande semirorho sineetjalo ezima-48 ezitjalwe emareyini. Kuneentjalo ezili-7 ereyini
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngayinye. Kunamareyi amangaki nasele awoke?
Ukusebenzisa ukubuyelela kabili ukusombulula imiraro
• UJustini uneminyaka ebu-8 ubudala
• Umfowabo omdala unobudala obubuyelwe kabili kunoJustini.
• Uyise unobudala obubuyelelwe kane kunoJustini.
• Ubamkhulu kaJustini mdala okubuyelelwe kabili kunoyise kaJustin.
• Buyini ubudala bomunye nomunye?
• Incwadi kaTjhepi inamakhasi ama-48 ubude. Sele asekhasini lama-26, ingabe sele
afunde ngaphezulu kwengcenye yencwadi?
EGreyidini yesi-3 abafundi balindeleke bonyana babone ukubuyabuyelela kweembalo
zamagama. Abafundi kufanele bakhuthazwe bonyana basebenzise iinomboro
nangeenthombe, kunokobanyana basebenzise ama-apharathasi nofana iinthombe
ngokwabo.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.9 Ukurarulula Ukurarulula NgeThemu le kuthulwa itshwayo lokuhlukanisa. Kuqakathekile bonyana abafundi bazwisise
Ukubuthele- imiraro yamagama imiraro yamagama imiqondo elandelako yokuhlukanisa ngaphambi kobana kusetjenziswe itshwayo:
la nok- ezisebujameni ezisebujameni Imiraro efaka hlangana ukwabelana kanengi imayelana no:
wabelana bewuhlathulule bewuhlathulule
Kwabelana ngokulinganako, begodu
okurholela iinsombululo zakho iinsombululo zakho
ufake ukwabelana ufake ukwabelana • Munye uthola okungangani?
ekuhlu-
kaniseni ngokulingana ngokulingana • Imiraro efaka hlangana ukwabelana kanengi imayelana :
nokubuthelela nokubuthelela Ziinqhema ezingaki ezingenziwa?
ngeenqhema ngeenqema
• Iimbonelo zemiraro engenziwa ngeThemu le.
kweenomboro kweenomboro
ezipheleleko ukufika ezipheleleko ukufika • Lokha kunabafundi abama-44 nabotitjhere aba-3 bafanele baye ekhonsadini, kodwana
e-100 kanye nempendulo e-50 kanye nempendulo iteksi ikhweza abantu abali-11 kwaphela, iteksi ezokubuyela kangaki ukuyothatha
ezingahle zifake iinsalela ezingahle zifake iinsalela abafundi, ngaphambi kobana boke abafundi baphelele ekhonsadini?
• UMongezi upaka izinto zokubala ezima-47 uzibeka ngamareyi ali-9. Kunezinto zokubala
ezingaki ereyini?
• Abantazana aba-35 bafuna ukudlala ibhola yezandla. Ziinqhema ezingaki
ezinabantazana abali-7 ezingabakhona?
• Linganisa maqangi:
• Kuzokuba kunengi nofana kuncani kune-10?
• Kuzokuba kunengi nofana kuncani kunama-20?
• UMarlina uthenga amaswidi ama-44. Uwahlukanisa ngokulinganako emaphaketheni
ama-4 azowathengisa. Kunamaswidi amangaki ngemgodleni?
• UMarlina uthenga amaswidi ama-48. Ufuna ukuwahlukanisa ngemigodla enamaswidi
asithandathu ngemgodleni ngamuny. Uthloga imigodla emingaki?
351
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
352 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.10 Ukurarulula Ukurarulula EGreyidini yesi-2 abafundi bathulwe emafraktjhinini begodu;
Ukwabelana bewuhlathulule bewuhlathulule • Babelana begodu babuthelela izinto ngokulinganako;
okurholela iinsombululo zemiraro iinsombululo zemiraro
• Batjho iingcenye zefraktjhini;
emafrak- ephathekako efaka ephathekako efaka
hlangana ukwabelana hlangana ukwabelana • Babona amafraktjhini ebujameni obuhlukeneko
tjhinini.
ngokulingana erholela ngokulingana erholela • Batlola amagama wamafraktjhini njenge 1 yesithathu, 1 yesihlanu
empendulweni empendulweni • Ukuthola amafraktjhini wokupheleleko; begodu
zamafraktjhini wohlavu zamafraktjhini wohlavu
• Ukuthola amafraktjhini webuthelelo lezinto.
olulodwa nalayo olulodwa nalayo
angenahlavu eyodwa. angenahlavu eyodwa. Ngikuphi okuhlukileko kune Greyidini yesi- 2?
1 1 1 1 1 1 1 1
isib. 2 , 4 , 3 , 5 njll. isib. 2 , 4 , 3 , 5 njll. NgeThemu le, abafundi baragela phambili nokusenza ngamafraktjhini anehlavu elilodwa
afana na: 1 isiquntu , 1 kokuthathu, 1 ikota, 1 kokuhlanu.
Abafundi bathulwa emafraktjhinini anganahlavu elilodwa. Isib. 3 amakota nofana o 2
kokuthathu.
Abafundi akutlhogeki bonyana basebenzise amagama athi anehlavu elilodwa nelithi
anganahlavu elilodwa
Iimbonelo zemiraro engenziwa ngeThemu le.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukwabelana okurholela emafraktjhinini.
Yabela abangani aba-3 iintina zetjhokolethi ezi-8 wenze bona boke bathole iintina
ezilinganako zetjhokolethi begodu kungasali litho.
• Ifraktjhini yebuthelelo
a) Thola ikota e-1 yamaswidi ali-16.
b) Amaswidi abu-8 alifraktjhini liphi lamaswidi ama-24?
c) Ugogo unikela uKiki R12, uKiki ufuna ukonga okuthathu kwemali. ufanele onge malini?
d) Umhlobo lo womraro ufanele ubuzwe ngemva kobana abafundi basombulule imiraro
emine nofana emihlanu “yokwabelana, okurholela emafraktjhinini” babe bazi umhlobo
namagama weengcezu zamafraktjhini.
Ukutlola amafraktjhini
Akuthlogeki bona abafundi batlole amatshwayo wamafraktjhini. Abafundi bafundile bonyana
bangazilebula bunjani iingcenye zamafraktjhini njengo 1 kokuhlanu, 3 yamakota nofana 3
kokusithandathu.
Lokhu kubasiza kokuthoma ngokuzwisisa bonyana amagama wamafraktjhini ahlathulula
bonyana kuneengcezu ezingaki ezilinganako zokupheleleko. Isibonelo isiquntu, kokuthathu,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
amakota njll. Kwesibili ziingcezu ezingaki ezitjhejwako, isib. 2 kokuthathu.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.10 Ukurarulula Ukurarulula Ukujamiselela imiraro yamagama yamafraktjhini.
Ukwabelana bewuhlathulule bewuhlathulule Abafundi bafanele bagwale iimpendulo zabo ukubonisa bonyana bayawuzwisisa umraro.
okurholela iinsombululo zemiraro iinsombululo zemiraro
Lindela bonyana abanye abafundi bangathala ifraktjhini ngendlela okungiyo kodwana
emafrak- ephathekako efaka ephathekako efaka
banganikeli igama ekungilo lengcenye yefraktjhini. Siza abafundi laba bonyana
tjhinini. hlangana ukwabelana hlangana ukwabelana
batjho ingcenye yefraktjhini ngendlela okungiyo (Qala amanothi ahlobana nokubizwa
ngokulingana erholela ngokulingana erholela
kwamafraktjhini angaphasi kobujamo obutjhaphulukileko bokubala)
empendulweni empendulweni
zamafraktjhini wohlavu zamafraktjhini wohlavu Abafundi bafanele batjho iingcezu ezabiweko ngokuzitlola njenge 2 yokuthathu.
olulodwa nalayo olulodwa nalayo
angenahlavu eyodwa. angenahlavu eyodwa.
1 1 1 1 1 1 1 1
isib. 2 , 4 , 3 , 5 njll. isib. 2 , 4 , 3 , 5 njll.
1.11 • Ukukhumbula • Ukukhumbula NgeThemu le abafundi baragela phambili nokurarulula imiraro yemali.
Imali nokubona iinhlavu nokubona iinhlavu Isibonelo:
nemali yephepha nemali yephepha
• Abafundi beGreyidi yesi-3 batlhoga R759 yekampa yetlasi. Babuthelele R250.
yeSewula Afrika yeSewula Afrika
Basatlhoga malini?
• Sombulula imiraro • Sombulula imiraro
• Tlola 325c ngamaranda namasende.
yemali efaka hlangana yemali efaka hlangana
amanani wemali amanani wemali • Ziindlela ezingaki ezihlukileko ongazenza ngazo i R400 usebenzisa imali yamaphepha
netjhentjii ngamaranda netjhentjii ngamaranda kwaphela? Wazi bunjani bonyana unazo zoke iinsombululo?
nofana ngamasende nofana ngamasende. • USiyabonga unehlavu le 50c neenhlamvu ezine za-20c. Amathofi abiza R1, 20.
• Tjhugulula hlangana Uzokuthola itjhentjhi yamalini?
namaranda • Nange itreksudu yesikolo ibiza R150, amatreksudu ama-2 azokubiza malini?
namasende Imiraro yokuthenga nokuthengisa
Isibonelo
• Ugogo ka Pitrosi umnikele iR5. Ngimaphi amaswidi ama-3 angawathenga? Itjhoku
tjhakile ibiza R2,70; amatjhapisi abiza R1,80; umzoka osiri R1,40; amaswidi weperegisi
R1,60; amaminthi R2,20; ithofi libiza R1,20.
• UDamon wathenga iincwadi ezintathu nge R80 incwadi ngayinye. Yimalini itjhentjhi
azoyithola nange aphethe R300?
• Amaphakethe wamaminti ama-5 abiza 44c ngalinye. Umnumzana King utlhoga 88
yamaminthi. Kufanele athenge amaphakethe amangaki? Uzokubhadela malini?
353
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
354 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
IIMBALO EZISEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Sebenzisa amathekhniki Sebenzisa amathekhniki Amathekhniki la azokusetjenziswa kikho kokubili ekusombululeni imiraro nasekubaleni
Amathek- alandelako lokha alandelako lokha okusebujameni obutjhaphulukileko:
iniki nawenza ukubalisisa: nawuwenza ukubalisisa: Ukwakha nokuphula
(iindlela • Ukwakha nokuphula • Ukwakha nokuphula Le ngenye yamathekhniki aqakatheke khulu eSigabeni eSisisekelo. Ukusetjenziswa
zokwenza iinomboro iinomboro kwethekhniki le kuvumela abafundi ukuhlukanisa (ukuphula ) nokubuye bahlanganise
namaqh- • Ukubuyelela kabili • Ukubuyelela kabili iinomboro ukubasiza ukwenza ukubala kubelula. Bazokusebenzisa ithekhniki le neSigabeni
inga) nokuhafula phakathi nokuhafula phakathi eSiphakathi. Kuqakathekile bonyana abafundi basebenzisa ilwazi elaziwako nabaphula
• Amanambalayini • Amanambalayini iinomboro. Isib.
• Ukutjhideza eduze • Ukuphula ngokusebenzisa ubukhulu bedijithi
kwetjhumi • Ukuphula ngokusetjenziswa ukubuyabuyelela kwe-10; begodu
• Ukuphula ngokuya kwenomboro zangakubili (iimpara).
Amanambalayini
Abafundi bazokuragela phambili nokusebenzisa nokwakha amanambalayini okungewabo
ukwezela ukubala. Kunekghonakalo yokobana inambalayini izokusetjenziswa kanengi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ekubaleni kokuhlanganisa nokukhupha.
Ukuhlanganisa nokukhupha
Abafundi bafanele bakhe inambalayini okungeyabo begodu baphule iinomboro
ngeengcenye elawulekako.
Isibonelo:
45 + 27
Inambalayini ifanele ithome ema-45 begodu abafundi bangatlama imeqo emi -2 yangali-10
begodu nomeqo owodwa otjengise uli-7.
Ukubuyabuyelela
Amanambalayini kufanele kuragelwe phambili nokuwasebenzisa ukusekela ukuhlanganisa
okubuyelelako. Ukweqa okulinganako kurekhodwa enambalayini begodu imitjho esekelako
nayo ingarekhodwa.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika NgeThemu le abafundi bazijayeza beba hlanganise umsebenzi owenziwa eGreyidini yesi-2.
Ukuh- ema-999 ema-99 Lokha abafundi:
langanisa • Khupha ukusuka ema- • Khupha ukusuka ema- • Basebenza ngezinto zokubala ezihlukeneko kuphela;
nokukhupha 999 99
• Gwala imifanekiso yanga 1 kwaphela; begodu
• Sebenzisa • Sebenzisa
amathswayo afaneleko amathswayo afaneleko • Bala koke ngaku-1
(+, –, =, ) (+, –, =, ) Lokha nawusebenza ngesamba esingaphezulu kwama-30, kubakhambisa buthaka, begodu
• Ukuphrakhthisa • Ukuphrakhthisa kwandisa amathuba wabo wokwenza amaphutha wokubala.
ukulumbana ukulumbana Lokhu kwenza kuqakatheke kibo ukuthuthukisa amaqhinga asiza khulu. Ukwakha
kwenomboro ukufika kwenomboro ukufika nokuphula iinomboro kuba ngelinye lamaqhinga aqakathekileko abafundi abazo
e-30 e-20 wasebenzisa ngeThemu le.
Iindlela ezingakghonakala ukutjengisa ukubala kokuhlanganisa nokukhupha.
Ukuphula inomboro ibe ziingcenye ezincani ukwenza ukubala kube lula.
Abafundi bangahle baphule inomboro ngeendlela zabo ezilawulekako. Lokhu kutjho
bonyana bazokwenza ngeendlela ezihlukileko.
Ukusebenzisa ilwazi lobukhulu bedijithi ukuphula iinomboro zibe matjhumi nemivo
• Ukuhlanganisa iinomboro zamadijithi amabili ngokuphula iinomboro zombili
43 + 36 =
43 + 36 = (40 + 3) + (30 + 6)
= (40 + 30) + (3 + 6)
= 70 + 9
= 79
• Ukuhlanganisa ngokuphula inomboro yinye
43 + 36 =
43 + (30 + 6)
43 + 30 → 73 + 6 = 79
• Ukuphula ngeeqhema zangalitjhumi
43 + 36 =
43 + (10 + 10 + 10 + 6)
43 + 10 → 53 + 10 → 63 + 10 → 73 + 6 = 79
355
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
356 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Ukukhupha
Ukuh- ema-999 ema-99 • Ukukhupha ngokuphula iinomboro zombili
langanisa • Khupha ukusuka ema- • Khupha ukusuka ema- 87– 56 =
nokukhupha 999 99
87– 56 = (80 + 7) – (50 + 6)
• Sebenzisa • Sebenzisa
amathswayo afaneleko amathswayo afaneleko = (80– 50) + (7– 6)
(+, –, =, ) (+, –, =, ) = 30 + 1
• Ukuphrakhthisa • Ukuphrakhthisa = 31
ukulumbana ukulumbana • Ukukhupha ngokuphula inomboro yinye
kwenomboro ukufika kwenomboro ukufika
87–56 =
e-30 e-20
87– (50 + 6)
87– 50 → 37 – 6 = 1
Lindela bonyana abanye abafundi bangaphula inomboro ngeendlela ezihlukileko ukwenza
ukubala kubelula:
• Ukuphula ngeeqhema zangalitjhumi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
87– 56 =
87– (20 + 20 + 10 + 6)
87– 20 → 67–20 → 47– 10 → 37– 6 → 31
Ukusebenzisa ilwazi elidlulileko njengethekhniki
• Ukusebenzisa ukuqunta phakathi ukuphula inomboro
69 + 12
69 + (6 + 6)
69 + 6 → 75 + 6 = 81
• Ukubala uye phambili nokuya emva
78 – 69 =
Ukubala ngakunye uye phezulu kusuka ema- 69 kuliqhinga elifaneleko ngombana
iinomboro ziseduze enye kwenye.
• Ukubona ukubuyelela kabili okuseduze
34 + 35 hlathulula bonyana kubuyelela kabili ama-34 hlanganisa naku- 1 nofana
ukubuyelela kabili ama-35 ukhupha ku-1.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
34 + 35 + 1
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika Abafundi bangahle barekhode amaqhinga wabo ngokusenzisa inothetjheni yabotjhobi
Ukuh- ema-999 ema-99 ukulandela ukubala kwabo
langanisa • Khupha ukusuka ema- • Khupha ukusuka ema- 34 + (30 + 4) + 1
nokukhupha 999 99 34 + 30 → 64 + 4 → 68 + 1 → 69
• Sebenzisa • Sebenzisa • Ukutjhugulula inomboro ibe sibuyabuyelelo setjhumi bese bakhupha nofana bahlanganise
amathswayo afaneleko amathswayo afaneleko imivo
(+, –, =, ) (+, –, =, )
Ukubala uyephezulu nofana uye phasi eduze kwetjhumi
• Ukuphrakhthisa • Ukuphrakhthisa
ukulumbana ukulumbana 58 + 19 =
kwenomboro ukufika kwenomboro ukufika Lapha abafundi kufanele bonyana bazitjele bona banamathuba wokukhetha amabili.
e-30 e-20 Ukutjhugulula ama-58 nofana i-19 eduze kwesibuyelelo se- 10. Ukuzikhethela kungekwabo.
Isibalo singatlolwa bunjesi: 58 + 19 = 58 + 20 – 1
58 + 20 → 78 – 1 = 77
Abanye abafundi bangahle baphule ama-20 kube ziinqhema ezimbili ze-10 ngokunembako.
Ukuzijayeza amabhondi ukufika ema-20
Amabhondi afika ema-20 kufanele enziwe ngokusebenzisa imihlohlobo yemifanekiso
esekelelako.
Ukuthuthukisa nokuzijayeza amakghono wokuhlanganisa nokukhupha
Abafundi kufanele bazijayeza eminye imihlobo yokuhlanganisa namakghono wokukhupha.
• Hlanganisa nofana ukhuphe inomboro ezinedijithi elilodwa kunanoma ngiziphi iinomboro
ezinamadijithi amabili ngaphandle kokweqela ematjhumini:
Isibonelo:
a) 65 + 4
b) 89 – 3
• Ukuhlanganisa inomboro yedijithi elilodwa esibuyelelweni se-10.
Isibonelo:
a) 70 + 5
b) 90 + 3
• Ukukhupha inomboro yedijithi elilodwa esibuyelelweni se-10.
Isibonelo:
a) 80 – 6
357 b) 50 – 3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
358 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Hlanganisa ukufika • Ukuhlanganisa nofana ukukhupha i-10 kunanoma ngiyiphi inomboro enamadijithi amabili
Ukuh- ema-999 ema-99 Isibonelo:
langanisa • Khupha ukusuka ema- • Khupha ukusuka ema-
nokukhupha 999 99 a) 56 + 10
• Sebenzisa • Sebenzisa
b) 68 + 10
amathswayo afaneleko amathswayo afaneleko
(+, –, =, ) (+, –, =, )
c) 79 – 10
• Ukuphrakhthisa • Ukuphrakhthisa
ukulumbana ukulumbana d) 57 – 10
kwenomboro ukufika kwenomboro ukufika
e-30 e-20 • Ukuhlanganisa nofana ukukhupha okukhamba ngakubili kwembuyeleli ze-10 ngaphandle
kokweqela e-100.
a) 40 + 30
b) 80 – 50
Ukuhlola umphumela wokubalisisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukujaja ngokuzwakalako iinsombululo.
Abafundi bafanele babandulwe ngokujaja okuzwakalako iinsombululo.
Enye yeendlela yokwenza lokho kulinganisa iimpendulo zabo ngaphambili kokubala.
Lokha uhlanganisa iinomboro ezimbili ezitjhideleneko enye kenye isib. 45 na 46, abafundi
bangasebenzisa ukubuyelela kabili njengendlela yokulinganisa iimpendulo zabo.
Ukuhlola iinsombululo
Abafundi bafanele bazi bonyana banga:
• hlola isibalo sokuhlanganisa ngokukhupha.
Isibonelo: nange 36 + 18 = 54; bese 54- 18 = 36
• hlola isibalo sokukhupha ngokuhlanganisa
Isibonelo 84- 48 = 36, bese 36 + 48 = 84
Ukusebenzisa itshwayo lokubala lokuphekguka ukuhlola iinsombululo kungesinye isizathu
sokufundisa ukuhlanganisa nokukhupha ngokuhlangeneko.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela EGreyidini yesi -2 abafundi babuyabuyelele iinomboro kusuka ku- kuya e- nga na ukufika
Ukuh- iinomboro ukusuka iinomboro ukusuka-1 ema- . Bathulwa etshwayweni begodu balisebenzise emitjhweni yeenomboro.
langanisa ku-1 ukufika e-10 ukufika e-10 ngaku 2, Abafundi eGreyidini yesi-3 bafanele baragele phambili nokuzijayeza bebasebenzise ilimi
okubuyele- ngaku 2, 3, 4, 5, 10 5, 3, 4 lokubuyabuyelela eensombululweni eziphathekako, ukubuyelela kabili, kabili, buyabuyelela,
lweko ukufika enanini lama- • Sebenzisa ukubuyabuyelela nga, okunengi kwa, iinqhema zaku, buyelela, ukubuyelela kathathu
okurholela 99 amatshwayo afaneleko ngokunengi.
ekubuy- • Sebenzisa (x, =, ) Ilimi nalo kufanele lisetjenziswe nakwenziwa ukubalisisa okubuyabuyelelako. NgeThemu le
abuyeleleni amatshwayo afaneleko abafundi bazobe bathoma ukubuyabuyelela ngakuthathu.
(x, =, )
Abafundi abangena eGreyidiniyesi-3 bafanele bakghone ukujamiselela ukuhlanganisa
okubuyelelweko basebenzisa itshwayo lokubuyabuyelela. Abafundi bakghona ukuhlathulula
ukubuyabuyelela ngendlela ezihlukileko. Bazwisisa bonyana iinqhema ezi- 3 zezinto ezisi-
6 nofana iinqhema ezi-3 zika-6 zingatlolwa njenge 6 + 6 + 6. Kunokuzwisisa bonyana
ukubuyabuyelela uku-3 kasi -6 kungatlolwa njenge
Ilwazi leli liragela phambili nokuthuthukiswa eGreyidini yesi-3. Abafundi bazokuragela
phambili ukusebenzisa ama-apharathasi aphathekako, ukurhemisa nenambalayini
ukuzwisisa nokujamiselela ukubuyabuyelela.
Kusuka eGreyidini yesi - 3 abafundi kufanele balemuka bonyana ukubuyabuyelela
kungenziwa nanyana ngayiphi indlela.
Isibonelo:
Abafundi bafanele bakghone ukuzwisisa begodu batlole okulandelako:
3 × 10 = 10 × 3 =
30 = 10 × 30 = 3 ×
Iintatimende ezingehla kufanele zisekelwe ngokusebenzisa imifanekiso evamileko evumela
abafundi bonyana babone bona u 3 × 10 ne 10 × 3 no kunikela ipendulo efanako.
Isibonelo:
and
ne
359
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
360 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Ekupheleni kweThemu abafundi bafanele bathome ukuzwisisa bonyana ukubuyabuyelela
Ukuh- iinomboro ukusuka iinomboro ukusuka-1 kungenziwa nanyana ngayiphi indlela. Umqondo lo ufanele uragele phambili nokujayezwa
langanisa ku-1 ukufika e-10 ukufika e-10 ngaku 2, unyaka woke.
okubuyele- ngaku 2, 3, 4, 5, 10 5, 3, 4 Abafundi bangasebenzisa itjhadinaneko ukurekhoda amaphuzu wokubuyabuyelela.
lweko ukufika enanini lama- • Sebenzisa Isibonelo
okurholela 99 amatshwayo afaneleko
ekubuy- • Sebenzisa (x, =, ) okungeniswako
Input umphumela
Output
abuyeleleni amatshwayo afaneleko 1 umthetho
Rule
(x, =, )
3
5
7
× !
9
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro Itshwayo lokkuhlukanisa lithulwa eGreyidini yesi-3. Eminyakeni emibili umqondo
Ukuhlu- ukufika ema-99 ngaku- ukufika ema-50 ngaku- wokwabelana nokubithelela bayijayezwa kwanjesi sekusikhathi sokuhlanganisa/
kanisa 2, 2, sokuhlobanisa imiqondo emibili le. Itshwayo lokuhlukanisa lingaziswa/lingathulwa
abafundi nabenza imiraro yamagama. Ukwaziswa/ukwethulwa kwetshwayo kungasekelwa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Sebenzisa • Sebenzisa
ngemifanekiso engenzasi elandelako. Kuqakathekile ukusebenzisa imifanekiso
amatshwayo afaneleko amatshwayo afaneleko ejayelekileko.
(÷,=, ) (÷,=, )
Isibonelo:
za 3 kukunikela 4 12 ubuthelelwe iinqhema ezi- 4 kukunikela 3
12 groupediinqhema
12 ubuthelelwe into 3s give 4 groups 12 grouped into 4s gives 3 groups
yeenqhema yeenqhema
3 × 4 = 12
4
12 ahlukaniselwa
12 shared aba-3 kunikela
between 3 gives 4oku-4
each
12 shared between 4 gives 3 each ngamunye
12 ahlukaniselwa 4 kukunikela 3 ngamunye
! × !
× 3 ==12 !"
! × ! = !"
4 x 3 = 12
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
i-12
lihlukaniselwa aba-4 kunikela oku-3 ngamunye
12 ÷ 3 = 4: Kutjho bonyana 12 abuthelelwe ngaku- 3 kukunikela iinqhema ezi-4 begodu
i-12 nalabiwa hlangana naba- 3 kukunikela iinqhema ezi-4 ngasinye.
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
YOKU-1
ama -24)
1.16 Umnqopho wenomboro: Umnqopho wenomboro: Amaqhinga wokubala, umqondo wenomboro, ilwazi nokwazi amaphuzu wenomboro
Iimbalo irherho 999 irherho 200 athuthukiswe ngokusombulula umraro nokubalisisa. Lokhu kujayezwa ngesikhathi
zehloko • Hlela isede enikelweko • Hlela isede sezembalo zehloko. Lokho kusiza abafundi bonyana bazijayeze zona bebakghone
yeenomboro ezikhethiweko onikelweyona ukuzisebenzisa ngobulula nababalako begodu basomulula imiraro esebujameni.
• Madanisa iinomboro kufika yeenomboro NgeThemu leli abafundi baragela phambili nekghono lokusebenza batjhaphulukile
ema-999 begodu utjho ezikhethiweko ngeenomboro. Amaqhinga wokubala ngehloko lawe abafundi abawathuthukisako
bonyana ngiyiphi enengi • Madanisa iinomboro azabasiza ngokubala okutloliweko begodu kuzokusiza abafundi lokha nabalinganisa.
nofana encani nga-1, 2, 3, ukufika ema-200
4, 5 ne-10. begodu utjho bonyana Iimbonelo zemibuzo engabuzwa:
Ukukhumbula masinyana: ngiyiphi enengi nofana Umqondo wenomboro:
encani nga-1, 2, 3, 4, 5 Amagama weenomboro namatshwayo
• Amaphuzu wokuhlanganisa ne-10
nawokukhupha kufika Phakamisa ikarada nofana tlola phasi igama lenomboro. Khetha umfundi bonyana
ema- 20 Ukukhumbula atlole inumerali emetjhako.
masinyana:
• Hlanganisa nofana Ukunengi nofana okuncani
ukhuphe imbuyeleli ze-10 • Ukukhumbula
kusuka e-0 kufika e-100 amaphuzu Khuyini
wokuhlanganisa • Okuncani ema-200 ngaku-1
• Amaphuzu nowokukhupha kufika
wokubuyabuyelela ema- 20 • Okunengi e-199 ngalu-1
nowokuhlukanisa we : • Okunengi e-102 ngaku-2
• Hlanganisa nofana
• thebula laku-2 kufika ku ukhuphe imbuyeleli • Okuncani e-105 ngaku-2
• thebula le-10 kufika e- ze-10 kusuka e-0 kufika • Okunengi ema-77 ngaku-3
Amaqhinga wokubala e-100
• Okuncani ema-51 ngaku-3
Ukusebenzisa amaqhinga Amaqhinga wembalo
wokubala alandelako : zehloko • Okunengi ema-68 ngaku-4
• Beka inomboro ekulu Ukusebenzisa amaqhinga • Okuncani e-167 ngaku-4
maqangi ukwenzela wokubala: • Okunengi e-129 ngaku-5
ukubala uye phambili • Beka inomboro ekulu • Okuncani e-185 ngaku-5
nofana ubale uye emuva maqangi ukuwenzela
• Inambalayini. ukubala uye phambili • Okunengi ema-90 nge-10
• Ukubuyelela kabili nofana ubale uye • Okuncani e-160 nge-10
nokuhafulaphakathi emuva.
Ngiliphi iledere lesi-5 lama -alfabethi?
• Ukwakha nokuphula • Inambalayini.
Ngiyiphi inyanga ye-9 yonyaka?
• Ukusebenzisa ubudlelwano • Ukubuyelela kabili
nokuhafulaphakathi Ukuhlela nokumadanisa
phakathi kokuhlanganisa
nokukhupha • Ukwakha nokuphula Ngikuphi okunengi: 21 nofana i-171?
• Ukusebenzisa ubudlelwano • Ukusebenzisa Nginikela inomboro ehlangana i-154 ne -159.
361 phakathi kokubuyabuyelela ubudlelwano phakathi
nokuhlukanisa kokuhlanganisa
nokukhupha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
362 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
ama -24)
1.16 Umnqopho wenomboro: Umnqopho wenomboro: Ukukhumbula ngokurhabako
Iimbalo irherho 999 irherho 200 Amaphuzu wokuhlanganisa nokukhupha:
zehloko • Hlela isede enikelweko • Hlela isede • Ukwazi ngenhloko koke ukuhlanganisa nokukhupha kokulumbana kweenomboro
yeenomboro ezikhethiweko onikelweyona
ukufika e-20
• Madanisa iinomboro kufika yeenomboro
ema-999 begodu utjho ezikhethiweko Isibonelo
bonyana ngiyiphi enengi • Madanisa iinomboro a) __________+ = 20
nofana encani nga-1, 2, 3, ukufika ema-200 b) __________+ = 16
4, 5 ne-10. begodu utjho bonyana Hlanganisa begodu ukhuphe amaphuzu wazozoke iinomboro ukufika nokufaka
Ukukhumbula masinyana: ngiyiphi enengi nofana
hlangana nama-20
encani nga-1, 2, 3, 4, 5
• Amaphuzu wokuhlanganisa ne-10 Iimbonelo
nawokukhupha kufika
ema- 20 Ukukhumbula a) 1 + 11 = 12 b) 18 – 4 = 14
masinyana:
• Hlanganisa nofana c) 11 + 1 = 12 d) 18 – 14 = 4
ukhuphe imbuyeleli ze-10 • Ukukhumbula
kusuka e-0 kufika e-100 amaphuzu e) 2 + 10 = 12 f) 18 – 5 = 13
wokuhlanganisa g) 10 + 2 = 12 h) 18 – 13 = 5
• Amaphuzu nowokukhupha kufika
ISIGABA ESISISEKELO AMAGREYIDI 1-3
wokubuyabuyelela ema- 20 i) 3 + 9 = 12 j) 18 – 6 = 12
nowokuhlukanisa we :
• Hlanganisa nofana k) 9 + 3 = 12 l) 18 – 12 = 6
• thebula laku-2 kufika ku ukhuphe imbuyeleli Ukukhumbula ngokurhabako ukuhlanganisa okubuyelela kabili ukufika ema-. Lokhu
• thebula le-10 kufika e- ze-10 kusuka e-0 kufika kufanelekufake hlangana amaphuzu akhambelanako wokukhupha.
Amaqhinga wokubala e-100
Iimbonelo:
Ukusebenzisa amaqhinga Amaqhinga wembalo
wokubala alandelako : zehloko a) 1+1=2 b) 6 + 6 = 12
• Beka inomboro ekulu Ukusebenzisa amaqhinga c) 2+2=4 d) 7 + 7 = 14
maqangi ukwenzela wokubala:
ukubala uye phambili e) 3+3=6 f) 8 + 8 = 16
• Beka inomboro ekulu
nofana ubale uye emuva maqangi ukuwenzela g) 4+4=8 h) 9 + 9 = 18
• Inambalayini. ukubala uye phambili i) 5 + 5 = 10 j) 10 + 10 = 20
• Ukubuyelela kabili nofana ubale uye
emuva. Iimbonelo:
nokuhafulaphakathi
• Inambalayini. Ngitjengisa inomboro okufanele uyihlanganise no.... ukukunikela inani lama-(
• Ukwakha nokuphula
• Ukubuyelela kabili ngokutlola phasi nofana ukusebenzisa ubukhulu bedijithi nofana amaFlardi karada)
• Ukusebenzisa ubudlelwano
nokuhafulaphakathi a) 8
phakathi kokuhlanganisa
nokukhupha • Ukwakha nokuphula b) 2
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukusebenzisa ubudlelwano • Ukusebenzisa c) 9
phakathi kokubuyabuyelela ubudlelwano phakathi d) 15
nokuhlukanisa kokuhlanganisa e) 3
nokukhupha
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
YOKU-1
ama -24)
1.16 Umnqopho wenomboro: Umnqopho wenomboro: Iimbonelo:
Iimbalo irherho 999 irherho 200
Ngitjengise inomboro ezokusala lokha u_________akhutjhwa ema-20 ( ngokutlola
zehloko • Hlela isede enikelweko • Hlela isede phasi nofana ukusebenzisa ubukhulu bedijithi nofana amaFlardi karada )
yeenomboro ezikhethiweko onikelweyona
• Madanisa iinomboro kufika yeenomboro a) 5
ema-999 begodu utjho ezikhethiweko
b) 18
bonyana ngiyiphi enengi • Madanisa iinomboro
nofana encani nga-1, 2, 3, ukufika ema-200 c) 0
4, 5 ne-10. begodu utjho bonyana
ngiyiphi enengi nofana d) 14
Ukukhumbula masinyana:
encani nga-1, 2, 3, 4, 5 e) 7
• Amaphuzu wokuhlanganisa ne-10
nawokukhupha kufika
Ukukhumbula Hlanganisa nofana ukhuphe imbuyabuyeleli ze-10 kusuka e-100
ema- 20
masinyana: Iimbonelo:
• Hlanganisa nofana
ukhuphe imbuyeleli ze-10 • Ukukhumbula
amaphuzu a) Yitjho bonyana magadango amangaki okufanele athathwe enambalayinini
kusuka e-0 kufika e-100
wokuhlanganisa ukusuka ema-30 ukuya e-100 nofana kusuka e-100 ukuya ema-50.
• Amaphuzu nowokukhupha kufika
wokubuyabuyelela b) Thola amakarada amabili enza i-100
ema- 20
nowokuhlukanisa we :
• Hlanganisa nofana c) Faka iinomboro ngemabhokhsini zenze i-100:
• thebula laku-2 kufika ku ukhuphe imbuyeleli
• thebula le-10 kufika e- + 70 = 100
ze-10 kusuka e-0 kufika
Amaqhinga wokubala e-100 20 + = 100
Ukusebenzisa amaqhinga Amaqhinga wembalo
100 – = 90
wokubala alandelako : zehloko
• Beka inomboro ekulu Ukusebenzisa amaqhinga 100 – 40 =
maqangi ukwenzela wokubala:
Amaqhinga wokubalisisa:
ukubala uye phambili • Beka inomboro ekulu
nofana ubale uye emuva maqangi ukuwenzela Sebenzisa amaqhinga wokubala ukuhlanganisa nokukhupha ngokuphumelela.
• Inambalayini. ukubala uye phambili
Hlanganisa iinomboro ezimbalwa ngokusebenzisa amaqhinga afana nokuthi:
• Ukubuyelela kabili nofana ubale uye
nokuhafulaphakathi emuva. • Funa iinomboro ezimbili ezenza i-10 begodu usebenzise zona kokuthoma
• Ukwakha nokuphula • Inambalayini.
2+7+8
• Ukusebenzisa ubudlelwano • Ukubuyelela kabili
nokuhafulaphakathi 2 + 8 kwenza 10 bese uhlanganise ne- 7
phakathi kokuhlanganisa
nokukhupha • Ukwakha nokuphula • Beka inomboro ekulu kokuthoma ukwenzela bona ukwazi ukubala uye phambili
• Ukusebenzisa ubudlelwano • Ukusebenzisa nofana ubale uye emva.
363 phakathi kokubuyabuyelela ubudlelwano phakathi
nokuhlukanisa kokuhlanganisa 5 + 15
nokukhupha Ukutjho godu umutjho wenomboro: 15 + 5 nokubala uye phambili ukufika ema- 20
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
364 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
ama -24)
1.16 Umnqopho wenomboro: Umnqopho wenomboro: • Tjhugulula inomboro ibe li-10 bese ukhuphe nofana uhlanganise na-1
Iimbalo irherho 999 irherho 200 Isibonelo:
zehloko • Hlela isede enikelweko • Hlela isede 8 + 9 = 17 bese uhlathulule bonyana umuntu angenza 8 + 9 = 8 + 10 – 1
yeenomboro ezikhethiweko onikelweyona
yeenomboro 6 + 11 = 17 uhlathulule bonyana umuntu angenza 6 + 10 + 1
• Madanisa iinomboro kufika
ema-999 begodu utjho ezikhethiweko 17 – 9 = 8 uhlathulule bonyana umuntu angenza 17 – 10 + 1
bonyana ngiyiphi enengi • Madanisa iinomboro • Ukuphula inomboro ibe ziingcenye bese uyahlanganisa
nofana encani nga-1, 2, 3, ukufika ema-200
4, 5 ne-10. begodu utjho bonyana Ukwakha nokuphula iinomboro
Ukukhumbula masinyana: ngiyiphi enengi nofana Ukuragela phambili nokuphula iinomboro zibe ziingcezu ezincani
encani nga-1, 2, 3, 4, 5 8 + 12 = 8+ (10+2)
• Amaphuzu wokuhlanganisa ne-10
nawokukhupha kufika
ema- 20 Ukukhumbula = 8 + 2 + 10
masinyana:
• Hlanganisa nofana
• Ukukhumbula = 10 + 10
ukhuphe imbuyeleli ze-10
kusuka e-0 kufika e-100 amaphuzu
wokuhlanganisa = 20
• Amaphuzu nowokukhupha kufika
ISIGABA ESISISEKELO AMAGREYIDI 1-3
wokubuyabuyelela ema- 20 • Ukusebenzisa ukubuyelela kabili njengeqhinga lokubala ngehloko
nowokuhlukanisa we : Ukubona ukubuyelela kabili okuseduze
• Hlanganisa nofana
• thebula laku-2 kufika ku ukhuphe imbuyeleli Isibonelo:
• thebula le-10 kufika e- ze-10 kusuka e-0 kufika 5 + 6 = 11 hlathulula bonyana kukubuyelela kabili uku- uhlanganise naku- nofana
Amaqhinga wokubala e-100
kukubuyelela kabili isi- 6 ukhuphe ku-
Ukusebenzisa amaqhinga Amaqhinga wembalo
zehloko Ukubona bonyana lokha iinomboro ezimbili zitjhidelene enye kenye ngesayizi lokho
wokubala alandelako :
kwenza kube lula ukufunyana umehluko ngokubala uye phambili ungabali uye emuva.
• Beka inomboro ekulu Ukusebenzisa amaqhinga
maqangi ukwenzela wokubala: 15 - 11 = 4 begodu uhlathulule bonyana ukubala uye phambili kusuka e- ukuya
ukubala uye phambili • Beka inomboro ekulu kukunikela
nofana ubale uye emuva maqangi ukuwenzela Ezinye iimbalo zehloko zingenziwa ngaphandle kwama-apharathasi, kodwana
• Inambalayini. ukubala uye phambili kuyasiza ukwenza iimbalo zehloko ngokusebenzisa ama-apharathasi.
• Ukubuyelela kabili nofana ubale uye Ama-apharathasi aphakamisiweko
nokuhafulaphakathi emuva.
• Inambalayini (ehlelekileko begodu engenalitho)
• Ukwakha nokuphula • Inambalayini.
• Igridi yeenomboro
• Ukusebenzisa ubudlelwano • Ukubuyelela kabili
nokuhafulaphakathi • Amakarada wobukhulu bedijithi (amaflardi karada)
phakathi kokuhlanganisa
nokukhupha • Ukwakha nokuphula • Umncamo wokubala.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukusebenzisa ubudlelwano • Ukusebenzisa
phakathi kokubuyabuyelela ubudlelwano phakathi
nokuhlukanisa kokuhlanganisa
nokukhupha
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
YOKU-1
ama -24)
1.17 • Sebenzisa begodu • Sebenzisa begodu utjho EGreyidini yesi-2 abafundi bathulwa emafraktjhinini. Ba:
Amafrak- utjho amafraktjhini amafraktjhini ebujameni • belana begodu babuthelela izinto ngokulinganako;
tjhini ebujameni obujayelekileko obujayelekileko
• tjho iingcezu zamafraktjhini ebujameni obunehlavu elilodwa;
afaka hlangana afaka hlangana
amahafu, iinkotara, amahafu, iinkotara, • bona amafraktjhini ebujameni obuhlukeneko;
kobunani, kobuthathu, kobunane, kobuthathu, • tlola amagama wefraktjhini njenge 1 yokuthathu, 1 yokuhlanu;
kwesithandathu, kwesithandathu, • thola ifraktjhini wezinto ezipheleleko ; begodu
kwesihlanu kwesihlanu.
• thola amafraktjhini wezinto ezibuthelelweko
• Ukukhumbula amafraktjhini • Ukukhumbula
NgeThemu le abafundi bathulwa emafraktjhinini anganahlavu elilodwa, isib. Amakotara
asebujameni bedayagramu amafraktjhini
ama -3 nofana ku-2 kokuthathu. Baragela phambili ngokusebenzisa ngamafraktjhini
• Ukuthoma ukukhumbula asebujameni
anehlavu elilodwa. Basenza godu ngokobunane nokwesithandathu.
bonyana amahafu bedayagramu
Iimbonelo zemibuzo:
amabili nofana ubuthathu • Ukuthoma
obuthathu benza kunye ukukhumbula bonyana Ubujamo ngabunye buhlukaniswe izingcezu/iingcenye ezingaki ezilinganako?
okupheleleko, ingcenye amahafu amabili Ngiyiphi ifraktjhini/ingcenye yobujamo ngabunye ehlikihliweko
yinye yehafu neenkotara nofana ubuthathu Ngiyiphi ifraktjhini/ ingcenye yobujamo ngabunye engakahlikihlwa?
ezimbili ziyalingana obuthathu benza
• Tlola amafraktjhini njenge, kunye okupheleleko, A.
1- yehafu, 2-kokuthathu ingcenye yinye yehafu
neenkotara ezimbili
ziyalingana
B
C
D
Abafundi bafanele banikelwe ithuba lokufaka umbala/lokuhlikihla ubujamo bona
ngokwabo
365
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
366 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
ama -24)
1.17 • Sebenzisa begodu • Sebenzisa begodu utjho Isibonelo:
Amafrak- utjho amafraktjhini amafraktjhini ebujameni Hlikihla oku-2 kokuthathu bobujamo lobu
tjhini ebujameni obujayelekileko obujayelekileko
A.
afaka hlangana afaka hlangana
amahafu, iinkotara, amahafu, iinkotara,
kobunani, kobuthathu, kobunane, kobuthathu,
kwesithandathu, kwesithandathu,
kwesihlanu kwesihlanu.
Hlikihla amakotara ama-2 wobujamo lobu
• Ukukhumbula amafraktjhini • Ukukhumbula
B
asebujameni bedayagramu amafraktjhini
• Ukuthoma ukukhumbula asebujameni
bonyana amahafu bedayagramu
amabili nofana ubuthathu • Ukuthoma
obuthathu benza kunye ukukhumbula bonyana Hlikihla ku-4 kokuhlanu bobujamo lobu
okupheleleko, ingcenye amahafu amabili C
yinye yehafu neenkotara nofana ubuthathu
ezimbili ziyalingana obuthathu benza
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Tlola amafraktjhini njenge, kunye okupheleleko,
1- yehafu, 2-kokuthathu ingcenye yinye yehafu
neenkotara ezimbili Hlikihla okusi-6 kokubunane bobujamo lobu
ziyalingana
D
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YESI-3 ITHEMU YOKU-1
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.1 Kopulula, ngezelela Kopulula, ngezelela EGreyidini yesi-3 abafundi bangasebenza ngamaphetheni lapho:
Amapheth- begodu uhlathulule begodu uhlathulule. • ilunga/ ama-elemende abuyelelwa khona ngendlela efanako;
eni weJi- Kopulula, ngezelela Kopulula, ngezelela • isayizi yobujamo itjhuguluka ngeendlela ezinikela ibonelo phambili; begodu
yomethri. begodu uhlathulule begodu uhlathulule • inani lobujamo nofana lezinto litkjhuguluka ngendlela enikela ibonelo phambili.
ngawakho amagama ngamagama
Amaphetheni angenziwa ngokusebenzisa ubujamo obubodwa kodwana umbala wobujamo
• amaphetheni alula • amaphetheni alula lobo utjhuguluke njalo njalo/ ngendlela ejayelekileko isib.
enziwe ngezinto enziwe ngezinto
eziphathekako eziphathekako
• amaphetheni alula • amaphetheni alula
Amaphetheni angenziwa ngokusebenzisa ubujamo nofana into eyodwa kodwana indawo
enziwe ngokugwala enziwe ngokugwala
yobujamo nofana into leyo itjhuguluke njalo njalo/ ngendlela ejayelekileko
imida, ubujamo nofana imida, ubujamo nofana
izinto. izinto. Isibonelo:
Ukuzakhela Irherho lamaphetheni: a)
amaphetheni wakho. Amaphetheni alula
Ukuzakhela amaphetheni lapho ubujamo, nofana
wakho weJiyomethri iinqhema zobujamo
• ngezinto zibuyelelwe ngendlela
efana poro. b)
eziphathekako
• ngokugwala
imida,ubujamo nofana Ukuzakhela
izinto amaphetheni wakho.
Amaphetheni • Ukuzakhela Amanye amaphetheni aneenqhema ezifananko zobujamo nofana izinto ezibuyelelweko,
asizungelezileko amaphetheni lapho ubukhulu bobujamo esiqhemenei ngasinye butjhuguluka ngendlela ejayelekileko,
Ukubona , ukuhlathulula weJiyomethri ngendlela enikela ibonelo phambili isib. Ubukhulu bobujamo buba bukhudlwana nofana
ngamagama • ngezinto buncazana.
nokukopulula eziphathekako Isibonelo: Ubukhulu bobujamo bubabukhudlwana
amaphetheni • ngokugwala
weJiyomethri imida,ubujamo nofana
• eemvelweni izinto.
• ebuphilweni
Isibonelo: Ubukhulu bobujamo buba buncazana
bangamalanga
banamhlanje
367 • elifeni lamasiko wethu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
368 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.1 Kopulula, ngezelela Kopulula, ngezelela Amaphetheni angenziwa ngokuthi kwenziwe iinqhema ezifanako, lapho isiqhema ngasinye Isifundo esi-1
Amapheth- begodu uhlathulule begodu uhlathulule. sinomhlobo owodwa kodwana indawo yezinto esiqhemeni iyatjhuguluka. Iinqhema
eni weJi- Kopulula, ngezelela Kopulula, ngezelela ezifanako ziyabuyelelwa.
yomethri. begodu uhlathulule begodu uhlathulule Isibonelo:
ngawakho amagama ngamagama
• amaphetheni alula • amaphetheni alula
enziwe ngezinto enziwe ngezinto
eziphathekako eziphathekako Amanye amaphetheni enziwe ngobujamo bomhlobo owodwa, kodwana isibonelo sobujamo
• amaphetheni alula • amaphetheni alula ngabuye Siyanda nofana siyehla ngobukhulu.
enziwe ngokugwala enziwe ngokugwala Isibonelo:
imida, ubujamo nofana imida, ubujamo nofana
izinto. izinto.
Ukuzakhela Irherho lamaphetheni:
amaphetheni wakho. Amaphetheni alula
Ukuzakhela amaphetheni lapho ubujamo, nofana Amanye amaphetheni enziwe ngeenqhema lapho kwenzeka khona ubujamo obufanako
wakho weJiyomethri iinqhema zobujamo bezintokodwana inani lomhlobo ngamunye wobujamo nofana izinto liyakhula nofana
• ngezinto zibuyelelwe ngendlela linciphe ngendlela ejayelekileko.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
eziphathekako efana poro. Isibonelo:
• ngokugwala
imida,ubujamo nofana Ukuzakhela
izinto amaphetheni wakho.
Amaphetheni • Ukuzakhela
asizungelezileko amaphetheni
Ukubona , ukuhlathulula weJiyomethri
ngamagama • ngezinto
nokukopulula eziphathekako • Ukukopa iphetheni kusiza abafundi bonyana babone ilojikhi yokuthi amaphetehni enziwe
amaphetheni • ngokugwala bunjani.
weJiyomethri imida,ubujamo nofana • Ukungezelela amaphetheni kusiza abafundi ukuhlola bonyana bayizwisise kuhle ilojikhi
• eemvelweni izinto. yephetheni.
• ebuphilweni • Ukuhlathulula amaphetheni kusiza abafundi bonyana bathuthukise ilimi namakghono
bangamalanga wabo wokukhuluma. Begodu kukusiza bonyana ubone bonyana abafundi bayihlathulule
banamhlanje bunjani iphetheni. Kuba lula bonyana abafundi bakhulume ngephetheni ngemva
• elifeni lamasiko wethu kokobana bayenzile.
Ngalesi sikhathi abafundi kufanele bakwazi ukuhlathulula amaphetheni ngaphandle
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
kokusebenzisa iinsiza zemibuzo ekhokhelako. Ragela phambili ngomnqopho
wokuthuthukisa ilimi abalitlhogako bonyana bahlathulule ngalo amaphetheni.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
CAPS
ama -24)
2.2 Kopulula, ngezelela Kopulula, ngezelela Ukulandelana kweenomboro kungahlanganiswa begodu kusekele ukubala. Lokha
Amaphe- begodu uhlathulule begodu uhlathulule amakghono wabafundi wokubala atjhuguluka begodu athuthuka, nemihlobo yokulandela
theni Kopulula, ngezelela Kopulula, ngezelela kweenomboro abafundi abasebenza ngazo kungathuthuka.
Weenom- begodu uhlathulule begodu uhlathulule Ukulandelana kufanele kubonise ukubala uye phambili nasemuva ngaku:
ukulandelana ukulandelana • ngabo ku-1 kusuka kunanyana ngiyiphi inomboro phakathi kwe- 0 nama- 200
boro
kweenomboro okulula kweenomboro okulula
ukufika okungasenani e- ukufika okungasenani • ngali- 10 kusuka kunanyana ngikuphi ukubuyabuyelela kwe- 10 phakathi kwe- 0 nama- 200
1 000. e-100. • ngaku 5 kusuka kunanyana ngikuphi ukubuyabuyelela kwaku- 5 phakathi kwe- 0 nama- 200.
• Ukulandelana kufanele • Ngaku- 2 kusuka kunanyana ngikuphi ukubuyabuyelela kwaka ku- 2 phakathi kwe- 0 nama-
Ukuzakhela kubonise ukubala uye
nokuhlathulula 200
phambili nemuva nga: • Ngaku- 3 kusuka kunanyana ngikuphi ukubuyabuyelela kwaka- 3 phakathi kwe- 0 nama- 200
amaphetheni wakho
-- Ku-1 ukusuka
Ukuzakhela amaphetheni kwenye nenye • Ngaku- 4 kusuka kunanyana ngikuphi ukubuyabuyelela kwa kaku- 4 phakathi kwe- 0 nama-
wakho weenomboro. inomboro hlangana 200
ne-0 ne-1000. • Ngali-100 kusuka kunanyana ngikuphi ukubuyabuyelela kwe-100 kufika okungasenani ema-
-- Li-10 ukusuka 500.
kesinye nesinye Abafundi bangakhomba iinomboro lokha nababalako. Kyasiza ukunikela abafundi
isibuyabuyelelo se- iinomboro ezilandelanako eenjamiselelweni ezihlukahlukeneko
10 hlangana ne-0 Isibonelo:
ne-1000.
• Ukulandelana kweenomboro okutloliweko
-- Ku-5 ukusuka
kesinye nesinye • Amanambalayini
isibuyabuyelelo saka -- Lapho kutjengiswa khona inomboro ebaliweko kuphela.
ku-5 hlangana ne-0 -- Iingcenye zamanambalayini isib.
ne-1000.
• Amagridi weenomboro
-- Ku-2 ukusuka
kesinye nesinye • Iinketani zeenomboro
isibuyabuyelelo saka Abafundi bangavala, banga faka umbala, nofana bazungulezele iinomboro njengombana
ku-2 hlangana ne -0 babala emanambalayinini nasemagridini weenomboro.
ne-1000. Abafundi bangazalisa iinomboro ezingekho emanambalayini, nemagridini weenomboro,
-- Ku-3 ukusuka emitjhweni yeenombo etlolweko, begodu neenketanini zeenomboro.
kesinye nesinye
Isibonelo
isibuyabuyelelo saka
ku-3 hlangana ne-0
110
+
10
+
10
+
10
120
130
ne-1000
-- Ku-4 ukusuka
kesinye nesinye
+
10
isibuyabuyelelo saka
+
10
+
10
+
10
ku-4 hlangana ne-0
ne-1000
369 -- Ma-20, 25, 50,
100 okungasenani
ukufika e-1000.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
370 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
2.2 Kopulula, ngezelela Kopulula, ngezelela Njengombana ukulandela kweenomboro kungasekela ukubala, ngokunjalo abafundi Iimfundo ezi-3
Amaphe- begodu uhlathulule begodu uhlathulule bangabala ngeenqhema, izinto nofana iinthombe, begodu batlole iinomboro emathebuleni
theni Kopulula, ngezelela Kopulula, ngezelela nematjhadininaneko njengendlela yokuthuthukisa nokusekela ukubuyabuyelela.
Weenom- begodu uhlathulule begodu uhlathulule Ethemini yoku- 1 umnqopho usekubaleni ngaku 2 , 5, nanga li 10 isib.
ukulandelana ukulandelana
boro Bala ngaku -5
kweenomboro okulula kweenomboro okulula
ukufika okungasenani e- ukufika okungasenani
e-100. Iinhlavu za 1 2 3 4 5 6 7 8 9
1 000.
• Ukulandelana kufanele Isamba semali R5 R10 R15 R20 R25 R30 R35 R40 R45
Ukuzakhela kubonise ukubala uye
nokuhlathulula phambili nemuva nga:
amaphetheni wakho
-- Ku-1 ukusuka okungeniswako
Input Output
okukhutjhwako
Ukuzakhela amaphetheni kwenye nenye
wakho weenomboro. inomboro hlangana 1 umthetho
Rule 5
ne-0 ne-1000. 2
-- Li-10 ukusuka
3 15
kesinye nesinye
isibuyabuyelelo se- 4
× !
10 hlangana ne-0 5 25
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ne-1000.
-- Ku-5 ukusuka Ekupheleni kweThemu le abafundi basebenza ngokubala ngokulandelana ukuya nokusuka
kesinye nesinye e - 100.
isibuyabuyelelo saka
ku-5 hlangana ne-0
ne-1000.
-- Ku-2 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-2 hlangana ne -0
ne-1000.
-- Ku-3 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-3 hlangana ne-0
ne-1000
-- Ku-4 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-4 hlangana ne-0
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ne-1000
-- Ma-20, 25, 50,
100 okungasenani
ukufika e-1000.
IGREYIDI YESI-3 ITHEMU YOKU-1
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.3 Irherho lamajamo Irherho lamajamo Ngikuphi okuhlukileko eGreyidini yesi-2?
Amajamo • iindulungu • iindulungu Egreyidini yesi-3 abafundi banzizisa umsebenzi owenziwe kubusobubili 2-D eGreyidini
abusobubili • aboncantathu • aboncantathu yesi- 2, kodwana banganqophi emasayizini nofana embaleni lokha kusetjenziswa
2-D ngamabumbeko.
• iinkwere • iinkwere
Lokhu kuvumela abafundi bonyana babe nesikhathi esaneleko ukunqophana nomsebenzi
• aboncande • aboncande omutjha wezinto ezibuso buthathu 3-D, ubujamo, ukujayeza umsebenzi nokubukela kanye
Ubujamo Ubujamo nesimethri.
bamabumbeko bamabumbeko Umsebenzi omunengi wamabumbeko eGreyidi yesi-3 wenziwa ngokuphathekako ngezinto
Hlathulula, uhlele begodu Hlathulula, uhlele begodu eziphathekako. Woke umsebenzi kufanele undzindziswe ngemisetjenzana etlolwako.
umadanise amajamo umadanise amajamo Ukukhumbula nukutjho amagama weendulungu,aboncantathu,iinkwere naboncande
abusobubili 2-D ngokuya abusobubili 2-D ngokuya Abafundi kufanele basebenze ngeendulungu neenkwere zamasayizi ahlukeneko begodu
nge: nge: nangaboncantathu bobujamo obuhlukahlukeneko.
• bumbeko • bumbeko Kuqakathekile bonyana abafundi bangaboni isibonelo sinye kwaphela samajamo
wamabumbeko. Amasede amanengi wamabumbeko aphathelene nezorhwebo anikela za
• amaqadi anqophileko • amqadi anqophileko
isibonelo sinye kwaphela sakancantathu. Abafundi bafanele bonyana bakhumbule
• amaqadi aziindulungu • amaqadi azindulungu
• Iindulungu ezihlukeneko ngamasayisi
Gwala ubujamo
Isibonelo:
• iindulungu
• aboncantathu
• iinkwere
• aboncande
• Aboncantathu ababumbeke ngokuhlukana babekwa ezindaweni ezihlukahlukeneko
Isibonelo:
Iinkwere ezihlukene ngamasayisi nezibekwe eendaweni ezihlukeneko
Isibonelo:
371
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
372 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YOKU-1 namaminithi
ama -24)
3.3 Irherho lamajamo Irherho lamajamo • Aboncande abanobujamo obuhlukahlukeneko babekwa eendaweni ezahlukeneko. Iimfundo ezi-2
Amajamo • iindulungu • iindulungu Isibonelo:
abusobubili • aboncantathu • aboncantathu
2-D
• iinkwere • iinkwere
• aboncande • aboncande
Ubujamo Ubujamo
bamabumbeko bamabumbeko
Hlathulula, uhlele begodu Hlathulula, uhlele begodu Kuqakathekile bonyana abafundi basebenze ngokusika imifanekiso yamajamo
umadanise amajamo umadanise amajamo ngamabhoksi. Lokhu kuvumela abafundi bonyana babone aboncantathu, iinkwere,
abusobubili 2-D ngokuya abusobubili 2-D ngokuya naboncande ababekwe endaweni ezihlukileko.
nge: nge: Abafundi bahlela amabumbeko ngokuya ngokuthi anamahlangothi anqophe poro nofana
• bumbeko • bumbeko ayindulungu.
• amaqadi anqophileko • amqadi anqophileko Abafundi bahlela bebabuthelele ndawonye amabumbeko ngokuya ngokuthi aboncantathu,
boncande, iinkwere nofana iindulungu.
• amaqadi aziindulungu • amaqadi azindulungu
Umsebenzi undindziswa ngokutlolwa kwemisetjenzana.
Gwala ubujamo
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• iindulungu
• aboncantathu
• iinkwere
• aboncande
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
IGREYIDI YESI- 3 ITHEMU YOKU-1
4. UKUMEDA
CAPS UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Ngikuphi okuhlukileko eGreyidini yesi-2?
Isikhathi • Ukufunda idadamu / • Ukufunda idadamu / Iintlabagelo zedijithali ziyethulwa
umuhla ekhalendeni. umuhla ekhalendeni. Egreyidini yesi-2 abafundi bafunda isikhathi ngama-iri, isiquntu se-iri begodu nekotara
• Ukubeka amalanga • Ukubeka amalanga ye-iri ewatjhini ye-analogo.
wamabeletho, wamabeletho,
amafestivali wezekolo, amafestivali wezekolo, Egreyini yesi-3 abafundi basebenza ngeentlabagelo zedijithali kokuthoma. Basagcina
amaholideyi amaholideyi isakhiwo se-iri le-12 begodu basebenzisa ekuseni nantambama nakutlhogekako.
womphakathi, iminyanya womphakathi, Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi begodu
yezomlando, izehlakalo iminyanya nangokulandelana kwesikhathi.
zesikolo ezisekhalendeni. wezomlando,
Ngesikhathi sokufundisa itlasi loke begodu nesikhathi sokunqopha esiqhemeni, abafundi
• Ukutjho isikhathi sama-iri izehlakalo zesikolo
ezisekhalendeni. baragela phambili nokukhuluma ngelanga leveke, iinyanga zonyaka begodu idadamu /
ali-12 ngama- ilanga lamhlokho, namalanga angaphambili begodu namalanga ezako.
-- -iri, • Ukutjho isikhathi sama-
-- ngesiquntu se-iri iri ali-12 ngama- • amalanga wamabeletho
-- ngekotara ye-iri -- -iri, • amafestivali wezekolo
-- minithi
-- ngesiquntu se-iri • iminyanya yezomlando,
ewatjhini le-analogo
nemawatjhini wedijithali -- ngekotara ye-iri • izehlakalo zesikolo
begodu nezinye -- minithi • amaholideyi womphakathi,
iintlabagelo zedijithali ewatjhini le-analogo Ragela phambili ngokubawa abafundi bonyana batjho isikhathi ngokuya ngama-iri,
ezitjengisa isikhathi, isib. nemawatjhini wedijithali
abomaliledinini iinquntu zama-iri begodu nekotara ye-iri ewatjhini ye-analogo njalo njalo. Isibonelo,
begodu nezinye abafundi bangabawiwa bonyana batjho isikhathi sokungena kwesikolo, isikhathi
Ukubala ubude besikhathi iintlabagelo zedijithali sokudla begodu nangesikhathi sokuphuma kwesikolo, nofana nabatjhintjha ukusuka
nokudlula kwesikhathi ezitjengisa isikhathi, isib.
kesinye isifundo ukuya kwesinye. Khetha isikhathi lapho iwatjhi litjengisa khona
Ukusebenzisa amakhalenda abomaliledinini
isikhathi poro phezu kwe iri , nofana isiquntu se-iri nofana ikotara ye-iri. Kuqakathekile
ukubala nokuhlathulula
ukuba newatjhi ekulu, esebenzako ebekwa ngeklasini, ukuze abafundi baqale kiyo.
ubude besikhathi
Abafundi bangazenzela imifanekiso yamawatjhi. Ungabawa abafundi batjengise
ngamalanga nofana
ngeemveke nofana iinyanga iinkhathi ezihlukileko begodu bafake hlangana nezinye iimbalo. ‘Ngitjengisa i-iri le-10.
ukufaka hlangana Bekusikhathi bani ikotara ye-awara ngaphambi kwe-iri le-10?
• ukutjhugulula hlangana Ngesikhathi sokusebenza ngokuzijamela abafundi baragela phambili nokwenza
kwamalanga neemveke imisebenzi ehlobene nokutjho isikhathi ngama-iri, ngesiquntu se-iri begodu nekotara
• ukutjhugulula hlangana ye-iri emawatjhini we-analogo. Abafundi bangabala ngeemveke nofana ngamalanga
kweemveke neenyanga nangabe banikelwe ikhalenda nofana ihlangothi lekhalenda, isib. Ukuthola amalanga
Sebenzisa amawatjhi nokubala umehluko wesikhathi hlangana nazo.
ukubala ubude besikhathi
373 ngama-iri nofana isiquntu
se-iri.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
374 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Isikhathi sedijithali Iimfundo ezi-3
Isikhathi • Ukufunda idadamu / • Ukufunda idadamu / • Isikhathi sitjengiswa ngesakhiwo sedijithali sama-iri ali-12 eensetjenzisweni
umuhla ekhalendeni. umuhla ekhalendeni. eziphathelene nezinto nekambiso yangekhaya, isib. Abomaliledinini, ama-oveni
• Ukubeka amalanga • Ukubeka amalanga apheka nanyana efuthumeza kokugoma msinyana, Imitjhini yamaCD namaDVD, njll.
wamabeletho, amafes- wamabeletho, Abafundi bangahle bajayele khulu umhlobo lo wesikhathi kunamawatjhi we-analogo.
tivali wezekolo, ama- amafestivali wezekolo, Sebnenzisa iimfundo ezingaba pheze zintathu ukujayeza abafundi isikhathi sefomethi
holideyi womphakathi, amaholideyi yama iri ali-12.
iminyanya yezomlando, womphakathi,
izehlakalo zesikolo ez- iminyanya • Khumbuza abafundi ngehlathululo yekuseni nantambama.
isekhalendeni. wezomlando, • Tjengisa abafundi bonyana ngiyiphi idijithi etjho ama-iri begodu ngiyiphi idijithi etjho
• Ukutjho isikhathi sama-iri izehlakalo zesikolo amaminithi esikhathini sedijityhali.
ali-12 ngama- ezisekhalendeni. • Hlathulula bonyana kunamaminithi ama-60 nge-iri, ngakho-ke kunamaminithi ama30
-- -iri, • Ukutjho isikhathi sama- esiquntini se-iri begodu namaminithi ali-15 ekotarini ye-iri. Lokhu kuzosiza abafundi
-- ngesiquntu se-iri iri ali-12 ngama- bonyana bahlanganisa amamimithi nokufunda ngama-iri, ngesiquntu se-iri begodu
-- ngekotara ye-iri -- -iri, nekotara ye-iri ewatjhini ye-analogo, okungilokho abakwenze eGreyidini yesi-2
-- minithi
ewatjhini le-analogo nema- -- ngesiquntu se-iri • Nikela abafundi isikhathi esinengi sokuzijayeza ukufunda ngesikhathi sedijithali
watjhini wedijithali begodu -- ngekotara ye-iri ngesakhiwo sama-iri ali-12.
nezinye iintlabagelo zedi- -- minithi • Yiba newatjhi yedijithali esebenzako ibekwe ngetlasini. Bawa abafundi banikele
ISIGABA ESISISEKELO AMAGREYIDI 1-3
jithali ezitjengisa isikhathi, ewatjhini le-analogo isikhathi njalo emini umnyaka woke. Vumela abafundi benze amawatjhi wesifanekiso,
isib. abomaliledinini nemawatjhini wedijithali abangawasebenzisa ukutjho isikhathi begodu nokubala umehluko wesikhathi.
Ukubala ubude besikhathi begodu nezinye
nokudlula kwesikhathi iintlabagelo zedijithali
Ukusebenzisa amakhalenda ezitjengisa isikhathi, isib.
ukubala nokuhlathulula abomaliledinini
ubude besikhathi ngama-
langa nofana ngeemveke
nofana iinyanga ukufaka
hlangana
• ukutjhugulula hlangana
kwamalanga neemveke
• ukutjhugulula hlangana
kweemveke neenyanga
Sebenzisa amawatjhi
ukubala ubude besikhathi
ngama-iri nofana isiquntu
se-iri.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
CAPS
ama -24)
4.2 Ukumeda okungakahleleki Egreyidini yesi-2 kuphakanyiswe bonyana abafundi banqophe ekulinganiseni,
Ubude • Ukulinganisa, ukumeda, ekumedeni, ekumadaniseni begodu nokurekhoda ubude, ububanzi begodu
ukumadanisa, ukuhlela nokuphakama.
ngemihlobo begodu • ngamayunithi ahlelekileko; begodu
urekhode ubude
ngokusebenzisa iimedo • ukumeda ngamamitha usebenzisa intongamamitha nofana intambo enobude bemitha
ezingakahleleki isib. li-1
Ubude besandla, Ngesikhathi sokusebenza ngokuzijamela abafundi bangazijayeza amakghono lawa
amagadango, ubude wokumeda.
bamapensela, izinto
Ukumeda ubude njengobujamo bokurarulula imiraro begodu nokubala
zokubala, njll.
• Ukuhlathulula ubude Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi bangararulula
bezinto ngokubala imiraro esebenzisa ubujamo bo
begodu nokutjho • kumeda ubude obungakahleleki; begodu
bonyana zinobude • kumeda ubude ngamamitha
obungangani bamayunithi
angakahleleki Yelela irherho leenomboro zeThemu, nomihlobo ehlukahlukeneko yemiraro efanele
iThemu.
• Ukusebenzisa
ilimi ukukhuluma Iimfundo ezinqophe ekumedeni ubude zizokuthoma ethemini yesi-2
ngokumadanisa,
isib. okudanyana
okufitjhazana, okude
khulu, okubanzi khulu.
Ukwethula ukumeda
okuhlelekileko
• Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela
begodu urekhode
ubude ngokusebenzisa
amamitha (amamitha
stiki nofana iintambo
ezinobude bemitha)
njengomuvosimedo
ojayelekileko.
• Ukulinganisa nokumeda
ubude ngamasenthimitha
ngokusebenzisa irula.
Akuthlogeki ukwenza
itjhuguluko hlangana
375 kwamamitha
namasenthimitha.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
376 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YOKU-1
ama -24)
4.3 Ukumeda okungakahleleki EGreyidini yesi-2 abafundi
Imasi/ • Ukulinganisa, ukumeda, • bameda ubudisi/ imasi ngokungakahleleki ngokusebenzisa isikala sokudzimelela;
Ubudisi ukumadanisa, ukuhlela, • hlela imikhiqizo ngokuya ngemasi etlolwe eempakaneni; begodu
bekurekhodwe ubungako
• ukufunda iinkala zangendlini yokuhlambela ( zombili iinkala zamambala neseenthombe).
/ imasi ngokusetjenzisa
iimedo ezingakahleleki Ngesikhathi sokusebenza ngokuzijamela abafundi bazijayela amakghono lawa wokumeda
begodu nesikala Ukumeda ubudisi / imasi njengobujamo bokurarulula imiraro begodu nokubala
sokudzimelela isib. Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi bangararulula imiraro esebenzisa ubujamo boku
Amabhlogo, iintina njll.
• meda ubungako/imasi obungakahleleki; begodu
• Ukusebenzisa
• meda ubungako ngamakhilogremu
ilimi ukukhuluma
ngokumadanisa isib. Yelela irherho leenomboro ezifaneleko zeThemu, nemihlobo ehlukahlukeneko yemiraro efaneleko yeThemu.
elula, ebudisi, elula-khulu, Iimfundo ezinqotjhiswe ekumedeni ubungako/ imasi zizokuthonywa eThemini yesi-2.
ebudisi-khulu.
Ukwethula ukumeda
okuhlelekileko
• Ukumadanisa, ukuhlela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokurekhoda ubudisi
bezinto ezipakelwe
ukuthengiswa
ezinobungako
obutjengiswe
ngamakhilogremu, isib.
amakhilogremu ama-2
wereyisi nekhiligremu
eli-1 leflowuru nofana
amakhilogremu ama-500
wetswayi
• Ukumeda ubudisi / imasi
yabo ngamakhilogremu
ngokusebenzisa isikala
sokumeda sangendlini
yokuhlambela
Akuthlogeki ukwenza
itjhuguluko hlangana
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
kwamamilimitha namalitha.
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : IMINQOPHO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
YETHEMU YOKU-1 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Ngikuphi okuhlukileko eGreyidini yesi-2? Iimfundo ezi-2
Umthamo/ • Ukulinganisa nokumeda, • Ukulinganisa nokumeda; ukumadanisa EGreyidini yesi-2 abafundi
Ivolumu ukumadanisa nokuhlela (isib. nokuhlela umthamo wesimumathii (o.u. • balinganise bebameda, bamadanise, bahlela begodu barekhoda
umthamo ongamumathwa umthamo ongamumathwa simumathi umthamo weemumathi nofana ivolumu engeemumathini
simumathii nasizeleko) nasizeleko) ngokusebenzisa iimedo ngokusebenzisa iimedo ezingakahleleki;
ngokusebenzisa iimedo ezingakahleleki isib. Iingobho namakopi. • bamadanisa begodu bahlele umthamo werherho lamabhodlelo begodu
ezingakahleleki isib. Iingobho • Ukuhlathulula umthamo wesimumathi nezinto ezithengiswa esitolo sokudla / igrozari nezinye iintwanyana
namakopi. ngokubala nokutjho bonyana mangaki zangekhaya lapho ivolumu itjengiswe khona eempakaneni
• Ukuhlathulula umthamo amayunithi angakahleleki angazalisa • basebenzisa ilitha li-1 lamabhodlelo nofana amajege welitha li-1
wesimumathi ngokubala isimumathi, isib. Ibhodlelo linobungako ukulinganisa nokumeda, ukumadanisa, ukuhlela begodu nokurekhoda
nokutjho bonyana mangaki bamakopi amane umthamo weemumathi nofana ivolumu eemumathini ngamalitha.
amayunithi angakahleleki Ukwethulwa kokumeda okuhlelekileko EGreyidini yesi-3 abafundi bethulwa kumamilimitha
angazalisa isimumathi, isib. • Ukulinganisa, ukumeda; ukumadanisa
Uyini umthamo? Iyini ivolumu
Ibhodlelo linobungako bamakopi nokuhlela nokurekhoda umthamo wezinto
ngokumeda ngamalitha, iinqunto zamalitha Ibhodlelo lingaba nomthamo welitha li-1, kodwana ngeze lazaliswa swi,
amane
begodu nangamakotara wamalitha. isibonelo, lingamumatha kwaphela ivolumu lekopi elilodwa lamanzi.
Ukwethulwa kokumeda
okuhlelekileko -- Ukusebenzisa amabhodlelo anomthamo Umthamo bungako bento engamumathwa simumathi (nofana ubungako
• Ukulinganisa, ukumeda; welitha li-1, nofana iimumathi besikhala esingaphakathi kwento).
ukumadanisa nokuhlela ezinomthamo otlolwe ngamamilimitha, Ivolumu bungako besikhala esithathwa simumathwa/ liketjezi.
nokurekhoda umthamo wezinto isib. amabhlegana wesiselo esimakhaza. Kesinye isikhathi abafundi bazokumeda bonyana lingangani iketjezi
ngokumeda ngamalitha, -- Amajege wokumeda anemida etjengisa (nofanaisanda nofana okhunye nje) elingesimumathini. Lokhu kukumeda
iinqunto zamalitha begodu amalitha, isiquntu samalitha begodu ivolumu yento engesimumathini.
nangamakotara wamalitha. namakotara wamalitha Kezinye iinkhathi abafundi bazokumeda bonyana isimumathi
• Ukumadanisa, ukuhlela -- Amajege wokumeda anemida etjengisa singamumatha kangangani lokha nasizele swi.
nokurekhoda umthamo amamililitha. Abafundi abakalindeleki Abafundi bafanele baragele phambili ngokumeda basebenzisa
wezinto ezipakelwe bonyana bafunde amavolumu amayunithi womthamo angakahleleki.
ukuthengiswa, ubungako angakameregwa emudeni. Ukumeda umthamo ongakahleleki ngokusebenzisa amayunithi
bazo butlolwa ngamalitha, -- Amakopi wokumeda namathispuni womthamo angakahleleki
isib. Amalitha ama-2 webisi, atjengisa umthamo wawo. Abafundi bangafunda zoke iinkambisolawulo neenkambiso zokumeda
ilitha li-1 lesiselo esimakhaza, -- Ukumadanisa, ukuhlela nokurekhoda ngokusebenzisa amayunithi angakahleleki. Ukumeda ngamayunithi
amalitha ama-5 wepende umthamo wezinto ezipakelwe angakahleleki kufanele bonyana kungaqaleki kwanga akukaqakatheki
nofana ngamamilimitha, isib. ukuthengiswa, ubungako bazo butlolwa kunokumeda ngamayunithi ahlelekileko.
Amamililitha ama-500 webisi, ngamalitha, isib. Amalitha ama-2 webisi, Abafundi bafanele bathole ithuba lokumeda ivolumu/ umthamo
• Amamililitha ama-340 wesiselo ilitha li-1 lesiselo esimakhaza, amalitha ngokusebenzisa izinto ezihlukahlukeneko njengamayunithi ahlelekileko,
esimakhaza, amamilimitha ama-5 wepende nofana ngamamilimitha, isib. Amakopi (kodwana ingasi amakopi wokumeda), iingobho, (kodwana
amamililitha ama-750 we-oli isib. Amamililitha ama-500 webisi, ingasi amathispuni wokumeda), iimvalo zamabhodlelo njengeemvalo
• Ukwazi bonyana ikopi • Amamililitha ama-340 wesiselo esimakhaza, zamabhodlelo webisi lamalitha ama-2, amabhlegana amancani,
elisezingeni elifaneleko amamilimitha amamililitha ama-750 we-oli amabhodlelo amancani, njll.
limamililitha ama-250 • Ukwazi bonyana ikopi elisezingeni Ukumeda ivolumu/umthamo ngamayunithi angakahleleki kufana ukubala
• Ukwazi bonyana ithispuni elifaneleko limamililitha ama-250 bonyana kukangaki lapho umuntu azalisa begodu athela khona eyunithini
limamililitha ama-5 • Ukwazi bonyana ithispuni limamililitha ekhethiweko ivolumu yakhona emedwako.
377 Akuthlogeki bonyana kube ama-5
Abafundi bafanele bafundiswe ngaso soke isikhathi ukutjho iyunithi, isib.
netjhuguluko hlangana Akuthlogeki bonyana kube netjhuguluko
Kuneengobho ezi-48 ezipheleleko zamanzi ngebhodlelweni nofana
kwamamilimitha namalitha hlangana kwamamilimitha namalitha
kunamanzi angaphasi kwekopi ngebhodlelweni.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : IMINQOPHO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
378 YETHEMU YOKU-1 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Lokha abafundi nasele bamede nanyana ngiyiphi iyunithi amahlandla Iimfundo ezi-2
Umthamo/ • Ukulinganisa nokumeda, • Ukulinganisa nokumeda; ukumadanisa ambalwa, bafanele balinganise umthamo/ ivolumu ngokusebenzisa
Ivolumu ukumadanisa nokuhlela (isib. nokuhlela umthamo wesimumathii (o.u. iyunithi leyo. Ukulinganisa ngaphambi kokumeda kuqakathekile, kodwana
umthamo ongamumathwa umthamo ongamumathwa simumathi kungenziwa kwaphela lokha abafundi nabasele bamede ngeyunithi leyo.
simumathii nasizeleko) nasizeleko) ngokusebenzisa iimedo Abafundi bafanele bafundiswe bonyana ukuze bamadanise ivolumu
ngokusebenzisa iimedo ezingakahleleki isib. Iingobho namakopi. nofana umthamo, iyunithi efana patsi ifanele isetjenziswe. Isib.nangabe
ezingakahleleki isib. Iingobho • Ukuhlathulula umthamo wesimumathi irhalasi Limimatha amathispuni ama-20 wamanzi begodu ikopi Limimatha
namakopi. ngokubala nokutjho bonyana mangaki amathispuni wamanzi ali-10, umuntu angekhe atjho bonyana irhalasi
• Ukuhlathulula umthamo amayunithi angakahleleki angazalisa Limimatha amanzi amanengi kunekopi.
wesimumathi ngokubala isimumathi, isib. Ibhodlelo linobungako Abafundi bafanele bamede ngamayunithi angakahleleki
nokutjho bonyana mangaki bamakopi amane ahlukahlukeneko, ukuze bakghone
amayunithi angakahleleki Ukwethulwa kokumeda okuhlelekileko • ukuthoma ukuzwisisa bonyana lokha iyunithi nayiyincani ,
angazalisa isimumathi, isib. • Ukulinganisa, ukumeda; ukumadanisa izokusetjenziswa amahlandla amanengana ukuzalisa isimumathi,
Ibhodlelo linobungako bamakopi nokuhlela nokurekhoda umthamo wezinto Isib. ivolumu engebhodlelweni ingaba ziingobho ezmai-20, kodwana
amane ngokumeda ngamalitha, iinqunto zamalitha ilingane nekopi yi-1;
Ukwethulwa kokumeda begodu nangamakotara wamalitha. • ukuthoma ukusebenzisa amayunithi afaneleko kilokho abakumedako,
okuhlelekileko -- Ukusebenzisa amabhodlelo anomthamo isib. Ukumeda amalitha ama-2 wamabhodlelo azeleko ngethispuni
• Ukulinganisa, ukumeda; welitha li-1, nofana iimumathi kukumotjha isikhathi.
ukumadanisa nokuhlela ezinomthamo otlolwe ngamamilimitha,
Ukwethula ukumeda okuhlelekileko
nokurekhoda umthamo wezinto isib. amabhlegana wesiselo esimakhaza.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Linganisa, meda, madanisa, hlela begodu urekhode amavolumu
ngokumeda ngamalitha, -- Amajege wokumeda anemida etjengisa
begodu nemithamo ngamalitha.
iinqunto zamalitha begodu amalitha, isiquntu samalitha begodu
namakotara wamalitha Khumbuza abafundi bonyana amalitha mayunithi ajayelekileko
nangamakotara wamalitha.
-- Amajege wokumeda anemida etjengisa asezingeni elifaneleko wokumeda umthamo begodu nevolumu. Indlela
• Ukumadanisa, ukuhlela
amamililitha. Abafundi abakalindeleki yokurhunyeza ( l ) iyasetjenziswa emajegeni wokumeda nezintweni
nokurekhoda umthamo
bonyana bafunde amavolumu zokurhweba ezithengiswa ngamavolumu. Hlolisisa bonyana abafundi
wezinto ezipakelwe
angakameregwa emudeni. bakhumbula isirhunyezo samalitha.
ukuthengiswa, ubungako
bazo butlolwa ngamalitha, -- Amakopi wokumeda namathispuni Abafundi bameda ngamalitha basebenzisa :
isib. Amalitha ama-2 webisi, atjengisa umthamo wawo. • Iimumathi ezimalitha li-1 njengamabhodlelo weenselo ezimakhaza,
ilitha li-1 lesiselo esimakhaza, -- Ukumadanisa, ukuhlela nokurekhoda amabhodlelo webisi, amakhathuni webisi, amakhathuni wejuzi; begodu
amalitha ama-5 wepende umthamo wezinto ezipakelwe • Amajege wokumeda etjengisa ilitha yi-1 yemida yekhalibhratjhini.
nofana ngamamilimitha, isib. ukuthengiswa, ubungako bazo butlolwa Bayalinganisa begodu bameda umthamo ohlukahlukeneko weemumathi
Amamililitha ama-500 webisi, ngamalitha, isib. Amalitha ama-2 webisi, njengeembhigiri ezikulu zeyogathi, iimbhigirana ze-ayisikhrimi,
• Amamililitha ama-340 wesiselo ilitha li-1 lesiselo esimakhaza, amalitha amabhoksi wokudla kwemini, amajege amakhulu, amabhodlelo
esimakhaza, amamilimitha ama-5 wepende nofana ngamamilimitha, amakhulu, amabhlege wepende angenalitho, amabhakede njll. Izinto
amamililitha ama-750 we-oli isib. Amamililitha ama-500 webisi, ezinomthamo ohlukahlukeneko zifanele zikhethwe.
• Ukwazi bonyana ikopi • Amamililitha ama-340 wesiselo esimakhaza, Abafundi bahlathulula umthamo njengo “ngaphasi kwelitha li-1, amalitha
elisezingeni elifaneleko amamilimitha amamililitha ama-750 we-oli ama-2, hlangana kwelitha li-1 nama-2, amalitha ama-5, njll.
limamililitha ama-250 • Ukwazi bonyana ikopi elisezingeni • Abafundi bamadanisa, bahlela begodu barekhoda umthamo wezinto
• Ukwazi bonyana ithispuni elifaneleko limamililitha ama-250 zerhwebo ezipakelwako, umthamo wabo otlolwe ngamalitha, isib.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
limamililitha ama-5 • Ukwazi bonyana ithispuni limamililitha amalitha ama-2 webisi, ilitha li-1 leeselo esimakhaza, amalitha ama-5
Akuthlogeki bonyana kube ama-5 wepende.
netjhuguluko hlangana Akuthlogeki bonyana kube netjhuguluko Ukulinganisa, ukumeda, ukumadanisa, ukuhlela nokurekhoda
kwamamilimitha namalith hlangana kwamamilimitha namalitha amavolumu begodu nomthamo ngamamilimitha.
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : IMINQOPHO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
YETHEMU YOKU-1 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ukumeda okungakahleleki Coca nabafundi bonyana amamililitha amayunithi wokumeda ahlelekileko Iimfundo ezi-2
Umthamo/ • Ukulinganisa nokumeda, • Ukulinganisa nokumeda; ukumadanisa ajayelekileko womthamo begodu nevolumu. Hlathulula bonyana
Ivolumu ukumadanisa nokuhlela (isib. nokuhlela umthamo wesimumathii (o.u. amamilimitha mancani kunamalitha.
umthamo ongamumathwa umthamo ongamumathwa simumathi Bafanele bafunde igama begodu nesirhunyezo, ngombana
simumathii nasizeleko) nasizeleko) ngokusebenzisa iimedo iimumathi ezinengi zerhwebo begodu neenjege ezinengi zokumeda
ngokusebenzisa iimedo ezingakahleleki isib. Iingobho namakopi. zineenrhunyezo zamagama.
ezingakahleleki isib. Iingobho • Ukuhlathulula umthamo wesimumathi Abafundi bafanele bamadanise, bahlele begogu barekhode umthamo
namakopi. ngokubala nokutjho bonyana mangaki wezinto ezipakelwe irhwebo, umthamo wazo otloleke ngamamilimitha,
• Ukuhlathulula umthamo amayunithi angakahleleki angazalisa isib. Amamilimitha webisi ama-500ml, ama-750ml weviniga, ama-330ml
wesimumathi ngokubala isimumathi, isib. Ibhodlelo linobungako weenselo ezimakhaza, ama-400ml weporitjhi yaphasi, njll.
nokutjho bonyana mangaki bamakopi amane Abafundi bafanele bamede njalo njalo ngokwaneleko nga:
amayunithi angakahleleki Ukwethulwa kokumeda okuhlelekileko • makopi wokumeda asezingeni elifaneleko ukuthoma ukwazi bonyana
angazalisa isimumathi, isib. • Ukulinganisa, ukumeda; ukumadanisa mangaki amamilimitha ama-250;
Ibhodlelo linobungako bamakopi nokuhlela nokurekhoda umthamo wezinto • mathispuni wokumeda ukuthoma ukwazi bonyana mangaki
amane ngokumeda ngamalitha, iinqunto zamalitha amamilimitha ama-5;
Ukwethulwa kokumeda begodu nangamakotara wamalitha.
• majege wokumeda amedwe ngamamilimitha- lapha kulindeleke
okuhlelekileko -- Ukusebenzisa amabhodlelo anomthamo
bonyana abafundi bafunde kwaphela imida etjengiswe ngeenomboro-
• Ukulinganisa, ukumeda; welitha li-1, nofana iimumathi
bazokunqopha ekufundeni imida engakanomborwa esiGabeni
ukumadanisa nokuhlela ezinomthamo otlolwe ngamamilimitha,
esiPhakathi.
nokurekhoda umthamo wezinto isib. amabhlegana wesiselo esimakhaza.
Ukulandela amaresibhi, ukufaka hlangana ukubhaga, kubujamo obulisizo
ngokumeda ngamalitha, -- Amajege wokumeda anemida etjengisa
lapho abantwana bangazijayeza khona ukumeda
iinqunto zamalitha begodu amalitha, isiquntu samalitha begodu
nangamakotara wamalitha. namakotara wamalitha Abafundi ABAKALINDELEKI bonyana
• Ukumadanisa, ukuhlela -- Amajege wokumeda anemida etjengisa • bazi bona ama-1 000 ml = 1 ilitha
nokurekhoda umthamo amamililitha. Abafundi abakalindeleki • ukwenza itjhuguluko hlangana kwamamilimitha namalitha, nofana
wezinto ezipakelwe bonyana bafunde amavolumu • bafunde imida engakanomborwa emajegeni amedako ( lokhu
ukuthengiswa, ubungako angakameregwa emudeni. kwenziwa ukusuka eGreyidini yesi-4).
bazo butlolwa ngamalitha, -- Amakopi wokumeda namathispuni Ukurekhoda ukumeda / iimedo
isib. Amalitha ama-2 webisi, atjengisa umthamo wawo. Nanyana ukumeda kulikghono eliphathekako, abafundi bafanele
ilitha li-1 lesiselo esimakhaza, -- Ukumadanisa, ukuhlela nokurekhoda barekhode ukumeda kwabo ngaso soke isikhathi, ukufaka hlangana koke
amalitha ama-5 wepende umthamo wezinto ezipakelwe ukumeda okuhlelekileko nokungakahleleki.
nofana ngamamilimitha, isib. ukuthengiswa, ubungako bazo butlolwa Ukumeda umthamo/ ivolumu njengobujamo bokurarulula imiraro
Amamililitha ama-500 webisi, ngamalitha, isib. Amalitha ama-2 webisi, nokubala
• Amamililitha ama-340 wesiselo ilitha li-1 lesiselo esimakhaza, amalitha Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana, abafundi
esimakhaza, amamilimitha ama-5 wepende nofana ngamamilimitha, bangararulula imiraro ngokusebenzisa ubujamo.
amamililitha ama-750 we-oli isib. Amamililitha ama-500 webisi, • ukumeda okungakahleleki komthamo / ivolumu besimedo,
• Ukwazi bonyana ikopi • Amamililitha ama-340 wesiselo esimakhaza, isibonelo, uGogo usebenzisa amakopi amabili webisi ukwenza
elisezingeni elifaneleko amamilimitha amamililitha ama-750 we-oli iphudinghi. Lokha nakangabuyelela kabili iresebhele le,
limamililitha ama-250 • Ukwazi bonyana ikopi elisezingeni
uzokuthloga ibisi elingangani?
• Ukwazi bonyana ithispuni elifaneleko limamililitha ama-250
limamililitha ama-5 • Ukwazi bonyana ithispuni limamililitha • amalitha
379 Akuthlogeki bonyana kube ama-5 • amamililitha
netjhuguluko hlangana Akuthlogeki bonyana kube netjhuguluko Yelela irherho leenomboro elifanako leThemu leyo, begodu nerherho
kwamamilimitha namalitha hlangana kwamamilimitha namalitha lemihlobo yemiraro ehlukahlukeneko.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YOKU-1
380
5. UKUPHATHA IDATHA
IMIQONDO UBUDE
IMIQONDO BESIKHATHI
NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA namaminithi
YOKU-1
KONYAKA ama -24)
5.4 Buthelela begodu Buthelela begodu Yini umehluko kune Greyidini yesi - 2?
Buthelela uhlele idatha uhlele idatha • Abafundi bahlela idatha ngama rhelo, thali, thebula
begodu uhlele • Buthelela idatha Buthelela idatha • Abafundi bathulwa kuma bha- grafu
idatha ngetlasi nofana ngetlasi nofana
• Abafundi baragela phambili nokusebenza ngama grafu weenthombe – kokubili
isikolo ukwenzela isikolo ukwenzela
ukuwakha njenge ngcenye yomzombe wedatha nokuhlaziya igrafu yeenthombe
ukuphendula imibuzo ukuphendula imibuzo
abanikelwe yona.
ebuzwa ngutitjhere. ebuzwa ngutitjhere.
Umzombe wedatha opheleleko
• Hlela idatha Sebenzisa amathali
oyinikelwe ngutitjhere ukurekhoda idatha Emzombeni wokuphatha idatha,
nofana yincwadi ngeengaba onikelwe • abafundi babuthelela ilwaziukwenzela ukuphendule imibuzo. Esigabeni Esisisekelo
• Hlela idatha ngama: zona. nesiGabeni Esiphakathi umbuzo lo unikelwa ngutitjhere nofana yincwadi;
-- Rhelo Jamisela idatha • abafundi bahlela ngamananeko begodu bajamisele ilwazi ngezindlela ezenza bona kube
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Jamisela idatha nge: lula ukuhlaziya. Iindlela zokutjengisa okusetjenzwa ngazo eGreyidini yesi-3 ngileszi:
-- Thali
amarhelo, amathali, amathebula, amagrafu weenthombe nama bha grafu; begodu
-- Thebula • Thebula
• abafundi bahlaziya ilwazi ngokuphendula imibuzo ebuzwa ngutitjhere.
• Bha grafu
5.5 Jamisela idatha Ibha grafu yetlasi
Hlaziya begodu
Jamisela idatha Jamisela idatha nge: urhumutjhe idatha Kuphakanyiswa bona abafundi beGreyidi yesi-3, basebenze ngawowoke umzombe
• Grafu yeenthombe wedatha okungasenani kanye ngonyaka: Ukusebenza baboke njenge tlasi kusiza abafundi
Phendula imibuzo
• Bha grafu bona bazibandakanye kizozoke iinteji ngaphandle kokuthi baduke ngemininingwana
ngedatha ethulwe
yesinye seenteji. Ukwenza ibha grafu yetlasi kukuvumela bona unqophise abafundi
kumabha grafu.
Hlaziya begodu emaphuzwini aqakathekileko wokuphatha idatha nokuthula abafundi ezakhiweni
5.6 urhumutjhe idatha eziqakathekileko ze bha grafu.
Hlaziya begodu Phendula imibuzo • Igrafu uyilebula kuphi begodu njani (isihloko segrafu)
uhlathulule ngedatha ethulwe nge: • Ama-eksisi uwalebula kuphi begodu njani (iinhloko se-eksisi)
idatha • Grafu yeenthombe • Ama-bha agwalwa bunjani
• Bha grafu. -- Gwala ama-bha, ubude obufaneleko ukutjengisa idatha
-- Yenza ama-bha abe nobubanzi obulinganako
-- Tjhiya isikhala hlangana nama-bha
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
-- Lebula ibha ngalinye ngokucacileko
• Uyifunda njani igrafu
IMIQONDO UBUDE
IMIQONDO BESIKHATHI
NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA namaminithi
YOKU-1
CAPS
KONYAKA ama -24)
Hlaziya begodu Abafundi kufanele bazi bona kuqakathekile ukufunda isihloko segrafu mantanzi, ukwenzela iimfundo ezi-3
5.6 urhumutjhe idatha bona bazi bonyana idatha iphathelene nani. Kufanele bafunde neenhloko kuma eksisi
Phendula imibuzo athabaleleko nama eksisis anqophe poro. Akuthlogeki bona abafundi bazi amaThemu
Hlaziya begodu
ngedatha ethulwe nge: asetjenzisiweko ukuhlathulula iingcenye zegrafu, okufanele bakwazi ngokuse ‘’eksisini
uhlathulule
ethabaleleko / ephasi’’ nalokho okuse ‘’ekzisini enqophe poro / eseqadi’’ ukubona bona
idatha • Grafu yeenthombe
igrafu ikhuluma ngani.
• Bha grafu.
Ngokujayelekileko, sifunda kusuka ngakwesesincele ukuya ngakwesokudla, kodwana
lokha abafundi bafunda igrafu, kufanele bafunde kusuka ngakwesesincele ukuya
ngakwesokudla begodu nakusuka phasi ukuya phezulu. Lokhu kufanele kuhlathululelwe
abafundi. Nabo kufanele bawa phrakthise amakghono la.
Ukusebenza ngawowoke umzombe wedatha kungathatha iimfundo ezi 3.
Buthelela begodu uhlele idatha
EGreyidini 3 kufanele ubuze imibuzo ovumela abafundi bona babuthewlele idatha
isib “Ngimiphi imibala ethandwa litlasi lethu?” Abotitjhere esigabeni lesi kufanele
bona baqinisekise bona iinhloko ezihlukahlukeneko zokubuthelela nokuhlaziya idatha
ziyakhethwa kwenye nenye igreyidini.
Iinhloko ezifaneleko kufaka hlangana imidlalo ethandwako , iinselo ezimakhaza
ezithandwako, imibala ethandwako, isikhathi sokuledlha abasithandako, ukudla
abakuthandako , amahlelo abawathandako wakamabonwakude , njll
Abafundi bangathoma ngokumemezela lokho abakucabangako. Nasele bathole ilwazi
lerherho leempendulo, kufanele ubeke ihlelo/ isigaba okufanele bakhethe kizo. Abafundi
kufanele baphrakthise koke “okungasi yigrafu” izinto ezizinjamiselo o.u. amarhelo, amathali
nama thebula, isib.
-- Rhemisa amagama wabafundi ngamunye ngaphasi kwe hlelo / kwesigaba
abasikhethe njengabasithandako;
-- Tjengisa abafundi bona bangayenza njani ithebula yamathali kususela erhelweni
(ukufundisa abafundi bona bangathaliya bunjani kungathatha isifundo soke); no
-- Kwenza ithebula ngeenomboro abazithethe ethebuleni yamathali.
Lokha idatha sele isethebuleni, tjengisa abafundi bona bangayigwala njani ibha grafu
(bona umhlahlandlela ongehla).
Hlaziya begodu urhumutjhe idatha
Abafundi baphendula imibuzo oyibuzako ngegrafu yeenthombe
Isibonelo:
a) “Ngimuphi umbala othandwa khulu ngetlasini lethu?”
b) “Ngimuphi umbala othandwa bafundi abambalwa ngetlasini?”
381 c) “Kgani abafundi abanengi bathanda …. nofana … ?”
d) “Banengi kangangani abafundi abakhetha … kuna … ?”
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI-2
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANA
382 UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
1.1 Bala izinto eziphathekako Buthelela okungasenani izinto Ngikuphi okuhlukileko eThemini yoku-1?
Ukubala Linganisa begodu zangamalanga ezima 500 Irherho leenomboro liyangezeleleka ukufika ema-500. Ukungezelela kurherho
izinto ubale ngokuthembeka ukulinganisa begodu nokubala leenomboro kucabangela bonyana abafundi banga:
okungasenani ukufika e-1000 ngokuthembeka.
• buthelela izinto ukwenzela ukubala;
izinto zangamalanga. Iqhinga Nikela isilinganiso esizwakalako
• bala ngalitjhumi ukufika ema-500 begodu utjho amagama seenomboro
lokubuthelela liyakhuthazwa. senani lezinto ezingahlolwa
ngokulandelana kwabo; begodu
ngokubala.
• madanisa itshwayo enanini elibaliweko ngokutlola inomboro nofana
ngokubonisa inomboro ngamakarada wobukhulu bedijithi.
Qala amanothi weThemu yoku-1
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko eThemini yoku-1?
Bala uye nemuva nga: nemuva nga:
• Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye nenye Ethemini le abafundi bathoma ukubala ngama-50. Irherho lenomboro njenganje
phambili liyangezeleleka ukufika e-1 000.
nenye inomboro hlangana inomboro hlangana ne-0 ne-
nemuva
ne-0 ne-1000. 500. Ethemini le abafundi baragela phambili ukusebenzisa ukubala ngokweqa
• Li-10 ukusuka kesinye • Li-10 ukusuka kesinye ethebuleni lokubuyabuyelela begodu kulandelaneni kweenomboro.
nesinye isibuyabuyelelo se- nesinye isibuyabuyelelo se-10
Qala amanothi weThemu yoku-1
10 hlangana ne-0 ne-1000. hlangana ne-0 ne-500.
• Ku-5 ukusuka kesinye • Ku-5 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo saka
saka ku-5 hlangana ne-0 ku-5 hlangana ne-0 ne-500.
ne-1000. • Ku-2 ukusuka kesinye
• Ku-2 ukusuka kesinye nesinye isibuyabuyelelo saka
nesinye isibuyabuyelelo ku-2 hlangana ne -0 ne-500.
saka ku-2 hlangana ne -0 • Ku-3 ukusuka kesinye
ne-1000. nesinye isibuyabuyelelo saka
• Ku-3 ukusuka kesinye ku-3 hlangana ne-0 ne-500
nesinye isibuyabuyelelo • Ku-4 ukusuka kesinye
saka ku-3 hlangana ne-0 nesinye isibuyabuyelelo saka
ne-1000 ku-4 hlangana ne-0 ne-500
• Ku-4 ukusuka kesinye • Ma-20, 25, 50, 100
nesinye isibuyabuyelelo okungasenani ukufika e-500.
saka ku-4 hlangana ne-0
ne-1000
• Ma-20, 25, 50, 100
okungasenani ukufika
e-1000.
383
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
384 IMINQOPHO YETHEMU YESI-2 YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
1.3 • Ukukhumbula, ukubona • Ukukhumbula, ukubona Amatshwayo weenomboro wokufunda nokutlola aragela phambili
Amat- begodu nokufunda nokufunda iinomboro ngokujayezwa lokha naka:
shwayo amatshwayo iinomboro • Khumbula, ubone begodu • bala izinto;
• Khumbula, ubone begodu ufunde amatshwayo
weenom- • bala aye phambili nemuva;
ufunde amatshwayo wenomboro ukusuka ku-0
boro wenomboro ukusuka ku-0 ukufika ku-1000. • qedelela ukulandelana kweenomboro;
begodu ukufika ku-1000. • Tlola amatshwayo wenomboro
namgama • hlela begodu amadanisa iinomboro
• Tlola amatshwayo ukusuka ku-0 ukufika ku-1000
weenom- wenomboro ukusuka ku-0 • Khumbula, ubone Qala amanithi weThemu yoku-1
boro ukufika ku-1000 begodu ufunde amagama
• Khumbula, ubone weenomboro ukusuka eli-0
begodu ufunde amagama ukufika ku-250.
weenomboro ukusuka ku-0 • Tlola amagama weenomboro
ukufika ku-1000. ukusuka ku-0 ukufika ku-250
• Tlola amagama
weenomboro ukusuka ku-0
ukufika ku-1000
1.4 Ukuhlathulula, ukumadanisa Ukuhlathulula, ukumadanisa Ethemini le irherho leenomboro liyangezeleleka ukusuka ema-99 ukufika
Hlathulula, nokuhlela iinomboro nokuhlela iinomboro ukufika ema-500. Abafundi kwanje bahlela iinomboro zamadijithi amathathu. Ukuhlela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
umadanise ukufika ema-999. ema-500 iinomboro zamadijithi amathathu, abafundi batlhoga uku:
• Ukuhlathulula • Ukuhlathulula begodu
begodu • tjho igama lenomboro;
nokumadanisa iinomboro nokumadanisa iinomboro
uhlele ezipheleleko ukufika ezipheleleko ukufika ema-500 • tlola inomboro; begodu
iinomboro ema- 999 ngokusebenzisa ngokusebenzisa okuncani • Khumbula ubungako bedijithi ngayinye
okuncani kuna, okukhulu kuna, okukhulu kuna, okunengi
kuna, okunengi kuna, kuna, okumbadlwana kuna Vumela abafundi ukusebenzisa inambalayini, umkhondo wenomboro, amagridi
okungaphasi kuna begodu begodu nokulinganako. wenomboro nofana ilwazi labo lokuphula iinomboro ngamakhulu, ngamatjhumi
nokulinganako. • Ukuhlathulula begodu nangakunye ukutjengisa ukuzwisia kwabo. Lokha nawuhlela iinomboro
• Ukuhlathulula nokuhlela nokuhlela iinomboro abafundi kufanele bakghone ukutjho bonyana kungani inomboro iyikulu
iinomboro ezipheleleko ezipheleleko ukufika ema 500 ukudlula enye usebenzisa ubungako bedijithi ukuzihlathulula.
ukufika ema-999 ukusuka ukusuka kwencani khulu ukuya Isibonelo:
kencani ukuya kekulu, kwekulu khulu, nokusuka
kunye nokusuka kekulu uye kwekulu khulu ukuya kwencani ama-239 mancani kuna-339 ngombana
kenca ni khulu. Umfundi kufanele akghone ukuhlathulula bonyana ama-300 manengi
Ukusebenzisa Ukusebenzisa kunama-200 ngokusebenzisa izinto ezibuthelelweko ukubonisa inomboro 100
inomborosikhundla inomborosikhundla enomborweni ngayinye. Abafundi bangakghona ukuthola ubujamo benomboro
ukutjengisa ukuhleleka, ukutjengisa ukuhleleka, emdeni ngokutjho bonyana ama-339 eza emva kwama-239, ngakho-ke ngiyazi
indawo namkha ubujamo indawo namkha ubujamo bonyana yikulu.
• Ukusebenzisa, • Ukusebenzisa, ukufunda
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ukufunda nokutlola nokutlola iinomborosikhundla,
iinomborosikhundla, ukufaka ukufaka hlangana
hlangana nezirhunyeziweko nezirhunyeziweko ezifika
ezifika ema-31. ema-31.
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
1.5 Ukulemuka ubukhulu Ukulemuka ubukhulu bedijithi Ngikuphi okuhlukileko kunethemini yoku-1?
Ubukhulu beenomboro zamadijithi beenomboro ukufikela ema Ethemini yesibili abafundi baphula iinomboro zamadijithi amathathu kokuthoma.
bedijithi ama-3 ukufika ema-999 500 Umthetho wobukhulu bedijithi ukhulisiwe ukufaka hlangana amakhulu.
• Ukwazi bonyana inomboro • Ukwazi bonyana inomboro Ukuzwisisa kwabafundi kobukhulu bedijithi kungathuthukiswa ngokuza
yedijithi yinye ijamele ini yedijithi ngayinye ijamele ini imibuzo, enjengokuthola okunengi ngalitjhumi nofana okuncani kunenomboro.
• Ukuphula iinomboro • Ukuphula iinomboro Ngesizathu samalemuko wanjalonjalo ekuthuthukiseni umqondo wobukhulu
zamadijithi ama-3 zamadijithi amathathu ukufika bedijithi, abafundi kufanele bakghone ukubala nokuzithemba ngama-100,
ukufika e-999 ukuya ema-500 ngokubuyabuyelela bavumbulule amaphetheni ahlobene nobukhulu bedijithi begodu nokwakha
ngokubuyebuyelela kwe- ngamakhulu, ngamatjhumi nokuphula iinomboro zamadijithi amabili namathathu.
100, ukubuyebuyelela kwe- nangemivo (KTU) Abafundi kufanele banikelwe ithuba elaneleko ukwakha iinomboro zamadijithi
10 begodu nemivo • Ukubona begodu nokutjho amathathu ngamabhlogo weDienes nofana isisekelo samabhlogo ali-10.
• Ukubona begodu nokutjho ubungako bedijithi ngayinye Kuqakathekile bonyana bakhe ukwenza i-100 begodu bathome ukubona i-100
ubungako bedijithi ngayinye njengento ezijameleko. Abafundi kufuze babuzwe bonyana ziiqhema ezingaki
zama-100 abanazo. Amakarada wobukhulu bedijithi kufuze busetjenziswe
ukutjengisa iinomboro.
Ukusebenzisa amaDienes nofana isisekelo samabhlogo ali-10, imibuzo nofana
iinyalelo ezilandelako zingabuzwa nofana zinikelwle:
• Ma-100 amangaki ange: 300, 400, 500?
• Yakha iinomboro ezilandelako: 256, 378, 499
Ethemini le abafundi bafunda ukutjho begodu nokutlola phasi ubungako
bedijithi enomborweni.
Ema-452, ubungako bo-5 matjhumi amahlanu.
Ema 325, ubungako bo-5 si-5.
Kuqakathekile ukuhlobanisa ilemuko lama-50 nebuthelelo eli5 lamatjhumi
begodu oku-5 nabokunye abahlanu abatjhaphulukileko.
Amakarada wobukhulu bedijithi aqakatheke ngokulinganako. Amakarada
wobukhulu bedijithi asetjenziselwa ukuphula iinomboro ukutjengisa ubungako
bedijithi ngayinye
Abafundi bangenza amasede wabo wamakarada wobukhulu bedijithi. Imvilobhu
ingananyatheliswa emuva kwencwadi zabo zomsebenzi begodu namakarada
ahlale lapho.
Amakarada angasetjenziswa lokha nabenza ukuhlanganisa begodu kungaba
ngenye indlela abayisebenzisako ukuhlola iimpendulo zabo.
385
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
386 IMINQOPHO YETHEMU YESI-2 YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
1.5 Ukulemuka ubukhulu Ukulemuka ubukhulu bedijithi Basebenzisa amakarada wabo wamafardi ukutjengisa lokhu:
Ubukhulu beenomboro zamadijithi beenomboro ukufikela ema
bedijithi ama-3 ukufika ema-999 500
• Ukwazi bonyana inomboro • Ukwazi bonyana inomboro
yedijithi yinye ijamele ini yedijithi ngayinye ijamele ini
• Ukuphula iinomboro • Ukuphula iinomboro
zamadijithi ama-3 zamadijithi amathathu ukufika
ukufika e-999 ukuya ema-500 ngokubuyabuyelela
ngokubuyebuyelela kwe- ngamakhulu, ngamatjhumi
100, ukubuyebuyelela kwe- nangemivo (KTU)
10 begodu nemivo • Ukubona begodu nokutjho
• Ukubona begodu nokutjho ubungako bedijithi ngayinye
ubungako bedijithi ngayinye Ukuphula iinomboro zamadijithi amabili ngokubuyabuyelela ngamakhulu,
ngamatjhumi nangamivo.
Abafundi bangaphula iinomboro nge:
• Ubungako bamakhulu, bamatjhumi nemivo isib. 273 = 200 + 70 + 3
(amakarada wobukhulu bedijithi alisizo ekwenzeni lokhu)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ukubuyabuyelela ngalitjhumi nangakakunye isib. 273 = 2 amakhulu, 7
amatjhumi + 3 emiveni
Ukwakha iinomboro zamadijithi amabili eengcenyeni zobukhulu bedijithi
Isibonelo:
Tlola inomboro:
• ikhulu eli 1 namatjhumi ama- 3
• amakhulu ama-2 namatjhumi ama-4 begodu nemivo emi-5
• amakhulu ama-3 namatjhumi ali-9 begodu nemivo emi-2
• amakhulu ama-4 namatjhumi ama-5 begodu nemivo eli-7
Isibonelo: Zalisa:
a) 346 = 300 + + 6
b) 400 + 20 + 8 =
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
UKURARULULA IMIRARO EBUJAMENI OBUTHILEKO.
1.6 Ukusebenzisa amathekhiniki Ukusebenzisa amathekhiniki Abafundi baragela phambili ngokurarulula imiraro yamagama basebenzisa
Amathek- alandelako nakurarululwa alandelako nakurarululwa amathekhiniki alandelako:
hiniki wok- imiraro begodu kuhlathululwa imiraro: • Ukwakha nokuphula iinomboro
urarulula iinsombululo zemiraro: • Ukwakha nokuphula • Ukubuyelela kabili nokuhafula phakathi
imiraro • Ukwakha nokuphula iinomboro
• Amanambalayini
iinomboro • Ukubuyelela kabili nokuhafula
Qala amanothi ethemini yoku-1
• Ukubuyelela kabili phakathi
nokuhafula phakathi Ngikuphi okuhlukileko kunethemini yoku-1
• Inambalayini
• Inambalayini Ukutjhideza
• Ukutjhideza etjhumini
• Ukutjhideza etjhumini Ethemini le abafundi bathoma ukutjhideza iinomboro eziseduze kwe-10.
Ukutjhideza kumhlobo wokulinganisa ojayeleke khulu. Nangabe umfundi naka
umlinganisi omuhle ikghono lakhe lokutjhideza lifanele libe ngelitjhugulukako
begodu nelizwisiseka kuhle. Ngaphambi kobana abafundi basebenzise
ukutjhideza njengethekhniki nabahlanganisa nofana bakhupha, badinga
bathome ngozijayeza ithekhniki.
Lokhu kungenziwa ngokusebenzisa inambalayini.
Isibonelo:
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Ama-33 aseduze kwama 30 nofana kwama 40?
Ama 37 aseduze kwama 30 nofana 37?
Abafundi kufuze bazwisise bonyana:
Ama-35 ahlangana kwama-30 begodu nama-40. Sithi i-10 eliseduze nama-
35 ma-40 ngombana sitjhideza eduze netjhumi lokha inomboro ihlangana
namatjhumi amabili. Qala amanothi ethemini yesi-2.
387
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
388 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Iimbonelo zemiraro engenziwa ngeThemu le
Ukuh- yamagama yamagama Imiraro yokuhlanganisa nokukhupha
langanisa ezisebujameni ezisebujameni
• UBuyaphi ubuthelele iimvalo zamabhodlela ezima-413. USolani nakangamnikela iimvalo
nokukhupha bewuhlathulule bewuhlathulule
zamabhodlela ezima 29, uzakuba nenani ezifanako noBuyaphi.
iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka -- Bazakuba nemuvalo zamabhodlela ezingaki bobabili?
ukuhlanganisa ukuhlanganisa -- Bekade aneemvalo zamabhodlela ezingaki uSolani ekuthomeni?
nokukhupha nempendulo nokukhupha nempendulo • UKsk.Masimula uboleke amaranda ama-R80.00 kuKsk. Msiza. UKsk. Masimula usele
ukufika e-99. ukufika e-400. ngamaranda ama-R366.00. Bekanamalini uKsk. Masimula ekuthomeni?
• UMsongelwa ufunda amakhasi ali-115. UTjhejeni ufunda amakhasi ali-126. Ufunde
amakhasi amangaki uTjhejeni ukudlula uMsongelwa?
• UMbalekwa unamamabula ama-218. Unamamabula ama-97 ngaphasi kewaka-Anna.
Unamamabula amangaki u-Anna?
1.8 Rarulula imiraro Rarulula imiraro Iimbonelo zemiraro engenziwa ethemini le
Ukuh- yamagama yamagama Qala ezinye iimbonelo zeThemu yoku-1 begodu utjhugulule irherho lenomboro ngefanelo
langanisa ezisebujameni ezisebujameni
• Umenenjari kufanele a-ode amatayere webhesi abu-8. Nakube ibhesi ngayinye itlhoga
okubuyele- bewuhlathulule bewuhlathulule
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amatayere asithandathu nespere, matayere amangaki okufuze bonyana umenenjara
lwako iinsombululo zakho iinsombululo zakho
awa-ode?
okurholela zemiraro, ezifaka zemiraro, ezifaka
ukubuyabuyelela ukubuyabuyelela • Idanyana lokududa lesikolo libubude bamamithara ali-10. Umenzi ududa ubude
ekubuy-
okunempendulo ufikela okunempendulo ufikela beengaba ezisithandathu. Udude wafika kuphi?
abuyeleleni
e-100. e-75. Umhlobo womraro : Irhemo
• Isivande somrorho sinamareyi ali-12 weentjalo. Ireyi ngayinye ineentjalo ezi-7. Ziintjalo
ezingaki ezikhona ngesivandeni?
• Isivande somrorho sinamareyi ali-12 weentjalo. Ireyi ngayinye inenani elifanako leentjalo.
Nakube kunenani leentjalo eli- 48, kuneentjalo ezingaki ereyini ngayinye?
• Isivande somrorho sineentjalo ezi-48 ezitjalwe ngereyi. Ireyi ngayinye ineentjalo ezi-7.
Kunamareyi amangaki?
Ukumadanisa/Iretjhiyo
• UDzubhana unamaswidi asi 6. UDzubhana unamaswidi abuyelelwe kathathu kunewaka
uLindokuhle. UMoeketsi unamaswidi amangaki?
• UKunubhe unamswidi ali-18. Lokhu kunengi ngokubuyelelwe kathathu ukudlula
uDzubhana anakho. UDzubhana unamaswidi amangaki?
Umhlobo lo womraro uthulwa kokuthoma ethemini yesi 2. Abafundi bangathatha isikhathi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
eside ukurarulula imiraro yemihlobo le.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
1.9 Ukurarulula Ukurarulula Iimbonelo zemiraro engenziwa ethemini le
imiraro yamagama imiraro yamagama Ziinkoloyi ezingaki ezizotlhogeka ukukhambisa abafundi aba-24 nakube abane
Uku- ezisebujameni ezisebujameni
buthelela bangalingana ekoloyini yinye?
bewuhlathulule bewuhlathulule
nokukwaba iinsombululo zakho iinsombululo zakho Kunamakowusu ama 65 ngelayini. Kunamapara wamakowusu amangaki?
okurholela ufake ukwabelana ufake ukwabelana Ukubuthelela Ukuhlanganisa iinomboro ezinamadijithi
ekuhlukaniseni ngokulingana ngokulingana ama-3 ngezinye
Ugijimani uthengisa imigodla enamalamune alitjhumi umgodla ngamunye.ezinamadijithi
Unamalamune ama-3
nokubuthelela nokubuthelela
ngeenqema ngeenqema ama 40. Angazalisa imigodla mingaki?
kweenomboro kweenomboro UMsongelwa unamaswidi ama-66. Udla amaswidi ama-3 ngelanga. Uzakudla amaswidi
ezipheleleko ukufika ezipheleleko ukufika amalanga amangaki?
e-100 kanye nempendulo e-75 kanye nempendulo
ezingahle zifaka iinsalela ezingahle zifaka iinsalela
1.10 Ukurarulula Ukurarulula Ethemini yoku-1 abafundi bathulelwa amafrakhtjhini angakahleleki isib. Amakotara ama-3
bewuhlathulule bewuhlathulule nofana uku-2 kokuthathu.
Ukwabelana
iinsombululo zemiraro iinsombululo zemiraro Iimbonelo zemiraro engenziwa ethemini le
okurholela
ephathekako efaka ephathekako efaka
ekuhlu- a) Ukwabelana, okurholela emafrakhtjhinini
hlangana ukwabelana hlangana ukwabelana
kaniseni b) Ukwaba amaqa weentina zetjhokoledi abu-8 hlangana kwabangani aba-3 ukuze boke
ngokulingana erholela ngokulingana erholela
empendulweni empendulweni bathole inani elilinganako lamaqa weentina zetjhokoledi begodu akukasali litho
zamafraktjhini wohlavu zamafraktjhini wohlavu c) Ifraktjhini yokubuthelela
olulodwa nalayo olulodwa nalayo d) Thola ikotara yi-1 yamaswidi ama-20.
angenahlavu eyodwa. angenahlavu eyodwa.
1 1 1 2 2 1 1 1 2 2 e) Amaswidi asi-6 ayifraktjhini yiphi yamaswidi ama-24
isib. 2 , 4 , 5 , 4 , 5 njll. isib. 2 , 4 , 5 , 4 , 5 njll.
f) Ugogo unikela uKiki amaranda ali-R12. Ukiki ufuna ukubulunga okuthathu kwemali.
Yimalini okufuze ayibulunge?
Umhlobo lo womraro kufuze ibuzwe kuphela ngemuva kokuba abafundi bararulule imiraro
emine nofana emihlanu yokwabelana, ukurholela emihlobeni yamafrakhtjhini nokwazi
amagama wengcenye zamafrakhtjhini.
Ukutlola
Abafundi akukafuneki bonyana batlole itshwayo lefrakhtjhini. Abafundi baragela phambili
ngokulebula ingcenye zamafrakhtjhini njengo 1 kokuhlanu, amakotara ama-3 nofana oku-3
kwesithandathu.
Ukujamela amafrakhtjhini wemiraro yamagama
Abafundi kufanele bagwale iimpendulo zabo ukutjengisa bonyana bazwisisa imiraro.
Lindela bonyana abanye abafundi bangagwala kuhle kodwana bahluleka ukubiza ingcenye
yefrakhtjhini. Siza abafundi laba ukubiza kuhle amafrakhtjhini ngefanelo (qala amanothi
389 wokutjho amafrakhtjhini ngaphasi kokubala zobujamo obutjhaphulukileko)
Abafundi bafanele batjho iingcenye ezabiweko ngokuzitlola njenga- 2 kobuthathu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
390 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.11 • Ukukhumbula • Ukukhumbula Iimbonelo zemiraro engenziwa ethemini le:
Imali nokubona iinhlavu nokubona iinhlavu • Ubungako bemali nokwenza amanani woke isib.
nemali yamaphepha nemali yamaphepha
-- Ukutlola ama-525c ngamaranda nangamasende.
yeSewula Afrika yeSewula Afrika
-- Kungeendlela ezihlukeneko ezingaki ongenza amaranda ama-R400 usebenzisa imali
• Ukurarulula imiraro • Ukurarulula imiraro
yamaphepha yodwa? Wazi bunjani bonyana unazo zoke iisombululo?
yemali efaka hlangana yemali efaka
inani loke begodu hlangana inani loke -- UThabo una-50c begodu nama-20c amane. Amathofi abiza i-R1,20. uzothola itjhentjhi
netjhentjhi emaranda begodu netjhentjhi yamalini?
namasende ngamaranda nofana • UMandla ubhadela ama-R2,50 ukukhwela iteksi eya esikoleni.
• Ukutjhugulula ngamasende -- Kumbiza malini ukuya nokubuya esikoleni ilanga ngalinye?
amaRandi namasende -- Isitimela sibiza amaranda asi R6 ukuya nokubuya. Ngiyiphi engabiziko, sitimela nofana
yiteksi?
• Imiraro yokuthenga nokuthengisa
-- Ugogo kaPendulo umnikele amaranda ama-R5. Amakuke wetjhokoladi ma-
R2,70, amatjhungamu a-R1,80; amaswidi weemzobe amunyu a-R1,40; amaswidi
wamaperegisi a-R1,60; amaminti womlingo ama-R2,20; amathofi a-R1,20. Angathenga
amaswidi maphi ama 3?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
-- UZumnandi uthenge iincwadi ezintathu ngama-R80 incwadi ngayinye; uzothola
itjhentjhi yamalini ma-R300?
-- Amaphakethe wamaminti ama-5 abiza ama-44c lilinye. UMnu. uMthimunye uthloga
amaminti ama-88. Kufanele athenge amaphakethe amangaki? Uzobhadela malini?
• Iimbhesi ezintathu zikhamba endleleni ekulu ebhadalelwako begodu zibhadale amaranda
ama-R40 ibhesi ngayinye. Babhadela malini nasele zizoke? ( kulindeleke bonyana
abafundi bazosebenzisa imiraro yokuhlanganisa okubuyelelweko lapho ubungako
beranda bubukhulu khona)
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
UBUJAMO BOKUBALA OBUTJHAPHULUKILEKO.
1.12 Ukusebenzisa Ukusebenzisa Abafundi balindeleke ukusebenzisa amathekniki alandelako nabenza iimbalo zobujamo
Amathek- amathekniki alandelako amathekniki alandelako obutjhaphulukile:
niki (Iindlela nakwenziwa iimbalo: nakwenziwa iimbalo: • Ukwakha nokuphula iinomboro
nofana am- • Ukwakha nokuphula • Ukwakha nokuphula • Ukubuyelela kabili nokuhafula phakathi
athekniki) iinomboro iinomboro
• Amanambalayini
• Ukubuyelela kabili • Ukubuyelela kabili
• Ukutjhideza ngamatjhumi
nokuhafula phakathi nokuhafula phakathi
Vumela abafundi bona bakhethe ithekiniki ezokwanelisa bona. Noma kunjalo, lokha
• Amanambalayini • Amanambalayini
abafundi basebenzisa amathekhiniki angabanikeli ikghono, kufaneke bayeleliswe
• Ukutjhideza • Ukutjhideza ngeendlela zokwenza ezingaba lirhelebho kibo.
ngamatjhumi ngamatjhumi
Qala amanothi wethemini yoku 1 aphathelene no
• kwakha nokuphula iinomboro
• kubuyelela kabili nokuhafula phakathi; begodu
• Amanambalayini
Ukutjhideza ngamatjhumi
Qala ihlathululo esigabeni sokurarulula imiraro sethemini yesi-2.
391
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
392 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Ngikuphi okuhlukileko eThemini yesi-2?
Ukuh- ukufikela ema -999 ukufikela ema -400 Ethemini le abafundi babala ngeenomboro zamadijithi amathathu kokuthoma. Ukuze ubale
langanisa • Ukukhupha ukusuka • Ukukhupha ukusuka ngeenomboro zamadijithi amathathu ngokuzithemba, kufanele ukuba sebakghona uku:
nokukhupha ema -999 ema -40 • Funda nokutlola amatshwayo weenomboro ukufika ema-400;
• Ukusebenzisa • Ukusebenzisa • Hlela begodu umadanise iinomboro ukufika okungasenani ema-400;
amatshwayo afaneleko amatshwayo afaneleko
(+, –, =, ) (+, –, =, ) • bala ngeenqhema ukufika ema-400; begodu
• Ukuzijayeza • Ukuzijayeza • Bala ngeenkhewu zanga 2, 3, 4, 5, 10, 50 begodu ne-100 ukufika ema-400.
ukulumbana ukulumbana Ethemini le abafundi baragela phambili ukuphula iinomboro ukuze babale. Ukwakha
kweenomboro ukufika kweenomboro ukufika nokuphula iinomboro kuhlala kungelinye lamaqhinga aqakathekile abafundi
ema-30 ema 30 abazowasebenzisa ngeThemu le.
Iindlela zamakghono ezenzekako zokutjengisa iimbalo zokuhlanganisa nokukhupha.
• Ukuphula inomboro ngeengcenye ezincani ukwenza ukubala kube lula.
Amaqhinga amanengi asetjenziswa bafundi afaka hlangana ukuphula iinomboro. Baragela
phambili ukwenza njalo ngeenomboro zamadijithi amathathu.
• Ukuhlanganisa ngokuphula inomboro yinye
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuhlanganisa amadijithi amathathu namadijithi amabili
Isibonelo:
324 + 82 =
324 + 82 = (300 + 20 + 4) + (80 + 2)
= 300 + (20 + 80)+ (4 + 2)
= (300 + 100) + 6
= 400 + 6
= 406
Isibonelo:
Ukuhlanganisa iinomboro ezinamadijithi amathathu nezinye ezinamadiji amathathu
Ukuphula iinomboro zombili
323 + 136 =
323 + 136 =(300 + 20 + 3) + (100 + 30 + 6)
= (300 + 100) + (20 + 30) + (3 + 6)
= 400 + 50 + 9
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
= 459
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa • Ukuhlanganisa (ngokuphula inomboro ezohlanganiswa)
Ukuh- ukufikela ema -999 ukufikela ema -400 Abafundi bazophula inomboro ngeendlela ezilawulekako kibo. Lokhu kutjho bonyana
langanisa • Ukukhupha ukusuka • Ukukhupha ukusuka bazokwenza ngeendlela ezihlukahlukeneko.
nokukhupha ema -999 ema -40 Isibonelo Isibonelo
• Ukusebenzisa • Ukusebenzisa 324 + 82 =
amatshwayo afaneleko amatshwayo afaneleko
(+, –, =, ) (+, –, =, )
324 + (40 + 40 + 2) 323 + 136 =
• Ukuzijayeza • Ukuzijayeza
ukulumbana ukulumbana 324 + 40 → 364 + 40 → 404 + 2 = 406 323 + 136 = 323 + (100 + 30 + 6)
kweenomboro ukufika kweenomboro ukufika = (323 + 100) + 30 + 6
ema-30 ema 30 = (423 + 30) + 6
= 453 + 6
= 459
Ukubala ngama-40 ukusukela ema-324 kungenziwa ngokubala ngali-10.
• Ukukhupha
• Ukuphula iinomboro zombili
Iinomboro zamadijithi amathathu ukhuphe zamadijithi amabili
Isibonelo:
389 – 137 =
389 – 137 = (300 + 80 + 9) – (100 + 30 + 7)
= (300 – 100) + (80 – 30) + (9 – 7)
= 200 + 50 + 2
= 252
Ukukhupha ngokuphula inomboro yinye
Isibonelo:
389- 137 =
389 – (100 + 30 + 7)
389- 100 → 289- 30 → 259- 7 = 252
Ukusebenzisa ukuhafula phakathi ukuphula inomboro
Isibonelo:
225 + 16 = 225 + 8 +8
393 = (225 + 8) + 8
= 233 + 8
= 241
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
394 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa • Bala uye phambili begodu nemuva
Ukuh- ukufikela ema -999 ukufikela ema -400 305 + 298 =
langanisa • Ukukhupha ukusuka • Ukukhupha ukusuka Ukubala uye phezulu ngakunye ukusuka ema-298 kuliqhinga elifaneleko ngombana
nokukhupha ema -999 ema -40 iinomboro zitjhidelene.
• Ukusebenzisa • Ukusebenzisa • Ukubona Ukubuyelela kabili okuseduze
amatshwayo afaneleko amatshwayo afaneleko
(+, –, =, ) (+, –, =, ) Isibonelo:
• Ukuzijayeza • Ukuzijayeza 145 + 146 = 191 ukuhlathulula bonyana kubuyabuyelela kabili kwe-145 hlanganisa na- 1
ukulumbana ukulumbana nofana ukubuyabuyelela kabili kwe-145 khupha ku-1.
kweenomboro ukufika kweenomboro ukufika 145 + 145 + 1
ema-30 ema 30 (100 + 40 + 5) + (100 + 40 + 5) + 1
(100 + 100) + (40 + 40) + (5 + 5 + 1)
200 + 80 + 11
280 + 11
280 + 10 + 1
290 + 1
ISIGABA ESISISEKELO AMAGREYIDI 1-3
291
• Tjhugululela inomboro ekubuyabuyeleni ngetjhumi begodu ukhuphe nofana uhlanganise
kanye.
Bala uye phezulu nofana ubale uye phansi eduze ne 10
Isibonelo:
288 + 11
288 + 10 = 298
298 – 1 = 297
Isibonelo:
188 + 19
188 + 20 = 208
208 – 1 = 207
Ukuthuthukisa nokujayeza amakghono wokuhlanganisa nokukhupha.
Abafundi kufanele bajayeze imihlobo eminye yamakghono wokuhlanganisa nokukhupha.
• Ukujayeza amabhondi ukufika ema 30
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Hlangansa begodu ukhuphe ukubuyabuyelela nge 10
Abafundi kufanele babe namathuba wokwenza imihlobo elandelako yokubala ngeenomboro
ezifika ema 400:
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Hlanganisa nofa ukhuphe ipara yokubuyabuyelela nge 10, uvkweqela ema- 100
Ukuh- ukufikela ema -999 ukufikela ema -400 40 + 70
langanisa • Ukukhupha ukusuka • Ukukhupha ukusuka 70 + 80
nokukhupha ema -999 ema -40 120 – 30
• Ukusebenzisa • Ukusebenzisa 150 – 60
amatshwayo afaneleko amatshwayo afaneleko Hlanganisa nofana ukhuphe i-10 ukuya nofana ukusuka kwenye nenye inomboro
(+, –, =, ) (+, –, =, ) yamadijithi amabili nofana amathathu, kufaka hlangana ukweqela ema 100..
• Ukuzijayeza • Ukuzijayeza Isibonelo:
ukulumbana ukulumbana
65 + 10
kweenomboro ukufika kweenomboro ukufika
ema-30 ema 30 124 + 10
326 - 10
358 - 10
Hlanganisa nofana ukhuphe inomboro enedijithi yinye nofana enomborweni enamadijithi
amathathu ngaphandle kokweqela ngematjhumini.
Isibonelo:
234 +5
475 + = 479
768 – 4
Hlanganisa begodu uhlukanise inomboro enedijithi yinye ukuya nokusuka ekubuyabuyeleni
nge 100.
Isibonelo:
200 + 4
300 + 3
300 - 6
400 - 5
Thoma ukuhlanganisa nokukhupha ipara yokubuyabuyelela nge 100
100 + 100
100 + 200
Abafundi kufanele banikelwe amathuba wokuzijayeza amaphetheni ekuhlanganiseni
nekukhupheni.
Nangazi bonyana 1+ 1 = 2
Ngakho-ke yini i:
10 + 10
395 100 + 100
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
396 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Ukuhlola imiphumela yokubala
Ukuh- ukufikela ema -999 ukufikela ema -400 Ukuhlola ukuzwakala kweensombululo
langanisa • Ukukhupha ukusuka • Ukukhupha ukusuka Abafundi kufanele babandulwe ukuhlola ukuzwakala kweensombululo. Enye indlela
nokukhupha ema -999 ema -40 yokwenza lokhu kulinganisa iimpendulo zabo ngaphambi kokubala. Lokha uhlanganisa
• Ukusebenzisa • Ukusebenzisa iinomboro ezimbili ezitjhideleneko isib. i-145 ne-146, abafundi bangasebenzisa ukubuyelela
amatshwayo afaneleko amatshwayo afaneleko kabili njengendlela yokulinganisa iimpendulo zabo.
(+, –, =, ) (+, –, =, ) Ukuhlola iinsombululo
• Ukuzijayeza • Ukuzijayeza Abafundi kufanele bazi bonyana banga
ukulumbana ukulumbana
• Hlola isibalo sokuhlanganisa ngokukhupha. Isibonelo: Nangabe 236 + 18 = 254; bese
kweenomboro ukufika kweenomboro ukufika
ama 254 – 18 = 236; begodu
ema-30 ema 30
• Hlola isibalo sokukhupha ngokuhlanganisa. Isibonelo: 384 – 48 = 336, bese 336 + 48 =
384.
Ukusebenzisa itshwayo lokubala eliphekghukileko ukuhlola iinsombululo ngesinye
seenzathu zokufundisa ukuhlanganisa nokukhupha ndawonye.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
red
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Ethemini le abafundi baragela phambili ngoku:
Ukuh- ukufikela ema -999 ukufikela ema -400 • sebenzisa nokuzwisisa ilimi lokubuyabuyelela;
langanisa • Ukukhupha ukusuka • Ukukhupha ukusuka • jamela ukubuyabuyelela njengerhemo;
nokukhupha ema -999 ema -40
• sebenzisa amatshwayo afaneleko ukurhumutjha imitjho yeenomboro;
• Ukusebenzisa • Ukusebenzisa
• zwisisa bonyana ukuhlanganisa okubuyelweko kungajanyelwa ngokusebenzisa itshwayo
amatshwayo afaneleko amatshwayo afaneleko
lokubuyabuyelela;
(+, –, =, ) (+, –, =, )
• jayeza begodu uzwisise bonyana ukubuyabuyelela kungenziwa ngenye nenye indlela
• Ukuzijayeza • Ukuzijayeza
(umthetho nofana ihlelo elihlanakelekako); begodu
ukulumbana ukulumbana
kweenomboro ukufika kweenomboro ukufika • sebenzisa inambalayini ukubonisa iimbalo zokubuyabuyelela begodu ukghone
ema-30 ema 30 ukuhlathulula ukujanyelwa (imeqo ikhomba bunjani ukuhlanganisa okubuyelelweko)
Abafundi bangaragela phambili ukusebenzisa amarhemo ukutlola ukuhlanganisa
okubuyelelweko nemitjho yokubuyabuyelela yeenomboro.
Isibonelo:
Tlola imitjho yeenomboro yokuhlanganisa kabili nokubuyabuyelela kabili kwerhemo.
orange
red
Imifanekiso esetjenziswe ukuhlathulula ukubuyabuyelela ingavulwa. dark
green
dark
green
Ithebula yokubuyabuyelela ingathulwa. Isibonelo: purple
purple
purple
purple
red
red
red
red
red
red
× 2 3 4 5 6 7 8 9 10
W
W
W
W
W
W
W
W
W
W
W
W
1
2
3
4
5
Ukuvuma/ukurhwelela amathebula kungenziwa. Abafundi abakafaneli ukwazi amathebula
eGreyidini yesi-3. Umnqopho uselimini, elivumela isithombe sehloko kwesiqhema.
397
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
398 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela ukuya Isibonelo:
Ukuh- iinomboro ukuya nga- nga-2, 4, 5, 10 kunani • okubili ngakunye kubili
langanisa 2, 3, 4, 5, 10 kunani lama-50
• okubili ngakubili kune
okubuyele- le-100. • Ukusebenzisa
• okubili ngakuthathu sithandathu
lwako • Ukusebenzisa amatshwayo afaneleko
okurholela amatshwayo afaneleko ( x, =, ) • okubili ngakune bunane
ekubuy- ( x, =, ) • okubili ngakuhlanu litjhumi
abuyeleleni • okubili ngasithandathu litjhumi nambili
• okubili ngakhomba litjhumi elinakune
• okubili ngobunane litjhumi nesithandathu
• okubili ngalithoba litjhumi nobunane
• okubili ngetjhumi matjhumi amabili
Ukukutjho ngalendlela kusekela ilwazi elithuthukiswe ekuhlanganiseni ngokubuyelela.
Ukuvuma/ukurhwelela kufanele kusekelwe ngokukhomba ekubaleni ngokulandelana nofana
inambalayini.
Abafundi bangasebenzisa amatjhadi naneko ukurekhoda amaphuzu wokubuyabuyelela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
isib.
isibonelo
Input
Okungeniswako Okuphumako
Output
1 Umthetho
Rule
3
5
7
× !
9
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
1.15 • Ukuhlukanisa • Ukuhlukanisa Ethemini yesibili abafundi baragela phambili ukujayeza nokuhlanganisa ndawonye
Ukuhlu- iinomboro ukufika iinomboro ukufika basebenzisa itshwayo lokuhlukanisa. Kufanele bazwisise bonyana umutjho wokuhlukanisa
kanisa kuma-99 nga- kuma-50 nga-,2,4,5,10 wenomboro ungahlathulula isimo esifaka hlangana ukubuthelela nofana ukwabelana.
1,2,3,4,5,10 • Ukusebenzisa Ngikuphi okuhlukileko kunethemini yoku-1?
• Ukusebenzisa amatshwayo Ethemini le abafundi bafanele bakghone ukutlola nokuhlathulula imitjho yokuhlukanisa
amatshwayo ngefanel ( ngefanelo. ( ÷, =, ) ekhambelanako:
÷, =, )
Abafundi bafanele bakghone ukurekhoda okulandelako:
30 ÷ 6 = begodu ama- 30 ÷ 5 =
Abafundi kufuze godu bathuthukise amaqhinga wokutlola iimbalo zokuhlukanisa.
Isibonelo:
Ukukhupha okubuyelelweko
Ukuze babale 12 ÷ 4 = Abafundi kufuze basebenzise iinthombe ukubonisa iinqhema
nokuwabelana.
One group
Isiqhema of 4
sinye Isiqhema
One groupsinye Isiqhema
of 4
One sinye
group of 4
sanga-4 sanga-4 sanga-4
Abela isiqhema sinye sanga-4 godu isiqhema sesibili sanga-4 begodu nesiqhema
sesithathu sanga-4.
12- 4 → 8 – 4 → 4- 4 = 0
Njengalokha isiqhema sinye sanga-4 sibekwa ngeqadi abafundi bangakhupha oku-4
kokuthoma begodu babale bonyana banazingaki eziseleko. Baragela phambili ngokwenza
lokhu babe bakhuphe koke. Ukugandelela egreyidini yesi-3 kufanele kube sesiqhemeni
kunokwabelana.
Ukwenza ukukhupha okubuyelelweko ngerherho lenomboro kulungile. Abafundi kuzofanele
banikelwe imitjho yokuhlukanisa yeenomboro ukuzalisa evumela ukwenza ukukhupha
okubuyelelweko. Ukwenza ukukhupha okubuyelelwe kwa 96 ÷ 3 akusiliqhinga elilungile
nofana iqhinga elisebenzako ngombana irherho leenomboro liphezulu khulu. Ekuthomeni
kungaba budisi ebafundini ukubona bonyana ngimiphi imitjho yeenomboro (ngiliphi irherho
leenomboro) elifaneleko ukwenza ukukhupha okubuyelelweko.
399
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
400 IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YESI-2
ama -24)
1.16 Umqondo nomboro: Irherho Umqondo nomboro: Umqondonomboro
Iimbalo ukufika 999 Irherho ukufika e-500 Iimbonelo zemibuzo engabuzwa:
zehloko • Hlela isede enikelweko • Hlela isede enikelweko Amabizo weenomboro namatshwayo
yeenomboro ezikhethiweko yeenomboro
Phakamisa ikarada nofana utlole phasi ibizo lenomboro. Khetha umfundi atlole
• Madanisa iinomboro ukufika ezikhethiweko. Irherho ukumadaniswa kweenomboro.
ema-999 begodu utjho bonyana ukufika ema-500
Okunengi nofana okumbadlwana
ngiyiphi enengi nofana encani • Madanisa iinomboro
Khuyini:
nga 1, 2, 3, 4, 5, begodu ne- 10 ukufika ema-500
begodu utjho bonyana • okuncani ngaku-1 kunama-500
Ukukhumbula msinyana:
ngiyiphi enengi nofana • okunengi ngaku-1 kunama-499
• Amaphuzu wokuhlanganisa
encani nga-1, 2, 3, 4, 5, • okunengi ngaku-2 kunama-502
nokukhupha ukufikela ema-20
ne 10
• Ukubuyabuyelela nge-10 • okumbadlwana ngaku-2 kunama-405
Ukukhumbula • okunengi ngaku-3 kunama-477
ngokuhlanganisa nofana
msinyana:
ngokukhupha ukusuka e-0 • okumbadlwana ngaku-3 kunama-251
ukufika e-100. • Ukukhumbula
• okumbadlwana ngaku-4 kune-185
amaphuzu
• Amaphuzu wokubuyabuyelela • okunengi nge-10 ngama-490
wokuhlanganisa
begodu nokuhlukanisawoku:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokukhupha ukufika • okumbadlwana nge-10 ngama-660
• Ithebula lokubuyabuyelela e- 20 Ngiyiphi iledere yesi-5 ye-alfabhethi?
ngaku-2 ukufika ku-2 x 10
• Hlanganisa Ngiyiphi inyanga ye-9 enyakeni?
• Ithebula nofana ukhuphe
lokubuyabuyelengali-10 ukufika Ukuhlela nokumadanisa
iimbuyabuyeleli ze-10
ku-10 x 10 ukusukela e-0 ukuya Ngiyiphi enengi: 621 nofana 671?
Amaqhinga wokubala e-100 Nikela inomboro ehlangana ne-154 ne-159.
Ukusebenzisa amaqhinga Amaqhinga wokubala Amaphuzu wokuhlanganisa nokukhupha:
wokubala alandelako: Sebenzisa amaqhinga Qala amanothi weThemi yoku-1.
• Beka inomboro ekulu maqangi wokubala alandelako:
ukuze ubale uye phambili Hlanganisa nofana ukhuphe ukubuyabuyelela ngali-10 ukusuka e 100.
• Beka inomboro ekulu
nofana uye emuva maqangi ukuze ubale Magadango amangaki okufanele athathwe enambalayini ukusuka e-30 ukufika
uye phambili nofana e-100 nofana ukusuka e-100 ukufika e-50.
• Inambalayini
uye emuva Thola amapara wamakarada ukwenza i -100.
• Ukubuyelela nokuhafula
• Inambalayini. Faka iinomboro ngemabhoksini ukwenza i-100.
• Ukwakha nokuphula
• Ukubuyelela nokuhafula + 70 = 100
• Ukusebenzisa ubudlelwana
obuphakathi kokuhlanganisa • Ukwakha nokuphula 20 + = 100
nokukhupha. • Ukusebenzisa 100 – = 90
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• sebenzisa ubudlelwano ubudlelwana hlangana 100 – 40 =
hlangana kokubuyabuyelela kokuhlanganisa Amaqhinga weembalo
nokuhlukanisa nokukhupha. Qala amanothi eThemu yoku-1
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YESI-2
CAPS
ama -24)
1.17 • Sebenzisa bewutjho Ethemini le abafundi baragela phambili uku:
Amafrak- amafraktjhini ajayelekileko • funda amabizo weengcenye zamafraktjhini;
tjhini akufaka hlangana iinquntu,
• sebenzisa amabizo ngebujameni obuhlukeneko;
amakota, iingcenye
zangobunane, iingcenye • fanisa ingcenye yefraktjhini;
zangobuthathu, iingcenye • thoma ukuzwisisa okuhlobene ngobukhulu;
zangasithandathu, iingcenye • thola amafraktjhini wezinto; begodu
zangahlanu
• Funda ngokulingana kwamafraktjhini.
• Ukubona amafraktjhini
Ethemini le abafundi bamadanisa amafraktjhini.
ebujameni obuyidayagremu
• Ukusebenzisa imitletle yamafraktjhini nofana neenlinganiso zeCuisenaire.
• Thoma ukubona bonyana
iinquntu ezi-2 nofana ubuthathu Isibonelo:
obu-3 benza kunye okuzeleko Imifuziselo le ilungele ukufundisa abafundi ukutjho amafraktjhini nokuwamadanisa.
nokuthi ihafu yinye namakotara Isibonelo:
ma-2 ayalingana.
orentji bomvu
hlaza satjani hlaza satjani
Tlola amafraktjhini njengehafu sasipiriti sasipiriti sasipiriti sasipiriti
yi-1, ku-2 kwethathu
bomvu bomvu bomvu bomvu bomvu bomvu
w w w w w w w w w w w w
Bonisa itjhadi lamafraktjhini akhombisa oku-1 okupheleko, iinquntu, ubuthathu,
amakotara, ubuhlanu, ubuthandathu, ububunane, ubulitjhumi. orange
red
Kuqakathekile bonyana abafundi basebenze ngensetjenziswa eziphathekako dark
green
dark
green
elineenthombe.
bangamadanisi amafrakhtjhini basebenzisa itjhadi lamafrakhtjhini purple
purple
purple
purple
nezinye.
Abafundi kufuze basebenzise izinto ngokuzimeda bazimadanise red
red
red
red
red
red
Imibuzo elandelako ingabuzwa: W
W
W
W
W
W
W
W
W
W
W
W
• Mangaki amahafu alingana nokupheleleko?
• Makotara amangaki alingana okupheleleko?
• Makotara amangaki asehafini eyodwa? Vumela abafundi babeke imitletlana
magega nayo ukuthola iimpendulo.
• Kukunye kwesithathau okungaki okulingana nokuphelelekko?
• Kukunye kwesithandathu okungaki okulingana nakunye kwesithathu?
• Kukunye kwesithandathu okungaki okulingana nehafu?
• Buthandathu obungaki obulungana isiquntu?
401 • Ngiyiphi ekulu, ku-1 kwesithathu nofana ihafu yi-1?
• Ngiyiphi ekulu ku-2 kwesithathu nofana amakotara ama-3?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI-2
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
402 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
2.1 Kopulula, ngezelela Kopulula, ngezelela Ragela phambili ngokunikela abafundi irherho elifanako lamaphetheni njengalawo Isifundo esi-1
Amapheth- begodu uhlathulule begodu uhlathulule. aseThemini yoku-1, kodwana ufake hlangana woke amajamo amatjha begodu nezinto
eni weJi- Kopulula, ungezelela Kopulula, ungezelela emaphethenini njengombana kusetjenzwa ngawo kusiKhala nobuJamo. Qala amanothi
yomethri begodu uhlathulule begodu uhlathulule wamaphetheni weThemu yoku-1 namanothi weSikhala Nobujamo eThemini yesi-2.
ngamagama ngamagama
• amaphetheni alula • amaphetheni alula Vumela abafundi bonyana bakopulule mantanzi, bese bayangezelele emaswapheleni
enziwe ngezinto enziwe ngezinto bahlathulule amaphetheni. Njenganje, bafanele bakwazi ukuhlathulula amaphetheni
eziphathekako eziphathekako ngaphandle kokurhelejwa imibuzo ebarholako. Ragela phambili nokunqophisa
• amaphetheni alula • amaphetheni alula ekuthuthukiseni ilimi abalitlhogako ukuhlathulula amaphetheni.
enziwe ngemigwalo enziwe ngemigwalo
yemida, amajamo yemida, amajamo
nofana izinto nofana izinto
Ukuzakhela Ukuzakhela
amaphetheni wakhe amaphetheni wakhe
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuzakhela amaphetheni Amaphetheni alula
wakhe weJiyomethri lapho ubujamo, nofana
ngezinto eziphathekako iinqhema zobujamo
zibuyelelwe ngendlela
ngokugwala imida,
efana poro
amajamo nofana izinto
Amaphetheni lapho
Amaphetheni
inomboro nofana
asizungelezileko
isayizi yamajamo
Ukubona , ukuhlathulula ezingeni ngalinye
ngamagama itjhuguluka ngendlela
nokukopulula enebonelo phambili o.u.
amaphetheni amaphetheni akhula
wejiyomethri ngendlela eqhelileko
• eemvelweni Ukuzakhela
• ebuphilweni amaphetheni wakhe
bangamalanga Ukuzakhela amaphetheni
banamhlanje wakhe wejiyomethri :
• elifeni lamasiko wethu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• ngezinto
eziphathekako
• ngokugwala imida,
amajamo nofana izinto
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
CAPS
ama -24)
2.2 Kopulula, ngezelela Kopulula, ngezelela Qala amanothi we Themu yoku- 1, Iimfundo ezi-3
Amaphe- begodu uhlathulule begodu uhlathulule Ngezelela irherho leenomboro nokulandelana kokubala ngendlela elandelako
theni Kopulula, ngezelela Kopulula, ngezelela • ngabo ku-1 ukusuka kunanyana ngiyiphi inomboro phakathi kwe-0 nama-500
weenom- begodu uhlathulule begodu uhlathulule
ukulandelana • ngali-10 ukusuka kunanyana ngikuphi ukubuyabuyelela kwe-10 hlangana kwe -0 nama-
boro ukulandelana
kweenomboro okulula 500
kweenomboro okulula
ukufika okungasenani • ngaku-5 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaka-5 hlangana kwe-0 nama-
Ukulandela- ukufika okungasenani e-150.
e-1 000 500.
na kufanele • Ukubala uye phambili
Ukuzakhela • Ngaku-2 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaka ku-2 hlangana kwe-0
kutjengise nemuva nga:
amaphetheni nama-500
ukubala uye • Ku-1 ukusuka kwenye
phambili ne- Ukuzakhela amaphetheni nenye inomboro • Nge-100 ukusuka kunanyana ngikuphi ukubuyabuyelela ukufika okungasenani e-1000
muva nga weenomboro. hlangana ne-0 ne-500. • Ngama-50 ukusuka kunanyana ngikuphi ukubuyabuyelela kwama-50 ukufika
• Li-10 ukusuka okungasenani e-1000
kesinye nesinye • Ngaku-3 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaka-3 hlangana kwe -0
isibuyabuyelelo se-10 nama-500
hlangana ne-0 ne-500.
• ngaku 4 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaka-4 hlangana kwe-0
• Ku-5 ukusuka nama-500
kesinye nesinye
isibuyabuyelelo saka Ukusebenzisa izinto, iinthombe, amathebula namatjhadi naneko ukusekela abafundi
ku-5 hlangana ne-0 ekutjhugulukeni ukusukela ekubaleni ngokweqa begodu nokulandelana ukuya
ne-500. ekubuyabuyeleleni ngali-10, 5, 2, 4.
• Ku-2 ukusuka Ukusiza abafundi ukusebenzisa amaphetheni abawaziko njengesisekelo sokuzijayeza
kesinye nesinye begodu nokufunda amanye amaphetheni isib.
isibuyabuyelelo saka • Ukulandelana kwabo ku-2 ukubeka isisekelo sokulandelana kwabo ku-4; begodu
ku-2 hlangana ne -0
ne-500. • Ukulandelana kwabo ku-5 njengesisekelo sokulandelana ngama-50.
• Ku-3 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-3 hlangana ne-0
ne-500
• Ku-4 ukusuka
kesinye nesinye
isibuyabuyelelo saka
ku-4 hlangana ne-0
ne-500
• Ma-20, 25, 50, 100
okungasenani ukufika
403 e-500.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI-2
ISIKHALA NOBUJAMO (JIYOMETHRI)
404 UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
: IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YOKU-1 namaminithi
ZOKUPHELA KONYAKA
ama -24)
3.1 Ubujamo nokubukela Ubujamo nokubukela Ngikuphi okuhlukileko eGreyidini yesi-2?
Ubujamo, • Madanisa imibono • Madanisa iimbono • Akunamnqopho onqophileko wokuthuthukisa ilimi lobujamo, njengombana lokhu
ukuzijayeza ehlukeneko ehlukahlukeneko yezinto kwenziwe eGreyidini yoku-1 neyesi-2.
nokubukela yezinto ezifanako ezifanako zangamalanga • Landela iinkombatjhuba ezinabako ngokungezelelweko isib.ukukhambakhamba
zangamalanga • Itjho into yangamalanga ngesikolweni, kunangetlasini nje.
• Yitjho into lokha nakuvezwa ihlangothi • Nikela iinkombatjhuba zendawo engetlasini nesikolweni.
yangamalanga elingakajayeleki layo.
• Imimebhe nokubukelwa okungaphezulu kwezinto ezibuthelelweko, lokhu
lokha nawutjengiswe Ubujamo nekombatjhuba kIMINQOPHO YETHEMU YESI-3.
ihlangothi
• Landela ikombatjhuba Umnqopho ophakanyisiweko weThemu yesi-2
elingakajayeleki layo.
ukukhamabakhamba
• Funda, rhumutjha KuThemu yesi-2, kutjhukunyiswa bonyana kubuyekezwe umsebenzi weGreyidi yesi-2
ngetlasini begodu
begodu ugwale begodu kuhlanganiswe,
nesikolweni
imebhe engakahleleki • Ukubona izinto eziseenthonjeni ezitjengisa ihlangothi elingakajayeleki noku:
Nikela ilayelo
nofana ukubukeka • Ukulandela iinkombatjhuba zeendawo ezihlukahlukeneko ngaphandle kwetlasi.
lokukhambakhamba
ISIGABA ESISISEKELO AMAGREYIDI 1-3
izinto eziphezulu
ngetlasini nesikolweni Thoma ngokuhlola lokho abafundi abakwaziko begodu ukhumbule ubujamo
ezibuthelelweko
nokuzijayeza
• Thola izinto emebheni
Ubujamo neenkombatjhuba
Ubujamo
• Ukulandela iinkombatjhuba
nekombatjhuba
Lokhu kufanele kwenziwe ngemisetjenzana ephathekako lapho abafundi
• Landela iinlayelo
bakhambakhamba ngokwabo ngokuya ngeenlayelo. Egreyidini yesi-3 abafundi
ukukhambakhamba
banganikelwa nofana iinlayelo ngamagama nofana zitlolwe.
ngetlasini
nasesikolweni. -- Ukukhambakhamba ngetlasini isib.” iza ngaphambili kwetlasi”, “jama hlanu
kwesitulo sakho”, “yeqa ngehla komgqomu wenzibi”; begodu
• Nikela ilayelo
zokukhambakhamba -- Ukhambakhambe ngetlasini nofana ngesikolweni, o.u: inkombatjhuba ezide,
ngetlasini nesikolweni “Khamba uphume emnyango, jikela ngesinceleni, ragela phambili wehlele
ngephasitjhi, yeqa itatawu, sewukuphi kwanjesi?
• Landela iinlayelo
ukusuka endaweni
enye ukuya
kwenye emebheni
engakahleleki
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
: IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YESI-2 namaminithi
ZOKUPHELA KONYAKA
CAPS
ama -24)
3.1 Ubujamo nokubukela Ubujamo nokubukela • Ukunikela iinlayelo. Iimfundo ezi-2
Ubujamo, • Madanisa imibono • Madanisa iimbono Abanye abafundi bafumana kulula ukunikela iinlayelo ngokutjengisa lokho
ukuzijayeza ehlukeneko ehlukahlukeneko yezinto abakutjhoko. Kwabanye abafundi kuyasiza ukunikela iinkombandlela zemininingwana
nokubukela yezinto ezifanako ezifanako zangamalanga eqakathekileko.
zangamalanga • Itjho into yangamalanga • Yitjho nanyana uragela phambili nofana ukhamba ngekomba oqalane nayo nofana
• Yitjho into lokha nakuvezwa ihlangothi uyajika.
yangamalanga elingakajayeleki layo. • Yitjho nanyana ukhamba bunqopha, ujikela ngesinceleni nofana ujikela ngesidleni.
lokha nawutjengiswe Ubujamo nekombatjhuba • Yipha iimmerego zalapho ufanele ujike khona isib. Nawuya e-ofisini lakamabhalana
ihlangothi
• Landela ikombatjhuba ujikela ngesinceleni; begodu itjho bonyana usazokukhamba kangangani.
elingakajayeleki layo.
ukukhamabakhamba • Yitjho bonyana ukude kangangani.Kuneendlela ezihlukahlukeneko zokutjho bonyana
• Funda, rhumutjha ngetlasini begodu kufanele ukhambe kangangani isib.
begodu ugwale nesikolweni
imebhe engakahleleki o Khamba amatriya ama- 30 nofana khamba amamitha ali-10
Nikela ilayelo
nofana ukubukeka o Khamba udlula amatlasi ama- 3, nofana bewudlule itlasi likaMnumzana
lokukhambakhamba
izinto eziphezulu uRhadebe nofana
ngetlasini nesikolweni
ezibuthelelweko
o Khamba isikhathi esingaba mzuzu mu-1.
• Thola izinto emebheni
Ubujamo nokubukela
Ubujamo
nekombatjhuba KuGreyidi yesi-3 abafundi bafanele banikelwe imisetjenzana lapho bangamadanisa
khona ukubukelwa okuhlukahlukeneko (bukela ukusukela phezulu, bukela ukusuka
• Landela iinlayelo
emaqadi, bukela ukusuka ngaphambili) kwezinto ezihlukahlukeneko zangamalanga.
ukukhambakhamba
ngetlasini Ekugcineni lokhu kuzokusiza abafundi bonyana barhumutjhe imigwalo yezinto
nasesikolweni. zeJiyomethri ezenziwe ngemibono ehlukahlukeneko.
• Nikela ilayelo Abafundi kufanele begodi banikelwe imisetjenzana lapho bazokubona izinto
zokukhambakhamba eenthombeni ezigwalweko, nofana ezithethwe ebujameni obungakajayeleki, isib.
ngetlasini nesikolweni ukubukeka kwelingaphezulu lekomo, nofana ingaphambili lebhorsolo yamazinyo.
• Landela iinlayelo
ukusuka endaweni
enye ukuya
kwenye emebheni
engakahleleki
405
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
406 : IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YESI-2 namaminithi
ZOKUPHELA KONYAKA
ama -24)
3.2 Irherho lezinto Irherho lezinto Ngikuphi okuhlukileko kuneGreyidi yesi-2?
Izinto ezi- Ukubona nokutjho izinto Ukubona nokutjho izinto • Abafundi abasaqali bonyana izinto zingagedeka nofana zingatjhelela; baqala
busontathu ezi 3-D ezingetlasini ezi 3-D ezingetlasini bonyana ingaphezulu nofana ilingaphandle lithabalele nofana ligobeneko.
neenthombeni
(3-D) neenthombeni • Lapho okunezinto ezinelingaphandle ngaphezulu elithabaleleko neligobeneko,
• Amajamo webhola
• Amajamo webhola (iindulungu) abafundi baqala kobana ilingaphandle leli lizinkwere, liboncantathu, liboncande
(iindulungu) • Amajamo webhoksi nofana liyindulungu.
• Amajamo webhoksi (amaphrizimu) • Amakhowuni nama phiramidi ayathulwa (Lokhu kungaba mnqopho weThemu yesi-3
(amaphrizimu) • Amasilinda begodu neye-4).
Amatshwayo wezinto
• Amasilinda Ukuhlathulula, ukubeka Umnqopho ophakanyisiweko weThemu yesi-2
• Iphiramidi ngeengaba nokumadanisa Abafundi basebenza ngezinto ezifanako njengombana bebenza eGreyidini yesi-2 o.u.
izinto ezi 3-D ngokuya: • Iimbholo nezinto ezibumbeke njengembholo;
• Iinkurwana
• amajamo we 2-D enza
(Amakhowuni) ubuso bezinto za3-D • Amasilinda nezinto ezinobujamo bebumbeko lamasilinda;
Amatshwayo wezinto • ilingaphandle elithabaleleko • Amabhoksi ahlukahlukeneko begodu nezinye izinto ezinobujamo obufana
Ukuhlathulula, nofana eligobeneko nobukancande, ncantathu, phrizimu nofana amakhyubhu.
ukubeka ngeengaba Imisetjenzana enqophiweko
Abafundi banganqopha ezintweni ezitjha (amaphiramidi namakhowuni) kuThemu yesi-3
• Tjheja begodu wakhe
nokumadanisa izinto ezi begodu ne-4.
izinto za 3-D ezinikelweko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
3-D ngokuya: Ukukhumbula nokutjho amagama weembholo (indulungu) namabhoksi (
ngokusebenzisa
• amajamo we 2-D enza amamathiriyeli iphrizimu) namasilinda
ubuso bezinto za3-D aphathekako • Abafundi baragela phambili nokutjho amagama, nokuhlela neengaba, nokubuthelela
• ilingaphandle njengamajamo wa 2-D izinto. Abafundi bafanele banikelwe izinto ezihlukahlukeneko abazokusebenza ngazo:
elithabaleleko nofana asikiweko, umdaka/ibumba,
iimbangulimazinyo, • Ezinobujamo obufana neendulungu, isib. iimbholo ezihlukahlukeneko ngamasayisi,
eligobeneko amamabula, amalamune njll. nofano
iphayiphi lokusela nezinye
Imisetjenzana izinto za 3-D zeJiyomethri • Ezinobujamo obufana nephrizimu isib. amabhlogo, iintina, amabhoksi
enqotjhiweko Irherho lamajamo ahlukahlukeneko ngamasayizi, amabhoksi womlilo,amabhoksi wamaseriyeli,
• Tjheja begodu • Iindulungu amabhoksi weentiye, amabhoksi weensibha zamazinyo; begodu
wakhe izinto za • Abocantathu
• Iinkwere • Ezinobujamo obufana namasilinda, ukufaka hlangana namasilinda amade
3-D ezinikelweko namatsikana isib.intokana zamaphayiphi anobujamo besilinda, amabhoksi
• Aboncande
ngokusebenzisa Amatshwayo wamajamo wamathawula agedekako wangekhwitjhini namkha amaphepha wangendlini
amamathiriyeli Ukuhlathulula,ukubeka yokuphumela, isib amabhlegana wephortjhi yamanyathelo, amabhlegana weeneyifu.
aphathekako ngeengaba nokumadanisa Abafundi bangathola izinto ezinobujamo beembholo (indulungu), nofana ezinobujamo
njengamajamo izinto ezinamajamo bebhoksi (iphrizimu) nofana ezinobujamo obufana nebesilinda nebanikelwe izinto
wa 2-D asikiweko, abobusobubili 2-D ngokuya ezibuthelelweko ukukhombisa ubujamo bazo. Abafundi bangathola nofana bakhombise
umdaka/ibumba, nga:
izinto ezinobujamo bamabhoksi (iphrizimu) ezingatlasini isib. “Lokho zingaba
iimbangulimazinyo, • Amajamo
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Amahlangothi anqophileko njengamatamati nofana ezizindulungu nfana ezinobujamo besilinda”.
iphayiphi lokusela
nezinye izinto za 3-D Amahlangthi andulungeleko Ngesikhathi sabafundi sokuzijamela bangaragela phambili benze iimbholo namasilinda
zeJiyomethri begodu namajamo wamabhoksi (amaphrizimu) avela emdakeni nofana emdakeni
wokudlala.
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
: IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YESI-2 namaminithi
ZOKUPHELA KONYAKA
CAPS
ama -24)
3.2 Irherho lezinto Irherho lezinto Umnqopho wamatshwayo wezinto zaka 3-D : ingaphezulu elithabaleleko nofana limfundo ezi-3
Izinto ezi- Ukubona nokutjho izinto Ukubona nokutjho izinto ingaphandle eligobekileko
busontathu ezi 3-D ezingetlasini ezi 3-D ezingetlasini • Yakha amabumbeko wezinto ezinobujamo ba 3-D.
neenthombeni
(3-D) neenthombeni Abafundi basebenzisa amabhoksi weenkwere nofana aboncande, aboncantathu,
• Amajamo webhola
• Amajamo webhola (iindulungu) ukwenza ibhoksi. Lokhu kwenza abafundi banqophe emajameni wengaphezulu
(iindulungu) • Amajamo webhoksi elithabaleleko.
• Amajamo webhoksi (amaphrizimu) Abafundi baqala amajamo welingaphezulu elithabaleleko nofana eligobeneko isb.
(amaphrizimu) • Amasilinda Iindulungu (iphrizimu) namasilinda bahlathulule ubujamo bazo ngokuya ngokuthi
Amatshwayo wezinto
• Amasilinda yindulungu, lisikwere, nguncantathu nofana nguncande.
Ukuhlathulula, ukubeka
• Iphiramidi ngeengaba nokumadanisa • Iingaphezulu nofana iingaphandle elithabaleleko nofana eligobeneko.
izinto ezi 3-D ngokuya: Ukwakha ibhoksi (iphrizimu) kusiza abafundi bonyana banqophe kulingaphezulu
• Iinkurwana
• amajamo we 2-D enza elithabaleleko lezinto.
(Amakhowuni) ubuso bezinto za3-D
Amatshwayo wezinto • ilingaphandle elithabaleleko Abafundi bangaqala bonyana ngabe zoke izinto eziyiJiyomethri zinelingaphezulu
nofana eligobeneko elithabaleleko kwaphela na? KuGreyidi yoku-1 neGreyidi yesi-2, abafundi bahlukanisa
Ukuhlathulula,
Imisetjenzana enqophiweko izinto zeJiyomethri ezigedekako nalezo ezitjhelelako. Lokhu kulingiselela abafundi
ukubeka ngeengaba
• Tjheja begodu wakhe ukubona banqophe ekuthini ilingaphezulu lithabaleleko (izinto ezitjhelelako) nofana
nokumadanisa izinto ezi
izinto za 3-D ezinikelweko ezigobeneko (izinto ezigedekako). Amasilinda anelingaphezulu elithabaleleko begodu
3-D ngokuya:
ngokusebenzisa anelingaphezulu eligobeneko.
• amajamo we 2-D enza amamathiriyeli Imisetjenzana etlolwako
ubuso bezinto za3-D aphathekako
njengamajamo wa 2-D Nanyana imisebenzi eminengi yezinto zabo 3-D zenziwe ngokuphathekako, umsebenzi
• ilingaphandle
asikiweko, umdaka/ibumba, ufanele uhlanganiswe ngokutlola imisetjenzana. Umnqopho we-Greyidi 3 ufanele
elithabaleleko nofana
iimbangulimazinyo, ube sekubizeni izinto ngamagama begodu kucoca bonyana ingaphezulu lazo nofana
eligobeneko
iphayiphi lokusela nezinye ingaphandle lazo libunjani. Akukalindeleki bonyana abafundi babale nofana bazi
Imisetjenzana izinto za 3-D zeJiyomethri inani leenkwere, laboncande, laboncantathu, leendulungu nofana ilingaphezulu
enqotjhiweko Irherho lamajamo nelingemaqadi elinazo.
• Tjheja begodu • Iindulungu
ILimi
wakhe izinto za • Abocantathu
• Iinkwere Ikghono elisetjenziswako zelimi ukucoca ngezinto zabo 3-D:
3-D ezinikelweko
• Aboncande Ilingaphezulu elithabaleleko, eligobeneko, amabhoksi, iimbholo, amasilinda.
ngokusebenzisa Amatshwayo wamajamo
amamathiriyeli Ukuhlathulula,ukubeka
aphathekako ngeengaba nokumadanisa
njengamajamo izinto ezinamajamo
wa 2-D asikiweko, abobusobubili 2-D ngokuya
umdaka/ibumba, nga:
iimbangulimazinyo, • Amajamo
iphayiphi lokusela • Amahlangothi anqophileko
407 nezinye izinto za 3-D Amahlangthi andulungeleko
zeJiyomethri
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
408 : IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YESI-2 namaminithi
ZOKUPHELA KONYAKA
ama -24)
3.3 Irhemo lobujamo Awukho umnqopho otjhukunyisiweko onqophe emajameni we 2-D kuThemu yesi-
Amajamo • Iindulungu 2. Nanyana abafundi bangahlanganisa lokho abakufundileko ngokutjheja nokutjho
abobusobu- amagama wamajamo wa 2-D eThemini yesi-2, ngokwenza imisetjenzana etlolwako
• Aboncantathu
bili (2-D) ngesikhathi sabafundu sokuzijamela.
• Iinkwere
• Aboncande
Amatshwayo
wobujamo
Ukuhlathulula,
ukubeka ngeengaba,
nokumadanisa amajamo
abo 2-D ngokuya nga:
• majamo
• mahlangothi
anqophileko
• mahlangothi
andulungileko
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Gwala amajamo
• iindulungu
• aboncantathu
• iinkwere
• aboncande
3.4 Isimethri Isimethri Ngikuphi okutjha eGreyidini yesi-3? limfundo ezi-2
Isimethri • Tjheja begodu ugwale • Khetha umuda wesimethri • Thola umuda wesimethri ngokubhinca amaphepha nokubonisa.
umuda wesimethri ngokubhinca amaphepha Umsetjenzana wokubhinca amaphepha othuthukisa ukuzwisisa kwesimethri kufaka
ngamajamo we nokubonisa hlangana:
2-D wejiyomethri
• imisetjenzana lapho kuthelwa ipende emanzi ephepheni ngaphambi kokuba
naleyo okungasiyo
libhincwe; begodu
yeJiyomethri
• imisetjenzana lapho iphepha lisikwa nofana lidatjulwa emudeni obhinciweko
• Khetha nofana jamisa
umuda wesimethri Lemisetjenzana ingenziwa esifundweni seeMbalo nezifundweni zamakghono wepilo.
abhincwako iphepha Bawa abafundi babonela bonyana phambili ngimaphi amajamo abazowathola
nangokubonisa godu. nabangathabulula nofana baqunta iphepha. Lokhu kusiza ukubabandula ekghonweni
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
labo lokubona ngelihlo lengqondo amajamo wesimethri.
IGREYIDI YESI- 3 ITHEMU YESI- 2
4. UKUMEDA
CAPS UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi Iimfundo ezi-2
Isikhathi • Ukufunda amalanga • Ukufunda amalanga emakhalendeni begodu nangokulandelana kwesikhathi.
emakhalendeni • Ukubeka amalanga wamabeletho, Ngesikhathi sokufundisa itlasi loke begodu nesikhathi sokunqopha
• Ukubeka amalanga amafestivali wezekolo, amaholideyi esiqhemeni, abafundi baragela phambili nokukhuluma ngamalanga
wamabeletho, amafestivali womphakathi, iminyanya yezomlando, weveke, iinyanga zonyaka begodu nelanga lamhloko, nangamalanga
wezekolo, amaholideyi izehlakalo zesikolo ezisekhalendeni. angaphambili begodu namalanga ezako. Abafundi baragela phambili
womphakathi, iminyanya • Ukutjho isikhathi sama-iri ali-12 ngokubeka okulandelako ekhalendeni njengombana izehlakalo zivela
yezomlando, izehlakalo ngama
zesikolo ezisekhalendeni. • amalanga wamabeletho
-- -iri, • amafestivali wezekolo
• Ukutjho isikhathi sama-iri
ali-12 ngama -- ngesiquntu sama-iri • iminyanya yezomlando,
-- -iri, -- ngekotara yama-iri
• izehlakalo zesikolo
-- ngesiquntu sama-iri -- amaminithi
• amaholideyi womphakathi
-- ngekotara yama-iri ewatjhini ze-analogo neenwatjhi
zedijithali begodu nezinye iintlabagelo Ragela phambili ngokubawa abafundi bonyana batjho isikhathi ngokuya
-- amaminithi zedijithali ezitjengisa isikhathi, isib. ngama-iri, iinquntu zama-iri begodu nekotara yama-iri ewatjhini ye-
ewatjhini ze-analogo abomaliledinini analogo njalo ngesikhathi sokuphumula ngamalanga.Qala amanothi
neenwatjhi zedijithali Ukubala ubude besikhathi nokudlula aseThemini yoku-1.
begodu nezinye iintlabagelo kwesikhathi Isikhathi sedijithali
zedijithali ezitjengisa
isikhathi, isib. abomaliledinini Ukusebenzisa amakhalenda ukubala Sebenzisa okungasenani iimfundo ezi-2 ubuyekeza ukufunda isikhathi
begodu nokuhlathulula ubude ewatjhini yedijithali. Qala amanothi weThemu yoku-1.
Ukubala ubude besikhathi besikhathi ngamalanga nofana
nokudlula kwesikhathi Ngesikhathi sokusebenza ngokuzijamela abantwana baragela phambili
ngeemveke nofana iinyanga ukufaka
Ukusebenzisa amakhalenda hlangana nokwenza umsebenzi ophathelene nokutjho isikhathi:
ukubala nokuhlathulula • Ukusebenzisa amawatjhi ukubala • ngama-iri, isiquntu sama-iri begodu nekotara yama-iri asewatjhini ye-
ubude besikhathi ubude besikhathi ngama-iri nofana analogo; begodu
ngamalanga nofana isiquntu se-iri • ngama-iri begodu nangamaminithi ewatjhini yedijithali.
ngeemveke nofana iinyanga
ukufaka hlangana Abafundi bangabala ngeemveke nofana ngamalanga nabanganikelwa
-- ukutjhugulula hlangana ikhalenda nofana isigaba sekhalenda, isib. Ukufunyana amalanga
kwamalanga neemveke begodu nokubala umahluko wesikhathi ohlangana naso.
-- ukutjhugulula hlangana
kweemveke neenyanga
Sebenzisa amawatjhi
ukubala ubude besikhathi
409 ngama-iri nofana isiquntu
sama-iri.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
410 IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
4.2 Ukumeda okungakahleleki Ukumeda okungakahleleki Ngikuphi okuhlukileko kuneGreyidini yesi-2?
Ubude • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, EGreyidini yesi-2 abafundi
ukumadanisa, ukuhlela ukumadanisa, ukuhlela begodu • banqopha ekumedeni okungakahleleki ngamayunithi wobude
begodu nokurekhoda nokurekhoda ubude ngokusebenzisa obungakahleleki; begodu
ubude ngokusebenzisa iimedo ezingakahleleki, isib. ubude
• bathulelwa ukumeda ngamamitha.
iimedo ezingakahleleki, besandla, amagadango, ubude
isib. ubude besandla, bamapensela, izinto zokubala, njll EThemini yesi-2 yeGreyidi yesi-3 abafundi bangaragele phambili
amagadango, ubude ngokumeda okungakahleleki ngokusebenzisa amayunithi angakahleleki
• Ukuhlathulula ubude bezinto
bamapensela, izinto begodu nokumeda ngamamitha.
ngokubala begodu nokutjho bonyana
zokubala, njll zinobude obungangani bamayunithi EThemini yesi-3 bangathoma ukumeda ngamasenthimitha
• Ukuhlathulula ubude angakahleleki ngokusebenzisa irula.
bezinto ngokubala • Ukusebenzisa ilimi ukukhuluma Ukulinganisa, ukumeda, ukumadanisa nokurekhoda ubude,
begodu nokutjho bonyana ngokumadanisa, isib.ubude, ukuphakama begodu nobubanzi ngokusebenzisa amayunithi
zinobude obungangani ubufitjhani, mude khulu , banzi khulu angakahleleki wobude.
bamayunithi angakahleleki Abafundi bangafunda zoke iinkambisolawulo neenkambiso zokumeda
Ukwethula ukumeda okuhlelekileko
• Ukusebenzisa ngokusebenzisa amayunithi angakahleleki. Ukumeda ngamayunithi
• Ukulinganisa, ukumeda,
ilimi ukukhuluma angakahleleki kufanele bonyana kungaqaleki kwanga akukaqakatheki
ukumadanisa, ukuhlela begodu
ngokumadanisa, isib.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kunokumeda ngamayunuthi ahlelekileko.
nokurekhoda ubudengokusebenzisa
ubude, ubufitjhani, mude Ukumeda ubude ngamayunithi angakahleleki kufaka ukubala bonyana
amamitha (iintonga ezimamitha
khulu , banzi khulu mangaki amayunithi akhethiweko anobude obufana nezinto ezimedwako.
nofana iintambo ezinobude bemitha)
Ukwethula ukumeda njengomuvosimedo ojayelekileko. Isib, Ubude bedeski bububude bezandla ezi-8.
okuhlelekileko Abafundi bafanele bamede izinto ezihlukahlukeneko ngokusebenzisa
• Ukulinganisa, ukumeda, Izinto ezihlukahlukenekonjengamayunithi angakahleleki.
ukumadanisa, ukuhlela Kuneendlela ezintathu zokusebenzisa amayunithi angakahleleki:
begodu nokurekhoda
• Ukubeka ngereyi buvundla into emedwako, izinto ezinengi zobude
ubudengokusebenzisa
obulinganako, njengamabhoksana womlilo, iimvadlwana zamabhodlela
amamitha (iintonga
ezinobujamo obufana patsi nofana izinto zokubala, amapensela
ezimamitha
amatjha, njll. Isibonelo, ukumeda ububanzi bedeski, amapensela
nofana iintambo
amatjha angabekwa ngokulandelana ukusuka ekuthomeni ukufika
ezinobude bemitha)
ekugcineni avundle itafula.
njengomuvosimedo
ojayelekileko. Lapha kuqakathekile bonyana
• Ukulinganisa nokumeda -- zoke izinto zinobude obulinganako. Angekhe utjho bonyana incwadi
ubude ngamasenthimitha yakho ibubanzi beemuvalo zamabhodlelo webisi ali-12 nangabe
ngokusebenzisa irula. iimvalo zamabhodlelo zinobukhulu obungalinganiko, isib. Iimvalo
zamabhodlelo webisi ezimalitha ama-2, iimvalo zamabhodlelo
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Alikho itjhuguluko elenzeka
wenamaneyidi weplastiki, iimvalo zamabhodlelo wesimbi, njll; begodu
hlangana kwamamitha
namasenthimitha -- Akunaankhala ezitjhiywa hlangana nezinto : zifanele zipakelwe
ngokulandelana ukuze zithintane
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
4.2 Ukumeda okungakahleleki Ukumeda okungakahleleki • Sebenzisa izinto ezimbili ezifana poro njengamayunithi angakahleleki.
Ubude • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, Beka into hlanu kwenye, begodu ubeka yokuthoma ngale kweyesibili.
ukumadanisa, ukuhlela ukumadanisa, ukuhlela begodu Lokhu kwenziwa nakusimedwa ngobude bezandla, ubude benyawo
begodu nokurekhoda nokurekhoda ubude ngokusebenzisa nofana amagadango.
ubude ngokusebenzisa iimedo ezingakahleleki, isib. ubude • Sebenzisa izinto ezimbili ezifana poro njengamayunithi angakahleleki.
iimedo ezingakahleleki, besandla, amagadango, ubude Beka yinye hlanu kwenye, bese ukhambisa yokuthoma uyise kelinye
isib. ubude besandla, bamapensela, izinto zokubala, njll ihlangothi lesibili. Lokhu kwenziwa nakumedwa ngobude besandla,
amagadango, ubude • Ukuhlathulula ubude bezinto ubude benyawo nofana amagadango
bamapensela, izinto ngokubala begodu nokutjho bonyana Ukusebenzisa into eyodwa kwaphela njengesimedo esingasisezingeni
zokubala, njll zinobude obungangani bamayunithi begodu ngokuyigeda nofana ukumerega lapho iphelela khona ngaphambi
• Ukuhlathulula ubude angakahleleki kokuyitjhelelisa.
bezinto ngokubala • Ukusebenzisa ilimi ukukhuluma Abafundi bafanele bafundiswe ukutjho iyunithi, isib. Incwadi inobubanzi
begodu nokutjho bonyana ngokumadanisa, isib.ubude, beemuvalo zebhodlelo ezi-12, ikumba yokufundela inobude
zinobude obungangani ubufitjhani, mude khulu , banzi khulu obumagadango ama-38.
bamayunithi angakahleleki
Ukwethula ukumeda okuhlelekileko Lokha abafundi nasele bamede ngananyana ngiyiphi iyunithi amahlandla
• Ukusebenzisa ambala, bafanele balinganise bonyana ingaba nobude obungangani
• Ukulinganisa, ukumeda,
ilimi ukukhuluma beyunithi into efanele imedwe. Ukulinganisa ngaphambi kokumeda
ukumadanisa, ukuhlela begodu
ngokumadanisa, isib. kuqakathekile, kodwana kungenziwa kwaphela lokha abafundi nabenze
nokurekhoda ubudengokusebenzisa
ubude, ubufitjhani, mude ukumeda ngeyunithi leyo.
amamitha (iintonga ezimamitha
khulu , banzi khulu
nofana iintambo ezinobude bemitha) Abafundi bafanele bafundiswe bonyana ukuze bakwazi ukumadanisa
Ukwethula ukumeda njengomuvosimedo ojayelekileko. ubude, ukuphakama nanyana ububanzi iyunithi efana poro ifanele
okuhlelekileko isetjenziswe. Isib.nangabe ububanzi bomnyango omedweko bububude
• Ukulinganisa, ukumeda, besandla obu-20 begodu ububanzi bedeski bububude bamapensela a-8,
ukumadanisa, ukuhlela angekhe utjho bonyana umnyango ubanzi kunedeski.
begodu nokurekhoda Abafundi bafanele bamede ngamayunithi angakahleleki ahlukahlukeneko,
ubudengokusebenzisa ukuze bakghone
amamitha (iintonga
• ukuthoma ukuzwisisa bonyana lokha iyunithi nayiyincani ,
ezimamitha
izokusetjenziswa amahlandla amanengana ,isib. ububanzi bekumba
nofana iintambo
yokufundela bungaba magadango ama-20 kodwana kube bubude
ezinobude bemitha)
beenyawo obuma-48.
njengomuvosimedo
ojayelekileko. • Thoma ukusebenzisa amayunithi afanele lokho abakumedako, isib.
ukumeda ububanzi bekumba yokufundela ngeemuvalo zamabhodlelo
• Ukulinganisa nokumeda
kukumorosa isikhathi.
ubude ngamasenthimitha
ngokusebenzisa irula.
Alikho itjhuguluko elenzeka
411 hlangana kwamamitha
namasenthimitha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
412 IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
4.2 Ukumeda okungakahleleki Ukumeda okungakahleleki Ukulinganisa, ukumeda, ukumadanisa begodu nokurekhoda ubude, Iinfundo ezi-2
Ubude • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, ububanzi begodu nokuphakama ngokusebenzisa amamitha.
ukumadanisa, ukuhlela ukumadanisa, ukuhlela begodu Abafundi bafanele bahlanganise ukuzwisisa kwabo kobude bemitha
begodu nokurekhoda nokurekhoda ubude ngokusebenzisa yi-1, begodu basebenzise ubude bemitha ukumeda okuthileko. Lokhu
ubude ngokusebenzisa iimedo ezingakahleleki, isib. ubude kwenzeka kuhle khulu nangabe abafundi bameda ngesitlabagelo
iimedo ezingakahleleki, besandla, amagadango, ubude esinobude bemitha yi-1 (njengemitha yerula; isigodo esiquntwe saba
isib. ubude besandla, bamapensela, izinto zokubala, njll yimitha yi-1 nofana intambo enobude bemitha). Ukubona imitha yi-1 isiza
amagadango, ubude • Ukuhlathulula ubude bezinto abafundi ukwakha umfanekiso wokobana singangani isilinganisa semitha.
bamapensela, izinto ngokubala begodu nokutjho bonyana Kuyakghonakala ukumeda ubude bamamitha ngevilo elitjhovwako
zokubala, njll zinobude obungangani bamayunithi eliyithrendlili, kodwana akusilula ukubona ubude bemitha.
• Ukuhlathulula ubude angakahleleki Abafundi bangathola izinto ezinobude bemitha yi-1 tere. Kuyasiza ukuba
bezinto ngokubala • Ukusebenzisa ilimi ukukhuluma nezinto ongaqala kizo njengeemadanisi, isib. ububanzi bomnyango
begodu nokutjho bonyana ngokumadanisa, isib.ubude, begodu nokuphakama wefesidere kanengi kuba yimithayi-1. Lokhu kusiza
zinobude obungangani ubufitjhani, mude khulu , banzi khulu abafundi bonyana basebenzise ubude/ ububanzi lobu abangabubona
bamayunithi angakahleleki ukulinganisa ubude nezine izinto abazimedako.
Ukwethula ukumeda okuhlelekileko
• Ukusebenzisa Abafundi bafanele balinganise ngaphambi kwaleso naleso isimedo.
• Ukulinganisa, ukumeda,
ilimi ukukhuluma Abafundi bangathola izinto ezingaba zide nofana zifitjhani kunemitha e-1.
ukumadanisa, ukuhlela begodu
ngokumadanisa, isib. Abafundi bangameda imihlobo ehlukahlukeneko yobude ngamamitha.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokurekhoda ubudengokusebenzisa
ubude, ubufitjhani, mude Kufanele kumadaniswe ubude obuhlukahlukeneko.
amamitha (iintonga ezimamitha
khulu , banzi khulu
nofana iintambo ezinobude bemitha) Ukurekhoda iimedo
Ukwethula ukumeda njengomuvosimedo ojayelekileko. Nanyana ukumeda kulikghono lokuzijayeza ukwenza, abafundi bafanele
okuhlelekileko
barekhode iimedo zabo ngaso soke isikhathi(ngawo womabili amayunithi
• Ukulinganisa, ukumeda, angakahleleki begodu na mamitha)
ukumadanisa, ukuhlela
Ukumeda ubude njengobujamo bokurarulula imiraro begodu
begodu nokurekhoda
nokubala
ubudengokusebenzisa
amamitha (iintonga Ngesikhathi esibekelwe Iinomboro, ama-Opheratjhini noBudlelwana,
ezimamitha abafundi bangararulula imiraro esebenzisa ubujamo:
nofana iintambo • bobude besimedo esingakahleleki, begodu
ezinobude bemitha) • bokumeda amamitha ngobude
njengomuvosimedo
Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yemiraro
ojayelekileko.
ehlukahlukeneko efaneleko yeThemu.
• Ukulinganisa nokumeda
ubude ngamasenthimitha
ngokusebenzisa irula.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Alikho itjhuguluko elenzeka
hlangana kwamamitha
namasenthimitha
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Ukumeda okungakahleleki Ngikuphi okuhlukileko egreyidini yesi-2?
Ubungako/ • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, ukumadanisa, EGreyidini yesi-2 abafundi banqopha ekumedeni okungakahleleki
ukumadanisa, ukuhlela begodu nokurekhoda ngamayunithi angakahleleki wobungako. Abafundi basebenzisa isikala
Ubudisi ubungako, ngokusebenzisa iimedo
ukuhlela, begodu sokumeda ukwenza lokhu. Bathome ngokusebenza ngamakhilogremu.
nokurekhoda ubungako, ezingakahleleki begodu nesikala
sokudzimelela isib. amabhlogo, iintina Bahlela imikhiqizo yangamalanga enobungako obutlolwe
ngokusebenzisa iimedo ngamakhilogremu. Bafunda ubungako bayo eenkaleni zangendlini
ezingakahleleki begodu njll.
• Ukusebenzisa ilimi ukukhuluma yokuhlambela.
nesikala sokudzimelela
isib. amabhlogo, iintina ngokumadanisa isib.lula, budisi, lula- Ukumeda ubudisi obungakahleleki ngokusebenzisa isikala
njll. khulu, budisi-khulu. sokumeda begodu amayunithi wokumeda angakahleleki.
Ukwethula ukumeda okuhlelekileko
• Ukusebenzisa Abafundi bangafunda zoke iinkambisolawulo begodu nekambiso
• Ukumadanisa, ukuhlela begodu
ilimi ukukhuluma yokumeda ngokusebenzisa amayunithi angakahleleki. Ukumeda
nokurekhoda ubungako bezinto
ngokumadanisa isib.lula, ezipakelwa ukuthengiswa ngamayunithi angakahleleki kufanele kungathathwa njengokunyazekako
budisi, lula-khulu, budisi- ezinobungako obutjengiswe kunokumeda ngamayunidi ahlelekileko.Abafundi bangahlanganisa
khulu. ngamakhilogremu, isib. amakghono wabo wokumeda ngokwenza obunye ubungako bokumeda
Ukwethula ukumeda amakhilogremu ama-2 wereyisi obungakahleleki ngamayunidi angakahleleki.
okuhlelekileko begodu nekhilogremu li-1 leflowuru Isikala sokuthengwa singasetjenziswa. Nawunganaso isikala
• Ukumadanisa, ukuhlela nofana ngamagremu, isib. amagremu sokuthengwa, ungazenzela ngokuhlanganisa kubili kwalokhu
begodu nokurekhoda ama-500 wetswayi okulandelako ehenghereni yejasi: ikopi leyogathi, ingaphasi lebodlelo
ubungako bezinto • Lapho okuneenkala zangeendlini eliquntiweko limalitha ama-2, ingaphasi lebhodlelo eliquntiweko lelitha
ezipakelwa ukuthengiswa yokuhlambela abafundi bangameda
yi-1 yebisi nofana ibhoksi lesiselo esimakhaza ( iimumathi ezifanako
ezinobungako ubungako babo ngamakhilogremu
zibotjhelelwa emahlangothini wehanghera yejasi).
obutjengiswe ngokusebenzisa sona
ngamakhilogremu, isib. • Lapho okuneenkala zangendlini Ukumeda ubungako ngamayunithi angakahleleki kufaka hlangana
amakhilogremu ama- yokuhlambela, abafundi bangameda ukubala bonyana mangaki amayunithi akhethiweko afanako ngobujamo
2 wereyisi begodu ubungako babo ngamakhilogremu njengento emedweko. Isib : irula inobungako obulingana namabhulogo
nekhiligremu li-1 leflowuru kusetjenziswa isikala sangendlini ali-9.
nofana amagremu isib. yokuhlambela. Okulindelekileko
Abafundi bafanele bamede izinto ezihlukahlukeneko ngokusebenzisa
ama-500 wamagremu kukobana abafundi bafunde kwaphela
izinto ezihlukeneko njengamayunidi angakahleleki.
wetswayi ukufikela emudeni omediweko
oseduzana Abafundi bafanele bafundiswe ngaso soke isikhathi ukutjho iyunidi
• Ukumeda ubungako
• Bahlathulula ubungako babo nabanikele ubungako, isib. Incwadi inobungako bamamabula ama-34.
babo ngamakhilogremu
ngokusebenzisa isikala njengokuthi pheze, / eduze / Lokha abafundi nasele bamede ngananyana ngiyiphi iyunidi amahllandla
sokumeda sangendlini okutjhideleneko/okunengana kuna/ ambalwa, bafanele balinganise bonyana mayunidi angaba mangaki
yokuhlambela pheze kube/ nofana inomboro poro angaba nobungako obulinganako nento emedwako. Ukulinganisa
(yamakhilogremu) bafunda ubungako
• Alikho itjhuguluko ngaphambi kukumeda kuqakathekile, kodwana kungenziwa nangabe
bamamitha.
elenzeka hlangana • Lapho okuneenkala zokudzimelelisa abafundi bakhe bameda ngeyunidi leyo.
kwamamilimitha namalitha ubungako beengcezu ezithalelwe Abafundi badinga ukufundiswa bonyana ukuze umadanise ubungako
ngamagremu, abafundi bangameda bezinto ezihlukahlukeneko,kusetjenziswa iyunidi efanako. Isibonelo,
413 ubungako bezinto ezihlukahlukeneko nangabe irula inobungako bamabhulogo ama-20 begodu isikere
Alikho itjhuguluko elenzeka hlangana sinobungako bamamabula ama-20, ngeze satjho bonyana zinobungako
kwamagremu namakhilogremu obufanako nofana obungafaniko, nofana ngikuphi okubudisi.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
414 IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Ukumeda okungakahleleki Ukurekhoda iimedo
Ubungako/ • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, ukumadanisa, Nanyana ukumeda kulikghono lokuzijayeza ukwenza okuthileko, abafundi
ukumadanisa, ukuhlela begodu nokurekhoda bafanele barekhode iimedo zabo ngaso soke isikhathi.
Ubudisi ubungako, ngokusebenzisa iimedo Ukusebenza ngamakhilogremu
ukuhlela, begodu
nokurekhoda ubungako, ezingakahleleki begodu nesikala Ukuhlela imikhiqizo ngokuya ngobudisi bayo.
ngokusebenzisa iimedo sokudzimelela isib. amabhlogo, iintina
Abafundi bangasebenza ngezinto ezithengiswa esitolo sokudla
ezingakahleleki begodu njll.
nezinye izintwanyana zangekhaya ezithengiswa ngamakhilogremu,
nesikala sokudzimelela • Ukusebenzisa ilimi ukukhuluma
lapho inomboro yamakhilogremu itlolwe eentweni eziphakethelwako.
isib. amabhlogo, iintina ngokumadanisa isib.lula, budisi, lula-
Abafundi bangamadanisa ubungako bezinto eziphakethelwako zezinto
njll. khulu, budisi-khulu.
ezihlukahlukeneko (njengereyisi, itjhukela, ipuphu, iflowuru nofana isibha
Ukwethula ukumeda okuhlelekileko
• Ukusebenzisa sokuvasa sepuphu ezithengiswa ngekhilogramu li-1. Bangakubeka
• Ukumadanisa, ukuhlela begodu
ilimi ukukhuluma esikaleni sokumeda ukwenzela ukubona bonyana nanyana ubungako
nokurekhoda ubungako bezinto
ngokumadanisa isib.lula, bempakana bungahluka, kodwana zinobungako obupheze bulingane.
ezipakelwa ukuthengiswa
budisi, lula-khulu, budisi- ezinobungako obutjengiswe Abafundi banganikelwa ke izinto ezihlukahlukeneko eziphakathelwako
khulu. ngamakhilogremu, isib. bonyana bazimadanise ukusuka kezibudisi khulu ukuya kezilula khulu,
Ukwethula ukumeda amakhilogremu ama-2 wereyisi lapho bamadanisa khona ngokuya ngobudisi bobujamo obutlolwe
okuhlelekileko begodu nekhilogremu li-1 leflowuru ephaketheni, isib. Ama-2kg wereyisi, i-1kg yetjhukela, ama-5kg wepuphu,
nofana ngamagremu, isib. amagremu ama-10kg westampa.
• Ukumadanisa, ukuhlela
ama-500 wetswayi Abafundi bazokudinga ukwazi isirhunyezo “kg” samakhilogremu.
begodu nokurekhoda
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Lapho okuneenkala zangeendlini Ukusebenza ngamagremu
ubungako bezinto
ezipakelwa ukuthengiswa yokuhlambela abafundi bangameda Ukuhlela imikhiqizo ngokuya ngobungako bento
ezinobungako ubungako babo ngamakhilogremu Abafundi bangasebenza ngezinto ezithengiswa esitolo sokudla nezinye
obutjengiswe ngokusebenzisa sona izintwanyana zangekhaya ezithengiswa ngamagremu, lapho inomboro
ngamakhilogremu, isib. • Lapho okuneenkala zangendlini yamagremu itlolwe khona eentweni eziphakethelwako. Abafundi
amakhilogremu ama- yokuhlambela, abafundi bangameda bangamadanisa ubungako bezinto eziphakethelwako ezihlukahlukeneko
2 wereyisi begodu ubungako babo ngamakhilogremu (njengamasiriyeli, itiye, ikofi, itswayi, amabhontjisi, iimpakana ezincani
nekhiligremu li-1 leflowuru kusetjenziswa isikala sangendlini zetjhukela, iimpakana ezincani zebisi lepuyera, amaphakethe wejeli,
nofana amagremu isib. yokuhlambela. Okulindelekileko amaphakethe amancani wereyisi, njll) athengiswa ngamagremu.
ama-500 wamagremu kukobana abafundi bafunde kwaphela Abafundi banganikelwa ke izinto ezihlukahlukeneko eziphakathelwako
wetswayi ukufikela emudeni omediweko bonyana bazilamanise ukusuka kwezibudisi ukuya kwezilula khulu, lapho
• Ukumeda ubungako oseduzana bazilamanise khona ngokuya ngobudisi bobujamo obutlolwe ephaketheni,
babo ngamakhilogremu • Bahlathulula ubungako babo isib. ama-2kg wereyisi, i-1kg yetjhukela, ama-5kg wepuphu, ama-10kg
ngokusebenzisa isikala njengokuthi pheze, / eduze / westampa.
sokumeda sangendlini okutjhideleneko/okunengana kuna/ Kuqakathekile bonyana abafundi bavezelwe epepeneneni izinto
yokuhlambela pheze kube/ nofana inomboro poro eziphakethelwako ezincani, ezibudisi ezinjengetswayi begodu eentweni
(yamakhilogremu) bafunda ubungako eziphakethelwako ezikulu kodwana zilula njengamarice crispies nofana
• Alikho itjhuguluko bamamitha. amacorn flakes. Lokhu kubenza bazwisise bonyana izinto ezikulu
elenzeka hlangana • Lapho okuneenkala zokudzimelelisa azisibudisi ngaso soke isikhathi kunezinto ezincani, ngaphandle kokuthi
kwamamilimitha namalitha ubungako beengcezu ezithalelwe kumadaniswa izinto ezifanako. Ungaqinisekisa kwaphela bonyana
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ngamagremu, abafundi bangameda izinto ezikulu zinobungako obukhulu nangabe
ubungako bezinto ezihlukahlukeneko • kumadaniswa izinto ezifanako; begodu
Alikho itjhuguluko elenzeka hlangana • uhlola ubungako bento esikaleni (esingadingekiko emaBangeni
kwamagremu namakhilogremu asiSekelo)
UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YETHEMU YESI-2 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Ukumeda okungakahleleki Abafundi badinga ukwazi bonyana isirhunyezo“g” esijamele amagremu Iimfundo ezi-3
Ubungako/ • Ukulinganisa, ukumeda, • Ukulinganisa, ukumeda, ukumadanisa, Abafundi abakalindeleki bonyana bafunde iinkala zangekhwitjhini
ukumadanisa, ukuhlela begodu nokurekhoda ngamagremu. Lokhu kwenziwa eBangeni eliSisekelo
Ubudisi ubungako, ngokusebenzisa iimedo Ukufunda iinkala zangeendlini yokuhlambela ngamakhilogremu
ukuhlela, begodu
nokurekhoda ubungako, ezingakahleleki begodu nesikala Lapho okuneenkala zangendlini yokuhlambela, abantwana
ngokusebenzisa iimedo sokudzimelela isib. amabhlogo, iintina bangazisebenzisa ukufunda ubudisi babo.
ezingakahleleki begodu njll. Kunemihlobo emibili yeenkala zokumeda ubudisi/ubungako: idijithali ne-
nesikala sokudzimelela • Ukusebenzisa ilimi ukukhuluma analogo.
isib. amabhlogo, iintina ngokumadanisa isib.lula, budisi, lula- Iinkala zedijithali zilula ukuzifunda ngombana ubungako butlolwe
njll. khulu, budisi-khulu. ngeenomboro. Nawunesikala sedijithali sangendlini yokuhlambela,
Ukwethula ukumeda okuhlelekileko hlola bonyana iveza ubungako ngamakhilogremu azeleko kwaphela.
• Ukusebenzisa • Ukumadanisa, ukuhlela begodu
ilimi ukukhuluma Ungakwazi ukubuyelela usede ngobutjha iinkala ezinye ukutjengisa
nokurekhoda ubungako bezinto amakhilogremu azeleko kwaphela. Nawungakwaziko ukuseda utjengise
ngokumadanisa isib.lula, ezipakelwa ukuthengiswa
budisi, lula-khulu, budisi- amakhilogremu azeleko kwaphela, fundisa abantwana bonyana balise
ezinobungako obutjengiswe ingcenye yamakhilogremu okwanje.
khulu. ngamakhilogremu, isib.
Ukwethula ukumeda Ezinye iinkala ze-analogo zangendlini yokuhlambela zinomboriwe kenye
amakhilogremu ama-2 wereyisi
okuhlelekileko nenye i-10 kg, nomuda omude otjengisa indawo yama-5kg. Imida ye-1kg
begodu nekhilogremu li-1 leflowuru
ayikanomboriwa. Lokhu kufana nendlela imida begodu neenomboro
• Ukumadanisa, ukuhlela nofana ngamagremu, isib. amagremu
zisebenza ngakho eruleni.
begodu nokurekhoda ama-500 wetswayi
• Lapho okuneenkala zangeendlini Vumela abafundi bathome ukubala ukuze babona bonyana kuneeenkhala
ubungako bezinto
yokuhlambela abafundi bangameda eziyi-10 ngaphambi kwemaraga yama -10 kg, ukuze isikhala ngasinye
ezipakelwa ukuthengiswa
ubungako babo ngamakhilogremu sijamele ikhilogremu yi-1, begodu umuda omude ujamele ama-5kg.
ezinobungako
ngokusebenzisa sona Abafundi bangafunda ukumeda esikaleni samambala sangendlini
obutjengiswe
• Lapho okuneenkala zangendlini yokuhlambela neethombe zeenkala zangendlini yokuhlambela.
ngamakhilogremu, isib.
yokuhlambela, abafundi bangameda Kulula khulu ukufunda ubungako esikaleni seenthombe sangendlini
amakhilogremu ama-
ubungako babo ngamakhilogremu yokuhlambela kunesikaleni sokumeda samambala.
2 wereyisi begodu
nekhiligremu li-1 leflowuru kusetjenziswa isikala sangendlini Ukurekhoda iimedo
nofana amagremu isib. yokuhlambela. Okulindelekileko Nanyana ukumeda kulikghono lokuzijayeza ukwenza, abafundi bafanele
ama-500 wamagremu kukobana abafundi bafunde kwaphela barekhode iimedo zabo ngaso soke isikhathi.
wetswayi ukufikela emudeni omediweko Ukumeda ubungako njengobujamo bokurarulula iinkinga begodu
oseduzana nokubala
• Ukumeda ubungako
babo ngamakhilogremu • Bahlathulula ubungako babo Ngesikhathi esibekelwe Iinomboro, ama-Opharetjhini noBudlelwana,
ngokusebenzisa isikala njengokuthi pheze, / eduze / abafundi bangararulula imiraro esebenzisa
sokumeda sangendlini okutjhideleneko/okunengana kuna/ • ubujamo
yokuhlambela pheze kube/ nofana inomboro poro • bobudisi besimedo ezingakahleleki, begodu
(yamakhilogremu) bafunda ubungako • bokumeda ubudisi ngamakhilogremu.
• Alikho itjhuguluko bamamitha.
elenzeka hlangana Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yemiraro
• Lapho okuneenkala zokudzimelelisa ezihlukahlukeneko ezifaneleko yeThemu.
kwamamilimitha namalitha ubungako beengcezu ezithalelwe
Abafundi abakalindeleki bonyana
ngamagremu, abafundi bangameda
415 ubungako bezinto ezihlukahlukeneko • bazi bonyana ama-1 000g= ne-1 kg; nofana
Alikho itjhuguluko elenzeka hlangana • ukwenza itjhuguluko hlangana kwamagremu begodu namakhilogremu.
kwamagremu namakhilogremu Ukubala ngamagremu kungakhethwa ukuze kungadluleli ngale kwe-1000 g.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
BESIKHATHI
IMIQONDO NAMAKGHONO : (eemfundweni
IINHLOKO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA YOKUFUNDISA
416 IIMFUNEKO ZOKUPHELA KONYAKA ze-iri -1 begodu
namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ngesikhathi sokusebenza ngokuzijamela abafundi bafanele baragele phambili noku:
Umthamo/ • Ukulinganisa, ukumeda, kumadanisa Linganisa, meda, madanisa, hlela nokurekhoda umthamo weemumathi nofana ivolumu engeemumathini
Ivolumu begodu nokuhlela (isib. umthamo ngokusebenzisa iimedo ezingakahleleki, Ukulandela amaresibhi, ukufaka hlangana ukubhaga kubujamo
ongamumathwa simumathii obusiza abafundi bonyana bazijayeze ukumeda. Khetha amaresibhi lapho iintlabagelo zakhona zinikelwa
nasizeleko) ngokusebenzisa iimedo ngamakopi ngamathispuni nofana ngamayunithi angakahleleki.
ezingakahleleki isib. Iingobho • Ukumadanisa begodu nokuhlela umthamo wamabhodlelo ahlukahlukeneko begodu nezinto zegrozari
namakopi. lapho umthamo otlolwe khona ezintweni eziphakethelwako.
• Ukuhlathulula umthamo wesimumathi • Sebenzisa nanyana amabhodlelo welitha li-1 nofana amajege welitha li-1 ukulinganisa begodu
ngokubala nokutjho bonyana nokumeda, ukumadanisa, ukuhlela begodu nokurekhoda umthamo weemumathi nofana ivolumu
mangaki amayunithi angakahleleki engeemumathini ngamalitha.
angazalisa isimumathi, isib. Ibhodlelo
Qala amanothi weThemu yesi-3
linobungako bamakopi ama-4
Abafundi bafanele banikelwe amathaski ukuhlanganisa okulandelako, ukufaka hlangana iinthombe
Ukwethulwa kokumeda
zokufunda:
okuhlelekileko
• imikhiqizo enomthamo otlolwe kiwo ukuze ilandelaniswe ngefanelo, begodu
• Ukulinganisa, ukumeda;
ukumadanisa nokuhlela begodu • iinthombe eziseenjegeni lapho ivolumu iseduze nalapho okunomborwe khona ilitha li-1 nofana izinga
nokurekhoda umthamo wezinto lomuda elimalitha ama-2.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngokumeda ngamalitha, iinqunto Kulindeleke bonyana abafundi bafunde kwaphela izinga lomuda eliseduze nenomboro .Bahlathulula
zamalitha begodu nangamakotara ivolumu yabo njengokuthi pheze, / eduze /okunengana/ pheze kube/ nofana inomboro poro ( yamalitha)
wamalitha. abawafunda ejegeni
• Ukumadanisa, ukuhlela begodu Ukumeda umthamo njengobujamo bokurarulula iinkinga begodu nokubala
nokurekhoda umthamo wezinto Ngesikhathi esibekelwe Iinomboro, ama-Opharetjhini noBudlelwana,abafundi bangararulula imiraro
ezipakelwe ukuthengiswa, ubungako esebenzisa ubujamo:
bazo butlolwa ngamalitha, isib.
• bokumeda okungakahleleki komthamo/ivolumu; isib. uGogo usebenzisa amakopi amabili webisi
amalitha ama-2 webisi, ilitha li-1
ukwenza ipudinghi. Nakayibuyelela kabili iresibhi, uzokusebenzisa ibisi elingangani?
lesiselo esimakhaza, amalitha ama-5
wepende nofana ngamamilimitha, • bamalitha
isib. ama-500 ml webisi, Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yeenkinga ezihlukahlukeneko
• amamililitha ama-340 wesiselo
esimakhaza, amamilimitha ama-750
we-oli
• Ukwazi bonyana ikopi elihlelekileko
limamililitha ama-250
• Ukwazi bonyana ithispuni imamililitha
ama-5
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Akukalindeleki bonyana kube
netjhugululko hlangana kwamamilimitha
namalitha
IGREYIDI YESI-3 ITHEMU YESI-2
5. UKUPHATHA IDATHA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-2 namaminithi
ama -24)
5.4 Ukubuthelela nokuhlela
Ukubuthelela idatha
nokuhlela idatha • Buthelela idatha
yetlasi nofana
yesikolo ukwenzela
ukuphendula imibuzo
ebuzwa ngutitjhere.
• Hlela idatha oyinikelwe
ngutitjhere nofana
etholakala encwadini
Hlela idatha ngama:
o Rhelo
o Thali
o Thebula
5.5 Jamisela idatha
Jamisela idatha Jamisela idatha nge:
• Grafu yeenthombe
• Bha grafu
5.6 Hlaziya begodu Hlaziya idatha kusukela Nangabe abafundi bawenze woke umzombe wedatha eThemini yoku-1, ukuhlaziya 1isifundoq
Hlaziya begodu urhumutjhe idatha esijamiselweni iinjamiselo zedatha ezihlukahlukeneko kuzakwenza umqondo ozwakalako.
urhumutjhe idatha Phendula imibuzo esinikelweko. Kuphakanyisiwe bona eThemini yesi-2 unikele abafundi idatha bona bayihlaziye
ngedatha ethulwe nge: okungasenani
• Grafu yeenthombve • Yi-1 igrafu yeenthombe
• Bha- grafu. • ithebula
Abafundi kufanele baphendule imibuzo obabuza yona ngegrafu begodu nethebula;
qala iThemu yoku-1 ukuthola imibuzo efaneleko
417
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI-3
1. IINOMBORO, AMA-OPHARETJHINI NOBUDLELWANE
418
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
1.1 Ukubala izinto Buthelela ngeenqhema Ngikuphi okuhlukileko kuneThemini yesi 2?
Ukubala eziphathekako ukufika okungasenani ema Irherho leenomboro lingezelelekile begodu abafundi bafanele banikelwe
izinto Linganisa begodu 700 izinto zangamalanga ithuba lokuthinta, ukukhambakhamba begodu nokubala izinto ezibuthelelweko
ngokuthembeka izinto ukulinganisa begodu nokubala
ezihlukeneko ezima- 700 ngeenqhema.
zangamalanga okungenani ngokuthembeka.
kufika e-1000.Iqhinga Nikela ukulinganisa Qala amanothi ethemini yoku-1 neye-2
leenqhema liyakhuthazwa. okuzwakalako kwenomboro
yezinto ezingahlolwa
ngokubala.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3
CAPS namaminithi
ama -24)
1.2 Ukubala uye phambili Ukubala uye phambili Ngikuphi okuhlukileko kuneThemini yesi 2?
Ukubala uye nemuva nga: nemuva nga: Irherho leenomboro liyangezeleleka ukufika ema 700.
phambili • Ku-1 ukusuka kwenye • Ku-1 ukusuka kwenye Qala amanothi weThemini yoku-1 neye-2
nemuva nenye inomboro hlangana nenye inomboro hlangana
ne-0 ne-1000. ne-0 ne-700.
• Li-10 ukusuka kesinye • Li-10 ukusuka kesinye
nesinye isibuyabuyelelo se- nesinye isibuyabuyelelo se-
10 hlangana ne-0 ne-1000. 10 hlangana ne-0 ne-700.
• Ku-5 ukusuka kesinye • Ku-5 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-5 hlangana ne-0 saka ku-5 hlangana ne-0
ne-1000. ne-700.
• Ku-2 ukusuka kesinye • Ku-2 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-2 hlangana ne -0 saka ku-2 hlangana ne -0
ne-1000. ne-700.
• Ku-3 ukusuka kesinye • Ku-3 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-3 hlangana ne-0 saka ku-3 hlangana ne-0
ne-1000 ne-700
• Ku-4 ukusuka kesinye • Ku-4 ukusuka kesinye
nesinye isibuyabuyelelo nesinye isibuyabuyelelo
saka ku-4 hlangana ne-0 saka ku-4 hlangana ne-0
ne-1000 ne-700
• Ma-20, 25, 50, 100 • Ma-20, 25, 50, 100
okungasenani ukufika okungasenani ukufika
e-1000. e-700.
419
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
420 YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
1.3 Ukukhumbula ukubona Ukukhumbula ukubona Ngikuphi okuhlukileko eThemini yesi-2?
Amat- begodu nokufunda iinomboro. begodu nokufunda iinomboro. Abafundi babona, bafunde begodu batlole:
shwayo • Khumbula,ubone begodu • Khumbula,ubone begodu • Amatshwayo weenomboro ukufika e-1 000; begodu
weenom- ufunde amatshwayo ufunde amatshwayo
wenomboro kusuka e-10 wenomboro kusuka e-10 • Amabizo weenomboro ukufika ema- 500.
boro
namagama ukufika e-1000. ukufika e-1000. Qala amanothi weThemini yesi- 2
weenom- • Tlola amatshwayo • Tlola amatshwayo
boro. wenomboro ukusuka ku-0 wenomboro kusuka ku-0
ukufika ku-1000 ukufika ku-1000
• Khumbula, ubone • Khumbula, ubone
begodu ufunde amagama begodu ufunde amagama
weenomboro ukusuka ku- 0 weenomboro ukusuka ku-0
ukufika e-1000. ukufika ku-500.
• Tlola amagama • Tlola amagama
weenomboro ukusuka ku- 0 weenomboro ukusuka ku-0
ukufika e-1000 ukufika ema-500
1.4 Hlela begodu umadanise Hlela begodu umadanise Ngikuphi okuhlukileko kuneThemini yesi 2?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukuhlathu- iinomboro ukufika ema 999 iinomboro ukufika ema 500 Abafundi bahlela begodu bamadanisa iinomboro ukufika ema-500
lula, uku- • Hlela iinomboro • Hlela iinomboro begodu baragela phambili ukusebenzisa indlela erhunyeziweko yokutlola
madanisa ezipheleleko ukufika ema ezipheleleko ukufika ema inomborosikhundla.......
nokuhlela 999 ukusuka kwencani 500 ukusukela kwencani
khulu ukuya kwekulu khulu, khulu ukuya kwekulu khulu, Qala amanothi weThemini yesi- 2
iinomboro
begodu ukusuka kwekulu begodu ukusuka kwekulu
khulu ukuya kwencani khulu ukuya kwencani khulu
khulu • Madanisa iinomboro
• Madanisa iinomboro ezipheleleko ukufika
ezipheleleko ukufika ema- 500 usebenzisa
ema 999 usebenzisa okuncani kuna, okukhulu
okuncani kuna, okukhulu kuna, okunengi kuna,
kuna, okunengi kuna, okumbadlwana kuna
okumbadlwana kuna nokulinganako.
nokulinganako.
Sebenzisa
Sebenzisa inomborosikhundla
inomborosikhundla ukutjengisa ukulandelana
ukutjengisa ukuhlela ,indawo namkha ubujamo
,indawo namkha ubujamo
• Sebenzisa ,funda nokutlola
• Sebenzisa ,funda nokutlola
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
iinomborosikhundla
iinomborosikhundla ukufaka hlangana indlela
ukufaka hlangana erhunyezwako ukufika
ezirhunyezwako ukufika ema-31.
ema-31.
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3
CAPS namaminithi
ama -24)
1.5 Ukukhumbula ubukhulu Ukukhumbula ubukhulu Ngikuphi okuhlukileko kuneThemini yesi-3?
Ubukhulu bedijithi beenomboro bedijithi beenomboro Imihlobo efanako yemibuzo neenyalelo inikelwe eThemini yesi-3. Irherho
bedijithi ezintathu zedijithi ukufika ukufika ema-750. leenomboro lingezelelekile kodwana abafundi basasebenza ngeenomboro
ema-999. • Ukwazi bonyana idijithi zamadijithi amathathu.
• Ukwazi bonyana idijithi ngayinye ijamele ini. Umnqopho weThemini le ufanele uragele phambili ngo:
ngayinye ijamele ini. • Hlukanisa iinomboro bungako benomboro;
• Hlukanisa iinomboro zamadijithi amathathu
kuhlukanisa iinomboro ngamakhulu, ngamatjhumi begodu nangemivo
zamadijithi amathathu ukufika ema-750
ngokusebenzisa amakarada wobukhulu bedijithi begodu nenomborosisekelo
ukufika ema- 999 ngeembuyabuyeleli
ezilitjhumi zamabhlogo; begodu
ngeembuyabuyeleli • zangali-100,
zangali-100, kutlola umhlobo weenomboro ezinabileko.
iimbuyabuyeleli zalitjhumi
iimbuyabuyeleli zalitjhumi begodu nemivo. Qala amanothi weThemini yesi- 2.
begodu nemivo.
• Ukufanisa nokutjho
• Ukubona begodu fanisa ubukhulu benye nenye
nokutjho ubukhulu bedijithi idijithi.
ngayinye.
IMIRARO YEENOMBORO
1.6 Sebenzisa amathekniki Sebenzisa amathekniki Abafundi kulindeleke bonyana bararulule imiraro yamagama ngokusebenzisa
Amaqhinga alandelako nawurarulula alandelako nawurarulula amathekniki alandelako:
wokuraru- imiraro begodu uhlathulule imiraro: • Ukwakha nofana ukuphula iinomboro
lula imiraro iinsombululo zemiraro: • Ukwakha nokuphula • Ukubuyelela kabili nokuhafula.
• Ukwakha nokuphula iinomboro
• Amanambalayini
iinomboro • Ukubuyelela kabili
• Ukutjhideza eduze.
• Ukubuyelela kabili nokuhafula.
nokuhafula. Qala amanothi weThemini yesi-2.
• Amanambalayini
• Amanambalayini • Ukutjhideza e-10
• Ukutjhideza e-10
421
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
422 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.7 Rarulula imiraro Rarulula imiraro Iimbonelo zemihlobo yemiraro engenziwa ngeThemu le
Ukuh- yamagama yamagama • Imiraro yokuhlanganisa begodu nokukhupha
langanisa ezisebujameni ezisebujameni
• UPhephelaphi ubuthelele iimvalo zamabhodlela ezima-413. UKunubhe nakangamnikela
nokukhupha bewuhlathulule bewuhlathulule
iimvalo zamabhodlela ezima 29, uzakuba nenani elifanako nelakaPhephelaphi.
iinsombululo zakho iinsombululo zakho
zemiraro ezifaka zemiraro ezifaka -- Bazokuba nemvalo zamabhodlela ezingaki babobabili?
ukuhlanganisa ukuhlanganisa -- UKunubhe bekaneemvalo zamabhodlela ezingaki kwasekuthomeni?
nokukhupha nempendulo nokukhupha nempendulo • Abafundi beGreyidi yesi-2 banebuthelelo lamamabula ama-500. Abafundi beGreyidi yesi
ukufika e-999. ukufika e-800. 3 banamamabula ambadlwana ngali-170 kunabafundi beGreyidi yesi-2. Banamamabula
amangaki abafundi beGreyidi yesi-3?
• ULingiwe noVamuhle babuthelele izinto zokunamathelisa ezi-250. UMark uthola ezili 160.
ULingiwe uthole izinto zokunamathelisa ezingaki?
1.8 Rarulula imiraro Rarulula imiraro Iimbonelo zemihlobo yemiraro engenziwa ngeThemu le.
Ukuh- yamagama yamagama Umhlobo womraro we-9: Irhemo
langanisa ezisebujameni ezisebujameni
• Isivande somrorho sinamareyi ali-12 weentjalo. Ireyi ngayinye ineentjalo ezi-7. Ziintjalo
okubuyele- bewuhlathulule bewuhlathulule
ezingaki ezikhona ngesivandeni?
iinsombululo zakho iinsombululo zakho
ISIGABA ESISISEKELO AMAGREYIDI 1-3
lweko
zemiraro, ezifaka zemiraro, ezifaka • Isivande somrorho sinamareyi ali 12 weentjalo. Ireyi ngayinye inenani elifanako leentjalo.
okurholela
ukubuyabuyelela ukubuyabuyelela Nakunenani leentjalo elima- 48, kuneentjalo ezingaki ereyini ngalinye?
ekubuy-
abuyeleleni okunempendulo ufikela okunempendulo ufikela • Isivande somrorho sineentjalo ezima-48 ezitjalwe ngereyi. Ireyi ngayinye ineentjalo ezi-7.
e-100. e-75. Kunamareyi amangaki?
Ukumadanisa/Iretjhiyo
USalelani unamaswidi asi 6. USalelani unamaswidi abuyelelwe kathathu ukudlula
kaMongezi. UMongezi unamaswidi amangaki?
UMavela unamswidi ali-18. Lokhu kunengi kathathu ukudlula lokha uSalelani. USalelani
unamaswidi amangaki?
Isilinganiso
Amaperegisi athengiswa ngamaranda abu- R8 ikhilogremu ngalinye. Lokha nangithenga
amakhilogremu amane, kuzokubiza malini? Amaperegisi abiza amaranda abu-R8
ikhilogremu ngayinye. Lokha nangina nama-R32, ngingathenga amakhilogremu amangaki?
Ngithenga amakhilogremu ama-4 wamaperegisi begodu kungibiza amaranda ama-R32.
Ikhilogremu eyodwa ithengwa ngamalini?
Ukusebenzisa ukutjhideza
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Iteksi ikhweza abakhweli abayi-15. Abantu abama-73 banganela emateksini ama-5?
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.9 Ukurarulula Ukurarulula Iimbonelo zemihlobo yemiraro engenziwa ngeThemu le
Ukubuthele- imiraro yamagama imiraro yamagama • UKosikazi Matjhiga upaka amamafini ama 66 ngeempakaneni ngasi-6. Uneempakana
la nok- ezisebujameni ezisebujameni ezingaki?
wabelana bewuhlathulule bewuhlathulule • USizani uthola imali ema-R72 ngokuthengisa amathikithi werafula ngamaranda ali-R9.
okurholela iinsombululo zakho iinsombululo zakho Mangaki amathikithi awathengisileko?
ekuhlu- ufake ukwabelana ufake ukwabelana • Umphakathi usiza imindeni eli-9 eyaloba izinto zayo ngebanga lomlilo. Kuneengubo
kaniseni. ngokulingana ngokulingana ezima-75 okufuze zabelwe imindeni ngokulinganako.
nokubuthelela nokubuthelela a) Umndeni ngamunye uzokuthola iingubo ezingaki?
.
ngeenqhema ngeenqhema b) Zingaki eziseleko?
kweenomboro kweenomboro Isilinganiso
ezipheleleko ukufika ezipheleleko ukufika • Amaperegisi abiza ama-R8 ikhilogremu ngayinye. Lokha nanginama- R32,
e-100 kanye nempendulo e-75 kanye nempendulo ngingathenga amakhilogremu amangaki?
ezingahle zifaka iinsalela ezingahle zifaka iinsalela • Ngithenga amakhilogremu ama-4 wamaperegisi begodu angibiza ama-R32. Ikhilogremu
yinye ithengwa ngamalini?
Imiraro yesilinganiso imihlobo emitjha yemiraro yeThemu yesi-3. Abafundi bangatlhoga
isikhathi esinengi nabararulula imiraro.
1.10 Ukurarulula Ukurarulula Iimbonelo zemiraro engenziwa ngeThemu le.
Ukwabelana bewuhlathulule bewuhlathulule Ukwabelana, okurholela emafraktjhinini
okurholela iinsombululo zemiraro iinsombululo zemiraro • Abela abangani bakho aba- 3 iintinyana zetjhokolede ezili- 7 ukuze boke bathole
emafrak- ephathekako efaka ephathekako efaka ngokulingana kungasali litho.
tjhinini. hlangana ukwabelana hlangana ukwabelana • Abela abantwana aba-4 iintinyana zetjhokolede ezili-13 ngokulinganako. Munye uthola
ngokulingana erholela ngokulingana erholela iintina ezingaki?
empendulweni empendulweni Ifraktjhini yokubuthelela
zamafraktjhini wohlavu zamafraktjhini wohlavu • Ugogo unikela uKiki ama- R12. UKiki ufuna ukubulunga isithathu semali. Yimalini
olulodwa nalayo olulodwa nalayo okufuze ayibulunge?
angenahlavu eyodwa. angenahlavu eyodwa.
1 1 3 1 1 3 • Kunamakuke ali 12 ngesitjeni. UNomonde uthatha ikotara yinye yamakuke. Kusele
isib. 2 , 4 , 4 njll. isib. 2 , 4 , 4 njll. mangaki?
Ukutlola
Abafundi akukafuneki bonyana batlole itshwayo lefraktjhini. Abafundi bafunda
ukulebula iingcenye zamafraktjhini njenga kunye kokuhlanu, amakotara ama 3 nofana
okuthathu kokusithandathu. Lokhu kubasiza kokuthoma ukuzwisisa bonyana amagama
wamafraktjhini ahlathulula bonyana ziingcenye ezingaki ezilinganako okupheleleko
okuhlukaniswe ngakho, isibonelo, amahafu, ubuthathu, amakotara, njll begodu okwesibili
ziingcenye ezingaki zalokho eziqaliweko, isib. Ubu 2 obuthathu.
Ukujamela imiraro yamagama yamafraktjhini
Abafundi kufuze bagwale iimpendulo zabo ukutjengisa bonyana bazwisisa umraro.
423 Lindela bonyana abanye abafundi bangagwala kuhle kodwana balebule kumbi ingcenye
yefraktjhini.
Abafundi kufuze batjho iingcenye ezabelenweko ngokuzitlola njengobu 2 bobuthathu.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
424 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.11 • Ukukhumbula • Ukukhumbula Iimbonelo zemiraro engenziwa ngeThemu le
Imali nokubona imali nokubona imali Ubungako bemali nokwenza amanani isib.
yeSewula Afrika yeSewula Afrika
Tlola ama 325c njengamaranda namsende.
eziinhlamvu begodu eziinhlamvu begodu
nemali yamaphepha nemali yamaphepha Kungezindlela ezihlukileko ezingaki ongenza ngazo amaranda ama R400 usebenzisa imali
yamaphepha yodwana? Wazi bunjani bonyana uneensombululo zoke?
• Ukurarulula imiraro • Ukurarulula imiraro
yemali efaka hlangana yemali efaka hlangana UMnu. Lebethe umumakhi begodu uthola ibhonasi ngokuqeda umsebenzi ngesikhathi.
inani netjhentjhi inani netjhentjhi Uqunta ukwaba ibhonasi le hlangana kwakhe nombazi.
kufikela emaranda kufikela emaranda Umuntu munye uthola amaranda ama R400. Each person receives R400.
namasende namasende Buyini ubungako bebhonasi?
• Tjhugulula hlangana • Tjhugulula hlangana UNina nabangani bakhe abathathu babelana amaranda ama R20-60. Munye uthole malini?
kwamaranda kwamaranda
namasende namasende
UKUBALA OBUSEBUJAMENI OBUTJHAPHULUKILEKO
1.12 Sebenzisa amaqhinga Sebenzisa amaqhinga Abafundi balindeleke bonyana babale imiraro yamagama basebenzisa akathekniki
Amathekniki alandelako lokha alandelako lokha alandelako:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
(iindlela nakubalwako nakubalwako • Ukwakha nokuphula iinomboro
namkha • Ukwakha nokuphula • Ukwakha nokuphula • Ukubuyelela kabili nokuhafula phakathi
amaqhinga) iinomboro iinomboro
• Amanambalayini
• Ukubuyelela kabili • Ukubuyelela kabili
• Ukutjhideza etjhumini
nokuhafula phakathi nokuhafula phakathi
Qala amanothi weThemu yoku 1
• Amanambalayini • Amanambalayini
• Ukutjhideza etjhumini • Ukutjhideza etjhumini
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Ethemini le abafundi baragela phambili ngokubala iinomboro zamadijithi amathathu ukufika
Ukuh- ukufikela ku-999 ukufikela ku-999 ema-800. Ukuze abale ngeenomboro zamadijithi amathathu abafundi bafanele bakghone
langanisa • Ukukhupha ku-999 • Ukukhupha ku-999 uku:
nofana uku- • funda nokutlole amatshwayo weenomboro ukufikela ema-800 ngokuzithemba;
• Ukusebenzisa • Ukusebenzisa
khupha amatshwayo afaneleko amatshwayo afaneleko • hlela amadanise iinomboro ukufika okungasenani ema-800 ngokuzithemba;
( +, -, =, ) ( +, -, =, ) • bala ngeenqhema ukufika ema 800 ngokuzithemba; begodu
• Ukujayeza • Ukujayeza • bala ngokuzithemba ngeenkhewu zanga ku 2, 3, 4, 5, 10, 50 ne 100 ukufika ema 800.
ukuhlangana ukuhlangana Iindlela ezinokwenzeka zokubonisa ukuhlanganisa neembalo zokukhupha.
kweenomboro kweenomboro ukufika • Ukuhlanganisa ngokuphula iinomboro zombili.
ukufikela ema-30 ema-30 Ukuhlanganisa amadijithi amathathu namadijithi amabili.
524 + 82 =
= (500 + 20 + 4) + (80 + 2)
= 500 + (20 + 80+ (4 + 2)
= (500 + 100) + 6
= 600 + 6
= 606
Ukuhlanganisa amadijithi amathathu begodu namadijithi amathathu.
323 + 436 =
323 + 436 = (300 + 20 + 3) + (400 + 30 + 6)
= (300 + 400) + (20 + 30) + (3 + 6)
= 700 + 50 + 9
= 759
• Ukuhlanganisa ( ngokuphula iinomboro ezokuhlanganiswa)
Abafundi bazokuphula inomboro ngeendlela zabo ezilawulekako kibo. Lokhu kutjho
bonyana bazokwenza ngeendlela ezihlukeneko.
524 + 82 =
524 + (40 + 40 + 2)
524 + 40 564 + 40 604 + 2 = 606
Ukubala uye phambili ukusuka ema 40 ukufika ema 524 kungenziwa ngokubala nge 10.
Ukuhlanganisa iinomboro zamadijithi amathathu nezinye iinomboro zamadijithi amathathu
323 + 436 =
= 323 + (400 + 20 + 6)
= (323 + 400) + 20 + 6
= (723 + 20) + 6
425 = 743 + 6
= 749
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
426 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa • Ukukhupha ngokuphula iinomboro zombili
Ukuh- ukufikela ku-999 ukufikela ku-999 Khupha inomboro enamadijithi amabili enomborweni enamadijithi amathathu
langanisa • Ukukhupha ku-999 • Ukukhupha ku-999 889 – 137 =
nofana uku- • Ukusebenzisa • Ukusebenzisa 889 – 137 = (800 + 80 + 9) – (100 + 30 + 7)
khupha amatshwayo afaneleko amatshwayo afaneleko = (800 – 100) + (80 – 30) + (9 – 7)
( +, -, =, ) ( +, -, =, )
= 700 + 50 + 2
• Ukujayeza • Ukujayeza = 752
ukuhlangana ukuhlangana
kweenomboro kweenomboro ukufika • Ukukhupha ngokuphula inomboro yinye
ukufikela ema-30 ema-30 889 – 137 =
889 – (100 + 30 + 7)
889 – 100 789 – 30 759 – 7 = 752
• Usebenzisa ukuhafula kabili ukuphula inomboro
525 + 16
= 525 + 8 + 8
= (525 + 8) + 8
ISIGABA ESISISEKELO AMAGREYIDI 1-3
= 533 + 8
= 541
• Bala uye phambili begodu nemuva
805 = 798 =
Ukubala uye phezulu ngakunye ukusuka ema 798 kuliqhinga elifaneleko ngombana
iinomboro zitjhidelene.
• ukubona ukubuyabuyelana okuseduze
245 + 246
kungatjhiwo bonyana isibalo esingehla singaba kubuyelela kabili kwama 245 + 1
kubuyelela kabili kwama 246 – 1
245 + 245 + 1
= (200 + 40 + 5) + (200 + 40 + 5) + 1
= (200 + 200) + (40 + 40) + (5 + 5) + 1
= 400 + 80 + 10 + 1
= 400 + (80 + 10) + 1
= 400 + 90 + 1
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
= 491
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa • Tjhugululela inomboro esibuyabuyelelo setjhumi begodu ukhuphe nofana uhlanganise
Ukuh- ukufikela ku-999 ukufikela ku-999 imivo.
langanisa • Ukukhupha ku-999 • Ukukhupha ku-999 Bala uye phambili nofana uye emuva ufike na-10
nofana uku- • Ukusebenzisa • Ukusebenzisa 588 + 9
khupha amatshwayo afaneleko amatshwayo afaneleko 588 + 10 = 598
( +, -, =, ) ( +, -, =, ) 598 – 1 = 597
• Ukujayeza • Ukujayeza 588 + 19
ukuhlangana ukuhlangana 588 + 20 = 608
kweenomboro kweenomboro ukufika
608 – 1 = 607
ukufikela ema-30 ema-30
Ukuthuthukisa nokujayeza amakghono wokuhlanganisa nokukhupha
Abafundi batlhoga ukuzijayeza ukwenza imihlobo eminye yamakghono wokuhlanganisa
nokukhupha.
Abafundi bafanele babe namathuba wokwenza imihlobo elandelako yeembalo
ngeenomboro ukufika ema 800:
Hlanganisa nofana ukhuphe ipara yesibuyabuyelelo se-10, ukudlulela ngale kwe-100.
• 40 + 70
• 70 + 80
• 120 – 30
• 150 – 60
Hlanganisa nofana ukhuphe i-10 kunanyana ngiyiphi inomboro enamadijithi amabili nofana
amathathu ukufaka hlangana ema-100.
Isibonelo:
• 65 + 10
• 124 + 10
• 326 – 10
• 358 - 10
Hlanganisa nofana ukhuphe idijithi yinye enomborweni enamadijithi amathathu ngaphandle
kokweqela ngale kwetjhumi.
Isibonelo:
• 634 + 5
• 775 + = 779
• 768 – 4
Hlanganisa begodu ukhuphe idijithi yinye ekubuyabuyeleni kwali 100. Add and subtract a
427 single digit to and from a multiple of 100
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
428 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.13 • Ukuhlanganisa • Ukuhlanganisa Isibonelo:
Ukuh- ukufikela ku-999 ukufikela ku-999 • 600 + 4
langanisa • Ukukhupha ku-999 • Ukukhupha ku-999 • 500 + 3
nofana uku- • Ukusebenzisa • Ukusebenzisa • 700 - 6
khupha amatshwayo afaneleko amatshwayo afaneleko • 800 - 5
( +, -, =, ) ( +, -, =, ) Thoma ngokuhlanganisa nokukhupha ipara yokubuyabuyelela kwali 100.
• Ukujayeza • Ukujayeza • 100 + 100
ukuhlangana ukuhlangana
• 100 + 200
kweenomboro kweenomboro ukufika
ukufikela ema-30 ema-30 • 200 + 200
• 300 + 400
Abafundi bafanele banikelwe amathuba wokuzijayeza amaphetheni wokuhlanganisa
nokukhupha.
Nangazi bonyana u-1+ 1 = 2
Bese liyini:
10 + 10
ISIGABA ESISISEKELO AMAGREYIDI 1-3
100 + 100
Thoma ukuhlanganisa nofana ukukhupha ipara yesibuyabuyelelo nofana ngiyiphi inomboro
enamadijithi amathathu.
Isibonelo:
675 + 100
762 – 100
Ukuhlola imiphumela yeembalo
Ukujaja ukuzwisiseka kweensombululo
Abafundi bafanele babandulwe ukujaja ukuzwisiseka kweensombululo. Indlela enye
yokwenza lokhu ngukulinganisa iimpendulo zabo ngaphambi kobana babale. Lokha
nawuhlanganisa iinomboro ezimbili ezitjhideleneko, isib. i-145 begodu ne 146, abafundi
bangasebenzisa ukubuyelela kabil njengendlela yokulinganisa iimpendulo zabo.
Ukuhlola iinsombululo
Abafundi bafanele bazi bonyana banga:
• Hlola isibalo sokuhlanganisa ngokukhupha. Isibonelo: lokha ama-436 + 118 = 454; bese
454 – 118 = 436
• Hlola isibalo sokukhupha ngokuhlanganisa. Isibonelo: 684 – 248 = 436, bese 436 + 248
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
= 684
Ukusebenzisa umbalopherhuko ukuhlola iinsombululo ngesinye seenzathu zokufundisa
ukuhlanganisa nokukhupha ndawonye.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Ethemini le abafundi baragela phambili ngoku:
Ukuh- iinomboro ngeye iinomboro ngeye • Sebenzisa begodu nokuzwisisa ilimi lokubuyabuyelela;
langanisa 2,3,4,5,10 2,3,4,5,10 • Jamela ukubuyabuyelela njengerhemo;
okubuyele- ukuhlanganisa ukufika ukuhlanganisa ukufika • Sebenzisa amatshwayo afaneleko ukurhumutjha imitjho yeenomboro;
lweko ema 99 ema 99
• Zwisisa bonyana ukuhlanganisa okubuyelelwako kungajanyelwa ngokusebenzisa
okurholela • Ukusebenzisa • Ukusebenzisa itshwayo lokubuyabuyelela;
ekubuy- amatshwayo amatshwayo • Jayeza begodu nokuzwisisa bonyana ukubuyabuyelela kungenziwa nanyana kungayiphi
abuyeleleni ngokufaneleko( x, =, ) ngokufaneleko( x, =, ) indlela (umthetho nofana ihlelo elihlanakelekako);
• Sebenzisa inambalayini ukubonisa iimbalo zokubuyabuyelela begodu ukghone
ukuhlathulula ukujanyelwa (iindlela imeqo ebonisa ngayo ukuhlanganisa
okubuyelelweko); begodu
• Thoma ukuzwisia ihlelo elabiweko lokubuyabuyelela.
Abafundi baragela phambili ukusebenzisa imihlobohlobo yemifanekiso ukuzwisisa
ukubuyabuyelela. Qala amanothi eThemini yesi -2.
Amaqhinga wokubuyabuyelela alisizo
Ukusebenzisa ukubuyelela kabili
Isibonelo:
Zalisa ithebula lokubuyelela ngakahlanu. Ngimaphi amaphetheni owabonako?
1 2 3 4 5 6 7 8 9 10
×5
× 10
Buyabuyelela iinomboro ethebuleni yokubuyabuyelela ngahlanu ukuthola iinomboro ereyini
yethebula yangetjhumi. Ubona amaphetheni maphi?
Zalisa ithebula lokubuyelela ngakubili.
1 2 3 4 5 6 7 8 9 10
×2
×4
Buyabuyelela iinomboro ngethebuleni lokubuyabuyelela ngakubili ukuthola iinomboro
ethebuleni lokubuyelela ngakune. Ngimaphi amaphetheni owabonako?
• Ukusebenzisa ukuhafula kabili
Iinqhema ezintathu obu-8 zilingana nama-24
Iinqhema ezisithandathu zanga-4 zilingana nama 24
4 + 4 + 4 + 4 + 4 + 4
429
Ngebanga lalokho:
8 + 8 + 8
Iinqhema zangasi-6 ezi-4 zifana neenqhema ezi 3 zango 8.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
430 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.14 • Buyabuyelela • Buyabuyelela Ngikuphi okuhlukileko kunethemini yesi 2?
Ukuh- iinomboro ngeye iinomboro ngeye Ethemini le irherho leenomboro abafundi abazosebenza ngazo lingezeleleke ukufika
langanisa 2,3,4,5,10 2,3,4,5,10 ema 99. Ukusebenza ngerherho leenomboro ezingezelelweko kutjho bonyana abafundi
okubuyele- ukuhlanganisa ukufika ukuhlanganisa ukufika kufuze bathome ukusebenza ngamaqhinga wokubala afaneleko begodu nangamarekhodi
lweko ema 99 ema 99 atloliweko ukufika eempendulweni zabo.
okurholela • Ukusebenzisa • Ukusebenzisa Amaqhinga wokurekhoda
ekubuy- amatshwayo amatshwayo
Ethemini yesi- 3 neye- 4 abafundi bazozijayeza ukurekhoda ukuhlukanisa basebenzisa
abuyeleleni ngokufaneleko( x, =, ) ngokufaneleko( x, =, )
iinomboro begodu bangabambeleleli emigwaleni. Amaqhinga wokurekhoda ngeze
asafumaneka ebafundini lokha nabangazwisisi ukusebenza. Nabalinga ukusebenzisa
indlela abangayizwisisiko kuzogcina kunemitjhapho abafundi ngokwabo abangeze baba
nekghono lokuyibona. Kuqakathekile bonyana abafundi bakghona ukubona ukuhlobana
hlangana kokubuyabuyelela begodu nokuhlukanisa. Umnqopho wamarekhodi atlolwako
ufanele uthuthukise ukuzwisisa kwabafundi kokuhlobana kweenomboro.
Ukusebenzisa ukubuyabuyelela
Abafundi bafanele bakwazi ukusebenzisa ilwazi labo lokubuyabuyelela. Bafanele bathome
ukutjho bonyana:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
“ Ngazini ngokubuyabuyelela ukuze ngithole ipendulo?”
96 ÷ 3 =
Ngiyazi bonyana: 10 x 3 = 30
Bese: 96 – 30 = 66
Ngiyazi bonyana: 10 x 3 = 30
Bese: 66 – 30 = 36
Ngiyazi bonyana: 10 x 3 = 30
Bese: 36 – 30 = 6
6÷3=2
Ngendlela engaphezulu, abafundi basebenzisa ukubuyabuyelela begodu bakhupha
ngokubuyelela ema 96.
Bese babala bonyana bakhuphe amahlandla amangaki : 2 + 10 + 10 + 10 = 32
Ukuphula iinomboro
Abafundi bangahlukanisa ama- 96 ngeenomboro ezikhambisana noku 3. Abafundi godu
basebenzisa ilwazi labo lokubuyabuyelela ukuze benze ukuhlukanisa kokubuyelela.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro 96 ÷ 3 =
Ukuhlu- ukufika ema-99 ngaku ukufika ema-99 ngaku
kanisa 2, 3, 4, 5, 10 2, 4, 5, 10, 3, 96 = 30 + 30 + 30 + 6
• Ukusebenzisa • Ukusebenzisa
amatshwayo afaneleko amatshwayo afaneleko
( ÷, =, ) ( ÷, =, ) iinqhema ezi10 iinqhema ezi10 iinqhema ezi10 iinqhema ezi 2
zanga 3 zanga 3 zanga 3 zanga 3
Lokho abafundi abakwenzako eembonelweni zombili basebenzisa ukukhupha
okubuyelelweko “ngeentokatokana”. Njengalokha ukubuyabuyelela “kwakha iinomboro”,
ukuhlukanisa kungabonwa “njengokuphulwa kweenomboro”. Ngalendlela ukuzwisiseka
kokuhlukanisa kuyaqiniswa njengompherhuko wokubuyabuyelela..
Abafundi bangasebenzisa ukukhupha okubuyelelweko njengentoka tokana , begodu
barekhode kuyo iindlela ezifana nalokha okuvezwe ngenzasi.
10 10 10
10 10 10
10 10 10
1 1 1
1 1 1
96 ÷ 3 =
96 ÷ 3 = 32
Ukusebenza ngeensalela
Abafundi bazakube basebenze ngeensalela nabenza ukubuthelela nokwabelana imiraro
yamagama. Kuqakathekile bonyana bathulelwe ngemitjho yeenomboro yokuhlukanisa
(ubujamo obutjhaphulukileko) evumela iinsalelo. Isibonelo:
Hlathululela abafundi bonyana:
Lokha nabazi bonyana 28 ÷ 7 = 4. Azakuba yini 29 ÷ 7 = 4? Kulindeleke bonyana abafundi
barekhode iimpendulo zabo ngendlela elandelako:29 ÷ 7 = 4 isalela yi-1. Sifuna abafundi
bakghone ukutjho bonyana ngimaphi amaphuzu wokuhlukanisa abawaziko, isib. 25 ÷ 5 = 5
ngebanga lalokho ama 26 ÷ 5 = 5 isalela yi-1
431
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
AMANYE AMANOTHI BESIKHATHI
IMIQONDO NAMAKGHONO : IIMFUNEKO ZOKUPHELA IMIQONDO NAMAKGHONO : IMINQOPHO WOKUTLHADLHULA (eemfundweni
IINHLOKO
432 KONYAKA YETHEMU YESI-3 NOFANA IMIHLAHLANDLELA ze-iri -1 begodu
YOKUFUNDISA namaminithi
ama -24)
1.16 Umqondonomboro: irherho lama 999 Umqondonomboro: irherho lama 700 Iimbalo zehloko
Iimbalo • Ukuhlela iinomboro ezikhethiweko ngokwesede • Ukuhlela iinomboro ezikhethiweko Qala amanothi weThemu
zehloko. enikeliweko. ngokwesede enikeliweko. yesi 2, kodwana sebenzisa
• Ukumadanisa iinomboro ukufika ku-999 begodu utjho • Ukumadanisa iinomboro ukufika ku-200 irherho leenomboro eziphezulu
bonyana ngiyiphi enengi nofana encani begodu utjho bonyana ngiyiphi enengi nofana ezinqiphisiweko ethemini yesi 3
• Ukwazi bonyana ngiyiphi inomboro: encani
• enengi nga-1 nofana encani nga-1 • Ukwazi bonyana ngiyiphi inomboro:
• Ukwazi bonyana ngiyiphi inomboro: • enengi nga-1 nofana encani nga-1
• enengi nga-2 nofana encani nga-2 • Ukwazi bonyana ngiyiphi inomboro:
• Ukwazi bonyana ngiyiphi inomboro: • enengi nga-2 nofana encani nga-2
• enengi nga-3 nofana encani nga-3 • Ukwazi bonyana ngiyiphi inomboro:
• Ukwazi bonyana ngiyiphi inomboro: • enengi nga-3 nofana encani nga-3
• enengi nga-4 nofana encani nga-4 • Ukwazi bonyana ngiyiphi inomboro:
• Ukwazi bonyana ngiyiphi inomboro: • enengi nga-4 nofana encani nga-4
• enengi nga-5 nofana encani nga-5 • Ukwazi bonyana ngiyiphi inomboro:
• Ukwazi bonyana ngiyiphi inomboro: • enengi nga-5 nofana encani nga-5
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• enengi nge-10 nofana encani nge-10 • Ukwazi bonyana ngiyiphi inomboro:
Ukukhumbula msinyana • enengi nge-10 nofana encani nge-10
• Ukuhlanganisa nokukhupha ukufika ema 20 Ukukhumbula msinyana
• Hlanganisa nofana ukhuphe ukubuyabuyelela nge 10 • Khumbula amaphuzu wokuhlanganisa
ukusuka eli 0 ukufika e 100 nokukhupha ukufika ema 20
• Amaphuzu wokubuyabuyelela nokuhlukanisa ngokwe: • Ukuhlanganisa nofana ukhuphe
ukubuyabuyelela nge 10 ukusuka eli 0
• ithebula yangakubili ukufika ku 2 x 10 ukufika e 100
• ithebula yangalitjhumi ukufika ku10 x 10 Amaqhinga wokubala ngehloko
Amaqhinga wokubala Ukusebenzisa amaqhinga wokubala
• Ukusebenzisa amaqhinga wokubala alandelako.: alandelako.
• Ukubeka inomboro ekulu maqangi ukuze ubale uye • Ukubeka inomboro ekulu maqangi ukuze
phambili nofana ubale uye emuva ubale uye phambili nofana ubale uye emuva
• Inambalayini. • Inambalayini.
• Ukubuyelela kabili nokuhafula phakathi • Ukubuyelela begodu nohafula phakathi
• Ukwakha nokuphula • Ukwakha nokuphula
• Ukusebenzisa ubudlelwana hlangana nokuhlanganisa
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
• Ukusebenzisa ubudlelwana hlangana
begodu nokukhupha. nokuhlanganisa begodu nokukhupha.
• Ukusebenzisa ubudlelwana hlangana nokubuyelela • Ukusebenzisa ubudlelwana hlangana
nokuhlukanisa. nokubuyelela nokuhlukanisa.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
1.17 • Sebenzisa begodu Ethemini le abafundi baragela phambili noku:
Amafrak- utjho amafraktjhini • Funda amagama weengcenye zamafraktjhini;
tjhini ukufaka hlangana
• Sebenzisa amagama ngebujameni ahlukeneko;
amahafu, amakotara,
ajayele- • bona ingcenye yamafraktjhini;
kobunane,kwesithathu,
kileko
kwesithandathu • Thoma ukuzwisisa bungako bamafraktjhini;
begodu nokwesihlanu • Thola amafraktjhini wezinto;
• Ukubona amafraktjhini • Funda ngokulingana kwamafraktjhini; begodu
wesakhiwo sesifaniso
• Madanisa amafraktjhini.
• Ukuthoma ukulemuka
Ethemini le abafundi bathoma ukubala iingcenye zamafraktjhini begodu bafunde
bonyana amahafu
amagama amatjha wamafraktjhini.
amabili namkha
kuthathu kwesithathu Ukubala iingcenye zamafraktjhini kuvumela abafundi ukubona iingcenye zokubuyabuyelela
begodu nokuthi zenza begodu ibanikela ilimi lamafraktjhini avangeneko nangasisezingeni. Amafraktjhini
into yinye epheleleko weendulungu alungile ukusebenzisa umqondo lo. Khuthaza abafundi ukubala ngombana
begodu nokuthi ihafu bazoku bala ibuthelelo lezinto, isib. kunye kwesine, okubili kwesine, okuthathu kwesinje,
yinye namakota okuhlanu kwesine ...ungabawa abafundi ukwenza kunye okupheleleko ngokusebenzisa
amabili ayalingana. abokune e begodu ubuze bonyana “lokha nasinakuhlanu kwesine, ngabe lokho kunengi
kunokupheleleko, kuncani kunokupheleleko, nofana kulingana nokupheleleko?” Thatha
• Ukutlola amafraktjhini
ithuba leli ukulungiselela umsebenzi osisekelo wamafraktjhini avangeneko ngokubuza
njengehafu yi-1 na 2
bonyana: “thatha okulikhomba kwesithathu. Ungenza okuzeleko okungaki? Ziingcenye
kwesithathu
ezingaki eziseleko?” Sifuna abafundi batjho bonyana : “kunokupheleleko okubili begodu
kusele kunye kokuthathu”
Umhlobo lo womsebenzi ukhuthaza:
• Ukuzwisisa inani lamahafu / leenquntu kokupheleleko
• Iindlela ezihlukahlukeneko zokukhuluma ngokubuyabuyelela iinomboro ngamahafu /
neenquntu.
433
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI- 3
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
434
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
: IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YESI-3 namaminithi
ZOKUPHELA KONYAKA
ama -24)
2.1 Ukukopulula, Ukukopulula, ukungezelela Ragela phambili nokunikela abafundi irherho elifanako lamaphetheni njengalawo isifundo si-1
Amapheth- ukungezelela begodu begodu nokuhlathulula. aku Themu yoku-1, kodwana faka hlangana woke amajamo amatjha begodu
eni weJi- nokuhlathulula Kopulula, ngezelela begodu emaphethenini njengoba kusetjenzwa ngawo eSikhaleni Nobujamo. Qala amanothi
yomethri Kopulula, ngezelela uhlathulule ngamagama wamaphetheni we Themu yoku-1 begodu namanothi weSikhala Nobujamo eThemini
begodu uhlathulule • amaphetheni alula enziwe yesi-2.
ngamagama ngezinto eziphathekako Vumela abafundi bakopulule mantanzi , bese bayangezelela begodu emaswapheleni
• amaphetheni alula • amaphetheni alula enziwe bahlathulule amaphetheni. Njenga nje,bafanele bonyana sebayakwazi ukuhlathulula
enziwe ngezinto ngemigwalo yemida, amaphetheni ngaphandle kokurhelejwa mibuzo ebarholako. Ragela phambili
eziphathekako yamajamo nofana ngezinto nokuqopha ekuthuthukiseni ilimi abalitlhogako lokuhlathulula amaphetheni.
• amaphetheni alula Amaphetheni lapho inomboro
enziwe ngemigwalo nofana ubukhulu wesinye
yemida, yamabujamo nesinye isigaba itjhuguluka
nofana ngezinto ngendlela abonela phambili
Ukuzakhela wakhe esigabeni esinye nesinye o.u.
amaphetheni akhula ngendlela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
amaphetheni
ehlelekileko eqelekileko
Ukuzakhela wakhe
amaphetheni Irherho lamaphetheni:
weJiyomethri Amaphetheni lapho inani
• ngezinto lamajamo kesinye nesinye
eziphathekako esigabaeni ngasinye itjhuguluka
ngendlela enebonelophambili
• ngokugwala o.u. amaphetheni akhula
imida,ubujamo nofana ngendlela eqakathekileko.
izinto
Ukuzakhela wakhe
Amaphetheni amaphetheni
asizungelezileko
Ukuzakhela wakhe
Ukubona , ukuhlathulula amaphetheni weJiyomethri :
ngamagama
nokukopulula • ngezinto eziphathekako
amaphetheni • ngokugwala imida,amajamo
weJiyomethri nofana izinto
• weemveleni
• ebuphilweni
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
bangamalanga
banamhlanje
• elifeni lamasiko wethu
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
: IIMFUNEKO YOKUFUNDISA ze-iri -1 begodu
YESI-3
CAPS namaminithi
ZOKUPHELA KONYAKA
ama -24)
2.2 Ukukopulula,uku Ukukopulula,ukungezelela Qala amanothi weThemu yoku-1 3 lessons
Amaphethe- ngezelela begodu begodu uhlathulule Ngezelela ukulandelana ufake hlangana abo:
ni weenom- uhlathulule Ukukopulula, ukungezelela • ngabo ku-1 ukusuka kunanyana ngiyiphi inomboro pha hlangana kwe- 0 nama-
boro Ukukopulula, begodu nokuhlathululea
750
ukungezelela begodu ukulandelana kweenomboro
okulula kufika okungasenani • ngali-10 ukusuka kunanyana ngikuphi ukubuyabuyelela kwe-10 hlangana kwe-0
nokuhlathulula
e-180 nama-750
ukulandelana
kweenomboro nokulula Ukulandelana kufanele • ngaku-5 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaku-5 hlangana kwe-0
ukufika okungasenani kutjengise ukubala uye phambili nama-750.
ema-700 nemuva nga:
• Ngaku-2 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaka ku-2 hlangana
• ku-1 ukusuka kunanyana kwe-0 nama -750
Ukuzakhela wakhe
ngiyiphi inomboro hlangana
amaphetheni ne-0 ne-750. • Nge-100 ukusuka kunanyana ngikuphi ukubuyabuyelela kwe-100 ukufika
Ukuzakhela amaphetheni okungasenani e-1000
• Li-10 ukusuka kunanyana
weenomboro. ngikuphi ukubuyabuyelela se- • ngama-50 ukusuka kunanyana ngikuphi ukubuyabuyelela kwama-50 ukufika
10 hlangana ne-0 ne-750. okungasenani e-1000
• Ku-5 ukusuka kunanyana • ngama-25 ukusuka kunanyana ngikuphi ukubuyabuyelela kwama-25 ukufika
ngikuphi ukubuyabuyelela okungasenani e-1000
kwaku ku-5 hlangana ne-0 • Ngama-20 ukusuka kunanyana ngikuphi ukubuyabuyelela kwama-20 ukufika
ne-750.
okungasenani e-1000
• Ku-2 ukusuka kunanyana
ngikuphi ukubuyabuyelela • Ngaku-3 ukusuka kunanyana ngikuphi ukubuyabuyelela kwaka 3 hlangana kwe-0
saka ku-2 hlangana ne -0 nama-750
ne-750. • ngaku -4 ukusuka kunanyana ngikuphi ukubuyabuyelela kwa ka 4 hlangana kwe-0
• Ku-3 ukusuka kunanyana nama-750
ngikuphi esinye nesinye Sebenzisa izinto, iinthombe, amathebula netjhadi naneko ukusekela abafundi
ukubuyabuyelela kwaku ku-3 ekutjhugulukeni kusukela ekubaleni ngokweqa begodu nokulandelandelana ukuya
hlangana ne-0 ne750 ekubuyabuyeleleni nga 10, 5, 2, 4, 3.
• Ku-4 ukusuka ukusuka Ukusiza abafundi basebenzise amaphetheni abawaziko njengesisekelo sokuzijayeza
nanyana ngikuphi kesinye
begodu nokufunda amanye amaphetheni isib.
nesinye ukubuyabuyelela
kwaku-4 hlangana ne-0 ne- Ukulandelana kwabo ku 2 ukubeka isisekelo sokulandelana kwabo ma 20.
750
• Ma-20, 25, 50, 100
okungasenani ukufika e-1000.
Ukutlama nokuhlathulula
amaphetheni wakho
435 Tlama begodu uhlathulule
amaphetheni wakho
weenomboro
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI-3
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
436
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
3.1 Ubujamo nokubukela Ubujamo nokubukela Ngikuphi okutjha eGreyidini yesi-3 limfundo ezi-3
Ubujamo, • Ukumadanisa • Ukufunda, • Imimebhe, iimplani begodu nelingaphezulu lezinto ezibuthelelweko.
ukuzijayeza ukuqaleka ukurhumutjha begodu -- Ukuthola izinto emimebheni.
nokubukela okuhlukahlukeneko nokugwala imimmebhe
-- Ukulandela iinkombatjhuba emimebheni
kwezinto ezifanako engakahleleki
zangamalanga. nofana ilingaphezulu -- Ukugwala imimebhe engakahleleki,iimplani nelingaphezulu lezinto zibuthelelweko
• Yitjho igama lento lebuthelelo lezinto . Ukufunda nokurhumutjha imimebhe
yangamalanga lokha • Ukuthola izinto Imimebhe isitayela esithize sokubona into kusukela ngehla kwendawo. Egreyidini 3
nawuyitjengiswe emimebheni. abafundi basebenza ngemimebhe angakahleleki kuphela, Lokhu akufaki hlangana
ihlangothini Ubujamo imimebhe yendlela evamileko nofana imimebhe avamileko wejiyografi.
elingakajayeleki. neenkombatjhuba Kungasiza abafundi ukuthoma ngeemplani nofana ukubukela ngehla kwendawana ezincani
• Ukufunda, Landela iinkombatjhuba isib.ithreyi yezinto nofana iplani yeetlasini ngaphambi kokubaqala imimebhe yendawo
ukurhumutjha begodu ukusukela endaweni ezikudlwana.
ugwale imimebhe eyodwa ukuya kwenye Ithemu yesi- 2 iphathelene nokumadanisa kokubukelwa ilingaphezulu, ilingeqadi begodu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
engakahleleki, emebheni ongakahleleki. nelingaphambili .Ukubona into ehlangothini eliyi obhligi kutjho ukubona ingcenye yayo
nofana ilingaphezulu kusukela ngaphezulu begodu uyibone ingenye yayo ukusukela ngehlangothini, Abantwana
lebuthelelo lezinto. abancani babona iobhligi yomhlaba kanengi khulu kunokubona ilingaphezulu. Kungasiza
• Ukuthola izinto abafundi ukuthoma ukumadanisa amahlangothi wendawo aqaleka ayi-obhligi nemimebhe
emebheni yendawo lezo. Nangabe kokubili okubonakalako (ukuqaleka kwe obhligi nokubona
• Ubujamo ilingaphezulu) anikelwe , abafundi bangamadanisa lokho abakubona kelinye ihlangothi
neenkombatjhuba nalokho okhunye abakubonako.
• Landela ikombatjhuba Thoma ngokusiza abafundi bonyana bazwisise imimebhe begodu namaplani bese
yokukhambakhamba uyababawa bonyana bafunyane iindawo emimebheni isib. “fumana
ngetlasini begodu iklinigi; kuyini okuseduze nayo?”
nesikolweni. Nasele abafundi bakgona ukuthola lula I ngokuzijamela emebheni, thoma ngokubanikela
• Ukunikela iinlayelo iinkombadlela zokusuka endaweni enye ukuya kwenye emebheni.
zokukhambakhamba Gwala ilingaphezulu lezinto ezibuthelelweko begodu nemimebhe engakahleleki
ngetlasini begodu
Kulula bonyana abafundi bagwale ilingaphezulu lento ethize abangayiqalela phasi
nasesikolweni .
kunokuba bagwale umebhe ngehloko nofana ngengqondo. Indawo ongathoma ngayo
• Landela ikombatjhuba ukugwala ilingaphezulu, ukuvumela abafundi ukuqalela phasi izinto ezibuthelelweko isib.
ukusuka endaweni izinto ezisedeskeni lakatitjhere, nofana ithreyi yezinto ezibekwe ehlabathini, begodu ubawe
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
eyodwa ukuya kwenye abafundi bayigwale kusukela ngaphezulu. Abafundi bangaragela phambili ngokugwala
emebheni ongakahleki iimplani ezingakahleleki begodu nemimebhe yeendawana ezincani isib.itlasi lokufundela,
ibala lesikolo.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
3.2 Irherho lezinto Irherho lezinto Isitjhukumiso somnqopho weThemu yesi-3
Izinto ezibo- Ukukhumbula begodu Ukukhumbula begodu -- Abafundi banganqopha ezintweni ezitja eGreyidini yesi-3, o.u.amaphiramidi begodu
busontathu nokutjho amagama nokutjho amaga wezinto neenkurwana/amakhowuni
(3-D) wezinto za- 3-D za-3-D ezingetlasini -- Abafundi bakha izinto ngamathunjana wokusela iinselo ezimakhaza nofana
ezingetlasini begodu begodu neethombeni amaphayiphu wokuhlwengisa nofana ngeembali mazinyo nofana ngamathunjana
neenthombeni • Amajamo webhola wamaphepha aphuthelweko.
• Amajamo webhola (indulungu) Yethula kubafundi amakhoni namaphiramidi.
(indulungu) • Amajamo bebhoksi Ukunqopha ematshwayeni wezinto za (3-D ): zelingaphezulu elithabaleleko nofana
• Amajamo bebhoksi (amaphrizimu) eligobeneko, ubujamo belingaphezulu elithabaleleko
(amaphrizimu) • Amasilinda • Ingaphezulu elithabaleleko nofana eligobeneko
• Amasilinda • Amaphiramidi EThemini yesi- 2
• Amaphiramidi • Iinkurwana (Amakhoni) • Abafundi banqopha ekuthini izinto zinelingaphezulu elithabaleleko nofana eligobeneko.
• Iinkurwana (Amakhoni) Amatshwayo wezinto • Abafundi bahlathula amajamo welingaphezulu elingemaqadi ngukutjho bonyana;
Amatshwayo wezinto Ukuhlathulula, ukuhlela iindulungu, aboncantathu, iinkwere nofana aboncande.
Ukuhlathulula, ukuhlela begodu nokumadanisa Abafundi baragela phambili nokwenza lokhu eThemini yesi-3 , kodwana kwanje baqala
begodu nokumadanisa izinto ezi 3-D ngokuya nama phiramidi neenkurwana (amakhowuni).
izinto ezi 3-D ngokuya nga/ngo:
• Ukwakha izinto ezi 3-D ezikhamba ngayinye .
nga/ngo: • majamo we 2-D
Abafundi basebenzisa iimbangulimazinyo, namathunjana wamaphepha aphuthelweko,
• majamo we 2-D ezenza ubuso bezinto
amathunjana wokusela iinselo ezimakhaza nofana amphayiphu wokuhlwengisa ukwenza
ezenza ubuso bezinto ze 3-D
iphiramidi. Lokhu kwenza abafundi banqophe emaphethelweni wephiramidi. Abafundi
ze 3-D • phezulu elisipara abakalindeleki bonyana babale inani lomiphetho nofana umakhona wephiramidi (lokhu
• phezulu elisipara nofana eligobeneko kwenziwa eGreyidini yesi-6).
nofana eligobeneko Imisetjanzana Ukukhumbula nokutjho amagama wezinto
Imisetjenzana enqotjhiweko
Abafundi bafanele banikelwe Izinto ezihlukahlukenekoabazokusebenza ngazo :
enqophiweko Imisetjenzana
-- Okujame njenge ndulungu, isib. iimbholo nofana ubukhulu bomabul , amalamune njll. ;
Tjheja godu wak he izinto Tjheja goduwak he izinto
za 3-D ezinikelweko -- Okujame onjenge phrizimu, isib. Amabhlogo , iintina , amabhoksi ahlukahlukeneko
za 3-D ezinikelweko
ngokusebenzisa ngobukhulu , isib.amabhoksi womlilo ,amabhoksi wesiriyeli ,amabhoksi wetiye
ngokusebenzisa
amamathiriyeli ,amabhoksi wenhlamba mazinyo ;
amamathiriyeli
aphathekako aphathekako -- Okujame njenge silinda, okufaka hlangana amade namatsikana, isib. inquntwana
afana namajamo afana namajamo zamaphayiphi ezinobujamo besilinda ,
we 2-D asikiweko we 2-D asikiweko -- Ikhadibhodi elingaphakathi lephepha lefoyili nofana iphepha lokuya ngendlwaneni
umdaka/ibumba, umdaka/ibumba, begodu namasilinda amafithjani, adage, isib amabhlegana wephoritjhi yamanyathelo,
iimbangulimazinyo, iimbangulimazinyo, amabhlegana wesineyifu njll.
437 amaphayiphi wokusela amaphayiphi wokusela -- Okujamo njeenkurwana ( amakhowuni); begodu
nezinye izinto eziyi 3-D nezinye izinto eziyi 3-D
zeJiyomethri -- Okujame njengephiramidi.
zeJiyomethri
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
438 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
3.2 Irherho lezinto Irherho lezinto Abafundi bafanele babawiwe batjengise izinto ezijame njengebholo (indulungu), Iimfundo
Izinto ezibo- Ukukhumbula begodu Ukukhumbula begodu nofana okujame njengebhoksi (phrizimu) , nofanaokujame njenge ( isilinda) , okujame
busontathu nokutjho amagama nokutjho amaga wezinto njengephiramidi, nonfana okujamw njengesikurwana .
(3-D) wezinto za- 3-D za-3-D ezingetlasini -- Lokha nabanikelwe ibuthelelo lezinto ; nofana
ezingetlasini begodu begodu neethombeni -- Ngetlasini,
neenthombeni • Amajamo webhola isib. Isitina lesi sinobujamo obufana nebebhoksi nofana ilamune leli linobujamo obufana
• Amajamo webhola (indulungu) nebholo.
(indulungu) • Amajamo bebhoksi Ngesikhathi sabafundi sokujamela bangenza iimbholo, bebodu namasilinda begodu
• Amajamo bebhoksi (amaphrizimu) nobujama bamabhoksi, (amaphrizimu ),amphiramidi ,begodu neenkurwana ngedaka
(amaphrizimu) • Amasilinda nofana ihlama yokudlala.
• Amasilinda • Amaphiramidi Umsetjenzana otlolwako
• Amaphiramidi • Iinkurwana (Amakhoni) Nanyana umsebenzi omnengi wezinto za-3-D wenziwa ngokuphathekako, kufanele
• Iinkurwana (Amakhoni) Amatshwayo wezinto uhlanganiswe noku tlola .Umnqopho weGreyidi yesi-3 ufanele ube sekutjhweni amagama
Amatshwayo wezinto wezinto begodu nokukhuluma ngobujamo belingaphezulu lento. . Akukalindeleki bonyana
Ukuhlathulula, ukuhlela
abafundi babale nofana bazi inani nomboro leenkwere, laboncande, aboncantathu nofana
Ukuhlathulula, ukuhlela begodu nokumadanisa
izinto ezinelingaphezulu eliyidulungu, nofana amawugu atholakala entweni leyo. izin
begodu nokumadanisa izinto ezi 3-D ngokuya
ISIGABA ESISISEKELO AMAGREYIDI 1-3
izinto ezi 3-D ngokuya nga/ngo: ILimi
nga/ngo: • majamo we 2-D ILimi elisebenzisekako lokha nawukhuluma ngezinto za-3-D:
• majamo we 2-D ezenza ubuso bezinto Ingaphezulu elithabaleleko , eligobeneko , amabhoksi , iimbholo , amasilinda ,
ezenza ubuso bezinto ze 3-D amaphiramidi , iinkurwana .
ze 3-D • phezulu elisipara
• phezulu elisipara nofana eligobeneko
nofana eligobeneko Imisetjanzana
Imisetjenzana enqotjhiweko
enqophiweko Imisetjenzana
Tjheja godu wak he izinto Tjheja goduwak he izinto
za 3-D ezinikelweko za 3-D ezinikelweko
ngokusebenzisa ngokusebenzisa
amamathiriyeli amamathiriyeli
aphathekako aphathekako
afana namajamo afana namajamo
we 2-D asikiweko we 2-D asikiweko
umdaka/ibumba, umdaka/ibumba,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
iimbangulimazinyo, iimbangulimazinyo,
amaphayiphi wokusela amaphayiphi wokusela
nezinye izinto eziyi 3-D nezinye izinto eziyi 3-D
zeJiyomethri zeJiyomethri
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
3.3 Irherho lamajamo Irherho lamajamo Qala amanothi weThemu yoku-1. Iimfundo ezi-2
Amajamo • iindulungu • iindulungu Abafundi bafanele bagcine nomnqopho ofanako , kodwana benze imisetjenzana
wa- (2-D) • aboncantathu • aboncantathu ehlukahlukeneko.
• iinkwere • iinkwere Abafundi basebenza ngendulungu nangeenkwere ezinesayizi /ubukhulu obuhlukahlukeneko
begodu nangabo ncatathu naboncande abanobujamo obuhlukahlukeneko. Bazihlela
• aboncande • aboncande
ngokuthi zinamahlangothi anqophileko / athabaleleko nofana amahlangothi azindulungu.
Amatshwayo Amatshwayo
Abafundi bahlela begodu babuthelele amajamo ngokuya ngokuthi aboncantathu,
wamajamo wamajamo
aziinkwere, aboncande nofana azindulungu.
Ukuhlathulula,ukuhlela Ukuhlathulula,ukuhlela
Umsebenzi uyahlanganiswa ngemisetjenzana otlolwako ofaka hlangana imigwalo
nokubeka begodu nokubeka begodu
yamajamo woke afunekako.
nokumadanisa izinto ezi- nokumadanisa izinto ezi-
( 2-D) ngokuya ngo: ( 2-D) ngokuya ngo:
• bujamo • bujamo
• amahlangothi anqophe • amahlangothi anqophe
thwi thwi.
• amahlangothi • amahlangothi
azindulungu . aziindulungu/arondo
Gwala amajamo Gwala ubujamo
• iindulungu • iindulungu
• aboncantathu • aboncantathu
• iinkwere • iinkwere
• aboncande • aboncande
439
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI -3 ITHEMU YESI- 3
4. UKUMEDA
440
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi
Isikhathi • Ukufunda amalanga • Ukufunda amalanga begodu nangokulandelana kwesikhathi.
emakhalendeni emakhalendeni Ngesikhathi sokufundisa itlasi loke begodu nangesikhathi sokunqopha
• Ukubeka amalanga • Ukubeka amalanga esiqhemeni, abafundi baragela phambili nokukhuluma ngamalanga weveke,
wamabeletho, amafestivali wamabeletho, amafestivali inyanga yonyaka begodu nedadamu yelanga lamhlokho , nangamalanga
wezekolo, amaholideyi wezekolo, amaholideyi angaphambili begodu namalanga asezako. Abafundi baragela phambili
womphakathi, iminyanya womphakathi, iminyanya nokubeka okulandelako ekhalendeni njengombana izehlakalo zivela
yezomlando, izehlakalo yezomlando, izehlakalo • amalanga wamabeletho ;
zesikolo ezisekhalendeni. zesikolo ezisekhalendeni. • amafestivali wezekolo ;
• Ukutjho isikhathi sama-iri • Ukutjho isikhathi sama-iri ali- • iminyanya yezomlando ;
ali-12 ngama 12 ngama
• izehlakalo zesikolo ; begodu
-- -iri, -- -iri,
-- ngesiquntu se-iri -- ngesiquntu se-iri • amaholideyi womphakathi.
-- ngekotara ye-iri -- ngekotara ye-iri Ragela phambili ngokutjela abafundi bonyana batjho isikhathi ngamakhefu
-- amaminithi -- amaminithi avamileko.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
wewatjhi le-analogo neenwatjhi wewatjhi le-analogo neenwatjhi -- ngama-iri begodu nangamaminithi wewatjhini ye-analogo; begodu
zedijithali begodu nezinye zedijithali begodu nezinye -- ngama-iri, iinquntu zama-iri, begodu nangamakotara wama-iri
iinsetjenziswa zedijithali iinsetjenziswa zedijithali ngokusebenzisa amawatjhi we analogo .
ezitjengisa isikhathi, isib. ezitjengisa isikhathi, isib.
abomaliledinini abomaliledinini Isibonelo, abafundi bangabawiwa bonyana batjho iskhathi sokungena
kwesikolo , isikhathi sokudla begodu nesikhathi sokuphuma kwesikolo ,
Ukubala ubude besikhathi Ukubala ubude besikhathi nofana batjhintja basuka kesinye isifundo baya kwesinye. Khetha iinkhathi
begodu nokudlula begodu nokudlula lapho iwatjhi litjengisa isikhathi poro nofana isiquntu se-iri nofana ikotara
kwesikhathi kwesikhathi ye-iri. Kuyarhelebha ukuba newatjhi elikhulu, elisebenzako libekwe
Ukusebenzisa amakhalenda Ukusebenzisa amakhalenda ngetlasini, fanelekile bonyana kube newatjhi esebenzako ebekwa ngetlasini,
ukubala begodu nokuhlathulula ukubala begodu nokuhlathulula uukwenzela bonyana abafundi baqale kilo isikhathi. Abafundi bangenza
ubude besikhathi ngokuya ubude besikhathi ngokuya imifaniso yamawatjhi. Ungababawa bonyana bakutjengise iinkhathi
ngamalanga nofana ngamalanga nofana ngeemveke ezihlukileko begodu nokufaka hlangana nokhunye ukubalisisa , isib.
ngeemveke nofana nofana ngeenyanga ukufaka “Ngitjengisa i-iri le-10 ehloko . Bekusukhathi bani ikotara ye-iri ngaphambi
ngeenyanga ukufaka hlangana hlangana kwe –iri letjhumi ?”
• ukutjhugulula hlangana • ukutjhugulula hlangana Qala amanothi weThemu yoku-1
kwamalanga neemveke kwamalanga neemveke Ngesikhathi sokusebenza ngokuzijamela , abafundi baragela phambili
• ukutjhugulula hlangana • ukutjhugulula hlangana nokwenza imisebenzi ephathelene nokutjho isikhathi:
kweemveke neenyanga kweemveke neenyanga -- ngama-iri, iinquntu zama-iri, begodu nangamakotara wama-iri ewatjhini
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Sebenzisa amawatjhi ukubala Sebenzisa amawatjhi ukubala ye-analogo; begodu
ubude besikhathi ngokuya ubude besikhathi ngokuya -- ngama-iri begodu nangamaminithi ewatjhini ye-dijithali
ngama-iri nofana iinquntu ngama-iri nofana iinquntu
zama-iri zama-iri
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-3
CAPS namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi bangabala ngeemveke nofana ngamalanga nabanganikelwa iimfundo ezi-4
Isikhathi • Ukufunda amalanga • Ukufunda amalanga ikhalenda nofana iingcenye zekhalenda , isib. Ukuthola idadamu begodu
emakhalendeni emakhalendeni nokubala umahluko hlangana nawo
• Ukubeka amalanga • Ukubeka amalanga Ukufunda isikhathi se-analogo ngamaminithi
wamabeletho, amafestivali wamabeletho, amafestivali Sebenzisa okungasenani iimfundo ezi-3 unqophise abafundi emakghonweni
wezekolo, amaholideyi wezekolo, amaholideyi afunekako bonyana bafunde isikhathi se-analogo ngamaminithi.
womphakathi, iminyanya womphakathi, iminyanya
yezomlando, izehlakalo yezomlando, izehlakalo -- Khumbuza abafundi ngehlathululo yekuseni (a.m) begodu
zesikolo ezisekhalendeni. zesikolo ezisekhalendeni. neyentambama (p.m.)
• Ukutjho isikhathi sama-iri • Ukutjho isikhathi sama-iri ali- -- Khumbuza abafundi bonyana kunamaminithi ama-60 e-irini linye;
ali-12 ngama 12 ngama ngakho-ke kunamaminithi ama-30 esinquntwini se-iri begodu
-- -iri, -- -iri, kunamaminithi ali-15 ekotareni ye-iri. Bavumele babale ngaku-5
-- ngesiquntu se-iri -- ngesiquntu se-iri nawukhomba iinomboro ewatjhini ye-analogo.
-- ngekotara ye-iri -- ngekotara ye-iri -- Hlathulula imithetho yesikhathi “ukudlula” begodu “nokuya”
-- amaminithi -- amaminithi
-- Nikela abafundi isikhathi esinengi sokuzijayeza ukufunda isikhathi se-
wewatjhi le-analogo neenwatjhi wewatjhi le-analogo neenwatjhi
zedijithali begodu nezinye zedijithali begodu nezinye analogo ngamaninithi
iinsetjenziswa zedijithali iinsetjenziswa zedijithali Bawa abafundi bonyana batjho isikhathi qho emini umnyaka woke. Abafundi
ezitjengisa isikhathi, isib. ezitjengisa isikhathi, isib. bangahlola ewatjhini ye-analogo bonyana banikele isikhathi esifaneleko
abomaliledinini abomaliledinini nabafunda iwatjhi ye-analogo. Vumela abafundi benze amawatjhi
Ukubala ubude besikhathi Ukubala ubude besikhathi wemifanekiso abangawasebenzisa ukutjho isikhathi begodu nokubala
begodu nokudlula begodu nokudlula ukuhluka kweekhathi
kwesikhathi kwesikhathi
Ukusebenzisa amakhalenda Ukusebenzisa amakhalenda
ukubala begodu nokuhlathulula ukubala begodu nokuhlathulula
ubude besikhathi ngokuya ubude besikhathi ngokuya
ngamalanga nofana ngamalanga nofana ngeemveke
ngeemveke nofana nofana ngeenyanga ukufaka
ngeenyanga ukufaka hlangana hlangana
• ukutjhugulula hlangana • ukutjhugulula hlangana
kwamalanga neemveke kwamalanga neemveke
• ukutjhugulula hlangana • ukutjhugulula hlangana
kweemveke neenyanga kweemveke neenyanga
Sebenzisa amawatjhi ukubala Sebenzisa amawatjhi ukubala
ubude besikhathi ngokuya ubude besikhathi ngokuya
ngama-iri nofana iinquntu ngama-iri nofana iinquntu
zama-iri zama-iri
441
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
442 : IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YETHEMU YESI-3
ama -24)
4.2 Ukumeda okungakahleleki Ukwethula ukumeda Ngikuphi okuhlukileko eThemini yesi-2
Ubude • Ukulinganisa, ukumeda, okuhlelekileko EThemini yesi-2 abafundi banqopha
ukumadanisa, ukuhlela • Ukulinganisa, • Ekumedeni okungakahleleki ngokusebenzisa amayunithi wobude angakahleleki :
begodu urekhode ukumeda, begodu
ubudengokusebenzisa ukumadanisa, • Nokumeda ngamamitha
iimedo ezingakahleleki, ukuhlela begodu EThemini yesi-3 abafundi bangathoma ukumeda ngamasenthimitha basebenzisa irula.
isib. Ubude besandla, urekhode ubude Lokhu kuzokuba sisetjenziswa sokuthoma sokumeda esisetjenziswa bafundi lokha
amagadango, ubude ngokusebenzisa nabatlhoga ukufunda iimedo emideni enomboriweko yeemedo.
bamapensela, izinto amamitha (iintonga
Ukulinganisa, ukumeda, ukumadanisa begodu nokurekhoda ubude, ukuphakama
zokubala, njll ezimamitha begodu nobubanzi ngokusebenzisa amamitha
• Ukuhlathulula ubude nofana iintambo
• Abafundi bafanele bahlanganise ukuzwisisa kwabo kobude bemitha yi-1 begodu
bezinto ngokubala ezinobude bemitha)
basebenzise ubude bemitha ukumeda into ethileko. Qala amanothi weThemu yesi-2
begodu nokutjho bonyana njengomuvosimedo
ohlelekileko. Ukulinganisa, ukumeda, ukumadanisa begodu nokurekhoda ubude, ukuphakama
zinobude obungangani begodu nobubanzi ngamasenthimitha ngokusebenzisa irula.
bamayunithi angakahleleki • Ukulinganisa
• Ukusebenzisa irula
• Ukusebenzisa nokumeda ubude
ngamasenthimitha Tjengisa abafundi bonyana kuthonywa njani ukumeda ukusuka kulize.
ilimi ukukhuluma Lokha abafundi nabasebenzisa amayunithi angakahleleki , bathoma ukubeka
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngokumadanisa, isib. ngokusebenzisa
izinto ezisetjenziswa njengamayunithi ekuthomeni kwento emedwako. Nawumeda
ubude, ubufitjhani, mude irula.
ngamasenthimitha, awubeki ekuthomeni kwerula into emedwako Ubeka into emedwako
khulu , banzi khulu • Alikho itjhuguluko elizeni lerula.
Ukwethula ukumeda elifuneka hlangana
okuhlelekileko kwamamitha
namasenthimitha.
• Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela
begodu urekhode
ubude ngokusebenzisa
amamitha (iintonga
ezimamitha Iraba inobude bama-2 cm
nofana iintambo Kuyakghonakala bonyana unqophise into emedwako ngekuthomeni kwayo nenye
ezinobude bemitha) inomboro eseruleni begodu ukhuphe inomboro esekuthomeni kwento emedwako
njengomuvosimedo enomborweni esekugcineni kwento emedwako.
ohlelekileko.
• Ukulinganisa nokumeda
ubude ngamasenthimitha
ngokusebenzisa irula.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Alikho itjhuguluko elifuneka
hlangana kwamamitha
namasenthimitha. Iraba inobude obuma- (3cm- 1cm) =2 cm
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
: IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
YETHEMU YESI-3
ama -24)
4.2 Ukumeda okungakahleleki Ukwethula ukumeda Ngaphandle kobana abafundi babuze ngayo, nofana bazitholele ngokwabo, ingaliselelwa lessons
Ubude • Ukulinganisa, ukumeda, okuhlelekileko iGreyidi yesi-4.
ukumadanisa, ukuhlela • Ukulinganisa, • Ukulinganisa ngamasenthimitha
begodu urekhode ukumeda, Abafundi bafanele bathole izinto ezinobude besenthimitha yi-1 tere. Mhlamunye
ubudengokusebenzisa ukumadanisa, munye wemino ububanzi be-1 cm. lokhu kungasetjenziswa njengendawo esitjengiso
iimedo ezingakahleleki, ukuhlela begodu yokulinganisa ubude, ubudege, begodu nokuphakamangamasentimitha. Lokha abafundi
isib. Ubude besandla, urekhode ubude nasele banekghono lokumeda ngamasentimitha, kufanele balinganise ngaphambi
amagadango, ubude ngokusebenzisa kokumeda okhunye nokhunye.
bamapensela, izinto amamitha (iintonga • Imida , imigwalo begodu nezinto
zokubala, njll ezimamitha Vumela abafundi bathome ukumeda imida. Kulula ukumeda ubude bemida eyenza
nofana iintambo ubude, ukuphakama nofana ububanzi bemigwalo yezinto nakusetjenziswa irula.
• Ukuhlathulula ubude
ezinobude bemitha) Kubudisi khulu ukumeda ubude, ukuphakama nofana ububanzi bezinto eziphathekako
bezinto ngokubala
njengomuvosimedo ngokusebenzisa irula.
begodu nokutjho bonyana
ohlelekileko. EGreyidini yesi-4 abafundi bazakumeda ngamasenthimitha nangamamilimitha.
zinobude obungangani
EGreyidini yesi-3 abakalindeleki bonyana
bamayunithi angakahleleki • Ukulinganisa
nokumeda ubude Basebenzise amamilimitha.
• Ukusebenzisa
ngamasenthimitha • Ukumadanisa iimedo ngamasenthimitha
ilimi ukukhuluma
ngokumadanisa, isib. ngokusebenzisa Abafundi bafanele bamadanise ubude, ububanzi begodu nokuphakama kwezinto
irula. ezimedwako ngamasenthimitha.
ubude, ubufitjhani, mude
khulu , banzi khulu • Alikho itjhuguluko • Ukurekhoda iimedo
elifuneka hlangana Nanyana ukumeda kulikghono lokuzijayeza, abafundi bafanele barekhode iimedo zabo
Ukwethula ukumeda
kwamamitha (ngawo womabili amayunithi angakahleleki begodu ngamamitha) ngaso soke isikhathi.
okuhlelekileko
namasenthimitha. Ukumeda ubude njengobujamo bokurarulula imiraro begodu nokubala
• Ukulinganisa, ukumeda,
Ngesikhathi esibekelwe Iinomboro, ama- Oparetjhiniimi noBudlelwana, abafundi
ukumadanisa, ukuhlela
bangararulula imiraro esebenzisa
begodu urekhode
ubujamo
ubude ngokusebenzisa
amamitha (iintonga • Bokumeda okungakahleleki kobude
ezimamitha • Ukumeda ngobude amamitha ;begodu
nofana iintambo • Ukumeda ubude ngamasenthimitha
ezinobude bemitha) Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yeenkinga ezihlukahlukeneko
njengomuvosimedo ezifaneleko zeThemu.
ohlelekileko. Abafundi ABAKALINDELEKI bonyana
• Ukulinganisa nokumeda • bazi bonyana i-100cm= 1 m;
ubude ngamasenthimitha • ukwenza itjhuguluko hlangana namasenthimitha namamitha;
ngokusebenzisa irula. • bafunde ubude ngamamilimitha ( lokhu kwenziwa ukusuka eGreyidini ye-4)
Alikho itjhuguluko elifuneka • bazi bonyana i-10 mm = 1 cm; nofana
443 hlangana kwamamitha • benze itjhuguluko hlangana namasenthimitha namamilimitha.
namasenthimitha.
Ukubala ngamasenthimitha kungakhethwa ukuze bangeqeli ngale kwe-100 cm.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO : NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
444 IIMFUNEKO ZOKUPHELA KONYAKA IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
YESI-3 namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Ngesikhathi sokusebenza ngokuzijamela abafundi bangaragela phambili
Imasi / • Ukulinganisa, ukumeda, noku:
Ubudisi ukumadanisa, ukuhlela, • Linganisa, ukumeda, ukuhlela, ukumadanisa begodu nokurekhoda
begodu kurekhodwe ubungako, ubungako bezinto ngokusebenzisa isikala sokudzimelela ngamayunithi
ngokusetjenzisa iimedo wokumeda angakahleleki.
ezingakahleleki begodu nesikala • Madanisa, uhlele begodu urekhoda abakufumeneko.
sokudzimelela isib. amabhulogo,
-- izinto ezithengiswa esitolo sokudla nezinye izintwanyana zangekhaya
iintina njll.
ngobungako obutlolwe ngamakhilogremu
• Ukusebenzisa ilimi ukukhuluma
-- izinto ezithengiswa esitolo esitolo sokudla nezinye izintwanyana
ngokumadanisa isib.elula, ebudisi,
zangekhaya ngobungako obutlolwe ngamagremu
elula-khulu, ebudisi-khulu.
Qala amanothi weThemu yesi-2.
Ukwethula ukumeda okuhlelekileko
Ukumeda ubungako njengobujamo bokuraralula imiraro nokubala
• Ukumadanisa, ukuhlela
nokurekhoda ubungako bezinto Ngesikhathi esabelwe Iinomboro, amaFanktjhini noBudlelwana, abafundi
ezipakelwe ukuthengiswa bangararulula imiraro esebenzisa
ezinobungako obutjengiswe ubujamo
ngamakhilogremu, isib.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Bokumeda obungakahleleki bobungako
amakhilogremu ama-2 wereyisi
• bobungako ngamakhilogremu
begodu nekhilogremu li-1 leflowuru
nofana amagremu ama-500 • bobungako ngamagremu
wetswayi Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yeenkinga
• Ukumeda ubungako babo ezihlukahlukeneko ezifaneleko zeThemu.
ngamakhilogremu ngokusebenzisa
isikala sokumeda sangendlini
yokuhlambela
Alikho itjhuguluko elifunekako
hlangana kwamamilimitha namalitha
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO : NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS IIMFUNEKO ZOKUPHELA KONYAKA IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
YESI-3 namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ngesikhathi sokusebenza ngokuzijamela abafundi bafanele baragele phambili
Umthamo/ • Ukulinganisa ,nokumeda , ngoku
Ivolumu Ukumadanisa nokuhlela umthamo Linganisa nokumeda, ukumadanisa, ukuhlela begodu nokurekhoda
weemumathi ( o.u. umthamo umthamo weemumathi nofana ivolumu yeemumathi ngokusebenzisa iimedo
ongamumathwa simumathii ezingakahleleki. Ukulandela amaresibhi, ukufaka hlangana ukubhaga ,
nasizeleko) ngokusebenzisa iimedo kubujamo obusibuzako lapho abafundi bangazijayeza khona ukumeda.
ezingakahleleki zokumeda isib.
Khetha amaresibhi lapho iinthako zakhona ziphiwa ngamakopi, amathispuni
Iingobho namakopi.
nofana ngamayunithi angakahleleki.
• Ukuhlathulula umthamo
wesimumathi ngokubalabegodu • Madanisa begodu uhlele umthamo wamabhodlelo ahlukahlukeneko begodu
nokutjho bonyana mangaki nangezinto ezithengiswa esitolo sokudla (igrozari) nezinye intwanyana
amayunithi angakahleleki angazalisa zangekhaya lapho umthamo utlolwe khona entweni eziphakethelweko.
isimumathi, isib. Ibhodlelo • Sebenzisa nanyana mabhodlelo welitha li-1 nanyana majege welitha
linobungako bamakopi ama-4 li-1 ukulinganisa begodu nokumeda, ukumadanisa, ukuhlela begodu
Ukwethulwa kokumeda nokurekhoda umthamo weemumathi nofana ivolumu engesimumathini
okuhlelekileko ngamalitha.
• Ukulinganisa, ukumeda; • Sebenzisa iimumathi ezimeregwe ngamamililitha, isib. 200 ml, 330 ml, 500
ukumadanisa ukuhlela begodu ml, 750 ml, nofana 250 ml yamakopi wokumeda, nofana 5ml yeengobho
nokurekhoda umthamo wezinto zokumeda nofana amajege anemida yamamilimitha ameregwe kiwo
ngokumeda ngamalitha, iinqunto ukumeda ivolumu nofana imithamo yeemumathi ezingakalebulwa.
zamalitha, ngamahafu wamalitha
begodu nangamakotara wamalitha. Qala amanothi weThemu yoku-1.
• Ukumadanisa, ukuhlela begodu Abafundi bafanelwe banikelwe amathaski atlolwako ukuhlanganisa
nokurekhoda umthamo wezinto okulandelako, ukufaka hlangana ukufunda iinthombe ze:
ezipakelwe ukuthengiswa, ubungako • mikhiqizo imithamo yazo etlolwe ngamalitha ukuze zilandelaniswe
bazo butlolwa ngamalitha, isib. ngendlela efaneleko.
Amalitha ama-2 webisi, ilitha li-1
lesiselo esimakhaza, amalitha ama- • iinthombe zamajege lapho ivolumu iseduze nomuda onomborwe ilith
5 wepende nofana ngamamilimitha li-1 nofana amalitha ama-2. Kulindeleke bonyana abafundi bafunde
isib. ama-500 ml yebisi, kwaphela umuda onomboriweko oseduze nomthamo. Bahlathulula ivolumu
• amamililitha ama-340 wesiselo njengokuthi pheze, / eduze /okunengana kuna/ pheze kube/ nofana
esimakhaza, amamilimitha ama-750 inomboro poro (yelitha) abayifunda ejegeni.
we-oli. • Imikhiqizo enomthamo otlolwe kiwo ngamamilimitha ukuze kulandelaniswe
• Ukwazi bonyana ikopi elisezingeni ngendlela efaneleko.
elifaneleko limamililitha ama-250. • Iinthombe zamajege lapho ivolumu iseduze nomuda wamamililitha
Ukwazi bonyana ithispuni imamililitha womthamo onomboriweko.
ama-5
Kulindeleke bonyana abafundi bafunde kwaphela umuda oseduze
Akukalindeleki bonyana kube omeregiweko.
445 netjhugululko hlangana kwamamililitha
namalitha
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO : NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
446 IIMFUNEKO ZOKUPHELA KONYAKA IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
YESI-3 namaminithi
ama -24)
4.4 Ukumeda umthamo njengobujamo bokurarulula imiraro begodu
Umthamo/ nokubala
Ivolumu Ngesikhathi esabelwe Iinomboro, ama-opharetjhini noBudlelwana, abafundi
bangararulula imiraro ngokusebenzisa
ubujamo be /bo
• bobungako / bevolumu yesimedo esingakahleleki, isibonelo, uGogo
usebenzisa amakopi amabili webisi ukwenza ipudinghi. Nakayibuyelela
kabili iresibhi yakhe, uzakutlhoga ibisi elingangani?
• Amalitha
• amamililitha
Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yeenkinga
ezihlukahlukeneko ezifaneleko zeThemu.
4.5 Ipherimitha Ipherimitha Ukumeda izinto mazombe nofana ukumeda ipherimitha kuyinto etjha
Ipherimitha • Phenya/rhubhulula ibanga • Phenya ibanga eGreyidini yesi-3
ne-eriya elizombeleze amajamo we- elizombeleze amajamo Ipherimitha imedwa ngokungakahleleki kwaphela eGreyidini yesi-3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
(2D) begodu nezinto ezi - (3D) we- (2D) begodu Nikela abafundi isikhathi esinengi sokuzijayeza ukusebenzisa iinquntu
ngokusebenzisa intambo nezinto ezi - (3D) zentambo ukumeda buzombeleza izinto ezinengi ezihlukahlukeneko
I-eriya ngokusebenzisa njengeenhloko, amabhodlelo (okufaka hlangan amabhodlelo amade aqaleka
intambo amatsikana begodu namabhodlelo amafitjhani aqaleka abanzi) amabhlege,
• Phenya/rhubhulula I –eriya
ngokusebenzisa ukuthayela iimbhigiri, amabhoksi, njll. Vumela abafundi balinganise maqangi bonyana
ngiziphi izinto abacabanga bonyana zinepherimitha ekudlwana bese uhlola
ngokumerega ubude eentokaneni zeeentanjana begodu nokuzimadanise.
Abafundi bangameda ipherimitha yamajamo wa- (2D) ngokusebenzisa
isitokana sentambo.
Abafundi bangameda amapherimitha ngokusebenzisa amayunuthi
angakahleleki wokumeda okufana neemvalo zamabhodlelo, amabhoksi
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) womlilo, njll.
IGREYIDI YESI-3 ITHEMU YESI-3
5. UKUPHATHA IDATHA
CAPS UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-3 namaminithi
ama -24)
5.4 Buthelela begodu Buthelela begodu Kuphakanyisiwe bonyana eThemini yoku 1 abafundi benze ibha grafu yetlasi ,nokuthi 3 lessons
Buthelela uhlele idatha uhlele idatha eThemini yesi- 2 bahlaziya amagrafu weenthombe namathebula obanikela wona.
begodu • Buthelela idatha Buthelela idatha EThemini yesi-3 abafundi bangasebenza ngawowoke umzombe wedatha (Qala amanothi
uhlele idatha ngetlasi nofana isikolo ngetlasi nofana isikolo weThemu yoku- 1) nofana bathome ngedatha ethulwe ngerhelo nofana ngamathali nofana
ukuphendula imibuzo ukuphendula imibuzo ngethebula begodu babuye bahlele koke lokhu nge- bha grafu.
ebuzwa ngutitjhere. ebuzwa ngutitjhere. Kulula khulu ebafundini ukugwala ama-bha grafu ngokusebenzisa amaphepha wesikotjhi.
• Hlela idatha oyinikelwe Jamisela idatha Kuzakuthlogeka bonyana ukhumbuze abafundi ngamatshwayo aqakathekileko we- bha
ngutitjhere nofana Jamisela idatha ngama grafu (Qala amanothi weThemu yoku-1).
incwadi bha. Abafundi bafanele baphendule imibuzo obabuza yona ngama grafu; qala iThemu yoku-
• Hlela idatha ngama: Hlaziya begodu 1 ukuthola imihlobo efaneleko yemibuzo
-- Rhelo urhumutjhe idatha
-- Thali Phendula imibuzo
-- Thebula ngedatha ethulwe
ngamabha
5.5 Jamisela idatha
Jamisela Jamisela idatha nge:
idatha • Grafu yeenthombve
• Bha grafu
5.6 Hlaziya begodu
Tsenga urhumutjhe idatha
begodu Phendula imibuzo
uhlathulule ngedatha ethulwe nge:
idatha • Grafu yeenthombve
• Bha grafu.
447
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI- 4
1. IINOMBORO , AMA-OPHARETJHINI NOBUDLELWANA
448
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Ekupheleni kweThemu le, abafandi bafanele bonyana sele babone, bathinta, bebatjhidisa
Ukubala eziphathekako eziphathekako izinto e-1000. Bafanele bonyana sele ‘banomuzwa wobunengi’ be-1000. Iqhinga
Linganisa bewubale Linganisa bewubale lokubuthelelwa ngeenqhema lifanele ligqugquzelwe.Ekupheleni kweThemu bafanele
izinto
ngokuthembeka ngokuthembeka bakghone ukuphendula imihlobo yemibuzo elandelako neenlayelo:
ukufika e-1000 izinto ukufika e-1000 izinto
zangamalanga. zangamalanga.
Amaqhinga Amaqhinga
wokubuthelela wokubuthelela
ayakhuthazwa. ayakhuthazwa.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Iinkulungwane Amakhulu Amatjhumi Imivo
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.1 Ukubala izinto Ukubala izinto Bala izinto zokubala ngeenqhema zangakuhlanu, namatjhumi. Babuyelele babuhlele begod
Ukubala eziphathekako eziphathekako babubale godu. Usese nezinto zobukubala ezisalingana naleza ogade unazo?
izinto Linganisa bewubale Linganisa bewubale • Nazi izinto zokubala ezima-200. Zibale ngokuzibuthelela ngeenqhema zangalitjhumi.
ngokuthembeka ngokuthembeka Ukubala zoke izinto zokubala ezima-200, unganyula ukuzibala ngeenqhema zama-20
ukufika e-1000 izinto ukufika e-1000 izinto nofana -25? Kubayini?
zangamalanga. zangamalanga. • Thatha isiqunto bonyana ngiyiphi indlela elula khulu ukubala ibuthelelo leempensela.
Amaqhinga Amaqhinga • Nanzi izinto zokubala ezima-80. Nange sibala ngakubili nofana ngamatjhumi, ingabe
wokubuthelela wokubuthelela isamba yezinto zokubala zisazokulingana nasekuthomeni?
ayakhuthazwa. ayakhuthazwa. • Bala izinto zokubala ezi-46 ngokuzibuthelela ngeenqhema zangakubili. Kumasinya
ukubala ngakubili kunokubala ngakhunye.
1.2 Ukubala uye phambili Ukubala uye phambili Ekupheleni kweThemu leli abafundi bafanele bakghone uku:
Ukubala uye nemuva nga: nemuva nga: Babala ngokuzethemba, ngokukhuluma ngakhunye, ngalitjhumi, ngakuhlanu, ngakubili,
phambili • Ku-1 kusuka kwenye • Ku-1 kusuka kwenye ngamatjhumi amabili, ngamatjhumi amabili nahlanu, amatjhumi amahlanu begodu
nemuva nenye inomboro nenye inomboro nangamakhulu ukufika e-1000.
hlangana ne-0 na- hlangana ne-0 na- Ukuphendula imbuzo efana na:
1000 1000 Ukubala ngamatjhumi ukusuka ema-400 ukuya -500. Manjesi bala ubuyele emuva godu.
• Li-10 kusukela kwenye • Li-10 kusukela kwenye Ukubala nga-2 ukusuka 564 ukuya 580. Manjesi bala ubuyele emuva godu.
nenye inomboro ebala nenye inomboro ebala
Ukubala uye emuva ngamatjhumi ukusuka ema-200 ukuya -40,
nga- li-10 ehlangana nga- li-10 ehlangana
ne -0 na 1000 ne -0 na 1000 Ukubala ngamatjhumi amahlanu ukusuka e-600 ukuya 800. Amatjhumi amahlanu amangaki
owabalileko?
• Ku-5 kusukele kwenye • Ku-5 kusukele kwenye
nenye inomboro ebala nenye inomboro ebala Ukubala uye emuva ngama-100 ukufika ema-620. Makhulu amangaki owabalileko?
nga ku-5 ehlangana ne nga ku-5 ehlangana ne Ukubala uye emuva ngakhunye ukusuka e-876 ukuya e-866. Ubale abokunye abangaki?
- 0 na 1000 - 0 na 1000 Ungaqinisekisa bunjani bonyana ulungile?
• Ku-2 kusukela kwenye • Ku-2 kusukela kwenye Ukubala uye phambili amagadango a-15 nga-5 ukusuka e-305. Ukuphi njenga nje?
nenye inomboro ebala nenye inomboro ebala Lokha ubala nga-25 ukusuka 525 ukuya 850 uzosebenzisa inomboro 725? Bala bewu hlole.
nga- 2 ehlangana ne-0 nga- 2 ehlangana ne-0 Ngiyiphi inomboro elandelako?
na 1000 na 1000 467, 468, 469,
• Ku-3 kusukela kwenye • Ku-3 kusukela kwenye 725, 750, 775,
nenye inomboro ebala nenye inomboro ebala
420, 440, 460
nga- 3 ehlangana ne - nga- 3 ehlangana ne -
820, 800, 780
0 na 1000 0 na 1000
Bala usebenzise inambalayini.
• Ku-4 kusukela kwenye • Ku-4 kusukela kwenye
nenye inomboro ebala nenye inomboro ebala Gwala inambambalayini enganalitho ukubonisa inomboro ezilandelako phezu kwayo:
nga- 4 ehlangana ne - nga- 4 ehlangana ne - 602, 604, 610. Kwanjesi ungawabeka kuphi ama-606? Bala usebenzise inambalayini yakho
449 0 na 1000 0 na 1000 ukusuka ema-602 ukufika 610.
• Ma- 20, 25, 50,100 • Ma- 20, 25, 50,100 Bala ngamatjhumi ukusuka e-314 ukuya e-344. Ngimaphi amadijithi atjhugulako? Ngimaphi
okungenani ukufikela okungenani ukufikela amadijithi angatjhugulukiko? Kungani amakhulu angatjhuguluki? Nawubala ubuyela emuva,
ISIGABA ESISISEKELO AMAGREYIDI 1-3
e-1 000 e-1 000 khuyini okwenzekako?
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
450 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.3 Ukubona nokufunda Ukubona nokufunda Ekupheleni kweThemu abafundi bafanele bakghone ukwenza okulandela:
Amat- iinomboro iinomboro Ukufunda nokutlola iinomboro okungasenani e-1000
shwayo • Ukubona nokufunda • Ukubona nokufunda Ukuphendula imibuzo efana na:
weenom- amatshwayo amatshwayo
• Ngiyiphi inomboro esekaradeni leli?
boro wenomboro kusukela wenomboro kusukela
namagama ku- 0 ukufika e-1000 ku- 0 ukufika e-1000
642
weenom- • Ukutlola amatshwayo • Ukutlola amatshwayo
boro weenomboro weenomboro • Thola ikarada elinenomboro 738 nofana amakhulu alikhomba namatjhumi amathathu
ukusukela ku -0 ukusukela ku -0 nobunane
ukufika e-1000 ukufika e-1000
Fundela phezulu iinomboro ezilandelako: 534, 947, 974, 345
• Ukubona nokufunda • Ukubona nokufunda
Funda amagama lawa:
amabizo wenomboro amabizo wenomboro
kusuka e-0 ukufika kusuka e-0 ukufika • Amakhulu amathathu namatjhumi amane nambili
e-1000 e-1000 • Amakhulu amane namtjhumi asithandathu nethoba
• Ukutlola amabizo • Ukutlola amabizo • Ikulungwane
wenomboro kusukela wenomboro kusukela • Amatjhumi amabili nethoba
e- 0 ukufika e-1000 e- 0 ukufika e-1000
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Tlola ngamatshwayo weenomboro
• Amakhulu amahlanu namatjhumi alikhomba
• Amakhulu amane
• Amakhulu asithandathu namatjhumi abunane nahlanu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.4 Ukumadanisa Ukumadanisa Ekupheleni kweThemu leli abafundi bafanele bakghone ukwenza okulandelako:
Ukuhlathu- nokuhlela iinomboro nokuhlela iinomboro Ukuhlela iinomboro okungasenani kufika e-1000
lula, uku- kufika e- 999 kufika e- 999 Ukuphendula imibuzo ebuzwe ngeendlela ezihlukeneko:
madanisa, • Ukuhlathulula • Ukuhlathulula Funda inambalayini.
nokuhlela nokumadanisa nokumadanisa
iinomboro iinomboro kufika e- iinomboro kufika e-
999 ngokusebenzisa 999 ngokusebenzisa
ngokunengi khulu, ngokunengi khulu, Ama-450 avela kuphi?
ngokuncani khulu, ngokuncani khulu, Ama-700 avela kuphi?
okunengi kuna, okunengi kuna, Ama-350 avela kuphi?
okuncani kuna, okuncani kuna,
Kwanjesi zalisa zoke iinomboro.
okulinganako. okulinganako.
Tlola iinomboro kusukela kekhulu khulu ukuya kencani khulu.
• Hlathulula bewuhlele • Hlathulula bewuhlele
345, 428, 389, 561, 600, 739, 620, 824
iinomboro kufika e- 999 iinomboro kufika e- 999
ezipheleleko. Kusukela ezipheleleko. Kusukela Madanisa iinomboro ukuya e-999
kencani khulu kufikela kencani khulu kufikela • Ngiyiphi inomboro enengi nga-1 kuna -563?
kekulu khulu begodu kekulu khulu begodu • Ngiyiphi inomboro eza ngemuva kwa-768?
kusukela kekulu khulu kusukela kekulu khulu • Ngiyiphi inomboro embadlwana nga-1 kuna-431
kuya kencani khulu kuya kencani khulu
• Ngiyiphi inomboro enengi nge-10 kuna-620
Ukusebenzisa Ukusebenzisa • Ngiyiphi inomboro embadlwana nga-10 kuna-650
iinomboro eziodinali iinomboro eziodinali
ukutjengisa ukutjengisa • Ngiyiphi inomboro enengi nga-20 kuna-480
ukuhlela,indawo nofana ukuhlela,indawo nofana • Ngiyiphi inomboro embadlwana nga-20 kuna-740
ubujamo ubujamo • Ngiyiphi inomboro enengi nga-25 kuna-625
• Ukusebenzisa, • Ukusebenzisa, • Ngiyiphi inomboro enengi nga-50 kuna-250
ukufunda nokutlola ukufunda nokutlola • Ngiyiphi inomboro embadlwana nga-50 kuna-700
iinomboro, ukufaka iinomboro, ukufaka • Ngiyiphi inomboro enengi nge-100 kuna-300
hlangana ibumbeko hlangana ibumbeko
Phendula ngokuthi liqiniso nofana mamanga. Nikela izizathu zempendulo zakho
elirhunyeziweko elirhunyeziweko
ukufika ku 31 ukufika ku 31 Ama-220 useduzana nama- 200 kuna- 250
Ama-403 awasiseduze ema- 400 kuna- 420
i-15 liseduzana e- 0 kune -30
Zaliselela ngo-nengi kuna nofana no-mbadlwana kuna.
I-145 li _________ 154
Ama-823 ma/a _________ 789
Ama-466 ma/a_________ 664A
451 Sebenzisa amadijithi 9, 0, 6 ukwenza inomboro ekulu kazi ongayikghona. Ngiyiphi
inomboro encani khulu ongayenza?
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
452 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.5 Thoma ukulemuka Thoma ukulemuka NgeThemu leli ukuhlanganiswa kwemiqondo elandelako kufanele aqinisekiswe
Ubukhulu ubukhulu bedijithi ubukhulu bedijithi bewagqugquzelwe:
bedijithi okungenani iinomboro okungenani iinomboro • Iinomboro zingaphulwa zibe makhulu, matjhumi nemivo
zamadijithi ama-3 zamadijithi ama-3
• Ukuzwisisa bonyana ama-51 makhulu kune-15 ngombana ama-51 uphethe iinqhema/
ukufika ema-999 ukufika ema-999
iinyanda ezi-5 zamatjhumi bese i-15 linesiqhema/inyanda sinye/yinye setjhumi/yetjhumi.
• Ukwazi bonyana idijithi • Ukwazi bonyana idijithi
• Newubala ngamatjhumi, abafundi nebafika e-40 bayazi bonyana sebabale amatjhumi a-4.
ngayinye ijameleni ngayinye ijameleni
Ekupheleni kweThemu leli abafundi bafanele bakghone uku:
• Ukuphula iinomboro • Ukuphula iinomboro
zamadijithi amathathu zamadijithi amathathu Sebenzisa, ukufunda nokutlola ilimi leli lokusebenza ngobukhulu bedijithi
ukufika e-999 ukufika e-999 nokulizwisisisa.
ukuya ngamatjhumi ukuya ngamatjhumi Amayunithi nofana imivo, amatjhumi, amakhulu, idijithi, idijithi elilodwa, amadijithi amabili,
nangakunye (KTV) nangakunye (KTV) amadijithi amathathu, ubukhulu bedijithi.......
• Bona bewutjho • Bona bewutjho 60
ubukhulu bedijithi ubukhulu bedijithi
305
ngayinye ngayinye
720
Ukuphula inomboro ukubonisa ubukhulu belinye nelinye idijithi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
637 = 600 + 30 + 7
Basebenzisa amakarada wabo wefladi ukutjengisa lokho
600
30
7
Basebenzisa amabhlogo weDienes ukutjengisa ubukhulu bedijithi yenomboro.
Ukuphendula imibuzo efana na:
Yitjho bonyana idijithi li-7 lijamele ini e-127? Bese u-2? No-1?
Makhulu amangaki kenye nenye inomboro elandelako: 300, 500, 700, 412, 568
Ziinyanda ezingaki zangalitjhumi ezikhona kuleyo naleyo nomboro elandelako?
50, 80, 100, 200, 700, 120
Tlola iinomboro:
Ikhulu linye nahlanu
Amakhulu asithandathu namatjhumi amabili nahlanu
Amakhulu amane amatjhumi abunane nethoba
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Amakhulu amathathu nantathu
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.5 Thoma ukulemuka Thoma ukulemuka Tlola iinomboro:
Ubukhulu ubukhulu bedijithi ubukhulu bedijithi Ikhulu elilodwa + namatjhumi -2
bedijithi okungenani iinomboro okungenani iinomboro
zamadijithi ama-3 zamadijithi ama-3 Amakhulu amabili + amatjhumi -3 + imivo -7
ukufika ema-999 ukufika ema-999 Amakhulu amane + amatjhumi -9 + imivo -3
• Ukwazi bonyana idijithi • Ukwazi bonyana idijithi Hlathulula bonyana ngiyiphi inomboro efanele ingene kelinye nelinye ibhoksi
ngayinye ijameleni ngayinye ijameleni
872 = + 70 + 2
• Ukuphula iinomboro • Ukuphula iinomboro
zamadijithi amathathu zamadijithi amathathu 129 = 100 + + 20 + 9
ukufika e-999 ukufika e-999 346 = 300 + 40 +
ukuya ngamatjhumi ukuya ngamatjhumi Tlola phasi ubungakho nedijithi ngayinye e-762.
nangakunye (KTV) nangakunye (KTV)
• Bona bewutjho • Bona bewutjho
ubukhulu bedijithi ubukhulu bedijithi
ngayinye ngayinye
UKURARULULA IMIRARO ESEBUJAMENI
453
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
454 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.6 Sebenzisa amathekhiniki Abafundi balindeleke ukusombulula imiraro yamagama kusetjenziswa amathekhiniki
Amathek- alandelako nawurarulula alandelako:
hiniki wok- imiraro uhlathulule • Ukwakha nokuphula iinomboro
urarulula neensombululo zemiraro: • Ukubuyelela nokuhafula phakathi
imiraro • Ukwakha nokuphula • Amanambalayini
iinomboro • Tjhideza ematjhumini
• Ukubuyelela Qala amanothi aseThemini 2 emaqhingeni alandelako
nokuhafula phakathi • Ukwakha nokuphula iinomboro
• Amanambalayini • Ukubuyelela nokuhafula phakathi
• Amanambalayini
• Ukutjhideza etjhumini
Ukutjhideza ematjhumini
NgeThemu leli abafundi bangenza amathekhiniki wokutjhideza nabenza imiraro yamagama.
Isibonelo:
UNowa una-R48, 00. Ipakana yamakarada awabuthelelako abiza R5, 00. Angathenga
iimpaka ezingaki zamakarada?
Umfundi angatjhideza eduze kwetjhumi, okutjho bonyana yi R50, 00. Lokhu kutjho bonyana
angathenga ‘cithe’ iimpakana ezi-10. Abafundi bazokusebenza ukubalisa bese basebenza
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ipendulo yabo bayitjhideza ngokuzwakalako eduze kwenani.
Vumela abafundi bakhethe ithekhniki abazigedla ngayo. Nanyana kunjalo nange abafundi
basebenzisa amathekhiniki lawo angaba phumelelisiko badinga ukukhokhelwa ukukhetha
amathekhiniki abaphumelelisako.
Akutlhogeki bonyana abafundi batjhelele emathekhniki lawo. Bazokukghona
ukuwasebenzisa godu eZingeni Eliphakathi.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.7 Rarulula iimbalo Rarulula iimbalo Ekupheleni kweThemu abafundi bafanele bakghone ukwenza imihlobo
Ukuh- zamagama zamagama ehlukahlukeneko yemihlobo yemiraro elandelako.
langanisa, ezisebujameni ezisebujameni Ukuhlanganisa nokukhupha
bewuhlathulule bewuhlathulule
nokukhupha Kunemihlobo okungenani emithathu esisekelo yokuhlanganisa nokukhupha omunye
iinsombululo zakho iinsombululo zakho
nomunye umhlobo ungabuzwa ngendlela ehlukileko.
zemiraro, ukufaka zemiraro, ukufaka
hlangana ukuhlanganisa hlangana ukuhlanganisa Imihlobo esisekelo yi:
nokukhupha nokukhupha Itjhentjhi
okuneempendulo ukufiika okuneempendulo ukufiika UNoluthando ubuthelele 234 yamastikha .USilo umnikela ezinye ezi- 80 ngaphezulu. Sele
ku-999. ku-999. amastikha amangaki nasele awoke?
Kunabakhweli abama-500 ngesitimeleni. Abakhweli aba-176 bayehla. Kusele abakhweli
abangaki ngesitimeleni?
Ukuhlanganisiweko
UNosisi ubuthelelela iphrojekthi yesikolo izinto ezisetjenzisiwe zabuye zasetjenziswe godu.
Ubuthelele 124 yamabhodlela weplastiki, namabhlege a-268. Ubuthelele izinto ezingaki
nasele zizoke?
Esitolo kuneempakana zamatjhipsi ezima 368, ezi-82 zimatjhiposi, aseleko maziksnacks.
Zimpakana ezingaki zamaziksnak ezilapho?
Ukumadanisa
AmaGreyidi 2 abuthelela R446. IGreyidi 3 ibuthelele R729. Yimali enengi kangangani
ebuthelelwe yiGreyidi 3?
Ukubuza omunye nomunye umraro ngendlela ehlukileko:
Imiraro ifanele ibuzwe ngeendlela ezihlukeneko. Isibonelo, yombili imiraro le ngefuna
itjhenthi kodwana “okungaziwako” kusendaweni ezihlukeneko emirarweni
Esitolo kuneempakana zepuphu, ezinye ezi-55 za-odwa ngaphezulu, manjesi
sekuneempakana zepuphu ezi-170. Bekuneempakana ezingaki ekuthomeni?
Esitolo kuneempakana ezi-500 zetjhukela, ngemuva kokuthengisa ezinye iimpakana,
basala neempakana ezi-324, bathengise iimpakana ezingaki?
455
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
456 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.8 Rarulula iimbalo Iimbonelo zemiraro ezingenziwa ngeThemu le
Ukuh- zamagama Ukuhlanganisa kokubuyelela
langanisa ezisebujameni
Iinkoloyi ezi-36 zinamavili amangaki?
okubuyele- bewuhlathulule
iinsombululo zakho Isilinganiso
lweko
kurholela zemiraro ngo UThami wonga 35c ngeveke, Wonga imalini ngemveke ezi-8?
ekubuy- kubuyabuyelela AmaGridi
abuyeleleni okuneempendulo ukufika
Umnumzana Khumalo utjala amareyi ama-20 wemithi yama lamula. Kunemithi eyi-12
e-99.
ereyini ngalinye. Kunemithi emingaki nasele awoke?
Ubujamo bemiraro enobudlelwana obuhlukahlukeneko beeMbalo
UHeila uthengisa amahotdogo nge R4 ngayinye. Yenza ithebula ukumlekelela ukuthola
inani le-oda ekulu.
Inani lamahotdogo 1 2 3 4 5 10 20
Imali ngama R 4 8
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Sebenzisa ithebula ukuthola inani lama hotdogo alikhomba namahotdogo ama-23.
USello uthlogomela abentwana. Ubhadelisa R20 imali yokukhamba, abhadelise R5 imali
yokuhlala nabantwana. Qedelela ithebula.
1.9 Rarulula iimbalo Iimbonelo zemiraro ezingenziwa ngeThemu leli
Ukubuthele- zamagama Ukubuthelela ngeeqhema
la nok- ezisebujameni
Ukubuthelela, ukulahla isalela
wabelana bewuhlathulule
iinsombululo zakho Umbhagi uthengisa amakuke ngomgodla ona 12. Banamakuke ali-118. Migodla emingaki
okurholela
ufake ukwabelana yamakuke a 12 ngamunye abangawenza?
ekuhlu-
kaniseni ngokulingana Ukubuthelela, okufaka isalela ependulweni
nokubuthelela Umlimi unamaqanda ama-227. Udinga amabhokhsi amangaki azokufaka amaqanda a-6
kwenomboro ngebhokhsini ngalinye?
ezipheleleko ukufika
Ukwabelana
e-100 begodu
nangempendulo Ukwebelana , ukulahla isalela
ezingafaka hlangana Abangani abahlanu babelana amaswidi ama-84 ukuze boke bathole inani elillinganako
okuseleko/ isalela lamaswidi. Umngani ngamunye uzokuthola amaswidi amangaki?
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.10 Rarulula begodu Iimbonelo zemiraro ezingenziwa ngeThemu leli
Ukwabelana uhlathulule Ukwabelana okurholela emafraktjhinini.
okurholela iinsombululo zemiraro
Yaba iintina zetjhokolethi ezi-15 wabele abangani aba-6 wenze boke bathole
emafrak- ephathekako efaka
ngokulinganako ukuze boke bathole inani elilinganako leentina zetjhokolethi bekungabi
tjhinini hlangana ukwabelana
nesalela.
ngokulingana ezirholela
eensombululweni ezifaka Yaba iintina zetjhokolethi ezi-7 wabele abangani aba-3 wenze boke bathole ngokulinganako
hlangana amafraktjhini ukuze boke bathole inani elilinganako leentina zetjhokolethi bekungabi nesalela.
wohlavu olulodwa isib. Ifraktjhini yebuthelelo
nalawo angenahlavu Ugogo unikela uKiki R12, uKiki ufuna ukonga okuthathu kwemali ufanele onge malini
1 1 3 2
olulodwa , 2 , 4 , 4 , 5 yemali anayo?
Umhlobo lo womraro ufanele ubuzwe ngemuva kobana basombulule imiraro emine
nofana emihlanu yokwabelana okurholela emafraktjhinini abe azi amagama weengcezu
zamafraktjhini.
Ukubeka amafraktjhini ndawonye
Umbanduli webhodla lezandla unikela umdlali ngamunye ingcenye yelamune.
Kunabadlali aba-14. Udinga amalamune amangaki? Umhlobo lo womraro ufanele ubuzwe
ngemuva kobana basombulule imiraro emine nofana emihlanu yokwabelana okurholela
emafraktjhinini abe azi amagama weengcezu zamafraktjhini
Ukutlola amafraktjhini
Abafundi abakalindelwa bonyana batlole amatshwayo wamafraktjhini. Abafundi bafundile
bonyana bangawalebula bunjani amafraktjhini njengo 1 esihlanwini, 3 yamakota nofana 3
kokusithandathu.
Lokhu kubasiza okukuthoma ngokuzwisisa bonyana amagama wamafraktjhini ahlathulula
bonyana kuneengcezu ezingaki ezilinganako zokupheleleko ezihlukanisiweko ukwenza.
Isibonelo isiquntu, kokuthathu, amakota njll. Begodu ziingcezu ezingaki eziqalekako, isib. 2
kokuthathu.
Ukujamiselela amafraktjhini wemiraro yamagama.
Abafundi bafanele bagwale iimpendulo ubonisa bonyana bayazwisisa umraro.
Lindela bonyana abanye babafundi bangagwala ifraktjhini ngendlela okungiyo kodwana
banganikeli igama ekungilo. Lekelela abafundi bonyana batjho ifraktjhini ngendlela
okungiyo (Qala amanothi ahlobana nokubizwa kwamafraktjhini angaphasi kobujamo
obutjhaphulukileko)
Abafundi bafanele batjho iingcezu ezabiweko ngokuzitlola njenge 2 yokwesithathu.
457
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
458 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.11 Khumbula bewufanise Iimbonelo zemiraro ezingenziwa ngeThemu leli
Imali imali yeSewula Afrika • Ubungako bemali nokwenza inani, Isibonelo
eziinhlavu -- Tlola 325c ngamaranda namasende.
kunye nemali -- Ziindlela ezingaki ezihlukileko ongazenza nga R400 usebenzisa imali yamaphepha
yamaphepha kwaphela? Wazi bunjani bonyana inazo zoke iinsombululo?
Sombulula imiraro -- UTravis une 50c neenhlamvu ezine za-20c. Amathofi abiza R1, 20. Uzokuthola itjhentjhi
efaka hlangana yemalini?
amanani wemali • UMandla ubhadela R5, 50 ukukhamba ngetekhsi ukuya esikoleni.
netjhentjii yamaranda
-- Kumbiza malini ukuya nokubuya esikoleni ngamalanga?
neyamasende
Imiraro yokuthenga nokuthengisa
Tjhugulula hlangana
• Ugogo ka Pedro umnikele iR5. Ngimaphi amaswidi a-3 angawathenga? Itjhoku tjhakile
namaranda namasende
Ibiza R2,70; amatjhapisi abiza R1,80; umzoka osiri R1,40; amaswidi weperegisi R1,60;
amaminthi R2,20; ithofi libiza R1,20.
• UDamon wathenga iincwadi ezintathu nge R80 incwadi ngayinye. Yimalini itjhentjhi
azoyithola nange aphethe R300?
• Amaphakethe wamaminti ayi-5 abiza 44c ngalinye. Umnumzana King udinga 88
ISIGABA ESISISEKELO AMAGREYIDI 1-3
yamaminti. Kufanele athenge amaphakethe okufanele amathenge? Uzokubhadela
imalini?
UKUBALA OKUSEBUJAMEN
1.12 Sebenzisa amathekhiniki Qala amanothi weThemu yesi-3.
Amathekh- alandelayo nawubalako
iniki • Ukwakha bewuphadhle
(iindlela iinomboro
namkha • Ukubuyelela
amaqhinga) nokuhafula phakathi
• Amanambalayini
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN) • Ukutjhideza etjhumini
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika NgeThemu leli abafundi baragela phambili ngokuphula iinomboro ukuze babale.
Ukuh- e-999 Iindlela ezingakghonakala ukutjengisa ukubala kokuhlanganisa nokukhupha.
langanisa • Khupha ukufika e- 999 Ukuphula iinomboro zibe ziingcenye ezincani ukwenza ukubala kube lula.
nokukhupha • Sebenzisa Ukusebenzisa ilwazi lobukhulu bedijithi ngokuphula ngamakhulu, ngamatjhumi
amatshwayo afaneleko nemivo
( +, -, =, )
• Ukuhlanganisa ngokuphula iinomboro zombili
• Ukuphrakhthisa
Ukuhlanganisa iinomboro zamadijithi amathathu nezamadijithi amabili ngokuphula
ukulumbana
iinomboro zombili
kwenomboro ukufika
e-30 524 + 82 =
= (500 + 20 + 4) + (80 + 2)
= 500 + (20 + 80+ (4 + 2)
= (500 + 100) + 6
= 600 + 6
= 606
Ukuhlanganisa iinomboro zamadijithi amathathu nezinye zamadijithi amathathu
323 + 436 =
323 + 436 = (300 + 20 + 3) + (400 + 30 + 6)
= (300 + 400) + (20 + 30) + (3 + 6)
= 700 + 50 + 9
= 759
• Ukuhlanganisa ( ngokuphula iinomboro ezizohlanganiswa)
Abafundi bazophula iinomboro ngendlela ezingaphathekako. Lokhu kutjho bonyana bazo
kwenza ngeendlela ezihlukeneko.
524 + 82 =
524 + (40 + 40 + 2)
524 + 40 → 564 + 40 → 604 + 2 = 606
Ukuhlanganisa iinomboro zamadijithi amathathu nezamadijithi amathathu
323 + 436 =
= 323 + (400 + 20 + 6)
= (323 + 400) + 20 + 6
= (723 + 20) + 6
= 743 + 6
459
= 749
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
460 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika • Ukukhupha ngokuphula iinomboro zombili
Ukuh- e-999 Ukukhupha inomboro enamadijithi amathathu kenamadijithi amathathu
langanisa • Khupha ukufika e- 999 889 – 137 =
nokukhupha • Sebenzisa 889 – 137 = (800 + 80 + 9) – (100 + 30 + 7)
amatshwayo afaneleko = (800 – 100) + (80 – 30) + (9 – 7)
( +, -, =, )
= 700 + 50 + 2
• Ukuphrakhthisa = 752
ukulumbana
kwenomboro ukufika • Ukukhupha ngokuphula inomboro yinye
e-30 Ukukhupha inomboro enamadijithi amathathu kenamadijithi amathathu
889 – 137 =
889 – (100 + 30 + 7)
889 – 100 → 789 – 30 → 759 – 7 = 752
Ukusebenzisa ukuqunta/ukuhafula phakathi ukuphula inomboro
525 + 16
= 525 + 8 + 8
ISIGABA ESISISEKELO AMAGREYIDI 1-3
= (525 + 8) + 8
= 533 + 8
= 541
• Ukubala uye phambili nokuya emuva
805 = 798 =
Ukubala ngakunye kusuka ema 798 kuliqhinga elifaneleko ngombana iinomboro ziseduze
enye kenye
• Ukubona ukubuyelela kabili okuseduze
245 + 246
Omunye umuntu angatjho bonyana isibalo esingehla sibuyelela kabili ama-245 + 1 nofana
246 - 1
245 + 245 + 1
= (200 + 40 + 5) + (200 + 40 + 5) + 1
= (200 + 200) + (40 + 40) + (5 + 5) + 1
= 400 + 80 + 10 + 1
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
= 400 + (80 + 10) + 1
= 400 + 90 + 1
= 491
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika Ukuthuthukisa nokuzijayeza amakghono wokuhlanganisa nokukhupha
Ukuh- e-999 Abafundi bafanele bazijayeze imihlobo ethize yamakghono wokuhlanganisa nokukhupha
langanisa • Khupha ukufika e- 999 Ukubala uye phezulu nofana uye phasi ngokuseduze netjhumi
nokukhupha • Sebenzisa 588 + 9
amatshwayo afaneleko
588 + 10 = 598
( +, -, =, )
598 - 1 = 597
• Ukuphrakhthisa
ukulumbana 588 + 19
kwenomboro ukufika 588 + 20 = 608
e-30 608 – 1 = 607
Abafundi banamathuba wokwenza imihlobo elandelako yokubala ngeenomboro ukufika
e-800:
Ukuhlanganisa nokukhupha okukhamba ngakubili kwembuyeleli ze-10 ngaphandle
kokweqela e-100.
40 + 70
70 + 80
120 – 30
150 – 60
Ukuhlanganisa nokukhupha -10 ukuya nofana kusuka kunanoma kuyiphi inomboro
ezinamadijithi amabili nofana amathathu efaka hlangana ukweqela e-100.
Isibonelo:
65 + 10
124 + 10
326 – 10
358 - 10
Ukuhlanganisa nokukhupha inomboro yedijithi elilodwa ukuya nofana kusuka enomborweni
yamadijithi amathathu ngaphandle kokweqela e-10.
Isibonelo:
634 +5
775 + = 779
768 – 4
461
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
462 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika Ukuhlanganisa inomboro yedijithi elilodwa ukuya nofana kusuka esibuyelelweni se-100.
Ukuh- e-999 Isibonelo:
langanisa • Khupha ukufika e- 999 600 + 4
nokukhupha • Sebenzisa 500 + 3
amatshwayo afaneleko
700 - 6
( +, -, =, )
800 - 5
• Ukuphrakhthisa
ukulumbana Ukuhlanganisa nokukhupha okukhamba ngakubili kwembuyeleli ze-100
kwenomboro ukufika 100 + 100
e-30 100 + 200
200 + 200
300 + 400
Abafundi kufanele banikelwe amathuba wokuzijayeza amaphetheni wokuhlanganisa
nokukhupa.
Lokha nangazi bonyana u 1+ 1 = 2
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Kwanjesi khuyini i:
10 + 10
100 + 100
Ukuthoma ukuhlanganisa nokukhupha okukhamba ngakubili kusuka kunoma ngiyiphi
inomboro enamadijithi amathathu.
Isibonelo:
675 + 100
762 - 100
Ukuzwisisisa ukuhlanganisa ekupheleni konyaka
Ekupheleni konyaka abafundi bafanele bakghone uku:
Ukusebenzisa nokuzwisisa ilimi lokuhlanganisa:
Okunengi, hlanganisa, isamba, inani, sekuhlangene, itshwayo lokulingana.....bekufundwe
kutlolwe itshwayo lokuhlanganisa (+) netshwayo lokulingana (=)
Ragela phambili nokuthuthukisa ukuzwisisa kokuhlanganisa kobala uye phambili bakhambe
magega nenambalayini
Isibonelo,
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Phendula imibuzo.
Ngithloga ini ukuhlanganisa ku- 67 ukwenza- 85?
Lo mumutjho wenomboro wombuzo wami: 67 + = 85.
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika Phendula imihlobo yemibuzo elandelako:
Ukuh- e-999 • ukuhlanganisa ndawonye a-43 ne-19
langanisa • Khupha ukufika e- 999 • ngezelela itjhumi e-167
nokukhupha • Sebenzisa • 51 hlanganisa na-83
amatshwayo afaneleko
• Hlanganisa amatjyumi ali-70 na-50
( +, -, =, )
• 280 = 120 + 80 +
• Ukuphrakhthisa
ukulumbana • Ngiyiphi inomboro edlula a-160 nga-30
kwenomboro ukufika • Thola isamba se-156 ne-14
e-30 • Hlanganisa itjhumi nambili ekhulwini namatjhumi alikhomba nahlanu
• Ngiyiphi inomboro edlula a-483 ngetjhumi?
• Ngiyiphi inomboro ongayihlanganisa na-45 ukwenza i-178?
• Ngiyiphi inomboro ongayihlanganisa na-25 ukwenza a-178?
• Ngiyiphi inomboro ekufanele ngiyihlanganise na-56 ukwenza a-170?
• Amakhulu amathathu uhlanganise namatjhumi amane uhlanganise nemivo emi-3
• Amatjhumi a-12 uhlanganise nemivo -8
• 245 + 10 = 245 + 20 = 245 + 30 =
Yazi bonyana ijamele inomboro engaziwako.
45 + 81 =
67 + = 125
47 + 32 + 8 =
31 + + 20 = 160
+ r = 100
+ r = 120
+ r = 450
Ukuzwisisa nokusebenzisa ilwazi lokobana ukuhlanganisa bungenziwa nanyana ngaliphi
ihlelo:
463 178 + 12 = 190 ngakhoke 12 + 178 = 190
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
464 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika Ukuzwisisa ukukhupha ekupheleni konyaka
Ukuh- e-999 Sebenzisa bewuzwisise ilimi lokukhupha:
langanisa • Khupha ukufika e- 999 Khupha, khupha, kusele mangaki, yincani kangangani............kune......, umehluko hlangana,
nokukhupha • Sebenzisa yikulu kangangani ......kune......, kufuneka okungangani okunengi ukwenza ......begodu
amatshwayo afaneleko ufunde utlole itshwayo lokukhupha (-)
( +, -, =, ) Ragela phambili ukuthuthukisa ukuzwisisisa kokukhupha njenge:
• Ukuphrakhthisa • Ukukhupha
ukulumbana • Ukuthola umehluko hlangana
kwenomboro ukufika
Ukuzwisisa bonyana nawukhupha ilize kutjhiya inomboro ingakatjhintjhi:
e-30
192 – 0 = 192 192 = 192 – 0
Ukuphendula imibuzo etloliweko ebuzwe ngeendlela ezitloliweko okufana nokuthi:
• 37 khupha 13
• Khupha 40 ema-80
• 162 khupha 42
• Khupha 45 e-390
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• Ngimuphi umehluko okhona hlangana na-738 ne-157?
• Lincani kangangani i-117 kuna-449
• Ngiyiphi inomboro ongayikhupha -56 ukuthola -122?
• Ngiyiphi inomboro ongayikhupha -56 ukuthola – 132?
• Ngiyiphi inomboro ongayikhupha -56 ukuthola – 142?
• Thola okukhamba ngabubili okunomehluko we-10
• Kunempensela e-45 ngelayini katitjhere. Ubanikela iimpensela e-17. Kusele ezingaki?
Thola iinomboro ezikhamba ngambili ezinomehluko wama-20.
Yazi bonyana ijamele inomboro engaziwa.
557 – 134 =
800 – 530 =
762 - = 448
598 – 42 =
687 - = 375
13 – 6 = 15 -
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
- 18 = 24
174 – 14 =
199 - = 25
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika Ukuthoma ukuzwisisa bonyana:
Ukuh- e-999 125 – 10 kuhlukile ku 10 - 125
langanisa • Khupha ukufika e- 999 Ukuzwisisa ubudlelwana obuphakathi kokuhlanganisa nokukhupha.
nokukhupha • Sebenzisa Yitjho bewutlole ukukhambelana okuliqiniso kokukhupha ekuhlanganiseni okulliqiniso
amatshwayo afaneleko okunikelweko begodu bahlanekezele.
( +, -, =, )
isibonelo:
• Ukuphrakhthisa
25 + 68 = 93 kutjho bonyana 93 – 68 = 25
ukulumbana
kwenomboro ukufika 68 + 25 = 93 kutjho bonyana 93 – 25 = 68
e-30 122 – 104 = 18 kutjho bonyana 18 + 104 = 122
Ngaphandle kokusebenzisa ama-apharathasi phendula okulandelako:
Nangabe uyazi bonyana 145 + 120 = 265
Uyini u :
120 + 145
265 – 120
265 – 145
Nangabe uyazi bonyana 154 – 38 = 116
Uyini u :
154 – 116
116 + 38
38 + 116
Tlola bewuphendule okulandelako:
64 – 37 = ngakho ke 37 + = 64
137 – 17 = ngakho ke + r = 137
200 - 100 = ngakho ke + 100 = 200
89 – 38 = 51 ; 51 ngumehluko ngombanyana + r = 89
Tlola inomboro mitjho emine usebenzise iinomboro lezi160, 35, 125
Ukuhlola imiphumela yokubala
Ukwahlulela iinsombuluko ngokuzwisiseka
Abafundi kufanele babandulwe ukwahlulela iinsombululo ngokuzwakalako.
Enye yeendlela yokwenza lokhu ukulinganisa iimpendulo ngaphambi kokubala. Lokha
465 uhlanganisa iinomboro ezimbili eziseduze kwenye nenye, isib. 45 na 46, abafundi
bangasebenzisa ukubuyelela kabili njengendlela yokulinganisa iimpendulo zabo.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
466 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.13 • Hlanganisa ukufika Ukuhlola imiphumela
Ukuh- e-999 Abafundi kufanele bazi bonyana bangakghona uku:
langanisa • Khupha ukufika e- 999 Hlola isibalo sokuhlangania ngokukhupha.Isibonelo: If 36 + 18 = 54; then 54 – 18 = 36
nokukhupha • Sebenzisa Hlola isibalo sokukhupha ngokuhlanganisa. Isibonelo 84 – 48 = 36, then 36 + 48 = 84
amatshwayo afaneleko
Ukusebenzisa itshwayo eliphekgukayo ukuhlola iinsombululo ngenye yesizathu sokufundisa
( +, -, =, )
ukuhlanganisa nokukhupha ndawonye
• Ukuphrakhthisa
ukulumbana
kwenomboro ukufika
e-30
1.14 • Buyabuyelela NgeThemu le abafundi baragela phambili ngoku:
Ukuh- iinomboro kusuka ku-1 • Sebenzisa bewuzwisise ilimi lokubuyabuyelela;
langanisa kufika e-10 ngo 1, 2, 3,
• Jamiselela ukubuyabuyelela njengerhemiso;
okubuyele- 4, 5, 10
• Sebenzisa amatshwayo alungileko ukuhlathulula imitjho yenomboro;
lweko • Sebenzisa
kurholela amatshwayo afaneleko • Ukuzwisisa bonyana ukuhlanganisa okubuyelelweko kungajamiselwa ngokusebenzisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ekubuy- (x, =, ) itshwayo lokubuyabuyelela;
abuyeleleni • Ukuzijayeza nokuzwisisia bonyana ukubuyabuyelela kungenziwa nanoma ngiyiphi indlela
(umthetho wecommutative nofana weprophathi);
• Sebenzisa inambalayini ukutjengisa iimbalo zokubuyabuyelela begodu bakghone
ukuhlathuthula ukujanyelwa (iimeqo ebonisa ukuhlanganisa okubuyelelweko);
• Bavuma ithebula lokubuyabuyelela
Ekupheleni kweThemu leli abafundi bafanele bakghone uku:
Ukusebenzisa ilimi lokubuyabuyelela ebujameni obuphathekako:
Kabili, buyabuyelela, buyabuyelela nga, isibuyabuyelelo sika, okunengi kwa, iinqhema za,
ukubuyabuyelela (ubukhulu, ubude, ububanzi....) kabili, buyelela kathathu ngobunengi
obungange, bafunde batlole itshwayo lokubuyabuyelela (x)
Sebenzisa ilimi leli ukwenza ukubala kokubuyabuyelela
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.14 • Buyabuyelela Ukuzwisisa ukubuyabuyelela njengokuhlanganisa okubuyelelweko
Ukuh- iinomboro kusuka ku-1 6 bahlanganiswe ndawonye ka-3 kulingana na:
langanisa kufika e-10 ngo 1, 2, 3,
6 + 6 + 6 = 18
okubuyele- 4, 5, 10
3 kanengi kwe 6 = 18
lweko • Sebenzisa
kurholela amatshwayo afaneleko 3 buyabuyelela 6 = 18
ekubuy- (x, =, ) 6 x 3 = 18
abuyeleleni 3 x 6 = 18
3 maal 6 = 18
6 x 3 = 18
3 x 6 = 18
Thoma ukukhumbula bonyana ukubuyabuyelela kungenziwa nanoma ngiyiphi indlela.
Ukuphendula imibuzo ebuzwe ngeendlela ezihlukeneko:
Abokuhlanu ababili
Ukubuyelela kabili i- 5
3 buyelela 5
Izinto zokubala ezintathu ereyini ngalinye. Kunamareyi amane. Kunezinto zokubala
ezingangani sezizoke?
2 ubuyabuyelelwa nga-7
16 buyelela ka 2
Understanding the commutative law of multiplication
3 x 4 = 12 ilingana na 4 x 3 = 12
Ukubona ukusebenziswa kwesibambelindawo ukujamela inomboro engaziwako
2+2+2=
2x=6
5 + 5 +5 + 5 + 5 ngakhoke 5 x r = 25
4 + 4 + 4 ngakhoke 4 x 3 =
10 + 10 + 10 + 10 + 10 ngakhoke 10 x = 50
5 x £ = x 5 = 45
467 4x8=x4
8 + 8 + 8 = abobunane-3 = 8 x = 24
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
468 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.14 • Buyabuyelela Ukuzwisisa ubudlelwano hlangana nokubuyelela nokubuyabuyelela kabili
Ukuh- iinomboro kusuka ku-1 Kopa ithebula elingezasi. Zalisa ireyi lokubuyelela nga-4
langanisa kufika e-10 ngo 1, 2, 3,
okubuyele- 4, 5, 10 1 2 3 4 5 6 7 8 9 10
lweko • Sebenzisa 4s
kurholela amatshwayo afaneleko 2s
ekubuy- (x, =, )
abuyeleleni
Ukusebenzisa imihlobo ehlukahlukeneko yemifanekiso yokubuyelela
• Igridi yokubuyabuyelela
• Itjhadi naneko
• Amathebula
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro Ngikuphi okuhlukileko kune Themu yesi-3?
Ukuhlu- ukufika e-99 ngo 1, 2, ukufika e-99 ngo 1, 2, Ekupheleni kweThemu kufanele kuqinisekiswe bonyana abafundi bakghona:
kanisa 3, 4, 5, 10 3, 4, 5, 10
• Ukuzwisisa bonyana ukuqunta phakathi liphekguko lokubuyelela kabili bebakhumbule
• Sebenzisa • Sebenzisa ukubuyelelwa kabili kweziinomboro ukufika e-20;
amatshwayo (÷, =, ) amatshwayo (÷, =, )
• Ukulemuka ukuhlukaniswa kabili njengebuthelelo;
• Ukuzwisisa bebajabulele ubudlelwano hlangana kokubuyabuyelela nokuhlukanisa
begodu ziyaphekgukelelana;
• Ukusebenzisa iindlela zokutlolwa zokwenza nezingakahleleki ukwenza ukuhlukanisa
iinomboro ezinamadijithi amabili ngenomboro yedijithi elilodwa;
• Basebenzisa ilwazi labo lobukhulu baedijithi ukwenza ukubala kokubuyelela
nokuhlukanisa.
• Bahluthulule bonyana ngikuphi ukubala abakwenzileko nokuthi kubayini;
• Bacocisana ngeempendulo zabo bebahlathulule ngokucanga kwabo;
• Ukusebenzisa ilwazi lamatshwayo wenomboro nokuhlobana kwephekguko, okufaka
hlangana ukubuyelela kabili nokuhlukanisa phakathi ukulinganisa nokuhlola.
Amaqhinga wokurekhoda
Kunamaqhinga athile wokurekhoda okufanele abafundi abangawasebenzise eGreyidini
3. Abafundi angeke batjhelele kuwo woke amaqhinga. Badinga ukukhokhelwa nakuqalwa
emutjhweni wenomboro wokuhlukanisa bebathathe isiqunto seqhinga elifaneleko, kufanele
kulindeleke bonyana abafundi angekhe basabambelela ekugwaleni iinthombe begodu
bazokusebenzisa iinomboro ukuhlathulula ukucabanga kwabo.
Ukukhupha okubuyelelweko
Iqhinga leli lizokusetjenziswa nakusombululwa imiraro yamagama begodu abafundi
badinga ukukhokhelwa ekuqaleni irherho leenomboro bebathate isiqunto sokubana ukubala
kungenziwa ngokusebenzisa ukukhupha okubuyelelweko.
40 ÷ 8 =
40 – 8 → 32 – 8 → 24 – 8 → 16 – 8 → 8 – 8 = 0
Abafundi babala inomboro yeenkhathi abakhuphe u-8 ngaso ukuthola i-0
Ukuhlanganisa okubuyelelweko
Abanye abafundi bangahle basebenzise iqhinga leli bazwisisa ubudlelwana obuphakathi
bokubuyabuyelela nokuhlukanisa. Msinyana ngemuva kwalokho irherho lenomboro
bazokukhetha bonyana iqhinga lifanele nofana awa.
40 ÷ 8 =
469 8 + 8 → 16 + 8 → 24+ 8 → 32 + 8 → 40
Abafundi babala inkhathi abahlanganise u-8 ukuthola ama-40.
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
470 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro Ukusebenzisa ukubuyelela
Ukuhlu- ukufika e-99 ngo 1, 2, ukufika e-99 ngo 1, 2, Abafundi bafanele bakghone bonyana “(ngazi ini ngokubuyabuyelela okungangisiza
kanisa 3, 4, 5, 10 3, 4, 5, 10 bonyana ngibale ukuhlukanisa?)”
• Sebenzisa • Sebenzisa Abafundi bakwazi ukkutlola phasi amaqiniso wokubuyabuyelela okusebhodini
amatshwayo (÷, =, ) amatshwayo (÷, =, ) yesinamathelisi, ukubalekelela ukuhlukanisa.
Ibhodi yomtlhala
Ngiyazi: 10 x 3 = 30
Ngiyazi: 4 x 3 = 12
72 ÷ 3 =
10 x 3 = 30
10 x 3 = 30
30 + 30 = 60
72 – 60 = 12.
4 x 3 = 12
ISIGABA ESISISEKELO AMAGREYIDI 1-3
10 + 10 + 4 = 24
Ngakhoke 72 ÷ 3 = 24
Ihlelo elabiweko
Ihlelo elabiwako lokuhlukanisa phezulu kokuhlanganisa okutjho bonyana inomboro
ingaphulwa ibe ziingcezu ezibaleka lula:
39 ÷ 3 =
= (30 + 9) ÷ 3
= (30 ÷ 3) + (9 ÷ 3)
= 10 + 3
= 13
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro Ukuphula iinomboro zibe mahafu: 60 ahletjhuliweko
Ukuhlu- ukufika e-99 ngo 1, 2, ukufika e-99 ngo 1, 2, Lapha abafundi bathi kibo ngokwabo “Yini engikwaziko ngokuhlukanisa nge-5?” abafundi
kanisa 3, 4, 5, 10 3, 4, 5, 10 bayazi bonyana a-30 ayahlukaniseka nga-5 ingatjhiyi isalela.
• Sebenzisa • Sebenzisa 60 ÷ 5 =
amatshwayo (÷, =, ) amatshwayo (÷, =, )
30 ÷ 5 = 6
30 ÷ 5 = 6
6 + 6 = 12
Ukusebenzisa ukuqunta phakathi ukuhlukanisa nga-4
Abafundi bebasenza ukubuyelela kabili nokuhafula phakathi iminyaka emithathu. Badinga
ukusebenzisa amakghono lawo njengamaqhinga wokubala. Ilwazi lokubuyelela kabili
nokuhafula phakathi lingasetjenziswa nakuhlukaniswako:
96 ÷ 4 =
96 ÷ 2 = 48
48 ÷ 2 = 24
Ekupheleni kweThemu leli abafundi bafanele ukukghona uku:
Zwisisa, ukusebennzisa nokuthoma ukufunda:
Umuntu ngamunye, kubili, omunye nomunye, yabelana, ihafu, hlukanisa nga-3, hlukanisa
nga-4, hlukanisa nga-2, hlukaniswa nga-3, iinsalela, hlukanisa nga, iinqhema ezilinganako
za, isalela.
Funda, tlola bewusebenzise itshwayo lokuhlukanisa (÷)
Ukusebenzisa ilimi lokubala ngokuhlukanisa
Ukuzwisisa ukuhlukanisa njengokubuthelela nofana ukukhupha okubuyelelweko.
Ukuphendula imibuzo ebuzwe ngeendlela ezihlukahlukaneko:
Yaba 16 nga-2
Hlukanisa 20 nga-5
Bokuhlanu abangaki abenza ama-50?
Zinhlamvu ezingaki ze-10c ezenza ama-50c?
Bokuhlanu abangaki abenza ama-50?
Bokune abangaki ema-20, e-28, e-36?
Bokuhlanu abangaki ema-20, e-40, e-50, e-60?
471
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
472 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro UAnnina uthi ufunda amagama amatjha ama-5 ngamalanga. Uthatha amalanga ukufunda
Ukuhlu- ukufika e-99 ngo 1, 2, ukufika e-99 ngo 1, 2, 40 yamagama.
kanisa 3, 4, 5, 10 3, 4, 5, 10 Amatjhumi a-6 ÷ 3 = amatjhumi
• Sebenzisa • Sebenzisa Ukubona ukusetjenziswa kwamatshwayo afana na weenomboro ezingaziwako.
amatshwayo (÷, =, ) amatshwayo (÷, =, )
Qala izinto zokubala ezingenzasi bese uqedelele umtjho weenomboro
kune zeenqhema zanga- 3
15 – 3 – 3 - - - = 0
15 ÷ 3 =
Qala umgwalo bese uqedelela umutjho:
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Kuna £ znazizoke bekuna r yeenqhema- 3 zngalinye nelinye. ngakhoke: £ ÷ 3 =
Kuna £ znazizoke bekuna begodu kuneenqhema ezi-4 ezinamathosi-3 elinye nelinye. .
ngakhoke : £ ÷ 4 =
Kopa bewuqedelele:
20 ÷ 2 = 20 ÷ = 10 20 ÷ = 2
21 ÷ 3 = 21 ÷ = 7 21 ÷ 7 =
Ukuzwisisa umthetho wokuhlukanisa ngo-1 ne-0
6 ÷1 =
8÷1=
12 ÷ = 12
6÷0=
÷4=0
1÷1=
0÷7=
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
CAPS
ama -24)
1.15 • Hlukanisa iinomboro • Hlukanisa iinomboro Sebenza, funda begodu bathoma ukutlola:
Ukuhlu- ukufika e-99 ngo 1, 2, ukufika e-99 ngo 1, 2, Iinsalela....
kanisa 3, 4, 5, 10 3, 4, 5, 10
Bala iinsalela nawenza ukubala kokuhlukanisa:
• Sebenzisa • Sebenzisa
12 ÷ 5 ngu 2 isalela ngu-2
amatshwayo (÷, =, ) amatshwayo (÷, =, )
23 ÷ 7 ngu 3 isalela ngu-2
Ukuzwisisa ubudlelwana obuphakathi kokubuyelela nokuqunta phakathi
Phendula imihlobo yemibuzo:
Kopa ithebula elingenzasi.
Zaliselela ngokubuyelela kwaka -4 ereyini. Ngiyiphi oyibonako?
1 2 3 4 5 6 7 8 9 10
4s
2s
Qunta iinomboro ezisereyini lesibuyabuyeleli -4 ukuthola iinomboro ezisereyini
lesibuyabuyeleli -2.
Ngiyiphi iphetheni oyibonako?
Ukuzwisisa bonyanya ukuhkiukanisa kuliphekguka lesibuyabuyeleli
Tjengisa imitjho yenomboro ngemigwalo
4 x 5 = 20 ÷ 5 =
12 x 4 = 48 ÷ 4 =
473
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO: AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
474 IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YETHEMU YESI-4
ama -24)
1.16 Umnqopho wenomboro: Iimbonelo zemibuzo engabuzwa:
Iimbalo irherho 999 Umqondo nomboro:
zehloko • Hlela isethi enikelweko Ibizo lenomboro namatshwayo
leenomboro ezikhethiweko
Phakamisa ikarada nofana tlola phasi ibizo lenomboro. Khetha umfundi ukutlola inomboro
• Madanisa iinomboro ema-999
bewutjho bonyana ngiyiphi emetjhako.
enengi nofana encani nga-1, Okunengi nofana okumbadlwana
2, 3, 4, 5 ne-10 khuyini
Ukukhumbula masinyana: okumbalwa nga-1 kuna 900
• Ukukhumbula amaphuzu
okunengi nga-1 kuna 899
wokuhlanganisa
nowokukhupha kufika e- 20 Okunengi nga-2 kuna 702
• Hlanganisa nofana ukhuphe Okuncani nga-2 kuna 405
imbuyeleli ze-10 kusuka e-0 Okunengi nga-3 kuna 477
kuya e-100
Okuncani nga-3 kuna 251
• Amaqiniso wokubuyabuyelela
nokuhlukanisa: Okunengi nga-4 kuna 868
ISIGABA ESISISEKELO AMAGREYIDI 1-3
-- Ithebula lika-2 ukufika 2 x Okuncani nga-4 kuna 967
10 Okunengi nga-5 kuna 729
-- Ithebula le-10 ukufika 10 Okuncani nga-5 kuna 685
x 10
Okunengi nga10 kuna 490
Amaqhinga wokubala
Okuncani nga-10 kuna 660
Ukusebenzisa amaqhinga
wokubala ukuhlanganisa Ngiliphi iledere lesi-5 alfabethi?
nokukhupha ngekghono Ngiyiphi inyanga ye-9 yonyaka?
elifaneleko:
Ukuhlela nokumadanisa
• Beka inomboro ekulu maqangi
ukuze ubale uye phambili Ngiyphi enokunengi: 621 nofana 671?
nofana ubale uye emuva Nginikela inomboro ehlangana 154 ne 159.
• Inambalayini.
• Ukubuyelela kabili
nokuhafulaphakathi
• Ukwakha nokuphhula
• Sebenzisa ubudlelwano
phakathi kokuhlanganisa
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
nokukhupha
• Sebenzisa ubudlelwano
phakathi kokubuyabuyelela
nokuhlukanisa
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO: AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
YETHEMU YESI-4
ama -24)
1.16 Umnqopho wenomboro: Amaphuzu aliqiniso ngokuhlanganisa nokukhupha:
Iimbalo irherho 999 • Ukwazi ngenhliziyo koke ukuhlanganisa nokukhupha iinomboro zebhodi ukufika e-20
zehloko • Hlela isethi enikelweko + r = 20
leenomboro ezikhethiweko
• Madanisa iinomboro ema-999 + r = 16
bewutjho bonyana ngiyiphi 20 = - r
enengi nofana encani nga-1,
2, 3, 4, 5 ne-10 Amaphuzu aliqiniso ngokuhlanganisa nokukhupha kufika e 20.
Ukukhumbula masinyana: 1 + 11 = 12 11 + 1 = 12
• Ukukhumbula amaphuzu 2 + 10 = 12 10 + 2 = 12
wokuhlanganisa 3 + 9 = 12 9 + 9 = 12
nowokukhupha kufika e- 20
18 – 4 = 14 18 – 14 = 4
• Hlanganisa nofana ukhuphe
imbuyeleli ze-10 kusuka e-0 18 – 5 = 13 18 – 13 = 5
kuya e-100 18 – 6 = 12 18 – 12 = 6
• Amaqiniso wokubuyabuyelela Ukukhumbula ngokurhabako ukuhlanganisa ukubuyelela kabili ukufika 20. Lokhu akufake
nokuhlukanisa: hlangana ukukhambelana
-- Ithebula lika-2 ukufika 2 x kwamaphuzu aliqiniso wokukhupha
10
• 1+1=2
-- Ithebula le-10 ukufika 10
x 10 • 2+2=4
Amaqhinga wokubala • 3+3=6
Ukusebenzisa amaqhinga • 4+4=8
wokubala ukuhlanganisa • 5 + 5 = 10
nokukhupha ngekghono
elifaneleko: • 6 + 6 = 12
• Beka inomboro ekulu maqangi • 7 + 7 = 14
ukuze ubale uye phambili • 8 + 8 = 16
nofana ubale uye emuva
• 9 + 9 = 18
• Inambalayini.
• 10 + 10 = 20
• Ukubuyelela kabili
nokuhafulaphakathi Ngitjengisa inomboro okufanele uyihlanganise nalezi ezilandelako ukwenza a-20
(ngokutlola nofana kusetjenziswe ubukhulu bedijithi namkha amakarada wefladi)
• Ukwakha nokuphhula
8
• Sebenzisa ubudlelwano
phakathi kokuhlanganisa 2
nokukhupha 9
475 • Sebenzisa ubudlelwano 15
phakathi kokubuyabuyelela
nokuhlukanisa 3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO: AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
476 IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
KONYAKA namaminithi
YETHEMU YESI-4
ama -24)
1.16 Umnqopho wenomboro: Ngitjengise inomboro ezokusala nange u_________akhitjhwa e-20 (ngokutlola nofana
Iimbalo irherho 999 kusetjenziswe ubukhulu bedijithi namkha amakarada wefladi)
zehloko • Hlela isethi enikelweko • 5
leenomboro ezikhethiweko
• 18
• Madanisa iinomboro ema-999
bewutjho bonyana ngiyiphi • 0
enengi nofana encani nga-1, • 14
2, 3, 4, 5 ne-10 • 7
Ukukhumbula masinyana: Amaqhinga wokubala:
• Ukukhumbula amaphuzu
Sebenzisa amaqhinga wokubala ukuhlanganisa nokukhupha ngokuphumelela.
wokuhlanganisa
nowokukhupha kufika e- 20 Hlanganisa iinomboro ezimbalwa ngokusebenzisa amaqhinga afana na:
• Hlanganisa nofana ukhuphe • Qala iinomboro ezimbili lezo ezenza -10 begodu uzisebenzise kokuthoma
imbuyeleli ze-10 kusuka e-0 2+7+8
kuya e-100
2 + 8 kwenza10 bese uhlanganisa 7.
• Amaqiniso wokubuyabuyelela
nokuhlukanisa: • Ukubeka inomboro ekulu phambili ukuze ubale uye phambili nofana ubalele emuva
ISIGABA ESISISEKELO AMAGREYIDI 1-3
-- Ithebula lika-2 ukufika 2 x 5 + 15
10 • Buya utjho umutjho wenomboro:15 + 5 nokubala uye phambili ukufika- 20
-- Ithebula le-10 ukufika 10 Tjhugulula inomboro ukuya e-10 bese ukhupha nofana uhlanganise oku-1
x 10
Isibonelo:
Amaqhinga wokubala
8 + 9 = 17 bese uhlathulule bonyana omunye angenza 8 + 9 = 8 + 10 – 1
Ukusebenzisa amaqhinga
wokubala ukuhlanganisa 6 + 11 = 17 bese uhlathulule bonyana omunye angenza 6 + 10 + 1
nokukhupha ngekghono 17 – 9 = 8 bese uhlathulule bonyana omunye angenza 17 – 10 + 1
elifaneleko:
• Ukuphula inomboro ibe ziingcezu bese uyahlanganisa
• Beka inomboro ekulu maqangi
ukuze ubale uye phambili ukwakha nokuphula iinomboro:
nofana ubale uye emuva isibonelo, sebenza ngehloko bese uhlathulule:
• Inambalayini. ragela phambili nokuphula iinomboro zibe ‘ziingcezu ezincani khulu’
• Ukubuyelela kabili 8 + 12
nokuhafulaphakathi
= 8 hlanganisa (10 + 2)
• Ukwakha nokuphhula
= 8 + 2 + 10
• Sebenzisa ubudlelwano
phakathi kokuhlanganisa = 10 + 10
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
nokukhupha =20
• Sebenzisa ubudlelwano
phakathi kokubuyabuyelela
nokuhlukanisa
UBUDE
IMIQONDO BESIKHATHI
IMIQONDO NAMAKGHONO
NAMAKGHONO: AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA
IMINQOPHO YOKUFUNDISA ze-iri -1 begodu
KONYAKA
CAPS namaminithi
YETHEMU YESI-4
ama -24)
1.16 Umnqopho wenomboro: • Sebenzisa ukubuyelela kabili njengeqhinga lokubala ngehloko
Iimbalo irherho 999 Ukubona ukutjhideza eduze kokubuyelela kabili.
zehloko • Hlela isethi enikelweko Isibonelo:
leenomboro ezikhethiweko
8 + 7 = 15 hlathulula bonyana ukubuyelela kabili i- 7uhlanganise na-1 nofana ukubuyelela
• Madanisa iinomboro ema-999
bewutjho bonyana ngiyiphi kabili u-8 ukhuphe- 1
enengi nofana encani nga-1, Ukubona bonyana nange iinomboro ezimbili zitjhidelene ngobukhulu enye kenye kulula
2, 3, 4, 5 ne-10 ukuthola umehluko ngokubala uye phezulu ingasi ukubala uye emuva.
Ukukhumbula masinyana: 17- 13 = 4 bewuhlathulule bonyana ukubala uye phezulu kusuka- 13 ukuya-17
• Ukukhumbula amaphuzu kukunikela- 4
wokuhlanganisa
nowokukhupha kufika e- 20 Ezinye iimbalo zehloko zingenziwa ngaphandle kokusenzisa ama-aapharathasi, nokho
kanengi kkulisizo ukwenza imbalo zehloko ngama-aplharathasi.
• Hlanganisa nofana ukhuphe
imbuyeleli ze-10 kusuka e-0 Ama-apharathasi aphakanyisiweko
kuya e-100 • Inambalayini (ehlelekileko begodu engenalitho)
• Amaqiniso wokubuyabuyelela • Igridi yeenomboro
nokuhlukanisa:
• Amakarada wobukhulu bedijithi (amafladi karada)
-- Ithebula lika-2 ukufika 2 x
10 • Imincamo yokubala
-- Ithebula le-10 ukufika 10
x 10
Amaqhinga wokubala
Ukusebenzisa amaqhinga
wokubala ukuhlanganisa
nokukhupha ngekghono
elifaneleko:
• Beka inomboro ekulu maqangi
ukuze ubale uye phambili
nofana ubale uye emuva
• Inambalayini.
• Ukubuyelela kabili
nokuhafulaphakathi
• Ukwakha nokuphhula
• Sebenzisa ubudlelwano
phakathi kokuhlanganisa
nokukhupha
477 • Sebenzisa ubudlelwano
phakathi kokubuyabuyelela
nokuhlukanisa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
478 : IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
1.17 • Sebenzisa begodu Ekupheleni kweThemu leli abafundi bafanele bakghone uku:
Amafrak- utjho amafraktjhini • Ukubona amafraktjhini wobujamo begodu baqinise ukuzwisisa bonyana iingcenye
tjhini ajayelekileko afaka kufanele zibe bukhulu obulinganako;
hlangana amahafu, • Ukwazi bonyana amakotara amane enza okuzeleko okupheleleko, begodu ikotara
ikotara, kobunani, enye nenye ifanele ibe nobukhulu obulinganako;
kobuthathu, • Thola amafraktjhini wesiqhema sezinto;
kwesithandathu,
kwesihlanu • Funda bewutlole amagama wamafraktjhini;
• Bewuhlele, uhlathulule bewumadanise amafraktjhini.
• Ukukhumbula
amafraktjhini Ekupheleni kweThemu abafundi bazwisise amafraktjhini njenge ngcenye yukupheleleko
asebujameni bebakghone ukuphendula imibuzo efanako
bedayagremu • zeenquntu = okupheleleko okukodwa
• Ukuthoma • yamakota = okupheleleko okukodwa
ukukhumbula bonyana • kwesithathu = okupheleleko okukodwa
amahafu amabili • zeenquntu = okupheleleko okukodwa
nofana ubuthathu • kwesihlanu = okupheleleko okukodwa
obuthathu benza
• kwesithandathu = okupheleleko okukodwa
ISIGABA ESISISEKELO AMAGREYIDI 1-3
kunye okupheleleko,
ingcenye yinye yehafu Ukuphendula imibuzo efana na:
nenkota ezimbili Nange ubujamo buhlukaniswa bube ezimbili, sizibiza
ziyalingana Nange ubujamo buhlukaniswa bube ziingcenye ezi-2 ezilinganako, sizibiza ___
• Tlola amafraktjhini Nange ubujamo buhlukaniswa bube ziingcenye ezi- 3 ezilinganako, sizibiza____
njenge, ingcenye Lokha ubujamo buhlukaniswe ngeengcenye ezilinganako______ sizibiza amakota.
yinye yehafu, izingcezu Bakghona ukumadanisa ubukhulu bamafratjhini
ezimbili zobuthathu
Ihafu -1 ikulu nofana incani kunamakota-3?
Makota amangaki alingana noku-1 okupheleleko?
Bobunane abangaki abalingana noku-1 okupheleleko?
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Ngabe amakota amibili alingana nehafu yi-1na?
Thola ifraktjhini yebuthelelo lezinto.
Kunemincamo e-12, e-8 ngepinki ne-4 emhlophe. Yifraktjhini yiphi yomncaamo
omhlophe?
IGREYIDI YESI-3 ITHEMU YESI- 4
2. AMAPHETHENI, AMAFANKTJHINI NE-ALJIBHRA
CAPS UBUDE
IMIQONDO BESIKHATHI
NAMAKGHONO IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YESI-4 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA namaminithi
ama -24)
2.1 Kopulula, ngezelela Amaphetheni asizungelezileko Abafundi bazakusebenza ngamaphetheni wokwemvelo, zesimanjemanje
Amapheth- begodu uhlathulule Ukubona , ukuhlathulula ngamagama zobuphilo bangamalanga ngamafa wamasiko wethu kusukela eGreyidini
eni weJi- Kopulula, ngezelela nokukopulula amaphetheni weJiyomethri yoku-1 ukuya eGreyidini 6. Lokhu kutjho bonyana akutlhogeki bona
yomethri begodu uhlathulule uthathe isikhathi esinengi esihlokweni lesi. Kufanele godu ukhethe
• eemvelweni
ngawakho amagama imisebenzi namaphetheni afaneleko egreyidini ngayinye.
• ebuphilweni bangamalanga
• amaphetheni alula Omunye umhlobo wamaphetheni abafundi abangawuqala yisimethri, isib.
banamhlanje
enziwe ngezinto Amakari amanengi neenlwana ziyi simethril. Zinjalo neenunwana ezinengi
• elifeni lamasiko wethu lokha uzibona kusukela ngaphezulu namaphetheni weenyoni ezinengi
eziphathekako
lokha uziqala kusukela ngaphasi.
• amaphetheni alula
enziwe ngokugwala EGreyidini 3 kunomqopho wokuthola umuda wesimethri ngokubhinca
imida, ubujamo nofana iphepha nesitjengiso. Abafundi bangenza amaphetheni ngokusika ubujamo
izinto emaphepheni abhinciweko. Lokhu kungafaka hlangana ukwenza amadoyili
namaphepha wamasiko anamaphetheni ongawasika. Abafundi bangaqala
Ukuzakhela
begodu bakhulume ngamaphetheni emadoyilini akorotjhiweko neenthombe
amaphetheni
zamaphetheni ezisikwe zaba maphepha wamasiko anamaphetheni.
Ukuzakhela amaphetheni
Abafundi bangafuna amaphetheni godu e :
weJiyomethri
• emafensini( idrada, okwenziwe ngekhuni nofana vibra krete);
• ngezinto
eziphathekako • umsebenzki weentina nama thayela wefluru;
• ngokugwala • imifulelo;
imida,ubujamo nofana • amatjhila nomunye umateriyali;
izinto • amapleyiti, iinkomitji neempiringi;
Amaphetheni • amabholo webholo yeenyawo;
asizungelezileko
• iinlwana ezifana neenkomo, iviyaviyani lebusuku, idube, ijirafi, izingwe,
Ukubona , ukuhlathulula iinyoni, iinunwana;
ngamagama
• amathuthumbo namakari;
nokukopulula
amaphetheni • iphepha lebodeni, okufaka hlangana amaphepha webodeni atloliweko
weJiyomethri avamise ukutholakala emikhukhwini neendaweni lapho abantu bakhe
khona ngokungasisemthethweni;
• eemvelweni
• umsebenzi womncamo wangokwesiko nofana wesimanjemanje; begodu
• ebuphilweni
bangamalanga • neempoto zebumba/ zomdaka zemandulo / zangokwesiko nofana
banamhlanje imimatjhi ethungiweko.
479
• elifeni lamasiko wethu
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO BESIKHATHI
NAMAKGHONO IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO
480 : IIMFUNEKO IMINQOPHO YETHEMU YESI-4 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA namaminithi
ama -24)
2.1 Kopulula, ngezelela Amaphetheni asizungelezileko Abafundi bangawa hlathulula bunjani amaphetheni abawabonako isifundo esi-1
Amapheth- begodu uhlathulule Ukubona , ukuhlathulula ngamagama abazombelezileko?
eni weJi- Kopulula, ngezelela nokukopulula amaphetheni weJiyomethri Kuneendlela ezahlukahlukeneko zokuhlathulula amaphetheni esiwabonako
yomethri begodu uhlathulule • eemvelweni asizombelezileko. Amaphetheni amanengi asizombelezileko enziwe
ngawakho amagama ngemida, ubujamo nofana izinto. Ubujamo nofana izinto akuthlogeki bona
• ebuphilweni bangamalanga
• amaphetheni alula zihlobaniswe nobujamo babobusobubili 2-D beJiyomethri namabumbeko
banamhlanje
enziwe ngezinto wabosobusontathu 3-D weJiyomethri okusetjenzwe ngawo eGreyidini yesi
• elifeni lamasiko wethu 2. Kuphela kwento okufanele bona abafundi bayicale yi :
eziphathekako
• amaphetheni alula • lokho okubuyelelwako isib.amadothi, imida, umhlobo omunye nomunye
enziwe ngokugwala wobujamo; nokuthi
imida, ubujamo nofana • bubuyelelwe njani isib.
izinto • Imida enqophileko evundlanako (njenge fadugwini), imida emagegana
Ukuzakhela nehlangothi eliphasi lomatheriyali nofana buvundla erhembheni, imida
amaphetheni egega nemilenze yamabrhugu;
Ukuzakhela amaphetheni • Imida egobeneko njenge mida ezindulungu oyibona lokha usika i-eyi;
weJiyomethri • Imida engalinganiko , njengemida yemino yesandla nemida yamadube
ISIGABA ESISISEKELO AMAGREYIDI 1-3
• ngezinto nemifinqo etholakala eendlovini, ubhejane nomuntu olupheleko;
eziphathekako • Imida esamagagasi oyitholako lokha usika ikhabitjhi buvundla, nofana
• ngokugwala oyithola emagagasini wehlabathi;
imida,ubujamo nofana • Amadothi alinganako ngesayizi, amadothi ahlukaniswe ngokulinganako;
izinto
• amajamo alinganako ngesayizi;
Amaphetheni
• amajamo afanako ngemibala; nofana
asizungelezileko
• amaphetheni enziwe ngobujamo obungafaniko boke :ubujamo obenza
Ukubona , ukuhlathulula
amaphetheni asesikhumbeni sejirafe woke akafani.
ngamagama
nokukopulula
amaphetheni
weJiyomethri
• eemvelweni
• ebuphilweni
bangamalanga
banamhlanje
• elifeni lamasiko wethu
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
UBUDE
IMIQONDO BESIKHATHI
NAMAKGHONO IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO
CAPS : IIMFUNEKO IMINQOPHO YETHEMU YESI-4 IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA namaminithi
ama -24)
2.2 Kopulula, ngezelela Kopulula, ngezelela begodu Qala amanothi weThemu yoku-1. Iimfundo ezi-3
Amaphe- begodu uhlathulule uhlathulule Ngezelela amaphetheni bona afake okulandelako
theni Kopulula, ngezelela Kopulula, ngezelela begodu uhlathulule • ngabo ku1 kusuka kunanyana ngiyiphi inomboro phakathi kwe 0 nama
weenom- begodu uhlathulule ukulandelana kweenomboro okulula
1000
boro ukulandelana ukufika okungasenani e 1000.
Ukulandelana kufanele kutjengise • ngali 10 kusuka kunanyana ngikuphi ukubuyabuyelela kwe 10 phakathi
kweenomboro okulula
ukubala uye phambili nemuva nga: kwe 0 nama 1000
ukufika okungasenani
ema • ngabo ku1 kusuka kunanyana ngiyiphi • ngaku 5 kusuka kunanyana ngikuphi ukubuyabuyelela kwaku 5 phakathi
inomboro phakathi kwe 0 nama 1000 kwe 0 nama 1000.
200.
• ngali 10 kusuka kunanyana ngikuphi • Ngaku 2 kusuka kunanyana ngikuphi ukubuyabuyelela kwaka ku 2
Ukuzakhela
ukubuyabuyelela kwe 10 phakathi kwe phakathi kwe 0 nama 1000
amaphetheni
0 nama 1000 • nge100 kusuka kunanyana ngikuphi ukubuyabuyelela kwe100 kufika
Ukuzakhela • ngaku 5 kusuka kunanyana ngikuphi okungasenani e 1 000
nokuhlathulula ukubuyabuyelela kwaku 5 phakathi kwe
amaphetheni • ngama 50 kusuka kunanyana ngikuphi ukubuyabuyelelakwama 50
0 nama 1000.
weenomboro. kufika okungasenani e 1 000
• Ngaku 2 kusuka kunanyana ngikuphi
ukubuyabuyelela kwaka ku 2 phakathi • ngama 25 kusuka kunanyana ngikuphi ukubuyabuyelela kwama 25
kwe 0 nama 1000 kufika okungasenani e 1 000
• nge100 kusuka kunanyana ngikuphi • ngama 20 kusuka kunanyana ngikuphi ukubuyabuyelela kwama 20
ukubuyabuyelela kwe100 kufika kufika okungasenani e 1 000
okungasenani e- 1 000 Sebenzisa izinto , iinthombe, amathebula netjhadi naneko ukusekela
• ngama 50 kusuka kunanyana ngikuphi ukutjhuguluka kwabafundi kusuka ekubaleni ngokweqa nokulandelanisa
ukubuyabuyelelakwama 50 kufika ukuya ekubuyabuyeleleni ngali: 10, 5, 2, 4, 3.
okungasenani e 1 000
• ngama 25 kusuka kunanyana ngikuphi
ukubuyabuyelela kwama 25 kufika
okungasenani e 1 000
• ngama 20 kusuka kunanyana ngikuphi
ukubuyabuyelela kwama 20 kufika
okungasenani e 1 000
Ukwakha nokuhlathulula amaphetheni
wakho
• Ukwakha nokuhlathulula amaphetheni
wakho weenomboro
• ngamakhefu anqotjhiswe / enziwe
egreyidini 2 ngerherho leenomboro
elingezelelweko
481 • ngama 20,25, 50,100 to ukufika
okungasenani e 1000
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI- 4
3. ISIKHALA NOBUJAMO (JIYOMETHRI)
482 UBUDE
IMIQONDO NAMAKGHONO BESIKHATHI
IMIQONDO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA (eemfundweni
IINHLOKO : IMINQOPHO YETHEMU
IIMFUNEKO ZOKUPHELA KONYAKA IMIHLAHLANDLELA YOKUFUNDISA ze-iri -1 begodu
YESI-4 namaminithi
ama -24)
3.2 Irherho lezinto Irherho lezinto Qala amanothi weThemu yesi-2. Isifundo esi-1
Izinto ezi- Ukukhumbula nokutjho ngamagama Ukukhumbula nokutjho NgeThemu le, ningazijayeza nibuyekeze begodu ninzinzise umsebenzi
busontathu izinto ezibusontathu (3-D) ngetlasini ngamagama izinto wezinto ezibusontathu (3-D) ngomsebenzi otlolwako.
(3-D) neenthombeni ezibusontathu (3-D)
• Ukunqopha ekukhumbuleni nokutjho ngamagama:
• Ubujamo obuziimbholo, (iindulungu) ngetlasini neenthombeni
• Ubujamo obuziimbholo, • Ubujamo obuziimbholo, (iindulungu);
• Ubujamo obumabhoksi (amaphrizimu)
(iindulungu) • Ubujamo obumabhoksi (amaphrizimu);
• amasilinda
• Ubujamo obumabhoksi • Amasilinda;
• amaphiramidi (amaphrizimu)
• iinkurwana • Amaphiramidi; nee
• amasilinda
Ubujamo bezinto • Iinkurwana
• amaphiramidi
Hlathulula, hlela ngamananeko begodu lokha nababoniswe iinthombe zeJiyomethri nofana izinto ezisetjenziswa
• iinkurwana ngamalanga .
umadanise izinto ezibusontathu (3-D)
mayelana ne: Ubujamo bezinto imibuzo kufanele inqophise abafundi e:
• ubujamo obubusobubili (2-D) obenza Hlathulula, hlela
• Kghani ingaphezulu lento ligobene nofana lithabalele; nokuthi
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ubuso bezinto ezibusontathu (3-D) ngamananeko begodu
umadanise izinto • Kghani ilingaphezulu elithabaleleko lezinto zibo ncantathu, ncamane,
• ilingaphezulu elithabaleleko nofana ezibusontathu (3-D) iinkwere nofana iindulungu.
ilingaphezulu eligobeneko mayelana ne:
Imisetjenzana enqotjhiweko • ubujamo obubusobubili (2-
• Tjheja begodu wakhe ubujamo D) obenza ubuso bezinto
babobusontathu (3-D)onikelwe bona ezibusontathu (3-D)
usebenzise izinto eziphathekako • ilingaphezulu
okufana nokusika ubujamo elithabaleleko nofana
obubusobubili ( 2-D), imdaka, ilingaphezulu eligobeneko
iingojwana zokukhupha ukudla
emazinyweni, ithunjana okuselwa
ngalo iinselo, nezinye izinto
ezinobujamo obubusontathu (3-D)
zeJiyomethri.
3.4 Isimethri Isimethri Umsebenzi wesimethri wokubhinca iphepha owenziwe eThemini yesi – 1 lesson
Isimethri • Ukukhumbula nokugwala imida • Ukukhumbula 2 kufanele irhelebhe abafundi ukubona imida yesimethri emigwalweni
yesimethri ebujameni beJiyomethri nokugwala imida yezinto zejiyomethri nalezo ezingasi ngezejiyomethri.
nebujameni obungasibo beJiyomethri yesimethri ebujameni Imisetjenzana etlolwako kufanele ifake hlangana iimbonelo lapho
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
emabumbekweni wabobusobubili ( 2-D) beJiyomethri nebujameni
obungasibo beJiyomethri • umuda wesimethri kungasimumuda ojame rwe; begodu
• Yenza umuda wesimethri ngokugoqa
iphepha nokutjengisa godu. emabumbekweni • kube nemida yesimethri edlula kowodwa ebujameni nofana entweni.
wabobusobubili ( 2-D).
IGREYIDI YESI- 3 ITHEMU YESI-4
4. UKUMEDA
CAPS UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-4 namaminithi
ama -24)
4.1 Ukutjho isikhathi Ukutjho isikhathi Abafundi baragela phambili ukuzijayeza ukukhuluma ngobude besikhathi begodu Iimfundo ezi-2
Isikhathi • Ukufunda amalanga • Ukufunda amalanga nangokulandelana kwesikhathi.
ekhalendeni ekhalendeni Ngesikhathi sokufundisa itlasi loke begodu nesikhathi sokunqopha esiqhemeni,
• Ukubeka amalanga • Ukubeka amalanga abafundi baragela phambili nokukhuluma ngamalanga weveke, iinyanga zonyaka
wamabeletho, amafestivali wamabeletho, amafestivali begodu nelanga lamhloko, nangamalanga angaphambili begodu namalanga ezako.
wezekolo, amaholide wezekolo, amaholide Abafundi baragela phambili nokubeka okulandelako ekhalendeni njengombana
womphakathi, iminyanya womphakathi, iminyanya izehlakalo zivela
wezomlando, izehlakalo wezomlando, izehlakalo • amalanga wamabeletho ;
zesikolo ezisekhalendeni. zesikolo ezisekhalendeni. • amafestivali wezekolo ;
• iminyanya wezomlando ;
• Ukutjho isikhathi sama-iri • Ukutjho isikhathi sama-iri • izehlakalo zesikolo ; begodu
ali-12 ngama ali-12 ngama • amaholideyi womphakathi .
o -iri, o -iri, Ragela phambili ngokutjela abafundi bonyana batjho isikhathi ngaso soke isikhathi
o ngesiquntu se-iri o ngesiquntu se-iri pheze ngamalanga
o ngekotara ye-iri o ngekotara ye-iri o ngama-iri begodu nangamaminithi wewatjhini ye-analogo; begodu
o amaminithi o amaminithi o ngama-iri, iinquntu zama-iri, begodu nangamakotara wama-iri
wewatjhi le-analogo wewatjhi le-analogo ngokusebenzisa amawatjhi wedijithali.
neenwatjhi zedijithali neenwatjhi zedijithali Isibonelo, abafundi bangabawiwa bonyana batjho bonyana isikolo singena sikhathi
begodu nezinye iintlabagelo begodu nezinye iintlabagelo bani, isikhathi sokudla sinini begodu isikolo siphuma nini, nofana batjhintja nini
ezitjengisa isikhathi, isib. ezitjengisa isikhathi, isib. ukusuka kesinye isifundo nabaya kwesinye. Khetha iinkhathi lapho iwatjhi itjengisa
abomaliledinini abomaliledinini isikhathi poro. Kufanelekile bonyana kube newatjhi esebenzako ebekwa ngetlasini,
Ukubala ubude nokudlula Ukubala ubude besikhathi ukuze abafundi baqale kiyo. Abafundi bangenza iimfaniso zamawatjhi. Ungababawa
kwesikhathi nokudlula kwesikhathi bonyana bakutjengise iinkhathi ezihlukileko, isib. Ngitjengisa i-iri le-10 ehloko.
Sebenzisa ikhalenda Sebenzisa amakhalenda Ngitjengise bonyana bekusikhathi bani ngephambi kwekotara ye-iri.
ukubalanokuhlathulula ukubala nokuhlathulula Ngesikhathi sokusebenza ngokuzijamela , abafundi baragela phambili nokwenza
ubude besikhathi ubude besikhathi imisebenzi ephathelene nokutjho isikhathi:
ngamalanga nofana iimveke ngamalanga nofana o ngama-iri, iinquntu zama-iri, begodu nangamakotara wama-iri ewatjhini ye-
nofana iinyanga okufaka ngeemveke nofana iinyanga analogo; begodu
hlangana ukufaka hlangana o ngama-iri begodu nangamaminithi ewatjhini ye-dijithali
• ukutjhuguluia hlangana • ukutjhugulula hlangana Abafundi bangabala ngokuya ngeemveke nofana amalanga nangabe banikelwe
kwamalanga neemveke. kwamalanga neemveke ikhalenda nofana isigaba sekhalenda, ukuthola amalanga begodu nokubala
• Ukutjhiugulula hlangana • ukutjhugulula hlangana ukuhluka kwesikhathi esihlangana nazo.
kweemveke neenyanag. kweemveke neenyanga Ukufunda isikhathi se-analogo ngamaminithi
Sebenzisa amawatjhi Sebenzisa amawatjhi Sebenzisa pheze iimfundo ezimbili unqophe ekuhlanganise abafundi ekghonweni
483 ukubala ubude besikhathi ukubala ubude besikhathi lokufunda isikhathi se-analogo ngamaminithi.
ngama-iri nofana isiquntu ngama-iri nofana isiquntu
se-iri se-iri Qala amanothi weThemu yesi-3
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
484 IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-4 namaminithi
ama -24)
4.2 Ukumeda okungakahleleki Yoke imihlobo yokumeda ubude eerhenyiswa magega nekholomu ingajayezwa
Ubude • Ukulinganisa, ukumeda, ngesikhathi sekusebenza ngokuzijamela ethemini yoke. Yoke imisebenzi ifanele
ukumadanisa, ukuhlela irekhodwe.
begodu urekhode
ubudengokusebenzisa
iimedo ezingakahleleki,
isib. Ubude besandla,
amagadango, ubude
bamapensela, izinto
zokubala, njll
• Ukuhlathulula ubude
bezinto ngokubala
begodu nokutjho bonyana
zinobude obungangani
bamayunithi angakahleleki
• Ukusebenzisa
ilimi ukukhuluma
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ngokumadanisa, isib.
ubude, ubufitjhani, mude
khulu , banzi khulu
Ukwethula ukumeda
okuhlelekileko
• Ukulinganisa, ukumeda,
ukumadanisa, ukuhlela
begodu urekhode
ubude ngokusebenzisa
amamitha (iintonga
eziyimitha nofana iintambo
ezinobude bemitha)
njengomuvosimedo
ojayelekileko.
• Ukulinganisa nokumeda
ubude ngamasenthimitha
ngokusebenzisa irula.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
Alikho itjhuguluko elenzeka
hlangana kwamamitha
namasenthimitha
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
CAPS KONYAKA YESI-4 namaminithi
ama -24)
4.3 Ukumeda okungakahleleki Ukwethula ukumeda Ukuhlanganisa umsebenzi owenziwe ngobungako emnyakeni woke, abafundi 1 lessons
Ubungako • Ukulinganisa, ukumeda, okuhlelekileko bafanele benze imisebenzi etlolwako lapho bazoku:
ukumadanisa, Abafundi benza amathaski • ukufunda iinthombe ezibavumela bonyana bamadanise ubungako bezinto
ukuhlela, begodu atlolwako ukuhlanganisa ezitjengiswe esikaleni sokumeda
urekhode ubungako, okulandelako, ukufaka • ukufunda iinthombe ezibavumela bonyana batjho ubungako bezinto esikaleni
ngokusetjenzisa iimedo hlangana ukufunda sokumeda ngamayunithi angakahleleki wokumeda.
ezingakahleleki begodu iinthombe ze:
• Ukumadanisa,ukuhlela begodu nokurekhoda abakufunyeneko
nesikala sokudzimelelisa • mikhiqizo yobungako
isib.amabhulogo, iintina o Iinthombe zezinto ezithengiswa esitolo sokudla nezinye izintwanyana
bento etlolwe kiyo. zangekhaya ezinobungako obutlolwe ngamakhilogremu; begodu
njll.
• Iinthombe zobungako o Iinthombe zezinto ezithengiswa esitolo sokudla nezinye izintwanyana
• Ukusebenzisa beenkala zangendlini zangekhaya ezinobungako obutlolwe ngamagremu
ilimi ukukhuluma yokuhlambela lapho
ngokumadanisa isib. • Ukufunda iinthombe zesikala sangendlini yokuhlambela lapho ubungako butjengisa
ivolumu iseduze khona
elula,ebudisi, elula- ukuba sedeze nekhilogremu ezeleko.
nomuda inalidi ekhombe
khulu,ebudisi-khulu khona umuda onenomboro Qala amanothi weThemu yesi-2
Ukwethula ukumeda emeregiweko Ukumeda ubungako njengobujamo bokurarulula imiraro begodu nokubala
okuhlelekileko Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana,abafundi bangararulula
• Ukumadanisa, ukuhlela imiraro ngokusebenzisa
nokurekhoda ubungako ubujamo
bezinto ezipakelwe
• bokumeda okungakahleleki kobungako
ukuthengiswae-
zinobungako obutjengiswe • ubungako ngamakhilogremu
ngamakhilogremu, isib. Ubungako ngamagremu
amakhilogremu ama-2 Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yeenkinga
wereyisi nekhiligremu ezihlukahlukeneko ezifaneleko zeThemu.
li-1 leflowuru nofana
amakhilogremu ama-500
wetswayi
• Ukumeda ubungako
babo ngamakhilogremu
ngokusebenzisa isikala
sokumeda sangendlini
yokuhlambela
Alikho itjhuguluko
elifunekako hlangana
kwamamilimitha namalitha
485
ISIGABA ESISISEKELO AMAGREYIDI 1-3
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
486 IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-4 namaminithi
ama -24)
4.4 Ukumeda okungakahleleki Ukwethula ukumeda Ngesikhathi sokusebenza ngokuzijamela abafundi bafanele baragele phambili Isifundo esi-1
Umthamo/ • Ukulinganisa nokumeda; okuhlelekileko noku:
ivolumu Ukumadanisa nokuhlela (isib. Abafundi benza amathaski • Ukulinganisa nokumeda; ukumadanisa, ukuhlela begodu nokurekhoda
umthamo ongamumathwa atlolwako ukuhlanganisa umthamo weemumathi nofana ivolumu yeemumathi ngokusebenzisa iimedo
simumathi nasizeleko) okulandeleko, ukufaka ezingakahleleki.
ngokusebenzisa iimedo hlangana ukufunda • Ukumadanisa begodu nokuhlela umthamo wamabhodlelo ahlukahlukeneko
ezingakahleleki isib. Iingobho iinthombe begodu nezinto zesitolo sokudla nezinye izintwanyana zangekhaya lapho
namakopi. • zemikhiqizo yobungako umthamo wakhona utlolwe ezintweni eziphakethelwako.
• Ukuhlathulula umthamo bento etlolwe kiyo ukuze • Sebenzisa nanyana amabhodlelo welitha li-1 nofana amajege welitha li-1
wesimumathi ngokubala nokutjho kulandelaniswe ngendlela ukulinganisa nokumeda, ukumadanisa,ukuhlela begodu nokurekhoda
bonyana mangaki amayunithi efeneleko. umthamo weemumathi nofana ivolumu engeemumathini ezingamalitha.
angakahleleki angazalisa
isimumathi, isib. Ibhodlelo • Iinthombe zamajege Qala amanothi weThemu yesi-3
linobungako bamakopi amane lapho ivolumu Abafundi bafanele banikelwe amathaski atlolwako ukuhlanganisa
Ukwethula ukumeda iseduze nelitha li-1 okulandeleko, ukufaka hlangana ukufunda iinthombe
okuhlelekileko elinomboriweko nofana • zemikhiqizo yobungako bento etlolwe kiyo ukuze kulandelaniswe ngendlela
umuda omeregweko efaneleko.
• Ukulinganisa, ukumeda;
otjengisa amalitha ama-2 • Iinthombe zamajege lapho ivolumu iseduze nelitha li-1 elinomboriweko
ukumadanisa nokuhlela
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nokurekhoda umthamo wezinto nofana isiquntu samalitha nofana umuda omeregweko otjengisa amalitha ama-2 nofana isiquntu
ngokumeda ngamalitha, iinqunto nofana ikotara yelitha. samalitha nofana ikotara yelitha.
zamalitha begodu nangamakotara • Iinthombe zamajege Iinthombe zamajege lapho ivolumu iseduze nemida emeregiweko
wamalitha. lapho ivolumu iseduze yamamilimitha.
• Ukumadanisa, ukuhlela nemida emeregiweko Kulindeleke bonyana abafundi bafunde kwaphela umuda oseduze
nokurekhoda umthamo wezinto yamamilimitha. emeregiweko yamamilimitha.
ezipakelwe ukuthengiswa, Kulindeleke bonyana Bahlathulula ivolumu yabo njengokuthi pheze, / eduze /okunengana kuna/
ubungako bazo butlolwa abafundi bafunde pheze kube/ nofana inomboro poro (yelitha) abayifunda ejegeni.
ngamalitha, isib. Amalitha
kwaphela umuda Alikho itjhuguluko elifuneka hlangana kwamamitha namasenthimitha
ama-2 webisi, ilitha li-1 lesiselo
esimakhaza, ama-5 l wepende oseduze emeregiweko Ukumeda ubungako njengobujamo bokurarulula imiraro begodu
nafana ngamamilimitha, isib. yamamilimitha. nokubala
ama-500 ml webisi, Bahlathulula ivolumu yabo Ngesikhathi esibekelwe Iinomboro, imiSebenzi noBudlelwana,abafundi
• Amamililitha ama-340 wesiselo njengokuthi pheze, / eduze bangararulula imiraro ngokusebenzisa
esimakhaza, amamilimitha ama- /okunengana kuna/ pheze
kube/ nofana inomboro poro ubujamo
750 we-oli
(yelitha) abayifunda ejegeni. • bobungako / ivolumu besimedo ezingakahleleki, isibonelo, uGogo
• Ukwazi bonyana ikopi usebenzisa amakopi amabili webisi ukwenza ipudinghi. Nakawabuyelela
elisezingeni limamililitha ama-250 Alikho itjhuguluko elifuneka
hlangana kwamamitha kabili, uzokusebenzisa ibisi elingangani?
• Ukwazi bonyana ithispuni namasenthimitha • amalitha
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
limamililitha ama-5
• amamililitha
akukalindeleki bonyana
Yelela irherho lenomboro elifaneleko leThemu, nemihlobo yeenkinga
kube netjhuguluko hlangana
ezihlukahlukeneko ezifaneleko zeThemu.
kwamamilimitha namalitha
UBUDE
IMIQONDO NAMAKGHONO IMIQONDO NAMAKGHONO BESIKHATHI
AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO : IIMFUNEKO ZOKUPHELA : IMINQOPHO YETHEMU
YOKUFUNDISA ze-iri -1 begodu
KONYAKA YESI-4
CAPS namaminithi
ama -24)
4.5 IPherimitha Ubukhulu bendawo Abafundi bangeniswa ekumedeni ubungako bendawo kokuthoma egreyidini Iimfundo ezi-2
Ipherimitha • Rhubhulula ibanga lobujamo Rhubhulula ubukhulu yesi-3. Egreyidini yesi-3 begodu nesikhathi esinengi sesiGabeni esisiSekelo
nobukhulu uzombelezele boke bendawo ngokusebenzisa ubungako bendawo bumedwa kwaphela ngokungakahleleki. Abafundi bathola
bendawo abobusobubili (2D) begodu ukuthayela bonyana mangaki amajamo nofana izinto ezivala ilingaphandle. Bapakela
nezinto zabosobusontathu ( 3D) amajamo nofana izinto ngaphandle kokutjhiya iinkhala hlangana namajamo
ngokusebenzisa intambo nofana izinto. Bese babala bonyana mangaki amajamo avala ilingaphandle.
Isib. Abafundi bangapakela iinkwere nofana aboncamane ekhasini; babala
Ubungako bendawo
bonyana nangaki amajamo avala ikhasi. Abafundi bafanele batjho ubungako
• Rhubhulula ubungako bendawo bendawo ngokuya ngamajamo, isib. Ikhasi lami linobungako bendawo
ngokusebenzisa ukuthayela obuboncamane abali-16. Kulindelekile bonyana amajamo angavali ikhasi
ngokupheleleko, njengesibonelweni esingenzasi.
Abafundi bafanele batjho ubungako bekhasi ngokuyelela lokhu, isib. Ikhasi
lami linobungako bendawo obungaphezu kwaboncamane abali-18 kodwana
mbadlwana kunaboncamane abama-28.
Vumela abafundi bafake amathayela endaweni enamajamo ahlukahlukeneko
begodu namajamo afanako wobungako obuhlukahlukeneko. Lokhu
kuzokuvumela abafundi babone bonyana.
• ijamo nalilincani, lenza bonyana abe manengi amajamo azokulingana
ilingaphandle, begodu
• ijamo olikhethako lizokuthinta iimpendulo zokubala ozitholako
Abafundi abakalindeleki banyana babale ubungako bendawo ngokubala
iinkwere ezisegridini yeenkwere; lokhu kuzokwenziwa esiGabeni esisiSekelo.
487
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YESI-3 ITHEMU YESI-4
5. UKUPHATHA IDATHA
488 UBUDE
IMIQONDO IMIQONDO BESIKHATHI
NAMAKGHONO NAMAKGHONO : AMANYE AMANOTHI WOKUTLHADLHULA NOFANA IMIHLAHLANDLELA (eemfundweni
IINHLOKO
: IIMFUNEKO IMINQOPHO YETHEMU YOKUFUNDISA ze-iri -1 begodu
ZOKUPHELA KONYAKA YESI-4 namaminithi
ama -24)
5.4 Ukubuthelela begodu
Ukubuthelela uhlele idatha
begodu uhlele • Buthelela idatha
idastha ngetlasi nofana
isikolo ukwenzela
ukuphendula imibuzo
ebuzwa ngutitjhere.
• Hlela idatha oyinikelwe
ngutitjhere nofana
incwadi
• Hlela idatha ngama:
-- Amarhelo
-- Amathali
-- Amathebula
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Ukujamisela idatha
5.5 Jamisela idatha nge:
Ukujamisela • Grafu yeenthombve
idatha • Bha grafu
5.6 Ukuhlaziya begodu Ukuhlaziya idatha Ngalesi isikhathi sonyaka, kufanele bona abafundi sele babandakanywe kiyoyoke Isifundo esi-1
Ukutsenga urhumutjhe idatha kusukela eenjamisweni imihlobo yokubuthelela idatha efunekako eGreyidini 3 (amarhelo, amathali, amathebula,
begodu Phendula imibuzo onikelwe zona. amagrafu weenthombe, amabha grafu). Kuphakanyisiwe bona ngeThyemu yesi 4
uhlathulule ngedatha ethulwe nge: abafundi banqophe ekuhlaziyeni idatha. Unikela abafundi idatha bona bayihlaziye
idatha okungasenani ema:
• Grafu yeenthombve
• Ibha grafu eyodwa; nase
• Bha grafu.
• Thebuleni eyodwa
Abafundi kufanele baphendule imibuzo obabuza yona ngama grafu nama thebula; bona
iThemu 1ukufumana imihlobo yemibuzo efaneleko.
ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISAHLUKO 4: UKUHLOLA
4.1 ISINGENISO
Ukuhlola yikambiso eragela phambili ehleliweko yokubona, ukubuthelela begodu nokurhumutjha ilwazi elimayelana
nokusebenza kwabafundi, ngokusebenzisa iindlela ezihlukeneko zokuhlola. Kufaka hlangana amagadango amane:
• ukukhiqiza begodu nokubuthelela ubufakazi bokuzuza,
• ukuhlola ubufakazi lobu:
• ukurekhoda lokho okutholakeleko begodu
• kusetjenziswa ilwazi leli ukuzwisisa begodu nokusiza ekuthuthukiseni umfundi ukuze kwenziwe ngcono
ikambiso yokufunda nokufundisa.
Ukuhlola kufanele kwenziwe ngazo zombili iindlela kube ngokungakahleleki (Ukuhlola mayelana nokufunda) nan-
gokuhlelekileko (Ukuhlola kokufunda). Kizo zombili iindlela zokuhlola umbiko obuyako kufanele unikelwe abafundi
ukuthuthukisa ilemuko lokufunda.
EsiGabeni esisiSekelo, amathekhiniki aqakathekileko wokuhlola okuhlelekileko begodu nokungakahlelekiko kutjhe-
jwa ngutitjhere, ukucocisana ngokomlomo, ukutjengisa wokwenzekako, begodu nerekhodi elitloliweko. Ukuhlola
kweGreyidi R kufanele kube ngokomlomo begodu nangokwenzeka
4.2 Ukuhlola okungakahleleki nanyana ukuhlola kwangamalanga
Ukuhlola kokufunda kuyikambiso yokuragela phambili yokubuthelela ilwazi ngalokho umfundi akuzuzileko okungas-
etjenziswa ukwenza ngcono ukufunda kwakhe. Lokhu kubizwa ukuhlola okungakahleleki..Kuyindlela yangamalanga
yokutjheja iragelo phambili labafundi. Lokhu kwenziwa ngendlela yokuqala, ukucocisana, ukutjengisa okwenzekako,
ukukhulumisana ngendlela engakahleleki ngetlasini, njll. Akukafaneli kubonakale njengento ehlukileko kunemise-
benzi efundwako leyo efundwa ngetlasini. Ukuhlola okungakahleleki kusiza utitjhere ukutjheja ituthuko yomfundi
nokwenza imiyalelo ngesiqunto sangamalanga woke. Ukuhlola okuhlelekileko kusetjenziseswa:
• ukunikela umbiko obuyako ebafundini
• ukwazisa ukutlamela ukufundisa
Kesinye isikhathi utitjhere angalondoloza irhelo lokuhlola nofana asebenzise itjhejuli yokuqala njengendlela yoku-
rekhoda iragelo phambili lomfundi. Kesinye isikhathi abafundi nofana utitjhere angatshwaya umsebenzi. Nanyana
kunjalo, ukuhlola okungahleleki akubi yingcenye yerekhodi elihlelekileko lomfundi. Imiphumela yemisebenzi yokuh-
lola okungakahleleki kwangamalanga ayitjhejwa nakukhutjhulwa abafundi begodu nalokha nakunehloso yokunikela
iintifikeyidi.
4.3 UKUHLOLA OKUHLELEKILEKO.
Yoke imisebenzi ehlolwako/amathaski abumba ihlelo elihlelekileko lokuhlola lomnyaka woke lithathwa njengokuHlo-
la okuHlelekileko. Amathaski/Imisebenzi yokuhlola okuhlelekileko iyatshwaywa begodu irekhodwe phasi ngutitjhere
ngendlela ehlelekileko mayelana neragelo phambili kanye nomnqophowokunmikelwa kwesitifikeyidi. Ukuhlola
okuhlelekile kunikela abotitjhere indllela yerherho yokuhlunga bonyana abafundi bathuthuka bunjani ngegreyidini
ngayinye begodu nasesifundweni esithize.
Utitjhere angaqala kwaphela abafundi abangaba li 10 ngesikhathi sinye, ngakho ke imisebenzi yokuhlola okuhlele-
kileko izokwenzeka khulu ekuhlanganeni okunqotjhiweko kweenqhema ezincani begodu kuzothatha amalanga uku-
hlola ikumba yoke yokufunda. Yoke imethiriyali neensetjenziswa lezo abafundi abanokuziberegisa kufanele zibe
khona njengasemihleni, (izinto zokubala, amatjhadi weenomboro,njll)
Iindlela zokuhlola ezisetjenziswako kufanele zilingane neminyaka begodu nezinga letuthuko elifaneleko. Ukuhlola
CAPS 489
ISIGABA ESISISEKELO AMAGREYIDI 1-3
okuhlelekileko kufanele kuvumele amazing ahlukahlukeneko wokufunda namakghono wabafundi, nobujamo bemise-
benzi le kufanele bulingane nokumumethweko kwesifundo ngeendlela ezihlukeneko.
Imihlobo ehlukeneko yokuhlola (ukuqala, komlomo, okwenziwako nokutlolwako) kufanele kuberegiswe ukunikela
umfundi ngamunye ithuba lokutjengisa abangakwenza. Lokhu kungombana abanye abafundi bakghona masinyana
ukubonisa lokhu abakwaziko kokhunye ukuhlola okuhlelekileko. Isibonelo,
• Abanye abafundi abathola bonyana ukufunda kubudisi bayazazi iimBalo.
• Abanye abafundi ngeze babe sezingeni elamukelekileko lokukghona ngelimini lokufunda nokufundisa.
Imisebenzi yokuhlola eemBalweni kufanele ifake imisebenzi begodu nemisetjenjana engakasekelwa elimini, begodu
engakasimi ekufundeni, ukuveza amakghono wamambala wabafundi laba.
Nanyana kunjalo, iyalelo lalokho okuhlolwako lifanele liqalwe. Ilwazi elithileko begodu, amakghono ahloleka kuhle
ngeendlela ezithileko zokuhlola. Imihlobo ehlukeneko yokuhlola ilungele amakghono begodu nemiqondo etlhogeka-
ko eenhlokwaneni ezihlukahlukene neenqhema zeminyaka ezihlukeneko. Kuyasiza ukusebenzisa irhelo lokuhlola
ukuhlola ukulinganisa abafundi emagreyidini aphasi.
Irubrikhi ingaberegiswa ukuhlola ikghono lomfundi ekurarululweni kwemiraro.
4.4 IHLELO LOKUHLOLA OKUHLELEKILEKO
Iimfuneko zokuhlola okuhlelekileko eemBalweni emaGreyidini 1-3 zirhenyiswe ethebuleni engenzasi:
ITHEMU 1 ITHEMU 2 ITHEMU 3 ITHEMU 4 INANI
IGreyidi 1 2 2 2 1 7
IGreyidi 2 2 2 2 2 8
IGreyidi 3 2 3 3 2 10
Abotitjhere bakhuthazwa bonyana benze ukuhlola okusisekelo ethemini yokuthoma. Imiphumela yabafundi ekuhlol-
weni okusisekelo akukafaneli bonyana isetjenziselwe ukulebula ikghono labo, kodwana ukuthatha isiquntu sokobana
imisetjenzana yokuthoma ibekwe kiliphi izinga begodu nokuhlola nokobana ngiziphi iingcenye zomsebenzi ezitlhoga
itjhejo elinengi. Abafundi bathuthuka ngamazinga ahlukahlukeneko. Abanye abafundi bathoma buthaka, kodwana
baye ngokurhaba eeMbalweni lokha nakukhamba isikhathi.
Umsebenzi wokuhlola okuhlelekile eemBalweni ufaka hlangana iinhloko ezidlula kwesisodwa eemBalweni. Uku-
hlola konyaka woke kufanele kumumathe zoke iingaba zokumumethweko neenhloko, kodwana akusingiyo yoke
into ekukharikhyulamu okufanele ihlolwe ngokuhlelekileko nofana kubikwe ngakho. Iinomboro ,Ama-opharetjhini no
Budlelwano kuthatha 60 % eemBalweni emaGreyidini 1-3. Lokhu kutjho bonyana amaphesende ama-60% yokuh-
lola okuhlelekileko ethemini ngayinye begodu nenyakeni kufanele unqotjhiswe Eenomborweni, Ama-opharetjhini no-
Budlelwano
Umsebenzi wokuhlola okuhlelekileko ngamunye akukafaneli bonyana kubonwe njengesehlakalo esihlukileko nofa-
na ukulingwa. Ezinye iinquntu zesilinganiso zingahlolwa ngasikhathi sinye, kodwana ezinye zizakuhlolwa enkathini
esihlukile. Isibonelo lokha ikghono labafundi lokubala ngokweqa lihlolwa, ikghono labo ukwenza okulandelako lin-
gahlolwa emsebenzini ofanako nofana isehlakalo:
• Ukuqedelela ilandelano lokubala
• Ukufunda nokuatlola amatshwayo weenomboro
• Ukubala
Nanyana kunjalo, uma umsebenzi wokuhlola umumethe kokubili ukurarululwa kwemiraro ngokweenqhema/ nofana
ukwabelana.
490 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
nangokuhlanganyela, begodu nokuhlola ikghono labafundi lokulinganisa umthamo;kuvamile bonyana amahlangothi
wobujamo weemBalo azokuhlolwa eenkathini ezihlukeneko begodu ngeendlela ezahlukeneko.
4.5. UKUREKHODA NOKUBIKA
Ukurekhoda yikambiso lapha utitjhere atlola phasi khona amazinga wokusebenza komfundi ekuhloleni umsebenzi
onqotjhiweko. Kutjengisa iragelo phambili lomfundi mayelana nokuzuza ilwazi njengombana kuquntwe ngakhona
esiTatimendeni somThetho-kambiso weKharikhyulamu nokuHlola. Amarekhodi wokusebenza komfundi kufanele an-
ikele ubufakazi beragelo phambili lemiqondo hlangana negreyidi nokulungela kwakhe ukuragela phambili nanyana
ukudluliselwa kugreyidi elandelako. Ukurekhodwa kokusebenza komfundi kufanele kusetjenziswe ukuqinisekisa ira-
gelo phambili elenziwa botitjhere nabafundi ekambisweni yokufunda kanye nokufundisa.
Ukubika yikambiso yokukhulumisana ngokusebenza komfundi kubafundi, kubabelethi, eenkolweni begodu nabanye
abahlanganyeli. Ukusebenza komfundi kungabikwa ngeendlela ezinengi. Lokhu kufaka hlangana amakarada wemi-
biko, imihlangano yababelethi, amalanga wokuvakatjhela iinkolo, amakhonferensi wabafundi nabotitjhere, imitato,
iincwadi, iincwadi zetlasi nanyana zesikolo, njll. Abotitjhere kiwo woke amagreyidi babika ngamaphesende kuneem-
fundo. Amazinga ahlukeneko wokuzuza kanye namazinga wamaphesende akhambisana nawo atjengisiwe kilethe-
bula engenzasi.
AMAKHOWUDU NAMAPHESENDE WOKUREKHODA NOKUBIKA
IKHOWUDU YAMANANI UKUHLATHULULWA KWEKGHONO AMAPHESENDE
7 Uphumelele kuhle tle 80 – 100
6 Uphumelele ngendlela ethokozisako 70 – 79
5 Uphumelele ngamandla 60 – 69
4 Uphumelele ngokwaneleko 50 – 59
3 Uphumelele ngokulingeneko 40 – 49
2 Uphumelele ngendlela ephasi 30 – 39
1 Akakaphumeleli 0 - 29
4.6 UKULINGANISA UKUHLOLA
Ukulinganisa kutjho ikambiso eqinisekisa bonyana ukuhlola umsebenzi kwenziwa ngendlela efaneleko, esemthethweni
nethembekileko. Ukulinganisa kufanele kwenziwe emazingeni wesikolweni , kudistrki, kusiyingi kuphrovinsi kanye
nezingeni lelizwe loke. Iindlela zokwenza zokullinganisa ezipheleleko nezifaneleko kufanele zibe khona mayelana
nokuqinisekiswa kwakho koke ukuhlola iimfundo.
4.7 OKUVAMILEKO
Umtlolo lo kufanele ufundwe ngokukhambisana nalokhu:
4.7.1 IKambiso yokuHlola yeliZwe loke, Imihlahlandlela yeenhlahlubo ezithileko zesifundo njengombana
simunyethwe emtlameni wetlhatlha lomgomo: Umgomo weliZwe loke ophathelene nehlelo kanye neendingo
zokuthuthukiswa kwesiTatimende seKharikhyulamu yeliZwe loke, kumaGreyidi R-12
4.7.2 Iimfuneko zokuRagela Phambili nokuKhutjhulwa Amagreyidi 1-12.
4.7.3 Umhlahlandlela wokuhlola onqotjhiswe esifundweni okhutjhwa njalo ngonyaka.
CAPS 491
ISIGABA ESISISEKELO AMAGREYIDI 1-3
4.8 iimbonelo zamathaski wokuhlola zamagreyidi woku-1 ukuya ku-3
Isibonelo samarhelo wokuhlola ukuhlola anikelwe ngenzasi. Umnqopho kusiza abotitjhere ngokutlama nokwenza
ukuhlola okuhlelekileko ngendlela eragako.
IGREYIDI 1
Irherho lokutjheja lomthamo/ivolumu
Isigaba soku-
Isihloko Isilinganiso nofana Imibono
mumethweko
Hlela begodu umadanise inani lokusaketjezi
(ivolumu) eemumathini ezimbili ezibekwe
esinye eqadi kwesinye.
Madanisa ivolumu yeemumathi ezimbili
Umthamo / Ivolumu
nofana ngaphezulu eziqaleka zihlukile
ngokuthela ngesimumathini sesithathu.
ukumeda
Rekhoda umthamo weemumathi
ngokusebenzisa izinto zokumeda
ezingakahleleki, isib. Iingobho namakomitji.
Phendula imibuzo emayelana nokuthi
ngisiphi isimumathi esithatha iketjezi
elinengi.
Sebenzisa ilimi ukukhuluma
ngokumadanisa, isib. Nengi kuna, ncani
kuna, kuzele, akunalitho.
IGREYIDI 1
Irherho lokutjheja lemasi
Isigaba soku-
Isihloko Isilinganiso nofana Imibono
mumethweko
Hlela begodu umadanise imasi yezinto
ezintathu nofana ngaphezulu, ngokubeka
izinto ngazimbili esikalini sokudzimelelisa,
kufikela lapho zoke izinto sele
zilandelanisiwe.
Ukumeda
Yitjho iyunidi lokha nawunikela imasi, isib.
Imasi Incwadi inemasi elingana namamabula
ama-34.
Sebenzisa ilimi ukukhuluma
ngokumadanisa, isib. Okulula, okubudisi,
okuludlana, okubudisana.
Ikghono lokurekhoda ukumeda.
Ukusebenzisa irubhrikhi ukuhlola / ukulinganisa ukurarulula imiraro
Ukurarulula imiraro kungahlolwa ngokusebenzisa irubhrikhi.
Okuthathwa njengendlela elungileko yokurarulula imiraro,
• kuyatjhuguluka lokha abafundi bathuthuka begodu bakhula ngokuzwisisa umqondo wenomboro begodu
nekghono lokusebenza kwabo; begodu
• kudzimelele kikho kokubili irherho lenomboro emrarweni begodu nehlobo lomraro.
492 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI 1
Irubhrikhi yokurarulula imiraro
Akazi bonyana athome kuphi nofana wenza into eseqadi. 1
Uzwisisa umraro begodu uyawuthoma kodwana akakghoni ukuwuqedelela kuhle. 2-3
Uzwisisa umraro begodu uyawurarulula ngokusebenzisa imigwalo (immeregi) nofana izinto zokubala. 4-5
Ukghona ukuhlathulula. Angahle enze iimphoso ezincani.
Uqedelela umraro ngefanelo. Angahlathulula ukucabanga kwakhe nokwabanye ngokuzethemba. 6-7
IGREYIDI 2
Irubhrikhi yokurarulula imiraro
Akazi bonyana athome kuphi nofana wenza into eseqadi. 1
Uzwisisa umraro begodu uyawuthoma kodwana akakghoni ukuwuqedelela kuhle. 2-3
nofana
Uzwisisa umraro begodu uyawurarulula ngokusebenzisa imigwalo (immeregi) nofana izinto zokubala kuphela. *
Uzwisisa umraro begodu uyawurarulula ngokusebenzisa iinomboro, kodwana wenza iimphoso ezincani. Ukghona 4-5
ukuhlathulula.
Uqedelela umraro ngefanelongokusebenzisa ilwazi lenomboro begodu namaqhinga afana nokuthi aphule begodu 6-7
abuyelele ahlanganise iinomboro, ukubuyelela kabili, ukuqunta phakathi, amanamba layini, njll. Angahlathulula
ukucabanga kwakhe nokwabanye ngokuzethemba.
* Irherho leenomboro ezisebenza ngabafundi beGreyidi yesi-2, lithoma ukwenza bonyana kube budisi/ kungak-
ghoneki ukubala ngokugwala iinthombe bese uyazibala. Umqondo weenomboro wabafundi kutlhogeka bonyana
uthuthuke ngokuzeleko ukwenzela bonyana bakghone ukusebenzisa iinomboro ukurarulula imiraro nokubala.
IGREYIDI 3
Irubhrikhi yokurarulula imiraro
Akazi bonyana athome kuphi nofana wenza into eseqadi. 1
Uzwisisa umraro begodu uyawuthoma kodwana akakghoni ukuwuqedelela kuhle, nofana usebenzisa immeregi
2-3
(imigwalo) nofana izinto zokubala.
Uzwisisa umraro begodu uyawurarulula ngokusebenzisa iinomboro. Ukghona ukuhlathulula. 4-5
Uqedelela umraro ngefanelo ngokusebenzisa ilwazi lenomboro begodu namaqhinga afana nokuthi aphule begodu
abuyelele ahlanganise iinomboro, ukubuyelela kabili, ukutjhideza eduze nokujamiselela , amanamba layini, njll 6-7
ngefanelo. Angahlathulula ukucabanga kwakhe nokwabanye ngokuzethemba.
Iimbonelo zokuthi ungayisebenzisa bunjani irubhrikhi le emirarweni erarululwe bafundi bamaGreyidi 1 – 3.
Inja inemilenze emi-4. Izinja ezili -12 zinemilenze emingaki?
IGreyidi 1: Isilinganiso 1.
Umfundi akawuzwisisi umraro, yekeke usebenzisa iqhinga
eliseqadi nofana itshwayo okungasingilo.
inja eyodwa ineenyawo ezi 4 IGreyidi 1: Isilinganiso 6
izinja ezili 12 zineenyawo ezingaki? 48 Umfundi uwuzwisisile umraro, urarulule umraro ngendlela
efaneleko eGreyidini yoku 1 begodu ukghona ukuhlathulula
umraro.
IGreyidi 2: Isilinganiso 4
Umfundi uwuzwisisisle begodu wawurarulula umraro.
Nanyana kunjalo, umfundi wegreyidi yesi 2 kufanele
asebenzise iinomboro namatshwayo ukuhlanganisa
ngokubuyelela (nofana ukubuyabuyelela, kuye ngokuthi
ngisiphi isikhathi sonyaka).
Umlimi utjala amareyi asi 6 wemithi. Ireyi ngalinye linemithi eli- 13. Utjala imithi emingaki nasele iyoke?
CAPS 493
ISIGABA ESISISEKELO AMAGREYIDI 1-3
Umfundi weGreyidi 2 , Isilinganiso 6
Umfundi uwuzwisisisle begodu wawurarulula umraro,
ngokusebenzisa inomboro efaneleko namatshwayo afaneleko
eGreyidini yesi 2.
Abafundi beGreyidi 3: Isilinganiso 4
Abafundi bawuzwisisisle begodu bawurarulula umraro
ngendlela elingeneko. Nanyana kunjalo, abatholi imaraga
lokusebenza ngokudluleleko ngombana abakatjengisi
amaqhinga akhona ebafundini beGreyidi yesi 3 o.u.
ukubuyabuyelela ngokusebenzisa ukuphula begodu
nokubuye uhlanganiseiinomboro : bona ngenzasi.
Umfundi weGreyidi 3: Isilinganiso 5
Uqedelela umraro ngefanelo ngokusebenzisa inomboro
namatshwayo afaneleko namaqhinga afana nokuthi aphule
begodu abuye ahlanganise iinomboro. Angahlathulula
ukucabanga kwakhe nokwabanye ngokuzethemba.
UJabu uneentikara ezima 258 begodu uJonasi uneentikara ezima 384. Baneentikara ezingaki nasele zihlangene
zoke?
IGreyidi 3: Isilinganiso 5
Uqedelela umraro ngefanelo ngokusebenzisa ilwazi
lenomboro begodu namaqhinga afana nokuthi aphule
begodu abuyelele ahlanganise iinomboro, ukubuyelela kabili,
ukutjhideza eduze nokujamiselela , amanamba layini, njll
ngefanelo. Angahlathulula ukucabanga kwakhe nokwabanye
ngokuzethemba.
Iyini ihafu yama 237?
IGreyidi 3. Isilinganiso 5
Urarulula umraro ngefanelo ngokusebenzisa ilwazi
lenomboro namathekiniki afana nokuphula ubuye godu
uhlanganise inomboro, ukubuyelela kabili, ukutjhideza
eduze nokujamiselela, amanamba layini. Angahlathulula
ukucabanga kwakhe nokwabanye ngokuzethemba.
494 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGREYIDI YOKU-1:
ITHEMU YOKU-1: Isibonelo esisisekelo sethaski yokuhlola
Imihlobo
Umbandela wokulinganisa nofana Iimbono
yemisebenzi
Zomlomo Umfundi uyakghona uku:
• ukubala izinto ukufikela e-10
• tjho bonyana ngiliphi ibuthelelo lezinto elincani khulu/elikhulu
khulu.
• Ukufunda amatshwayo weenomboro ukufika ku- 5?
Okwenziwako Umfundi uyakghona uku:
• Ukulandelanisa izinto?
• Ukukopa amaphetheni?
• Ukubeka izinto ngaphambi kwakhe?
• Ukubeka izinto ngemuva kwakhe?
• Ukuhlukanisa izinto ngokuya ngakunye okuphawulekako?.
• Ukuzibandakanya emrarweni ukwenzela ukuthola isisombululo?
IGreyidi yoku-1
IThemu yoku-1: Isibonelo somsebenzi wokuhlola ithaski yoku-1
ISIGABA
ISIHLOKO ISILINGANISO SOMSEBENZI WOKJULINGA
SOKUMUMETHWEKO
IINOMBORO, AMA- Umqondo nomboro Bala izinto ezi-10 ngokuthembeka,ngokutjho amagama
OPHARETJHINI ngokulandelana.
NOBUDLELWANA
Ukutlola nokufunda amatshwayo wenomboro ukusuka keyoku-1
ukufika keye-5
Ukuhlela iinomboro ukusuka keyoku-1 ukufika keye -5 Ukusuka
kencani ukufika kokukhulu.
Ukusebenzisa ilimi ukuhlathulula ubudlelwana bobukhulu
beenomboro: ngaphambili, ngemuva, nahlangana.
Ukurarulula imiraro Ukusombulula imiraro yamagama asebujameni okufaka
ukuhlanganisa, ukukhupha kube neempendulo ukufikela keyesi-5
Ngokusebenzisa ama-apharethasi nofana imigwalo begodu
nokuhlathulula iinsombululo zakhe emirarweni.
Ukusombulula imiraro eyenzekako efaka ukwabelana
ngokulinganako begodu nokuhlela ngeenqhema iinomboro
ezipheleleko ukufika keye-5 nangeempendulo ezingafaka iinsalela
ngokusebenzisa ama-apharethasi nofana imigwalo,
Ukubalisisa Ukuhlanganisa ukufikela ku- 5 ngokusebenzisa ama-apharethasi
nofana imigwalo
Ukukhupha kusukela keye-5 nofana ezimbadlwana ngokusebenzisa
ama-apharethasi nofana imigwalo
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kwenomboro nawubala ngakunye
AMAFANKTJHINI NE- weenomboro ukufikela e-10. isib.1, 2, 3, 4, __, __, __, __, 9, 10
ALJIBHRA
CAPS 495
ISIGABA ESISISEKELO AMAGREYIDI 1-3
ISIKHALA NOBUJAMO Indawo Ukulandela iinlayelo ukubeka into yinye ehlobana nenye isib. faka
(JIYOMETHRI) ipensela ngaphakathi kwebhoksi, faka ipensela ngesandleni sokudla
sebhoksi.
Izinto Ukubona nokutjho
Ezi- 3D • ubujamo bebhola (indulungu)
• ibhoksi (iphrizimimu)
UKUMEDA Isikhathi Ukuhlathulula lokha nakwenzeka okuthileko ngokusebenzisa ilimi
isib. ekuseni, ngemuva kwedina, ebesuku ngamasa, ngamarhwalala.
Ubude Ukumeda ubude, ububanzi, nofana ukuphakama ngokusebenzisa
iimedo ezingakahleleki. Itjho ukulinganisa ngamayunithi
angakahleleki.
Ubudisi/imasi Ukumeda nokumadanisa ubudisi bezinto ezintathu nezinengi
kusetjenziswa isikala esidzimeleleko kusetjenziswa isilinganiso
esingakahleleki. Hlela izinto ngokuya ngobudisi. Hlathulula
ukuhleleka ngokusebenzisa okulula, okubudisi nokubudisi khulu.
UKUPHATHA IDATHA Ukuhlukanisa ibuthelelo Ukubuthelela nokuhlela ngeengaba izinto ezibonakalako
lezinto zangamalanga ngokuya ngombandela wesilinganiso esinikelwe
ngutitjhere. Ukugwala isithombe sezinto ezihleliweko nofana
ukuhlathulula ibuthelelo elihleliweko.
496 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yoku-1 IThemu yesi-2: Isibonelo sokuhlola Ithaski yoku-1
ISIGABA
ISIHLOKO UMBANDELA WESILINGANISO
SOKUMUMETHWEKO
IINOMBORO, AMA- Umqondonomboro Ukubala izinto ezima-20 ngokuthembeka, ngokutjho amagama
OPHARETJHINI ngokulandelana.
NOBUDLELWANA
Ukutjho bonyana ngiyiphi into kulezo ezimbili ezibuthelelweko
enokunengi nofana okumbalwa lapho amabuthelelo womabili ana-
10 nofana okumbalwa.
Ukufunda amatshwayo wenomboro ukufika ema-30
Ukutlola amatshwayo wenomboro ukufika e-10
Ukusombulula imiraro Ukusombulula imiraro yamagama ngobujamo obufaka
ukuhlanganisa, ukukhupha okuneempendulo ukufika e-10
ngokusebenzisa kunye kwalokhu okulandelako:
• Ama-apharethasi
• Imigwalo
• Ukwakha nokuphula iinomboro
• Amanambalayini
• Ukubuyelela nokuhlukanisa begodu
bahlathulule impendulo zemiraro yabo.
Ukubalisisa Ukuhlanganisa kufikela e-10. ngokusebenzisa kunye kwalokhu
okulandelako:
• Ama-apharethasi
• Imigwalo
• Ukwakha nokuphula iinomboro
• Amanambalayini
• Ukubuyelela nokuhlukanisa
Ukutlola umutjho wenomboro ngokusebenzisa u +
Ukukhupha kusukela e-10 nofana ngaphasi. Ngokusebenzisa kunye
kwalokhu okulandelako.
• Ama-apharethasi.
• Imigwalo
• Ukwakha nokuphula iinomboro
• Amanambalayini
• Ukubuyelela nokuhlukanisa
Ukutlola umutjho wenomboro ngokusebenzisa u -
AMAPHETHENI, Amaphetheni wenomboro Ukuqedelela ukulandelana kweenomboro zokubala ukufika ema-30
AMAFANKTJHINI NE- • Ngakunye isib. 20, 21, 22, 23, __, __, __, __, 28; __; 30.
ALJIBHRA
• Ngakuhlanu isib. 5, 10, 15, __, __, 30,
Amaphetheni Ukukopa nokwandisa iphetheni
weJiyomethri • Kwenziwa ngokusebenzisa into eyodwa kodwana imibala yezinto
itjhugululwe ngendlela ejayelekileko nofana.
• Yenziwe ngokusebenzisa izinto ezifanako zobukhulu
obuhlukeneko.
ISIKHALA Ama 2-D Ukubona nokutjho amagama
NOBUJAMO Weendulungu
(JIYOMETHRI)
Iinkwere
aboncantathu
CAPS 497
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yoku-1 iThemu yesi-2:Isibonelo sokuhlola ithaski 2
ISIGABA
ISIHLOKO UMBANDELA WESILINGANISO
SOKUMUMETHWEKO
IINOMBORO, AMA- Umqondonomboro Ukubala uye phambili nemuva ngaku-1 hlangana nakunye-1 ukufika ema-
OPHARETJHINI 50
NOBUDLELWANA Ukubala uye phambili ngaku-5, ku-2 ukufika ema-50
Ukusebenzisa ilimi ukuhlathulula ukuhlobana kobukhulu benomboro:
ngaphambili, ngemuva, nahlangana
Ukumadanisa ubukhulu beenomboro ukufika e-10 ngokusebenzisa ilimi
isib. Okunengi kuna, okumbalwa kuna njll.
Ukusebenzisa ilimi ukuhlathulula ubukhulu beenomboro: ngaphambili,
ngemuva,nahlangana
Ukuhlela iinomboro ukusukela keyoku-1-10 ukusukela kencani khulu
ukuya kekhulu khulu.
Ukufunda amatshwayo wenomboro ukufika ema-50.
Ukusombulula Ukusombulula imiraro yokwenziwako efaka ukwabelana ngokulinganako
imiraro begodu nokubuthelelwa kweenomboro ezipheleleko ukufika e-10 begodu
neempendulo ezingafaka hlangana iinsalela.
Ngokukodwa okulandelako
• Ama-apharethasi.
• Imigwalo
• Amanambalayini
Bahlathulule iinsombululo
Ukusombulula Ukusombulula imiraro yamagama asebujameni efaka hlangana
imiraro ukuhlanganisa kokubuyelela, okuneempendulo ukufika e-10
ngokusebenzisa kunye kwalokhu okulandelako:
• Ama-apharethasi.
• Imigwalo
• Ukwakha nokuphula iinomboro
• Inambalayini
• Ukubuyelela nokuhafula begodu
Bahlathulule iinsombululo zemiraro okungeyabo.
Imali Ukubona imali yeSewula Afrika amasende 5c, 10c, 20, 50c, R1, R2; R5
Ukusombulula imiraro yemali efaka inani liloke netjhentjhi ya- R10
namasende ukufika ema -20c
Ukubalisisa Ukuhlanganisa okubuyabuyelweko ukufika e- 10
Ngokusebenzisa okukodwa okulandelako:
• Ama-apharethasi.
• Imigwalo
• Ukwakha nokuphula iinomboro
• Amanambalayini
• Ukubuyelela nokuhafula begodu
Ukutlola umutjho wenomboro kusetjenziswa u +
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro zokubala
AMAFANKTJHINI NE- weenomboro • Ngakunye kubuyelwa emuva ukusukela e- 50 isib. 50, 49, 48, __, __, 45,
ALJIBHRA __, __, 42; __; 40.
• Ngalitjhumi ukufika ema- 50 isib.10, 20, 30, __, __,
UKUMEDA Umthamo/ivolumu Ukulinganisa, ukumeda, ukumadanisa, ukuhlela begodu nokurekhoda
umthamo weemumathi ngokusebenzisa iinlinganiso ezingakahleleki isib.
Iingobho namakopi.
UKUPHATHA IDATHA Ukuhlela Ukubuthelela begodu nokuhlela ngamananeko izinto ezibonakalako
ngemihlobo zangamalanga ngokuya ngemibandela yokulinganisa enikelwe ngutitjhere.
ibuthelelo lezinto Ukugwala isithombe sezinto ezihlelwe ngemihlobo nofana ukuhlathulula
ibuthelelo elihlelwe ngokweengaba.
498 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yoku-1 iThemu yesi-3:Isibonelo sokuhlola Ithaski yoku-1
OKUMUMETHWEKO
ISIHLOKO UMBANDELA WESILINGANISO
ISIGABA
IINOMBORO, AMA- Umqondonomboro Ukubala izinto ezi-40 ngokuthembeka, utjho namagama
OPHARETJHINI ngokulandelana.
NOBUDLELWANA
Ukutjho bonyana ngiyiphi yezinto ezimbili ezinikelweko enengi nofana
encani nangabe zombili zilibuthelelo le-15 nofana zincani.
Funda amatshwayo weenomboro ukufika e-70.
Tlola amatshwayo weenomboro ukufika e- 20
Ukusombulula imiraro Ukusombulula imiraro yamagama asebujameni efaka hlangana
ukuhlanganisa ,ukukhupha okuneempendulo ukufika e-15.
Ngokusebenzisa kunye kwalokhu okulandelako
• Ama-apharethasi
• iimigwalo
• ukwakha nokuphula iinomboro
• Amanambalayini
• ukubuyelela nokuhafula.
bebahlathulule nensombululo zemiraro yabo
Ukubala Yenza ukuhlanganisa ukufika e-15 nofana ngaphasi
Sebenzisa kunye kwalokhu okulandelako
• Ama-apharethasi
• Imigwalo
• ukwakha nokuphula iinomboro
• iinamba-layini
• ukubuyelela nokuhafula
Tlola umutjho weenomboro usebenzise +,=
Yenza ukukhupha kenye nenye inomboro ye-15 nofana encani
Sebenzisa kunye kwalokhu okulandelayo
• Ama-apharethasi.
• Imigwalo.
• ukwakha nokuphula iinomboro
• Amanambalayini
• ukubuyelela nokuhafula.
Tlola umutjho weenomboron ngokusebenzisa -,=
AMAPHETHENI, Amaphetheni Qedelela ukubala ukulandelana kweenomboro nga:
AMAFANKTJHINI NE- weenomboro • yinye .ubalele emuva ukusuka e-60 isib. 60, 59, 58, __, __, __, 54,
ALJIBHRA __, __, 51.
• ngakubili, isib. 44, 46, 48, __, __, __,56; __, 60
Amaphetheni Ukukopa, ukungezelela nokuhlathulula amaphetheni lokhana
weJiyomethriki kusetjenziswa amajamo ahlukahlukeneko ukwenza ukwakha isiqhema
,kodwana iinqhema zezinto ziyabuyelelwa ngokunemba ngendlela
efanako.
ISIKHALA NOBUJAMO Ama-3-D Ukubona begodu nokutjho
(JIYOMETHRI) • ubujamo bendulungu (indulungu)
• ubujamo bebhoksi (iphrizimu)
Hlela izinto ngokuya ngokugedeka nofana ngokutjhelela kwazo.
CAPS 499
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yoku-1 iThemu yesi-3 isibonelo sokuhlola ithaski yesi-2
ISIGABA
ISIHLOKO UMBANDELA WESILINGANISO
SOKUMUMETHWEKO
IINOMBORO, AMA- Umqondonomboro Balela phambili nga:-10, 5, 2, kufika ku-80
OPHARETJHINI
NOBUDLELWANA Sebenzisa ilimi ukuhlathulula ukuhlobana kobukhulu kwenomboro:
ngaphambi,ngemuva, hlangana
Madanisa ubukhulu beenomboro ukufika e-15 ngokusebenzisa ilimi isib.
kunengi-kune, kumbalwa kuna njll.
Rhatjha iinomboro ye- 11 – 15 nga- 10 + kunye isib. 12 = 10 + 2
Sombulula imiraro Ukusombulula imiraro yamagama asebujameni efaka hlangana
ukuhlanganisa okubuyelelwako, okuneempendulo ukufika e-
15.
Ngokusebenzisa kunye kokulandelako.
• Ama-apharethasi.
• Imigwalo.
• ukwakha nokuphula iinomboro
• Amanambalayini
• ukubuyelela nokuhafula
begodu bewuhlathulula iinsombuluko zemiraro ekungeyakho.
Sombulula imiraro yokwenziwako efaka ukwabelana ngokulingana
nokubuthelela ngeenomboro ezipheleleko ukufika e-15 zifake begodu
ezineempendulo ezingafaka iinsalelo.
Ngakunye kwalokhu okulandelako.
• Ama-apharethasi.
• Imigwalo.
• Amanambalayini
Hlathulula iinsombululo
Imali Bona imali yesewula Afrika emasende 5c, 10c, 20, 50c, R1, R2; R5
Sombulula imiraro yemali inani loke netjhentjhi ukufika e- R20 namasende
ukufika emasendeni ama -20
Ukubalisisa Ukwenza ukuhlanganisa okubuyelelweko ukufika -15
ngokusebenzisa kunye kokulandelako
• Ama-apharethasi
• Imigwalo.
• ukwakha nokuphula iinomboro.
• ukubuyelela nokuhafula.
Ukutlola umutjho wenomboro ngokusebenzisa +,=
AMAPHETHENI, Amaphetheni Qedelela ukulandelana kweenomboro zokubala.
AMAFANKTJHINI NE- weeNomboro • ngaku- 1 ubalela emuva ukusuka 80 isib. 80, 79, 78, __, __, __, __, 73,
ALJIBHRA ___; __; 70.
• ngali – 10 ukufika 80 isib.10, 20, 30, __, __,__, __, __,
• nga-5 isib .5, 10, 15, __, __, 30, __, __.45, __, __, 60, __, __, __, 80
ISIKHALA NOBUJAMO isimethri Ukubona begodu ugwale umuda wesimethri wamajamo we 2D
(JIYOMETHRI) weJiyomethri nekungasiyo yejiyomethri yobujamo.
UKUMEDA Ubude Linganisa, meda, madanisa, hlela,begodu bewurekhode ubude
ngokusebenzisa isimedo esingakahleleki isib.izandla, igadango, ubude
bepensela, izinto zokubala njll.
UKUPHATHA IDATHA Idatha Ukuphendula imibuzo ngedatha yephikthografi
500 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yoku-1 iThemu yesi-4: isibonelo sokuhlola Ithaski yoku-1
ISIGABA SOKUMU-
ISIHLOKO UMBANDELA WESILINGANISO
METHWE
IINOMBORO, AMA- Umqondonomboro Ukubala izinto ezi-50 ngokuthembeka, utjho amagama ngokulandelana..
OPHARETJHINI
NOBUDLELWANA Utjho bonyana ngiliphi ibuthelelo lezinto ezinengi nofana ezimbalwa
lapho amabuthelelo ama-20 nofana ambalwa.
Ukufunda amatshwayo wenomboro kufikela ema-80
Ukusombulula Ukusombulula imiraro yamagama asebujameni okufaka, ukuhlanganisa,
imiraro ukukhupha okuneempendulo ukufika ku-20.
Ukusebenzisa khunye kwalokhu okulandlayo
• Ama-apharethasi
• Imigwalo
• ukwakha nokuphula iinomboro
• Amanambalayini
• ukubuyelela noku hafula
Ukuhlathulula iinsombululo zemiraro okungezabo
Ukubalisisa Ukuhlanganisa ukufika ngo-20
Ngokusebenzisa kunye kwalokhu okulandelako
• Ama-apharethasi.
• imigwalo
• Ukwakha nokuphula iinomboro
• Anambalayini
• Ukubuyelela nokuhafula.
Ukutlola umutjho ngokusebenzisa +, =
Susa ukufika ema-20 nofana ngaphasi
Ngokusebenzisa kunye kwalokhu.
• Ama-apharethasi
• Imigwalo
• Ukwakha nokuphula iinomboro
• Amanambalayini
• Ukubuyelele noku hafula
Ukutlola umutjho ngokusebenzisa +, =
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kokubala iinomboro
AMAFANKTJHINI NE- weenmboro • Ngaku-1 isib. Ubalela emuva ukusuka 80: 80, 79, 78, __, __, __, 74,
ALJIBHRA __, __, 71.
• Ngaku-2 isib. 64, 66, 68, __, __, __,76; __, 80
ISIKHALA NOBUJAMO Amajamo Ukubona begodu utjho.
(JIYOMETHRI) abusobubili (2-D) • Iindulungu
• Uncantathu
• Iinkwere
Ukuhlela ngokuya ngokuthi ziyindulungu nofana mahlangothi
anqophileko.
UKUMEDA Ubudisi/imasi • Ukulinganisa,ukumeda,ukumadanisa, ukuhlela nokurekhoda ubudisi
ngesimedo esingakahleleki isib.iintina,amabhlogo njll.
• Ukusebenzisa ilimi ukukhuluma ngokumadanisa isib.elula,ebudisi,ebul
udlana,ebudisana njll.
CAPS 501
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yoku-1 iThemu yesi-4: isibonelo sokuhlola ithaski 2
ISIGABA SOKUMU-
ISIHLOKO UMBANDELA WESILINGANISO
METHWEKO
IINOMBORO, AMA- Umqondonomboro Ukubala ukuya phambili nga-10, 5, 2 ukuya e-100
OPHARETJHINI Ukusebenzisa ilimi ukuhlathulula, ukukhambelena kobukhulu beenomboro
NOBUDLELWANA ngaphambili, nangemuva nahlangana
Ukumadanisa ubukhulu beenomboro ukufika ema-20 ngokusebenzisa ilimi
isib. Khulu kuna, kumbalwa kuna, njll.
Ukuhlela iinomboro ukusuka keyoku-1- 20 ukusuka kwekulu ukuya
kwencani
Ungahlukanisa iinomboro ukusuka -11-20 kube 11- 10 kube 10+ imivo
,isib. 14=10+ 4
Ukufunda amatshwayo wenomboro ukufika e- 100.
Ukutlola amatshwayo wenomboro ukufika ku-20
Ukurarulula imibala Ukurarulula imiraro yamagama kummongo ofaka hlangana ukubala
okubuyelelwako neempendulo ukufika ema -20 Ngokusebenzisa kunye
kwalokhu okulandelako
• Ama apharethasi
• imigwalo
• ukwakha nokuhlephula iinomboro
• Amanambalayini
ukubuyelela kabili nokuhafula begodu nokuhlathulula isisombululo semiraro
Ukusombulula imiraro yokwenziwako efaka hlangana ukwabelana
ngokulinganako nokubuthelela ngeenomboro ezipheleleko ukuya ema-20
eneempendulo ezingafaka iinsalela ngalokhu okulandelako:
• Ama-apharathasi
• imigwalo
• Amanambalayini
Ukuhlathulula iinsombululo
Ukukhumbula iinhlavu zemali yeSewula Afrika 5c, 10c, 20c, 50c, R1,R2,R5
Imali Ukusombulula imiraro yemali ukufaka hlangana amanani begodu
netjhentjhi ukufika ema-R20 begodu nangamasende ukuya
emasendeni ema-50c
Ukwenza ukuhlanganisa okubuyabuyelelako ukufika ema- 20 usebenzisa
Ukubalisisa / kunye kwalokhu
Ukubala • i-apharathasi
• imigwalo
• Ukwakha nokuphula iinomboro
• amanambalayini
• Ukubuyelelakabili begodu nokuqunta phakathi
Ukutlola umutjho weenomboro ngokusebenzisa +, =
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro zokubala
AMAFANKTJHINI NE- wenomboro • Ngabo kunye ukuya emuva, isib. 99, 98, __, 96, __, __, __, 92, ___;
ALJIBHRA __; 89.
• ngalitjhumi ukuya e-100 , isib.10, 20, 30, __, __, __, __, __, 90, __.
ngakuhlanu isib. 20, 25, 30, __, __.45, __, __, 60, __, 70__, __,__, 90
ISIKHALA NOBUJAMO Ubujamo Ukusebenzisa ilimi lobujamo ukulandela iinkombatjhuba ukukhamba
(JIYOMETHRI) uzombeleza ikumba yokufundela
ukumetjhisa ukuqalela okuhlukahlukeneko kwento efaneleko
UKUMEDA Isikhathi Ukwazi amalanga weveke
Ukwazi iinyanga zonyaka
UKUPHATHA IDATHA Idatha Ukuphendula imibuzo ngedatha esegrafini yeenthombe
502 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 iThemu yoku-1: Ukuhlola 1
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondo Ukubuthelela nokubala ukufika ezintweni ezi-100
OPHARETJHINI wenomboro
NOBUDLELWANA Ukumadanisa nokuhlela iinomboro ezipheleleko ukufika ema-25
Ukuhlahlela iinomboro ezinamadijithi amabili ukufika ema-25 ngamatjhumi
begodu nangakunye, isib. 23= 20+3
Ukufunda nokutlola amatshwayo weenomboro ukusuka eli-0 ukuya e-100
Ukurarulula Ukurarulula imiraro yamagama ebujameni okufaka hlangana ukuhlanganisa
imiraro , ukukhupha ,neempendulo ukufika ema -20 usebenzisa kunye kwalokhu
okulandelako
• ama-apharathasi
• imigwalo
• ukwakha nokuphula iinomboro
• amanabalayini
ukubuyelela kabili nokuqunta phakathi begodu uhlathulule iinsombululo zakho
semiraro
Imali Ukukhumbula iinhlavu zemali yeSewula Afrika 5c, 10c, 20c, 50c, R1,R2,R5
begodu nemali yamaphepha R10, R20, R50
Ukusombulula imiraro yemali ukufaka hlangana amanani begodu netjhentjhi
ukufika ema-R20 begodu nangamasende ukuya emasendeni ema-50c
Ukubala Ukwenza ukuhlanganisa ukufika ema- 20 ngokusebenzisa kunye kokulandelako
• ama-apharathasi
• imigwalo
• Ukwakha nokuphula iinomboro
• amanambalayini
• ukubuyelela kabili nokuqunta phakathi
Ukutlola umutjho weenomboro ngokusebenzisa +, =
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro zokubala ukuya phambili begodu
AMAFANKTJHINI NE- weenomboro nokuya emuva
ALJIBHRA • Ngabokunye ukusuka ku-0- 100, isib. 99, 98, 97 __, __, __,93, __, 91, 90.
• ngamatjhumi ukusuka ku-0 -i00 , isib.10, 20, 30, __, __, __, 70__, __, 100.
• ngabokubili ukusuka ku -0-100, isib. 80 82, 84, __, __, 90, _, __, __, ___,
100
ISIKHALA NOBUJAMO Izintho ezi ukukhumbula nokutjho
(JIYOMETHRI) (3-D) • Amajamo webholo ( iindulungu)
• Amajamo webhoksi( amaphrizimu)
Amajamo we Ukukhumbula nokutjho
(2-D) iindulungu, aobncantathu, iinkwere begodu naboncamane
Isikhathi Ukutjho /ukutjela isikhathi ewatjhini ye-analogo ngama-iri
UKUMEDA Ubude Linganisa, meda, madanisa, hlela begodu urekhode ubude, ububanzi nofana
ukuphakama ngamamitha
CAPS 503
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 iThemu yesi-2: Ukuhlola 1
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondo wenomboro Ukubala iinthombe zezinto ezibuthelelweko ukufika e-150
OPHARETJHINI
NOBUDLELWANA ukumadanisa iinomboro ukufika e-50
Ukufunda nokutlola iinomboro kusuka e-0- 150
ukubala uye phambili nemuva nga-10, 2, 5 ukuya e- 150
Ukurarulula imiraro Ukurarulula imiraro ephathekako okufaka hlangana ukwabelana
ngokulinganako begodu nokubuthelela ngeenomboro ezipheleleko
ukufika e-50 usebenzisa kunye kokulandelako
• ama-apharathasi
• imigwalo
• ukwakha nokphula iinomboro
• amanambalayini
• ukubuyelela kabili nokuqunta phakathi begodu
nokuhlathulula iinsombululo zemiraro
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro zokubala ukuya phambili
AMAFANKTJHINI NE- weenomboro begodu nokuya emuva ngabo kunye ukusukela eli-0 -150
ALJIBHRA isib.131,132,133,_,_,_,137,_,_,_,14111 in ones from 0 - 150 e.g.131,
132, 133, __, __, __, 137, __, ___, ___, 141
• Ngamatjhumi hlangana ne-0 &200 isib.150, 140, 130, __, __, 100,
__, __.70, __, __, 40
• Ukubala ngabokubili isib. 150, 148, 146, 144, __, __, 138, __, __,
132.
• Ukubala ngabo kuhlanu ukusuka e-0 – 150 isib. 105, 110, 115, __,
__, __, 135, __, __, 150
Kopulula ,ngezelala begodu uhlathululeamphetheni lapho amajamo
ahlukahlukeneko asetjenziswa khona ukwenza isiqhema ,kodwana iin
qhema zamajamo zibuyelelwa ngendlela efana poro
UKUMEDA Isikhathi Yitjho /tjela isikhathi ewatjhini ye-analogo ngama-iri begodu
nangeenquntu zama-iri
504 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 iThemu yesi-2: Ukuhlola 2
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Imqondo Bala uye phambili ngaku- 3, 4
OPHARETJHINI nomboro
NOBUDLELWANA
Ukurarulula imiraro Ukurarulula nokuhlathulula iinsombululo zemirao efaka hlangana
ukwabelena ngokulingana okurholela emafraktjhini
Amafraktjhini
Ukukhumbula nokusebenzisa amahafu ,kukothathu,a makotara, kokuhlanu
ebujameni obujayelekileko
Ukukhumbula amafraktjhini asebujameni bamadayagramu
Ukutlola amafraktjhini ngendlela yehafu yi-1, ku-1 kokuthathu, ,njll
Ukuhlanganisa ukufika ema-50 usebenzisa kunye kokulandelako
Ukubala Ukukhupha ukufika ema-50 usebenzisa kunye kokulandelako
• ama-apharathasi
• imigwalo
• ukwakha nokphula iinomboro
• amanambalayini
• ukubuyelela kabili nokuqunta phakathi
Ukutlola umutjho weenomboro ngokusebenzisa +,=
Ukukhupha ukufika ema-50 usebenzisa kunye kokulandelako
• ama-apharathasi
• imigwalo
• ukwakha nokphula iinomboro
• amanambalayini
• ukubuyelela kabili nokuqunta phakathi
Ukutlola umutjho wenomboro uberegisa _ ,=
AMAPHETHENI, Amaphetheni ukuqedelela ukulandelana kweenomboro hlangana kwe-0 ne 150
AMAFANKTJHINI NE- weenomboro • ukubala ngokunye
ALJIBHRA
• ukubala ngabokune, isib..4, 8, 12 __, __, 24, __, 32, __, __, __, 48
• . ukubala ngabokuthathu ,isib. 3, 6, 9, __, __,21, __, __,__, 33, 36.
UKUMEDA Ubungako/imasi Linganisa, meda, madanisa, hlela begodu ukurekhode imasi
ngokusebenzisa iimedo ezingakahleleki begodu nesikala sokudzimelela ,
isib. Amablogo, iintini, njll
ukuhlela imikhiqizo lapho imasi itlolwe ngamakhilogremu
CAPS 505
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 iThemu yesi-3: Ukuhlola 1
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondonomboro Ubala iinthombe zeenqhema zezinto ukufika ema-180
OPHARETJHINI
NOBUDLELWANA Umadanisa abuye ahlele iinomboro ukufikela ema-75
Ufunda atlole amatshwayo weenomboro ukufikela ema-180
Ubalela phambili nasemuva ngaku-2, ngali-10, ngaku 5 hlangana ne-0
nama-180
Uphula iinomboro ezinamdijithi amabili ukufikela ema-75 ngalitjhumi
nangakunye isib. 48=40 + 8
Rarulula Imiraro Urarulula imibuzo yemitjho ngobujamo okubandakanya
ukuhlanganyela okubuyelelwako erholela ekubuyabuyeleleni ukufika
ema-40
• aberegisa kunye kokulandelako
• iinsetjenziswa
• imigwalo
• ukwakha nokuphula iinomboro
• inambalayini
ukubuyelela kabili nokuqunta begodu ahlathulule isisombululo sakhe
emirarweni
Ukubalisisa Angabuyabuyelela iinomboro ukusukela kwe-1 ukuya e-10 ngaku-5, 4
uberegisa okulandelako
• iinsetjenziswa
• imigwalo
• inambalayini
Tlola umutjho weenomboro usebenzisa u- x, =
AMAPHETHENI, Iphetheni yeenomboro Uqedelela ukulandelana kweenomboro ze
AMAFANKTJHINI NE- • Ukubala uye phambili nasemuva ngakunye hlangana kwe-0 nama-
ALJIBHRA 180
• 180, 170, 160, __, __, 120, __,__ 90,
• ukubala ngakubili isib. 150, 152, 154, __, 156, __, 160, __, __,
166
• ukubala ngakuhlanu ukusuka eli-0 ukuya ema – 150 isib.120, 125,
130, 135, __, __, __, 155, __, __, 170, __, 180
ISIKHALA NOBUJAMO Ubujamo Usebenzisa ilimi yobujamo ukulandela ikombatjhuba
(JIYOMETHRI) ukukhambakhamba ngekombeni
506 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 iThemu yesi-3: Ukuhlola 2
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondonomboro Ubalela phambili ngaku-4, nangaku-3
OPHARETJHINI
NOBUDLELWANA Rarulula Imiraro Urarulula abuye ahlathulule iinsombululo zemibuzo ebandakanya
ukuhlukaniselana ngokulinganako okurholela emafraktjhinini
Amafraktjhini Ulemuka asebenzise iinquntu, ubuthathu,iinkota, kokuhlanu ebujameni
obujayelekile
Ulemuka amafraktjhini ngendlela yemifanekiso
Utlola amafraktjhini ngendlela yesiquntu 1, isithathu si-1 njll.
AMAPHETHENI, Amaphetheni Uqedelela ukulandelana kweenomboro hlangana kwe-0 nama-180
AMAFANKTJHINI NE- weenomboro • ukubala ngakunye
ALJIBHRA
• ukubala ngakune isib.
104,108, 112 __, __, 124, __, 132, __, __, __, 148
• ukubala ngakuthathu isib.
103, 106, 109, __, __,121, __, __,__, 133, 136.
Amaphetheni Ukhopha, angezelele begodu ahlathulule amaphetheni wejeomethri lapho
wejiyomethri kuvela khona ubujamo obufanako, kodwana inani lobujamo ngabunye
buyangezeleleka nofana buphunguleke ngendlela ejayelekile.
ISIKHALA NOBUJAMO Ubujamo Ukumetjhisa imibono ehlukahlukeneko yezinto ezifanako
(JIYOMETHRI)
Ubujamo Ulemuka atjho amabizoi indulungu, aboncantathu, iinkwere, aboncamane
obubusobubili
Uhlukanisa ubujamo ngamahlangothi athe thwi nalawo anamahlangothi
(2-D) ayindulungu
UKUMEDA Umthamo Ulinganisa, meda, madanisa, hlela begodu urekhode umthamo
wesimumathi ngokusebenzisa iimedo ezingakahleleki isib. Iingobho
neenkomitji
Isikhathi Ufunda isikhathi sama-analogo nge-iri, ngesiquntu se-iri, ngekotara ye-iri
Usebenzisa ikhalenda ukubala ubude besikhathi ngamalanga nofana
ngeenveke
UKUPHATHA IDATHA Idatha Wakha igrafu yesithombe ngephepheni elinamabhogo nakanikelwa idatha
CAPS 507
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 iThemu yesi-4: Ukuhlola 1
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondonomboro Ubala iinthombe zezinto ezingeenqhemeni ukjufikela ema-200
OPHARETJHINI
NOBUDLELWANA Uhlela amadanise iinomboro ukufikela ema-99
Rarula Imiraro Urarulula imibuzo yemitjho ngebujameni obuhlanganisa ukwenza iinqhema
nofana ukuhlukaniselana ukufikela ema-99 nezipendulo ezifaka ukusalela e
• aberegisa kunye kokulandelako
• iinsetjenziswa
• imigwalo
• ukwakha nokuphula iinomboro
• inambalayini
ukubuyelela kabili nokuqunta begodu ahlathulule isisombululo sakhe
emirarweni
Imali Ulemuka imali yangeSewula Afrika ezinhlamvu zama -5c, 10c, 20c, 50c,
R1, R2, R5nemali yamaphepha R10, R20, R50
Urarulula imiraro yemali efaka amanani netjhentji ukya ema-99 begodu
namasende afika ema-95c wamasende
AMAPHETHENI, Amaphetheni Uqedelela ukulandelana kweenomboro zokubalela emuva naphambili
AMAFANKTJHINI NE- weenomboro ngakunye hlangana kwe-0 nama-200
ALJIBHRA
ngalitjhumi hlangana kwe-0 nama-200 isib. 130, 140, 150, -__, ___, ___,
__, 200
ISIKHALA NOBUJAMO Obubusobubili Ulemuka atjho amagama
(JIYOMETHRI) (2-D) • iindulungu
• aboncantathu
• iinkwere
• Aboncamane
Uhlukanisa ngokuya ngokuthi ihlangothi lithwi nofana liyindulungu
UKUMEDA Isikhathi Usebenisa iwatjhi ukubala ubude besikhathi ukudlula ama-iri, ama-iri
nesiquntu nofana ikotara yama-iri aberegisa kunye kokulandelako
• iinsetjenziswa
• imigwalo
• ukwakha nokuphula iinomboro
• inambalayini
• ukubuyelela kabili nokuqunta
begodu ahlathulule isisombululo sakhe emirarweni
508 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 IThemu yesi-4: Ukuhlola 2
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondonomboro. Ukubala uye phambili nemuva ngaku 2, 5, ukufika ema-200
OPHARETJHINI
NOBUDLELWANA. Ukufunda nokutlola amatshwayo weenomboro ukufoka ema200
Ukubalisisa Ukwenza ukubalisisa ukufika ema 99
Ngokusebenzisa kunye kwalokhu okulandelako
• ama-apharathasi
• imigwalo
• ukwakha nokuphula iinomboro
• amanamba layini
• ukubuyelela kabili nokuqunta phakathi
Ukutlola umutjho wenomboro ngokusebenzisa +, =
Ukususa ukufika ema 99
Ngokusebenzisa kunye kwalokhu okulandelako
• ama-apharathasi
• imigwalo
• ukwakha nokuphula iinomboro
• amanamba layini
• ukubuyelela kabili nokuqunta phakathi
Ukutlola umutjho wenomboro ngokusebenzisa -, =
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro hlangana kwe 0 nama 200
AMAFANKTJHINI NE- weenomboro • ukubala ngakubili isib. 160, 162, 164, _, 166,_, 170, _, _, 176,_, 180
ALJIBHRA
• ukubala ngakuhlanu kusukela e 0-200 isib. 160, 165, 170,
_,_,_,190, _, 200
UKUPHATHA IDATHA Idatha Ukuphendula imibuzo ngedatha esesithombeni
CAPS 509
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-2 IThemu yesi-4: Ukuhlola 3
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO ESISQUNTU.
METHWEKO
IINOMBORO, AMA- Imiqondonomboro Balela phambili ngaku 4,3
OPHARETJHINI
NOBUDLELWANA Rarulula imiraro. Ukurarulula imibuzo yemitjho ebujameni obufaka ukuhlanganisa
okubuyelelweko ekurholela ekubuyebuyeleleni ngeempendulo ukufika ema-
50.
• Ngokusebenzisa kunye kwalokhu okulandelako.
• iintlabagelo
• imigwalo
• ukwakha nokuphula iinomboro
• inambalayini
Ukubuyelela kabili nokuqunta begodu ahlathulule iinsombululo zakhe
emirarweni.
Ukubala Angabuyebuyelela iinomboro 1-10 ngaku 3
ngokusebenzisa kunye kwalokhu okulandelako.
• iintlabagelo
• imigwalo
• inambalayini
• ukubuyelela kabili
Tlola imitjho embalwa ngokusebenzisa x,=
AMAPHETHENI, Amaphetheni Qedelela ukulamana kweenomboro ezihlangana kwe 0 ne-180
AMAFANKTJHINI NE- weenomboro • Bala ngakunye.
ALJIBHRA
• Balela emuva ngakune Isib .48,44, 40 __, __, 28, __, __, 16, __, __, 0
• Balela emuva ngakuthathu.Isib . 36, 33, 30, __, __, 21, 18, __,__, 9, __,
__, 0.
ISIKHALA NOBUJAMO Abobusontathu Ukulemuka namabizo
(JIYOMETHRI) (3-D) • ubujamo bebholo(ndulungu)
• Ubujamo bebhoksi (phrizimu)
• Isilinda
Ukuhlela izinto ukuya ngalezo ezigedekako nalezo ezitjhelelako
Isimethri Ukulemuka nokugwala imida yesimethri yobujamo obubusobubili
beJiyomethri nalezo ezingasizo zeJiyomethri.
UKUMEDA Umthamo/ Ivolumu Ukuhlela imikhiqizo yangamalanga yemithamo etlolwe phezu kwazo
ngamalitha.
Ukufunda umthamo wamalitha eenthombeni ezilinganiswe ngamajege.
510 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 IThemu yoku-1: Ukuhlola 1
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO ESISQUNTU
METHWEKO
IINOMBORO,AMA- umqondonomboro Ukukhetha nokubala ukufika ezintweni ezima-200
OPHARETJHINI Ukumadanisa nokuhlela iinomboro ngokupheleleko ukufika ema-99
NOBUDLELWANA
Ukufunda nokutlola amatshwayo weenomboro ukusuka e-0 ukufika ema-500.
Ukuhlahlela iinomboro zamadijithi amabili ukufika ema-99 ngalisumi begodu
ngakunye Isib. 78 = 70 + 8
Rarulula imibuzo Rarulula imibuzo yemitjho ebujameni ebufaka ukuhlanganisa , ukukhupha
ngeempendulo ukufika ema-99 ngokusebenzisa kunye kwalokhu
okulandelako.
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta/nokuhafula
• Ukutjhideza e-10
Begodu ahlathulule iinsombululo zakhe emibuzweni.
Imali Rarulula imibuzo yemali efaka hlangana inani loke begodu netjhentjhi
yamaranda namasende.
Ukubala Ukubala ukufika ema-99 ngokusebenzisa kunye kwalokhu okulandelako.
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta.
• Ukutjhideza e-10
Tlola umutjho wenomboro ngokusebenzisa +, =
Ukukhupha ukufika ema-99 ngokusebenzisa kunye kwalokhu okulandelako.
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta.
• Ukutjhideza e-10
Tlola umutjho wenomboro ngokusebenzisa +, =
AMAPHETHENI, Amaphetheni Qedelela ukulamana kweenomboro kukubala uye phambili nemuva.
AMAFANKTJHINI NE- weenomboro • Ngakunye hlangana kwe 0 nama 200 Isib 199,1 98, 197, __, __, __, 13,
ALJIBHRA __, 191, 190
• Ngalisumi hlangana kwe 0 nama 200 Isib. 110, 120, 130, __, __, __,
170__, __, 200
• Ngamakhulu hlangana kwe 0 nama 500 Isib 100, 200, 300, __, __,
• Ngakuhlanu hlangana kwe 0 nama 200 Isib 150, 155, 160, __, __, __, 180,
__, __, 195, __
• Ngakubili hlangana kwe 0 nama 200 Isib 180,182, 184, __, __, 190, _, __,
__, ___, 200
ISIKHALA NOBUJAMO Abobusobubili Ukulemuka nokunikela amabizo
(JIYOMETHRI) (2-D) Iindulungu, aboncantathu, iinkwere naboncamane.
Ukuhlela ubujamo bezinto lezo ezinamahlangothi athwi kunye nalezo
ezizombelezako.
UKUMEDA Isikhathi Ukufunda amalanga ekhalendeni
Ukutjela isikhathi ewatjhini ye-analogo ngama iri,ngeenquntu ze- iri
nangamakota we-iri
Umthamo Ukulinganisa, isilinganiso, ukumadanisa,ukuhlela nokurekhoda imithamo
yeemumathi ngokusebenzisa iinlinganiso ezingakahleleki Isib isigobho
nekomitji.
Ukuhlela imikhiqizo yangamalanga leyo imithamo yayo itlolwe
nagamamililitha phezu kwayo.
CAPS 511
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 IThemu yesi-2: Ukuhlola 1
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO ESISQUNTU
METHWEKO
IINOMBORO, AMA- Umqondonomboro Ukubala iinthombe zezinto ezikhetheke ngeenqhema (Isib. iinqhema nga-
OPHARETJHINI 10,25,50 namkha 100) ukufika ema 500
NOBUDLELWANA
Ukuhlela nokumadanisa iinomboro ukufika ema 500
Ukufunda nokutlola iinomboro ukusuka e 0 – 1 000
Rarulula imibuzo Uku rarulula imibuzo ebonakalako efaka hlangana ukwabelana
ngokulingana nokwenza iinqhema zeenomboro ngokupheleleko ukufika
ema 75 ngokusebenzisa kunye kwalokhu okulandelako.
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta.
• Ukutjhideza e-10
Begodu ahlathulule iinsombululo zakhe zemibuzo
Ukubala Hlukanisa iinomboro ema 50 ngaku 2,5,10
AMAPHETHENI, Amaphetheni Qedelela ukulandelana kweenomboro kokubalela phambili nemuva
AMAFANKTJHINI NE- weenomboro • Ngakunye hlangana kwe 0 nama 500 Isib 389, 399, 400, , __, __, __, 404,
ALJIBHRA __, ___, ___, 408
• Ngalisumi hlangana kwe 0 nama 500 Isib 300, 310, 320, __, __, 350, __,
__.370, __, __, 400
• Ngamakhulu hlangana kwe 0 ne 1000 Isib 1000, 900, 800, __, __, 500,
__, __.200, __, 0
ISIKHALA NOBUJAMO Izinto Ukulemuka nokunikela amabizo
(JIYOMETHRI) Ezibusontathu • ubujamo bebholo (indulungu)
(3-D) • Ubujamo bebhoksi (phrizimu)
• Isilinda
Ukuhlela izinto ukuya ngalezo ezizombelezako begodu nalezo ezinebala
eliparaleleko.
UKUMEDA Ubude Ukulinganisa, isilinganiso ,ukuhlela nokumadanisa ubude, ubungako
nobubanzi i ngokusebenzisa iinlinganiso ezingakahleleki
Ukulinganisa ,isilinganiso,ukuhlela nokumadanisa ubude ngosebenzisa
amamitha.
512 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 iThemu yesi-2: Ukuhlola 2
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO SESIQUNTU
METHWEKO
IINOMBORO, AMA- Umqomdonomboro Balela phambili nemuva ngaku 2,4 namkha ku-3 ukufika ema-500
OPHARETJHINI
NOBUDLELWANA Ukubala Ukwenza ukubala ukufika ema-400
ngokusebenzisa kunye kwalokhu okulandelako
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta/nokuhafula
• Ukutjhideza e-10
Tlola umutjho wenomboro ngokusebenzisa +, =
Ukukhupha ukusuka ema 400 namkha okumbalwa ngokusebenzisa kunye
kwalokhu
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta/nokuhafula.
• rounding off to 10
Tlola umutjho wenomboro ngokusebenzisa _, =
AMAPHETHENI, Amaphetheni Qedelela ukulandelana kweenomboro
AMAFANKTJHINI NE- weenomboro • kokubala ngakubili hlangana kwe 0 nama-500 Isib. 450, 448, 446, 444,
ALJIBHRA __, __, 438, __, __, 432.
• Ngokubala ngakune hlangana kwe 0 nama 500 Isib. 404, 408, 412 __,
__, 424, __, 432, __, __, __, 448
• Ngokubala ngakuthathu kwe 0 nama 500 Isib. 403,406, 409, __,
__,421, __, __,__, 433, 436.
Amaphetheni Ukukopa , ukungezelela nokuhlathulula amaphetheni wobujamo
weJiyomethri obuhlukeneko ayasetjenziswa ukwenza iinqhema ,kodwana iinqhema
zobujamo ziyabuyelelwa ngendlela efanako.
IGreyidi yesi-3 iThemu yesi-2: Ukuhlola 3
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO SESIQUNTU
METHWEKO
IINOMBORO, AMA- Umqomdonomboro Bala uye phambili ngaku 5, 50, 100, hlangana ne-0 nama-500
OPHARETJHINI Ukuphula iinomboro ezinamadijithi amathathu zibe makhulu, amatjhumi
NOBUDLELWANA. begodu nangabokunye, isib. 247= 200+40+7
Ukurarulula imiraro Ukurarulula begodu nokuhlathulula iinsombululo zemiraro efakahlangana
ukwabelana ngokulinganako okurholela emafraktjhinini.
Amafraktjhini Ukukhumbula nokusebenzisa amahafu, amakota, kobunane, kwesithathu,
kwesihlanu ebujamweni obujayelekileko.
Ukukhumbula amafraktjhini asebujamweni bedayagramu.
Ukutlola amafraktjhini ngendlela yokuthi ihafu yi-1, ku-2 kokuthathu, njll.
AMAPHETHENI, Amaphetheni Qedelela ukulandelana kweenomboro
AMAFANKTJHINI NE- weenomboro • Ukubala ngakuhlanu hlangana ne 0-500, isib. 105, 110, 115, _,_,_,135,
ALJIBHRA. _,_,150
• Ukubala ngamatjhumi amahlanu hlangana ne 0-1000, isib. 550, 600, 650,
_,_,800,_,_,_,1000
ISIKHALA NOBUJAMO Ubujamo Ukulandela indlela/ilayelo lokukhamba khamba esikolweni.
(JIYOMETHRI). nekombatjhuba Nikela indlela/ilayelo yokukhamba khamba esikolweni.
UKUMEDA Imasi Linganisa, meda, madanisa hlela ngemihlobo begodu urekhode imasi
ngokusebenzisa iimedo ezingakahleleki nesikala sokudzimelelisa isib.
Amabhlogo, iintina, njll.
Ukuhlela imikhiqizo enobudisi /imasi etlolwe ngamagremu.
CAPS 513
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 iThemu yesi-3: Ukuhlola 1
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO SESIQUNTU
METHWEKO
IINOMBORO, AMA- Umqomdonomboro Ukubala iinthombe zezinto ezibuthelelweko ukufika ema- 750 ( isib.
OPHARETJHINI Ezibuthelelwe ngama 20, 25, 50, nofana i- 100)
NOBUDLELWANA.
Ukumadanisa nokuhlela iinomboro ukufika ema-750.
Ukufunda nokutlola amatshwayo weenomboro ukufika ema-100.
Ukurarulula imiraro. Ukurarulula imiraro yamagama ebujameni okufaka hlangana
ukubuyabuyelela ukufika ema75 usebenzisa okukodwa kwalokhu
• Ukwakha nokuphula iinomboro.
• Inambalayini.
• Ukubuyelela ngakubili nokuqunta/nokuhafula
• Ukutjhideza eduze ne 10
begodu bahlathulule iinsombululo zabo zemiraro.
Ukubalisisa Bangakghona ukubuyabuyelela ngaku 2, 5, 10 ukufika enanini lama 99
ngokusebenzisa kunye kwalokhu okulandelako
• iintlabagelo / ama-apharathasi
• imigwalo
• amanambalayini
Ukutlola umutjho weenomboro ngokusebenzisa x, =
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelanakweenomboro zokubala uye phambili nemuva
AMAFANKTJHINI NE- weenomboro • ngakunye hlangana ne 0 nama 750 isb. 665, 666, 667, _ ,_, _, 671, _, _,
ALJIBHRA. _, 675, _, _, 678
• ngalitjhumi hlangana ne 0 nama 750 isib. 650, 660, 670, __, _, 700, _, _,
730, _, _, 760
• ngekhulu hlangana ne 0 ne 1000 isib. 0, 100, 200, _, _, 500, _, _, 800, _,
1000
IGreyidi yesi-3 iThemu yesi-3: Ukuhlola 2
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO SESIQUNTU
METHWEKO
IINOMBORO, AMA- Umqomdonomboro Ukubala uyephambili nemuva ngaku 2, 20, 4, 3, ukufika ema- 750
OPHARETJHINI
Ukuphula iinomboro ezinamadijithi amathathu ukufika ema750 zibe
NOBUDLELWANA.
makhulu, matjhumi, begodu nabo kunye isib. 648= 600+40+8
Ukubalisisa Bangabuyabuyelela ngaku 3, 4, ukufika enanini lama 99 ngokusebenzisa
okukodwa kwalokhu
• iintlabagelo / ama-apharathasi
• imigwalo
• amanambalayini
• ukubuyelela kabili
ukutlola umutjho weenomboro ngokusebenzisa x, +
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro zaku
AMAFANKTJHINI NE- weenomboro • ukubala ngakubili hlangana ne 0 nama750 isib. 750, 749, 748, _, _, 445,_,
ALJIBHRA. _, 742
• ukubala ngamatjhumi amabili hlangana ne 0 ne 1000 isib. 800, 820,840,
860, _, _, 920, _, _, 980
• ukubala ngakune hlangana ne 0 nama 750 isib. 704, 708, 712, _, _, 724,
_, 732, _, _, _, 748
• ukubala ngakuthathu hlangana ne 0 nama 750 isib, 630, 633, 639, 641, _,
_, 650, _, _, _, 661
Amaphetheni Ukukopulula, ukungezelela nokuhlathulula iphetheni yejiyomethri lapho
wejiyomethri kwenzeka khona ubujamo obufanako, kodwana inani lobujamo ngabunye
buyanda nofana buya ncipha ngendlela efanako
ISIKHALA NOBUJAMO Ubujamo Ukukhumbula nokutjho ngegama
(JIYOMETHRI obubusobubili 2 D Iindulungu, aboncantathu, iinkwere, naboncamane.
Ukugwala iindulungu, iinkwere, aboncamane, aboncantathu
UKUPHATHA IDATHA Idatha Yakha ibha-grafu ephepheni elinamabhlogo lokha nawunikelwe idatha.
514 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 iThemu yesi-3: Ukuhlola 3.
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO SESIQUNTU
METHWEKO
IINOMBORO, AMA- Umqomdonomboro. Ukubala uye phambili ngaku 5, 50, 25, ukufika ema- 750
OPHARETJHINI Ukurarulula imiraro Ukurarulula nokuhlathulula iinsombululo zemiraro efakahlangana
NOBUDLELWANA. ukwabelana ngokulinganako okurholela emafraktjhinini.
Amafraktjhini Ukukhumbula nokusebenzisa amahafu, amakota, kobunane, kwesithathu,
kwesithandathu, kwesihlanu ebujameni obujayelekileko
Ukukhumbula amafraktjhinio asebujamweni bedayagramu
Ukukhumbula bonyana amahafu ama 2 enza okuzeleko
Ukutlola amafraktjhini ngendlela yokuthi ihafu yi 1, kunye kokuthathu, njll.
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro
AMAFANKTJHINI NE- weenomboro • ukubala ngakuhlanu hlangana ne 0-750 isib. 705, 710, 715, _, _, _, 735,
ALJIBHRA. _, _, 750
• ukubala ngakuhlanu hlangana ne 0-1000 isib. 1000, 950, 800, _, _, 650,
_, _, _, 750
• ukubala ngamatjhumi amabili nakuhlanu hlangana ne 0-1000 iosib. 525,
550, 575, _, _, 650, _, _, _, 750
ISIKHALA NOBUJAMO Ubujamo Ukulandela indlela/ilayelo lokukhamba ukusuka endaweni enye ukuya
(JIYOMETHRI kwenye.
Ukmeda Isikhathi Ukutjho isikhathi ewatjhini ledijithali
Ukusebenzisa ikhalenda ukubala ubude besikhathi nga,malanga nofana
iimveke
IGreyidi yesi-3 iThemu yesi-4: Ukuhlola 1.
ISIGABA SOKUMU-
IINHLOKO ISILINGANISO SESIQUNTU
METHWEKO
IINOMBORO, AMA- Umqomdonomboro. Ukubala iinthombe zezinto ezibuthelelweko ukufika ema- 1000
OPHARETJHINI Ukuhlela nokumadanisa iinomboro ukufika ema -99
NOBUDLELWANA
Ukurarulula imiraro. Ukurarulula imiraro efaka hlangana ukubuthelela nofana ukwabelana
ngokulinganako ebujameni ukufika e-100 neempendulo ezifaka hlangana
iinsalela ngokusebenzisa kunye kwalokhu
• ukwakha nokuphula iinomboro
• amanamba layini
• ukubuyelela kabili nokuqunta/nokuhafula phakathi
• ukutjhideza eduze ne10
begodu nokuhlathulula iinsombululo zemiraro
Ukubalisisa . Hlukanisa iinomboro ukufika ema-99 ngaku 2, 4, 5, 10, 3
Imali Ukurarulula imiraro yemali efaka hlangana amanani netjhentjhi ngamaranda
nofana ngamasende.
AMAPHETHENI, Amaphetheni Ukuqedelela ukulandelana kweenomboro zokubalela phambili nemuva
AMAFANKTJHINI NE- weenomboro • ngakunye hlangana ne 0 ne 1000 isib. 889, 890, 891, _, _, _, 892
ALJIBHRA
• ngamatjhumi hlangana ne 0 ne 1000 isib. 1000, 990, 980, _, _, 950, _, _,
920, _, _, 890
Ukumeda Isikhathi Sebenzisa iwatjhi ukubala ubude besikhathi esidlulako ngama iri
namaminithi
CAPS 515
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 iThemu yesi-4: Ukuhlola 2
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- Umqondonomboro Ubala uyaphambili nemuva ngaku-2,ngaku-4, ngaku 3, ukuya e-1000
OPHARETJHINI N
Ufunda abuye atlole amatshwayo weenomboro ukufikela e-1 000
OBUDLELWANA ukubala Ukuhlanganisa ukufika e-999 uberegisa okunye kwalokhu
• ukwakha nokuhlephula iinomboro
• inamabalayini
• Ukubuyelela kabili nokuqunta
• Ukutjhideza e-10
Ukutlola umutjho wenomboro +,=
Ukhupha kunanoma ngiyiphi inomboro ema-999 nofana ngaphasi
aberegisa kunye kwalokhu okulandelako
• Ukwakha nokuphula iinomboro
• Inamabalayini
• Ukubuyelela kabili nokuqunta
• Ukutjhideza e-10
utlola inomboro yomutjho aberegisa -, =
AMAPHETHENI, Amaphetheni Uqedelela ukulandelana kweenomboro ko
AMAFANKTJHINI NE- weenomboro • Ukubala ngakubili hlangana kwe- 0 ne-1 000 e.g. 1000, 998, 996, __,
ALJIBHRA __, 990, __, __, 984
• Ukubala ngakune hlangana kwe- 0 ne-1 000 e.g. 840, 844, 852 __, __,
864, __, 872, __, __, __, 894
• Ukubala ngakuthathu hlangana kwe- 0 ne-1 000 e.g. 960,963, 966, 969,
971,
• __, __,980, __, __,__, 691
ISIKHALA NOBUJAMO Isimethri Ulemuka begodu agwale imida yesimethri ngobubusobubili bejeometri
(JIYOMETHRI) nobujamo obungasibo bejeomethri
UKUPHATHA IDATHA Idatha Uphendula imibuzo ngedatha ngamagrafu weenthombe
516 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
IGreyidi yesi-3 IThemu yesi-4: Ukuhlola 3
ISIGABA SOKUMU-
ISIHLOKO ISILINGANISO SESIQUNTO
METHWEKO
IINOMBORO, AMA- umqondonomboro Ubalela phambili nga- 5s, 50s, 25s hlangana kwe-0 ne-1 000
OPHARETJHINI Ukurarulula Urarulula imibuzo yemitjho ngobujamo okubandakanya ukuhlanganyela
NOBUDLELWANA imiraro okubuyelelwako erholela ekubuyabuyeleleni ngeenpendulo ezifika ema-50
• iinsetjenziswa
• imigwalo
• ukwakha nokuhlephula iinomboro
• inamabalayini
• ukubuyelela kabili
begodu ahlathulule isisombululo sakhe emirarweni
Ukubala Angabuyabuyelela ngantathu ukufikela ema-99 uberegisa kunye
kokulandelako
• iinsetjenziswa
• imigwalo
• inamabalayini
• ukubuyelela kabili
utlola inomboro yomutjho aberegisa x, =
AMAPHETHENI, Amaphetheni Uqedelela ukulandelana kweenomboro
AMAFANKTJHINI NE- weenomboro • ukubala ngakuhlanu hlangana kwe- 0 – 1000 e.g. 1 000, 995, 990, 985, __,
ALJIBHRA __, __, 965, __, __, 950
• ukubala ngamasumi amahlanu hlangana kwe- 0 – 1000 isib.600, 650, 700,
__, __, 850, __, __, __,
• ukubala ngamasumi amahlanu hlangana kwe- 0 – 1000 isib.1 000, 975,
950, __, __, 875, __, __, __, 775
ISIKHALA NOBUJAMO Abobusontathu Ulemuka atjho negama
(JIYOMETHRI) (3-D) • ubujamo bebholo (iindulungu)
• ubujamo obusabhoksi
• amasilinda
• umgolojo
• iinkurwana
Uhlukanisa izinto ukuya ngalezi eziparaleleko nalezo ezinobujamo
obuzombelezako
Ufanisa ubujamo obubusobubili (2-D) obenza nengaphezulu eliparaleleko
ezintweni ezibusontathu (3-D) ezitjhiwo ngaphezulu
UKUMEDA Umthamo Ufunda umthamo ngamalitha eenthombeni zamajege wokumeda
Ufunda umthamo ngamamilimitha enthombeni zamajege wokumeda
CAPS 517
ISIGABA ESISISEKELO AMAGREYIDI 1-3
518 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
ISIGABA ESISISEKELO AMAGREYIDI 1-3
CAPS 519
ISIGABA ESISISEKELO AMAGREYIDI 1-3
520 ISITATIMENDE SOMTHETHO-KAMBISO WEKHARIKHYULAMU NOKUHLOLA (TTKN)
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