CAPS MATHS ISIZULU GR 1-3 FS.pdf

National Curriculum Statement (NCS) ISIZULU MATHEMATICS Curriculum and Assessment Policy Statement Foundation Phase Grades 1-3    

Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola IBANGA 1-3 Izibalo CAPS

Izibalo IBANGA 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: 978-1-4315-0450-3 Design and Layout by: Ndabase Printing Solution Printed by: Government Printing Works Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 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) to produce this document. From 2012 the two 2002 curricula, 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 accordingly replaces the Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines with the (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

Izibalo IBANGA 1-3 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 OKUMUMETHWE ISIGABA SESI – 2: ANCAZELO, IZINHLOSO, IMAKHONO NOKUQUKETHWE .................................. 9 2.1 Isingeniso ......................................................................................................................................................9 2.2 Ziyini izibalo. ...................................................................................................................................................9 2.3 Imiphumela eqondile .....................................................................................................................................9 2.4 Amakhono aqondile......................................................................................................................................10 2.5 Izingxenye zolwazi okugxilwe kulo ............................................................................................................10 2.6 Isisindo sezingxenye zolwazi. .....................................................................................................................12 2.7 Izibalo emabangeni aphansi........................................................................................................................12 2.7.1 Imigomo ephakanyisiwe yokuphatha ikilasi .........................................................................................12 2.7.2 Abafundi abanezingqinamba ekufundeni izibalo. .................................................................................14 2.7.3 Izibalo zekhanda...................................................................................................................................15 2.8 Ibanga R ....................................................................................................................................................15 2.9 Izinsizakufundisa ezinconyiwe kumabanga aphansi ekilasini lezibalo...................................................18 ISIGABA SESI – 3: UKUCACISA OKUQUKETHWE NOKUQONDWE NGQO..................................... 19 3.1 Isingeniso 19 3.2 Okuqukethwe okuqondwe ngqo okukhombisa inqubekela phambili .....................................................19 • Izinombolo, izimpawu kanye nobudlelwano bazo......................................................................................20 • Amaphethini, ukuxhumanakanye ne-aljebhra............................................................................................29 • Indawo nesimo (ijiyometri).........................................................................................................................30 • Isilinganiso................................................................................................................................................. 34 • Ukuqokelelwa kolwazi lwezibalo................................................................................................................ 40 3.3 Ukucacisa okuqukethwa..............................................................................................................................42 3.4 Isivinini nokulandelanisa okuqukethwe. ....................................................................................................43 3.4.1 Ibanga 1 ulwazi jikelele ngethemu........................................................................................................46 3.4.2 Ulwazi jikelele lebanga 2 ngethemu. ....................................................................................................64 3.4.3 Ibanga lesi-3 ulwazi jikelele ngethemu.................................................................................................84 3.5 Amanothi achazayo kanye nomhlahlandlela wokufundisa ....................................................................106 3.5.1 Amanothi achazayo: Ibanga 1............................................................................................................106 3.5.2 Ukuchaza okuqukethwe kwebanga 2.................................................................................................249 3.5.3 Incazelo yokuqukethwe ebangeni lesi-3.............................................................................................397 CAPS 1

Izibalo IBANGA 1-3 ISIGABA SESI – 4: UKUHLOLA........................................................................................................... 572 4.1 Isingeniso ..................................................................................................................................................572 4.2 Uhlola ngongakuhlelekile /ukuhlola kwansukuzonke.............................................................................572 4.3 Ukuhlola okuhlelekile.................................................................................................................................572 4.4 Uhlelo lokuhlola ukuhlola okuhlelekile.....................................................................................................573 4.5 Ukubhala nokubika ngokusebenza kwabafundi......................................................................................574 4.6 Ukuqinisekisa ukuhlola okuhleliwe...........................................................................................................574 4.7 Jikelele.........................................................................................................................................................574 4.8 Izibonelo zezinhla zokuhlola zamabanga 1-3...........................................................................................575 2 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 ISIGABA SOKU – 1: ISINGENISO NESENDLALELO 1.1 Isendlalelo IsiTatimende SoHlelo LweziFundo LukaZwelonke seBanga-R kuya kwele-12 (uTaHFuZwe) sikhombisa inqubomgomo yezinhlelo zezifundo kanye nezokuhlola emkhakheni wokufunda esikoleni. Ukuze kwenziwe ngcono ukusetshenziswa kwaso, kwadingeka ukuthi kube nezichibiyelo ezithile ezizoqala ukusebenza ngoMasingana ngonyaka wezi-2012. Kwabe sekubhalwa umqulu owodwa odidiyele IsiTatimende SeNqubomgomo YoHlelo LweziFundo NokuHlola saleso naleso sifundo, okuwumqulu othatha isikhundla seziTatimende zesiFundo, umHlahlandlela woHlelo lokuFunda kanye nomHlahlandlela wokuHlola Izifundo eBangeni-R kuya kwele-12. 1.2 Ukubuka ngamafuphi (a) IsiTatimende SoHlelo LweziFundo LukaZwelonke seBanga-R kuya kwele-12 (kuMasingana ngonyaka wezi- 2012) simele inqubomgomo yokufunda nokufundisa ezikoleni zaseNingizimu Afrika futhi siqukethe lokhu: (i) NesiTatimende seNqubomgomo yoHlelo LweziFundo nokuHlola kuleso naleso sifundo esifundwayo. (ii) Umqulu weNqubomgomo, i-National Policy pertaining to the programme and promotion requirements of the National Curriculum Statement IBanga-R kuya kwele-12,kanye (iii) Nomqulu weNqubomgomo, i-National Protocol for Assessment IBanga-R kuya kwele-12 kuMasingana ngonyaka we-2012). (b) IsiTatimende SoHlelo LweziFundo LukaZwelonke seBanga-R-12 (kuMasingana 2012), sithatha indawo yeziTatimende zoHlelo LweziFundo lukaZwelonke ezimbili ezikhona njengamanje; okuyilezi (i) IsiTatimende soHlelo LweziFundo LukaZwelonke Olubukeziwe IBanga-R kuya kwelesi-9, IGazethi KaHulumeni ye-23406 zingama-31 kuNhlaba ngonyaka wezi -2002 kanye (ii) IsiTatimende soHlelo LweziFundo LukaZwelonke IBanga le-10 kuya kwele-12, IGazethi KaHulumeni ye-25545 ziyi-6 kuMfumfu ngonyaka we-2003 neye-27594 ziyi-17 kuNhlaba ngonyaka we-2005. (c) IsiTatimende soHlelo LweziFundo lukaZwelonke esibekwe sacaciswa esigabeni u-b(i) kanye no- (ii) siqukethe le miqulu yenqubomgomo elandelayo esizomiswa ukusetshenziswa kuthi esikhundleni sayo kungene isiTatimende soHlelo LweziFundo IBanga-R kuya kwele -12 kusuka ngonyaka wezi-2012 kuya kowezi-2014: (i) Isifundo/isiTatimende sesiFundo, umHlahlandlela woHlelo lokuFunda kanye nomHlahlandlela wokuHlola kwesiFundo IBanga-R kuya kwelesi-9 kanye neBanga le-10 kuya kwele -12; (ii) Umqulu wenqubomgomo, iNational Policy on Assessment and Qualification for Schools in the General Education and Training Band okwashicilelwa kwaba umthetho kuGovernment Notice No.124 kuGovernment Gazette No. 29626 mhla ziyi-12 kuNhlolanja ngonyaka wezi-2007. (iii) Umqulu weNqubomgomo, i-National Senior Certificate: iKhwalifikheshini yezinga lesi-4 kuNational Qualifications Framework (NQF), elishicilelwa laba semthethweni kuGovernment Gazette No. 27819 mhla zingama- 20 kuNtulikazi ngonyaka wezi-2005; CAPS 3

Izibalo IBANGA 1-3 (iv) Umqulu weNqubomgomo, isichibiyelo somqulu wenqubomgomo, weNational Senior Certificate: iKhwalifikheshini yezinga lesi-4 kuNational Qualifications Framework (NQF), ukubhekelela izingane ezinezidingo eziyisipesheli, elethulwa kuGovernment Gazette, No. 29466 mhla ziyi-11 kuZibandlela ngonyaka wezi-2006, lifakiwe nalo kulo mqulu wenqubomgomo, i-National Policy pertaining to the programme and promotion requirements of the National Curriculum Statement IBanga-R kuya kwele-12; kanye; (v) Nomqulu wenqubomgomo,isichibiyelo somqulu wenqubomgomo, weNational Senior Certificate: iKhwalifikheshini yezinga lesi-4 kuNational Qualifications Framework (NQF), ukubhekelela i-National Protocol for Assessment (IBanga-R kuya kwele-12), elashicilelwa laba semthethweni kuGovernment Notice No. 1267 kuGovernment Gazette No. 29467 mhla ziyi-11 kuZibandlela ngonyaka wezi-2006; (d) Umqulu wenqubomgomo, i-National policy pertaining to the programme and promotion requirements of the National Curriculum Statement IBanga-R kuya kwele-12, kanye nezigaba ezitholakala esiTatimendeni seNqubomgomo soHlelo lweziFundo nokuHlola njengoba kubekiwe ezahlukweni kusuka kwesesi-2,3 kanye nesesi-4 kulo mqulu kuyingxenye yemithetho nemigomo yesiTatimende soHlelo lweziFundo IBanga-R kuya kwele-12. Ngalokho-ke, ngokuka Section 6 A weSouth African Schools Act,1996 (Act No.84 of 1996,) kwakha isisekelo sokuthi uNgqongqoshe weMfundo esemaZingeni aPhansi akwazi ukunquma imiphumela kanye nemigomo emincane nje okungasukelwa kuyo, kanye nenqubo, nendlela yokwenza ukuhlola kokuphumelela komfundi ukuba kusetshenziswe ezikoleni zomphakathi nalezo ezizimele. 1.3 Izinhloso ezivamile zohlelo LweziFundo zaseNingizimu Afrika (a) IsiTatimende soHlelo lweziFundo lukaZwelonke IBanga-R kuya kwele-12 sikhombisa lokho okuthathwa ngokuthi kungulwazi, amakhono namagugu adinga ukufundwa ezikoleni zaseNingizimu Afrika. Lolu Hlelo lweziFundo luhlose ukuqinisekisa ukuthi abafundi bathola babuye basebenzise ulwazi namakhono njengendlela ahambisana ngayo nezimpilo zabo. Ngale ndlela uHlelo lweziFundo lukhulisa ulwazi lwezimo abaphila kuzona, babenozwelo kuzibopho zomhlaba jikelele. (b) IsiTatimende SoHlelo LweziFundo LukaZwelonke seBanga-R kuya kwele-12 sihlose lokhu: • Ukuhlomisa abafundi, noma ngabe bavela kuziphi izimo zenhlalo yomphakathi nezomnotho, ubuzwe, ubulili, ukukwazi ukusebenzisa umzimba nengqondo/ukuhlakanipha, ngolwazi, amasu nokungamagugu adingekayo ukuze bakwazi ukuzenelisa, nokubamba iqhaza elibonakalayo emphakathini njengezakhamuzi zezwe elikhululekile. • Ukuvumela abafundi ukuba bangene emikhakheni yemfundo ephakeme. • Ukwenza kube lula kubafundi ukwedlulela ezikhungweni zemisebenzi ngemuva kokuqeda esikoleni/ imfundo yamabanga aphakeme; kanye • Nokwedlulisela kubaqashi ulwazi oluphelele ngamakhono nakwazi ukukwenza ngempumelelo umfundi. (c) IsiTatimende soHlelo lweziFundo lukaZwelonke seBanga-R kuya kwele -12 sesekwe yile migomo elandelayo: • Ukuguquka kwezenhlalo yomphakathi; ukubhekelela ukungalingani kwezemfundo ngesikhathi esedlule ukuze kulungiswe, nokuthi amathuba okufunda alinganayo atholwe yiwo wonke umphakathi; • Ukufunda ngokuphapheme nangokuhlolisisa; ukukhuthaza indlela yokufunda ngokuphapheme nangokuhlolisisa ekufundeni , kunokuthi abafundi bamane bagxishe emakhanda lokho abanikwe khona bebe bengayiqondi incazelo yakho; 4 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 • Ulwazi oluphakeme namakhono aphakeme, ubuncane obemukelekile umthetho wokulinganisa ulwazi okumele luzuzwe ebangeni ngalinye kumele bucaciswe, kubekwe nemigomo ephezulu okumele izuzwe kuzo zonke izifundo; • Inqubekela phambili yolwazi; okuqukethwe nengqikithi yalelo nalelo banga kukhombise inqubekela phambili ukusuka kokulula kuya kokulukhuni. • Amalungelo esintu, ukudidiyela, ubulungiswa bezemvelo nezenhlalo yomphakathi; ukufaka imigomo nenkambiso yobulungiswa bezemvelo nezenhlalo kanye namalungelo esintu njengoba echaziwe kumThethosisekelo waseNingizimu Afrika. IsiTatimende soHlelo lweziFundo lukaZwelonke seBanga-R kuya kwele-12 (Jikelele) sinozwela ezindabeni zokwehlukahlukana kwesintu njengobuphofu, ukungalingani, ubuzwe, ubulili, ulimi, ubudala nokukhubazeka kanye nezinye izimo; • Ukwazisa ngezinhlelo zolwazi lwendabuko, ukwazisa ukunotha komlando namasiko aleli zwe, nomthelela obalulekile wokufundisa ngamagugu aqukethwe ngumThethosisekelo okube nawo njengomsuka wenguquko ukusiza ekuguquleni amagugu abafundi; kanye • Nokukholakala, uhlonze kanye nokwenza ngempumelelo, ukuhlinzeka ngohlobo lwemfundo olungaqhathaniseka ngokuqeqesheka nangazo zonke ezinye izindlela njengakwamanye amazwe. (d) Isitatimende Sohlelo LweziFundo Lukazwelonke seBanga-R kuya kwele-12 sihlose ukukhiqiza abafundi abazokwazi: • Ukubona baxazulule izinkinga, bakwazi nokwenza izinqumo besebenzisa ukucabanga ngokuhlaziya nangobuchule; • Ukusebenza ngokuzinikela nabanye njengamalungu eqembu; • Ukulungiselela, bakwazi ukuziphatha bona baphathe nemisebenzi yabo ngokuyikho; • Ukuqoqa, bahlaziye, bahlele, bahlanganise, bahlolisise ngokucubungula ulwazi. • Ukuxoxisana ngempumelelo besebenzisa izinto ezibukwayo, ukufanekisa ngezimpawu kanye namanye amakhono olimi ezimweni ezahlukene; • Ukusebenzisa isayensi nobuchwepheshe ngempumelelo nangokuhlolisisa bekhombisa nokuzinikela kwezemvelo kanye nempilo yabanye; kanye • Nokukhombisa ukuqondisisa umhlaba njengenkundla yezinhlelo ezihlobene ngokubona ukuthi izimo zokuxazulula izinkinga azenzeki ngazodwana. (e) Ukuhlanganisa izinhlobo zabafundi yikho okumele kube ngumgogodla wokuhlela, ukulungiselela, nokufundisa kuleso naleso sikole. Lokhu kungenzeka kuphela uma bonke othisha bekuqonda kahle ukuthi bazobabona futhi babasize kanjani abafundi abanezihibe ekufundeni, nokuthi bazokuhlelela kanjani ukwehlukahlukana kwabafundi. Okusemqoka ngokuhlanganisa izinhlobo zabafundi, ukuqinisekisa ukuthi zonke izithiyo ziyabonwa zigudluzwe ngayo yonke indlela ezikoleni, kumbandakanya othisha, amakomidi asemahhovisi ezemfundo, amakomidi ezikoleni, abazali kanye nezikole ezikhethekile ezisetshenziswa njengemithombo yolwazi. Ukugudluza izithiyo emakilasini, othisha bangasebenzisa amaqhinga ahlukene ezinhlelo zezifundo njengalezo ezitholakala eMnyangweni wezeMfundo eyisisekelo: Guidelines for Inclusive Teaching and Learning (2010). CAPS 5

Izibalo IBANGA 1-3 1.4 Ukwabiwa kwesikhathi 1.4.1 IsiGaba esiyisiSekelo (a) Isikhathi sokufundisa emkhakheni weSigaba Esiyisekelo sinjengoba sikhonjisiwe kuleli thebula elingezansi: Ibanga loku-1 IBANGA-R IBANGA LESI-3 ISIFUNDO KUYA KWELESI-2 (AMAHORA) (AMAHORA) (AMAHORA) ULimi lwaseKhaya 10 7/8 7/8 ULimi lokuQala lokwEngeza 2/3 3/4 Izibalo 7 7 7 Amakhono Empilo: 6 6 7 • Ulwazi lokuqala (1) (1) (2) • Ubuciko bokusungula (2) (2) (2) • Isifundo sokuzivocavoca (2) (2) (2) • Okuqondene nomuntu uqobo kanye nokuphila (1) (1) (1) emphakathini ISAMBA 23 23 25 (b) Isikhathi sokufundisa seBanga-R, 1 neBanga lesi-2, amahora angama-23 kuthi IBanga lesi-3 kube ngamahora angama-25. (c) Izilimi zabelwe amahora ayi-10 eBangeni-R kuya kwelesi-2 kanye namahora ayi-11 eBangeni lesi-3. Isibalo esiphezulu samahora ayisi-8 nesibalo esiphansi esingamahora ayi-7 sabelwe ULimi lwaseKhaya kanye nesibalo esiphansi esingamahora ama-2 nesibalo esiphezulu esingamahora ama-3 soLimi lokuQala lokwEngeza eBangeni loku-1 kuya kwelesi-2. EBangeni lesi-3 isibalo esiphezulu esingamahora ayisi-8 nobuncane obungamahora ayisi-7 sabelwe iziLimi zaseKhaya kanye nobuncane obungamahora ama-3 nobuningi obungamahora ama-4 oLimini lokuQala lokwEngeza. (d) Esifundweni samakhono olwazi lokuqala, kwabiwe Ihora eli-1 eBangeni-R kuya kwelesi-2 kanye namahora ama-2 njengoba kukhonjisiwe ngamahora akubakaki ethebulini eBangeni lesi-3: 6 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 1.4.2 IsiGaba esiPhakathi neNdawo (iBanga lesi- 4 kuya kwelesi-6) (a) Leli thebula elingezansi likhombisa izifundo nesikhathi sokufundisa esibekiwe sesigaba esiphakathi nendawo: ISIFUNDO AMAHORA ULimi lwaseKhaya 6 ULimi lokuQala lokwEngeza 5 Izibalo 6 Isayensi nobuchwepheshe 3,5 Isayensi yezokuhlalisana kwabantu 3 Amakhono Empilo 4 • Ubuciko bokusungula (1.5) • Isifundo sokuvocavoca umzimba (1) • Okuqondene nomuntu uqobo kanye nokuphila (1.5) emphakathini ISAMBA 27,5 1.4.3 IsiGaba esiPhakeme (a) Isikhathi sokufundisa IsiGaba EsiPhakeme simi ngale ndlela: ISIFUNDO AMAHORA ULimi LwaseKhaya 5 ULimi lokuQala lokwEngeza 4 Izibalo 4.5 Isayensi yezemvelo 3 Isayensi yokuhlalisana komphakathi 3 Ezobuchwepheshe 2 Isayensi yokuphathwa komnotho 2 Ukwazi ngamakhono empilo 2 Ubuciko bokusungula 2 ISAMBA 27,5 CAPS 7

Izibalo IBANGA 1-3 1.4.4 IBanga le-10 kuya kwele-12 (a) Isikhathi sokufundisa eBangeni le 10 kuya kwele-12 simi ngale ndlela: ISIFUNDO UKWABIWA KWESIKHATHI NGESONTO (AMAHORA) ULimi LwaseKhaya 4.5 ULimi lokuQala lokwEngeza 4.5 Izibalo 4.5 Ukwazi amakhono empilo 2 Okungenani kungakhethwa izifundo ezintathu eqoqweni 12 (3xAmahora ama-4) B Isengezelelo B, Ithebula B1 kuya ku-B8 kumqulu wenqubomgomo, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement IBanga-R kuya kwele-12, isifundo ngenkombandlela ebhalwe esigabeni sama-28 kumqulu weNqubomgomo obhalwe ngenhla. ISAMBA 27,5 Ukwabiwa kwesikhathi ngesonto kungasetshenziswa kuphela esibalweni esiphansi esidingekayo sezifundo zesiTati- mende soHlelo LweziFundo lukaZwelonke (TAHFUZWE) njengoba kukhonjisiwe ngenhla, akumele kusetshenziswe kunoma yiziphi izifundo ezengeziwe ohlwini lwenani lezifundo ezivunyelwe. Uma umfundi efisa ukwengeza ezinye izifundo, isikhathi kumele sandiswe ukwenelisa lezo zifundo.. 8 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 ISIGABA SESI – 2: ANCAZELO, IZINHLOSO, IMAKHONO NOKUQUKETHWE 2.1 Isingeniso Kulengxenye yesibili, imfundo yezibalo kumaBanga aphansi kwisitatimende senqubomgomo yohlelo lwezifundo lukazwelonke luzonika othisha incazelo yezibalo, imiphumela eqondile namakhono aqondile, igxile ezingxenyeni zokuqukethwe, isisindo sezingxenye zokuqukethwe ezibalweni, izinsiza kufundisa ezinconyiwe kwizifundo zamaBanga aphansi ezibalweni, inqubomgomo enconyiwe ukwelekelela izingane ezinezinkinga ekufundeni izibalo, izibalo zekhanda kanye nokukhulisa amakhono okufundisa izibalo eBangeni – R. 2.2 Ziyini Izibalo Izibalo ulimi olusebenzisa uphawu nezimpawu ukuchaza uphawu olumele inombolo, okusejiyometri nokukhombi- sa ubudlelwano ngegrafu. Kuwumsebenzi lapho abantu bebuka, bebeka okumele kanye nokuphenya amaphethini nobudlelwano obuphusile okwenzeka ngokwenza enhlalweni yabo naphakathi kwezinto eziphathelene nezibalo. Igqugquzela ukusebenza ngengqondo okuthuthukisa ukucaBanga ngokuhlelekile nangokujulile, ngokucophelelekile nokuxazulula izinkinga ezinomthelela ekuthatheni izinqumo ezifanele. 2.3 Imiphumela eqondile Ukufunda nokufundiswa kwezibalo, kuhlose ukuthuthukisa umfundi kulokhu okulandelayo: • ukuqaphela ngobumqoka bokuthi busebenza kanjani ubudlelwano bezibalo ngokwenhlalo, ngokwemvelo, ngokwamasiko nangokomnotho. • ukuzethemba nokukwazi ukubhekana nezimo ezahlukene zezibalo ngaphandle kokungabaza nokwesaba ukwenza izibalo. • uthando nentshisakalo yezibalo. • ukuncoma ubuhle bezibalo. • ukubona ukuthi izibalo ziwubuchwepheshe bomsebenzi wabantu • ukuba nomcabango ojulile wokuqonda izibalo; kanye • nokuthola ulwazi namakhono aqondile adingekayo: -- ukusetshenziswa kwezibalo ngokwenza, ngokwenhlalo nezinkinga zezibalo; -- ukufundiswa kwesifundo ezincike ezibalweni (isib.ezinye izifundo); kanye -- nokuqhuba ulwazi lwezibalo. CAPS 9

Izibalo IBANGA 1-3 2.4 Amakhono aqondile Ukuthuthukisa amakhono adingekayo ezibalo, umfundi kufanele: • ukuthuthukisa ulwazi olufanele lokusebenzisa ulimi lwezibalo; • ukuthuthukisa ulimi lwezibalo nolwazi lwezinombolo, namakhono okubala nokusebenzisa izinombolo; • afunde ukulalela, ukuxhumana, ukucaBanga ngokuhlelekile, kanye nokusebenzisa ulwazi lwezibalo alufundile • afunde ukuphenya, ukuhlaziya, ukubeka okumele ulwazi nokulihumusha • afunde ukubuza nokuxazulula izinkinga zezibalo; kanye • nokwakha ngokuqaphela ukubaluleka kwezibalo ezimweni zempilweni nasekukhuleni komfundi. 2.5 Izingxenye zolwazi okugxilwe kulo Izibalo emaBangeni aphansi zinezingxenye ezinhlanu. Ingxenye ngayinye ilekelela ekutholeni amakhono athile. Ithebula elilandelayo likhombisa okuqukethwe yizingxenye ngokuvulelekile nezikhethekile emaBangeni aphansi. Ithebula 2.1 Izibalo zamaBanga aphansi nolwazi okugxilwe kulo ULWAZI LWEZIBALO Ingxenye Ulwazi Oluvulelekile Ulwazi Olukhethekile EmaBangeni Aphansi Yolwazi Ukuthuthukisa ulwazi lwezinombolo Uhla lwezinombolo okufanele luthuthukiswe kuyofika olufaka: ekupheleni kweBanga lesi 3 lufaka izinombolo eziphelele kuze kufinyele e 1000 kanye namaqhezu ajwayelekile. • incazelo yezinhlobo ezahlukene KumaBanga aphansi ukufundwa kolwazi lwezinombolo zezinombolo; luphathelene nezinsiza kufunda eziphathekayo ukuze • ubudlelwano phakathi bakwazi ukubala, bahlukanise, bahlanganise, babale kwezinhlobo ezahlukene ngokweqa izinombolo ngezindlela ezahlukene, baxazulule zezinombolo; izinkinga zezibalo (zamagama), bese bekwazi ukwakha nokuhlakaza izinombolo • ubudlelwano bobungako bazo ezahlukene; • Ukubala kusiza abafundi ukuba bathuthukise ulwazi lwezinombolo, izibalo zekhanda, ukuqagela, amakhono • ukubekwa okumele izinombolo okubala nokwazi ukubona amaphethini. ezinhlobonhlobo ngezindlela ezahlukene; kanye • Ukuthuthuka kolwazi lwezinombolo lusiza abafundi ukuba Izinombolo, bazi izakhiwo zezinombolo kanye namasu angabasiza • nomphumela wokusebenza izimpawu kanye ukuthuthukisa ukubala kalula. ngezinombolo nobudlelwano • Ukukwazi ukuxazulula izinkinga kusiza abafundi ukukwazi bazo ukuxoxa nokubhala imicabango yabo besebenzisa imidwebo nezimpawu. • Abafundi bakhula ekuqondeni indlela yokusebenzisa izinombolo behlanganisa, besusa, behlukanisa nokuphindaphinda. • Abafundi bathuthukisa ulwazi ngamaqhezu ukuxazulula izinkinga zezibalo besebenzisa ukucazelana izinto eziphathekayo nokusebenzisa imidwebo. Izinkinga zezibalo abazenzayo aziveze imiphumela enezinombolo eziphelele kanye nezinsalela noma amaqhezu. Ukucazelana akumele kufake kuphela inani lamaqoqo kodwa kubhekwe ukuthi kungaki eqoqweni ngalinye. Kulesisigaba abafundi akufanele bafunde noma babhale izimpawu zamaqhezu. 10 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 ULWAZI LWEZIBALO INGXENYE ULWAZI OLUVULELEKILE ULWAZI OLUKHETHEKILE EmaBangeni APHANSI YOLWAZI I-aljebhra ulimi lokuphenya KuleliBanga abafundi basebenza ngakho kokubili: nokuxhumana ngokwezibalo • amaphethini ezinombolo (isib.ukubala weqa inombolo); olungabuye lusetshenziswe kanye ekufundweni kwemisebenzi kanye nobudlelwano phakathi • nokusazibalo mdwebo (isib.izithombe) kwezingxenyana zezibalo. Abafundi kumele basebenzise izinto eziphathekayo, Umgogodla wolwazi lwalengxenye imdwebo kanye nezimpawu ukukopisha, ukwandisa, yezibalo udinga ukuba umfundi ukuchaza nokwakha amaphethini. akwazi ukusebenzisa amakhono ngendlela efanele ye-aljebhra. Ukukopisha iphethini kusiza abafundi ukuba babone ukuthi Iphinde ibheke: iphethini yakheke kanjani. Amaphethini, ukuxhumana kanye • ukuchaza amaphethini Ukuchaza iphethini kusiza abafundi ukuthuthukisa amakhono ne-aljebhra nobudlelwane ngokusebenzisa olimi. izimpawu zokuchaza , amagrafu namathebula; kanye Ukugxila ekulandelaneni kwephethini kusiza ekuthuthukiseni amakhono okucaBanga nge-aljebhra. • nokukhomba nokuhlaziya okuvamile nokushintsha Amaphethini ezinombolo asiza ekuthuthukiseni ulwazi kwamaphethini, nobudlelwano lwezinombolo, nokwakheka komqondo wezinombolo obusiza abafundi ukuthi baqagele ukusebenza kanye nobudlelwano bazo. babuye baxazulule izinkinga Okusejiyometri kuhlanganisa imigqa, izimo, nezinto, kanye zezibalo. namaphethini akhona ezweni. Kulokhu okusazibalo mdwebo abafundi basebenzisa ulwazi lwabo lwezindawo nesimo. Ukufunda ngendawo nesimo KuleliBanga abafundi bagxila kwizinto ezinhlangothintathu (3-D), kuthuthukisa ukuqonda nokuncoma izimo ezinhlangothimbili (2-D), isikhundla nezinkomba. amaphethini, ukucacisa, • Abafundi bahlola izinto ezinhlangothintathu nezimo ukuphumelela nobuhle bendalo ezinhlangothimbli ngokuhlela, nokuhlukanisa ngamaqoqo, namasiko. Kugxila kulokhu: ukuchaza nokuzisho ngamagama. • Izakhiwo nobudlelwano bazo ; Indawo nesimo • Abafundi badweba izimo bakhe ngezinto. (ijiyometri) • Isimo, izikhundla kanye • Abafundi babona babuye bachaze izimo nezinto • Nezinguquko zezimo ezisezindaweni zabo ezifana nezinto nezimo ezisebenza ezinhlangothimbili nezinto ezibalweni. ezinhlangothintathu • Abafundi bachaza isikhundla sezinto, ezabo, nezabanye besebenzisa amagama afanele. • Abafundi balandela babuye banike izinkomba. Isilinganiso kugxile ekukhetheni KulamaBanga ulwazi lwabafundi lokulinganisa luthuthukiswa nasekusebenziseni amayunithi ngokusebenzisa izinto eziphathekayo nezimo, befunda ngendlela efanele, izinsizakukala izakhiwo zobude,zomthamo, zesisindo, zobungako bendawo kanye namafomula ukunika inani kanye nesikhathi. lobunjalo bezehlakalo,izimo, • Abafundi balinganisa izakhiwo zezimo, nezinto izinto kanye nendawo. besebenzisa amayunithi angalinganisiwe njengezandla, Kuhambelana ncamashi nobuciko, amagxathu, izitsha njll. nobuchwepheshe, nomnotho Isilinganiso wokuqonda komfundi ngokwezinga • Abafundi baqhathanisa izinto besebenzisa amagama lakhe. Lokhu kumsiza ukuba: okuqhathanisa njengokuthi kude kuna/kufishane kuna, kuyasinda kuna kulula kuna njll. • aqagele ngokuyikho, kanye • Abafundi bethulwa kumayunithi ahleliwe njengama gramu, • nokukwazi ukuqikelela isilinganiso khilogramu; ilitha, imililitha; imitha, isentimitha. ngokuyikho nokuthola imiphumela eyiyo. Imisebenzi ephathalene nesikhathi kufanele ihlelwe ngokwazi ukuthi abafundi banalo ulwazi ngokudlula kwesikhathi ngaphambi kokuba bafunde ngesikhathi. CAPS 11

Izibalo IBANGA 1-3 ULWAZI LWEZIBALO INGXENYE ULWAZI OLUVULELEKILE ULWAZI OLUKHETHEKILE EmaBangeni APHANSI YOLWAZI Ngesifundo sokuqokelelwa kolwazi, Okugxilwa kukho uma kufundiswa, kufundwa umfundi uthuthukisa amakhono oku: ngokuqokelelwa kolwazi emaBangeni aphansi kusekuhlelweni kwezinto nolwazi ngezindlela ezahlukene • qoqa kube kuncike ezimpawini ezahlukene zezinto noma ulwazi. Ukuqokelelwa • hlela kolwazi lwezibalo • Kulindeleke ukuthi abafundi bahumushe baphinde bakhe • khangisa; igrafu yezithombe nebar grafu ngokukodwa nokukodwa okuhambisanayo olwazini olunikiwe. • ukuhlaziya nokuhumusha ulwazi alunikiwe. 2.6 Isisindo sezingxenye zolwazi Isisindo sezingxenye zolwazi lwezibalo kunezinhloso ezimbili: eyokuqala isisindo seluleka ngobungako besikhathi esidingekayo ukufundisa ulwazi engxenyeni ngayinye ngokwanele; eyesibili isisindo seluleka ngokusabalalisa ulwazi ekuhlolweni. Isisindo sezingxenye zolwazi siyehlukahlukana ngokwamaBanga emaBangeni aphansi. Ithebula 2.2 isisindo sezingxenye zolwazi emaBangeni aphansi ISISINDO SEZINGXENYE ZOLWAZI Ibanga IBANGA IBANGA Ingxenye yokuqukethwe loku-1 LESI-2 LESI-3 Izinombolo, izimpawu kanye nobudlelwano bazo* 65% 60% 58% Amaphethini, ukuxhumana kanye ne-aljebhra 10% 10% 10% Indawo nesimo (Ijiyometri) 11% 13% 13% Isilinganiso 9% 12% 14% Ukuqokelelwa kolwazi lwezibalo 5% 5% 5% 100% 100% 100% * Ebangeni R-3, kusemqoka ukuthi izinombolo, ukusebenza kanye nobudlelwano bazo iyona esemqoka ohlelweni lwezibalo. Abafundi ku- fanele bakwazi ukusebenzisa izinombolo ngokukhululekile lapho sebeqede iBanga lesithathu. Inhloso ukuba abafundi bakwazi ukusebenzisa izinombolo ngokukhululeka nangokuzethemba. Ngalesizathu isikhathi sokufundisa izinombolo, ukusebenza kanye nobudlelwano bazo ses- engeziwe. Umsebenzi omningi wamaphethini kufanele ubheke kakhulu ekwenzeni amaphethini ezinombolo ukuhlanganisa ulwazi lwabafundi lokusebenza ngezinombolo ngokuqhubekayo. 2.7 Izibalo emaBangeni aphansi Izibalo emaBangeni aphansi ziqinisekisa ukuxhumana kolwazi lwezibalo ebangeni – R, empilweni ngaphandle kwesikole nasemaBangeni aphakeme emfundo. Abafundi emaBangeni aphansi kumele bakhonjiswe ulwazi lwezibalo oluzobanika amathuba okwenza, ukukhuluma, nokubhala imcabango yabo. Isikhathi esisetshenziswa ekufundiseni izibalo yisona esiveza umphumela wokuthuthuka olwazini nasemakhonweni ezibalo. Imisebenzi enikwa abafundi kumele kube ezobakhulisa olwazini lwezibalo njengoba kubekiwe kunqubomgomo hayi umsebenzi nje. 2.7.1 Imigomo ephakanyisiwe yokuphatha ikilasi Sonke isikhathi esibekelwe ukufundisa izibalo ngelanga kufanele sithathwe njengesifundo esisodwa. Ngesikhathi sokufundwa kwezibalo kufanele kwenzeke lokhu okulandelayo: 12 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 • Umsebenzi wekilasi -- Izibalo zekhanda -- ukuhlanganisa ubukeze ulwazi olufundiwe -- ukuphathwa kwekilasi (ukwabiwa komsebenzi ozimele,njll) • Ukufundisa abafundi ngamaqembu -- Ukubala -- Ukuthuthukisa ulwazi lwezinombolo (ngokukhuluma nangokwenza) -- Ukuxazulula izinkinga zezibalo (ngokukhuluma nangokwenza) -- Umsebenzi wokubhala -- Ukuthuthukisa amasu okubala (ngokukhuluma nangokwenza) -- Amaphethini -- Isimo neNdawo -- Isilinganiso -- ukuqokelelwa kolwazi lwezibalo • Umsebenzi abawenza ngokuzimela Abafundi bazokwenza bese behlanganisa babukeze ulwazi lwezibalo abalufunde beyikilasi nasemaqenjini. Umsebenzi wekilasi: lapho kugxilwa khona kakhulu ezibalweni zekhanda, ukuhlanganiswa kolwazi nokwabiwa kwemisebenzi ezimele okungenani imizuzu engama 20 ngosuku ekuqaleni kwesifundo sezibalo.kulesikhathi uthisha uzophinda asebenze nekilasi lonke ukubona abhale (uma sekufanele)igama losuku,usuku, abafundi abakhona nabangekho, nesimo sezulu.izibalo zekhanda zifaka ukubala ngokushesha njengoku “inombolo engemuva/ngaphambili kwesi 8 ingu; 2 ngaphezulu/ngaphansi kwesi 8 ngu; 4+2; 5+2; 6+2” ngalesikhathi uthisha angahlanganisa ulwazi olubukhunyana.Futhi kubalulekile ukuthi uthisha anike ikilasi umsebenzi ojwayelekille wekilasi kanye nalowo msebenzi wokuzimela abazowenza ngokwabo ngesikhathi yena eqhubeka neqembu agxile kulo. Izifundo ezigxile emaqenjini:zisebenza kahle kakhulu uma uthisha ethatha abafundi abayiqembu elincane (aBangaba 8 kuya e 12) abasezingeni elifanayo lokusebenza basebenze naye eceleni ngesikhathi amanye amaqembu esebenza ngokuzimela umsebenzi osufundiwe. Kuleliqembu elinothisha benza umsebenzi wokukhuluma nokwenza emisebenzini efana nokubala, ukuqagela, ukuthuthukisa ulwazi lwezinombolo nokuxazulula izinkinga, kanye nemisebenzi ethinta amaphethini, isimo nendawo, isilinganiso kanye nokuqokelelwa kolwazi lwezibalo, okufanele kube kulungiselelwe ngokucophelela. Ukuze ugcizelele ukufunda, umsebenzi wokubhala (incwadi yokusebenza, iphepha lokusebenzela, amakhadi okusebenza njll) kufanele ube yingxenye yomsebenzi weqembu uma kungenzeka. Abafundi kumele babe ne- zinto zokubhala (izincwadi zokusebenza ekilasini, njll)zokwenza imisebenzi yokuxazulula izinkinga.Ngesikha- CAPS 13

Izibalo IBANGA 1-3 thi sokusebenza ngamaqembu kumele abafundi basebenzisane bagqugquzelwe ukuba “benze, bakhulume, batshengise bese bebhala ulwazi nemicaBanga yabo yezibalo”. Othisha kufanele Bangababukeli phansi abafundi abathatha kancane;kufanele nabo banikwe imisebenzi ezo- bathuthukisa olwazini lwabo.Kulula ukuqondanisa izinga lomsebenzi othe thuthu nabafundi uma iqembu uthi- sha asebenza nalo lisezingeni elifanayo lokusebenza.Kodwa-ke,iqembu elixube amazinga ahlukene okusae- benza lingasebenza kahle uma lenza imisebenzi efana nokwakha, isilinganiso ukwakha amaphethini noma imisebenzi yokuhlela, noma imidlalo. Imisebenzi yomfundi ngamunye: Ngesikhathi uthisha esebenza neqembu agxile kulo,abanye abafundi bazo- kwenza imisebenzi eminingi eyahlukene yezibalo egcizelela ihlanganise ulwazi namakhono asefundiwe nge- sikhathi sokufunda emaqenjini nothisha.Lemisebenzi yokuzimela kufanele ihlelwe ngokwehlukana kwamaz- inga abafundi abakuwo.Imisebenzi yokuzimela ingafaka: -- Incwadi yokusebenzela; -- Amaphepha/amakhadi okusebenzela asemazingeni ahlukene uma bebala, besebenza ngezinombolo, bex- azulula izinkinga zezibalo ezilula ezisesimweni esejwayelekile(izinkinga zezibalo zamagama), njll; -- Imidlalo yezibalo njenge Ludo,amadomino, amaphazili;kanye -- Imisebenzi efaka ukwakha, ukuhlela, ukwakha amaphethini noma isilinganiso. Isikhathi sezibalo kufanele silekelele abafundi abanezinkinga ekufundeni kwabo,imisebenzi yokwandisa ul- wazi kulabo abafunda ngokushesha, imisebenzi yokuhlola,njll. Imisebenzi yezifundo yokuzimela neyamaqembu kufanele ibhekwe (ngokwenziwayo, nokuxoxwayo),imakwe bese ibhekwa uthisha njengemsebenzi yokuhlola ehleliwe nengahleliwe. Ukubhekisisa izimpendulo zabafundi (ngokukhuluma, ngokuxoxa, ngokwenza, ngokubhala) ezimweni zoku- funda nokufundisa kusiza uthisha ukuba enze ukuhlola okuqhubekayo,ukubheka inqubekela phambili yaba- fundi nokuhlela nokulekelela okufanele abafundi abanezinkinga ekufundeni kwabo. 2.7.2 Abafundi abanezingqinamba ekufundeni izibalo Kusemqoka ukuthi abafundi abanezingqinamba banikwe umsebenzi yokwenza befunda.Izibonelo zokwenza use- benzisa izinto eziphathekayo nemisebenzi yokwenza kufanele yenziwe isikhathi esithe xaxa kunabanye abafundi, uma siqhubekela emsebenzini ofuna ukucatshangwa ungaholela ekudidekeni nasekudikibaleni. La bafundi Bangad- inga ukunikezwa isikhathi esingaphezulu soku; • qedela imisebenzi yokuhlola; • ukuthola amakhono okucaBanga (amaqhinga akhe) Inani lemisebenzi okufanele iqedwe kufanele ihambisane nezinga lokufunda lomfundi ngaphandle kokwehlisa izinga lolwazi namakhono. 2.7.3 Izibalo zekhanda Izibalo zekhanda zinendima enkulu kwinqubomgomo yezibalo. Amabhondi ezinombolo namathebula okuphindaphin- da okufanele abafundi bawazi noma bawakhumbule ngokushesha abhalwe ohlwini lweBanga neBanga. Ngaphezulu 14 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 kwalokho , izibalo zekhala zisetshenziswa kakhulu ukuthola uhla lwezinimbolo oluphezulu ngokusebenzisa ukubal- weqe izinombolo nokwenza imisebenzi efana “nokwehla wenyuka isitbhisi sezinombolo”,isib. Uthisha weBanga le 3 angabuza imibuzo exhumene “Qala ngo 796. Yenza kube kuningi ngokuyi 7.Yebo, kuwu 803. Yenza lokho kuke nga- phansi ngoku 5. Yebo, kuwu 798. Yenza lokho kube ngaphezulu ngoku 10…ngaphezulu ngoku 2….ngokungaphezu- lu noku 90… ngokungaphansi ngiku 5…” njll. Lemisebenzi isiza abafundi ukwakha umugqa wezinombolo sakuhuba. Ngakhoke izibalo zekhanda zingena kakhulu kukona kokubili ukubala nokuthuthuka kolwazi lwezinombolo ngokux- humana ngezinombolo namaphethini, kungenzeka futhi ngokulinganisa nemisebenzi yokuqokelelwa kolwazi. Uma wenza izibalo zekhanda , uthisha akufanale aphoqe abafundi ukwenza izibalo zekhanda abangeke bakwazi ukuzik- hona –izinto zokubhala noma zokubala kufanele zihlale zikhona lezo abafundi aBangazidinga. 2.8 IBanga R Indlela yokufunda izibalo eBangeni – R kufanele incike emigomeni yokuhlanganisa konke abakwenzayo nasekufun- deni sakudlala. Uthisha kufanele akhuthale, njengomxhumanisi kunokuba umfundisi. Umxhumanisi wenza amathu- ba amaningi okufunda benganakile okwenzeka ngesikhathi benza imisebenzi eminingi yobuntwana njengokudlala ngokukhululeka ekhoneni labo lamaphupho noma esizindeni sokwakha amabhuloki,iimidlalo yesihlabathi namanzi elawulwa uthisha egxile olwazini lwezibalo njengokubala, ukuthuthukiswa kolwazi lwezinombolo, indawo nesimo, amaphethini, isikhathi nezinye imisebenzi ezingenelayo yezibalo. Umbala awusilo ulwazi lwezibalo ngokuzimele, kodwa lungasetshenziswa ekuthuthukisweni kokukhuliswa kolwazi lwezibalo emsebenzise efana nokuhlele, ukwen- za amaqoqo nokuhlela ngendlela ethile. Konke okufundwa eBangeni – R okufaka impilo yasekilasini nokufunda nokufundiswa, kufanele kubasize, kubakhu- lise kwizingxenye zonke zempilo. Ukuthuthukiswa kuyingxenye kokwenzeka ezibalweni okufaka nokuthuthuka ngokwengqondo (ukuxazulula izinkinga, ukucaBanga ngendlela ehlelekile), ukuthuthukiswa kolimi (ulimi lwezibalo) imicabango nemizwa kanye nokuthuthuka ngokwenhlalo. Konke lokhu kungathuthukiswa, ngezindaba, amaculo, imilolozelo, imidlalo Yeminwe neyamanzi, izinto zokudlala ezifundisayo okufaka kuzo imidlalo yamabhodi, yokwakha nokubona (isisindo, isikhathi, umthamo, isilinganiso, njll), imidlalo yemicabango, imidlalo yangaphandle” nemidlalo yasenkundleni”. Izinhlobo eziningi zemidlalo zingafaka izingxenye zezibalo, isibonelo: ukukala ngesikhathi sokukha- thi sokupheka noma ukubala ngesikhathi sokuthenga. Ngamanye amagama ukufundwa kwezibalo zokuqala nolwazi oluhambisana nazo njengokufundisa okufanele, ku- hambisana nemigomo elanselayo lapho khona abantwana bedlula kuwona womathathu amazinga okufunda, lawa: • Ukusetshenziswa komzimba (ukufunda ulwazi ngomzimba nemizwa); • ukusetshenziswa kwezinsiza kufunda eziphathekayo (3-D, ukusetshenziswa kwezinhlobo ezahlukene zez- into njengamabhuloki, izivalo zamabhodlela, izinti zokubala nezinye izinto ezibazungezile); kanye • Ukusetshensizwa komfanekiso osephepheni (imidwebo njengezithombe, amakhadi okuqondanisa njll) Onyakeni weBanga R uhlelo lwesikhathi lubizwa ngokuthi uhlelo losuku (bheka umbhalo 1)lwakhiwe izinhlaka ez- intathu ezibizwa: • Imisebenzi eholwa uthisha; • Imisebenzi yansukuzonke;kanye • Imisebenzi esungulwa abafundi noma imidlalo ekhululekile. Ukugcizelela kukona konke kufanele kube sekusebenziseni lezi zingxenye zohlelo losuku ukuthuthukisa ukufunda izibalo zokuqala ngokuthokozisayo nokwenzeka kungalindelekile esimweni esejwayelekile. Isibonelo: ukufundwa CAPS 15

Izibalo IBANGA 1-3 kwezibalo ezilawulwa uthisha ngesikhathi seringi. Amaringi amaningi anganikwa isikhathi sokugxila ezibalweni. Iringi yasekuseni ngesikhathi sokubingelela nokubizwa kwamagama kunikeza amathuba okudlala ngezinombolo, njengokubala.Amanye amaringi, njengeringi yezibalo , amaringi emicabango, eminyakazo, umculo nobuchwepheshe zingagxila ekunikezeni izibalo. Imisebenzi yokuzenzela ingagcizelela izibalo, kusetshenziswa izimo ezisazibalo mdwebo ezifana njengezindilinga, nezikwele ukwenza ikholaji noma ukwakha iphethini yokufaka isithombe. Ishadi lesimo sezulu, ikhalenda neringi yezinsuku zokuzalwa nacho kunika amathuba okuvaza ulwazi lwezibalo.Ulwazi lukathisha nokuzinikela olungenyusa izinga lokufunda. • Okwenziwa njalo, Lapho abafundi befunda ngokwenza, njengesikhathi sokudla, ukufika, ukugoduka/ukuya ekhaya, nokuya endlini encane, kunganikwa ukugxilwa ezibalweni. Abantwana abagqoke okubomvu, isibonelo, baya endlini encane kuqala (umbala nenombolo esho isikhundla), umntwana ngamunye uthola ipuleti nesinkwa (okukodwa nokukodwa okuqondanayo), UThandi angathanda isinkwa sesibili, uSipho akasithandi esesibili. Lokhu kulekelela ekuboneni nasekufundiseni , Ngamanye amazwi kuba umxhumanisi wokufunda. • Ngesikhathi sokudlala ngokukhululekile uthisha angathuthukisa ulwazi lwezibalo zokuqala ngokuhlela kahle indawo yokudlala ngokukhululekile.Ukudlala okukhululekile okuphandle okunjengokugibela isitebhisi esenziwe ngezingodo kungathuthukisa ulwazi lolimi lwezibalo olufana nophezulu/phansi, ngenhla/ ngenzansi, ukushesha / nokuhamba kancane, njll. Umdlalo wamanzi nesihlabathi kungathuthukisa ukuqonda ulwazi njenge isisindo, umthamo nokumumethwe. Yonke lemisebenzi izothuthukisa amakhono okusebenza kwengqondo, okuholela ekutholeni ukufunda okuhlelekile kolimi nezibalo. Izibonelo zalamakhono: -- ukuthuthukiswa kolwazi lokuqonda isikhundla sakhe nendawo isib. Ngemuva, ngaphambili, ngaphansi noma eceleleni kwento (lokhu kunga xhumana nesikhundla senombolo ezibalweni); kanye -- ukuqonda izinkomba kanye nezinhlangothi (lokhu kungaxhumana nezinombolo nokwakheka kwezinhlamvu, kanye nokufunda kusukela kwesokudla kuya kwesobunxele) Ukwenza okuchazwe ngenhla kuchaza indlela yokusebenza kweBanga -R ekuxazululeni izinkinga ekucaBangani okuhlelekile, kanye nemfundo yobuzwe egxile ekubambisaneni nasekuxoxisaneni. Ngokusebenzisa izikhathi zokufundisa uthisha angagqugquzela abantwana ukubheka izinqumo abazenzayo nokuqagela okungase kwenzeke, isib. Uma bebuka isitsha samanzi okudlala asetshenziswe emdlalweni wamanzi singamumatha amanzi amningi ukunanoma isiphi esinye isitsha. Ngokwenza izincomo ezilekelelayo nokumenza umntwana ukuba acabange ngezinye izindlela zokuxazulula izinkinga, uthisha angagqugquzela abantwana ukuba bacabange kabanzi ngalento nokuthola izizathu ezifanele zezinqumo ezifanele. Ngalendlela akuzona kuphela izibalo ezithuthukayo kodwa ukuthuthuka komntwana ngokuphelele nezizinda ezisekele amaCAPS ziyasebenza. Ukuhlolwa eBangeni – R kumele kungabi okuhlelekile nabafundi Bangakuzweli ukuhlolwa. Ngakho – ke akukho ukuhlola eBangeni – R. Umsebenzi ngamunye kufanele ulungiselelwe kahle ukuze kuthuthukiswe amakhono. Ukuhlola eBangeni – R kwenzeka ngenkathi uthisha ebabuka benza bese ebhala phansi akubonile ngokwenza komfundi, kumele akwenze ngokusebenzisa uhlu lwezinto azibhekayo. Ngokuqhubeka konyaka uthisha uzokwakha isithombe esiphelele somntwana, esiveza lokho akwazi ukukwenza nangakwazi ukukwenza. Lokhu kunika ithuba lokuthi lokhu angakwazi ukukwenza kubhekisiswe nalokho akwazi ukukwenza kuthuthukiswe. Ikilasi leBanga – R elihlelwe ngendlela yokubheka phambili, elilandela imigomo yokufunda ngendlela engaguquki “nenemigomo emile” kufanele ligwenywe, njengoba ingavumeli ukutholakala kolwazi lwezibalo emntwaneni weBanga –R. IBanga –R akufanele libe ikilasi elibukeka njengeleBanga-1. Linezinto zalo ezehlukile ezincike 16 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 ekutheni abantwana baleliBanga bazibona kanjani izinto emhlabeni wobuntwana bebebethola nolwazi, amakhono, nezimfundiso ezizobavumela ukwenyusa amathuba atholakala eminyakeni yokufunda okuhlelekile. Umbhalo 1: Uhlelo Lwansuku zonke IBanga R (UKUSUKA ± 7:30 – 13:00) IZIBALO UKUFIKA NEMIDLALO EKHULULEKILE • Imisebenzi ehlelwe Ukubingelela Izindaba Izibalo nge-(caps) yezibalo Ishadi lesimo sezulu Iregista • Imisebenzi yomculo namaculo Ulimi, Amakhono empilo Imizuzu: • Imisebenzi emayelana 36 nokucaBanga UMSEBENZI OHOLWA UTHISHA Izibalo; Ulimi; Amakhono Empilo • Imilolozelo enokubala • Ingxoxo ngezihlokwana • Ubuciko bokuhlola • UMSEBENZI WAMAKHONO • Ukudlala ngokukhululeka (nsukuzonke: OKUMQOKA oku-1 kanye 2/3 imisebenzana • Imidlalo yokuzenzisa • Inqubo yokulekelela • Ukulingisa Imizuzu: 50 • UKUDLALA • Ukudlala ngokwakha ULIMI OKUKHULULEKILE • Amabhuloki • Imisebenzi ngokwe • UKUHLANZWA • ukufunda nqutahlelo (ulimi KWANGAPHAKATHI lwasekhaya) • Amathoyisi • Imidlalo ecabangisayo • Izindaba • Iphazeli • Ukulingisa Imizuzu: ISIKHATHI SOKUZIKHULULA ULimi, 30 Izibalo, Amakhono Empilo • Ikhona lezincwadi • Izincwadi / izithombe • Isikhathi sokuthula • Ukufunda ngezithombe • Indawo enokuthula • Ukuxoxa ngezithombe Imizuzu: UMSEBENZI OHOLWA UTHISHA Izibalo; • Imisebenzi emayelana 10 Ulimi; Amakhono Empilo nokucaBanga • Iphosta yabazali Imizuzu: ISIKHATHI SOKUDLA Ulimi, Izibalo, Amak- • Incwadi yabazali 20 hono Empilo • Izindaba • Umdlalo wamanzi • Imilolozelo nezinkondlo • Umdlalo wesihlabathi • Okuqoshiwe • Ukulingisa Imidlalu ekhululekile • Ukuxoxa ngezihlokwana • Umdanso Imizuzu: ngaphandle nokuqoqa • Imidlalo yokunyakazisa 60 • Imijikelo/ozwingi imizimba • Amathoyizi • Inqubo anamasondo • Imidlao ekhululekile • Amathoyizi okufundisa • Ukudlala ngokukhululeka • Amathayi Imizuzu: Isikhathi sokuzikhulula • Ukunyakaziswa 10 Izibalo, Ulimi, Amakhono Empilo komzimba AMAKHONO EMPILO • Imidlalo • Imisebenzi ehlelwe ngokwe- caps (amakhono empilo) Imizuzu: UMSEBENZI OHOLWA UTHISH • Imidlalo yokunyakazisa 30 Izibalo, Ulimi, Amakhono Empilo umzimba • Ukucula namaculo Imizuzu: • Imilolozelo nezinkondlo INDABA nsuku zonke 30 • Ingxoxo ngezihlokwana • Izinsuku zokuzalwa Isikhathi sokuphumula/esokuthula kanye nosokuhamba • Inqubo • Ukudlala ngokukhululeka CAPS 17

Izibalo IBANGA 1-3 2.9 Izinsizakufundisa ezinconyiwe kumaBanga aphansi ekilasini lezibalo • Izinto zokubala • Idayisi elikhulu • Ibhodi lezinombolo elikhulu • Ishadi lobude • Igridi enkulu tezinombolo esukela 1-100 nesuka ku 101-200 (amashadi-100) • Imigqa yezinombolo ehlukene (ovundlile nosuka phezulu uya phansi) • Amafuladi khadi • Imali yokudlala-ewuhlweza nengamaphepha • Ikhalenda yalowo nyaka • Iwashi elikhulu lezinti lasodongeni • Isilinganiso sokuzimelela • Amabhuloki okwakha • Ubumba lokudlala • Izinhlobo ezahlukene zamabhokisi ezinezimo nobungako obungafani ezitholakala emakhaya • Amabhodlela ayiplastiki anhlobonhlobo nezitsha zokuchaza nokuqhathanisa okumemethwe • Izibonelo ezinhle zokuyindilinga (Ibhola), iprizimu ewunxande (ibhokisi), ikhiyubhu, ikhoni, iphiramadi nesilinda.uthisha angazenzela lezinto ngokwakhe. • Izikwele ezingamaplasitiki noma ezingamakhadibhodi, onxande abahlukene, izindilinga, onxantathu abahlukene abawubungakho obuhlukene • Imidlalo yezibalo, isib uLudo, Izinyoka nezitebhisi, amaphazili, amadomino, aTangrams njll. • Okudingeka ebangeni R no 1 -- Izindawo zemidlalo yamanzi nesihlabathi -- Izinto zokugibela, ezokuzimelela, ezokujikela nezokweqa -- Isitolo sokudlala esinezinto zokuthengwa ngemali yokudlala -- Izinhlobo zemidlalo ehlukene njengokuthi ‘yini esesikweleni? -- Amabhuloki 18 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 ISIGABA SESI – 3: UKUCACISA OKUQUKETHWE NOKUQONDWE NGQO 3.1 Isingeniso Emfundweni yamazinga aphansi kunezingxenye ezinhlanu zolwazi lwezibalo: • Izinombolo, izimpawu kanye nobudlelwano bazo • Amaphethini, ukuxhumana kanye ne-Aljebhra • Indawo nesimo (Ijiyometri) • Isilinganiso • Ukuqokelelwa kolwazi lwezibalo Ezibalweni ingxenye ngayinye yolwazi yehlukaniswe ngezihlok , njenge ndawo nesimo emaBangeni aphansi esinye isihloko singe zimo ezinhlangothi mbili.Isihloko ngasinye siluveza kahle ulwazi namakhono. Ingxenye yesi-3 kumaBanga aphansi kumaCAPS ezibalo iveza iphinde icacise ngolwazi oludingekayo. 3.2 OKUQUKETHWE OKUQONDWE NGQO OKUKHOMBISA INQUBEKELA PHAMBILI Ithebula lolwazi oluqukethwe emaBangeni aphansi lukhombisa ngqo inqubekela phambili yolwazi namakhono kusuka eBangeni R kuya eBangeni 3. Ithebula leBanga likhombisa inqubekela phambili yolwazi namakhono kuwona omane amathemu onyaka. Kwezinye izihloko ulwazi namakhono kuyafana kwamanye amaBanga amabili noma amathathu alandelanayo. Incazelo yolwazi inika inqubomgomo emayelana nokuthi inqubekela phambili izohamba kanjani kulamaBanga. Incazelo enemininingwane yolwazi kufanele ifundwe ngokuhlanganyela nencazelo yolwazi. Ulwazi jikelele emaBangeni aphansi lukhombisa ingqubekela phambili yengxenye yolwazi; izinombolo, ukusebenza kanye nobudlelwano bazo, amaphethini, imisebenzi kanye ne-aljibhra, indawo nesimo, isilinganiso, ukuqokelelwa kolwazi lwezibalo kumaBanga aphansi kusetshenziswa lelithebula elilandelayo: CAPS 19

ULWAZI JIKELELE EmaBangeni APHANSI 20 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO INQUBEKELAPHAMBILI KWIZINOMBOLO, UKUSEBENZA KANYE NOBUDLELWANO • Inqubekela phambili ebalulekile kwizinombolo, ukusebenza kanye nobudlelwano yenzeka ngezindlela ezintathu: -- Uhlelo lwezinombolo luyakhula -- Ukwethulwa kwezinhlobo ezahlukahlukene zezinombolo -- Ukushintsha kwamasu okubala • Ngesikhathi uhlelo lokuthuthukisa izinombolo lukhula kuze kufinyelele ebangeni le – 3, kulindeleke ukuthi abafundi bathuthuke kangcono kumasu okubala. Izibalo IBANGA 1-3 • Izinkinga ezisesimweni esejwayelekile kumele zithathe uhla lwezinombolo zeBanga kanye nokubala kwabafundi okusezingeni elifanele. ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Ukubala kusetshenziswa izinombolo eziphelele 1.1 Bala izinto eziphathekayo Bala izinto eziphathekayo Bala izinto eziphathekayo Bala izinto eziphathekayo Bala izinto Qagela bese ubala izinto okungenani Qagela bese ubala izinto okungenani Qagela bese ubala izinto okungenani Qagela bese ubala izinto okungenani eziyi – 10 ngokuyikho nsukuzonke. ezingama – 50 ngokuyikho ezingama – 200 ngokuyikho ezingama – 1000 ngokuyikho nsukuzonke. Gqugquzela ukubala nsukuzonke. Gqugquzela ukubala nsukuzonke. Gqugquzela ukubala ngamaqoqo. ngamaqoqo. ngamaqoqo. 1.2 Bala ukusuka phambili uye emuva Bala uya phambili ubuye uye emumva Bala uye phambili ubuye uye Bala uye phambili ubuye uye ngakunye kusukela koku 1 – 10; ngakunye kusukela kunoma iyiphi emumva: emumva: Bala uye inombolo phakathi kuka 0 – 100; • Ngakunye kusukela kunoma iyiphi phambili Sebenzisa imilolozelo efaka • Ngakunye kusukela kunoma iyiphi nasemuva izinombolo kanye namaculo Bala uye phambili: inombolo phakathi kuka 0-kuya e inombolo phakathi kuka 0-kuya e 200 1000 • Bala ngama -10 phakathi kuka - 0 • Bala ngama – 10 kusukela kunoma • Bala ngama – 10 kusukela kunoma kuya e – 100 iyiphi inombolo phakathi kuka -0 iyiphi inombolo phakathi kuka -0 kuya e – 200 kuya e – 1000 • Bala ngokuyisi – 5 phakathi kuka -0 • Bala ngokuyisi – 5 kusukela • Bala ngokuyisi – 5 kusukela kuya e – 100 kunoma iyiphi inombolo phakathi kunoma iyiphi inombolo phakathi kuka – 0 kuya e – 200 kuka – 0 kuya e – 1000 • Bala ngoku -2 phakathi kuka -0 • Bala ngaku – 2 kusukela kunoma • Bala ngaku – 2 kusukela kunoma kuya e – 100 iyiphi inombolo phakathi kuka iyiphi inombolo phakathi kuka 0- 0-kuya e 200 kuya e-1000 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Bala ngaku – 3 kusukela kunoma • Bala ngaku – 3 kusukela kunoma iyiphi inombolo phakathi kuka – 0 iyiphi inombolo phakathi kuka – 0 kuya e – 200 kuya e – 1000 • Bala ngaku – 4 kusukela kunoma • Bala ngaku – 4 kusukela kunoma iyiphi inombolo phakathi kuka – 0 iyiphi inombolo phakathi kuka – 0 kuya e – 200 kuya e – 1000 • Ngama – 20, 25, 50, 100 kuze kufike okungenani e – 1000

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Okumele izinombolo eziphelele 1.3 Buka, ukhombe ubuye ufunde Buka, ukhombe ubuye ufunde Buka, ukhombe ubuye ufunde Buka, ukhombe ubuye ufunde CAPS izinombolo izimpawu zezinombolo izinombol izinombolo Izimpawu namagama • Buka, ukhombe ubuye ufunde • Buka, ukhombe ubuye ufunde • Buka, ukhombe ubuye ufunde • Buka, ukhombe ubuye ufunde ezinombolo uphawu lwezinombolo kusukela uphawu lwezinombolo kusukela uphawu lwezinombolo kusukela ku uphawu lwezinombolo kusukela ku koku – 1 kuya e – 10. koku – 1 kuya e – 100. – 0 kuya e – 200. – 0 kuya e – 1 000. • Buka, ukhombe ubuye ufunde • Bhala izimpawu zezinombolo • Bhala izimpawu zezinombolo • Bhala izimpawu zezinombolo amagama ezinombolo kusukela kusuka ko -1 kuya ema - 20 kusuka ko -1 kuya ema - 200 kusuka ko -1 kuya ema – 1 000 koku – 1 kuya e – 10 • Buka, ukhombe ubuye ufunde • Buka, ukhombe ubuye ufunde • Buka, ukhombe ubuye ufunde amagama ezinombolo kusukela amagama ezinombolo kusukela ku amagama ezinombolo kusukela ku koku – 1 kuya e – 10. – 0 kuya e – 100. – 0 kuya e – 1 000. • Bhala amagama ezinombolo • Bhala amagama ezinombolo • Bhala amagama ezinombolo kusukela koku – 1 kuya e - 10 kusukela ku – 0 kuya e - 100 kusukela ku – 0 kuya e – 1 000 • UKUTHUTHUKISWA KOLWAZI L WEZINOMBOLO: Chaza, qhathanisa uphinde uhlele izinombolo eziphelele 1.4 Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela izinto iqoqo lezinto kuyofika e-10. kuyofika e-20. Chaza, qhathanisa ubuye • Chaza izinombolo eziphelele kuya • Chaza uqhathanise iqoqo lezinto uhlele izinombolo e-10. ngokuningi, okuncane, okulinganayo • Qhathanisa lezizinto ezimbili • Chaza uhlele iqoqo lezinto kusukela ozinikiwe ngobukhulu, ngobuncane, kokuningi kuya kokuncane, okuncane kunokunye, okukhulu nokuncane kuya kokuningi kunokunye, okungaphezulu kunokunye, okungaphansi kunokunye, okulinganayo, okuningi kakhulu, okuncane kakhulu, okumbalwa kuze kufike e-10. • Hlela izinto eziqoqiwe ezingaphezu kokubili kusuka kokuncane kakhulu kuya kokukhulu kakhulu kuze kufike e-10. 21 Izibalo IBANGA 1-3

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 1.4 Chaza, qhathanisa bese uhlela Chaza, uqhathanise ubuye uhlele Chaza, uqhathanise ubuye uhlele 22 izinombolo kuyofika e-20. izinombolo kuya ema – 99 izinombolo kuya ema – 999 Chaza, qhathanisa ubuye • Chaza bese uqhathanisa izinombolo • Chaza bese uqhathanisa izinombolo • Chaza bese uqhathanisa izinombolo uhlele izinombolo eziphelele ngokubancane eziphelele kuze ufike ema – 99 eziphelele kuze ufike ema – 999 ukunenye,enkulu ukunenye kanye usebenzisa okuncane kunokunye, usebenzisa okuncane kunokunye, neningi ukunenye, nengaphansi okukhulu kunokunye, okungaphezulu okukhulu kunokunye, okungaphezulu ukunenye, nelinganayo kunokunye, okungaphansi kunokunye, okungaphansi kunokunye kanye nokulinganayo kunokunye kanye nokulinganayo • Chaza bese uhlela izinombolo • Chaza bese uhlela izinombolo • Chaza bese uhlela izinombolo Izibalo IBANGA 1-3 kusukela kwencane kakhulu kuyofika eziphelele kuyofika ema-99 kusukela eziphelele kuze kufike ema - 999 kwenkulu kakhulu nakwenkulu kwencane kakhulu kuyofika kusukela kwezincane kakhulu kakhulu kuyofika kwencane kakhulu kwenkulu kakhulu nakwenkulu kuya kwezinkulu kakhulu, ezinkulu kakhulu kuyofika kwencane kakhulu kakhulu kuya kwezincane kakhulu. Sebenzisa izinombolo ezisho Sebenzisa izinombolo ezisho Sebenzisa izinombolo ezisho Sebenzisa izinombolo ezisho isikhundla ukukhombisa ukuhleleka, isikhundla ukukhombisa ukuhleleka, isikhundla ukukhombisa ukuhleleka, isikhundla ukukhombisa ukuhleleka, indawo noma isikhundla. indawo noma isikhundla. indawo noma isikhundla. indawo noma isikhundla. • Thuthukusa ukuqaphela izinombolo • Beka izinto emugqeni • Beka izinto emugqeni • Sebenzisa, ufunde uphinde ubhale ezisho isikhumdla isib. Okokuqala, ngokulandelana kusukela ngokulandelana kusukela izinombolo ezimele isikhundla okwesibili, okwesithathu kuyofika kweyokuqala kuya kweyeshumi kweyokuqala kuya kweyamashumi kwesithupha nokokugcina noma eyokuqala kuya amabili noma eyokuqala kuya kweyokugcina. Isib. Okokuqala, kweyokugcina. Isib. Okokuqala, okwesibili, okwesithathu ... okwesibili, okwesithathu ... okweshumi okwamashumi amabili UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Ubungako benani lenombolo 1.5 Qala ukubona ubungako benani Qala ukubona ubungako benani Qala ukubona ubungako benani benombolo okungenani izinombolo benombolo okungenani izinombolo benombolo okungenani izinombolo Ubungako ezingambili kufinyelela ema – 20 ezingambili kufinyelela ema – 99 ezingantathu kufinyelela ema – 999 benani lenombolo • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba ezingambili kubalwa ngamashumi ngambili kufinyelela ema – ngantathu kufinyelela kuma – 999 nangokukodwa /imivo. 99 kubalwa ngamashumi bebala ngamakhulu, ngamashumi nangokukodwa /imivo. nangokukodwa/imivo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukukhomba ubuye usho ubungako • Ukukhomba ubuye usho ubungako benombolo ngayinye. benombolo ngayinye

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 XAZULULA IZINKINGA ezisesimweni ESEJWAYELEKILE 1.6 Sebenzisa lamasu kuze kufike e - 10: Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo CAPS ukuxazulula izinkinga nokuchaza ukuxazulula izinkinga nokuchaza ukuxazulula izinkinga nokuchaza Amasu izixazululo zezinkinga: izixazululo zezinkinga: izixazululo zezinkinga: okuxazulula izinkinga • Izinsiza kufundisa eziphathekayo, • Izinsiza kufundisa eziphathekayo, • Imidwebo noma izinsiza kufundisa Isib. Izinto zokubala isib. (izinto zokubala)Amatshe, eziphathekayo, isib. (izinto ummbila, ubhontshisi njll. zokubala) amatshe, ummbila, • Isitebhisi sezinombolo ubhontshisi esiphathekayo • Izithombe ukuze kudwetshwe izibalo zengxoxo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili ngokulingana kabili ngokulingana kabili ngokulingana • Umugqa wezinombolo ohambisana • Umugqa wezinombolo • Umugqa wezinombolo nezinto eziphathekayo • Sondezela emashumini 1.7 Xazulula izibalo zamagama Xazulula izibalo zamagama Xazulula izibalo zamagama Xazulula izibalo zamagama (izibalo zengxoxo) ngokwesimo ngokwesimo esejwayelekile ngokwesimo esejwayelekile ngokwesimo esejwayelekile Ukuhlanganisa esejwayelekile ubuye uchaze ubuye uchaze isixazululo sakho ubuye uchaze isixazululo sakho ubuye uchaze isixazululo sakho nokususa isixazululo sakho esifaka esifaka ukuhlanganisa nokususa esifaka ukuhlanganisa nokususa ezinkingeni ezifaka ukuhlanganisa ukuhlanganisa nokususa esinezimpendulo ezifinyelela ema – esinezimpendulo ezifinyelela ema – nokususa eziholela ezimpendulweni esinezimpendulo ezifinyelela e – 10. 20. 99 kufinyelela ema – 999 1.8 Xazulula izibalo zamagama Xazulula izibalo zamagama Xazulula izibalo zamagama ngokwesimo esejwayelekile ubuye ngokwesimo esejwayelekile ubuye ngokwesimo esejwayelekile ubuye Ukuhlanganisa uchaze isixazululo sakho esifaka uchaze isixazululo sakho esifaka uchaze isixazululo sakho esifaka okuphindaphin- ukuhlanganisa okuphindaphindayo ukuhlanganisa okuphindaphindayo ukuhlanganisa okuphindaphindayo dayo okuholela okunemiphumela efinyelela ema – 20. okunemiphumela efinyelela ema – 50 okunemiphumela efinyelela e – 100 ekuphindaphinde- ni 23 Izibalo IBANGA 1-3

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 1.9 Chaza uxazulule izisombululo Xazulula uchaze izixazululo Xazulula uchaze izixazululo Xazulula uchaze izixazululo 24 ezimayelana nezibalo zamagama zezinkinga eziphathekayo kufaka zezinkinga eziphathekayo kufaka zezinkinga eziphathekayo kufaka Ukuhlela nga- ngokwesimo esejwayelikle (izibalo ukwahlukaniselana ngokulinganayo, ukwahlukaniselana ngokulinganayo, ukwahlukaniselana ngokulinganayo, maqoqo nokuh- zengxoxo) okufaka ukwahlukaniseana uhlele ngamaqoqo ezinombolo uhlele ngamaqoqo kufinyelela ema – uhlele ngamaqoqo kufinyelela e – lukaniselana ngokulinganayo, ukuhlele ngamaqoqo eziphelele kuze kufike ema – 20 50 kanye nezimpendulo ezingafaka 100 kanye nezimpendulo ezingafaka okuholela ekwahl- izinombolo eziphelele kuze kufike e kanye nezimpendulo ezingafaka izinsalela. izinsalela. ukaniseni 10 kanye nezimpendulo ezingafaka izinsalela. izinsalela. UKUXAZULULA IZINKINGA ezisesimweni ESEJWAYELEKILE Izibalo IBANGA 1-3 1.10 Xazulula uchaze izixazulo Xazulula uchaze izixazulo ngezinkinga eziphathekayo ezifaka ngezinkinga eziphathekayo ezifaka Ukuhlukaniselana ukwabelana ngokulinganayo ukwabelana ngokulinganayo okuholela okuholela kwizixazululo ezifaka okuholela kwizixazululi ezifaka kumaqhezu ingxenye eyodwa kokuphelele. ingxenye eyodwa kokuphelele kanye nezingxenye ezingaphezu kweyodwa kokuphelele. 1.11 Thuthukisa ulwazi lwemali • Ukukwazi ukubona nokukhomba • Ukuwazi ukubona nokukhomba • Ukuwazi ukubona nokukhomba esetshenziswa eNingizimu Afrika imali yaseNingizimu Afrika imali yaseNingizimu Afrika yonke imali ewuhlweza Imali ewuhlweza nengamaphepha. ewuhlweza (5c, 10c, 50c,R1, R2, ewuhlweza (5c, 10c, 50c,R1, nengamaphepha esetshenziswa R5), nengamaphepha (R10, R20) R2, R5), nengamaphepha (R10, eNingizimu Africa R20,R50) • Ukuxazululwa kwezinkinga zemali • Ukuxazululwa kwezinkinga zemali • Ukuxazululwa kwezinkinga ezifaka isamba noshintshi kulemali ezifaka isamba noshintshi kulemali zemali ezifaka isamba noshintshi – 20c, R20 – 90c, R99 owuhlweza nemali yamaphepha • Guqula imali ewuhlweza ibe amaphepha; eyamaphepha ibe uhlweza . UKUBALA OKUKHULULEKILE 1.12 Sebenzisa lamasu alandelayo uma Sebenzisa lamasu alandelayo uma Sebenzisa lamasu alandelayo uma ubala: ubala: ubala: Amasu (izindlela noma amaqhinga) • Imidwebo noma izinsiza kufundisa • Imidwebo noma izinsiza kufundisa eziphathekayo zokubala eziphathekayo zokubala Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili ngokulingana kabili ngokulingana kabili ngokulingana • Umugqa wezinombolo ohambisana • Umugqa wezinombolo • Umugqa wezinombolo nezinto eziphathekayo. • Ukusondezela emashumini

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 1.13 Xazulula ngomlomo izinkinga • Hlanganisa kuze kufike kuma – 20 • Hlanganisa kuze kufike kuma – 99 • Hlanganisa kuze kufike kuma – zokuhlukanisa nokuhlanganisa 999 Ukuhlanganisa • Susa ema – 20 • Susa ema – 99 CAPS ezinezixazululo ezifinyelela e-10. nokususa • Susa ema – 999 • Sebenzisa izimpawu ezifanele (+, • Sebenzisa izimpawu ezifanele (+, –, =, ) –, =, ) • Sebenzisa izimpawu ezifanele (+, –, =, ) • Yenza uphindelela amabhondi kuze • Yenza uphindelela amabhondi kuze kufike e – 10 kufike e – 20 • Yenza uphindelela amabhondi kuze kufike ema – 30 1.14 • Hlanganisa inombolo efanayo • phindaphinda izinombolo kusukela • Phindaphinda noma iyiphi Ukuhlanganisa ngokuphindelela kufinyelela ema kweyodwa kuya kwezilishumi ngoku inombolo ngoku -2,3,4,5,10 kuze ngokuphindelela – 20 - 2,5,3 nangoku-4 kuze kufike ema kufike e– 100 okuholela • Sebenzisa izimpawu ezifanele (+, – 50 • Sebenzisa izimpawu ezifanele (x, ezibalweni =, ) • Sebenzisa izimpawu ezifanele (+, ) zokuphindaphinda x, =, ) 1.15 • Hlukanisa izinombolo kufinyelela Ukwahlukanisa e - 100 ngalezi zinombolo: 2,3,4,5,10 • Sebenzisa izimpawu ezifanele (÷, =, ) 25 Izibalo IBANGA 1-3

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 1.16 Ulwazi lwezinombolo: Uhla Ulwazi lwezinombolo: uhla Ulwazi lwezinombolo: uhla Ulwazi lwezinombolo: uhla 26 olufinyelela e-10 olufinyelela e – 20 olufinyelela e – 99 olufinyelela e –1000 Izibalo zekhanda Umsebenzi ngamunye uqala • Shono inombolo engaphambi noma ngezibalo zekhanda: emuva kwenombolo enikiwe. • Hlela iqoqo olinikwe lezinombolo • Hlela iqoqo olinikwe lezinombolo • Bala izinto zansukuzonke • Hlela iqoqo olinikwe lezinombolo ezikhethiwe. ezikhethiwe. • Bala uye phambili ubuye uye ezikhethiwe. • Qhathanisa izinombolo kufinyelela • Qhathanisa izinombolo kufinyelela emumva • Qhathanisa izinombolo kufinyelela ema-99 bese usho ukuthi iyiphi ema-1000 usho ukuthi iyiphi • Ukubala ngezinombolo ezisho ema-20 usho ukuthi iyiphi enkulu enkulu noma encane ngoku enkulu noma encane ngoku isikhundla noma encane ngokukodwa noma -1.2,3,4,5,10 -1.2,3,4,5,10 Izibalo IBANGA 1-3 okubili. • Shaya izandla kaningi/ kambalwa • Ikuphi ukushaya okuningi/ okuncane/okungaphezulu/ okumbalwa • Iyiphi inombolo eba ngaphambili/ ngemimva/ ephakathi Ukukhumbula okusheshayo: Ukukhumbula okusheshayo: Ukukhumbula okusheshayo: • Imigomo yokuhlanganisa nokususa • Imigomo yokuhlanganisa nokususa • Khumbula imigomo ukufika e -10. kufika ema-20 yokuhlanganisa nokususa kufika • Susa noma uhlanganise ubala ema-20 ngokuyishumi kusukela ku-0 kuya • Susa noma uhlanganise ubala e-100 ngokuyishumi kusukela ku-0 kuya e-100 • Imigomo yikuphindaphinda usebenzisa: -- Ithebula lokuphindaphinda ngokubili kufika ema - 20 -- Ithebula lokuphindaphinda ngokuyi - 10 kufika e – 100 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 1.16 • Imigomo yokuhlukanisa izinombolo: Izibalo zekhanda CAPS -- Hlukanisa ngokubili kufinyelela ema – 20 -- Hlukanisa ngokuyi – 10 kufinyelela e – 100 Amaqhinga okubala: Amaqhinga okubala: Amaqhinga okubala: Sebenzisa amaqhinga okuhlanganisa Sebenzisa amaqhinga okuhlanganisa Sebenzisa lamaqhinga alandelayo: nokususa ngokuyikho: nokususa ngokuyikho: • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala ukuze • Beka inombolo enkulu kuqala ukuze ukuze ubale uqhubeke noma ubale uqhubeke noma ubala uya ubale uqhubeke noma ubala uya ubala uya emumva. emumva. emumva. • Umugqa wezinombolo. • Umugqa wezinombolo. • Umugqa wezinombolo. • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili ngokulingana kabili ngokulingana kabili ngokulingana • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi kokuhlanganisa nokususa. kokuhlanganisa nokususa. • Sebenzisa ubudlelwano phakathi kokuphindaphinda nokuhlukanisa. 27 Izibalo IBANGA 1-3

ULWAZI IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 1.17 • Sebenzisa bese usho ingxenye • Sebenzisa bese usho ingxenye 28 eyodwa kokuphelele kwizimo eyodwa kokuphelele kanye Amaqhezu ezejwayelekile ufaka ohhafu, nezingxenye ezingaphezulu amakota, okukodwa kokuthathu kweyodwa kokuphelele nokukodwa kokuhlanu. kwizimo ezejwayelekile kufaka ohhafu, amakota, okukodwa kokuyisishiyagalombili, okukodwa kokuthathu, okukodwa kokuhlanu, okukodwa kokuyisithupha. Izibalo IBANGA 1-3 • Ukukwazi ukubona amaqhezu • Ukukwazi ukubona amaqhezu emidwebweni kwimidwebo • Ukukwazi ukubona ukuthi ohhafu ababili noma okuthathu kokuthathu kwenza okuphelele, nokuthi uhhafu owodwa kanye namakota amabili kuyalingana. • Bhala amaqhezu kahhafu o-1 • Bhala amaqhezu njengohhafu, nokubili kokuthathu (Isib. ½) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE EmaBangeni APHANSI 2. AMAPHETHINI, UkuxhumanaKANYE NE-ALJEBHRA Inqubekela phambili kumaphethini, imisebenzi kanye ne-Aljebhra CAPS • Kumaphethini, Imisebenzi kanye ne-Aljebhra, abafundi bathola amathuba oku: -- qedela bese uqhubeke amaphethini lela ezahlukene; kanye -- nokukhomba nokuchaza amaphethini. • Ukuchaza amaphethini kwenza isisekelo kubafundi bamaBanga Aphakathi (Intermediate Phase) ukuchaza imithetho yamaphethini. Lokho kuphenduka kube ngokuhleliwe emsebenzini wama-aljebhra kumaBanga Aphezulu (Senior Phase). IZIHLOKO IBanga- R IBanga-1 IBanga-2 IBanga-3 2.1 Kopisha bese uqhubeka Kopisha, uqhubeke bese uchaza Kopisha, uqhubeke bese uchaza Kopisha, uqhubeke bese uchaza Amaphethini Kopisha bese uqhubeka Kopisha, uqhubeke bese uchaza Kopisha, uqhubeke bese uchaza Kopisha, uqhubeke bese uchaza asejiyometri namaphethini alula usebenzisa • ngamagama • ngamagama • ngamagama izinto eziphathekayo nemidwebo • Amaphethini alula enziwe • Amaphethini alula enziwe • Amaphethini alula enziwe (Isib: usebenzisa imibala nezimo). ngezinto eziphathekayo. ngezinto eziphathekayo. ngezinto eziphathekayo • Amaphethini alula enziwe • Amaphethini axube izinto eziningi • Amaphethini axube izinto eziningi ngemidwebo yemigqa, izimo enziwe ngemidwebo yemigqa, ezenziwe ngemidwebo yemigqa, noma izinto izimo noma izinto izimo noma izinto Ukwakha amaphethini akho Ukwakha nokuchaza amaphethini Ukwakha nokuchaza amaphethini Akha amaphethini akho akho akho okusazibalo mdwebo • Ngezinto eziphathekayo • Ngezinto eziphathekayo • Ngezinto eziphathekayo • Ngokudweba imigqa, izimo noma • Ngokudweba imigqa, izimo noma • Ngokudweba imigqa, izimo noma izinto izinto izinto Amaphethini asizungezile Amaphethini asizungezile Amaphethini asizungezile Khomba, uchaze ngamagama Khomba, uchaza ngamagama Khomba, uchaze ngamagama bese ukopishe amaphethini okusazibalo ukopishe amaphethini okusazibalo ukopisha amaphethini okusazibalo mdwebo mdwebo mdwebo • emvelweni • emvelweni • emvelweni • kusuka empilweni yesimanje • kusuka empilweni yesimanje • kusuka empilweni yesimanje yansuku zonke, yansuku zonke. yansuku zonke. • kusuka emasikweni ethu ayigugu • kusuka emasikweni ethu ayigugu • kusuka emasikweni ethu ayigugu 2.2 Kopisha, uqhubeke bese uchaza Kopisha, uqhubeke bese uchaza Kopisha, uqhubeke bese uchaza Amaphethini Kopisha, uqhubeke bese Kopisha, uqhubeke bese Kopisha, uqhubeke bese ezinombolo uchaza ukulandelana okulula uchaza ukulandelana okulula uchaza ukulandelana okulula 29 kwezinombolo okungenani kufike kwezinombolo okungenani kufike kwezinombolo okungenani kufike e - 100 e - 200 e - 999 Ukwakha nokuchaza amaphethini Ukwakha nokuchaza amaphethini Ukwakha nokuchaza amaphethini Izibalo IBANGA 1-3 akho akho akho

ULWAZI JIKELELE EmaBangeni APHANSI 3. INDAWO NESIMO (IJIYOMETRI) 30 Inqubekela phambili yendawo nesimo Ingqubekela phambili ebalulekile kwindawo nesimo yenzeka ngoku: • ngokugxila ezakhiweni ezintsha nasezimpawini zezimo nezinto kumaBanga onke; kanye • noukusuka ekufundeni ulimi lwesikhundla kanye nokuqondanisa ukubukeka okwahlukene kwezinto ezifanayo kuya ekufundeni nasekulandeleni izinkomba kumabalazwe angahlelekile. IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 Izibalo IBANGA 1-3 3.1 Ulimi lwesikhundla Ulimi lwesikhundla Ulimi lwesikhundla Isikhundla, isimo Chaza isikhundla sento eyodwa Chaza isikhundla sento eyodwa Chaza isikhundla sento eyodwa nokubukeka kwento kwenye. isib: phezu kwe-, phambi kwenye. isib: phezu kwe-, phambi kwenye. isib: phezu kwe-, phambi kwe;ngemuva kwe-; kwesokunxele; kwe;ngemuva kwe-; kwesokunxele; kwe;ngemuva kwe-; kwesokunxele; kwesokudla; phezulu; phansi; eduze kwesokudla; phezulu; phansi; eduze kwesokudla; phezulu; phansi; eduze kwe- kwe- kwe- Isikhundla nokubuka Isikhundla nokubuka Isikhundla nokubuka • Bona bese uqondanisa ukubukeka • Bona bese uqondanisa ukubukeka • Bona bese uqondanisa ukubukeka okwahlukene kwezinto ezifanayo okwahlukene kwezinto ezifanayo okwahlukene kwezinto ezifanayo zansuku zonke zansuku zonke zansuku zonke • Isho into yansuku zonke uma ikhonjiswe ngendlela engajwayelekile • Funda, humusha bese udweba ibalazwe elingahlelekile, noma ukubuka ngaphezulu iqoqo lezinto. • Thola izinto kubalazwe Isikhundla nezinkomba Isikhundla nezinkomba Isikhundla nezinkomba • Landela izinkomba ulokhu uhamba Isikhundla nezinkomba ekilasini nasesikoleni. • Landela izinkomba ulokhu uhamba • Landela izinkomba ulokhu uhamba • Landela izinkomba ulokhu uhamba ekilasini ekilasini • Nika izinkomba zokulokhu uhamba ekilasini Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Landela imiyalelo ukubeka into ekilasini nasesikoleni. eyodwa enobudlelwano nokunye • Landela izinkomba ezisuka isib: beka ipeni emuva kwebhokisi endaweni eyodwa kuya kwenye ebalazweni elingahlelekile.

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 3.2 Uhla lwezinto Uhla lwezinto Uhla lwezinto Uhla lwezinto Izinto ezinhlangothi Bona uphinde ubize izinto Bona uphinde ubize izinto Bona uphinde ubize izinto Bona uphinde ubize izinto CAPS ntathu (3-D) ezinhlangothi ntathu (3-D) ekilasini ezinhlangothi ntathu (3-D) ekilasini ezinhlangothi ntathu (3-D) ekilasini ezinhlangothi ntathu (3-D) ekilasini Izinto ezisabhola nasezithombeni. nasezithombeni. nasezithombeni. • Izinto ezisabhola (imbulunga) • Izinto ezisabhola (imbulunga) • Izinto ezisabhola • Izinto ezisabhokisi • Izinto ezisabhokisi (iphrizimu) • Izinto ezisabhokisi (iphrizimu) • (imbulunga) • isilinda • Izinto ezisabhokisi • (iphrizimu) • isilinda Izimpawu zezinto Izimpawu zezinto Izimpawu zezinto • iphiramidi Chaza, hlela bese uqhathanisa izinto Chaza, hlela bese uqhathanise izinto Chaza, hlela bese uqhathanise izinto • ikhoni ezinhlangothi ntathu (3-D) ngoku: ezinhlangothi ntathu (3-D) ngoku: ezinhlangothi ntathu (3-D) ngoku: Izimpawu zezinto • wobungako • wobungako • wobungako • Chaza, hlela bese uqhathanise • imibala • imibala • izinto eziginqikayo izinto ezinhlangothi ntathu (3-D) ngoku: • izinto eziginqikayo • izinto eziginqikayo • izinto ezishelelayo • izimo ezinhlangothi mbili (2- • izinto ezishelelayo • izinto ezishelelayo D) ezenza ubuso bezinto Imisebenzi okugxilwa kuyo Imisebenzi okugxilwa kuyo Imisebenzi okugxilwa kuyo ezinhlangothi ntathu • Sebenzisa izinto ezinhlangothi • Bheka futhi wakhe izinto • Bheka futhi wakhe izinto • ingaphezulu lendawo endlalekile ntathu (3-D) njengamabhuloki ezinhlangothi ntathu (3-D) ezinhlangothi ntathu (3-D) noma emagwingci okwakha, okusetshenziswa usebenzisa izinto eziphathekayo usebenzisa izinto eziphathekayo, Imisebenzi okugxilwa kuyo kabusha, njll ukwakha izinto njengamabhuloki okwakha, izimo ezinhlangothi mbili, ezakhiwe ngezinto ezahlukene. okusetshenziswa kabusha, izinto amabhuloki okwakha, • Bheka futhi wakhe izinto Isib: umbhoshongo, ibhuloho njll zokwakha. okusetshenziswa kabusha, izinto ezinhlangothi ntathu (3- zokwakha nezinto ezinhlangothi D) usebenzisa izinto ntathu ezisazibalo mdwebo. eziphathekayo njengezimo ezinhlangothi mbili ezisikiwe, ubumba, izinti zokuvungula, izinti zokuphuza,nezinye izinto ezinhlangothi ntathu ezisazibalo mdwebo. 31 Izibalo IBANGA 1-3

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 3.3 Uhla lwezimo Uhla lwezimo Uhla lwezimo Uhla lwezimo 32 Izimo ezinhlangothi • Bona bese usho izimo Bona bese usho izimo ezinhlangothi Bona bese usho izimo ezinhlangothi Bona bese usho izimo ezinhlangothi mbili (2-D) ezinhlangothi mbili (2-D) mbili (2-D) mbili (2-D) mbiliu (2-D) • indilinga • indilinga • indilinga • indilinga • unxantathu • unxantathu • unxantathu • unxantathu Ukukhumbula, ukubona nokusho • isikwele • isikwele • isikwele amagama ezimo ezinhlangothi mbili • unxande • unxande ekilasini nasezithombeni, ukufaka: Izibalo IBANGA 1-3 Izimpawu zezimo Izimpawu zezimo Izimpawu zezimo • izimpawu zabafundi • Chaza, hlela bese uqhathanise • Chaza, hlela uphinde uqhathanise • Chaza, hlela uphinde uqhathanise • igama lekilasi izimo ezinhlangothi mbili (2-D) izimo ezinhlangothi mbili (2-D) izimo ezinhlangothi mbili (2-D) • isikwele ngoko: ngoko: ngoko: • bungako • wobungako • isimo Izimpawu zezimo • imibala • isimo • amacala aqondile • Chaza, hlela bese uqhathanise • amacala aqondile • amacala aqondile • amacala ayindilinga izimo ezinhlangothi mbili (2-D) • amacala ayindilinga • amacala ayindilinga ngoko: Dweba izimo • bungako • izindilinga • imibala • onxantathu • amacala aqondile • izikwele • amacala ayindilinga • onxande Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 3.4 Okufananse nxazombili Okufananse nxazombili Okufananse nxazombili Okufananse nxazombili Okufana nse • Ukubona ukuhlukana komzimba • Ukubona ukuhlukana komzimba CAPS nxazombili wakhe kabili izingxenye ezifana wakhe kabili izingxenye ezifana nse. nse. • Bona uphinde udwebe umugqa • Bona uphinde udwebe umugqa • Bona uphinde udwebe umugqa ohlukanisa izimo ezinhlangothi ohlukanisa izimo ezinhlangothi ohlukanisa izimo ezinhlangothi mbili ezisazibalo mdwebo nalezo mbili ezisazibalo mdwebo nalezo mbili ezisazibalo mdwebo nalezo ezingezona ijiyometri. ezingezona ijiyometri. ezingezona ijiyometri. • Thola umugqa ohlukanisa izinto phakathi zilingane ngokugoqa iphepha phakathi nendawo lihlukane kabili. 33 Izibalo IBANGA 1-3

ULWAZI JIKELELE EmaBangeni APHANSI 34 4. ISILINGANISO Ingqubekela phambili ekulinganiseni • Ingqubekela phambili ebalulekile ekulinganiseni kuwo wonke amaBanga yenzeka ngokwethulwa kwalokhu: -- Izindlela ezintsha zokulinganisa; -- Amathulusi amasha okulinganisa, kuqala emathulizini angahlelekile kuya kumathuluzi ahlelekile kumaBanga 2 no 3; -- Izikali ezintsha zokulinganisa, ikakhulukazi kumaBanga 2 no 3, Izibalo IBANGA 1-3 • Ukubala nokuxazululwa kwezinkinga zokulinganisa kumele kunakekekelwe ukuthi kusetshenziswe izinombolo esezifundiwe. IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 4.1 Ukudlula kwesikhathi Ukudlula kwesikhathi Isikhathi Ukuxoxa ngokudlula kwesikhathi Ukuxoxa ngokudlula kwesikhathi • Kuxoxwa ngezinto ezenzeke emini • Hlela izigameko ezenzeka nasebusuku ezimpilweni zabo. • Abafundi balandelanisa izigameko • Qhathanisa ubude besikhathi ezenzeke emini usebenzisa ulimi isib. side kuna, sifushane kuna, siyashesha kuna, • Abafundi bahlela izigameko sihamba kancane kuna. ezenzeka njalo ezimpilweni zabo • Hlela izigameko usebenzisa ulimi njengokuthi izolo, namuhla, kusasa. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 4.1 Ukusho isikhathi Ukusho isikhathi Ukusho isikhathi Isikhathi • Chaza ukuthi into yenzeka nini CAPS ngokusebenzisa ulimi isib ekuseni, ntambama, ebusuku, ngaphambi kwesikhathi, ngemuva kwesikhathi. • Shono bese ulandelanisa izinsuku • Shono bese ulandelanisa izinsuku • Funda izinsuku (umhlaka bani) zesonto nezinyanga zonyaka. zesonto nezinyanga zonyaka. ekhalendeni • Faka izinsuku zokuzalwa • Faka izinsuku zokuzalwa, • Faka izinsuku zokuzalwa, ekhalendeni. imugubho yezenkolo, amaholidi, imugubho yezenkolo, amaholidi, izigameko zomlando, izigameko izigameko zomlando, izigameko zesikole ekhalendeni. zesikole ekhalendeni. • Isho isikhathi ngokwa mahora, • Isho isikhathi ngokwa isigamu sehora kanye nekota -- amahora lehora. -- uhhafu wehora -- ikota lehora -- amaminithi usebenzisa iwashi lezinti nelezinombolo nezinye izinto zokukala isikhathi isib. umakhalekhukhwini Bala ubude besikhathi nokudlula Bala ubude besikhathi nokudlula kwesikhathi kwesikhathi • Sebenzisa ikhalenda ukubala • Sebenzisa ikhalenda ukubala nokuchaza ubude besikhathi: nokuchaza ubude besikhathi: -- Ngezinsuku, -- Ngezinsuku, -- Ngamasonto -- Ngamasonto -- Ngezinyanga • Ukushintsha kusuka ezinsukwini kuya evikini • Ukushintsha kusuka emavikini kuya ezinyangeni • Sebenzisa iwashi ukubala ubude • Sebenzisa iwashi ukubala ubude besikhathi: besikhathi: -- Ngamahora -- ngamahora 35 -- Uhhafu wehora -- ngohhafu wehora -- ngekota lehora Izibalo IBANGA 1-3

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 4.2 Ukukala okungahlelekile Ukukala okungahlelekile Ukukala okungahlelekile Ukukala okungahlelekile 36 Ubude • Qhathanisa bese uhlela ubude, • Qhathanisa bese uhlela ubude, ukuphakama noma ububanzi ukuphakama noma ububanzi bezinto ezimbili noma ngaphezulu bezinto ezimbili noma ngaphezulu ngokuzibeka eduze kwenye. ngokuzibeka eduze kwenye. Sebenzisa ulimi ukukhuluma Sebenzisa ulimi ukukhuluma ngokuqhathanisa Isib. Okude kuna, ngokuqhathanisa Isib. Okude kuna, okufushane kuna, okude kuna, okufushane kuna, okude kuna, okubanzi ngokuthe xaxa, okubanzi ngokuthe xaxa, Izibalo IBANGA 1-3 • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, hlela bese ubhala phansi hlela bese ubhala phansi hlela bese ubhala phansi ubude usebenzisa ukukala ubude usebenzisa ukukala ubude usebenzisa ukukala okungenasilinganiso Isib. okungenasilinganiso Isib. okungenasilinganiso Isib. ngezandla, amagxathu, ubude ngezandla, amagxathu, ubude ngezandla, amagxathu, ubude bamapensela, nezinto zokubala bamapensela, nezinto zokubala bamapensela, nezinto zokubala • Chaza ubude bezinto ngokubala • Chaza ubude bezinto ngokubala • Chaza ubude bento bese usho ubude ngokwezikali bese usho ubude ngokwezikali ngokubala bese usho ukuthi ezingahlelekile. ezingahlelekile. kude kangakanani ngesikali esingahlelekile. Ukwethulwa kokulinganisa Ukwethulwa kokulinganisa ngokuhlelekile ngokuhlelekile • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, hlela bese ubhala ubude hlela bese ubhala ubude usebenzisa amamitha (induku usebenzisa amamitha (induku eyimitha noma intambo eyimitha) eyimitha noma intambo eyimitha) njengesikali esilinganisiwe sobude. njengesikali esilinganisiwe sobude. • Qagela bese ulinganisa ubude ngamasentimitha usebenzisa irula (akudingekile ukuguqula amamitha abe amasentimitha) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 4.3 Isilinganiso okungahlelekile Isilinganiso okungahlelekile Isilinganiso okungahlelekile Isilinganiso okungahelekile CAPS Isisindo • Qhathanisa bese uhlela isisindo • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, • Qagela,linganisa,qhathanisa,hlela sezinto ezimbili noma ngaphezulu hlela, bese ubhala hlela, bese ubhala ,bese ubhala isisindo usebenzise ngokuzizwa noma usebenzise isisindo usebenzise isikali isisindo usebenzise isikali isikali sokuzimelela kanye isikali sokuzimelela. sokuzimelela kanye nokukala sokuzimelela kanye nokukala nokukala okungenasilinganiso Isib. okungenasilinganiso Isib. okungenasilinganiso Isib. amablokisi,izitena amabhulokisi, izitini. amabhulokisi, izitini. • Chaza isisindo sezinto ngokubala • Chaza isisindo sezinto ngokubala • Chaza isisindo sezinto ngokubala ukhombise isisindo ngokwe zikali ukhombise isisindo ngokwe zikali ukhombise isisindo ngokwe zikali ezingahlelekile. ezingahlelekile ezingahlelekile • Sebenzisa ulimi ukuqhathanisa, • Sebenzisa ulimi ukuqhathanisa, • Sebenzisa ulimi ukuqhathanisa, • Sebenzisa ulimi ukuqhathanisa, Isib. kulula, kuyesinda, kulula kuna, Isib. kulula, kuyesinda, kulula kuna, Isib. kulula, kuyesinda, kulula kuna, Isib. kulula, kuyesinda, kulula kune, kusinda kune kusinda kune kusinda kune kusinda kune Ukwethulwa kokulinganisa Ukwethulwa kokulinganisa okukuhlelekiIe okukuhlelekiIe • Qhathanisa, hlela ubhale isisindo • Qhathanisa, uhlele bese ubhala sezinto ezithengisayo ezinesisindo isisindo sezimpahla ezipakishiwe esikaliwe esingama khilogram sabhalwa: Isib.2 amakhilogramu elayisi,1 -- ngamakhilogramu. isib 2 ikhilogramu ka fulawa. amakhilogramu wempuphu no 1 khilogramu washukela. -- Amagramu isib 500g kasawoti • Linganisa isisindo sakho • Linganisa isisindo sakho ngamakhilogramu usebenzisa ngamakilogramu usebenzisa isikali isikali sasendlini yokugeza sasendlini yokugeza.. Ayikho inguquko edingekayo phakathi kwamagramu namakhilogramu 4.4 Ukukala okungahlelekile Ukukala okungahlelekile Ukukala okungahlelekile Ukukala okungahlelekile Umthamo / • Qhathanisa bese uhlela umthamo • Qhathanisa bese uhlele umthamo okumumethwe woketshezi olusezitsheni ezimbili woketshezi olusezitsheni ezimbili ezibekwe ndawonye. Abafundi ezibekwe ndawonye. Abafundi bazohlola ngokuthi bathele bazohlola ngokuthi bathele uketshezi esitsheni sesithathu. uketshezi esitsheni sesithathu. • Qhathanisa bese uhlela umthamo • Qhathanisa bese uhlela umthamo woketshezi olungamumathwa woketshezi olungamumathwa izitsha ezimbili uma zigcwele. izitsha ezimbili uma zigcwele. • Sebenzisa ulimi uqhathanise Isb. • Sebenzisa ulimi ukuqhathanise 37 okuningi kunokunye, okuncane Isib. okuningi kunokunye, kunokunye, okugcwele, okungekho okuncane kunokunye, okugcwele, lutho. okungekho lutho. Izibalo IBANGA 1-3

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 4.4 • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, 38 hlela bese ubhala umthamo hlela bese ubhala umthamo hlela bese ubhala umthamo Umthamo / wezitsha usebenzisa ukukala wezitsha (Isib.umthamo wezitsha (Isib.umthamo okumumethwe okungenasilinganiso Isib.izipuni ongagcwalisa isitsha) usebenzisa ongagcwalisa isitsha) usebenzisa kanye nezinkomishi. ukukala okungenasilinganiso Isib. ukukala okungenasilinganiso Isib. izipuni kanye nezinkomishi. izipuni kanye nezinkomishi. • Chaza umthamo wesitsha • Chaza umthamo wesitsha • Chaza umthamo wesitsha ngokubala bese usho ukuthi ngokubala bese usho ukuthi ngokubala bese usho ukuthi ugcwala ngezikali ezingaki ugcwala ngezikali ezingaki ugcwala ngezikali ezingaki ezingahlelekile Isib.ibhodlela ezingahlelekile Isib.ibhodlela ezingahlelekile Isib.ibhodlela Izibalo IBANGA 1-3 lithatha umthamo wezinkomishi lithatha umthamo wezinkomishi lithatha umthamo wezinkomishi ezine. ezine. ezine. Ukuthulwa kokulinganisa Ukuthulwa kokulinganisa okuhlelekile okuhlelekile • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, uhlele bese ubhala umthamo uhlele bese ubhala umthamo wezinto ezikalwe ngamalitha. wezinto ezikalwe ngamalitha, uhhafu welitha nekota yelitha. • Qhathanisa, hlela bese ubhalea • Qhathanisa, hlela bese ubhala umthamo wezinto ezithengisayo umthamo wezinto ezithengisayo ezikaliwe ezingamalitha Isib.2 ezikaliwe ezingamalitha isib 2 amalitha obisi, 1 ilitha lesiphuzo, 5 amalitha obibs, 1 ilitha lesiphuzo, amalitha kapende. 5 amalitha kapende noma ibhalwe ngamamililitha isib 500 amamililitha wobisi, 340mamililitha wesiphuzo, 750 amililitha kawoyela • Inkomishi yetiye ejwayelekile ingamamililitha angama 250. • Ithisipuni ejwayelekile ingamamililitha ama 5. (Ayikho inguquko edingekayo phakathi kwamamililitha namalitha ) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 4.5 Ubude bengaphandle lento CAPS Ubude Phenya iBanga lezimo ezinhlangothi bengaphandle lento mbili 2-D nezinto ezinhlangothintathu kanye nobubanzi 3-D usebenzisa ukuqhathanisa ngqo bendawo noma isikali esingahlelekile. Ububanzi bendawo Phenya ububanzi bendawo ngokusebenzisa amathayela (aphansi / obondeni) 39 Izibalo IBANGA 1-3

ULWAZI JIKELELE EmaBangeni APHANSI 40 5. UKUQOKELELWA KOLWAZI LWEZIBALO Inqubekela phambili kokuqokelelwa kolwazi lwezibalo • Inqubekela phambili ebalulekile ekuqokelelweni kolwazi lwezibalo kumaBanga ahlukene yenzeka ngoku: -- Ukusuka ekusebenzeni ngezinto uye ekusebenzeni ngolwazi, futhi -- Usebenza ngezindlela ezintsha zokukhombisa ulwazi lwezibalo. • Abafundi kufanele basebenze ngolwazi lwezibalo oluphelele okungenani kanye ngonyaka – lokhu kufaka ukuqoqa kanye nokuhlela ulwazi, ukwethulwa kolwa, ukuhlaziya, ukuhumusha kanye nombiko wolwazi. Izibalo IBANGA 1-3 • Ezinye izingxenye zolwazi oluqokelelwe lungenzeka kweminye imisebenzi yezibalo. IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 5.1 Ukuqoqa nokuhlela izinto Ukuqoqa nokuhlela izinto Ukuqoqa Qoqa bese uhlela izinto Qoqa bese uhlela izinto nokuhlela izinto eziphathekayo zansukuzonke eziphathekayo zansukuzonke 5.2 Beka okumele iqoqo lezinto Beka okumele iqoqo lezinto eziphathekayo ezihlelekile . eziphathekayo ezihlelekile Okumele iqoqo lezinto Dweba isithombe sezinto eziqoqiwe Dweba isithombe sezinto eziqoqiwe eziphathekayo ezihlelekile 5.3 Xoxa ubike ngeqoqo lezinto Xoxa nubike ngeqoqo lezinto eziphathekayo ezihlelekile eziphathekayo ezihlelekile Ukuxoxa nokubika ngeqoqo lezinto • Nika izizathu ngokuthi okuqoqiwe eziphathekayo kuhlelwe kanjani ; ezihlelekile • Phendula imibuzo ngoku: • Phendula imibuzo ngoku: -- kuhlelwe kanjani okuqoqiwe -- Zihlelwe kanjani izinto (indlela owenze ngayo) -- kudwetshwe kanjani okuqoqiwe -- Okuhleliwe kwaqoqwa kubukeka kanjani Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Chaza okuqoqiwe / umdwebo • Chaza ukuthi okuqoqiwe kuhlelwe kanjani

IZIHLOKO IBanga R Ibanga loku-1 IBANGA LESI-2 IBANGA LESI-3 5.4 Qoqa uphinde uhlele ulwazi Qoqa uphinde uhlele ulwazi Qoqa uphinde uhlele ulwazi lwezibalo lwezibalo CAPS Ukuqoqa bese • Qoqa ulwazi ngekilasi noma isikole uhlela ulwazi • Qoqa ulwazi ngekilasi noma isikole • Qoqa ulwazi ngekilasi noma isikole ukuze uphendule imibuzo ethulwa ukuze uphendule imibuzo ethulwa ukuze uphendule imibuzo ethulwa uthisha uthisha uthisha • Hlela ulwazi olwethulwe uthisha noma incwadi yomfundi noma yokusebenza • Hlela ulwazi lwezibalo kulokhu: -- Uhla -- amathalisi -- amathebula 5.5 Ukubeka okumele ulwazi Ukubeka okumele ulwazi Ukubeka okumele ulwazi Ukubeka okumele • Beka okumele ulwazi • Beka okumele ulwazi • Beka okumele ulwazi: ulwazi ngokusebenzisa igrafu yezithombe ngokusebenzisa igrafu yezithombe -- Ngokwenza igrafu yezithombe • Sebenzisa igrafu yezithombe • Sebenzisa igrafu yezithombe (Sebenzisa igrafu yezithombe okukodwa nokukodwa okukodwa nokukodwa okukodwa nokukodwa okuhambisanayo. okuhambisanayo. okuhambisanayo) -- amabhagrafu 5.6 Ukuhlaziya nokuhumusha ulwazi Ukuhlaziya nokuhumusha ulwazi Ukuhlaziya nokuhumusha ulwazi Ukuhlaziya Phendula imibuzo ngolwazi kwigrafu Phendula imibuzo ngolwazi kwigrafu Phendula imibuzo ngokumele ulwazi nokuhumusha yezithombe yezithombe ngo: ulwazi • Sebenzisa igrafu yezithombe • Sebenzisa igrafu yezithombe • Ngokwenza igrafu yezithombe okukodwa nokukodwa okukodwa nokukodwa (Sebenzisa igrafu yezithombe okuhambisanayo. okuhambisanayo. okukodwa nokukodwa okuhambisanayo) • Bhagrafu 41 Izibalo IBANGA 1-3

Izibalo IBANGA 1-3 3.3 Ukucacisa OKUQUKETHWA Kulengxenye yokucaciswa kolwazi, othisha banikezwa lokhu: • Ulwazi jikelele lweThemu lwamaBanga R - 3; • Iziphakamiso zokulandelana kwezihloko ngokwamathemu: akuzona zonke izingxenye zezihloko ezifundiswayo ithemu ngayinye; ezinye izingxenye zezinye izihloko kumele zifundiswe ngaphambili kwezinye izingxenye zalezo zihloko. • Iziphakamiso zezikhathi ezibekelwe izihloko onyakeni. Njengoba ezinye izingxenye zolwazi zidinga isikhathi esiningi kezinye, ngakhoke ezinye izihloko zidinga isikhathi esiningi kunezinye; kanye • NAmanothi Acacisayokanye nomhlahlandlela wokufundisa onezibonelo ezifanele. Ingxenye ngayinye yolwazi ihlukaniswe ngezihloko. Zonke izingxenye zolwazi kufanele zifundiswe ngethemu. Ukuhleleka kwezihloko ngamathemu kunika umqondo wokusabalalisa nokubukeza izihloko kuwona wonke amathemu onyakeni. Akubalulekile ukufundisa zonke izihloko zendawo nesimo, isilinganiso kanye ukuqokelelwa kolwazi kuwo wonke amathemu. Kodwa ke akuqikelelwe ukuthi zonke izihloko ziyafundiswa ngonyaka. Kwingxenye ye – 2 (isigamu 2.6) unikeziwe isisindo sezingxenye zolwazi. Uma kuhlanganiswa amahora anikeziwe onyakeni, ungakwazi ukubala isikhathi sokufundisa sengxenye ngayinye yolwazi. Othisha Bangakhetha ukuhlela ulwazi balwabele isikhathi ngokwehlukile kunalokho okuphakanyisiwe kule sahluko. Othisha Bangashintsha isikhathi esiphakanyisiwe sesahluko kancane Kodwa ke, kufanele kuqashelwe isisindo esisondelene kanye namahora okufundisa izingxenye zolwazi lwezibalo emaBangeni aphansi. • Ebangeni R izibalo zisemazingeni okuqala ngakhoke akumele zibe nezikhathi zokuzifundisa ezihleliwe. Uthisha weBanga R kufanele afake ukufundiswa kwezibalo emisebenzini yansuku zonke nakuba izikhathi uthisha kufanele abe nesikhathi lapho egxila khona emsebenzini yezibalo, ngaphandle kwalokho abafundi bangeke bathuthuke olwazini namakhono adingekayo ezibalweni. • Izikhathi zamaBanga R – 3 zibekwe ngalendlela: -- Amahora ayisikhombisa kufanele asetshenziselwe izibalo ngesonto (amasonto ayi -10 x 4 amathemu x 7 amahora = 280 amahora ngonyaka). -- Isifundo ngasinye sezibalo kufanele sibe yihora eli-1 namaminithi angama 24 ngosuku kumaBanga 1 – 3. -- Lokhu kusho ukuthi kunamathemu amane anamasonto ayi 10 anezifundo ezinhlanu ngesonto (uMsombuluko kuya koLwesihlanu). -- Banike isonto lokuqala ethemini ukuthi bajwayele futhi babukeze umsebenzi abawenzile, njengoba abafundi bavame ukukhohlwa ulwazi abalufundile ngesikhathi samaholide babuye bakhohlwe inqubo abayejwayele yesikole. Banike isonto lokugcina ethemini ukuba babukeze ulwazi abalufundile. Lokhu kunika 8 x 4 x 5 = 160 izifundo. 42 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 3.4 ISIVININI NOKULANDELANISA OKUQUKETHWE Amathebula alandelayo awamaBanga R – 3: • Ukulandelana kwezihloko onyakeni (kukhombisa ukuhlelwa kwezihloko ngamathemu kanye nokuncoma ubude besikhathi isihlokweni ngasinye ingxenye yokuqukethwe) • Ukulandelanisa kwezihloko onyakeni (kukhombisa ukuthi izihloko zifakwe kanjani ngamathemu nenqubekela phambili yilwazi namakhono ngamathemu) • Amanothi Acacisayoisihloko ngasinye - amathebhula anika incazelo yolwazi nomhlahlandlela wokufundisa ngesihloko ngasinye ngokulandelana kwazo ngamathemu Ukuhlelwa okuzofundiswa – Ukuhlelwa kwezihloko ngethemu EmaBangeni aphansi isihloko sezinombolo yisona esisemqoka ekufundweni kwezibalo. Ezikhathini eziningi ezifundweni zezibalo ngesonto, ngethemu nangonyaka kugxilwa ekufundweni kwi - Izinombolo, Ukusebenza kanye Nobudlelwane bazo. Okungenani kathathu noma ngaphezulu ngesonto makugxilwe ezifundweni ze - Izinombolo, Ukusebenza kanye Nobudlelwane bazo. Isikhathi esisele asihlukaniselwe ezinye izingxenye zolwazi lwezibalo. INdawo neSimo kanye nokuLinganisa kudinga kunikwe isikhathi esiningi kunokuQokelelwa koLwazi, kanye namaPhethini,Imisebenzi kanye ne Aljebhra. Amathebula alandelayo akhombisa ukuthi zingaki izifundo okufanele zenziwe kwingxenye ngayinye yolwazi nesihloko ebangeni ngalinye kumaPhethini, Imisebenzi kanye neAljebhra; Indawo neSimo; Isilinganiso kanye noKuqokelelwa koLwazi. • IBanga R: Ukuhlelwa kwezingxenye zolwazi nezihloko zezifundo Izibalo eBangeni R zisezingeni loqala kolwazi lwezibalo, ngakhoke isikhathi esiphakamisiwe sokufundisa sisetshenziselwa ukufundiswa kwezibalo ezihleliwe nalezo ezixubene nezinye izifundo ezingahlelelwe.Lokhu kwenzelwe ukukhombisa ukusebenzisa lonke ulwazi olumele lufundiswe. Imisebenzi yezibalo zokuqala ingaba ukubala inani lamapuleti nezinkomishi abazokusebenzisa, imidlalo yokubala abayidlala ngaphandle, imidlalo yasendlini njengamadomino namaphazili,njll. Uthisha kufanele ahlele imisebenzi, alungise izinsiza kufundisa kuye ngokwezidingo zabafundi. Indawo neSimo iyingxenye esemqoka ekuthuthukisweni kokufundwa kwezibalo kubafundi abasebancane, okufanele isabalaliswe kwisonto lonke, lapho izingxenye ezithile ziholwa uthisha, kuthi amathuba amaningi okwakha, imidlalo yasesihlabathini nasemanzini yenziwe abafundi. Isilinganiso kufanele kuhlanganiswe nemisebenzi yokubala, njengokuqagela nokubala uma kukalwa iBanga ngezandla, ngezinyawo namanyathelo. Irejista yansukuzonke kanye neshadi lesimo sezulu kunikeza abafundi ithuba lokusebenza ngokuqokelela ulwazi. CAPS 43

Izibalo IBANGA 1-3 Ithebula lesi- 3.1: ukwabiwa kwesikhathi sengxenye yolwazi ngalunye ngesonto Isikhathi Ingxenye yokuqukethwe Izihloko Esiphakanyisiwe Izinombolo Izimpawu kanye Ukubala nobudlelwane bazo Ukubona izinombolo Ukukhomba nokuchaza izinombolo 120 imizuzu Ulwazi lwezinombolo Ukuxazulula izinkinga zezibalo Amaphethini, Ukuxhumana Ukukopisha, ukwandisa, ukwakha iphethini lakhe 80 imizuzu kanye ne-Aljebhra Indawo neSimo (Ijiyometri) Ukubona, ukukhomba nokusho izimo ezinhlangothi mbili/ izithombe Izibalomdwebo Ukwakha izinto ezinhlangothintathu ngokusebenzisa izinto 80 imizuzu eziphathekayo Ubudlelwane nendawo Izinkomba Isilinganiso Isikhathi Ubude 80 imizuzu Isisindo Umthamo Ukuqokelelwa kolwazi Qoqa, hlela, dweba, funda bese ubeka okumele ulwazi. 60 imizuzu 420 imizuzu ISAMBA 7 amahora ngesonto Ibanga 1: Ukwabiwa kwezingxenye zolwazi nezihloko ezifundweni zamaBanga loku-1 kuya kwele-3 1 Okungenani izifundo ezintathu (phakathi kwamahora ama - 4 kuya kwa 42) ngesonto azosetshenziswa ukufundisa Izinombolo, izimpawu kanye nobudlelwane bazo emaBangeni oku-1, 2 nele-3. Izifundo ezimbili ezisele (phakathi 1 kwamahora 22 kuya kwa -3) ahlukaniselwa izihloko zezinye izinxenye zolwazi lwezibalo njengoba kunconyiwe nge- zansi. Ithebula lesi- 3.2: Inani lezifundo eliphakanyisiwe lengxenye ngayinye yeBanga loku- 1 Inani Lezifundo Ingxenye yokuqukethwe Isihloko Ithemu 1 Ithemu 2 Ithemu 3 Ithemu 4 Isamba Izinombolo kanye Zonke izihloko zezinombolo kanye 22 30 28 25 105 nobudlelwane bazo nobudlelwane bazo Amaphethini, Amaphethini ezinombolo 3 3 3 3 12 Ukuxhumana kanye ne- Aljebhra Amaphethini ayizibalomdwebo 1 1 1 1 4 Izimo ezinhlangothi mbili 3 3 6 Indawo neSimo Izinto ezinhlangothi ntathu 3 2 1 6 (Ijiyometri) Isikhundla, isimo nokubukeka kwento 2 1 3 Okufana nse nxazombili 1 1 2 Isikhathi 2 2 Ubude 2 2 4 Isilinganiso Isisindo 2 2 4 Umthamo / okumumethwe 1 2 1 4 Ukuqoqa, ukuhlela, ukubeka okumele 2 1 3 ulwazi nokuhlaziya izinto Ukuqokelelwa kolwazi Ulwazi oluphelele 3 3 Izingxenye zolwazi oluphelele 2 2 Inani Lezifundo 40 40 40 40 160 44 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Ithebula lesi- 3.3: Inani lezifundo eliphakanyisiwe lengxenye ngayinye yeBanga lesi- 2 Inani Lezifundo Ingxenye yokuqukethwe Isihloko Ithemu 1 Ithemu 2 Ithemu 3 Ithemu 4 Isamba Izinombolo kanye Zonke izihloko zezinombolo kanye 24 25 24 26 99 nobudlelwane bazo nobudlelwane bazo Amaphethini, Amaphethini ezinombolo 3 3 3 3 12 Ukuxhumanakanye ne- Aljebhra Amaphethini ayizibalomdwebo 1 1 1 1 4 Izimo ezinhlangothi mbili 3 3 6 Indawo neSimo Izinto ezinhlangothi ntathu 3 2 1 6 (Ijiyometri) Isikhundla, isimo nokubukeka kwento 2 1 3 Okufana nse nxazombili 1 1 2 Isikhathi 3 1 3 1 8 Ubude 3 1 4 Isilinganiso Isisindo 3 1 4 Umthamo / okumumethwe 3 1 4 Ukuqoqa, ukuhlela, ukubeka okumele ulwazi nokuhlaziya izinto Ukuqokelelwa kolwazi Ulwazi oluphelele 3 3 6 Izingxenye zolwazi oluphelele 1 1 2 Inani Lezifundo 40 40 40 40 160 Ithebula lesi- 3.4: Inani lezifundo eliphakanyisiwe lengxenye ngayinye yeBanga lesi- 3 Inani Lezifundo Ingxenye yokuqukethwe Isihloko Ithemu 1 Ithemu 2 Ithemu 3 Ithemu 4 Isamba Izinombolo kanye Zonke izihloko zezinombolo kanye 26 22 19 27 94 nobudlelwane bazo nobudlelwane bazo Amaphethini, Amaphethini ezinombolo 3 3 3 3 12 Ukuxhumana kanye ne- Aljebhra Amaphethini ayizibalomdwebo 1 1 1 1 4 Izimo ezinhlangothi mbili 2 2 4 Indawo neSimo Izinto ezinhlangothi ntathu 3 3 1 7 (Ijiyometri) Isikhundla, isimo nokubukeka kwento 2 3 5 Okufana nse nxazombili 2 1 3 Isikhathi 3 2 3 2 10 Ubude 2 2 4 Isilinganiso Isisindo 2 1 3 Umthamo 2 1 3 Ubude bengaphandle lento 1 1 Ububanzi bendawo 2 2 Ulwazi oluphelele 3 3 6 Ukuqokelelwa kolwazi Izingxenye zolwazi oluphelele 1 1 2 Inani Lezifundo 40 40 40 40 160 CAPS 45

3.4.1 Ibanga 1 Ulwazi jikelele ngethemu ULWAZI JIKELELE LEBANGA 1 46 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 UKUTHUTHUKISA ULWAZI LWEZINOMBOLO: Ukubala usebenzisa izinombolo eziphelele 1.1 Bala izinto eziphathekayo kuya Bala izinto eziphathekayo kuya Bala izinto eziphathekayo kuya Bala izinto eziphathekayo kuya kweziyi-10 kwezingama-20 ngokuyikho. kuma-40 ngokuyikho. kuma-50 ngokuyikho. Bala izinto eziphathekayo Qagela inani lezinto esingazibala Qagela inani lezinto esingazibala Qagela inani lezinto esingazibala Qagela inani lezinto esingazibala ngokuyikho. ngokuyikho. ngokuyiko. ngokuyiko. Izibalo IBANGA 1-3 Gqugquzela ukubala izinto Gqugquzela ukubala izinto Gqugquzela ukubala izinto ngamaqoqo ngamaqoqo. ngamaqoqo. 1.2 Bala uyaphambili ubuye uye Bala uyaphambili ubuye uye Bala uyaphambili ubuye uye Bala uyaphambili ubuye uye emumva kanje: emumva kanje: emumva kanje: emumva kanje: Bala uyaphambili ubuye uye emumva • Ngakunye kusukela kunoma iyiphi • Ngakunye kusukela kunoma iyiphi • Ngakunye kusukela kunoma iyiphi • Ngakunye kusukela kunoma iyiphi inombolo phakathi kuka -1 kuya inombolo phakathi kuka -1 kuya inombolo phakathi kuka -1 kuya inombolo phakathi kuka -1 kuya kuma 20. kuma 50. kuma 80. kuma 100. Bala uya phambili kanje: Bala uya phambili kanje: Bala uya phambili kanje: • Ngama-10 kusuka kunoma iyiphi • Ngama-10 kusuka kunoma iyiphi • Ngama-10 kusuka kunoma iyiphi inombolo phakathi kuka -0 kuya inombolo phakathi kuka -0 kuya inombolo phakathi kuka -0 kuya kuma -50. kuma -80. kuma -100. • Ngaku -5 kusuka kunoma iyiphi • Ngaku -5 kusuka kunoma iyiphi • Ngaku -5 kusuka kunoma iyiphi inombolo phakathi kuka 0 kuya inombolo phakathi kuka 0 kuya inombolo phakathi kuka 0 kuya kuma -50. kma -80 kma -100 • Ngaku -2 kusuka kunoma iyiphi • Ngaku -2 kusuka kunoma iyiphi • Ngaku -2 kusuka kunoma iyiphi inombolo phakathi kuka 0 kuya inombolo phakathi kuka 0 kuya inombolo phakathi kuka 0 kuya kuma -20 kuma -80 kuma -100 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 UKUTHUTHUKISA ULWAZI LWEZINOMBOLO: Beka okumele izinombolo eziphelele 1.3 Ukubona, akhombe nokufunda Ukubona, akhombe nokufunda Ukubona, akhombe nokufunda Ukubona, akhombe nokufunda CAPS izinombolo izinombolo izinombolo izinombolo Uphawu negama lenombolo • Bona, khomba bese ufunda • Bona, khomba bese ufunda • Bona, khomba bese ufunda • Bona, khomba bese ufunda izimpawu zezinombolo kusukela izimpawu zezinombolo kusukela izimpawu zezinombolo kusukela izimpawu zezinombolo kusukela koku -1 kuya kuma -20 koku -1 kuya kuma -50 koku -1 kuya kuma -80 koku -1 kuya kuma -100 • Bhala izimpawu zezinombolo • Bhala izimpawu zezinombolo • Bhala izimpawu zezinombolo • Bhala izimpawu zezinombolo kusukela koku -1 kuya koku -5 kusukela koku -1 kuya koku -10 kusukela koku -1 kuya koku -20 kusukela koku -1 kuya koku -20 • Bona, khombea bese ufunda • Bona, khombea bese ufunda • Bona, khombea bese ufunda • Bona, khombea bese ufunda amagama ezinombolo kusukela amagama ezinombolo kusukela amagama ezinombolo kusukela amagama ezinombolo kusukela koku -1 kuya koku -5 koku -1 kuya koku -10 koku -1 kuya koku -10 koku -1 kuya koku -10 • Bhala amagama ezinombolo • Bhala amagama ezinombolo • Bhala amagama ezinombolo • Bhala amagama ezinombolo kusuka koku - 1 kuya koku -5. kusuka koku - 1 kuya koku -10. kusuka koku - 1 kuya koku -10 kusuka koku - 1 kuya koku -10 UKUTHUTHUKISA ULWAZI LWEZINOMBOLO: Chaza, qhathanisa bese uhlela izinombolo eziphelele 1.4 Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela izinto kuye kufike koku -5 izinto kuye kufike koku -10 izinto kuye kufike koku -15 izinto kuye kufike koku -20 Chaza, qhathanisa bese uhlela • Qhathanisa amaqoqo ezinto • Qhathanisa amaqoqo ezinto • Qhathanisa amaqoqo ezinto • Qhathanisa amaqoqo ezinto izinombolo ngobuningi, okumbalwa; ngobuningi, okumbalwa; ngobuningi, okumbalwa; ngobuningi, okumbalwa; ngokuningi kakhulu, okuncane ngokuningi kakhulu, okuncane ngokuningi kakhulu, okuncane ngokuningi kakhulu, okuncane kakhulu; kuningi kuna, kunca kuna; kakhulu; kuningi kuna, kunca kuna; kakhulu; kuningi kuna, kunca kuna; kakhulu; kuningi kuna, kunca kuna; kuyalingana, kuhlukile kuyalingana, kuhlukile kuyalingana, kuhlukile kuyalingana, kuhlukile • Hlela iqoqo lezinto kusukela • Hlela iqoqo lezinto kusukela • Hlela iqoqo lezinto kusukela • Hlela iqoqo lezinto kusukela kweziningi kakhulu kuya kweziningi kakhulu kuya kweziningi kakhulu kuya kweziningi kakhulu kuya kwezincane kakhulu nakwezincane kwezincane kakhulu nakwezincane kwezincane kakhulu nakwezincane kwezincane kakhulu nakwezincane kakhulukuya kweziningi kakhulu kakhulukuya kweziningi kakhulu kakhulukuya kweziningi kakhulu kakhulukuya kweziningi kakhulu 47 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.4 Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela Chaza, qhathanisa bese uhlela 48 izinomboli kuye kufike koku -5 izinombolo kuye kufike koku -10 izinombolo kuye kufike koku -15 izinombolo kuye kufike koku -20 Chaza, qhathanisa bese uhlela • Chaza, qhathanisa izinombolo • Chaza, qhathanisa izinombolo • Chaza, qhathanisa izinombolo • Chaza, qhathanisa izinombolo izinombolo ngokuthi inkulu kuna, incane kuna, ngokuthi inkulu kuna, incane kuna, ngokuthi inkulu kuna, incane kuna, ngokuthi inkulu kuna, incane kuna, iningi kuna,kungaphansi kuna; iningi kuna,kungaphansi kuna; iningi kuna,kungaphansi kuna; iningi kuna,kungaphansi kuna; kuyalingana kuyalingana kuyalingana kuyalingana • Chaza bese uhlela izinombolo • Chaza bese uhlela izinombolo • Chaza bese uhlela izinombolo • Chaza bese uhlela izinombolo - Kusukela kokuncane kakhulu - Kusukela kokuncane kakhulu - Kusukela kokuncane kakhulu - Kusukela kokuncane kakhulu Izibalo IBANGA 1-3 kuya kokukhulu kakhulu, kuya kokukhulu kakhulu, kuya kokukhulu kakhulu, kuya kokukhulu kakhulu, kusuka kokukhulu kakhulu, kuya kusuka kokukhulu kakhulu, kuya kusuka kokukhulu kakhulu, kuya kusuka kokukhulu kakhulu, kuya kokuncane kakhulu kokuncane kakhulu kokuncane kakhulu kokuncane kakhulu - Usebenzisa umugqa - engaphambi, engemumva, - engaphambi, engemumva, - engaphambi, engemumva, wezinombolo kusuka ku 1 kuya ephakathi nendawo ephakathi nendawo ephakathi nendawo kuoku -5 - Usebenzisa umugqa - Usebenzisa umugqa - Usebenzisa umugqa wezinombolo kusuka ku 0 kuya wezinombolo kusuka ku 0 kuya wezinombolo kusuka ku 0 kuya -10 -15 -20 Usebenzisa izinombolo zesikhundla ukuhlela, ukulandelana nangokwendawo • Beka izinto emgqeni ngokulan- delana kusukela kweyokuqala kuya kweyeshumi. Isib okokuqala, okwesibili, ikwesithathu,….okwe- shumi, okokugcina. • Ukuhlela izinombolo ngokwesikhundla ngokulandelana ukusuka kweyokuqala ukuya kweyeshumi. UKUTHUTHUKISA ULWAZI LWEZINOMBOLO: Ubungako benani lenombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 1.5 Ukubona ubungako benani Ukubona ubungako benani lezinombolo usuka e-11 -kuya e-15. lezinombolo usuka e-11 -kuya e-19 Ubungako benani lenombolo • Ukuhlakaza izinamba ezihamba Ukuhlakaza izinombolo ezihamba ngambili uzise emashumini ngambili uzise emashumini nasemiveni. Isib. 12 ungu 10 no 2 nasemiveni. Isib. 18 ungu 10 no 8

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 XAZULULA IZINKINGA ZEZIBALO ESIMWENI ESIJWAYELEKILE 1.6 Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo Sebenzisa lamaqhinga alandelayo Sebenzisa lamaqhinga alandelayo CAPS ukuxazulula izinkinga zezibalo bese ukuxazulula izinkinga zezibalo bese ukuxazulula izinkinga zezibalo bese ukuxazulula izinkinga zezibalo bese Amasu okuxazulula uchaza isisombululo kanje: uchaza isisombululo kanje: uchaza isisombululo kanje: uchaza isisombululo kanje: izinkinga zezibalo • Sebenzisa izinsizakufunda • Sebenzisa izinsizakufunda • Sebenzisa izinsizakufunda • Sebenzisa izinsizakufunda eziphathekayo njengezinto eziphathekayo njengezinto eziphathekayo njengezinto eziphathekayo njengezinto zokubala. zokubala zokubala zokubala • Sebenzisa izithombe ukubonisa • Sebenzisa izithombe ukubonisa • Sebenzisa izithombe ukubonisa • Sebenzisa izithombe ukubonisa izibalo eziyingxoxo izibalo eziyingxoxo izibalo eziyingxoxo izibalo eziyingxoxo • Sebenzisa umugqa wezinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo owakhiwe ngezinto eziphathekayo • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise njengobuhlalu kabili izinombolo kabili izinombolo kabili izinombolo • Sebenzisa umugqa wezinombolo • Sebenzisa umugqa wezinombolo • Sebenzisa umugqa wezinombolo owakhiwe ngezinto eziphathekayo owakhiwe ngezinto eziphathekayo owakhiwe ngezinto eziphathekayo njengobuhlalu njengobuhlalu njengobuhlalu 1.7 Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo eziyingxoxo ezisesimweni zamagama ezisesimweni zamagama ezisesimweni zamagama ezisesimweni Ukuhlanganisa esijwayelekile bese uchaza esijwayelekile bese uchaza esijwayelekile bese uchaza esijwayelekile bese uchaza nokususa isisombululo usebenzisa isisombululo usebenzisa isisombululo usebenzisa isisombululo usebenzisa ukuhlanganisa, ukususa ezibalweni ukuhlanganisa, ukususa ezibalweni ukuhlanganisa, ukususa ezibalweni ukuhlanganisa, ukususa ezibalweni ezinika umphumela ofika esi -5. ezinika umphumela ofika esi -10. ezinika umphumela ofika esi -15 ezinika umphumela ofika esi -20 1.8 Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo zamagama ezisesimweni zamagama ezisesimweni zamagama ezisesimweni Ukuhlanganisa esijwayelekile bese uchaza esijwayelekile bese uchaza esijwayelekile bese uchaza okuphindayo isisombululo usebenzisa isisombululo usebenzisa isisombululo usebenzisa okuholela ukuhlanganisa okuphindayo ukuhlanganisa okuphindayo ukuhlanganisa okuphindayo ekuphindaphindeni ezibalweni ezinika umphumela ofika ezibalweni ezinika umphumela ofika ezibalweni ezinika umphumela ofika e -10. e -15 e -20. 49 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.9 Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo Uxazulula izinkinga zezibalo 50 zamagama ezisezimweni zamagama ezisezimweni zamagama ezisezimweni zamagama ezisezimweni Ukwenza ezijwayelekile bese bechaza ezijwayelekile bese bechaza ezijwayelekile bese bechaza ezijwayelekile bese bechaza amaqoqo kanye isisombululo besebenzisa ukwenza isisombululo besebenzisa ukwenza isisombululo besebenzisa ukwenza isisombululo besebenzisa ukwenza nokuhlukaniselana amaqoqo nokuhlukaniselana amaqoqo nokuhlukaniselana amaqoqo nokuhlukaniselana amaqoqo nokuhlukaniselana okuholela ezinombolo eziphelele ezibalweni ezinombolo eziphelele ezibalweni ezinombolo eziphelele ezibalweni ezinombolo eziphelele ezibalweni ezibalweni ezinemiphumela efika esi -5 ezinemiphumela efika esi -10 ezinemiphumela efika esi -15 ezinemiphumela efika esi -20 zokuhlukanisa ezingaba nezinsalela.. ezingaba nezinsalela ezingaba nezinsalela.. ezingaba nezinsalela 1.11 • Ukubona bese ukhomba imali • Ukubona bese ukhomba imali • Ukubona bese ukhomba imali Izibalo IBANGA 1-3 yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika Imali 5c, 10c, 20, 50c, R1, R2; R5 5c, 10c, 20, 50c, R1, R2; R5 - ewuhlweza 5c, 10c, 20, 50c, R1, • Ukuxazulula izinkinga zemali • Ukuxazulula izinkinga zemali R2; R5 ezifaka isamba noshintshi kuyofika ezifaka isamba noshintshi kuyofika - eyamaphepha R10 no R20 ku R10 no 20c ku R20 no 20c • Ukuxazulula izinkinga zemali ezifaka isamba noshintshi kuyofika ku R20 no 20c. UKUBALA NGOKUKHULULEKA 1.12 Sebenzisa amasu alandelayo uma Sebenzisa lamasu alandelayo uma Sebenzisa lamasu alandelayo uma Sebenzisa lamasu alandelayo uma ubala: ubala: ubala: ubala: Amasu • Izinsizakufunda eziphathekayo Isib. • Sebenzisa izinsizakufunda • Sebenzisa izinsizakufunda • Sebenzisa izinsizakufunda (izindlela zokwenza izinto zokubala eziphathekayo. Isib.izinto zokubala eziphathekayo. Isib.izinto zokubala eziphathekayo. Isib.izinto zokubala noma amaqhinga) • Dweba izithombe • Dweba izithombe • Dweba izithombe • Dweba izithombe • Umugqa wezinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo owenziwe izinto eziphathekayo • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise njengobuhlalu. kabili kabili kabili • Sebenzisa umugqa wezinombolo • Sebenzisa umugqa wezinombolo • Sebenzisa umugqa wezinombolo owakhiwe ngezinto eziphathekayo owakhiwe ngezinto eziphathekayo owakhiwe ngezinto eziphathekayo njengobuhlalu njengobuhlalu njengobuhlalu Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.13 Uhla lwezinombolo: 1 - 5 Uhla lwezinombolo: 1 - 10 Uhla lwezinombolo: 1 - 15 Uhla lwezinombolo: 1 - 20 Ukuhlanganisa • Hlanganisa kuze kufike okuyi -5 • Hlanganisa kuyofika e- 10 • Hlanganisa kuyofika e- 15 • Hlanganisa kuyofika e- 20 CAPS nokususa • Susa kokuyi -5 • Susa koku -10 • Susa koku -15 • Susa koku -20 • Enza uphindelela amabhondi kuze • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele kufike kwinombolo yesi -5 (+, –, =, ) (+, –, =, ) (+, –, =, ) • Enza uphindelela amabhondi kuze • Enza uphindelela amabhondi kuze • Enza uphindelela amabhondi kuze kufike kwinombolo yesi - 7 kufike kwinombolo yesi - 9 kufike kwinombolo yesi - 10 1.14 • Izibalo zokuhlanganisa • Izibalo zokuhlanganisa • Izibalo zokuhlanganisa okuphindayo (ukuphinda inombolo okuphindayo (ukuphinda inombolo okuphindayo 9 ukuphinda Ukuhlanganisa efanayo) kuyofika e -10. efanayo) kuyofika e -15. inombolo) kuyofika e -20. okuphindayo okuholela • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele ezibalweni (+, –, =, ) (+, –, =, ) (+, –, =, ) zokuphindaphinda 51 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.16 Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla 52 olufinyelela esi -5 olufinyelela esi -10 olufinyelela esi -15 olufinyelela esi -20 Izibalo Zekhanda • Hlela iqoqo lezinombolo olunikiwe. • Hlela iqoqo lezinombolo olunikiwe. • Hlela iqoqo lezinombolo olunikiwe. • Hlela iqoqo lezinombolo olunikiwe. • Qhathanisa izinombolo kusukela • Qhathanisa izinombolo kusukela • Qhathanisa izinombolo kusukela • Qhathanisa izinombolo kusukela kweyo -1 kuya e -5,yisho ukuthi kweyo -1 kuya e -10,yisho ukuthi kweyo -1 kuya e -15,yisho ukuthi kweyo -1 kuya e -20,yisho ukuthi iyiphi encane noma enkulu iyiphi encane noma enkulu iyiphi encane noma enkulu iyiphi encane noma enkulu ngokukodwa noma ngokubili. ngokukodwa noma ngokubili. ngokukodwa noma ngokubili. ngokukodwa noma ngokubili. Ukukhumbula okusheshayo: Ukukhumbula okusheshayo: Izibalo IBANGA 1-3 • Amabhondi ezinombolo kuya e -5 • Amabhondi kuya e -10 • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa nokususa kuya e -5 nokususa kuya e -10 Amaqhinga okubala Amaqhinga okubala Sebenzisa amaqhinga okuhlanganisa Sebenzisa amaqhinga okuhlanganisa nokususa ngokugculisayo: nokususa ngokugculisayo: • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala ukuze ubale uqhubeke noma uye ukuze ubale uqhubeke noma uye emumva. emumva. • Umugqa wezinombolo • Umugqa wezinombolo • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili kabili • Ukwakha nokuhlakaza inombolo • Ukwakha nokuhlakaza inombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Izinhlobo zezinkinga zezibalo: Ibanga 1 Lezi yizibonelo zezinhlobo zezinkinga ezibalulekile okufanele ukuthi uthisha azethule ngokuziphindaphinda ekilasni lakhe. Uma uthisha esebenza ngeqembu elincana, kufanele ayisho ngomlomo inkinga. Uma abafundi sebekwazi ukufunda, usengabanikeza izinkinga zezibalo ezibhalwe phansi, kodwa futhi ayisho inking ngomlomo. Izinkinga ezisesimweni esejwayelekile zingafakwa encwadini yokusebenzela, kodwa kube kufishane, iqonde ngqo kube ejwayelekile, uthisha kufanele aqiniseke ukuthi bonke abafundi bayaziqonda lezinkinga. Amaqoqo Ukwenza amaqoqo, kulahlwa izinsalela UNokwethaba uthengisa amahhabhula asezikhwameni ezinamahhabhula ngamathathu ngasinye. Unamahhabhula ayi - 14. Zingaki izikhwama ezinamahhabhula amathathu angazenza? Ukwenza amaqoqo, kufakwa nezinsalela ezimpendulweni USimanga ufuna ukunikeza ugogo wakhe ibhokisi lamaqanda ayi - 15. Mangaki amabhokisi azowadinga ukufaka amaqanda ayisithupha ibhokisi ngalinye? Ukuhlukaniselana Ukuhlukaniselana, kulahlwa insalela Hlukanisa uswidi oyi - 14 kubafundi abathathu ukuze bonke bathole alinganayo. Ukuhlanganisa okuphindayo Mangaki amasondo emabhayisikilini amane? Ukuhlanganisa nokususa Kunezinhlobo eziyisisekelo okungenani ezintathu zokuhlanganisa nokususa, inhlobo ngayinye ingavezwa ngezindlela ezehlukene. Izinhlobo eziyisisekelo: Ushintshol ekubekeni inkinga UNoluthando ubenamahhabhula amahlanu. USipho umuphe amanye ayisishiyagalombili. Mangaki amahhabhula kaNoluthando esewonke? UNoluthando ubenamahhabhula ayi - 13, unikeze uSipho amahhabhula amahlanu. Mangaki amahhabhula asele nawo manje? Hlanganisa UNomfundo unomabuli abahlanu abaluhlaza kanye nabayisishiyagalombili ababomvu. Unomabuli abangaki sebebonke? UNomfundo unomabuli abayi - 13. Abahlanu babo baluhlaza, bonke abanye babomvu. Bangaki omabuli ababomvu anabo? CAPS 53

Izibalo IBANGA 1-3 Qhathanisa UNomfundo unobhanana abayi - 13. UThemba unobhanana abahlanu. Bangaki obhanana uNoluthando anabo abangaphezulu kwabakaThemba? Veza inkinga ngayinye ngezindlela ezahlukene Izinkinga ingavezwa ngezindlela ezahlukene. Isibonelo, zombili lezizinkinga ezoshintsho, kodwa okungaziwa ku- sezindaweni ezahlukene. • UNoluthando ubekade enamahhabhula. UThemba wamupha amanye ayisishiyagolombili. Manje usenamahhabhula ayi - 13. Ubekade enamahhabhula amangaki uNoluthando ekuqaleni? • UNoluthando ubekade enamahhabhula amahlanu. UPhilasande wamupha amanye. Manje unamahhabhula ayi - 13. Mangaki amahhabhula amnike wona uPhilasande? Izimo zezinkinga ezinobudlelwano obusebenzayo obehlukene UNokwethaba uthengisa amawolintshi abiza amarandi amane (R4) lilinye. Yenza ithebula lokumsiza ukuthola inani lamaoda amakhulu. Inani lamawolintshi 1 2 3 4 5 6 7 Inani ngokwamarandi 4 8 Sebenzisa ithebula ukuthola inani lamawolintshi ayisi - 7 Lezizinhlobo zezinkinga zezenzelwe ukusiza uthisha. Abafundi akumele baxinwe ngamagama alezizinkinga. Khum- bula ukuthi abafundi bajwayele ukusebenzisa izindlela ezahlukene zokuxazulula izinkinga okungenzeka kungabi yilokhu okulindelwe nguthisha. 54 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 1 2. AMAPHETHINI, UBUDLELWANE NE-ALJEBHRA IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 CAPS 2.1 Ukukopisha nokwandisa Ukukopisha, ukwandisa bese Ukukopisha, ukwandisa bese Amaphethini asizungezile uchaza uchaza OKUSEjiyometri Khomba, chaza nganagama bese Ukukopisha nokwandisa amaphethini Ukukopisha, ukwandisa bese uchaza Ukukopisha, ukwandisa bese uchaza ukopisha amaphethini asejiyometri alula usebenzisa: ngamagama. ngamagama. • emvelo • Izinto eziphathekayo; • Amaphethini alula enziwe ngezinto • Amaphethini alula enziwe ngezinto • awesimamje eziphathekayo eziphathekayo • Izithombe (usebenzise imibala • nasemasikweni nasemagugwini nezimo) • Amaphethini alula enziwe • Amaphethini alula enziwe ethu ngokudweba imidwebo eyenziwe ngokudweba imidwebo eyenziwe ngemigqa, ngezimo noma ngezinto ngemigqa, ngezimo noma ngezinto eziphathekay eziphathekayo Akha uchaze amaphethini akho Akha uchaze amaphethini l akho Akha uchaze amaphethini l akho • Akha amaphethini akho • Akha amaphethini akho • Akha amaphethini akho asejiyometri asejiyometri asejiyometri - Usebenzisa izinto eziphathekayo - Usebenzisa izinto eziphathekayo - Usebenzisa izinto eziphathekayo - Ngokudweba imigqa, izimo noma - Ngokudweba imigqa, izimo noma - Ngokudweba imigqa, izimo noma izinto eziphathekayo izinto eziphathekayo izinto eziphathekayo • Chaza amaphethini akho. • Chaza amaphethini akho. • Chaza amaphethini akho. Isiphakamiso sokulandelanisa Qala ukopishe bese wandisa amaphethini usebenzisa izinto eziphathekayo. Uma abafundi sebekwazi ukusebenzisa amakhrayoni namapensela, sebengaqala ukukopisha nokwandisa amaphethini ngokuwadweba. 55 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 2.2 Ukukopisha, ukwandisa bese Ukukopisha, ukwandisa bese Ukukopisha, ukwandisa bese Ukukopisha, ukwandisa bese 56 uchaza uchaza uchaza uchaza AMAPHETHINI EZINOMBOLO Ukukopisha, ukwandisa nokuchaza Ukukopisha, ukwandisa nokuchaza Ukukopisha, ukwandisa nokuchaza Ukukopisha, ukwandisa nokuchaza ukulandela okulula kwezinombolo ukulandela okulula kwezinombolo ukulandela okulula kwezinombolo ukulandela okulula kwezinombolo kuyofika kuma 20. kuyofika kuma 50 kuyofika kuma 80 kuyofika kuma 100 Ukulandelana kwezinombolo Ukulandelana kwezinombolo Ukulandelana kwezinombolo Ukulandelana kwezinombolo kufanele kufanele kokhombise ukubala uya kufanele kokhombise ukubala uya kufanele kokhombise ukubala uya kokhombise ukubala uya phambili phambili nokubala uya emumva phambili nokubala uya emumva phambili nokubala uya emumva nokubala uya emumva kanye: kanye: kanye: kanye: Izibalo IBANGA 1-3 • Ngaku 1 usuka kunoma iyiphi • Ngakunye usuka kunoma iyiphi • Ngaku 1 usuka kunoma iyiphi • Ngaku 1 usuka kunoma iyiphi inombolo phakathi kuka 1 no 100 inombolo phakathi kuka 1 kuya inombolo phakathi kuka 1 no 50 inombolo phakathi kuka 1 no 80 kuma -20 Ubala uya phambili ngo: Ubala uya phambili ngo: Ubala uya phambili ngo: • Ngama 10 kusuka kunoma iyiphi • Ngama 10 kusuka kunoma iyiphi • Ngama10 kusuka kunoma iyiphi inombolo ephakathi,kuka 0 kuya inombolo ephakathi,kuka 0 kuya inombolo ephakathi,kuka 0 kuya ku 50 ku 80 ku 100 • Ngaku 5 kusukela kunoma iyiphi • Ngaku 5 kusukela kunoma iyiphi • Ngaku 5 kusukela kunoma iyiphi inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya ku 50 ku80 ku 100 • Ngaku 2 kusukela kunoma iyiphi • Ngaku 2 kusukela kunoma iyiphi • Ngaku 2 kusukela kunoma iyiphi inombolo ephakathi kuka o kuya inombolo ephakathi kuka o kuya inombolo ephakathi kuka o kuya ku 50 ku 80 ku 100 Akha bese uchaza amaphethini Akha bese uchaza amaphethini Akhabese uchaza amaphethini akho akho akho • Akha uchaze iphethini lakho • Akha uchaze iphethini lakho • Akha uchaze iphethini lakho lezinombolo lezinombolo lezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 1 3. INDAWO NEZIMO (IJIYOMETRI) IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 CAPS 3.1 Ulimi olusho ukuthi into ikuphi Ulimi olusho ukuthi into ikuphi Isikhundla, Chaza ukuthi into ikuphi uma Chaza ukuthi into ikuphi uma inkomba uqhathanisa nenye. Isibonelo: phezu uqhathanisa nenye. Isibonelo: phezu nokubukeka kwe, phambili kwe, emumva kwe, kwe, phambili kwe, emumva kwe, kwento kwesobunxele, kwesokudla, phezulu, kwesobunxele, kwesokudla, phezulu, phansi, eduze kwe. phansi, eduze kwe. Indawo nezinkomba Indawo nezinkomba • Landela izinkomba ukunyakaza • Landela izinkomba ukunyakaza ekilasini. ekilasini. • Landela imiyalelo ukubeka into • Landela imiyalelo ukubeka into uyiqhathanisa nenye. Isib. Faka uyiqhathanisa nenye. Isib. Faka ipensela phakathi ebhokisini ipensela phakathi ebhokisini Iziphakamisozokugxilwa kukho Iziphakamisozokugxilwa kukho ngokulandelana komsebenzi ngokulandelana komsebenzi wethemu yokuqala wethemu 4 • Ulimi lwesikhundla kufanele • Umsebenzi wesikhundla lwethulwe ngemisebenzi lapho nezinkomba ungahlanganiswa abafundi benyakazisa umzimba. ngokubhala njengokudweba, ukufaka imibala noma • Lokhu kungahlanganiswa ukuqondanisa umdwebo negama. nangemisebenzi yokubhala efana nokudweba, ukufaka imibala • Amanye amagama amasha noma ukuqondanisa amagama esikhundla angathulwa nezithombe. ngemisebenzi efaka ukunyakaza kwabafundi. • Sebenzisa undile uma ulandela izinkomba. • Izinkomba zingenziwa ngokuphindelela ngokwenza • Izinkomba zingenziwa imisenzi lapho abafundi benyakaza ngokuphindelela ngokwenza noma benyakazisa izinto imisenzi lapho abafundi benyakaza ngokwemyalelo. noma benyakazisa izinto ngokwemyalelo. Isikhundla nokubukeka kwento • Qondanisa ukubukeka kwento efanayo nsukuzonke. 57 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.2 Uhla Lwezinto Uhla Lwezinto Uhla Lwezinto 58 Izinto ezinhlangoth- Bona bese unika igama lezinto Bona bese unika igama lezinto Bona bese unika igama lezinto intathu ezinhlangothi ntathu ezikhona ezinhlangothi ntathu ezikhona ezinhlangothi ntathu ezikhona ekilasini kanye nasezithombeni ekilasini kanye nasezithombeni ekilasini kanye nasezithombeni • Izinto eziyibhola nasezithombeni nasezithombeni • Izinto eziyibhokisi • Izinto eziyibhola • Izinto eziyibhola • Izinto eziyibhokisi • Izinto eziyibhokisi Izibalo IBANGA 1-3 Izimpawu zezinto Izimpawu zezinto Izimpawu zezinto Chaza, uhlele bese uqhathanisa Chaza, uhlele bese uqhathanisa Chaza, uhlele bese uqhathanisa izinto ezinhlangothi ntathu ngokwe: izinto ezinhlangoth intathu ngokwe: izinto ezinhlangothi ntathu ngokwe: • ngokobungako • ngobungako • ngobungako • ngokombala • umbala • umbala Imisebenzi okugxilwa kuyo • izinto ezigingqikayo • izinto ezigingqikayo Buka bese wakha izinto • iznto ezishelelayo • iznto ezishelelayo ozinikiwe ezinhlangothi ntathu usebenzisa izinto eziphathekayo njengamabhuloki nezinye izinto ezingabuye zisebenziseke., izinto zokwakha Iziphakamiso zemisebenzi Iziphakamiso zemisebenzi I Iziphakamiso zemisebenzi okugxilwe kuyo ngokulandelana okugxilwe kuyo ngokulandelana okugxilwe kuyo ngokulandelana eThemu 1: eThemu 3: eThemu 4: • Imidlalo ekhululekile lapho • Sebenzisa izinto eziphathekayo kusethenziswa izinto ezinhlangothi ezinomumo webhola, namabhokisi ntathu. Ukwakha izinto ozithandayo ahlukene nokunye okunezimo usebenzisa amabhuloki,izinto eziyiprizimu kanxande noma zokwakha noma izinto ezingabuye eyekhiyubhu. Phenya ikuphi zisebenziseke. Lokhu kungenziwa okukwazi ukugingqika, ukushelela ngesikhathi sokusebenza kanye nongakubekwa phezulu ngokuzimela. kokunye. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Kopisha isimo sento elethiwe • Khomba bese uchaza uthisha.Lokhu kungenziwa izibalomdwebo kanye nezinye ngesikhathi sokusebenza izinto bese usho ukthi zakheke ngokuzimela. njengebhola noma njengebhokisi. • Umsebenzi uphethwa Umsebenzi uphethwa ngomsebenzi ngomsebenzi obhalwayo. obhalwayo.

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 • Qhathanisa ubungako bezinto CAPS ezifanayo e. g. isho ukuthi iliphi ibhola elikhulu • Khuluma bese uhlela izinto eziphathekayo ngokombala. • Khomba bese uchaze izibalomdwebo nezinye izinto usho ukuthi zimi njengebhola noma njengebhokisi. • Umsebenzi uphethwa ngomsebenzi obhalwayo. 3.3 Uhla lwezimo Uhla lwezimo IZIMO Bona bese usho amagama ezinto Bona bese usho amagama ezinto EZINHLANGOTHI ezinhlangothi mbili: ezinhlangothi mbili: MBILI 2-D • indilinga • indilinga • unxantathu • unxantathu • isikwele • isikwele Izimpawu zezimo Izimpawu zezimo Chaza, hlela bese uqhathanise izimo Chaza, hlela bese uqhathanise izimo ezinhlangothi mbili kanje: ezinhlangothi mbili kanje: • ngobungako • ngobungako • ngombala • ngombala • amacala aqondile • amacala aqondile • amacala ayizindilinga • amacala ayizindilinga Iziphakamiso zemisebenzi Iziphakamiso zemisebenzi okugxilwe kuyo ngokulandelana okugxilwe kuyo ngokulandelana eThemu 2 eThemu 4 • Qala ngokudlala okukhululekile ngezimo ezahlukene okufaka ukwenza izithombe ngezimo eziyizibalo mdwebo ezisikiwe. Lokhu kungenziwa ngesikhathi sokusebenza ngokuzimela. Lokhu 59 kungenzeka ngesikha sezifundo zamakhono empilo. Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 • Kopisha isithombe esakhiwe 60 ngesimo esiyisibalomdwebo. Lokhu kungenzeka ngesikhathi sokusebenza ngokuzimela. • Qhathanisa ubungako bezinto ezifanayo njengengezikwele zihlelwa kusukela kwesincane kuya kwesikhulu, bese usebenzisa ulimi lobungako ukuchaza izimo. Izibalo IBANGA 1-3 • Xoxa ngemibala yezimo bese uhlela izimo ngemibala yazo. • Sebenzisa izindilinga, nezikwele • Sebenzisa izindilinga, izikwele eziwungako obungafani nonxantathu bese ukuhlela nonxantathu abayimo ezahlukene. ngokwamacala ayindilinga Bahlele ngokuthi banamacala naqondile. aqondile noma ayindilinga. • Hlela ubeke izimo ngamaqoqo • Hlela ubeke izimo ngamaqoqo njengonxantathu, izikwele, njengonxantathu, izikwele, onxande noma izindilinga izindilinga. • Phetha lengxenye ngemisebenzi • Phetha lengxenye ngemisebenzi ebhalwayo. ebhalwayo. 3.4 Okufana nse nxazombili Okufana nse nxazombili Okufana nse • Ukubona izinhlangothi ezimbili • Ukubona bese udweba nxazombili zomzimba wakho ezifanayo. umugqa ohlukanisa kabili izimo ezinhlangothimbili nokungezona • Ukubona bese udweba izibalomdwebo. umugqa ohlukanisa kabili izimo ezinhlangothimbili nokungezona izibalomdwebo. I Iziphakamiso zemisebenzi Iziphakamiso zemisebenzi okugxilwe kuyo ngokulandelana okugxilwe kuyo ngokulandelana eThemu 3 eThemu 4 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Bheka imigqa ehlukanisa izinto kabili zifane nse • Imisebenzi yokubhala akufanele • Imisebenzi yokubhala kufanele ibe “dweba ingxenye enye” ifake izibonelo lapho umugqa ohlu- kodwa kubekhona izibonelo kanisa kabili kufane ungabi osuka lapho abafundi bedweba umugqa phezulu wehle kuphela. ohlukanisa kabili kufane nse.

ULWAZI JIKELELE LEBANGA 1 4. ISILINGANISO IZIHLOKO Ithemu loku-1 Ithemu lesi-2 TERM 3 TERM 4 CAPS 4.1 Ukudlula kwesikhathi Isikhathi siyafundwa ngenkathi Isikhathi siyafundwa ngenkathi Isikhathi siyafundwa ngenkathi yezifundo zekilasi yezifundo zekilasi yezifundo zekilasi. ISIKHATHI Khuluma ngokudlula kwesikhathi • Hlela izehlakalo ezejwayelekile ezenzeka ezimpilweni zabo. • Qhathanisa ubude besikhathi usebenzisa ulimi lwesikhathi njen- gokuthi isikhathi eside / esifushane, esisheshayo, esamba kancane • Landelanisa ukwenzeka kwezinto usebenzise amagama afana: izolo, namuhla, kusasa, Ukusho isikhathi • Chaza ukuthi izinto zenzeke nini usebenzisa amagama afana: ekuseni, ebusuku, ntambama, emva kwesikhathi, ngaphambi kwsikhathi • Isho ngokulandelana izinsuku zes- into nezinyanga zonyaka. • Faka izinsuku zokuzalwa zabafundi kwikhalenda. 4.2 • UKULINGANISE esingahlelekile • UKULINGANISE esingahlelekile Ubude • Qhathanisa bese uhlela ubude, • Qagela,l inganisa, qhathanisa, ukuphakama noma ububanzi hlela bese ubhala ubude useben- bezinto ezimbili noma ngaphezulu zisa ukukala okungenasilinganiso ngokuzibeka enye eduze kwenye. njengezandla, ubude bepensela, amagxathu, okokubala njll. • Sebenzisa amagama akhuluma ngokuqhathanisa njengikuthi: kude kune, kufushane kune, okude ngokuthe xaxa, okubanzi kune, • Qagela, linganisa, qhathanisa, hlela bese ubhala ubude useben- 61 zisa ukukala okungenasilinganiso njengezandla, ubude bepensela, amagxathu, okokubala njll. Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 TERM 3 TERM 4 62 4.3 • UKULINGANISE esingahlelekile • UKULINGANISE esingahlelekile Isisindo • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, hlela bese ubhala phansi isisindo hlela bese ubhala phansi isisindo usebenzisa isikali sokuzimelela usebenzisa isikali sokuzimelela kanye nokulinganisa okungenasi kanye nokulinganisa okungenasi linganiso, njengebhuloki njll. linganiso, njengebhuloki njll. • Sebenzisa amagama ukuqhathani- • Sebenzisa amagama ukuqhathani- sa izinto. Isibonelo kulula, kuyasin- sa izinto. Isibonelo kulula, kuyasin- Izibalo IBANGA 1-3 da, kulula kuna, kusinda kuna da, kulula kuna, kusinda kuna 4.4 • Ukulimganisa okungahlelekile • Ukulimganisa okungahlelekile • Ukulimganisa okungahlelekile Umthamo/ oku- • Qhathanisa bese uhlela inani • Qhathanisa bese uhlela inani loket- mumethwe loketshezi olusezitsheni ezimbili shezi olungena ezitsheni ezimbil ezibekwe eduze nesinye. uma zigcwele (umthamo). • Abafundi babheka ngokuthela • Sebenzisa amagama ukuqhatha- esitsheni sesithathu nisa njengokuthi kuningi kuna, kugcwele, kuncane kuna, aku- nalutho • Qagela, linganisa, qhathanisa, • Qagela, linganisa, qhathanisa, uhlele bese ubhala umthamo uhlele bese ubhala umthamo wezitsha usebenzisa isilinganiso wezitsha usebenzisa isilinganiso esingenasilinganiso Isib izipuni esingenasilinganiso Isib izipuni nezinkomishi. nezinkomishi. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 1 5. UKUQOKELELWA KOLWAZI IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 CAPS 5.1 Qoqa bese uhlela izinto Qoqa bese uhlela izinto eziphathekayo ezisebenza eziphathekayo ezisebenza Qoqa bese nsukuzonke. nsukuzonke. uhlela izinto eziphathekayo 5.2 Dweba isithombe sezinto Dweba isithombe sezinto esezihleliwe. esezihleliwe. Okumele iqoqo lezinto eziphathekayo ezihlelekile • Chaza ukuthi amaqoqo ahlelwe • Chaza ukuthi amaqoqo ahlelwe kanjani kanjani 5.3 Phendula imibuzo ngalokhu: Phendula imibuzo ngalokhu: Ukuxoxa - Zihlelwe kanjani izinto - Zihlelwe kanjani izinto nokubika ngeqoqo lezinto - Libukeka kanjani iqoqo elihleliwe - Libukeka kanjani iqoqo elihleliwe eziphathekayo • Chaza iqoqo elihleliwe • Chaza iqoqo elihleliwe ezihlelekile 5.4 Okunconywayo: Qoqa bese uhlela Ulwazi oluphelele lokwenza igrafu ulwazi yezithombe yekilasi 5.5 • Qoqa bese uhlela ulwazi Okumele ulwazi - Izinto eziphathelene nekilasi noma nesikole 5.6 Hlaziya ulwazi olukwigrafu olubekiwe. - Izimpendulo zemibuzo ebuzwe Hlaziya bese uthisha. Okungenani abafundi abenze uyahumusha amagrfu ezithombe amabili ulwazi • Beka ulwazi kwigrafu yezithombe. • Phendula imibuzo ngolwazi lwegrafu yezithombe 63 Izibalo IBANGA 1-3

3.4.2 ULWAZI JIKELELE LEBANGA 2 ngethemu 64 ULWAZI JIKELELE LEBANGA 2 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Bala usebenzisa izinombolo eziphelele 1.1 • Bala ngokuyikho izinto • Bala ngokuyikho izinto • Bala ngokuyikho izinto • Bala ngokuyikho izinto ezisetshenziswa njalo okungenani ezisetshenziswa njalo okungenani ezisetshenziswa njalo okungenani ezisetshenziswa njalo okungenani Bala izinto kuye kufike e -100 kuye kufike e -150 kuye kufike e -180 kuye kufike e -200 Izibalo IBANGA 1-3 eziphathekayo • Qagela inombolo esondelela • Qagela inombolo esondelela • Qagela inombolo esondelela • Qagela inombolo esondelela ngakhona yezinto ezingabhkwa ngakhona yezinto ezingabhkwa ngakhona yezinto ezingabhkwa ngakhona yezinto ezingabhkwa ngokubala ngokubala ngokubala ngokubala • Amaqhinga okubala ngamaqoqo • Amaqhinga okubala ngamaqoqo • Amaqhinga okubala ngamaqoqo • Amaqhinga okubala ngamaqoqo kuyakhuthazwa. kuyakhuthazwa. kuyakhuthazwa. kuyakhuthazwa. 1.2 Bala uyephambili ubuye uye Bala uyephambili ubuye uye Bala uyephambili ubuye uye Bala uyephambili ubuye uye emumva kanje: emumva kanje: emumva kanje: emumva kanje: Bala uyephambili ubuye emumva • Ngaku 1 kusukela kunoma iyiphi • Ngaku 1 kusukela kunoma iyiphi • Ngaku 1 kusukela kunoma iyiphi • Ngaku 1 kusukela kunoma iyiphi inombolo ephakathi kuka -0 ne inombolo ephakathi kuka -0 ne inombolo ephakathi kuka -0 ne inombolo ephakathi kuka -0 ne -100 -150 -180 -200 • Ngokuyi -10 kusukela kunoma • Ngokuyi -10 kusukela kunoma • Ngokuyi -10 kusukela kunoma • Ngokuyi -10 kusukela kunoma iyiphi inombolo ephakathi 0 ne -100 iyiphi inombolo ephakathi 0 ne -150 iyiphi inombolo ephakathi 0 ne -180 iyiphi inombolo ephakathi 0 ne -200 • Ngokuyi -5 kusukela kunoma iyiphi • Nokuyi -5 kusukela kunoma iyiphi • Nokuyi -5 kusukela kunoma iyiphi • Nokuyi -5 kusukela kunoma iyiphi inombolo ephakathi kuka 0 ne 100 inombolo ephakathi kuka 0 ne 150 inombolo ephakathi kuka 0 ne 180 inombolo ephakathi kuka 0 ne 200 • Ngaku 2 kusukela kunoma iyiphi • Ngaku 2 kusukela kunoma iyiphi • Ngaku 2 kusukela kunoma iyiphi • Ngaku 2 kusukela kunoma iyiphi inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya koku 100 koku 150 koku 180 koku 200 • Ngoku 3 usukela kunoma iyiphi • Ngoku 3 usukela kunoma iyiphi • Ngoku 3 usukela kunoma iyiphi inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya koku 99 koku 180 koku 200 • Ngoku4 kusukela kunoma iyiphi • Ngoku 4 kusukela kunoma iyiphi • Ngoku 4 kusukela kunoma iyiphi inombolo ephakathi kuka 0 okuya inombolo ephakathi kuka 0 okuya inombolo ephakathi kuka 0 okuya Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola koku 100 koku 180 koku 200

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Ukumela izinombolo eziphelele 1.3 Khomba, ubone, bese ufunda Khomba, ubone, bese ufunda Khomba, ubone, bese ufunda Khomba, ubone, bese ufunda CAPS izinombolo izinombolo izinombolo izinombolo Uphawu negama lenombolo • Khomba, ubone, bese ufunda • Khomba, ubone, bese ufunda • Khomba, ubone, bese ufunda • Khomba, ubone, bese ufunda izimpawu zezinombolo kusukela ku izimpawu zezinombolo kusukela ku izimpawu zezinombolo kusukela ku izimpawu zezinombolo kusukela ku 0 kuya e 100 0 kuya ema- 150 0 kuya ema- 180 0 kuya e 200 • Bhala uphawu lenombolo kusukela • Bhala uphawu lenombolo kusukela • Bhala uphawu lenombolo kusukela • Bhala uphawu lenombolo kusukela ku 0 kuya e 100 ku 0 kuya ema- 150 ku 0 kuya ema- 180 ku 0 kuya e 200 • Khomba, ubone, bese ufunda • Khomba, ubone, bese ufunda • Khomba, ubone, bese ufunda • Khomba, ubone, bese ufunda amagama ezinombolo kusuka ku 0 amagama ezinombolo kusuka ku 0 amagama ezinombolo kusuka ku 0 amagama ezinombolo kusuka ku 0 kuye ema 25 kuye ema -50 kuye ema -75 kuye e100 • Bhala amagama ezinombolo • Bhala amagama ezinombolo • Bhala amagama ezinombolo • Bhala amagama ezinombolo kusuka ku 0 kuye ema 25 kusuka ku 0 kuye ema- 50 kusuka ku 0 kuye ema 75 kusuka ku 0 kuye e100 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Chaza, qhathanisa, bese uhlele izinombolo 1.4 Chaza, qhathanisa, bese uhlela Chaza, qhathanisa, bese uhlela Chaza, qhathanisa, bese uhlela Chaza, qhathanisa, bese uhlela izinombolo kuye kufike ema -25 izinombolo kuye kufike ema -50 izinombolo kuye kufike ema -75 izinombolo kuye kufike ema -99 Chaza, qhathanisa, bese uhlela • Qhathanisa izinombolo eziphelele • Qhathanisa izinombolo eziphelele • Qhathanisa izinombolo eziphelele • Qhathanisa izinombolo eziphelele izinombolo usebenzise amagama njenga usebenzise amagama njenga usebenzise amagama njenga usebenzise amagama njenga okuncane kuna, okukhulu kuna, okuncane kuna, okukhulu kuna, okuncane kuna, okukhulu kuna, okuncane kuna, okukhulu kuna, kungaphezulu kunokunye, kungaphezulu kunokunye, kungaphezulu kunokunye, kungaphezulu kunokunye, okungaphansi kunokunye, okungaphansi kunokunye, okungaphansi kunokunye, okungaphansi kunokunye, okulingana okulingana okulingana okulingana • Hlela izinombolo eziphelele • Hlela izinombolo eziphelele • Hlela izinombolo eziphelele • Hlela izinombolo eziphelele kusukela kwencane kakhulu kuya kusukela kwencane kakhulu kuya kusukela kwencane kakhulu kuya kusukela kwencane kakhulu kuya kwenkulu kakhulu kanye nezinkulu kwenkulu kakhulu kanye nezinkulu kwenkulu kakhulu kanye nezinkulu kwenkulu kakhulu kanye nezinkulu kakhulu kuya kwezincane kakhulu. kakhulu kuya kwezincane kakhulu. kakhulu kuya kwezincane kakhulu. kakhulu kuya kwezincane kakhulu. Sebenzisa izinombolo zesikhundla Sebenzisa izinombolo zesikhundla ukukhombisa ukuhleleka ukukhombisa ukuhleleka kwezinombolo, ngokwesikhundla kwezinombolo, ngokwesikhundla • Beka izinto eziphathekayo • Beka izinto eziphathekayo ngokulandelana kusukela ngokulandelana kusukela kweyokuqala kuya kweyamashumi kweyokuqala kuya kweyamashumi amabili noma eyokuqala kuya amabili noma eyokuqala kuya kweyokugcina Isib eyokuqala, kweyokugcina Isib eyesibili, eyesithathu…eyeshumi. Eyokuqala, eyesibili, eyesithathu 65 kuye kuyofika kweyamashumi amabili. Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Ubungako benani lenombolo 66 1.5 Ukubona ubungako benombolo Ukubona ubungako benombolo Ukubona ubungako benombolo Ukubona ubungako benombolo kusuka kwi -11 kuya kuma -25 kusuka kwi -11 kuya kuma -50 kusuka kwi -11 kuya kuma -75 kusuka kwi -11 kuya kuma -99 Ubungako benani lenombolo • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba ngazimbili sizise kumashumi ngazimbili sizise kumashumi ngazimbili sizise kumashumi ngazimbili sizise kumashumi nemivo nemivo nemivo nemivo • Khomba bese usho ubungako • Khomba bese usho ubungako • Khomba bese usho ubungako • Khomba bese usho ubungako benani benombolo ngayinye benani benombolo ngayinye benani benombolo ngayinye benani benombolo ngayinye Izibalo IBANGA 1-3 UKUXAZULULA IZINKINGA ZEZIBALO ESIMWENI ESIJWAYELEKILE 1.6 Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo ukuxazulula izinkinga zezibalo bese ukuxazulula izinkinga zezibalo bese ukuxazulula izinkinga zezibalo bese ukuxazulula izinkinga zezibalo bese Amasu okuxazulula uchaza isixazululo sakho: uchaza isixazululo sakho: uchaza isixazululo sakho: uchaza isixazululo sakho: izinkinga zezibalo • Imidwebo noma izinto • Imidwebo noma izinto • Imidwebo noma izinto • Imidwebo noma izinto eziphathekayo Isib izinto zokubala eziphathekayo Isib izinto zokubala eziphathekayo Isib izinto zokubala eziphathekayo Isib izinto zokubala • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukphinda kabili nokuhlukanisa • Ukphinda kabili nokuhlukanisa • Ukphinda kabili nokuhlukanisa • Ukphinda kabili nokuhlukanisa kabili kabili kabili kabili • Umugqa wezinombolo osebenzisa • Umugqa wezinombolo osebenzisa • Umugqa wezinombolo. • Umugqa wezinombolo. izinto eziphathekayo izinto eziphathekayo 1.7 Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile Ukuhlanganisa bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo nokususa ngokusebenzisa ukuhlanganisa ngokusebenzisa ukuhlanganisa ngokusebenzisa ukuhlanganisa ngokusebenzisa ukuhlanganisa nokususa. Izimpendulo zibe nokususa. Izimpendulo zibe nokususa. Izimpendulo zibe nokususa. Izimpendulo zibe nezisombululo ezifika kuma -20. nezisombululo ezifika kuma -50. nezisombululo ezifika kuma -75. nezisombululo ezifika kuma -99. 1.8 Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile Ukuhlanganisa bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo okuphindayo ngokusebenzisa ukuhlanganisa ngokusebenzisa ukuhlanganisa ngokusebenzisa ukuhlanganisa ngokusebenzisa ukuhlanganisa okuholela okuphindayo okuholela ezibalweni okuphindayo okuholela ezibalweni okuphindayo okuholela ezibalweni okuphindayo okuholela ezibalweni Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ezibalweni zokuphindaphinda. Izimpendulo zibe zokuphindaphinda. Izimpendulo zibe zokuphindaphinda. Izimpendulo zibe zokuphindaphinda. Izimpendulo zibe zokuphindaphinda nesisombululo ezifika kuma -20. nesisombululo ezifika kuma -30. nesisombululo ezifika kuma -40. nesisombululo ezifika kuma -50.

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.9 Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile zamagama esimweni esijwayelekile Ukwenza amaqoqo CAPS bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo nokuhlukaniselana ngokusebenzisa ukwabelana ngokusebenzisa ukwabelana ngokusebenzisa ukwabelana ngokusebenzisa ukwabelana okuholela ngokulinganayo nokwenza amaqoqo ngokulinganayo nokwenza amaqoqo ngokulinganayo nokwenza amaqoqo ngokulinganayo nokwenza amaqoqo ezibalweni ukufika kuma 20. Izimpendulo ukufika kuma 30. Izimpendulo ukufika kuma 40. Izimpendulo ukufika kuma 50. Izimpendulo ezifaka zokuhlukanisa ezingafaka izinsalela. ezingafaka izinsalela. ezingafaka izinsalela. izinsalela. 1.10 Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo Xazulula izinkinga zezibalo zamagama esimweni esijwayelekile zamagama esimweni esjwayelekile zamagama esimweni esjwayelekile Ukuhlukanisa bese uchaza isisombululo bese uchaza isisombululo bese uchaza isisombululo okuholela ngokusebenzisa ukwabelana ngokusebenzisa ukwabelana ngokusebenzisa ukwabelana emaqhezwini ngokulingana okuholela okuholela kuzisombululo ezifaka okuholela kuzisombululo ezifaka kuzisombululo ezifaka ingxenye ingxenye eyodwa yeqhezu.Isibonelo ingxenye eyodwa yeqhezu.Isibonelo 1 1 1 1 1 1 1 1 1 1 1 1 eyodwa yeqhezu.Isibonelo 2 , 4 , 3 , 5 2 , 4 , 3 , 5 njll 2 , 4 , 3 , 5 njll njll 1.11 • Ukubona bese ukhomba imli • Ukubona bese ukhomba imli • Ukubona bese ukhomba imli • Ukubona bese ukhomba imli yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza Imali 5c, 10c, 20c, 50c, R1, R2, R5, 5c, 10c, 20c, 50c, R1, R2, R5, 5c, 10c, 20c, 50c, R1, R2, R5, 5c, 10c, 20c, 50c, R1, R2, R5, neyamaphepha R10, R20, R50 neyamaphepha R10, R20, R50 neyamaphepha R10, R20, R50 neyamaphepha R10, R20, R50 • Xazulula izinkinga zezimali • Xazulula izinkinga zezimali • Xazulula izinkinga zezimali • Xazulula izinkinga zezimali eziyisamba noshinntshi eziyisamba noshinntshi eziyisamba noshinntshi eziyisamba noshinntshi ongamasenti ogcina ku 50c, ongamasenti ogcina ku 50c, ongamasenti ogcina ku 75c, ongamasenti ogcina ku 90c, namarandi agcina ku R20. namarandi agcina ku R50. namarandi agcina ku R75. namarandi agcina ku R99. UKUBALA ESIMWENI ESIKHULULEKILE 1.12 Ukusebenzisa amsu alandelayo uma Ukusebenzisa amasu alandelayo Ukusebenzisa amasu alandelayo Ukusebenzisa amasu alandelayo uhlanganisa: uma uhlanganisa: uma uhlanganisa: uma uhlanganisa: Amasu • Ukudweba noma ukusebenzisa • Ukudweba noma ukusebenzisa • Ukudweba noma ukusebenzisa • Ukudweba noma ukusebenzisa (izindlela noma izinto eziphathekayo.Isib izinto izinto eziphathekayo. Isib izinto izinto eziphathekayo.Isib izinto izinto eziphathekayo. Isib izinto amaqhimga) zokubala zokubala zokubala zokubala • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili kabili kabili kabili • Umugqa wezinombolo owenziwe • Umugqa wezinombolo owenziwe • Umugqa wezinombolo • Umugqa wezinombolo izinto eziphathekayo izinto eziphathekayo 67 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.13 • Izibalo zokuhlanganisa ukuyofika • Izibalo zokuhlanganisa ukuyofika • Izibalo zokuhlanganisa ukuyofika • Izibalo zokuhlanganisa ukuyofika 68 ema 20 ema 50 ema 75 ema 99 Ukuhlanganisa nokususa • Izibalo zokususa besukela kuma • Izibalo zokususa besukela kuma • Izibalo zokususa besukela kuma • Izibalo zokususa besukela kuma 20 50 75 99 • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele (+, –, =, ) (+, –, =, ) (+, –, =, ) (+, –, =, ) • Enza uphindelela amabhondi • Enza uphindelela amabhondi • Enza uphindelela amabhondi • Enza uphindelela amabhondi ezinombolo kuyofika e 10 ezinombolo kuyofika e 15 ezinombolo kuyofika ema 20 ezinombolo kuyofika ema 20 Izibalo IBANGA 1-3 1.14 • Hlanganisa izinombolo ezifanayo • Phindaphinda izinombolo ngo 2 • Phindaphinda izinombolo ngo 2 u 5 • Phindaphinda izinombolo ngo 2, ngokuphindayo kufika kuma 20 kanye no 5 kusukela ku 1kuya e 10 kanye no 4 kusukela ku 1kuya e 10 u 5, u3 kanye no 4 kusukela ku Ukuhlanganisa 1kuya e 10 okuphindayo • Phindaphinda izinombolo ngoku 2 • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele okuholela kusukela ku 1 kuya e 10 (+, x, =, ) (+, x, =, ) • Sebenzisa izimpawu ezifanele ezibalweni (+, x, =, ) • Sebenzisa izimpawu ezifanele zokuphindaphinda (+, x, =, ) 1.16 Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Lwezinombolo kufinyelela ku 25 Lwezinombolo kufinyelela ku 50 Lwezinombolo kufinyelela ku 75 Lwezinombolo kufinyelela ku 99 Izibalo zekhanda • Hlela iqoqo lezinombolo ozinikiwe. • Hlela iqoqo lezinombolo. • Hlela iqoqo lezinombolo. • Hlela iqoqo lezinombolo. • Qhathanisa izinombolo kuya kuma • Qhathanisa izinombolo kuya kuma • Qhathanisa izinombolo kuya kuma • Qhathanisa izinombolo kuya kuma -25 usho ukuthi iyiphi: -50 usho ukuthi iyiphi: -75 usho ukuthi iyiphi: -99 usho ukuthi iyiphi: - Eningi noma encane ngoku 1 - Eningi noma encane ngoku 1 - Eningi noma encane ngoku 1 - Ening noma encane ngoku 1 - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 2 - Eningi noma encane nge 10 - Eningi noma encane ngoku 3 - Eningi noma encane ngoku 3 - Eningi noma encane ngoku 3 - Eningi noma encane ngoku 4 - Eningi noma encane ngoku 4 - Eningi noma encane ngoku 4 - Eningi noma encane ngoku 5 - Eningi noma encane ngoku 5 - Eningi noma nvane ngoku 5 - Eningi noma encane nge 10 - Eningi noma encane nge 10 - Eningi noma encane nge 10 Khumbula ngokushesha: Khumbula ngokushesha: Khumbula ngokushesha: Khumbula ngokushesha: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa nokususa kuyofinyelela e10 nokususa kuyofinyelela e10 nokususa kuyofinyelela e15 nokususa kuyofinyelela e15 • Ukuhlanganisa noma ususe • Ukuhlanganisa noma ususe okubalwa ngamashumi kusukela okubalwa ngamashumi kusukela ku 0 kuya ema 50 ku 0 kuya ema 50

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 1.16 Amaqhinga okuhlanganisa: Amaqhinga okuhlanganisa: Amaqhinga okuhlanganisa: Amaqhinga okuhlanganisa: Izibalo zekhanda Sebenzisa amaqhinga okuhlanganisa Sebenzisa amaqhinga okuhlanganisa Sebenzisa amaqhinga okuhlanganisa Sebenzisa amaqhinga okuhlanganisa CAPS nokususa ngendlela efanele: nokususa ngendlela efanele: nokususa ngendlela efanele: nokususa ngendlela efanele: • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala ukuze ubale uye phambili noma ukuze ubale uye phambili noma ukuze ubale uye phambili noma ukuze ubale uye phambili noma emumva. emumva. emumva. emumva. • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise kabili kabili kabili kabili • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi kokuhlanganisa nokususa kokuhlanganisa nokususa kokuhlanganisa nokususa kokuhlanganisa nokususa 1.17 • Sebenzisa ubuye unike amagama • Sebenzisa ubuye unike amagama • Sebenzisa ubuye unike amagama amaqhezu njengo: uhhafu, ikota, amaqhezu njengo: uhhafu, ikota, amaqhezu njengo: uhhafu, ikota, Amaqhezu okukodwa kokuthathu, nokukodwa okukodwa kokuthathu, nokukodwa okukodwa kokuthathu, nokukodwa kokuhlanu kokuhlanu kokuhlanu • Bona amaqhezu asemidwebeni • Bona amaqhezu asemidwebeni • Bona amaqhezu asemidwebeni • Bhala amaqhezu njenge okukodwa • Bhala amaqhezu njenge okukodwa • Bhala amaqhezu njenge okukodwa kokubili, okubili kokuthathu. kokubili, okubili kokuthathu. kokubili, okubili kokuthathu. 69 Izibalo IBANGA 1-3

Izibalo IBANGA 1-3 Izinhlobo zezinkinga zebanga lesi - 2 Lezi yizibonelo zezinhlobo zezinkinga ezibalulekile okufanele ukuthi uthisha azethule ngokuziphinda ekilasni. Uma uthisha esebenza ngamaqoqo amancane, kufanele ayisho ngomlomo inkinga. Uma abafundi sebekwazi ukufunda, usengabanikeza izinkinga zezibalo ezibhalwe phansi, kodwa futhi akayisho inkinga ngomlomo. Izinkinga ezisesimweni esejwayelekile zingafakwa ephepheni lokusebenzela, kodwa kube kufishane, iqonde ngqo kube ejwayelekile, uthisha kufanele aqiniseke ukuthi bonke abafundi bayaziqonda lezizinkinga. Amaqoqo Ukwenza amaqoqo, kulahlwa izinsalela UPhilasande uthengisa amahhabhula asezikhwameni, isikhwama ngasinye siphethe amahhabhula ayi - 10. Un- amahhabhula angama - 81. Zingaki izikhwama zamahhabhula angazenza ngamahhabhula angama - 81? Ukwenza amaqoqo, ukufakwa nezinsalela ezimpendulweni Umlimi unamaqanda angama - 47. Mangaki amabhokisi amaqanda azowadinga uma ibhokisi ngalinye lifaka amaqanda ayi - 6? Ukuhlukanisa Ukuhlukanisa, kulahlwa insalela Hlukanisa ngokulinganayo uswidi ongama - 54 phakathi kwabangane abayisikhombisa. Ukuhlukanisa, okuholela emaqhezwini Hlukanisa amawolintshi ayi - 11 phakathi kwabangani ezine ukuze bonke bathole amawolintshi ngokulinganayo kungasali lutho. Iqhezu lokuqoqelwe ndawonye Ugogo unikeze uNobuhle amawolintshi ayi - 12. UNobuhle wenza ujusi ngoku - 1/3 kwamawolintshi. Mangaki ama- wolintshi awasebenzisile? Loluhlobo lwezinkinga kufanele luvezwe kuphela uma abafundi sebexazulule izinkinga ezine noma ezinhlanu zokuhlukaniselana, kuholela kwizinhlobo zamaqhezu kanye nokwazi amagama ezingcezu zamaqhezu. Ukubekwa kwamaqhezu ndawonye Umqeqeshi webhola lomnqakiswano unikeza abadlali abayi - 14 uhhafu wewolintshi umdlali ngamunye. Udinga amawolintshi amangaki? Loluhlobo lwezinkinga kufanele luvezwe kuphela uma abafundi sebexazulule izinkinga ezine noma ezinhlanu zokuhlukaniselana, kuholela kwizinhlobo zamaqhezu kanye nokwazi amagama ezingcezu zamaqhezu. Ukuhlanganisa okuphindayo Mangaki amasondo kumabhayisikili angama - 20? 70 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Izinga UThami uhamba amabhuloki ayisithupha ngelanga. Uhamba amabhuloki amangaki ngesonto? Igridi Ubaba uKhumalo utshala imigqa eyi - 7 yamaklabishi. Umugqa ngamunye unamaklabishi ayisi - 8. Mangaki amaklabishi esewonke? Ukuhlanganisa nokususa Kunezinhlobo okungenani ezintathu eziyisisekelo zezinkinga zokuhlanganisa nokususa, uhlobo ngalunye lungavezwa ngezindlela ezahlukene. Izinhlobo eziyisisekelo: Ushintshol ekubekeni inkinga UNoluthando unamahhabhula angama - 25. USiphlo umuphe amanye ayi - 18. Mangaki amahhabhula kaNoluthando esewonke? UNoluthando unamahhabhula angama - 53, unikeza uSipho amahhabhula angama - 32. Mangaki amahhabhula asele nawo? Hlanganisa Ibanga lesi - 2 linonxantathu abangama - 37 abaluhlaza kanye nabayi - 19 ababomvu. Bangaki onxantathu sebebonke? Kunezindilinga ezingama - 63; ezingama - 27 ziluhlaza, bese kuthi zonke ezinye zibebomvu. Zingaki izindilinga ezibomvu? Qhathanisa UNomfundo unobhanana abayi - 13. UThemba unobhanana abahlanu. Bangaki obhanana uNoluthando anabo abangaphezulu kwabakaThemba? Veza inkinga ngayinye ngezindlela ezahlukene Izinkinga zingavezwa ngezindlela ezahlukene. Isibonelo, zombili lezizinkinga ezoshintsho, kodwa okungaziwa kusezindaweni ezahlukene. UNoluthando ubekade enamahhabhula. UThemba wamupha amanye ayi - 18, manje usenamahhabhula angama - 43. Ubekade enamahhabhula amangaki uNoluthando ekuqaleni? UNoluthando ubekade enamahhabhula angama - 25. UPhilasande wamupha amanye. Manje unamahhabhula angama - 43. Mangaki amahhabhula amnike wona uPhilasande? Izimo zezinkinga ezinobudlelwano obusebenzayo obehlukene UNokwethaba uthengisa amawolintshi abiza amarandi amane (R4) lilinye. Yenza ithebula lokumsiza ukuthola inani lama oda amakhulu. Inani lamawolintshi 1 2 3 4 5 6 7 8 9 10 Inani ngokwamarandi 4 8 CAPS 71

Izibalo IBANGA 1-3 Sebenzisa lelithebula ukuthola inani lamawolintshi ayisi - 7 kanye nayi - 15. UNomusa ugada ingane. Ubiza amarandi angama - 20 imali yokuhamba, kube amarandi ama 5 ngehora ukugada ingane. Qedela lelithebula lakhe. Inani lamahora 1 2 3 4 5 10 Inani ngokwamarandi (R) 25 30 Qaphela ukuthi izinkinga zikaNokwethaba noNomusa zisebenza ngokungafani. Lezizinhlobo zezinkinga zezenzelwe ukusiza uthisha. Abafundi akumele baxinwe ngalezizinkinga. Khumbula ukuthi abafundi bajwayele ukusebenzisa izindlela ezahlukene zokuxazulula izinkinga okungenzeka kungabi yilokhu okulindelwe nguthisha. Isibonelo,inkinga yokuhlukanisa ingaxazululwa ngokususa okuphindayo,ukuhlanganisa noma ngokuphindaphinda. Izindlela ezisetshenziswa abafundi zingashintsha ngokuqhubeka konyaka ngokukhula kolwazi nokujwayela izinhlobo zezinkinga,nokukhula kolwazi lwazi lwabo lwezinombolo. 72 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 2 2. AMAPHETHINI, UBUDLELWANE NE - ALJIBHRA ISIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 CAPS 2.1 Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Amaphethini asizungezile Okusejiyometri Kopisha, wandisa bese uchaza Kopisha, wandisa bese uchaza Kopisha, wandisa bese uchaza Bona,chaza ngamagama usebenzisa amagama usebenzisa amagama usebenzisa amagama bese ukopisha amaphethini okusazbalomdwebo • Amaphethini alula enziwe izinto • Amaphethini alula enziwe izinto • Amaphethini alula enziwe izinto eziphathekayo eziphathekayo eziphathekayo • Emvelweni • Amaphethini alula enziwe • Amaphethini alula enziwe • Amaphethini alula enziwe • Empilweni yesimanje ngemidwebo, izimo noma izinto ngemidwebo, izimo noma izinto ngemidwebo, izimo noma izinto • emasikweni nasemagugwini ethu eziphathekayo. eziphathekayo. eziphathekayo. Uhla lwamaphethini: Uhla lwamaphethini: Uhla lwamaphethini: Amaphethini alula anezimo noma Amaphethini alula anezimo noma amaqoqo ezimo aphindaphindayo amaqoqo ezimo aphindaphindayo Amaphethini lapho inani noma ngendlela efanayo. ngendlela efanayo. ubungako bezimo buyashintsha Amaphethini lapho inani noma ngendlela engaqageleka okusho ubungako bezimo buyashintsha ukuthi amaphethini aya ngokukhula. ngendlela engaqageleka okusho ukuthi amaphethini aya ngokukhula. Akha bese uchaza amaphethini Akha bese uchaza amaphethini Akha bese uchaza amaphethini akho: akho: akho: • Akha amaphethini akho • Akha amaphethini akho • Akha amaphethini akho okusamdwebo okusamdwebo okusamdwebo - Usebenzisa izinto eziphathekayo - Usebenzisa izinto eziphathekayo - Usebenzisa izinto eziphathekayo - Ngokudweba imigqa, izimo - Ngokudweba imigqa, izimo - Ngokudweba imigqa, izimo noma izinto eziphathekayo noma izinto eziphathekayo noma izinto eziphathekayo • Chaza amaphethini akho • Chaza amaphethini akho • Chaza amaphethini akho 73 Izibalo IBANGA 1-3

ISIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 74 2.2 Kopisha, wandisa bese uchaza. Kopisha,wandise bese uchaza. Kopisha,wandise bese uchaza. Kopisha,wandise bese uchaza. Amaphethini Kopisha, wandise bese uchaza Kopisha, w andise bese uchaza Kopisha, w andise bese uchaza Kopisha, w andise bese uchaza ezinombolo ukulandelana kwezinombolo ukulandelana kwezinombolo ukulandelana kwezinombolo ukulandelana kwezinombolo ezilulakuya e 100. ezilulakuya e 150. ezilulakuya e 180. ezilulakuya e 200. Ukulandelana kwezinombolo Ukulandelana kwezinombolo Ukulandelana kwezinombolo Ukulandelana kwezinombolo kufanele ukhombise ukubala uya kufanele kukhombise ukubala uya kufanele kukhombise ukubala uya kufanele kukhombise ukubala uya phambili ubuye uye emumva kanje: phambili ubuye uhlehle kanje: phambili ubuye uhlehle kanje: phambili ubuye uhlehle kanje: Izibalo IBANGA 1-3 • Ngaku 1kusukela kunoma iyiphi in- • Ngaku 1 kusukela kunoma iyiphi • Ngaku 1 kusukela kunoma iyiphi • Ngaku 1 kusukela kunoma iyiphi ombolo ephakathi kuka -0 ne -100 inombolo ephakathi kuka -0 ne inombolo ephakathi kuka -0 ne inombolo ephakathi kuka -0 nama- -150 -180 200 • Ngokuyi -10 kusukela kunoma iy- iphi inombolo ephakathi 0 ne -100 • Ngokuyi -10 kusukela kunoma iy- • Ngokuyi -10 kusukela kunoma iy- • Ngokuyi -10 kusukela kunoma iphi inombolo ephakathi 0 ne -150 iphi inombolo ephakathi 0 ne -180 iyiphi inombolo ephakathi 0 nama • Nokuyi - 5 kusukela kunoma iyiphi -200 inombolo ephakathi kuka 0 ne 100 • Nokuyi - 5 kusukela kunoma iyiphi • Nokuyi - 5 kusukela kunoma iyiphi inombolo ephakathi kuka 0 ne 150 inombolo ephakathi kuka 0 ne 180 • Nokuyi - 5 kusukela kunoma • Ngaku 2 kusukela kunoma iyiphi iyiphi inombolo ephakathi kuka 0 inombolo ephakathi kuka 0 kuya • Ngaku 2 kusukela kunoma iyiphi • Ngaku 2 kusukela kunoma iyiphi nama200 koku 100 inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya koku 150 koku 180 • Ngaku 2 kusukela kunoma iyiphi inombolo ephakathi kuka 0 nama • Ngoku 3 usukela kunoma iyiphi • Ngoku 3 usukela kunoma iyiphi 200 inombolo ephakathi kuka 0 kuya inombolo ephakathi kuka 0 kuya koku 150 koku 180 • Ngoku 3 usukela kunoma iyiphi in- ombolo ephakathi kuka 0 nama200 • Ngoku 4 kusukela kunoma iyiphi • Ngoku 4 kusukela kunoma iyiphi inombolo ephakathi kuka okuya inombolo ephakathi kuka okuya • Ngoku 4 kusukela kunoma iyiphi koku 150 koku 180 inombolo ephakathi kuka 0 nama 200 Akha eyakho iphethini Akha eyakho iphethini lezinombolo lezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 2 3. INDAWO NEZIMO (IJIYOMETRI) CAPS IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.1 Ulimi lwesikhundla Isikhundla nokubukeka kwento Isikhundla, inkomba • Chaza ukuthi into ikuphi uma • Qondanisa ukubukeka okwehlukene nokubukeka kwento uqhathanisa nenye. Isibonelo kwento eyodwa yazozonke izinsuku. phezu kwe, phambili kwe, emumva kwe,kwesobunxele, kwesokudla, phezulu, phansi, eduze kwe. Indawo nezinkomba Indawo nezinkomba • Landela izinkomba ukunyakaza • Landela izinkomba ukunyakaza ekilasini. ekilasini. 3.2 Uhla lwezinto eziphathekayo Uhla lwezinto eziphathekayo Uhla lwezinto eziphathekayo Izinto Bona bese usho izinto eziphathekayo Bona bese usho izinto eziphathekayo Bona bese usho izinto eziphathekayo ezinhlangothintathu ezinhlangothintathu ezithombeni ezinhlangothintathu ezithombeni ezinhlangothintathu ezithombeni nezisekilasini. nezisekilasini. nezisekilasini. 3-D Izimo zamabhola (imbulunga) • okusabhola • okusabhola • okusabhola • okusabhokisi • okusabhokisi Izimo zamabhokisi (iphirizimu) • isilinda • isilinda • okusabhokisi izimpawu zezinto izimpawu zezinto izimpawu zezinto Chaza, hlela bese uqhathanisa izinto Chaza, hlela bese uqhathanisa izinto Chaza, hlela bese uqhathanisa izinto ezinhlangothintathu ngoku: ezinhlangothintathu ngoku:: ezinhlangothintathu ngoku:: • ubungako • ubungako • ubungako • izinto ezigingqikayo • izinto ezigingqikayo • izinto ezigingqikayo • izinto ezishibilikayo • izinto ezishibilikayo • izinto ezishibilikayo imisebenzi okugxilwe kuyo • Buka bese wakha izinto ezinhlangothintathu usebenzisa izinto eziphathekayo njengezimo ezinhlangothimbili, amabhuloki, nezinye izinto ongabuye uzisebenzise, izinto zokwakha kanye 75 nezinto ezinhlangothi ntathu. Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.2 Iziphakamiso zomsebenzi Iziphakamiso zomsebenzi Iziphakamiso okuzogxilwa kuzo 76 okuzogxilwa kuwo nokulandelana okuzogxilwa kuwo nokulandelana kwi themu 4 Izinto ezinhlangoth- kwemisebenzi ku themu 1 kwemisebenzi ku themu 3 intathu • Kopisha isimo sento oyinikwe 3-D uthisha. Isimo sento singenziwa ngamabhuloki, izinto ongabuye uzisebenzise, izinto zokwakha, ezinye izinto ezinhlangothi ntathu 3-D, nokunye okuyizimo Izibalo IBANGA 1-3 ezinhlangothi mbili 2-D ezisikiwe. Lokhu kungenziwa ngesikhathi sokusebenza ngokuzimela • Qhathanisa bese uchaza ubungako bezinto ezifanayo kusukela kwenkulu kuya kwencane. Isibonelo, beka amabhokisi kusuka kwelikhulu kuya kwelincane. Sebenzisa: Sebenzisa: • Amabhola kanye nezinto ezinesimo • Amabhola kanye nezinto ezinesimo samabhola. samabhola. • Amabhokisi ahlukene nezinye • Amabhokisi ahlukene nezinye izinto njengamaprizimu awunxande izinto njengamaprizimu awunxande noma amakhiyubhu. noma amakhiyubhu. Phenya ukuthi iziphi izinto Phenya ukuthi iziphi izinto ezikwazi ukugingqika, ezishelelayo ezikwazi ukugingqika, ezishelelayo nezingabekwa phezulu kwenye.. nezingabekwa phezulu kwenye.. Khomba bese uchaza Khomba bese uchaza okuzibalomdwebo nezinto zansuku okuzibalomdwebo nezinto zansuku zonke ngokusho ukuthi zakhiwe zonke ngokusho ukuthi zakhiwe njengebhola, njengebhokisi noma njengebhola, njengebhokisi noma isilinda. isilinda. Phetha lengxenye yomsebenzi Phetha lengxenye yomsebenzi Phetha lengxenje yomsebenzi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ngokunika umsebenzi wokubhala. ngokunika umsebenzi wokubhala. ngokunika umsebenzi wokubhala

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.3 Uhla Lwezimo Uhla Lwezimo Izimo Bona bese usho igama lezimo Bona bese usho igama lezimo CAPS ezinhlangothimbili ezinhlangothimbili ezinhlangothimbili 2-D • indilinga • indilinga • unxantathu • unxantathu • isikwele • isikwele • unxande • unxande Izimpawu zezimo Izimpawu zezimo Chaza, hlela bese uqhathanisa izimo Chaza, hlela bese uqhathanisa izimo ezinhlangothimbili ngokwe: ezinhlangothimbili ngokwe: • ubungako • ubungako • umbala • umbala • ngokwesimo • ngokwesimo • izinhlangothi eziqondile • izinhlangothi eziqondile • izinhlangothi eziyindilinga • izinhlangothi eziyindilinga 77 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.3 Ukulandelana komsebenzi Ukulandelana komsebenzi 78 okuzogxilwa kuwo kwi themu 2 okuzogxilwa kuwo kwi themu 4 Izimo ezinhlangothimbili • Dlala ngokukhululekile usebenzisa izimo ezahlukene kanye 2-D nokwakha izithombe ngezimo eziyizibalo mdwebo.Lokhu kungenziwa ngesikhathi sokudlala ngokukhululekile. • Kopisha esenziwe izimo Izibalo IBANGA 1-3 eziyizibalo mdwebo.Lokhu kungenziwa ngezikhathi zokudlala ngokukhululekile. • Qhathanisa ubungako bezimo ezifanayo isib. Hlela onxande kusukela komncane kakhulu kuya komkhulu kakhulu usebenzisa ulimi lobungako ukuchaza izimo. • Xoxa ngemibala yezimo bese uhlela izimo ngemibala. • Hlela izimo ngokuthi zinamacala • Hlela izimo ngokuthi zinamacala aqondilie noma ayindilinga. aqondilie noma ayindilinga. sebenzisa izindilinga nezikwele sebenzisa izindilinga nezikwele ezinobumo obuhlukene nonxande ezinobumo obuhlukene nonxande nonxantathu abanezimo nonxantathu abanezimo ezihlukene. ezihlukene. • Hlela bese wenza amaqoqo ezimo • Abafundi bahlela bese benza ngokuthi angonxantathu, izikwele, amaqoqo ezimo ngokuthi ziwo unxande noma izindilinga. nxantathu, izikwele, onxande noma izindilinga. • Phetha lengxenye ngemisebenzi ebhalwayo. • Phetha lengxenye ngemisebenzi ebhalwayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.4 Okufana nse nxazombili Okufana nse nxazombili Okufana nse Bona bese udweba umugqa Bona bese udweba umugqa CAPS nxazombili ohlukanisa kabili kufane ohlukanisa kabili kufane nse nxazombili 2-D kwizimo nse nxazombili kwizimo ezinhlangothimbili eziyizibalomdwebo ezinhlangothimbili eziyizibalomdwebo nezingeziyizo izibalomdwebo. nezingeziyizo izibalomdwebo. Ukulandelana komsebenzi Ukulandelana komsebenzi okuzogxilwa kuwo kwi themu 2 okuzogxilwa kuwo kwi themu 4 • Dweba imigqa ehlukanisanisa ka- • Dweba imigqa ehlukanisanisa ka- bili kufane nse izinto eziphathekayo bili kufane nse izinto eziphathekayo nezithombe. nezithombe. • Imisebenzi ebhalwayo kufanele • Imisebenzi ebhalwayo kufanele ifake nezibonelo lapho umugqa ifake nezibonelo lapho umugqa ohlukanisa kabili ungasuki phe- ohlukanisa kabili ungasuki phe- zulu uya phansi kuphela. zulu uya phansi kuphela. 79 Izibalo IBANGA 1-3

ULWAZI JIKELELE LEBANGA 2 4. ISILINGANISO 80 IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.1 Ukufunda Isikhathi Ukufunda Isikhathi Ukufunda Isikhathi Ukufunda Isikhathi Isikhathi • Isho igama bese ulandelanisa • Isho igama bese ulandelanisa izinsuku zesonto. izinsuku zesonto. • Isho bese ulandelanisa izinyanga • Isho bese ulandelanisa izinyanga zonyaka. zonyaka. • Faka izinsuku zokuzalwa, imigubho • Faka izinsuku zokuzalwa, imigubho yokholo, izinsuku zokuphumula, yokholo, izinsuku zokuphumula, Izibalo IBANGA 1-3 izinsuku zezigameko zomlando, izinsuku zezigameko zomlando, imicimbi yesikole kwikhalenda. imicimbi yesikole kwikhalenda. • Funda iwashi lezinti ngamahora • Funda iwashi lezinti ngamahora • Funda iwashi lezinti ngamahora • Funda iwashi lezinti ngamahora nangesigamu sehora nangesigamu sehora nangesigamu sehora ayi-12 nangesigamu sehora nekota yehora. Bala ubude besikhathi nokudlula Bala ubude besikhathi nokudlula Bala ubude besikhathi nokudlula kwesikhathi kwesikhathi kwesikhathi Bala ubude besikhathi nokudlula • Sebenzisa ikhalenda ukubala kwesikhathi nokuchaza ubude besikhathi ngezinsuku noma ngamasonto. • Sebenzisa iwashi ukubala ubude • Sebenzisa iwashi ukubala ubude besikhathi ngamahora noma besikhathi ngamahora noma • Sebenzisa iwashi ukubala ubude • Sebenzisa iwashi ukubala ubude ngesigamu sehora. ngesigamu sehora besikhathi ngamahora noma besikhathi ngamahora nesigamu ngesigamu sehora sehora 4.2 Isilinganiso esingahlelekile Ubude • Qagela, linganisa, qhathanisa, hlela bese ubhala ubude usebenzisa isilinganiso okungenasilinganiso isibonelo. izandla, amagxathu, ubude bepensela, izinto zokubala njll. • Chaza ubude bezinto eziphathekayo ngokubala usho nobude besilinganiso usebenzisa amayunithi angahleliwe. • Sebenzisa ulimi ukukhuluma Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ngokuqhathanisa isib. kude kuna, kufushane kuna, kuphakeme kuna, kubanzi kuna njll. Ukuthula Isilinganiso esingahlelekile Ukuthula Isilinganiso esingahlelekile • Qagela, linganisa, hlela bese ubhala • Qagela, linganisa, hlela bese ubhala ubude usebenzisa amamitha (uthi ubude usebenzisa amamitha (uthi oluyimitha, intambo eyimitha) oluyimitha, intambo eyimitha) ngesikalo esilinganisiwe sobude. ngesikalo esilinganisiwe sobude.

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.3 Isilinganiso esingahlelekile CAPS Isisindo • Qagela, linganisa, qhathanisa,hlela bese ubhala isisindo usebenzisa isikali sokuzimelela kanye nezikali ezingenasilinganiso isibonelo. njengamabhuloki, izitini. • Chaza isisisindo sezinto eziphathekayo ngokubala nokusho ngama ngezilinganiso angahleliwe • Sebenzisa ulimi ukukhuluma ngokuqhathanisa isisindo isibonelo. okulula, okusindayo, okulula kuno, okusinda kuno. Ukwethula Isilinganiso esingahlelekile Ukwethula Isilinganiso esingahlelekile • Qhathanisa, hlela bese ubhala isisindo sezinto ezithengiswayo afundi benza umsebenzi wokubhala ezinesisindo esibhalwe ukuphetha okulandelayo kufaka ngamakhilogramu,isib. 2kg nokufunda izithombe zalokhu yempuphu ne 1kg kafulawa. • Imikhiqizo enesisindo esibhaliwe • Uma sikhona isikali sasendlini kuyo yokugeza, abafundi bangazikala • Izakali zasendlini yokugeza lapho izisindo zabo besebenzisa isikali uthi lwesikali lukhomba inombolo sasendlini yokugeza. Okulindelekile yesisindo. ukuba abafundi bafunde isisindo esisondelene nothi lwesikali.. bachaza isisindo sabo njengesicishe / sisondelene / siseduze / sikhudlwana / esifanayo (amakhiligramu) abawafunda esikalini. 81 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.4 Isilinganiso esingahlelekile 82 Umthamo • Qagela, linganisa, qhathanisa, hlela bese ubhala umthamo wezitsha • (Isibonelo. umthamo isitsha esingawumumatha uma sigcwele) ngokusebenzisa izikali ezingenasilinganiso njengezipuni nezinkomishi. • Chaza umthamo wesitsha ngokubala Izibalo IBANGA 1-3 nokusho ukuthi mangaki amayunithi angahlelekile angagcwalisa lesisitsha isibonelo.ibhodlela linomthamo wezinkomishi ezine Ukwethula Isilinganiso esingahlelekile Ukwethula Isilinganiso • Qagela, linganisa, qhathanisa, esingahlelekile hlela bese uyabhala umthamo wezinto ngokulinganisa ngamalitha Imisebenzi yokubhala ukuphetha usebenzisa: okulandelayo, ifaka nokufunda izithombe zalokhu - Amabhodlela anomthamo welitha • Imikhiqizo enomthamo obhaliwe - Ujeke wokukala onamagabelo kuyona ukuze ikwazi ukuhleleka akhombisa ilitha ngokulandelana • Qhathanisa, hlela bese ubhala • Izithombe zojeke lapho umthamo wezinto ezithengisayo okumumethwe kucishe kufike umthamo wazo obhalwe ngamalitha emgqeni wegabelo lelitha elilodwa isibonelo. 2 amalitha obisi, 1 ilitha noma amabili yesiphuzo, 5 amalitha kapende. • Funda ngokusondezela emgqeni wegabelo elilandelayo, chaza umthamo wazo njengokucishe, okuningana, okuningi noma okuncane noma okulingana ncamashi (namalitha) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 2 5. UKUQOKELELWA KOLWAZI IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 CAPS 5.4 Izincomo: Qoqa bese Ukusebenzisa ulwazi oluphelele uhlela ulwazi ngekilasi ukwenza igrafu yezithombe usebenzisa okukodwa nokukodwa 5.5 okuhambisanayo Okumele Ulwazi • Qoqa ulwazi ngezinto ezisekilasini 5.6 noma esikoleni ukuze uphendule Hlaziya ulwazi lwezithombe ezimele imibuzo ebuzwe uthisha. izinto ezibonakalayo. Hlaziya bese Hlaziya ulwazi olumele olunikiwe uhumusha • Ukubeka ulwazi kwigrafu Izincomo Izincomo: Ulwazi yezithombe usebenzisa okukodwa • Okungenani akwenziwe igrafu nokukodwa okuhambisanayo. • Okungenani akwenziwe igrafu Yenza igrafu yakho yezithombe eyodwa yezithombe usebenzisa eyodwa yezithombe usebenzisa ngolwazi olunikiwe oluyizithombe okukodwa nokukodwa • Phendula imibuzo ngegrafu okukodwa nokukodwa noma ithebula.. okuhambisanayo. yezithombe usebenzisa okukodwa okuhambisanayo. • Qoqa ulwazi ngezinto ezisekilasini nokukodwa okuhambisanayo. noma esikoleni ukuze uphendule imibuzo ebuzwe uthisha. • Ukubeka ulwazi kwigrafu yezithombe usebenzisa okukodwa nokukodwa okuhambisanayo. Phendula imibuzo ngegrafu yezithombe usebenzisa okukodwa nokukodwa okuhambisanayo. 83 Izibalo IBANGA 1-3

3.4.3 IBANGA LESI-3 Ulwazi jikelele ngethemu 84 ULWAZI JIKELELE LEBANGA 3 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Bala usebenzisa izinombolo eziphelele 1.1 Yenza iqoqo lezinto okungenani Yenza iqoqo lezinto okungenani Yenza iqoqo lezinto okungenani Yenza iqoqo lezinto okungenani ezingama - 200 ukuze uqagele ubuye ezingama - 500 ukuze uqagele ubuye ezingama - 700 ukuze uqagele ubuye ezingama - 1000 ukuze uqagele Bala izinto ubale ngokuyikho. ubale ngokuyikho. ubale ngokuyikho. ubuye ubale ngokuyikho. Izibalo IBANGA 1-3 eziphathekayo Qagela inombolo yezinto Qagela inombolo yezinto Qagela inombolo yezinto Qagela inombolo yezinto ezingabhekwa ngokubala. ezingabhekwa ngokubala. ezingabhekwa ngokubala. ezingabhekwa ngokubala. Gqugquzela amaqhinga okusebenza Gqugquzela amaqhinga okusebenza Gqugquzela amaqhinga okusebenza Gqugquzela amaqhinga okusebenza ngamaqoqo. ngamaqoqo. ngamaqoqo. ngamaqoqo5 1.2 Bala uye phambili nasemumva Bala uye phambili nasemuva ngoku: Bala uye phambili nasemuva ngoku: Bala uye phambili nasemuva ngoku: ngoku: Bala uye phambili • 1, kusukela kunoma iyiphi inombolo • 1, kusukela kunoma iyiphi inombolo • 1, kusukela kunoma iyiphi inombolo ubuye uye emumva • 1, kusukela kunoma iyiphi inombolo phakathi kuka - 0 kuya ema - 500 phakathi kuka - 0 kuya ema - 700 phakathi kuka - 0 kuya ema - 1000 phakathi kuka - 0 kuya ema - 200 • Ngama - 10, kusukela kunoma • Ngama - 10, kusukela kunoma • Ngama - 10, kusukela kunoma • Ngama - 10, kusukela kunoma iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 nama - 500 nama - 700 nama -1000 nama - 200 • Ngaku 5 kusukela kunoma • Ngaku 5 kusukela kunoma • Ngaku 5 kusukela kunoma • Ngaku 5 kusukela kunoma iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 kuya ema - 500 kuya ema - 700 kuya ema -1000 kuya ema - 200 • Ngaku 2 kusukela kunoma • Ngaku 2 kusukela kunoma • Ngaku 2 kusukela kunoma • Ngaku 2 kusukela kunoma iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 kuya ema - 500 kuya ema - 700 kuya ema - 1000 kuya ema - 200 • 10 Ngaku 3 kusukela kunoma • 10 Ngaku 3 kusukela kunoma • 10 Ngaku 3 kusukela kunoma • 10 Ngaku 3 kusukela kunoma iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola izinombolo eziphakathi kwe - 0 kuya ema - 500 kuya ema - 700 kuya ema - 1000 kuya ema - 200 • Ngaku 4 kusukela kunoma • Ngaku 4 kusukela kunoma • Ngaku 4 kusukela kunoma • Ngaku 4 kusukela kunoma iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda iyiphi indlela yokuphindaphinda izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 izinombolo eziphakathi kwe - 0 kuya ema - 500 kuya ema - 700 kuya ema - 1000 kuya ema - 200 • Ngama 50, 100 kufinyelela • Ngama - 20, 25, 50 nge - 100 • Ngama - 20, 25, 50 nge - 100 • Ngama 100 kufinyelela okungenani okungenani ema - 1 000 kufinyelela okungenani ema - 1 000 kufinyelela okungenani ema - 1 000 ema - 500

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 UKUTHUTHKISWA KOLWAZI LWEZINOMBOLO: Ukumela inombolo ephelele 1.3 Khomba, bona, ufunde izinombolo Khomba, bona, ufunde izinombolo Khomba, bona, ufunde izinombolo Khomba, bona, ufunde izinombolo CAPS Uphawu negama • Khomba, bona, ufunde uphawu • Khomba, bona, ufunde uphawu • Khomba, bona, ufunde uphawu • Khomba, bona, ufunde uphawu lwenombolo lwezinombolo eziphakathi kwe - 0 lwezinombolo eziphakathi kwe - 0 lwezinombolo eziphakathi kwe - 0 lwezinombolo eziphakathi kwe - 0 kuya ema - 500. kuya ema - 1 000. kuya ema - 1 000. kuya ema - 1 000. • Bhala uphawu lwezinombolo • Bhala uphawu lwezinombolo • Bhala uphawu lwezinombolo • Bhala uphawu lwezinombolo eziphakathi kwe - 0 kuya ema - 500 eziphakathi kwe - 0 kuya ema - 1 eziphakathi kwe - 0 kuya ema - 1 eziphakathi kwe - 0 kuya ema - 1 000 000 000 • Khomba, bona ufunde amagama ezinombolo eziphakathi kwe - 0 • Khomba, bona ufunde amagama • Khomba, bona ufunde amagama • Khomba, bona ufunde amagama nama - 250 ezinombolo eziphakathi kwe - 0 ezinombolo eziphakathi kwe - 0 ezinombolo eziphakathi kwe - 0 nama - 250 nama - 500 nama - 1 000 • Bhala amagama ezinombolo eziphakathi kwe - 0 ne - 100 • Bhala amagama ezinombolo • Bhala amagama ezinombolo • Bhala amagama ezinombolo eziphakathi kwe - 0 ne - 250 eziphakathi kwe - 0 ne - 500 eziphakathi kwe - 0 ne - 1 000 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: chaza, qhathanisa uhlele izinombolo eziphelele 1.4 Chaza, uqhathanise bese uhlela Chaza, uqhathanise bese uhlela Chaza, uqhathanise bese uhlela Chaza, uqhathanise bese uhlela izinombolo kuze kufinyelele ema-99 izinombolo kuze kufinyelele ema-500 izinombolo kuze kufinyelele ema-700 izinombolo kuze kufinyelele ema-999 Chaza, uqhathanise bese uhlela • Qhathanisa izinombolo • Qhathanisa izinombolo • Qhathanisa izinombolo • Qhathanisa izinombolo izinombolo eziphelele kuze kufinyelele eziphelele kuze kufinyelele eziphelele kuze kufinyelele eziphelele kuze kufinyelele ema - 99 usebenzisa okuncane ema - 500 usebenzisa okuncane ema - 700 usebenzisa okuncane ema - 999 usebenzisa okuncane kunokunye, okukhulu kunokunye, kunokunye, okukhulu kunokunye, kunokunye, okukhulu kunokunye, kunokunye, okukhulu kunokunye, okungaphansi kunokunye okungaphansi kunokunye okungaphansi kunokunye okungaphansi kunokunye nokulingana nokunye. nokulingana nokunye. nokulingana nokunye. nokulingana nokunye. • Hlela izinombolo eziphelele • Hlela izinombolo eziphelele • Hlela izinombolo eziphelele • Hlela izinombolo eziphelele kufinyelela ema-99 kusukela kufinyelela ema-500 kusukela kufinyelela ema-700 kusukela kufinyelela ema-999 kusukela kokuncane kakhulu kuya kokukhulu kokuncane kakhulu kuya kokukhulu kokuncane kakhulu kuya kokukhulu kokuncane kakhulu kuya kokukhulu kakhulu kanye nokukhulu kakhulu kakhulu kanye nokukhulu kakhulu kakhulu kanye nokukhulu kakhulu kakhulu kanye nokukhulu kakhulu kuya kokuncane kakhulu. kuya kokuncane kakhulu kuya kokuncane kakhulu kuya kokuncane kakhulu Sebenzisa izinombolozesikhunbdla ukukhombisa ukuhleleka, indawo noma isikhundla. • Sebenzisa, funda bese ubhale izinombolo zesikhundla kufinyelela ema - 31 85 Izibalo IBANGA 1-3

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO: Ubungako benani lenombolo 86 1.5 Ukubona ubungako bezinombolo Ukubona ubungako bezinombolo Ukubona ubungako bezinombolo Ukubona ubungako bezinombolo kufinyelela ema - 99 kufinyelela ema - 500 kufinyelela ema - 700 kufinyelela ema - 999 Ubungako benani lenombolo • Ukukwazi ukubona ukuthi inombolo • Ukukwazi ukubona ukuthi inombolo • Ukukwazi ukubona ukuthi inombolo • Ukukwazi ukubona ukuthi inombolo ngayinye imeleni ngayinye imeleni ngayinye imeleni ngayinye imeleni • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba • Hlakaza izinombolo ezihamba ngazimbili kufinyelela ema - 99 ngantathu kufinyelela ema - 500 ngantathu kufinyelela ema - 700 ngantathu kufinyelela ema - 999 ngamashumi nemivo ngama - khulu, -shumi ngemivo ngama - khulu, -shumi ngemivo ngama - khulu, -shumi ngemivo Izibalo IBANGA 1-3 • Khomba usho ubungako bedijithi • Khomba usho ubungako bedijithi • Khomba usho ubungako bedijithi • Khomba usho ubungako bedijithi ngayinye ngayinye ngayinye ngayinye UKUXAZULULA IZINKINGA ZEZIBALO ESIMWENI ESIJWAYELEKILE 1.6 Sebenzisa lamasu alandelayo uma Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo Sebenzisa lamasu alandelayo uxazulula izinkinga zezibalo: ukuxazulula lezinkinga zezibalo: ukuxazulula lezinkinga zezibalo: ukuxazulula lezinkinga zezibalo Amasu okuxazulula ubuye uchaze izixazululo zezinkinga: izinkinga zezibalo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili kabili kabili • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo ngokulinganayo ngokulinganayo ngokulinganayo • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Ukusondezela emashumini • Ukusondezela emashumini • Ukusondezela emashumini 1.7 Xazulula izibalo zamagama Xazulula izibalo zamagama Xazulula izibalo zamagama Xazulula izibalo zamagama ezimweni ezijwayelekile, ezimweni ezijwayelekile, ezimweni ezijwayelekile, ezimweni ezijwayelekile, Ukuhlanganisa ezinezimpendulo ezifinyelela ema - ezinezimpendulo ezifinyelela ema - ezinezimpendulo ezifinyelela ema - ezinezimpendulo ezifinyelela ema - nokususa 99, uchaze isixazululi sakho kufaka 400, uchaze isixazululi sakho kufaka 800, uchaze isixazululi sakho kufaka 999, uchaze isixazululi sakho kufaka ukuhlanganisa nokususa ukuhlanganisa nokususa ukuhlanganisa nokususa ukuhlanganisa nokususa 1.8 Xazulula izibalo zezinombolo Xazulula izibalo zezinombolo Xazulula izibalo zezinombolo Xazulula izibalo zezinombolo Ukuhlanganisa ezimweni ezijwayelekile, ezimweni ezijwayelekile, ezimweni ezijwayelekile, ezimweni ezijwayelekile, okuphindayo ezinezimpendulo ezifinyelela ema - ezinezimpendulo ezifinyelela ema - ezinezimpendulo ezifinyelela ema - ezinezimpendulo ezifinyelela ema - Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola okuholela 50, uchaze isixazululi sakho kufaka 75, uchaze isixazululi sakho kufaka 75, uchaze isixazululi sakho kufaka 100, uchaze isixazululi sakho kufaka ezibalweni ukuphindaphinda ukuphindaphinda ukuphindaphinda ukuphindaphinda zokuphindaphinda

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 1.9 Xazulula izibalo zezinombolo Xazulula izibalo zezinombolo Xazulula izibalo zezinombolo Xazulula izibalo zezinombolo ezimweni ezijwayelekile, uchaze ezimweni ezijwayelekile, uchaze ezimweni ezijwayelekile, uchaze ezimweni ezijwayelekile, uchaze Ukwenza amaqoqo CAPS isixazululi sakho okufaka isixazululi sakho okufaka isixazululi sakho okufaka isixazululi sakho okufaka nokuhlukaniselana ukuhlukaniselana ngokulinganayo ukuhlukaniselana ngokulinganayo ukuhlukaniselana ngokulinganayo ukuhlukaniselana ngokulinganayo okuholela nangokwenza amaqoqo kuze nangokwenza amaqoqo kuze nangokwenza amaqoqo kuze nangokwenza amaqoqo kuze ezibalweni kufinyelele ema - 50 kube kufinyelele ema - 75 kube kufinyelele ema - 75 kube kufinyelele ema - 100 kube zokuhlukanisa nezimpendulo ezingafaka izinsalela. nezimpendulo ezingafaka izinsalela. nezimpendulo ezingafaka izinsalela. nezimpendulo ezingafaka izinsalela. 1.10 Xazulula uchaze izixazululo Xazulula uchaze izixazululo Xazulula uchaze izixazululo Xazulula uchaze izixazululo zezinkinga eziphathekayo kufaka zezinkinga eziphathekayo kufaka zezinkinga eziphathekayo kufaka zezinkinga eziphathekayo kufaka Ukuhlukanisa ukuhlukaniselana ngokulinganayo ukuhlukaniselana ngokulinganayo ukuhlukaniselana ngokulinganayo ukuhlukaniselana ngokulinganayo okuholela okuholela kwizixazululo ezifaka okuholela kwizixazululo ezifaka okuholela kwizixazululo ezifaka okuholela kwizixazululo ezifaka emaqhezwini izingcezu ezizodwa namaqhezu izingcezu ezizodwa namaqhezu izingcezu ezizodwa namaqhezu izingcezu ezizodwa namaqhezu anezingcezu ezingaphezu kolulodwa, anezingcezu ezingaphezu kolulodwa anezingcezu ezingaphezu kolulodwa anezingcezu ezingaphezu kolulodwa 1 1 3 1 1 3 2 1 1 3 2 1 1 1 3 2 Isib. 2 , 4 , 4 , njll. Isib. 2 , 4 , 4 , 5 , njll. Isib. 2 , 4 , 4 , 5 , njll. Isib. 2 , 3 , 4 , 4 , 5 ,njll. 1.11 • bona bese ukhomba imali • Ukubona bese ukhomba imli • Ukubona bese ukhomba imli • Ukubona bese ukhomba imli yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza yaseNingizimu Afrika ewuhlweza Imali kanye neyamaphepha kanye neyamaphepha kanye neyamaphepha kanye neyamaphepha • Xazulula izinkinga zezimali • Xazulula izinkinga zezimali • Xazulula izinkinga zezimali • Xazulula izinkinga zezimali eziyisamba noshinntshi eziyisamba noshinntshi eziyisamba noshinntshi eziyisamba noshinntshi ongamarandi noma namasenti. ongamarandi noma namasenti. ongamarandi noma namasenti. ongamarandi noma namasenti. • Guqula phakathi kwamarandi • Guqula phakathi kwamarandi namasenti nasenti UKUBALA ESIMWENI ESIKHULULEKILE 1.12 Sebenzisa amasu alandelayo uma Sebenzisa amasu alandelayo uma Sebenzisa amasu alandelayo uma Sebenzisa amasu alandelayo uma ubala: ubala: ubala: ubala: Amasua (izindlela noma amaqhinga) • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa • Ukuphinda kabili nokuhlukanisa kabili kabili kabili kabili • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Ukusondezela emashumini • Ukusondezela emashumini • Ukusondezela emashumini 87 Izibalo IBANGA 1-3

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 1.13 • Izibalo zokuhlanganisa ukuyofika • Izibalo zokuhlanganisa ukuyofika • Izibalo zokuhlanganisa ukuyofika • Izibalo zokuhlanganisa ukuyofika 88 ema 99 ema 400 ema 800 ema 999 Ukuhlanganisa nokususa • Izibalo zokususa besukela kuma 99 • Izibalo zokususa besukela kuma • Izibalo zokususa besukela kuma • Izibalo zokususa besukela kuma 400 800 999 • Sebenzisa izimpawu ezifanele (+, –, =, ) • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele (+, –, =, ) (+, –, =, ) (+, –, =, ) • Yenza amabhondi ezinombolo kuyofika e 20 • Yenza amabhondi ezinombolo • Yenza mabhondi ezinombolo kuy- • Yenza amabhondi ezinombolo kuyofika e 30 ofika e 30 kuyofika e 30 Izibalo IBANGA 1-3 1.14 • Phindaphinda izinombolo kusukela • Phindaphinda ngoku 2, 4, 5, 10, 3 • Phindaphinda ngoku 2, 3, 4, 5, 10, • Phindaphinda ngoku 2, 3, 4, 5, 10, kwe - 1 kuya kwezi - 10 ngo 2, 5, kuya kwisamba esingama - 50 kuya kwisamba esiyi - 100 kuya kwisamba esiyi - 100 Ukuhlanganisa 3, 4 okuphindayo • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele okuholela • Sebenzisa izimpawu ezifanele (x, =, ) (x, =, ) (x, =, ) ezibalweni (x, =, ) zokuphindaphinda 1.15 • Hlukanisa izinombolo kufinyelela • Hlukanisa izinombolo kufinyelela • Hlukanisa izinombolo kufinyelela • Hlukanisa izinombolo kufinyelela ema - 50 ngo 2, 5, 10 ema - 50 ngo 2, 4, 5, 10 ema - 99 ngo 2, 3, 4, 5, 10 ema - 99 ngo 2, 3, 4, 5, 10 Ukuhlukanisa • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele • Sebenzisa izimpawu ezifanele (÷, =, ) (÷, =, ) (÷, =, ) (÷, =, ) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 1.16 Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Ulwazi Lwezinombolo: Uhla Lwezinombolo kufinyelela ku 200 Lwezinombolo kufinyelela ku 500 Lwezinombolo kufinyelela ku 750 Lwezinombolo kufinyelela ku 999 Izibalo zekhanda CAPS • Hlela izinombolo ezikhethiwe • Hlela izinombolo ezikhethiwe • Hlela izinombolo ezikhethiwe • Hlela izinombolo ezikhethiwe ngokwamaqoqo. Uhla ngokwamaqoqo. Uhla ngokwamaqoqo. ngokwamaqoqo. lwezinombolo kufinyelela ema - lwezinombolo kufinyelela ema - • Qhathanisa izinombolo kuya ema - • Qhathanisa izinombolo kuya ema - 200 500 200 bese uyasho ukuthi eyiphi: 1 000 bese uyasho ukuthi eyiphi: • Qhathanisa izinombolo kuya ema - • Qhathanisa izinombolo kuya ema - - Eningi noma encane ngoku 1 - Eningi noma encane ngoku 1 200 bese uyasho ukuthi eyiphi: 500 bese uyasho ukuthi eyiphi: - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 1 - Eningi noma encane ngoku 1 - Eningi noma encane ngoku 3 - Eningi noma encane ngoku 3 - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 2 - Eningi noma encane ngoku 4 - Eningi noma encane ngoku 4 - Eningi noma encane ngoku 3 - Eningi noma encane ngoku 3 - Eningi noma ncane ngoku 5 - Eningi noma nvane ngoku 5 - Eningi noma encane ngoku 4 - Eningi noma encane ngoku 4 - Eningi noma encane nge 10 - Eningi noma encane nge 10 - Eningi noma nvane ngoku 5 - Eningi noma nvane ngoku 5 - Eningi noma encane nge 10 - Eningi noma encane nge 10 Khumbula ngokushesha: Khumbula ngokushesha: Khumbula ngokushesha: Khumbula ngokushesha: • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa • Khumbula izindlela zokuhlanganisa nokususa kuyofinyelela ema - 20 nokususa kuyofinyelela ema - 20 nokususa kuyofinyelela ema - 20 nokususa kuyofinyelela ema - 20 • Hlanganisa noma ususe okubalwa • Hlanganisa noma ususe okubalwa • Hlanganisa noma ususe okubalwa • Hlanganisa noma ususe okubalwa ngama 10 kusukela ku 0 kuya e ngama 10 kusukela ku o kuya e ngama 10 kusukela ku o kuya e ngama 10 kusukela ku o kuya e 100 100 100 100 • Izindlela zokuphindaphinda nokuhlukanisa: - Ithebula lika 2 kufinyelela 2 x 10 - Ithebula lika 10 kufinyelela ku 10 x 10 89 Izibalo IBANGA 1-3

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 1.16 Amaqhinga okubala ngekhanda: Amaqhinga okubala ngekhanda: Amaqhinga okubala ngekhanda: Amaqhinga okubala ngekhanda: 90 Izibalo zekhanda Sebenzisa amaqhinga okubala: Sebenzisa amaqhinga okubala: Sebenzisa amaqhinga okubala: Sebenzisa amaqhinga okubala: • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala • Beka inombolo enkulu kuqala ukuze ubale uye phambili noma ukuze ubale uye phambili noma ukuze ubale uye phambili noma ukuze ubale uye phambili noma emumva. emumva. emumva. emumva. • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Umugqa wezinombolo • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise • Phinda kabili ubuye uhlukanise kabili kabili kabili kabili Izibalo IBANGA 1-3 • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi kokuhlanganisa nokususa kokuhlanganisa nokususa kokuhlanganisa nokususa kokuhlanganisa nokususa • Sebenzisa ubudlelwano phakathi • Sebenzisa ubudlelwano phakathi kokuphindaphinda nokuhlukanisa kokuphindaphinda nokuhlukanisa 1.17 • Sebenzisa ubuye unike • Sebenzisa ubuye unike • Sebenzisa ubuye unike • Sebenzisa ubuye unike amagama izingcezu ezizodwa amagama izingcezu ezizodwa amagama izingcezu ezizodwa amagama izingcezu ezizodwa Amaqhezu ezifaka: uhhafu, ikota, okukodwa zifaka: uhhafu, ikota, okukodwa zifaka: uhhafu, ikota, okukodwa zifaka: uhhafu, ikota, okukodwa kokuthathu, nokukodwa kokuhlanu kokuyisishiyagalombili, kokuyisishiyagalombili, kokuyisishiyagalombili, nokukodwa kokuthathu, okukodwa nokukodwa kokuthathu, okukodwa nokukodwa kokuthathu, okukodwa kokuyisithupha, okukodwa kokuyisithupha, okukodwa kokuyisithupha, okukodwa kokuhlanu kokuhlanu kokuhlanu • Bona amaqhezu asemidwebeni • Bona amaqhezu asemidwebeni • Bona amaqhezu asemidwebeni • Bona amaqhezu asemidwebeni • Bhala amaqhezu abe ngokukodwa • Bhala amaqhezu abe ngokukodwa • Qala ukubona ukuthi ohhafu • Qala ukubona ukuthi ohhafu kokubili, okukodwa kokuthathu. kokubili, okukodwa kokuthathu. ababili noma okuthathu kokuthathu ababili noma okuthathu kokuthathu kwenza okukodwa okuphelele, kwenza okukodwa okuphelele, uhhafu owodwa namakota amabili uhhafu owodwa namakota amabili kuyalingana kuyalingana • Bhala amaqhezu abe ngokukodwa • Bhala amaqhezu abe ngokukodwa kokubili, okubili kokuthathu. kokubili, okubili kokuthathu. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Izinhlobo zezinkinga zeBanga lesi - 3 Lezi yizibonelo zezinhlobo zezinkinga ezibalulekile okufanele ukuthi uthisha azethule ngokuziphinda ekilasni. Uma uthisha esebenza ngamaqoqo amancane, kufanele ayisho ngomlomo inkinga. Uma abafundi sebekwazi ukufunda, usengabanikeza izinkinga zezibalo ezibhalwe phansi, kodwa futhi akayisho inkinga ngomlomo. Izinkinga ezisesimweni esejwayelekile zingafakwa ephepheni lokusebenzela, kodwa kube kufishane, iqonde ngqo kube ejwayelekile, uthisha kufanele aqiniseke ukuthi bonke abafundi bayaziqonda lezizinkinga. Amaqoqo Ukwenza amaqoqo, kulahlwa izinsalela Ibhikawozi lithengisa izinkwa eziyi - 12 esikhwameni ngasiynye. Banezinkwa eziyi - 118. Zingaki izikhwama ezifaka izinkwa eziyi 12 abazozenza? Ukwenza amaqoqo, kufakwa izinsalela ezimpemdulweni Umlimi unamaqanda angama - 227. Mangaki amabhokisi amaqanda azowathola uma ibhokisi ngalinye lifaka amaqanda ayi - 6? Ukuhlukanisa Ukuhlukanisa, kulahlwa insalela Abangane bahlukaniselana ibhokisi elinamaswidi angama - 84 ukuze bonke bathole amaswidi alinganayo. Ukuhlukanisa okuholela emaqhezwini Hlukanisa amawolintshi ayi - 15 phakathi kwabangane abayisithupha ukuze bonke bathole amawolintshi ngokulinganayo kungabibikho asalayo. Ingxenye yeqoqo Ugogo unikeza uNoluthando imali engamarandi ayi - 12. UNoluthando ufuna ukonga ingxenye yokukodwa kokuthathu. Malini azoyonga? Ukubekwa kwamaqhezu ndawonye Umqeqeshi webhola lomnqakiswano unikeza umdlali ngamunye uhhafu wewolintshi. Kunabadlali abayi - 14. Udinga amawolintshi amangaki? Loluhlobo lwezinkinga kufanele luvezwe kuphela uma abafundi sebexazulule izinkinga ezine noma ezinhlanu zokuhlukaniselana, kuholela kwizinhlobo zamaqhezu kanye nokwazi amagama ezingcezu zamaqhezu. Ukwabelana ngokulingana UnoMfundo mncane kunoNokwethaba. Uma uNomfundo edla ucezu olulodwa lwesinkwa uNokwethaba ufuna izingcezu ezimbili. Uma uNomfundo edla izingcezu ezimbili, uNokwethaba ufuna izingcezu ezine. Ngemumva kwezinsukwana, bazobe bedle izingcezu eziyi - 12. Zingaki izingcezu ezidliwe nguNomfundo, zingaki ezidliwe nguNokwethaba? CAPS 91

Izibalo IBANGA 1-3 UThemba noSimanga benza umsebenzi othile ndawonye. UThemba usebenza amahora amathathu, uSimanga usebenza ihora elilodwa. Bakhokhelwe imali engangamarandi - 60. Bazoyihlukanisa kanjani lemali? Ukuhlanganisa okuphindayo Mangaki amasondo ezimotweni ezingama - 36? Izinga UThami ukwazi ukugcina imali engango - 35c ngesonto. Malini akwazi ukuyigcina ngamasonto ayisi - 8? Igridi Umnumzane uKhumalo utshale imigqa yezihlahla zamawolintshi engama - 20. Kunezihlahla eziyi - 12 umugqa ngamunye. Zingaki izihlahla ezitshaliwe sezizonke? Ukuhlanganisa nokuhlukanisa Kunezinhlobo okungenani ezintathu zezinkinga zokuhlanganisa nokuhlukanisa. Uhlobo ngalunye lungavezwa ngezindlela ezahlukene. Izinhlobo eziyisisekelo yilezi: Ushintsho UNoluthando uqoqe izivalo zamabhodlela ezingama - 234. UPhilasande umnikeze ezingama - 80 ngaphezulu. Zingaki izivalo zamabhodlela anazo? Bekunabagibeli abangama - 500 esitimeleni. Kwehla abayi - 176. Bangaki abagibeli abasele esitimeleni? Hlanganisa UNomali uqoqela isikole sakhe amabhodlela namathini. Uqoqe amabhodlela ayi - 124 kanye namathini angama - 268. Mangaki amabhodlela namathini awaqoqile? Isitolo sinamaphakethe angama - 368 amakhekhe; angama - 82 asonakele. Mangaki angakonakali? Qhathanisa IBanga lesi 2 liqoqe imali engango R446. IBanga lesi 3 laqoqa imali engango R729. Ingakanani imali eqoqwe yiBanga lesi 3 ngaphezulu kunaleyo eqoqwe yiBanga lesi 2? Ukuvezwa kwenkinga ngayinye ngezindlela ezahlukene Izinkinga kufanele zivezwe ngezindlela ezahlukene. Isibonelo, zombili lezizinkinga ezoshintsho, kodwa okungaziwa kusezindaweni ezahlukene. Isitolo sinamasaka empuphu, bathenga amanye angama - 55. Isitolo manje sesinamasaka ayi - 170. Mangaki amasaka empuphu ebekade esesitolo ekuqaleni? Isitolo besinamaphakethe angama - 500 kashukela. Ngemuva kokuthengisa amanye alamaphakethe, babenamaphakethe angama - 324 asele. Bathengise amaphakethe amangaki? 92 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Izimo zezinkinga ezinobudlelwano obusebenzayo obehlukene UNokwethaba uthengisa amawolintshi abiza amarandi amane (R4) lilinye. Yenza ithebula lokumsiza ukuthola inani lama oda amakhulu. Inani lamawolintshi 1 2 3 4 5 10 20 Inani ngokwamarandi 4 8 Sebenzisa lelithebula ukuthola inani lamawolintshi ayisi - 7 kanye nangama - 23. UNomusa ugada ingane. Ubiza amarandi angama - 20 imali yokuhamba, kube amarandi ama 5 ngehora ukugada ingane. Qedela lelithebula lakhe. Inani lamahora 1 2 3 4 5 10 Inani ngokwamarandi (R) 25 30 Qaphela ukuthi izinkinga zikaNokwethaba noNomusa zisebenza ngokungafani. Lezizinhlobo zezinkinga zezenzelwe ukusiza uthisha. Abafundi akumele baxinwe ngalezizinkinga. Khumbula ukuthi abafundi bajwayele ukusebenzisa izindlela ezahlukene zokuxazulula izinkinga okungenzeka kungabi yilokhu okulindelwe nguthisha. Isibonelo,inkinga yokuhlukanisa ingaxazululwa ngokususa okuphindayo,ukuhlanganisa noma ngokuphindaphinda. Izindlela ezisetshenziswa abafundi zingashintsha ngokuqhubeka konyaka ngokukhula kolwazi nokujwayela izinhlobo zezinkinga,nokukhula kolwazi lwazi lwabo lwezinombolo. CAPS 93

ULWAZI JIKELELE LEBANGA 3 2. AMAPHETHINI, UBUDLELWANE, I-ALJEBHRA 94 IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 2.1 Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Amaphethini asizungezile Amaphethini Kopisha, wandise bese uchaza use- Kopisha, wandise bese uchaza use- Kopisha, wandise bese uchaza use- Bona,chaza ngamagama bese ukopi- ejiyometri benzisa amagama benzisa amagama benzisa amagama sha amaphethini asejiyometri • Amaphethini alula enziwe ngezinto • Amaphethini alula enziwe ngezinto • Amaphethini alula enziwe ngezinto • emvelweni eziphathekayo eziphathekayo eziphathekayo • empilweni yesimanje yansuku Izibalo IBANGA 1-3 • Amaphethini alula enziwe imidwe- • Amaphethini alula enziwe imidwe- • Amaphethini alula enziwe imidwe- zonke bo, izimo noma izinto eziphathek- bo, izimo noma izinto eziphathek- bo, izimo noma izinto eziphathek- • kumasiko namagugu ethu ayo. ayo. ayo. Uhla lwamaphethini: Uhla lwamaphethini: Uhla lwamaphethini: • Amaphethini alula lapho izimo • Amaphethini alula lapho izimo noma amaqoqo ezimoephindiwe. noma amaqoqo ezimo ephindiwe. • Amaphethini lapho inombolo noma • Amaphethini lapho inombolo noma usayizi wesimo ushintsha ngendle- usayizi wesimo ushintsha ngendle- la eqagelekayo, Isib. amaphethini la eqagelekayo, Isib. amaphethini akhulayo akhulayo Akha bese uchaza amaphethini Akha bese uchaza amaphethini Akha bese uchaza amaphethini akho: akho: akho: • Akha amaphethini okusamdwebo • Akha amaphethini okusamdwebo • Akha amaphethini okusamdwebo - Usebenzisa izinto eziphathekayo - Usebenzisa izinto eziphathekayo - Usebenzisa izinto eziphathekayo - Ngokudweba imigqa, izimo noma - Ngokudweba imigqa, izimo noma - Ngokudweba imigqa, izimo noma izinto eziphathekayo izinto eziphathekayo izinto eziphathekayo • Chaza amaphethini akho • Chaza amaphethini akho • Chaza amaphethini akho Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO ITHEMU YOKU - 1 ITHEMU YE - 2 ITHEMU YE - 3 ITHEMU YE - 4 2.2 Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Kopisha, wandise bese uchaza. Iphethini Kopisha wandise bese uchaza Kopisha wandise bese uchaza Kopisha wandise bese uchaza Kopisha wandise bese uchaza CAPS yezinombolo ukulandelana okulula kwezinombolo ukulandelana okulula kwezinombolo ukulandelana okulula kwezinombolo ukulandelana okulula kwezinombolo okungenani kuyofika kuma 200. okungenani kuyofika kuma 200. okungenani kuyofika kuma 200. okungenani kuyofika kuma 200. Ukulandelana kwezinombolo Ukulandelana kwezinombolo Ukulandelana kwezinombolo . kufanele kukhombise ukubala uya kufanele kukhombise ukubala uya kufanele kukhombise ukubala uya Ukulandelana kwezinombolo phambili ubuye uye emumva kanje: phambili ubuye uye emumva kanje: phambili ubuye uye emumva kanje: kufanele kukhombise ukubala uya • sebenzisa izikhawu njengoba • sebenzisa izikhawu njengoba • sebenzisa izikhawu njengoba phambili ubuye uye emumva kanje: kuchaziwe eBangeni le - 2 nohla kuchaziwe eBangeni le - 2 nohla kuchaziwe eBangeni le - 2 nohla • sebenzisa izikhawu njengoba lwezinombolo olukhulayo lwezinombolo olukhulayo lwezinombolo olukhulayo kuchaziwe eBangeni le - 2 nohla • ngama 100 kuya okungenani • ngama 50,100 kuya okungenani • ngama 20, 25, 50,100 kuya lwezinombolo olukhulayo kwangama - 500 kwangama - 1000 okungenani kwangama - 1000 • ngama 20, 25, 50,100 kuya akha uchaze iphethini yakho okungenani kwangama - 1000 yezinombolo akha uchaze iphethini yakho yezinombolo 95 Izibalo IBANGA 1-3

ULWAZI JIKELELE LEBANGA 3 3. INDAWO NEZIMO (IJIYOMETRI) 96 IZIHLOKO ITHEMU YOKU - 1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.1 Isikhundla nokubukeka kwento Isikhundla nokubukeka kwento Isikhundla, inkomba • qondanida ukubukeka kwezinto • Funda, humusha bese udweba nokubukeka kwento ezifanayo zansuku zonke ibalazwe elingahlelekile noma. • Isho into yansuku zonke • Thola izinto kwibalazwe uma iboniswa ngendlela Indawo nezinkomba engajwayelekile. Izibalo IBANGA 1-3 • Landela izinkomba usuka Isikhundla nezinkomba endawieni eyodwa uya kwenye • Landela izinkomba uma unyakaza usebenzisa ibalazwe ekilasini nasesikoleni • Nika izinkomba zokunyakaza ekilasini nasesikoleni. 3.2 Uhla lwezinto Eziphathekayo Uhla lwezinto Eziphathekayo Uhla lwezinto Eziphathekayo Izinto Bona bese usho izinto ezinhlangothi Bona bese usho izinto ezinhlangothi Bona bese usho izinto ezinhlangothi ezinhlangothintathu ntathu ezitholakala ekilasini ntathu ezitholakala ekilasini ntathu ezitholakala ekilasini nasezithombeni nasezithombeni nasezithombeni 3-D • Okusabhola • Okusabhola • Okusabhola • Okusabhokisi • Okusabhokisi • Okusabhokisi • Amasilinda • Amasilinda • Amasilinda • Iphiramidi • Iphiramidi • Ikhoni • Ikhoni Izimpawu zezinto Izimpawu zezinto Izimpawu zezinto Chaza, hlela bese uqhathanisa izinto Chaza, hlela bese uqhathanisa izinto Chaza, hlela bese uqhathanisa izinto ezinhlangothi ntathu ngokuthi: ezinhlangothi ntathu ngokuthi: ezinhlangothi ntathu ngokuthi: • Usebenzise izimo ezinhlangothi • Usebenzise izinto ezinhlangothi • Usebenzise izinto ezinhlangothi mbili ukwenza ubuso bezinto mbili ukwenza ubuso bezinto mbili ukwenza ubuso bezinto Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ezinhlangothi ntathu ezinhlangothi ntathu ezinhlangothi ntathu • Usebenzise izicaba noma • Usebenzise izicaba noma • Usebenzise izicaba noma okugwingcizayo. okugwingcizayo. okugwingcizayo.

IZIHLOKO ITHEMU YOKU - 1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.2 Umsebenzi Okugxilwa kuwo Umsebenzi Okugxilwa kuwo Izinto • Bona bese wakha izinto • Bona bese wakha izinto CAPS ezinhlangothintathu ezinhlangothi ntathu ozinikiwe ezinhlangothi ntathu ozinikiwe usebenzisa izinto eziphathekayo usebenzisa izinto eziphathekayo njengezimo ezinhlangothi mbili, njengezimo ezinhlangothi mbili, ubumba, izinti zokuphuza, izinti ubumba, izinti zokuphuza, izinti zokuvungula nezinye izinto zokuvungula nezinye izinto ezinhlangothi ntathu. ezinhlangothi ntathu. Ukulandelana komsebenzi Ukulandelana komsebenzi Ukulandelana komsebenzi okuzugxilwa kuwo eThemu 2 okuzugxilwa kuwo eThemu 3 okuzugxilwa kuwo eThemu 4 Sebenzisa okusamabhola, Sebenzisa okusamabhola, okusamabhokisi, amasilinda okusamabhokisi, amasilinda njengoenzile eBangeni 2; nika njengoba senzile eBangeni 2; amagama azo beseuwenza nika amagama azo beseuwenza amaqoqo. amaqoqo. Gxila ebusweni bohlobo ngalunye Gxila ebusweni bohlobo ngalunye lwento. Bheka ukuthi ubuso lwento. Bheka ukuthi ubuso buyisicaba noma buyagwingciza. buyisicaba noma buyagwingciza. Xoxa ngobuso obuyisicaba obukumaprizimu namasilinda bese uyabuchaza ukuthi buyindilinga, buyisikwele, buwunxande noma buwunxantathu. Nika igama bese wenza iqoqo Sebenzisa izingqwembe ezisikwe lezinto ezinhlanothi ntathu izikwele ukwenza ibhokisi. Khuluma ezingenhla. ngobuso obuyisicaba obusesimweni esisabhokisi nakwisilinda bese uchaza ukuthi ayindilinga, isikwele Sebenzisa izinti zokvungula, izinti noma unxande. zokuphuza noma iphepha eligoqiwe laba umbhobho ukwenza iphiramidi. Qedela lengxenye yomsebenzi Qedela lengxenye yomsebenzi Qedela lengxenye yomsebenzi ngokwenza umsebenzi obhalwayo. ngokwenza umsebenzi obhalwayo. ngokwenza umsebenzi obhalwayo. 97 Izibalo IBANGA 1-3

IZIHLOKO ITHEMU YOKU - 1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.3 Uhla Lwezimo Uhla Lwezimo 98 Izimo • Indilinga • Indilinga ezinhlangothimbili • Unxantathu • Unxantathu 2-D • Isikwele • Isikwele • Unxande • Unxande Izimpawu Zezimo Izimpawu Zezimo Chaza, uhlele bese uqhathanisa Chaza, uhlele bese uqhathanisa Izibalo IBANGA 1-3 izimo ezinhlangothimbili ngoku: izimo ezinhlangothimbili ngoku: • izimo • izimo • amacala aqondile • amacala aqondile • amacala ayindilinga • amacala ayindilinga Ukulandelana komsebenzi Ukulandelana komsebenzi okuzugxilwa kuwa eThemu 1 okuzugxilwa kuwa eThemu 3 Nika amagama bese ubeka izimo Nika amagama bese ubeka izimo ngamaqoqo. ngamaqoqo. Gxila ezinhlobeni zamacala Gxila ezinhlobeni zamacala akumumo ngamunye. Hlukanisa akumumo ngamunye. Hlukanisa izimo ngokubuka ukuthi amacala izimo ngokubuka ukuthi amacala ayindingila noma aqondile. ayindingila noma aqondile. Dweba indilinga, isikwele, unxande, Dweba indilinga, isikwele, unxande, nonxantathu. nonxantathu. Qedela lengxenye yomsebenzi Qedela lengxenye yomsebenzi ngokwenza umsebenzi obhalwayo. ngokwenza umsebenzi obhalwayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO ITHEMU YOKU - 1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 3.4 Okufana nse nxazombili Okufana nse nxazombili Okufana nse Thola lapho kuhamba khona • Bona bese udweba umugqa CAPS nxazombili umugqa ohlukanisa phakathi ohlukanisa kabili ezintweni nendawo ngoku eziyizimo ezinhlangothi mbili eziyizibalo mdwebo nezingeyizo Imisebenzi yokugoqwa izibalo mdwebo. kwamaphepha goqa amaphepha Okugxilwa kukho eThemu 2 Okugxilwa kukho eThemu 4 ithuthukisa ulwazi lokuhlukanisa Imisebenzi yokubhala kufanele ifake kabili kufane futhi kulingane izibonelo lapho: nxazombili lufaka: • Umugqa ohlukanisa kabili kufane • imisebenzi lapho upende omanzi nse nxa zombili akumele kube unindwa ephepheni ngaphambi osuka phezulu uye phansi kokugoqa iphepha. kuphela. • Imisebenzi lapho iphepha lisikwa • Umugqa ohlukanisa kabili kufane noma lidatshulwa emgqeni ingaba sezindaweni ezahlukene eligoqwe kuwo. kwezinye izimo nima izinto. 99 Izibalo IBANGA 1-3

ULWAZI JIKELELE LEBANGA 3 4. ISILINGANISO 100 IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.1 Ukufunda Isikhathi Ukufunda Isikhathi Ukufunda Isikhathi Ukufunda Isikhathi Isikhathi • Funda izinsuku kukhalenda • Funda izinsuku kukhalenda • Funda izinsuku kukhalenda • Funda izinsuku kukhalenda • Faka izinsuku zokuzala, imigubho • Faka izinsuku zokuzala, imigubho • Faka izinsuku zokuzala, imigubho • Faka izinsuku zokuzala, imigubho yokholo, izinsuku zokuphumula, yokholo, izinsuku zokuphumula, yokholo, izinsuku zokuphumula, yokholo, izinsuku zokuphumula, izigameko zomlando, imicimbi izigameko zomlando, imicimbi izigameko zomlando, imicimbi izigameko zomlando, imicimbi yesikole kwikhalenda. yesikole kwikhalenda. yesikole kwikhalenda. yesikole kwikhalenda. Izibalo IBANGA 1-3 • Yisho isikhathi ngamahora • Yisho isikhathi ngamahora • Yisho isikhathi ngamahora • Yisho isikhathi ngamahora ayishumi nambili ayishumi nambili ayishumi nambili ayishumi nambili - amahora - amahora - amahora - amahora - isigamu sehora - isigamu sehora - isigamu sehora - isigamu sehora - ikota yehora - ikota yehora - ikota yehora - ikota yehora - imizuzu - imizuzu - imizuzu - imizuzu Sebenzisa iwashi lezinti Sebenzisa iwashi lezinti Sebenzisa iwashi lezinti Sebenzisa iwashi lezinti nelezinombolo nezinye nelezinombolo nezinye nelezinombolo nezinye nelezinombolo nezinye izinto ezikhombisa isikhathi izinto ezikhombisa isikhathi izinto ezikhombisa isikhathi izinto ezikhombisa isikhathi njengomakhalekhukhwini. njengomakhalekhukhwini. njengomakhalekhukhwini. njengomakhalekhukhwini. Bala ubude nokudlula kwesikhathi Bala ubude nokudlula kwesikhathi Bala ubude nokudlula kwesikhathi Sebenzisa ikhalenda ukubala bese Sebenzisa ikhalenda ukubala bese Sebenzisa ikhalenda ukubala bese uchaza ubude besikhathi usebenzise uchaza ubude besikhathi usebenzise uchaza ubude besikhathi usebenzise izinsuku, amasonto noma izinyanga. izinsuku, amasonto, izinyanga kanye izinsuku, amasonto, izinyanga kanye noku: noku: • Sebenzisa iwashi ukubala ubude besikhathi ngamahora noma • ukushintsha usuka ezinsukwini uya • ukushintsha usuka ezinsukwini uya ngesigamu samahora. emasontweni emasontweni • Ukushintsha usuka emasontweni • Ukushintsha usuka emasontweni uya ezinyangeni. uya ezinyangeni. Sebenzisa iwashi ukubala ubude Sebenzisa iwashi ukubala ubude besikhathi ngamahora, ngesigamu besikhathi ngamahora, ngesigamu Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola samahora nangekota lamahora. samahora nangekota lamahora

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.2 Isilinganiso esingahlelekile Ubude • Qagela, linganisa, qhathanisa, CAPS hlela bese ubhala ubude usebenzisa ukukala okungenasilinganiso njengezandla, amagxathu, ubude bepensela, izinto zokubala njll. • Chaza ubude bezinto eziphathekayo ngokubala usho nobude usebenzisa amayunithi angahleliwe. • Sebenzisa ulimi olukhuluma ngokuqhathanisa ubude; njengokuthi kude kuna, kufushane kuna, kuphakeme kuna, kubanzi kuna Ukwethula Isilinganiso Ukwethula Isilinganiso esingahlelekile esingahlelekile • Qagela, linganisa, hlela bese • Qagela, linganisa, hlela bese ubhala ubude usebenzisa ubhala ubude usebenzisa amamitha (irula eliyimitha, amamitha (irula eliyimitha, intambo eyimitha) njengesikali intambo eyimitha) njengesikali esilinganisiwe sobude. esilinganisiwe sobude. • Qagela bese ukala ubude • Qagela bese ukala ubude ngamasentimitha usebenzisa irula. ngamasentimitha usebenzisa irula. (Akudingekile ukushintsha amasentimitha aye kumamitha.) 101 Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.3 Isilinganiso esingahlelekile 102 Isisindo • Qagela, linganisa, qhathanisa, hle- la bese ubhala isisindo usebenzisa isikali sokuzimelela kanye nokukala okungenasilinganiso njengamabhu- loki, izitini njll • Sebenzisa ulimi ukukhuluma ngokuqhathanisa isisisindo njen- gokuthi kulula, kuyasinda, kulula Izibalo IBANGA 1-3 kuna, kuyasinda kuna Ukwethula Isilinganiso esihleliwe Ukwethula Isilinganiso esihleliwe • Qhathanisa, hlela bese ubhala Abafundi kufanele benze imisebenzi isisindo sezinto ezithengiswayo yokubhala ukuphetha lokhu, okufaka ezinesisindo esibhaliwe esinan- nokufundwa kwezithombe: gamakhilogramu, njengokuthi 2kg • Imikhiqizo enesisisindo esibhaliwe yempuphu ne 1kg kafulawa noma kuyo ngamagramu Isib. 500g zikasawoti • Izikali zasendlini yokugeza lapho • Uma sikhona isikali sasendlini uthi lukhomba amagabelo esikali. yokugeza, abafundi bangazikala izisindo zabo besebenzisa isikali sasendlini yokugeza. Okulindelekile ukuba abafundi bafunde isisindo esisondelene nothi lwesikali.. bac- haza isisindo sabo njengesicishe / sisondelene / siseduze / sikhudl- wana / esifanayo (amakhiligramu) abawafunda esikalini. • Lapho kukhona izikali zokuzimelela ezikhombisa amagramu, abafundi bangakala isisindo noma izinto ezahlukene. (Akudingeki ukushinntsha amagramu abe amakhilogramu) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 4.4 ISILINGANISO okungahlelekile umthamo • Qagela, kala, qhathanisabese CAPS u hlela umthamo wezitsha (umthamo ongamumathwa isitsha uma sigcwele) usebenzisa izikali ezingenasilinganiso njengezipuni nezinkomishi • Chaza umthamo wesitsha ngokubala usho ukuthi kungena okungaki okuyizilinganiso ezingahleliwe ukugcwalisa isitsha Isib ibhodlela linomthamo wezinkomishi ezine. Ukwethulwa kokukala Okuhleliwe Ukwethulwa kokukala Okuhleliwe • Qagela, kala, qhathanisa, Abafundi kufanele benze imisebenzi hlela bese uyabhala umthamo yokubhala ukuphetha lokhu, okufaka usebenzisa izikalo zamalitha, nokufundwa kwezithombe: isigamu selitha nekota lelitha. • Imikhiqizo yokudayisa enomthamo - Usebenzisa amabhodlela obhaliwe kuzo ukuze bakwazi angumthamo we 1 litha, noma ukuzihlela ngokulandelana izitsha ezinomthamo obhalwe • Ojeke lapho okumumethwe ngamamililitha. Isib. Amakani kucishe kulingane namagabelo esiphuzo. akhombisa 1 litha noma 2 amalitha - Ujeke onamagabelo akhombisa noma isigamu selitha noma ikota amalitha, uhhafu welitha nekota lelitha yelitha • Ojeke lapho okumumethwe - Ujeke onamagabelo akhombisa kucishekulingane amamililitha namagabeloakhombisa amamililitha. Okulindelekile ukuthi - Izinkomishi zokukala kanye abafundi abafunde ukufunda namathisipuni akhombisa besondezela kumagabelo. umthamo. Bachaze umthamo njengocishe • Qhathanisa, hlela bese ubhala / kusondele / kuthi ukuba umthamo obhaliwe ezintweni ngaphezulu / ungaphezulu noma ezipakishelwe ukudayisa ngaphansi / noma olingana lakusetshenziswe amalitha. (amalitha) abakufanda kujeke. Isibonelo 5 amalitha kapendi, 1 litha wesiphuzo, 2 amalitha 103 ob noma ngamamililitha noma amamililithaIsib. 500 ml yobisi, 340ml yesiphuzo, 750ml yamafutha Izibalo IBANGA 1-3

IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 • Azi ukuthi inkomishi ekaliwe Akudingeki ukushinntsha amagramu 104 ingamamililitha angama -250 abe amakhilogramu • Azi ukuthi isipuni singamamililitha ayisi -5 Akudingeki ukushintsha amagramu abe amakhilogramu 4.5 Ubude obungaphandle bento Ubude Phenya ubude obuzungeze Izibalo IBANGA 1-3 obungaphandle izimo ezinhlangothi mbili nezinto bento ezinhlangothi ntathu kusetshenziswa ukuqhathanisa ngqo noma amayunithi angahleliwe. 4.6 Ububanzi bendawo Ububanzi bendawo Phenya ububanzi bendawo usebenzisa amathayela. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI JIKELELE LEBANGA 3 5. UKUQOKELELWA KOLWAZI IZIHLOKO Ithemu loku-1 Ithemu lesi-2 Ithemu lesi-3 Ithemu lesi-4 CAPS 5.4 Izincomo: Izincomo: Qoqa bese uhlele Ukusebenzisa ulwazi oluphelele Hlela kabusha ulwazi olunikiwe ulwazi ukwakha ibar grafu. olusohlwini noma kumathalisi noma amathebula noma i bar grafu. 5.5 Qoqa ulwazi ngekilasi noma nge- sikole bese uphendula imibuzo Bhala ulwazi kwi bar grafu Okumele Ulwazi ebuzwe uthisha. Phendula imibuzo ngolwazi olukwi 5.6 Sebenzisa amathalisi ukubhala ul- Hlaziya okumele ulwazi okunikiwe. bar grafu. Hlaziya okumele ulwazi olunikiwe. wazi ngezigaba zalo ezinikiwe kanje: Hlaziya bese Izincomo Izincomo uhumusha ulwazi • amathebula • Abafundi abenze okungenani eyo- • Abafundi abenze okungenani eyo- • Bar grafu dwa igrafu yezithombe okukodwa dwa igrafu yezithombe okukodwa Xoxa bese uphendula imibuzo nokukodwa okuhambisanayo. nokukodwa okuhambisanayo. ngolwazi olukumathebula nakwi bar • Okungenani eyodwa ibar grafu. • Okungenani eyodwa ibar grafu. grafu. 105 Izibalo IBANGA 1-3

3.5 AMANOTHI ACHAZAYO KANYE NOMHLAHLANDLELA WOKUFUNDISA 106 Amathebula angezansi anikeza uthisha lokhu: • Ingxenye yolwazi nezihloko kw iBanga ngalinye neThemu ngayinye; • Ulwazi namakhono okuphakanyisiwe okuzogxilwa kukho eThemu ngayinye; • Amanothi achazayo nomhlahlandlela wokufundisa; Izibalo IBANGA 1-3 • Isikhathi esabelwe isihloko ngasinye sezifundo ezethulwa nge 1hora namaminithi angama - 24. 3.5.1 AMANOTHI ACHAZAYO: Ibanga 1 ithemu YOKU-1 YEbanga LOKU- 1 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO Ngethemu yokuqala isikhathi sisetshenziselwa ukuthuthukisa ulwazi lokuqala lwezinombolo. Amakhono okuqalwa ngawo awokuthuthukiswa kwamaphethini, indawo nesimo, ISILIN- GANISO nolwazikha isisekelo samakhono okufunda ngokuvulelekile namakhono ezinombolo ngokukhethekile. Ukuqondanisa Ukuqondanisa kuholela ekuqondeni ulwazi lokufunda ukuqondanisa okukodwa nokukodwa okuhambisanayo, okwakha isisekelo sokuqhathanisa inani lezinto eqoqweni. Uma umfundi ekwazi ukubona “okufanayo”, kwenza kubelula ukuqondanisa amasethi amabili. Ukufanisa kuyisiqalo sokwazi ukugcina ulwazi. Ukugcina ulwazi kuyikhono elibalulekile ekulinganiseni, inombolo nendawo nesimo. Ukuhlela Uma kuhlelwa, abafundi babheka okufanayo nokwehlukile. Abafundi babuye bathuthukise ukukwazi ukuchaza nokukhomba. Ukuchaza kusho ukuthi abafundi bangakwazi ukubona nokusho izinto ezibazungezile. Ukukhomba kusho ukuthi abafundi bangakwazi ukuthatha into uma ichaziwe. Abafundi bakhomba ngokwezakhiwo ezithile. Abafundi bahlela izinto ngokobungako, umbala, isimo, ubude, isisindo, umthamo nokumumethwe. Ukuhlela kwenziwa ngoku: • Uk ukuqokelelwa kolwazi lwez izinto zansuku zonke; • Izimo ezisejiyometri nezinto eziphathekayo kwisimo nendawo; kanye • Izakhiwo zezinto zokulinganisa. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukuqhathanisa Uma abafundi beqhathanisa izinto eziphathekayo babhekisisa okwenza umehluko phakathi kwezinto ezimbili. Abafundi bangagxila kulokhu • Kukhulu noma kuncane; • Kuyasinda noma kulula; • Kude noma kufishane; • Kuyashisa noma kuyabanda;

ithemu YOKU-1 YEbanga LOKU- 1 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO • Akukho noma kugcwele; CAPS • Kuningi noma kumbalwa; kanye • Okokuqala, okokugcina noma kuphakathi. Ukufunda ukuqhathanisa kuyinto okugxilwa kuyo:- • Imisebenzi yokuqala yokulinganisa; • Imisebenzi yokuqala yezimo nendawo (kufaka imisebenzi yesikhundla) kanye • nemisebenzi yokuqala uma kwenziwa amaphethini. Emisebenzini yezinombolo, abafundi baqondanisa izinto eziphathekayo ngamaqoqo ahlukene. Bafunda ukubona amaqoqo anezinto ezilinganayo ngenani, nokuhlukanisa amaqoqo anezinto eziningi noma ezimbalwa kunezinye. Ukuhlela ngokulandelanisa Ukuhlela ngokulandelanisa kuyisisekelo somsebenzi wezinombolo. Ukubeka nokubala izinto ngokulandelana kwazo kusiza abafundi abasebancane ukuqinisekisa ukuthi into bayibala kanye. Ukubeka izinto ngokulandelana kwacha isisekelo solwazi lokulandelanisa izinombolo. Umsebenzi wokuqala wamaphethini ofaka izimo noma izinto usiza abafundi bagxile ekulandelaniseni izinombolo. Abafundi bazolisebenzisa lelikhono ukwenza amaphethini. Ukuqagela inani lezinto eqoqweni Ukuqagela inani lezinto eziyiqoqo ngaphandle kokuzibala. Lokhu kusiza abafundi ukubona iqoqo elincane njengento eyodwa. Lokhu kunika abafundi ulwazi lokuqala oluyisisekelo sokusebenza ngezinombolo. 107 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 108 NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA engu -24) 1.1 Bala izinto ngokuyikho Bala izinto ngokuyikho Ukubala kusiza abafundi ukuthuthukisa ukwazi ubungako bezinombolo bese kufika ema -50. Nikeza kufika e -10. kwenza isisekelo sokubala ngezinombolo eziphelele. Ngethemu yokuqala abafundi Bala izinto inombolo oyiqagele bathuthukisa lamakhono: Nikeza inombolo ngokusondelele oyiqagele ngokusondelele • Ukubala konke nengatholakala ngokubala. nengatholakala ngokubala. • Ukubala ngokuqhubeka Izibalo IBANGA 1-3 • Indlela yokusebenza kwezinombolo ezijwajelekile • Ukusebenza ngokubhaliwe Ngethemu yoku - 1 ukubala kugxila ekuthuthukiseni amakhono okubala. Ukuthuthuka kwamakhono okubala kubasiza ukuba: • Ukubala izinto ezingamaqoqo nezingewona amaqoqo; • Ukubalal uyaphambili nasemumva; • Ukubala ngokwenza; • Ukubalala ngokulandelanisa kumugqa wezinombolo; • Ukuthuthukisa ulwazi lobungako benombolo ngokuzihlela nangokuziqhathanisa; kanye • Ukuhlawumbisela nokuqagela. Ukubala izinto Ngaphambi kokuba abafundi babale izinto badinga amathuba okubala ngokwenza ngokuphindelela bekhuluma. Abafundi kufanele bathole uhla lwezinombolo ngamagama ngokulandelana: kunye, kubili, kuthathu kuze kufike kuma -20. Khuthaza abafundi ukusho imilolozelo enezinombolo badlale nemidlalo ezogxilisa ukushiwo kwezinombolo. Lelikhono lokubala ngokuphimisa libalulekile ukuthuthukisa ulwazi lwezinombolomagama kanye nomuzwa wesigqi / iphethini ezinombolweni. Abafundi bazobe sebebala into ngayinye baqondanise igama lenombolo nenani lezinto. Lokhu kusho ukuthinta nokunyakazisa into ube usho igama lenombolo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Kubalulekile ukuthi abafundi baqonde ukuthi inombologama yokugcina isho inombolo yento yokugcina eqoqweni. Kumele baqonde ukuthi inombolo magama yokugcina ikhombisa inani lezinto eqoqweni noma isikhundla seqoqo. Akubona bonke abafundi abakwazi ukubala ngokuphimisa izinombolomagama ngendlela ezilandelana ngayo abangakwazi ukunikeza umqondo entweni ebalwayo. Bangeqa izinombolo bese bethi zine izinto zokubala kodwa zibe zinhlanu.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA CAPS engu -24) 1.1 Bala izinto ngokuyikho Bala izinto ngokuyikho Kubalulekile ukuthi abafundi babale inombolo efanayo yezinto ezihlukene. kufika ema -50. Nikeza kufika e -10. Bala izinto Isibonelo: inombolo oyiqagele Nikeza inombolo ngokusondelele oyiqagele ngokusondelele • Bala izinto eziyisithuph zokubala nengatholakala ngokubala. nengatholakala ngokubala. • Letha amapensela ayisithupha • Bala izinkinobho eziyisithupha Ukulondoloza / Ukugcina Abafundi bazoqala ukubona uma bebala inombolo yezinto, ukuthi inamba ayiphazamiswa ubungako noma isikhundla ekuyo. Omunye angabuza: zingaki izinkanyezi ekhadini ngalinye?   Isikhumdla noma ukuhlelwa kwezinkanyezi akufani kodwa inombolo yezinkanyezi ilingana ncimishi. Kubalulekile ukuthi uma ubala izinto eziphathekayo, abafundi babone izinto ezimbalwa ngaphandle kokubala. Isibonelo, ukubona • Okuhlanu, njengenombolo yeminwe emihlanu esandleni. • Izinto zokubala ezintathu, zihlelwe noma ngayiphi indlela. • Okukodwa ukuya kokuyisithupha, kubukwa indlela okuhlelwe ngayo amachashazi edayisini • Lokhu kwaziwa njengokuqagela inani lezinto eqoqweni Ngakho ke: Ulwazi lwezinombolo eziyisisekelo luthuthukiswa ngokubala izinto eziphathekayo. Abafundi bafunda: • Ukuhlanganisa amagama ezinombolo neqoqo lezinto; • Ukwakha isithombe sengqondo ukuthi inombolo isho ukuthini okuwukuthi inkulu kangakanani; kanye 109 • Ukuthi igama lenombolo lento yokugcina ebaliwe imela inombolo yeqoqo lezinto. Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 110 NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA engu -24) 1.1 Bala izinto ngokuyikho Bala izinto ngokuyikho Imiyalelo nemibuzo yokulekelela ukubalwa kwezinto kufika ema -50. Nikeza kufika e -10. Bala izinto • Bala 10 izinduku zokubala. Zihlele uzibeke ngomugqa. inombolo oyiqagele Nikeza inombolo ngokusondelele oyiqagele ngokusondelele • Phinda uzihlele ngenye indlela izinduku bese uyazibala. Inamba isafana na? nengatholakala ngokubala. nengatholakala ngokubala. • Bala lezi zivalo zamabhodlela ngaphandle kokuzithinta. Izibalo IBANGA 1-3 • Ngabe inamba isafana yini? • Mangaki amakhilayoni ocabanga ukuthi akhona? • Maningi noma ambalwa kunalokho obokucabanga? • Wazi kanjani ukuthi unaleyo nombolo? • Wazi kanjani ukuthi ubale wonke amakhilayoni? • Ungayihlola kanjani impendulo yakho? Ukudlulela emsebenzini obhalwayo Abafundi kudingeka banikwe amathuba okubala imidwebo yezinto. isibonelo: Kungaki? Ukubala uqhubeka Uma abafundi sebakwazi ukubala ngokuzethemba zonke izinto kusukela kweyodwa, sebengabala ebaqhubeka kusuka eqoqweni abanalo. isibonelo: Yalela abafundi babale izinto eziyisikhombisa bese, beqala kweyesikhombisa, balale ezintathu ngaphezulu baze bafike kweziyi 10. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukubala uqhubeka yiqhinga elisebenza kangcono kunokubala konke futhi abafundi bazobenzisa ukubala beqhubeka uma benza izibalo. Izinsizakufunda: Kuyasiza ukwakha iqoqo elinezinto ezingafani abafundi abangazisa njengezinto zokubala.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA CAPS engu -24) 1.1 Bala izinto ngokuyikho Bala izinto ngokuyikho Isibonelo: kufika ema -50. Nikeza kufika e -10. Bala izinto • Izinti zikamentshisi inombolo oyiqagele Nikeza inombolo ngokusondelele oyiqagele ngokusondelele • izinti za -ayisikhilimi nengatholakala ngokubala. nengatholakala ngokubala. • izinhlamvu zepentshisi • ubhontshisi • izivalo zamabhodlela 111 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 112 NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA engu -24) 1.2 Ukubala uye phambili Ukubalal uyaphambili Ukubala uyaphambili ngakunye ubuye uye emumva ubuye uye emumva Ukubala uye Ukubala ngokuphimisela kuyisinyathelo esisemqoka uma usho amagama ezinombolo ngakunye kusukela ngakunye kusukela phambili ngokulandelana. Uma abafundi bekwazi ukwenza loku, akusho ukuthi bayabazi kunoma yiphi inombolo kunoma iyiphi inombolo ubuye uye ubungako benombolo abayishoyo. Abukho ubudlelwano phakathi kwenombolo nenani ephakathi kuka 0 ne 100 ephakathi kuka 1 no 20 emumva noma ubungako benombolo. Ukubala uye phambili Izibalo IBANGA 1-3 kanje EThemu 1 kulindeleke ukuthi abafundi bakwazi ukubala beyaphambili nasemumva ngakunye kuze kufike kuma 20. • bala ngama 10 ukusuka kunoma iyiphi inom- Ukubala uya phambili nasemumva kungenziwa abafundi bonke ekilasini. bolo ebala ngama 10 Makwenziwe isiqinesikiso sokuthi abafundi abasho nje bengaqondi ukuthi bathini. phakathi kuka 0 no 100 Emaqenjini okugxilwe kuwo nasemsebenzini wokuzimela lemsebenzi elandelayo ingenziwa ukunika umqondo ekubaleni: • bala ngoku 5 ukusuka kunoma iyiphi inombolo • Qala kokubili ubale uye kokuyisishiyagalombili ebala ngoku 5 phakathi • Bala kusukela kokune uya e 10 kuka 0 no 100 • Bala kusukela kokubili kuya kokuyisishiyagalombili. Zingaki izinombolo ozibalile? • bala ngoku 2 ukusuka kunoma iyiphi inombolo Ukubala kufinyelela e 10 ebala ngoku 5 phakathi Abafundi bazoqala ukubala kufinyelela eshumini bese benza bephinda amagama kuka 0 no 100 ezinombolo ngokulandelana. Abafundi bangakhathala ukubala ngokuphimisela badinga ukubala besebenzisa izindlela eziningi ezahlukene, ngaphandle kwaloko bayasho nje okungenamqondo. Ukubala ngokuphimisela kudinga ukulekelelwa ngokufunda izimpawu zezinombolo nokubala izinto eziphathekayo. Abafundi badinga ukuboniswa imifanekiso yezinombolo ngokulandelana. Lemifanekiso elandelayo ingasetshenziswa: • Ubuhlalu bokubala • I-abhakhasi • Umugqa wezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ekuqaleni umugqa wezinombolo kufanele ukhombise zonke izinombolo, emuva kwalokho ungasetshenziswa unezinombolo ezingakhonjisiwe noma ezeqiwe. Lokhu kusho ukuthi abafundi kufanele bazazi izinombolo ngokulandelana ukuze bakwazi ukugcwalisa izikhala.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA CAPS engu -24) 1.2 Ukubala uye phambili Ukubalal uyaphambili Ukubala uya emumva ubuye uye emumva ubuye uye emumva Ukubala uye Ukubala uya emumva kuyikhono elibukhuni kubafundi kanti ukulokhu benza ngakunye kusukela ngakunye kusukela phambili bephindelela kuyadingeka. Qala ukubala uye emumva kusukela enombolweni kunoma yiphi inombolo kunoma iyiphi inombolo ubuye uye abafundi abayijwayele,isibonelo sukela ku 2 uye emumva, uma sebemazi u 3 sukela ephakathi kuka 0 ne 100 ephakathi kuka 1 no 20 emumva kuye uye emumva njll. Ukubala uye phambili kanje Ukubala kufinyelelwa ema 20 • bala ngama 10 ukusuka Ukubala udlule eshumini kungadinga abafundi ukuba basho kulandelana kunoma iyiphi inom- kwezinombolo emva kukathisha. Kubaluleke kakhulu ukukhuthaza abafundi ukuthi bolo ebala ngama 10 baqale ukubala kunoma iyiphi inombolo. Ukuqala koku -8 kuthanda ukubanzima phakathi kuka 0 no 100 kunokuqala koku -1. Abafundi bazolisebenzisa lelikhono uma sebebala beqhubeka lapho behlanganisa. • bala ngoku 5 ukusuka kunoma iyiphi inombolo Izinsiza kufundisa ebala ngoku 5 phakathi • Ubuhlalu bokubala kufinyelele ku 20 kuka 0 no 100 • I-abhakhasi • bala ngoku 2 ukusuka kunoma iyiphi inombolo • Igridi yezinombolo isiza ukuthuthukisa izinga lokufunda imininingwane ethebulini. ebala ngoku 5 phakathi Ngoba abafundi babala bafinyelele eshumini, igrid kufanele iveze kuphela leminin- kuka 0 no 100 ingwane: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 • Umugqa wezinombolo okhombisa kufinyelele ema-20 113 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 114 NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA engu -24) 1.3 Khomba, bona bese Khomba, bona bese Ukufunda nokubhala izimpawu zezinombolo namagama. ufunda izinombolo ufunda izinombolo Izimpawu Abafundi kufanele bafunde ukuthi kwenziwa kanjani uku: zezinombolo • Khomba, bona bese • Khomba, bona bese • Bhala izimpawu zezinombolo namagama namagama ukufunda izimpawu ukufunda izimpawu ezinombolo zezinombolo oku 1kuya zezinombolo oku 1kuya • Ukufunda izimpawu zezinombolo e 100 e 20 • Ukusho izinombolo Izibalo IBANGA 1-3 • bhala izimpawu • bhala izimpawu Ukufunda nokubhala izimpawu zezinombolo namagama kufanele kuxhumane zezinombolo oku 1kuya zezinombolo oku 1 kuya nemisebenzi yokubala.Abafundi kufanele banikezwe amathuba ukuqondanisa kuma 20 e- 5 uphawu lwenombolo negama lenombolo ezintweni eziqoqiwe abazibalayo. • Khomba, bona bese • Khomba, bona bese Ngalendlela abafundi bahlanganisa uphawu lenombolo, igama lenombolo, okumele ufunda amagama ufunda amagama inombolo nokuchazwa inombolo. ezinombolo oku 1 kuya ezinombolo oku 1 kuya Eminye imisebenzi e- 10 e- 5 Ukuzijwayeza ukubhala • Bhala amagama • Bhala amagama Abafundi bangazijwayeza ukubhala izimpawu zezinombolo ngezindlela ezehlukene ezinombolo oku 1 kuya ezinombolo oku 1 kuya ngoku: e- 10 e -5 • Ngokubhala ngaphezu kwezinombolo • Ukubhala ‘ukuhlanganisa amachashaza’ imisebenzi enemigqa elandela ukubhaleka kwenombolo • Ukubhala esihlabathini • Ukubhala ebhodini noma kusimende • Ngokupenda • Ukuthunga izinombolo kusetshenziswa iwuli. Konke loku kugcizelela lapho kuqala khona ukubhalwa kwenombolo. • Ngokubhala ngaphezulu kwenombolo enkulu eyakhiwe ngephepha elinamathiselwe isihlabathi noma endwangwini Ukufunda izinombolo Lokhu kungenziwa ngoku: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukukhomba inombolo emugqeni wezinombolo noma kugridi yezinombolo • Ukufunda amakhadi ezinombolo Ukuqondanisa izimpawu zezinombolo eqoqweni lezinto Kungenziwa kanje: • Ukuqondanisa inombolo nenani lezinto • Ukubala iqoqo lezinto ngokukhetha ikhadi lenombolo elifanele lenani lezinto. • Ukubala izinto ezisesithombeni bese ubhala upawu lwenombolo.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA CAPS engu -24) 1.4 Chaza, uqhathanise, bese Chaza, uqhathanise, bese Ukuqhathanisa nokuhlela izinombolo kusiza abafundi ukuhlaziya ukuqonda uhlela izinto kufinyelela uhlela izinto kufinyelele e 5 nobungako bezinombolo. Kuzobasiza ukuthuthukisa umqondo wokuthi inkulu noma Chaza, e- 20 incane kunezinye. Uma abafundi beqonda ubungako bezinombolo, bazothola qhathanisa • Chaza bese uqhathanisa izimpawu zokubala zilula. Emabangeni aphansi loku kubizwa ngokuthi ukwakheka bese uhlela • Chaza bese uqhathanisa amaqoqo ezinto ngoku: kwenombolo. Amakhono okubala abalulekile ukuqhathanisa nokuhlela izinombolo. izinombolo iqoqo lezinto ngoku: ningi, kuncane, okuningi Ukuhlelwa kwezinombolo kufaka: ningi, okumbalwa, kakhulu, okuncane okufanayo kakhulu, kulingana, • ukufunda ngezinombolo ezimele inani lenombolo (cardinal numbers) kuningi ngango, akufani. • Usebenzisa, ukufunda nokubhala amagama nezimpawu zezinombolo • Chaza bese uhlela • Ulumi lokuqhathanisa izinombolo iqoqo lezinto • Chaza bese uhlela Ukuqhathanisa inombolo yezinto kusukela kokuningi iqoqo lezinto kuya kokumbalwa kusukela kokuningi Loku kwenzeka kaningi ngokusebenzisa okukodwa kokukodwa okuhambisanayo. nokumbalwa kuya kuya kokumbalwa Abafundi babala izinto eziqoqiwe bese beqondanisa amagama ezinombolo nezinto kokuningi nokumbalwa kuya ngokukodwa nokokukodwa okuhambisanayo. Ukuqhathanisa izinto eziqoqiwe kokuningi kuncike olwazini lokubala lwabafundi. • Uhla lwezinto Kubalulekile ukugxila olwazini loku ‘kuningi no kuncane’ uma uqhathanisa amanani. ezifinyelela esihlanwini. Uma uqhathanisa izinto ulimi lokuqhathanisa luyathuthuka. Chaza, uqhathanise, Chaza, uqhathanise Isibonelo: okuningi njenge, okuyinani elilingana noku, kulingana ne, kuningi kune, bese uhlela izinombolo bese uhlela izinombolo kuncane kune, kumbalwa kune kufinyelela e 20. kufinyelela e- 5. • Chaza bese uqhathanisa Ukuhlela amaqoqo ezinto • Chaza bese izinombolo eziphelele Ekubaleni nokuqhathanisa izinto ezingamaqoqo amabili, abafundi bathola bese uqhathanisa izinimbolo ngokuthi encane kuno. befunda ubudlelwano obubili obubalulekile: eziphelele kufinyelela enkulu kune, okuningi e- 5 usebenzisa ulimi. • Izinto ezingamaqoqqo amabili ziyalingana uma zinenani lezinto ezilinganayo yize kuno,okumbalwa Isib. okuncane kuna, okuqoqiwe kungahleliwe ngendlela efanayo. kuno,kulingana ne okukhulu kuna, okuningi kuna, okumbalwa kuna • Ukubala izinombolo kumela ukulandelana kwezinombolo eziya ngokukhula ngokukodwa njalo, isib. Okuhlanu kuza emva kokune, njengoba izinto ezinhlanu • Chaza bese uhlela • Chaza bese uhlela: eziqoqiwe ziningi ngeyodwa kunezine noma iqoqo lezinto ezine lincane ngeyodwa izinombolo kusukela kwezinhlanu. - Izinombolo eziqala kwencane kakhulu kwezincane kakhulu Ukuhlela nokuqhathanisa izinombolo kuye kufike kokukhulu kuya kwezinkulu kakhulu kanye Uma abafundi behlela izinombolo, bangasebenzisa ukulandelana kwezinombolo kakhulu nakwezinkulu nokukhulu kakhulu kuya ukubona ukuthi iyiphi inombolo enkulu. Isibonelo, bangathi oku 5 kukhulu kuno 2 kakhulu kuya kokuncane kakhulu ngoba oku 5 kuza emva koku 2. Abafundi badinga ukubona ukuxhumana ekubaleni kwezincane kakhulu izinto bese beqhathanisa iqoqo lezinto eziyisishiyagalolunye nalelo elinezinto ezimbili. - Usebenzisa ulumi isib. EBangeni lesi 2 nele 3abafundi bazohlela baqhathanise izinombolo ngokuthi bachaze 115 Ngaphambi, emumva, ubungako bezinombolo. Abafundi bangahlela basebenzisa izithombe ezahlukene. maphakathi nendawo/ Izibalo IBANGA 1-3 phakathi naphakathi

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO KWI AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 116 NGOKUPHELA 1 ihora nemizuzu THEMU 1 KONYAKA engu -24) 1.4 Chaza, uqhathanise, bese Chaza, uqhathanise, bese Abafundi futhi bangahlela izinombolo ngokusebenzisa umugqa wezinombolo. uhlela izinto kufinyelela uhlela izinto kufinyelele e 5 Chaza, isibonelo: e- 20 qhathanisa • Chaza bese uqhathanisa • Thatha inombolo 3 uyibeke emgqeni wezinombolo bese uhlela • Chaza bese uqhathanisa amaqoqo ezinto ngoku: izinombolo iqoqo lezinto ngoku: ningi, kuncane, okuningi • Khetha inombolo eza emumva kuka 4 uyibeke endaweni yayo efanele emugqeni ningi, okumbalwa, kakhulu, okuncane wezinombolo Izibalo IBANGA 1-3 okufanayo kakhulu, kulingana, • Khetha inombolo ephakathi kuka 3 no 5 uyibeke endaweni yayo efanele emugqeni kuningi ngango, akufani. wezinombolo • Khetha inombolo eza ngaphambi kuka 2 uyibeke endaweni yayo efanele emugqeni • Chaza bese uhlela • Chaza bese uhlela wezinombolo iqoqo lezinto iqoqo lezinto kusukela kokuningi kusukela kokuningi • Khetha inombolo eza ngaphambi kuka 3 uyibeke endaweni yayo efanele emugqeni kuya kokumbalwa kuya kokumbalwa wezinombolo nokumbalwa kuya nokumbalwa kuya Amakhadi ezinombolo kokuningi kokuningi Isibonelo: Abafundi bangabeka amakhadi ngokulandelana. • Uhla lwezinto ezifinyelela esihlanwini. 1 2 3 4 5 Chaza, uqhathanise, Chaza, uqhathanise bese uhlela izinombolo bese uhlela izinombolo kufinyelela e 20. kufinyelela e- 5. Ukudlulela emsebenzini obhaliwe • Chaza bese uqhathanisa • Chaza bese Abafundi bangaphetha ulwazi lwabo ngokuqedela umsebenzi ezincwadini zabo izinombolo eziphelele uqhathanisa izinimbolo zokusebenzela. Loku kungenziwa ngesikhathi somsebenzi wokuzimela. ngokuthi encane kuno. eziphelele kufinyelela enkulu kune, okuningi e- 5 usebenzisa ulimi. Izinombolo ezejwayelekile nezinombolo ezisho isikhundla (cardinality and kuno,okumbalwa Isib. okuncane kuna, ordinality) kuno,kulingana ne okukhulu kuna, okuningi kuna, okumbalwa kuna Izinombolo ezejwayelekile zisho inani lezinto eqoqweni. Izinombolo ezisho isikhundla sento eqoqweni. Ukuxhumana phakathi kwezinombolo ezejwayelekile kanye nezisho • Chaza bese uhlela • Chaza bese uhlela: isikhundla kufanele kwakhiwe. Abafundi bazokubona lapho bebala iqoqo lezinto izinombolo kusukela bese bazi ukuthi uma bethinta into yesihlanu bazobe sebebale izinto eziyisihlanu. - Izinombolo eziqala Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kwencane kakhulu Izinombolo ezisho isikhundla zizokwenziwa kuphela ngethemu yesi 4. kwezincane kakhulu kuye kufike kokukhulu kuya kwezinkulu kakhulu kanye kakhulu nakwezinkulu nokukhulu kakhulu kuya kakhulu kuya kokuncane kakhulu kwezincane kakhulu - Usebenzisa ulumi isib. Ngaphambi, emumva, maphakathi nendawo/ phakathi naphakathi

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) UKUXAZULULA IZI NKINGA EZISESIMWENI ESIJWAYELEKILE 1.6 Sebenzisa amasu Sebenzisa amasu Kulethemu abafundi bazoqala ukuxazulula izinkinga zamagama besebenzisa alandelayo uma alandelayo uma lamasu alandelayo: Amasu uxazulula izinkinga bese uxazulula izinkinga bese okuxazulula uchaza izixazululo: uchaza izixazululo: • Izinto eziphathekayo izinkinga • Izinto eziphhathekayo • Izinto eziphhathekayo • imidwebo isib. Izinto zokubala isib. Izinto zokubala • imigqa yezinombolo • Izithombe zokwakha • Izithombe zokwakha Imidwebo nezinsiza kufundisa eziphathekayo izibalo zengxoxo izibalo zengxoxo Abafundi bazodweba izithombe besebenzisa izinto eziphathekayo ukuxazulula • Ukwakha nokuhlakaza • Imigqa yezinombolo izinkinga. Ngasekupheleni kwethemu abafundi bangadweba izithombe izinombolo ilekelelwa izinto ezinezinombolo ukuchaza ukusebenza nezixazululo. Kubalukekile ukuthi eziphathekayo isb. izithombe noma imidwebo ibe nezinombolo ukuchaza ukusebenza nezixazululo • Ukuphinda kabili Ubuhlalu bokubala nge: nokuhlukanisa kabili ngokulingayo • ngezinto ezikhombisa igabelo elimele into eyodwa • Imigqa yezinombolo • izinombolo Imigqa yezinombolo Ukusebenzisa imigqa yezinombolo kuzobasiza ukubala nokubhala imicabango yabo ukulandelela kulokho abasukele kukho. Kuphinde kuvumele abafundi ukuthi babhale izithombe abangazisebenzisa ukuchaza ukuthi bazixazulule kanjani izinkinga. Kulethemu abafundi bazothulelwa umugqa wezinombolo baqale nokusebenzisa loku uma besebenzisa amaqhinga okubala. Uma uqala ukusebenzisa umugqa wezinombolo ubuhlalu obusentanjeni bungabekwa ngenhla noma ngezanzi ukulekelela abafundi ekubaleni. Ngaphambi kokuba abafundi basebenzise umugqa wezinombolo njengeqhinga lokubala kufanele bayisebenzisele: • ukubala uya phambili nasemuva • ukufunda izimpawu zezinombolo • ukubhala izimpawu zezinombolo • ukubeka izinombolo esikhundleni esifanele emugqeni wezinombolo • ukuhlela nokuqhathanisa izinombolo Uma usebenzisa umugqa wezinombolo njengesithombe sokubala, ulwazi loku ‘gxuma’ lungafundwa ngokusebenzisa iminwe noma ngokwakha umugqa 117 ngaphandle noma ukugxuma usuka kwenye inombolo uya kwenye. Lezizinhlobo zemisebenzi zisiza abafundi ukubona ukuthi zikuphi izinombolo kwezinye. Kufanele bakwazi ukuthi: ukusuka koku 3 kuya 5 kulingana nokugxuma ka 2”. Izibalo IBANGA 1-3 Abafundi kufanele banikezwe amathuba okuqagela ukuthi kugxunywe kangaki, kusuka ku 2 kuya 5.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 118 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 1.6 Sebenzisa amasu Sebenzisa amasu Isibonelo sokuthi abafundi bangawusebenzisa kanjani umugqa wezinombolo alandelayo uma alandelayo uma kulethemu: Amasu uxazulula izinkinga bese uxazulula izinkinga bese okuxazulula uchaza izixazululo: uchaza izixazululo: Kunabafana abathathu namantombazane amabili abenza izifundo izinkinga zobuchwepheshe ezengeziwe esikoleni. Bangaki abafundi abenza isifundo • Izinto eziphhathekayo • Izinto eziphhathekayo sobuchwepheshe? isib. Izinto zokubala isib. Izinto zokubala Izibalo IBANGA 1-3 Abafundandi bangasebenzisa umugqa wezinombolo ngalendlela ukufinyelela • Izithombe zokwakha • Izithombe zokwakha empendulweni. izibalo zengxoxo izibalo zengxoxo   • Ukwakha nokuhlakaza • Imigqa yezinombolo izinombolo ilekelelwa izinto eziphathekayo isb. • Ukuphinda kabili 0 1 2 3 4 5 6 7 8 9 Ubuhlalu bokubala nokuhlukanisa kabili ngokulingayo Bheka amanothi engezansi ‘izindlela zokwenza noma amaqhinga’ ukwethula • Imigqa yezinombolo umugqa wezinombolo. Khumbula ukuthi abafundi bangaxazulula izinkinga ngendlela engalindelwe uthisha. Isibonelo, ukuxazulula inkinga engenhla, abafundi bangakhetha ukuqala ukubala ngenombolo yamantombazana, 2, bese befaka ama 3. Indlela esetshenziseswa abafundi ingashintsha uma kuqhubeka unyaka njengoba bejwayela abafundi ukuxazulula izinhlobo zezinkinga, nolwazi lwabo lwezinombolo luthuthuka. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 1.7 Xazulula izikinga Xazulula ngokwenza Izibalo zamagama zijwayele ukusetshenziswa njengendlela yokuqala zezibalo zamagama izinkinga zezibalo yokusebenzisa izimpawu zezibalo. Abafundi baqala ngokusebenzisa izinto Ukuhlanganisa nokususa ezimweni ezijwayelekile zamagama ezimweni eziphathekayo ukuxazulula izinkinga; okube sekuthuthukisa: bese uchaza izixazululo ezijwayelekile bese • Ukudweba izithombe; ngokusebenzisa uchaza izixazululo ukuhlanganisa nokususa zezinkinga ezifaka • Ukudweba izithombe nokubhala izinombolo ukuchaza izimpawu ezisebenzile; okunezixazululo ukuhlanganisa nokususa noku ezifinyelela kuma - 20. nezixazululo ezifika • sebenzisa izinombolo kuphela. kokuyisihlanu. Isibonelo: Kunabantwana abahlanu kuginqi-gonqo. Abathathu babo basohlangothini olulodwa. Bangaki abakolunye uhlangothi? Ngethemu yokuqala abafundi bengabhala izinkinga zamagama ngalendlela. Amaqhinga okubala Usebenzisa ukubala ukuxazulula inkinga kaginqi-gonqo 1, 2, 3 kuloluhlangothi ku 2 kuloluhlangothi Lapha abafundi babala iqoqo ngalinye kanye neqembu lonke seliphelele, ngakho- ke babala okungenani kathathu. Ukusebenzisa ukubala ukuxazulula inkinga kaginqi-gonqo. Abafundi babala baqhubeke ukusukela kokuthathu baze bafike kokuhlanu. Leli iqhinga elisebenza kahle. “ngiyazi ukuthi kunezingane ezintathu uma kungena enye kwenza ezine, kuphinde kungene enye kwenze ezinhlanu. Zimbili izingane ezikolunye uhlangothi”. Ukusebenzisa ukuhlanganisa nokususa kusetshenziswa izinsizakufunda 119 eziphathekayo Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 120 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 1.7 Xazulula izikinga Xazulula ngokwenza Abafundi basebenzisa izinto eziphathekayo ngezindlela ezithile ukuthola zezibalo zamagama izinkinga zezibalo impendulo. Abafundi basebenzisa izinto eziphathekayo ukwakha umqondo Ukuhlanganisa nokususa ezimweni ezijwayelekile zamagama ezimweni wokuhlanganisa nokususa besebenzisa izinto abangazithinta, bazibambe futhi bese uchaza izixazululo ezijwayelekile bese bezinyakazisa. Indlela abafundi abasebenzisa ngayo izinto eziphathekayo ngokusebenzisa uchaza izixazululo ilawulwa ingxoxo yesibalo. ukuhlanganisa nokususa zezinkinga ezifaka Ukubhala izithombe zokuhlanganisa nokususa Izibalo IBANGA 1-3 okunezixazululo ukuhlanganisa nokususa ezifinyelela kuma - 20. nezixazululo ezifika • Ukubhala besebenzisa izinto eziphathekayo kokuyisihlanu. Abafundi bangasebenzisa izinto eziphathekayo ukubala konke noma bebala beqhubeka. Yize abafundi bengakwazi ukusebenzisa lamaqhinga ngokudweba izithombe ukuveza imicabango yabo, kanye namaqhinga okubala nezixazilulo. • Ukubhala kusetshenziswa izithombe kuphela Isibonelo   Ukubhala kusetshenziswa izithombe nezinombolo Ukuze abafundi basebenzise izithombe nezinombolo ukuveza imicabango yabo badinga uku: • Ukwazi ukubona izinombolo 1-5 • Ukubala izinto ezinhlanu bese bekwazi ukubona ukuthi oku 5 kumele izinto ezibalwe zanhlanu. • Ukubhala izinombolo • Ukuhlela nokuqhathanisa izinombolo Kunezingane ezinhlanu ezigibele uginqi-gonqo. Abathathu bagibele ohlangothini elilodwa. Bangaki abagibele kolunye uhlangothi lukagiqi-gonqo? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Izinhlobo zezinkinga zokuhlanganisa nokususa Kunezinhlobo okungenani ezintathu eziyisisekelo sezinkinga zokuhlanganisa nokususa, ngayinye ingathulwa ngezindlela ezahlukene. Izinhlobo eziyisisekelo yilezi: Ushintsho UNoluthando ubenama apula amabili. USilo wamnika amanye amathathu. Mangaki ama apula asenawo esephelele?

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 1.7 Xazulula izikinga Xazulula ngokwenza UNoluthando ubenama apula amahlanu. Ube esenikeza uSilo amane. Mangaki zezibalo zamagama izinkinga zezibalo ama apula asenawo esephelele? Ukuhlanganisa nokususa ezimweni ezijwayelekile zamagama ezimweni Ukuhlanganisa bese uchaza izixazululo ezijwayelekile bese ngokusebenzisa uchaza izixazululo UNolwazi unamamabula amabili aluhlaza okotshani namabili aluhlaza ukuhlanganisa nokususa zezinkinga ezifaka okwesibhakabhaka. Mangaki amamabula asenawo esephelele? okunezixazululo ukuhlanganisa nokususa UNolwazi unamamabula amane. Amathathu aluhlaza okotshani amanye aluhlaza ezifinyelela kuma - 20. nezixazululo ezifika okwesibhakabhaka. Mangaki amamabula aluhlaza okotshani anawo esephelele? kokuyisihlanu. Ukuqhathanisa UNoma unamaswidi amahlanu. UThemba unoswidi owodwa. Manngaki amaswidi uNoma anawo owedlula okaThemba? Izinsiza kufunda: Abafundi bengasebenzisa izinto zokubala ezihamba ngazodwana, ukuze zibasize ukubona ukuthi kwenzekani uma bebeka inani elithile ndawonye, noma bezihlukanisa. Izinto zokubala ezihamba ngazodwana zibasiza ukuthi babone ukuthi kwenzekani uma bezibala zonke. • Izibonelo zezinto zokubala ezahlukene kungaba: • Izinto zokubala • Izinti zokubala • Izivalo zamabhodlela • Izinhlamvu zamapetshisi • Amatshe • Amabhulokisi axhumanayo • Ukusebenza ngohla lwezinombolo1 kuya 5, abafundi bangasebenzisa iminwe yabo njengezinto zokubala ezihamba ngazodwana. 121 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 122 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 1.9 Xazulula bese uchaza Xazulula bese uchaza EBangeni 1ulwazi lokuhlukanisa lwethulwa ngokunika abafundi izinkinga izixazululo zezinkinga izixazululo zezinkinga eziphathekayo ezifaka ukuhlukaniselana nokwenza amaqoqo. KuseBangeni lesi Ukwakha amaqoqo eziphathekayo ezifaka eziphathekayo ezifaka nokuhlukaniselana -3 lapho uphawu lokuhlukanisa lwethulwa khona. ukuhlukaniselana ukuhlukaniselana okuholela ngokulingana ngokulingana Ngezansi izibonelo zezinhlobo zezinkinga zamagama ezingenziwa ekuhlukaniseni nokuhlukanisa nokuhlukanisa Ukwakha amaqoqo ngamaqoqo izinombolo ngamaqoqo izinombolo Izibalo IBANGA 1-3 eziphelele ezifinyelela eziphelele ezifinyelela Ukwakha amaqoqo, kulahlwa izinsalela kuma - 20 nezimpendulo e 5 nezimpendulo ezingaba nezinsalela. ezingaba nezinsalela. USiza udayisa amapentshisi asephaketheni elinapentshisi amabili ngalinye. Usalelwe amapentshisi amahlanu. Zingakai izikhwama zamapentshisi amabili isikhwama ngasinye ezingenziwa? Ukwakha amaqoqo, ufaka izinsalela ezimpendulweni Kunamapulamusi amane.Zingaki izikhwama ezinamapulamusi amabili ngasinye ezingenziwa? Ukuhlukaniselana Ukuhlukaniselana, kulahlwe insalela Hlukanisa amaswidi amahlanu kubangani abathathu bonke bathole ngokulingana. Ukubhala ngemifanekiso ukwakha amaqoqo nokuhlukaniselana Uma kukhonjiswa izinkinga zokuhlukaniselana zezibalo zamagama, abafundi “bazohlukaniselana’” into eyodwa ngesikhathi. Abafundi bebanga 1 bangakwazi ukuhlukaniselana into eyodwa ngesikhathi lokhu Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kuzokhonjiswa emidwebeni yabo. Ngokuqhubeka konyaka abafundi bazokwazi ukubhala besebenzisa izithombe nezinombolo ukukhombisa inombolo ehlukaniswayo.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) UKUBALA ESIMWENI ESIKHULULEKILE Ziningi izindlela zokucabanga ngokulungiselela ukufundisa nokufunda ukubala. Enye indlela ukucabanga ngohla lwezinombolo ozosebenza ngalo. Uhla lwezinombolo osebenzela ngalo luzosho izinhlobo zezinsiza kufunda ezizosetshenziswa nokuthi zizobhalwa kanjani izixazululo. Ngakhoke enye indlela yokucabanga ngokubala emabangeni aphansi indlela okukhonjiswe ngayo ukubala. Loku kwenziwa ngoku: • Ukusebenzisa izinto eziphathekayo; • Ukudweba izithombe; • Ukusebenzisa izithombe nezimpawu; • Ukusebenzisa izinombolo nezinkomba; noma • Izibalo eziyimisho. Abafundi basuka ekusebenziseni izinto eziphathekayo baye ekusebenzeni ngengqondo uma besebenza ngezimpawu zezinombolo nezibalo zemisho. Ukubala kungena ngaphansi kwezimo zokuxazulula izinkinga.Abafundi bathuthukisa amakhono okuxazulula izinkinga ukuze bakwazi ukusebenza ngezinombolo. Abafundi kudinga babale esimweni esikhululekile. 1.12 Sebenzisa lamasu Sebenzisa lamasu Ngethemu yokuqala abafundi bazoxazulula izinkinga besebenzisa izinto alandelayo uma alandelayo uma eziphathekayo.kubalulekile ukuthi abafundi basebenzise izinsiza kufunda Amasu (izindlela kwenziwa izibalo: uxazulula izinkinga ezahlukene ezikhethwe ngokucopheIela ukulekelela ukuthuthukisa ulwazi noma amaqhinga) nalapho uchaza • Izinto eziphathekayo olufundiswayo. izixazululo zezinkinga: isib. Izinto zokubala Njengoba abafundi bekhula ekuzethembeni ukusebenzisa izinsiza kufunda, • Izinto eziphathekayo ukukhombisa imicabango yabo bangabhala ukubala kwabo besebenzisa • Ukudweba izithombe isib. Izinto zokubala imidwebo.lindela ukuthi imidwebo yabo ikhombise izinsiza kufundisa • Ukwakha nokuhlakaza • Izithombe zokudweba eziphathekayo. Kungabakhona abanye abafundi abangavele bakhombise izinombolo izibalo zengxoxo ukubala kwabo ngokudweba bengasebenzisi zinto eziphathekayo. • Ukuphinda kabili • Imigqa yezinombolo Imigqa yezinombolo elekelelwa izinto eziphathekayo nokuhlukanisa kabili ehambisana nezinto ngokulinganayo Uma kusetshenziswa imigqa yezinombolo njengesu lokubala abafundi kufanele eziphathekayo isib. ukuba baqale basebenzise: • Imigqa yezinombolo Ubuhlalu bokubala • Ezinye izinsiza kufundisa zomugqa (‘line apparatus’) isib. ubuhlalu bokubala; • Umugqa wezinombolo ukubala uya phambili noma uya emumva; kanye • Umugqa wezinombolo ukuze kunikwe izikhundla bese kuhlelwa izinombolo. Umugqa wezinombolo ohlelekile ungasetshenziswa (kanti ulungele kakhulu) uma abafundi benza ukuhlanganisa nokususa. Umugqa wezinombolo ohleliwe kufanele ukhombise zonke izinombolo ezikuwo. 123 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 124 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 1.12 • Thula ukuhlanganisa usebenzisa umugqa wezinombolo Amasu (izindlela a) Uthisha ubeka umugqa wezinombolo ebhodini oqala ku 0 kuya 10. noma amaqhinga) Ukhombisa abafundi ukuthi ixazululwa kanjani inkinga 3 + 2 esebenzisa umugqa wezinombolo. Ubeka isithombe sikanogwaja ku 0. Isibonelo: unogwaja ugxuma usuka ku 0 kuya 5 bese ebuya egxuma kabili. Ugxume kangaki sekukonke? Izibalo IBANGA 1-3 b) Abafundi bazosebenzisa iminwe yabo ukugxuma emugqeni wabo wezinombolo osemadeskini abo, njengoba uthisha ebanikeza imisho yezinombolo enezimpendulo ezifinyelela e 10, Isibonelo: 1 + 2 =3. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 1.13 Uhla lwezinombolo: 1 -20 Uhla lwezinombolo: 1 -5 Ngethemu 1 abafundi bazi ukuhlanganisa njengokuhlanganisa amaqoqo nanjengokubala uqhubeka. Basebenzisa ulwazi lwabo lokuthi ukuhlanganisa Ukuhlanganisa • Hlanganisa ukuya 20 • Hlanganisa kufinyelele kungenziwa noma ngayiphi indlela ukukhetha ukuthi ubala kanjani. Basebenzisa nokususa ku 5 • Ukususa ku 20 ubuhlalu obusentanjeni, ukudweba izithombe noma umugqa wezinombolo • Susa ku 5 ukwenza izibalo njenge 3 + 2 noma 1 + 4 ngokubala uqhubeka. Bangahlakaza • Sebenzisa izmpawu izinombolo ukuze bahlanganise. ezifanele (+, –, =, ) • Sebenzisa amabhondi ukuya 5 Ngethemu 1 abafundi bahumusha ukususa njengoku’khipha’. Basebenzisa • Sebenzisa amabhondi ukubonakalisa “ukususa” ngokusebenzisa izinto eziphathekayo noma ukudweba ezinombolo ukuya ku izithombe kanye nezibalo eziyimisho. Bakhumbula ukuthi inombolo yezinto 10 ezisalile iyimpendulo esibalweni. Bangabhala ukuhlanganisa nokususa besebenzisa: • Izinto eziphathekayo; • Izithombe noma nemidwebo; noma • Izithombe nezinombolo. Ukusebenza ngohla lwezinombolo 1 - 5 Uma abafundi besebenza noma bebala kuloluhla lwezinombolo bangakha ulwazi lokuhlanganisa nelokususa ngalendlela: • Ukusebenzisa izinto eziphathekayo ukumela inombolo nokubala • Ukubhala okubalwayo kusetshenziswa izithombe nemifanekiso • Ukubhala okubalwayo ngokusebenzisa inhlanganisela yezithombe nezinom- bolo Ukwakha nokuhlakaza izinombolo Ukuhlanganisa nokususa eBangeni 1 kugxile ekutheni abafundi abacabange ngezinombolo ngokuthi zakhiwe ezinye izinombolo. Isikhathi esiningi abafundi benza ingxenye-nengxenye yemisebenzi ephelele. lemisebenzi igxile enombolweni ehamba ngayodwa. Isibonelo, uma usebenza ngenombolo 4 abafundi bazo: 125 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 126 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 1.13 Uhla lwezinombolo: 1 -20 Uhla lwezinombolo: 1 -5 • Hlakaza oku 4 ngezindlela ezahlukene; Ukuhlanganisa • Hlanganisa ukuya 20 • Hlanganisa kufinyelele • bazosho noma bafunde izingxenye kuzwakale; noma nokususa ku 5 • Ukususa ku 20 • badwebe noma babhale phansi. • Susa ku 5 • Sebenzisa izmpawu   ezifanele (+, –, =, ) • Sebenzisa amabhondi 1 Izibalo IBANGA 1-3 ukuya 5 • Sebenzisa amabhondi 4 ezinombolo ukuya ku 10 3 Abafundi bangasebenzisa namakhadi ezinombolo ukukhombisa izingxenye zezinombolo. Ukukhombisa oku 4, amanye alamakhadi alandelayo angasetshenziswa:   1 3 2 2 Lolu lwazi lungalekelelwa ngokubhala ezincwadini zokusebenzela ngesikhathi sokusebenza ngokuzimela.   4 1 3 Uma kwenziwa ukususa abafundi bajwayele ukwenziswa izibalo sengxoxo ukuthuthukisa ukuqonda ukususa njengokuthi ‘khipha’ noma ‘ukubala ukhipha’. Abafundi badinga ukwenza nemisebenzi yokulahlekile. Lemisebenzi ilekelela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ukuqonda ukususa futhi kufuna enye ingxenye ifihlakale noma ingazeki. Isibonelo:   Ngina ngifisa ukuba bengino- 5

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 1.13 Uhla lwezinombolo: 1 -20 Uhla lwezinombolo: 1 -5 Uphawu alwethulwa kulethemu. Abafundi kufanele bakhonjiswe ngezindlela eziningi ukubhalwa kwemisho okuzosiza abafundi uma sekuthulwa uphawu Ukuhlanganisa • Hlanganisa ukuya 20 • Hlanganisa kufinyelele ngethemu 2. nokususa ku 5 • Ukususa ku 20 • Susa ku 5   Isibonelo  1   Isibonelo  2   • Sebenzisa izmpawu ezifanele (+, –, =, ) • Sebenzisa amabhondi ukuya 5 • Sebenzisa amabhondi ezinombolo ukuya ku 10  no   kwenza     3    no   kwenza   2   Amabhondi ezinombolo Ngalethemu abafundi bazokwenza baphindelele amabhondi ezinombolo kuya ku 5. Lokhu kungavezwa ngezithombe nangemisho yezinombolo kusetshenziswa imifanekiso ehlukene. Ukuhlanganisa Isibonelo: Ukwakha oku 5 noma uthole abangani aba 5 kusetshenziswa izithombe nezinombolo Faka imibala ezikweleni ukwakha oku 5 Isibonelo: ________ no __________ kwenza 5 ________ no __________ kwenza 5 ________ no __________ kwenza 5 ________ no __________ kwenza 5 127 Ulimi lokuhlanganisa nokususa Abafundi kufanele basebenzise ulimi lokuhlanganisa nokususa. Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 128 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 1.13 Uhla lwezinombolo: 1 -20 Uhla lwezinombolo: 1 -5 Ukuhlanganisa: Ukuhlanganisa • Hlanganisa ukuya 20 • Hlanganisa kufinyelele Hlanganisa bese wandise, konke ndawonye, akha,isamba nokususa ku 5 • Ukususa ku 20 Ukususa: • Susa ku 5 • Sebenzisa izmpawu Susa,khipha, umehluko, okuphakathi koku, okungaphansi, okunciphisiwe ngoku ezifanele (+, –, =, ) • Sebenzisa amabhondi Izibalo IBANGA 1-3 EThemu 2 abafundi bazohumusha ngokusebenzisa ulimi lokuhlanganisa ukuya 5 • Sebenzisa amabhondi nokususa ngezimpawu. ezinombolo ukuya ku Abafundi bazokwazi ukwenza belandela imiyalelo ehlukene elandelayo: 10 • Akha okungaphezulu ngoku 3 • Yengeza oku 1 ngaphezulu • Susa oku 3 • Nciphisa ngoku 1 • 3 no 2 ngaphezulu • 4 ususe oku 2 • 3 yengeza 1 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 1.16 Ulwazi lwezinombolo: Ulwazi lwezinombolo: Isikhathi sezibalo zekhanda zithuthukisa abafundi: uhla kuya ku 20 uhla kuya koku 5 Izibalo zekhanda • Olwazini lwezinombolo; • Hlela iqoqo elinikiwe • Hlela iqoqo elinikiwe • Olimini lwezibalo; lezinombolo lezinombolo ezikhethiwe ezikhethiwe. • Kumakhono okucabanga; kanye • Qhathanisa izinombolo • Qhathanisa izinombolo • nakumakhono okulalela. kufinyelele e 100 kufinyelele e 10 Ngesikhathi sezibalo zekhanda abafundi kufanele banikezwe amathuba bese besho ukuthi bese besho ukuthi okuchaza izindlela abazisebenzisile. Isikhathi sezibalo zekhanda sakha ukwazi ikuphi okuningi noma ikuphi okuningi noma kangcono ngezinombolo (ukuba ‘nomuzwa’lwezinombolo) kuqale nokufundisa okumbalwa okumbalwa abafundi ukuthi kusetshenzwa kanjani ngokukhululekile ngezinombolo. Inombolo • Ukwazi ukuthi iyiphi • Ukwazi ukuthi iyiphi 5 akuyona nje kuphela inombolo. inombolo enkulu ngoku inombolo enkulu ngoku isibonelo, inombolo 5, abafundi mabazi lokhu: 1 noma encane ngoku 1 noma encane ngoku 1 1 • iza ngemumva kuka 4; • Ukwazi ukuthi iyiphi • Ukwazi ukuthi iyiphi • iza phambi kuka 6; inombolo enkulu inombolo enkulu ngoku 2 noma encane ngoku 2 noma encane • ingahambisana nezinto ezi 5; ngoku 2 kunenombolo ngoku 2 kunenombolo • bangabhala uphawu; kanye enikeziwe. enikeziwe. • negama lenombolo. • Ukwazi ukuthi iyiphi inombolo enkulu nge Ulwazi lwenombolo 10 noma encane nge Izibonelo zemibuzo nemisebenzi engebuzwa noma engenziwa: 10 kwenikeziwe • abafundi bama umugqa bese ubuza: ubani owokuqala, owesibili, owesithathu Ukukhumbula noma owokugcina? ngokushesha: • Ikuphi okungaphansi,oku 3 noma 5? • Amabhondi ezinombolo kufike e-10 • Ikuphi okuningi, oku 2 noma 4? • Ukukhumbula • Nginike inombolo ephakathi koku 1 noku 3, ukuhlanganisa • Nginike inombolo ephakathi koku 2 noku 5. Kunenombolo eyodwa kuphela? nokususa kufike e-10 • Beka lamakhadi ezinombolo ngokuhlelekile kusuka kwencane kakhulu ukuya Amaqhinga okubala kwenkulu kakhulu. ngekhanda Imibuzo yokubala ingabuzwa: Sebenzisa amaqhinga 129 okuhlanganisa nokususa • Qala ngoku 3 bese ubala uye phambili ngokukodwa kuya e 10. ngokufanele: Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 130 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) • Beka inombolo enkulu kuqala ukuze ubale uqhubeka noma uya emumva • Umugqa wezinombolo Izibalo IBANGA 1-3 • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo • Ukwakha nokuhlakaza inombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YOKU- 1 YEBANGA LOKU-1 2. AMAPHETHINI, IMISEBEZI NE ALJEBHRA ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 2.1 Kopisha,wandise bese Kopisha,bese wandisa Ukukopisha iphethini kusiza abafundi ukuthi babone ukuthi iphethini yakhiwe uchaza kanjani. Amaphethini Kopisha bese wandisa asazibalo- Kopisha,wandise bese amaphethini alula Ukwandisa iphethini kusiza abafundi ukuthi baqonde kahle ukuthi iphethini mdwebo uchaza ngamagama usebenzisa: lakhiwe kanjani. • Amaphethini alula • izinto eziphathekayo Abafundi bangakopisha bese bandisa amaphethini enziwe ngezinto enziwe ngezinto eziphathekayo nangaphambi kokuthi bakhululeke ukusebenzisa amakhilayoni • imidwebo (isib. eziphathekayo noma ipensela ukuqala ukukopisha nokwandisa amaphethini ngokudweba. usebenzisa imibala • Amaphethini alula nezimo) Amaphethini angenziwa ngezinto zansuku zonke ezikhona ekilasini, njengezinto enziwe ngemigqa zokubala, umentshisi, amabhokisi amentshisi, izimo ezisejiyometri, ubuhlal yemidwebo, u,amabhokisi,amabhola,amakhirayoni,amapensela njll. Abafundi bengenza izimo noma izinto izinto ngobumba noma badlale ngenhlama futhi loku kungasebenza ukwenza eziphathekayo amaphethini. Akha awakho EBangeni loku -1 abafundi bangagxila kumaphethini lapho izimo noma izinto amaphethini eziphathekayo (noma amaqoqo ezimo noma ezinto eziphathekayo) ziphindwe ngendlela efana ngqo. Akha awakho amaphethini asejiyometri Isibonelo 1: • Ngezinto Kwamanye amaphethini ubungako bezinto eqoqweni kuyashintshana, kodwa eziphathekayo amaqoqo aphinda ngendlela efana ngqo • Ngokudweba   imigqa,izimo noma izinto eziphathekayo Isibonelo 2: Amaphethini Amaphethini angakhiwa ngokusebenzisa into oyodwa kodwa imibala yayo asizungezile ishintshane ngendlela ethile. Khomba,chaza   ngamagama bese ukopisha amaphethini asejiyometri Isibonelo 3: • ngokwemvelo Kwamanye amaphethini izinto ezahlukene ziyasetshenziswa ukwakha iqoqo, • empilweni yesimanje kodwa amaqoqo ezinto aphindwa ngendlela efana ngqo 131 • emasikweni namagugu   Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 132 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 2.1 Kopisha,wandise bese Kopisha,bese wandisa Ukusiza abafundi bebanga 1 ukubona ukuthi iliphi iqoqo eliphindwayo, Isifundo - 1 uchaza kuyasebenza ukubeka iqoqo ephepheni elehlukile kwelinye noma ukhombise Amaphethini Kopisha bese wandisa iqoqo ebhokisini ngalinye. asazibalo- Kopisha,wandise bese amaphethini alula mdwebo uchaza ngamagama usebenzisa: Isibonelo 4: • Amaphethini alula • izinto eziphathekayo Amaphethini angenziwa ngokuphinda amaqoqo ezinto. Amaqoqo angenziwa Izibalo IBANGA 1-3 enziwe ngezinto izinto eziningi ezifanayo ezibekwe ngezindlela ezahlukene. • imidwebo (isib. eziphathekayo usebenzisa imibala • Amaphethini alula nezimo) enziwe ngemigqa yemidwebo, izimo noma izinto eziphathekayo Amaphethini ayingxenye ebalulekile emfundo yokuqala, ngakho ke enzeka Akha awakho esifundweni soLimi, Amakhono Empilo neziBalo. amaphethini Isibonelo, amaphethini ayingxenye yamaculo nomculo, imilolozelo, ukudansa Akha awakho njengenye indlela yesifundo sobuciko obubonakalayo. Kunamathuba kubafundi amaphethini asejiyometri ukwenza amaphethini abonakalayo namakhono okusebenzisa izibalo uma • Ngezinto befunda isifundo samakhono Empilo ikakhulu ekutshutsheni ubuhlalu noma eziphathekayo ukudweba amaphethini. • Ngokudweba imigqa,izimo noma izinto eziphathekayo Amaphethini asizungezile Khomba,chaza ngamagama bese ukopisha amaphethini asejiyometri • ngokwemvelo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • empilweni yesimanje • emasikweni namagugu

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 2.2 Kopisha,andisa bese Kopisha,andisa bese Emabangeni aphansi, amaphethini ezinombolo athuthukisa ulwazi lwezinombolo Izifundo ezi 3 uchaza uchaza kubafundi. Amaphethini ezinombolo axhumene nezinombolo, izimpawu Amaphethini nobudlelwano bazo. ezinombolo Kopisha,wandise bese Kopisha,wandise bese uchaza ukulandela uchaza ukulandela Ukulandelana kwezinombolo kungaxhumana nokubala. Ukulandelanisa kahle okulula kwezinombolo okulula kwezinombolo izinombolo kuthuthukisa futhi kuhlanganise amakhono okubala kwabafundi. kufinyelele okungenani kufinyelele okungenani Njengoba amakhono okubala abafundi eshintsha futhi ethuthuka kanjalo e-100 e-20 nokulandelana kwezinombolo. Akha awakho Ukulandelana Uma abafundi bebala bekhuluma bangakhonjiswa ukulandelana kwezinombolo amaphethini makukhombise ukubala kubhalwe phansi ngezindlela ezahlukene isib. uya phambili nokuya Akha awakho emumva ku: amaphethini ezinombolo · ngakunye kusuka kunoma iyiphi inombolo ephakathi koku 1 noku 20 Abafundi bangagcwalisa izinombolo ezingekho ezinikeziwe kunoma iyiphi indlela kulezi ezinikwe ngenhla. Khumbula, ukuthi abafundi babhala izinombolo kufinyelela ku 5. Abafundi bangafaka izinombolo ezisele ngokuphimisela bese besebenzisa amakhadi ezinombolo ukuqedela ukulandelana kwazo. Bheka amanothi okuchaza, uqhathanise, uhlele. Isibonelo 1: igridi yezinombolo Isibonelo 2: ukulandelana kwezinombolo   1 2 4 5 6 8 Ngasekupheleni kwethemu, uhla lwezinombolo ezibekiwe lufinyelelela ku 20. Abafundi bangasebenza ngokulandelana kwezinombolo kusuka ku 1 - 20 noma izingxenye zokulandelana kwezinombolo. isibonelo 3: umugqa wezinombolo 133 1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 18 20 Izibalo IBANGA 1-3

ITHEMU YOKU- 1 YEBANGA LOKU-1 3. INDAWO NESIMO (IJIYOMETRI) 134 ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 3.1. Ulimi lwesikhundla Ulimi lwesikhundla Ulimi lwesikhundla Izifundo 2 Isikhundla, Chaza isikhundla sento Chaza isikhundla sento Ulimi lwesikhundla kufane luthulwe ngemisebenzi eyenziwayo efaka inkomba eyodwa nokuhlobana eyodwa nokuhlobana ukunyakazisa umzimba kwabafundi njengamaculo nemilolozelo enokunyakazisa Izibalo IBANGA 1-3 nokubukeka nenye isib. Ngaphezulu, nenye isib. Ngaphezulu, imizimba kanye namagama anyakazisayo.Lokhu kungenziwa ngesikhathi kwento ngaphambili, ngaphambili, ufundisa ikilasi lonke.noma uqondanise ngesikhathi sokufundisa amaqembu. ngemuva, kwesokudla, ngemuva, kwesokudla, Kungakuhle uchithe isikhathi sezifundo ezimbili ngemisebenzi yesikhundla kwesokunxele, phezulu, kwesokunxele, phezulu, ngethemu 1,kodwa uqhubeke ukwethula nokwenza uphindelela amagama phansi, eceleni kwe. phansi, eceleni kwe. ezikhundla ngezikhathi ezimfishane zekilasi lonke, amagqembu, nomfundi ngamunye.Ulimi lwesikhundla lungabuye lusetshenziswe nangesikhathi Isikhundla nokubukeka sokufundisa ulimi namaKhono empilo. kwento Kuyasiza ukwethula amagama ahambisanayo ezikhundla ngesikhathi esisodwa Qondanisa ukubukeka isib. Phansi naphezulu, phakathi nangaphandle. ngokwehlukile kwento eyodwa yansukuzonke. Amagama ezikhundla angakusiza kungayilawa: Izikhundla nezinkomba Isikhundla nezinkomba • Kwesokudla/kwesokunxele, • Sebenzisa ulimi • Ngaphambili /ngemuva, lwesikhundla olufudwe • ngemuva kwe/ngaphambi kwe ngenkathi ulandela izinkomba • ngaphezulu/ngaphansi; • Landela izinkomba • Landela izinkomba • phakathi/phandle unyakaze ekilasini. unyakaze ekilasini. • ngaphansi/ngale kwe • Landela imiyalo • Landela imiyalo • ngaphansi /ngaphezu kwe ukubeka into eyo- ukubeka into eyo- dwa ngokuhlobana dwa ngokuhlobana • eduze/kude nenye isb. Beka ipeni nenye isb. Beka ipeni • phakathi kwe phakathi ebhokisini phakathi ebhokisini Ulimi lwesikhundla lungaphethwa ngemisebenzi ebhalwayo njengokudweba, Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ufaka imibala noma baqondanise imidwebo ngamagama.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 3.1 Isikhundla nezinkomba Isikhundla, Abafundi bangaqala ukufunda amagama ezikhundla bese usebenzisa lolulwazi inkomba kanje nokubukeka • Imiyalezo yokunyakaza noma ukubeka izinto ngokuhlobana kwazo isib.beka kwento ikrayoni eduze netafula; beka ikhadi lezinombolo phezu kwesitulo • Izinkomba ezizobenza banyakaze ekilasini.isib. Wozani ngaphambili kwekilasi;yima eduze nesitulo sakho; gxumela ngale komgqomo wezibi njll. Ukufundisa abafundi ukulandela izinkomba kufanela kwenziwe ngemisebenzi yokwenza ezokwenza abafundi banyakaze noma benyakazisa izinto belandela imiyalelo 3.2 Uhla lwezinto Uhla lwezinto Imisebenzi eminingi yezinto ezinhlangothi ntathu eBangeni 1 kumele yenziwe Izifundo 3 ngezinto eziphathekayo.Sifunda umhlaba ngezinto ezinhlangothi ntathu Izinto Bona bese usho izinto Bona bese usho izinto ngokho ke ukuqala ngezinto eziphathekayo kusiza abafundi ukwakha ulwazi ezinhlangothi zonhlangothi ntathu zonhlangothi ntathu abazolusebenzisa esikoleni. ntathu ekilasini nasezithombeni ekilasini nasezithombeni Abafundi abaningi bayehluleka ukuhumusha izinto ezinhlangothi ntathu • Ezisabhola • Ezisabhola esisejiyometri ezisezithombeni.Ukusebenza ngezinto eziphathekayo • Ezisabhokisi (iprizimu) • Ezisabhokisi (iprizimu) kuyabasiza abafundi bakwazi ukuhumusha izithombe zezinto ezisazibalodwebo ngokuhamba kweskhathi.Uma umfundi ebona izinto eziphathekayo angazibuka Izimpawu zezinto Izimpawu zezinto aziphenduphendule ebuka macala onke, bese ekwazi ukusho ukuthi lesosimo Chaza uhlele bese Chaza uhlele bese simi kanjani ngasemumva nangaphansi. uqhathanise izinto uqhathanise izinto Uma unesithombe kuphela kufanele uzakhele emqondweni izingxenye ezinhlangothi ntathu ezinhlangothi ntathu ezingabonakali emdwebeni.Akulula ukubona lokhu kubafundi abansebancane. ngoku: ngoku: uma abafundi benikwe incazelo yento ngaphandle kokuyibona noma ukuyithinta • Ubungako • Ubungako akulula ukwazi izingxenye zento ngokugcwele. • umbala • umbala • izinto eziginqikayo • izinto ezishibilikayo 135 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 136 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 3.2 Imisebenzi okugxilwa Imisebenzi okugxilwa Ukwakha izinto ezinhlangothi ntathu 3-D kuyo kuyo Izinto Abafundi baqala ngokudlala ngezinto ezinhlangothi ntathu ezahlukene bese ezinhlangothi Buka bese wakha Buka bese wakha bakha izinto abazithandayo besebenzisa amabhuloki okwakha noma izinto ntathu izinto esinhlangothi izinto esinhlangothi zokwakha.Kungenziwa ngesikhathi sokusebenza ngokuzimela. ntathu 3-D usebenzisa ntathu usebenzisa Ungasebenzisa izinto ezike zasebenza njengebhokisi likametshisi noma izinto eziphathekayo izinto eziphathekayo Izibalo IBANGA 1-3 amabhuloki okwakha noma izinto zokwakha ukubumba noma ukwakha njengamabhuloki njengamabhuloki okuthile isib. Umbhoshongo, irobhothi, isitimela, imoto, inqaba njll.abafundi okwakha;izinto okwakha;izinto bangenza umfanekiso wokwenziwe. Lokhu kungenziwa ngesikhathi somsebenzi ezingabuye ezingabuye wokuzimela, kodwa kusemqoka ukuxoxa nabafundi ukuthi kungani kuyizinhlo zisetshenziswe;izinto zisetshenziswe;izinto ezithile zezinto ezisetshenziselwa ukwakha imifanekiso.Lokhu kusiza abafundi zokwakha zokwakha bagxile ezimpawini ezisambhalomdwebo zezinto.isib.uma umbhoshongo ungakhiwa ngamabhokisi noma ngamabhuloki, ungababuza abafundi ukuthi ‘”Ungawakha umbhoshongo ngamabhola kuphela?”kufanele bachaze izimpendulo zabo. Ukuwabona nokunika amagama okusamabhola nokusamabhokisi (iprizimu) Abafundi babona bese bechaza izimo ezisabhola nezisamabhokisi Abafundi kumele bachaze izinto zansukuzonke ngokusho ukuthi zinesimo esisabhola noma esisabhokisi isib. Isitini simise okwebhokisi noma iwolintshi limise okwebhola. Kusemqoka ukuthi abafundi babone futhi basebenze ngezibonelo eziningi ezisabhola nezamabhokisi. Abafundi kumele banikwe uhla lwezinto zezimo zezimbulunga ukusebenza ngazo isib.amabhola anobungako obuhlukene, izimabuli, amawolintshi njll. Abafundi kumele banikwe uhla lwezinto zezimo zeprizimu ukuze basebenze ngazo isb, izitini, amabhuloki, namabhokisi anobungako obuhlukene Abafundi kumele bathole babuye bahlele izimo njengamabhola, okusambulunga noma amabhokisi iprizimu uma benikiwe iqoqo lezinto.Abafundi bangathola bakhombise bese benika amagama ezinto ezinesimo esisabhokisi ekilasini. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi bangayalelwa ukuba benze izinto ezinezimo ezisabhola noma ezisabhokisi besebenzisa ubumba.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA CAPS engu -24) 3.2 Ukuqhathanisa nokuchaza izinto ezinhlangothi ntathu 3-D: ubungako Izinto Abafundi baqhathanisa ubungako bezinto ezifanayo ezinhlangothi Isibonelo: ntathu • Hlela amabhola ngobungako bawo • Sebenzisa ulimi olukhuluma ngobungako “ibhokisi likhulu kunebhola ngoba uyakwazi ukufaka ibhola phakathi ebhokisini”. Chaza izinto ezinhlangothi ntathu 3-D: umbala Abafundi baxoxa ngemibala yezinto bese behlela izinto ngokwemibala Ukubona bese besho amagama ezinto kanye nemibala yazo kanye nokuqhathanisa ubungako bezinto kungenziwa ngokuphindelela ngesikhathi benza amaphethini imisebenzi yokubhala Nakuba imisebenzi yezinto ezinhlangothi ntathu yenziwa ngokwenza,umsebenzi kufanele uphethwe ngemisebenzi ebhalwayo. Ulimi Kusemqoka ukuthuthukisa ikhono labafundi ukuthi bakhulume ngezinto ezinhlangothi ntathu • Ulimi lobungako: kukhulu,kukhudlwana,kukhulu kakhulu,kuncane,kuncanyana, kuncane kakhulu • Imibala • Ulimi lwezinto;amabhokisi,amabhola(abafundi akumele bazi amagamausphere,no prizimu) • Ulimi lwesikhundla lokuchaza isakhiwo 137 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (ezifundweni ze IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 138 NGOKUPHELA 1 ihora nemizuzu KWI THEMU 1 KONYAKA engu -24) 3.2 isibonelo: Izinto - Ngaphezu kwe; ngaphansi ezinhlangothi - Ngaphambili,ngemuva ntathu - Eceleni kwe,kuhambisana Izibalo IBANGA 1-3 - Ngaphansi,ngale - Eduze,phakathi kwe - Ngaphakathi, ngaphandle Ulimi lobungako nemibala lungathuthukiswa ngesikhathi kufundiswa izifunod zoLimi noma zamakhono eMpilo bese kwenziwa ngokuphindelela ngesikhathi sesifundo sezibalo.ULimi lwesikhundla lungathuthukiswa ngesikhathi sesifundo soLimi noma samaKhono eMpilo nangesikhathi abafundi begxile nqo esikhundleni.kungasetshenziswa noma kwenziwe ngokuphindelela ngesikhathi abafundi besebenza ngezinto ezinhlangothi ntathu. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

iThemu YOKU- 1 YEbanga LOKU- 1 4. isilinganiso ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO (esifundweni ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA sehora eli 1 NGOKUPHELA KWI THEMU 1 nemizuzu engama KONYAKA 24) 4.1 Abafundi abafunde ukukhuluma ngalokhu: ISIKHATHI • Ukulandelanisa izigameko kanye • Ubude besikhathi Umsebenzi omningi wenziwa nsukuzonke ngesikhathi ufundisa ikilasi noma ngesikhathi samaqembu. Abafundi abakhulume bese bephendula imibuzo uma izinto zenzeka besebenzisa uLimi olufana; ekuseni, ntambama, ebusuku, usheshile, uphuzile. Ukudlula kwesikhathi Ukudlula kwesikhathi Ukudlula kwesikhathi Khuluma ngokudlula Khuluma ngokudlula Abafundi balandelanisa izigameko besebenzisa uLimi oluna njengo-izolo, kwesikhathi kwesikhathi namuhla, kusasa. • Hlela izigameko • Hlela izigameko Abafundi baqhathanisa ubude besikhathi besebenzisa uLimi olufanele njenga; ezejwayelekile ezejwayelekile ubude obuthe xaxa, isikhathi esifishanyana, esishesha kakhudlwana, esihamba ezimpilweni zabo ezimpilweni zabo kancane. • Qhathanisa ubude • Qhathanisa ubude Abafundi balandelanisa izigameko ezenzeka ezimpilweni zabo.Babuye besikhathi usebenzisa besikhathi usebenzisa balandelanise izithombe njenge uLimi olufanele isib. uLimi olufanele isib. Ubude obuthe xaxa, Ubude obuthe xaxa, • Izindlela zokwenza inkomishi yetiye isikhathi esifishanyana, isikhathi esifishanyana, • Izithombe zengane ikhula ize ibe umuntu omdala esishesha esishesha kakhudlwana, kakhudlwana, • Impilo yokukhula kwezilwane isib. Kusuka eqandeni kuya enkukhwini ephelele esihamba kancane esihamba kancane noma iqanda kuya kwixoxo eliphelele noma iqanda kuya kwimpukane; kanye • Landelanisa izigameko • Landelanisa izigameko • Nezigameko ezijwayelekile zosuku (evuka, eya esikoleni, edlala, edla,elala). usebenzisa ulimi usebenzisa ulimi olufanele njega izolo, olufanele njega izolo, namuhla, kusasa. namuhla, kusasa. 139 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (esifundweni ADINGEKAYO 140 IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA sehora eli 1 NGOKUPHELA KWI THEMU 1 nemizuzu engama KONYAKA 24) 4.1 Khuluma ngesikhathi Khuluma ngesikhathi Khuluma ngesikhathi ISIKHATHI • Chaza ukuthi • Chaza ukuthi • Abafundi bafunda ngezinsuku zesonto becula besho nemilolozelo. Lokhu kwenzeke nini kwenzeke nini kwenziwa nsukuzonke. usebenzisa uLimi usebenzisa uLimi • Izinsuku zabo zokuzalwa zifakwa ekhalendeni ngosuku olufanele. olufanele isib. olufanele isib. Izibalo IBANGA 1-3 ekuseni, ntambama, ekuseni, ntambama, • Abafundi bafunda ngezinyanga zonyaka ngomculo nangemilolozelo ebusuku,ngaphambi ebusuku,ngaphambi kwesikhathi,ngemumva kwesikhathi,ngemumva kwesikhathi kwesikhathi • Shono bese • Shono bese ulandelanisa isizinsuku ulandelanisa isizinsuku zesonto zesonto • Shono bese • Shono bese ulandelanisa izinyanga • ulandelanisa izinyanga zonyaka zonyaka • Faka izinsuku • Faka izinsuku zokuzalwa zabafundi zokuzalwa zabafundi ekhalendeni ekhalendeni Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (esifundweni ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA sehora eli 1 NGOKUPHELA KWI THEMU 1 CAPS KONYAKA nemizuzu engama 24) 4.2 Isilinganiso Isilinganiso Zonke izilinganiso eBangeni l azihleliwe.Azikho izilinganiso ezihleliwe zokukala Izifundo ezi-2 esingahlelekile esingahlelekile ubude ezenziwayo UBUDE • Qhathanisa • Qhathanisa Kuyanconywa ukuthi izifundo zezibalo ezifundisa ngobude zifundiswe kabili bese uhlela bese uhlela ngonyaka.(iThemu 1 neThemu 3.NgeThemu 1 kugxilwa ekuqhathaniseni ubude,ukuphakama, ubude,ukuphakama, bese kuthi ngoThemu 3 abafundi ngezikali ezingahleliwe.Abafundi bangenza noma ububanzi noma ububanzi ngokuphindelela bese bephetha loluLwazi ngesikhathi sokusebenza ngokuzimela bezinto ezimbili bezinto ezimbili unyaka wonke. noma ngaphezulu noma ngaphezulu Ukuqhathanisa okuqondile kobude ngezinto eziphathekayo ngokuzibeka eduze ngokuzibeka eduze nenye nenye Thuthukisa ulwazi lobude nolimi lokukhuluma ngakho. • Sebenzisa uLimi • Sebenzisa uLimi Abafundi baqale bacabange ngakho babuye baxoxe ngobude baphinde olufanele ukukhuluma olufanele ukukhuluma baqhathanise izinto ezimbili (imidwebo yezinto ezimbili) ngokwazi ukubona ngokuqhathanisa isib. ngokuqhathanisa isib. umehluko obonakalayo wobude. kude kune, kufushane kude kune, kufushane Izibonelo kune, kuphakeme kune, kuphakeme kune, kubanzi kune. kune, kubanzi kune. • Intambo ende nentambo emfishane • Qagela, linganisa, • Isihlahla eside nesifishane qhathanisa bese ubhala ubude • Umfula ovulekile nowumngcingo usebenzisa izikalo Abafundi bangenza noma badwebe izibonelo njenge esingenasilinganiso isib.izandla, • Sebenzisa ubumba ukwenza inyoka ende nemfishane amagxathu, ubude • Sebenzisa amabhuloki ukwenza umbhoshongo omude nomfishane bepensela, okokubala njll. • Dweba uthisha omude nomfishane • Chaza ubude bezinto Uma abafundi sebengakhuluma ngobude ngamagama aphikisayo, usengathula ngokubala usho ulimi lokuqhathanisa isib, Mina ngenze isitimela eside kodwa uSihle wenza ubude ngesilinganiso isitimela eside ngokuthe xaxa. ezingahlelekile. Qhathanisa ubude ngokubeka izinto eduze kwenye 141 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (esifundweni ADINGEKAYO 142 IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA sehora eli 1 NGOKUPHELA KWI THEMU 1 nemizuzu engama KONYAKA 24) 4.2 Uma abafundi sebekwazi ukukhuluma ngobude obudlulele (phakama,fishane njll)bese beqhathanisa ubude bezinto lezo ezibonakalayo nezisobala., UBUDE bangaqhubeka nezinye izibonelo ezilukhunyana nezidinga ukucabanga bese zibekwa eduze kwezinye kuqhathaniswa isib. • Thola ukuthi iyiphi phakathi kwalezizingane ende kunenye uma bema Izibalo IBANGA 1-3 behlangene ngemihlane’ • Beka amakrayoni amabili uwaqhathanise ubuka amakhanda amakrayoni ukuthola ukuthi yiliphi elifishane kunelinye. Abafundi kumele bathole ithuba lokuqhathanisa izibonelo ezimbili zezinto eziningi ezahlukene njengezinduku, amapensela, izintambo ezinde, amaphepha asikiwe, njll. Imidwebo yezinto ezimbilii ingaqhathaniswa ume zibekwe zasondelana futhi ziqondanisiwe ngezansi noma ngenhla. Abafundi bangaqhubeka baqhathanise futhi bahlele izinto ezintathu noma ngaphezulu.Lokhu kubizwa ngokuthi ukuhlela izinto ngobude bazo (seriation) izibonelo zifaka • Amaqembu abafundi bemi imihlane yabo ihlangene emugqeni ngababili ukuze kubonakale ukuthi ubani omude nomfishane kunomunye • Ukuhlela amaqoqo ezinto ezintathu noma ngaphezulu kusuka kokude kakhulu/ okuphakeme kuya kokufishane kakhulu/ okubanzi kuya kokumngcingo.Izinto ezifanelekile njengamapensela, amakrayoni,amabhodlela, izinti, izicathulo, izintambo,njll. Abafundi bathuthuka kulwazi lobude ngesikhathi bethuthuka olimini lokuchaza ubude. Njegoba lokhu kungazidingi izinombolo, kungafundiswa ekuqaleni kweThemu 1 ngaphambi kokuba abafundi baphethe ulwazi lwezinombolo nokusebenza kwazo kuze kufinyelele ku 5. Noma ISILINGANISO kuyikhono lokwenza, abafundi kufanele benze imisebenzi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola yokubhala efaka ukudweba nokufaka imibala, ukuze bazijwayeze ukusebenzisa amakrayoni noma amapensela bese bezijwayeza nokubhala uma bekala.

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (esifundweni sehora IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA eli 1 nemizuzu KWI THEMU 1 KONYAKA CAPS engama 24) 4.3 Isilinganiso Isilinganiso Zonke izilinganiso eBangeni l azihleliwe.Azikho izilinganiso ezihleliwe zokukala izifundo ezi-2 esingahlelekile esingahlelekile isisindo ezenziwayo Isisindo • Qagela, linganisa, • Qagela, linganisa, Kuyanconywa ukuthi izifundo zezibalo zigxile kwisisindo zifundiswe kabili qhathanisa, hlela qhathanisa, hlela ngonyaka.(iThemu 1 neThemu 4.NgeThemu 1 kugxilwa ekuqhathaniseni bese ubhala isisindo bese ubhala isisindo bese kuthi ngoThemu 4 abafundi ngezikali ezingahleliwe.Abafundi bangenza usebenzisa isikalo usebenzisa isikalo ngokuphindelela bese bephetha loluLwazi ngesikhathi sokusebenza esingalinganisiwe esingalinganisiwe ngokuzimela unyaka wonke. nokuzimelela. isib. nokuzimelela. isib. Ukuqhathanisa okuqondile kwesisindo sezinto eziphathekayo amabhuloki, izitini njll. amabhuloki, izitini njll. • Ukuthuthukisa ulwazi lwesisindo kanye nolimi olusetshenziswayo. • Sebenzisa ulimi • Sebenzisa ulimi olufaneleyo olufaneleyo Abafundi baqala ukucabanga babuye bakhulume ngesisindo ukukhuluma ukukhuluma ngokuqhathanisa izinto ezisindayo nezilula.Bazophakamisa into elula ngokuqhathanisa isib. ngokuqhathanisa isib. kakhulu babuye baphakamise into esinda kakhulu. Lokhu kungaphethwa kulula, kuyasinda, kulula, kuyasinda, ngokukhombisa imidwebo eqhathanisa izinto ezisinda kakhulu nezilula kulula kune. kulula kune. kakhulu. • Chaza isisndo sezinto Uma abafundi sebekwazi ukukhuluma ngesisindo ngokusebenzisa amagama ngokubala bese usho aphikisayo isib, kulula noma kuyasinda, abafundi bangaqhathanisa izinto isindo ngamayunithi ezimbili,bese basho ukuthi iyiphi ekulula kakhulu noma esinda kakhulu.Lokhu angahleliwe. kungenziwa ngokukuphatha izinto ezehlukene esandleni ngasinye bese uqhathanisa ukuthi iyiphi esinda kakhulu noma elula kunenye. Abafundi kumele bakubhale phansi lokho abakutholile ngemisebenzi yokudweba noma yokuqondanisa • Qhathanisa isisindo usebenzisa isikali sokuzimelela Isilinganiso sesindo esithengwayo singasetshenziswa. uma ungenaso ungazenzela esakho ungasebenzisa ikhothenga okubili kwalokhu: inkomishi yeyogathi (yoghurt), isinqe sebhodlela lamalitha ama 2 noma isinqe sebhodlela lobisi eliyilitha (izitsha ezifanayo zifakwa emacaleni omabili ekhothenga) - Abafundi bangaqala babeke izinto ezifanayo emacaleni womabili esikali, ukubona ukuthi ikhothenga lima liqonde uma isisindo sezinto silingana. - Abafundi bangaqhathanisa izinto ezehlukene ngokuzibeka ezitsheni zombili esikalini ukubona ukuthi iyiphi esindayo nelula. 143 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (esifundweni sehora IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 144 NGOKUPHELA eli 1 nemizuzu KWI THEMU 1 KONYAKA engama 24) - Abafundi bangaqhqthanisa izinto ngokubeka izinto ezingaphezulu kweyo- dwa esitsheni esisodwa noma zombili ukubona ukuthi zingaki izinto zohlobo olulodwa ezinesisindo esifanayo njengesinye.isib.amakrayoni ayi 5 anesisindo esilingana nesesikelo. - Lokhu kungaqhubeka kwenziwe ngezinye izinto ezihamba ngazimbili kuze kulandelanise izinto ngazintathu noma ngaphezulu kusukela kwelula Izibalo IBANGA 1-3 kakhulu kuya kwesinda kakhulu noma kwesinda kakhulu kuya kwelula kakhulu. Izinto ezingasetshenziswa zingakhethwa zifake izinto ezilula nezinto ezincane kodwa ezisindayo njengalokhu 250g iphakethe leswayi uliqhathanisa no 500g iphakethe letiye. Lokhu kuyosiza abafundi ukuqonda ukuthi isisindo siyahambisana nobungako bokukaliwe. Abafundi bathuthukisa ulwazi lwesisindo ngesikhathi bethuthukisa ulimi lokuchaza isisindo. Njegoba lokhu kungazidingi izinombolo. Kungafundiswa ekuqaleni kweThemu 1 ngaphambi kokuba abafundi baphethe ulwazi lwezinombolo nokusebenza kwazo kuze kufinyelele ku 5. Ukubhala Noma ISILINGANISO kuyikhono lokwenza, abafundi kufanele benze imisebenzi yokubhala efaka ukudweba nokufaka imibala, ukuze bazijwayeze ukusebenzisa amakrayoni noma amapensela bese bezijwayeza nokubhala uma bekala. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (esifundweni sehora IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA eli 1 nemizuzu KWI THEMU 1 KONYAKA CAPS engama 24) 4.4 Isilinganiso Isilinganiso Yini umthamo? Umthamo ubungako obungamumathwa ilesositsha (ukuvuleka 1 lisifundo esingahlelekile esingahlelekile kwaleso sitsha sokuthwala okusaketshezi) ubungako beisikhala esithathwa Umuthamo/ okusaketshezi.Ibhodlela lingaba nomthamo wezinkomishi ezigcwele ezi-4 okumumethwe • Qhathanisa • Qhathanisa kodwa kwesinye isikhathi ingaba noketshezi olungangenkomishi eyodwa. uhlele umthamo uhlele umthamo Abafundi beBanga 1 akulindelekile ukwazi umehluko phakathi komthamo wokusaketshezi, wokusaketshezi, nokumumethwe. bezintsha ezimbili bezintsha ezimbili uzibeke eduze uzibeke eduze Zonke izilinganiso eBangeni l azihleliwe.Azikho izilinganiso ezihleliwe zokukala Kwesinye. Abafundi Kwesinye. Abafundi umthamo ezenziwayo bathela okusaketshezi bathela okusaketshezi Kuyanconywa ukuthi izifundo zezibalo zigxile kumthamo zifundiswe kumathemu esitsheni sesithathu esitsheni sesithathu amathathu ngonyaka (iThemu 1, 2 no 4.) NgeThemu 1 kungagxilwa uma kunesidingo uma kunesidingo ekuthuthukiseni ulimi bese uqhathanisa umthamo, eThemu 2 kungenziwa • Qhathanisa • Sebenzisa uLimi ukuqhathanisa okuqondile bese eThemu 3 abafundi bangasebenzisa uhlele umthamo olufanele ukukhuluma izilinganiso ezingahleliwe. Abafundi bangenza ngokuphindelela bese bephetha wokusaketshezi ngokuqhathanisa isib. loluLwazi ngesikhathi sokusebenza ngokuzimela unyaka wonke. olungamumathwa kuningi kune, Ukuqhathanisa okuqondile komthamo wezitsha izitsha ezimbili uma zigcwele. kuncane kune, Ukuthuthukisa ulwazi lwesisindo kanye nolimi olusetshenziswayo.Abafundi baqala ukucabanga babuye bakhulume ngomthamo ngokuqhathanisa izintsha • Sebenzisa uLimi kugcwele.,akunlutho ezimbili ezifanayo (noma imidwebo yezitsha ezimbili ezifanayo) gxila kulokhu; olufanele ukukhuluma ngokuqhathanisa isib. • Kugcwele /akunalutho kuningi kune, • Kuningi kuno/ kuncane kuno kuncane kune, • Kuyalingana Abafundi abagcwalise izitsha ezingenalutho besbenzisa amanzi noma kugcwele,akunalutho isihlabathi njll. Kungafundiswa ekuqaleni kweThemu 1 ngaphambi kokuba • Qagela, linganisa, abafundi baphethe ulwazi lwezinombolo nokusebenza kwazo kuze kufinyelele qhathanisa, hlela ku 5. bese ubhala Ukubhala umthamo wezitsha ngokusebenzisa izikali Noma ukulinganisa kuyikhono lokwenza, abafundi kufanele benze ezingenasilinganiso imisebenzi yokubhala efaka ukudweba nokufaka imibala, ukuze bazijwayeze isib. Izipuni ukusebenzisa: nezinkomishi. • amakrayoni noma amapensela; kanye • nokubhala uma bekala. 145 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ISIKHATHI ULWAZI NAMAKHONO ADINGEKAYO (esifundweni sehora IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA 146 NGOKUPHELA eli 1 nemizuzu KWI THEMU 1 KONYAKA engama 24) • Chaza umthamo wesitsha ngokubala bese usho ukuthi mangaki amayunithi angahleliwe istsha esikwazi Izibalo IBANGA 1-3 ukuwamumatha isib. ibhodlela ligcwaliswa ngezinkomishi ezi-4 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YOKU- 1 YEBANGA LOKU-1 5. ukuqokekelwa kolwazi ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO (esifundweni sehora IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA eli 1 nemizuzu KWI THEMU 1 KONYAKA engama 24) Ukusebenza ngamaqoqo ezinto 5.1 Qoqa bese uhlela izinto Qoqa bese uhlela Ukuhlela,okumele okuqoqiwe,nokuchaza okuqoqiwe kwahlelwa kungamakhono izifundo ezi 2 izinto alusizo oluzothuthukisa abafundi besaqala ukufika esikoleni (bheka amanothi Ukuqoqa nohlela Qoqa bese uhlela amakhono okuqalisa izinombolo ekuqaleni kwamanothi achazayo)Lokhu izinto izinto eziphathekayo Qoqa bese uhlela kwenza kuthuthuke amakhono kubafundi ngesikhathi sebeqala ukwenza zansukuzonke. izinto eziphathekayo ukuqokelela ulwazi oluqoqiwe. zansukuzonke. Abafundi banganikwa izinto ezinhlobonhlobo bacelwe ukuba bazihlele.isib. Beka okumele iqoqo 5.2 Beka okumele iqoqo nika amaqembu izinto zokubala ezifanayo bese ubacela ukuba bazihlele lezinto eziqoqiwe lezinto eziqoqiwe ngokwemibala, ubanike izinhlobo ezehlukene zezinto zokubala njengobuhlal Beka okumele zahlelwa zahlelwa u,umetshiso,izinhlavu zamapentshisi,izivalo zamabhodlela kuhlangene bese iqoqo lezinto Dweba isithombe ubacela bakuhlele ngamaqoqo ahlukene. eziqoqiwe zahlelwa Dweba isithombe sezinto sezinto eziqoqiwe eziqoqiwe Abafundi badweba isithombe samaqoqo abawenzile. Ngalendlela babhala Chaza okuqoqiwe abakwenzile. Baphendula imibuzo ngamaqoqo. 5.3 Xoxa bese ubika nemidwebo. ngeqoqo lezinto Isibonelo Xoxa ubike Xoxa bese ubika ezihleliwe ngeqoqo lezinto Uwenze kanjani amaqoqo ezinto zokubala? Ngihlele ngemibala ngezinto eziqoqiwe zahlelwa • Nika izizathu zokuthi ezihleliwe Iqoqo elikhulu lezinto zokubala linombala onjani? Iqoqo elikhulu linombala iqoqo lihlelwe kanjani • Nika izizathu zokuthi obomvu • Phendula imibuzo iqoqo lihlelwe kanjani Unemibala emingaki ezintweni zakho zokubala? Nginemibala emihlanu ngalokhu; • Phendula imibuzo eyahlukene. - Kuhlelwe kanjani ngalokhu; Bangabuye bazitholele ezinye izindlela zokuthola amaqoqo ahlukene isib. - Kubukeka kanjani - Kuhlelwe kanjani Bangaqoqa amacembe egcekeni lesikole noma balethe amathini ahlukene lokhu okuhleliwe angenalutho emakhaya. - Kubukeka kanjani • Chaza okuqoqiwe lokhu okuhleliwe nemidwebo • Chaza okuqoqiwe • Chaza ukuthi nemidwebo okuqoqiwe kuhlelwe • Chaza ukuthi kanjani okuqoqiwe kuhlelwe kanjani 147 Izibalo IBANGA 1-3

ITHEMU YESI-2 YEBANGA 1 1. IZINOMBOLO UKUSEBENZA KANYE NOBUDLELWANO BEZINOMBOLO 148 ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA UKUTHUTHUKISWA KOLWAZI LWEZINOMBOLO:Bala ngezinombolo eziphelele 1.1 Bala izinto eziphathekayo Bala izinto eziphathekayo Kuyini okwehlukile eThemu 2? ngokuyiko kuya kuma-50. ngokuyiko kuya kuma-20 Bala izinto EThemu 2, luyakhula uhla lwezinombolo lokubala Kusagxilwa elwazini lokuthi Izibalo IBANGA 1-3 eziphathekayo • Qagela • Qagela inombolo yokugcina eshiwo ikhomba inani lezinto eqoqweni. Abafundi babala ngokusondezela inani ngokusondelela inani izinto eziningi bese kuthi eThemu 2 kufanele bafunde ukumisa izinto ngendlela lezinto ezingabhekwa lezinto ezingabhekwa ukuze uma behlola ukubala kwabo kubasize babale kalula. ngokubala. ngokubala. Isibonelo: • Ukubala ngokwenza amaqoqo kuyakhuthazwa. Kulethemu abafundi baqhubeka nokwandisa amakhono abo okubala nokwenza: • Ukubala konke; • Ukubala beqhubeka;. • Indlela yokusebenza yezinombolo ezejwayelekile; kanye • Nokusebenza ngokubhaliwe. Ngethemu yesibili abafundi baqala uku: • Ukubala izinto abangeke bazithinte noma baziphathe. Isibonelo: Sibuza abafundi: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Zingaki izingxenye ezisefasiteleni? • Bala ngokulingisa Isibonelo: Shaya izandla izikhathi eziyi-15. Phakamisa iminwe eyi-8.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.1 Ukuqagela Bala izinto Ukuqagela inombolo yezinto kumaqoqo kuthuthukisa amakhono abalulekile eziphathekayo okuqagela. Kusiza abafundi ukubona noma baqagele ngokuyikona. Kubalulekile lokhu uma bebala: bangazibhekela ukuqinisekisa ukuthi baphendule ngokuyikho. Kuyabasebenzela abafundi ukubala imidwebo yezithombe ezingamaqoqo kanye nokungewona amaqoqo. Zama ukuphambanisa amaqoqo ezinto ahleliwe nangahleliwe bese abafundi beqagela ukuthi iliphi iqoqo elinezinto eziningi. Abafundi bangaqagela inani lezinto esithombeni ngasinye. Abafundi sebengabala. Kufanele baqhathanise nombolo abayithole beqagela naleyo abayithole sebebala izinto. Abafundi mabakhulume ngendlela ababale ngayo. Zama ukuthola noma abanye abafundi babale ngamaqoqo. Ukuqagela inombolo eyakha iqoqo Abafundi bakhulisa amakhono abo okubona iqoqo elincane lezinto. Ukubala ngamaqoqo Ukusiza abafundi ukubala ngezikhawu zoku-2, 5, nokuyi-10 kufanele benze amaqoqo ezinto ezinga-2,-5,nokuyi-10. Amakhadi ezinombolo kufanele akhonjiswe eduze kweqoqo ngalinye ukuze kubonakale inani lezinto ezibaliwe. Ukubala ngamaqoqa kulungiselela abafundi ukuqonda ukuphindaphinda kumazinga aphezulu. Izinsiza kufundisa Qaphela ukubheka izinhlobo zezinsiza kufundisa ezisetshenziswayo. • Izinsiza kufundisa ezihleliwe njenge ubuhlalu obusentangeni • iAbhakhasi ukuzilungiselela ukubala ngamaqoqo ngokuyishumi • ukwenza izinyanda zoku-2, izinyanda zoku-5 nokuyishumi kanye nokubala konke. 149 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 150 KWI THEMU 1 KONYAKA 1.2 Bala uya phambili Bala uya phambili Yimuphi umehluko eThemu 2? ubuye uye emumva ubuye uye emumva Bala uya phambili EThemu 2 abafundi manje babala kufinyelela ema-50 ngokukodwa. ngoku: ngoku: ubuye uye Bangabala ngezikhawu zokuyi-10, 5, kanye noku-2. emumva • ngokukodwa kusukela • ngokukodwa kusukela kunoma iyiphi kunoma iyiphi Ukubala ngokweqa bekhuluma inombolo phakathi inombolo phakathi Ukubala ngokweqa elinye igama lokubala ngamaqoqo. Lokhu kusiza Izibalo IBANGA 1-3 kuka 1 - 100 kuka 0 - 50 ukuthuthukisa ukuqonda amaphethini ezinombolo.Ukubala ngokweqa kukhuthaza Bala uya phambili Bala uya phambili abafundi ukubala bacabange ngamaqoqo okubenza babe nekhono lokubala ngama- ngama- ngokuzethemba. Lokhu kubasiza ukuba bathuthuke kamakhono abo okuqagela. • 10 kusukela kunoma • 10 kusukela kunoma Ukubala ngamaqoqo kwenza bazi ubudlelwano phakathi kwezinombolo iyikuphi inombolo iyikuphi inombolo ezingalandelani. Kubanika isisekelo sokwenza amaphethini ezinomolo kanye ephindaphinda ngama- ephindaphinda ngama- nokuphindaphinda. 10 phakathi koku- 10 phakathi koku- 1kanye ne- 100 1kanye nama- 50 Eminye Imisebenzi • 5 kusukela kunoma • 5 kusukela kunoma Nazi ezinye iziphakamiso zezindlela ezihlukene zokubala ngokweqa.: iyikuphi inombolo iyikuphi inombolo • Qala ngokubala izinombolo ezilandelanayo kodwa ugcizelela njalo kweyesibili. ephindaphinda ngoku- ephindaphinda ngoku- Isib.Abafundi bashaya izandla besho kakhulu njalo uma bebiza inombolo 5 phakathi koku- 5 phakathi koku- yesibili. Cela abafundi babale kodwa m basho inombolo yesibili ngekhanda. 1kanye ne- 100 1kanye nama- 50 Lokhu kungandiswa ngokuthi abafundi basho inombolo yesithathu, eyesine, • 2 kusukela kunoma • 2 kusukela kunoma noma eyesihlanu. iyikuphi inombolo iyikuphi inombolo • Ungahlukanisa ikilasi ngamaqoqo, iqoqo ngalinye lingashintshana namaye ephindaphinda ngoku- ephindaphinda ngoku- ngokusho inombolo elandelayo.Isib. ungahlukanisa ikilasi libe ngamaqoqo 2 phakathi koku- 2 phakathi koku- amahlanu iqoqo ngalinye kufanele libable njalo inombolo yesihlanu. 1kanye ne- 100 1kanye nama- 20 • Cela abafundi benzae amaphethini ngemizimba yabo njengokuthinta amakhanda abo ngokubala kokuqala,baphambanisa izandla bese bethinta amahlombe ngokubala kwesibili, bese bezishaya amathanga bememeza njalo inombolo yesithathu.. • Ukushaya izandla ngesigqi somculo kungasetshenziswa nokubala ngokweqa. Ukubala izinto kungathuthukisa amakhono okubala ukhuluma. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Imisebenzi yokubala ekilasini ithuthukisa amakhono ahlukene. Ukubala ngokweqa kwethuleka kangcono uma benza amaqoqo ezinto eziphathekayo.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.2 Eminye Imisebenzi Bala uya phambili Ishadi lezinombolo ubuye uye Cela abafundi bagqamisa izinombolo abakwazi ukuzibona ngenkathi bebala emumva ngaku- 2, 5, 10. Buza abafundi abakuqaphele ngezinombolo. Shintsha izinombolo abafundi abaqala kuzo uma bebala. Ukuqhubekela kokubhalwayo • Umugqa wezinombolo -abafundi bakhombisa ukubala ngokweqa besebenzisa umugqa wezinombolo. • Ukulandelana kwezinombolo- ngasekupheleni kweThemu abafundi bangaqede- la izinombolo ezilandelanayo ezilula (bheka amanothi amaphethini ezinombolo) Isibonelo: - 2, 4, 6, 8, – - 5, 10, 15, 20, – - 10, 20, 30, 40, – 1.3 Bona, khomba,bese Bona, khomba,bese Yimuphi umehluko eThemu - 1? ufunda izinombolo ufunda izinombolo Izimpawu EThemu yesi- 2 luyakhula uhla lwezinombolo: ukwazi, ukufunda, nokubhala namagama • Bona, khomba, bese • Bona, khomba, bese izimpawu zezinombolo. ezinombolo ufunda izimpawu ufunda izimpawu zezinombolo - 1 kuya zezinombolo - 1 kuya Ukubala emugqeni wezinombolo nakwishadi lezinombolo kunika abafundi e- 100. e- 100. ithuba lokuzilungiselela ukukhomba, ukubona, ukusho nokufunda izimpawu zezinombolo. • Bhala izimpawu • Bhala izimpawu zezinombolo - 1kuya zezinombolo - 1kuya Nika abafundi amathuba okuzilungiselela uqhaphele ukubagxilisa kwizimpawu ema- 20. ema- 20. zezinombolo kwindawo abakuyo nokokubhaliwe. • Bona, khomba, bese • Bona, khomba, bese Isibonelo: ufunda amagama ufunda amagama • Babheka emakhasini ezincwadi. ezinombolo - 1 kuya ezinombolo - 1 kuya e-10. e-10. • Bakhomba izinsuku zokuzalwa kwikhalenda. • Bhala amagama • Bhala amagama ezinombolo - 1 kuya ezinombolo - 1 kuya e- 10. e- 10. 151 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 152 KWI THEMU 1 KONYAKA 1.3 Eminye Imisebenzi Izimpawu • Uthisha unika lemiyalelo elandelayo ukuthola inombolo, bese abafundi namagama basebenzisa amafuladi khadi (flard card) ukukhombisa izimpendulo.. ezinombolo - Thola inombolo engaphambi kokuyi-12 - Thola inombolo engemuva kokuyi- 12 Izibalo IBANGA 1-3 - Inombolo engaphezulu ngokuthathu kokuyi-11 - Inombolo encane ngokukodwa kokuyi-14 1.4 Chaza, qhathanisa, Chaza, qhathanisa, Yimuphi umehluko eThemu - 1? bese uhlela izinto bese uhlela izinto Chaza, qhathanisa kufinyelela ema- 20 kufinyelela ema- 10 EThemu-2 abafundi baqhubeka noku: bese uhlela • Chaza, bese • Chaza, bese • Hlela bese uqhathanisa izinto; izinombolo. uqhathanisea iqoqo uqhathanisea iqoqo • Hlela bese uqhathanisa izinombolo; kanye lezinto ngoku - lezinto ngoku - okuningi, okuncane, okuningi, okuncane, • nokusebenzisa ulimi lokuhlela nokuqhathanisa. okuningi kakhulu, okuningi kakhulu, Ngalethemu abafundi bayaqhubeka nokuhlela bese beqhathanisa izinto. Abafundi okuncane kakhulu, okuncane kakhulu, bangaqala ukwenza ubudlelano phakathi kwezinombolo ngokugxila kokukodwa okuningi kunokunye, okuningi kunokunye, nokubili okungaphezulu, okukodwa nokubili okuncane. okuncane kunokunye, okuncane kunokunye, • Uma beqhathanisa amaqoqo kufanele bakwazi ukuchaza ngokusho lokhu, okulinganayo, okulinganayo, “nginezinto zokubala ezingaphezulu ngokubili kunaye” noma, “unokuncane nokuhlukile. nokuhlukile. ngokukodwa kunokwami”. • Chaza bese uhlela • Chaza bese uhlela • Uma beqhathanisa izinombolo kufanele bakwazi ukuthi “okukodwa ngaphezulu iqoqo lezinto kusukela iqoqo lezinto kusukela kokune kuhlanu’ noma okuyisikhombisa kungaphezulu ngokubili kokuhlanu” kokuningi kakhulu kuya kokuningi kakhulu kuya kokuncane kakhulu kokuncane kakhulu Ukwakha ulwazi “lokungaphezulu gokukodwa “ kanye nokuncane kanye nokuncane Ulwazi lokungaphezulu kuna nokungaphansi kuna kuwukuqa kuhlanganisa kakhulu kuya kokuningi kakhulu kuya kokuningi nokususa okungahlelwe.Lokhu kusiza abafundi ukwazi ubungako benombolo kakhulu. kakhulu. kanye nokuhlelwa kwezinombolo. • Yalela abafundi ukuthi babeke into yokubala eyodwa esikhaleni sokuqala esin- genalutho ekhadini lokubala elinezikhala ezinhlanu “5 frame card”. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Yalela abafundi babeke enye into eyodwa yokubala eduze kwento yokuqala yokubala   Buza: Kungaki onakho manje? Kungaki osekungaphezulu ngokukodwa kokukodwa?

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.4 Chaza, uqhathanise, Chaza, uqhathanise, • Yalela abafundi ukuthi babeke into yokubala eyodwa ngaphezulu ekhadini loku- bese uhlela izinombolo uhlele izinombolo bala elinezikhala ezinhlanu “5 frame card”. Chaza, qhathanisa kufinyelela ema-20 kufinyelela e-10 bese uhlela izinombolo. • Chaza bese • Chaza bese   uqhathanisa uqhathanisa Buza: izinombolo eziphelele izinombolo eziphelele ngoku -okungancane ngoku -okungancane Kungaki ongako manje? kunokunye, okukhulu kunokunye, okukhulu Kungakanani okungaphezulu ngokukodwa kokubili? kunokunye, okuningi kunokunye, kunokunye, okuncane okuningi kunokunye, • Yalela abafundi babeke into eyodwa ngaphezulu ekhadini lokubala elinezikhala kunokunye, okuncane kunokunye, ezinhlanu “5 frame card”. okulinganayo. okulinganayo.   • Chaza bese uhlele • Chaza bese uhlele izinombolo: izinombolo: Buza imibuzo: - Kusukela kokuncane - Kusukela kokuncane kungaki onakho manje? kakhulu kuya kakhulu kuya Kungakanani okungaphezulu ngokukodwa kokuthathu? kokukhulu kakhulu kokukhulu kakhulu nokukhulu kakhulu nokukhulu kakhulu Zingaki izinto zokubala ozidingayo ukwenza okuhlanu? kuya kokuncane kuya kokuncane Buza, “ Yini ongangitshela kona ngenombolo- 4?(kuncane ngokukodwa kakhulu. kakhulu. kokuhlanu.) - Ngaphambi, - Ngaphambi, Yini ongangitshela yona ngenombolo- 2? (kuncane ngokuthathu kokuhlanu 5.) emumva, emumva, Ukuhlela izinombolo okuphakathi okuphakathi nendawo / phakathi. nendawo / phakathi. Abafundi kufanele bahlele izinombolo besebenzisa izinhlobo ezahlukene zemifanekiso. - Sebenzisa umugqa - Sebenzisa umugqa wezinombolo wezinombolo • Benza amaqoqo emifanekiso. kusukela koku- 0 kusukela koku- 0 Abafundi baqhathanisa iqoqo lezinto eziyi-9 neqoqo lezinto ezi-2. - 20 - 10 • Umugqa wemifanekiso. • Chaza uhlele • Chaza uhlele usebenzisa ulimi Isib. usebenzisa ulimi Isib. Uma abafundi behlela izinombolo bangasebenzisa ibanga phakathi kwezinombolo ngaphambi, emumva, ngaphambi, emumva, ukwazi ukuthi iyiphi inombolo enkulu ngokuthe xaxa. Isibonelo, bazosho ukuthi okuphakathi nendawo / okuphakathi nendawo / okuyi-9 kukhulu ngokuthe xaxa kunoku-2 ngoba okuyi-9 kuza emuva koku-2. phakathi. phakathi. Ukuhlelwa kwezinombolo kungenziwa ngesikhathi sokusebenza ngokuzimela / ngayedwa. 153 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 154 KWI THEMU 1 KONYAKA 1.4 Eminye Imisebenzi Chaza, qhathanisa Ukuhlela izinombolo bese uhlela Abafundi bahlela amakhadi ezinombolo -1 kuya kokuyi-13 kusukela kokuncane izinombolo. kakhulu kuya kokukhulu kakhulu. Abafundi babhekisa phansi amakhadi abo ezinombolo. Bakhetha amakhadi Izibalo IBANGA 1-3 ama-4, bawahlele kusuka kokuncane kakhulu kuya kokukhulu kakhulu bese ucela umngani abheke ukuthi abekwe ngakho yini.Uma sebewaqonda amakhadi ama-4 bangakhetha amakhadi ama-5. Bawahlele ngendlela efanele bese bekopisha izinombolo kusuka kwencane kakhulu kuya kwenkulu kakhulu. Imisebenzi ebhalwayo Abafundi kufanele baphethe ulwazi lwabo ngokwenza imisebenzi ebhalwayo. Izibonelo: Kufanele kuthi kuphela iThemu babe bekwazi ukuqedela imisho efanayo: Okuningi ngoku-1 koku- 3 ________ Okuningi ngoku-1 koku- 4 _______ Okuncane ngoku-1 koku-2 ________ ____ okuningi ngoku- 1 koku- 4 ____ okuncane ngoku-1 koku- 3 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.6 Sebenzisa lamasu Sebenzisa lamasu Yimuphi umehluko eThemu - 2 alandelayo ukuxazulula alandelayo ukuxazulula Amasu izinkinga bese uchazea izinkinga bese uchazea NgaleThemu kwethulwa kubafundi ukuphinda kabili nokuhlukanisa kabili okuxazulula izixazululo: izixazululo: ngokulingana okokuqala. Bheka amanothi ngaphansi kwengxenye yezibalo. izinkinga Kufanele kuthi kuphela iThemu abafundi baqale ukuxazulula izinkinga zamagama • Izinsiza kufundisa • Izinsiza kufundisa besebenzisa lamasu: eziphathekayo Isib. eziphathekayo Isib. Izinto zokubala. Izinto zokubala. • Imidwebo noma izinto eziphathekayo. • Izithombe zokudweba • Izithombe zokudweba • Ukwakha noma ukuhlakaza izinombolo. izibalo zengxoxo. izibalo zengxoxo. • Ukwakha nokuhlakaza izinombolo. • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza • Ukuphinda kabili nokuhlukanisa kabili ngokulingana. izinombolo. izinombolo. • Umugqa wezinombolo • Ukuphinda kabili • Ukuphinda kabili nokuhlukanisa kabili nokuhlukanisa kabili Imidwebo noma izinsiza kufundisa eziphathekayo ngokulingana. ngokulingana. Abafundi baqhubeka nokudweba izithombe nokusebenzisa izinsiza kufundisa • Umugqa wezinombolo • Umugqa wezinom- eziphathekayo ukuxazulula izinkinga. Kubalulekile ukuthi izithombe noma bolo ilekelelwa izinto imidwebo ibe nezinombolo kanye nomusho wezinombolo. eziphathekayo. Isib. Ukwakha nokuhlakaza Ubulalo bokubala Kuyisuqhinga elibaluleke kakhulu emazingeni aphansi. Ukusebenzisa lelisu kuvumela abafundi ukuhlukanisa babuye bahlanganise izinombolo ukusiza ukwenza ukubala kubelula. Isibonelo 6 + 4 → 5 + 1 + 4 → 5 + 5 → 10 Lelisu lisetshenziswa kaningi emazingeni aphakathi. Ukuphinda kabili nokuhlukanisa kabili ngokulingana Lelisu linobucayi obuthile lidinga ulwazi lwezinombolo olujulile.Abafundi abakwazi ukukhetha lelisu bayakwazi ukusebenzisa amaqhinga ngokhululeka. NgaleThemu abafundi baqala ukuphinda kabili izinombolo ngoba babala kufinyelela e-10. Ngaphambi kokusetshenziswa kokuphinda kabili nokuhlukanisa kabili ngokulingana njengeqhinga kufanele abafundi bakufundiswe. 155 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 156 KWI THEMU 1 KONYAKA 1.6 EBangeni 2 abafundi bethulelwa ngomusho wezinombolo bese bebuzwa: “ Singazisebenzisa kanjani izinombolo eziseduze kweziphindeke kabili ukuthola Amasu impendulo yoku- 5 + 6 = ?”Abafundi bayaqonda ukuthi oku-5 kanye nokuyi-6 okuxazulula kusondelene nokunye. Izinsiza kufundisa eziphathekayo ziyasetshenziswa izinkinga ukukhombisa ukuthi “Ngizokwenza oku-5 okuphindwe kabili okungamaqoqo amabili okuhlanu. Ngihlanganisa okubili okuhlanu ngithole okuyishumi bese ngisala nokukodwa okufanele ngikwengeze. Impendulo kube okuyi-11. Izibalo IBANGA 1-3 Besebenzisa ulimi lwabo noma imidwebo, abafundi bangalisebenzisa lelisu. Uma abafundi befika eBangeni-3 bazokwazi ukusebenzisa lelisu uma bebala izinombolo ezinamadijithi amathathu. NgaleThemu abafundi bazosebenzisa ukuphinda kabili nokuhlukanisa kabili ngokulingana ngalendlela: ukuphinda kabili: • Amabhayisekili amabli amasondo mathathu, anamasondo amangaki? • USipho noThemba banomabuli aba-4 eyedwa. Bangaki omabuli bebonke? Abafundi bangadweba izithombe basebenzise izinsiza kufundisa eziphathekayo ukukhombisa ukuthi inombolo iphindwe kabili. Ukuhlukanisa kabili ngokulingana: • EThemu 2 abafundi benza ngokuphindelela ukuhlukaniseni kabili ngokulingana ukuze basebenzise lelesu eThemu 3. • Ukuphinda kabili nokuhlukanisa kabili ngokulingana kufanele bakwenze ngoku- phindelela kwizimo ezikhululekile. Umugqa wezinombolo Ukubala usebenzisa umugqa wezinombolo kusiza abafundi uku: • Babhala ukucabanga kwabo; • Bahlale belandelela imicamango yabo; kanye • Babe nesithombe abangasisebenzisa ukuchaza indlela abaxazulule ngayo inkinga. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi kade besebenzisa umugqa wezinombolo kusukela eThemu 1 Njengoba abafundi beqhubekela phambili emazingeni aphansi kufanele bakhuthazwe ukusebenzisa umugqqa wezimombolo ngendlela ekhombisa inqubekela phambili ekusebenziseni umugqa wezinombolo.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.6 EThemu 1 abafundi babala ngakunye, lokhu kukhonjiswa kumugqa wezinombolo ngokugxuma ngakunye. Amasu okuxazulula Isibonelo 1: izinkinga Kunabafana aba-5 kanye namantombazana ama-4 benza izifundo ezengeziwe zobuciko esikoleni. Bangaki abafundi abasekilasini lezifundo zobuciko? EThemu 2 abafundi basangabala ngakunye, kepha bangakhuthazwa ukusebenzisa umugqa wezinombolo ukukhombisa ukubala uqhubeka ngamaqoqo. Isibonelo 2: Abafundi bangahlakaza oku-4 kube ngamaqoqo ama-2. Umugqa wezinombolo uzokhombisa ngokugxuma kabili kusuka koku-5. 1.7 Xazulula izinkinga Xazulula izinkinga Yimuphi umehluko eThemu 1? zamagama ezimweni zamagama ezimweni Ukuhlanganisa KuleThemu abafundi benza bephindelela izinkinga zamagama besebenzela nokususa ezijwayelekile uchaze ezijwayelekile uchaze ukuzethemba ekusebenziseni amanye amasu uma bexazulula izinkinga. isixazululo ezinkingeni isixazululo ezinkingeni KuleThemu kufanele kugxilwe ekubhaleni phansi, abafundi kufanele babhale ezifaka ukuhlanganisa ezifaka ukuhlanganisa phansi imisho yezinombolo njengezinkinga ezibhalwe phansi kufinyelela koku- nokususa nezimpendulo nokususa nezimpendulo 5. Abafundi bazoqhubeka nokusebenzisa izinsiza kufundisa eziphathekayo ezifinyelela ema-20. ezifinyelela ema-10. nemidwebo ukwethula izibalo zabo kusukela esi-5 kufinyelela e-10. Bheka amanothi eThemu 1 izinhlobo zezinkiga ezingenziwa ngaleThemu, uhla lwezinombolo luyakhula kufinyelela e-10. 157 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 158 KWI THEMU 1 KONYAKA 1.8 Xazulula izinkinga Xazulula izinkinga Uhla lwezinombolo ekubalwa ngazo kuleThemu luvumela abafundi ukuqala zamagama ezimweni zamagama ezimweni ukuhlanganisa okuphindayo. Ukwenza izibalo ezifinyelela e-10 kuvumela Ukuhlanganisa ezijwayelekile uchaze ezijwayelekile uchaze ukubhala phansi. ngokuphindel- isixazululo ezinkingeni isixazululo ezinkingeni ela okuholela eku- Isibonelo: ezifaka ukuhlanganisa ezifaka ukuhlanganisa phindaphindeni ngokuphindelela ngokuphindelela • 1+1+1 kufinyelela ema-20. kufinyelela e-10. Izibalo IBANGA 1-3 • 2+2+2+2 • 3+3+3 EThemu 1 kwakhiwa umqondo wokuqonda ukuhlanganisa, bese abafundi kufanele bakwazi ukuhlanganisa amaqoqo alinganayo. KuleThemu abafundi basebenza ngezinkinga zamagama ezizovumela imifanekiso yokuhlanganisa ngokuphindayo. Ukuhlanganisa ngokuphindayo kwethulwa kubafundi ngamaqoqo ezinombolo ezilinganayo. Ekuqaleni kngethulwa ngamaqoqo alinganayo ansukuzonke. Izinkinga ezifaka ukuhlanganisa ngokuphindaphinda: • Amaqoqo oku-2: izandla, amasokisi, izicathulo, amehlo,izinyawo, amasondo ebhayisikili. • Amaqoqo oku-3: amasondo ebhayisikili elinamasondo amathathu, unqenqema kunxantathu. • Amaqoqo oku-4: amasondo emoto, imilenze yezihlalo. • Amaqoqo oku-5: iminwe, izinzwane. Ulimi lokuhlanganisa ngokuphindayo lubalulekile. Kufanele abafundi banikwe ithuba lokuchaza ngokukhuluma abakubonayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.11 • Bona, bese ukhomba • Bona, bese ukhomba Fundisa abafundi ngemali, uchaza lolulwazi olulandelayo: imali yaseNingizimu imali yaseNingizimu Imali • yini imali Afrika Afrika • ibaluleke ngani imali - uhlweza 5c, 10c, - uhlweza 5c, 10c, 20c, 50c, R1, R2 20c, 50c • isetshenziswa kanjani imali empilweni yansukuzonke - amaphepha R10 • Xazulula izinkinga • bayibala kanjani abafundi imali kanye R20 zezimali kufaka isamba Abafundi bafunda ngemali phambi kokuya esikoleni. Abanye abafundi bangaba noshintshi oluhlweza • Xazulula izinkinga nalo ulwazi lwenani lemali bese bekwazi ukubona basho uhlweza nemali kufinyelela ema- 20c zezimali kufaka isamba engamaphepha. noma amarandi noshintshi oluhlweza kufinyelela kwayi-R10. KuleThemu kufanele abafundi bafunde ulwazi oluyisisekelo lokusebenzisa imali kufinyelela ema- 20c ngokwenza. Lokhu kungenziwa ngokudlala umdlalo wesitolo. noma amarandi kufinyelela kwangama- • Leha uhlweza kanye nemali engamaphepha -R20 kanye ne-R10 yaseNingizimu R20. Afrika esikoleni. Abafundi bathinta unqenqema lohlweza bachaze indlela oluhluka ngayo. Bachaza izimpawu ezisohlwezeni ngalunye nemali yamaphepha. • Abafundi babeka uhlweza ngaphansi kwephepha elilula usebenzise okokubhala okuthambile uhlikihle ngaphezu kwalo Isib.amapeni okufaka umbala.basika amakhophi, banamathisele ezincwadini zabo babhale igama lohlweza. • Basika izithombe zohlweza olungo- 5c, 10c kanye no- 20c. Banamathisela yonke inhlanganisela yohlweza oluzokwenza-20c kanye no- 10c Isib. 20c = 10c 5c 5c • 20c = 5c 5c 5c 5c • Isamba kufinyelela e- 20c -uhlweza kuphela. • Abafundi sebeyakwazi ukubala ngoku-5 nokuyi-10 bazobenzisa lolu lwazi ukuthola isamba. • Uthisha unika umfundi ngamunye ikhophi lephepha lohlweza olungo-5c, 10c kanye nama-20c. Ubatshela ukuthi iluphi uhlweza okufanele balukhiphe Isib.uhlweza oluthathu lama-5c. 159 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 160 KWI THEMU 1 KONYAKA 1.11 Babala ngoku-5 noma benze ukuhlanganisa okuphindayo, 5c+5c+5c. Imali - Uthisha ucela abafundi bakhiphe uhlweza olungama-20c besebenzisa izinhlobo ezihlukene zohlweza. Bazobona ukuthi bakhiphe uhlweza olubili olungo-5c nohlweza olulodwa lo-10c. - Abafundi bagcwalisa iphepha lokusebenzela bekhombisa uhlweza abaludingayo ukwenza isamba sohlweza olungama-20c. Izibalo IBANGA 1-3 Isibonelo: 20c = 10c + 10c noma 5c+ 5c + 5c + 5c= 20c noma 5c+5c + 10c =20c • Nika ushintshi usebenzisa uhlweza kuphela - Uthisha wenza izibalo zokususa esebenzisa uhlweza kanye nabafundi Isib. Bakhipha uhlweza olungo-5 olwenza ama-20c. - Uthisha uyabuza: “uma ukhokhela umthengisi imali ama-15c kusele malini?” abafundi abakuthola kunzima ngohlweza kuphela basebenzisa izinto zokubala ukubasiza. - Abafundi bagcwalisa amaphepha okusebenzela lapho bebala ushintshi wezinto abazithengile ngama-20c noma ngaphansi. Isibonelo: - 10c - 5c = 5c - 20c - 10c =10c - amashumi aphelele - 20 -5c - 5c - 5c = 5c -ukususa ngokuphindelela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS UKUBALA EZIMWENI EZIKHULULEKILE 1.12 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Yimuphi umehluko kuThemu 2? alandelayo uma wenza alandelayo uma wenza Amasu (izindlela izibalo: izibalo: EThemu 2, abafundi baqala ukubala kufinyelela e-10.Ukusebenza phakathi noma amaqhinga) kwaloluhla lwezinombolo kusho ukuthi amasu okwenza izibalo angathuthukiswa • Izinsiza kufundisa • Izinsiza kufundisa enziwe ngokuphindelela. eziphathekayo Isib. eziphathekayo Isib. izinto zokubala izinto zokubala Lamaqhinga angeziwa ngokuphindelela kwingxenye yezinkinga zezinombolo. • Dweba izithombe • Ukwakha nokuhlakaza Ukwakha nokuhlakaza izinombolo izinombolo. Imisebenzi yokwakha nokuhlakaza kuthuthukisela phambili ulwazi lwabafundi • Ukwakha nokuhlakaza izinombolo. • Ukuphinda kabili lobungako bezinombolo ezisondelene. Lemisebenzi yenza isisekelo sokufundwa nokuhlukanisa kabili kwezibalo. Ukuhlakaza nokwakha izinombolo kusiza ukwenza izibalo zibelula. • Ukuphinda kabili Ukwenza ngokuphindelela kuloluhlobo lwemisebenzi kugqugquzela abafundi ngokulingana nokuhlukanisa kabili ukukusebenzisa njengeqhinga kufunda izibalo. ngokulingana • Umugqa wezinombolo wesekwa izinsiza ku- Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo • Umugqa wezinombolo fundisa eziphathekayo Ngaphambi kokusetshenziswa kokuphinda kabili nokuhlukanisa kabili Isib.ubuhlalu bokubala ngokulingana njengeqhinga lokwenza izibalo kufanele kuqondwe futhi kwenziwe ngokuphindelela kuqala. • Sebenzisa izinsiza kufundisa eziphathekayo. Lokhu kungenziwa ngokunika imiyalelo eqondile.Yisho bese ukhombisa abafundi ukuthi kunenduku zokubala ezinhlanu nokuthi uzokwazi ukuziphinda kabili ngokubeka izinduku zokubala ezinhlanu ngaphezulu. • Qhubekela kokubhalwayo usebenzisa izithombe. • Abafundi banganikezwa imifanekiso yokuphinda kabili bangabuye bayikhom- bise ngezithombe. • Ukusebenzisa izinombolo Abafundi bangaqala ngokuqedela imisho njengo: • Phinda kabili oku- 1 kwenze... • Phinda kabili oku- 2 kwenze... • Phinda kabili oku- 3 kwenze... • Phinda kabili oku- 4 kwenze... 161 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 162 KWI THEMU 1 KONYAKA 1.12 Umugqa wezinombolo wesekwa izinsiza kufundisa eziphathekayo Amasu (izindlela Uma usebenzisa umugqa wezinombolo njengesu ukwenza izibalo, abafundi noma amaqhinga) kufanele babebeqale ngokusesebenzisa: • Ezinye ezinsiza kufundisa ezisemgqeni Isib. ubuhlalu bokubala • Umugqa wezinombolo ubale uya phambili ibuye uye emumva; kanye Izibalo IBANGA 1-3 • Nomugqa wezinombolo ukuze abeke abuye ahlele izinombolo ngokwendawo. Umugqa wezinombolo ohlelekile kufanele usetshenziswe uma abafundi behlanganisa noma besusa. Umugqa wezinombolo ohlelekile kufanele ukhombise zonke izinombolo okusetshenzwa ngazo. 1.13 Uhla lwezinombolo: 1 -20 Uhla lwezinombolo: 1 -10 Yimuphi umehluko eThemu 1? Ukuhlanganisa • Hlanganisa kufinyelela • Hlanganisa kufinyelela EThemu 2 uhla lwezinombolo luyakhula kusuka koku-5 kufinyelela e-10. nokususa ema-20 e-10 NgaleThemu abafundi bazoqala ukwazi: • Susa kusuka ema- 20 • Susa kusuka e- 10 • Ukuguquguqulwa kwezinombolo uhlanganisa (The commutative property of addition); kanye • Sebenzisa izimpawu • Sebenzisa izimpawu ezifanele (+, –, =, ) ezifanele (+, –, =, ) • Nobudlelwano phakathi kokuhlanganisa nokususa • Yenza uphindelela • Yenza uphindelela Ngaphambi kokwethula abafundi kwizimpawu zokuhlanganisa nokususa kufanele amabhondi ezinombolo amabhondi ezinombolo abafundi babe nolwazi olwanele: kufinyelela e-10 kufinyelela e-7 • Ukubala konke; • Ukubala uqhubeka kusukela kwinombolo enkulu kakhulu; • Ukusebenzisa nokuqonda ulimi lokuhlanganisa nokususa; • Nokuhlela nokuqhathanisa izinombolo. KuleThemu, abafundi baqhubeka nokukhulisa ukuqonda ukuhlanganisa nokususa. Ukuhlanganisa nokususa kusahlobene ngokuqinile nokubala. Ulwazi lokukodwa ngaphezulu nokubili ngaphansi lusasetshenziswa ngoba luhambisana nenombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola elandelayo uma kubalwa ngokulandelana.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.13 NgaleThemu abafundi basosebenzisa izimpawu ukubhala imisho yezinombolo njalo nangokuzethemba. Inqubekelaphambili ekusebenziseni izimpawu kufanele Ukuhlanganisa kusetshenziswe ngokukhulu ukucophelela. Kubalulekile ukuthi abafundi baqonde nokususa izincazelo ezahlukene ezihambisana nezimpawu. Abafundi kufanele bakwazi ukuqonda basebenzise amagama njengo: engeza, hlanganisa, sekukonke, konke, susa, okuhlukile phakathi, nokususa ngaphambi kophawu ayethulwa kubafundi. Abafundi kufanele baqale bakwazi ukuphendula imibuzo efana njengo: oku-3 noku-2; oku-5 uthathe oku-3; ngaphambi kokusebenzisa uphawu. Ukubhala phansi imifanekiso Ukwenza izibalo kufinyelela e-10 kusho ukuthi abafundi basazibhala phansi izibalo zabo besebenzisa: • Imidwebo noma izinsiza kufundisa eziphathekayo; • Izithombe kanye nezinombolo; noma • Izinombolo kuphela. Ngasekupheleni kweThemu ngaphakathi kohla lwezinombolo oku-1 kufinyelela koku-5 abafundi kufanele babenokuzethemba ekusebenziseni izinombolo kuphela bengadwebi izithombe ukumela izibalo zabo. Amaqhinga okwenza izibalo uma uhlanganisa noma ususa Ukuhlanganisa ngokubala konke. Abafundi bazoqala koku-1 babale kufinyelela koku-5 baqhubeke bebala kufinyelela kokuyi-7. ukuhlanganisa ubala uqhubeka. 5 Abafundi bazobala kusukela koku-5 kufinyelela kokuyi-7 Lelisu lisebenza kangcono kakhulu kunokubala uqhubeka ngokukodwa. Abafundi bazosebenzisa lelisu kakhulu uma uhla lwezinombolo zokubala lukhula. 163 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 164 KWI THEMU 1 KONYAKA 1.13 Bala uqhubeka kusukela kwinombolo enkulu kakhulu. Ukuhlanganisa 6 nokususa Abafundi babala beqhubeka kusukela kwinombolo enkulu kakhulu oku-6 babale beqhubeka kufinyelela esi-8 Izibalo IBANGA 1-3 Benza ukususa ngokukhipha okunye 7-3=   7- 3 = 4 Uma bebhala phansi izibalo zokususa abafundi bangadweba umugqa phezu komfanekiso ukukhombisa ukususa. Susa ngokubala uqhubeka 6–2= Abafundi bangabala beqhubeka kusukela koku-2 kufinyelela kokuyi-6. Kufanele baqaphele ukuthi zingaki izinombolo abazibalile kusuka koku-2 kufinyelela kokuyi-6. Susa ngokubala uya emuva 8–2= Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi bangaqala kwizinombolo ezinkulu kakhulu okungoku-8, babale beya emuva ngezinyathelo ezi-2 kufinyelela kokuyi-6.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.13 Ukwakha nokuhlakaza izinombolo Ukuhlanganisa Lokhu kungenziwa ngezindlela ezinhlobonhlobo. nokususa 7=4+3   7=4+3 Amabhondi ezinombolo NgaleThemu abafundi benza ngokuphinda amabhondi ezinombolo kufinyelela kokuyi-7. Lokhu kungethulwa ngezithombe nemisho yezinombolo kusetshenziswa izinhlobonhlobo zemifanekiso. 165 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 166 KWI THEMU 1 KONYAKA 1.13 Ukuhlanganisa Ukuhlanganisa Isibonelo: nokususa ukwenza okuyi-6 noma uthole abangane abayi-6 usebenzisa izithombe nezinombolo   Izibalo IBANGA 1-3 Isibonelo  1   noku   kwenza   6   Isibonelo  2   noku   kwenza   6   Isibonelo  3   noku   kwenza   6   Ukwenza okuyi- 6 usebenzisa izithombe nezinombolo Faka umbala ukukhombisa okuyisi-6 ngezindlela ezihlukene.   Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola __________ noku ________ kwenza 6

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.13 Sebenzisa izinombolo kuphela Ukuhlanganisa Qondanisa izinomblo ezihamba ngambili ukwenza okuyi- 6: nokususa   1 2 3 4 5 5 4 3 2 1 Ukushintsha izikhundla zezinombolo Ngalethemu abafundi bazoqala ukubona ukusebenza ngezinombolo ngendlela yokushintsha izikhundla behlanganisa ngaphandle kokuthi bazi igama ukubizwa ngalo lelohlelo. Isibonelo: Bala onxantathu   6+2=   2+6= Ukubhala okuhlobene nokuhlanganisa nokususa imisho yezinombolo - ukuqonda ubudlelwane phakathi kokuhlanganisa nokususa. KuleThemu abafundi bafunda ukuthi bangabhala umugqa wezinombolo wokususa nokuhlanganisa. Isibonelo:   4+2=6 noku 6 – 2 = 4 167 2+4=6 noku 6 – 4 = 2 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 168 KWI THEMU 1 KONYAKA 1.13 Uphawu lokulinganisa Ukuhlanganisa Uphawu lokulinganisa akufanele lwethulwe / lufundiswe masishane. nokususa Kungaba usizo ukusebenzisa izimpawu ngendlela ekhululekile bese unika abafundi ithuba lokusebenzisa imicibisholo endaweni yophawu lokulinganisa. Isibonelo: Izibalo IBANGA 1-3 kukonke kwenza 4 noku 2 →   6   Ukusebenzisa umugqa wezinombolo Yethula / fundisa ukususa kufinyelela e-10 emugqa wezinombolo. Uthisha usebenzisa umugqa wezinombolo ukususa izinombolo kufinyelela e-10 Isib. 5 – 2 = Isibonelo: unogwaja ugxuma kuya ku-5, waphinde wagxuma izinombolo ezimbili ukuya emumva wabe esema koku-3. Ngakhoke oku 5 – 2 = 3 Umsebenzi obhaliwe Abafundi kufanele banikwe izinhlobonhlobo zemifanekiso ukubasiza ukuqonda ukuhlanganisa nokususa. Badinga ukwenza umsebenzi obhaliwe obuza ngokucacile: • Ukubala beqhubeka; Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukuhlanganisa ngokubala beqhubeka kusukela kwinombolo enkulu; noma • Ukususa ngokudweba umugqa phezu komfanekiso ukukhombisa ukususa

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.13 Ulwazi lokuphinda kabili Ukuhlanganisa Uhla lwezinombolo abafundi abasebenza ngalo lubavumela ukuthi baqale nokususa ukuphinda kabili. Lokhu kungethulwa ngezindlela eziningi futhi kungenziwa uma abafundi bebala izinto. Isibonelo:abafundi bangenza amaqoqo ezinto zokubala ezi-2, ezi-4, eziyisi-6, 8,10. Imisho yezinombolo kufanele ihambisane nemifanekiso.   Phinda kabili Phinda kabili Phinda kabili oku 1…… oku 2…… oku 3…… Phinda kabili Phinda kabili oku 4…… oku 5…… 169 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 170 KWI THEMU 1 KONYAKA 1.14 • Ukuhlanganisa • Ukuhlanganisa Yimuphi umehluko eThemu 1? okuphindayo okuphindayo Ukuhlanganisa EThemu 2 abafundi baqala ukwenza ukuhlanganisa okuphindayo kufinyelela (i.e.izinombolo (i.e.izinombolo okuphindayo e-10. ezifanayo) kufinyelela ezifanayo) kufinyelela okuholela ema- 20 e-10 Uma abafundi sebenolwazi oluqinile lwezinombolo 1 kufinyelela esi-5, ekuphindaphindeni ukuhlanganisa uphindayo kuzokwenza umqondo kubafundi. • Sebenzisa izimpawu • Sebenzisa izimpawu Izibalo IBANGA 1-3 ezifanele (+, –, =, ) ezifanele (+, –, =, ) Ukuhlanganisa okuphindayo kufanele kwethulwe kubafundi ngamaqoqo ezinombolo ezilinganayo. Ukusebenza ngezinto ezingamaqoqo kubalulekile ukwazi ukuphindaphinda. Abafundi kufanele bakwazi uku: • Ukwenza amaqoqo ezinto ezilinganayo; • Chaza ukuhleleka; bese • ubala inani eliphelele lezinto. Okokuqala abafundi bazobala ngakunye uma sebebala ngokukhulleka beqa izinomboli kufanele babale izinto ezihlelwe ngakubili, ngakuhlanu, noma ngamashumi. Abafundi kufanele bavezelwe izinhlobo eziningi zemifanekiso ehlukile ukubasiza baqonde ukuhlanganisa bephindayo. Kungaba usizo ukwethula izithombe kubafundi zansukuzonke zezinto eziqoqelwe ndawonye ezilinganayo.Isib. • Amaqoqo oku-2: izandla, amasokisi, izicathulo, amehlo,izinyawo, amasondo ebhayisikili. • Amaqoqo oku-3: amasondo ebhayisikili elinamasondo amathathu, unqen- qema kunxantathu. isibonelo: Mangaki amasondo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola esewonke?

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA KWI THEMU 1 KONYAKA CAPS 1.14 Mingaki iminwe? Ukuhlanganisa Qedela lomusho okuphindayo wezinombolo ongenzansi. okuholela  +  +  = 15 ekuphindaphindeni Ukubhala phansi iukubhala phansi imifanekiso yokuhlanganisa okuphindayo kugxilwa ekuthuthukiseni ulimi ukulekelela ulwazi lokuphindaphinda. Abafundi bazobhala phansi ulwazi lwabo besebenzisa izithombe. Abafundi kufanele banikwe izithombe zezinto eziqoqiwe badwebe izindilinga bazizungeze ukukhombisa amaqoqo ezinto.   Ulimi olungasetshenziswa lungathi amaqoqo ama 2 oku 3. Uma abafundi sebenokuzethemba lapho bechaza kumelwe ngezithombe besebenzisa ulimi sebengakwazi kuchaza lokhu ngomusho wezinombolo. Umusho wezinombolo: 3 + 3 = 6 171 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA NGOKUPHELA 172 KWI THEMU 1 KONYAKA 1.16 Ulwazi lwezinombolo: Ulwazi lwezinombolo: Yimuphi umehluko kuThemu 1? Uhla- 20 Uhla- 10 Izibalo zekhanda Kuthemu 2 uhla lwezinombolo luyakhula kusukela koku-5 kuya e-10. • Hlela uhla lweziombolo • Hlela uhla lweziombolo Izibonelo zemibuzo kanye nemisebenzi engabuzwa nengenziwa: ezikhethiwe ezikhethiwe ozinikezwe. ozinikezwe. • Qala koku-3 ubale uya phambili ngokukodwa kufinyelela e-10. • Qhathanisa izinombolo • Qhathanisa izinombolo • Yikuphi okuncane oku- 8 noma oku-5? Izibalo IBANGA 1-3 kufinyelela e-20 kufinyelela e-10 • Yikuphi okuningi oku- 8 noma oku- 4? usho ukuthi iyiphi usho ukuthi iyiphi engaphezulu noma engaphezulu noma • Yikuphi okuncane oku- 2 noma oku 9? ngaphansi ngoku - 1, 2 ngaphansi ngo - 1, no ne-10. ku 2. • Yikuphi okungaphezulu ngoku- 2 koku 3? Ukukhumbula • Nginike inombolo ephakathi koku-1 noku- 3. ngokushesha: • Nginike inombolo ephakathi kokuyi -6 nokuyi -10. • Amabhondi • Nginike inombolo ephakathi koku 6 ne 10. Ngabe iyodwa yini inombolo? ezinombolo kufinyelela e- 10 • Beka lamakhadi ezinombolo ngokulandelana kusukela enombolweni encane kakhulu kuya kwenkulu kakhulu. • Khumbula amaphuzu okuhlanganisa nokususa kufinyelela e- 10 Amqhinga okubala ngekhanda Sebenzisa amaqhinga okwenza izibalo zokuhlanganisa nokususa ngendlela eyiyo: • Beka inombolo enkulu kuqala ukuze babale Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola beqhubeka noma beya emumva. • Umugqa wezinombolo • Ukuphinda kabili nokuhlukanisa kabili kulingane • Ukwakha nokuhlakaza izinombolo

ITHEMU YESI- 2 YEBANGA LOKU 1 2. AMAPHETHINI, UBUDLELWANE, KANYE NE-ALJIBHRA UMQONDO KANYE UMQONDO CAPS NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 2.1 Kopisha, uqhubeke Kopisha, uqhubeke Ukukopisha amaphethini kusiza abafundi ukubona indlela yokuthi iphethini Isifundo esi-1 bese uchaza bese uchaza yenziwe kanjani. Amaphethini okusejiyometri Kopisha, uqhubeke bese Kopisha, uqhubeke bese Ukuqhubeka nephethini kusiza abafundi ukubheka ukuthi bayiqonda kahle uchaza uchaza indlela iphethini eyenziwe ngayo. ngamagama ngamagama Ukuchaza iphethini kusiza abafundi ukuthuthukisa amakhono abo olimi kanye nokukhuluma. Kuyakusiza ukubona indlela abafundi abahumushe ngayo • Amaphethini alula • Amaphethini alula iphethini. enziwe ngezinto enziwe ngezinto eziphathekayo. eziphathekayo. EBangeni 1 abafundi bangagxila kumaphethini lapho izinto noma amaqoqo ezinto eziphindwe ngendlela efanayo. • Amaphethini alula • Amaphethini alula enziwe ngemidwebo enziwe ngemidwebo NgeThemu ye-2 abafundi abaningi sebesebenzisa ngokukhululeka amakrayoni yemigqa, izimo noma yemigqa, izimo noma noma ipeni lomsizi ukudweba. Abafundi bangaqhubekela phambili ukukopisha izinto izinto nokuqhubeka namaphethini enziwe ngezithombe esikhundleni sezinto eziphathekayo. Kufanele bagxile ekuchazeni amaphethini. Akulula kubafundi Akha amaphethini akho Akha amaphethini akho ukuchaza iphethini. Ungabasiza bafunde okulindeleke bakhulume ngako Akha amaphethini Akha amaphethini ngokubuza imibuzo efana no: okusejiyometri okusejiyometri “Yiziphi izimo ozibonayo kulephethini?” • Ngezinto • Ngezinto “Ziwumbala ofanayo zonke yini?” eziphathekayo eziphathekayo “Ubona isimo esisodwa noma ngaphezulu kwiphethini?” • Ngokudweba imigqa, • Ngokudweba imigqa, izimo noma izinto izimo noma izinto “Ingabe zonke izinto zibheke endaweni efanayo?” Amaphethini “Ngabe kunenombolo efanayo yezinto kwiqoqo ngalinye?” asizungezile “Zingaki izinto kwiqoqo ngalinye?” Khomba, chaza “Ingabe zonke izimo zinkulu ngokulinganayo?” njll. ngamagama bese nikopisha amaphethini EThemu ye-2 okunye okungagxilwa ekusebenziseni izimo zokunhlangothi okusejiyometri mbili nezinto zokunhlangothi ntathu abafundi abafunde ngakho eThemu yo-1. Abafundi bangenza izimo ezinhlangothimbili ngokusika iphepha noma ikhadi, • kwimvelo noma bangakudweba. Bangenza amaphethini ngamabhokisi noma amabhola • kusuka kwimpilo abawenze ngobumba noma inhlama. yesimanje, Amaphethini angenziwa ngokusebenzisa isimo esisodwa kepha umbala wento • kusuka emasikweni ushintshe njalo.Isib. 173 ayigugu Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 174 KUPHELA UNYAKA NGETHEMU YE-2 2.1 Kuyasiza eBangeni 1 ukusiza abafundi babone ukuthi iliphi iqoqo eliphindayo, ngokubeka iqoqo ngalinye ephepheni lalo, noma ukukhombise ebhulokini lalo Amaphethini ekhasini. okusejiyometri Amaphethini angenziwa ngamaqoqo afana nse aphindayo, lapho iqoqo ngalinye linohlobo olulodwa lwezinto kepha isikhundla sezinto siyashintsha, amaqoqo afana nse ayaphinda.Isib. Izibalo IBANGA 1-3   Kwamanye amaphethini kusetshenziswa izinto ezihlukene ukwenza iqoqo, kepha amaqoqo ezinto aphindwe ngendlela efanayo.Isib.   Kwamanye amaphethini ubungako bezinto eqoqweni buyashintsha, kepha amaqoqo aphindwe ngendlela efanayo.   Abafundi bangenza amaphethini ngokutshu0tsha ubuhlalu, amaphethini angabuye enziwe kwisifundo samakhono empilo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 2.2 Kopisha, uqhubeke Ukulandelana Ukulandelana kwezinombolo kungahlanganiswa nokubala. Uma amakhono bese uchaza kwezinombolo kufanele abafundi okubala esintsha futhi ethuthuka, izinhlobo zezinombolo ezilandelanayo Amaphethini kukhombise ukubala uya abafundi abasebenza ngazo zingathuthuka. ezinombolo Kopisha, uqhubeke bese phambili nokubala uya uchaza Ukulandelana kwezinombolo kufanele kukhombise ukubala uya phambili emumva kanye: nokubala uya emumva kanye: izinombolo ezilula • Ngaku 1 usuka ngokulandelanisa • Ngakunye usuka kunoma iyiphi inombolo phakathi kuka 1 no 50 kunoma iyiphi okungenani ufike ku- 100 inombolo phakathi • Ngamashumi kusuka kunoma iyiphi inombolo ephakathi,kuka 0 kuya ku 50 kuka 1 no 50 • Ngakuhlanu kusukela kunoma iyiphi inombolo ephakathi kuka 0 kuya ku 50 Uya phambili: • Ngakubili kusukela kunoma iyiphi inombolo ephakathi kuka o kuya ku 20 • Ngama 10 kusuka Uma abafundi bebala bephimisa bangakhonjiswa ukulandelana kwezinombolo kunoma iyiphi inombolo okubhalwe phansi ngezindlela ezihlukile. Bangakhomba inombolo ebalwayo.Isib. ephakathi,kuka 0 kuya ku 50 1 2 3 4 5 6 7 8 9 10 • Ngaku 5 kusukela 11 12 13 14 15 16 17 18 19 20 kunoma iyiphi inombolo ephakathi Abafundi sebengagcwalisa izinombolo ezishiyiwe ku noma iyiphi indlela kuka 0 kuya ku 50 yokulandelana engenhla. • Ngaku 2 kusukela Khumbula abafundi babhala izimpawu zezinombolo kuphela kufinyelela e-10. kunoma iyiphi Abafundi bangagcwalisa izinombolo ezishiyiwe ngokulandelana ukwedlula e-10 inombolo ephakathi uma: kuka o kuya ku 20 • Bekwenza bekhuluma / bephimisa; Akha amaphethini akho Akha amaphethini akho • Banikwa amakhadi ezinombolo ukuba bawafake ezikhaleni; noma Akha amaphethini akho Akha amaphethini akho ezinombolo. ezinombolo • Banikezwa uhla lwezimpawu zezinombolo. Abafundi bangadweba umugqa besusela kwinombolo ekhethiwe iye kwisikhundla okufanele kusona. Ezinye izibonelo ozinekeziwe: Umugqa wezinombolo onezinombolo ezeqiwe   30   31   32   34   36   38   40   41   43   46   47   48   50   Ukulandelana okukhombisa ukubala uya phambili nasemumva ngokukodwa ezinye izinombolo zishiyiwe. 175 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 176 KUPHELA UNYAKA NGETHEMU YE-2 2.2 Abafundi baqondanisa izinombolo kuhla abalunikiwe. Badweba umugqa Izifundo ezi-3 ukukhombisa lapho inombolo ekhethiwe izofakwa khona. Amaphethini ezinombolo 40, 41, 42, __, 44; __, __, 47, ___, 49, 50. 50, 49, 48, __, __, 45, 44, ___, ____, 41, 40 Okubhalwe ngolulandelana kuya phambili ngokuphindaphinda okushiwo ngenhla Izibalo IBANGA 1-3 ezinye izinombolo zeqiwe Umugqa wezinombolo okhombisa ukuqala kwezikhawu, abafundi bagcwalisa ezinye.   0   2   4   6   8   Igridi yezinombolo ezibalwa ngoklandelana ezinye zivaliwe noma ezeqiwe. 1 3 5 7 9 11 13 15 17 19 Abafundi bangafaka umbala noma bamboze izinombolo lapho bebala ngokweqa. Uma kuphela iThemu uhla lwezinombolo luyakhuphuka kufinyelela ema-50. Abafundi bangasebenza ngokulandelanisa okuphelele 1-50 noma ngezingxenye zokulandelanisa. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YE - 2 YEBANGA LOKU - 1 3. INDAWO NESIMO(IJIYOMETRI) UMQONDO ISIKHATHI CAPS UMQONDO KANYE NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 3.1. ULimi oluchaza ukuthi ULimi oluchaza ukuthi into ikusiphi isikhundla olwathuthukiswa eThemu into ikusiphi isikhundla yokuqala kufanele lwenziwe njalo ngesikhathi sokufundiswa kwekilasi lonke Isikhundla, nangesikhathi sokufunda ngokugxila kumaqoqo kuze kuphele iThemu; chitha ukubonisa kanye Chaza isikhundla izikhashana nenza lolulimi lwesikhundla. nendlela into sento ngayinye ukuthi ebukeka ngayo ikuphi kunenye, isib. Umsebenzi woLimi lwesikhundla ungaphethwa ngmsebenzi wokubhala ngaphezulu kwe-, njengokudweba, ukufaka umbala noma ukuqondanisa imidwebo namagama. ngaphambi kwe- Lokhu kungenziwa ngesikhathi sokusebenza ngokuzimela. , ngemuva kwe, Olunye uLimi lwesikhundla lungasetshenziswa uma abafundi besebenza ngakwesonxele, ngezimo ezinhlangothimbili. (2-D) ngakwesokudla, phezulu, phansi, eduze kwe- Isikhundla nendlela into ebukeka ngayo Qondanisa izindlela ezahlukene into efanayo yansuku zonke ebukeka ngayo. Isikhundla kanye nezinkomba Landela izinkomba ukunyakaza ekilasini. Landela imiyalelo ukubeka into ngayinye ngokuhlobana nokunye., isib. faka ipensela ebhokisini. 177 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 178 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 3.2 Bona bese usho izinto Abafundi bangaqhubeka bakhe izinto besebenzisa izinto esezike zasebenza ezinhlangothintathu noma amabhuloki noma amabhokisi kamentshisi noma izinto zokwakha Izinto ezisekilasini kanye ngesikhathi sokusebenza ngokuzimela. ezinhlangothintathu nasezithombeni (3-D) • okuyimbulunga (spheres) Izibalo IBANGA 1-3 • iprizimu (prisms) Izimpawu zezinto chaza, hlela bese uqhathanisa izimo ezinhlangothintathu ngo- • bungako • ngombala • izinto ezigingqikayo • izinto ezishelelayo Imisebenzi okugxilwa kuyo Buka bese wakha izinto ezinhlangothintathu usebenzisa izinto eziphathekayo ezifana namabhuloki, izinto esezike zasebenza, izinto zokwakha. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 3.3 Uhla lwezimo Uhla lwezimo Umsebenzi omningi wezimo oseBangeni lokuqala wenziwa ngezinto Izifundo - 3 eziphathekayo. Wonke umsebenzi kumele uphethwe ngokwenza imisebenzi Izimo Bona bese usho izimo Bona bese usho izimo ebhalwayo. ezinhlangothimbili ezinhlangothimbili ezinhlangothimbili (2-D) Abafundi baqala ngokudlala bekhululekile ngezimo ezahlukene, kufaka ukwenza • izindilinga • izindilinga izithombe ezenziwe ngezimo ezisejiyometri. Lokhu kungenziwa nagesikhathi • onxantathu • onxantathu sezifundo zamakhono empilo. • izikwele • izikwele Abafundi bakopisha izithombe ezenziwe ngezimo ezisejiyometri. Lezizithombe zingavela kuthisha noma encwadini. Lokhu kwenza abafundi babone izindilinga Izimpawu zezinto Izimpawu zezinto nezikwele ezinobungako obehlukene, izikwele nonxantathu abasezikhundleni Chaza, hlela, bese Chaza, hlela, bese ezahlukene, kanye nonxantathu abanezimo ezahlukene. Lokhu kungenziwa uqhathanisa izimo uqhathanisa izimo ngesikhathi sokusebenza ngokuzimela. ezinhlangothimbili ngo: ezinhlangothimbili ngo: Lokhu kungenziwa nagesikhathi sezifundo zamakhono empilo. • bungako • bungako Ukuqhathanisa nokuchaza izimo ezinhlangothimbili: ubungako • ngombala • ngombala Abafundi baqhathanisa ubungako bezimo ezifanayo, isib. • ngezimo • ngezimo • hlela izindilinga kusukela kwencane kahkulu kuya kwenkulu kakhulu;bese • izinhlangothi eziqondile • izinhlangothi • ufaka zonke izikwele noma okulinanayo ndawonye. eziqondile • amacala ayindilinga Sebenzisa uLimi oluchaza ubungako ukuqhathanisa izimo ezahlukene, isib. • amacala ayindilinga “Ngidwebe unxantathu phakathi esikweleni, ngakhoke unxantathu mncane kunesikwele”. Ukuchazwa izimo ezinhlangothimbili: umbala Abafundi bakhuluma ngemibala yezimo bese behlela izimo ngokwemibala yazo. Ukukhomba bese usho izinto nemibala yazo, kanye nokuqhathanisa ubungako bezinto kungenziwa ngesikhathi kwenziwa amaphethini. Ukubona bese usho izindilinga, onxantathu nezikwele Abafundi kufanele basebenze ngezindilinga nezikwele ezinobungako obehlukene, kanye nonxantathu abame ngezindlela ezingafani. Kubalulekile ukuthi abafundi bangaboni kuphela isibonelo esisodwa sesimo. Amasethi amaningi athengiswayo ezimo anikeza isibonelo esisodwa vo sikanxantathu. Abafundi kufanele bakwazi ukubona: 179 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 180 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 3.3 • Onxantathu abame ngezindlela ezahlukene babuye babheke ezindaweni ezahlukene. Abanye onxantathu bafaka laba abalandelayo: Izimo ezinhlangothimbili   (2-D) Izibalo IBANGA 1-3 • Izikwele zobungako abehlukene zibekwe ezindaweni ezahlukene. Lezi ngezinye zezikwele:   • Izindilinga zobungako obehlukene: Kuyasiza ukuthi abafundi basebenze ngezimo zemifanekiso esezisikiwe. Lokhu kuvumela abafundi ukuthi babone onxantathu abehlukene nezikwele ezibekwe kwizikhundla ezahlukene. Abafundi bahlela izimo ngokuma kwazo, njengokuthi: zinamacala ayindilinga noma aqondile. Abafundi bahlela baqoqele ndawonye izimo ngokuma kwazo: izikwele ndawonye, ngonxantathu, izindilinga izikwele, njll. Umsebenzi uphethwa ngokuthi babhale. Lemisebenzi ingafaka umsebenzi wokufaka umbala, ukuqondanisa amagama nezimo njll. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI - 2 YEBANGA LOKU-1 4. ISILINGANISO UMQONDO ISIKHATHI CAPS UMQONDO KANYE NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.1 Ukudlula kwesikhathi Abafundi kufanele bafunde ukukhuluma ngalokhu: Isikhathi Khuluma ngokudlula • Ukulandelana kwezigameko kwesikhathi • Ubude besikhathi • Hlela izigameko Abafundi baqhubeka nokufunda izindlela zokukhuluma ngesikhathi nsukuzonke ezivamile empilweni ngesikhathi sokufundiswa kwekilasi lonke noma iqembu okugxilwe kulo. yabo (abafundi) Abafundi bakhuluma babuye baphendule imibuzo uma kwenzeka izinto • Qhathanisa ubude besebenzisa ulimi njengokuthi: ekuseni, ntambama, ebusuku. besikhathi usebenzisa ulimi, isib. okude Abafundi balandelanisa izigameko besebenzisa ulimi njengokuthi: izolo, namuhla, ngokuthe xaxa, kusasa, izinsuku zesonto kanye nezinynga zonyaka. okushesha ngokuthe Abafundi baqhathanisa ubude besikhathi besebenzisa ulimi njengokuthi: esikhathi xaxa, kuhamba eside ngokuthe xaxa, esifushane ngokuthe xaxa, nesishesha ngokuthe xaxa, kancane esihamba kancanyana. • Hlela izigameko Abafundi bakhuluma ngokuhlelwa kwezigameko ezenzeka empilweni yabo. usebenzisa ulimi Babuye bahlele izithombe ngokulandelana kwazo njengokuhti: njengokuthi: izolo, namuhla, kusasa • Izindlela zokwenza itiye; Ukusho isikhathi • Izithombe ezikhombisa ukukhula kwengane ize ibe ndala; • Sebenzisa ulimi • Ukukhula kwesilwane; ukuchaza isikhathi uma into yenzeka, isib. • Izigameko ezejwale ukwenzeka ngosuku (ukuvuka, ukuba sesikoleni, ukudlala, ekuseni, ntambama, ukudla isidlo santambama, ukulala). ebusuku, ngaphambi Abafundi bayaqhubeka bakhombise izinsuku zabo zokuzalwa kwikhalenda kwesikhathi, unyaka wonke. ngemumva kwesikhathi • Ukukwazi izinsuku zesonto • Ukwazi izinyanga zonyaka • Ukufaka izinsuku 181 zabo zokuzalwa kwikhalenda Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 182 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.2 Ukukala Ubude okungahlelekile • Qhathanisa bese uhlela ubude, ukuphakama, noma ububanzi bezinto Izibalo IBANGA 1-3 ezimbili nangaphezulu ngokuzibeka eduze kwezinye Zonke izilinganiso eBangeni 1 azihlelekile. Asikho isikali sobude esinesilinganiso • Sebenzisa ulimi esenziwayo. ukukhuluma EThemu yokuqala, isiphakamiso wukuthi abafundi kumele bagxile kulokhu: ngokuqhathanisa, isib. okude ngokuthe xaxa, • Ukuqhathanisa okuqondile kwezinto ngokuzibeka eduze kwenye; okufishane kakhulu, • Ukuhlela nokuqhathanisa ubude noma ukuphakama kwezinto ezintathu okude kakhulu, nangaphezulu, ngokubeka izinto ezihamba ngazimbili eduze kwenye kuze kube okubanzi ngokuthe zonke izinto sezilandelaniswe kahle; kanye xaxa • Ukuthuthukiswa kolimi ukuze kuxoxwe ngobude, ngokuphakama, ngobubanzi, • Qagela, linganisa, njll. qhathanisa, hlela, Ngesikhathi sokusebenza ngayedwa ithemu yonke, abafundi bangenza babuye bese ubhala phansi bahlanganise ukuhlela nokuqhathanisa ubude, ububanzi, bezinto ezihamba ubude bento ngantathu nangaphezulu nokubeka izinto ezihamba ngakubili eduze kwenye usebenzisa isikali ukuze zonke izinto zibekeke ngokulandelana. esingenasilinganiso, isib. izandla, izinto Wonke umsebenzi kufanele ubhalwe phansi. zokubala, njll. 4.3 ISILINGANISO okungahlelekile Zonke izilinganiso eBangeni 1 azihlelekile. Asikho isikali sobude esinesilinganiso Isisindo esenziwayo. • Qagela, linganisa, qhathanisa, hlela bese EThemu yokuqala, isiphakamiso wukuthi abafundi kumele bagxile kulokhu: ubhal phansi isisindo • Qhathanisa ngokuqondile isisndo sezinto; usebenzisa isikali • Ukuhlela nokuqhathanisa isisindo sezinto ezintathu nangaphezulu ngokuthi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola esingenasilinganiso abeke izinto ezihamba ngazimbili kuze kulingane nxazombili, kuze kuhlelke nokukala zonke izinto; ngokulinganisa • Ukuthuthukiswa kolimi ngokukhuluma ngokwehluna kwezisindo. • Sebenzisa ulimi ukukhuluma Ngesikhathi sokusebenza ngayedwa iThemu yonke, abafundi bangenza babuye ngokuqhathanisa, isib. bahlanganise ukuhlela nokuqhathanisa ubude, ububanzi, bezinto ezihamba kulula, kuyesinda, ngantathu nangaphezulu nokubeka izinto ezihamba ngakubili eduze kwenye kulula kakhulu, kusinda ukuze zonke izinto zibekeke ngokulandelana. kakhulu Wonke umsebenzi kufanele ubhalwe phansi.

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 4.4 Isilinganiso Isilinganiso Zonke izilinganiso eBangeni 1 azihlelekile. Asikho isikali sobude esinesilinganiso Izifundo 2 esingahlelekile esingahlelekile esenziwayo. Umthamo • Qhathanisa ubuye • Qhathanisa uhlele Isiphakamiso sokugxilwa kukho ngeThemu yoku - 1 kusekuthuthukisweni koLimi uhlele inani lomthamo inani lomthamo ngokuxoxa ngokuqhathanisa umthamo kwizitsha ezimbili osezitsheni ezimbili NgeThemu yei - 2, kugxilwa ekuqhathanisweni okuqondile. ezibekwe eduze ezibekwe ndawonye. kwesinye. Abafundi Abafundi bahlola NgeThemu yesi - 4 kugxilwa ekusebenzeni ngamaunithi angahlelekile baqinisekisa ngokuthi umthamo ngokuthi okulinganisa. Abafundi benza bahlanganise imiqondo ngesikhathi sokusebenza babuye bathele bathele esitsheni ngabodwa unyaka wonke. esitsheni sesithathu sesithathu uma Ukuqhathaniswa okuqondile komthamo osezitsheni uma kunesidingo kunesidingo • Ukuthuthukiswa kokuqonda umthamo kusetsheenziswa uLimi. • Qhathanisa ubuye • Qhathanisa uhlele uhlele inani lomthamo inani lomthamo Abafundi baqala ukucabanga nokukhuluma ngomthamo ngokuqhathanisa ongathathwa izitsha elingathathwa izitsha umthamo osezitsheni ezimbili (noma imidwebo yezitsha emibili efanayo). ezimbili ezigcwele ezimbili uma zigcwele Kugxilwa kulokhu: • Sebenzisa ukukhuluma • Sebenzisa uLimi - Kugcwele noma akunalutho; ngokuqhathanisa, isib. ukukhuluma okungaphezu kokunye, ngokuqhathanisa, isib. - Okungaphezu kwe / okungaphansi kwe-; okungaphansi okungaphezu kwe-, - Okufana ne-. kokunye, okugcwele, okugcwele okungenalutho Abafundi bagcwalisa babuye bathulule izitsha • Hlawumbisela, • Qqgela bese ulinganise, • Qhathanisa umthamo wokubili nokungaphezulu kwizitsha ezingafani ngokuthi ulinganisa, uqhathanise, uhlele bathele kwesesithathu isitsha. uqhathanisa ubuye ubhale phansi Uma abafundi sebengakhuluma ngemithamo (kugcwele, akunalutho njll), bese ubuye uhlele umthamo wezitsha beqhathanisa imithamo (ebonakalayo ukuthi ayifani uma uyibuka) esezitsheni umthamo wezitsha ngokusebenzisa isikali ezifanayo, bangaqhubeka baqhathanise umthamo osezitsheni ezimbili usebenzisa isikali esingenasilinganiso, ezingafani. Gxila ikakhulukazi ezitsheni ezibanzi neziwumtshumo, isib. esingenasilinganiso, isib. izinkomishi, izipuni isib. izipuni, izinkomishi - Gcwalisa ngokufanayo amabhodlela angamalitha amabili kanye nebhodlela elinguhhafu welitha; - Buza abafundi ukuthi yimaphi amabhodlela aphethe okuningi. Abafundi bahlola ngokuthi bathele uketshezi esitsheni sesithathu bese bebeka umaka. 183 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 184 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.4 Abafundi abancane esikhathini esiningi abakubheki ububanzi besitsha uma bephawula ngomthamo; esikhathini esiningi babheka ukuthi kugcwele Umthamo kangakanani. Abafundi kufanele banikezwe ulwazi olwanele ekuqhathaniseni umthamo ezitsheni ezinobubanzi obehlukene. Izibalo IBANGA 1-3 Ukubhala phansi Abafundi kufanele babhale phansi wonke umsebenzi abawenzile. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Ibanga 1 ITHEMU YESI - 2 5. UKUQOKELELWA KOLWAZI UMQONDO CAPS UMQONDO KANYE ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho KUPHELA UNYAKA enga - 24 isifundo) ngeThemu ye - 2 Ukusebenza ngezinto eziqoqiwe 5.1 Qoqa bese uhlela izinto Qoqa bese uhlela izinto Bheka amanothi kathemu 1 Isifundo 1 Qoqa bese uhlela Qoqa bese uhlela izinto Qoqa bese uhlela izinto NgeThemu yesi - 2 abafundi bayaqhubeka basebenze ngezinto eziqoqiwe izinto nsukuzonke nsukuzonke ngendlela efanayo kodwa usizo lube luncane. 5.2 Okumele iqoqo lezinto Okumele iqoqo lezinto Uma abafundi sebenikeziwe umhlahlandlela ngokuhlela nokumela okuqoqiwe eziqoqiwe eziqoqiwe ngesikhathi sokufunda ngamaqoqo. Okumele iqoqo lezinto eziqoqiwe Dweba isithombe sezinto Dweba isithombe sezinto Uma abafundi sebezilolongile ukuphendula imibuzo ngamaqoqo, sebengaqala eziqoqiwe. eziqoqiwe ukubuzwa nokuchazwa kwamaqoqo ezinto ngaphandle kokubanikeza izinkombandlela zemibuzo. 5.3 Xoxa ubuye ubike Xoxa ubuye ubike ngezinto eziqoqiwe ngezinto eziqoqiwe Xoxa ubuye ubike ngezinto eziqoqiwe • Nika izizathu zokuthi • Nika izizathu zokuthi okuqoqiwe kuhlelwe okuqoqiwe kuhlelwe kanjani kanjani. • Phendula imibuzo • Phendula imibuzo ngalokhu ngalokhu - Zihlelwe kanjani - Zihlelwe kanjani izinto izinto - Lokhu okuqoqiwe - Lokhu okuqoqiwe kubukeka kanjani kubukeka kanjani • Chaza ukuqoqeka • Chaza ukuqoqeka nokudwetshwa nokudwetshwa kwezinto. Chaza ukuthi kwezinto kuhlelwe kanjani Chaza ukuthi kuhlelwe kanjani Okuphakanyisiwe: ukusebenza ngokuqokelelwa nokuhlelwa kolwazi lwezibalo kugxilwa kukho ngeThemu yes - 3 neye - 4 185 Izibalo IBANGA 1-3

ITHEMU YESI - 3 YEBANGA LOKU-1 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANE BAZO 186 ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) UKUTHUTHUKISA ULWAZI LWEZINOMBOLO: Ukubala usebenzisa izinombolo eziphelele Izibalo IBANGA 1-3 1.1 Bala izinto eziphathekayo Bala izinto eziphathekayo Yimuphi umehluko ku-Themu 2? kuya ezingama-50 kuya ezingama-40 Bala izinto Kuthemu 3, abafundi bangeza uhla lokubala. Kusekhona ukubheka ngokuqonda eziphathekayo Qagela inani lezinto Qagela inani lezinto indlela emiselwe yokusenza kwenombolo nhloko. Ngalethemu abafundi kumele esingaziibala ngokuyikho. esingaziibala bafunde indlela yokubeka izinto eziphathekayo ngokulandelana uma bebala ngokuyikho. ukuze uma bebheka ukubala, amalungiselelo abasiza ekubaleni kakhulu kalula. Isibonelo, ukubala kubekwe emgqeni. Ngalethemu abafundi baqhubeka nokwengeza amakhono okubala nokufunda. • Ukubala konke • Ukuqhubeka nokubala • Indlela emiselwe yokusenza kwenombolo nhloko kanye • Ukusebnza ngethekisthi ebhaliwe. Ukuqagela inombolo eyakhe iqoqo Abafundi baqhubeka nokufunda nokubona iqoqo elincane lezinto. ukubala ngamaqembu Ukuze kusizwe abafundi ukubala ngezikhawu ezimbili, ezinhlanu nezi - 10, kudingeka bahlanganise izinto ngokubili, ngokuhlanu kanye nokuyi- 10 ukuze kubalwe iqoqo lezinto. Amakhadi ezinombolo kufanele abonise kuko konke Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola okuqoqiwe ukubonisa izinombolo zezinto ezibaliwe. Ukubala ngamaqembu kuzolungiseslela abafundi ekwazini ukuphindaphinda. Izinsiza: Qaphela ukubheka izinhlobo zezinsiza ezisetshenziswayo. • Izinsiza ezihlelekile, ubuhlalo bokubala obusentanjeni bungasetshenziswa. • I-abhakhasi ingasetshenziswa ukufunda ukubala ngeqembu leshumi. • Bangenza inyanda yokubili, inyanda yoku-5 kanye neyeshumi ngezinti zikamentshisi noma ngezingodo zokubala bese uzibala zonke.

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.2 Bala uyaphambili Bala uyaphambili Yimuphi umehluko ku-Themu 1? Bala uyaphambili ubuye uhlehle kanje ubuye uhlehle kanje Ku-Themu 3, abafundi babala ukufika ku-80 ubuye uhlehle • Ngakunye kusukela • Ngakunye kusukela Baqhubeka nokubala ngokuphindiwa oku-2, 5 noku- 10. kunoma iyiphi kunoma iyiphi Umsebenzi oqhubekayo: inombolo phakathi inombolo phakathi Umsebenzi wekilasi lonke kuka -0 kuya ku-100. kuka -0 kuya kuma 80. Bala uyaphambili ubuye uhlehle kuya kuma- 80 Bala uya phambili Bala uya phambili • Abafundi babala baye phambili babuye bahlehle. kanje: kanje: • Uthisha ukhomba izinombolo eziseshadini abafundi bebala kuya ku-70. • Ngama-10 kusuka • Ngama-10 kusuka • Abafundi babala ngokuhlanu kusuka kuma-25 kuya ku- 60. kunoma iyiphi kunoma iyiphi inombolo phakathi inombolo phakathi • Abafundi babala ngeshumi beya phambili kusoka ku- 0 kuya ku- 80. kuka -0 kuya kuma kuka -0 kuya kuma -80. Ukubala wenqa usebenza ngokuhlanu nangeshumi kuya kuma- 80. -100. • Ngaku -5 kusuka • Abafundi babala ngeshumi kuya kuma - 50 uthisha ekhomba ishadi lezinombolo. • Ngaku -5 kusuka kunoma iyiphi • Uthisha ukhomba ukuphindaphinda ngokuhlanu kushadi le - 100 abafundi kunoma iyiphi inombolo kuya kma -80 bebala. inombolo kuya kma • Ngaku -2 kusuka -100 • Abafundi babala baye phambili babuye bahlehle ngeshumi. kunoma iyiphi • Ngaku -2 kusuka inombolo kuya kuma Basebenzisa ishadi le -100, kumele basebenzise imiyalelo efanayo: kunoma iyiphi -80 • Ukubala ngeshumi uqale kuma-20. inombolo kuya kuma -100 • Ukubala uhlehle ngokukodwa kusuka kuma-56. • 80, 70, 60: shono izinombolo ezintathu ezilandelayo usebenzisa ishadi le-100. Ukusebenza ngokuzimela Amakhono okubala ngokwenqa kufanele asetshenziswe emsebenzini obhaliwe. Isibonelo: Abafundi bazobuka behambisa amehlo: • Beqedela uhla lwezinombolo ngokulandelana; kanye • Gcwalisa ngezinombolo ezishodayo emgqeni olandelanayo kanye nasemgqeni wezinombolo. • Bhala ezinye izinombolo ezimbili 66, 65, 64,__, __, 187 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 188 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.3 Ukufunda nokwazi Ukufunda nokwazi Yimuphi umehluko ku-Themu 2? izinombolo izinombolo Uphawu negama Ku-Themu 3, uhla lwezinombolo lukhulu kuya ku-80. Kulindeleke ukuthi lenombolo • Ukufunda nokwazi • Ukufunda nokwazi abafundi babhale izimpawu zezinombolo ukufika ku-20. Kudingeka ukuthi uphawu lwezinombolo uphawu lwezinombolo bakwazi ukwenza lokhu ngoba bazobala bafike kuma- 20 bese bebhala izibalo Izibalo IBANGA 1-3 kusuka ku-0 kuya kusuka ku-0 kuya eziwumugqa. Abafundi baqhubeka nokufunda nokubhala amagama ezinombolo. kwi-100. ku-80 Kumele bakwazi ukuqhathanisa izimpawu emagameni ezinombolo. Imisebenzi esencwadini yokusebenzela kanye nokubhalwa kwaseklasini - imisebenzi • Bhala izimpawu • Bhala izimpawu esencwadini ingenziwa ngesikhathi sokukhululeka. zezinombolo kusuka zezinombolo kusuka ku-0 kuya kwi-100 ku-0 kuya ku-80 Isibonelo somsebenzi obhaliwe: • Ukufunda nokwazi • Ukufunda nokwazi Qondanisa amagama ezintweni amagama ezinombolo amagama ezinombolo kusuka ku-1 kuya kusuka ku-1 kuya Kanye  kwi-10 kwi-10 Kubili     • Bhala amagama • Bhala amagama Kuthathu  ezinombolo kusuka ezinombolo kusuka ku-1 kuya kwi-10 ku-1 kuya kwi-10 Kune  Kuhlanu  Isithupha  Isikhombisa  Isishiyagalombili      Shumi  Yini okulindelekile kubafundi? • Ukuthi bangafunda izimpawu zezinombolo kuya ku-50 • Ukuthi bangabhala izimpawu zezinombolo kuya ku-20 • Ukuthi bangafunda amagama ezinombolo kuya ku-10 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukuthi bangabhala amagama ezinombolo kuya ku-10

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.4 Hlela uqhathanise Hlela uqhathanise Yimuphi umehluko ku-Themu 2? izinto izinto eziyi-15 Chaza, qhathanisa Ku-Themu 3, abafundi baqhubeka: bese uhlela • Qhathanisa amaqoqo • Qhathanisa amaqoqo ezinto ngobuningi ezinto ngobuningi / • Hlela uqhathanise ukuqoqwa kwezinto; izinombolo / okumbalwa; okumbalwa; ngokuningi • Hlela uqhathanise izinombolo; uphinde ngokuningi kuno; kuno; okuncane kuno; okuncane kuno; kuningi ngango, • Usebenzise ulimi lokuhlela nokuqhathanisa. kuningi ngango, okuhlukene Umsebenzi oqhubekayo: okuhlukene • Qoqa uhllele izinto Uthisha uzosho izinamba isibonelo: 12 • Qoqa uhllele ngokuningi kuya Uthisha uzobuza imibuzo: Iphi inamba emgqeni wezinombolo? izinto ngokuningi kokuncane nokuncane kuya kokuncane kuya kokuningi. Iyiphi inamba eza ngaphambi kwe-12? nokuncane kuya • Uhla kufinyelela Iyiphi inamba eza ngemuva kwe-12 kokuningi. ezintweni eziyi-15 i-12 likhulu ngoku-1 kune _________ • Uhla kufinyelela ezintweni eziyi-100 i-12 lincane ngoku-1 kune ________ Hlela uqhathanise Hlela uqhathanise izinamba izinamba ufike ku-15 • Hlela izinamba • Hlela izinamba - Kusukela - Kusukela kokuncane kokuncane kuya kuya kokukhulu; kokukhulu; kusuka kusuka kokukhulu kokukhulu kuya kuya kokuncane kokuncane - engaphambi li, - engaphambi li, engmuva, ephakathi engmuva, ephakathi nendawo nendawo - Usebenzisa umugqa - Usebenzisa wezinombolo ka 0 umugqa kuya kuoku -80 wezinombolo ka 0 kuya kuoku -100 189 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 190 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.4 • Qhathanisa • Qhathanisa izinombolo izinombolo ngokuthi ngokuthi inkulu kuna Chaza, qhathanisa inkulu kuna / incane / incane kuna ining bese uhlela kuna ining kuna / kuna / kumbalwa kuna; izinombolo kumbalwa kuna; kulingana na Izibalo IBANGA 1-3 kulingana na • Okukodwa nokukodwa • Okukodwa okuhambisanayo nokukodwa • Uhla lwezinombolo okuhambisanayo kufinyelela kweziyi-15 • Uhla lwezinombolo kufinyelela kweziyi-100 Sebenzisa izinombolo Sebenzisa izinombolo ezijwayelekile ezijwayelekile ukubonisa ukuhleleka, ukubonisa ukuhleleka, indawo noma indawo noma isikhundla isikhundla • Hlela izinto • Hlela izinto ngokulandelana ngokulandelana kusukela kusukela kweyokuqala kweyokuqala kuya kuya kweyeshumi, kweyeshumi. yokugcina (izinombolo ezilandelanayo). Hlela izinombolo ngokulandelana ukusuka kweyokuqala ukuya kweyeshumi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.5 Ukubona ubungako Ukubona ubungako Yimuphi umehluko ku-Themu 2? benani lezinombolo benani lezinombolo Ubungako benani Kuleli Themu abafundi baqala ukuhlukanisa izinombolo ngeshumi nangokukodwa ezimbili zedigithi -kuya ezimbili zedigithi -kuya lenombolo usebenzisa: ku-20. ku-15. • Amaqoqo ezinto eziyishumu • Hlukanisa izinombolo • Hlukanisa izinombolo ezingamadigithi ezingamadigithi • Indlela yokubhala 14 = 10 no 4. ahamba ngamabili ahamba ngamabili Ukuqonda okuphelele kobungakho benani kuthuthuka kudlulele eBangeni eliphan- ngeshumi ngeshumi si naseBangeni eliphakathi. Ku-Banga 1 abafundi baqala ukucabanga ngamaqo- nangokukodwa kuya nangokukodwa kuya qoq ezinto eziyishumu noma izinto ezingamaqoqoq. Baqala ukwenza ushintsho ku-20 Isib: i-12 yi-10 ku-15 Isi: i-12 yi-10 ekuboneni okuyishumi iqoqo elilodwa noma ishumi elilodwa. kanye no-2 kanye no-2 Ukuqala ukuqonda ubungakho benani kuleli - Themu, abafundi kudingeka: • Bazi amagama ezinombolo bazibale ngokulandelana ngokuzethemba okunge- nani kuya ku-20 • Bhala ufunde uphawu lwezinombolo, • Yenza ukubala nokususa okulula; • Ukubala izinto eziphathekayo ngokuzibeka ngamaqoqo, kanye • Ukwazi ukwethula ngamaqoqoqo. Ukuhlakaza izinombolo ngamashumi nangokukodwa ngamaqoqo Ku-Banga 1 kubhekwa ukwenza amaqoqo ezinto eziyishumi nokukodwa okusece- leni. Ngaphambi kokuhlakaza izinombolo ngamashumu nangokukodwa, abafundi kumele bazilungiselele ngokwanele ukuhlakaza izinombolo ngokuhlukana ku- Themu 1 no-2. Lokhu kumele kwenziwe nangendlela yokubhalwa. Sebenzisa izinsizakufunda eziphathekayo Izinto eziphathekayo zisebenza kangcono ukuqonda kwabo izinombolo, ukumela izinombolo nendlela okumele zisebenze ngayo nobungakho benani. Uma ubala ngamashumi uhlele amaqoqoqo ngamashumi, abafundi bazoqala ukuqonda ukuthi ukuphindaphinda kwe-10 kuholela olwazini lokubala isib: 26, 27, 28, 29, 30, 31. Kumele babenolwazi kuqala lokuthi amagama nezimpawu eziyi-10 zimele oku- kodwa. 191 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 192 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.5 Ukusebenza ngezinsizakufunda eziphathekayo ngokwamaqoqoqo ezinto ukwakha ngamashumi kokukodwa ukwazi ukuthi - 10 iqembu leshumi nokukodwa okuse- Ubungako benani celeni. Bonisa abafundi kalula amaqoqoq ngokweshumu batshelwe ukuthi u-14 lenombolo okuyishumi kanye no-4 nokukodwa okuseceleni. Amaqoqoqo ezinto eziseceleni enza amaqoqoqo okuyishumi okuletha umqondo. Izibalo IBANGA 1-3 Ukusebenzisa i-abacus, abafundi bakwazi: Ishumi elilodwa, ishumi elilodwa nemivo e-2, ishumi elilodwa nemivo e-3 ishumi elilodwa nemivo e-4 Lindela abafundi ukuthi babale umuvo ukwenza amaqoqoqo alishumi. Kwabaningi kuzoba yiyona ndlela yamagama ezinombolo noma uthi mangakhi. Kunezinduku eziyi-11. Abafundi bazokwakha inyanda yezinduku eyi-10 bese kusala induku eyodwa eceleni. Amabhulokhi angaxhunywa ukwakha umbhoshongo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ubungakho benani lamakhadi kungasetshenziswa ukubonisa okuyishumi noku- kodwa.

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.5 Baqhubekela kokubhalwayo Ubungako benani Izithombe ezizomela izinto eziyishumi nokuseceleni lenombolo Abafundi bangavezwa nezithombe ezivumela amaqoqoqo ayishumi nokuseceleni okusele. Isibonelo: Ekupheleni kwe-Themu abafundi kumele bakwazi ukubhala: 13 = 1 okuyishumu noku- 3 nokukodwa okusecelelni 13 = 10 noku- 3   Izinsiza ezinconywayo Izinto zingahlelwa ngamaqoqoqo: • Izinduku zokubala • Okubalwayo okubhekwayo • Izinti zikamentshisi • Izinti zika-ayisikhilimu • Amabhulokhi ahlanganayo • Ubuhlalu bokubala • Ama-abakhasi 193 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 194 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.6 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Yimuphi umehluko ku-Themu 2? alandelayo ukuxazulula alandelayo ukuxazulula Amaqhinga okuxa- Amaqhinga okubala uqhubeke nokuphindaphinda. izinkinga zezibalo bese izinkinga zezibalo bese zulula izinkinga Ukuphinda kabili nokuhlukanisa phakathi kokubili kungasetshenziswa kumaqhinga uchaza isisombululo uchaza isisombululo zezibalo okubala kule-Themu. Abafundi baqhubeke bephindaphinda kabili nokuhlukanisa kanje: kanje: Izibalo IBANGA 1-3 ezinkingeni zamagama ezimo ezijwayelekile ezimweni ezikhululekile. • Sebenzisa • Sebenzisa izinsizakufunda izinsizakufunda Ekuqcineni kwaleli-Themu abafundi baqala ukucazulula izinkinga zamagama basebenzisa lamaqhinga eziphathekayo eziphathekayo • Dweba noma izinsizakufunda • Sebenzisa izithombe • Sebenzisa izithombe ukubonisa izibalo ukubonisa izibalo • Ukwakha nokuhlakaza izinombolo eziyingxoxo eziyingxoxo • Phindaphinda kabili ubuye uhlukanise kabili • Ukwakha • Ukwakha nokuhlakaza nokuhlakaza izinombolo • Umugqa wezinombolo izinombolo Bheka amanothi e-Themu 2 • Phinda kabili ubuye • Phinda kabili ubuye uhlukanise kabili uhlukanise kabili • Sebenzisa umugqa • Sebenzisa umugqa wezinombolo owakhiwe ngezinto eziphathekayo 1.7 Uxazulula izinkinga Uxazulula izinkinga Yimuphi umehluko ku-Themu 2? zezibalo zamagama zezibalo zamagama Ukuhlanganisa Buka amanothi e-Themu 2 kodwa usebenze ngezinombolo kuya ku-15. nokususa ezisesimweni ezisesimweni esijwayelekile bese esijwayelekile bese uchaza isisombululo uchaza isisombululo esebenzisa esebenzisa ukuhlanganisa ukuhlanganisa nokususa nokususa ezibalweni ezibalweni ezinika ezinika umphumela umphumela ofika ku-15. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ofika ku-20.

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.8 Uxazulula izinkinga Uxazulula izinkinga Buka uThemu 2 isibonelo senkinga kodwa sebenza ngezinombolo kuya ku- 15. zezibalo zamagama zezibalo zamagama Ukuphindaphinda ezisesimweni ezisesimweni ukuhlanganisa esijwayelekile bese esijwayelekile bese okuzoholela uchaza isisombululo uchaza isisombululo ekuphindaphindeni esebenzisa esebenzisa ukuhlanganisa ukuhlanganisa nokususa nokususa ezibalweni ezibalweni ezinika ezinika umphumela umphumela ofika ku-15 ofika ku -20 1.9 Uxazulula izinkinga Uxazulula izinkinga Buka uThemu 2 isibonelo senkinga kodwa sebenza ngezinombolo kuya ku- 15 zezibalo zamagama zezibalo zamagama Ukwenza ezisesimweni esij- ezisesimweni esij- amaqoqo kanye wayelekile bese uchaza wayelekile bese uchaza nokuhlukaniselana isisombululo esebenzisa isisombululo esebenzisa okuholela ukuhlanganisa noku- ukuhlanganisa noku- ezibalweni susa ezibalweni ezinika susa ezibalweni ezinika zokuhlukanisa umphumela ofika ku-20 umphumela ofika ku-15 kanye nezimpendulo kanye nezimpendulo ezifaka izinsalela ezifaka izinsalela. 195 Izibalo IBANGA 1-3

ITHEMU YESI - 3 YEBANGA LOKU-1 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANE BAZO 196 ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) • Ukubona ukhombe • Ukubona ukhombe Inani - eliwuhlweza imali yaseNingizimu imali yaseNingizimu Izibalo IBANGA 1-3 Abafundi basebenza ngama- R1, R2, R5, R10 no R20 yephepha. Bahlanganisa Afrika Afrika ewuhlweza 5c, inani elifika ku-R20 ngokusebenzisa umdlalo wumali. 10c, 20, 50c, R1, R2; - ewuhlweza 5c, 10c, R5 Isibonelo: 20, 50c, R1, R2; R5 • Ukuxazulula izinkiknga R5 + R10 = R15 - yephepha R10 no zemali eziyingxoxo ezi- R20 R10 + R10 + R10 =R30 - ukuhlanganisa okuphindiwe faka isamba noshintshi • Ukuxazulula izinkiknga kuyofika ku R20 no 20c R5 +R2 + R8 = R15 - gcwalisa kuya ku- 10 1.11 zemali eziyingxoxo ezi- Ushintshi owuhlweza Imali faka isamba noshintshi kuyofika ku R20 no 20c Abafundi basebenza ngama- R1, R2, R5, R10 no R20 yephepha. Bakhipha inani ngokusebenzisa imali yephepha. Abafundi baqedela umsebenzi lapho besebenza ngoshintshi wezinto abazithengile ngo-R20 nama ngemali engaphansi. Isibonelo: R10 - R8 =R2 R15 - R5 =R10 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) UKUBALA 1.12 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Kulindeleke ukuthi abafundi baxazulule ukubala esimweni esikhululekile alandelayo ukuxazulula alandelayo ukuxazulula basebenzisa amaqhinga alandelayo: Amaqhinga izinkinga zezibalo bese izinkinga zezibalo bese • Ukwakha nokuhlakaza izinombolo (izindlela noma uchaza isisombululo uchaza isisombululo amasu) kanje: kanje: • Phindaphinda kabili ubuye uhlukanise kabili • Sebenzisa • Sebenzisa • Umugqa wezinombolo izinsizakufunda izinsizakufunda Bheka amanothi e-Themu 2 eziphathekayo eziphathekayo • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza izinombolo izinombolo • Phinda kabili ubuye • Phinda kabili ubuye uhlukanise kabili uhlukanise kabili • Sebenzisa umugqa • Sebenzisa umugqa wezinombolo wezinombolo owakhiwe ngezinto eziphathekayo njengobuhlalu 197 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 198 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.13 Uhla lwezinombolo: Uhla lwezinombolo: Yimuphi umehluko ku-Themu 3? 0 - 20 0 - 15 Ukuhlanganisa Ku-Themu 2, uhla lwezinamba zokubala lwengezeke kusuka ku-10 kuya ku- 15 nokususa • Izibalo hlanganisa • Izibalo hlanganisa Ukuze usebenze ngezimpawu zokuhlanganisa nokukhipha abafundi kumele babe kuyofika ku- 20 kuyofika ku- 15 nolwazi oluthuthukile. Izibalo IBANGA 1-3 • Izibalo zokususa ku 20 • Izibalo zokususa ku 15 • Sebenzisa uqonde ulimi lokuhlanganisa nelokususa. • Sebenzisa izimpawu • Sebenzisa izimpawu • Bala konke ezifanele (+, –, =, ) ezifanele(+, –, =, ) • Bala uqhubeke kuzinombolo ezinkulu • Enza uphindelela • Enza uphindelela amabhondi kuze kufike amabhondi kuze kufike • Hlela uqhathanise izinombolo ku-10 ku 9 Amaqhinga okubala uma uhlanganisa noma ukukhipha Kuleli Themu abafundi bazoqhubeka nokusebenzisa lamaqhinga • Wenze ukuhlanganisa ngokubala konke. • Wenze ukuhlanganisa ngokubala ngokuqhubeka • Bala uqale ngezinombolo ezinkulu • Sebenzisa ukususa ngokukhipha • Susa ngokubala uhlehla Kuleli-Themu abafundi bazo: Shintsha inombolo kuya eshumini baphinde basebenzise ukuhlanganisa okuyimivo. Lamaqhinga angafundiswa kusetshenziswa uhla lwezinombolo olusezingeni oluphansi asetshenziswa nasezingeni eliphezulu.. Isibonelo: 9+6= Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi bangazitshela ukuthi: “Ngizosusa okukodwa kokuyi-6 ngikuhlanganise nokuyi-9 kuzokwenzwa i-10” Kuwukuthi i-9 + 6 kungabhalwa kube i- 10 + 5 = 15 Isibonelo: 8+5=

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.13 Abafundi bangazithsela ukuthi: “Ngizosusa oku-2 kokuyi-5 ngihlanganise nokuyi- 8 kuzokwenza i- 10 Ukuhlanganisa nokususa Kuwukuthi 8 + 5 kungabhalwa kube i-10 + 3 = 13 Uma ufunda lamaqhinga, abafundi bazosebenzisa izinsizakufunda eziphathekayo ukuqonda iqhinga. Isibonelo: Enza iqoqo ngezinja ukwenza i-10 9+4 10 + 3     9   +  4   =  10   +  3   =  13   Hlakaza inombolo ibe izicucu ezincane ukuze ukubala kube lula Abafundi bazohlukanisa izinombolo ngezinxenye ezahlukene. Bazohlukanisa izinxenye zezinombolo ezisebenzisekayo kubona. 199 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 200 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.13 • Ukusebenzisa imicibisholo nezinombolo ukubonisa ukucabanga. Ukuhlanganisa 8+6= nokususa 8+2+4 Izibalo IBANGA 1-3 8 + 2 → 10 + 4 = 14 8+7=V 8+2+5 8 + 2 → 10 + 5 = 15 15 - 9 =  15 - (5+4) 15 - 5 → 10 - 4 = 6 Sebensisa ulwazi lwngaphambili lube amaqhinga Amaqhinga aboniswe ngenhla avumela abafundi ukuthi bazi ukubala izinombolo ngokunikeza umqondo. Enza uphindelela amaqhinga ngaphansi kuzogqugquzela abafundi ukuthi babonise ubudlelwano phakathi kwezinombolo nokufundisa abafundi ukuthi basebenzise ulwazi ukuze bahlanganise. Beka izinombolo ezinkulu kuqala ukuze kubalwe kuya phambili noma kuh- lehle 4 + 12 =  Hlela 4 + 12 as 12 + 2 uphinde ubale oku-4 uqale 12. Ukubona izinombolo eziseduze kweziphindeke kabili “ Identify near dou- bles” 7+6 Abafundi bangachaza izibalo ezingabhaleka kanje: 6 + 6 -1 noma 7 + 7 - 1 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi bangahle babhale amaqhinga besebenzisa imicibisholo 6 + 6 → 12 + 1 = 13

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.13 Sebenzisa ulwazi lokuphikisa phakathikokuhlanganisa nokususa Ukuhlanganisa 15 - 9 =  nokususa Abafundi bayazi ukuthi ukubala kungabhalwa ngokuhlanganisa: “ngiyazi ukuthi 9 + = 15.” Abafundi bangase basebenzise ukubala ukuze bakwazi ukwenza izibalo Izinombolo ezakha inombolo Ukuze usebenze uphindelele izinombolo ezakha izinombolo abafundi okumele banikezwe imisebenzi ehlukahlukene abazoyenza. Lokhu kwenziwa ngesikhathi sokukhululeka. Umugqa wezinombolo ungasetshenziswa enza uphindelela amabhondi kuze kufike ku 9 Umqondo wokuphindaphinda Abafundi kumele babhale umusho wezinombolo kule-Themu.. 1+1= 2-1= 2+2= 4-2= 3+3= 6 - 3=  4+4= 8-4= Abafundi kumele baphendule imibuzo elandelayo: • Okuphindwe 3. • Yini okubili 3s? • Uginqike ka-6 okuphindwe kabili. Ufake okungaki? • Mangakhi amasokisi kumapheya ama-5? 201 Izibalo IBANGA 1-3

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora 202 IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.14 • Ukuhlanganisa • Ukuhlanganisa Yimuphi umehluko ku-Themu 2? ngokuphindaphinda ngokuphindaphinda Ukuphindaphinda Ku-Themu 3, abafundi baqhubeka nokwakha ulimi ngokuphindaphinda (izinombolo ezifanayo) (izinombolo ezifanayo) kokuhlanganisa kokuhlanganisa. Isibonelo: kuya ku- 20 kuya ku- 15 okuholela • Amaqoqo ama-2 ezinto ezi-3 Izibalo IBANGA 1-3 ezibalweni • Sebenzisa izimpawu • Sebenzisa izimpawu zokuphindaphinda ezifanele (+, –, =, ) ezifanele (+, –, =, ) • Amaqoqo ama-4 ezinto ezi-2 Abafundi baqhubeka nokubhala imisho yezinombolo okwethulwa okusazithombe. Ukubala okweqayo kumele kuqhubeke ukuze kusize abafundi ekubala izinto eziqoqelwe ezithombeni. Uma izithombe noma izinto eziqoqwe ngokubili abafundi kumele babale ngokubili hhayi ngokukodwa ukuze bathole isamba sezinto. 1.16 Ulwazi Lewzibalo: Uhla Ulwazi Lewzibalo: Uhla Yimuphi umehluko ku-Themu 2? olufinyelela ku-20 olufinyelela kwi -15 Izibalo Zekhanda Ku-Themu, uhla lwezinombolo lukhula kusuka ku-10 kuya ku-15 • Hlela iqoqo • Hlela iqoqo Isibonelo semibuzo kanye nomsebenzi engahle ibuzwe futhi yenziwe: lezinombolo olunikiwe. lezinombolo olunikiwe. • Qala ngoku-3 ubale uya phambili ngakunye kuya kwi-10. • Qhathanisa izinombolo • Qhathanisa izinombolo kusukela ku-20 ngokusho ukuthi iyiphi • Abafundi bama umugqa babuze: ngubani owokuqala, owesibili, owesithathu yisho ukuthi iyiphi encane noma enkulu noma wokugcina? encane noma enkulu ngokukodwa noma • Ikuphi okuncane oku-14 noma ku-8? ngokukodwa noma ngokubili. ngokubili. • Ikuphi okuningi oku-8 noma oku-4? • Yazi ukuthi iyiphi • Yazi ukuthi iyiphi encane noma enkulu • Yini okuncane ngoku-2 ukunokuyi-13? encane noma enkulu ngoku-1. ngoku-1. • Yini okuningi nkoku-2 ukunokuyi-8? • Yazi ukuthi iyiphi • Yazi ukuthi iyiphi encane noma enkulu • Nginike inombolo ephakathi koku-1 noku-3. encane noma enkulu ngoku-2. • Nginike inombolo ephakathi kwe-10 ne-13. Ingabe kunenamba eyodwa? ngoku-2. • Hlela lezi zinombolo zamakhadi ngokuyikho usuka kwezincane uya kwezinkulu. • Yazi ukuthi iyiphi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola encane noma enkulu ngoku-10.

ISIKHATHI UKUQONDA UKUQONDA (ezifundweni OKUFUNDWAYO OKUFUNDWAYO ezingamahora IZIHLOKO NAMAKHONO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS Okudingekayo Okubhekwayo amaminithi ekupheleni konyaka ku-Themu 1 angama-24) 1.16 Ukukhumbula Ukukhumbula Ukukhumbula ngokushesha Izibalo Zekhanda ngokushesha ngokushesha Bonisa izinombolo zokuhlanganisa ezenza oku-5 (zibhale phansi noma • Izinombolo ezakha • Izinombolo ezakha usebenzisa ubungakho benani lezinombolo noma amakhadi okusebenza inombolo kufika kwi-10 inombolo kufika okwakha izinombolo) • Khumbula izindlela kwezi-5 • 1 zokuhlanganisa • Khumbula • 2 nokususa kuya e -10 izindlela okuyizo zokuhlanganisa • 3 nokususa kuya ku-5 • 4 Amasu okubala Amasu okubala Bonisa izinombolo ngakwesokunxele uma....kususiwe kusuka ku-5 (zibhala Sebenzisa amasu phansi noma usebenzisa ubungakho benani lezinombolo noma amakhadi okuhlanganisa nokususa Sebenzisa amaqhinga ngekhono lokusebenzisa okusebenza okwakha ubungako bezinombolo) ngokugculisayo: ukubala kokuhlanganisa • 1 • Beka inombolo enkulu nokususa kuqala ukuze ubale • 2 uqhubeke noma • Beka inombolo enkulu • 3 uhlehle kuqala ukuze ubale uqhubeke noma • 4 • Umugqa wezinombolo uhlehle 1 + 2 = 3 yini oku- 2 + 1? Ingabe impendulo iyafana? • Ukuphinda kabili • Umugqa wezinombolo 3 + 1 = 4 yini oku- 1 + 3? Ingabe impendulo iyafana? nokuhlukanisa kabili inombolo • Ukuphinda kabili Amasu okubala nokuhlukanisa kabili Sebenzisa amasu okuhlanganisa nokususa ngokugculisayo: • Ukwakha nokuhlakaza inombolo inombolo Hlanganisa okulandelayo ngokufaka izinombolo ezinkulu kuqala bese uqhubeka • Ukuphinda kabili nokubala: nokuhlukanisa kabili inombolo 1+2 • Ukwakha nokuhlakaza 2+3 inombolo 1+4 Okuphindwe 1 Yini okubili 2s? Yini okuyinxenye we-4? Sebenzisa umugqa wezinombolo Ugxuma kangakhi ukusuka koku-3 kuya koku-5? 203 Ugxuma kangakhi usuhlehla usuku koku-5 uya koku-2? Izibalo IBANGA 1-3

ITHEMU YESI- 3 YEBANGA LOKU-1 2. AMAPHETHINI, UBUDLELWANE NE-ALJIBHRA 204 UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO (ezifundweni OKUFUNDWAYO NAMAKHONO ezingamahora IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA OKUDINGEKAYO ama- 2 ihora OKUBHEKWAYO amaminithi EKUPHELENI KU-THEMU 3 angama-24) KONYAKA 2.1 Ukukopisha, ukuqhuba Ukukopisha, ukuqhuba eBangni 1 abafundi bangagxila kumaphethini lapho izinto ziphindwe ngendlela Isifundo esisodwa Izibalo IBANGA 1-3 AMAPHETHINI bese uchaza bese uchaza eqondile. OKUSEjiyometri Ukukopisha, ukuqhubeka Ukukopisha, ukuqhubeka nokuchaza ngamagama nokuchaza ngamagama • Amaphethini alula • Amaphethini alula enziwe ngezinto enziwe ngezinto eziphathekayo eziphathekayo • Amaphethini alula • Amaphethini alula enziwe ngokudweba enziwe ngokudweba imidwebo eyenziwe imidwebo eyenziwe ngemigqa, ngezimo ngemigqa, ngezimo noma ngezinto noma ngezinto eziphathekayo eziphathekayo Akha amaphethini akho Akha amaphethini Akha amaphethini akho lakho asejiyometri Create own Akha amaphethini akho geometric patterns asejiyometri • Izinto eziphathekayo • Izinto eziphathekayo with physical objects • Ngokudweba olayini, • Ngokudweba olayini, izimo noma izinto izimo noma izinto eziphathekayo eziphathekayo Amaphethini asizungezile Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Khomba, uchaze ngamagama uphinde ukope amaphethini asejiyometri • Kwimvelo • Empilweni yesimanje yansuku zonke • Emasikweni ethu

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO (ezifundweni OKUFUNDWAYO NAMAKHONO ezingamahora IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ama- 2 ihora CAPS OKUDINGEKAYO OKUBHEKWAYO amaminithi EKUPHELENI KU-THEMU 3 angama-24) KONYAKA 2.2 Ukukopisha, ukuqhuba Ukukopisha, ukuqhuba Ukulandelana kwezinombolo kungahlanganiswa nokubala. Njengoba abafundi Izifiundo ezintathu bese uchaza bese uchaza bebala amakhono ayashintsha aphinde akhekhe njengezinhlobo zezinombolo AMAPHETHINI ezilandelanayo abafundi basebenza ngolwazi lokwakha. EZINOMBOLO Ukukopisha, ukuqhubeka Ukukopisha, ukuqhubeka nokuchaza ngamagama nokuchaza ngamagama Ukulandelana kwezinombolo kufanele kokhombise ukubala uya phambili alula ngokulandelana alula ngokulandelana nokubala uhlehla kanye: okungenani ufike ku-100. okungenani ufike ku-80. Ukulandelana akuveze ukubala uya phambili uphinde uhlehle: Akha amaphethini Ukulandelana akuveze • Ngakunye usuka kunoma iyiphi inombolo phakathi kuka 1 no 80 lakho ukubala uya phambili uphinde uhlehle: • Ngamashumi kusuka kunoma yikuphi ukuphindana kwe-10 okuphakathi,kuka 0 Akha amaphethini akho kuya ku 80 ezinimbolo • Ngakunye usuka kunoma iyiphi • Ngakuhlanu kusukela kunoma yikuphi ukuphindana kwe-5 okuphakathi kuka 0 inombolo phakathi kuya ku80 kuka 1 no 80 • Ngokubili kusukela kunoma yikuphi ukuphindana kwe-2 okuphakathi kuka 0 Ukubala uya phambili kuya ku80 kulokhu: Uma abafundi bebala bephimisa bangabonisa ukulandelana kwezinombolo • Ngamashumi kusuka ezibhalwe phansi ngezindlela ezahlukene. Bangakhombisa izinombolo kunoma yikuphi ezibalwayo. ukuphindana kwe-10 Isibonelo 1: Sebenzisa ishadi lezinombolo okuphakathi,kuka 0 kuya ku 80 1 2 3 4 5 6 7 8 9 10 • Ngakuhlanu kusukela 11 12 13 14 15 16 17 18 19 20 kunoma yikuphi ukuphindana kwe-5 21 22 23 24 25 26 27 28 29 30 okuphakathi kuka 0 31 32 33 34 35 36 37 38 39 40 kuya ku80 • Ngokubili kusukela Isibonelo 2: Sebenzisa umugqa wezinombolo ukuchaza iphethini kunoma yikuphi ukuphindana kwe-2 Bala ngama- 10 uqale kuma-50 kuya kuma- 80 okuphakathi kuka 0 kuya ku80 205 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO (ezifundweni OKUFUNDWAYO NAMAKHONO ezingamahora 206 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA OKUDINGEKAYO ama- 2 ihora OKUBHEKWAYO amaminithi EKUPHELENI KU-THEMU 3 angama-24) KONYAKA 2.2 Akha amaphethini Abafundi bafunda izinombolo ukufika ku-80, kodwa ukubhala kuphela izinombolo lakho kusuka kokukodwa kuya kwi-15. Amaphethini ezinombolo anezinombolo AMAPHETHINI ezingaphezulu kwe-15 zingenziwa ngoku: EZINOMBOLO Akha amaphethini akho ezinimbolo • Ukufaka imibala ehlukene kumaphethini, kugridi yezinombolo, Izibalo IBANGA 1-3 • Ukukokelezela izinombolo kumaphethini, kugridi yezinombolo noma emgqeni wezinombolo; • Ukusebenzisa amakhadi ezinombolo ukuqoqa isinombolo ngokulandelana; • Ukusebenzisa amakhadi ezinombolo abonisa izinombolo ezingekho embhalweni onikiwe olandelanayo; noma • Ukusebenzisa uhla lwezimpawu zezinombolo ezilethelwe ukudweba umugqa kwizinombolo ezikhethiwe ezilungile endaweni okumele zibe kuyona. • Abafundi banganikezwa ukubhalwa okulandelanayo kwezinombolo okunezinombolo ezingekho. Kumele banikezwe uhla lwezinombolo ezingasetshenziswa, kulokho abangakhetha impendulo okuyiyona. Abafundi bazogcwalisa izinombolo ezingekho ezinikiwe zilandelana ngaphezulu, bagcwalise izinombolo ezingekho ngendlela yokubhala izinombolo zilandelana, isibonelo: 2, 12, 22, ___, 42, 52, 62. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI-3 YEBANGA LOKU - 1 3. INDAWO NESIMO (IJIYOMETRI) ISIKHATHI CAPS UKUQONDA UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI kumaminithi anga NGETHEMU 3 KONYAKA 24) 3.1 Ulimi oluchaza ukuthi Ulimi oluchaza isikhundla olwakheke eThemini 1 kufanele abafundi balwenze leyonto ikusiphi njalo ngesikhathi sokufunda beyiqoqo eliphelele nangesikhathi befunda Isikhundla, isikhundla. kugxilwe emaqoqweni kuze kuphele iThemu. Kumele kube nesikhashana ukubonisa sokuzilugisela ukusetshenzisa ulimi. into nendlela Chaza isikhundla sento okubonakala ngayo usiqhathanisa nenye. Olunye ulimi oluchaza isikhundla lungafundwa ngesikhathi abafundi befunda Isibonelo: ingaphezulu, ngesimo ezinhlangothintathu. ingaphambi, ingemumva, Umsebenzi okhuluma ngesikhundla nangezinkomba uqoqwa ugoqwe ingakwesokunxele, ngomsebenzi obhalwayo. Isibonelo: imidwebo, ukufaka imibala, noma ingakwesokudla, iphansi, ukuqondanisa imidwebo namagama. Abafundi bangenza lomsebenzi iseduze kwalokhu, njll. ngesikhathi sokusebenza ngamunye Isikhundla sento nokubukeka kwayo. • Qondanisa ukubukeka kwento eyodwa efanayo ngokubukeka kwayo okwahlukene. Isikhundla nezinkomba • Landlela izinkomba ukunyakaza uzungeza ekilasini. Landela imiyalelo ukubeka into ibe nobudlelwane nenye. Isibonelo: Faka ipeni phakathi ebhokisini. 207 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO 208 IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI kumaminithi anga NGETHEMU 3 KONYAKA 24) 3.2 Uhla lwezinto Uhla lwezinto Ukugxila ezimpawini zezinto ezinhlangothintathu Izifundo ezimbili Isimo Ukubona ashonizinto Ukubona ashonizinto Abafundi basebenzisa amabhola nezimo ezisabhola, amabhokisi esinhlangothintathu ezinhlangothintathu ezinhlangothintathu ahlukahlukene nezinye izinto ezinizimo ezingonxande, amaphrizimu ekilasini nasezithombeni. ekilasini nasezithombeni. namabhuloki. Abafundi bangakha izinto ezishelelayo noma eziginqikayo bese bezibeka endaweni ephakeme ukuze babone bazitholele okushelelayo Izibalo IBANGA 1-3 • Isimo esiyibhola • Isimo esiyibhola nokugingqikayo. (imbulunga) (imbulunga) • Isimo esiyibhokisi • Isimo esyiibhokis (iphrizimu) (iphrizimu) Izimpawu zezinto Izimpawu zezinto Chaza,uhlele bese Chaza,uhlele bese Abafundi bangathola ukuthi bangakwazi ukwakha umbhoshongo besebenzisa uqhathanisa izimo uqhathanisa izimo amabhola odwa noma amabhokisi odwa.. ezinhlangothintathu ezinhlangothintathu Ngesikhathi sokusebenza ngabodwa abafundi bangaqhubeka nokwenza ngokwe: ngokwe: lomsebenzi: • ubungako • ubungako • ukuhlela izinto ngobungako; • umbala • umbala • ukuhlela izinto ngokwemibala; • izinto eziginqikayo • izinto eziginqikayo • ukwakha ngezinto ezikhona eklasini • izinto esishibilikayo • izinto esishibilikayo • ukwakha amabhola noma amabhokisi ngobumba noma ngenhlama. Imisebenzi okugxile Ukubona nokusho amabhola (okuyimbulunga)namabhokisi(amaphrizimu) kuyo. Abafundi bayaqhubeka bakhombe bese bechaza okusejiyometri nokutholakala Buka bese wakha isimo ezimpilweni zansukuzonke, basho ukuthi kunesimo esisabhola noma esinhlangothintathu esisabhokisi. Isibonelo: isitini sime njengebhokisi, noma iwolintshi limi usebenzisa izinto njengebhola. eziphathekayo njengamabhulokhi, Umsebenzi obhalwayo nokuphinde Umsebenzi owenziwayo wezinto ezinezimo ezinhlangothintathu ungasongwa kusebenziseke uphethwe ngomsebenzi obhalwayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kabusha, nokunye okuyizinsizakufundisa

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI CAPS NGETHEMU 3 kumaminithi anga KONYAKA 24) 3.3 Uhla lwezimo Azikho izimo ezinxambili ezinconywe ukuba kugxilwe kuzo kuthemu 3, kodwa abafundi bangaqhubeka ngokwakha izithombe ezinhlangothimbili noma benze umsebenzi obhalwayo ngesikhathi sokusebenza Izimo Ukubona bese esho ngabodwa. Lokhu bangakwenza ngesikhathi sezibalo nangesamakhono empilo. ezinhlangothimbili izimo ezinhlangothimbili • indilinga • unxantathu • izkwele Izimpawu zezimo Chaza, uhlele bese uqhathanisa izimo ezinhlangothimbili ngokwe • bungakho • umbala • isimo • amacala aqondile • amacala ayindinga 3.4 Okufana nse Okufana nse Abafundi abathole umugqa ohlukanisa izinto eziphathekayo nezithombe kufane Isifundo esisodwa nxazombili nxazombili nse nxazombili. Okufana nse nxazombili • ukubona okufana • ukubona okufana Umsebenzi obhalwayo akumele ube imidwebo kodwa kufanele ufake nxazombili emzimbeni nxazombili emzimbeni umsebenzi wokudweba umugqa ohlukanisa phakathi kufane nse nxazombili wakhe. wakhe. emidwebeni eyizibalomdwebo. Isibonelo: unxantathu, imidwebo engesizo izibalo nokudweba umugqa ohlukanisa umzimba kufane nse nxazombili • Ukubona bese edweba • Ukubona bese edweba umugqa ohlukanisa umugqa ohlukanisa kabili kufane nse kabili kufane nse nxazombili izimo nxazombili izimo ezinhlangothimbili ezinhlangothimbili eziyizibalomdwebo eziyizibalomdwebo nengezibalomdwebe. nengezibalomdwebe. 209 Izibalo IBANGA 1-3

ITHEMU YESI- 3 YEBANGA LOKU- 1 4. ISILINGANISO 210 UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI kumaminithi anga NGETHEMU 3 KONYAKA 24) 4.1 UKUDLULA Abafundi kumele bafunde ukukhuluma ngalokhu: KWESIKHATHI ISIKHATHI • Ukulandelana kwezigameko Izibalo IBANGA 1-3 Ukuxoxa ngokudlula • Ubude besikhathi kwesikhathi Abafundi bayaqhubeka nokuhlanganisa izindlela zokukhuluma ngesikhathi • Ukuhlela kwezigameko nsukuzonke ngesikhathi sokufunda bebonke njengekilasi noma ngesikhathi ezejwayelekile sokufundiswaa ngamaqembu. ezimpilweni zabo ngokulandelana. Abafundi baxoxa baphendule imibuzo ngokwenzeka kwezinto besebenzisa amagama afana nokuthi ekuseni,ebusuku, emini, njll • Ukuqhathanisa ubude besikhathi Abafundi balandelanisa izigameko besebenzisa ulimi olufana nokuthi izolo, kusetshenziswa ulimi namuhla, kusasa, izinsuku zesonto nezinyanga zonyaka. oluchazayo Abafundi baqhanisa ubude besikhathi nobufushane baso nokushesha kwaso • Ukuqhanisa ubude Abafundi baxoxa ngokuhlela izigameko zempilo yabo. besikhathi usebenzisa ulimi olufanele. Balandelanisa bahlele izithombe ezifana Isibonelo:kude ngokuthe xaxa, • Izinyathelo ozilandelayo uma wenza inkomishi yetiye. kufushane ngokuthe • Izithombe ezikhombisa ingane ekhulayo ize ibe umuntu omdala xaxa kuyashesha, kuhamba kancane njll • Impilo nokukhula kwezilwane. Isibonelo iqanda liba inkukhu. • Ukulandelanisa • Izehlakalo ezenzeka njalo ngosuku ukusuka ekuseni kuze koshona ilanga. izigameko usebenzisa Abafundi baqhubeka nokukhombisa izinsuku zabo zokuzalwa kwikhalenda ulimi olufanele unyaka wonke. njengokuthi: izolo, namuhla kusasa. Ukusho isikhathi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukuchaza ukwenzeka kwezinto kusetshenziswa ulimi olufanele. Isibonelo: Ekuseni, ntambama, ebusuku.

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI CAPS NGETHEMU 3 kumaminithi anga KONYAKA 24) 4.1 • Ukwazi izinsuku zeviki ISIKHATHI • Ukwazi izinyanga zonyaka. • Ukukhombisa izinsuku zabo zokuzalwa kwikhalenda ngezindlela ezahlukene. 4.2 Isilinganiso Isilinganiso Yikuphi okwahlukile eThemini 3? Izifundo ezimbili esingahlelekile esingahlelekile UBUDE Konke ukukala eBangeni 1 akunasilinganiso. Ubude abulinganiswa • ukuqhathanisa • Ukuhlawumbisela, ngesilinganiso esihleliwe nesilinganisiwe. nokuhlela ubude, ISILINGANISO, EThemini 1 kunconywa ukuba abafundi bagxile kulokhu: ukuphakama, noma ukuqhathanisa, ububanzi phakathi ukuhlela, • Ukuqhathanisa ubude beizinto ezibekwe zasondelana kwezinto ezimbili nokubhala ubude • Ukuhlela nokuqhanisa ubude nokuphakama nobubanzi bezinto ezintathu nezingaphezulu ukusebenzisa izikali nangaphezulu ngokuzibeka ngambili ezinye eduze kwezinye. bese ezibeka ezingenasilinganiso. ngokulandelana enye Isibonelo: ubude • Ukukhulisa ulimi olukhuluma ngomehluko okhona uma kukhulunywa ngobude, emva kwenye. bezandla, amagxatho, ukuphakama ububanzi, njll ubude bepensela, • Ukusebenzisa Ngesikhathi sokusebenza ngokuzimela ngeThemu abafundi bangazilungiselela nezinto zokubala, njll ulimi olufanele ngokuphindelela behlanganisa behlela bese beqhathanisa ubude, ukuphakama ukuqhathanisa. noma ububanzi bezinto ezintathu nangaphezulu ngokuzibeka ngazimbili ezinye Isibonelo: kude eduze kwezinye zize zilandelane ngokufanele. ngokuthe xaxa, kufishane ngokuthe Umsebenzi wonke kumele ubhalwe, abafundi bebhala abakutholayo nothisha xaxa, kubanzi ebhala ukusebenza kwabafundi. ngokuthe xaxa, njll EThemini lesi 3 abafundi bangagxila ekulinganiseni okungenasilinganiso belinganisa ubude. 211 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO 212 IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI kumaminithi anga NGETHEMU 3 KONYAKA 24) 4.2 • Ukuhlawumbisela, Ukulinganisa okungahlelekile kobude kusetshenzisa isilinganiso Izifundo ezimbili Ukulinganisa, okungenasilinganiso sobude. UBUDE ukuqhathanisa, Abafundi bangafunda imigomo nemikhuba yokulinganisa besebenzisa ukukala ukuhlela, okunganasilinganiso. Ukukala ngesilinganiso esingahlelekile akumele kuthathwe nokubhala ubude njengokungenasidingo. Izibalo IBANGA 1-3 ukusebenzisa izikali ezingenasilinganiso. Ukulinganisa ubude ngesikalo esingahlelekile kufaka ukubala izilinganiso Isibonelo: ubude ezilinganayo bese kubalwa izinto ebekulinganiswa ngazo. Isibonelo: ubude bezandla, amagxatho, bedesiki buyizandla eziyi 8. ubude bepensela, Abafundi kumele balinganise izinto ezahlukene besebenzisa uhla lwezinto nezinto zokubala, njll belinganisa ngesilinganiso esingalinganisiwe. Zintathu izindlela zokulinganisa okungahlelekile; • Qoqa ubeke ngomugqa izinto ezizolinganiswa eziwubude obufanayo njengamabhokisi kamantshisi,izivalo zamabhodlela ezinezimo ezifanayo,njll ungasebenzisa lokhu kulinganisa ubude bedesiki. Kusemqoka ukuthi: • Konke okuzosetshenziswa kuwubude obufanayo. Ungeke usho ukuthi incwadi iyizivalo eziyi 12 ngoba nazo azilingani futhi • Azikho izikhala ezishiywa phakathi kwezinto ezilinganisayo, izinto ziqoqwa kungasali sikhala phakathi kwazo • Ukusebenzisa izinto ezifana nse ukukala ngesilinganiso esingahlelekile. Lokhu ungakwenza uma ulinganisa ubude bezinyawo.. • Ukusebenzisa into eyodwa kuphela njengesilinganiso esingahlelekile noma uyiphendulele kolunye uhlangothi ukuyenza umkhawulo ngaphambi kokuyishishilizisa. Abafundi abafundiswe ukuchaza ukukala abakusebenzisile okungalinganisiwe. Isibonelo: ikilasi liyizinyawo ezingama 38 Uma abafundi sebelinganise izikhashana bangajwayezwa ukuhlawumbisela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ubungako bobude bento elinganiswayo. Ukuhlawumbisela ngaphambi kokulinganisa kusemqoka kodwa abafundi bangakwenza emva kokuba sebeke balinganisa ngaleso silinganiso.

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI CAPS NGETHEMU 3 kumaminithi anga KONYAKA 24) 4.2 Abafundi kumele bafunde ukukwazi ukuqhathanisa ubude, nokuphakama nobubanzi kusetshenziswa izilinganiso ezifanayo. isibonelo: uma umnyango UBUDE uyizandla ezingama 20 ububanzi kanti idesiki lingamapensela ayisi 8 lokho akusho ukuthi ububanzi bomnyango bukhulu kunobedesiki. Abafundi badinga ukulinganisa ngohla lwezilinganiso ukuze:- • Bazi ukuthi uma isilinganiso sisincane isilinganiso siba siningi kanti uma sisikhulu isilinganiso isilinganiso siba sincane. Isibonelo: ububanzi beklasi amanyathelo angama20 kodwa libe anagxatho angama 48 ukuphapama futhi • Bazi uksebenzisa izilinganiso ezifanele zokulinganisa. Isibonelo: ukusebezisa izivalo zamabhodlela okulinganisa ububanzi beklasi kuchitha isikhathi. Ukubhala isilinganiso Ukulinganisa kuyikhono elenziwayo kodwa abafundi bangakubhala njalo phansi abakuthola uma kade belinganisa. Ukulinganisa ubude esimweni sokuxazulula izinkinga nezokubala Ngesikhathi sokusebenza ngezinombolo, ubudlelwane nokusebenza kwazo abafundi bangaxazulula izinkinga zokulinganisa okungahlelekile kobude. Isibonelo: ubude bebhokisi lensipho lingaba izinti eziyi 8 zikamentshisi. Ibhokisi lamakhekhe liyizinti eziyi 13 zikamentshiso. Lide kangakanani ibhokisilamakhekhe kwelensipho? Makunakekelwe uhla lwezinombolo ezisetshenziswa eThemu ngokwazi izinhlobo zezinkinga ezihambisana neThemu. 213 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO 214 IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI kumaminithi anga NGETHEMU 3 KONYAKA 24) 4.3 ISILINGANISO Konke ukulinganisa eBangeni 1 akuhlelekile. Akukho ukulinganiswa kwesisindo okungahlelekile okuhlelekile nokusebenzisa ukulinganisa okungahlelekile. ISISINDO • ukuhlawumbisele, EThemini 1 kunconywa ukuba abafundi bagxile isilinganiso, • Ekuqhathaniseni isisindo sezinto ukuqhathanisa, Izibalo IBANGA 1-3 • Ukuhlela bese uqhathanisa izisindo zezinto ezintathu nezingaphezulu • ukuhlela, ngokuzibeka ngambili uzilinganisa zilandelane ngokwesisindo. nokubhala isisindo besebenzisa izikali • Ukukhulisa ulimi olukhuluma ngomahluko wesisindo. ezingalinganisiwe Ngesikhathi sokusebenza ngokuzimela ngeThemu abafundi bangazilungiselela nokulinganisa macala ngokuphindelela behlanganisa behlela bese beqhathanisa ubude, ukuphakama onke. Isibonelo: noma ububanzi bezinto ezintathu nangaphezulu ngokuzibeka ngazimbili ezinye amabhulokisi, nezitini, eduze kwezinye zize zilandelane ngokufanele. njll Wonke umsebenzi uyabhalwa abafundi nothisha • Ukusebenzisa ulimi olufanele ukuqhathanisa. Isibonelo: kuyasinda, kulula, kulula kakhulu, kusinda kakhulu. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO (ezifundweni eziyi NAMAKHONO IZIHLOKO ADINGIKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa elilodwa kuya OKUGXILWA KUWO EKUPHELENI CAPS NGETHEMU 3 kumaminithi anga KONYAKA 24) 4.4 Isilinganiso Konke ukulinganisa eBangeni 1 akuhlelekile. Akukho ukulinganisa isisindo esingahlelekile okuhlelekile nokusebenzisa ukulinganisa okulingahlelekile. UMTHAMO / OKUMUMETHWE • ukuqhathanisa Ngalesisikhathi sonyaka kugxilwa kokumumethwe nomthamo ngoku nokuhlela ukungako • Khulisa ulimi oluqondene nokumumethwe nomthamo boketshezi olumumethwe izitsha • Qhathanisa umthamo wezitsha ezimbili ezifanayo; bese ezimbili ezibekwe • Qhathinisa umthamo wezitsha ezinobubanzi obungafani ngokuthela esitsheni zasondelana. sesithathu Abafundi bangathola ubungako boketshezi Bheka amanothi eThemu 2. ngokuluthela esitsheni sesithathu. Abafundi bangahlanganisa ulwazi abaluzuzile ngesikhathi sokufunda ngokuzimela . • Ukuqhathanisa nokuhlela ubungako boketshezi olungamumathwa izitsha ezimbili. • Ukusebenzisa ulimi olufanele ukuqhathanisa. Isibonelo:kugcwele kunokunye, akunalutho. • Ukuhlawumbisela bese ukala uhlele umthamo wezitsha usebenzisa ukukala okungalinganisiwe. Isibonelo:amathisipuni nezinkomishi. 215 Izibalo IBANGA 1-3

ITHEMU YESI-3 YEBANGA LOKU -1 5. UKUQOKELELWA KOLWAZI 216 UKUQONDA UKUQONDA ABAKUFUNDAYO ISIKHATHI OKUFUNDWAYO NAMAKHONO (ezifundweni eziyi- IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO hora nemizuzu OKUGXILWA KUWO NGOKUPHELA engama-24) NGETHEMU -I KONYAKA Ukusebenza ngeqoqo lezinto Izibalo IBANGA 1-3 5.1 Qoqa bese uhlela izinto Ukuhlela izinto eziqoqiwe akuyona into okugxilwa Qoqa bese uhlela Qoqa bese uhlela kuyo ngesigamu sesibili izinto izinto eziphathekayo sonyaka kodwa ingenziwa nsukuzonke ngesikhathi semisebenzi 5.2 Okumele izinto yokuzimela ezihleliwe eziqoqiwe Izincomo zokugxila kukho Okumele izinto ezihleliwe Dweba isithombe sezinto ngeThemu 3 indlela eziqoqiwe eziqoqiwe. ukuqokelelwa kolwazi okusebenza ngayo 5.3 Ukuxoxa bese kubikwa kusuka ekuqaleni kuze ngezinto ezihleliwe kuyofika ekugcineni. Ukuxoxa bese eziqoqiwe kubikwa ngezinto Bheka isibonelo olunikiwe ezihleliwe • Nika isizathu sokuqoqa ngezansi. eziqoqiwe izinto nokuzihlela ngendlela ezihlelwe ngayo. • Phendula imibuzo - Ukuthi ukuhlela kwenziwe kanjani. (inqubo) - Izinto ezihleliwe zibukeka Kanjani. (umkhiqizo) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Chaza iqoqo nemidwebo. • Nikeza incazelo yokuhlela kezinto Ukusebenza ngolwazi

UKUQONDA UKUQONDA ABAKUFUNDAYO ISIKHATHI OKUFUNDWAYO NAMAKHONO (ezifundweni eziyi- IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO hora nemizuzu CAPS OKUGXILWA KUWO NGOKUPHELA engama-24) NGETHEMU -I KONYAKA 5.4 Qoqa bese uhlela Qoqa bese uhlela Izincomo zokugxila kukho: ukusebenza ngolwazioluqokelelwe oluphelele Izifundo ezi-3 ulwazi ulwazi kusuka ekuqaleni kuze kube sekugcineni. Qoqa bese uhlela ulwazi Qoqa ulwazi ngekilasi Qoqa ulwazi ngekilasi Ulwazi oluqokelelwe oluphelele noma ngesikole noma ngesikole abafundi baqoqa ulwazi ukuphendula imibuzo. EmaBangeni Aphansi ukuphendula imibuzo ukuphendula imibuzo nasemazingeni Aphakathi imibuzo itholakala kuthisha noma encwadini ebuzwa uthisha ebuzwa uthisha okufundwa ngayo. Okumele ulwazi • Abafundi bahlela babhale okumele ulwazi ngendlela elula ukuluhlaziya. Okumele ulwazi kwi Abafundi beBanga -1 banendlela yokubhala okumele ulwazi ngokbhala igrafu grafu yezithombe yezithombe Hlaziya bese • Abafundi bahlaziya ulwazi lwegrafu yezithombe ngokuphendula imibuzo uhumusha ulwazi ebuzwa uthisha. • ukuphendula imibuzo Igrafu yezithombe yekilasi ngegrafu yezithombe. eBangeni -1 kuyasiza ukuqala ulwazi oluqokelelwe ngokwenza igrafu yesithombe sekilasi. Ukusebenza ndawonye kubenza basizane besebenza bonke bengasali ndawo. Ukwenza igrafu yezithombe kwenza uthisha agxile ezingxenyeni ezimqoka esifundweni solwazi oloqokelelwe. Uthisha akafundise abafundi ukubona izimpawu zegrafu yezithombe • Ukulebhelwa kwegrafu(izihloko zegrafu) • Ukulebhela izingxenye zegrafu • Izithombe kumele zibe nencazelo yezikumele • Kumele kube nezikhala phakathi phakathi kwezithombe • Izithombe kufanele zibe nobukhulu obulinganayo • Ukufundwa kwegrafu Ukusebenza ngolwazi oluqokelelwe oluphelele kusuka ekuqaleni kuya ekugcineni kuthatha izifundo eziningana. 217 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA ABAKUFUNDAYO ISIKHATHI OKUFUNDWAYO NAMAKHONO (ezifundweni eziyi- 218 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO hora nemizuzu OKUGXILWA KUWO NGOKUPHELA engama-24) NGETHEMU -I KONYAKA 5.4 Ukuqoqa, uhlele bese ubhala okumele ulwazi oluphelele Qoqa bese uhlela Othisha emeBangeni aphansi kumele basebenzise izihloko ezahlukahlukene ulwazi eziqokwa ukufundisa kuqoqwa ulwazi nokuluhlaziya ezingeni nasezingeni ngalinye. izibonelo ezifanele Izibalo IBANGA 1-3 zifaka ukuhlela ishadi lesimo sezulu lenyanga edlule bese kwenziwa igrafu yezithombe. Noma ukwakha igrafu yezithombe yezinsuku zokuzalwa zabafundi Ukuhlaziya ulwazi Abafundi baphendula imibuzo efana nalena: Iluphi uhlobo lwezulu olube luningi kulenyanga ? Iluphi uhlobo lwezulu olube luncane kulenyanga? Zibe zingaki ezibe nelanga elibalele? Ukusebenza ngolwazi oluqokelelwe oluphelele kusuka ekuqaleni kuya ekugcineni kuthatha izifundo eziningana. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI-4 YEBANGA LOKU -1 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANE BAZO UKUQONDA CAPS UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA UKUTHUTHUKISA ULWAZI LWEZINOMBOLO: Ukubala usebenzisa izinombolo eziphelele 1.1 Bala izinto eziphathekayo Bala izinto eziphathekayo Yimuphi umehluko ku-Themu 2? Bala izinto kuya ezingama-50 kuya ezingama-50 Ku-themu 4, abafundi bangeza uhla lokubala. Kusekhona ukubheka ngokuqonda eziphathekayo Qagela inani lezinto Qagela inani lezinto indlela emiselwe yokusenza kwenombolo nhloko. Ngalethemu abafundi kumele esingaziibala esingaziibala bafunde indlela yokubeka izinto eziphathekayo ngokulandelana uma bebala ngokuyikho. ngokuyikho. ukuze uma bebheka ukubala, amalungiselelo abasiza ekubaleni kakhulu kalula. Isibonelo, ukubala kubekwe emgqeni. Ngalethemu abafundi baqhubeka nokwengeza amakhono okubala nokufunda. • Ukubala konke • Ukuqhubeka nokubala • Indlela emiselwe yokusenza kwenombolo nhloko kanye • Ukusebnza ngethekisthi ebhaliwe. Abafundi badinga ukuxhumana phakathi kokubala okujwayelekile nezinombolo ezisho isikhundla. Lokhu kwenzeka uma bethola ukuthi ukugcina ukubala kufike ku-50 wezinto kusho ukuthi babale izinto ezingama-50.. Futhi bayazi ukuthi indlela umuntu abala ngayo izinto ayithikamezi ukubala. ukubala ngamaqoqo Ukuze kusizwe abafundi ukubala ngezikhawu ezimbili, ezinhlanu nezi - 10, kudingeka bahlanganise izinto ngokubili, ngokuhlanu kanye nokuyi- 10 ukuze kubalwe iqoqo lezinto. Amakhadi ezinombolo kufanele abonise kuko konke okuqoqiwe ukubonisa izinombolo zezinto ezibaliwe. Ukubala ngamaqembu kuzolungiseslela abafundi ekwazini ukuphindaphinda. Ekupheleni kwe-Themu abafundi kumele bakwazi ukubona ukuqoqwa ngokuhlukanisa izinombolo. Isibonelo: “Ngiyazi ukuthi kuyi-10 ngoba ngibeka oku-4 kwelinye icala ngibeke okuyi-6 kwelinye icala” Izinsiza: Qaphela ukubheka izinhlobo zezinsiza ezisetshenziswayo. • Izinsiza ezihlelekile, ubuhlalo bokubala obusentanjeni bungasetshenziswa. 219 • I-abhakhasi ingasetshenziswa ukufunda ukubala ngeqembu leshumi. • Abafundi bangenza inyanda yoku-2, inyanda yoku-5 neyeshumi bese bezibala Izibalo IBANGA 1-3 zonke.

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 220 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.2 Bala uyaphambili Bala uyaphambili Yimuphi umehluko ku-Themu 1? ubuye uhlehle kanje ubuye uhlehle kanje Bala uyaphambili Ku-Themu 4, abafundi babala izikhawu ze-10, 5 ne-2 ukufika ku-100. Ukubala ubuye uhlehle • Ngakunye kusukela • Ngakunye kusukela ngezikhawu kuba ikhono elibalulekile abafundi abazolisebenzisa ku-Banga 2 ne 3 kunoma iyiphi kunoma iyiphi kubasize uma benza izibalo. Izibalo IBANGA 1-3 inombolo phakathi inombolo phakathi Ekupheleni kwe-Themu abafundi bazokwazi lokhu: kuka -0 kuya ku-100. kuka -0 kuya ku-100. Ukubala uphimisa uphinde uphendule imibuzo enjengale: Bala uya phambili Bala uya phambili kanje: kanje: • Qala kuma- 52, bala uqhubeke ngokubala ngakunye ufike kuma-70 • Ngama-10 kusuka • Ngama-10 kusuka • Qala kuma- 88, bala uqhubeke ngokubala uhlehle ngakunye ufike kuma-70 kunoma iyiphi kunoma iyiphi • Qala kuma- 38, uphinde uqhubeke ngokubala ngakubili ufike kuma-50 inombolo phakathi inombolo phakathi kuka -0 kuya kuma kuka -0 kuya ku-100. • Qala kuma-45, uphinde uqhubeke ngokuhlanu ufike ku-100 -100. • Ngaku -5 kusuka • Qala ku-10, uphinde uqhubeke ngokuyishumi ufike ku-100 • Ngaku -5 kusuka kunoma iyiphi kunoma iyiphi inombolo ku-100 Abafundi kumele bakwazi ukusebenzisa amakhono okubala emsebenzini inombolo kuya kma obhalwayo. Isibonelo: • Ngaku -2 kusuka -100 • Kopisha wenabe izinombolo ezilula ngokulandelana okungenani kuya ku-100. kunoma iyiphi • Ngaku -2 kusuka inombolo kuya ku-100 Bheka ingxenye kumaphethini ezinombolo kunoma iyiphi inombolo kuya kuma Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola -100

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.3 Ukufunda nokwazi Ukufunda nokwazi Yimuphi umehluko ku-Themu 3? izinombolo izinombolo Uphawu negama Ku-Themu 4, uhla lwezinombolo luthuthuka kuya ku-100. Ukubhala izimpawu lenombolo • Ukufunda nokwazi • Ukufunda nokwazi zezinombolo nezinombolo magama ziyahlanganiswa ngaleli-Themu. Alukho uphawu lwezinombolo uphawu lwezinombolo olwazi olusha olufundwayo. Kubalulekile ukuthi ukuqagela inombolo eyakhe kusuka ku-0 kuya kwi- kusuka ku-0 kuya kwi- iqoqo nokubala kuncike kwenzeni ngokucophelela nokusebenzisa izinombolo 100. 100. zamagama. Abafundi kumele basebenzise babhale izinombolo zamagama zezinhlobo ezahlukene zesimo. • Bhala izimpawu • Bhala izimpawu zezinombolo kusuka zezinombolo kusuka Ekugcineni kwe-Themu kufanele bakwazi ukwenza lemisebenzi elandelayo: ku-0 kuya ku-20 ku-0 kuya ku-20 Uqondanisa izimpawu, izithombe noma izinto zezithombe • Ukufunda nokwazi • Ukufunda nokwazi amagama ezinombolo amagama ezinombolo Leli khadi lith ku--6 Leli kadi lithini? kusuka ku-1 kuya kusuka ku-1 kuya kwi-10 kwi-10 6 11 • Bhala amagama • Bhala amagama ezinombolo kusuka ezinombolo kusuka Qondanisa amagama nezinto ku-1 kuya kwi-10 ku-1 kuya kwi-10 Kanye  Kubili ã ã ã  Kuthathu ì   Kune ëëëëë Kuhlanu  Isithupha õõ Isikhombisa ðððððð Isishiyagalombili ø ø ø ø  Shumi ööööööö 221 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 222 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.4 Hlela uqhathanise Ngokuhlela nokuqhathanisa izinto nezinombolo abafundi bafunda ukuthi: izinto zifike ku-20 Chaza, qhathanisa • Izinombolo ezisho isikhundla zisetshenziswa ukuchaza izinamba eziseqoqweni. bese uhlela • Qhathanisa amaqoqo ezinto ngobuningi / Yimuphi umehluko ku-Themu 3? izinombolo Izibalo IBANGA 1-3 okumbalwa; ngokuningi Abafundi baqala ukufundiswa ukubala okujwayelekile. kuno; okuncane kuno; kuningi ngango, Ekupheleni kwe-Themu nasekupheleni konyaka abafundi kumele bakwazi okuhlukene. ukusebenzisa ulimi oluhlelekile noluqhathanisayo ezindleleni ezithile: • Qoqa uhllele izinto Okokuqala, okwesibili, okwesithathu, okwesine, okwesihlanu, ngokuningi kuya okuyisithupha............. kokuncane nokuncane Bangakhi.......... kuya kokuningi. Okuningi njenge, izinombolo ezifanayo njenge..... • Uhla kufinyelela ezintweni ezi-20 Okulingana no, kukhulu kuno, kuncane kuno, kuyingcosana kono, kuningi kuno, Hlela uqhathanise Hlela, okokuqala, okokugcina, ngaphambi, emva, eduze, phakathi izinamba Izinombolo • Hlela izinamba Okokuqala, okwesibili, okwesithathu, okwesine, okwesihlanu, - Kusukela kokuncane okuyisithupha............. kuya kokukhulu; Bangakhi.......... kusuka kokukhulu kuya kokuncane Okuningi njenge, izinombolo ezifanayo njenge..... - engaphambi li, Okulingana no, kukhulu kuno, kuncane kuno, kuyingcosana kono, kuningi kuno, engmuva, ephakathi Hlela, okokuqala, okokugcina, ngaphambi, emva, eduze, phakathi nendawo - Usebenzisa umugqa wezinombolo ka 0 kuya ku -20 Faka umbala ophuzi endilingeni yesihlanu. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Qhathanisa izinombolo Faka umbala obomvu endilingeni yokuqala. ngokuthi inkulu kuna Faka umbala oluhlaza okwesibhakabhaka endilingeni yesishiyagalombili / incane kuna ining kuna / kumbalwa kuna; kulingana na

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.4 • Okukodwa nokukodwa Abafundi abaphendule imibuzo enjenga le okuhambisanayo Chaza, qhathanisa Ubani owokuqala emugqeni? bese uhlela • Uhla lwezinombolo Ubani owesibili emgqeni? izinombolo kufinyelela kwezi-20 UMthunzi unamakhilayoni ama-5. UCally unamakhilayoni ayisi-8 Sebenzisa izinombolo ezijwayelekile Ubani onamakhilayoni ambalwa? ukubonisa ukuhleleka, indawo noma Nginike inombolo ephakathi kwe-15 no- 17? isikhundla Bhala phansi izinombolo eziphakathi kwe-4 neziyi- 10 • Hlela izinto 1, 2, 3, 4, _, _, _, _, _, 10 ngokulandelana Gcwalisa izinombolo ezingekho kusukela kweyokuqala kuya kweyeshumi. Ngaphambili Izinombolo Ngemuva Hlela izinombolo 17 ngokulandelana ukusuka kweyokuqala ukuya 12 kweyeshumi 14 9 6 Bhala lezi zinombolo zihleleke kusuka kwezinkulu uya kwezincane Bhala lezi zinombolo usuka kwezincane uye kwezinkulu Kopisha ugcwalise usebenzise amagama “ngaphansi” noma “ngaphezulu”: • 35 anga _______ kunama- 38 • 79 anga __________kunama 65 Ukwazi ukuthi inombolo eza ngaphambili ingaphansi ngokukodwa kanti inomba eza ngemuva ingaphezulu ngenamba eyodwa. Iyiphi inamba efika ngaphambi kwe-17? Iyiphi inamba eza ngemuva kwama-82? 223 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 224 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.4 Gcwalisa izinombolo ezingekho emgqeni wezinombolo Chaza, qhathanisa   bese uhlela 85   86   87   88   89   90   91   92   93   94   95   izinombolo Beka isinombolo zamakhadi ezilandelayo ngohlelo: Izibalo IBANGA 1-3 yiziphi izinombolo eziphakathi kwama-25 no 30 Nginikeze inamba enkulu ngokukodwa engaphezulu kuka-76 Nginikeze inamba enkulu ngokubili engaphezulu kuka-76 Iyiphi inombolo engaphansi ngokukodwa kuno-45? Iyiphi inombolo engaphansi ngokubili kuno-39? 1.5 Ukubona ubungako Yimuphi umehluko ku-Themu 3? Ubungako benani benani lezinombolo Kuleli Themu abafundi baqhubeka nokwakha nokukhulisa ukuqonda ubungakho lenombolo ezimbili zedigithi -kuya benani lenombolo ku-20. Ku-Themu 4, abafundi basebenza ngohla lwezinombolo ezinkulu baqhubeke: • Hlukanisa izinombolo ezingamadigithi • Bala wenze amaqoqo ezinto ezilishumi nokukodwa okuseceleni; ahamba ngamabili • Bhala oku-18 = 1 okulishumi noku- 8 nokukodwa okuseceleni; ngeshumi • Bese ubhala oku- 14 = 10 no 4. nangokukodwa kuya ku-20 Isi: i-12 yi-10 Abafundi kumele baqhubeke nokusebenza bethinta izinsizakufunda kanye no-2 eziphathekayo ngokwamaqoqoqo ezinto ukwakha ngamashumi kokukodwa ukuze bakhe ukuqonda ukuthi iqembu leshumi nokukodwa okuseceleni Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Besebenzisa iabhakhasi (abucus)abafundi kufane bakwazi ukukhomba: • Ishumi elilodwa • Ishumi elilodwa nemivo emihlanu • Ishumi elilodwa nemivo eyisithupha

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.5 Lindela abafundi ukubala ngemivo ukwenza amaqoqo okuyishumi.kwabaningi kuphela kwendlela yokusho inombolo noma zingaki izinto ezilapho. Ubungako benani lenombolo Amakhadi asho ubungako benombolo (Place value cards/Flard cards) Amakhadi asho ubungako benombolo kufanele asetshenziswe ngaleThemu ukukhombisa indlela okwakhiwe ngayo inombolo.amakhadi asho ubungako benombolo angakhhonjiswa eceleni kwezinyanda noma amaqoqo ezinto. Izinsiza Izinto ezingaqoqwa: • Izinduku zokubala • Izinto zokubala ezingantshuntshwa • Izinti zikamentshisi • Izinti zika-ayisikhilimu • Amabhulokhi ahlanganayo • Amakhadi amele ubungakho benombolo • Imali yokudlala Kuyasiza ukuba namaqoqo okuyishumi ahlezi elungile abafundi abawaqoqile bawagcina ezitsheni. 225 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 226 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.6 Sebenzisa lamaqhinga Yini okwehlukile eThemu ye-3? Amaqhinga alandelayo ukuxazulula Uma kuphela leThemu abafundi baqala ukuxazulula izinkinga zamagama okuxazulula izinkinga zezibalo bese besebenzisa lamaqhinga: izinkinga uchaza isisombululo • Dweba noma izinsizakufunda Izibalo IBANGA 1-3 kanje: • Sebenzisa • Ukwakha nokuhlakaza izinombolo izinsizakufunda • Phindaphinda kabili ubuye uhlukanise kabili eziphathekayo • Umugqa wezinombolo • Sebenzisa izithombe Bheka amanothi e-Themu 2 ukubonisa izibalo eziyingxoxo • Ukwakha nokuhlakaza izinombolo • Phinda kabili ubuye uhlukanise kabili • Umugqa wezinombolo 1.7 Uxazulula izinkinga Uma kuphela leThemu abafundi kufanele babe bekwazi ukwenza / ukuxazulula Ukuhlanganisa zezibalo zamagama izinkinga ezifana nalezi ezingaphansi. nokususa ezisesimweni ushintsho esijwayelekile bese uchaza isisombululo uNoluthando unama apula ama- 5. uSilo umunika ama apula ayi- 8. Mangaki esebenzisa ama apula anowo manje? ukuhlanganisa nokususa Noluthando ubenama apula ayi-13. wanika uSilo ama apula ama- 5. mangaki ezibalweni ezinika ama apula asenawo manje? umphumela ofika ku-20. hlanganisa Nosisi unomabuli aba-5 aluhlaza satshani kanye nayisi-8 aluhlaza sasibhakabhaka. Bangaki omabuli anabo? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Nosisi unomabuli abayi- 13. aba-5 baluhlaza satshani abanye bonke baluhlaza sasibhakabhaka. Bangaki omabuli abaluhlaza sasibhakabhaka uNosisi anabo? Qhathanisa uNosisi unobhanana abayi-13. uThemba unobhanana aba- 5. bangaki ngaphezulu obhanana Nosisi anabo kunoThemba?

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.8 Uxazulula izinkinga Uma kuphela iThemu abafundi kufanele babe bekwazi ukwenza izinkinga Ukuphindaphinda zezibalo zamagama ezifana nalezi ezingaphansi. ukuhlanganisa ezisesimweni Ukuhlanganisa ngokuphindelela okuzoholela esijwayelekile bese uchaza isisombululo Amabhayisikili ama-4 anamasondo amangaki? ekuphindaphindeni esebenzisa Izinga ukuhlanganisa nokususa UThami uphuza izinkomishi ezi-2 zobisi nsuku zonke. Zingaki izinkomishi zobisi ezibalweni ezinika aziphuzayo ngesonto? umphumela ofika ku -20. amaGridi uMnu Khumalo utshala imigqa emi-3 yeklabishi. Kunezithombo ezi-5 emugqeni. Zingaki izithombo zeklabishi zizonke? 1.9 Uxazulula izinkinga Umakuphela iThemu kufanele abafundi babe bekwazi ukwenza izinkinga Ukwenza zezibalo zamagama ezifana nalezi ezishiwo ngezansi. amaqoqo kanye ezisesimweni esijwayelekile bese Ukwenza amaqoqo nokuhlukaniselana okuholela uchaza isisombululo Ukwenza amaqoqo, ulahle izinsalela ezibalweni esebenzisa ukuhlanganisa nokususa uStella ama apula angama-3 esikhwameni sisinye. Unama apula ayi-13. Zingaki zokuhlukanisa izikhwama ezinama apula ama-3 agazenza? ezibalweni ezinika umphumela ofika ku-20 Ukwenza amaqoqo, ufaka insalela kwimpendulo kanye nezimpendulo ezifaka izinsalela uBen ufuna ukuthatha amaqanda ayi- 15 awayise kugogo wakhe. Mangaki amabhokisi angathahta amaqanda ayi-6 lilinye awadingayo ukupakisha wonke amaqanda? Ukwehlukanisa ngokulinganayo Hlukanisa, ulahle insalela Hlukanisela abangani aba-3 ngokulingana oswidi abayi - 14 bathole inombolo elinganayo yoswidi. Hlukanisa, okuholela emaqhezwini Hlukanisela abangani aba-3 oshokoledi aba-4 bathole ngokulinganayo bonke kungasali lutho. (abafundi abavumelekile ukubiza ingxenye yeqhezu ngokukodwa kokuthathu.bangayichaza ingxenye yeqhezu kalula ngokuth:i “ okuncane”.) 227 Amaqoqo amaqhezu Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 228 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.11 • Ukubona ukhombe Uma kuphela iThemu abafundi kufanele babe bekwazi ukwenza izinkinga imali yaseNingizimu ezifana nalezi ezishiwo ngezansi. imali Afrika ewuhlweza 5c, uJohn uthenge isinkwa ngama- R8. Usikhokhele nge- R10 eliphepha. Yimalini 10c, 20, 50c, R1, R2; ushintshi awutholile? Izibalo IBANGA 1-3 R5 yephepha R10 no R20 Umama kaRosy’s uthenge isikhafu ngama- R17.usikhokhele ngamarandi ayishumi ama-2 anhamaphephayimalini ushintshi awutholile? • Ukuxazulula izinkiknga zemali ezifaka isamba Usuku lokuzalwa lukaJudy lwalungesonto. Uthole ama- R5 kudade wabo, ama-R2 umfowabo kanye nayi-R10 kumza wakhe.yimalini iyonke ayitholile? noshintshi kuyofika ku R20 no 20c UKUBALA Sebenzisa lamaqhinga Yimuphi umehluko eThemu 3? alandelayo ukwenza Abafundi kulindeleke baxazulile izibalo esimweni esikhululekile besebenzisa izibalo: lamaqhinga alandelayo: 1.12 • Imidwebo noma • imidwebo noma izinsizakufunda eziphathekayo izinsizakufunda Amaqhinga eziphathekayo • imidwebo yabafundi iqala ukubukela ngokohlelo kufanele bakwazi ukuchaza (izindlela noma izibalo zabo esekelwe kwimidwebo yabo. • Ukwakha nokuhlakaza amasu) izinombolo • Ukwakha nokuhlakaza izinombolo • ukuphinda kabili • ukuphinda kabili nokuhlukanisa kabili ngokulingana nokuhlukanisa kabili • umugqa wezinombolo ngokulingana bheka amanothi eThemu ye-2. • umugqa wezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.13 • Hlanganisa kufike Ukuhlanganisa nokususa phakathi kohla lwezinombolo 0 - 20 abafundi bazo: ema- 20 Ukuhlanganisa • Baqala ukuthuthukisa ulwazi lobumeli bungako bamashumi nemivo; nokususa • Susa kusukela ema- • Baqhubeka ukubala ngamaqoqo; kanye noku 20 • Kuqala ukubona ukuthi ukubala uqhubeka ngemivo akulona isu eliphusile. • Sebenzisa izimpawu ezifanele (+, –, =, ) Abafundi bazoqhubeka Learners will continue to: • Enza uphindelela • Bala izinto; amabhondi ezinombolo • Ukubona, ukufunda nokubhala izinombolo; kuze kufike ku-10 • Ukuqhqthanisa nokuhlela izinombolo. Ukuze usebenze ngezimpawu zokuhlanganisa nokususa; abafundi kufanele babe nolwazi oluphusile loku: • Bala konkecount all; • Bala uqhubeka kusukela kwinombolo enkulu ngokuthe xaxa; • Ukusebenzisa nokuqonda ulimi lokuhlanganisa nokususa; kanye • Hlela nokuqhathanisa izinombolo. Abafundi bazoqhubeka nokwakha ukuqonda ukuhlanganisa nokususa. Uma kuphela unyaka kufanele abafundi bakwazi uku: • Ukusebenzisa amagama asetshenziswayo ahlobene nokuhlanganisa nokususa kanye nezimpawu ukuchaza nokubhala phansi imisho yezinombolo yokuhlanganisa nokususa; • Sebenzisa izindlela ezingahleliwe ukwenza kanye nokubhala ukuhlanganisa nokususa; • Xazulula izibalo zokuhlanganisa nokususa kanye nokubhala phansi izimpendulo zabo ngemisho yezinombolo; • Ukuqonda ukuthi ukuhlanganisa akufani nokususa kanye nokususa akufani nokuhlanganisa ukusebenzise ukuthola nokubhala phansi izibalo. 229 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 230 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.13 Ukuqonda ukuhlanganisa nokususa sbafundi kufanele bakwazi uku: Ukuhlanganisa • Kukwazi ukusebenzisa iphuzu lokuthi indlela ukuhlanganisa oukuhleleke nokususa ngayo akusho lutho; Izibalo IBANGA 1-3 • ukusebenzisa izimpawu +, - kanye =; • ukwazi ukuthi  kumele inombolo engaziwa; • ukuqonda ukususa njengo “kuthahta konako” kanye “nokuthola umehluko phakathi”’; kanye • ukusho nokubhala namaphuzu ezinombolo ezihambisanayo kwiphuzu elinikeziwe lokuhlanganisa ngokuguquka.Isib. 8 + 6 = 14 kusho ukuthi 14 - 6 = 8. Ukubhala phansi imifanekiso yokuhlanganisa nokususa: Ngenkathi abanye abafundi besafuna ukubhala phansi nokubala ngemivo,badinga ukusizwa ukuqala ukubhala nokubala ngamaqoqo. Kufanele bakwazi uku: Dweba izithombe nokusebenzisa izinombolo,ngokugqamile bekhombisa amaqoqo. Ukuhlakaza izinombolo kube yizingxenye ezincane ukwenza izibalo zibe lula Abafundi bazohlakaza izinombolo kube izingxenye ezihlukene eziphathekayo. Abafundi bazoqala ngokuhlakaza okuyisikhombisa ngemivo; kepha ngesikhathi amaphuzu enombolo kufinyelela e-10 esesemqondweni abafundi bangasebenza ngezinombolo kwizinga eliphezulu, kufanele bahlakaze okuyisikhombisa kube izingxenye ezihlukene. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.13 Sebenzisa imicibisholo kanye nezinombolo ukukhombisa ukucabanga Ukuhlanganisa 11 + 7 =  nokususa 11 + 4 + 3 11 + 4 → 15 + 3 = 18 11 + 7 =  11 + 5 + 2 11 + 5 → 16 + 2 = 18 17 - 9 =  17 - (7 + 2) 17 - 7 → 10 - 2 = 8 Amabhondi ezinombolo Ukuzijwayeza amabondi ezinombolo, kufanele abafundi banikezwe imisebenzi ehlukahlukene ukuba bayenze,lokhu kwenzeka kahle ngesikhathi esikhululekile. Umugqa wezinombolo ungasetshenziswa ukuzijwayeza amabondi kufinyelela e-10. Basebenzisa ulwazi abaluthole ngaphimbilini njengeqhinga Lamaqhinga okhonjiswe ngezansi kuvumela abafundi ngokuhlela ukubala kwabo kanye nomqondo wezinombolo.ukuzilungiselela lamaqhinga engezansi azokhuthaza abafundi ukucabanga ngobudlelwane phakathi kwezinombolo kanye nokufundisa abafundi ukusebenzisa ulwazi ukubasiza ukwenza izibolo. Beka inombolo enkulu kakhulu kuqala ukuze ubale uqhubeka noma uye emuva. 4 + 12 =  Hlela kabusha 4 + 12 njenga 12 + 4 ubale uqhubeka kusukela e-12. 231 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 232 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.13 Bala uqhubeka kusukela kwinombolo enkulu kakhulu Ukuhlanganisa Abafundi kufanele bakwazi kubala beqhubeka kusukela kwinombolo enkulu nokususa kakhulu.lokhu kuyiqhinga elilunge kakhulu kunokubala ngemivo kufiytelela e-14 kanye nokubala ngokuhlanu nangaphezulu. Izibalo IBANGA 1-3 14 + 5 =  Abfundi babala kusukela kokuyi 14, kuqhubeke kuye 15, 16, 17, 18, 19. Khomba izinombolo eziseduze kweziphindeke kabili 8+7 Abafundi bangachaza ukuthi isibalo singabhalwa kanje 8 + 8 -1 (okuphindwe kabili 8 hlanganisa 1) noma 7 + 7 + 1 (okuphindwe kabili 7 hlanganisa 1). Abafundi bangabhala phansi amasu abo besebenzisa imicibisholo: 8 + 8 → 16 + 1 = 17 Shintsha inombolo iye eshumini bese ususa noma wengeze okukodwa Lelisu lingafundiswa ngezinombolo ezisohleni oluphansi lungasetshenziswa kwizinombolo eziphezulu. 9+6= Abafundi bangasho: “ngikhipha okukodwa kokuyi-6 ngiyokwengeza ngokuyi-9 ukwenza okuyi-10.” Okuyi- 9 + 6 kungabhalwa kanje 10 + 5 = 15 8+5= Abafundi bangasho kuboThe learners can say to themselves: “ngikhipha okubili koku-5 ngiyokwengeza kokuyi-8 ukwenza okuyi-10.” Okuyi- 8 + 5kungabhalwa kanje 10 + 3 = 13 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.13 Sebenzisa ulwazi ekuphambaneni kobudlelwane phakathi kokuhlanganisa nokususa Ukuhlanganisa nokususa 15 - 9 =  Umfundi uyazi ukuthi isibalo singaphinde sibhalwe njengesibala sokuhlanganisa “ngiyazi ukuthi 9 +  = 15.” Umfundi angasebenzisa ukubala ukwenza izibalo. Umugqa wezinombolo Kufanale bakwazi ukusebenzisa umugqa wezinombolo ukweseka ukwenza kwabo izibalo.Isib. 13 + 6 1.14 • hlanganisa inombolo Yimuphi umehluko eThemu 3? efanayo ngokuphin- Ukubala Ku-Themu 4, abafundi baqhubeka nokwakha ulimi ngokuphindaphinda daphinda kufinyelela ngokuphindaphinda kokuhlanganisa. Isibonelo: ema- 20 okuholela • Amaqoqo ama-2 ezinto ezi-3 ekuphindaphindeni • sebenzisa izimpawu ezifanele (+, =, ) • Amaqoqo ama-4 ezinto ezi-2 Abafundi baqhubeka nokubhala imisho yezinombolo okwethulwa okusazithombe. Ukubala okweqayo kumele kuqhubeke ukuze kusize abafundi ekubala izinto eziqoqelwe ezithombeni. Uma izithombe noma izinto eziqoqwe ngokubili abafundi kumele babale ngokubili hhayi ngokukodwa ukuze bathole isamba sezinto. Ukuphela kweThemu abafundi kufanele bakwazi uku: • Ukuqonda ukuhlanganisa ngokuphindaphinda njengokwenza amaqoqo okul- inganayo; • Khombisa ukuhlanganisa ngokuphindaphinda usebenzisa izinto eziphathek- ayo kanye nemidwebo; • Bhala phansi imisho yezinombolo ezihambisanayo nokwenziwayo noma imidwebo; • sebenzisa umugqa wezinombolo ukufinyelela kwimpendulo. 233 Izibalo IBANGA 1-3

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO 234 IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.16 Number concept: Yimuphi umehluko eThemu 3? Range 20 Izibalo zekhanda eThemu 4, uhla lwezinombolo luyakhula kusuka e-15 kufinyelela ema- 20. • isho inombolo Isibonelo semibuzo nemisebenzi engabuzwa noma yenziwe: engaphambi Izibalo IBANGA 1-3 kanye nasemuva • Qala ngoku-3 ubale uya phambili ngakunye kuya kwi-10. kwenombolo • Abafundi bama umugqa babuze: ngobani wokuqala, wesibili, wesithathu noma oyinikeziwe.hlela wokugcina? iqoqo lezinombolo ozinikeziwe • Ngubane ongaphansi kuka-14 noma ku-8? ezikhethiwe. • Ngubane ongaphezulu ku-8 noma ko-4? • Qhathanisa izinombolo kufinyelela ema- • Yini oku-2 okuncane kunaku-13? 20 usho okuphi • Yini oku-2 okwedlula u-8? okungaphezu nokungaphansi. • Nginike inombolo ephakathi kuka-1 no-3. • Yazi ukuthi iyiphi • Nginike inombolo ephakathi kwe-10 ne-13. Ingabe kunenamba eyodwa? inombolo engaphezu • Hlela lezi zinombolo zamakhadi ngokuyikho usuka kwezincane uya kwezinkulu. ngokukodwa noma ngaphansi. Ukukhumbula ngokushesha • Yazi ukuthi iyiphi Bonisa izinombolo zokuhlanganisa ezenza okuyi-10 (zibhale phansi noma inombolo engaphezu usebenzisa ubungakho benani lezinombolo noma amakhadi okusebenza noma ngaphansi okwakha izinombolo) ngoku-2 nangaphansi a) 1 Ukukhumbula b) 2 ngokushesha: c) 3 • Amphuzu okuhlanganisa d) 4 nokususa kufinyelela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola -10

UKUQONDA UKUQONDA OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO CAPS IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI OKUDINGEKAYO OKUBHEKWAYO EKUPHELENI KU-THEMU 1 KONYAKA 1.16 Amaqhinga okubala Bonisa izinombolo ngakwesokunxele uma....kususiwe kusuka kuyi-10 (zibhala phansi noma usebenzisa ubungakho benani lezinombolo noma amakhadi Izibalo zekhanda Sebenzisa amasu okusebenza okwakha izinombolo) okuhlanganisa nokususa ngokugculisayo: a) 1 • Beka inombolo enkulu b) 2 kuqala ukuze ubale c) 3 uqhubeke noma uhlehle d) 4 • Umugqa wezinombolo e) 6+ 4 = 10 yini oku- 4 + 6? Ingabe impendulo iyafana? • Ukuphinda kabili f) 5 + 2 = 7 yini oku- 2 + 5? Ingabe impendulo iyafana? nokuhlukanisa kabili Amasu okubala inombolo Sebenzisa amasu okuhlanganisa nokususa ngokugculisayo: • Ukwakha nokuhlakaza inombolo Hlanganisa okulandelayo ngokufaka izinombolo ezinkulu kuqala bese uqhubeka nokubala: 1+9 2+6 1+4 Okuphindwe 1 Yini okubili 2s? Yini okuyinxenye we-4? Sebenzisa umugqa wezinombolo Ugxuma kangakhi ukusuka koku-3 kuya koku-5? Ugxuma kangakhi uhlehla usuka koku-5 kuya koku-2? 235 Izibalo IBANGA 1-3

236 ITHEMU YESI-4 YEBANGA LOKU -1 2. AMAPHETHINI, UBUDLELWANE, NE - ALJEBHRA UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 2.1 Kopisha, uqhubeke Amaphethini atholakala Abafundi bazosebenza ngamaphethini akwimvelo, ngokwempilo ephilwa manje Isifundo 1 Izibalo IBANGA 1-3 uchaze lapho siphila khona nangokwamasiko kusukela eBangeni loku - 1 kuya kwelsi - 6. Lokhu kusho ukuthi Amaphethini akudingeki uchithe isikhathi esiningi kulesisihloko. Kumele ukhethe imisebenzi okusejiyometri Kopisha, uqhubeke Bona, uchaze namaphethini alungele ibanga ngalinye. uchaze ngamagama ngamagama ubuye ukopishe amaphethini EBangeni loku - 1 abafundi bangenza amaphethini abawathathela kwamanye. • Amaphethini alula okusejiyometri enziwe ngezinto Ezinye zezibonelo zamaphethini amacembe ezihlahla, amagxolo, insoli ezphathekayo • kwimvelo yezicathulo, amathayi, njll. • Amaphethini alula • kusuka kwimpilo Inhlobo eyodwa yephethini izingane ezingabuka kuyo okufana nse nxa zombili enziwe ngokudweba yesimanje (symmetry) isib.amacembe amaningi afana nse nxa zombili. imigqa, izimo, noma • kusuka emasikweni Abafundi bangabuye babuke amaphethini ocingweni (ucingo, ukhuni) izinto ayigugu Izitini ezisebhilidini kanye nesiyingi esinamathayili; Akha amphethini akho Akha amphethini akho Izingubo nezinto; Akha amaphethini Akha amaphethini okusejiyometri Amapuleti, izinkomishi, amasoso; okusejiyometri • Ngezinto Amabhola; • Ngezinto eziphathekayo eziphathekayo Izilwane ezifana nezinkomo, ibhu, umvemvane, idumbe, indlulamithi, izinyoni, • Ngokudweba imigqa, izintethe, izimbali, izinto ezenziwe ngobumba • Ngokudweba imigqa, izimo noma izinto izimo noma izinto Kunezindlela ezahlukene zokuchaza amaphethini atholakala endaweni Amaphethini atholakala eseduzane. Amaphethinin amaningi atholakala eduze / kalula enziwe ngemigqa, lapho siphila khona ngezimo noma ngezinto. Izimo noma izinto azidingi ukuxhunyaniswa nezimo zezinto ezisejiyometri ezinhlangothimbili esenziwe eBangeni 1. Abafundi Bona, uchaze bangabheka bachaze ngamagama ubuye ukopishe amaphethini • Ukuthi yikuphi ngokuphindelela, isib. imigqa, noma iyiphi inhlobo yesimo, Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola okusejiyometri amachashaza • kwimvelo • Olayini abaphindaphindiwe isib. ingabe olayini bayaphambana njengalabo abakwindwang yezitsha, ngabe amachasha angosayizi abalinganayo, ngabe • kusuka kwimpilo imibala iyefana, ingabe babheke endaweni eyodwa, njll. yesimanje • kusuka emasikweni ayigugu

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 2.2 Kopisha, qhubezela, Kopisha, qhubezela, Ukulandelana kwezinombolo kungahlanganiswa nokubala. Njengoba ikhono Izifundo ezi - 3 chaza chaza labafundi lokubala liya ngokuthuthuka nangokushintsha, izinhlobo zokuhlelwa Amaphethini kwezinombolo abafundi abasenza ngazo zingathuthuka. ezinombolo Kopisha, qhubezela Kopisha, qhubezela uchaze ukuhlelka uchaze ukuhlelka Ukulandelana kwezinto kufanele zikhombise: kwezinombolo ezilula kwezinombolo ezilula • Ukubala uye phambili nasemuva ngoku - 1 kusukela kunoma iyiphi inombolo kufinyelela okungenani kufinyelela okungenani phakathi koku 1 kuya e - 100 e - 100. e - 100. • Ukubala uye phambili ngama-: Akha amaphethini akho Ukulandelana kwezinto kufanele zikhombise: - Shumi kusukela kunoma yiziphi izinombolo eziphinda ngama - 10s phakathi Qamba amaphethini kwe - 0 kuze kufike e - 100 akho ezinombolo. • Ukubala uye phambili nasemuva ngoku - 1 - Ngoku - 5s kusukela ku - 5 kuya e - 100 kusukela kunoma iyiphi - Ngoku - 2s phakathi kwe - 0 ne - 100 inombolo phakathi koku 1 kuya e - 100 Abafundi bangakhomba izinombolo ezisemgqeni wezinombolo, kwigridi yezinombolo, noma ngokulandelana kwezinombolo okubhalwe phansi. • Ukubala uye phambili ngama-: Abafundi bangagcwalisa izinombolo ezimgekho kuhlelo lwezinombolo, emgqeni wezinombolo noma kwigridi yezinombolo ukuzilungiselela ukubala. Abafundi - Shumi kusukela babhala kuze kufike ema - 20. Bheka amanothi eThemu yes - 3 ukutze ubone kunoma yiziphi ukuthi abafundi bangasebenza kanjani ngohlelo lwezinombolo ukwedlula ema - izinombolo ez- 20. iphinda ngama - 10s phakathi kwe - 0 kuze kufike e - 100 - Ngoku - 5s kusukela ku - 5 kuya e - 100 - Ngoku - 2s phakathi kwe - 0 ne - 100 Akha awakho amaphethini akho Akha izinombolo zamaphethini akho. 237 Izibalo IBANGA 1-3

ITHEMU YESI-4 YEBANGA LOKU -1 3. INDAWO NESIMO (IJIYOMETRI) 238 UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO NAMAKHONO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA (ezifundweni eziyi ULWAZI ALINDELEKILE OKUQXILWA KUWO WOKUFUNDISA awa elilodwa kuya EKUPHELENI NGETHEMU 3 kumaminithi anga 24) KONYAKA 3.1 Ulimi oluchaza ukuthi Ulimi oluchaza ukuthi Isikhundla nezinkomba Isifundo esisodwa leyonto ikusiphi leyonto ikusiphi Isi Isikhundla, Bheka amanothi aku Themu 1 isikhundla. isikhundla. Izibalo IBANGA 1-3 inkomba Ulimi olusha olusetshenziselwa isikhundla kumele luthulwe kusebenzisiswa nokubukeka Chaza isikhundla sento Chaza isikhundla sento imisebenzi enezinto eziphathekayo ezizokwenza abafundi banyakazise kwento usiqhathanisa nenye. usiqhathanisa nenye. imizimba yabo. Lokhu kungenziwa ngesikhathi befunda beliklasi lonke Isibonelo: ingaphezulu, Isibonelo: ingaphezulu, bephelele noma befunda besemaqoqweni. ingaphambi, ingemumva, ingaphambi, ingemumva, ingakwesokunxele, ingakwesokunxele, Izinkombandlela zifundwa ngokufundisa abafundi isifundo esenza ingakwesokudla, iphansi, ingakwesokudla, iphansi, banyakaze noma basebenzisa izinto eziphathekayo ngokuyalela kukathisha. iseduze kwalokhu, njll. iseduze kwalokhu, njll. Kungafundwa lokhu abafundi bafunda bephelele noma ngesikhathi sokufunda ngamaqembu. Isikhundla nezinkomba Isikhundla nezinkomba Isikhundla sento nokubukeka kwayo. • Landela izinkomba • Landela izinkomba Abafundi abasemazingeni ayisisekelo kumele bakwazi ukuthi izinto zibukeka ukunyakaza uzungeza ukunyakaza uzungeza ngezindlela ezingafani uma ukwesinye isikhundla. Abafundi bangacabanga ekilasini. ekilasini. ukuthi izinto zibukeka ngokufana noma uzibuka ungakuliphi icala. Isibonelo imoto ingabukeka incane uma ukude. Abafundi noma besebenzisa izincwadi • Landela imiyalelo • Landela imiyalelo kumele bakwazi ukubona isithombe engaphambili sinesithombe esikhulu ukubeka into ibe ukubeka into ibe kunesingemumva. Uma sekufundwa ngamaqoqo abafundi bengenza nobudlelwane nenye. nobudlelwane nenye. belinganisa ngokubeka izandla phambi kwaboe ukusitha ukubo na into Isibonelo: Faka ipeni Isibonelo: Faka ipeni enkulu ekude. EBangeni -I abafundi kumele banikwe umsebenzi wokubuka phakathiebhokisini. phakathiebhokisini. izinto zisesikhundleni esihlukile. (Isibonelo: Ukubuka ungaphezulu, ukubuka Isikhundla sento Isikhundla sento useceleni,ukubuka ungaphambili) ezintweni abazibona nsukuzonke. nokubukeka kwayo. nokubukeka kwayo. Lokhu kungaholela ekutheni abafundi bakwazi ukuhumusha iimidwebo Qondanisa ukubukeka Qondanisa ukubukeka eyizibalomdwebo zenziwa ngezindlela ezahlukahlukene. kwento eyodwa efanayo kwento eyodwa efanayo ngokubukeka kwayo ngokubukeka kwayo okwahlukene okwahlukene Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO NAMAKHONO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA (ezifundweni eziyi ULWAZI ALINDELEKILE OKUQXILWA KUWO WOKUFUNDISA awa elilodwa kuya EKUPHELENI CAPS NGETHEMU 3 kumaminithi anga 24) KONYAKA 3.2 Uhla lwezinto Uhla lwezinto Ukusebenza ngezinto ezinhlangothintathu (3-D) ukuhlanganisa kunenziwa Isifundo esi-1 ngomsebenzi obhalwayo. Izinto ezinhlang- Ukubona bese esho Ukubona bese esho othintathu 3-D izinto ezinhlangothintathu izinto ezinhlangothintathu ekilasini nasezithombeni. ekilasini nasezithombeni. • Izimo esiyibhola • Izimo esiyibhola (izimbulunga) (izimbulunga) • Izimo zisamabhokisi • Izimo zisamabhokisi (iphrizimu) (iphrizimu) Izimpawu zezinto Izimpawu zezinto Chaza, uhlele bese Chaza, uhlele bese uqhathanisa izinto uqhathanisa izinto ezinhlangothintathu ezinhlangothintathu ngoko: ngoko: • Bungako • Bungako • Mbala • Mbala • Izinto eziginqikayo • Izinto eziginqikayo • Izinto esishelelayo • Izinto esishelelayo Imisebenzi okugxilwa kuyo Buka bese wakha izinto ezinhlangothintathu usebenzisa izinto eziphathekayo njengamabhuloki okwakha nokusebenziswa kabusha nezinto ezisekhithini yokwakha. 239 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA NAMAKHONO NAMAKHONO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA (ezifundweni eziyi ULWAZI ALINDELEKILE 240 OKUQXILWA KUWO WOKUFUNDISA awa elilodwa kuya EKUPHELENI NGETHEMU 3 kumaminithi anga 24) KONYAKA 3.3 Uhla lwezimo Uhla lwezimo Bheka amanothi akuThemu 2 Izifundo ezi-3 Izinto ezinesimo Ukubona usho izimo Ukubona usho izimo Abafundi basebenza ngendilinga nangezikwele zobungako obungafani esinhlangothimbili ezinhlangothimbili ezinhlangothimbili onxande abanezimo ezingafani. Bawahlela ngokwamacala aqondile nayindilinga. • Okuzindilinga • Okuzindilinga Abafundi bahlela bese bebeka ngamaqoqo izimo ngokuthi Izibalo IBANGA 1-3 • unxantathu • unxantathu ziwunxande,isikwele noma indilinga. • izikwele • izikwele Ukusebenza ukuhlanganisa kungenziwa ngomsebenzi obhalwayo. Izimpawu zezimo Izimpawu zezimo Chaza, uhlele bese Chaza, uhlele bese uqhathanisa izimo uqhathanisa izimo ezinhlangothimbili ngoko: ezinhlangothimbili ngoko: • bungako • bungako • mbala • mbala • amacala aqondile • amacala aqondile • amacala ayindilinga • amacala ayindilinga 3.4 Okufana nse nhlangathi Okufana nse nhlangothi Abafundi kufanele bathole umugqa ohlukanisa izinto eziphathekayo Isifundo esi-1 zombili nezithombe kulingane kufane nse nhlangothi zombili. Okufana nse • Ukubona bese nhlangothi zombili • Ukubona umugqa udweba umugqa Imisebenzi ebhalwayo ohlukanisa umzimba ohlukanisa kufane nse • Akufanele ibe imiyalelo yokudweba ” ingxenye esele” kodwa phakathi nendawo nhlangothizombili izimo izinhlangothi zombili ezinhlangothimbili • Ayifake izibonelo ezifuna abantwana badwebe umugqa ohlukanisa izinto zifane nse. ezintweni kulingane nse nhlangothi zombili.umugqa ohlukanisa kabili kufane nse eziyizibalomdwebo akumele uhlale njalo usuka phezulu uya phansi. • Ukubona bese nezingejiyometri. udweba umugqa ohlukanisa kufane nse nhlangothizombili izimo ezinhlangothimbili Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ezintweni eziyizibalomdwebo nezingejiyometri.

Ibanga 1 ITHEMU YE - 4 4. ISILINGANISO UMQONDO ISIKHATHI CAPS UMQONDO KANYE NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.1 Ukwedlula kwesikhathi Ukwedlula kwesikhathi Abafundi kumele bakwazi ukukhuluma ngalokhu: Isifundo esi-2 Isikhathi Khuluma ngokwedlula Khuluma ngokwedlula • Ukuhleleka kwezigameko kwesikhathi kwesikhathi • ngesikhathi. • Hlela izigameko • Hlela izigameko Abafundi bayaqhubeka bahlanganise izindlela zokukhuluma ngesikhathi ezivamise ukwenzeka ezivamise ukwenzeka nsukuzonke ngesikhathi sokufunda kwekilasi lonke noma iqoqo okugxilwa kulo empilweni (yakhe empilweni (yakhe umfundi) umfundi) Abafundi bakhuluma ngezimpendulo ngokwenzekile, kusetshenziswa uLimi olufana nalolu: ekuseni, ntambama, ebusuku. • Qhathanisa ubude • Qhathanisa ubude besikhathi usebenzisa besikhathi usebenzisa Abafundi bahlela izigameko besebenzisa uLimi olufana nalolu: izolo, namuhla, uLimi, isib. okude uLimi, isib. okude kusasa, izinsuku zesonto kanye nezinyanga zonyaka. ngokuthe xaxa, ngokuthe xaxa, okushesha ngokuthe okushesha ngokuthe xaxa, kancane kahulu xaxa, kancane kahulu Abafundi baqhathanisa ubude besikhathi kusetshenziswa uLimi olufana nalolu: okude kunku-, okufishane kune-, okusheshayo, okuhamba kancane • Hlela izigameko • Hlela izigameko usebenzisa uLimi usebenzisa uLimi Abafundi bahuluma ngokuhlela izigameko bezisusela ezimpilweni zabo. Babuye njengokuthi: izolo, njengokuthi: izolo, bahlele izithombe ezifana nalezi: namuhla, kusasa namuhla, kusasa • izindlela zokwenza itiye; Ukusho isikhathi Ukusho isikhathi • izithombe ezikhombisa ukukhula kwengane ize ndala; • Sebenzisa uLimi • Sebenzisa uLimi ukuchaza uma into ukuchaza uma into • impilo yezilwane - kusukela zizalwa zize zibendala, yenzeka, isib. ekuseni, yenzeka, isib. ekuseni, • izigameko ezejwayelekile nosuku (ukuvuka, ukuba sesikoleni, ukudla isidlo ntambama, ebusuku ntambama, ebusuku sasebusuku, ukudlala, ukulala). • Ukukwazi izinsuku • Ukukwazi izinsuku Abafundi bayaqhubeka babhale izinsuku zokuzalwa kwabo kwikhalenda. zesonto zesonto • Ukukwazi izinyanga • Ukukwazi izinyanga zonyaka zonyaka • Ukukhombisa izinsuku • Ukukhombisa izinsuku zabo zokuzalwa zabo zokuzalwa kwikhalenda kwikhalenda 241 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 242 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.2 Ukukala Zonke izilinganiso okungahlelekile eBangeni 1azihlelekile. Ubude Azikho izilinganiso • qhathanisa uhlele ezihlelekile ubude, ukuphakama, zobude ezinezikali noma ububanzi bezinto ezinesilinganiso ezimbili nangaphezulu Izibalo IBANGA 1-3 ezenziwayo. ngokuzibeka eduze kwezinye Ngesikhathi sokusebenza ngokuzimela iThemu • Sebenzisa uLimi yonke, abafundi ukukhuluma bangenza bahlanagnise ngokuqhathanisa, isib. isilinganiso sobude, okude ngokuthe xaxa, ububanzi, kanye nokuya okufishane kakhulu, phezulu okunamaunithi okude kakhulu, ahlelekile. Wonke okubanzi ngokuthe umsebenzi kufanele xaxa ubhalwe phansi. Bheka • Hlawumbisela, amanothi aeThemu yesi linganisa, qhathanisa, - 3. hlela, ubuye ubhale phansi ubude bento usebenzisa isikali esingenasilinganiso, isib. Izandla, izinto Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola zokubala, njll.

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 4.3 Isilinganiso Isilinganiso Konke ukulinganisa eBangeni 1 akuhlelekile. Akukho ukulinganisa okuhlelekile 2 izifundo esingahlelekile esingahlelekile kwesisindo okwenziwa ngesikali esihlelekile. Isisindo • hlawumbisela, • Hlawumbisela, Yini okwehlukile kuThemu yesi - 4? linganisa, qhathanisa, qhathanisa, hlela ngThemu yoku - 1 kwaphakamiswa ukuthi abafundi kumele kugxilwe kulokhu: hlela ubuye ubhale ubuye ubhale phansi phansi isisindo usebenzisa izikali • Ukuqhathanisa ngqo isisndo sezinto; usebenzisa isikali ezingenasilinganiso • Hlela ubuye uqhathanise izisindo zezinto ezintathu nangaphezulu ngokubeka esingenasilinganiso nokuzimelela, isib. izinto ngazimbili zizimelele kuze kube zonke izinto zihleleke ngokwezisindo nokukala amabhuloki, izitini njll. ngokulinganisa • Ukuthuthukiswa koLimi ukukhuluma ngezisindo ezahlukene. • Sebenzisa uLimi • Sebenzisa uLimi ukuhuluma NgeThemu yesi - 4 abafundi bagxila ekwenzeni ukulinganisa okungahlelekile ukukhuluma ngokuqhathanisa, kusetshenziswa isikali esingenasilinganiso. ngokuqhathanisa, isib. isib. kulula, kusinda kulula, kuyesinda, kakhulu, kulula kakhulu Ukulinganisa okungahlelekile kwesisindo kusetshenziswa isikali kulula kakhulu, kusinda esingenasilinganiso ukukala amayunithi kakhulu Abafundi bangafunda yonke imigomo nokwenza kokulinganisa kusetshenziswa isikali esingenasilinganiso smaunithi. Ukulinganisa ngesikali esingenasilinganiso samaunithi akufanele sithathwe njengesingabalulekileukulinganisa ngesikali esinesilinganiso. ukulinganisa isisndo ngesikali esingenasilinganiso kufaka ukubala ukuthi mangaki amaunithi anesisindo esifanayo uma kukalwa amaunithi. Isib. irula linesisindo esifanayo namabhuloki ayisi - 9. Abafundi kufanele balinganise izinto ezihlukene besebenzisa uhla lwezinto ezinamayunithi angahlelkile. Abafundi kufanele bafundiswe izindlela zokuthi bekwazi ukusho uma iyunithi ikhombisa isisindo, isib. incwadi inesisindo esifanayo nomabuli abangama - 34. Uma abafundi selinganisile amayunithi izikhathi eziningana, kufanele bahlawumbisele ukuthi mangaki amayunithi alingana nesisindo sento ethile ekaliwe. Ukuhlawumbisela kubalulekile, kodwa kungenziwa kuphela uma abafundi sebeke benza ukulinganisa ngaleyoyunithi. 243 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 244 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.3 Abafundi kufanele bafundiswe ukuze bakwazi ukuqhathanisa isisndo sezinto ezihlukene, abafundi kufanele bafundiswe ukuze bakwazi ukuqhathanisa Isisindo izinto ezahlukene, kufanele kube iyunithi efanayo. Isib. uma irula linesisindosamabhuloki esingama - 20 nesikelo esinesisindo somabuli abagama 20, angeke ukwazi ukusho ukuthi kuesisindo esifanayo noma qha,noma yikuphi okusinda ukwedlula okunye. Izibalo IBANGA 1-3 Ukubhalwa phansi kokulinganisa Nakuba ukulinganisa kuyikhono elenziwayo, abafundi kufanele babhale izilinganiso zabo. Ukulinganiswa kwesisindo ngesimo esejwayelekile ukuze kubalwe kubuye kuxazululwe izinkinga zezibalo Ngesikhathi esinikezwe inombolo, ukusebenza kanye nobudlelwane bezinombolo, abafundi bangaxazulula izinkinga ezisebenzisa isimo esejwayelekile sokulinganisa isisind. Isib. Indwango yokwesula ibhodi inesisindo somabuli abayi -11. Ibhokisi lamakhrayoni linesisindo somabuli abayi - 8. Sekukonke kunesisindo somabuli abangaki? Bheka uhla lwezinombolo lweThemu, nohla lwezinhlobo zezinkinga ezilungele iThemu. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 4.4 Isilinganiso Isilinganiso Konke ukulinganisa eBangeni 1 akuhlelekile. Akukho ukulinganisa okuhlelekile Isifundo esi - 1 esingahlelekile esingahlelekile kwesisindo okwenziwa ngesikali esihlelekile. Umthamo • Qhathanisa ubuye • Hlawumbisela, Yini okwehlukile kuThemu yesi - 4? uhlele inani lomthamo qhathanisa, hlela, ngeThemu yoku - 1 kwaphakamiswa ukuthi abafundi kumele kugxilwe kulokhu: kwizitsha ezimbili ubuye ubhale phansi ezibekwe eduze umthamo osezitsheni • Ukuthuthukiswa koLimi ukuxoxa umehluko phakathi komthamo; kwesinye. Abafundi ngokusebenzisa isikali • Ukuqhathaniswa komthamo osezitsheni ezifanayo ezitsheni baqinisekisa ngokuthi esingenasilinganiso, babuye bathele isib. izipuni, izinkomishi • Qhathanisa umthamo osezitsheni ezimbili ezibukeka ngokufana, ikakhulukazi esitsheni sesithathu lezo ezibanzi neziwumncingo. uma kunesidingo NgeThemu yesi - 4 abafundi bagxila ekwenzeni ukulinganisa okungahlelekile • Qhathanisa ubuye kusetshenziswa isikali esingenasilinganiso somthamo. uhlele inani lomthamo ongathathwa izitsha Yini umthamo? ezimbili ezigcwele Ibhodlela lingathatha umthamo oyizinkomishi ezine, kodwa kunokwenzeka • Sebenzisa ukukhuluma lingagcwali nswi, lingathatha umthamo wenkomishi eyodwa yamanzi ngesikhathi ngokuqhathanisa, isib. esithile. okungaphezu kokunye, Umthamo inani elingathathwa into ethile (noma ubungako bendawo ngaphakathi okungaphansi kwento ethile). kokunye, okugcwele, okungenalutho Uthamo yinani lendawo elithathwa yilokho okuthelwe entweni. • Hlawumbisela ubuye Ngesinye isikhathi anafundi bangalinganisa ukuthi ungakanani umthamo ulinganise, qhathanisa wonketshezi osesitsheni. Lokhu kulinganisa umthamo wokusaketshezi ubuye uhlele okusesitsheni. umthamo wezitsha Kokunye abafundi bazobe belinganisa ukuthi isitsha singathatha umthamo usebenzisa isikali ongakanani. esingenasilinganiso, isib. izipuni, izinkomishi Ukulinganisa okungahlelekile kobude kusetshenziswa isikali esingenasilinganiso Abafundi bangafunda imigomo babuye benze ngokuphindaphinda ukulinganisa kusetshenziswa isikali esingenasilinganiso ngamayunithi. ukulinganisa amayunithi ngesikali esingenasilinganiso akufanele kunakwe uma kulinganiswa ngesikali esinesilinganiso ngokwamayunithi. Abafundi kufanele banikezwe ithuba lokulinganisa umthamo besbenzisa uhla lwezinto ngamayunithi angahlelekile, isib. Izinkomishi, izipuni, izivalo zamabhodlela, amathini, amabhodlela, njll. 245 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 246 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 4.4 Ukulinganisa umthamo ngesikali esingenasilinganiso ngamayunithi kufaka ukubala izikhathi ogcwalisa ngazo into kuze kufike kumthamoofunekayo. Umthamo Abafundi kufanele bafundiswe ngasosonke iskhathi ukusho amayunithi, isib. Kunezipuni ezingama 48 zamanzi ebhodlelni. Uma abafundi sebelinganisile amayunithi izikhathashana, kufanele Izibalo IBANGA 1-3 bahlawumbisele ngaphambi kokulinganisa umthamo weyunithi. Ukuhlawumbisela kubaluleke kakhulu, kodwa kungenzeka kuphela uma abafundi sebeke benza ukilinganisa ngamayunithi. Abafundi kufanele bafundiswe ukuthi ukuze bakwazi ukuqhathanisa umthamo, kufanele kusetshenziswe iyunithi efanayo. Isb. Uma ingilazi ithatha umthamo ongamathesipuni angama 20 amanzi kanye nezinkomishi ezingathatha amathesipuni ayi - 10 amanzi, angeke uthi ingilazi ithatha umthamo omkhulu wamanzi. Abafundi badinga ukulinganisa uhla lwamayunithi angahlelekile ukuze: • Baqala ukuqonda ukuthi uma amayunithi amancane kakhulu udinga isikhathi esithe xaxa ukuwagcwalisa. Isib. Umthamo webhodlela ungaba amathesipuni angama -20. • Qala ukusebenzisa amayunithi afanele kulokho okulinganiswayo isib. Ukulin- ganiswa kwebhodlela elingamalitha amabili kusetshenziswa ithispuni kuwuku- chitha isikhathi. Ukubhalwa phansi kokulinganisa Nakuba ISILINGANISO kulikhono, abafundi kufanele babhale phansi lokho abakulinganisile ngasosonke isikhathi. Ukulinganiswa kwesisindo ngesimo esejwayelekile ukuze kubalwe kubuye kuxazululwe izinkinga Ngesikhathi esinikezwe iainombolo, ukusebenza kanye nobudlelwane bezinombolo, abafundi bangaxazulula izinkinga ezisebenzisa isimo esejwayelekile sokulinganisa isisind. Isib. Indwango yokwesula ibhodi inesisindo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola somabuli abayi -11. Ibhokisi lamakhrayoni linesisindo somabuli abayi - 8. Sekukonke kunesisindo somabuli abangaki?

YEBANGA LOKU- 1 ITHEMU YESI-4 5. UKUQOKELELWA KOLWAZI ISIKHATHI CAPS UKUQODA NANKHONO ULWAZI NAMAKHONO ALINDELEKILE (ezifundweni eziyi ULWAZI OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYONNOMA UMHLAHLANDLELA EKUPHELENI awa elilodwa kuya NGETHEMU -4 KONYAKA kumaminithi anga- 24 Ukusebenza ngezinto eziqoqiwe 5.1 Qoqa bese uhlela izinto Ukuhlela izinto eziqoqiwe akuseyiyo into okugxilwa kuyo kulengxenye yesibili yonyaka. Inganikezwa imisebenzi engenziwa ngesikhathi sokusebenza Qoqa bese uhlela Qoqa bese uhlela ngokuzimela. izinto izinto eziphathakayo zansukuzonke Izincomo okugxilwa kuzo ngeThemu 4 elokufunda kuhlaziywe igrafu lezithombe.. 5.2 Bhala okumele izinto eziqoqiwe Bhala okumele izinto eziqoqiwe Dweba igrafu yezinto zahlelwa eziqoqiwe. 5.3 Xoxa bese ubika ngezinto eziqoqiwe Xoxa bese ubika zahlelwa ezinto eziqoqiwe • nika izizathu zokuhlela izinto • phendula imibuzo ngalokhu - zihlelwe kanjani izinto - kubukeka kanjani okuqoqiwe kwahlelwa • chaza okuqoqiwe nemidwebo • nika incazelo yokuhlela kokuqoqiwe 247 Izibalo IBANGA 1-3

UKUQODA NANKHONO ISIKHATHI ULWAZI NAMAKHONO ALINDELEKILE (ezifundweni eziyi ULWAZI OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYONNOMA UMHLAHLANDLELA 248 EKUPHELENI awa elilodwa kuya NGETHEMU -4 KONYAKA kumaminithi anga- 24 Ukusebenza ngezinto eziqoqiwe 5.4 Ukuqoqa bese uhlela ulwazi Qoqa bese uhlela izinto • Qoqa ulwazi ngeklasi noma ngesikole Izibalo IBANGA 1-3 ukuphendula imibuzo ebuzwa uthisha. 5.5 Bhala okumele ulwazi Bhala okumele Bhala ulwazi kwigrafu ulwazi yezithombe 5.6 Hlaziya bese uhumusha Hlaziya ulwazi olunikiwe. Uma abafundi sebenolwazi oluphelele ukusuka ekuqaleni kuya ekugcineni Izifundo ezi-2 ulwazi. (okunconywe eThemini 3) bangagxila ekuhlaziyeni imifanekiso abayinikiwe. Analyse and Interpret data Phendula imibuzo Kuyanconywa ukuthi ngeThemu 4 abafundi bahlaziya (ngokuphendula ngolwazi olukwigrafu imibuzo) ngamagrafu ezithombe okungenani amabili. yezithombe. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

3.5.2 UKUCHAZA OKUQUKETHWE KWEBANGA 2 ithemu YOKU-1 YEbanga LESI-2 CAPS 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BEZINOMBOLO UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA UKUSEBENZISA IZINOMBOLO EZIMWENI EZIJWAYELEKILE: Bala usebenzise izinombolo eziphelele 1.1 ukubala izinto Ukubala ngokuyikho Bheka amanothi ebanga 1,ithemu 3 no 4 eziphathekayo okungenani ukuya e 100 Ukubala izinto Ithemu 1 eBangeni 2 ukuhlanganiswa komsebenzi owenziwe ngethemu kwezinto zansukuzonke. ukuqagela nokubala 4yebanga 1. okuyikho kuze kufinyelele Nikeza ukuqagela okulindelekile kwezinto Ukubala ngamaqoqo ema 200 ezinto zansuku zonke. Isu lokwakha ezingabhekwa ngokuthi Kulethemu kugxilwe ekubaleni nangamaqoqo. amaqoqo liyakhuthazwa. zibalwe. Lekelela abafundi ukubala izinombolo ezinkulu ngezinto, ukugqugquzela ekwenzeni amaqoqo okubala ngakubili, ngakuhlanu, nangamashumi. Amakhadi ezinombolo kufanele abekwe eduze kweqoqo ngalinye akhombise inani lezinto. Ukubala ngamaqoqo kulungiselela abafundi ukubala ngokuphindaphinda. Abafundi kufanele banikezwe amathuba okubala ngamaqoqo e 100 ingenziwa ngezindlela ezahlukene,isibonelo: • 10 amaqoqo ezinto eziyishumi; • 100 wezinto ezehlukene; noma • 2 amaqoqo oku- 50. Ukubala ukuqhubeka Abafundi bazodinga uukukhonjiswa amaqoqo ezinto bese beqhubeka nokubala. Izinsiza kufunda: Ukubhekisisa kahle izinto eziphathekayo ukukhuthaza abafundi ukubala ngamaqoqo. Izinsiza ezilungile zifaka nalezi: • Izinto eziphathekayo ezihlelekile, njengobuhlalu bokubala obusentanjeni • I - abhakhasi ukujwayeza ukubala ngama qoqo amashumi 249 • Ukwakha izinyanda ngoku 2, izinyanda yoku 5 nokuyishumi besekubalwa konke ngezinti noma umentshisi • Imali yokudlala Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 250 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.1 Uma abafundi beke babona izinto zokubala ezihleliwe noma ezenziwe amaqoqo, bakhuthaze ukuba benze amaqqoqo ngezinto ngesikhathi bebala. Ukubala izinto Abafundi kufanele benze ukuxhumana ezinombolweni ezejwayelekile nezinom- bolo ezisho isikhundla uma bebala ‘ ordinal and cardinal’. Loku kucaca kahle Izibalo IBANGA 1-3 uma bema ema-50 ukubala izinro ezingama- 50 ukuthi sebebale izinto ezin- ga-50. Ngokuphela kwethemu abafundi bazobe sebekwazi uku: • Ukubala izinto abangazithinta noma bazibambe; • Ukubala izinto zokubala ezenziwe amqoqo ezinto ezi 5 nezingama 10; kanye • Ukuhlela kabusha baphinde babale. Abafundi kufanele bakwazi ukuphendula imibuzo: “izinto ezikhona zisalingana nezasekuqaleni?” Eiminye imisebenzi: Abafundi kufanele baphendule lemiyalelo nemibuzo: • Kunezinto zokubala eziyi 100. Ukuzibala ngokwenza amaqoqo ezinto ezin- gamashumi. Ubheke ngokubala ngakunye. Ngaphambi kokuqala, ucabanga ukuthi impendulo izofana? • Ukubala izinto zokubala eziyi 100,ungakhetha ukubala ngamaqoqo ama 20noma25?Ngobani ? • Khetha ukuthi iyiphi indlela yokubala amapensela aqoqiwe. • Kunezinto zokubala ezinga 80. Uma sibala ngakubili noma ngamashumi, ucabanga ukuthi impendulo izofana? • Bala izinto zokubala ezi 46 ngokwenza amaqoqo okubili. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.2 Ukubala kuyiwe phambili Ukubala kuyiwe phambili Ithemu 1 eBangeni 2 kusuke kuhlanganiswa umsebenzi owenziwe kuthemu 4 Ukubala kuyiwe nasemumva ngo: nasemumva ngo: eBangeni 1. phambili nase • nga1, kusukela • nga1, kusukela Ukubala weqe izinombolo kuzohlala kubalulekile ukulekelela abafundi uma muva kunoma iyiphi kunoma iyiphi benza izibalo. Ukusho izinombolo ngokulandelana kuzohlala kuyikhono inombolo ephakathi inombolo ephakathi elidingekayo uma kubalwa. Ukubala kufanele kuqhubeke nokuba yimpilo kuka 0 no 200 kuka 0 no 100 yansukuzonke yabafundi nemilolozelo, amaculo nezindaba okungabamba iqhaza ekubaleni. • nga10, kusukela • nga10, kusukela kunoma iyiphi kunoma iyiphi EBangeni 1 abafundi kufanele bathuthukise lolwazi lokuqonda ekubaleni: inombolo ephakathi inombolo ephakathi • Ukuqonda ngokulondoloza kuka 0 no 200 kuka 0 no 100 • Imigomo yezinombolo - ukusho okuqoqiwe • nga 5, kusukela • nga 5, kusukela kunoma iyiphi kunoma iyiphi • Ukuqagela inombolo eyakhe iqoqo inombolo ephakathi inombolo ephakathi • Ukuqondanisa okukodwa nokukodwa kuka 0 no 200 kuka 0 no 100 Ukubala ngokweqa • nga2, kusukela • nga2, kusukela kunoma iyiphi kunoma iyiphi Ukubala ngokweqa elinye igama lokubala ngamaqoqo. Kusiza ukuthuthukisa inombolo ephakathi inombolo ephakathi ukuqaphela amaphethini. Ukubala ngokweqa kukhuthaza abafundi ukucabanga kuka 0 no 200 kuka 0 no 100 ngamaqoqo, okwenza kube yimpumelelo. Kuphinde kubasize ukuthuthukisa amakhono ukuqagela. • nga3, kusukela kunoma iyiphi Ukubala ngamaqoqo kwenza banake ubudlelwano phakathi kwezinombolo inombolo ephakathi ezingalandelani. Kwenza isizinda samaphethini ezinombolo nokuphindaphinda. kuka 0 no 200 Abafundi kufanele baqhubeke nokulekelelwa ngemifanekisoukubasiza ekubaleni • nga1, kusukela ngokweqa. isibonelo: kunoma iyiphi inombolo ephakathi 2 4 6 8 10 kuka 0 no 200 12 14 16 18 20 • nga 4, kusukela 22 24 26 8 30 kunoma iyiphi 32 34 36 38 40 inombolo ephakathi 42 44 46 48 50 kuka 0 no 200 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 251 92 94 96 98 100 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 252 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.2 Imisebenzi eqhubekayo: Ukubala kuyiwe Ukubala uyephambili nasemumva kufinyelela ku 100 usebenzise ishadi phambili nase elikhulu elifinyelela e 100: (5 - 7 imizuzu ngosuku) qala ukubala nekilasi muva lonke kanyekanyeume enombolweni ethile isib. 24. Abafundi bayashintshana Izibalo IBANGA 1-3 ngokubala beqhubeka kuleyonombolo benza ngamaqoqo / ngababili / ngamunye njengoba kusho uthisha ukubhala, ukubhala inombolo abama kuyo. Ubuze imibuzo efana nokuthi iyiphi iphethini oyibonayo? Igcina kuphi iphethini yokuqala? (isibonelo: iphethini yokubala nga 2s: 2; 4; 6; 8; 10) Ngokuphela kwethemu abafundi kufanele bakwazi uku: Ukubala ngokuphimisa nokuphendula emibuzweni efana nokuthi: • Qala e-52, ubale ngakunye ufinyelele e-72 • Qala e-88, ubale ngakunye uye emumva ufinyelele e-70 • Qala e-38, ubale ngakubili ufinyelele e-50 • Qala e-45, ubale ngakuhlanu ufinyelele e-100 • Qala e-10, ubale ngamashumi ufinyelele e-100 Abafana kufanele basebenzise amakhono abo okubala emsebenzini obhalwayo. Isibonelo,emsebenzini wokuzimela bengaqedela ukulandelana kwezinombolo: Abafundi ababukele baqedele ukulandelana kwezinombolo okwahlukene iaib. • 76; 75; 74; __; 72; __; __; __; 68 (kuyiwa emumva ngakunye) • 27; 28; 29; __; __; 32; __ (ngakunye kuyaphambili) • 8; 10; __; 14, __ (ngakubili noma ngezinombolo ezihamba ngazimbili) • 5; 10, 15; 20; 25; ____ (ngakuhlanu) • 90; __; 70 60; __ (kubalwa kuyiwa emumva ngamashumi) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • 10, 20, 30, 40, ___, 60, 70, ___ (ukubala kuyiwa phambili ngamashumi).

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.3 Ukwazi nokufunda Ukwazi nokufunda Ngalethemu abafundi baqhubeka no izinombolo izinombolo Izimpawu • Bhala ufunde iizimpawu zezinombolo kufinyelele e 100; bese zezinombolo nezi- • Ukwazi nokufunda • Ukwazi nokufunda • Bhala ufunde izinombolomagama kufinyelele ema-25. nombolomagama izimpawu zezinombolo izimpawu zezinombolo 0 - 200 0 - 100 Ngokuphela kwe themu abafundi bazobe sebekwazi uku: • Ukubhala izimpawu • Ukubhala izimpawu Bhala uphawu lwenombolo ebekwe ngenombolomagama: zezinombolo 0-200 zezinombolo 0- 100 • Ishumi nesikhombisa • Ukwazi nokufunda • Ukwazi nokufunda • Amashumi amabili nantathu izinombolomagama izinombolomagama 0-100 0- 25 Qondanisa uphawu nenombolomagama • Ukubhala izinombolo- • Ukubhala izinombolo- 66 Amashumi ayisishiyagalolunye nanye magama 0-100 magama 0- 25 8 Amashumi amahlanu nantathu 172 Amashumi amane 109 Amashumi amathathu nesishagalombili 91 Ikhulu namashumi ayisikhombisa nambili 40 Amashumi ayisithupha nesithupha 53 Isishiyagalombili 38 Ikhulu nesishiyagalolunye Funda izinombolo ekhadini ngalinye: 253 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 254 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.4 Hlela bese uqhathanisa Hlela bese uqhathanisa Uhla lwezinombolo ukuhlela nokuqhathanisa kuhambisana nokubala izinombolo izinombolo kufinyelele izinombolo kufinyelele ezisehlwini. Loku kusho ukuthi ukuze ubale kufinyelele ema 99,abafundi Chaza, 99 ema 25 ngendlela abaqonda ngayo izinombolo kufanele kuthuthukiswe ukufinyelela uqhathanise, nkuh- esixazululweni. Uma umfundi engehlela aqhathanise ngokuzethemba ngaphezu lela • Hlela izinombolo • Hlela kokudingekayo kuzobe sekukhuphuka ukuqonda inombolo nokuyisebenzisa. Izibalo IBANGA 1-3 izinombolo eziphelele kufinyelele izinomboloeziphelele ema -99 kusukela kusukela kokuncane Abafundi kufanele baqhubeke nokusebenzisa ulimi lokuhlela nokuqhathanisa: kokuncane kakhulu kakhulu kuya • Okokuqala, okwesibili, okwesithathu, okwesine, okwesihlanu, kuya kokukhulu kokukhulu kakhulu. okwesithupha………….. kakhulu, nokukhulu • Qhathanisa izinombolo kakhulu kuya • kungaki………… eziphelele usebenzisa kokuncane kakhulu. okuncane okune, • kuningi njenge, inombolo efanayo ne… • Qhathanisa izinombolo kukhulu ukune,kuningi • kulingana ne, kuningi ukune, kungaphansi ukune, okumbalwa ukune, okukhulu eziphelele kufinyelele ukune, kungaphansi ukune, kuncane kune, okubanzi ukune……… ema 99 usebenzisa ukune, kulingana ne. okuncane okune, • Okokuqala, okokugcina, emva, okulandelayo, phakathi ne kukhulu ukune,kuningi ukune, kungaphansi Ngokuhlela nokuqhathanisa izinto nezinombolo abafundi bafunde lokhu: ukune, kulingana ne. • Indawo ethile yezinombolo isetshenziswa ukuchaza inombolo eziseqoqweni; Sebenzisa izinombolo • Indawo ethile yezinombolo ezisho indawo nobudlelwano ngendawo ekuyo ukukhombisa eqoqweni. Isibonelo: mfaka umbala ophuzi endilingeni yesithathu. ukuhleleka, indawo noma nesikhundla Imisebenzi eqhubekayo Beka izinto emugqeni • Izinombolo ezisho isikhundla: chaza umehluko phakathi kwamagama kusukela kokokuqala ‘kunye’ no ‘okokuqala’; ‘kubili’ ‘okwesibili’ njll: ungalisebenzisa kanjani igama kuya kokweshumi ‘okuthathu’ nanini ‘okwesithathu’? mona okokuqala kuya • Hlukanisa ikilasi amaqoqoq amathathu noma amane alinganayo: umfundi kokokugcina isib. ngamunye uthola ikhadi azobhala kulo igama lakhe. Iqoqo lizobe selibeka Okokuqala, ukwesibili, amakhadi ngokulandelana kokuhleleka kwezinhlamvu. Uthisha nomfundi okwesithathu.... bangabuza umbuzo, isib. Ubani owesine eqoqweni lenu? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola okwamashumi amabili.

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.5 Ukubona ubungako Ukubona ubungako Yini ehlukile eBangeni 1? benombolo benombolo Ubungako benani Ngethemu 1,abafundi basebenza ngohlu lwezinombolo ezinkulu uku: yezinombolo ezihamba yezinombolo ezihamba lenombolo ngambili kufinyelele ngambili kufinyelele • Ukubala nokuqoqa amaqoqo amashumi nokuhamba ngakodwana; kanye ku 99 ku 25 • Bhala i-18 = ishumi eli-1 noku -8 okuhamba ngakodwana • Ukwazi ukuthi idigithi • Ukwazi ukuthi idigithi 13 = 10 no-3. ngayinye imeleni ngayinye imeleni Ngalethemu abafundi bazoqhubeka nokwenza ngezindlela ezahlukene • Ukuhlakaza izinombolo • Ukuhlakaza izinombolo nokusebenzisa Ishumi njengento ewumkhawulo nokukodwa okuseceleni. ishumi ezingama digit amabili ezingama digit okuyi-10 okukodwa. ‘Ishumi elejwayelekile nokukodwa’ (24 kusho 2 amaqoqo kufinyelele ema amabili ngokuphinda okuyi- 10 noku- 4 okuyimivo noma 2 amashumi nku- 4 okuyimivo) kudingwa -99 ngokuphinda ngamashumi ukusetshenziswa njalo ukugcina ulimi oolusho ukucaza nokuhlanganisa. ngamashumi nokungezinombol nokungezinombol ezingazodwana Ukusebenza ngezinto eziphathekayo ezingazodwana • Ukukhomba usho • Izinti zokubala / izinti zamentshisi • Ukukhomba usho nesimo senani ledijithi nesimo senani ledijithi Izinti zokubala noma umentshisi ongaqoqelwa ndawonye ukukhombimbisa izinto eziqoqelwe ndawonye inyanda yezinto eziyishuminokungakodwana. Isibonelo: Kukhombisa i- 12 Kukhombisa i- 18 Kukhombisa ama- 25 • I - abhakhasi Abafundi kufanele baqedele ngokusebenzisa izinto eziphathekayo ngokwenza amaqoqo lezinto eziyishumi ukuqonda ukuthi iqoqo lenziwa okuyishumi okungakodwana. 255 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 256 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.5 Ukusebenzisa i -abhakhasi, umfundi makakwazi ukukhombisa: Ubungako benani - Ishumi elilodwa; lenombolo - Ishumi elilodwa noku 5 okungakodwana; Izibalo IBANGA 1-3 - Ishumi elilodwa noku 6 okungakodwana; - Ishumi elilodwa noku 7 okungakodwana; - Ishumi elilodwa noku 8 okungakodwana; ne - Ishumi elilodwa noku 9 okungakodwana. • Amabhuloki kaDienes Ngalethemu izinsiza kufundisa zingandiswa ukufundisa ubungako benani lenombolo.Beka ishumi lamabhuloki (part of the Dienes blocks) ingathulwa ingathulwa ukuthuthukisa umcabango weshumi njengento eyodwa kanye loko: - 10 elilodwa lenza ishumi eli 1; - 20 elilodwa lenza amashumi ama 2; kanye - 16 okungakodwana kwenza 1 ishumi 6 okungakodwana. Yize abafundi besadinga ukubala nokwenza amaqoqo amashumi,bengaphinde bakhombise ama-18 ngokubeka ishumi lokuqala lamabhuloki nayisishiyagalombili angawodwana ukukhombisa izinombolo. Abafundi kuzofanele benze amaqoqo ukukhombisa ama-20. • Okumele okulingene Ngalethemu kugxilwe ekukhombiseni okumele okulingene inombolo efanayo. Amashumi amababili angachazwa ngokuthi 2 amashumi (kusetshenziswe inyanda noma amaqoqo ezinto) nomaamaqoqo amashumi. Kubalulekile ukukhombisa abafundi ukuthi 20 ungabukeka ngendlela ehlukene. Ngakho khombisa 20 izinto ezihlakazekile, iqoqo leshumi kanye ne10 lokungakodwana Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola namaqoqo ama 2 amashumi. Abafundi mabanikezwe amathuba okuchaza indlela okuhlelwe ngayo, suusho ukuthi yini ehlukile nefanayo.

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.5 • Amakhadi obungako benani Ubungako benani Amakhadi obungako benani angathulwa asetshenziswe ngalethemu lenombolo ukukhombisa ukuthi zakheke kanjani izinombolo amakhadi obungako benani lezinombolo ahambisane nenyanda noma iqoqo lezinto. • Ubungako bedijithi Abafundi kufanele baqale ukusho ukuthi idijithi imelelni. Buza abafundi: • Imeleni inombolo 7 ema- 27? • Imeleni inombolo 2 ema- 29? Abafundi kufanele basebenzise ikhadi lobungako benombolo ukufakazela abakushilo. • Ukudlulela kokubhaliwe Ngesikhathi esikhululekile abafundi kufanele benziswe imisebenzi ebhalwayo ukwakha nokuhlanganisa: - Umqondo weqoqo leshumi nokungakodwana; kanye - Ubungako bedujithi. Isibonelo: Faka umbala ebuhlalwini obu-12 Faka umbala ebuhlalwini obu-16 Faka inombolo engekho (loku kungenziwa noma kuchazwe ngokusebenzisa izinto eziphathekayo) 18 = 1 ishumi ne ____ okungakodwana 23 = __ amashumi ne 3 okungakodwana 257 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 258 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.5 Izinsiza ezinconywayo Ubungako benani Izinto ezingenziwa amaqoqo: lenombolo • Izinti zokubala Izibalo IBANGA 1-3 • Izinto zokubalwa ezingatshutshwa • Izinti zamentshisi • Izinti zokumunca • Amabhuloki axhumanayo 1.6 Sebenzisa amasu Sebenzisa amasu Abafundi kulindeleke ukuthi baxazulue izinginga zamagama usebenzise lamasu alandelayo uma alandelayo uma alandelayo: Amasu okuxazulula uxazulula uchaze uxazulula uchaze izinkinga • Ukwakha nokuhlakaza izinombolo izixazululo enkingeni: izixazululo enkingeni: • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo • Imidwebo nezinto • Imidwebo nezinto ezibambekayo isib. ezibambekayo isib. • Umugqa wezinombolo Izinto zokubala Izinto zokubala Imidwebo noma izinto eziphathekayo • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza Abafundi bazoqhubeka nokudweba izithombe nokusebenzisa izinto izinombolo izinombolo eziphathekayo ukuxazulula izinkinga. Kubalulekile ukuthi izithombe kubalulekile • Ukuphinda kabili • Ukuphinda kabili ukuthi izithombe nemidwebo enezinombolo kanye nemisho yezinombolo. nokuhlukanisa kabili nokuhlukanisa kabili Ukwakha nokuhlakaza ngokulinganayo ngokulinganayo Leli elinye lamasu abaluleke emabangenini abansi. Lelisu libavumela • Umugqa wezinombolo • Umugqa wezinombolo ukuhlakaza (decompose) nokuhlanganisa ukuze babale kalula. Bazolisebenzisa kakhulu lelisu emabangeni aphakathi. Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo Lelisu libucayi lidingalidinga ukuqonda okujulile kwezinombolo. Abafundi bayakwazi ukukhetha isu elikhululekile emaqhingeni abawasebenzisayo: Inking yamagama: ngelinye ilanga emtholampilo abantwana abayi- 17 bathola Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola imjovo womkhuhlane. Ngosuku olulandelayo abantwana abayi- 16 bajovwa. Bangaki abantwana abajovwa uma sebebonke? Inkinga ingaxazululwa ngokusebenzisa ukuphinda kabili. Umfundi angathi ukuphinda kabilli i- 16 uhlangana no1 noma ukuphinda kabili 17 ususa 1.

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.6 Umugqa wezinombolo Amasu okuxazulula Ukusebenzisa umugqa wezinombolo ukuze ukulekelele ukubala okungasiza izinkinga abafundi ukubhala imicabango yabo baphinde bayilandelele. Kuvumela abafundi ukubhala ngemifanekiso leyo abangayisebenzisa ukuchaza ukuthi inking bayixazulule kanjani inkinga. Abafundi baqale eBangeni lokuqala eBangeni 1. Njengamanje sebeyakwazi ukwakha umugqa wezinombolo ongenazo izinombolo la befaka inombolo yokuqala bese bephokophelela ukuqala bese beqhubekele kwenye. Ngalethemu kuzobakhona ukuqhubekela phambili nokwakhiwa komugqa wezinombolo. Isibonelo zokukhombisa ukuthi abafundi bangasebenzisa maphi amaqhinga okubala: UZonke umamathoyizi ayi- 6 antofontofo. UZola unamaningi ngayi- 6 ukunakaZonke.UZola unamathoyizi amangaki antofontofo? Abafundi bazokwenza umugqa wezinombolo ukubasiza bafinyelele empendulweni.   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Abafundi bengaphinde bahlakaze okuyi- 6 kube amaqoqoq ama 2. Umugqa wezinombolo uzokhombisa ukugxuma ngaku- 2s kusukela koku 6. isibonelo: Uma abafundi sebenokuzethemba ekubaleni besukela enombolweni zabayinikeziwe.Umugqa wezinombolo izoqala enombolweni eyi- 6. Indlela yomugqa wezinombolo eyenziwa ihambisana nomqondo wokubala beqhubeka. Kubalulekile ukuthi abafundi bawubone umugqa wezinombolo oqala kunoma iyiphi inombolouma bebala noma behlela izinombolo. Usenga hlukanisa inombolo eyi -6 enze amaqoqo ezinto ezihamba ngambili aphinde ahlanganise 259 esukela enombolweni eyi-6 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 260 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.6 Isibonelo: Amasu okuxazulula izinkinga Izibalo IBANGA 1-3 6 ungahlukaniswa kabili ngokulinganayo bese kugxunywa ka 2 kubhalwe oku3. Isibonelo: Abafundi kufanele banikezwe ithuba eliningi ukusho ukuthi bangafinyelela kanjani enombolweni besebenzisa umugqa wezinombolo. Kungabuzwa ukuthi:yikuphi ukugxuma okuhlukene esingakwenza ukze sifinyelele e - 15? Ukuze kugxunywe kusondelwe ezinombolweni, abafundi kufanele bazi amabhondi afinyelela e- 15noma bakwazi ukusebenzisa umugqa wezinombolo ukufinyelela empendulweni. Kubalulekile ukuthi abafundi bakhulume ngokuthi kube kukhulu kangakanani ukugxuma. Ukwenza loluhlobo lalomsebenzi kulungiselela abafundi ukuthi bakwazi ukusebenzisa imigqa engenalutho. Uma kusetshenzwa ngomugqa wezinombolo,abanye abafundi bangadinga ukubamba ubuhlalu obusentanjeni ngaphezu noma ngaphansi komugqa wezinombolo ukubasiza ukubala. Vumela abfundi ukuthi abafundi benze iqhinga elibasebenzela kangcono. Bese kuthi uma abafundi besebenzisa iqhinga elingasebenzi kahle balekelelwe ngelingabasebenzela kangcono. Abafundi bayawasebenzisa lamasu akufanele baze babe yizingcweti ukuze bakwazi ekuwasebenziseni. Khumbula ukuthi abafundi banokusebenzisa izindlela ezehlukene ukuxazulula izinkinga okungenzeka kungabi yilezo ezilindelwe uthisha. Isibonelo. Inkinga yokuhlukanisa ingaxazululwa ngokusebenzisa ukususa ngokuphindelela, Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ukuhlanganisa, noma ukuphindaphinda. Izindlela ezisetshenziswa abafundi zizishintsha ngokuqhubeka konyaka njengoba ukujwayela nokuqonda kwaboizinhlobo zezinkinga kukhula

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.7 Xazulula izinking a Xazulula izinking a Yini ehlukile eBangeni loku- 1 zezibalo zamagama zezibalo zamagama Ukuhlanganisa Ngalethemu abafundi bazokwenza ngokuphindelela izinkinga zamagama nokususa esimweni esijwayelekile, esimweni esijwayelekile, nokusebenzela ukuzethemba ekusebenziseni amaqhinga alandelayo uma uchaze nendlela uchaze nendlela kuxazululwa izinkinga: oxazulule ngayo oxazulule ngayo inking okufakaka inking okufakaka • Imidwebo noma izinto eziphathekayo ukuhlanganisa, ukususa, ukuhlanganisa, ukususa, • Ukwakha nokuhlakaza izimpendulo ezifinyelela izimpendulo ezifinyelela ema -99. ema -20. • Ukuphinda kabili nokuhlukanisa kabili ngokulingana nse • Umugqa wezinombolo Kulethemu, lekelela abafundi kakhudlwana emizamweni yabo yokubhala nokwethula izibalo zabo. Abafundi badinga ukulekelelwa okuningi emizamweni . yabo yokubhala nokwethula izibalo zabo. Abafundi kufanele babhale phansi imisho yezinombolo njengendlela yokuqopha inkinga exazululiwe. Kubalulekile ukubona ukuthi ibaphi abantwana abasebenza kanzima ukubhala imisho yezinombolo ukubona inkinga ethize. Inhlobo yenkinga 1: Ushintsho Ukuxhuma Hlukanisa Imiphumela UMoeketsi unamaswidi ayi Kunamaswidi ayi 15. engaziwa 6. UMahlodi umnika ayi 9 UMoeketsie wadla 6. Mangaki ngaphezulu. UMoeketsi asalele uMahlodi? unamaswidi amangaki esewonke? Ushintsho UMoeketsi unamaswidi ayi 6. UMoeketsi unamaswidi ayi- olungaziiwa mangaki amanye awadingayo 15. UMahlodi udla amanye. ukuze abe yi -15? Kusele ayi- 9. Mangaki adliwe uMahlodi? Ukuqala UMoeketsi ubenamaswidi. UMoeketsi udla amanye. okungaziwa UMahlodi umunika ayi - 9. Unikeze uMahlodi ayi -6. Manje Manje usenangama 15. unamaswidi ayi - 8 asele. Mangaki uMoeketsi aqale Mangaki aqale enaye? ngawo? 261 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 262 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.7 Inhlobo yenkinga 2: Qhathanisa Ukuhlanganisa Ukuxhuma Hlukanisa nokususa Imiphumela UMoeketsi unamaswidi ayi - 6. UMahlodi unamaswidi ayi -15. engaziwa Izibalo IBANGA 1-3 Ushintsho UMahlodi une 9. Mangaki UMahlodi unamaswidi ayi - 6. olungaziiwa amanye amaswidi uMahlodi Awakhe angaphansi ngayi- 9 anawo ngaphezu kuka ukunaka Moeketsi. UMahlodi Moeketsi? unamaswidi amangaki? Ukuqala UMahlodi unamaswidi ayi- 15. UMahlodi unamaswidi ayi -16. okungaziwa Unamaswidi amaningi ngayi- 9 UMoeketsi unamaswidi ayi- 9 ukunaka Moeketsi. Unamaswidi angaphansi kuka Mahlodi. amangaki uMoeketsi? Mangaki amaswidi anawo uMahlodi? Unhlobo yenkinga 3: Linganisa Ukuxhuma Hlukanisa Imiphumela UMahlodi unamaswidi ayi -16. UMahlodi unamaswidi ayi- engaziwa 16. UMoeketsi unamaswidi UMoeketsi unayi - 6. Mangaki ayi- 6. Kufanele aphinde adle amaswidiHow many more amangaki amaswidi UMahlodi sweets must Moeketsi get to ukuze alingane naka Moeketsi? have as many as Mahlodi? Ushintsho UMoeketsi unamaswidi ayi- 6. UMoeketsi unamaswidi olungaziiwa Uma ethenga amaswidi ayi- 9 ayi -6. Uma uMahlodi edla uzoba namaningi njengaka amaswidi ayi 9 uzoba Mahlodi. Unamangaki nenombolo yamaswidi efana uMahlodi? neka. Unamangaki amaswidi uMoeketsi? Ukuqala UMahlodi unamaswidi UMahlodi unamaswidi ayi- 16. okungaziwa ayi-15. Uma uMoeketsi Uma edla amaswidi ayi- 9 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ethengaamaswidi ayi - 9 uzoba nenombolo yamaswidi ngaphezulu uzoba nenombolo efanayo neka Moeketsi. yamaswidi efanayo neka Unamangaki amaswidi Mahlodi. Mangaki amaswidi uMoeketsi? uMoeketsi?

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.8 Ukuxazulula izinkinga Ukuxazulula izinkinga Ukuphindaphinda Ukuhlanganisa zezibalo ezisesimweni zezibalo ezisesimweni ngokuphindelela esejwayelekile esejwayelekile Ukuqala ukuqonda ukuphindaphinda kulelibanga amaqoqo. Ukwenza amaqoqo kuholela kuchazwe nendlela kuchazwe nendlela kungasiza umfundi ezimweni zokumela ukuphindaphinda. ekuphindaphindeni okuxazulwe ngayo okuxazulwe ngayo inking kusetshenziswa inking kusetshenziswa Kunezinhla ezintathu eziyisisekelo zezimo zenkinga ezifaka ukuphindaphinda ukuhlanganisa ukuhlanganisa ngezinombolo eziphelele: ngokuphindaphinda ngokuphindaphinda • Amaqoqo alinganayo (isib.amatafula amathathu, lilinye linabafundi abane):a noma ukuphindaphinda okuholela mele amaqoqo aphindaphindiwe kufinyelela e- 50. ukuphindaphindeni kufinyelela e- 20. • Ukuqhathanisa ngokuphindelela (isib. Okuphindwe kathathu njengobuningi babafana namantombana): okumele okuningi kokuvumelanayo • Izinhlelo ezinxande (isib. Imigqa emithathu yabantwana abane): emelwe uhla uluvundlile nolwehlayo Isimo ngasinye kulezi singahlanganiswa nezindlela ezithile zokubuza imibuzo (bheka Izinhlobo Ukuxazululwa Kwezinkinga IBANGA LESI-2 lsahluko 2). Izimo zezinkinga zokuphindaphinda ezifaka izinombolo ezintantunubudlelanweni bezibalo: • Inombolo yezinto kwisethi ngayinye • Inombolo yamasethi • Inombolo ephelele Izibonelo zezinkinga ezingenziwa kulethemu Kulindelekile ukuthi uma kuxazululwa izinkinga ezingezansi, abafundi bazosebenzisa izithombe, imidwebo noma izinto eziphathekayo ukulekelela ukubala. Uma abafundi bedweba izithombe ukubasiza ukubala, imidwebo ayiveze isimo samaqoqo.abafundi kumele bakhuthazwe ukubhala imisho yezinombolo kuzona zonke izinkinga zezibalo zamagama. Labo bafundi abanolwazi olukhulu basebenzise izibalo eziyimisho zokuhlanganisa ngokuphindaphinda ukukhombisa isixazululo. 263 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 264 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.8 Izibonelo zezinkinga ezingenziwa: Ukuhlanganisa Ukuhlanganisa ngokuphindaphinda ngokuphindelela kuholela • Amabhayisikili ama- 4 anamasondo amangaki? ekuphindaphindeni Izibalo IBANGA 1-3 • Abantwana abayi- 7 banamehlo amangaki? Abafundi bangayixazulula inkinga ngalendlela: • Izithombe noma imidwebo mayikhombise amaqoqo. Abafundi mabakhuthazwe ukubala ngaku - 2 bafinyelele empendulweni. Kufanele bakhuthazwe ukukhombisa ukubala kwabo ngomusho wezinombolo.      2      +    2      +      2    +      2      +    2    +    2    +    2        =    14   Isilinganiso UThami uphuza izinkomishi ezi- 3 zobisi nsukuzonke. Zingaki izinkomishi zobisi aziphuzayo ngesonto? Amagridi nezinhlelo UMnu. Khumalo itshala imigqa emi- 3 yezithombo zeklabishi. Kunezithombo ezi- 5 emugqeni. Zingaki izithombo zamaklabishi ezikhona zizonke? • Ingadi yemifino inemigqa emi - 5 yezithombo. Yonke imigqa inenombolo elin- ganayo yezithombo. Uma kunesamba sezithombo ezi -15, zingaki izithomnbo emugqeni ngamunye? • Ingadi yemifino inezithombo ezi- 18 ezitshalwe emigqeni. Kunezithombo eziyi- Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 6 emgqeni ngamunye. Mingaki imigqa ekhona?

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.9 Xazulula uchaze Xazulula uchaze Njengoba kwenzeka ekuphindaphindeni, ukuqonda ukuhlukanisa okuyisizinda izixazululo ezinkingeni izixazululo ezinkingeni kulelibanga, ukucazelana ngokulingana, nokwakha amaqoqo Amaqoqo nokucaza ezenzekayo ezifaka kuholela ezibalweni ezenzekayo ezifaka ukucazelana ukucazelana • Ukwenza amaqoqo (isib. Izingane eziyishuminambili ematafuleni amane, zokuhlukanisa ngokulingana namaqoqo ngokulingana namaqoqo mangaki amatafula) kufinyelela ema -99 kufinyelela ema -99 • ukucazelana (isib. Abantwana abayishuminambili ematafuleni amane, bangaki anezimpendulo ezingaba anezimpendulo ezingaba nezinsalela. kwelilodwa) nezinsalela. abanye abafundi bafika esikoleni bekwazi ukutshengisa kokubili ukwenza amaqoqo nokucaza izinkinga zokuhlukanisa nezinto eziphathekayo. Izimo zezinkinga zokuphindaphinda nokuhlukanisa zifaka izinombolo ezintathu ezilandelayo ebudlelwaneni bezibalo: • inombolo yezinto kwisethi • inombolo yamasethi • isamba senombolo Izinombolo zezinkinga ezingenziwa kulethemu Ukucaza • nginamapensela ayi- 12 ukucaza ngokulinganayo phakathi kwethu sobathathu; umuntu emunye uzothola amangaki? • Kunezimoto zamathoyizi eziyi -18; ningawahlukanisa kanjani ngokulinganayo phakathi kwenu nobabili? • Kunamapulamisi ayi - 16 nezingane eziyi - 8 ezihlukaniselana ngokulinganayo. Mangaki amapulamusi azotholwa yingane eyodwa? • UNaomi unezimbali ezi - 20. Uwafake emavazini ama- 2. Zingaki izimbali evazini eyodwa? • UTom ubhake amakhekhe ayi -8. unamaSmarties angama- 40. Mangaki amaSmarties angawafaka ekhekheni? 265 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 266 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.9 Ukwenza amaqoqo Amaqoqo nokucaza • Zingaki izimoto ongazenza uma unamasondo ayi- 8? Zingaki izithuthuthu? kuholela ezibalweni zokuhlukanisa • Kunama apula ayi - 18 ebhokisini. Zingaki izikhwama zama apula ama- 3 angagcwaliswa? Izibalo IBANGA 1-3 • Umbhaki ubhake amabhanisi. Ufaka amabhanisi a-6 kuwona wonke amabhokisi. Mangaki amabhokisi angawagcwalisa? • Kunezingane eziyi-16 lapha namuhla. Mangaki amaqembu ezingane ezine esingawenza? Ukuhlela UMongezi uqoqe izinto zokubala ezi- 20 zakha imigqa eyi- 10. Zingaki izinto zokubala emugqeni? 1.11. • Ukukhumbula • Ukukhumbula Yini ehlukile ebange lokuqala 1 nokubona imali nokubona imali Imali Ngalethemu abafundi bazilungiselela ukubona imali bayihlakaze ibe amanani ewuhlweza yase ewuhlweza yase amancane. South Africa, 5c, 10c, South Africa, 5c, 10c, 20c, 50c, R1, R2, R5, 20c, 50c, R1, R2, R5, Izibonelo zezinkinga ezingenziwa kulethemu nengamaphephaR10, nengamaphephaR10, • Ungasicaza isi- 50c ngokulinganayo ezinganeni ezine? Chaza kanjani. R20, R50 R20, R50 • Ushingamu ubiza u- 10c umunye. UBusi usebenziseisi-50c. Uthenge • Xazulula • Xazulula oshingami abangaki? izinkinga zemali izinkinga zemali ezimbandakanya ezimbandakanya • UThenje ukhokhe ama-R5 ukuhamba ngetekisi ukuya esikoleni ekuseni. isamba noshintshi isamba noshintshi Wakhokha ngamarandi anga- R20ayiphepha. Uthola ushintshi ongakanani? kufinyelele ema- R99 kufinyelele ema- R20 Imalini azobe esele nayo uma ephindela ekhaya? amasenti kufinyelele amasenti kufinyelele • Ufizipopo ubiza ama-R2, 50. UPalesa ufuna ukuthenga ufizipopo o- 4. Unama- 90c 50c R8,00. Unemali eyanele? Uma kungenjalo, imalini ayidingayo? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.12 Sebenzisa lamasu Sebenzisa lamasu Yini ehlukile eBangeni 1 alandelayo uma ubala: alandelayo uma ubala: Abafundi balindeleke ukuxazulu izinkinga ezisesimweni esejwayelekile Amasu (izindlela zokwenza • Imidwebo noma izinto • Imidwebo noma izinto ezinokubala okukhululekile besebenzisa lamasu alandelayo: namaqhinga) eziphathekayo isib. eziphathekayo isib. Imidwebo noma izinto eziphathekayo isib. Izinto zokubala Izinto zokubala Izinto zokubala Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza Ukuphinda kabili nokuhlukanisa kabili okulingana nse izinombolo izinombolo Umugqa wezinombolo • Ukuphinda kabili • Ukuphinda kabili nokuhlukanisa kabili nokuhlukanisa kabili • Imidwebo noma izinto eziphathekayo okulingana nse okulingana nse Abafundi bayaqhubeka nokudweba izithombe basebenzise nezinto • Umugqa wezinombolo • Umugqa wezinombolo eziphathekayo ukuxazulula izinkinga. Kubalulekile ukuthi isithombe noma imdwebo ibe nezinombolo kanye nemisho yezinombolo. Ukwakha nokuhlakaza Lena enye yezindlela ezibaluleke kakhulu emabangeni aphansi (abafundi bangasebenzisa ukuhlakaza ngokuqhubekayonemabangeni aphakathi). Ukusebenzisa lelisu kuvumela abafundi ukuhlukanisa nokuzihlanganisa izinombolo ukulekelela kubelula ukubala. Ngalethemu abafundi bazo: • Ukuhlakaza ibreak up numbers using place value; • Hlakaza izinombolo usebenzisa ukuphinda nga-10; noku • Ukuhlakaza inombolo ukwakha izinombolo ezimili ezifanayo nezihambisanayo isib. Ipheya elenza 20. Ukuphinda kabili nokuhlukanisa kabili ngokulingana nse Abafundi bayaqhubeka nokusebenzisa ukuphinda kabili nokuhlukanisa kabili ngokulinganayo njengeqhinga lokuballa. Umugqa wezinombolo Bheka amanothi ezinye izibonelo zokwenza umugqa wezinombolo ekuxazululeni izinkinga. • Ukuhlanganisa nokususa Abafundi kufanele bakhe izinombolo owabo umugqa wezinombolo behlakaza izinombolo zibe ngezikhonekayo. 267 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 268 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.12 Isibonelo: Amasu (izindlela 8 + 12 zokwenza Umugqa wezinombolo kumele uqale kwisi- 8 nabafundi bangakha: namaqhinga) Izibalo IBANGA 1-3 • Ukugxuma ka-2 ka- 6 • Ukugxuma ka-4 ka- 3 • Ukugxuma ka-3 ka- 4 • Ukugxuma ka-10 ka- 2 • ukuphindaphinda umugqa wezinombolo kumele uqhubeke nokusebenza ukulekelela ukuhlanganisa ngokuphindaphinda. Ukugxuma okulinganayo kuyabhalwa emugqeni wezinombolo nemisho elekelelayo ingabhalwa. Isibonelo: 5 + 5 + 5 + 5 + 5 = 25 Ukugxuma ka-5 oku- 5 kwenza 25 5 amaqoqo ka 5 = 25 5 x 5 = 25 Ukuphindaphinda okunikeziwe, abafundi kufanele bakwazi ukuchaza ukuthi bagxume kanjani ukwenza umugqa wezinombolo. Vumela abafundi ukukhetha amasu abazizwa kangcono ngawo. Kodwa-ke, uma abafundi besebenzisa amasu angasebenzi kahle badinga ukulawulwa ukusebenzisa ukuba basebenzise angasebenza kangcono. Khumbula ukthi abafundi bangaxazulula inking ngendlela engalindelwe uthisha. Isibonelo,inking yesibalo sokuhlukanisa ingaxazululwa ngokususa ngokuphindelela, ukuhlanganisa, noma ukuphindaphinda. Indlela umfundi ayisebenzisayo ingashintsha ngesikhathi unyaka uqhubeka njengoba ukwazi nokujwayela kwabo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola izinkinga kukhula, kanye nokuqonda kwabo izinombolo kuthuthuka.

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.13 • hlanganisa kufinyelele • hlanganisa kufinyelele Yini eyehlukile eBangeni 1? e- 99 e- 20 Ukuhlanganisa Kugxilwe kakhulu ekuthuthukiseni amasu namaqhinga okubala kulethemu. Uku- nokususa • susa kusukela e- 99 • susa kusukela e- 20 hlakaza izinombolo ukuze ukubala kube iqhinga elibalulekile abafundi abangaj- wayezwa lona. • ukusebenza • ukusebenza kwezimpawu ezifanele kwezimpawu ezifanele Lethemu igxile kwi: (+, -, =, ) (+, -, =, ) Ukusebenzisa ukuhlakaza nokwakha imisebenzi yezinombolo engasiza • ukuzijwayeza ukuzijwayeza amabhondi ekuthuthukisweni kokwazi ukuhlanganisa nokususa amabhondi ezinombolo ezinombolo kufinyelele Abafundi benza bephindelela izibalo zokuhlanganisa nezokususa kufinyelele kufinyelele e- 20 e- 20. Kuphakathi kwalezizilinganiso sezinombolo lapho abafundi bangaqala bathuthukise ukuqonda ubungako benombolo ngamashumi nangemivo. Ukubala ngamaoqo kuzohlala kubalulekile nabafundi bangaqala ukubona ukuthi ukubala ngakunye akulona isu elisebenza kangcono. Kukulesi silinganiso senombolo lap- pho abafundi okumele abafundi bacabange kanzima ngamasu abazowaseben- zisa. Ukukhetha indlela yokubala eyiyonayona kusiza abafundi ukuba baphume- lele ekubaleni. Ukuze babale esilinganisweni senombolo esukela e- 0-20 ulwazi lwabafundi lungafaka: • ukubala izinto; • ukubona,ukufunda nokubhala izinombolo; • ukuqhathanisa nokuhlela izinombolo; • ukwakha nokubhidliza izinombolo; • ukwenza ngokuphindelela ukuhlanganisa nokususa kufinyelele e- 20; • ukuphindaphinda nokuhlukanisa kabili ngokulinganayo; noku • ukuzikhumbuza okubalulekile ngezinombolo. Amasu angenzeka uma kuhlanganiswa noma kususwa Amasu akhonjiswe ngezansi avumela abafundi ukuba bazinzise ukubala noku- qonda kwabo izinombolo. Ukuzijwayeza amasu angezansi azokhuthaza abafun- di ukubheka ubudlelwano phakathi kwezinombolo nokufundisa abafundi ukuthi bangakwazi ukusebenzisa ulwazi ukuze babale. 269 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 270 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.13 Beka inombolo enkulu kuqala ukuze kubalwe kuqhubeke noma kuhlehlwe Ukuhlanganisa 4 + 12 =  nokususa Hlela kabusha 4 + 12 njengo 12 + 2 uqhubeke nokubala usukela e- 12. Izibalo IBANGA 1-3 Ukubona okungaseduze kokuphindwe kabili 8+7 Umfundi engachaza ukuthi isibalo singabhalwa kanje 8 + 8 -1 (phindaphinda i- 8 susa oku- 1) noma 7 + 7 + 1 (phindaphinda i- 7 uhlanganise oku- 1). Abafundi bangabhala amasu besebenzisa imicibisholo 8+ 8 →16, 16− 1→ 15 Shintsha inombolo iye eshumini bese ususa noma uhlanganise noku- kodwa Lelisu lingafundiswa nezimombolo ezisezingeni eliphansi lisebenze kuyofinyelela ezinombolweni ezinkulu. 9+6= Abafundi bangathi kubo: “ngithatha indlela eyodwa ukusuka ku- 6 ngawengeza ku- 9 ukwakha i-10.” Ngakho-ke 9 + 6 angabhalwa njengo 10 + 5 = 15. 8+5= Abafundi bangathi kubo: “ngizothatha izindlela ezimbili ukusukela ku 5 nga- wengeza ku 8 ukwakha i10.” Ngakho-ke 8 + 5 angabhalwa njenge 10 + 3 = 13. Ukuhlakaza inombolo ibe izingxenye ezincane ukwenza ukubala kube lula Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi bangahlakaza inombolo kube izingxenye ezikhonekayo kubo.

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.13 Ukubala kuqhubeka ngokuhlakaza inombolo Ukuhlanganisa 11 + 7 =  nokususa 11 + 4 + 3 11 + 4 15 + 3 = 18 11 + 7 =  11 + 5 + 2 11 + 5 16 + 2 = 18 17 - 9 =  17 - (7 + 2) 17 - 7 10 - 2 = 8 12 + 7 =  10 + 2 + 7 7 + 2 9 + 10 = 19 Sebenzisa ulwazi lokusebenza ngokuhlanekezela phakathi kokuhlanganisa nokususa 15 - 9 =  Umfundi uyazi ukuthi isibalo singaphinde sibhalwe njengesibalo sokuhlanganisa: “ngiyazi ukuthi 9 +  = 15.” Umfundi angasebenzisa ukubala ukuze ukwazi ukubala. Amabhondi ezinombolo Ukuze kwenziwe amabhondi ezinombolo, izinhlobonhlobo zemisebenzi kufanele zinikezwe abafundi. loku kulungele kahle ukwenziwa ngesikhathi sokusebenza ngokuzimela. Umugqa wezinombolo ungasetshenziswa ukuzijwayeza amabhondi kufinyelele e 10. 271 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 272 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.14 • hlanganisa • hlanganisa Ulaphi umehluko eBangeni loku-1 inombolo efanayo inombolo efanayo Ukuhlanganisa Abafunsi bazokwenza ushintsho ukusukela eekuhlanganiseni ngokuphindaphinda ngokuphindaphinda ngokuphindaphin- ngokuphindaphinda kuya ezibalweni zokuphindaphinda. Baqala ukwazi kufinyelele ema- 50 kufinyelele ema- 20 da okuholela umqondo wezibalo zokuphindaphinda. Bazokwenza umsebenzi obavumela Izibalo IBANGA 1-3 ezibalweni • ukuphindaphinda • ukuphindaphinda ukubona ubudlelwano phakathi kwezinombolo: zokuphindaphinda izinombolo izinombolo • inombolo yezinto eqoqweni e-1kufinyelele e-10 ngo e-1kufinyelele e-10 1, 2, 5, 3 no 4 ngo 2, • inombolo yamasethi noma amaqoqo • sebenzisa izimpawu • sebenzisa izimpawu • inombolo eyisamba ezifanele(+, x, =, ) ezifanele(+, x, =, ) abafundi bafika eBangeni lesibili bekwazi ukuhlanganisa ngokuphindelela. Ngasekupheleni kwethemu kumele bebesebekwazi uku: • ukuhlobanisa ukubala ngokweqa nokuhlanganisa ngokuphindelela ekwazini ukuphindaphinda; • sebenzisa, ukufunda nokubhala uphawu lokuphindaphinda; • bhala izibalo zemisho zokuphinda; kanye • phindaphinda izinombolo 1 kuya 10 ngo 2. Uma kuxazululwa izinkinga zezibalo zamagama abafundi bazothanda ukusebenzisa ukuhlanganisa nokuphindelela, ngaphandle kwalezo zibalo ezinomfanekisa wokuhleliwe. Kusesimweni esijwayelekile sezimo ezikhululekile Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola yezimo ezikhululekile eminye imifanekiso yokuphindaphinda ingasetshenziswa.

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.14 Ukuhlela Ukuhlanganisa Njengoba abafundi bethola ulwazi ngezinhlobo ezahlukene zezibalo ngokuphindaphin- zokuphindaphinda, ukubeka amaqoqo kuhleleke kunganikezela uhlelo da okuholela lokukhombisa ukwakheka kokuphindaphina isib. 2 x 4 kufana nokuthi 4 x 2. ezibalweni zokuphindaphinda ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ 4+4=8 ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ 2 + 2 + 2 + 2 = 8Ukusebenzisa uhlelo kukuvumela uku: • ukwakha nokuhlakaza izinombolo; • ukuxhumanisa ukuphindaphinda nokuhlanganisa ngokuphindelela; • ukucabanga ngokuphindaphinda njengohlelo; noku • lukundlala isizinda semithetho yokuphindaphinda Gxilisa ukuthi abafundi banake inombolo yemigqa nenombolo yezinto zokubala emigqeni. ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ 4+4=8 273 Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 274 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.14 kukhona 4 imigqa yoku 2, okuyi 8 sekukonke. Ukuhlanganisa Abafundi kufanele babhale ngalendlela elandelayo: ngokuphindaphin- da okuholela ¥ ¥ ¥ ¥ Izibalo IBANGA 1-3 ezibalweni zokuphindaphinda ¥ ¥ ¥ ¥ 2+2+2+2=8 kukhona 2 imigqa yoku 4 yoku 8 sekukonke. Igama “isikhathi” sebengathulelwa: 4 kuphindwa 2 kwakha 8. Uma abafundi sebenolwazi olwanele, uphawu lokuphindaphinda lungathulwa kanye nolimi olulandelayo useluthuthukisiwe: • 4 amaqoqo ka 2 • 4 okungakubili • 2+2+2+2=8 • 4 amaqoqo okubili noma 4 kuphindwa 2 yi 8 Ngisho noma uphawu seluthuliwe, amagama, izithombe zokuphindaphinda imifanekiso yokulekelela ukuqondisisa uphawu kuhlale kubalulekile. Imifanekiso yokuqondisisa ukuphindaphinda: • Amabhuloki axhumekayo angasetshenziswa axhunywe abe uhla loku 4 ohleni ngalunye kungaba amabhuloki a 2. Loku kuvumela abafundi ukuba bathi: there are four stacks and there are 2 in each stack.. Kubavumela ukubhala 2 +2 + 2 + 2 namaqoqo a- 4 oku 2 kusho 4 x 2. • Umugqa wezinombolo ungasetshenziswa ukukhombisa ukuhlanganisa ngokuphindelela noma amaqoqo ezinombolo. Loku kuxhunyaniswa nokubala ngokweqa. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi kufanele bakwazi ukubhala loku okulandelayo: 1 iqoqo lika 2 kwakha 2 noma 1 kuphindwe ka 2 kwakha 2 noma 1 x 2 = 2 2 iqoqo lika 2 kwakha 4 noma 2 kuphindwe ka 2 kwakha 4 noma 2 x 2 = 4 3 iqoqo lika 2 kwakha 6 noma 3 kuphindwe ka 2 kwakha 6 noma 3 x 2 = 6

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA 1.16 Ulwazi Lwezinombolo: Ulwazi Lwezinombolo: Ulaphi umehluko eBangeni 1 Uhla Lwezinombolo Uhla Lwezinombolo Izibalo zekhanda Lethemu igxile kulokhu: kufinyelela ku 99 kufinyelela ku 99 Izibalo zekhanda kumele zithuthukiswe ngendlela ethile onyakeni. • Hlela iqoqo • Hlela iqoqo Abafundi akufanele batshelwe ukwenza ukubala okungaheliwe ngelanga. lezinombolo. lezinombolo. Njengoba abafundi bafunda izihloko nokuthuthukiswa kwamasu okubala • Qhathanisa izinombolo • Qhathanisa izinombolo engxenyeni enkulu yesifundo, ezinye izinto ezenziwayo zingafakwa ohlelweni kuya kuma -99: kuya kuma -99: lwezibalo zekhanda ukuthuthukisa ukuqonda namakhono esifundweni sezibalo,okwenziwayo ngesinye isikhathi ngezinombolo elisezingeni elincane, • Eningi noma encane • Eningi noma encane ezibalweni zekhanda. ngo 1 ngo 1 Ungayigcina inombolo iphansi ngethemu 1 bese uyinyusa maphakathi nonyaka. • Eningi noma encane • Eningi noma encane Ekuqaleni konyaka, izinga lezinombolo namasu okubala angancika kulawo ngo 2i ngo 2 athuthukiswa eBangeni 1. • Eningi noma encane • Eningi noma encane Umqondo wezinombolo: ngo 3 nge10 Izibonelo zemibuzo engabuzwa: • Eningi noma encane ngo 4 Izinombolomagama nezimpawu • Eningi noma encane Bamba uphakamise ikhadi noma ubhale phansi inombolomagama. Khetha ngo 5 umfundi ozoqondanisa nenombolo. • Eningi noma encane Okungaphezulu nokungaphansi nge10 Yini • 1 ngaphansi kwe 15 • 1 ngaphezu kwe 9 • 10 ngaphezu kwe 15 • 10 ngaphansi kwe 16 Iyiphi i-alfabheti ye 5th ? Iyiphi inyanga ye- 9th yonyaka? Ukuhlela nokuqhathanisa Ikuphi okungaphezulu: 12 noma 21? 275 Nginike inombolo ephakathi kuka 17 no 19. Izibalo IBANGA 1-3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu 276 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA Khumbula Khumbula Amaphuzu okuhlanganisa nokususa: ngokushesha: ngokushesha: • Ukwazi ngengqondo wonke amabondi okuhlanganisa nokususa kufinyelele e • Khumbula izindlela • Khumbula izindlela 10 zokuhlangani sa zokuhlangani sa  + r = 10 Izibalo IBANGA 1-3 nokususa kuyofinyelela nokususa kuyofinyelela e 20 e 10 +r=8 • Hlanganisa noma Okuyiko ngokuhlanganisa nokususa zonke izinombolo kufinyelele e 10 ususe kusukela ngama 1 + 9 = 10 9 + 1 = 10 10 kusukela e-0 kufinyelele e 100 2 + 8 = 10 8 + 2 = 10 Amasu okubala Amasu okubala 8-4=4 8-4=4 Sebenzisa amasu Sebenzisa amasu 8-5=3 8-3=5 okubala ukuhlanganisa okubala ukuhlanganisa nokususa ngempumelelo: nokususa ngempumelelo: Ukukhumbula ngokushesha okuphindwe kabili kufinyelele e 10. Lokhu kumele kufake okuhambisana nokuyikho ngokususa. • Beka inombolo enkulu • Beka inombolo enkulu kuqala ukuze ubale kuqala ukuze ubale • 1+1=2 uqhubeke noma uye uqhubeke noma uye emuva • 2+2=4 emuva • Umugqa wezinombolo • 3+3=6 • Umugqa wezinombolo zekhanda • 4+4=8 • Ukuphinda kabili nokuhlukanisa kabili • Ukuphinda kabili • 5 + 5 = 10 ngokulinganayo nokuhlukanisa kabili ngokulinganayo Ngikhombise inombolo okufanele ngihlanganise nayo...... ukwakha i- 10 (bhala • Ukwakha nokuhlakaza phansi noma sebenzisa amakhadi enani lezinombolo nama Flard cards) • Ukwakha nokuhlakaza • Sebenzisa ubudlel- • 8 wane phakathi kokuh- • Sebenzisa langanisa nokususa ubudlelwane phakathi • 2 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kokuhlanganisa • 9 nokususa • 5 • 3

UKUQONDA UKUQONGA ISIKHATHI OKUFUNDWAYO OKUFUNDWAYO NAMAKHONO (ihora nemizuzu ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO enga - 24 CAPS ABHEKWA NGOKUPHELA isifundo) NGETHEMU 1 KONYAKA Ngikhombise inombolo esele uma …. Kususwe e 10(bhala phansi noma sebenzisa amakhadi enani lezinombolo nama Flard cards) • 5 • 3 • 6 • 1 • 7 Ezinye izibalo zekhanda zingenziwa ngaphandle kokusebenzisa izinsiza, kodwa njalo kuyasebenza ukwenza izibalo zekhanda ngezinsiza nokubhala okwenziwe. Izinsiza ezinconywayo • Umugqa wezinombolo (ohleliwe nongenalutho) • igrid yezinombolo • amakhadi enani lenombolo (Flard cards) • ubuhlalu bokubala 277 Izibalo IBANGA 1-3

ITHEMU YOKU-1 YEBANGA LESI-2 2. AMAPHETHINI, UBUDLELWANE NE ALJEBHRA 278 UKUQONDA ISIKHATHI UKUQONGA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora eli- ADINGEKAYO ABHEKWA 1 nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 2.1 Ukubukela, Ukubukela, Ukubukela kusiza abafundi ukubona ukuthi iphethini yakheke kanjani. 1 isifundo ukuqhubeka nokuchaza ukuqhubeka nokuchaza Izibalo IBANGA 1-3 Amaphethini Ukuqhubeka nephethini kusiza abafundi ukuba babheke ukuthi bayiqondisisa okusejiyometri ukubukela, ukuqhubeka ukubukela, ukuqhubeka kahle yini iphethini nokulandelana kwayo. nokuchaza ngamagama nokuchaza ngamagama Ukuchaza iphethini kusiza abafundi ukuthuthukisa ulimi lwabo namakhono • amaphethini alula • amaphethini alula okukhuluma. Kuphinda kusize nawe ukubona ukuthi abafundi bayihumusha enziwe ngezinto enziwe ngezinto kanjani iphethini. eziphathekayo eziphathekayo Kuhlale kulula kufafundi ukukhuluma ngephethini uma yenziwe yibona. Abafundi • amaphethini • amaphethini badinga ukuqeqeshwa ukuthi yini abayibhekayo nokuthi bayichaza kanjani elulaenziwe elulaenziwe iphethini. Ungabakhombisa loku ngokubuza imibuzo efana nale. ngemidwebo yemigqa, ngemidwebo yemigqa, “iziphi izakhiwo ozibonayo kulephethini?” “ izimu noma izinto. izimu noma izinto. “ngabe wonke anombala ofanayo?” Ukwakha nokuchaza Ukwakha nokuchaza amaphethini amaphethini “ubuna isimo esisodwa noma eziningi kulephethini?” angawakho angawakho “ngabe zonke izinto zibheke endaweni efanayo?” Ukwakha amaphethini Ukwakha amaphethini “ngabe inombolo yezinto iyafana eqoqweni ngalinye?” akho ngokusejiyometri akho ngokusejiyometri “zingaki izinto ezikhona eqoqweni ngalinye?” • ngezinto • ngezinto eziphathekayo eziphathekayo “ngabe zonke izimo nobungako kuyafana?”njll. • ngokudweba imigqa, • ngokudweba imigqa, Ukufaka okunhlangothimbili (2-D) izimo ezisejiyometri nokunhlangothi izimo noma izinto izimo noma izinto ntathu (3-D) izinto ezisazibalo mdwebo abafundi okufanele bafunde ngazo. Abafundi bangazakha izimo ezi 2-D ngokusika amaphepha noma amakhadi, Amaphethini noma bengazidweba. Bengakaha amaphethini ngezimo zamabhokisi, izimo asizungezile zamabhola namasilinda lezo abazenze ngobumba noma inhlama yokudlala. Khomba, uchaze Amaphethini angenziwa ngokusebenzisa into eyodwa kodwa imibala yazo ngamagama ishintsha ngendlela efanayo. ubukele amaphethini Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola okusejiyometri Isibonelo: • ngokwemvelo   • empilweni yesimanje yansukuzonke • emagugwini amasiko ethu

UKUQONDA ISIKHATHI UKUQONGA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora eli- ADINGEKAYO CAPS ABHEKWA 1 nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 2.1 Amaphethini angenziwa kusetshenziswa amaqoqo afanayo aphindaphindayo, lapho iqoqo ngalinyelinenhlobo eyodwa yento kodwa isikhundla sento Amaphethini sishintshe. Amaqoqo afanayo ayaphindwa. okusejiyometri Isibonelo:   Kwamanye amaphethini izinto ezahlukene ziyasetshenziswa ukwakha iqoqo, kodwa iqoqo lezinto liphindwe ngendlela efanayo. Isibonelo:   Amaphethini angenziwa lapho ubungako bezinto zishintshashintsha ngendlela efanayo.   Abafundi bengenza amaphethini ngokutshutsha ubuhlalu. Amaphethini angenziwa nasesifundweni saMakhono Empilo. 279 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONGA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni NAMAKHONO 280 ISIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora eli- ADINGEKAYO ABHEKWA 1 nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 2.2 Ukubukela, Ukubukela, Ukulandelana kwezinombolo kungaxhunyaniswa futhi kulekelelwe ukubala. 3 izifundo ukuqhubeka nokuchaza ukuqhubeka nokuchaza Njengoba amakhono abafundi okubala eshintsha futhi ethuthuka, izinhlobo Amaphethini zezinombolo ezilandelayo abafundi abasebenza ngazo zingathuthuka. ezinombolo Ukubukela, ukuqhubeka Ukubukela, ukuqhubeka nokuchaza izinombolo nokuchaza izinombolo Ukulandelana kufanele kukhombise ukubala okuqhubekayo nokuya emumva Izibalo IBANGA 1-3 ezilula ezilandelanayo ezilula ezilandelanayo ngo: kufinyelele e 200 kufinyelele e 100 • Nga-1 ukuphindaphinda kusukela kunoma iyiphi inombolo ephakathi kuka 1 Ukwakha nokuchaza Ukulandelana kubalwa no 100 amaphethini kuyiwa phambili • Nga-10 ukuphindaphinda kusukela kunoma iyiphi inombolo ephakathi kuka 1 okungawakho nasemuva ngo: no 100 Ukwakha awakho • nga-1 kusukela ku- • Nga-5 ukuphindaphinda kusukela kunoma iyiphi inombolo ephakathi kuka 1 amaphethini ezinombolo noma iyiphi inombolo no 100 ephakathi 1 and 100 • Nga-2 ukuphindaphinda kusukela kunoma iyiphi inombolo ephakathi kuka 1 • nga-10 ukuphinda no 100 nga10 kusukele ku- noma iyiphi inombolo EBangeni lesi- 2 abafundi babala baye emuva nga10, 5, no 2 okokuqala. phakathi kuka 1 no 100 Abafundi bangakhomba izinombolo ngesikhathi bebala. Kuyasebenza ukunika • nga-5 ukuphinda nga 5 abafundi izinombolo ezilandelanayo ekuthuleni okuhlukahlukene isib. kusukele kunoma iyiphi • Ukulandelana okubhaliwe kwezinombolo 100; 99; 98.97; 96, …… inombolo phakathi kuka 1 no 100 • umugqawezinombolo • nga-2 ukuphinda nga 2 • igridi lezinombolo kusukele kunoma iyiphi • iketanga lezinombolo inombolo phakathi Abafundi bangenza, umbala, nokuzungezela izinombolo bebebebala beqhubeka kuka 1 no 100 emugqeni wezinombolo negrid yezinombolo. Abafundi bangagcwalisa izikhala ezinezinombolo ezingekho emugqeni wezinombolo, igrid yezinombolo,ukulandelana kwezinombolo eketangeni lezinombolo. Isib. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ngasekupheleni kwethemu abafundi babala umsebenzi onezinombolo ezilandelanayo uksuka nokufinyelela e 100.

ITHEMU YOKU-1 YEBANGA LESI- 2 3. INDAWO NESIMO (IJIYOMETRI) UKUQONDA ISIKHATHI CAPS OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora eli- ADINGEKAYO NAMAKHONO NGOKUPHELA ABHEKWA NGETHEMU 1 nemizuzu KONYAKA engama-24) 3.2 Uhla lwezintoezi-3-D Uhla lwezintoezi-3-D Yini okwehlukile eBangeni 1 3 lessons Onhlangothintathu Buka bese usho izinto Buka bese usho izinto • Amasilinda masha eBangeni 2 kodwa angafundiswa ethulwe ngoThemu 3. ezi-3-D lapha ekilasini ezi-3-D lapha ekilasini 3-D KuThemu 1abafundi babukeziswa futhi kulanganiwse nalokho abakwenzile nasezithombeni. nasezithombeni. nabakufundile eBangeni 1.Abafundi mabagxiliswe kumasilinda ngoThemu 3 • Izimo ezisabhola, • Izimo ezisabhola, Umsebenzi omningi wonhlangothintathu 3-D useBangeni 2 kumele wenziwe (imbulunga) (imbulunga) ngezinto eziphathekayo.Thina siwazi umhlaba ngezindlela ezintathu ngakho • Okusabhokisi (iprizimu) • Okusabhokisi (iprizimu) kuyasisa ukuqala ngokusebenzisa izinto eziphathekayo ukuze umfundi asebenzise ulwazi analo alulethe esikoleni. • Amasilinda • Amasilinda Abafundi abaningi bayehluleka ukuhumusha onhlangothintathu 3-D nezinto Izimpawu zezinto Izimpawu zezinto ezisazibalombhalo ezithombeni.Ukusebenza ngezinto eziphathekayo ezi3-D ezi3-D kuyabasiza abafundi ukuthi bakwazi ukuhumusha kahle izithombe ezinezinto Chaza, uhlele ubuye Chaza, uhlele ubuye ezisazibalombhalo ngokuhamba kwesikhathi.Uma uphethe into ephathekayo uqhathanise izinto ezi- uqhathanise izinto ezi- bese ulokhu uyibukabuka kuwowonke amacala,yilapho ubona khona ukuthi lento 3-D ngokwe; 3-D ngokwe; oyibukayo ngaphansi nangemumva ifana nani. • ubungako • ubungako Uma unesithombe unakho ukubuka ngoqondo ubone izingxenye ezingabonakali entweni edwetshiwe,lokhu akulula kubafundi abasebancane ukwenzeka.Uma • izinto ezigingqikayo • izinto ezigingqikayo abafundi bangatshelwa incazelo yaleyonto ngaphandle kokuthi bayibone noma • izinto ezishelelayo • izinto ezishelelayo bayithinte,yingakho kulukhuni ukuthi aziqonde izimpawu zaleyonto ngokugcwele. Imisebenzi okugxilwe Imisebenzi okugxilwe Ukwakha izinto ngonhlangothintathu 3-D kuyo kuyo Abafundi abakopele umfanekiso wento abayikwe uthisha isib.umbhoshongo,iro Buka bese wenza Buka bese wenza bhothi,isitimela,inqaba,njll.Imifanekiso noma okokwakhiwe kungasetshenziswa izinto ezi-3-D usebenzisa izinto ezi-3-D usebenzisa amabhuloki,izinto ezike zasebenza, ikhithi yokwakha,neziny izinto izinto eziphathekayonjen- izinto eziphathekayonjen- zezibalombhalo ze 3-D Kusikwe izimo zo2-D Lokhu kungenzeka ngesikhathi gokusika ukhipha gokusika ukhipha sokufunda ngokuzimela. Kusemqoka ukuthi abafundi bakhulume ngalemifanekiso onhlangothimbili 2-D, onhlangothimbili 2-D, abayenzile, njengokwakha umbhoshongo owakhiwe ngamabhuloki amabhulokI amabhulokI nangamabhokisi. Ubabuzu imibuzo “Ungakwazi ukwakha umbhoshongo okwakha, izinto ezike okwakha, izinto ezike ngamabhola?Bazochaza bephendula imibuzo. zasebenza,ikhithi zasebenza,ikhithi Chaza uqhathanise izinto eziingo 3-D yokwakha,onhlangothi- yokwakha,onhlangothi- ntathu-3-D nezinto ntathu-3-D nezinto Abafundi baqhathanisa ubungako bezinto ezifanayo ezi- 3-D isib. 281 ezisazibalombhalo, ezisazibalombhalo, • Hlela amabhola ngobungako bawo • Sebenzisa uLimi lobungako nokuqhathanisa izinto. Ibhokisi likhulu kunebhola Izibalo IBANGA 1-3 ngoba ngiyakwazi ukufaka ibhola ebhokisini

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni 282 IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora eli- ADINGEKAYO NAMAKHONO NGOKUPHELA ABHEKWA NGETHEMU 1 nemizuzu KONYAKA engama-24) 3.2 Chaza izinto 3-D;Imibala Onhlangothintathu Abafundi bakhuluma ngemibala yezinto bese behlela izinto ngemibala 3-D Khomba ubuye usho izinto ngemibala yazo babuye baqhathanise ngobungako bezinto kubuye kjwenziwe ngesikhathi sokufunda ngamaphethini. Izibalo IBANGA 1-3 Izinto ezi-3-D zeBanga 2 Abafundi basebenza ngalokhu • Amabhola nezinto ezisabhola • Izinhlobo zamabhola nezinye izimo ezime njengonxande amaprizimu noma amakhiyubhi.Abafundi bazozifunela ukuthi yiziphi izinto eziginqikayo nezi shele- layo. Ukugqamisa izimpwu zezinto ze-3-D Abafundi bakha int eshelelayo noma utshekise ibhokisi ngokulibeka ngaphansi kwengxenye yencwadi.Yilapho bezobona khona ukuthi abakubekayo kuzoshelelela noma kuginqike Lapha, siqhubeka kumsebenzi esiwenze eBangeni 1 kodwa manje sifaka namasilinda. Abafundi bathola ithuba lokuziphenyela ukuthi bangazenza yini izitaki noma umbhoshongo usebenzisa amabhola noma amabhokisi kuphela. Ukubona nokusho amabhola (okusambulunga) Abafundi bathola izinto ezinhlobonhlobo ukuze bazisebenzise Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Izimo njengokusambulunga isib.amabhola anobungako obungalingani, izimabuli, amawolintshi njll. • Izimo ezinjengamaprizimu njengamabhuloki, izitini, amabhokisi isib. Amabhokisi kametshiso, etiye, noma yiliphi ibhokisi elingenalutho elingakusiza.

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora eli- ADINGEKAYO NAMAKHONO CAPS NGOKUPHELA ABHEKWA NGETHEMU 1 nemizuzu KONYAKA engama-24) 3.2 Abafundi bathola izinto ezisabhola (imbulunga,) noma okumise okusabhokisi (okweprizimu) ngenkathi bethola amaqoqo ezinto.Abafundi bazothola noma Onhlangothintathu batshengise ngezinto ezisabhokisi (iprizimu) ezisekilasini isib. Isitini simi noma leli 3-D wolintshi lifana nebhola.njengebhokisi. Ngesikhathi sokufunda ngokuzimele bangaqhubeka benze lokhu; • Hlela izinto ngobungako • Hlela izinto ngemibala; • Yakha izinto ezithiile • Benza amabhola nangamabhokisi (iprizimu) ngodongwe /ubumba Imisebenzi ebhalwayo Noma imisebenzi eminingi ephathekayo seyenziwe ngo3-D makuhlanganiswe nomsebenzi wokubhala. uLimi Kusemqoka ukuthuthukisa amakhono okukhuluma ngezimo ezingonhlangothintathu-3-D • ULimi olufanele lobungako; amazing a okukhula • Imibala • ULimi lwezinto olufanele; amabhokisi, amabhola, (Asikho isidingo sokuthi abafundi bazi igama (imbulunga) • ULimi lwesikhundla olufanele ukuchaza ukwakha isisb. Ngaphezu kwe...,ngaphansi.ngemumva,ngphambili, Eduze kwe, okuhambisana nen- gaphansi, ngale eduze, phakathi nengaphakathi, ngaphandle ULimi olufanele lobungako nemibala kungathuthukiswa ngesikhathi kufundiswa uLimi kanye namaKhono eMpilobese isetshenziswa nangenkathi kufundiswa iziBalo.ULimi lwesikhundla olufanele luthuthukiswe ngesikhathi sokufundisa izifundo zoLimi nesifundo samaKhono eMpilo nangesikhathi abafundi begxile kakhulu ngokufunda ngesikhundla.Lungasetshenziswa futhi lwenziwe ngesikhathi benza izinto zo 3-D 283 Izibalo IBANGA 1-3

ITHEMU YOKU- 1 YEBANGA LESI- 2 4. ISILINGANISO 284 UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 4.1 UKUKHULUMA UKUKHULUMA EBangeni 1abafundi bakhulume ngalokhu 2 izifundo NGESIKHATHI NGESIKHATHI Izibalo IBANGA 1-3 ISIKHATHI • Ukulandelanisa izigameko • Ukwazi ngezinsuku • Ukwazi ngezinsuku • Isikhathi esingakanani. zeviki • Ukwazi ngezinyanga Abafundi bafundile ngezinsuku zeviki nangezinyanga zonyaka bakusebenzisa zonyaka • Ukwazi ngezinyanga nakwezinye iziLimibelandelanisa izigameko ngezimpilo zabo.Bakhuluma besho zonyaka • Beka ishadi lokuzalwa, ukuthi izinto zenzeka isikhathi esingakanani, besbenzisa ulimi njengokudana, imigubho yezinkolo, • Beka ishadi lokuzalwa, kufishane, kusheshilenoma kunensile kune.. amaholide, izigameko imigubho yezinkolo, Abafundi bahlela ukulandelana kwezzithombe eziwumlando, izigameko amaholide,izigameko zesikole kuyikhalenda eziwumlando, izigameko • Iizindlela zokwenza inkomishi yetiye; zesikole kuyikhalenda • Batshele ngamahora • Izithombe zokukhula komuntu azabe mdalanphotographs ayi-12, uHafu • Batshele ngamahora ayi • Impilo yovemvane wehora,iKota yehora 12, uHafu wehora,iKota yehora • izigameko ezejwayelekile zosuku (ukuvuka,ukuba UKUBALA UBUDE sesikoleni,udlala,udla,ulala). NOKUDLULA KWESIKHATHI Babeka izinsuku zabo zokuzalwa kwikhalenda unyaka wonke Sebenzisa ikhalenda EBangeni 2 abafundi bayaqhubeka bekhuluma ngbude besikhathi ukubala nokuchaza ubude nangokulandelana kwaso.Ngesikhathi kufundiswa ikilasi lonke nesikhathi besikhathi ngezinsuku samaqembu abafundi bayaqhubeka bekhuluma ngezinsuku zesonto noma ngamasonto. nangezinyanga zonyaka nokuthi ulwesingaki namhlanje,kusasa ulwesingaki. Sebenzisa iwashi Abafundi bayayijwayela ikhalenda beqhubeka bebeka. ukubala ubude besikhathi • izinsuku zokuzalwa; ngamahora, nangohafu wehora noma ikota yehora • imigubho yezenkolo . • iziigameko eziwumlando Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • izigameko zesikole • amaholide kuyikhalenda Ngesikhathi abafundi befunda ngokuzimela bayaqhubeka bebelandelanisa izigameko ezenzeka nsuku zonke ezimpilweni zabo nokulandelanisa izigameko bezihlela ngezithombe.

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO CAPS NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 4.1 Yini umehluko eBangeni loku-1? ISIKHATHI Lapha eBangeni lesi- 2 kuyakhulunywa ngesikhathi ikakhulukazi ukufunda ngewashi.KuThemu 1 abafundi bagxilisa ukukhuluma ngesikhathi,amahora,iwashi elinezinti. Noma kunjalo abaqhubeke bakhulume ngezigigaba zosuku. Isib, abasho iukuthi isikole siqla nini,isikhathi sokuphumula,ufika nini ekhaya,noma isifudo sithatha isikhathi esingakanani. Khetha isikhathi lapho iwashi lishaya nqo ihora.Kuyasiza ukuba newashi elikhulu obondeni, ukuze abafundi balibone bakhombe kulo.Bayazakhela imifanekiso yamawashi.Ungabacela bakutshele ezinye izinhlobo zezikhathi. bafake nokubala.isib.Ngitshengise ihora leshumi.Ngitshene ukuthi kuzobe kusikhathi bani emva kwamahora ama-2 uma manje kuyihora le-10 4.2 sikali esingenasiliganiso Isikali esingenasiliganiso Yini umehluko eBangeni loku-1? UBUDE • Hlawumbisela, • Hlawumbisela, EBangeni loku-1 abafundi bagxiliswe - isilinganiso,uqhathanise, isilinganiso,uqhathanise, • Ngokubeka izinto maduze nezinye ukuqhathanisa ubude, ukuphakama, uhlele bese ubhala ubde uhlele bese ubhala ubde kanye nobubanzi placing usebenzisa amayunithi usebenzisa amayunithi angalinganisiwe isib. angalinganisiwe isib. • Isikali esingenasilnganiso kanye namayunithi angalinganiselwe obude Isandla, izinyathelo, Isandla, izinyathelo, Ithemu 1 eBangeni 2 abafundi bayaqhubeka bagxile kuso ipensela, ubude, ipensela, ubude, isikaliesingenasilinganiso kusetshenziswa amayunithi angalinganisiwe, futhi okokubala njll. okokubala njll. kungathulwa amamitha njengeyunithi yokulinganisa • Usebenzisa amayunithi • Usebenzisa amayunithi Isikali esingalinganisiwe sobude usebenzisa amayunithi angalinganisiwe angahleliweChaza angahleliwe.Chaza ubude bezinto ubala ubude bezinto ubala Abafundi bangafunda yonke imigomo yokulingnisa futhi bayisebenzise usebenzisa amayunithi usebenzisa amayunithi ngamayunithi angalinganisiwe.ISILINGANISO ngesikali esingalinganisiwe amade angahleliwe amade angahleliwe angeke usibukele phansi kunesikali samayunithi alinganisiwe • Ukusebenzisa • Ukusebenzisa Ukukala ubude ngesikali samayunithi angenasilinganisio ubuye ubale ukhetha uLimi ukhuluma uLimi ukhuluma amayunithi obude obulinganayo ngesikhathi leyonto ikalwa isib. Ubude ngokuqhathanisa isib. ngokuqhathanisa isib. bedesiki buyizandla eziyi-8. kude kune..., kufushane kude kune..., kufushane kune...., kuphakeme kune...., kuphakeme Abafundi kumele bakale izinto ezinhlobonhlobo besebenzisa uhla lwezinto kune..., kubanzi kune... kune..., kubanzi kune... njenamayunithi angalinganisiwe. 285 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni 286 IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 4.2 IUkwethula isikali Zintathu izindlela zokusebenzisa amayunithi angalinganisiwe,ubude, ibanga esingenasilinganiso nokuphakama UBUDE Hlawumbisela,isilinganiso, • Layisha izinto uzimake lezo osuzikalile emgqeni izinto eziningi zobude uqhathanise, uhlele bese obulinganayo njengamabhokisi kametshisi,amabhodlela anezimo nezivalo Izibalo IBANGA 1-3 ubhala ubde usebenzisa ezifanayo, noma okokubala amapensela njll.isib. ukukala ubunzi bedesiki, amamitha (induku umthwalo wamapensela amasha uwabeke ekugcineni nasekuvundleni yamamitha noma intambo kwedesiki ende) njengendlela Nakhu okusemqoka, ehleliwe yobude • zonke izinto zinobude obulinganayo,Angeke usho ukuthi ibhuku linobubanzi obulingana nezivalo zamabhodlela ayi-12 uma izivalo zamabhodlela zi- nobungako obungafani.isib.Izivalo zamabhodlela obisi,izivalo zamabhodlela kajusi,izivalo zamabhodlela ewuthayela. • Azikho izikhala ezisele phakathi kwezinto;Badinga ukubekwa ngandawonye ukuze bathintane. Sebenzisa izinto ezifanayo njengamayunithi angalinganisiwe. Beka enye eduze kwenye, susa eyokuqala, uyigudlukisele kwelinye icala lesibili.Lokhu kwenzeka ngesikhathi ukala ngesandla, nangobude bonyawo noma amagxathu. • Sebenzisa into eyodwa njengesikali esingalinganisiwe, yenza uphawu lokut- shengisa, lapho ugcine khona. Abafundi kumele bafundise njalo basho iyunithi leyo. Isib.incwadi inobubanzi obungangezivalo zamabhodlela ayi-12, ikilasi lona lide ngamagxathu angama 38. Uma abafundi sebeke balinganisa ngamayunithi izikhathi eziningana, kumele baqagele ukuthi zingaki izinto ezinamayunithi amade akaliwe.Ukuqagela isilinganiso ngaphambili kusemqoka kodwa kungenziwa uma sebeke bazenza ezinye izilinganiso ngamayunithi. Abafundi badinga ukufundiswa ukuze bakwazi ukuqagela ubude, ukuphakama, Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola noma ububanzi iyunithi afanayo kumele isetshenziswe.isib. Uma ububanzi bomnyango bulinganiswa ngezandla ezinga-20 bese kuthi ububanzi bedesiki sibe amapensela ayi- 8 ubude,ungeke usho ukuthi umnyango unobubanzi obuvulekile kunedesiki

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO CAPS NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 4.2 Abafundi kumele bakale ngohla ngamayunithi angenasilinganiso,yingakho; Izifundo ezi-3 UBUDE • Baqala ukuqonda ukwazi amayunithi amancane,amade adinga isikhathi esiningi sokukwenza.isib.ububanzi bekilasi bungalingana namagxathu an- gama-20 bese ubude bube iznyawo ezingama-48 • Baqala ukusebenzisa amayunithi okuyiwonawona kulokho abakukalayo isib. Ukukala ububanzi bekilasi usebenzisa izivalo zamabhodlela kuwukuchitha isikhathi Ukwethula isilinganiso esihleliwe Isikhathi esiningi eBangeni 2 kumele sisichithwe ngsikali esingalinganisiwe. Abafundi abathole ithuba lokuthuthukisa ulwazi lokubona ubude bemitha.Lokhu kwenzeka kahle uma abafundi sebekala besenzisa ubude bemitha”ithulusi” (njengeirula eliyimitha,induku engangemitha ubude).Ngokubona ubude bemitha kusiza abafundi bakwazi ukuba nesithombe sokwazi ukuthi imitha lide kangakanani.Kuyenzeka ukukala ngamamitha ngesondo lamamitha,kodwa ubude bemitha akulula ukububona Abafundi sebengaqala ukuthola izinto ezifana ncimishi nobungako bemitha. Kuyasiza ukuba nezinto esingaqhathanisa ngazo izilinganiso ezehlukene. Isib. Ububanzi bomnyango nokuphakama kwefasitela kunaba imtha 1m. Lokhu kungasiza abafundi bakwazi ukusebenzisa lobobude babone ngokuqagela ubude bezinto abangazikala.. Uma abafundi sebenolwazi lokukala ngamamitha sebengaqagela ngaphambi kokwazi isilinganiso. Abafundi sebengathola izinto ezindana noma ezimfishana kune mitha elilodwa. Ekugcineni sebengakala izinto ezinobude nobubanzi obuhlukene ngamamitha. Ukubhala izilinganiso Ukulinganisa kulikhono eliphathekayo, abafundi kumele babhale izilinganiso abazitholile.(zombili zamayunithi angahleliwe namamitha) ngazozonke izikhathi Ukukala ubude njengesimo esijwayelekile ukuxazulula izinkinga nokubala Ngesikhathi esinikeziwe sezinombolo,ukusebenza kanye nokusebenza kwazo abafundi baxazulula izinkinga besebenzisa isimo esijwayelekile njenge- • Isikali esingahlelekile sobude isib.idesiki lika Lebo liyizandla ezi 11 ubude, idesiki likathisha liyizandla ezingu -19 ubude. Lide kangakanani idesiki likathisha? 287 • Ukukala ubude ngamamitha Qikelela ubheke uhla lwezinombolo eziqondene neThemu, bese ubheka uhla Izibalo IBANGA 1-3 lwezinhlobo zezinkinga eziqondene naleyo themu..

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni 288 IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 4.3 Isilinganiso EBangeni loku-1 bekuncomeka ukuthi abafundi bagxiliswe ngokusebenzisa Isisindo esingahlelekile isilinganiso sesisindo • Hlawumbisela, • Qhathanisa isisindo sezinto bezibona; ulinganise, • Hlela bese uqhathanisa isisindo sezinto ezintathu noma uqhathanise, uhlele Izibalo IBANGA 1-3 ngaphezulu,ngokubeka phezu kwesisindo izinto ezihamba ngakubili,uze bese ubhala isisindo ubeke zonke izinto ngokulandelana usebenzisa amayunithi • Thola isisindo sento usebenzisa amayunithi angenasilinganiso. angalinganisiwe isib. Amabhuloki, izitini njll. Abafundi bagxila ekuthuthukisweni ulimi lokukhuluma ngesisindo. • Ukusebenzisa Ngesikhathi benza umsebenzi wokuzimela bangasebenzisa ukuqhathinisa, uLimi ukhuluma balinganise, bahlele, bese bebhala isisindo ngokusebenzisa ukuzimelela ngokuqhathanisa isib. namayunithi angenasilinganiso. kulula,kuyasinda,kulula Ukulinganisa ubude njengesimo esijwayelekile sokuxazulula izinkinga kakhulu, kusinda nokubala kakhulu njll Ukuxazulula izinkinga nukubala kungqhubeka usebenzisa isisindo esimeni Ukwethula isikali esijwayelekile esingenasilinganiso Ngesikhathi esinikeziwe sezinombolo, ukusebenza kanye nokusebenza kwazo • Qhathanisa, uhlele abafundi baxazulula izinkinga besebenzisa isimo esijwayelekile sesisindo isib.. bese ubhala,i sisindo Indwangu yokwesula ibhodi inesisindo sezimabuli eziyi-11,Ibhokisi lamakrayoni salezizimpahla linesisindo sezimabuli ayi-8.Sekuhlangene kuzoba nesisindo sezimabula ezidayisayo ezinesisindo ezingaki? esibhalwe kuyona Qikelela ubheke uhla lwezinombolo eziqondene neThemu, bese ubheka uhla ngamakilogramu isib. lwezinhlobo zezinkinga eziqondene naleyo themu.. 2kg erayisi, no 1kg kafulawa • Bazilinganisa, izisindo zabo besebenzisa isilinganiso sasendlini yokugeza. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO CAPS NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 4.4 Isikali esingenasiliganiso EBangeni 1 bekuncomeka ukuthi abafundi bagxiliswe kulokhu Umthamo/ • Qagela bese ulinganisa, • Ukuthuthukisa ulimi lokukhuluma ngamithamo eyahlukene okumumethwe qhathanisa bese uhlela • Ukuqhathanisa imithamo yezitsha ezifanyo umthamo wezitsha (isib, inani lomthamo • Ukuqhathanisa umthamo wezitsha ezibukeka zingafani, nengobubanzi ongaphathwa isitsha nangokuncipha kwazo. uma sigcwalisiwe). • Ukulinganisa umthamo ngezilinganiso namayunithi angalinganiswe. • Chaza umthamo Yini umthamo? Yini okumumethwe? wezitsha ngokubala nokusho ukuthi Ibhodlela lingaba nomthamo wazinkomishi ezine agcwele, kodwa ngeke mangaki amayunithi ligcwale lidlulele, lingafaka umthamo wenkomishi eyodwa ngesikhathi. angenasilinganiso Okumumethwe kuwubungako baleyonto ethwalwayo (isikhala esingaphakathi akwazi ukugcwalisa kuleyonto) isitsha isi. Ibhodlela Umthamo ubungako bendawo engathathwa okuthile linezinkomishi ezinel (Kwesinye isikhathi abafundi bayolinganisa okusaketshezi (noma Ukwethula isikali isihlabathi,noma ngabe yini) okusesitsheni.Lokhu kuwukulinganisa esingenasilinganiso okumumethwe kulesositsha. • Qagela, linganisa, Ngezikhathi ezithile abafundi bazolinganisa ukuthi isitsha leso singamumatha chathanisa, hlela sigcwalise umthamo ongaphezulu) bese ubhala umthamo wezinto ngokulinganisa Ngesikhathi sokwenza ngokuzimela bangazijwayeza ukuqagela, balinganise, ngamalitha bahlele, bese bebhala umthamo nokumumethwe ngezlinganso nangamayunithi angalinganisiwe. isib. Ukupheka nokubhaka kuyizimo ezijwayelekile lapho • Qhathanisa, uhlele, abafundi bazokwenza balinganise umthamo.Khetha isu lapho uzosebenzisa bese ubhala umthamo khona izilinganiso kuzoba izinkomishi,amathisuni kanye namayunithi wezinto ezipakishelwe angenasilinganiso. ukuthengisa ezinesisindo esichazwe Ukulinganisa umthamo njengesimo esijwayelekile sokuxazulula izinkinga ngamalitha isib, amalitha nokubala ama-2 obisi, ilitha e-1 Ngesikhathi esinikeziwe sezinombolo, ukusebenza kanye nokusebenza kwazo yesiphuzo esibandayo, abafundi baxazulula izinkinga besebenzisa isimo esijwayelekile somthamo amalitha ama-5 noma isib.Ugogo usebenzisa izinkomishi ezimbili zobisi ukwenza uphudingi. kapende. Uma efaka izinkomshi ezimbili, uzodinga ubisi olungakanani?. Qikelela ubheke uhla lwezinombolo eziqondene neThemu, bese ubheka uhla lwezinhlobo zezinkinga. 289 Izibalo IBANGA 1-3

ITHEMU YOKU-1 YEBANGA LESI- 2 5. UKUQOKELELWA KOLWAZI 290 UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 5.4 ukuqoqa nokuhlela ukuqoqa nokuhlela Yini umahluko eBangeni 1 Ukuqoqa ulwazi ulwazi • abafundi abasasebenzisi amaqoqo ezinto Izibalo IBANGA 1-3 nokuhlele ulwazi • Qoqa ulwazi ngekilasi Qoqa ulwazi ngekilasi • Abafundi bayaqhubeka ngokusebenza ngegrafu yezithombe - ngokunikezwa noma ngesikole noma ngesikole zona zombili zibe yingxenye yolwazi oluphelele nokuhlaziya amagrafu yez- uphendule imibuzo uphendule imibuzo thombe. ebuzwe uthisha ebuzwe uthisha ukubhala okumele Ulwazi olwanele oluqokelelwe ngokuphelele ulwazi Ulwazi oluqokelelwe ngokuphelele, Bhala okumele ulwazi • Abafundi baqoqa ulwazi ukuphendula umbuzo. Emazingeni aphansi naphakathi Ukuhlaziya lombuzo uyabuzwa uthisha noma incwadi. nokuhumusha ulwazi • Abafundi bayahlela babhale okumele ulwazi ngendlela ezokwenza kube lula Phendula kubafundi ukuthi bakwazi ukuyihlaziya. Indlela yokubhala okumele ulwazi imibuzongegrafu yikuthi abafundi beBanga 2 bayisebenzise igrafu yesithombe. yezithombe • Abafundi bahlaziya ulwazi ngegrafu yesithombe ngokuphendule imibuzo ezobuzwa uthisha. Igrafu yesithombe yekilasi Kuyancomeka ukuthi eBangeni 2 abafundi basebenza ngolwazi olwanele lokuqokelelwe ngokuphelele, ukwenza igrafu yesithombe yekilasi kabili ngonyaka(kanye ngethemu1 nethemu 3)Ukusebenza ndawonye njengekilasi kusiza abafundi bambandakanye kuzozonke izigaba ngaphandle kokulahlekelwa esinye isigaba.isib.dweba zonke izithombe.Benza igrafu yekilasi ezokwenza uthisha akwazi ukubamba abafundi banakisise ukuze babheke ukuqokelela kolwazi kulokho abafuna ukukwazi ngezimpawu ezisemqoka zegrafu yesithombe. Izimpawu zegrafu yesithombe abafundi okumele bazifundiswe: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • igrafu ilebulwa kuphi nakanjani (isihloko segrafu) • imikhakha ibebulwa kuphi nakanjani. • igrafu yesithombe idinga ube nendlela yokuchaza isithombe ngasinye sisho ukuthiniThe • izithombe noma izikhala zazo kumele zibe nobungako obulinganayo • zibekwa kanjani izithombe ziqonde emgqeniHow • ifundwa kanjani igrafu

UKUQONDA ISIKHATHI OKUFUNDWAYO UKUQONDA NAMAKHONO OKUFUNDWAYO (ezifundweni IZIHLOKO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA zehora ADINGEKAYO NAMAKHONO CAPS NGOKUPHELA ABHEKWA NGETHEMU eli-1 nemizuzu KONYAKA engama-24) 5.4 Abafundi bayadinga ukwazi ubumqoka bokuqala ngokufunda isihloko, ukuze 3 lessons Ukuqoqa bakwazi ukuthi igrafu ikhuluma ngani. Bayadinga ukwazi ukufunda amagama nokuhlele ulwazi asuka phansi uye phezulu nalawo asuka kwesokudla kuya kwesokunxele. Abafundi abadingi ukwazi ulimi olunobuchwepheshe oluthile ukuze alusebenzise ukuchaza izingxenye zegrafu, kuphela uma bezofunda ngaphansi nasemaceleni ukuthola ukuthi igrafu ikhuluma ngani. Uma sifunda siqala kwesokunxele siya kwesokudla, kodwa uma abafundi befunda igrafu bayifunda kusuka phansi kuya phezulu.Lokhu kudinga abafundi bachazelwe.Abafundi kumele bawenze lamakhono. Khetha isihloko ubuye ubabuze imibuzo ngokuqokelela ulwazi EBangeni 2 kumele babuzwe lemibuzo, isib. Yiziphi izinhlelo zeTV enizikhonzile? Othisha balelozinga kumele baqikelele ukuthi akufundiswe izihloko ezahlukene ezikhethiwe ukuze ulwazi oluqoqiwe luhlaziwe kulelo nalelobanga. Iziihloko ezifanele kumele zifake ezemidlalo iziphuzo engizithandayo,imibala engiyithandayo,izinkathi ezedlule,ukudla engikuthandayo,izinhlelo zeTV engizithandayo njll Ukuhlela imikhakha yokuqoqa ulwazi Nika abafundi uhlelo lwemikhakha lapho bezokhetha khona. Ukubhala okumele ulwazi Abafundi abathole iphepha elinobungako obufanayo lapho bezodweba noma babhale izimpendulo khona. Imidwebo kumele ihlelwe ngemigqa lapho bezodweba khona igrafu yezithombe. izihloko ziyengezwa ezimpambanweni negrafu. Ukuhlaziya nokuhumushe ulwazi Abafundi baphendula imibuzo leyo ebuziwe ngegrafu yezithombe isib. Yiziphi izinhlelo ezaziwayo zeTV ekilasini lakho.? Yiziphi izinhlelo abafundi abambalwa abazithandayo ekilasini lakho? Abafundi abaningi bathanda...noma...? Baningi bangakanani abathanda...ne...? 5.5 ukubhala okumele ukubhala okumele ulwazi ulwazi Bhala okumele ulwazi ngegrafu yezithombe 5.6 Ukuhlaziya Ukuhlaziya nokuhumusha ulwazi 291 nokuhumusha Phendula imibuzo ulwazi ngolwazi ngegrafu Izibalo IBANGA 1-3 yezithombe

ITHEMU YESI - 2 YEBANGA LESI-2 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANE BEZINOMBOLO 292 UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.1 Ukubala izinto Bala okungenani Yini okwehlukile kunakuThemu 1? eziphathekayo ufinyelele e- 150 Bala izinto ngokwethembeka NgeThemu lesi - 2 uhla lwezinombolo seluthe ukuthuthuka nabafundi sebebala Hlawumbisela ubuye izinto eziyi - 150. Ngenxa yokuthi lena inombolo enkulu ukuyibala, kufanele Izibalo IBANGA 1-3 nsukuzonke. ubale ufinyelele kugxilwe ekubaleni ngamaqembu. Leli yikhono abafundi abalenze kusukela okungenani ema - 200 Nikeza eBangeni loku - 1, manje osekufanele basisebenzise kwizinga eliphakeme lohla izinto zansukuzonke ngokuhlawumbisela inani lwezinombolo. ngokwethembeka. lezinto ezingahlolwa ngokubala. Kubalulekile ukuthi kuphela iThemu abafundi babe sebelibonile iqoqo lezinto eziyi Aligqugquzelwe isu - 150 bangenza isiphakamiso sendlela yokubala ebasizayo. lokusebenza ngamaqoqo Ukubalwa kwezinto kuleThemu kusekela: • Ikhono lokubala elidingekayo ukuqonda ubungako benombolo; • Ukubala bephimisela; • Ukushiwo kwamagama ezinombolo; • Ukubona izimpawu zezinombolo; • Ikhono lokubala elidingekayo ekubaleni Izinsizakufundisa: Kufanele kubhekelelwe izinhlobo zezizinsiza ezisetshenzisiwe. • Izinsiza ezihleliwe, njengobuhlalu bokubala obusentanjeni • I-abhakhasi ukuzilungiselela ukubala ngamaqembu • Inyanda yoku - 2, inyanda yoku - 5 kanye nenyanda yokuyi - 10 bese kuy- abalwa konke. • Amabhuloki • Imali yokudlala Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.2 Bala uye phambili ubuye Bala uye phambili ubuye Yikuphi okwahlukile kusukela kwiThemi - 1 uye emuva ngo: uye emuva ngo: Bala uyephambili NgeThemu yesi - 2 uhla lokubala izinombolo seluthe ukuthi xaxa nabafundi abuye uye emuva • Nakunye kunoma iyiphi • Nakunye kunoma iyiphi baqala ukubala ngakuthathu nangakune okokuqala. inombolo ephakathi inombolo ephakathi Ngokuphela kweThemu abafundi kufanele babe bekwazi ukuphendula imibuzo kwe - 0 kuya ema - 200 kwe - 0 kuya ema - 150 efana nale: • Ngokuyi - 10 • Ngokuyi - 10 • Qala e - 132, bala uye phambili ngakunye uze ufinyelele e - 150. okuphakathi kwe - 0 okuphakathi kwe - 0 kuya ema - 200 kuya ema - 150 • Qala e - 120 ubale uye emuva ngakunye uze ufinyelele ema - 98. • Ngokuyisi - 5 • Ngokuyisi - 5 • Qala ema - 60 ubale ngakubili uze ufinyelele e - 100. okuphakathi kwe - 0 okuphakathi kwe - 0 • Qala e - 100 ubale ngakubili uze ufinyelele e - 138. kuya ema - 200 kuya ema - 150 • Qala koku - 3 ubale ngakuthathu uze ufinyelele ema - 30. • Ngaku - 2 phakathi • Ngaku - 2 phakathi koku - 0 kuya ema - koku - 0 kuya ema - • Qala ema - 60, ubale uye emuva ngakuthathu uze ufinyelele ema - 42. 200 150 • Qala kokune ubale ngakune uze ufinyelele ema - 40. • Ngaku - 3 phakathi • Ngaku - 3 phakathi koku - 0 kuya ema - koku - 0 kuya ema - 99 • Qala ema - 84 ubale uye emuva ngakune uze ufinyelele ema - 68. 200 • Qala ema - 45 ubale ngakuhlanu uze ufinyelele e - 100. • Ngaku - 4 phakathi • Ngaku - 4 phakathi koku - 100 • Qala e - 100 ubale uya emuva ngamashumi ngamashumi uze ufinyelele koku - 0 kuya - 200 eshumini. Abafundi kufanele babale beya emuva ukusukela kunoma iyiphi inombolo. 293 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 294 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.3 Bona, ufunde Bona ufunde Yini eyahlukile ukusukela eThemu loku - 1? izinombolo izinombolo Uphawu Abafundi bayqhubeka bafunde babuye babhale izimpawu izimpawu zezinombolo lwezinombolo • Bona ufunde izim- • Bona ufunde izim- ngokhla lwezinombolo oluthe thuthu. Abafundi bazobe bebona, befunda, bebhala kanye namagama pawu zezinombolo pawu zezinombolo izimpawu ezingaphezu kwekhulu babuye babhale amagama ezinombolo kuze ezinombolo eziphakathi kwe - eziphakathi 0 - 150. kufinyelele ema - 50. nama - 200. Izibalo IBANGA 1-3 • Bhala izimpawu zezi- Kufanele kuqashelwe uma kukhulunywa ngezinombolo ezinamadijithi amathathu, • Bhala izimpawu zezi- nombolo eziphakathi njengokuthi: amakhulu amathathu namashumi amabili nantathu. nombolo eziphakathi 0 -150. Uma sibhala izinombolo ezinamadijithi amathathu eziphakathi kwekhulu nekhulu 0 - 200 • Bona ufunde amag- neshumi, idijitji emele amashumi u - 1. Abanye abafundi baba nobunzima • Bona ufunde amag- ama ezinombolo ukubhala lezizinombolo benikezwe izimpawu ezingamagama. Isib. Ukubhala - ama ezinombolo eziphakathi 0 - 50. 102 kungaba nzima kwabanye abafundi, bangabhala - 1002. Amakhadi amele eziphakathi 0 - 100 isikhundla senombolo ayabasiza abafundi ukuqonda ukuthi ungazisebenzisa • Bhala amagama kanjani izikhundla zezinombolo. Abafundi kufanele babuye banikezwe ithuba • Bhala amagama ezinombolo aphakathi elanele loubhala lezizinombolo. ezinombolo phakathi 0 - 50. 0 - 100. Izibonelo zokubhalwe phansi: • Bhala izimpawu zezinombolo. Ikhulu namashumi amathathu nantathu Ikhulu nashumi amne nesikhombisa • Qondanisa amagama ezinombolo nezimpawu zakhona • Qedela uhla lwezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Qedela umugqa wezinombolo nokulandelana kwazo

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.4 Chaza, Chaza, qhathanisa Yini eyahlukile ukusukela eThemu loku - 1? Chaza, qhathanisa qhathanisa,uhlele uhlele izinombolo uze NgaleThemu abafundi bayaqhubeka bahlele baqhathanise izinombolo. izinombolo kuze ufinyelele ema - 50 ubuye ubhale Umugqa wezinombolo uhlala uyisithombe esibalulekile esilusizo ekuhloleni izinombolo kufinyelele ema - 99 • Chaza uuqhathanise izikhundla zezinombolo ngokuhlobana nezinye iznombolo. • Chaza uqhathanise izinombolo eziphelele usebenzisa okuncane Imisebenzi yokuzimela eyengeziwe: izinombolo ezigcwele kuze kufinyelele kune-, okukhulu kune-, Babhala ngokuphindaphinda izinombolo ngokwezikhundla zazo. ema - 99 useben- okungaphezulu kune-, Bhala phansi lokhu okulandelayo ekilasini encwadini yakho yokusebenzela: zisa okuncane kune-, okulinganayo • Iyiphi inombolo eza ngaphambi kwama - 46? okungaphezulu kwe-, • Chaza uhlele izinom- • Iyiphi inombolo eza ngemuva kwama - 48? okungaphansi kwe-, bolo eziphelele okulingana ne-. • Iziphi izinombolo eziphakathi kwalezi - 45 no 47? Kusukela kwencane • Chaza uhlele izinom- kuya kwenkulu, kusukela • Sebenzisa umugqa wezinombolo onikezwe wona uqedela ngezinombolo ez- bolo eziphelele kwenkulu kuya kwencane ishodayo. Kusukela kwencane • Bhala okukodwa ngaphezulu kwenombolo ngayinye: kuya kwenkulu, kusukela - Okukodwa ngaphezulu kwama - 23 ___ kwenkulu kuya kwencane Sebenzisa izinombolo - Okukodwa ngaphezulu kwama - 29 ___ Sebenzisa izinombolo zesikhundla ukuhombisa ukuhleleka - Okukodwa ngaphezulu kwama - 42 ___ zesikhundla ukukhombisa kwezinombolo, indawo • Bhala okukodwa ngaphezulu kwenombolo ngayinye: nesikhundla sazo - Okukodwa ngaphansi kwama - 20 ___ ukuhleleka, indawo nesikhundla Beka izinto ezisemgqeni - Okukodwa ngaphansi kwama - 31 ___ ngezikhundla zazo Isikhundla sezinto - Okukodwa ngaphansi kwama - 42 ___ kusukela kweyokuqala ezisemgqeni • Bhala okuyishumi ngaphezulu kwenombolo ngayinye: kuya kweyeshumi ngokulandelana kwazo nanhlanu, kanje: - Okuyishumi ngaphezu kwama - 20 ___ kusukela kowokuqala, okokuqala, okwesibili, - Okuyishumi ngaphezu kwama - 30 ___ owesibili, owesithathu, njll. owesine, owesihlanu, njll. • Bhala okuyishumi ngaphansi kulezizinombolo ezilandelayo - Bhala okuyishumi okungaphansi kwama - 50 ____ - Bhala okuyishumi okungaphansi kwama - 40 ____ • Bhala lezizinombolo uzihlele kusukela kwenkulu kuya kwencane. (130, 133, 123, 143, 103, 113) • Qedela lomusho. Gcwalisa ngokuningi nokuncane: - Ama - 26 ma _______ kunama - 24 - Ama - 36 ma _______ kunama - 19 295 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 296 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.5 Bona ubungako Bona ubungako Yini eyahlukile ukusukela eThemu loku - 1? benombolo okungenani benombolo okungenani Ubungako inombolo enamadijithi inombolo enamadijithi NgaleThemu uhla lwezinombolo luyakhula lusuke ema - 25 kuya ema - 50. benombolo amabili kuze amabili kuze Abafundi manje basebensiza ulwazi nomqondo wobungako bezinombolo ukuya kufinyelele ema - 99 kufinyelele ema - 50 kwizinga eliphezulu lohla lwezinombolo. • Bona ukuthi idijithi • Bona ukuthi idijithi ngaleThemu abafundi bayaqhubeka uku: Izibalo IBANGA 1-3 ngayinye imeleni ngayinye imeleni • Bala ubuye uhlele ngamaqoqo ukhombise amashumi nemivo ngezindlela • Hlakaza inombolo • Hlakaza inombolo ezahlukene enamadijithi amabili enamadijithi amabili • Bala izinto ezingamaqoqo ezihleliiwe anamashumi nemivo anamashumi nemivo (TU) (TU) • Sebenzisa amakhadi obungako benombolo ukukhombisa inombolo ekwiqoqo naleyo ebaliwe, isib. ama - 35 angakhonjiswa ngezinto ezingama - 35 ezih- • Bheka usho ubungako • Bheka usho ubungako lukene, ngamashumi (3 tens) nokuyisihlanu okwahlukene kubekwe ngakunye, bedjithi ngayinye bedjithi ngayinye amaqoqo amashumi • Shono ubungako bedijithi ngayinye. Lomsebenzi ongenhla wenziwa emaqenjini okugxilwa kuwona, ngesikhathi esikhululekile abafundi bangabhala lokhu okulandelayo: 48 = namaqembu a - 4 awamashumi kanye nesi - 8 sokuhlukene 48 = 40 kanye nesi - 8 Lokhu kwelekelelwa ukusetshenziswa kwaflathi khadi. Ubungako bamadijithi Abafundi kufanele baqale basho ukuthi idijithi ngayinye imeleni. Buza abafundi: • Iyiphi inombolo emelwe yi - 7 ku - 27? • Iyiphi inombolo emelwe o- 4 ku - 49? Abafundi kufanele basebenzise amakhadi obungako benombolo ukufakazela izitatimende zabo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) UKUXAZULULWA KWEZINKINGA ZESIMO ESEJWAYELEKILE 1.6 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Kulindeleke ukuthi abafundi baxazulule izinkinga besebenzisa lamaqhinga alandelayo uma alandelayo uma alandelayo: Amaqhinga uxazulula izinkinga uxazulula izinkinga okuxazulula ubuye uchaze uchaze • Imidwebo noma izinto eziphathekayo, isib. izinto zokubala ubuye uchaze uchaze izinkinga izixazululo zezinkinga: izixazululo zezinkinga: • Ukwakha nokuhlakaza izinombolo • Imidwebo nezinto • Imidwebo nezinto • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo eziphathekayo isib. eziphathekayo isib. izinto zokubala • Umugqa wezinombolo izinto zokubala • Ukwakha nokuhlakaza Imidwebo noma izinto eziphathekayo • Ukwakha nokuhlakaza izinombolo izinombolo Abafundi bazoqhubeka nokudweba izithombe nokusebenzisa izinto eziphathekayo ukuxazulula izinkinga. Ukudweba izinto kusukela kwezingama - 30 • Ukuphinda kabili • Ukuphinda kabili noma kwezingama - 50 ngamunye kufanele kungagqugquzelwa. Gqugquzela nokuhlukanisa kabili nokuhlukanisa kabili abafundi ukuthi bafake izimpawu zezinombolo uma bebhala phansi kufaka ngoklinganayo ngoklinganayo nalokho okumele izithombe. Abafundi bangabuye bagqugquzelwe ukuthi babhale • Umugqa wezinombolo umusho wezinombolo. • Umugqa wezinombolo Bheka amanothi Themu yoku - 1 1.7 Xazulula izibalo Xazulula izibalo Yini okwehlukile kuThemu loku - 1 zenxoxo ngokwe simo zenxoxo ngokwe simo Ukuhlanganisa NgaleThemu abfundi bayaqhubeka benze ngokuphindaphinda izinkinga zezibalo esejwayelekile ubuye esejwayelekile ubuye nokususa zamagama babuye basebenzise lamaqhinga alandelayo uma bexazulula uchaze izixazululo uchaze izixazululo izinkinga: zezinkinga kufaka zezinkinga kufaka ukuhlanganisa, ukususa, ukuhlanganisa, ukususa, • Imidwebo noma nezinto eziphathekayo kanye nezinmpendulo kanye nezinmpendulo • Ukwakha nokuhlakazwa kwezinombonolo kufinyelela ema - 99. kufinyelela ema - 50. • Ukuphindaphinda kabili nokuhlukanisa kabili ngokulinganayo • Umugqa wezinombolo Imidwebo noma izinto eziphathekayo Abafundi bazoqhubeka nokudweba izithombe nokusebenzisa izinto eziphathekayo ukuxazulula izinkinga. Ukudweba izinto kusukela kwezingama - 30 noma kwezingama - 50 ngamunye kufanele kungagqugquzelwa. Gqugquzela abafundi ukuthi bafake izimpawu zezinombolo uma bebhala phansi kufaka nalokho okumele izithombe. Abafundi bangabuye bagqugquzelwe ukuthi babhale umusho wezinombolo. 297 Bheka amanothi aeThemu yoku - 2 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 298 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.8 Xazulula izinkinga Xazulula izinkinga Yini eyahlukile eThemu yoku - 1 zezibalo ezisesimweni zezibalo ezisesimweni Ukuhlanganisa Uhla lwezinombolo selukhulile lwafinyelela ema - 30. Abafundi kufanele esjwayelekile ubuye esjwayelekile ubuye okuziphindaphin- bagqugquzelwe ukubhala umusho wezinombolo kuzona zonke izinkinga uchaze izixazululo zakho uchaze izixazululo zakho dayo okuholela zezibalo ezibhalwayo. Kulindeleke ukuthi abafundi basebenzise ukuhlanganisa ezinkingeni usebenzisa ezinkingeni usebenzisa ekuphindaphindeni ngokuphindelela emgqeni wezinombolo ukukhombisa izixazululo. NgaleThemu ukuhlanganisa ukuhlanganisa abafundi kufanele babhale umugqa wokuphindaphinda wezinombolo Izibalo IBANGA 1-3 ngokuphindelela noma ngokuphindelela noma wezimpendulo zabo. Abafundi sebelwenzile uphawu lokuphindaphinda eThemu ukuphindaphinda ukuphindaphinda yoku - 1 kufanele basebenzise ulwazi lwangaphambili uma bexazulula izinkinga kanye nezimpendulo kanye nezimpendulo zokuphindaphinda izinkinga zezinombolo. Ukuhlanganisa ngokuphindelela ezifinyelela ema - 50. ezifinyelela ema - 30. kanye nenhlobo yegridi, izinkinga kufanele zikhombise umusho wezinombolo. Kunabanye abafundi asebenokuzethemba okukhulu ekubhaleni phansi imiphumela kusetshenziswa ukuhlanganisa ngokuphindelela kodwa hhayi ukuphindaphinda. Izibonelo zezinkinga ezingenziwa kuleThemba Ukuhlanganisa ngokuphindelela a) Mangaki amasondo asemabhayisikilini ayisi - 8? b) Mangaki amehlo ezinganeni eziyi - 9? Izinga UThami uphuza izingilazi eziyisi - 6 zamanzi ngosuku. Zingaki izingilazi zamanzi aziphuzayo ngesonto? Igridi /ukuhleleka (array) Umnumzane uKhumalo utshale imigqa yamakhabishi eyisi - 6. Kunezihlahla ezi - 5 umugqa ngamunye. Mangaki amakhabishi atshalwe uKhumalo eswonke? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.9 Uxazulula achaze Uxazulula achaze Izibonelo zezinkinga ezingenziwa kuleThemu izixazululo ezifaka izixazululo ezifaka Ukwenza amaqoqo NgaleliThemu bavumele abafundi ukuthi ukuthi basebenzise imidwebo kanye ukuhlukaniselana ukuhlukaniselana nokuhlukanisa nezinto eziphathekayo ukukhombisa izixazululo zabo. Umusho wezinombolo ngokulinganayo ngokulinganayo okuholela ungasetshenziswa. Umfundi angasebenzisa ukususa ngokuphindelela nokwenza amaqoqo nokwenza amaqoqo ekwehlukaniseni ukukhombisa ukuthi bafike kanjani kwimpendulo. kuze kufinyelele ema - kuze kufinyelele ema - 99 kanye nezimpendulo 50 kanye nezimpendulo ukuhleleka (array) / igridi ezifaka izinsalela. ezifaka izinsalela. UMongezi uqoqa izinto zokubala ezingama - 20 ngemigqa eyi - 10. Zingaki izinto zokubala umugqa ngamunye? Ukwenza amaqoqo Ukwenza amaqoqo, ukulahlwa kwensalela UPhilasande uthengisa amahhabhula asezikhwameni, isikhwama ngesinye sinamahhabhula ayisi - 6. Unamahhabhula angama - 40, zingaki izikhwama samahhabhula angazenza uma isikhwama ngasinye sifaka amahhabhula ayi - 6? Ukwenza amaqoqo, ukuhlanganiswa kwensalela kwimpendulo USimanga ufuna ukuthatha amaqanda angama - 35. Mangaki amabhokisi amaqanda azowadinga uma ibhokisi ngalinye lifaka amaqanda ayisithupha? Ukwahlukanisa Ukwahlukanisa, nokulahlwa kwensalela Hlukanisela izingane ezinengokulinganayo amaswidi angama - 45. UPhilasande noNothando basebenza ndawonye. UPhilasande usebenza amahora ama - 3, unoThando usebenze ihora elilodwa. Bakhokhelwe imali engangama - R40. Bazohlukaniselana kanjani lemali? 299 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 300 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.10 Xazulula ubuye uchaze Xazulula ubuye uchaze Yini eyahlukile kunaseBangeni loku - 1 izixazululo ezinkingeni izixazululo ezinkingeni Ukwahlukanisa Enye yezinhloso ekuthuthukisweni kwamaqhezu kufanele kube ukusiza okuholela ezifaka ukuhlukaniselana ezifaka ukuhlukaniselana abafundi ukwenza umqondo wezingxenye zamaqhezu okuphelele - izingxenye emaqhezwini ngokulinganayo ngokulinganayo eziphumayo uma okugcwele kwehlukaniswa ngokulinganayo noma okuholela kwizixazululo okuholela kwizixazululo ngokwenelisayo. Abafundi babonakala bekuqonda ukwahlukanisa umthamo ezifaka iqhezu elilodwa ezifaka iqhezu elilodwa wezingxenye kabili nangaphezulu ngokulinganayo phakathi kwabafundi. Izibalo IBANGA 1-3 1 1 1 1 kokuphelele, isib. 2 , 4 , kokuphelele, isib. 2 , 4 , Bagcina benza ukuxhumana phakathi kokuqonda phakathi kokuhlukanisa 1 1 ngokwanelisayo izingxenye zamaqhezu. Imisebenzi eyahlukanisiwe iyindawo 5 , njll. 5 , njll. enhle ukuqala umqondo wamaqhezu. Inqubomgomo yethu ingenisa umqondo wokwahlukaniselana oholela ezingxenyeni zamaqhezu. Imisebenzi yokwahlukaniselana ivezwa ngokujwayelekile ngendlela elula yamagama. Uma kuqalwa abafundi benza imisebenzi yokwahlukaniselana, bathola ukwahlukanisa noma ukwahlukaniselana kushiya izinsalela. Babuye bahlukanise izinsalela futhi. ULimi lwamaqhezu lungethulwa - ke. Sebengabhala amagama amaqhezu, isib. Uhhafu oyedwa, ikota elilodwa, okukodwa kokuthathu. Uma kubhala ngezingxenye zamaqhezu, isib. Ohhafu abathathu, amakota amathathu, bhala lokhu njenganombolo nangamagama. U 3 ∕2 noma 3∕ 4 akachazi lutho futhi, ngakho ke kungcono ukuwayekelela izinga lamabanga amaphakathi ((Intermediate Phase). Ukwahlukanisa Kwizibonelo ezingezansi isimo sokwahlukanisa ngokulinganayo esinezinselela esingabuye sehlukaniselwane singasetshenziswa Izingane ezimbili zehlukaniselana oshokoledi abathathu ukuze umuntu ngayedwa athole okulinganayo. Angathola amangaki umuntu ngamunye? Abafundi bazonikeza umfundi ngamunye amabili bese kuthi amanye ahlukaniswe kabili.   Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.10 Izinsalela Ukwahlukanisa Kubalulekile ukuthi abafundi badwebe izimpendulo zabo. Qala uvumele okuholela abafundi ukuthi bachaza ngamazwi abo ingxenye abayihlakazile. Lindela emaqhezwini ukuthi uma abafundi besika izicucu ezisele, kunokwenzeka ukuthi lezocucu zingalingani. Lokhu akufanele kube nomthelela kwindlela okuchazwa indlela yokwahlukaninselana. Uma abafundi sebkwazi ukwahlukaniselana ngokwanelisayo, amagama amaqhezu anganikezwa izingxenye. Ukwedlula ezinkingeni zokuhlukanisa ezinezixazululo ezinezinsalela kwizixazululo zezinombolo eziphelele nezingxenye zamaqhezu. Lokhu kusho ukuthi abafundi kumele bakhonjiswe / baboniswe amaqhezu mbumbulonezinombolo ezixubene. Akulindelekile ukuthi abafundi bazi babuye basebenziseulwazimagama. Isib. okubili nohhafu kungabhalwa kanj: 2 ½, okuyinombolo exubile. Ukuhlukanisa imisebenzi kanye noLimi lwamaqhezu Ingxoxo yezixazululo zabafundi yisikhathi esihle sokubangenisa kulwazi magama lwezingxenye zamaqhezu. Uma ushokoledi uqheshulwe ngamaqhezu alinganayo, vele uthi “lokhu sikubiza ngamakota”. Ikhekhe lehlukaniswe izingxenye ezine. Zonke izingxenye zinobungako obulinganayo. Abafundi kumele bazi izingxenye ezimbili zamaqhezu: • Inani lezingxenye • Izinga lezingxenye. Ukuhlukaniswa kwemisebenzi kuyabasiza abafundi ukuthi bathuthukise lemiqon- do elandelayo: • Uma sihlukanisa into izingxenye ezimbili ezilinganayo, lezozingxenye zibizwa ngokuthi ohhavu. • Uma sihlukanisa into ngezingxenye ezintathu ezilinganayo, lezingxenye zibizwa ngokuthi izingxenye zokuthathu. • Uma sihlukanisa into ngezinxenye ezine ezilinganayo, lezozingxenye zibizwa ngokuthi amakota. • Uma sihlukanisa into ngezinxenye ezinhlanu ezilinganayo, lezozingxenye sizi- biza ngokuthi okuhlanu 301 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 302 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.10 Ukugxila kwezinkinga zamagama amaqhezu kuleThemu zivumela abafundi ukuthi ba-: Ukwahlukanisa okuholela • Bahlukanise babuye bahlele ngamaqembu izinto ngokulinganayo; emaqhezwini • Basho izingxenye zamaqhezu; • Ukuthola amaqhezu okuphelele ezinto; kanye Izibalo IBANGA 1-3 • Nokubona ukuthi iiqhezu liyingxenye yokuphelele. Izibonele zezinkina ezifanele iThemu yesi - 2 • UThemba, uSimanga, kanye noNdalwenhle kufanele bahlukaniselane os- hokoledi ababili ngokulinganayo. Umuntu emunye uzothola oshokoledi aban- gaki? Dweba isithombe ukukhombisa impendulo yakho. • UNothando, uNokwethanba, uNomfundo, kanye noNdaweni behlukaniselana amawolintshi amahlanu. Bangawahlukanisa kanjani ukuze bathole alinganayo? Dweba isithombe ukukhombisa impendulo yakho • UPhilasande noNomfundo bahlukaniselana ihhabhula. UNomfundouthi emunye kufanele athole uhhafu, ingabe uqinisile? Dweba isithombe ukukhombisa im- pendulo yakho. Kubalulekile ukthi uma abafundi bedweba izixazululo, bakwazi nokuchaza ukuthi bahlukaniselane kanjani. Qalangokusebenzisa uLimi labafundi olungahlelekile ukuchaza izingxeneye zamaqhezu. Uma sebzethemba futhi bewuqonda umqon- do “wokuphelele nokuyimbijana” igama leqhezu lingangeniswa noma lingaset- shenziswa.umuntu usengalibhala igama leqhezu, isib. uhhafu, ikota elilodwa, okukodwa kokuthathu. Uphawu lweqhezu alukafundiswa, ngenxa yokuthi uma sikhuluma ngo 1∕5, kungakasho lutho futhi kungcono ukuyeka lokhu baze bakut- hole emaBangeni alandelayo ngokuhamba kwesikhathi. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.11 • Bona ubalule/ukhombe • Bona ubalule/ukhombe Yini eyahlukile kusukela kwiThemi yoku - 1 imali ewuhlweza imali ewuhlweza Imali NgaleThemu abafundi benza bephindelela ukubona imali babuye bayihlakaze ibe yaseNingizimu Afrika yaseNingizimu Afrika yizingxenye ezincane. 5c, 10c, 20c, 50c, 5c, 10c, 20c, 50c, R1, R2, R5, kanye R1, R2, R5, kanye Iziboneleo zezinkinga ezingenziwa kuleliThemu nengamaphepha R10, nengamaphepha R10, • Ungakwazi ukuhlukanisa imali engango - 50c ngokulinganayo kubafundi R20, R50 R20, R50 amane? Chaza ukuthi kanjani. • Xazulula izinkinga • Xazulula izinkinga • UMthandazo usebenzise u - 50c ukuthenga uswidi obiza u - 10c.Bangaki oswidi zemali kufaka zemali kufaka abathengile? nezamba noshintshi nezamba kanye kufinyelela emalini noshintshi • USipho ukhokha u - R5 ukuya esikoleni ngetekisi ekuseni. Ukhokhe ngo R20. engangamarandi ngemali ewuhleza Malini ushintshi azowuthola? Malini azosala nayo uma esebuyela ekhaya? angama - R99 nengamaphepha • UMondli ukhokhela itekisi uR5,50. Uzothola ushintshi wamalini uma ekhokha kufinyelela ku - 90c kufinyelela emalini ngoR10? engangama- 50c ornemali eyiphepha • UZandile ukhokhe uR38. Ubekade eno R50. Malini asele nayo? efinyelela emarandini angama - R50 303 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 304 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) ISIMO ESEJWAYEKILE - UKUBALA OKUKHULULEKILE 1.12 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Yini okwehlukile eThemu loku - 1 alandelayo ukubala: alandelayo uma Amaqhinga uxazulula izinkinga Kulindeleke ukuthi abafundi baxazulule ukubala okukhuluklekile kwizimo Imidwebo noma izinto ubuye uchaze izixazululo ezejwayelekile besebenzisa lamaqhinga alandelayo: eziphathekayo, isib. ezinkingeni: • Ukwakhiwa nokuhlakazwa kwezinombolo Izibalo IBANGA 1-3 izinto zokubala • Imidwebo noma izinto • Ukuphindaphinda kabili nokwehlukanisa kabili ngokulinganayo • Ukwakhiwa eziphathekayo, isib. nokuhlakazwa izinto zokubala • Umugqa wezinombolo kwezinombolo • Ukwakhiwa Imidwebo noma izinto eziphathekayo • Ukuphindaphinda kabili nokuhlakazawa Abafundi bazoqhubeka badwebe izithombe babuye basebenzise izinto nokwehlukanisa kabili kwezinombolo eziphathekayo ukuxazulula izinkinga. Kubalulekile ukuthi izithombe noma ngokulinganayo imidwebo ibe nezinombolo kanye nemisho yezinombolo. • Ukuphindaphinda kabili • Umugqa wezinombolo nokwehlukanisa kabili Ukwakha nokuhlakaza ngokulinganayo Leli ngelinye lamaqhinga abalulekie kakhulu kwimfundo yeSisekelo (ibuye • Umugqa wezinombolo isetshenziswe kaningana kumaBanga amaphakathi) ukusebenzisa leliqhinga kuvumela abafundi ukuthi bahlakaze babuye bahlanganise izinombolo ukwenza ukubala kube lula. Kubalulekile ukuthi abafundi basebenzise ulwazi abanalo uma behlakaza izinombolo, isib. • Ukuhlakazwa kwenombolo kusetshenziswa ubungako benombolo; • Ukuhlakaza izinombolo kusetshenziswa iziphindaphindi zokuyishumi; kanye • Nokuhlakaza izinombolo zihambe ngambili isib. izinombolo ezihamba ngambili ema - 20 ziyaziwa kanti futhi zingahlakazwa ngezindlela ezahlukene. Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo Abafundi bakuthola kulula ukuphinda kabili, kodwa futhi kubalulekile ukubenza ukuthi bakwazi ukusebenzisa ulwazi labanalo lokuphinda kabili: • Sebenzisa ulwazi lokubona ukuphinda kabili ukuze babone izinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola eziseduze kweziphindeke kabili Ukuphinda kabili izinombolo eziseduze kweziphindeke kabili 12 + 12 12 + 13 25 + 25 25 + 24

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.12 • Sebenzisa indlela yokuphinda kabili bese unxephezela ukwehlukana kwazo, isib. 13 + 14 = phinda kabili u - 13 uhlanganise nokukodwa Amaqhinga Leliqhinga linobucayi obuthile futhi lifuna ukuthi umfundi abe nolwazi lwezinom- bolo olusezingeni eliphezulu. Abafundi akakwazi ukuzikhethela leliqhinga kusho ukuthi bayakwazi ukusebenzisa amaqhinga amaningi ngokuwashintshashintsha. Isibonelo: Ngelinye ilanga ekliniki abantwana abangama - 24 banikezwa umjovo womkhuh- lane. Ngelanga elilandelayo abanye abangama - 25 bajova. Bangaki abantwana abajova sebebonke? Inking ingaxazululwa ngokusebenzisa ukuphinda kabili. Umfundi angasho ukuthi phinda u - 24 kabili uhlanganise nokukodwa noma phinda u - 25 kabili ususe okukodwa. Umugqa wezinombolo Ukusebenzisa umugqa wezinombolo ukusiza abafundi ngokubala kuzobanikeza indlela yokubhala phansi abakucabangayo babuye bakulandele futhi. Ibuye isize abafundi ukuthi babe nomfanekiso wokubhala phansi abangawusebenzisa ukuc- haza ukuthi bazixazulule kanjani izinkinga. Abafundi bebesebenzisa umugqa wezinombolo kusukela eBangeni loku - 1. Kulindeleke ukuthi manje bebe bekwazi ukwakha umugqa wezinombolo on- genalutho lapho bezokwazi khona ukufaka inombolo yokuqala bese bebona ukuthi baqhubeka kanjani nokufaka ezinye izinombolo. Isibonelo esikhombisa ukuthi abafundi banngawusebenzisa kanjani umugqa wezinombolo: • Ukuhlanganisa nokususa Abafundi kufanele bakhe eyabo imigqa yezinombolo babuye bahlakaze izinom- bolo ngezingxenye eziphathekayo noma ezisebenzisekayo. Isibonelo: 45 + 27   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   305 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 306 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.12 • Ukuphindaphinda Amaqhinga Umugqa wezinombolo kufanele uqhubeke usetshenziswe ukwelekelela ekuhlanganiseni ngokuphindelela. Amagxathu alinganayo angabhalwa phansi emgqeni wezinombolo kanye nemisho eyelekelelayo nayo ingabhalwa futhi. isibonelo:   Izibalo IBANGA 1-3 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 3 ukukheleza oku - 8 kwenza ama - 24 3 amaqoqo oku - 8 = 24 3 x 8 = 24 Ekuphindahindeni okunikeziwe abafundi kufanele bakwazi ukuchaza ukuthi angenziwa kanjani amagxathu emgqeni wezinombolo. 1.13 • Hlanganisa uze • Hlanganisa kufinyelele Yini eyahlukile eThemu yoku - 1? ufinyelele ema - 99 ema - 50 Ukuhlanganisa Abafundi beBanga lesi - 2 bazoqhubeka basebenzise izinto eziphathekayo nokususa • Susa kuze kufinyelele • Susa ema - 50 neminye imifanekiso ukusiza ekwakheni umqondo wezinombolo nasekubaleni. ema - 99 Ukusebenza kwalemifanekiso kuzoya ngokuya kube lukhuni ngokuhamba • Sebenzisa izimpwu kwesikhathi. Uma kuphela unyaka eBangeni lesi - 3, abafundi kufanele bekwazi • Sebenzisa izimpawu ezifanele (+, –, =, ) ukubala kuze kufinyelele kwizinombolo ezinamadijitji amathathu ngaphandle ezifanele (+, –, =, ) • Sebenzisa kokusebenzisa izinto zokubala eziphathekayo. Abafundi bebanga lesi - 2 • Sebenzisa ngokuphindelela bayaqhubeka basebenzise babuye bapholishe amaqhinga abo okubala. Badinga ngokuphindelela amabhondi ezinombolo ukusizwa ukuqinisekisa ukuthi lokho abakubhala phansi kuhamba ngokohlelo amabhondi ezinombolo kufinyelela e - 15 ukuze bakwazi ukukufunda nabanye abafundi bakwazi ukukufunda. Ibanga kuze kufinyelele ema lesi - 2 lizosebenzisa izindlela ezahlukene zokubhala phansi babuye babe - 20 nokuzethemba ekusebenziseni izinombolo nezimpawu njengendlela yokubhala phansi. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi kufanele bakwazi “ukucabanga” ngombuzo obuziwe babuye babheke inking yohla lwezinombolo ukuze bacabange iqhinga elingcono. Ngokuxazulula izinkinga abafundi kufanele baqale ukuthuthukisa amaqhinga abo okubala nendlela yokubhala phansi. EBangeni lesi - 2 bazokuthuthukisa lokho. ngaleThemu, kufanele babe nokuzethemba ngendlela yokubhala phansi abyisebenzisayo babuye bachaze ukuthi bafike kanjani kwimpendulo.

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.13 Abafundi kufanele bakwazi ukwenza lokhu okulandelayo ngokuhlanganisa noku- susa: Ukuhlanganisa nokususa Nakuba abafundi besebenzisa izinto zokbala eziphathekayo nemifanekiso ukwelekelela ukubala kwabo, uma kufika ekusebenzeni ngezinombolo, kufanele bakwazi ukubala ngendlela esezingeni eliphezulu. NgaleThemu abafundi kufanele baqhubeke babale ngokuphindaphinda imibuzo ngezindlela ezahlukene ukuze bakwazi ukusebenzisa izinombolo eziseduze kweziphindeke kabili njengeqhinga lokubala. Isibonelo: Phinda ama - 20 kabili. Kubhale lokhu njengomusho wezinombolo Kopisha uqedele: • 12 + 12 =  • 14 + 14 =  • 15 +  = 30 • 16 +  = 32 • 17 + 17 =  • 36 = 18 +  • 38 =  + 19 Izindlela ezinga khombisa ukubala ngokhlangansia nokususa. Ukuhlakaza inombolo ngezingxeneye ezincane ukwenza ukubala kube lula Ukusebenzisa ulwazi lobungako benomboloukuhlakaza izinombolo nga- mashumi nangemivo Ukuhlanganisa izinombolo ezinamadijithi amabili ngokuzihlakaza zombili 23 + 36 =  23 + 36 = (20 + 3) + (30 + 6) = (20 + 30) + (3 + 6) = 50 + 9 307 = 59 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 308 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.13 Ukuhlanganisa ngokuhlakaza inombolo eyodwa Ukuhlanganisa Ukuhlanganisa izinombolo ezinamadijithi amabili ngokuhlakaza inombolo eyodwa nokususa 23 + 36 =  23 + (30 + 6) Izibalo IBANGA 1-3 23 + 30 → 53 + 6 = 59 Abafundi bangahlakaza inombolo ngezindlela ezizokwenza kubelula ukusebenza kwabo. Lokho kusho ukuthi bazokwenza ngezindlela ezhlukene: 23 + 36 =  23 + (10 + 10 + 10 + 6) 23 + 10 → 33 + 10 → 43 + 10 → 53 + 6 = 59 Ukususa • Ukuhlakazwa kwezinombolo 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 12 - 6 = 6 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 10 + 6 = 16

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.13 • Ukususa ngokuhlakaza inombolo eyodwa Ukuhlanganisa 47 - 26 =  nokususa 47 - (20 + 6) 47 - 20=27 27 - 6 = 21 42 - 26 =  (30 + 12) - 26 30 - 26 = 4 12 + 4 = 16 • Kulindele ukuthi abanye abafundi kungenzeka bahlakaze inombolo ngezindlela ezenza kube lula kubo ukubala: 47 - 26 =  47 - (10 + 10 + 6) 47 - 10 → 37 -10 → 27 - 6 = 21 Ukusebenzisa ulwazi oluqoqiwe njengamaqhinga Amaqhinga akhonjisiwe ngezansi avumela abafundi ukuthi bahlele ukubala kwabo nolwazi lwezinombolo. Ukwenza amaqhinga alandelayo azogqugquzela abafundi ukuthi bakhombise ubudlelwane phakathi kwezinombolo abuye afundise abafundi ukuthi bangasebenzisa ulwazi abaluqoqile ukubasiza uma bebala. Ukubala uye phambili nokubala uye emuva 48 - 39 =  Ukubala ngakunye kusukela ema - 9 kuyiqhinga elifanele ngoba izinombolo zisondelene. Bona izinombolo eziseduze kweziphindeke kabili 24 + 25 chaza ukuthi u - 24 uphindeke kabili kwahlanganiswa nokukodwa noma u - 25 ususa okukodwa 24 + 24 + 1 309 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 310 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.13 Abafundi bangabhala phansi amaqhinga besebnzisa imicibisholo Ukuhlanganisa 24 + (20 + 4) + 1 nokususa 24 + 20 → 44 + 4 → 48 + 1 = 49 Ukusebenzisa ukuhlukanisa kabili ukubhidliza inombolo Izibalo IBANGA 1-3 29 + 12 29 + (6 + 6) 29 + 6 → 35 + 6 = 41 Shintsha inmbolo ibe ibe yisiphindaphindi sokweshumi bese uyasusa noma uhlanganise ngokukodwa Bala wenyuke noma wehle usondele eshumini 28 + 19 =  Lapha abafundi kufanele bazitshele ukuthi bayakhetha phakathi kwezinto ezimbili. Ukushintsha ama - 28 noma i - 19 babe seduze kweshumi, bayazikhethela. Isibalo singabhalwa kanje: 28 + 19 = 28 + 20 - 1 28 + 20 → 48 - 1 = 47 Abanye abafundi bangabhidliza u - 20 abe ngamaqoqo amabili anezinto eziyishu- mi iqoqo ngalinye ukuze babale kahle. Kusiza abafundi ukuthi babe nesibindi nokuzimela ezibalweni uma benamaqhinga • Ukuhlola izixazululo zabo;kanye • Nokwahlulela izixazululo zabo ngendlela ezwakalayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.14 • Phindaphinda • Phindaphinda Yini eyahlukile eThemu lesi - 2? izinombolo kusukela izinombolo kusukela Ukuhlanganisa NgeThemu yes - 2, abafundi benza ngokuphindelela nangokuqonda kweyodwa kufinyelela kweyodwa kufinyelelle ngokuphindaphin- ukuphindaphinda. Phindaphinda okukodwa kufinyelela e - 10 ngoku - 5 e - 10 ngo - 1, 2, 5, 3, 4 e - 10 ngo- 2, 5 da kuholela eku- kuyethulwa. phindaphindeni • Sebenzisa izimpawu • Sebenzisa izimpawu Ukwethulwa kokuphindaphinda ngoku - 5, bheka amanothi okuphindaphinda ezifanele (+, x, =, ) ezifanele (+, x, =, ) ngakubili eThemu yoku - 1 Ekupheleni kweThemu abafundi kufanele bakwazi ukubhala phansi lokhu okulandelayo: 1 iqoqo loku 5 ngu 5 noma 1kuphindwaphindwa ngaku - 2 kwenza - 2 Noma 1 x 2 = 4 2 iqoqo lokubili 2 nga - 4 noma 2 kuphindwa ngoku - 2 kwenza 4 2x2=4 3 iqoqo loku - 2 kukunikeza oku -6 3 uphindaphinda 2 kwenza oku - 6 noma 3 x 2=6 Akugxilwa ekukhumbuleni kwamathebula kodwa ekwakhiweni komqondo wokuphindaphinda. Abafundi babuye bafunde ukufunda baqonde nokuphindaphinda umusho wezinombolo. Imifanekiso eminingi yokuphindaphinda kufanele ibekhona nokubhala okuningi kwenziwe encwadini yomsebenzi wasekilasini. Isibonelo somsebenzi obhalwayo Ukubhala phansi ngethebula: Inombolo yezingane 1 2 3 4 5 6 7 8 9 Inombolo yemilenze Umfanekiso ogelezayo   1 2 3 4 ×  !     5 311 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 312 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.14 Uma usebenza ngamaphethini ezinombolo, ukuphindaphinda kungahlanganiswa nokweqa ube ubala ngokuphenya amaphethini okuphindaphinda kwigridi Ukuhlanganisa yezinombolo. ngokuphindaphin- da kuholela eku- Isibonelo: abafundi bangabhala phansi okungakubili nokungakuhlanu kwigridi phindaphindeni yezinombolo. Bankakhuluma ngokuthi yiziphi izinombolo ezisebenza kwithebula lokubili nelokuhlanu. Izibalo IBANGA 1-3 1.16 Uhla lomqondo Uhla lomqondo Umqondo wezinombolo: wezinombolo wezinombolo: Izibalo zekhanda Amaqhinga okubala, umqondo wezinombolo, ulwazi kanye namaphuzu kufinyelela ema - 99: kufinyelela ema - 50 ezinombolo aziwayo kuyathuthukiswa ngokubala nokuxazululwe izinking. • Hlela isethi • Hlela isethi Lokhu kwenziwa ngokuphindelela ngesikhathi sezibalo zekhanda. Lokhu kusiza yezinombolo yezinombolo abafundi ukuthi babenolwazi babuye bakwazi ukulusebenzisa kalula uma bebala ezikhethiwe ezikhethiwe noma bexazulula izinkinga zesimo esejwayelekile. • Qhathanisa izinombolo • Qhathanisa izinombolo Izibonelo zemibuzo engahle ibuzwe: kufinyelela ema - 99 kufinyelela e - 100 Amagama ezinombolo kanye nezimpawu ubuye usho ukuthi ubuye usho ukuthi iyiphi 1, 2, 3, 4, 5, iyiphi kulezi: 1, 2, 3, 4, Phakamisa ikhadi noma ubhale phansi igama lezinombolo. Khetha umfundi ukuthi nokuyi - 10 ngaphezulu 5, 10 ezingaphezulu abhale izinombolo eziqondanayo. nma ngaphansi nangaphansi Okungaphezulu noma ngaphansi Khumbula Khumbula Yini? ngokushehsa: ngokushehsa: • Oku-1 okungaphansi kwama - 50 • Ukuhlanganisa Khumbula ukuhlanganisa nokususa kufinyelela nokususa kufinyelela • Oku-1 okungaohezulu kwama - 39 ema - 20 e - 10 • Oku-3 ngaphansi kwama - 27 • Hlanganisa noma usue iziphindaphindi zokwe • Oku-10 okungaphezu kwama - 20 - 10 kusukela e - 0 Iluphi uhlamvu okungolwesi-5 ezinhlamvini zamagama? kufinyelela e - 100 Iyiphi inyanga engeyesi-9 onyakeni? Ngaphambili nangasemuva Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Iziphi izinombolo eziza ngaphambi kwama - 37? Iyiphi inombolo eza ngemuva kwama - 39?

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 1.16 Amaqhinga okubala Amasu engqondo Ukuhlela nokuqhathanisa Izibalo zekhanda Sebenzisa amaqhinga Sebenzisa amaqhinga Yikuphi okuningi: 21 noma 41? ukuhlanganisa ngendlela ukuhlanganisa ngendlela Ngiphe inombolo ephakathi kwama - 37 kanye nama - 39. efanele: efanele: Amaphuzu okuhlanganisa nokususa: • Beka inombolo enkulu • Beka inombolo enkulu Bona amanothi aeThemu yoku - 1 kuqala ukubala kuqala ukubala uyephambii nasemuva uyephambii nasemuva Amaqhinga okubala: • Umugqa wezinombolo • Umugqa wezinombolo Sebenzisa amaqhinga okubala ukuhlanganisa nokususa ngendlela. • Ukuphinda kabili • Ukuphinda kabili Hlanganisa izinombolo ngokusebenzisa amaqhinga afana nalokhu: nokwehlukanisa nokwehlukanisa • Buka izinombolo ezihamba ngambili ezenza ishumi bese usebenzisa lezi ngokulinganayo ngokulinganayo ezilandelayo kuqala: • Ukwakha • Ukwakha 2+7+8 nokubhidlizwa nokubhidlizwa 2 + 8 kwenza I - 10 bese wengeza ngo - 7 kwezinombolo kwezinombolo Beka inombolo enkulu kuqala ukuze ubale uye emuva naphambili • Sebenzisa • Sebenzisa • Qala ngenombolo enkulu kakhulu ubu phakathi ubu phakathi kokuhlanganisa kokuhlanganisa 3+6 nokususa nokususa Phinda usho umusho wezinombolo: 6 + 3 ubuye ubale ufinyelele esi - 9 • Sebenzisa ukuphinda kabili njengesu lokubala ngekhanda Bona izinombolo eziseduze kweziphindene kabili. Isibonelo: 5 + 4 = 9 chaza ukuthi okune kuphindeke kabili wengeze ngokukodwa, noma okuhlanhu okuphindeke kabili ususe okukodwa Bona ukuthi uma izinombolo zisondelene ngokobungako bazo kulula ukthola umehluko ngokuthi ubaleuye phambili kunkuya emuva. 8 - 6 = 2 ubuye uchaze ukuthi ukubala kusukela kwisi - 6 kuya kwisi - 8 kukunika okubili. E izibalo zekhanda zingenziwa ngaphandle kwezinsiza kufunda, kodwa ijwale ukusetshenziswa ukwenza izibalo zekhanda kusetshenziswa izinsiza. Izinsiza ezinconyiwe • Umugqa wezinombolo (enesimo nengenzso) • Igridi yenombolo • Amakhadi obungako benombolo • Ubuhlalu bokubala 313 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 314 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 1.17 • Sebenzisa ubuye usho • Sebenzisa ubuye usho leThemu igxila kulokhu: igama lamaqhezu igama lamaqhezu Amaqhezu NgaleThemu abafundi bafundiswa amaqhezu. Abafundi bazofundiswa amaqhezu afaka ohhafu, ikota, afaka ohhafu, ikota, ngokwehlukaniselana izinkinga zagama nemissebenzi. okuthathu, okuhlanu okuthathu, okuhlanu Umqondo wezingxenye zamaqhezu ubalulekeile ukuthi ithuthukise imisebenzi • Bona amaqhezu • Bona amaqhezu yokuhlanganisa. asesimweni asesimweni Izibalo IBANGA 1-3 esisamdwebo esisamdwebo • Yenza uhhafu noma ikota lesimo ngokugoqa ubuye usike • Bhala amaqhezu • Bhala amaqhezu Abafundi bangagoqa iphepha libe uhhafu bese benikeza ingxenye ngayinye ngohhafu owodwa, ngohhafu owodwa, igama. Kubalulekile ukuthi baqonde ukuthi uma wenza izingxenye ezimbili okubili kokuthathu okubili kokuthathu ezilinganayo entweni. Bangabuye bagoqe futhi iphepha libe nguhhafu. Okubalulekile la ukugoqa ikhasi ngezindlela ezahlukene ukuthola izindlela ezahlukene zokubukeka kohhafu.   or   Buza njalo abafundi ukuthin zingaki izingcezu abazozithola ubuye ubavumele ukuqaq ikhasi bahlole. Qhathanisa izimo zohhafu ababili abehlukene noma izimo zamakota amabili kungaholela kwingxoxo emnandi ngezimo nangobungako. Ungababuza abafundi: Ngizibiza lezizimo ngegama lezinombolo elifanayo, uhhafu owodwa? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) Ngikhombise ukuthi ngingazibiza lezimo ezimbili ngegama lezinombolo “ikota elilodwa”.   Abafundi kufanele basho ingxenye ngayinye, lokho kungenziwa ngokubhala amaqhezu. Isibonelo: Ikota Uhhafu owodwa • Ukuhlanganisa ukwenza okugcwele Abafundi abasebenzise izindilinga zamaqhezu noma izindilinga ezisikwe ephep- heni ukuthola ukthi isimo sikahhafu nekota singahlanganiswa kanjani ukwenza okukodwa okugcwele. • Ukufaka umbala noma ukufaka umbala emaqhezwini Lezizinhlobo zemisebenzi zigqugquzela: • Ukwazi ukuthi amaqhezu izingxenye ezilinganayo; • Ukubona izingxenye zamaqhezu kanye nokuzisho. Ukubhala amagama amaqhezu Asibangenisi abafundi ekubhaleni izimpawu zamaqhezu. Abafundi bafunda ukuthi balebula kanjani izingxenye zamaqhezu ngokubhala uhhafu owodwa noma ikota elilodwa. 315 Izibalo IBANGA 1-3

ITHEMU YESI- 2 YEBANGA LESI- 2 2. AMAPHETHINI, UBUDLELWANO, KANYE NE-ALJIBHRA 316 UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 2.1 Kopela, uqhubeke Kopela, uqhubeke Bangeni 1 kanye naeThemu1 kwBanga 2 kwanconywa ukuthi abafundi Isifundo esi-1 uphinde uchaze uphinde uchaze basebenze ngamaphethini anezingxenye (izimo, imigqa noma izinto) Amaphethini eziphindaphindayo ngendlela efanayo. eThemu 2 yeBanga 2 abafundi bangaqala ejiyometri Kopela, uqhubeke Kopela, uqhubeke ukusebenza ngamaphethini lapho khona ubungakho besimo noma inombolo Izibalo IBANGA 1-3 uphinde uchaza uphinde uchaza yesimo ishintsha ngendlela engaqageleka. ngamagama ngamagama Amanye amaphethini amaqoqo ezimo noma izinto ezifanayo aphindaphindayo, • Amaphethini alula • Amaphethini alula lapho ubungakho besimo kwiqoqo ngalinye lishintsha ngendlela ejwayelekile enziwe ngezinto enziwe ngezinto neqagelekayo.Isib.isimo siya ngokuba sincane. eziphathekayo. eziphathekayo.   • Amaphethini alula • Amaphethini alula enziwe ngemidwebo enziwe ngemidwebo yemigqa, izimo noma yemigqa, izimo noma izinto izinto Amanye amaphethini enziwe kusukela kuhlobo olulodwa lwesimo, kepha Ukwakha nokuchaza Ukwakha nokuchaza isibonelo ngasinye sesimo siyakhula nona siyehla ngokobungakho. amaphethini akho amaphethini akho Isibonelo ukwakha nokuchaza ukwakha nokuchaza amaphethini akho amaphethini akho   ejiyometri ejiyometri • Ngezinto • Ngezinto eziphathekayo eziphathekayo Amanye amaphethini enziwe ngamaqoqo lapho khona izimo zezinto ezingafani • Ngokudweba imigqa, • Ngokudweba imigqa, enzeka,kepha inombolo yenhlobo ngayinye yesimo noma into iyakhula noma izimo noma izinto izimo noma izinto iyehla ngendlela ejwayelekile.Isib. Amaphethini   asizungezile Khomba, uchaza Ukukopisha iphethini kusiza umfundi ukubona indlela iphethini eyenziwe ngayo. ngamagama ukopela Ukuqhubeka nephethini kusiza abafundi ukubheka ukuthi bayiqonde ngendlela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola amaphethini ejiyometri efanele indlela yokwenza yephethini. • kwimvelo Ukuchaza iphethini kusiza abafundi ukuthuthukisa amakhono abo olimi • kusuka kwimpilo nokukhuluma. Kuyakusiza ukubona indlela abafundi abawahumushe ngayo yesimanje, amaphethini.kuyane kube lula kubafundi ukukhuluma ngephethini uma sebeyenzile.ngalenkathi abafundi kufanele bakwazi ukuchaza iphethini • kusuka emasikweni ngaphandle kosizo lwemibuzo eholayo.qhubeka nokugxila ekuthuthukiseni ulimi ayigugu abaludingayo ukuchaza amaphethini.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 2.2 Kopela, uqhubeke Kopela, andisa bese Bheka amanothi eThemu 1, kepha ukhulise uhla lwezinombolo kufinyelele e-150 Izifundo ezi 3 uphinde uchaze uchaza. Amaphethini ezinombolo Kopela, uqhubeke Kopela andisa bese uphinde uchaza uchaza ukulandelana kwezinombolo izinombolo ezilula ezilulakuya e 150. ngokulandelanisa okungenani ufike ku- 200 Ukulandelana kwezinombolo kufanele Ukwakha nokuchaza kukhombise ukubala uya amaphethini akho phambili ubuye uhlehle Ukwakha awakho kanje: amaphethini ezinombolo • Ngakunye kusukela kunoma iyiphi inombolo ephakathi kuka -0 ne -150 • Ngokuyi -10 kusukela kunoma iyiphi inombolo ephindaphindayo nge- 10 ephakathi 0 no -150 • Nokuyi - 5 kusukela kunoma iyiphi inombolo ephindaphindayo nga- 5 ephakathi kuka 0 no 150 • Ngakubili kusukela kunoma iyiphi inombolo ephindaphindayo nga- 2 ephakathi kuka 0 no-150 • Ngokuthathu nokune usukela kunoma iyiphi inombolo ephindaphindayo nga- 3; 4 ephakathi kuka 0 kuya no- 150 317 Izibalo IBANGA 1-3

ITHEMU YESI- 2 YEBANGA LESI-2 3. INDAWO NESIMO (IJIYOMETRI) 318 UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 3.1 Amagama asho ukuthi Amagama asho ukuthi Okunconyiwe okufanele kugxilwe kukho eThemu 2: ulimi lwendawo, Izifundo ezi 2 into ikuphi into ikuphi ulandela izinkomba Isikhundla, inkomba Chaza ukuthi into ikuphi Chaza ukuthi into ikuphi Okugxilwa kukho eThemu 2 kungaba ukusho ukuthi into ikuphi.eThemu Izibalo IBANGA 1-3 nokubukeka uma uqhathanisa nenye. uma uqhathanisa nenye. 3 abafundi bangasebenza ngokubuka izinto, qala ngokuhlola okwaziyo kwento Isibinelo phezu kwe, Isibinelo phezu kwe, nobakukhumbulayo abafundi ngesikhundla nokubukeka kwento. phambili kwe, emuva phambili kwe, emuva Yimuphi umehluko eBangeni 1 kwe, kwesobunxele, kwe, kwesobunxele, kwesokudla, phezulu, kwesokudla, phezulu, EBangeni 2 abafundi bahlanganisa umsebenzi abawenzile ngesikhundla nokusho phansi, eceleni. phansi, eceleni. ukuthi into ikuphi eBangeni 1. Isikhundla nokubuka Indawo nezinkomba Ulimi olusho isikhundla into Landela izinkomba Ulimi lwesikhundla lungethula baphindaphinde imisebenzi eyenziwayo efaka Qhathanisa ukubuka unyakaza ekilasini. abafundi ngokunyakazisa imizimba, kufaka imilolozelo namaculo ayankazisayo okuhlukene into efanayo nemidlalo enamagama eminyakazo.lokhu kungenziwa ngesikhathi sokufundiswa nsukuzonke. kwekilasi lonke noma ngesikhathi sokufundisa kugxilwe emaqoqweni. kuphakanyiswa ukuthi wenze izifundo ezimbili wenza imisebenzi ngesikhundla Isikhundla nezinkomba eThemu 2,kepha qhubeka wethule / ufundise bazilungiselele amagama Landela izinkomba akhuluma ngesikhundla kusetshenziswa izingxenye ezimfishane ekilasini.lolu limi unyakaza ekilasini. lungasetshenziswa kwizifundo zolimi kanye nezamakhono empilo. Ulimi lwesikhundla lungahlanganiswa ngokwenza okubhalwayo njengo, ukufaka umbala noma ukuqondanisa imidwebo namagama, ukudweba into noma isimo uma utsheliwe isikhundla sayo uma uyiqhathanisa nenye into noma isikhundla. ukufaka umbala noma ukuqondanisa imidwebo namagama. Isikhundla nezinkomba Ukufundisa abafundi ukulandela izinkomba fanele kwenziwe ngokwenza lapho abafundi benyakaza belandela imiyalelo kathisha.eBangeni 2 abafundi banganikwa izinkomba ngokukhuluma noma ebhaliwe ukumyakaza ekilasini, Isib. “woza ngaphambili ekilasini”; “ ima eduze kwesihlalo sakho”; “gxuma weqe Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola umgqomo wezibi”.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 3.2 Uhla lwezinto Akukho okuthize okugxilwa kuko kwizinto ezi-3-D nokunconyiwe eThemu 2, eziphathekayo kepha umsebenzi ngezinto ezi-3-D ungahlanganiswa ngemisebenzi ebhalwayo. Izinto ezi-3-D abafundi bangaqhubeka nokwakha izinto ezi-3-D besebenzisa izinto esezike Ukubona futhi asho zasebenza ngsikhathi sokusebenza esikhululekile. amagama ezinto eziphathekayo ezi- 3-D ezithombeni nezisekilasini. • okusabhola • okusabhokisi • amasilinda Izimpawu zezinto Chaza, hlela bese uqhathanisa izinto ezi- 3-D ngoku:: • ubungako • izinto ezigingqikayol • izinto ezishibilikayo Ukulandelana komsebenzi okuzogxilwa kowo kuthemu 1 Kopela isimo sento oyinikwe uthisha. Isimo sento singenziwa ngamabhuloki, izinto ongabuye uzisebenzise nokunye. 319 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 320 KUPHELA UNYAKA NGETHEMU YE-2 3.3 Uhla Lwezimo Uhla Lwezimo Yini okusha eBangeni 2 Izimo-2-D Bona bese unika igama Bona bese unika igama • unxande lezimo ezi-2-D lezimo ezi-2-D Omningi ngezimo eBangeni 2 bayenza ngokusebenza ngezinto eziphathekayo, • indlinga • indlinga yonke imisebenzi ingahlanganiswa ngemisebenzi ebhalwayo. • unxantathu • unxantathu Abafundi baqala ukudlala ngokukhululekile ngezimo ezihlukene kufaka izithombe Izibalo IBANGA 1-3 ezisikiwe zezimo zejiyometri.ilokhu kungenziwa ngesikhathi esikhululekile, lokhu • isikwele • isikwele kungenziwa kwizifundo zamakhono empilo. • unxande • unxande Abafundi bakopisha izithombe ezenziwe ngezimo zejiyometri, lezi zithombe Izimpawu zezimo Izimpawu zezimo zinganikezwa uthisha noma ezincwadini, kusiza abafundi ukukwazi ukukhomba. Chaza, uhlele bese Chaza, uhlele bese • Izindilinga nezikwele zobungako obungafani; uqhathanisa izimo ezi- uqhathanisa izimo ezi- • Izikwele, onxande kanye nonxantathu kwizikhundla ezihlukene. and, 2-D ngokwe: 2-D ngokwe: • Onxantathu nonxande okunezimo ezihlukene, lokhu kungenziwa ngesikhathi • ubungako • ubungako esikhululekile nangesikhathi sezifundo zamakhono empilo. • umbala • umbala Qhathanisa uchaze izimo ezinhlangothimbili: ubungako • ngokwesimo • ngokwesimo Abafundi baqhathanisa ubungako bezimo ezifanayo Isib. • izinhlangothi eziqondile • izinhlangothi eziqondile • Uhlela izindilinga kusukela kokuncane kakhulu kuya kokukhulu kakhulu, • izinhlangothi • izinhlangothi • Beka zonke izikwele zobungakho okulinganayo ndawonye, eziyindilinga eziyindilinga Sebenzisa ulimi lobungakho ukuqhathanisa izimo ezihlukene Isib.“ ngidwebele unxantathu phakathi kwesikwele, unxantathu mncane kunesikwele.” Ukuchaza izimo ezi-2-D: umbala Abafundi bakhuluma ngemibala yezimo bahlele izimo ngokwemibala. Khomba usho izimo nemibala yazo; uqhathanise ubungako bezinto, lokhu kungaphindaphindwa uma kusetshenzwa ngamaphethini. Ukubona nokusho izindilinga, onxantathu, izikwele kanye nonxande Babfundi kufanele basebenze ngezindilinga nezikwele eziwubungako obehlukile Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kanye nonxantathu abanezimo ezehlukile. Kubalulekile ukuthi abafundi bangaboniswa isibonelo esisodwa sesimo ngasinye. izinsiza kufundisa eziningi ezithengiswayo zikhombisa uhlobo olulodwa lwesimo. abafundi kufanele bakwazi ukubona:

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 3.3 • Onxantathu abayizimo ezihlukene kwizikhundla ezihlukene.lezi ezinye izibonelo Izifundo ezi 3 zonxantathu: Izimo-2-D   • Izikwele eziwubungako obuhlukene kwizikhundla ezihlukene. Lezi ezinye izibonelo zezikwele:   • Onxande obayizimo ezihlukene kwizikhundla ezihlukene. Lezi ezinye izibonele zonxande:   • Izindilinga eziwubungako obuhlukene. Lezi ezinye izibonelo zezindilinga: noma Kuyabasiza abafundi ukusebenza ngezimo zezinto esezisikiwe kusetshenziswa amakhalibhodi anemifanekiso ezimo.loku kuvumela abafundi ukubona onxantathu, izikwele, nonxande abahlukene kwizikhundla ezihlukene. Abafundi bahlela izimo ngokwezinhlangothi eziqondile noma eziyindilinga. Abafundi bahlela benze amaqoqo ezimo ngoko nxantathu, izikwele noma izindilinga. Kuhlanganiswa umsebenzi ngokwenza umsebenzi obhalwayo, lemisebenzi ingafaka ukufaka umbala, ukuqhathanisa amagama nezimo njll.. 321 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI 322 ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 3.4 Okufana nse Okufana nse Abafundi kufanele babuka umugqa ohlukanisa kufane nse nxazombili kwizinto Isifundo esi 1 nxazombili nxazombili eziphathekayo nezithombe. Okufana nse nxazombili Bona bese udweba Bona bese udweba Imisebenzi ebhalwayo umugqa ohlukanisa kabili umugqa ohlukanisa kabili • Akungabi umyalelo othi “ dweba ingxenye esele’; kuphela. izimo ezinhlangothimbili. izimo ezinhlangothimbili. • Kufanele kubandakanye izibonelo lapho abafundi bedweba umugqa ohlukanisa Izibalo IBANGA 1-3 okufana nse nxazombili.umugqa ohlukanisa okufana nse nxazombili akufanele uhlezi udweba umugqa oya eceleni noma osuka phezulu uye phansi. • Kufaka izibonelo lapho umugqa ohlukanisa okufana nse nxazombili ungaphezu kowodwa. Uma abafundi bengaqinisekile noma isithombe / isimo sinawo yini umugqa ohlukanisa okufana nse nxazombili, bangakuhlola ngokugoqa iphepha babuke noma ohhafu ababili baqondene nse, uma kuqondene nse la zihlangana khona umugqa wokufana nse nxazombili. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI-2 YEBANGA LESI- 2 ISILINGANISO UMQONDO KANYE UMQONDO CAPS NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 4.1 Ukufunda isikhathi Ukufunda isikhathi Abafundi baqhubeka nokuzilungiselela bekhuluma ngobude besikhathi kanye isifundo1 nokulandelana kwesikhathi. Isikhathi • Ukwazi izinsuku zeviki • Ukwazi izinsuku zeviki Ngesikhathi sokufundiswa kwekilasi lonke nesokugxila emaqoqweni abafundi • Ukwazi izinyanga • Ukwazi izinyanga baqhubeka nokukhuluma ngezinsuku zeviki, izinyanga zonyaka kanye nosuku zonyaka zonyaka lwangalelolanga kanye nezinsuku ezandulelayo nezizolandela.abafundi • Faka izinsuku • Faka izinsuku bayalijwayela ikhalenda ngokulisebenzisa njalo ngokufaka lokhu: zokuzalwa, imigubho zokuzalwa, imigubho • Izinsuku zokuzalwa; yokholo, izinsuku yokholo, izinsuku zokuphumula, izinsuku zokuphumula, izinsuku • Imigubho yokholo; zezigameko zomlando, zezigameko zomlando, • Izinsuku zezigameko zomlando; imicimbi yesikole imicimbi yesikole kwikhalenda. kwikhalenda. • Imicimbi yesikole, kanye • Ukufunda ngokusho • Ukufunda iwashi • Izinsuku zokuphumula isikhathi ngamahora lezinti ngokusho Kwikhalenda. nangesigamu sehora isikhathi ngamahora nangesigamu sehora Ngesikhathi sokusebenza esikhululekile abafundi baqhubeka nokulandelelanisa Bala ubude besikhathi izigameko ezenzeka nsuku zonke ezimpilweni zabo kanye nokulandelelanisa nokudlula kwesikhathi Bala ubude besikhathi izithombe zezigameko.abafundi benza imisebenzi ehlobene nokusho isikhathi nokudlula kwesikhathi • Sebenzisa ikhalenda ngamahora. ukubala uchaze ubude • Sebenzisa iwashi Yini okwehlukile kuThemu 1? besikhathi ngezinsuku ukubala ubude noma amasonto. besikhathi ngamahora eThemu 2 kugxilwa ekufundiseni isikhathi ngamahora kanye nesigamu sehora noma isigamu sehora. kusetshenziswa iwashi lezinti.lokhu kungaba isifundo okuzogxilwa kuso, • Sebenzisa iwashi kufanele kufake ukukhuluma ngaso besebenzisa isikhathi sasekuseni (a.m.) ukubala ubude kanye nantambama (p.m.) ukusho isikhathi kufanele kwenziwe njalo ngethemu besikhathi ngamahora ngokuqhubekayo. Isib.abafundi bangecelwa ukusho isikhathi uma kugena isikole, nesigamu sehora ngesikhathi sekhefu, isikhathi sokugoduka, noma beshintsha isifundo beya kwesinye. Khetha isikhathi lapho iwashi likhombisa ihora noma isigamu sehora. kuyasiza ukukhombisa iwashi elikhulu ekilasini ukuze abafundi bamane bebheka kulo.abafundi bangenza imifanekiso yamawashi. Ungabacela bakhombise izikhathi ezihlukene kufaka nezibalo.Isib. “Ngikhombise ihora leshumi ngqo.” “Ngikhombise ukuthi kuzobe kuyisikhathi sini emuva kwesigamu sehora.” 323 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 324 KUPHELA UNYAKA NGETHEMU YE-2 4.2 ISILINGANISO Okun- NgeThemu 1 kwakunconyiwe ukuthi abafundi bagxile ekuhlawumbiseleni, linganisa, qhathanisa kanye nokubhala phansi ubude, gahlelekile ububanzi kanye nokuphakama ngezikali ezingahlelekile kepha bangakwenza okuye ukuhlawumbisela, ukuqhathanisa kanye nokub- ubude hala phansi ISILINGANISO ngamamiyha. • Qagela, linganisa, Qhathanisa, hlela Zombili lezindlela zokulinganisa ngobude kungenziwa ngokuphindaphinda ngesikhathi sokwenza umsebenzi ngokuzimela ithemu bese ubhala ubu- yonke.wonke umsebenzi kufanele ubhalwe phansi. deusebenzisa ukukala Ngesikhathi esabelwe izinombolo,izimpawu nobudlelwane abafundi bangaxazulula izinkinga zezibalo ezisesimweni ngoku; Izibalo IBANGA 1-3 okungenasilinganiso njengezandla, izinyat- • ukulinganisa okungahlelekile kobude; kanye helo, ubude bepensela • Nokulinganisa ubude ngamamitha. njll. Qaphela uhla lwezinombolo olulungele leyo Themu,kanye nohla lwezinhlobo zezinkinga zezinkinga zezibalo ezilungele iThemu. • Chaza ubude bezinto eziphathekayongoku- bala usho nobude be- silinganiso usebenzisa amayunithi angalingan- isiwe • Sebenzisa ulimi ukhu- luma uqhathanisa Isb. Okude ngokuthe xaxa, okufishane ngokuthe xaxa, okuphakeme ngokuthe xaxa, ku- banzi Ukukala okulinganisiwe • Qagela, Linganisa, qhathanisa,hlela bese ubhala ubude useben- zisa amamitha (irula eliyimitha, intambo eyimitha) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 4.3 Isilinganiso Isilinganiso Yini okuhlukile eBangeni 2? esingahlelekile esingahlelekile Isisindo eBangeni 1 kwakunconyiwe ukuthi abafundi bagxile ekusebenzeni ngokulinganisa • Qagela, linganisa, • Qagela, linganisa, nokuzimelela qhathanisa, hlela qhathanisa, hlela • Ukulinganisa ngqo isisindo sezinyo, ubhale phansi isisindo ubhale phansi isisindo usebenzise amayunithi usebenzise amayunithi • Ukuhlela nokuqhathanisa isisindo sezinto ezi-3 noma ngaphezulu, ngokubeka angalinganisiwe angalinganisiwe izinto ezihamba ngambili entweni yokuzimelela, kuze zonke izinto zilandelane. nokuzimelela Isib. nokuzimelela Isib. • Thola isisindo sezinto usebenzisa amayunithi esisindo esingahlelekile. Amabhuloki nezitina Amabhuloki nezitina njll. njll. Abafundi bagxila ekuthuthukiseni ulimi bekhuluma ngesisindo. • Sebenzisa amagama • Sebenzisa amagama Abafundi kufanele baqale ukuhlanganisa abakwaziyo besebenzisa ukuzimelela ukhuluma uqhathanisa ukhuluma uqhathanisa nama unithi angahlelekile ukulinganisa isisindo. Isib.okulula, Isib.okulula, okusindayo,okulula okusindayo,okulula Sebengavezelwa isisindo ngamakhilogremu. kakhulu, okusinda kakhulu, okusinda Ukulinganisa okungahlelekile kwesisindo usebenzisa ukuzimelela kanye kakhulu. kakhulu. namayunithi angahleliwe. Yethula Isilinganiso Yethula Isilinganiso Abafundi bangafunda yonke imigomo benze bephindaphinda ulinganisa bese- esihleliwe esihleliwe benzisa amayunithi angahleliwe,ukulingani ngamayunithi angahleliwe akufanele • Qhathanisa, hlela, • Qhathanisa, hlela, sithathelwe phansi njengesingabalulekile kunamayunithi alinganisiwe. ubhale phansi ubhale phansi Izizimeleli ezithengisayo zesisindo zingasetshenziswa, uma ungenazo izizimeli isisindo sezinto isisindo sezinto ezithengisayo ungazenzela ngokubeka izinto ezihamba ngambil zalokhu oku- eziqoqelwe ndawonye eziqoqelwe ndawonye landelayo: inkomishi kayogathi, ingxenye yangaphansi yebhodlela lobisi noma ezithengisayo ezithengisayo isiphuzo esibandayo (izitsha ezifanayo zingafakwa kuhlangothi ngalunye kwinto ezinesisindo esibhalwe ezinesisindo esibhalwe yokulengisa izimpahla). ngamakhilogremu ngamakhilogremu Isib. Amakhilogremu Isib. Amakhilogremu Ukulinganisa isisindo ngamayunithi angahleliwe kufaka ukubala ukuthi mangaki amabili elayisi kanye amabili elayisi kanye amayunithi akhethiwe anesisindo afanayo uma izinto zilinganiswa.Isibonelo. Irula nekhilogremu eyodwa nekhilogremu eyodwa inesisindo esilinganayo namabhuloki ayisi-9. yofulawa. yofulawa. Abafundi fanele balinganise izinhlobo ezihlukene zezinto usebenzisa uhla lwez- • Balinganisa isisindo into njengamayunithi ahleliwe. sabo ngamakhilogremu Abafundi fanele bafundiswe kusho iyunithi njalo uma benika isisindo.Isib.incwadi besebenzisa isikali inesisindo esilinganayo nezezimabuli ezinga-34. sasendlini yokugeza. Uma abafundi sebelinganisile nanoma ngayiphi iyunithi izikhathi eziningana, ku- fanele bahlawumbisele ukuthi mangaki amayunithi anesisindo esilinganayo nento elinganiswayo / ekalwayo.ukuhlawumbisela ngaphambi kokulinganisa kubalulekile kepha kungenziwa kuphela uma abafundi sebenze ukulinganisa ngaleyo yunithi. 325 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 326 KUPHELA UNYAKA NGETHEMU YE-2 4.3 • Lapho isikali sasendlini Abafundi fanele bafundiswe ukuze bakwazi ukuqhathanisa isisindo esihlukene yokugeza sikhona, sezinto lapho amayunithi afanayo kufanele asetshenziswe.Isib.uma irula inesisin- Isisindo abafundi balinganisa do samabhuloki ayi-20, isikele sinesisindo somabuli abangama-20, ngeke ukwazi isisindo sabo ukusho ukuthi kunesisindo esilinganayo noma cha,noma okuphi okusinda kakhulu ngamakhilogremu kunokunye. besebenzisa isikali Ukubhala phansi izilinganiso sasendlini yokugeza. Izibalo IBANGA 1-3 okulindelekile ukuthi Nakuba ukulinganisa kuyikhono lokwenza abafundibakwazi ukukala kodwa ku- abafundi bafunde fanele babhale phansi izilinganiso zabo zonke izikhathi. kuphela ukusondezela Ukusebenza ngamakhilogremu kwikhilogremu eliphelele. Abafundi bangaqala ukwethulwa / ukufundiswa ngamakhilogremu ngokusebenza ngokudla okuthengiswa ngamakhilogremu, lapho inombolo yekhilogremu ishiwo empahleni. Isib.abafundi bangaqathanisa isisindo sezimpahla ezinezinto ezingafani (njenge layisi, impuphu, ushukela, ufulawa noma insipho yokuwasha) okuthengiswa ngesilinganiso esingamakhilogremu a-1.bangafaka lokhu kwisizimeleli ukubona ukuthi noma ubungako bezimpahla bungafani kepha kunesisindo okungenani esingaphezulu noma esingaphansi. Abafundi banganikezwa uhla lwezimpahla lwezinto ezihlukene bazilandelelanise ezisinda kakhulu kuya kwezilula kakhulu,lapho bezilandelelanisa ngokwesisindo esizempahleni Isib.ilayisi 2 kg, ushukela 1 kg, impuphu 5 kg, isitambu 10 kg. Ukufunda isikali sasendlini yokugeza Uma izikali zasendlini yokugeza zikhona abafundi bangazisebenzisa ukufunda isisindo sabo. Kunezinhlobo ezimbili zamamitha esisindo: isikali sezinti nesezinombolo. Isikalisilinganiso sezinombolo kulula ukusifunda ngoba isisindo sibhalwe ngezi- nombolo.uma unesikali sezinombolo sasendlini yokugeza bheka ukuthi isisindo singamakhilogremu aphelele, ezinye izikalisilinganiso uyazicupha ziveze ama- khilogremu aphelele kuphela, uma ungakwazi ukusicupha siveze amakhilogremu Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola aphelele, fundisa abafundi ukuzishaya indiva izingxenye zamakhilogremu okwa- manje. Iningi lezikali zezinti zasendlini yokugeza zonke zinezinombolo ezingama- 10 kg, nomugqa omude okhomba isikhundla sama-5 kg. Imigqa yama-1 kg ngokuvamile ayinazo izinombolo.lokhu kuyafana nendlela imigqa nezinombolo ezisebenza ngayo kwirula.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 4.3 Ithi abafundi baqale ngokubala ukubona ukuthi kunezikhala eziyi-10 phambi ko- Izifundo 3 phawu lwama 10 kg, ukuze isikhala ngasinye simele ikhilogremu elilodwa, ubude Isisindo bomugqa bumele amakhilogremu amahlanu. Abafundi bangafunda isilinganiso sezikali zasendlini yokugeza nakwizithombe zezikali zasendlini yokugeza kunezokwangempela. Ukubhala izilinganiso Noma ukulinganisa kuyikhono lokwenza, abafundi kufanele babhale phansi isilin- ganiso sabo nkathi zonke. Sebenzisa ukulinganisa isisindo njengengqikithi yokuxazulula izinkinga zezibalo Ngesikhathi esabelwe izinombolo, ukusebenza, nobudlelwane bezinombolo abafundi bangaxazulula izinkinga kwizimo: • Ukulinganis okungahlelekile kwesisindo. Isibonelo: indwangu yokusula ibhodi inesisindo somabuli abayi-11.ibhokisi lokhirayoni linesisindo somabuli abayi-8, kukonke kunganesisindo somabuli abangaki? • Isilinganiso sesisindo ngamakhilogremu Isibonelo: uSipho uthenge impuphu engama-12 kg, ushukela ama-5 kg, ilayisi ama-2 kg.singakanani isisindo sezimpahla ezithengiwe zizonke? Bhekelela uhla lwezinombolo olulungele iThemu, kanye nohla lwezinhlobo zezink- inga zokulinganisa ezilungele iThemu. 327 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 328 KUPHELA UNYAKA NGETHEMU YE-2 4.4 Isilinganiso Uhla lokwenza kufaka olokubhaka luyasiza kwisimo lapho abafundi benza bephindaphinda isilinganiso.khetha uhla lapho izithako Umthamo esingahlelekile zinikeziwe ngezinkomishi, izipuni noma amayunithi angahleliwe. • Qagela ulinganise, Kulonyaka kunconyiwe ukuthi abafundi bagxile eku: qhathanisa uhlele • Thuthukiseni ulimi bekhuluma ngomehluko womthamo. umthamo wezitsha • Qhathanisa umthamo osezitsheni ezimbili ezifanayo, (Isib.umthamo ongathwalwa isitsha • Qhathanisa umthamo osezitsheni ezimbili ezifanayo kakhulukazi okubanzi ngokuthe xaxa nokungumcingo Izibalo IBANGA 1-3 uma sigcwele) • Ukulinganisa umthamo nokumumethwe ngezinsiza ezingahleliwe namayunithi. usebenzisa izikali Ngesikhathi sokusebenza ngokuzimela abafundi bangahlawumbisela, baqhathanise, bahlele babhale phansi umthamo ezingahleliwe Isib. nokumumethwe ngezinsiza ezingahleliwe kanye namayunithi angahleliwe omthamo.ukubhaka nokupheka kuyisimo esisizayo lapho izipuni nezinkomishi. abafundi bengenza bephindaphinda ukulinganisa umthamo. Khetha uhla lapho izilinganiso zinikezwe ngezinkomishi, izipuni kanye • Chaza umthamo namayunithi angahleliwe. wesitsha ngokubala Sebenzisa isilinganiso njengengqikithi yokuxazulula izinkinga zezibalo usho ukuthi zingaki Ngesikhathi esabelwe izinombolo, ukusebenza, nobudlelwane bezinombolo abafundi bangaxazulula izinkinga kwizimo izikali ezingahleliwe zokulinganisa okungahlelekile zomthamo / okumumethwe Isib.uGogo usebenzise izinkomishi ezimbili zobisi ukweza iyite, uma ezingagcwalisa ephinda kabili loku,angadinga ubisi olungakanani ? isitsha Isib.ibhodlela linomthamo Bhekelela uhla lwezinombolo olulungele iThemu, kanye nohla lwezinhlobo zezinkinga zokulinganisa. wezinkomishi ezine. Yethula Isilinganiso esihleliwe • Qagela, uqhathanisa, hlela, ubhale phansi umthamo wezinto ngokulinganisa ngamalitha. • Qhathanisa, hlela ubhale phansi umthamo wezinto eziyiqoqo ezithengisayo umthamo wazo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ochaziwe ngamalitha Isib.amalitha amabili obisi, ilitha eyodwa yesiphuzo esibandayo,amalitha amahlanu opened.

ITHEMU YESI-2 YEBANGA LESI-2 5. UKUQOKELELWA KOLWAZI UMQONDO KANYE UMQONDO CAPS NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 5.4 Qoqa bese uhlela ulwazi Qoqa bese uhlela ulwazi • Qoqa ulwazi ngezinto ezisekilasini noma esikoleni ukuze aphendule imibuzo ebuzwe uthisha.. • Hlela ulwazi ngamathali 5.5 Okumele Ulwazi Okumele Ulwazi yethula lwazi ngegirafu yezithombe emele izithombe. 5.6 • Hlaziya bese Hlaziya ulwazi lwezinto Abafundi kufanele babenolwazi lwakHo konke okuqokelelwe eThemu 1, Isifundo 1 uhumusha Ulwazi ezinikeziwe. bangagxila ekuhlaziyeni okumelwe abakunikeziwe.yo yonke. Hlaziya bese Phendula imibuzo uhumusha Ulwazi Kuyanconywa ukuthi kwThemu 2 abafundi bahlaziye (baphendule imibuzo ngezi:) ngolwazi kwigrafu okungenani igrafu yezithombe eyodwa. yezithombe. Abafundi baphendula imibuzo ebuzwa nguthisha ngegrafu yezithombe Isib. • “yiluphi uhlelo lwamabonakude oluthandwa ngabaningi ekilasini?” • “yiluphi uhlelo oluthandwa ngabafundi abambalwa ekilasini?” • “ngabe abafundi abaningi abaningi bathanda …. noma …..?” • “bangaki ngaphezulu abafundi abathanda …. kuna ….?” 329 Izibalo IBANGA 1-3

ITHEMU YESI-3 YEBANGA LESI- 2 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANE BAZO 330 ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA 1.1 Ukubala izinto Ukubala okungenani Ikuphi okwahlukile kuThemu 2? eziphathekayo izinto zansukuzonke eziyi Bala izinto - 180 ngokuyikho EThemu 2 uhla lwezinombolo olusetshenziswayo luyenyuka, nabafundi babala Qagela bese ubala izinto kuyofika e 180. Ukubala izinto kulethemu kuyaqhubeka ukweseka: Izibalo IBANGA 1-3 okungenani izinto Nika ukuqagela okusondelele kwezinto • Amakhono okubala adingekile ekuqondeni ubungako besikhundla senombolo; zansukuzonke ezingama -200 ngokuyikho. Iqhinga ezingatholwa ngokubala • Ukubala uphimisela; lokubala ngamaqoqo • Ukusho amagama ezinombolo; liyagqugquzelwa. • Ukubona izimpawu zezinombolo; kanye • namakhono okubala adingekelayo ukubala. Kugxilwa ekubaleni ngamaqoqo kusetshenziswa izinto zokubala ezahlukahlukene ezibekwe ngamaqoqo. Kuyasiza ukusebenzisa izinto ezihlelekile uma sifundisa ubungako bezinombolo, Isibonelo: abafundi bangasebenzisa amabhuloki ahamba ngama 10 ukubala ngamashumi bese ukhombisa amaqoqo okuyi 10. Imibuzo ewusizo engabuzwa abafundi uma kubalwa ngezinto • Wazi kanjani ukuthi usuyibalile leyo nombolo ? • Ungayibona ngani impendulo yakho ukuthi iyiyo ? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS 1.2 Bala uya phambili bese Bala uya phambili bese Ikuphi okwahlukili kokukwaThemu 2? uya emumva ngoku: uya emumva: Ukubala uya EThemu 3 uhla lwezinombolo olusetshenziswayo luyenyuka kubafundi phambili ubuye • Ngoku -1 ukusuka • Ngoku -1 ukusuka sebebabala ukusuka e 150 ukuyofika e 180. uye emumva kunoma iyiphi kunoma iyiphi Uma abafundi bebala bephimisela kusemqoka ukwenza abafundi bagxile inombolo phakathi inombolo phakathi ezinombolweni abazibalayo. Isibonelo, buza: Uma sibala ngakubili ukusuka e- kuka 0 nama 200. kuka 0 nama 180. 120 ukufika e 140 siyambala yini u 121? kungani singambali ? • Ngama - 10 ukusuka • Ngama - 10 ukusuka Kusesemqoka ukusebenzisa umugqa wezinombolo neshadi lezinombolo eziyi kunoma iyiphi kunoma ikuphi ukubala -100 ukuze babone ukuthi amagama abashoyo ahambisana kanjani nesakhiwo inombolo ephinda ngamashumi phakathi sezinombolo. Abafundi kumele babe negridi yezinombolo esukela e 100 kuya e ephinda ngamashumi kuka o ukuya kuma 200 ukuthi bayisebenziseukukhomba nokubala. phakathi kuka o ukuya 180 kuma 200. Bheka amanothi kaThemu 2 • Ngoku -5 kusuka • Ngoku -5 kusuka kunoma ikuphi ukubala kunoma iyiphi ngasihlanu phakathi inombolo ephinda kuka 0 nama 180 ngokuyisihlanu • Ngoku -2 kusuka phakathi kuka 0 nama kunoma ikuphi ukubala 200 ngabili phakathi kuka 0 • Ngoku -2 kusuka nama 180 kunoma iyipi inombolo • Ngoku -3 kusuka ephinda ngokubili kunoma ikuphi ukubala phakathi kuka 0 nama ngakuthathu phakathi 200 kuka 0 nama 180 • Ngoku -3 kusuka • Ngoku -4 kusuka kunoma iyiphi kunoma ikuphi ukubala inombolo ephinda ngakune phakathi kuka ngakuthathu phakathi 0 nama 180 kuka 0 nama 200 • Ngoku -4 kusuka kunoma iyiphi ukubala ngakune phakathi kuka 0 nama 200 331 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 332 NGETHEMU 3 KONYAKA UKUMELA IZINOMBOLO EZIPHELELE 1.3 Ukwazi nokufunda Ukwazi nokufunda Ikuphi okwahlukile kuThemu 2? izinombolo izinombolo izimpawu Uhla lwezinombolo; namagama • Ukwazi nokufunda • Ukwazi nokufunda • Ukukwazi, ukufunda nokubhala izimpawu zezinombolo kukhula kuyofika e 180; ezinombolo. izimpawu zezinombolo izimpawu zezinombolo kanye ukusuka ku 0 - 200 ukusuka ku 0 - 180 Izibalo IBANGA 1-3 • Ukukwazi, ukufunda nokubhala kuyofika e 75 • Ukubhala izimpawu • Ukubhala izimpawu zesinombolo ukusuka zesinombolo ukusuka Abafundi kumele bakwazi ukubona izinombolo bakwazi nokuchaza umehluko ku 0 kuya ema -200. ku 0 kuya ema -180 ngawabo amagama. • Ukwazi nokufunda • Ukwazi nokufunda Isibonelo: Kufanele babheke kulamakhadi ezinombolo alandelayo bese bekwazi izinombolo ukusuka ku izinombolo ukusuka ku ukubona umehluko phakathi kwanoma iziphi izinombolo ezimbili: 0 kuya ema 100 0 kuya ema 75.   16 11 16 13 16 • Ukubhala amagama • Ukubhala amagama ezinombolo ukusuka ezinombolo ukusuka ku 0 kuya e- 100 ku 0 kuya ema -75 Bheka amanothi kaThemu 2 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS 1.4 Hlela bese uqhathanisa Hlela bese uqhathanisa Ikuphi okwahlukili kuThemu 2? izinombolo kuyofika izinombolo ukofika Chaza, uqhatha- KuleThemu abafundi bahlela bese beqhathanisa izinombolo ukuya e -75. kuma -99 kuma -75 nise bese uhlela Kuze kufike manje abafundi bebeqhathanisa bese behlela izinombolo ukukhulisa izinombolo • Hlela izinombolo • Hlela izinombolo ulwazi lobungako bezinombolo uma uziqhathanisa nezinye. Imibuzo esezibalweni eziphelele kuyofika eziphelele ukusuka kumele ikhethwe ngokucophelela ukuze abafundi bakhuliswe emakhonweni kuma -99 ukusuka kwencane ukuya okucabanga okufaka izinombolo nobungako bazo. Abafundi kumele babuzwe kwencane ukuya kwenkulu nakwenkulu imibuzo yezinga eliphezulu ukukhulia izinga lokucabanga. kwenkulu nakwenkulu kuya kwencane. kuya kwencane. Kumele abafundi bakhuliswe olimini lokucabanga nabalusebenzisa uma bechaza. • Qhathanisa • Qhathanisa izinombolo eziphelele Izibonelo zemibuzo engabuzwa: izinombolo eziphelele usebenzisa okuncane • Nginikeze inombolo ephakathi kwama-50 nama- 60. Ingabe lenamba kuyofika kuma -99 kuna, okukhulu isondelene no 50 noma u 60? Nika incazelo yempendulo yakho usebenzisa usebenzisa okuncane kuna, okuningi kuna, umugqa wezinombolo. kuna, okukhulu okungaphansi kuna kuna, okuningi kuna, nokulingana na. • Abafundi kumele bafundiswe ukukwazi ukucabanga bakwazi ukuhlela okungaphansi kuna izinombolo. Abafundi abachaze ukuthi kungani ama- 15 abe mncane kunama- Ukusebenzisa izinamba nokulingana na. 50. Incazelo ingasekelwa ngokusebenzisa izinto eziphathekayo. zesikhundla ukubonisa Ukusebenzisa ukuhleleka, isikhundla Ekupheleni kweThemu abafundi kumele, Isib. izinombolo zesikhundla sento. ukubonisa ukuhleleka, • Azi ukuthi iziphi izinombolo ezincane kunama- 50 neziningi kunama- 50; kanye Ukubeka izinto indawo noma zilandelane emugqeni • Ukukwazi ukukhomba isikhundla sazo zonke izinombolo eziko 30; 40; njll isikhundla. kube eyokuqala kuyofika usebenzisa igridi yezinombolo. Ukubeka izinto kweyamashumi amabili Esikhundleni sokunika abafundi izibalo eziyimisho ukuba baqedele, kokunye noma eyokuqala kuya zilandelane emugqeni ungabatshela ukuba benze eyabo imisho,ukubonisa ukuhambisana kobungako kweyokugcina,Isib. kube eyokuqala, eyesibili Eyokuqala, eyesibili, bezinombolo. Isibonelo: kuyofika kweyeshumi eyesithathu...eyeshumi noma eyokuqala kuyofika Yenza le misho yezinamba ibe iqiniso : kweyokugcina, Isib. •  kukhulu ngoku- 1u kunoku  Eyokuqala, eyesibili, eyesithathu... kweyama •  kuncane ngoku- 1 ukunoku  20 njll •  kukhulu ngoku- 10 ukunoku  •  kuncane ngoku- 10 ukunoku  Bheka amanothi kaThemu 2 333 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 334 NGETHEMU 3 KONYAKA 1.5 Ukubona ubungako Ukubona ubungako Ikuphi okwahlukile kuThemu 2? benani lenombolo benani lenombolo Ubungako benani Ngalethemu abafundi baqhubeka nokukhulisa ulwazi lokuqonda ubungako benani okungenani ezingambili okungenani ezingambili lenombolo lenombolo ukuyofika kuma 75. ukofika kuma 99 ukofika kuma 75 kuleThemu abafundi baqhubeka noku: • Ukwazi ukuthi idijithi • Ukwazi ukuthi idijithi ngalinye limeleni. ngalinye limeleni. • Bala bese ubeka amaqoqo abonisa amashumi nokungakunye ngezindlela Izibalo IBANGA 1-3 ezahlukene; • Ukuhlakaza izinombolo • Ukuhlakaza izinombolo ezingambili ukuyofika ezingambili ukuyofika • Ukubala izinto ezihleliwe; kuma -99 ngokubala kuma -99 ngokubala • Ukusebenzisa amakhadi obungako benombolo ukukhombisa inani lezinto ngamashumi ngamashumi eziqoqiwe zabalwa; bese nangokukodwa (TU). nangokukodwa (TU). • Bonisa ukuhlelwangezindlela ezahlukene kwezinombolo Isibonelo: u 35 • Ukubona bese esho • Ukubona bese esho angabakhonjiswa njengezinto ezingu 35 ezihamba ngazodwa, amashumi ayi 3 ubungako bedijithi ubungako bedijithi noku 5 okuhamba ngakodwa kanye namaqoqo amabili okuyishumi nokuyi 15 ngalinye ngalinye okuhamba ngakunye. Lomsebenzi ongenhla ungenziwa ngesikhathi sokufundiswa kugxilwe emaqenjini noma ngesikhathi sokufunda ngokuzimela. Abafundi bangabhala lokhu okulande- layo: 68 = 6 wamaqoqo okuyi 10 noku 8 okuhamba ngakunye. 68 = 60 no 8 Lokhu kungenziwa kusetshenziswa amafladikhadi noma amakhadi obungako besikhundla senombolo. Abafundi kumele bakwazi ukuphendula imibuzo noma imiyalelo efana nalena: • Iyiphi inombolo efana nama 50 kanye 7? • Ngikhombise ama -75 usebenzisa amakhadi ubongako benombolo.. • Ngikhombise ama- 75 kwi abhakhasi.. • Ngikhombise ama- 75 kumabhulokisi ayishumi. • Ngikhombise ama- 75 usebenzisa amakhiyubhi.. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ngikhombise ama- 75 usebenzisa intambo yobuhlalu. • Bala ukhipha izinti zikamentshisi ezinga 70 usebenzisa amaqoqo okuyishumi. Mangaki amaqoqo amashumi owatholayo? Ukubhala encwadini yokusebenzela yeklasi noma yokusebenzela ngamunye ingaqhubeka ngesikhathi sokufunda ngokuzimela.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS UKUXAZULULA IZINKINGA ESIMWENI ESIJWAYELEKILE 1.6 Ukusebenzisa amasu Ukusebenzisa amasu Abafundi kulindeleke ukuba baxazulule izinkinga zezibalo zamagama beseben- alandelayo uma alandelayo uma zisa lamasu alandelayo: Amasu okuxazulula kuxazululwa izinkinga kuxazululwa izinkinga izinkinga zezibalo. • Imidwebo noma izinto eziphathekayo. Isibonelo izinto zokubala bese uchaza izixazululo. bese uchaza izixazululo. • Ukwakha izinombolo nokuzihlakaza • Imidwebo noma • Imidwebo noma izinto eziphathekayo. izinto eziphathekayo. • Ukuphinda kabili nokuhlukanisa phakathi kulingane Isibonelo, izinto Isibonelo, izinto • imigqa yezinombolo zokubala. zokubala. Bheka amanothi kaThemu 2 • Ukwakha izinombolo • Ukwakha izinombolo nokuzihlakaza nokuzihlakaza • Ukuphinda kabili • Ukuphinda kabili nokuhlukanisa nokuhlukanisa phakathi kulingane phakathi kulingane • umugqa wezinombolo • umugqa wezinombolo 1.7 Ukuxazulula izinkinga Ukuxazulula izinkinga Ikuphi okwahlukile kuThemu 2? zezibalo zamagama zezibalo zamagama Ukuhlanganisa Abafundi baqhubeka ngokusebenzangalezinhlobozezinkinga zezibalo zamagama nokususa ezimenwi ezijwayelekile ezimenwi ezijwayelekile ezichazwe esahlukweni 2 kodwa uhla lwezinombolo lukhule lwafika ema 75 bese uchaza isixazululo bese uchaza isixazululo sezinkinga ezifaka sezinkinga ezifaka Bheka amanothi eThemi 2. ukuhlanganisa ukuhlanganisa nokususa nokususa okumezimpendulo ezifka okumezimpendulo kuma -75. ezifka kuma -99. 1.8 Ukuxazulula izinkinga Ukuxazulula izinkinga Ikuphi okwahlukile kuThemu 2? zezibalo zamagama zezibalo zamagama Ukuhlanganisa Abafundi baqhubeka ngokusebenzangalezinhlobozezinkinga zezibalo zamagama ezimenwi ezijwayelekile ezimenwi ezijwayelekile ngokuphindelela ezichazwe esahlukweni 2 kodwa uhla lwezinombolo lukhule lwafika ema 40 bese uchaza isixazululo bese uchaza isixazululo okuholela sezinkinga usebenzisa sezinkinga usebenzisa ezibalweni ukuhlanganisa ukuhlanganisa uphindayo zokuphindaphinda Bheka amanothi kaThemu 2 uphindayo noma noma ukuphindaphinda ukuphindaphinda okunezimpendulo ezifka okunezimpendulo ezifka kuma -40. kuma -50. 335 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 336 NGETHEMU 3 KONYAKA 1.9 Ukuxazulula izinkinga Ukuxazulula izinkinga Ngalethemu abafundi baqhubeka nokusebenzisa imidwebo nezinto zokubala zezibalo bese uchaza zezibalo bese uchaza eziphathekayo ukubonisa izixazululo zabo. Imisho yezinombolo kufanele Ukwenza amaqoqo nokuhlukaniselana izixazululo ezifaka izixazululo ezifaka isetshenziswe. Abafundi bazosebenzisa ukususa okuphindayo ukubonisa ukuthi okuholela ukuhlukaniselana ukuhlukaniselana bafika kanjani empendulweni. ekwahlukaniseni. ngokulingana ngokulingana Bheka amanothi kaThemu 2 nokwenza amaqoqo nokwenza amaqoqo ukuyofka kokungama ukuyofka kokungama Izibalo IBANGA 1-3 99 okunezimpendulo 75 okunezimpendulo ezingafaka izinsalela. ezingafaka izinsalela 1.10 Ukuxazulula izinkinga Ukuxazulula izinkinga Ukugxila ezibalweni zamaqhezu ezinkinga zamagama kulethemu kuyaqhubeka ukuvumela abafund ukwenza: Ukuhlukanisa zezibalo bese uchaza zezibalo bese uchaza okuholela izixazululo ezifaka izixazululo ezifaka • ukwabelana nokwenza amaqoqo ngokulinganayo; emaqhezwini ukuhlukaniselana ukuhlukaniselana • ukusho izingxenyana zamaqhezu; ngokulingana ngokulingana okuholela okuholela kwizixazululo kwizixazululo ezifaka • ukuthola amaqhezu ezinto eziphelele; ezifaka amaqhezu amaqhezu angokukodwa • ukubona ukuthi iqhezu lingxenye yokuphelele; kanye angokukodwa 1 kokuphelele. Isibonelo 2 , kokuphelele. Isibonelo 1 1 1 • ukubhala amaqhezu njengokukodwa kokuthathu. 1 1 1 4 , 3 , 5 njll. 2 4 5 , , njll. Ngalethemu abafundi basho okukodwa kokuthathu kanye nokukodwa kokuhlanu. Kusemqoka ukuba abafundi bavezelwe ulwazi lwamaqhezu ahlukene ngaphandle kwawohhafu nekota. Izibonelo zezinkinga ezingenziwa ngaleThemu. • Abangani abayisi -6 bahlukaniselana amaswidi ayi 7 ngokulingana. Dweba isithombe ukukhombisa impendulo yakho. Qhathanisa impendulo yakho neyomngani. • Abangani abayi 8 bahlukaniselana amaswidi ayi 9 ngokulingana. Dweba isithombe ukukhombisa impendulo yakho. Qhathanisa impendulo yakho neyomngani. • Ikota e- 1 Bheka amanothi kaThemu 2 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS 1.11 • Ukubona nokukhomba Izibonelo zezinkinga ezingenziwa ngaleThemu. • Ukubona nokukhomba imali yaseNingizimu Imali imali yaseNingizimu • Abafundi abangama 35 nothisha o 1 bahamba nesikole baya esiqiwini. Isikole Afrika ewuhlweza (5c, Afrika ewuhlweza (5c, sikhokhe R1,20 ngomfundi ngamunye ukungena esiqiwini. Imalini efanele 10c, 20c, 50c, R1, R2, 10c, 20c, 50c, R1, R2, ikhokhwe? R5,) R5,)nengamaphepha ( R10, R20, R50) • UMakhoba uthengela umndeni wakhe izinkwa ezi -2 besinkwa ngosuku. Ulofu • Nengamaphepha owodwa wesinkwa ubiza R4, 99. Ukhokha malini ngezinsuku eziyisi 5 ? • Ukuxazulula izinkinga (R10, R20, R50) zemali ezifaka isamba Bheka amanothi kaThemu 2 • Ukuxazulula izinkinga noshintshi ukufika zemali ezifaka isamba kuma R 99 nama senti noshintshi ukufika afika kwangama 90. kuma R 75 nama senti afika kwangama 75. UKUBALA ESIMWENI ESIJWAYELEKILE NESIKHULULEKILE. 1.12 Sebenzisa lamasu Sebenzisa lamasu Abafundi balindeleke ukuxazulula izinkinga ezisesimweni esikhululekile alandelayo wenza alandelayo ukubala besebenzisa lamasu alandelayo: Amasu izibalo: izibalo: Ukwakha nokuhlakaza izinombolo (izindlela noma • Imidwebo noma • Imidwebo noma Ukuphinda kabili nokuhlukanisa kabili amaqhinga) izinto eziphathekayo, izinto eziphathekayo, isibonelo: izinto isibonelo: izinto Imigqa yezinombolo zokubala zokubala Bheka amanothi kaThemu 2 • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza izinombolo izinombolo • Ukuphinda kabili • Ukuphinda kabili nokuhlukanisa kabili nokuhlukanisa kabili • Imigqa yezinombolo • Imigqa yezinombolo 337 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 338 NGETHEMU 3 KONYAKA 1.13 • Ukuhlanganisa kufike • Ukuhlanganisa kufike Bheka amanothi kaThemu 2 kuma 99 kuma 75 Ukuhlanganisa Abafundi baqhubeka nokuhlakaza izinombolo bathole ukuzethemba ekusebsn- nokususa • Ukususa kusuka kuma • Ukususa kusuka kuma ziseni lamaqhinga okubhala. 99 75 Izindlela ezingasetshenziswa ukwenza izibalo zokuhlanganisa nokususa • Sebenzisa izimpawu • Sebenzisa izimpawu Ukuhlakaza inombolo uyenze izingxenye ezincane ukuze ukubala kubelula ezifanele ezifanele Izibalo IBANGA 1-3 (+, x, =, ) (+, x, =, ) Ukusebenzisa ulwazi lobungako benani lenombolo ukuhlakaza izinombolo zibe amashumi nemivo. • Yenza uphindelela • Yenza uphindelela amabhondi ezinombolo amabhondi ezinombolo Ukuhlanganisa izinombolo ezihamba ngambili ngokuzihlakaza. kufika kuma 20 kufika kuma 20 33 + 36 =  33 + 36 = (30 + 3) + (30 + 6) = (30 + 30) + (3 + 6) = 60 + 9 = 69 Ukuhlanganisa ngokuhlakaza inombolo eyodwa 33 + 36 =  33 + (30 + 6) 33 + 30 → 63 + 6 = 69 Abafundi bangayihlakaza inombolo ngezindlela abangazisebenzisa. Lokho kusho ukuthi bazokwenza ngezindlela ezahlukene. 33 + 36 =  33 + (10 + 10 + 10 + 6) 33 + 10 → 43 + 10 → 53 + 10 → 63 + 6 = 69 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS 1.13 Ukususa Ukuhlanganisa • Ukuhlakaza zombili izinombolo nokususa 75 - 54 =  75 - 54 = (70 + 7) - (50 + 4) = (70 - 50) + (7 -4) = 20 + 3 = 23 • Ukususa ngokuhlakaza eyodwa inombolo 75 - 54 =  75 - (50 + 4) 75 - 50 → 27 - 4 = 23 Ungakulindela ukuthi abafundi bangazihlakaza inombolo ngezindlela ezahlukene ukuze kube lula kubo uma benza izibalo 75 - 54 =  75 - (20 + 20 + 10 + 6) 75 - 20 57 -20 37 - 10 = 27 - 4 = 23 Ukusebenzisa uhuhlukanisa kabili ukuhlakaza inombolo 59 + 12 59 + (6 + 6) 59 + 6 65 + 6 = 71 Ukusebenzisa ulwazi onalo lwezibalo njengamasu Amasu akhonjiswe ngezansi avumela abafundi ukuba babale futhi nolwazi lwezinombolo ngokuhlelekile. Ukwenza ngokuphindelela amasu angezansi enza abafundi bakwazi ukubona ubudlelwano obukhona phakathi kwezinombolo nokukwazi ukusebenza ngezinombolokwenzeni izibalo. 339 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 340 NGETHEMU 3 KONYAKA 1.13 Ukubala uqhubeka ubuye uye emumva Ukuhlanganisa 68 - 59 =  nokususa Ukubala uya phezulu ngakunye kusukela kuma 59 kuyiqhinga elifanele ngoba izinombolo zisondelene. Ukubona izinombolo eziphindayo ezisondelene Izibalo IBANGA 1-3 34 + 35 ukuchaza ukuthi ukuphindeka kabili u 34 umhlanganisa noku 1 noma ukuphinda kabili u 35 ususe u 1 34 + 34 + 1 Abafundi bangabhala phansi amaqhinga abawasebenzisile besebenzisa imici- bisholo: 34 + (30 + 4) + 1 34 + 30 → 64 + 4 → 68 + 1 = 69 Ukushintsha inombolo ibale ngamasumi bese ususa noma uhlanganisa okukodwa. Ukubala wenyuke noma wehla usondezele koku 10 58 + 19 =  Lapha abafundi kumele bazitshele ukuthi bangakhetha phakathi kwezindlela ezimbili. Shintsha ama 58 noma i 19 kusondelele enombolweni ephinda nge 10. Ukuzikhethela okwabo. Isibalo singabhalwa kanjena: 58 + 19 = 58 + 20 - 1 58 + 20 → 78 - 1 = 77 Abanye abafundi bangahlakaza ama 20 benze amaqoqo amabili ama 10 ukubala ngokuyikho. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS 1.14 • Phindaphinda • Phindaphinda Ikuphi okwahlukile kuThemu 2? izinombolo kusukela izinombolo kusukela Ukuhlanganisa NgeThemu yesithathu abafundi baqhubeka nokwenza bephindelela ukuqonda koku 1 ukufika e 10 koku 1 ukufika e 10 okuphiphindayo kwabo ukuphindaphinda nokusebenzisa igridi yokuphinaphinda okokuqala. ngoku 1,2,5,3, noku 4. ngoku 2,5, 4. okuholela ekuphin- Baqhubeka uku: daphindeni • Sebenzisa izimpawu • Sebenzisa izimpawu ezifanele (+, x, =, ) ezifanele (+, x, =, ) • Bebhala ngendlela elandelayo: Iqoqo eli-1 loku - 2 lenza oku-2 noma oku- 1 ukuphinda ka 2 kwenza 2 noma 1 x 2=2 Amaqoqo ama 2 oku 2 enza oku- 4 noma oku- 2 ukuphinda ka2 kwenza 4 noma 2x2=4 Amaqoqo ama 3 oku 2 enza oku- 6 noma oku- 3 ukuphinda ka2 kwenza 6 noma 3x2=6 NgaleThemu abafundi baqala izibalo zokuphindaphinda ngo 4. Ukuphindaphinda ngo 2, nangoku 5 kuyaqhubeka nokwenziwa ngokuphindelela. Imifanekiso yokuphindaphinda kumele iqhubeke inikezwe kanye nokubhala phansi okuningi kufanele kwenziwe emsebenzini wasekilasini. Ukuqonda kwabafundi kungenziwa nasezincwadini zokusebenzela. Imigqa yezinombolo, imidwebo ebonisa ukuxhumana kanye namathebula kungasetshenziswa ukwakha ulwazi lwezimpawu ezisetshenziswa ezibalweni. Abafundi banganikwa izibalo eziyimisho ukuqedela izibalo kanje: 6x2= 5x7= 4x6= Abafundi bangasebenzisa igridi yokuphindaphinda ukuthola izimpendulo zezibalo. Lokhu kungabasiza ekufundeni nasekuqondeni amathebula nezibalo zokuphindaphinda: x 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 50 341 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 342 NGETHEMU 3 KONYAKA 1.16 Ulwazi lwezinombolo: Ulwazi lwezinombolo: Izibonelo zemibuzo engabuzwa: uhla olufika kuma 99 uhla olufika kuma 75 Izibalo zekhanda Ulwazi lwezinombolo: • Hlela iqoqo • Hlela iqoqo Amagama nezimpawu zezinombolo lezinombolo ozinikiwe lezinombolo ozinikiwe Bamba ikhadi noma bhala phansi igama lenombolo. Khetha umfundi ukuba • Qhathanisa izinombolo • Qhathanisa izinombolo abhale inombolo ehambisanayo. ukufika kuma 99 bese ukufika kuma 75 bese Izibalo IBANGA 1-3 usho iyiphi eningi usho iyiphi eningi Okuningi noma okuncane noma encane ngoku noma encane ngoku Yikuphi oku 1,2,3,4,5, no 10 1,2,3,4,5, no 10 • oku -1 okuncane kunama 45 Ukukhumbula Ukukhumbula ngokushesha: ngokushesha: • oku- 1 okuningi kunama 69 • Izindlela • Khumbula izindlela • kuncane ngoku 5 kunama 36 zokuhlanganisa zokuhlanganisa • okuningi ngoku10 kunama 30 nokususa ukufika nokususa ukufika e 15. Uluphi uhlamvu lwesihlanu kwizinhlamvu ze alfabhethi ? kuma 20. • Hlanganisa noma susa Iyiphi inyanga yesi 9 onyakeni ? • Hlanganisa noma susa ngokuphinda ngoku 10 ngokuphinda ngoku 10 ukusuka koku 0 kuya ukuhlela nokuqhathanisa ukusuka koku 0 kuya ema 50 Ikuphi okuningi: 21 noma 171 ? e 100. Nika noma iyiphi inombolo ephakathi kuka 154 no 159. Amaqhinga okwenza Amaqhinga okwenza izibalo izibalo Izindlela zokuhlanganisa nokususa: Sebenzisa amaqhinga Sebenzisa amaqhinga • Ukwazi ngekhandawonke amabhondi ezinombolo okuhlanganisa nokususa ukuhlanganisa nokususa ukuhlanganisa nokususa kufika ema -20 ngokuyikho: ngokuyikho:  + r = 20 • Beka inombolo enkulu • Beka inombolo enkulu  + r = 16 kuqala ukuze ubale kuqala ukuze ubale 18 =  - r uqhubeka noma uya uqhubeka noma uya emumva emumva Izindlela zokuhlanganisa nok ususa zonke izinombolo kufike e -15. • Umugqa wezinombolo • Umugqa wezinombolo Isibonelo: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Phinda kabili noma • Phinda kabili noma 1 + 14 = 15 14 + 1 = 15 hlukanisa kabili hlukanisa kabili 2 + 13 = 12 13 + 2 = 15 • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza 15 - 4 = 11 15 - 11 = 4 inombolo inombolo 15 - 5 = 10 15 - 10 = 5

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA NGETHEMU 3 KONYAKA CAPS 1.16 • Sebenzisa • Sebenzisa Ukukhumbula ngokushesha kwezinombolo eziphindayo kufike e 15. Lokhu ubudlelwano phakathi ubudlelwano phakathi kufanele kufake zokususa ezihambisanayo. Izibalo zekhanda kokuhlanganisa kokuhlanganisa • 1+1=2 nokususa. nokususa. • 2+2=4 • 3+3=6 • 4+4=8 Ngibonise inombolo ongayihlanganisa ukwenza okuyi 15.(ungayibhala phansi noma usebenzise amafladikhadi ukwenza lezizibalo) • 8 • 2 • 9 Ngibonise inombolo esele uma.......esuswa e-15. (ungayibhala phansi noma usebenzise amafladikhadi ukwenza lezizibalo) • 5 • 13 • 0 Amasu okubala: Bheka amanothi eThemu 2 343 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO ISIKHATHI EKUPHELENI WOKUFUNDISA 344 NGETHEMU 3 KONYAKA 1.17 • Sebenzisa bese usho • Sebenzisa bese usho Ikuphi okwahlukile kuyhemu 2? amaqhezu ezimweni amaqhezu ezimweni Amaqhezu NgaleThemu abafundi bagxila ekufundeni ukuthi igama leqhezu lixhumene ezijwayelekile ezifaka ezijwayelekile ezifaka kanjani kwinani lezingxenye ezenza okuphelele. Imidwebo eyahlukene ohhafu, amakota ohhafu, amakota ingasetshenziswa ukwakha ulwazi lwamaqhezu kubafundi. okukodwa kokuthathu okukodwa kokuthathu nokukodwa kokuhlanu nokukodwa kokuhlanu Isibonelo: Izibalo IBANGA 1-3 • Ukubona amaqhezu • Ukubona amaqhezu   asemidwebeni. asemidwebeni. • Ukubhala amaqhezu • Ukubhala amaqhezu ngokuthi uhhafu ngokuthi uhhafu owodwa, okubili owodwa, okubili Imibuzo elandelayo ingabuzwa: kokuthathu. kokuthathu. Zingaki izingxenye ezilinganayo ? Ibizwa ngokuthini ingxenye ngayinye ? Zingaki izingxenye ezilinganayo ? Siyibiza ngokuthini ingxenye ngayinye? Zingaki izingxenye ezikhona ? Ibizwa ngani ingxenye ngayinye ? Imisebenzi yalolu hlobo igquzela: Ukuba abafundi bazi ukuthi amaqhezu ayizingxenye ezilinganayo; • Ukubona izingxenye zamaqhezu; kanye • nokusho izingxenye zamaqhezu Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukubhala Asiwethuli amaqhezu kubafundi ukuba bawabhale ngezimpawu zawo.Aabafundi bafunda ukuthi bangawafaka kanjani amagama ezingxenye zamaqhezu njengekota e 1, oku 1 kokuhlanu.

ITHEMU YESI- 3 YEBANGA LESI-2 2. AMAPHETHINI, UBUDLELWANO NE ALJEBHRA. ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 2.1 Kopisha, wandise bese Kopisha, wandise bese Qhubeka unike abafundi uhla lwamaphethini olufanayo njengaeThemu yesi 2. uchaza uchaza Bheka amanothi kathemu 2 Amaphethini ayizibalomdwebo Kopisha, wandise bese Kopisha, wandise bese Vumela abafundi ukuba bakopishe, bese bandisa bagcine ngokuchaza uchaza ngamagama: uchaza ngamagama: amaphethini. Kufanele ngabe sebeyakwazi ukuchaza amaphethini ngaphandle kwemibuzo ebasizayo. Qhubeka ugxile ekuthuthukiseni ulimi abaludingayo • amaphethini alula • amaphethini alula ukuchaza amaphethini. enziwe ngezinto enziwe ngezinto eziphathekayo. eziphathekayo. • amaphethini alula • amaphethini alula enziwe ngemidwebo enziwe ngemidwebo yemigqa, ngezimo yemigqa, ngezimo noma ngezinto noma ngezinto ezahlukene. ezahlukene. Akha amaphethini akho Akha amaphethini akho Akha amaphethini akho Akha amaphethini akho ayizibalomdwebo. ayizibalomdwebo. • sebenzisa izinto • sebenzisa izinto eziphathekayo. eziphathekayo. • Ngokudwebw imigqa, • Ngokudwebw imigqa, nezimo noma izinto nezimo noma izinto Amaphethini asizungezile Khomba, chaza ngamagama bese ukopisha amaphethini ayizibalomdwebo • emvelweni • empilweni yesimanje yansukuzonke. 345 • Ezintweni ezingamagugu abantu Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 346 IZIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 2.2 Kopisha, wandise bese Kopisha, wandise bese Bheka amanothi kaThemu 1, ubungako bezinombolo kunganyuka ukofika e-180 Izifundo ezi - 3 Amaphethini uchaza uchaza ezinombolo Kopisha, wandise bese Kopisha, wandise bese uchaza ukulandelana uchaza ukulandelana okulula kwezinombolo okulula kwezinombolo Izibalo IBANGA 1-3 ukuyofika okungenani ukuyofika okungenani e ema -200 -180 Akha amaphethini akho Ukulandealana Yakha amaphethini lakho kwezinombolo kumele lezinombolo. kubonise ukubala uya phambili nokuya emumva noku: • Ngoku -1 beqala kunoma iyiphi inambolo phakathi koku - 0 noku yi 180. • Ngokuyi -10 ukusuka kunoma iyphi inombolo ephinda ngokuyi 10 phakathi kuka 0 kuya koku yi 180. • Ngokuyi -5 ukusukakuinoma iyiphi inombolo ephinda ngokuyi 5 phakathi kuka 0 kuya koku 180 • Ngoku -2 ukusuka kunoma iyiphi inombolo ephinda ngokuyi2 kusuka ku 0 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kuya koku yi 180 • Ngoku -3 noku 4 ukusuka ku noma iyiphi inombolo ephinda ngoku 3 noku 4 phakathi kuka 0 kuya kokuyi 180 Ukwakha amaphethini akhe

ITHEMU YESI -3 YEBANGA LESI-2 3. INDAWO NESIMO (IJIYOMETRI) ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO hora eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 3.1 Ulimi lwesikhundla Okunconyiwe okuzogxilwa kukho ngeThemu 3: Isikhundla Nokubukeka Isifundo esisodwa kwento Isikhundla, Chaza iskhundla sento inkomba kwenye. Iisibonelo: Yini ehlukile eBangeni 1 nokubukeka kungaphezulu kwe, EBangeni 2 abafundi benza ngokuphindelela bebukeza abakufunde kwento kungaphambili, ngokuqondanisa ukubukeka okwehlukene kwento efanayo yansuku zonke. ngemumva, ngakwesokunxele, Isikhundla nokubukeka kwento ngakwesokundla, Abafundi emaBangeni aphansi kumele baqonde ukuthi izinto zibukeka phezulu, phansi, eduze gokwehlukile uma uzibheka ezikhundleni ezahlukene. Abafundi bangakubuka kwe ngokunganaki ukuthi izinto ezifana nezimoto zibukeka zincane uma zikude. Isikhundla nokubukeka Isikhundla nokubukeka Abafundi abasebenze kakhulu ngezincwadi kanye nemidwebo esezincwadini, kwento kwento kudinga bazi ukuthi into esesithombeni esiphambili sibukeka sisikhulu kunento. Qondanisa ukubukeka Ngesikhathi sokufunda samaqoqo abafundi bangabeka izandla basithe amehlo, Qondanisa ukubukeka okwehlukene kwento ukuze kumvibeke isithombe sento enkulu ekude. okwehlukene kwento efanayo yansukuzonke. efanayo yansukuzonke. EBangeni lesiBili abafund kufanele banikwe imisebenzi lapho bengaqondanisa Isikhundla nezinkomba ukubukeka okwehlukene (ukubukeka okuvela phezulu, ukubukeka okuvela Isikhundla nezinkomba emaceleni, ukubukeka okuvela ngaphambili)kwezinto ezahlukene zansuku zonke. Landela izinkomba Landela izinkomba ukunyakaza ekilasini. Lokhu kuzogcina kusiza abafundi bakwazi ukuhumusha imidwebo yejiyometri ukunyakaza ekilasini. eyenziwa kusukela kukubukeka okwehlukene. 347 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 348 ISIHLOKO OKUGXILWA KUWO hora eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 3.2 Uhla lwezinto Uhla lwezinto Yini entsha ngethemu yesi-3: Izinto ezinhlang- Ukubona bese usho Ukubona bese usho Amasilinda ayangezwa ezintweni zokufunda. othintathu (3-D) izinto ezinhlangothintathu izinto ezinhlangothintathu Izinto ezinhlangothintathu eBangeni lesiBili. (3-D) eziseklasini (3-D) eziseklasini nasezithombeni. nasezithombeni. Abafundi bazosebenza ngalokhu: Izibalo IBANGA 1-3 • Izimo ezisabhola • Izimo ezisabhola • amabhola nezinto ezinezimo ezisabhola (okuyindilinga) (okuyindilinga) • amasilinda nezinto ezinezimo ezisasilinda; kanye • Izimo ezisamabhokisi • Izimo ezisamabhokisi • izinhlobonhlobo zamabhokisi nezinto ezenezimo ezingonxande, namaphrizimu (amaphrizimu) (amaphrizimu) kanye namakhiyubhu. • Amasilinda • Amasilinda Ukugxila ezimpawini zezinto ezinhlangothintathu: eziginqikayo Izimpawu zezinto nezishelelayo. Izimpawu zezinto Chaza, uhlele bese Lokhu kuqhubeka emsebenzini ofundwe eBangeni 1 eThemini 1 kodwa uqhathanisa izinto amasilinda angeziwe kuleliBanga. Chaza, uhlele bese ezinhlangothintathu uqhathanisa izinto ngoku: ezinhlangothintathu ngoku: • bungakho • bungakho • izinto eziginqikayo • izinto eziginqikayo • izinto ezishibilikayo Abafundi bangaphenya ukuthi bangakwazi yini ukwakha umbhoshongo besebenzisa amabhola odwa, noma amabhokisi odwa,namasilinda odwa. • izinto ezishibilikayo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO hora eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 CAPS KONYAKA nemizuzu engama-24) 3.2 Imisebenzi Okugxilwa Ukubona bese besho amabhola (okuyindilinga) namabhokisi (iphrizimu) Izifundo ezi - 2 kuyo nama silinda. Izinto ezinhlang- othintathu (3-D) Buka bese wakha izinto Abafundi,baqhubeka nokusho,bahlele, bese benza amaqoqo ezinto, kodwa ezinhlangothintathu manje sekufakwe namasilinda. Abafundi kumele banikwe uhla lwezinto ukuze usebenzisa izinto basebenze ngezimo ezifana: eziphathekayo • Okuyimbulunga, isibonelo amabhola awubungako obungalingani, amamabhula, njengezinto amawolintshi, njll ezisikiwe eziyizimo enhlangothimbili, • Amaphrizimu, isibonelo amabhuloki, izitini, amabhokisi awubungako obungal- amabhulokhi okwakha, ingani njengamabhokisi kamentshiso, amabhokisi ensipho, ibhokisi lomuthi izinto ezike zasebenza, wamazinyo, ibhokisi letiye; kanye izinto zokwakha • Amasilinda: ufaka amade na wumtshumo, isibonelo ipayipi elinesimo esyis- nokunye kokwakha ilinda, ingaphakathi lebhokisi elinamaphepha, ibhokisi elisonga amaphepha nokuyibalomdwebo. asendlini yangasese, kanye namasilinda amafushane abanzi njengamathini kapholishi nedosha lesinemfu. Abafundi bangathola izinto ezinezimo ezifana nebhola (okuyimbulunga) nezimo esimise okwamabhokisi (iphrizimu) nezimo ezimise okwamasilinda ezintweni azinikiwe. Abafundi bangathola noma bakhombe izinto ezinezimo ezimise okwamabhokisi (amaphrizimu) eklasini, isibonelo: “ Leli thini lelikhofi limise okwesilinda”. Ngesikhathi sokufunda ngokuzimela abafundi baqhubeka: • Nokwakha ngezinto; kanye • Nokwenza izimo ezingamabhola, amabhokisi namasilinda ngobumba noma ngenhlama yokudlala Umsebenzi obhalwayo Nakuba umsebenzi omningi wenzinto ezinhlangothintathu wenziwa ngezandla kufanele umsebenzi uphethwe ngomsebenzi obhalwayo. Ulimi Qhubeka nokukhulisa ikhono kubafundi lokukhuluma ngezinto ezinhlangothintathu. Bheka amanothi kaThemu -1 349 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 350 ISIHLOKO OKUGXILWA KUWO hora eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 3.3 Uhla lwezimo Akukho ukugxila kakhulu okubhekiswa ezimeni ezinhlangothimbili kodwa akukho okunconyiwe kuThemu -2. Kodwa - ke umsebenzi wezimo ezinhlangothi mbili ungaphethwa ngemisebenzi ebhalwayo ngesikhathi sokusebenza ngokuzimela. Abafundi Izimo Ukubona bese usho bangaqhubeka nokwenza izithombe ngzimo ezinhlangothimbili ngesikhathi sokusebenza ngokuzimela nangesikhathi sobuciko ezinhlangothimbili izimo namasiko (2-D) Bona bese usho izimo Izibalo IBANGA 1-3 ezinhlangothimbili • Izindilinga • Onxantathu • Izikwele • Onxande Izimpawu zezimo Chaza, uhlele bese uqathanisa izimo ezinhlangothimbili ngoko: • Bungako • mbala • ngesimo • amacala aqondile Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • amacala ayindilinga

ITHEMU YESI-3 YEBANGA 2 4. ISILINGANISO ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 4.1 Ukusho isikhathi Ukusho isikhathi Abafundi bayaqhubeka bekhuluma bephindelela ngobude besikhathi Izifundo ezi -3 nokulandelana kwesikhathi. Isikhathi • Yisho bese • Yisho bese ulandelanisa izinsuku ulandelanisa izinsuku Ngesikhathi sokufunda iklasi lilonke nangesikhathi sokufunda ngamaqoqo zeviki zeviki abafundi baqhubeka nokukhuluma ngezinsuku zesonto, izizinyanga zonyaka nosuku lwangalelolanga kanye nezinsuku ezidlule nezizofika. Abafundi • Yisho bese • Yisho bese bayawajwayela amakhalenda ngokukwazi ukafaka: ulandelanisa izinyanga ulandelanisa izinyanga zonyaka zonyaka • Izinsuku zokuzalwa; • Ukufaka ekhalendeni • Ukufaka ekhalendeni • Imigubho yezenkolo; izinsuku zokuzalwa, izinsuku zokuzalwa, • Izehlakalo eziwumlando; imigubho yezenkolo, imigubho yezenkolo, amaholide, izehlakalo amaholide, izehlakalo • Izehlakalo zesikole eziwumlando, eziwumlando, • Amaholide izehlakalo zesikole. izehlakalo zesikole. Konke lokhu bakwenza besebenzisa ikhalenda. • Yisho sikhathi • Yisho sikhathi samahora ayi- 12, samahora ayi- 12, Ngesikhathi sokufunda ngabodwa abafundi baqhubeka nokuhlela ngokulandelana isigamu sehora, nekota isigamu sehora, nekota izehlakalo ezenzeka nsukuzonke ezimpilweni zabo kanye nokulandelanisa ye hora. ye hora. izithombe nezehlakalo ngendlela ehlelekile.Abafundi benza imisebenzi ehambisana nokusho iskhathi ngamahora nangesigamu sehora. Bala ubude bese ubala Bala ubude bese ubala ukudlula kwesikhathi ukudlula kwesikhathi Yikuphi okwehlukile kuThemu 2 ? • Sebenzisa ikhalenda • Sebenzisa ikhalenda • Ukusho isikhathi ngamahora, isigamu sehora nekota yehora. KuThemu yesi- 3 ukubala uchaze ubude ukubala uchaze ubude kugxilwa ekushweni isikhathi ngamahora, ngesigamu sehora, kusetshenziswa besikhathi ngezinsuku besikhathi ngezinsuku iwashi lezinti. Lokhu kungagxilwa kukho ezifundweni ezimbili. noma namasonto noma namasonto Ukusho isikhathi kufanele kwenziwe ngokukuphinda eThemini ngezikhathi Sebenzisa iwashi • Sebenzisa iwashi zonke. ukubala ubude besikhathi ukubala ubude ngamahora ngengxenye besikhathi ngamahora ngekota yehora. ngengxenye ngekota yehora. 351 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 352 ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 4.1 Isibonelo, abafundi babuzwa ngesikhathi sokuqala kwesikole, isikhathi sekhefu, nesikhathi sokuya emakhaya noma isikhathi sokushintsha izifundo ukuqala Isikhathi kwesinye isifundo. Bakhetha izikhathi lapho iwashi libonisa izikhathi ngqo noma isigamu sehora noma ikota yehora. Kuyasiza ukuthi kube newashi elikhulu elisebenzayo ekilasini khona abafundi bangabuka kulo. Abafundi bangenza Izibalo IBANGA 1-3 amawashi ayimifanekiso. Uthisha angabuza imibuzo ezodinga basho izikhathi ezahlukene. Isibonelo:”khombisa isikhathi esiyihora le -10. Khombisa ukuthi bekuwubani isikhathi ikota lehora” Abafundi kufanele benze izibalo besebenzisa iwashi, Isibonelo, bakhombisa isikhathi esiwu 12 emini; babuze ukuthi isikhathi sizobe sithini emahoreni amathathu ezayo. Bahambisa izinti emawashini abo ayimifanekiso (noma babheke iwashi elisekilasini noma elisesithombeni) ukubala bathole izimpendulo. Abafundi akumele babale ubude besikhathi ngamahora nangesigamu sehora ngaphandle kokusebenzisa amawashi. • Basebenzisa ikhalenda ukubala nokuchaza ubude besikhathi sezinsuku noma samasonto. Abafundi bagxila ekufundeni amakhalenda. Bafunda ukuthola izinsuku ezithile kwikhalenda. Abafundi babala ubude besikhathi ngezinsuku noma amasonto bebe bebuka kwikhalenda. Abafundi abalindelekile ukuphendula izinsuku namasonto. Abafundi abalindelekile ukubala isikhathi okufaka ukubala isikhathi phakathi kwezinsuku uma bengenawo amakhalenda. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 CAPS KONYAKA nemizuzu engama-24) 4.2 Isilinganiso NgeThemu 1 kwanconywa ukuba abafundi bagxile ekuqageleni, ekulinganeseni, ekuqhathaniseni nasekubhaleni phansi ubude, Ubude esingahlelekile ububanzi nokuphakama besebenzisa izilinganiso ezingahleliwe kodwa benze ukuqagela, isilinganiso, ukuqhathanisa nokubhala • Qagela, linganisa, isilinganiso ngamamitha. qhathanisa, uhlele, Zombili lezizindlela zokulunganisa ubude zingenziwa kuphindelelwa ngezikhathi zokusebenza ngokuzimela kuze kuyophela bese ubhala ubude iThemu.Wonke umsebenzi kumele ubhalwe phansi usebenzisa isilinganiso Ukulinganisa ubude njengesimo sokuxazulula izinkinga nokwenza izibalo. esingalinganisiwe Ngesikhathi esisetshenziselwa Izinombolo, Izimpawu nobudlelwane bazo, abafundi bangaxazulula izinkinga ezisesimweni soku: Isibonelo: ubude besandla,amagxathu, • linganisa okungahlelekile kobude. Isibonelo: kungamagxatho anga 27 ukuyofika endlini kathishanhloko. Kungamagxatho angama ubude bepensela, 36 ukuya esangweni lesikole. Kude kangakanani ukuyofika esangweni lesikole? izinto zokubala, njll. • Ukulinganisa ubude ngamamitha. • Chaza ubude Kumele uthisha akhumbule uhla lwezinombolo olusezingeni lweThemu nezinkinga ezahlukene ezingaxazululwa. bezinto ngokubala usho izilinganiso ezingahleliwe ukuthi zingaki nokuthi zinde kangakanani. • Ukusebenzisa ulimi lokuqhathanisa, isibonelo okude kuna,, okufushane kuna, okuphakeme kuna, okubanzi kuna Ukwethula Isilinganiso esihlelekile Qagela, linganis, qhathanise, uhlele bese ubhala ubude usebenzisa amamitha, (ngokusebenzisa induku eyimitha noma ubude obungangemitha bentambo) bangasebenzisa lokhu njengezkali ezilinganisiwe zobude. 353 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 354 ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 4.3 Isilinganiso Abafundi bangaqhubeka benza bephindelela ukuqagela, isilinganiso, ukuqhathanisa bese kubhalwa phansi isisindo esingahlelekile kusetsthenziswa ukulinganisa okungahlelekile nolinganisa ukuzimelela ngesikhathi sokusebenza ngokuzimela isisindo • Qagela, linganise, Ukulinganisa isisindo njengesimo sokuxazulula izinkinga nokwenza izibalo. qhathanise, uhlele Ngesikhathi esisetshenziselwa Izinombolo, Izimpawu nobudlelwane bazo, abafundi bangaxazulula izinkinga ezisesimweni soku: bese ubhala isisindo Izibalo IBANGA 1-3 usebenzisa isikalo • Ukulinganisa okungahlelekile kwesisindo; kanye esingalinganisiwe. • nokulinganisa isisindo ngamakilogremu. Isibonelo amabhuloki, izitini, njll Kumele uthisha akhumbule uhla lwezinombolo olusezingeni lweThemu nezinkinga ezahlukene ezingaxazululwa. • Ukusebenzisa ulimi lokuqhathanisa, Isib. okulula, okusindayo, okulula ngokuthe xaxa, okusinda ngokuthe xaxa Ukwethula Isilinganiso esihlelekile • Qhathanisa,hlela bese ubhala isisindo sezimpahla zokuthengisa ezinesisindo esibhalwe ngamakhilogremu isibonelo: amakhilogremu amabili erayisi nekhilogremu elilodwa likaflawa. • Balinganisa ubungako bemizimba yabo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola besebenzisa isilinganiso sasendlini yokugeza.

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 CAPS KONYAKA nemizuzu engama-24) 4.4 ISILINGANISO ISILINGANISO Okuhlukile kuBanga 1 Izifundo ezi -3 okungahlelekile okungahlelekile Umthamo / eBangeni 1 kunconywa ukuba abafundi bagxile okumumethwe • Qagela bese • Qagela bese • Ukuthuthukisa ulimi lokhuluma ngomehluko kumthamo. ulinganisa, ulinganisa, uqhathanise bese, uqhathanise bese, • Ukuqhathanisa umthamo osezitsheni ezimbili ezifanayo. uhlele umthamo uhlele umthamo • Ukuqhathanisa umthamo osezitsheni ezimbili ezingafani, isitsha esivulekile osezitsheni (umthamo osezitsheni (umthamo neside esiwumtshumo; kanye ongamumathwa isitsha ongamumathwa isitsha uma sigcwalisiwe) uma sigcwalisiwe) • ukulinganisa okungahlelekile usebenzisa amayunithi anglinganisiwe. ukusebenzisa ukusebenzisa isilinganiso isilinganiso EBangeni 2 abafundi baqhubeka nokugxila ekwenzeni ukulinganisa esingenasilinganiso, esingenasilinganiso, okungahlelekile ngamayunithiangalinganisiwe omthamo. isibonelo: izipuni isibonelo: izipuni Abafundi bathola ulwazi lokuthi ilitha liwumthamo ongakanani. nezinkomishi. nezinkomishi. Yini umthamo yini okumumethwe ? • Chaza umthamo • Chaza umthamo omumethwe isitsha omumethwe isitsha Umthamo uwubungako obungagcwala kuleyonto(ubungako besikhala ngokubala usho ukuthi ngokubala usho ukuthi esingaphakathi kwesitsha) zingaki izilinganiso zingaki izilinganiso Okumumethwe yilikho okungangena esikhaleni salesositsha esisebenzisiwe. ezingahleliwe ezingahleliwe ezigcwalisa isitsha. ezigcwalisa isitsha Ibhodlela lingaba nomthamo welitha elilodwa, kodwakungenzeka lingagcwali; Isibonelo: ibhodlela Isibonelo: ibhodlela kungenzeka limumathe uketshezi eliwumthamo wenkomishi eyodwa. ligcwaliswa izinkomishi ligcwaliswa izinkomishi Ukulinganisa okungahlelekile komthamo kusetshenziswa isilingaane, ezine. ezine. amabhodlela amancane, njll. Ukwethula Isilinganiso Ukwethula Isilinganiso Ukulinganisa umthamo / okumumethwe usebenzisa amayunithi anglinganisiwe esihlelekile esihlelekile kufaka ukubala ukuthi kuthatha izikhathi ezingaki ukugcwalisa ngamayunithi • Qagela, linganisa, Qagela, linganisa, angenasilinganiso akungathathwa njengokungenamsebenzi kunokulinganisa qhathanisa, hlela, qhathanisa, hlela, ngamayunithi abesilinganiso. bese ubhala bese ubhala umthamo Abafundi bamele bathole ithuba lokulinganisa umthamo noma okumumethwe umthamo wezinto wezinto ngokuzilinganisa besebenzisa izinto ezahlukene ezingenasilinganiso esilingahleliweIsibonelo: ngokuzilinganisa ngamalitha usebenzisa: izinkomishi (kungezona izinkomishi zokulinganisa) izipuni (kungezona ezokukala) ngamalitha. izivalo zamabhodlela njengamabhodlela obisi, amathini amancvalo zamathini, • amabhodlela anomthamo oyilitha amathini amancanenamabhodlela amancane, elilodwa Ukulinganisa umthamo noma okumethwe ngezilinganiso ezingenazinganiso zingafaka ukubala ukuthi kuthatha izikhathi ezingaki ukugcwalisa isitsha usebenzisa iyunithi ekhethiwe. 355 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 356 ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 nemizuzu KONYAKA engama-24) 4.4 • Qhathanisa,uhlele • Ujeke wokulinganisa Abafundi kumele bafundiswe njalo ukusho iyunithi, isib. kunamathisipuni angama bese ubhala onamagabelo 48 amanzi ebhodleleni noma kunamanzi angaphansi kwenkomishi ebhodleleni. Umthamo / umthamo wezimpahla angamalitha okumumethwe Uma abantwana sebelinganise ngezilinganiso ezahlukene izikhashana zokuthengisa umthamo • Qhathanisa,uhlele bangaqagela umthamo / okumumethwe besebenzisa amayunithi. Ukuqagela wazo obhalwe bese ubhala ngaphambi kokulinganisa kubalulekile kodwa kungenzeka uma abafundi sebene Izibalo IBANGA 1-3 ngamalitha.isibonelo: umthamo wezimpahla ISILINGANISO ngaleyo yunithi.. amalitha ama -2 obisi, zokuthengisa umthamo ilitha eli -1 lesiphuzo, Abantwana kumele bafundiswe isilinganiso ukuze bakwazi ukuqhathanisa wazo obhalwe amalitha ama-5 imithamo noma okumumethwe okunamayunithi afanayo. Isibonelo: uma ingilazi ngamalitha.isibonelo: kapende. imumatha amathisipuni angama -20 amanzi, inkomishi imumatha izipuni eziyi -10 amalitha ama -2 obisi, angeke uthi leyongilazi imumatha amanzi amaningi ngokubala ngamathisipuni ilitha eli -1 lesiphuzo, amalitha ama-5 Abafundi kumele belinganise ngohla lwamayunithi angahleliwe ukuze kapende. • Baqale ukuqonda uma amayunithi emancane, siningi isikhathi ozosidinga ukugcwalisa.. Isibonelo: Ibhodlela lingagcwaliswa izipuni ezingama -20 kodwa noma inkomishi eyodwa. - Bakwazi ukusebenzisa amyunithi afanele okulinganisa ahambisana nokul- inganiswayo. Isibonelo, ISILINGANISO ibhodlela eligcwele eli 2 amalitha nezipuni ezincane ukuchitha isikhathi. Ukwethula ukulinganisa okuhlelekile • Ukujwayela ukulinganisa ngamalitha Abafundi batshelwa ukuthi amalitha ayizilinganiso ezijwayelekile zokulinganisa umthamo nokumumethwe. Bafunda igama bese bazi ukuthi linqanyulelwa kanjani ngoba lisetshenziswa kanjalo ezintweni ezithengiswayo. Abafundi kufanele babe nolwazi ukuthi amalitha mangaki ngokusebenzisa • Amabhodlela angafani amalitha isibonelo:amabhodlela esiphuzo esibandayo, ibhodlela lobisi, ikhathoni lobisi, njll • Ukusebenza ngojeke onamazinga okulinganisa obonisa amalitha. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA ISIHLOKO OKUGXILWA KUWO awa eleodwa EKUPHELENI WOKUFUNDISA NGETHEMU 3 CAPS KONYAKA nemizuzu engama-24) 4.4 Abafundi balinganisa ngamalitha izitsha ezibalwe ngenhla. Abafundi Izifundo ezi -3 bayaqagela bese bayalinganisa umthamo wezinto ezahlukahlukene Umthamo / njengezitsha zeyogathi, amabhokisi ezitsha zika ayisikhrimu, amabhokisi okumumethwe aphatha isidlo sasemini, ojeke abakhullu, amabhodlela amakhulu, amthini kapende angenalutho, amabhakede, njll. Izinto zomthamo owahlukahlukene kumele zikhethwe. Abafundi bachaza umthamo ngokuthi kuncane kunelitha, kuncane kunamalitha amabili kuphakathi kwelitha namalitha amabili, kungamalitha ama-5, njll Qhathanisa, ulandelanise bese ubhala phansi umthamo wezimpahla eziyiqoqo eziqoqelwe ndawonye zokudayisa ezibhalwe umthamo ngaphandle ngamalitha. Isibonelo amalitha ama -2 obisi, iltha eli -1 lesiphuzo esibandayo, amalitha amahlanu kapende, njll Ukubhala phansi isilinganiso Nakubauku;linganisa kuyikhono elenziwayo abafundi bayadinga ukwazi ukubhala phansi abakulinganisayo zonke izikhathi bebhalaukulinganisa okungahlelekile nokuhleliwe. Ukulinganisa umthamo ezimeni ezijwayelekile nokuxazulula izinkinga zokubala. Ngesikhathi se zinombolo, izimpawu nobudlelwane bazo, abafundi baxazulula izinkinga ezihambisana • Ukulinganis okungahlelekile komthamo/ okumumethwe. Isibonelo: Ugogo use- benzisa izinkomishi ezimbili zobisi ukwenza ukhasitadi, uma engaphinda kabili uhla lwezinto azozidinga lungakanani ubisi azoludinga • amalitha Kumele uthisha akhumbule uhla lwezinombolo olusezingeni lweThemu nezinkinga ezahlukene ezingaxazululwa. 357 Izibalo IBANGA 1-3

ITHEMU YESI- 3 YEBANGA LESI-2 5. ULWAZI OLUQOKELELWE 358 ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ezifundweni eziyi ISIHLOKO ADINGEKAYO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa EKUPHELENI KONYAKA NGETHEMU 3 nemizuzu engama-24) 5.4 Qoqa bese uhlela Qoqa bese uhlela Qoqa bese uhlela ulwazi Izifundo ezi-3 ulwazi ulwazi Qoqa bese uhlela Kuyancomeka ukuba abafundi basebenze ngolwazi oluqokelelwe oluphelele ulwazi • Qoqa ulwazi ngekilasi Qoqa ulwazi ngekilasi olukuThemu 1. Kuyancomeka nokuthi abafundi eThemini 3 benze amagrafu Izibalo IBANGA 1-3 noma isikole bese noma isikole bese ezithombe ngokuzimela ngamunye isuselwa olwazini olusezithombeni noma uphendula imibuzo uphendula imibuzo kumathebula. ebuzwa uthisha ebuzwa uthisha Bhala okumele ulwazi • Hlela ulwazi Ngoba abafundi bazobe bezidwebela izithombe abazozisebenzisa ukwenza ngamathalizi Bhala okumele ulwazi igrafu yezithombe, kusemqoka ukukhetha izihloko ezizodwebeka kalula. Isibonelo 5.5 Bhala okumele ulwazi izithombe zamakani eiiphuzo azibandayo, ngoba kulula ukudweba, izithelo Bhala okumele ulwazi zilula ukudwebeka kanti ukudweba umdlalo awuthandayo kulukhuni, uhlelo Bhala okumele • Bhala okumele ulwazi kwigrafu yezithombe lukamabonakude aluthandayo, njll kungalukhuni kubafundi bebanga lesibili. ulwazi kwigrafu yezithombe Kulula kubafundi ukwenza igrafu emaphepheni ayizikwele. Khumbuza abafundi 5.6 Hlaziya bese ubhala Hlaziya bese ubhala ngezimpawu ezimseqoka zegrafu yezithombe. (bheka iThemu 1) okumele ulwazi okumele ulwazi Hlaziya bese Hlaziya bese uhumusha ulwazi uhumusha ulwazi • Phendula imibuzo • Phendula imibuzo ngegrafu yezithombe. Abafundi kumele baphendule imibuzo ebuziwe emayelana negrafu yezithombe. ngegrafu yezithombe. Bheka iThemu 1 ukuthola izinhlobo zemibuzo efanele. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

iTHEMU YESI-4 YEbanga LESI-2 1. IZINOMBOLO, IZIMPAWU NOBUDLELWANO BAZO UKUQONDA ISIKHATHI CAPS UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.1 ukubala izinto ukubala izinto Yini ehlukile kuthemu 3? eziphathekayo eziphathekayo Bala izinto Kulethemu abafundi bazobala izinto ezi-200. Ngasekupheleni kwalethemu ukuqagela, nokubala ukuqagela, nokubala abafundi kumele babesebebone, bathinta banyakazisa izinto ezingama- 200. okuyikho kuze kufinyelele okuyikho kuze kufinyelele Qhubeka nokugxila ezintweni ezingamaqoqo. ema-200 ezinto zansuku ema-200 ezinto zansuku zonke. Iqhinga lokwakha zonke. Iqhinga lokwakha Ngokuphela kwethemu abafundi kumele baphendule lezizinhlobo zemibuzo amaqoqo liyakhuthazwa. amaqoqo liyakhuthazwa. nemiyalelo elandelayo: • Bala izinto zokubala ngamaqoqo okuhlanu, amshumi. Hlela kabusha uphinde ubale. Inombolo yezinto zokubala isafana? • Lezi zinto zokubala zinga-200. zibale zonke lezinto ezingama-200, ungancame- la ukuzibala ngamaqoqo ama- 20 noma-25? Ngobani? • Khetha ukuthi iyiphi indlela engaba ngcono kunazozonke ukubala iqoqo lamap- ensela. • Kunezinto ezingama-80 zokubala. Uma sibala nga-2 noma nga-10, ingabe isamba ekugcineni sizofana? • Bala izinto ezingama 46 ngokuzenza amaqoqo nga- 2. Ngabe kuyashesha ukubala ngakubili ukunokubala ngakunye? • Mangaki amaqoqo ama-10 uma ubala izinto ezinga-120 zokubala? 359 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 360 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.2 Ukubala uya phambili Ukubala uya phambili Yini ehlukile kuthemu 3? nasemuva nga: nasemuva nga: Bala uye phambili Ngalethemu abafundi babala baye phambili nasemumva bafinyelele ema-200. ubuye uye • 1 kusukela kunoma • 1 kusukela kunoma Ngasekupheleni kwethemu abafundi bazohlanganisa ukubala kwabo kuxhumane emumva iyiphi inombolo iyiphi inombolo nokubala beqe ethebulini lokuphindaphinda. Abafundi kumele bachaze ukuthi Izibalo IBANGA 1-3 ephakathi kuka-0 no- ephakathi kuka-0 no- yini abayiqaphelile kade bebala ngokuphindaphinda bakwazi nokubona uma 200 200 bebala ngokweqa. Kumele baqale ukusebenzisa lelikhono ukuthi bekuzoba iyiphi inombolo ekubaleni. Isibonelo: • Ngokuphindaphinda • Ngokuphindaphinda nga-10 kusukela nga-10 kusukela Buza abafundi: uma sibala ngakubili, singayisebenzisa inombolo-20? Ikhonayini kunoma iyiphi kunoma iyiphi inombolo-20 ethebulini lokuphindaphindaloku-2? inombolo ephakathi inombolo ephakathi Ngasekupheleni kwethemu kumele bakwazi ukuphendula imibuzo ethi: kuka-0 no-200 kuka-0 no-200 • Bala ngamashumi usukela e -170 kufinyelele e-200. • Ngokuphindaphinda • Ngokuphindaphinda nga-5 kusukela nga 5s kusukela • Bala uye emuva ngamashumi usukela e- 80 kufinyelele e-140. kunoma iyiphi kunoma iyiphi • Bala ngakuhlanu usukela e -115 kufinyelele e- 145. inombolo ephakathi inombolo ephakathi kuka-0 no-200 kuka-0 no-200 • Bala uye emuva ngakuhlanu usukela e- 135 kufinyelele e-110. • Ngokuphindaphinda • Ngokuphindaphinda • Bala ngakuthathu usukela e -66 kufinyelele e- 81. nga-2 kusukela nga-2 kusukela kunoma iyiphi kunoma iyiphi • Bala uye emuva ngakuthathu usukela e- 190 kufinyelele e-169. inombolo ephakathi inombolo ephakathi • Bala ngakune usukela e -120 kufinyelele e-140. kuka-0 no-200 kuka-0 no-200 • Bala uye emuva ngane usukela e-180 kufinyelele e-160. • Ngokuphindaphinda • Ngokuphindaphinda nga-3 kusukela nga-3 kusukela Abafundi bengasebenzisa amagrid ezinombolo, umugqa wezinombolo, kunoma iyiphi kunoma iyiphi ukulandelela izinombolo, i-abhakhasi nokubala ngobuhlalu ukulekelela ukubala. inombolo ephakathi inombolo ephakathi kuka-0 no-200 kuka-0 no-200 • Ngokuphindaphinda • Ngokuphindaphinda nga-4 kusukela nga-4 kusukela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kunoma iyiphi kunoma iyiphi inombolo ephakathi inombolo ephakathi kuka-0 no-200 kuka-0 no- 200

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.3 Ukwazi nokufunda Yini ehlukile kuthemu 3? izinombolo Izimpawu zezinom- Ngalethemu abafundi sebebona, bafunde, babhale izimpawu zezinombolo ku- bolo namagama • Ukwazi nokufunda finyelele e- 200. Ulwazi lwezimpawu zezinombolo luyaqina uma kubalwa izinto ezinombolo izimpawu zezinombolo noma uma kubalwa kuyiwa phambili nasemuva. 0 - 200 Ngasekupheleni kwethemu abafundi kumele baphendule kulezinhlobo zemibuzo • Ukubhala izimpawu ezilandelayo nemiyalelo: zezinombolo 0-200 Bhala izimpawu zezinombolo: • Ukwazi nokufunda Amashumi amathathu nantathu izmpawu zezinombolo 0-100 Amashumi amahlanu nesikhombisa • Ukubhala izimpawu Amashumi ayisishiyagalolunye nambili zezinombolo- 0-100 Ikhulu nesishiyagalolunye Ikhulu neshumi nanye Ikhulu namashumi ambili nesikhombisa Qondanisa uphawu nenombolomagama 66 Amashumi ayisishiyagalolunye nanye 8 Amashumi amahlanu nantathu 172 Amashumi amane 109 Amashumi amathathu nesishagalombili 91 Ikhulu namashumi ayisikhombisa nambili 40 Amashumi ayisithupha nesithupha 53 Isishiyagalombili 38 Ikhulu nesishiyagalolunye 361 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 362 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA Funda kuzwakale izinombolo ezisekhadini ngalinye: 30 Amashumi amathathu 16 Ishumi nesithupa Izibalo IBANGA 1-3 19 Ishumi nesishiyagalolunye 70 Amashumi ayisikhobisa 198 67 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.4 Hlela bese uqhathanisa Yini ehlukile kuthemu 3? izinombolo kufinyelele Chaza, uqhatha- Izinga lezinombolo lenyuke layofinyelela e- 99. ema-99 nise, nkuhlela Ngasekupheleni kwethemu abafundi kumele ba: izinombolo • Hlela izinombolo eziphelele kufinyelele Ukusebenzisa ngokubhala nokufunda ema-99 kusukela Okokuqala, okwesibili, okwesithathu, okwesine, okwesihlanu, okwesithu- kokuncane kakhulu pha………….. asinayo indlela enqamulelayo yokubhala lokhu kuya kokukhulu kakhulu, nokukhulu ka- Sebenzisa, ukufunda nokubhala ulimi olulandelayo lokuhlela nokuqhathanisa khulu kuya kokuncane kakhulu. • kungaki………… • Qhathanisa izinombolo • okuningi njenge, okuyinombolo elingana ne… eziphelele kufinyelele • kulingana no, kungaphezu nge, kumbalwa kune, kukhulu kune, kuncane kune, ema- 99 usebenzisa kubanzi kune………… okuncane kune, kukhu- lu kune,nokulinganayo • ubuningi, ubuncane, okuncane kakhulu, ukukhulu kakhulu Sebenzisa izinombolo • hlela, okokuqala, okokugcina, ngaphambi, ngemuva, okulandelayo, oku- ezisho isikhundla, uku- phakathi kwe, engxenyeni ethile maphakathi ne khombisa ukuhleleka, Sebenzisa uphawu = ukubambela okulinganayo indawo noma nesik- hundla Abafundi kuzomele baphenduleimibuzo efana ne: Beka izinto emugqeni Ubani owesibili ome emigqeni? kusukela kokoku- Iliphi ipensela elifishane kakhulu? qala kuya kokweshumi noma okokuqala kuya Hlela izinombolo kufinyelela e-100 uzibeke emgqeni wezinombolo noma kuse- kokokugcina isib. Okoku- benze igridi yezinombolo. qala, ukwesibili, okwesit- hathu.... okwamashumi Faka izinombolo ezingekho ezikhaleni zegridi ye-100 amabili. 363 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 364 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.4 Bhala lapho iziombolo kumele zibe khona:88, 90, 92... Chaza, uqhatha- Gcwalisa ngenombolo engekho: nise, nkuhlela izinombolo 115 117 Izibalo IBANGA 1-3 139 141 187 185 Phendula ngokukhuluma lemibuzo elandela: Iziphi izinombolo eziphakathi kuka 82 no 87? Iziphi izinombolo eziphakathi kuka 45 no 50? Iziphi izinombolo eziphakathi kukaa 69 no 75? Bhala izinombolo ngokuhleleka kusukela kwenkulu kuya kwencane: 127, 132, 165, 111, 189, 173, 156 Bhala izinombolo ngokuhleleka kusukela kwencane kuya kwenkulu: 89, 62, 56, 72, 45, 39, 17 Khombisa, ufunde ubhale izinombolo ezisho isikhundla. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA UBUNGAKO BENANI LENOMBOLO 1.5 Ukubona ubunga- Ngasekupheleni kwethemu abafundi kumele ba: kobenani lezinombolo Ubungako benani • Ukuqondisisa nokusebenzisa amagama amasha okumele ubungako: ezinamadijithi amabili lenombolo ufinyelele ku-99 • Sebenzisa,funda uqale ukubhala: • Ukwazi ukubona • Imivo,nomaamayunithi,amashumi, idijithi, inombolo enedijithi eyodwa,inombolo idijithi ukuthi ngayinye enamadijithi amabilii,....ubungako benani lenombolo.... imeleni • Hlukanisa izinombolo ezingamadijithi amabili ngokuphinda kashumi nangemi- • Ukuhlakaza izinom- vo kanye bolo ezingamadijithi • Bhala izinombolo: amabili kufinyelele ema -99 ngoku- • Amashumi ayi-6 nemivo emi-3 ____________________ phinda ngamashumi nangemivo • Amashumi ayi-2 nemivo emi- 5 ____________________ • Ukukhomba usho • Amashumi ayi-12 nemivo eyi- 8 ____________________ nesimo senani ledijithi • Amashumi ayi-18 nemivo eyi- 4 ___________________ • Ukusebenzisa izinsiza: Amashumi ayi-4 nemivo emi-5 kusetshenziswa i-abhakhasi. Amashumi eyi-7 nemivo eyi-6 kusetshenziswa i-abhakhasi. Isho ukuthi iyiphi idijithi emelwe isi-8 ku 28. Noku-2? Isho ukuthi iyiphi inombolo elingana noma efana no: - Amashumi ayi-6 - Amashumi ayisishiyagalolunye nemivo emithathu - Amashumi amahlanu nemivo eyisishiyagalolunye 365 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 366 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA Iyiphi inombolo okufanele ingene ebhokisini ngalinye? a) 34 =  + 4 b) 78 = 70 +  Izibalo IBANGA 1-3 Izinsiza kufundisa Izinto ezingenza amaqoqo: • Izinti zokubala • Izinto zokubala ezingatshutshwa • Izinti zikamentshisi • Izinti zika Ice cream • Amabhuloki axhumanayo UKUXAZULULA UZINKINGA EZISESIMWENI ESEJWAYELEKILE 1.6 Sebenzisa amasu Abafundi kulindeleke ukuthi baxazulule izinkinga zezibalo zamagama alandelayo uma besebenzisa amasu alandelayo: Amasu uxazulula ubuye uchaze okuxazulula • Ukwakha nokuhlakaza izinombolo izixazululo enkingeni: izinkinga • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo • Imidwebo nezinto ezibambekayo isib. • Umugqa wezinombolo Izinto zokubala Bheka amanothi ethemu 1 no 2 yama: • Ukwakha nokuhlakaza • Imidwebo nezinto eziphathekayo izinombolo • Ukwakha nokuhlakaza • Ukuphinda kabili nokuhlukanisa kabili • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo ngokulinganayo Umugqa wezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Umugqa wezinombolo Sebenzisa umugqa wezinombolo ukuze balekelelwe ukubala okungasiza abafundi babhale imicabango yabo baphinde bayilandelele. Kubuye kuvumele abafundi bakwazi ukubhala imifanekiso leyo abazoyisebenzisa ukuchaza ukuthi inkinga ixazululeke kanjani.

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.6 Abafundi bebesebenzisa umugqa wezinombolo besafunda Ibanga 1. Kulethemu 4 njengamanje sebezokwazi ukuzakhela umugqa wezinombolo ongenazo Amasu izinombolo befaka inombolo yokuqala bese bephokophelela ukuqala bese okuxazulula beqhubekele kwezinye. izinkinga Isibonelo abafundi bazokwazi ukusebenzisa umugqa wezinombolo. Abantwana abanga-23 bahambe beyovakasha nesikole namuhla. Kunabantwana abanga 63 esikoleni. Bangaki abantwana ekade bekhona kuqalwa? Vumela abafundi ukuthi benze isu elibasebenzela kangcono. Bese kuthi uma abafundi besebenzisa amasu angasebenza kahle ukuze balekelelwe ukusebenza kangcono. Khumbula ukuthi abafundi banokusebenzisa izindlela ezehlukene ukuxazulula izinkinga okungenzeka kungabi yilezo ezilindelwe uthisha. Isibonelo. Inkinga yokuhlukanisa ingaxazululwa ngokusebenzisauphindelela ukususa,ukuhlanganisa noma ukuphindaphinda, Izindlela zabafundi zizoshintsha ngokuqhubeka konyaka nokuqonda ukujwayela kwaboizinhlobo zezinkinga zikukhula nolwazi lwezinombolo luthuthuka. 367 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 368 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.7 Xazulula izinkinga zezi- Izibonelo zezinkinga abafundi okumele bazenze ngasekupheleni kwethemu balo zamagama esimwe- Ukuhlanganisa Ukuhlanganisa nokususa nokususa ni esijwayelekile, uchaze nendlela oxazulule Kunezinhlobo ezintathu zezinkinga eziyisisekelo zokuhlanganisa nokususa ngayo inkingangokufaka inhlobo ngayinye ingabuzwa ngezindlela ezahlukene. Eziyisisekelo yilezi: Izibalo IBANGA 1-3 ukuhlanganisa, ukususa, Ushintsho izimpendulo ezifinyelela ema -99. UNoluthando unamaswidi anga-25. Wanikwa uSilo amanye amaswidi ay- 18 sweets. Unamaswidi amangaki manje? UNoluthando unamaswidi anga-53. Wanikeza uSilo anga-32. Unamaswidi aman- gaki manje? Ukuxuba Ikilasi lebanga 2 linonxantathu abangama-37 abaluhlaza okotshani nayi-19 aluhlaza okwesibhakabhaka. Bangaki onxantathu abanawo? Banezindilinga ezingama-63 angama-27aluhlaza okotshani wonke amanye aluhlaza okwesibhakabhaka. Zingaki eziluhlaza okwesibhakabhaka abanazo? Qhathanisa UNosisi unobhanana abayi-13. UThemba unobhanana aba-5. Bangaki obhanana uNosisi anabo ukunabaka Themba? Ukubuza inkinga eyodwa ngezindlela ezahlukene Izinkinga kufanele zibuzwe ngezindlela ezahlukene. isib, zombili lezi ziyizinkinga zoshintsho, kodwa “okungaziwa” zisezindaweni ezehlukene zenkinga. UNoluthando unamaswidi. USilo umnike abayi-18 ngaphezulu. Manje usenamas- widi angama-43. UNoluthando ubenamaswidi amangaki ekuqaleni? UNoluthando ubenama-apula angama-25. USilo umnike amanye ama-apula. Njengamanje usenama-apula anga-43. Mangaki usilo amnikewona? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.8 Xazulula izinkinga Izibonelo zezinkinga okumele bakwazi ukuzenza ngokuphela kwethemu zezibalo ezisesimweni TOPIC ? Ukuhlanganisa ngokuphindelela esejwayelekile kuchazwe nendlela Amabhayisikili angama-20 anamasondo amangaki? okuxazulwe ngayo Isilinganiso inking kusetshenziswa ukuhlanganisa UThami uhamba amabhuloki ayi-6 ngelanga. Mangaki amabhuloki awahamba ngokuphindaphinda ngesonto? noma ukuphindaphinda ufinyelela e- 50. Amagridi UMnu. Khumalo utshala imigqa eyi-7 yezithombo zeklabishi. Kunezithombo ezi-8 emugqeni. Zingaki izithombo zamaklabishi ezikhona zizonke? 1.9 Xazulula uchaze Izibonelo zezinkinga okumele bakwazi ukuzenza ngokuphela kwethemu izixazululo ezinkingeni Amaqoqo nokuh- Ukwakha amaqoqo lukanisaokuholela ezenzekayo ezifaka ezibalweni zokuh- ukuhlukanisa Ukwakha amaqoqo, ukulahla, nezinsalela lukanisa ngokulingana namaqoqo UStella udayisa ama-apula ayi-10 esikhwameni ngasinye. Unama-apula ayi-80. kufinyelela ema Zingaki izikhwama zama-apula ayi-10 angazenza? -99 anezimpendulo ezinezinsalela. Ukwakha amaqoqo, afaka izinsalela empendulweni? Umlimi unamaqanda ayi-47. Mangaki amabhokisi amaqanda afaka amaqanda ayi 6 ngalinye awadingayo? Ukuhlukaniselana Ukuhlukaniselana, ukulahla nezinsalela Hlukanisa amaswidi ayi-54 kubangani abayi-7 ukuze bonke bathole inombolo yamaswidi elinganayo. 369 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 370 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.10 Xazulula uchaze isixazu- Ukugxila kumaqhezu ezibalweni zamagama kulethemu kuvumela abafundi ba: lulo ezinkingeni ezen- Ukuhlukanisa zekayo ezifaka ukuhlu- • hlukanise nokwenza amaqoqo ezinto ngokulingana; okuholela kanisa ngokulinganayo ezibalweni • sho izingxenye zamaqhezu; okuholela esixazululweni zamaqhezu Izibalo IBANGA 1-3 esifaka amaqhezu ukuh- • thole amaqhezu ezinto eziphelele; lukanisa okukodwa isib. 1 1 1 1 • bone ukuthi iqhezu liyingxenye yokuphelele; 2 , 4 , 3 , 5 , njll. • bhale amaqhezu njengo 1 kokuthathu. Ngalethemu abafundi bazosho amaqhezu amaningi. Kubalulekile ukuthi abafundi baboniswe amanye amaqhezu ngale kuka hhafu oyedwa nekota eyodwa. Izibonelo zezinkinga ezingenziwa: Ukuhlukaniselana, kuholela ezibalweni zamaqhezu • Hlukanisa oshokoledi abayi-7 kubangani aba-3 khona bonke bezothola inombolo efanayo yaoshokoledi kungasali lutho. • Amakhekhe amathathu ahlukaniselwa abangani abathathu ngokulinganayo. Emunye uthola amangaki? Ngasekupheleni kwethemu abafundi kumele bazi lomqondo olandelayo: Uma uhlukanisa okuthile ngoku: • Izingxenye ezimbili ezilinganayo zibizwa uhhafu. Ingxenye ngayinye ibizwa ngohhafu; • Izingxenye ezintathu ezilinganayo, ingxenye ngayinye ibizwa okukodwa kokuthathu; • Izingxenye ezine ezilinganayo, ingxenye ngayinye ibizwa ikota; • Izingxenye ezinhlanu ezilinganayo; ingxenye ngayinye ibizwa okukodwa kokuhlanu; kanye Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • ne izingxenye eziyisithupha ezilinganayo, ingxenye ngayinye ibizwa ekuko kokuyisithupha. Izibonelo zezinkinga abafundi okumele bakwazi ukuzenza kulethemu

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA Ukuhlukanisa, okuholela ezibalweni zamaqhezu Hlukanisa oshokodeni abayi-11 kubangani aba-4 khona bonke bazothola oshokoledi abalinganayo kungasali lutho. Amaqhezu ezinto eziqoqelwe ndawonye Ugogo unika uKiki amawolintshi ayi- 12. UKiki wakha ujuzi ngengxenye yokukodwa kokuthathu. Mangaki amawolintshi awasebenzisile? Lenhlobo yenkinga ingabuzwa kuphela uma abafundi sebenza izinkinga ezine kuya kwezinhlanu izinhlobo zezinkinga ‘zokucazelana okuholela ezibalweni zamaqhezu’, sebazi namagama amaqhezu. Ukubeka amaqhezu ndawonye Umqeqeshi webhola lezandla unikeza umdlali ngamunye uhhafu wewolontshi. Kunabadlali abayi-14. Udinga amawolintshi amangaki? Lenhlobo yenkinga ingabuzwa kuphela uma abafundi sebenza izinkinga ezine kuya kwezinhlanu izinhlobo zezinkinga ‘zokuhlukaniselana okuholela emaqhezwini’, sebazi namagama amaqhezu. 1.11 • Ukukhumbula nokubo- Izibonelo zezinkinga abafundi okumele bakwazi ukuzenza ngasekupheleni na imali ewuhlweza kwethemu Imali yase South Africa, 5c, Izimo zezinkinga ezisebenza ngokuxhumana okwahlukene 10c, 20c, 50c, R1, R2, R5, nengamaphep- UHeila udayisa amagwinya nga R4 lilinye. Yakha ithebula ukumsiza ukuthola haR10, R20, R50 isamba esikhulu sama oda. • Xazulula izinkinga ze- Inombolo yamagwinya 1 2 3 4 5 6 7 8 9 10 mali ezimbandakanya isamba noshintshi Inani ngama R 4 8 kufinyelele ema- R99 Sebenzisa ithebula ukuthola amanani amagwinya ayi 7 kanye nayi 15. amasenti kufinyelele 99c USizile ugada ingane. Ubiza R20 yezindleko zokuhamba, bese kuba R5 ngehora lokugada. Mqedelele lelithebula lakhe. Inombolo yamahora 1 2 3 4 5 10 Inani ngama R 25 30 Qaphela ukuthi inkinga ka Heila’s kanye nenkinga ka Sedick’s zisebenza ngok- 371 wehlukana. Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 372 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA IZIBALO EZISESIMWENI ESIKHULULEKILE 1.12 Sebenzisa lamasu Abafundi balindeleke ukuxazulula izibalo ezisesimweni esejwayelekile alandelayo uma ubala: esikhululekile besebenzisa lamasu: Amasu (izindlela zokwenza namaqh- • Imidwebo noma izinto • Ukwakha nokuhlakaza izinombolo Izibalo IBANGA 1-3 inga) eziphathekayo isib. • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo Izinto zokubala • Imigqa yezinombolo • Ukwakha nokuhlakaza izinombolo Bheka amanothi akathemu 1 no 2. • Ukuphinda kabili nokuhlukanisa kabili kulingane nse • Umugqa wezinombolo 1.13 • hlanganisa kufinyelele Ngalethemu abafundi baqhubeka nokuhlakaza izinombolo khona bezokwazi e- 99 ukubala. Ukuhlanganisa nokususa • susa kusukela e- 99 Izindlela ezingasebenziseka ukukhombisa izibalo zokuhlanganisa nokususa • ukusebenza Ukuhlakaza inombolo ibe yizingxenye ezincane ukwenza ukubala kubelula kwezimpawu ezifanele Ukusebenzisa ulwazi lobungako benani lenombolo ukuhlakaza izinombolo (+, -, =, ) ngamashumi nangemivo • ukuzijwayeza Ukuhlanganisa izinombolo ezingamadijithi amabili nokuhlakaza zombili izinom- amabhondi ezinombolo bolo kufinyelele e-20 43 + 36 =  43 + 36 = (40 + 3) + (30 + 6) = (40 + 30) + (3 + 6) = 70 + 9 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola = 79 Ukuhlanganisa ngokuhlakaza inombolo eyodwa 43 + 36 =  43 + (30 + 6) 43 + 30 → 73 + 6 = 79

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.13 Abafundi bangahlakaza inombolo ngezindlela abakwazi ukuzikhona. Lokhu kusho ukuthi bengakwenza ngezindlela ezehlukene. Ukuhlanganisa nokususa 43 + 36 =  43 + (10 + 10 + 10 + 6) 43 + 10 → 53 + 10 → 63 + 10 → 73 + 6 = 79 Ukususa • Ukuhlakaza zombili izinombolo 87 - 56 =  87 - 56 = (80 + 7) - (50 + 6) = (80 - 50) + (7 -6) = 30 + 1 = 31 • Ukususa ngokuhlakaza inombolo eyodwa 87 - 56 =  87 - (50 + 6) 87 - 50 → 37 - 6 = 31 • Lindela ukuthi abanye abafundi bengahlakaza inombolo ngezindlela ezahluke- ne ukuze kube lula kubo ukubala: 87 - 56 =  87 - (20 + 20 + 10 + 6) 87 - 20 → 67 -20 47 - 10 = 37 - 6 = 31 Ukusebenzisa ukuhlukanisa kabili ukuhlakaza inombolo 69 + 12 69 + (6 + 6) 69 + 6 → 75 + 6 = 81 373 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 374 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.13 Ukubala uye phambili babuye baye emumva Ukuhlanganisa 78 - 69 =  nokususa Ukubala uqhubeka usukela ema 69 kuyisu elingcono ngoba izinombolo zisonde- lene. Izibalo IBANGA 1-3 Ukukhomba izinombolo eziseduze kwezihamba ngazimbili 34 + 35 okuchaza ukuthi kuhambangakubili ama- 34 ehlanganiswa no 1 noma ukuhamba ngakubili ama-35 kususwa o 1. 34 + 34 + 1 Abafundi bangabhala amaqhinga abo besebenzisa imicibisholo 34 + (30 + 4) + 1 34 + 30 → 64 + 4 → 68 + 1 = 69 Shintsha inombolo iphindaphinde kashumi bese ususa noma uhlanganise imivo Bala ukhuphuke noma wehle ukusondelela e-10 58 + 19 =  Lapha abafundi badinga ukuthi bakhethe kukho kokubili. Shintsha ama-58 noma ama-19 ukusondelela e-10. Ibona bazozikhethela. Isibalo singabhalwa kanje: 58 + 19 = 58 + 20 - 1 58 + 20 → 78 - 1 = 77 Abanye abafundi bangahlakaza amashumi amabili abe ngamaqoqo ama-2 e-10 ukubala ngokucophelela. Ngasekupheleni konyaka abafundi kumele besekwazi uku: Ukusebenzisa nokuqonda ulimi lokuhlanganisa Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukuqonda ukuthi ukuhlanganisa no -0 kushiya inombolo ingashintshile 75 + 0 = 75 0 + 75 = 75 75 = 75 + 0 75 = 0 + 75

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.13 Ukuphendula imibuzo ebhaliwe ebekwe ngezindlela eziningi ezinjengalezi: Ukuhlanganisa • hlanganisa ndawonye 43 no 9 nokususa • yengeza ngeshumi ema 67 • 11 ehlanganiswa nama 83 • 80 = 62 + 8 +  • Yini ama 30 ngaphezu kwa 60 • Thola isamba sama 56 ne 14 • Yengeza ishumi nambili emashumini ayisikhombisa nanhlanu • Iyiphi inombolo enkulu ngeshumi ngaphezu kwama 83 • Iyiphi inombolo okufanele uyengeze ema 45 ikuthola ama 78? • Amashumi amane ehlanganiswa namashumi ama-3 • Amashumi ama-12 ehlanganiswa nemivo eyi-8 • 45 + 10 =  45 + 20 =  45 + 30 =  Yazi ukuthi ¨ kumele inombolo engaziwa 42 + 44 =  5 + 7 +  = 80 57 +  = 95  + 15 = 81 Ngosizo lezinsiza: hlanganisa izinombolo ezintathu ndawonye 26 +  +  = 72 Khetha ezintathu zalezi zinombolo: 15, 19, 22, 25 Zihlanganise zonke. Iziphi izamba ezahlukene ongazenza? 375 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 376 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.13 Ukuphendula emibuzweni ebhaliwe bese kuchazwa ukuthi kufikwe kanjani empendulweni: Ukuhlanganisa nokususa • Hlanganisa 6, 12 ne 14. • Yini isamba se 10, 5 ne 19. Izibalo IBANGA 1-3 Ukuqonda ukususa ngasekupheleni konyaka. Ngasekupheleni konyaka abafundi kumele bebesebekwazi uku: Ukuqondisisa nokusebenzisa amagama amasha ezibalo zokususa: Ukuthatha,susa, kungaki okusele, kungaphansi kangakanani...kuno, umehluko phakathi, kuningi ngokungakanani... kuno, kungaki ngaphezulu ukwenza... noku- funda nokubhala uphawu lokususa (-) Qhubeka nokuthuthukisa ukuqonda ukususa njengo: • ukususa; noku • thola umehluko phakathi. Ukuqonda ukuthi ukususa u-0 kushiya inombolo ingashintshile: 92 - 0 = 92 92 = 92 - 0 Phendula imibuzo ebhaliwe ebekwe ngezindlela ezahlukene ezinjengalezi: • 37 ususa oku-3 • Thatha 40 ku 80 • 62 susa 42 • susa 45 ku 90 • yini umehluko phakathi kwa 38 nama 57? • Kungaphansi ngokungaki i-17 ukuna 49 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Iyiphi inombolo okufanele uyisuse ku 56 ukuthola 22? • Iyiphi inombolo okufanele uyisuse ku 56 ukuthola 32? • Iyiphi inombolo okufanele uyisuse ku 56 ukuthola 22? • Thola izinombolo ezihambisanayo ezinomehluko we 10

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.13 Yazi ukuthi  kumele inombolo engaziwa. Ukuhlanganisa 57 - 34 =  nokususa 80 - 30 =  62 -  = 48 98 - 42 =  87 -  = 75 13 - 6 = 15 -   - 18 = 24 Qala ukuqondisisa ukuthi: 25 - 10 kuhlukile ku 10 - 25 Sebenzisa ubudlelwane phakathi kokuhlanganisa nokususa Yisho ubhale ukususa okuhambisanayo okuyikho ekuhlanganiseni okuyikho oku- nikeziwe noma kushintshana. Isibonelo: 73 + 17 =90 kusho ukuthi 90 - 17 = 73 17 + 73 = 90 kusho ukuthi 90 - 73 = 17 42 - 18 = 24 kusho ukuthi 24 + 18 = 42 42 - 24 = 18 kusho ukuthi 18 + 24 = 42 Ngaphandle kokusebenzisa izinsiza, phendula loku okulandelayo: Ingabe bewazi ukuthi 62 + 29 = 91. Yini: 29 + 62 91 - 29 91 - 62 377 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 378 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.13 Ingabe bewazi ukuthi 66 - 50 = 16 Ukuhlanganisa Yini: nokususa 66 - 16 Izibalo IBANGA 1-3 50 + 16 16 + 50 Bhala bese uphendule loku okulandelayo: 57 - 34 = 23  + 23 = 57  - 23 = 34 34 + 23 =  12 + 46 = 58 12 +  = 58 58 -  = 12  - 46 = 12 Bhala imisho yezibalo emine ehlukene usebenzise izinombolo ez-3. Isibonelo: 20, 30 no 50 20 + 30 = 50 30 + 20 = 50 50 - 30 = 20 50 - 20 = 30 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.14 • Ukuphindaphinda Yini ehlukile kuthemu 4? izinombolo nga-1 Ukuhlanganisa Kulethemu abafundi bazobe bephindaphinda ngakuthathu okokuqala. Bheka kufike e-10 ngaku 1, amanothi kuthemu 1 ukwethulwa komqondo omusha ngokuphindelela 2, 5, 3 no 4 kufinyelele okuholela ezibal- Ngasekupheleni kwethemu abafundi kumele bebesebekwazi uku: ku- 50 weni zokuphin- daphinda • Sebenzisa izimpawu Ukusebenzisa ulimi lwezibalo zokuphindaphinda ezimweni abenza kuzo: ezifanele(+, x, =, ) Ukuphinda kabili, ukuphindaphinda, okuphindiwe, ukuphindaphinda ngo,isamba, amaqoqo oku ukuphinda ka, isikhathi njengo (kakhulu, kade, kabanzi...), kabili, ngokuphindwe kathathu, nokufunda nokubhala uphawu lokuphindaphinda (x) Sebenzisa lolulimi ukwenza izibalo zokuphindaphinda Ukuqonda ukuphindaphinda njengokuhlanganisa ngokuphindelela Isibonelo Okuyisithupha okuhlanganiswe kathathu kuyafana nalokhu: 6 + 6 + 6 = 18 Amaqoqo ama-3aphindwe ka 6 = 18 Oku-3 kuphindwe ka- 6 = 18 6 x 3 = 18 3 x 5 = 18 Qondisisa ukuphindaphinda njengokuchaza ukuhleleka ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ 5 x 3 =15 ¥ ¥ ¥ ¥ ¥ ¥ 3 x 5 = 15 379 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 380 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.14 Phendula imibuzo efana nale: Ukuhlanganisa Okuhlanu okune ngokuphindelela kuholela Ukuphinda kabili oku-6 Izibalo IBANGA 1-3 ezibalweni zokuphindaphinda Oku-6 ukuphinde ka- 5 Izinto zokubala ezintathu emugqeni. Kunemigqa e-4. Zingaki izinto zokubala sezizonke Oku-2 uphindaphindwe ka-4 Oku-8 kuphindweka-2 Ukubona ukusebenza kwesibambeli  esimele inombolo engaziwa. 3 amaqoqo oku 2 kwenza 6 noma 3 kuphindwe 2 kwenza 6 noma 3 x 2 =  4 amaqoqo oku 3 kwenza 12 noma 4 kuphindwe 3 kwenza 12 noma 4 x 3 =  6 amaqoqo oku 3 kwenza 18 noma 6 kuphindwe 3 kwenza 18 noma 6 x  = 18 7 +  = 14 2 amaqoqo oku 7 =  2 +  +  +  +  +  +  = 14  x 7 = 14 1x2= 2x2= 3x2= Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 1x5= 2x5= 3x5=

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.16 Ulwazi lwezinombolo: Izibonelo zemibuzo engabuzwa: Uhla lwezinombolo Izibalo zekhanda Ulwazi Lwezinombolo kufinyelela ku- 99 Amagama ezinombolo nezimpawu zazo • Hlela iqoqo lezinom- bolo ezikhethiwe. Bamba uphakamise ikhadi noma ubhale phansi amagama ezinombolo. Khetha umfundi ozobhola zoqondanisa nenombolo. • Qhathanisa izinombolo kuya kuma -99bese Okungaphezulu nokungaphansi usho ukuthi iyiphi Yini enkulu noma encane ngo 1, 2, 3, 4, 5 ne-10 • 1 ngaphansi kwe 70 Khumbula ngokushe- • 1 ngaphezu kwe 80 sha: • 3 ngaphansi kwa 51 • Khumbula izindlela zokuhlanganisa noku- • 4 ngaphansi kwa 67 susa kuyofinyelela • 5 ngaphansi kwe 85 e-20 • 10 ngaphezu kwe 90 • Hlanganisa noma ususe kusukela • 10 ngaphansi kwe 80 ngama-10 kusukela Iyiphi i-alfabheti yesi- 5? e-0 kufinyelele e-100 Iyiphi inyanga ye- 9yonyaka? Amaqhinga okubala ngekhanda Ukuhlela nokuqhathanisa Sebenzisa amaqhinga Ikuphi okungaphezulu: 21 noma171? okubala ukuhlanganisa Nginike inombolo ephakathi kuka 154 no 159. nokususa ngempume- lelo: • Beka inombolo enkulu kuqala ukuze ubale uqhubeke noma uye emuva 381 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 382 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.16 • Umugqa wezinombolo Amaphuzu okuhlanganisa nokususa: Izibalo zekhanda • Ukuphinda kabili • Ukwazi ngengqondo wonke amabhondi okuhlanganisa nokususa kufinyelele nokuhlukanisa kabili e-20 ngokulinganayo  + ∆ = 20 Izibalo IBANGA 1-3 • Ukwakha nokuhlakaza  + ∆ = 16 Sebenzisa ubudlelwane 19 =  - ∆ phakathi kokuhlanganisa nokususa Okuyikho ngokuhlanganisa nokususa zonke izinombolo kufinyelele e-20 1 + 11 = 12 11 + 1 = 12 2 + 10 = 12 10 + 2 = 12 3 + 9 = 12 9 + 3 = 12 18 - 4 = 14 18 - 14 = 4 18 - 5 = 13 18 - 13 = 5 18 - 6 = 12 18 - 12 = 6 Khumbula ngokushesha ukuhlanganisa okuphindwe kabili kufinyelele e-20. Loku kumele kufake ukususa okuyikho okuqondene. • 1+1=2 • 2+2=4 • 3+3=6 • 4+4=8 • 5 + 5 = 10 • 6 + 6 = 12 • 7 + 7 = 14 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • 8 + 8 = 16 • 9 + 9 = 18 • 10 + 10 = 20

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.16 Ngikhombise inombolo engingayengeza ukwenza ama 20 (bhala phansi useben- zisa amakhadi obungako benani lenombolo). Izibalo zekhanda • 8 • 2 • 9 • 15 • 3 Ngikhombise inombolo esele uma ….kuthathiwe kokunga 20 (bhala phansi use- benzisa amakhadi obungako benani lenombolo). • 5 • 18 • 0 • 14 • 7 Amaqhinga okubala: Bheka amanothi kuthemu 2. 383 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO 384 ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.17 • Sebenzisa usho • Sebenzisa usho Yini okwehlukile kuthemu 4? amaqhezu ezimweni amaqhezu ezimweni Amaqhezu Ngalethemu yesi-3 abafundi bazogxiliswa ekutheni lihlangana kanjani igama ezejwayelekile ezejwayelekile leqhezu enombolweni elingana nezingxenye zokuphelele okuhlukanisiwe. nezaziwayo okufaka nezaziwayo okufaka Imidwebo enhlobonhlobo isetshenzisiwe ukwakha ukuqondisisa okuqhubekayo. uhhafu, ikota, uhhafu, ikota, Izibalo IBANGA 1-3 okukodwa kokuthathu, okukodwa kokuthathu, Abafundi baqhubeka nokusho amaqhezu emdwebeni kulethemu. Baphinda nokukodwa kokuhlanu nokukodwa kokuhlanu basho amagama ezingxenye uma benza izibalo. Izingxenye zamaqhezu ezikhonjiwe zibhalwa kanje 1kuhhafu, 1 kokuthathu, 1 ikota. • Bona amaqhezu • Bona amaqhezu ezimweni ezidwetshiwe ezimweni ezidwetshiwe Kulethemu kufanele kugxilwe kokuphelele. Abafundi bazokwazi uku: • Bhala amaqhezu • Bhala amaqhezu Qedela imisho njenge 1 uhhafu, 2 njenge 1 uhhafu, 2 Ohhafu ababili bafana ne _____ kokuphelele kokuthathu kokuthathu Okuthathu kokuthathu kufana ne ____ kokuphelele Okune kwekota kufana ne ____ kokuphelele Ngalethemu abafundi bazothola amaqhezu eqoqo lezinto. Isibonelo: Abafundi bazothola izinto zokubala ezibekwe ngokuhleleka: 1 uhhafu we 8 wezinto zokubala. ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ Abafundi bangahlukanisa izinto zokubala ezi- 8 kube amaqoqo ama-2 oku- 4. ¥ ¥ Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ¥ ¥ ¥ ¥ ¥ ¥

UKUQONDA ISIKHATHI UKUQONDA OKUFUNDWAYO OKUFUNDWAYO (ezifundweni eziyi NAMAKHONO ISIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA awa eleodwa ADINGEKAYO CAPS ABHEKWA nemizuzu NGOKUPHELA NGETHEMU 1 engama-24) KONYAKA 1.17 Vumela abafundi ukusebenzisa izinto eziphathekayo okwenza loku nokuzibeka ngohlelo olufanele. Amaqhezu Ngasekupheleni kwethemu abafundi kumele bebesebekwazi ukuthola: • 1 uhhafu wezinto eziqoqiwe; • 1 ikota yezinto eziqoqiwe; • 1 kokuthathu kwezinto eziqoqiwe; kanye • 1 kokuhlanu kwezinto eziqoqiwe. 385 Izibalo IBANGA 1-3

ITHEMU YESI-4 YEBANGA LESI- 2 2. AMAPHETHINI, UBUDLELWANO, I-ALJEBHRA 386 UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 2.1 Kopisha, wandise bese Amaphethini Abafundi bazosebenza ngamaphethini emvelo, awesimanje nansukuzonke kanye uchaza asizungezule nawamasiko angamagugu kusukela eBangeni loku - 1 kuya kwelesi - 6. Lokhu Amaphethini kusho ukuthi akudingeki ukuthi uchithe isikhathi ngalesisihloko. Kufanele ukuthi ejiyometri Kopisha, wandise ubuye Khomba,uchaze Izibalo IBANGA 1-3 kubuye kukhethwe imisebenzi kanye namaphethini alungele iBanga ngalinge. uchaze ngamagama ngamagama ubuye ukopishe amaphethini Inhlobo eyodwa yamaphethini abafundi ingabukeka njengomugqa ohlukanise kabili • Amaphethini alula ejiyometri kufane nxa zombili, isib. Amacembe amaningi nobuso bezilwane kuwumugqa ohlu- enziwe ngezinto kanisa kabili kufane nxa zonke. Kanjalo nezinambuzane uma uzibuka ngaphezulu eziphathekayo; kanye • Ngokwemvelo kanye namaphethini kwizinyoni eziningi uma uzibuka ngaphansi. • Namaphethini alula • Empilweni yesimanje Abafundi bangabuka amaphethini: enziwe ngokudweba yansukuzonke imigqa, izimo noma • Uthango (oluwucingo, izingodo); • Amasiko angamagugu izinto • Umsebenzi wezitini kanye namathayili aphansi; Sungula uchaze • uphahla; amaphethini akho • izimpahla kanye nezindwangu; Sungula amaphethini akho ejiyometri • amapuleti, izinkomishi, amasosa; • Ngezinto • amabhola; eziphathekayo • izilwane ezifana nezinkomo, izimvemvane, amadumbe, indlulamithi, ingwe, • Ngokudweba imigqa, izintuthwane, izinyoni; izimo noma izinto • izimbali nacembe; Amaphethini • iphepha lokuhlobisa ubonda olwenziwe ngephepha elihlotshiwe elitholakala asizungezile ikakhulukazi emikhukhwini. Bona, chaza • Umsebenzi wobuhlalu wesimanje nowakudala; kanye ngamagama ubuye ukopishe amaphethini • Nezitsha zobumba/dongo noma obhasikidi abelukiwe ejiyometri Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Bangawachaza kanjani abafundi amaphethini abawathola lapho behlala • Ngokwemvelo khona? • Kwimpilo yesimanje Kunezindlela ezahlukene zokuchaza amaphethini esiwathola lapho sihlala khona. yansukuzonke Amaphethini amaningi atholakala lapho sihlala khona enziwe ngemigqa, ngezimo noma izinto. Isimo noma izinto azidingi ukuxhumana nejiyometri eziyizimo ezi-2-D • Amasiko angamagugu nezi-3-D okusethsenzisiwe eBangeni lesi - 2. Bonke abafundi babheka: • Lokho ngokuphindelela, njengamachashaza, imigqa, nanoma iyiphi inhlobo yesimo; nokuthi

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA CAPS ngeThemu ye - 2 isifundo) 2.1 • Iphindeke kanjani. 1 isifundo Amaphethini Izibonelo: ejiyometri - Imigqa eqondile enqamula eminye, imigqa ehambisana nengezansi lento/ lendwangu noma umugqa osuka phezulu/ onqamulayo, imigqa ehamba emilenzeni yamabhulukwe, - Imigqa ezungezayo njengaleyo etholakala uma usika u-anyanisi. - Imigqa engaqondile, njengaleyo eseminweni kanye nedumbe, nemibimbi yendlovu naleyo ekubantu asebegugile. - Imigqa ejikajikayo efana naleyo etholakala uma usika ikhabishi. - Amachashaza afanayo, amachashaza ahlukene ngokulinganayo - Izimo ezilinganayo, isib. iphethini yezitini obondeni naphansi, - Izimo ezinombala ofanayo - Amaphethini enziwe ngesimo esifanayo ebheke ezindaweni ezehlukene, isib. unxantathu obheke phezulu naphansi owenziwe ngobuhlalu besintu, izitini zaphansi ezibheke ezindaweni ezahlukene. - Amaphethini enziwe ngezimo ezahlukene, njengawendlulamithi. 387 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO ISIKHATHI NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (ihora nemizuzu 388 ADINGEKAYO UMA Okugxilwa kukho enga - 24 KUPHELA UNYAKA ngeThemu ye - 2 isifundo) 2.2 Kopisha, wandise Kopisha, wandise Buka amanothi eThemu yoku - 1, kodwa ukhulise uhla lwezinombolo lufinyelele Izifundo ezi - 3 Amaphethini ubuye uchaze ubuye uchaze ema - 200 ezinombolo Kopisha,wandise ubuye Kopisha, wandise ubuye uchaze uhla olulula uchaze okulula ukulan- lwezinombolo kufinyelele delanalwezinombolo okungenani ema - 200. kufinyelele okungenani Izibalo IBANGA 1-3 Sungula awakho ema - 200. amaphethini Ukulandelana kufanele Sungula awakho kukhombise ukubala amaphethini ezinombolo. uyaphambili uye nase- muva ngo-: • Kukodwa, kusukela kunoma iyiphi inom- bolo ephakathi kwe - 0 no - 200 • Ngokwamashumi kusukela kunoma iyiphi inombolo phakathi kwe - o nama - 200 • Ngakuhlanu kusukela kunoma iyiphi inom- bolo ephakathi kwe - 0 kufinyelela ema - 200 • Ngakubili kusukela kunoma iyiphi inom- bolo ephakathi kwe - 0 kufinyelela ema - 200 • Ngakuthathu kusukela kunoma iyiphi inom- bolo ephakathi kwe - 0 kufinyelela ema - 200 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 2.2 • Ngakune kusukela Amaphethini kunoma iyiphi ezinombolo inombolo ephakathi kwe - 0 kufinyelela ema - 200 Yakha awakho amaphethini ezinombolo

ITHEMU YESI-4 YEBANGA LESI-2 3. INDAWO NESIMO (IJIYOMETRI) ISIKHATHI CAPS UKUQONDA UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO ADINGEKAYO WOKUFUNDISA sehora eli 1 ABHEKWA NGETHEMU NGOKUPHELA nemizuzu engama 1 KONYAKA 24) 3.2 Uhla lwezinto Uhla lwezinto Okunconywayo okugxilwa kukhoku Themu- 4 Isifundo esi-1 Izinto ezi-3-D Bona usho izinto ezi- Bona usho izinto ezi- Ukusebenza kuhlanganiswe nemisebenzi ebhaliwe. 3-D ezilapha ekilasini 3-D ezilapha ekilasini nezithombe nezithombe • Isimo sebhola • Isimo sebhola (Okusambulunga,) (Okusambulunga,) • Izimo ezisabhokisi • Izimo ezisabhokisi (iprizimu) (iprizimu) • amasilinda • amasilinda Izimpawu zezinto Izimpawu zezinto Chaza, uhlele bese Chaza, uhlele bese uqhathanisa izinto ezi- uqhathanisa izinto ezi- 3-D ngalokhu-: 3-D ngaloku-: • ubungako • ubungako • izinto ezigingqikayo • izinto ezigingqikayo • izinto ezishelelayo • izinto ezishelelayo Imisebenzi ekugxiliwe kuyo • Bukela bese wakhe izinto ezi- 3-D. Izinto usebenzisa izinto eziphathekayo njengezimo ezisikiwe ezi-2-D amabhuloki, okusetshenzisiwe nekhithi yokwakha nezinye izinto ezi-3-D 389 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 390 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO ADINGEKAYO WOKUFUNDISA sehora eli 1 ABHEKWA NGETHEMU NGOKUPHELA nemizuzu engama 1 KONYAKA 24) 3.3 Uhla lwezinto Uhla lwezinto Bheka amanothi kuThemu 2 Izimo-2-D Bona usho izimo ezi-2-D Bona usho izimo ezi-2-D KuleThemu kubukezwa kuhlanganiswa umsebenzi wezimo ezi-2-D.Kugxiliswa ekubukeni nokubiza ngamagama izindilinga, izikwele,onxande, nonxantathu bese • indilinga • indilinga bekhuluma ngamacala aqondile nazindilinga.Benza imisebenzi kuleyo ekuiThemu Izibalo IBANGA 1-3 • onxantathu • onxantathu 2, kodwa bagcine begxilisa kuzimpawu zezimo namagama azo. • izikwele • izikwele • onxande • onxande izimpawu zezimo izimpawu zezimo Chaza uhlele bese Chaza uhlele bese uqhathanisa izimo ezi- uqhathanisa izimo ezi- 2-D ngalokhu: 2-D ngalokhu: • ubungako • ubungako • umbala • umbala • isimo • isimo • amacala aqondile • amacala aqondile • amacala asandilinga • amacala asandilinga Izifundo ezi-3 3.4 Okufana nse nxazom- Okufana nse Bheka amanothi kaThemu 2. bili nxazombili Okufana nse nxazombili Bona udwebe Bukela udwebe umugqa okufana nse izimo ulayini ofana nxazombili ngejiyometri nse ngejiyometri nokungesiwo nokungesiwo izibalomdwebo. izibalomdwebo. isifundo1 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI-4 YEBANGA LESI- 2 4.ISILINGANISO ISIKHATHI CAPS UKUQONDA UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.1 Ukukhuluma Ukukhuluma Abafundi bayaqhubeka ngokukhuluma besebenzisa ubude besikhathi Isifundo 1 ngesikhathi ngesikhathi nokulandelanisa sona Isikhathi • ukubiza ngamagama • Khuluma ngesikhathi Ngesikhathi sokufundisa ikilasi lonke nokugxila emaqenjini, abafundi ukulandelanisa ngamahora ngohhafu bayakhuluma ngezinsuku zamasonto, izinyanga zonyaka,namhlanje zingaki izolo izinsuku zamasonto wehora nangekota nakusasa.Abafundi bayazijwayeza ikhalenda ngokufaka lokhu; yehora ewashini lezinti • Ukubiza ngamagama • Izinsuku zokuzalwa; izinyanga ngesizulu Ukubala ubude • imigubho yezenkolo; ngesikhathi nokudlula • Izinsuku zokuzalwa, kwaso • izigameko zomlando; imigubho yezenkolo, amaholide, izigameko • Sebenzisa iwashi • izigameko zesikole zomlando, izigameko ukubala ubude • Amaholide zesikole ekhalandeni. besikhathi ngamahora uhhafu wehora noma ekhalendeni. • Khuluma ngesikhathi ikota yehora. ngamahora ngohhafu Shono isikhathi ngamahora,ngohhafu wehora nekota yehora wehora nangekota yehora. Bheka amanothi kaThemu 3 Ukubala ubude ngesikhathi nokudlula kwaso • Sebenzisa amamkhalenda ukubala ubuye uchaze ubude ubude besikhathi ngezinsuku zeviki • Sebenzisa iwashi ukubala ubude besikhathi ngamahora uhhafu wehora noma amakota. 391 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO 392 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.2 Isilinganiso Ukwethula isinganiso Yini umahluko kuThemu 1 isifundo1 esingahlelekile esingahlelekile Ubude, KuThemu 1 kuyancomeka ukuba abafundi bagxiliswe ekuqageleni, belinganisa, • Qagela, ulinganise, • Qagela, ulinganise, beqagela, bese bebhala ubude, ububanzi kanye nokuphakama ngamayunithi uqhathanise, uhlele uqhathanisa, angahleliwe beqala ISILINGANISO ngamamitha. Izibalo IBANGA 1-3 bese ubhala ubude uhlele bese ubhala KuThemu 4 bangagxila ngokuqagela, isilinganiso, baqagela, nokubhala usebenzisa isilinganiso ubude usebenzisa ubude,ukuphakama, nobubanzi ngamamitha kuThemu 1. Bheka amanothi esingalinganisiwe isib, amamitha (izinduku kuThemu1 isandla, amanyathelo, zamamitha,noma ubude bepensela, ubude bentambo Lokhu kungahlanganiswa nomsebenzi obhalwayo. izintozokokubala.njll. ngamamitha) njenge yunithi engahleliwe • Chaza ubude bezinto ngokubala uqala ngokuqagela ukuthi bungakanani ubude bamayunithi angahleliwe • Sebenzisa ulimi ukhuluma ngokuqhathanisa isib, kude xaxa, kufishane xaxa, kuphakeme xaxa kubanzi xaxa Ukwethula isinganiso esingahlelekile • Qagela, ulinganise, uqhathanise, uhlele bese ubhala ubude ngamamitha (kungaba Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola amamitha ngezinduku noma ubude bentambo ngamamitha) ngesilinganiso esilingene sobude.

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.3 Isilinganiso esingahl- Ukwethula isilinganiso Kuthemu 2 isifundo1 elekile esingahlelekile Isisindo • Kulinganiswe isisindo ngokungahlelekile besebenzisa ukuzimelela; • Qagela, ulinganise, Abafundi babhala • Kuhlelwe izinto ngokwezisindo ezihalwe emaphaketheni uqhathanise, uhlele imisebenzi bese ubhala isisindo ngokuhlanganyela • Kufundwa izikali zasendlini yokugeza (izikali zombili nezithombe zezikali) bheka usebenzisa isilinganiso nokufunda izithombe; amanothi kathemu 2 esingalinganisiwe. • Izinto ezine sisindo Kuthemu 4 abafundi kumele bahlanganise amakhono okufunda isikali nokuzimelela isib, esibhalwe kuzo, sasendlini yokugeza nezithombe kusondezela kukilogremu eliphelele.Lokhu amabhuloki, izitini njll, kungahlanganiswa nomsebenzi obhalwayo. • Isisindo sezithombe • Sebenzisa ulimi esikalini sasendlini lokukhuluma ngoku- yokugeza lapho uthi qhathanisa, isib, lukhomba ikilogremu kulula, kuyasinda, liphelele. kulula ngokuthe xaxa, kuyasinda ngokuthe xaxa Ukwethula isilinganiso esingahlelekile • Qhathanisa, uhlele bese ubhala isisindo esiveziwe ephaketheni ezinto ezithengisayo ngokwamakilogremu isib amakilogremu ama 2 erayisi,ne1 kilogremu likafulawa • Balinganisa izisindo zabo ngokuseben- zisa isikali sasendlini yokugeza. 393 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO 394 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.4 Isilinganiso Ukwethula isinganiso Ngesikhathi sokusebenza ngokuzimela abafundi bangaqhubeka ngoku- isifundo1 l esingahlelekile esingahlelekile Umthamo • Qagela nokulinganisa baqhathanise, bahlele bese bebhala umthamo wesitsha • Qagela ulinganise, Abafundi babhala noma okumumethwe yisitsha leso besebenzisa isilinganiso esingalinganisiwe. uqhathanise uhlele imisebenzi Ukulandela uhlelo lwezinto ezizosetshenziswa njengokubhaka,usebenzisa Izibalo IBANGA 1-3 umthamo wesitsha ngokuhlanganyela isimo esijwayelekile lapho abafundi bezozijwayeza khona UKULINGANISA. isib. umthamo (isitsha nokufunda izithombe; Khetha uhla lwezinto abazozisebenzisa ngezithako ezinikwe ngamankomishi esingakumumatha amathisipuni,noma amayunithi angenasilinganiso. • Imiphumela uma sigcwalisiwe) ngomthamo obhaliwe • Qhathanisa uhlele umthamo wamabhodlela ahlukene nohla lwezinto noma okumumethwe kuwo ngokuhlela ozozithenga lapho umthamo azokhangisa ngawo ephaketheni lelo. isitsha ngokusebenzisa ngokulandelana isilinganiso • Ukusebenza ngo 1litha angamabhodlela, noma 1ilitha lojeke ukuqagela okuhleliwe. esingalinganisiwe isib. nokulinganisa uqhathanisa ubhala. Umthamo wezitsha noma okumumethwe isipuni namankomishi • Izithombe zojeke yilezo zitsha ngamalitha. lapho umthamo • Chaza umthamo Bheka amanothi kuthemu 3 usondezelayo kulitha wesitsha ngokubala e-1 noma 2 kulayini Abafundi kumele banikwe umsebenzi obhaliwe ohlanganisa nokufunda izithombe ukuthi mangaki obhaliwe. amayunithi angahleliwe • Imiphumela yomthamo obhaliwe kuwona ukuze kuhlelwe ngokulandelana angagcwalisa • Okulindelekile ukuthi kwawo lesositsha isib. abafundi bazofunda ibhodlela lingagcwala • Izithombe zojeke lapho umthamo usondelene nenombolo 1 yelitha noma 2 inombolo leyo ebhaliwe izinkomishi ezi-4. wamalitha kulayini obhaliwe duze komugqa wesindi Ukwethula isinganiso Okulindelekile ukuba abafundi bodwa bafunde inombolo eseduze kolayini. • Chaza umthamo esingahlelekile Lokho kuchaza ukuthi umthamo (cishe ugcwale.ngaphezulu ngaphansi. njengokuthi cishe kube kancane, noma kuyalingana ngamalitha) befunda ejekeni. (gcwale, ngaphansi, • Qagela, linganisa, ngaphezulu njll) Isilinganiso somthamo njengesimo esejwayelekile sokuxazulula izinkinga uqhathanise,uhlele befunda kujeke nokubala bese ubhala umthamo waleyonto Esikhathini esimiselwe iziNombolo iziMpawu noBudlelwano bazo abafundi ngokulinganisa sebengaxazulula izinkinga besebenzisa isimo esijwayelekile ngoku; ngamalitha Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Isilinganiso esingahlelekile somthamo nokumumethwe isib. Ugogo usebenzisa izinkomishi ezi 2 zobisi ukwenza uphudingi uma engaziphinda kabili izinto azisebenzisile, angadinga ubisi olungakanani? • Amamlitha

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.4 • Qhathanisa uhlele, Bhekisisa ukuthi ithemu inohlelo lwezinombolo ezifanele lona;kanjalo nohlobo ubhale umthamo lwezinkinga oluhlukene. Umthamo wezinto eziveziwe ephaketheni ngokwamalitha isib. Amalitha 2 obisi,ilitha 1yobisi, amalitha 5 kapende. 395 Izibalo IBANGA 1-3

ITHEMU YESI-4 YEBANGA LESI-2 5.ULWAZI OLUQOQELWE 396 UKUQONDA ISIKHATHI OFUNDWAYO UKUQONDA ESINQUNYIW NAMAKHONO OKUFUNDWAYO (esifundweni IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO NAMAKHONO sehora eli 1 NGOKUPHELA ABHEKWA NGETHEMU 1 nemizuzu engama KONYAKA 24) 5.4 Ukuqoqa nokuhlela ulwazi Qoqa nokuhlela Izibalo IBANGA 1-3 ulwazi • Ukuqokelelwa kolwazi ngekilasi lakho noma isikole ukuphendula imibuzo ezobe ibuzwa uthisha • Ukuhlela ulwazi ngamathali. 5.5 Ukubhala okumele ulwazi Bhala okumele ulwazi Ukubhala okumele ulwazi ngegrafu yezithombe 5.6 Ukuhlaziya Ukuhlaziya nokuhusha Ukuhlaziya nokuhumusha ulwazi olunikiwe 1isifundo nokuhumusha ulwazi ulwazi Hlaziya Kulesisikhathi sonyaka,abafundi kumele ngabe sebeyijwayele igrafu yezithombe. nokuhumusha Ukuphendula imibuzo Ukuhlaziya ulwazi kuyancomeka ukuthi kuthemu 4abafundi bagxiliswa ekuhlaziyeni ulwazi.Nika ulwazi ngolwazi egrafini kulokho okumele ulwazi abafundi ulwazi lokuhlaziya okungenani eyo-1igrafu yezithombe.. yezithombe. olubhaliwe. Abafundi abaphendule imibuzo leyo ezobuzwa uthisha ngegrafu nethebula. Bheka Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola uthemu 1nemibuzo efanele nenhlobonhlobo.

3.5.3 INCAZELO YOKUQUKETHWE EBANGENI LESI-3 YEBANGA LESI- 3 ITHEMU YOKU-1 CAPS 1. IZINOMBOLO, IZIMPAWU NOBUDLELWANE BAZO ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA EBangeni 3 abafundi bazohlanganisa bephetha abakufunde eBangeni 2 bese besenzisa lamakhono ekusebenzeni izinombolo phakathi kuka 0 kuya e - 999. Abafundi manje eBangeni lesithathu 3 bazokwenza lokhu • Bazofunda baphinde babhale izinombolo nezimpawu kanye namagama ukuya e 1000 • Buqhubeke nokukhomba nokuzibeka esikhundleni esifanele. • Besebenzisa ulwazi lwabo lobungako benani lenombolo ukuthola amakhulu, amashumi nemivo bese bechaza ubudlelwano bakho. • Ukuhlukanise izinombolo ezihamba ngantathu. Bazosebenzisa ulwazi lwabo lobungako benani lenimbolo ukuqathanisa nokuhlela izinombolo bese benika izizathu ngokukhetha kwabo. • Baqhubeke nokubala beya phambili babuye baye emumva, ngezikhawu zama 20,25, 50 kanye 100; bazoqala ke manje babona ubudlelwano phakathi kokubala ngaku 2 kanye noku 4 • Babe nolwazi lokubala isamba esikhulu sezinto ngamaqoqo. Sebeyakwazi kubala gokuhleleka, ngokuyikho futhi bangakwazi ukunika indlela yokubheka imiphumela; • Behlanganisa babuye basuse izinombolo ngekhanda uze ufike kuma 50 • Bexazulula izinkinga ezahlukene bese befunda ukuhlela izimpendulo ezibhaliwe ngendlela ehlelekile. • Bakhethe izimpawu ezifanele uma bexazulula izinkinga ezimweni ezijwayelekile. • Bangabhala ukubala kwabo besebenzisa ukhlananisa (+), ukususa (-) kanye nokulingana (=). Bayakwazi ukuchaza izimpendulo zabo nezindlela abazisebenzisile. • Besebenzisa izindlela ezihlelekile ukubhala izibalo zokuhlanganisa nokususa. Isibonelo:bazohlakaza eyodwa noma ezimbili kuhlanganisa nokususa; bese bekwazi ukukhetha ohlwini lamaqhinga abazolisebenzisa ukuxazulu inkinga. Isibonelo: ukususa: 135 - 131, umfundi uzokwazi ukususa ngokubala eqhubeka noma eya emumva. • Inqubo mgomo ilindele ukuthi umfudi webanga 3 uzisebenzisa kancane izinto zokubala eziphathekayo ukumela ukulanganisa nokususa. Ngokuphela konyaka balindeleke ukuba bakwazi ukuhlanganisa nokususa besebenzisa indlela yephepha nepensela. • Uma umfundi efika eBangeni lesi 3 kufanele azi ubungako benani lenombolo nokuhlakaza izinombolo ukuze akwazi ukwenza izibalo. Umfundi uzobeseqala ukwazi ukuthi ama 78 angama ayimivo engama 78 namashumi ayi 7 nemivo eyi 8.Umfundi akadingi izinto zokubala eziphathekayo ukumsiza ukwazi lokhu. EBangeni 3 abafundi bazodinga amathuba aqhubekayo ukwenza bephindelela ukuhlakaza izinombolo ukuze bazi ubungako benani lezinombolo bese besebenzisa lolulwazi ukuhlakaza izinombolo ma behlanganisa futhi besusa. 397 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 398 KUTHEMU 1 KONYAKA 1.1 Bala ngokujulile izinto • Yenza amaqoqo ezinto EBangeni lesi 3 abafundi baqhubeka nkubala izinto zansuku zonke. Uhla eziphathekayo ezingaba ama 200 lwezinombolo lukhula lufike e-1000 ngokuphela konyaka. Lokhu kusho ukuthi Ukubala izinto kudinga ukuketha ngokucophelela izinsizakufundisa ezizosetshenziswa: kuqagela nokubala Qagela bese ubala ngokwethembeka • Amabhuloki kaDienes ngokwethembeka kufinyelela okungenani • Nikeza ukuqagela • Amakhadi obungako lenani lenombolo izinto ezi- 1000 lezinto. okusondelele kwezinto Ngethemu lokuqala abafundi benza bephindelela bebukeza ukubala izinto Izibalo IBANGA 1-3 Iqhinga lokwenza ezingabhekwa amaqoqo liyakhuthazwa. ngokuzibala. kufinyelela e- 200. Kugxilwa ekwenzeni amaqoqo ezinto. Abafundi kufanele babe nokuqonda ukuthi kungcono, kuyashesha futhi kusebenza kangcono ukubala ngamaqoqo okuyishumi, amashumi amabili, amashumi amahlanu nekhulu nangakunye. Baqala ukubala ngamakhulu, uya phambili ubuye uye emumva ngethemu yokuqala. Ukulekelela ukubala bephimisela, abafundi bangahlela izinto ngamaqoqo ngokuyi 100. Isibonelo Iqoqo ngalinye likhombisa okuyikhulu. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ngalethemu kanye nonyaka wonke abafundi kumele benziwe bazi ukuthi ukubala izinto kuzosiza ezibalweni.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.1 Isibonelo Ukubala izinto Ukubala izinto ngokuzihlakaza zibe ngamaqoqo okuyishumi, 20, 50 ngisho namakhulu azobenza abafundi bahlakaze izinimbolo uma behlanganisa noma besusa. Ukuhlanganisa 362 + 527, abafundi bangayihlakaza inombolo ngobungako bamanani njenge 362 + 527 =(300+60+2)+(500+20+) Abafundi bangabala ngamakhulu ngoba bakwenzile lokho ngesikhathi bebala izinto ngamaqoqo amakhulu. Abafundi bazobala ngamashumi (benzile kanjalo kusukela eBangeni 1) kanye nangakunye. Abafundi kufanele baqonde ukuthi kungani bechitha isikhathi bebala izinto.Ukuxhumana kufanele kwenziwe kucace. Ngalethemu abafundi bangasebenzisa amanhuloki kaDiens ukumela izinombolo noma amabhloki ayishumi. Abafundi basebenzisa kezizinsiza kufunda eBangeni 2 Abafundi kufanele bakwazi ukuqedela lesisitatimende esilandelayo: Inani lamabhuloki ayi 10 a_____________ Abafundi bangasebenzisa amakhadi obungako benani ukukhombisa ubungako bedijithi ngayinye. Izinhlobo zalemisebenzi zigxile ekukhombiseni ukuthi akukona ukubala izinto kuphela. Ngalesosikhathi abafundi ba: • Bayokuqonda ubungako bamadijithi. • Ukuhlakaza nokwakha izinombolo, kanye • Nokufunda izimpawu zezinombolo. 399 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 400 KUTHEMU 1 KONYAKA 1.2 Bala uyephambili Bala uyephambili Yini okwahlukileyo eBangeni 2? ubuye uye emumva ubuye uye emumva Bala uyephambili Abafundi babala nge 100s okokuqala. Bakwenza lokhu kuyofika e 500. Abafundi nge: nge: ubuye uye badinga izinsiza ezizoba isizida seshumi njenge; emumva • Ngezikhawu ezinikiwe • Ngezikhawu • Ubuhlalu bokubala eBangeni 2 ngokukhula ezinikiwe eBangeni kohla lwezinombolo 2 ngokukhula kohla • Amabhuloki kaDiens Izibalo IBANGA 1-3 kusuka kunoma iyiphi lwezinombolo. • Umugqa wezinombolo inombolo oyinikiwe. • 100 kuyofika • Igridi yezinombolo • Ngama 20, 25, 50, okungenani ema 500 100 ukuze kuyofika Ukubala ngokweqa kudina kuxhunyaniswe nethebula lokuphindaphinda. Ukubala okungenani e1000 ngaku 4 kuzosiza abafyndi uma bethi: • Oku 4 oku 1 kwenza oku - 4 • Oku 2 okune kwenza okuyi - 8 • Oku 3 okune kwenza oku - 12 Lokubala weqa kusekela ulwazi lokuphindaphinda futhi kusize abafundi uma beqedela ukulandelana kwezinombolo. 1.3 Khomba, bona bese Khomba, bona bese Yini umehluko eBangeni 2? ufunda izinombolo ufunda izinombolo Amagama Ngalethemu abafundi babona, bafunde bese bebhala izimpawu zezinombolo kufike nezimpawu • Khomba, bona bese • Khomba, bona bese ema 500. Bafunda amagama ezinombolo kufike ema 250 bese bebhala amagama zezinimbolo ufunda zimpawu ufunda zimpawu ezinombolo kufike e 100. zezinombolo 0 - 1000 zezinombolo 0 - 500 Ukufunda nokubhala izimpawu zezinombolo kuyenziwa kuphindelelwe uma: • Bhala izimpawu • Bhala izimpawu • Bebala izinto zezinombolo 0 - 1000 zezinombolo 0 - 500 • Bebala beya phambili babuye baye emumva • Khomba, bona bese • Khomba, bona bese ufunda amagama ufunda amagama • Beqedela ukulandelana kweziombolo; kanye ezinombolo 0-1000 ezinombolo 0-250 • Nokuhlela nokuqhathanisa izinombolo • Bhala amagama • Bhala amagama Kufanele kuqikelelwe ukusho izinombolo ngendlela eyiyo; kufanele kuthiwe 323 ezinombolo 0 kuya e ezinombolo 0 kuya e Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola njenge “amakhulu amathathu, amashumi amabili nantathu”, hhayi njenge “323” -1000 -100 Uma ubhala izinombolo ezihamba ngantathu izinombolo eziphakathi kwe 100 no 110; 200 ne210; 300 ne 310, 400 ne 410, idijithi esesikhundleni sokuyishumi u 0. Abanye abafundi bakuthola kunzima ukubhala lezizimpawu zezinombolo uma benikwe inombolo ngamagama. Isibonelo, Kungabanzima kwabanye abafundi ukubhala “amakhulu amathathu nane” ngezimpawu, bangabhala ama 3004. Amakhadi amele ubungako benani lenombolo angasiza ukusiza abafundi ukuqonda ukuthi zingabekwa kanjani lezizinombolo ngokuyikho. Abafundi kufanele banikwe isikhathi esiningi ukwenza bephindelela bebhala lezizinombolo.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.4 Chaza, qhathanisa Chaza, qhathanisa Yini umahluko eBangeni 2? bese uhlela izinombolo bese uhlela izinombolo Chaza, Ngalethemu abafundi babukeza ukuhlela nokuqhathanisa iznombolo kufike ema 99 kufike ema 999 kufike ema 99 qhathanisa bebe bekwazi ukunika iziathu ukuthi yini inimbolo inkulu kunenye. Vumela abafundi bese uhlela • Chaza bese • Chaza bese ukuthi asebenzise umugqa wezinombolo, igridi yezinombolo noma ulwazi lwabo izinombolo uqathanisa izinombolo uqathanisa izinombolo lokuhlakaza izinombolo zibe amashumi nokuyimivo ukukhombisa ulwazi lwabo. eziphelele kufike eziphelele kufike Uma kuhlelwa izinombolo abafundi kfanele bakwazi ukusho kthi kungani inombolo ema 999 usebenzisa ema 99 usebenzisa inkulu kunenye besebenzisa ubungako bamadijthi ukunika incazelo. okuncane kuna, enkulu okuncane kuna, enkulu Izibonelo kuna, eningi kuna, kuna, eningi kuna, engaphansi kuna engaphansi kuna 39 mcane kuno 59 ngoba: nelingana ne nelingana ne Ngiyazi ukuthi 39= 30 kanye ne 9, kanye 59 = 50 kanye ne 9. Futhi ama 30 • Chaza bese uhlela • Chaza bese uhlela ayizinyanda ezintathu zokuyishumi no 50 uyizinyanda ezinhlanu zokuyishumi. izinombolo eziphelele izinombolo eziphelele Kunezinyanda eziningi zokuyishumi ema 50 kunama 30. kufike ema 999 kusuka kufike ema 99 kusuka Ukusebenza ngezinombolo zesikhundla ikhalenda iyona efanelekile ngoba ivumela kokuncane kakhulu kokuncane kakhulu abafundi bakhulume ngesikhundla senombolo esisekhalendeni. kuya kokukhulu kuya kokukhulu kakhulu, kanye kakhulu, kanye kokukhulu kakhulu kokukhulu kakhulu kuya kokukhulu kuya kokukhulu kakhulu kakhulu Sebenzisa izinombolo Sebenzisa izinombolo ezimele isikhundla ezimele isikhundla ukukhombisa ukukhombisa ukuhleleka, indawo ukuhleleka, indawo noma isikhundla. noma isikhundla. Sebenzisa, funda bese Sebenzisa, funda bese ubhala izinombolo ubhala izinombolo ezimele izikhundla ezimele izikhundla kuyofika kuma 31 kuyofika kuma 31 401 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 402 KUTHEMU 1 KONYAKA 1.5 Bona ubungako Bona ubungako Yini umahluko kuBanga 2? bezinombolo ezihamba bezinombolo ezihamba Ubungako Ngalethemu kubukezwa ulwazi lobungako benani lenombolo kusuka eBangeni 2. benani ngantathu kufike kuma ngantathu kufike kuma Abafundi baqhubeka nokwenza imisebenzi efana neyenziwa eBangeni 2 ngethemu lenombolo 999 99 4 • Bona ukuthi idijithi • Bona ukuthi idijithi Ulwazi nokusebenzisa amagama obungako benani lenombolo: ngayinye imeleni ngayinye imeleni Izibalo IBANGA 1-3 Sebenzisa, funda bese uqala ukubhala: • Hlakaza izinombolo • Hlakaza izinombolo ezihamba ngantathu ezihamba ngantathu Ngakunye noma ngokwamayunithi, ngamashumi, amadijithi, inombolo ehamba kufike ema 999 zibe kufike ema 99 zibe yodwa, inombolo ehamba ngambili....ubungako benani lenombolo... izinombolo eziphinda izinombolo eziphinda Hlakaza izinombolo ezihamba ngambili ibe ngokuphinda ngamashumi ne- ngama 100, eziphinda ngamashumi nangemi- mivo. ngamashumi nangemi- vo. vo. Abafundi bangahlakaza izinombolo zibe: • Khomba bese usho • Khomba bese usho ubungako bedijithi • Ubungako bamashumi nobungako bemivo isibonelo: 73=70+3 (amakhadi amele ubungako bedijithi ngayinye. ubungako benani ayasiza ukwenza loku) ngayinye. • Ukuphindaphinda ngamashumi kanye nemivo Isib. 73= 7 amashumi+ 3 imivo Ukwakhiwa kwezinombolo ezihamba ngambili kusukela kwizingxenye zobun- gako benani lenombolo Isibonelo: Bhala inombolo: a) 6 amashumi noku 3 okukodwa ___________________ b) 2 amashumi noku 5 okukodwa ___________________ c) 12 amashumi noku 8 okukodwa ___________________ d) 18 amashumi noku 4 okukodwa ___________________ Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.5 Sebenzisa izinsiza kufunda ukukhombisa ukuhlukaniseka kwezinombolo: Ubungako • Abhakhasi benani lenombolo a) Bonisa 4 amashumi kanye 5 okukodwa ukusebenzisa i- abhakhasi b) Bonisa 7 amashumi kanye 6 okukodwa ukusebenzisa i- abhakhasi • Amakhadi obungako benani lenombolo Abafundi basebenzisa amakhadi obungako benani lenombolo ukukhombisa izingxenye zenombolo Ezibonelo: Lokhu okulandelayo izinhlobo zemibuzo engabuzwa • Yisho ukuthi idijithi ayi-8 ku 28 limeleni? Elika 2? • Yisho ukuthi iyiphi inombolo elingana noma efana no: a) 6 amashumi b) Amashumi ayisishiyagalolunye nokuthathu okuyimivo c) Amashumi amahlanu kanye nokuyisishiyagalolunye okuyimivo. 403 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 404 KUTHEMU 1 KONYAKA Xazulula izinkinga ezisesimweni esijwayelekile 1.6 Sebenzisa lamasu Sebenzisa lamasu Yini umahluko kubanga 2? alandelayo ukuxazulula alandelayo ukuxazulula Amasu Abafundi balindeleke ukuxazulula izinkinga zezibalo zamagama besebenzisa izinkinga bese uchaza izinkinga okuxazulula lamasu alandelayo: isixazululo izinkinga • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza izinombolo • Ukwakha nokuhlakaza izinombolo Izibalo IBANGA 1-3 izinombolo • Ukuphinda kabili nokuhlukanisa kabili kulingane • Ukuphinda kabili • Ukuphindakabili nokuhlukanisa kabili • Imigqa yezinombolo nokuhlukanisa kabili kulingane Ukudweba izinto ezifika kuma 99 ngakodwa akubi namphumela futhi kufanele kulingane kungakhuthazwa. Akukhuthazwe ukufakwa kwezimpawu zezinombolo uma • Imigqa yezinombolo • Imigqa yezinombolo bebhala, kufakwa nezithombe. Abafundi bangakhuthazwa ukubhala imisho yezinombolo. • Ukusondezela emashumini Vumela abafundi ukukhetha isu abazokhululeka ukulisebenzisa. Uhlu lwezinombolo kanye nezinhlobo zezinkinga luzonika isu elizosetshenziswa. Kodwa-ke uma abafundi besebenzisa amasu angafanelekile badinga ukwesekelwa ukusebenzisa izidlela okuyizo. Ukwakha nokuhlakaza izinombolo Leli elinye lamasu asemqoka emabangeni aphansi. Ukusebenzisa lelisu kuvumela abafundi ukuhlakaza kanye nokuhlanganisa izinombolo okusiza ukwenza izibalo kubelula. Bazolisebenzisa lelisu nasemabangeni aphakathi. Ukuphinda kabili nokuhlukanisa kulingane Lelisu libucayi futhi lidinga ulwazi oluqinile lwezinombolo. Abafundi abakwazi ukuqoka lelisu basebenza ngokukhululeka emaqhingeni abawasebenzisayo. Ukwazi ukuphinda kabili kuzovumela abafundi ukusebenzisa iqhinga lokusondezela ekuphindeni kabili. Isibonelo: Izinkinga zezibalo zamagama: Ngelanga elilodwa emtholampilo izingane ezingama 45 zagomela umkhuhlane. Ngosuku olulandelayo kwagonywa ezingama 46. Zingaki izingane ezagonywa zizonke? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Lenkinga ingaxazululwa ngokusebenzisa ukuphinda kabili. Umfundi angaphinda kabili ama 45 uhlanganisa noku 1 noma aphinde kabili ama 46 asuse oku 1.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.6 Umugqa wezinombolo Amasu Ukusebenzisa umugqa wezinombolo ukubasiza ukwenza izibalo kuzonika abafundi okuxazulula indlela yokubhala imicabango yabo nokukwazi ukuyilandela. Kubuye kuvumele izinkinga abafundi ukuba nomfanekiso obhaliwe abangawusebenzisa ukuchaza indlela abaxazulule ngayo inkinga. Abafundi babelokhu besebenzisa imigqa yezinombolo kusuka eBangeni 1. Abafundi kufanele bakwazi ukwakha umugqa wezinombolo ongenalutho abazobhala inombolo abaqala kuyo bese bekwazi ukubona kuthi basuka kanjani kwenye eya kwenye. Isibonelo esikhombisa ukuthi abafundi bangawusebenzisa kanjani umugqa wezinombolo: Abafundi abangama 23 bathathe uhambo namuhla. Kusenabafundi abangama 63 esikoleni. Bebebangaki abafundi ekuqaleni?   +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 Xazulula izinkinga Xazulula izinkinga Izibonelo zezinkinga zezibalo ezingenziwa kulethemu zezibalo zamagama zezibalo zamagama Ukuhlanganisa esimweni esijwayelekile esimweni esijwayelekile Ngalethemu, abafundi babukeza umsebenzi owenziwe eBangeni 2. Bheka nokususa bese uchaza bese uchaza amanothi ezinhlobo zokuxazulula izinkinga eBangeni 2, Ingxenye 2. isixazululo sakho isixazululo sakho kufaka ukuhlanganisa, kufaka ukuhlanganisa, ukususa okuholela ukususa okuholela ezimpendulweni kufike ezimpendulweni kufike kuma 999. kuma 99. 405 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 406 KUTHEMU 1 KONYAKA 1.8 Xazulula izinkinga Xazulula izinkinga Izibonelo zezinkinga ezingenziwa kulethemu. zezibalo zamagama zezibalo ezezinombolo Ukuhlanganisa ezisesimweni ezisesimweni • Umakhi udinga ukubeka imigqa eyi 6 yezitini, umugqa ngamunye unezitini eziyi 8. okuphindayo esijwayelekile bese esijwayelekile bese Zingaki izitini azozidinga? okuholela eku- uchaza izixazululo uchaza izixazululo phindaphindeni • UNosipho unamaphakethe ama 4 amaswidi. Iphakethe ngalinye linamaswidi ayi usebenzisa usebenzisa 6. Mangaki amaswidi anawo esewonke? ukuphindaphinda ukuphindaphinda Izibalo IBANGA 1-3 okunezimpendulo okunezimpendulo • Umama ufuna ukubhaka amakhekhe ayi 12. Uma ikhekhe ngalinye lidinga kufinyelele ema 99 kufinyelele ema 50 amaqanda ama 2, mangaki amaqanda umama okumele awathenge? • Uma umfundi ngamunye efunda izincwadi eziyi 3 enyangeni kaJulayi, zingaki izincwadi ezingafundwa ikilasi lafundi abangama 20? Uhlobo lwenkinga: Ukuhleleka/ Array • Ingadi yemifino inemigqa eyi 12 yezitshalo.Umugqa ngamunye unezitshalo eziyi 7. Zingaki izitshalo ezisengadini zizonke? • Ingadi yemifino inemigqa eyi 12 yezitshalo. Umugqa ngamunye unenani lezithombo ezilinganayo. Uma ngabe kunesamba esingama 48 sezitshalo, zingaki izitshalo kumugqa ngamunye? • Ingadi yemifino inezitshalo ezingama 48 ezitshalwe emigqeni. Kunezitshalo eziyi 7 umugqa ngamunye. Minga imigqa ekhona? Ukusebenzisa ukuphinda kabili ukuxazulula izinkinga • UThemba uneminyaka eyi 8. • Umfowabo omdala mudala ngokuphindwe kabili kunoThemba. • Ubaba wakhe mdala ngobudala ngokuphindwe kane kunoThemba. • Umkhulu wakhe mdala ngokuphindwe kabili kunobaba kaThemba. • Mingakhi iminyaka yabo ngamunye? • Incwadi ka Sipho inamakhasi angama 48 ubude. Yena usekhasini lama 26; Ingabe usefunde ngaphezulu kukahhafu wencwadi? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola EBangeni 3 abafundi balindeleke ukubona izibalo zamagama eziphindaphindayo. Abafundi kufanele bakhuthazwe ukusebenzisa izinombolo nezithombe kunokusebenzisa izinsiza kufunda noma izithombe ngokwabo.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.9 Xazulula bese Xazulula bese Ngalethemu uphawu lokuhlukanisa luyethulwa. Kusemqoka ukuthi abafundi uchaza izixazululo uchaza izixazululo bayaluqonda ulwazi lokuhlukania ngaphambi kokuthula uphawu: Ukwenza ezinkingeni ezenziwayo ezinkingeni ezenziwayo amaqoqo nokuh- ezifaka ukwabelana ezifaka ukwabelana Izinkinga ezifaka ukwabelana zivamisa ukuba: lukaniselana ngokulingana nokwenza ngokulingana nokwenza okuholela ekuh- • Ukwabelana ngokulingana: kanye amaqoqo kufike ema amaqoqo kufike ema lukaniseni 200 okunezimpendulo 50 okunezimpendulo • Ngamunye uthola okungakanani ezingafaka izinsalela. ezingafaka izinsalela. Izinkinga ezifaka kwabelana zivamise ukufaka: • Mangakhi amaqoqo angenziwa? Izibonelo zezinkinga ezingenziwa ngalethemu • Uma abafundi abangama 44 nothisha aba 3 beya ekhonsathini, ibhasi ifaka abayi 11, ibhasi lizothutha kangaki ngaphambi kokuba bonke bafike ekhonsathini? • UMongezi upakisha izinto zokubala ezingama 47 emgqeni eyi 9. Zingaki emgqeni ngamunye? • Amantombazane angama 35 afuna ukudlala ibhola, mangakhi amaqembu amantombazane ayi 7 azobakhona? • Qagela kuqala: • Azoba maningi noma mancane kune 10? • Azoba maningi noma mancane kune 20? • UJabu uthenga amaswidi angama 44. Uwahlukanisa ngokulinganayo emaphaketheni ama 4 ukuwathengisa. Mangaki amaswidi ephaketheni ngalinye? • UJabu uthenga amaswidi angama 48. Ufuna ukuwahlukanisa abe yisithupha esikhwameni ngasinye. Udinga izikhwama ezingaki? 407 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 408 KUTHEMU 1 KONYAKA 1.10 Xazulula bese uchaza Xazulula bese uchaza Ebangeni 2 abafundi bethulelwa amaqhezu: kanye izixazululo ezinkingeni izixazululo ezinkingeni Amaqhezu • behlukaniselana, benza amaqoqo ngokulingana, ezenziwayo ezifaka ezenziwayo ezifaka ukwabelana ngokulinga- ukwabelana ngokulinga- • benikeza amagama amaqhezu na okuholela ezixazulul- na okuholela ezixazulul- • bekhomba amaqhezu ezimweni ezahlukene; weni ezifaka amaqhezu weni ezifaka amaqhezu okukodwa okuphelele okukodwa okuphelele • bebhala amagama amaqhezu njengoku 1 kokuthathu 3, noku 1 kokuhlanu Izibalo IBANGA 1-3 kanye nokubgaphezu kanye nokubgaphezu kokukodwa kokuphelele. kokukodwa kokuphelele. • bethole amaqhezu ezinto eziphelele; kanye 1 1 3 2 1 1 3 2 • namaqhezu amaqoqo ezinto. Isib. 2 , 4 , 4 , 5 njll Isib. 2 , 4 , 4 , 5 njll Yini okwehlukile eBangeni 2? Ngalethemu, abafundi bazoqhubeka nokusebenza ngamaqhezu awokukodwa kokuphelele afana noku 1 kahhafu, 1 yokuthathu, 1 yekota, 1 yokuhlanu. Abafundi bethulwa nsemaqhezwini angaphezu kokukodwa kokuphelele. Isib. 3 amakota noma 2 kokuyhathu. Abafundi abalindelekile ukusebenzisa ulimi olufana nokuthi okukodwa kokuphelele noluthi okungaphezu kokukodwa kokuphelele. Izibonelo zezinkinga ezingenziwa kulethemu • Ukwabelana okuholela emaqhezwini. Hlukanisela abangani aba 3 oshokoleti abayi 8ukuze bathole oshokoleti abalinga- nayo kungasali lutho. • Iqhezu leqoqo a) Thola 1 kota lamaswidi ayi 16 b) Amaswidi ayi 8 ayiqhezu lini lamaswidi angama 24? c) Ugogo unikeza uKiki iR12, uKiki ufuna ukonga okukodwa kokuthathu. Uzokonga malini? d) Loluhlobo wenkinga kufanele lwethulwe emva kokuba abafundi sebexazulule izinkinga ezine noma ezinhlanu zokwabelana okuholela emaqhezwini futhi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola sebazi amagama ezingxenye zamaqhezu

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.10 Ukubhala amaqhezu Amaqhezu Abafundi abalindelekile ukubhala uphawu lweqhezu. Abafundi sebefundile ukule- bula izingxenye zeqhezu njengo 1kokuhlanu, 3 amakota, noma 3 kokuyisithupha. Lokhu kubasiza kuqala ukuqonda ukuthi amagama amaqhezu achaza ukuthi zingaki izingxenye okuphelele okuhlukaniswe kwayizo, isib. ohhafu, okuthathu, amakota njll. Bese okwesibili babone ukuthi zingaki izingxenye ezisetshenzisiwe, isib. 2 kokuthathu. Ukubeka izinkinga zamaqhezu ngamagama • Abafundi kufanele badwebe izimpendulo zabo ukukhombisa ukuthi bayayiqonda inkinga. • Lindela ukuthi abanye abafundi bangadwea amaqhezu ngokuyikho kodwa ban- gasho igama laleloqhezu. Siza labafundi ukusho amaqhezu ngokuyikho.(bheka amanothi ahambisana nokushiwo ngamaqhezu pansi kwesimo esikhululekile sokwenza izibalo) • Abafundi kufanele basho izingxenye ezihlukanisiwe ngokuzibhala njengoku 2 kokuthathu. 1.11 • Bona bese ukhomba • Bona bese ukhomba Ngalethemu abafundi baqhubeka nokuxazulula izinkinga zezimali. imali yaseNingizimu imali yaseNingizimu Imali Izibonelo: Afrika ewuhlweza Afrika ewuhlweza nengamaphepha. nengamaphepha. • Abafundi beBanga lesi 3 badinga R759 ukuze baye ekhempini yekilasi labo. Baqoqe imali engama R250, badinga malini ngaphezulu? • Xazulula izinkinga • Xazulula izinkinga zemali ezifaka isamba zemali ezifaka isamba • Bhala 325c njenga marandi namasenti kanye noshintshi kanye noshintshi • Zingaki izindlela ezahlukene ongenza ngazo ama R400 usebenzisa imali ngamarandi noma ngamarandi noma yamaphepha kuphela? Uzokwazi kanjani ukuthi unazo zonke izixazululo? ngamasenti ngamasenti • UThami unohlamvu olungama 50c nezinhlamvu ezine zama 20c. Uswidi ubiza • Guqula phakathi R1, 20. Imalini ushintshi okufanele awuthole? kwarandi namasenti. • Uma ingubo yesikole ibiza R150, zingaba yimalini ezimbili? Izinkinga zokuthenga nokuthengisa Isibonelo • Ugogo kaXolo wamnikeza ama R5. Imaphi amaswidi amathathu angawuthenga? Uswidi wezinti R2,70; uguduza R1,80, ushampiyoni R1,40, isimutisi R2,20 namathofi R1,20 • UThabo uthenge izincwadi ezintathu ezibiza ama R80 iyinye, uzothola ushintshi ongakanani uma ekhokha ngama R300? 409 • Amaphakethe amaminti ama 5 abiza 44c lilinye. Ubaba uNkosi ufuna amaminti angama 88. Mangaki amaphakethe okufanele awathenge? Uzokhokha malini? Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 410 KUTHEMU 1 KONYAKA Ukwenza izibalo esimweni esikhululekile 1.12 Sebenzisa lamasu Sebenzisa lamasu Lamasu azosetshenziswa kuko kokubili ukuxazulula izinkinga kanye nokwenza alandelayo uma wenza alandelayo uma wenza izibalo ezimwe ezikhululekile Amasu izibalo: izibalo: (izindlela noma Ukwakha nokuhlakaza izinombolo amaqhinga) • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza Leli elinye lamasu asemqoka emabangeni aphansi. Ukusebenzisa lelisu kuvumela izinombolo izinombolo Izibalo IBANGA 1-3 abafundi ukuhlakaza kanye nokuhlanganisa izinombolo okusiza ukwenza izibalo • Ukuphinda • Ukuphinda kubelula. Bazolisebenzisa lelisu nasemabangeni aphakathi. Kusemqoka ukuthi nokuhlukanisa kabili nokuhlukanisa kabili abafundi basebenzise ulwazi abanalo lapho behlakaza izinombolo. Isib. • Imigqa yezinombolo • Imigqa yezinombolo • Ukuhlakaza inombolo usebenzisa ubungako benani lenombolo; • Sondezela emashumini • Ukuhlakaza inombolo usebenzisa ukubala ngamashumi; noku • Hlakaza izinombolo kwenziwa izinombolo ezihamba ngambili Imigqa yezinombolo Abafundi bazoqhubeka nokusebenzisa bese bakha eyabo imigqa yezinombolo ukuze benze izibalo. Kunokwenzeka ukuthi imigqa yezinombolo isetshenziswe kakhulu ekwenzeni izibalo zokuhlanganisa nokususa. Ukuhlanganisa nokususa Abafundi kumele bazakhele eyabo imgqa yezinombolo bese behlakaza izinombolo zibe izingxenyana okungasetshenzwa ngazo. Isibonelo: 45 + 27 Umugqa wezinombolo kufanele uqale ema 45 bese abafundi bakha kweqa okubili kwama 10 kanye nokukodwa okukhombisa okuyi 7. Ukuphindaphinda Imigqa yezinombolo kufanele iqhubeke nokusetshenziswa ukweseka ukuhlanganisa okuphinday. Ukweqa okulinganayo kubhalwa emigqeni yezinombolo nemisho esekayo ingabhalwa nayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.13 • Hlanganisa kuyofika • Hlanganisa kuyofika Ngalethemu abafundi benza ngokuphindelela bese bephetha umsebenzi owenziwe kuma 999 kuma 99 eBangeni 2. Ukuhlanganisa nokususa • Susa kusukela 999 • Susa kusukela 99 Uma ngabe abafundi: • Sebenzisa izimpawu • Sebenzisa izimpawu • Besebenza kuphela ngezinto zokubala ezihamba ngazinye; ezifanele ezifanele (+, –, =, ) • Bedweba imifanekiso yokunga 1 kuphela; noku (+, –, =, ) • Yenza uphindelela • Bala konke ngaku 1 • Yenza uphindelela amabhondi ezinombolo amabhondi ezinombolo kuyofika kuma 20 Uma besebenza ngezamba ezingaphezu kwama 30, kwehlisa isivinini sabo kodwa kuyofika kuma 30 futhi kwandisa amathuba okwenza amaphutha uma benza izibalo. Lokhu kwenza kubaluleke kubona ukuthuthukisa amaqhinga amaningi. Ukwakha nokuhlakaza izinombolo kuba elinye lamaqhinga abalulekile abafundi abazowase- benzisa kulethemu. Izindlela ezingasetshenziswa ukukhombisa ukwenza izibalo Ukuhlakaza inombolo ibe izingxenye ezincane kwenza isibalo kubelula Abafundi bangahlakaza inombolo ngezindlela ezizobalula kubona. Lokhu kusho ukuthi bazokwenza ngezindlela ezahlukene. Sebenzisa ulwazi lobungako benani lenombolo ukuhlakaza izinombolo zibe ngamashumi nemivo. • Ukuhlanganisa izinombolo ezihamba ngambili ngokuzihlakaza zombili 43 + 36 =  43 + 36 = (40 + 3) + (30 + 6) = (40 + 30) + (3 + 6) = 70 + 9 = 79 • Ukuhlanganisa ngokuhlakaza eyodwa inombolo 43 + 36 =  43 + (30 + 6) 43 + 30 → 73 + 6 = 79 411 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 412 KUTHEMU 1 KONYAKA 1.13 • Ukuhlakaza kube amaqoqo okuyishumi Ukuhlanganisa 43 + 36 =  nokususa 43 + (10 + 10 + 10 + 6) 43 + 10→ 53 + 10→ 63 + 10→ 73 + 6 = 79 Ukususa Izibalo IBANGA 1-3 • Ukususa ngokuhlakaza zombili izinombolo 87– 56 =  87– 56 = (80 + 7) – (50 + 6) = (80– 50) + (7– 6) = 30 + 1 = 31 • Ukususa ngokuhlakaza eyodwa inombolo 87–56 =  87– (50 + 6) 87– 50 → 37 – 6 = 1 Lindela ukuthi abanye abafundi bangahlakaza inombolo ngezindlela ezahlukene kwenza kubelula kubo ukubala: • Ukuhlakaza inombolo ibe izinomblo eziphinda nge 10. 87– 56 =  87– (20 + 20 + 10 + 6) 87– 20 → 67–20 → 47– 10 → 37– 6 → 31 Ukusebenzisa ulwazi olufundile njengesu lokubala • Sebenzisa ukuhlukaniselana ukuhlakaza inombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 69 + 12 69 + (6 + 6) 69 + 6 → 75 + 6 = 81

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.13 • Ukubala uqhubeka nokubala uya emumva Ukuhlanganisa 78 – 69 =  nokususa Ukubala ngokukodwa kusuka ema 69 kuyiqhinga elifanele ngoba izinombolo zison- delene. • Ukukhomba izinombolo ezisondezela ekuphindeni kabili 34 + 35 chaza ukuthi ama 34 aphinde kabili uhlanganisa noku 1noma ama 35 aphinde kabili ususe oku 1 34 + 34 + 1 Abafundi bangabhala phansi amaqhinga abo besebenzisa imicibisholo ukulandela indlela abenze ngayo izibalo. 34 + (30 + 4) + 1 34 + 30 → 64 + 4 → 68 + 1 → 69 • Guqula inombolo ibe ukuphinda ngamashumi ususe noma wengeze okukodwa Bala uqhubeka noma wehle usondezela emashumini eliseduze 58 + 19 =  Lapha abafundi kufanele bazitshele ukuthi kunezindlela ezimbili abangakhetha kuzo. Guqula ama 58 noma i 19 usondelane ema 10. Bazozikhethela ngokwabo Isibalo singabhalwa kanje: 58 + 19 = 58 + 20 – 1 58 + 20 → 78 – 1 = 77 Abanye abafundi bangahlakaza ama 20 abe amaqoqo ama 2 okungama 10 uku- bala ngokuyikho. Ukubala ngokuphindelela amabhondi ama 20 Amabhondi kufinyelela kuma 20 kumele kusetshenziswa imifanekiso eyahlukene esekayo. Thuthukisa bese wenza ngokuphindelela amakhono okuhlanganisa nokususa Abafundi kufanele benze ngokuphindelela izindlela ezithize zamakhono okuhlan- ganisa nokususa • Hlanganisa noma susa izinombolo ezihamba ngazinye kwezihamba ngazimbili 413 ngaphandle kokuthinta amashumi: Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 414 KUTHEMU 1 KONYAKA 1.13 Izibonelo: Ukuhlanganisa a) 65 + 4 nokususa b) 89 – 3 • Hlanganisa inombolo ehamba ngayinye kwinombolo ephinda ngama 10 isibonelo Izibalo IBANGA 1-3 a) 70 + 5 b) 90 + 3 • Susa inombolo ehamba ngayinye kwinombolo ephinda ngama 10 isibonelo a) 80 – 6 b) 50 – 3 • Hlanganisa noma susa okuyi 10 kunoma iziphi izinombolo ezihamba ngambili Isibonelo a) 56 + 10 b) 68 + 10 c) 79 – 10 d) 57 – 10 • Hlanganisa noma ususe izinombolo ezihamba ngambili eziphinda ngama 10 ungathinti ama 100 a) 40 + 30 b) 80 – 50 Ukubheka imiphumela yezibalo ezenziwe. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukubheka ubuqiniso bezixazululo Abafundi kufanele bafundiswe ukubheka ubuqiniso bezixazululo Enye indlela yokwenza lokhu ukuqagela izimpendulo ngaphambi kokubala. Uma uhlanganisa izinombolo ezimbili ezisondelene, isib. 45 no 46, abafundi bangas- ebenzisa indlela yokuphinda kabili uma beqagela izimpendulo.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.13 Ukuhlola izixazululo Ukuhlanganisa Abafundi kufanele bazi ukuthi banga: nokususa • Bheka isibalo sokuhlanganisa ngokususa. Isibonelo: Uma ama 36 + 18 = 54; ngakho ke ama 54– 18 = 36 • Bheka isibalo sokususa ngokuhlanganisa Isibonelo: 84– 48 = 36, ngakho ke 36 + 48 = 84 Ukusebenzisa izindlela zokuphambanisa uphawu lokuhlanganisa nolokususa isona sizathu esenza ukuthi kufundiswe kanye kanye. 1.14 • Phindaphinda • Phindaphinda EBangeni 2 abafundi baphindaphinde izinombolo 1 kuya e 10 ngo1, 2, 5, 3 kanye izinombolo kusuka izinombolo kusuka noku 4 kuze kufike ema 50. Bethulwa kuphawu base belusebenzisa emishweni Ukuhlanganisa 1 kuya e 10 ngo 1 kuya e 10 ngo yezinombolo. okuphindayo 2,3,4,5,10 kuze kufike 2,5,3,4,10 okuholela eku- Abafundi eBangeni lesi 3 kufanele bqhubeke benze bephindelela futhi basebenzise e 99 phindaphindeni • Sebenzisa izimpawu ulimi lokuphindaphinda kwizimo lapho bezosebenzisa izinto eziphathekayo; phinda • Sebenzisa izimpawu (x, =, ) kabili, phindaphinda, phindaphinda ngo, okuningi kwe, amaqoqooku, izikhathi, (x, =, ) okuphindwe kathathu. Ulimi kufanele lusetshenziswe uma kwenziwa izibalo zokuphindaphinda. Ngalethemu abafundi bazophinda phinda ngokuthathu okokuqala. Abafundi abangena abangeni 3 kufanele bakwazi ukwethula ukuhlanganisa okuphindayo besebenzisa uphawu lokuphindaphinda. Abafundi bayakwazi ukuchaza ukuphindaphinda ngezindlela ezahlukene. Bayakuqonda ukuthi amaqoqo ama 3 okuwuyisi 6 angabhalwa kanje 6 + 6 + 6. Kukhona nokuqonda ukuthi oku 3 kuphindwa ka 6 kungabhalwa kanje 3 x 6. Lolu ulwazi luyaqhubeka nokuthuthukiswa eBangeni 3. Abafundi bazoqhubeka nokusebenzisa izinsiza kufunda eziphathekayo, kanye nemigqa yezinombolo ukuqonda nokwethula ukuphindaphinda. Ukusukela eBangeni lesi 3 abafundi kufanele bazi ukuthi ukuphindaphinda kungenziwa noma ingayiphi indlela. 415 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 416 KUTHEMU 1 KONYAKA 1.14 Isibonelo: Ukuhlanganisa Abafundi kufanele bakwazi ukuqonda nokubhala lokhu okulandelayo: okuphindayo 3 x 10 =  10 x 3 =  okuholela eku- phindaphindeni 30 = 10 x  30 = 3 x  Lezizitatimendi eziphezulu kufanele zisekelwe ngokusebenzisa imifanekiso ej- Izibalo IBANGA 1-3 wayelekile evumela abafundi ukuba babone lokhu 3 x 10 kanye 10 x 3 kunikeza umphumela ofanayo. Isibonelo:   and no Ekupheleni kwethemu abafundi kufanele bakwazi ukuqala ukuqonda ukuthi uku- phindaphinda kungenziwa noma ikanjani. Lolulwazi kufanele lwenziwe ngokuphin- delela unya wonke Abafundi bangasebenzisa imidwebo ekhombisa ukuxhumana kwezinto ukubhala izindlela zokuphindaphinda Isibonelo: Inombolo osebenza   Input ngayo Output umphumela 1 Rule umthetho 3 5 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 7 ×  !     9

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.15 Hlukanisa izinombolo Hlukanisa izinombolo Uphawu lokuhlukanisa lwethulwa eBangeni 3. Eminyaka emibili ulwazi lkuhlukanisa ufike ema 99 ngo 2, 3, 4, ufike ema 50 ngo 2, 5, 10 nokwenza amaqoqo lwenziwe, manje sekuyisikhathi sokuxhumanisa lolu lwazi. ukuhlukanisa 5, 10 Uphawu lokuhlukanisa lungethulwa uma abafundi benza izinkinga zezibalo zamag- Sebenzisa izimpawu ama. Ukwethulwa kophawu kungelekelelwa nangemifanekiso engenzansi.Kubalule- Sebenzisa izimpawu ezifanele (÷,=, ) kile ukusebenzisa imifanekiso abayijwayele. ezifanele (÷,=, ) Isibonelo: ngaku 12 grouped 12   kuqoqwe into 3s kunika 4 give 3 amaqoqo 4 groups 12 kuqoqwe 12 grouped ngakuinto kunika 4 4s amaqoqo gives 33groups     12 12 shared uhlukaniswabetween ka 43gives unika3 4 eachngakunye 12 12 uhlukaniswa between shared ka 3 3 unika gives44 each ngakunye !  ×  !   =  !"   !  ×  !   =  !"   12 ÷ 3 = 4 Kusho ukuthi: 12 ehlukaniswe ka 3 kunikeza 4 amaqoqo, kanye 12 ehlu- kaniswe  ka 3 kunikeza 4 ngakunye.   417 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 418 KUTHEMU 1 KONYAKA 1.16 Ulwazi lwezinombolo: Ulwazi lwezinombolo: Amaqhinga okwenza izibalo, ulwazi lwezibalo, nolwazi nemigomo yezinombolo uhla 999 uhla 200 luthuhukiswa ngokuxazulula izinkinga nokwenza izibalo. Lokhu kungenziwa Izibalo zekhanda. ngesikhathi sezibalo zekhanda. Lokhu kusiza abafundi ukuba bazejwayele futhi • Hlela iqoqo • Hlela iqoqo bakwazi ukuzisebenzisa kalula uma benza izibalo futhi bexazulula izinkinga lezinombolo lezinombolo esimweni esejwayelekile. ezikhethiwe. ezikhethiwe. Ngalethemu abafunda bayaqhubeka nokuthuthukisa amakhono okusebenza • Qhathanisa izinombolo • Qhathanisa izinombolo Izibalo IBANGA 1-3 ngokukhululekile ngezinombolo. Amaqhinga okubala ngekhanda abafundi kufike ema 999 bese kufike ema 200 bese abathuthuka kuwo azobasiza ngokwenza izibalo ezibhalwayo futhi kuzobasiza usho usho bakwazi ukuqagela. ukuthi iyiphi ukuthi iyiphi Izibonelo zemibuzo engabuzwa: engaphezulu noma engaphezulu noma ngaphansi ngoku ngaphansi ngoku Ulwazi lwezinombolo: 1,2,3,4,5, kanye 10 1,2,3,4,5, kanye 10 Amagama nezimpawu zezinombolo Ukukhumbula Ukukhumbula Phakamisa ikhadi noma ubhale phansi igamal lenombolo. Khetha umfundi abhale okusheshayo okusheshayo uphawu aluqondanise negama • Izindlela • Izindlela Okungaphezulu noma okungaphansi zokuhlanganisa zokuhlanganisa nokususa kufike ema nokususa kufike ema Yini oku: 20 20 • Oku 1 ngaphansi kwama 200 • Hlanganisa noma • Hlanganisa noma • Oku 1 ngaphezulu kwe 199 ususe izinombolo ususe izinombolo eziphinda nge 10 eziphinda nge 10 • Oku 2 ngaphezulu kwe 102 kusuka k u 0 kuya e kusuka ku 0 kuya e 100. 100. • Oku 2 ngaphansi kwe 105 • Izindlela • Oku 3 ngaphezulu kwa 77 zokuphindaphinda • Oku 3 ngaphansi kwa 51 kanye nokuhlukanisa kwe: • Oku 4 ngaphezulu kwa 68 • Ithebla lika 2 kufike • Oku 4 ngaphansi kwe 167 koku 2 x 10 • Oku 5 ngaphezulu kwe 169 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ithebula leshumi kufike • Oku 5 ngaphansi kwe185 e 10 x10 • Okuyi 10 ngaphezulu kwa 90 • Okuyi 10 ngaphansi kwe 160

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.16 Amaqhinga okwenza Amaqhinga okwenza Yiluphi uhlamvu lwesi 5 konobumbani? izibalo izibalo Izibalo zekhanda. Iyiphi inyanga yesi 9 onyakeni? Sebenzisa lamaqhinga Sebenzisa lamaqhinga Ukuhlela nokuqhathanisa alandelayo ukwenza alandelayo ukwenza izibalo: izibalo: Ikuphi okuningi: 21 noma 171? • Beka inombolo enkulu • Beka inombolo enkulu Nginike inombolo ephakathi kuka 154 no 159 kuqala ukuze ubale kuqala ukuze ubale Ukukhumbula ngokushesha: uqhubeke noma uye uqhubeke noma uye emumva emumva Izindlela zokuhlanganisa nokususa • Umugqa wezinombolo • Umugqa wezinombolo Azi ngekhanda ukuhlanganisa nokususa amabhondi ezinombolo kufike ema 20 • Ukuphinda nokuhlu- • Ukuphinda nokuhlu- Isibonelo kanisa kabili kanisa kabili a) __________+  = 20 b) __________+  = 16 • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza Izindlela zokuhlanganisa nokususa zazo zonke izinombolo kuyofka kuhlanganisa izinombolo izinombolo nama 20 Izibonelo • Sebenzisa ubudlel- • Sebenzisa ubudlel- wano phakathi kokuh- wano phakathi kokuh- a) 1 + 11 = 12 b) 18 – 4 = 14 langanisa nokususa langanisa nokususa c) 11 + 1 = 12 d) 18 – 14 = 4 • Sebenzisa ubudle- e) 2 + 10 = 12 f) 18 – 5 = 13 lwano obuphakathi g) 10 + 2 = 12 h) 18 – 13 = 5 kokuphindaphinda nokuhlukanisa. i) 3 + 9 = 12 j) 18 – 6 = 12 k) 9 + 3 = 12 l) 18 – 12 = 6 Khumbula ngokushesha kuhlanganisa okuphinda kabili ufike ema 20. Lkhu kufanele kufake izindlela zokususa ezifanele: Izibonelo: a) 1+1=2 b) 6 + 6 = 12 c) 2+2=4 d) 7 + 7 = 14 e) 3+3=6 f) 8 + 8 = 16 g) 4+4=8 h) 9 + 9 = 18 i) 5 + 5 = 10 j) 10 + 10 = 20 419 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 420 KUTHEMU 1 KONYAKA 1.16 Izibonelo: Izibalo zekhanda. Ngibonise inombolo yokuhlanganisa... ukwenza am 20. (ukubhala phansi noma usebenzise amakhadi obungako benani lenombolo). a) 8 b) 2 Izibalo IBANGA 1-3 c) 9 d) 15 e) 3 Izibonelo: Ngibonise inombolo esalayo uma... isuswa ema 20 (ukubhala phansi noma useben- zise amakhadi obungako benani lenombolo). a) 5 b) 18 c) 0 d) 14 e) 7 Hlanganisa noma susa izinombolo eziphindaphinda nge 10 ukusuka e 100 Izibonelo: a) Yisho ukuthi mangakhi amagxathu angathathwa kumugqa wezinombolo ubala ngama 10 usuka kuma 30 kufika e 100 noma kusuka e 100 kufika ema 50 b) Thola amakhadi ahambisanayo kwenza i 100 c) Faka izinombolo emabhokisini ukwenza i 100  + 70 = 100 20 +  = 100 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 100 –  = 90 100 – 40 = 

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.16 Amaqhinga okwenza izibalo: Izibalo zekhanda. Sebenzisa amaqhinga ukwenza izibalo ukwenza ukuhlanganisa nokususa ngoku- yikho. Hlanganisa izinombolo ezihlukene ngokusebenzisa amaqhinga afana no: • Bheka izinombolo ezihamba ngambili ezenza i -10 usebenzise lezi kuqala 2+7+8 2 + 8 kwenza 10 bese wengeze 7. Beka inombolo enkulu kuqala ukuze ubale uqhubekele phambili noma ubale uye emumva. • Qala ngenombolo enkulu kakhulu 5 + 15 Buye ubhale lomusho wenombolo: 15+5 bese ubala uqhubeka ufika ema 20 • Guqula inombolo ibe i-10 bese ususa noma wengeze Isibonelo: 8 + 9 = 17 uphinde uchaze ukuthi ungenza kanje 8 + 9 = 8 + 10 - 1 6 + 11 = 17 uphinde uchaze ukuthi ungenza kanje 6 + 10 + 1 17 - 9 = 8 uphinde uchaze ukuthi ungenza kanje 17 - 10 + 1 • Hlakaza inombolo ibe izingxenye bese uyihlanganisa Akha bese uhlakaza izinombolo: Qhubeka nokuhlakaza izinombolo zibe “ izingxenye ezincane”. 8 + 12 = 8+ (10+2) = 8 + 2 + 10 = 10 + 10 = 20 • Sebenzisa ukuphinda kabili njengeqhinga lokwenza izibalo zekhanda. Khomba izinombolo ezisondelela ekuphindeni kabili. 421 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 422 KUTHEMU 1 KONYAKA 1.16 Isibonelo Izibalo zekhanda. 5+6=11 uchaze ukuthi ukuphinda kabili oku 5 ufake noku 1noma ukuphinda kabili okuyi 6 ususe oku 1 Bona ukuthi uma izinombolo ezimbili ezisondelene ngobungako kubalula ukuthola umehluko ngokubala uye phambili ungabali uye emumva. Izibalo IBANGA 1-3 5 + 6 = 11 ubuye uchaze ukuthi ukubala usuka kwi 11 uze ufike kwi 15 kunikeza 4 Ezinye izibalo zekhanda zingenziwa ngaphandle kwezinsiza kufunda, kodwa ku- yasiza ukwenza izibalo ngekhanda usebenzisa izinsiza kufunda. Izinsiza kufunda ezinconyiwe • Umugqa wezinombolo (owenziwe ongenalutho) • Igridi yezinombolo • Amakhadi amele ubungako benani lenombolo (flard cards) • Ubuhlalu bokubala Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA KUTHEMU 1 KONYAKA CAPS 1.17 • Sebenzisa bese usho • Sebenzisa bese usho EBangeni 2 kwathulwa amaqhezu kubafundi. Bona: amaqhezu ezimweni amaqhezu ezimweni Amaqhezu • Behlukaniselana benza amaqoqo ezinto ngokulingana; ezejwayelekle ezejwayelekle ajwayelekile okufaka ohhafu, okufaka ohhafu, • Banika amagama ezingxenye zamaqhezu ezihamba ngayinye kwamaningi amakota, okukodwa amakota, okukodwa • Bekhomba amaqhezu ezimweni ezahlukene. kokuyisishiyagalombili, kokuyisishiyagalombili, okukodwa kokuthathu, okukodwa kokuthathu, • Bebhala amagama amaqhezu ngoku 1 kokuthathu, 1 kokuhlanu; okukodwa okukodwa kokuyisithupha, kokuyisithupha, • Bethola amaqhezu ezinto eziphelele; kanye okukodwa okukodwa • Bethola amaqhezu amaqoqo ezinto kokuyisihlanu. kokuyisihlanu. Ngalethemu abafundi bethulwa kumaqhezu angaphezulu kwelilodwa, isib. • Bona amaqhezu • Bona amaqhezu 3 amakota noma 2 kokuthathu. Baqhubeka nokusebenza ngamaqhezu emidwebeni emidwebeni angaphezulu kwelilodwa. Basebenza ngeqhezu elilodwa kwayisithupha nelilodwa • Qala ukubona ukuthi • Qala ukubona ukuthi kwayisishiyagalombili. ohhafu ababili noma ohhafu ababili noma Izibonelo zemibuzo: okuthathu kokuthathu okuthathu kokuthathu kwenza okukodwa kwenza okukodwa Isimo sihlukaniswe izingxenye ezingaki ezilinganayo? okuphelele nokuthi okuphelele nokuthi Zingaki izingxenye zesimo ezihlikihliwe? uhhafu owodwa kanye uhhafu owodwa kanye namakota amabili namakota amabili Iqhezu elingakanani lesimo ngasinye elihlikihliwe? kuyalingana kuyalingana Iqhezu elingakanani lesimo elingahlikihliwe? • Bhala amaqhezu • Bhala amaqhezu A. njengo 1 uhhafu, 2 njengo 1 uhhafu, 2 kokuthathu kokuthathu B C D 423 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI NGOKUPHELA 424 KUTHEMU 1 KONYAKA 1.17 Abafundi kufanele banikezwe ithuba lokufaka umbala ezimweni ngokwabo. Amaqhezu Isibonelo: ajwayelekile Faka umbala koku 2 kokuthathu kwalesimo. A. Izibalo IBANGA 1-3 Faka umbala koku 2 amakota alesimo. B Faka umbala ok 4 kokuhlanu kwalesimo. B Faka umbala kokuyi 6 kokuyisishiyagalombili kwalesimo. D Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

YEBANGA LESI- 3 ITHEMU YOKU-1 2. AMAPHETHINI, UBUDLELWANO NEALJEBRA ULWAZI NAMAKHONO CAPS ULWAZI NAMAKHONO ISIKHATHI ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO NGOKUPHELA WOKUFUNDISA (ngokwamahora) KUTHEMU 1 KONYAKA 2.1 Ukukopisha, ukwandisa Ukukopisha, ukwandisa EBangeni lesi-3 abafundi bangasebenza ngamaphethini lapho: kanye nokuchaza kanye nokuchaza Amaphethini • amalungu aphindaphindiwe ngendlela efanayo; Asejiyometri Ukukopisha, ukwandisa Ukukopisha, ukwandisa • ubungako bezimo bushintsha ngendlela engaqageleka; kanye kanye nokuchaza kanye nokuchaza ngamagama ngamagama • nokutshitsha kwenani lezimo noma izinto ngendlela engaqageleka • amaphethini alula • amaphethini alula Amaphethini angenziwa esuselwa entweni eyodwa kodwa kube enziwe ngezinto enziwe ngezinto nokushintshashintsha kwemibabala ngendlela ethize isib. eziphathekayo eziphathekayo   • amaphethini • amaphethini alula enziwe alula enziwe Amaphethini angenziwa ngokusebenzisa isimo noma into eyodwa kodwa ngokudwetshwa ngokudwetshwa isikhundla sesimo noma into sishintshe ngendlela ethize. kwemingqa, izimo kwemingqa, izimo noma izinto noma izinto Isibonelo: Ukuzakhela Uhla lwamaphethini: a) amaphethini   Amaphethini alula lapho Ukuzakhela amaphethini izimo, noma iqoqo ache asamibalomdwebo lezimo kuphindaphindiwe ngendlela efana ngqo. • ngeizinto b) eziphathekayo Ukuzakhela amaphethini   • ngokudwetshwa kwemingqa, izimo Ukuzakhela amaphethini noma izinto akhe asamibalomdwebo Amaphethini • ngeizinto Amanye amaphethini aphindaphinda amaqoqo ezimo noma ezinto ezifanayo, asizungezile eziphathekayo lapho ubungako besimo kwiqoqo ngalinye buguquka ngendlela evamile futhi Khomba, chaza • ngokudwetshwa eqagekelayo. Isib. Ubungako besimo buyanda noma buyancipha. ngamagama bese kwemingqa, izimo Isibonelo: Ubungako besimo buyakhula ukopisha amaphethini noma izinto asamibalomdwebo   • ngokwemvelo • ngokwesimo senhlalo yesimanje 425 yansukuzonke • ngokwamasiko Izibalo IBANGA 1-3 namagugu emvelo

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ISIKHATHI ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO NGOKUPHELA WOKUFUNDISA (ngokwamahora) 426 KUTHEMU 1 KONYAKA 2.1 Isibonelo: Ubungako besimo buyancipha Isifundo 1 Amaphethini   Asejiyometri Izibalo IBANGA 1-3 Amaphethini angenziwa ngokuthi kwenziwe amaqoqo afanayo, lapho iqoqo ngalinye linenhlobo eyodwa yento kodwa isikhundla sento kulelo naleloqoqo siyaguquka. Amaqoqo afanayo ayaphindwa. Isibonelo:   Amanye amaphethini asuselwe kwisimo esithile esisodwa, kodwa ubungako besibonelo sesimo siyakhula noma sinciphe.isib:   Amanye amaphethini asuselwe kwizimo ezinezinto ezifanayo, kodwa inani lohlobo ngalunye lwesimo noma into luyakhula noma lunciphe ngendlela eyewayelekile. Isibonelo:   Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ukukopisha amaphethini kusiza ukuba abafundi babone ukuthi ukuhleleka kwephethini kwakheke kanjani. • Ukwandisa iphethini kusiza abafundi ukuba bahlole ukuthi ingabe bakuqondis- ise kahle ukuhleleka kwamaphethini.

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ISIKHATHI ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO NGOKUPHELA WOKUFUNDISA (ngokwamahora) KUTHEMU 1 KONYAKA CAPS 2.1 • Ukuchaza amaphethini kusiza abafundi ukuthuthukisa amakhono olimi kanye nokukhuluma. Kubuye kukusize ukuba ukwazi ukubona ukuthi ingabe abafundi Amaphethini bawahumushe kanjani amaphethini. Kuvame ukubalula kubafundi ukukhuluma Asejiyometri ngamaphethini emveni kokuba sebewenzile. Kulesisikhathi samanje abafundi kumele bakwazi ukuchaza amaphethini ngaphandle kosizo lwemibuzo ebaholayo. Qhubeka ugxile ekuthuthukiseni ulimi abaludingayo ukuze bakwazi ukuchaza amaphethini 2.2 Ukukopisha, ukwandisa Ukukopisha, ukwandisa Ukulandelana kwezinombolo kungaxhunyaniswa nezinombolo kanti futhi kanye nokuchaza kanye nokuchaza kusekele ukubala. Njengoba amakhono abafundi okubala eshintsha futhi Amaphethini ethuthuka, izinhlobo zokulandelanda kwezinombolo abafundi abasebenza ngazo ezinombolo Ukukopisha, ukwandisa Ukukopisha, ukwandisa zingathuthuka kanye nokuchaza kanye nokuchaza ukulandelana okulula ukulandelana okulula Ukulandelana kwezinombolo kufanele kubonise ukubala uya phambili noma kwezinombolo kuze kwezinombolo kuze ukubala uya emumva ngoku: kufike okungenani kwi kufike okungenani kwi • 1 ukusukela kunoma kuyiphi inombolo ephakathi kuka 0 no 200 1000 100 • 10 ukusukela kunoma ikuphi ukuphindaphinda ngoku 10 okuphakathi kuka 0 no Ukwakha nokuchaza • Ukulandelana kumele 200 amaphethini akhe kubonise ukubala uya phambili noma uya • 5 ukusukela kunoma ikuphi ukuphindaphinda ngoku 5 okuphakathi kuka 0 no Ukuzakhela amaphethini 200 emumva ngoku: akhe ezinombolo. • 1 ukusukela kunoma • 2 ukusukela kunoma ikuphi ukuphindaphinda ngoku 2 okuphakathi kuka 0 no kuyiphi inombolo 200 ephakathi kuka 0 no • 3 ukusukela kunoma ikuphi ukuphindaphinda ngoku 3 okuphakathi kuka 0 no 200 200 • 10 ukusukela • 4 ukusukela kunoma ikuphi ukuphindaphinda ngoku 4 okuphakathi kuka 0 no kunoma ikuphi 200 ukuphindaphinda ngoku 10 okuphakathi • 100 ukusukela noma ikuphi kuphindaphinda nge 100 ukufika okungenani 500 kuka 0 no 200 Abafundi bangakhomba izinombolo ngenkathi bebala. Kubalulekile ukunika • 5 ukusukela abafundi ukuandelana kwezinombolo ngezindlela ezihlukene kunoma ikuphi ukuphindaphinda ngoku 5 okuphakathi kuka 0 no 200 427 Izibalo IBANGA 1-3

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ISIKHATHI ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO NGOKUPHELA WOKUFUNDISA (ngokwamahora) 428 KUTHEMU 1 KONYAKA 2.2 • 2 ukusukela Isibonelo: 3 Izifundo kunoma ikuphi Amaphethini • Ukulandelana kwezinombolo okubhalwe phansi 200; 199; 198; 197; 196,..... ukuphindaphinda ezinombolo ngoku 2 okuphakathi • Umgqa wezinombolo kuka 0 no 200 - Okukhombisa izinombolo ezibalwayo kuphela. • 3 ukusukela - Izingxenye zemigqa yezinombolo isib. 150-200 Izibalo IBANGA 1-3 kunoma ikuphi ukuphindaphinda • Igridi yezinombolo ngoku 3 okuphakathi kuka 0 no 200 • Izinombolo ezixhumanayo • 4 ukusukela Abafundi bangemboza, bafake umbala, noma bakokelezele izinombolo kunoma ikuphi njengoba beqhubeka bebala emgqeni wezinombolo nakugridi, nokulandelana ukuphindaphinda kwezinombolo okubhaliwe. ngoku 4 okuphakathi Abafundi bangafakela izinombolo ezisele emgqeni wezinombolo, amagridi kuka 0 no 200 ezinombolo, nokulandelanda kwezinombolo kanye nezinombolo ezixhumanayo - 100 ukufika Isibonelo: okungenani kuma 500   110    +  10    +  10    +  10   120   130      +  10    +  10      +  10    +  10         Njengoba ukulandelanda kwezinombolo kungasekela ukubala, ngakho-ke abafundi bangakwazi ukubala ngamaqoqo, kungaba izinto noma izithombe, baphinde babhale lezizinombolo kumathebula kanye namashadi okulandenayo, okuyindlela yokuthuthukisa nokusekela ukuphindaphinda. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ULWAZI NAMAKHONO ULWAZI NAMAKHONO ISIKHATHI ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO NGOKUPHELA WOKUFUNDISA (ngokwamahora) KUTHEMU 1 KONYAKA CAPS Kuthemu yokuqala kugxilwa kakhulu koku 2, 5 kanye nokuyi 10. Isib. Ukubala ngaku 5 R5 izinhamvu 1 2 3 4 5 6 7 8 9 zemali Isamba R5 R10 R15 R20 R25 R30 R35 R40 R45 semali Inombolo osebenza ngayo   Input Output Umphumela 1 Rule Umthetho 5 2 3 15 4 ×  !     5 25 Ekupheleni kwethemu abafundi basebenza ngokubala ngendlela efanele, nokulandelana okufanele ukusuka nokuya e100. 429 Izibalo IBANGA 1-3

ITHEMU YOKU-1 YEBANGA LESI-3 3. INDAWO NESIMO (IJIYOMETRI) 430 ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangeha NGOKUPHELA KUTHEMU 1 nemizuzu engu KONYAKA 24) 3.3 Uhla lwezimo: Uhla lwezimo: Yini okwehlukile eBangeni 2? Izifundo ezi 2 Izimo ezinhlang- • indilinga • indilinga Kubanga 3 abafundi babukeza wonke umsebenzi owenziwe ngezimo ezinh- Izibalo IBANGA 1-3 othimbili langothi mbili eBangeni 2, kodwa kungagxilwa kubungako noma umbala uma • unxantathu • unxantathu kusetshenzwa ngezimo. (2-D) • isikwele • isikwele Lokhu kunika abafundi isikhathi esanele sokugxila emsebenzini omusha wezinto • unxande • unxande ezinnhlangothi ntathu, isikhundla, ukubonisa nkoubukeka kwento kanye nokufana nse nxazombili. Izimpawu zezimo Izimpawu zezimo Umsebenzi omningi wezimo kulelIBANGA LESI-3 wenziwa ngezinto eziphathek- Chaza, hlela bese Chaza, hlela bese ayo. Wonke umsebenzi kufanele uhethwe ngemisebenzi ebhalwayo. uqhathanisa izimo ezinh- uqhathanisa izimo ezinh- langothi mbili ngokwe: langothi mbili ngokwe: Ukubona nokusho izindilinga, onxantathu, izikwele kanye nonxande • simo • simo Abafundi kumele basebenze ngezindilinga kanye nezikwele znobungako obuh- lukene kanye nonxantathu abanezimo ezahlukene. • izihlangothi eziqondile • izihlangothi eziqondile Kubalulekile ukuthi abafundi bangaboni isibonelo esisodwa nje kuphela sosimo • amacala ayindilinga • amacala ayindilinga ngasinye. Amasethi amaningi athengisayo ezimo anika isibonelo esisodwa vo Dweba izimo sonxantathu. Abafundi kumele bakwazi ukubona: • indilinga • Izindilinga ezinobungako obahlukene • unxantathu Isibonelo: • isikwele   • unxande • Onxantathu abanezimo ezahlukene, babekwa ezikhundleni ezahlukene Isibonelo: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO IZIHLOKO OKUGXILWA KUWO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangeha NGOKUPHELA KUTHEMU 1 CAPS KONYAKA nemizuzu engu 24) • Izikwele ezahlukene ngobungako bazo, ezikhundleni ezahlukene Isibonelo:   • Onxande abanezimo ezahlukene babekwa ezikhundleni ezahlukene Isibonelo:   Kuyasiza ukuthi abafundi basebenze ngemifanekiso enezimo ezakhiwe ngama- bhokisi asikiwe. Lokhu kuvumela ukuba abafundi bakwazi ukubona onxantathu, izikwele kanye nonxande abehlukene bebekwe ezikhundleni ezehlukene. Abafundi bahlela izimo ngokuthi zinamacala aqondile noma ayindilinga. Abafundi bahlela bese benza amaqoqo ezimo ngokuthi zingonxantathu, unxande, izikwele noma izindilinga. Umsebenzi uphethwa ngokwenza imisebenzi ebhalwayo. 431 Izibalo IBANGA 1-3

ITHEMU YOKU-1 YEBANGA LESI-3 4. ISILINGANISO 432 ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) 4.1 Ukusho isikhathi Ukusho isikhathi Yini okwehlukile eBangeni 2? Izifundo ezi 4 Isikhathi • Ukufunda izinsuku • Ukufunda izinsuku Izinto ezikhombisa isikhathi ziyethulwa. Izibalo IBANGA 1-3 ekhalendeni ekhalendeni EBangeni 2 abafundi bafunda isikhathi ngamahora, isigamu sehora kanye nekota • Ukufaka izinsuku • Ukufaka izinsuku emawashini ezinti. zokuzalwa, imigubho zokuzalwa, imigubho EBangeni lesi 3 abafundi basebenza ngezinto ezikhombisa isikhathi okokuqala. yezenkolo, amaholide yezenkolo, amaholide Balokhu besagxile esikhathini sesimo samahora ayi 12 bese besebenzisa omphakathi, izehlakalo omphakathi, izehlakalo amagama asho ukuthi kusekeni noma kuntambama lapho kudingeka (am / pm). eziwumlando, eziwumlando, izehlakalo zezikole izehlakalo zezikole Abafundi balokhu beqhubekile njalo benza ngokuphindelele bekhuluma ngobude kwikhalenda kwikhalenda besikhathi, kanye nokulandelana kwesikhathi. • Ukusho isikhathi • Ukusho isikhathi Ngenkathi kufundiswa ikilasi lonke, kanye nangenkathi kugxilwe ekufundiseni samahora ayi 12 samahora ayi 12 amaqembu, abafundi baqhubeka ngokukhuluma ngosuku lwesonto, inyanga yonyaka, lolosuku lwenyanga onyakeni, kanye nezinsuku eziphambili/ ezedlule - amahora - amahora kanye nezinsuku ezizayo. Abafundi baqhubeka nokufaka loku okulandelayo uma - isigamu sehora - isigamu sehora kufika leyo migubho - ikota lehora - ikota lehora • izinsuku zokuzalwa, - amaminithi - amaminithi • imigubho yezenkolo, kumawashi ezinti kumawashi ezinti • amaholide omphakathi, kanye namawashi kanye namawashi • izehlakalo eziwumlando, anezinombolo, anezinombolo, kanye nezinye izinto kanye nezinye izinto • izehlakalo zezikole ezikwikhalenda ezibonisa isikhathi isib. ezibonisa isikhathi isib. Qhubeka ucela abafundi ukuba basho isikhathi ngokwamahora, isigamu sehora, umakhalekhukhwini umakhalekhukhwini ikota lehora usebenzisa amawashi ezinti ngezikhathi ezejwayelekile zonke Ukubala ubude izinsuku. Isibonelo, abafundi bangacelwa ukuba basho isikhathi sokuqala besikhathi kanye kwesikole, isikhathi sekhefu kanye nesikhathi sokuya ekhaya, noma uma Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola nokundlula kwesikhathi beshintsha isifundo kwesinye.Khetha isikhathi lapho iwashi liqonde ngqo kwihora noma isigamu sehora noma ikota lehora.Kuyasiza ukuba newashi elikhulu Ukusebenzisa elibekiwe elisebenzayo ekilasini ukuze abafundi bakwazi ukulokhu bebheka kulo. amakhalenda Abafundi bangabuye benze imifanekiso yamawashi. Ungabacela abafundi ukuthi ukubala nokuchaza babonise izikhathi ezahlukile ubuye wengeze nokubala. Isib. Ngibonise u 10 ubude besikhathi ngqo.Bekuwubani isikhathi esingangekota lehora eliphambi kuka 10? ngokwamalanga noma amasonto noma izinyanga kanye

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 CAPS KONYAKA nemizuzu engu 24) 4.1 • nokuguqula okupkathi Ngesikhathi sokusebenza ngokuzimela abafundi baqhubeke benze imisebenzi kwamalanga ehambisana nokushiwo kwesikhathi ngokwamahora, isigamu sehora kanye Isikhathi namasonto nekota lehora njengoba kukhonjisiwe kumawashi lezinti. Abafundi bangenza izibalo besebenzisa amasonto noma izinsuku uma benikeziwe ikhalenda noma • nokuguqula ingxenye yekhalenda, isib. Ukubheka izinsuku bese bebala umehluko wesikhathi okuphakathi phakathi kwazo. kwamasonto nezinyanga Isikhathi Sewashi Ukusebenzisa amawashi • Isikhathi siboniswe ngesikhathi sosuku esithatha isimo samahora angu 12 ez- ukubala ubude besikhathi intweni eziningi ezisetshenziswa ekhaya.isib. omakhalekhukhwini, iziifudumezi ngokwamahora noma zokudla (microwaves) imisakazo yokudlala ama CD nama DVD njll. Abafundi isigamu sehorase. bangabuye balwejwayele kangcono loluhlobo lwesikhathi kunohlobo lwama- washi ezinti. Izifundo ezintathu zingakusiza ukthi ukwazi ukwejwayeza abafundi isimo sesikhathi sosuku esingamahora ayi 12. • Khumbuza abafundi ukuthi lokhu kuchaza ini a.m. and p.m. • Khombisa abafundi ukuthi yiziphi izinombolo ezimele amahora, kanti futhi yiz- iphi ezimele imizuzu ngesikhathi sosuku. • Chaza ukuthi kunemizuzu engu 60 kwihora; ngakhoke kunemizizu engu 30 esigamini sehora kanti kunemizuzu engu 15 kwikota lehora. Lokhu kuzosiza abafundi ukuba bakwazi ukuxhumana okuphakathi kwamahora kanye nemi- zuzu, izigamu zehora, ikota lehora kanye namawashi ezinti, okuyizinto ebebez- enza eBangeni lesi 2. • Nikeza abafundi isikhathi esanele sokubuyekeza ukufunda isikhathi sewashi lezinti esingamahora ayi 12. Iba newashi lezinto elibekiwe ekilasini.Cela abafundi ukuthi balokhu bekutshela isikhathi phakathi nosuku unyaka wonke. Abafundi abenze imifanekiso yamawashi, abangawasebenzisa ukusho isikhathi babuye babale umehluko wezikhathi. 433 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 434 IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) 4.2 ISILINGANISO EBangeni lesi 2 kwakunconyiwe ukuthi abafundi bagxile ekuqageleni, okungahlelekile ekulinganiseni, ekuqhathaniseni kanye nokubhala phansi ubude, ububanzi kanye Ubude nokuphakama • Qagela, linganisa, qhathanisa, hlela • Ngamayunithi angahlelekile, kanye bese ubhala ubude Izibalo IBANGA 1-3 • Nokukala besebenzisa irula eliyimitha noma intambo eyimitha usebenzisa izikali ezingenasilinganiso Ngesikhathi sokusebenza ngokuzimela abafundi bangazilolongela lamakhono isib. izandla, okulinganisa amagxathu, ubude Ukulinganisa ubude njengendlela yokuxazulula izikinga zezibalo bepensela, izinto zokubala njll. Ngesikhathi esibekelwe ukufundisa Izinombolo, Izimpawu kanye nobudlelwano bazo, abafundi bangaxazulula izinkinga ezimweni • Chaza ubude bezinto ngokubala • Zezilinganiso ezingahlelekile zobude, kanye bese ushoubude bamayunithi • Nokulinganisa ubude ngamamitha angahlelekile. Nakisisa uhla lwezinimbolo olufanele lethemu, kanye nohla lwezinhlobo • Sebenzisa ulimi zezinkinga ezifanele kulethemu. ukukhuluma Izifundo ezizogxila ekulinganiseni ubude zizoqala eThemu 2 ngokuqhathanisa isb. Kude kuna, kufishane kuna, kuphakeme kuna nokubanzi. Ukwethula Isilinganiso esihlelekile • Qagela, linganisa, qhathanisa, hlela bese ubhala ubude usebenzisa imitha(noma irula Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola eliyimitha, noma intambo eyimitha) njengesikali sobude esilinganisiwe.

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 CAPS KONYAKA nemizuzu engu 24) 4.2 • Qagela bese ulinganisa ubude Ubude ngamasentimitha usebenzisa irula Akudingekile ukwenziwa inguguquko phakathi kwamamitha kanye namasentimitha 4.3 izilinganiso EBangeni lesi 2 abafundi ezingahlelekile Isisindo • Balinganisa isisindo ngokungahlelekile besebenzisa ISILINGANISO • Qagela, linganisa, okuzimelele; qhathanisa, hlela • Bahlele izinto ngokwesisindo esichaziwe ephaketheni; noku bese ubhala isisindo usebenzisa izilinganiso • Funda izikali zasendlini yokugeza (kokubili izikalo zangempela kanye nezikalo ezingahlelekile zezithombe). kanye nokulinganisa Ngesikhathi sokusebenza ngokuzimela, abafundi bangenza ngokuphindelela okuzimelele isib lamakhono okulinganisa. amabhuloki, izitini njl. Ukulinganisa isisindo njengendlela yokuxazulula izinkinga nokwenza izibalo • Sebenzisa ulimi ukukhuluma Ngesikhathi esibekelwe ukufundisa Izinombolo, Izimpawu kanye nobudlelwano ngokuqhathanisa isb. bazo, abafundi bangaxazulula izinkinga ezimweni lula, sinda,elula kuna, esinda kuna • Izilinganiso ezingahlelekile zesisindo; kanye Ukwethula isilinganiso • Nokulinganisa isisindo ngamakhilogremu okuhlelekile. Nakisisa uhla lwezinimbolo olufanele lethemu, kanye nohla lwezinhlobo • Qhathanisa, hlela bese zezinkinga ezifanele kulethemu. ubhala isisindo sezinto Izifundo ezizogxila ekulinganiseni isisindo zizoqala eThemu 2 ezithengisayo isisindo sazo esibhalwe ngamakhilogramu isib. 2 amakhilogremu yelayisi kanye no 1 kilogram kafulawa noma ngamagremu 435 isib 500 amagremu kasawoti Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 436 IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) 4.3 • Ukuzikala isisindo sabo ngokwamakhilogremu Isisindo besebenzisa isikali sasendlini yokugeza Akudingeki nguquko Izibalo IBANGA 1-3 phakathi kwamagremu kanye namakhilogremu 4.4 Izilinganiso Izilinganiso Yini okwehlukile eBangeni 2? ezingahlelekile ezingahlelekile Umthamo/o ku- EBangeni 2 abafundi mumethwe • Qagela bese • Qagela bese • baqagelile, balinganisa,baqhathanisa,bahlela base bebhala phansi umthamo ulinganisa, qhathanisa ulinganisa, qhathanisa wezitsha noma okumumethwe besebenzisa izikali ezingenasilinganiso bese uhlela umthamo bese uhlela umthamo wezitsha (isib. wezitsha (isib. • baqhathanisile, bahlela umthamo wamabhodlela ahlukene nezinto umthamo isitsha umthamo isitsha ezisetshenziswa ekhaya lapho umthamo wazo ubhaliwe emaphaketheni; esingawumumatha esingawumumatha baphinde uma sigcwele) uma sigcwele) • Basebenzise noma ilitha elilodwa lebhodlela noma ilitha elilodwa likajeke usebenzisa izilinganiso usebenzisa izilinganiso ukuqagela, nokulinganisa, ukuqhathanisa, ukuhlela bese ubhala sezitsha noma ezingahleliwe isib. ezingahleliwe isib. okumumethwe ngokwamalitha izipuni kanye izipuni kanye nezinkomishi. nezinkomishi. EBangeni lesi 3 abafundi bethulwa kumamililitha. • Chaza uthamo • Chaza uthamo Yini umthamo? Yini okumumethwe? wesitsha ngokubala wesitsha ngokubala Ibhodlela lingaba nomthamo welitha elilodwa kodwa lingase lingagcwali mfi, nokusho ukuthi nokusho ukuthi lingase Isib. limumathe umthamo wenkomishi eyodwa yamanzi. kuthatha amayunithi kuthatha amayunithi angahlelekile angahlelekile Umthamo ubungako bento engamumathwa isitsha (noma ubungako besikhala amangaki ukugcwalisa amangaki ukugcwalisa esingaphakathi kwento). isitsha isib.ibhodlela isitsha isib.ibhodlela linomthamo linomthamo Umthamo ubungako besikhala into enga naso. wezinkomishi ezine wezinkomishi ezine Ngesinye isikhathi abafundi bazobe belinganisa ukuthi kunoketshezi olungakanani (noma isihlabathi noma ngabe uhlobo oluthile) kulesositsha. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Lokhu kuwisilinganiso umthamo wento esesitsheni. Ngezinge izikhathi abafundi bazobe belinganisa ukuthi isitsha uma sigcwele singamumatha umthamo ongakanani.

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 CAPS KONYAKA nemizuzu engu 24) 4.4 Ukwethula isilinganiso Ukwethula isilinganiso Abafundi kumele baqhubeke isilinganiso besebenzisa amayunithi 2 Izifundo okuhlelekile. okuhlelekile. angenasilinganiso. Umthamo/o kumumethwe • Qagela, linganisa • Qagela, linganisa isilinganiso okungahlelekile komthamo kusetshenziswa amayunithi qhathanisa,hlela qhathanisa,hlela angalinganisiwe. bese ubhala phansi bese ubhala phansi Abafundi bangafunda imigomo nezindlela zokulinganisa besebenzisa amayunithi umthamo wezinto umthamo wezinto angalinganisiwe. isilinganiso kusetshenziswa amayunithi angesilinganiso ngokulinganisa ngokulinganisa makungathathwa njengento engabalulekile kunesikalo ezilinganisiwe. ngakwamalitha, ngakwamalitha, isigamu samalitha, isigamu samalitha, Abafundi kumele bathole ithuba lokulinganisa umthamo/okumumethwe kanye nekota kanye nekota besebenzisa izinhlobo zezinto njengamayunithi angalinganisiwe. Isib. Izinkomishi, yamalitha yamalitha (kungesizo ezokulinganisa okwangempela), izipuni (kungesizo izipuni zokulinganisa okwangempela), izivalo zamabhodlela njengezivalo zamabhodlela • Qhathanisa, hlela • Usebenzisa obisi angamalitha ama 2, amathini amancane, amabhodlela amancane njll. bese ubhala phansi amabhodlela izinto ezihlelelwe anesisindo selitha 1 Isilinganiso umthamo/ okumumethwe ngamayunithi angenasilinganiso ukuthengisa umthamo noma isitsha, umthamo kubandakanya ukubala ukuthi uthele izikhathi ezingaki kuthathwa wazo obhalwe wazo obhalwe kulesosilinganiso esilinganiswayo. ngokwamalitha isib 2 ngokwamamililitha isib Abafundi kumele bafundiswe ukuhlala njalo bechaza amayunithi isib.kunezipuni amalitha obisi, ilitha amakani eziphuzo. ezincane zamanzi ezingama 48 ebhodleleni noma kunamanzi angaphansi nje elilodwa yesiphuzo • Ojeke abanamagabelo kwesigamu senkomishi ebhodleleni. esibandayo, 5 amalitha, izigamu amalitha kapende Uma abafundi sebelinganisile nganoma iyiphi iyunithi izikhashana ezimbalwa nje, zamalitha namakota noma ngamamililitha, kufanele baqagele umthamo/ okumumethwe besebenzisa leloyunithi.Ukuqagela elitha. isib. 500 ml yobisi, ngaphambi kokulinganisa kubalulekile, kodwa kungenziwa kuphela uma abafundi 340 amamillilitha • Ojeke abanamagabelo sebeke balinganisa ngaleyoyunithi ngaphambilini. wesiphuzi, 750 ama akhombisa millilitha kawoyela Abafundi kumele bafundiswe ukuthi ukuze bakwazi ukuqhathanisa umthamo amamamililitha. noma okumumethwe, kumele kusetshenziswe iyunithi elifananayo. Isibonelo, Abafundi abalindelekile • Yazi ukuthi inkomishi uma ingilazi iphatha izipuni ezincane zamanzi ezingu20, kanti inkomishi iphatha ukuba bakwazi enesilinganiso izipuni zokudla eziyi 10 zamanzi, ungeze washo ukuthi ingilazi iphethe amanzi ukufunda umthamo inamamililitha awu 250 amaningi. wamagabelo • Yazi ukthi isipuni setiye angenazinombolo singamamililitha awu 5 • Izinkomishi Akukho nguquko zokulinganisa nezipuni elindelekile phakathi zetiye ezikhombisa kwamamililitha namalitha umthamo. 437 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 438 IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) 4.4 • Qhathanisa, hlela Abafundi kumele balinganise izinhlobo ezahlukane zamayunithi bese ubhala phansi alinganisiwe,ukuze Umthamo/o izinto ezihlelelwe kumumethwe • Bakwazi ukuqonda ukuthi ubuncane beyunithi, busho isikhathi esengeziwe ukuthengisa umthamo ozosidinga ukusisebenzisa ukugcwalisa into ethile isib. Umthamo webhodlela wazo obhalwe ungase ube yizipuni zokudla ezi 20 ezigcwele mfi, kodwa futhi inkomishi e 1; Izibalo IBANGA 1-3 ngokwamalitha isib 2 amalitha obisi, ilitha • Baqala ukusebenzisa amayunithi ahambisana nalokho okulinganiswayo. elilodwa yesiphuzo Isib.ISILINGANISO ibhodlela eligcwele lamalitha a-2 ngezipuni kuyasichitha esibandayo, 5 isikhathi. amalitha kapende Ukwethula isilinganiso okuhlelekile. noma ngamamililitha, isib. 500 ml yobisi, Qagela, linganisa, qhathanisa, hlela bese ubhala phansi umthamo kanye 340 amamillilitha nokumumethwe ngokwamalitha. wesiphuzi, 750 ama millilitha kawoyela Khumbuza abafundi ukuthi amalitha angamayunithi ayisilinganiso esejwayelekile okulinganisa umthano kanye nokumumethwe.Indlela efingqiwe (l) isetshenziswa • Yazi ukuthi inkomishi kakhulu kojeke bokulinganisa kanye nasezimpahleni zokuthengisa, ezithengiswa enesilinganiso ngomthamo. Hlola ukuthi abafundi bayasikhumbula ukusho ngokufingqiwe inamamililitha awu 250 amalitha. • Yazi ukthi isipuni setiye Abafundi balinganisa ngamalitha besebenzisa: singamamililitha awu 5 • Izitsha ezinelitha eli1 ezifana namabhodlela eziphuzo ezibandayo, amabhodlela Akukho nguquko obisi, amakhathoni obisi, amakhathoni eziphuzo; kanye elindelekile phakathi kwamamililitha namalitha • ojeke bokulinganisa ababonisa amagabelo akhombisa ilitha. Bayaqagela babuye balinganise umthamo wezitsha ezahlukahlukene ezifana nezitsha ezinkulu eziphatha uyogadi, u ayisikhilimu, izitsha zokufaka ukudla kwesidlo sasemini, ojeke abakhulu, amabhodlela amakhulu, amathini angenalutho opende, amabhakede njll. Kufanele kukhethwe izinto ezinemithamo eyahlukene. Abafundi bachaza umthamo ngokuthi bathi “ngaphansi kwelitha elilodwa, amalitha amabili, phakathi kwelitha eli 1 noma amalitha ama 2, amalitha ama 5” njll. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Abafundi baqhathanisa, bahlele bese bebhala phansi umthamo wezinto ezihlelelwe ukuthengisa umthamo wazo obhalwe ngokwamalitha isib 2 amalitha obisi, ilitha elilodwa yesiphuzo esibandayo, 5 amalitha kapende • Qagela, linganisa, qhathanisa, hlela bese ubhala umthamo nokumumethwe ngamamililitha.

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 CAPS KONYAKA nemizuzu engu 24) 4.4 Khuluma nabafundi mayelana namamililitha njengesilinganiso esejwayelekile sokulinganisa umthamo kanye nokumumethwe. Bachazele ukuthi amamililitha Umthamo/o angamayunithi amancane kunamalitha. Kumele bafunde igama kanye kumumethwe nendlela efingqiwe, ngoba ezitsheni eziningi zokuthengiswayo kanye nojeke bokulinganisa kusetshenziswa indlela efingqiwe yamagama. Abafundi kumele baqhathanisa, bahlele, bese bebhala phansi izinto ezihlelelwe ukuthengiswa, umthamo wazo obhalwe ngamamililitha, isib. 500ml yobisi, 750ml kaviniga, 330ml wesiphuzo esibandayo, 400ml kapholishi waphansi njll. Abafundi kumele balinganise njalo futhi ngokwanele nge: • sikali esilinganisiwe senkomishi, ukuze bakwazi ukuqonda ukuthi kungakanani okuwu 250 ml • izipuni zetiye zokulinganisa ukuze bakwazi ukuqonda ukuthi kungakanani okuwu 5 ml; • ojeke bokulinganisa abanamagabelo angamamililitha - lapha kulindeleke ukuba abafundi bakwazwi ukufunda izinombolo zamagabelo okulinganisa ezibhaliwe kuphela- bazogxila ekufundeni amagabelo okulinganisa angenazinombolo uma sebefunda emabangeni aphakathi. Ukulandela uhla lwezinto ozozisebenzisa, ufaka ubhaka, kuyisimo esingasiza abafundi ukuzilolongela isilinganiso. Abafundi abalindelekile • ukwazi ukuthi 1 000 ml = 1 ilitha • ukwenza uguquko phakathi kwamamililitha, kanye namalitha, noma • Ukufunda amagabelo ojeke bokulinganisa angenazinombolo (lokhu kwenziwa eBangeni lesi 4) Ukubhalwa phansi kwezilinganiso Noma isilinganiso kuyikhono lokwenza, abafundi kumele bazibhale phansi ngaso sonke isikhathi izilinganiso zabo, ezimbandakanya isilinganiso okungahlelekile noma okuhlelekile. 439 Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 440 IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) 4.4 Ukulinganisa umthamo/ okumumethwe njengesimo yokuxazulula izinkinga kanye nokwenza izibalo Umthamo/o kumumethwe Ngesikhathi esibekelwe ukufundisa Izinombolo, Izimpawu kanye nobudlelwano bazo, abafundi bangaxazulula izinkinga ezimweni Izibalo IBANGA 1-3 • isilinganiso okungahlelekile komthamo/ okumumethwe: isib.Ugogo usebenzisa izinkomishi ezimbili zobisi ukwenza uphudini. Uma ephinda kabili uhla lwezinto okumele azisebenzise (iresiphi), uzodigna ubisi olungakanani? • amalitha • amamililitha Nakisisa uhlelo lokuthuthukisa izinombolo olufanele ltthemu, kanye nohlelo lwezinkinga ezahlukene ezifanele. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YOKU- 1 YEBANGA LESI-3 5. UKUQOKELELWA KOLWAZI ISIKHATHI CAPS ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) 5.4 Qoqa bese uhlela ulwazi Qoqa bese uhlela ulwazi Yini okwahlukile eBangeni 2? 3 Izifundo Qoqa bese uhlela • Qoqa ulwazi • Qoqa ulwazi • Abafundi bahlela ulwazi benze uhla, amathali, namathebula ulwazi olumayelana nekilasi olumayelana nekilasi • Abafundi bathulwa kuma bar grafu noma isikole ukuze noma isikole ukuze bakwazi ukuphendula bakwazi ukuphendula • Abafundi baqhubeka ngokusebenza negrafu yezithombe - besebenzisa imibuzo ebuzwe imibuzo ebuzwe womabili amagrafu njengengxenye yolwazi oluphelele bebe behlaziya igrafu wuthisha wuthisha yezithombe abayinikiwe. • Hela ulwazi oluvela Ukusebenzisa amathali Ulwazi oluphelele kuthisha noma ukubhala phansi ulwazi Ekuqoqweni nasekuhleleni kolwazi oluphelele encwadini ohleni olunikeziwe • Abafundi baqoqa ulwazi ukuphendula imibuzo. Emabangeni aphansi kanye • Hlela ulwazi naphakathi lombuzo uvame ukuvezwa wuthisha noma ubesencwadi; olutholakala: • Abafundi bahlela bamele ulwazi ngezindlela ezenza kubelula ukuhlaziya. - kuhlu Indlela yesifanekiso esisetshenziswa ngabafundi bebanga lesithathu; uhla, - kumathali amathali, amathebula, igrafu yezithombe kanye ne bar grafu; kanye - kumathebula • abafundi bahlaziya ulwazi ngokuphendula imibuzo ebuzwe wuthisha. Bhala ukumela ulwazi 5.5 Bhala ukumela ulwazi I bar grafu yekilasi Bhala ukumela ulwazi Bhala ukumela Bhala ukumela ulwazi Kuyanconywa ukuthi abafundi bebanga lesithathu basebenze ngalolonke ulwazi • Ithebula oluphelele okungenani kanye ngonyaka: Ukusebenza bebonke njengekilasi ulwazi • Igrafu yezithombe • Bar grafu kusiza abafundi ukuba bazimbandakanye kuwo wonke amabanga ohlelo ngaphandle ngokuduka nakunoma ikusiphi isigaba. Ukwakha bar grafu yekilasi • Bar grafu kukuvumela ukuba ugxile kumaphuzu abalulekile okuqoqa nokuhlela ulwazi 5.6 Hlaziya bese uhumusha kanye nokwethula abafundi kumaphuzu asemqoka e bar grafu Ukuhlaziya bese ulwazi uhumusha ulwazi • ukuthi kubhalwa kuphi futhi kanjani kwigrafu (isihloko segrafu) Hlaziya bese uhumusha ulwazi Phendula imibuzo Phendula imibuzo • ukuthi kubhalwa kuphi futhi kanjani emigqeni yegrafu ngolwazi olumelwe ngolwazi olutholakala • ukuthi udweba kanjani ama bar • Igrafu yezithombe kubar grafu k - dweba ubude be bar ngendlela efanele ukukhombisa ulwazi. • ibha grafu - yenza ama bar grafu alingane ngobubanzi 441 - shiya isikhala phakathi kwama bar - bhala ibar ngayinye ngokucacile Izibalo IBANGA 1-3

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA 442 IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 nemizuzu engu KONYAKA 24) - indlela yokufunda igrafu Abafundi kumele bazi ukuthi kubalulekile ukufunda isihloko segrafu kuqala, ukuze bazi ukuthi lololwazi lumayelana nani. Kumele babuye bafunde izihloko emigqeni ehamba ivundle noma yehle Abafundi akudingekile ukuba bawazi amagama asetshenziswayo ukuchaza izingxenye zegrafu, Izibalo IBANGA 1-3 okubalulekile nje ukuthi bafunde “eceleni” nange “zansi” ukuze babone ukuthi igrafu imayelana nani. Sivamise ukufunda ukusuka ngasesandleni sobunxele ukuya ngakwesokudla, kodwa uma abafundi befunda amagrafu kumele bafunde ukusuka ngakwesobunxele ukuya ngakwesokudla nokusuka phansi ukuya phezulu. Lokhu kumele kuchazwe kubafundi. Kudingeka babuye bazilolonge kulamakhono. Ukusebenza ngolwazi oluphelele kungathatha izifundo ezintathu. Ukuqoqa nokuhlela ulwazi EBangeni lesithathu kumele ubuze imibuzo ezovumela abafundi ukuthi baqoqe ulwazi isib. Yimiphi imibala ethandwa kakhulu ekilasini lethu? Othisha bakulamabanga kumele baqiniseke ukuthi kukhethwa izihloko ezahlukene ukuqokelela ulwazi bese belihlaziya kumabanga ahlukene. Izihloko ezifanele zifaka ezemidlalo, iziphuzo ezibandayo ezithadwayo, imiba eyintandokazi, izikhathi ezedlule eziyintandokazi, izidlo eziyintandokazi, uhlelo oluyintandokazi lukamabonakude njll. Abafundi bangaqale basho imibono yabo. Uma nje uthola ulwazi lwezimpendulo ezahlukahlukene kumele ubekele abafundi izinhla abangakwazi ukukhetha kuzona.Yenza abafundi ukuba bazilolongele kwizindlela ezehlukene zokuhlela ulwazi ezingeyona igrafu, njengamathali, uhla kanye namathebula. isib.: • yeza uhla lwamagama lwabafundi ngaphansi kwesihloko abasikhethile; • Khombisa abafundi ukuthi enziwa kanjani amathali esuselwa ohleni (ukufundisa amathali kungathatha isifundo sonke); Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Enza ithebula ngezinombolo eziphuma kumathali akumathebula Uma ulwazi selukumathebula, khombisa abafundi ukuthi idwetshwa kanjani ibar grafu (bheka imihlahlandlela ebhalwe ngaphezulu).

ISIKHATHI ULWAZI NAMAKHONO ULWAZI NAMAKHONO (ngokwesifundo ADINGEKAYO AMANYE AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA IZIHLOKO OKUGXILWA KUWO esingangehora NGOKUPHELA WOKUFUNDISA KUTHEMU 1 CAPS KONYAKA nemizuzu engu 24) Ukuhlaziya nokuhumusha kolwazi Abafundi baphendula imibuzo oyibuzayo mayelana negarafu yezithombe Isib: a) “Yimuphi umbala ovamile ekilasini lethu?” b) “Yimuphi umbala oyintandokazi wabafundi abambalwa ekilasini?” c) “Ingabe abafundi abaningi bathanda …. noma … ?” d) “Bangaki ngaphezulu abafundi abakhetha uku … kunoku … ?” 443 Izibalo IBANGA 1-3

ITHEMU YESI-2 YEBANGA LESI- 3 1. IZINOMBOLO, IZIMPAWU KANYE NOBUDLELWANO BAZO 444 IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.1 Ukubala izinto Iqembu okungenani inani Yini umehluko kusukela kuthemu1? Ukubala izinto eziqotho. 500 Inani linwebeka laze lafika 500. Ukunwebeka kwaleli nani lisho ukuthi abafundi Qagela uphinde ubale Izinto mihlayonke banga: Izibalo IBANGA 1-3 ngokwethembeka ziqagelwa ngokwethembeka. • izinto zibalwa ngamaqembu okungenani 1000 izinto Nikeza isizathu • Ukubala ngamashumi ukuze kufike ku 500.bese usho izinombolo ngokulande- mihlayonke. esizwakalayo, ngezinto lanisa. Futhi Ikhono lamaqembu ezingahlolwa ngokubala. liyakhuthazwa. • Hlela izimpawu ukuze kufike esibalweni ngokubhala izinombolo noma ubonise inamba ngendawo ye value cards. • Bona amanothi ethemu 1 1.2 Ukubala uya phambili • ukubala nga-1 Yini umehluko kusukela kuthemu1? Ukubala ubuye uye emumva: kusukela noma kuyiphi Kulelithemu abafundi bayoqala ukubala ngamashumi amahlanu 50. Inombolo uqhubekela pham- inombolo esukela 0 liyakhuphuka lize lifike ku 1000. • 1 ukubala ngakunye bili uphinde ubale naku 500 Kulelithemu abafundi bayoqhubeka nokuthi benze ukweqa bebala bephin- uhlehlele emuva. kusukela noma kuyiphi daphinde ngamatafula kanye nokunikeza izinombolo izehlakalo. inombolo esukela 0 • Ngama-10 kusukela Bona amanothi ethemu 1 naku 1000 kusukela kunanoma • Ngama-10 kusukela iyiphi inombolo kusukela kunanoma ngokuphindaphinda iyiphi inombolo phakathi koku-0 kuya ngokuphindaphinda e-500 phakathi koku-0 kuya • Ngaku-5 e-1000 ngokuphindaphinda • Ngaku-5 phakathi koku-0 kuya ngokuphindaphinda e-500 phakathi koku-0 kuya • Ngaku-2 e-1000 ngokuphindaphinda Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ngaku-2 phakathi koku-0 kuya ngokuphindaphinda e-500 phakathi koku-0 kuya • Ngaku-3 e-1000 ngokuphindaphinda • Ngaku-3 phakathi koku-0 kuya ngokuphindaphinda e-500 phakathi koku-0 kuya • Ngaku-4 e-1000 ngokuphindaphinda phakathi koku-0 kuya e-500

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.2 • Ngaku-4 • Ngama-50, 100 Ukubala ngokuphindaphinda kuyofika 1 000 uqhubekela pham- phakathi koku-0 kuya bili uphinde ubale e-1000 uhlehlele emuva. • Ngama-20, 25, 50, 100 kuyofika 1 000 1.3 Bona,ukhombe uphinde Bona,ukhombe uphinde Ukufunda nokubhala izimpawu zezinombolo kuyaqhutshekwa nokwenziwa Nikeza izinto ufunde izinombolo ufunde izinombolo ngoku: amagama bese • Ukubala ngezinto • Bona,ukhhombe • Nikeza,ukubona lamagama uphinde ufunde uphinde ufunde enikezwa • Ukubala uye phambili nokubala uye emuva izinombolo. izimpawu izinombolo izimpawu zezinombolo ngezinto kusukela kusukela koku-0 - 1000 • Ukuqedela ukulandelana kwezinombolo, futhi koku-0 -1000 • Bhala izimpawu • Ukuhlela nokuqhathanisa izinombolo • Bhala izimpawu ngezinombolo ziqala zezinombolo ziqala koku-0-1 000 Bheka amanothi kathemu 1 koku- 0-1 000 • Bhala izimpawu • Bhala izimpawu zezinombolo ziqala zezinombolo ziqala koku- 0-250 koku-0-1 000 • Bhala izimpawu • Bhala izimpawu zezinombolo ziqala koku- 0-250 • zezinombolo ziqala koku- 0-1 000 445 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 446 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.4 Hlela bese uqhathanisa Hlela bese uqhathanisa Kulelithemu inani liyanwebeka ukusuka 99 kufike 500. Abafundi manje bahlela izinombolo ufinyelele izinombolo ufinyelele amadijithi amathathu ezinombolo. Ukuhlela amadijithi amathathu, abafundi Chaza, uqhatha- bafanele: nise bese uhlela ama- 999 ama- 500 izinombolo • Chaza ubuye uqatha- • Chaza ubuye • Basho igama lenombolo nise izinomboloeziph- uqathanise Izibalo IBANGA 1-3 • Babhale inombolo; futhi elele kufinyelele ema- izinomboloeziphelele 999 usebenzisa inani kufinyelele ema- 500 • Babone ukubaluleka kwedijithi ngalinye elincane kunelinye, usebenzisa inani Abafundi kufanele bavunyelwe basebenzise inamba layini, ukulalndela noma elikhulu elincane kunelinye, umkhondo, amagridi ezinombolo kanye futhi nolwazi lwabo lokusebenzisa kunelinye, eliningi noma elikhulu izinombolo nokwenza izibalo. Ukusebenzisa izinombolo ukwenza amakhulu, kunelinye, elincanyana kunelinye, eliningi amashumi, kanye nokwenza okunye, ukuze kubonakale ukuthi bayaqonda. kanye nokulinganayo kunelinye, elincanyana Uma abafundi begunyaza izinombolo, bayakwazi uksebenzisa inombolo enkulu kanye nokulinganayo kunenye kanti nesiko lamadijithi lizichaza kwalona. • Chaza ubuye uqatha- nise izinomboloez- • Chaza ubuye Isibonelo: iphelele kufinyelele uqathanise 239 incane kuno 339 ngoba ema- 999 uzisusela izinomboloeziphelele kunani elincane, ukuya kufinyelele ema- 999 Umfundi uzokwazi ukuchaza ukuthi 300 mkhulu kuno 200 ngokusebenzisa kwelikhulu, uphinde uzisusela kunani izinsiza ezibunjiwe ukukhombisa inani 100s kunombolo ngayinye. Abafundi bangathola isikhundla senamba kunambalayini ngokusho ukuthi 339 uza emuva usuke kwelikhulu uyek- elincane, ukuya 239 ngakhoke ngiyazi ukuthi yiyo inamba enkulu. welincane. kwelikhulu, uphinde usuke kwelikhulu Sebenzisa izinombolo zesikhundla ukubonisa uyekwelincane. uhla, indawo nesikhun- Sebenzisa izinombolo dla zesikhundla ukubonisa uhla, indawo • Sebenzisa ukubhala nesikhundla ukufunda nokubhala ngezinombolo zezik- • Sebenzisa ukubhala hundla zifinyelele ukufunda nokubhala ema- 31 ngezinombolo zezikhundla. zifinyelele Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ema- 31.

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.5 Bonisa Indawo Bonisa Indawo Yini umehluko kusukela kuthemu1? nokubaluleka kwayo nokubaluleka kwayo Inani lenombolo Kulelithemu lesibili abafundi bayohlakaza amadijithi amathathu ngesi khathi ngezinombolo ngezinombolo sokuqala. Indawo nokubaluleka kwayo, yengeziwe ukufakela amakhulu. zamadijithi amathathu zamadijithi amathathu Abafundi bayoqonda ukubaluleka kwendawo, nokuyithuthukisa ngokubuza afika 999 afika 999 imibuzo enjengo thola ishumi, okuningi noma okuncane kunenombolo. Njenge • Kufanele ukuthi idijithi • Kufanele ukuthi idijithi nhlalayenza ukuthuthukisa ukubaluleka kwesimo, abafundi kufanele bakwazi ngalinye lisho ukthini ngalinye lisho ukthini ukubala ngokuzethemba ngama -100, bazitholele amaphethini ahlobene nokubaluleka kwendawo, bakwazi ukuzakhekhela izibalo bahlanganise babuye • Hlakaza amadijithi • Hlakaza amadijithi 3 bahlukanise ngokubili nokuthathu kwamadijithi 3 kuze kufike 999 kuze kufike 500 ngokuphindaphinda Abafundi bafanele banikezwe isikhathi esilingeneyo, amathuba okwakha • ngokuphindaphinda ka 100, amadijithi amathathu ngezinombolo besebenzisa amabhuloki kadienes ka 100, ngokuphindaphinda ka namabhuloki kanye namabhulokiesisekelo sokwakha. Kubalulekile ukuhlanganisa ngokuphindaphinda ka 10, kayishumi kanye ukuze kwenzeke 100 nokuqala ukubona 100 njengento eyodwa. Abafundi 10, kayishumi kanye nokuphiondaphinda kufanele babuzwe ukuthi mangakhi amaqembu 100 abanawo. Ukubaluleka nokuphiondaphinda kanye (HTU) kwamakhadi endawo kufanele kusetshenziswe ukuveva izinombolo. kanye (HTU) • Bonisa uphinde uchaze Ukusebenzisa u diens nesisekeko sika 10 samabhuloki lokhu okulandelayo • Bonisa uphinde uchaze idijithi ngayinye. imibuzo nemithetho ingabuzwa noma inikezwe. idijithi ngayinye. • Mangakhi 100 aku 300,400,500 • Bhala lezizinombolo ezilandelayo: 256,387,499 Kuleli themu abafundi bafunda okushiwoyo nokubhalwayo phansi kanye nokubaluleka kwamadijithi ezinombolweni ngo 452 ukubaluleka kuka 5 emashumini amahlanu. Ngo 325, ukubaluleka kuka 5 okuhlanu. Kubaluleke kakhulu ukuhlanganisa nokuqonda ukuthi 50 ku 5 wezinyada ezinhlanukubalulekile ukuhlnganisa nokuqonda ukuthi Indawo nokubaluleka kwamakhadi iyalingana ngokubaluleka. Indawo nokubaluleka kwamakhadi kusetshenziswa ukuhlakaza izinombolo ukuze kuvele ukubaluleka kwedijithi ngalinye. 637 = 600 + 30 + 7 Abafundi bangenza amasethi abo endawo nokubaluleka kwamakhadi. I -emvilophi inganamekwa emuva encwadini yokufundela yomsebenzi wasekilasini amakhadi afkwe kuyo lemvilophi. Amakhadi angasetshenziswa noma kubalwa futhi kungaba yenye indlela abathola ngayo imiphumela. 447 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 448 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.5 Sebenzisa ama Amakhadi enani nobungako benombolo ukufundisa ngalokhu. Inani lenombolo Izibalo IBANGA 1-3 Hlakaza amadijithi amabili ezinombolo uwaphindephinde abe ngamakhulu, amashumi kanye nokunye Abafundi bangahlakaza izinombolo bazenze: Amakhulu,amshumi kanye nokunye okubalulekile e.g. 273 = 200 + 70 + 3 (Amakhadi endawo ayasetshenziswa ukwenza lokhu) • Ukuphindaphinda ngamashumi nokunye e.g. 273=2 amakhulu, 7 amashumi + 3 okunye Ukwakha amadijithi amabili ezinombolo kususelwa ukbaluleka kwamakhadi endawo Isibonelo: Bhala lenombolo 1 ikhulu namashumi amathathu 2 amakhulu kanye 4 amashumi kanye 5 ngakunye 2 amakhulu +9 amashumi + 2 okunye Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 3 amakhulu +5 amashumi + 7 okunye Isibonelo: Esiphelele: a) 346 = 300 +  + 6 b) 400 + 20 + 8 = 

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) Ukuxazulula izinkinga ezisesimweni esejwayelekile 1.6 Sebenzisa lamathekinisi Sebenzisa lamathekinisi Abafundi bazoqubeka besenzisa izinkinga zamagama besenzisa lamathekisi alandelayo uma alandelayo uma alandelayo. Amathekinisi okuxazulula izink- uxazulula izinkinga, uxazulula izinkinga, • Ukwakha nokuhlakaza izinombolo inga uphinde uchaze ukuthi uphinde uchaze ukuthi izinkinga lezo: izinkinga lezo: • Ukuphindaphinda nokugamula • Ukwakha izinombolo • Ukwakha izinombolo • Inamba layini nokuzihlakaza futhi. nokuzihlakaza futhi. Yini umahluko kumehluko kusukela kuthemu 1 • Ukuphindaphinda • Ukuphindaphinda Kuleli themu abafundi bangaqalisa ukufinyezela mduzane 10. Ukusondezela nokugamula nokugamula lokhu okujwayelekile kwendlela eqagelayo. Uma umfundi emuhle ngokuqagela • Inamba layini • Inamba layini amakhono akhe mawaqikelelwe aphinde alalelwe. Phambi kokuthi abafundi bangasebenzisa leliqhinga lokusondezela uma • Ukuqoqela • Ukuqoqela behlanganisa, besusa kufanele bazilolonge ngalethekinisi kuqala. okwamashumi okwamashumi Lokhu kungenziwa ngokusebenzisa inamba layini: Isibonelo:   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   • Ama- 33 asondele kuma- 30 noma ama-40? • Ama-37 asondele kuma-30 noma ama 40? Abafundi kufanele bakwazi lokhu: Ama-35 aphakathi nendawo nama- 30 kanye nama-40. Sithi ngaloko ukusondelela e-10 eliseduze kuma-35 kuya ema- 40 ngoba siyayisondezela eshumini elikhulu inombolo uma isuka kuhhafu nangaphezulu we-10. Bheka amanothi kathemu 2. 449 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 450 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.7 • Hlahlela igama • Hlahlela igama Izinkinga ngezibonelo ezingenziwa kulelithemu esibalweni uphinde esibalweni uphinde Ukuhlanagnisa Izibalo noku hlanganisa kanye nokususa nokususa uchaze ukuthi uchaze ukuthi ufike kanjani ufike kanjani • UPhamela wqokelela 413 izivalo zamabhodlela. Uma ngabe UKen 29 kuleyompendulo kuleyompendulo amabhodlela uzobe enenani elilanganayo nawakaPamela. Izibalo IBANGA 1-3 • Yokuphindaphinda Yokuphindaphinda • Zingakhi izivalo zamabhodlela abobonke. ngezimpendulo uze ngezimpendulo uze ufike • Zingakhi izivalo zamabhodlela uKen asenazo kusukela ekuqaleni ufike 999 400 • Unkosinkazi Zibi weboleke unkosikazi Magadla R80,00. Unkosinkazi Zibi manje usene R366, 00 eyayiesele wayenemalini unkosikazi unkosikazi Zibi kwasekuqaleni? • UJan ufunde amakhasi 115. UNandi ufunde amakhasi 126. Mangakhi amakhasi adlulele kunalawa uNandi edlule weqa kuNandi? • UBonga unamamabuli 218. Unamamabula ehlile kunani lika Anna nge 97 unamamabula angakanani u- Anna? 1.8 • Hlahlela igama • Hlahlela igama Izinkinga ngezibonelo ezingenziwa kulelithemu esibalweni uphinde esibalweni uphinde Ukuhlanganisa Bheka kulelithemu 1 ukuzobona izibonelo uzokwazi izinombolo uzenwebe ngokuphindelela uchaze ukuthi uchaze ukuthi njengoba. okuholela ufike kanjani ufike kanjani ezibalweni kuleyompendulo kuleyompendulo • Umanenja kufanele afake isicelo samathaya emabhisini 8, uma ibhasi lilinye zokuphindaphinda lidinga amathaya 6 nesphele esisodwa, manje mangakhi amathya okufanele • Yokuphindaphinda • Yokuphindaphinda imenenja iwacele? ngezimpendulo uze ngezimpendulo uze ufike 99 ufike 75 • Idamu lokubhukuda lesikole ling 10 amamitha ubude. ULuvuyo ubhukude amamitha angamaxadu 6. Usebhukude kangakanani? Uhlobo lwenkinga: Uhlelo ngononina • Ingadi yamaveje inemigqa 12 etshalwe izivande. Umagqa ngamunye unezivande 7 ngakho zingakhi izivande engadini? • Ingadi yamaveje inemigqa 12 etshalwe izivande. Yonke imigqa inenani Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola elilinganayo lezivande. Uma kunesamba senani 48 izivande. Zingakhi izivande emgqeni ngamunye • Izivande zamaveji engadini inani 48 ezilinyiwe ngemigqa. Kunezivande 7 emgqeni ngamunye, mingakhi imigqa isiyonke?

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.8 Ubungako kuqatha nobunye Ukuhlanganisa • USamuweli unamaswidi 6 nayisithupha. USamuweli unamaswidi aphindwe ngokuphindelela kathathu kunamaswidi oMoeketsi okuholela ezibalweni • uMarlene unaswidi 18. Lamaswidi aphindwe kathathu kuna Samuel. USamuel zokuphindaphinda unaswidi angakanani. Lolu hlobo lwezibalo luyethulwa okokuqala kuthemu 2. Abafunda bangathatha isikhathi eside benza loluhlobo lwezibalo. 1.9 Yenza lezibalo wenze Yenza lezibalo wenze Izibonelo zezinkinga ezingenziwa kuleli themu. uchaze nezimpendulo uchaze nezimpendulo Ukwakha amaqoqo Zingakhi izimoto ezidingekayo ukuhambisa izingane 24 uma ngabe abafundi nokuhlukaniselana ngezibalo ezenziwa ngezibalo ezenziwa abane bengalingana eqoleni eyodwa? okuholela njalo njalo nabanye njalo njalo nabanye ezibalweni ngamaqembu abunjwa ngamaqembu abunjwa Kunamasokisi angama-65 ediloweni. Mangakhi amapheya amasokisi? aze afike 100 kwenziwe aze afike 75 kwenziwe Ukubumba zokuhlukanisa nezimpendulo ezizofaka nezimpendulo ezizofaka izinsalela izinsalela uDavide uthengisa izikhwama ezinama- olintshi ayishumi. Unama-olintshi 40. Zingakhi izikhwama angazigcwalisa? uThabo unamaswidi 66. Imihla yonke udla amaswidi 3. Mangakhi amalanga angadla ngawo amalanga? 1.10 Xazulula bese Xazulula bese Kulelithemu 1abafundi bethulwa ku zingqezu ezihlukene isib. 3 amakota noma 2 uchaza izixazululo uchaza izixazululo thirds. Ulwazi olwaneleyo lwethulwe ukuze kwaziwe leziziqhezu. Ukuhlukaniselana okuholela izinkingeni ezenziwayo izinkingeni ezenziwayo Izibonelo zezinkinga ezingenziwa kuleli themu. ezibalweni ezifaka ukwabelana ezifaka ukwabelana zokuhlukanisa ngokulingana okuholela ngokulingana okuholela a) Ukwehlukanisa okuholela ezibalweni zamaqhezu ezixazululweni ezifaka ezixazululweni ezifaka b) Hlukanisa oshokolezi aba-8 phakathi kwabangani aba-3 ukuze bathole inani amaqhezu okuphelele amaqhezu okuphelele elilinganayo kuphinde kungasali lutho nalawo okungewona nalawo okungewona c) Iqhezu lokuqoqelwe ndawonye 1 1 1 3 1 1 1 3 okuphelele isib. 2 , 4 , 5 , 4 , okuphelele isib.2 , 4 , 5 , 4 , d) Thola ikota lamaswidini ama- 20. 2 2 5 , njll njll. 5 , njll. e) Amaswid ayi- 6 angamaqhezu amangakhi amaswidi angama- 24 f) Ugogo wanikeza amA- R12. Ukiki ugcina okwesithathu ye mali. Yimalini ayigcinile. Loluhlobo lwezibalo lungenziwa ngabafundi, uma sebekhonile ukwenza izibalo ngazine, nanhlanu behlukaniselana ngokuholelayo iziqhezu baphinde 451 bazi izingcezu ezahlukene. Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 452 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.10 Ukubhala Ukuhlukaniselana Abafundi akumele babhale izimpawu zamaqhezu. Abafundi bayoqhubeka bele- okuholela bula amaqhezu oku-1 kokuhlanu, oku-3 kwekota noma oku-3 kokuyisithupha. ezibalweni zokuhlukanisa Ukwethula amaqhezu ngezinkinga zamagama Izibalo IBANGA 1-3 Abafundi kufanele bazitholele izimpendulo ukuveza ukuthi bayazithola noma bayakwazi ukwenza izibalo. Kuyadingeka ukuthi abafundi bangathola izimpendulo kahle bangazinikezi igama eliqondile loqhezu. Siza lababafundi ukunikeza igama eliqondile leqhezu. Abafundi kufanele banikeze amaqhezu lezi abazihlukaniselana ngokubhala njenga ku 2 thirds. 1.11 • Bona uphinde uphinde • Bona uphinde uphinde Izibonelo zezinkinga ezingenziwa kuleli themu: ukhombe ukhombe Imali • Ukubaluleka kwemali nokwenza amathothali isib • iImali ewuhlweza noma • iImali ewuhlweza noma - Bhala 525c ngamarandi namasenti engamaphepha yaseN- engamaphepha yaseN- ingizimu Afrika ingizimu Afrika - Ngezindlela ezingakhi ungenza iR400 usebenzisa amabhangi nothi, ube sewazi kanjani unazo zonke izimpendulo? • Xazilula izinkinga ze- • Xazilula izinkinga ze- mali ngokufaka isamba mali ngokufaka isamba - UPhilasande uno 50c kanye nezingcezu ezine zika - 20c. Ushokoledi ubiza uwaguqule abe ama- uwaguqule abe ama- u - 20c. Uzothola ushintshi wamalini? Randi noma masenti. Randi noma masenti. • UMandla ukhokhe u - R2, 50 ukukhwela itekisi eya esikoleni. • Guqula phakathi kwa- - Kumbiza malini ukuya nokubuya esikoleni nsukuzonke? maRandi namasenti - Isitimela sibiza R6 ukuya nokubuya ithikithi. Yikuphi okushibhile i train noma taxi? • Ukuthenga nokuthengisa nezibalo - Ugogo kaNothando umnikeze u - R5, yimaphi amaswidi amathathu angahle awathenge? Ushokoledi ubiza u - R2, 70; ushingamu ubiza u - R1, 80; isi- tokswidi sibiza u - R1, 40; ithofi u - R1, 20. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola - UNdalwenhle uthenge izincwadi ezintathu, iyinyeibiza u - R80 iyodwa; malini ushuntshi azowuthola uma ekhokhe ng - R300? - Iphakethe elinoswidi oyi - 5 libiza u - 44c lilinye. Umnumzane uNtshangase ufuna uswidi ongama - 88. Mangaki amaphakethe okufanele awathenge? Malini azoyikhoka?

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.11 • Amabhasi amthathu ahamba emgwaqeni omkhulu okhokhelwayo obiza u - R40 ibhasi ngalinye. Malini ekhokhwa yilamabhasi esewonke? (kulindeleke uku- Imali thi abafundi basebenzise ukuhlanganisa ngokuphindelela lapho inani lerandi liphakeme kakhulu) IZIBALO EZISESIMWENI ESIKHULULEKILE 1.12 Sebenzisa amaqhinga Sebenzisa amaqhinga Abafundi balindeleke ukuba basebenzise lamaqhinga alandelayo uma benza alandelayo uma alandelayo uma izibalo esimweni esikhululekile: Amasu (izindlela zokwenza noma kwenziwa izibalo: kwenziwa izibalo: • Uwakha nokuhlakaza izinombolo namaqhinga) • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza • Ukuphinda kabili nokuhlukanisa izinombolo ngokulinganayo izinombolo izinombolo • Umugqa wezinombolo • Ukuphinda kabili • Ukuphinda kabili nokuhlukanisa kabili nokuhlukanisa kabili • Ukusondezela eshumini ngokulinganayo ngokulinganayo Vumela abafundi ukukhetha amaqhinga abakwazi kangcono ukusebenza ngawo, izinombolo izinombolo kodwa-ke, uma abafundi besebenzisa amaqhinga angasebenzi kahle badinga • Umugqa wezinombolo • Umugqa wezinombolo ukulawulwa ukuthi basebenzise amaqhinga angasebenza kangcono. • Osondezela eshumini • Osondezela eshumini Bheka amanothi kathemu 1 kuloku • Ukwakha nokuhlakaza; • Ukuphinda nokuhlukanisa kabili ngokulandelayo; kanye • Umugqa wezinombolo. Ukusondezela eshumini Bheka incazelo ekuxazululeni izinkinga engxenyeni yesi-2. 453 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 454 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.13 • Ukubala ufike 999 • Hlanganisa ufinyelele Yini eyehlukile kuthemu 2 ema- 400 Ukuhlanganisa • Susa kusukela 999 Kulethemu abafundi babala ngezinombolo ezakhiwe amadijithi amathathu okoku- nokususa • Susa kusukela ema- qala. Ukuze babale ngezinombolo ezinamadijithi amathathu ngokuzethemba, • Sebenzisa izimpawu 400 kufanele bebe sebekwazi uku: ezifanelekile Izibalo IBANGA 1-3 (+, –, =, ) • Sebenzisa izimpawu • Funda nokubhala izimpawu zezinombolo kufike ema-400; ezifanele (+, –, =, ) • Sebenzisa amabhondi • Hlela nokuqhananisa izinombolo kufinyelele ema-400; ezinombolo ufike ema- • Sebenzisa amabhondi • Bala ngamaqoqo kufike ema-400; noku 30 ezinombolo ufike ema- 30 • Bala ngezikhawu zoku-2,3,4,5,10,50,ne-100 kufike ema-400 Ngalethemu abafundi bazoqhubeka nokuhlakaza izinomboloukuze bawazi uku- bala. Ukwakha nokuhlakaza izinombolo kuhlala kuyiqhinga elibalulekile abafundi abangalisebenzisa ngalethemu. Izindlela ezingasebenza ukubala ngokuhlanganisa nokususa. • Ukuhlakaza inombolo ibe izingxenyana ezincane ukwenza ukubala kube lula. Amaqhinga amaningi asetshenziswa abafundi ukubala afaka ukuhlakaza izinom- bolo. Bayaqhubeka nokwenze njalo nangezinombolo ezingamadijithi amathathu. • Ukuhlanganisa ngendlela yokuhlakaza inombolo eyodwa 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 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola = 406

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.13 Isibonelo: Ukuhlanganisa Ukuhlanganisa amadijithi amathathu namadijithi amathathu nokususa Hlakaza zombili izinombolo 323 + 136 =  323 + 136 =(300 + 20 + 3) + (100 + 30 + 6) = (300 + 100) + (20 + 30) + (3 + 6) = 400 + 50 + 9 = 459 Ukuhlanganisa (ngokuhlakaza izinombolo ezizohlanganiswa) Abafundi bazohlakaza inombolo abangayikhona bona. Loku kusho ukuthi ben- gakwenza ngezindlela ezehlukene. Isibonelo: ukuhlanganisa izinombolo ezinamadigiti 324 + 82 =  amathathu nezinye futhi ezinamadigiti amathathu 324 + (40 + 40 + 2) 323 + 136 =  324 + 40→ 364 + 40→ 404 + 2 = 406 323 + 136 = 323 + (100 + 30 + 6) = (323 + 100) + 30 + 6 = (423 + 30) + 6 = 453 + 6 = 459 Ukubala kuqhutshekwe ngama 40 ukusukela kuma-324 kungenziwa ngokubala ngama-10. • Ukususa • Ukuhlakaza zombili izinombolo 455 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 456 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.13 Kususwa amadijithi amabili kumadijithi amathathu. Ukuhlanganisa Isibonelo: nokususa 389 – 137 =  389 – 137 = (300 + 80 + 9) – (100 + 30 + 7) Izibalo IBANGA 1-3 = (300 – 100) + (80 – 30) + (9 – 7) = 200 + 50 + 2 = 252 Ukususa ngokuhlaza inombolo eyodwa Isibonelo: 389- 137 =  389 – (100 + 30 + 7) 389- 100 → 289- 30 → 259- 7 = 252 • Ukususa ngokuhlakaza inombolo eyodwar Isibonelo: 389- 137 =  389 – (100 + 30 + 7) 389- 100 → 289- 30 → 259- 7 = 252 • Ukusebenzisa ukuhlukanisa kabili ngokulinganayo ngokuhlakaza inombolo Isibonelo: 225 + 16 = 225 + 8 +8 = (225 + 8) + 8 = 233 + 8 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola = 241 • Bala uye phambili ubuye uye emumva 305 + 298 =  Bala uqhubeke ngakunye usukela ema-298 kuyiqhinga elisebenzayo ngoba izinombolo ziyesondelana.

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.13 • Khomba eduze kweziphinda kabili Ukuhlanganisa Isibonelo: nokususa 145 + 146 = 191kuchaza ukuphindeka kabili145 kuhlangana noku- 1 noma ku- phinde kabili i-146 kususe oku- 1. 145 + 145 + 1 (100 + 40 + 5) + (100 + 40 + 5) + 1 (100 + 100) + (40 + 40) + (5 + 5 + 1) 200 + 80 + 11 280 + 11 280 + 10 + 1 290 + 1 291 • Shintsha inombolo ibe ngephinda kashumi bese ususa noma uhlanganise imivo Bala ukhuphuke noma wehle ukusondezela e-10 eliseduze Isibonelo: 288 + 11 288 + 10 = 298 298 – 1 = 297 Isibonelo: 188 + 19 188 + 20 = 208 208 – 1 = 207 457 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 458 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.13 Ukuthuthukisa amakhono ngokwenza ukuhlanganisa nokususa. Ukuhlanganisa Abafundi badinga ukusebenzisa amakhono ukwenza izinhlobo ezithile zezibalo nokususa zokuhlanganisa nokususa. • Ukwenza ambhodi afika kuma-30 Izibalo IBANGA 1-3 • Hlanganisa uphinde ususe ngokuphinda ka- 10 Abafundi kuzofanele bathole amathuba okwenza lezinhlobo ezilandelayo zezibalo ngezinombolo ezifinyelela ema- 400: Hlanganisa noma ususe ubala ngama-10 okuhamba ngakubili kweqe e-100 40 + 70 70 + 80 120 - 30 150 - 60 Hlanganisa noma ususe i-10 ezinombolweni ezingamadijithi amabili noma amath- athu, ezifaka ukweqa ema- 100. Isibonelo: 65 + 10 124 + 10 326 - 10 358 - 10 Hlanganisa ususe inombolo enedijithi eyodwa kwenamadijithi amabili ngaphandle kokweqa amashumi. Isibonelo: 234 +5 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 475 +  = 479 768 - 4

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.13 Hlanganisa uphinde ususe inombolo enedijithi eyodwa kwephinda ngama- 100 Ukuhlanganisa Isibonelo: nokususa 200 + 4 300 + 3 300 - 6 400 - 5 Qala ukuhlanganisa uphinde ususe okuphinda ka- 100 okuhamba ngakubili. 100 + 100 100 + 200 Abafundi kufanele banikezwe amathuba okwenza amaphethini ngokuhlanganisa nokususa. Uma ngazi ukuthi 1+ 1 = 2 Okusho ukuthi yini: 10 + 10 100 + 100 Ukubheka imphumela yokubala Ukubheka ukuthembeka kwesixazululo Abafundi kumele baqeqesheke ekubhekeni ukuthembeka kwezixazululo. Enye indlela yokwenza loku ukuqagela izimpendulo zabo ngaphambi kokubala. Uma kuhlanganiswa izinombolo ezimbili ezisondele kwenye isib. 145 nama 146,abafundi bangasebenzisa ukuphinda kabili inombolo kube indlela yokuqagela izimpendulo zabo. Ukuhlola izimpendulo Abafundi kufanele bazi ukuthi banga: • Hlola ukuhlanganisa ngokususa. Isibonelo: uma ama- 236 + 18 = 254;bese ama- 254 - 18 = 236;noku • Hlola izibalo zokususa ngokuhlanganisa. Isibonelo, ama- 384 - 48 = 336, bese ama- 336 + 48 = 384. Ukusebenzisa uphawu olusebenza ngokuphikisana nolunye ukuhlola izimpendulo 459 esinye isizathu sokufundisa ukuhlanganisa nokususa kanyekanye Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 460 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.14 • Phindaphinda • Phindaphinda Kuleli themu abafundi bozoqhubeka noku: izinombolo 1 kuya 10 2,4,5,10,3,kuye Ukuhlanganisa • Basebenzise babuye baqonde ulimi ngokuphindaphinda; ngo 2,3,4,5,10 ukuze esambeni sama-50 ngokuphindelela kufike 99 • Bethula ukuphindaphinda njengononina. Sebenzisa izimpawu ezifanele kuholela • Sebenzisa izimpawu ukuchaza imisho; ezibalweni • Sebenzisa izimpawu ezifanele Izibalo IBANGA 1-3 zokuphindaphinda ezifanele • Qonda loku ngokuphindelela okubhaliwe lokhu okungethulwa ngezimpawu (x, =, ) (x, =, ) zokuphindaphinda • Zilolonge uphinde uqonde ukthi ukuphindaphinda kungenziwa nomi ikanjani (ukusebenzisa izinombolo ngokuphambanisa izikhundla zazo); • Sebenzisa umugqa wezinomboloukubonisa ukuphindaphinda ubale uphinde uchaze ngokuzethula (ukugxuma kukuveza kanjani ukuhlanganisa ngokuphindelela). Abafundi bangaqhubeka nokusebenza njengononina bebhala behlanganisa kanye nokuphinda izinombolo ngemisho Isibonelo: Bhala izibonelo ezimbili zokuhlanganisa, nokubili ukuphinda phinda bhala lezinombolo ngemisho ibe ngononina. Imifanekiso engasetshenziswa ukuphindaphinda kungandiswa. Ithebula lokuphindaphinda lingethulwa. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.14 Isibonelo: Ukuhlanganisa × 2 3 4 5 6 7 8 9 10 ngokuphindelela 1 kuholela ezibal- 2 weni zokuphin- daphinda 3 4 5 Okusho kwama thebula ngokumemeza kungenziwa. Abafundi akufanele bazi amathebula eBangeni lesithathu 3. Ukugxila olimini, oluvumela izibalo ngekhanda ezivumela amaqembu. Isibonelo: • Okubili okudodwa kwenza okubili • Okubili okubili kwenza okune • Okubili okuthathu kwenza okuyisithupha • Okubili okune kwenza okuyisishiyagalombili • Ababili okuhlanu kwenza okuyishumi • Okubili okuyisithupha kwenza okuyishuminambili • Okubili okuyisikhombisa kwenza okuyishuminane • Okubili okuyisishiyagalombili kwenza okuyishuminesithupha • Okubili okuyisishigalolunye kwenza okuyishumi nesishiyagalombili • Okubili okuyishumi kwenza okungamashumi amabili 461 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 462 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.14 Ukusho lokhu ngalendlela kwelekelela ukuthuthuka kolwazi ekuhlanganiseni okuphindelelayo. Ukuhlanganisa ngokuphindelela Abafundi bangaphinde basebenzise umdwebo wokubala ngokuqhubeka kuholela ezibal- isibonelo weni zokuphin- Izibalo IBANGA 1-3 daphinda   Inombolo osebenza ngayo umphumela 1 umthetho 3 5 7 X  3   9 1.15 • Hlukanisa izinombolo • Hlukanisa izinombolo Kuleli themu lesibili abafundi nokuzilolonga baphinde bahlanganise beseben- ufike ema -99 ngoku- ufike ema -50 ngoku- zisa umpawu lokwehlukanisa. Kufanele bazi ukuthi izimpawu zokuhlakanisa ukuhlukanisa ngezinombolo emshweni kungachaza isimo esiphalene nokubumba amaqembu 1, 2, 3, 4, 5, 10 2, 4, 5, 10 nokwehlukanisa. • Sebenzisa izimpawu • Sebenzisa izimpawu ezifanele ezifanele Yini umahluko kusukela kuthemu 1? (÷, =, ) (÷, =, ) Kuleli themu abafundi kufanele bakwazi ukubhala bechaza izimpawu zokwehlu- kanisa emshweni. Abafundi kufanele bakwazi ukulekhoda lokhu okulandelayo: 30 ÷ 6 =  nokuthi 30 ÷ 5 =  Abafundi bafanele futhi bakwazi ukuthuthukisa izindlela ezahlukene zokwehlu- kanisa uma ubala. Izibonelo: ukususa ngokuphindelela Ukuze sikwazi ukubala 12 ÷ 4 =  abafundi bafanele bakwazi izithombe zabo ukuma kwamaqembu.   Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola                  Iqoqo elilodwa Iqoqo elilodwa Iqoqo elilodwa loku-4   loku-4   loku-4

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.15 Hlukanisa iqembu elilodwa 4 futhi iqembu lesibili 4 neqembu lesithathu 4 ukuhlukanisa 12- 4 → 8 – 4 → 4- 4 = 0 Njenge qembu elilodwa lika 4 libekwa nganhlanye ngakhoke abafundi bangasusa 4 okokuqala bese bebala ukuthi kusele okungakanani. Bazoqhubeka bekwenza lokhu kuze kufike lapho baze basuse konke okususwayo. Okugcizelelwayo eBan- geni 3 kufanele bazibumbe ngokwamaqembu kunokuhlukana. Ukwenza okuphindaphinda ukususa ngaleli nani linwebeke ngokufaneleyo. Abafundi bazokuba nokwahlukano okunikezelwe, ngokuhlukaniswa ngemisho ukuze kuvunyelwe ukususa ngokuphindelela. Ukwenza ukususa ngokuphindelela 96 ÷ 3 Akusikho okushaye esikhonkosini inqobo nje wukuthi inani linwebeke laya phe- zulu Okokuqala kungabanzima ukuthi abafundi babone yiyiphi inombolo emshweni, futhi yiyiphi inombolo enwetshiwe nokuthi emishweni kungenziwa ukususa oku- phindiwe. (yiziphi izinhla zezinombolo) ezilungele ukwenza ukususa ngokuphin- delela? 1.16 Ulwazi lwezinombolo: Ulwazi lwezinombolo: Ulwazi lwezinombolo uhla 999 uhla 500 Izibalo zekhanda. Izinhlobo zemibuzo engabuzwa: • Hlela izinombolo • Hlela izinombolo Amagama nezimpawu zezinombolo ezikhethiwe zeqoqo ezikhethiwe zeqoqo elinikeziwe. elinikeziwe. Zohla 500. Phakamisa ikhadi noma ubhale igama lenombolo. Khetha umfundi ukuba abhale uphawu lwenombolo. • Qhathanisa izinombolo • Qhathanisa izinombolo kufinyelele ema-999 kufinyelele ema-500 Kuningana ukunokunye nokuncanyana ukunokunye bese usho ukuthi bese usho ukuthi Yini?: ikuphi okunga phezulu ikuphi okunga phezulu noma okungaphansi noma okungaphansi • Okuncane ngoku-1 kokungama-500 ngoku-1, 2,3,4,5, ngoku-1, 2,3,4,5, kanye ne-10 kanye ne-10 • okuningi ngoku-1 kokungama-499 • okuningi ngoku-2 kokungama-502 • Okuncane ngoku-2 kokungama-405 • okuningi ngoku-3 kokungama-477 • Okuncane ngoku-3 kokungama-251 463 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 464 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI nemizuzu engu THEMU1 KONYAKA 24) 1.16 Khumbula Khumbula • Okuncane ngoku-4 kokungama-185 ngokushesha: ngokushesha: Izibalo zekhanda. • okuningi ngoku-10 kokungama-490 • Okuyikho • Okuyikho • Okuncane ngoku-10 kokungama-660 ngokuhlanganisa ngokuhlanganisa nokususa kufinyelela nokususa kufinyelela Iluphi uhlamvu lwesi-5 ezinhlamvini zama-alfabhethi? Izibalo IBANGA 1-3 ema-20 ema-20 Iyiphi inyanga yesi-9 onyakeni? • Susa noma uhla • Susa noma uhla Ukuhlela nokuqhathanisa nganise okuphinda nganise okuphinda ka-10 kusukela koku-0 ka-10 kusukela koku-0 Ikuphi okuningi: kuya e-100 kuya e-100 621 noma 671? • Okuyikho Amaqhinga okubala ngokuphindaphinda ngekhanda Nginike inombolo ephakathi koku-154 noku-159. nokuhlukanisa u: Okuyikho ngokuhlanganisa noma ukususa: sebenzisa lamaqhinga • Ithebula lokuphinda okubala alandelayo: Bheka amanothi eThemu yoku-1. kabili kufinyelele koku- • Beka inombolo enkulu Hlanganisa noma ususe okuphindwe ka-10 kokuyi-100 2x10 kuqala ukuze ubala • Ithebula lokuphinda uqhubeke noma uye Yisho ukuthi amagxathu okumele athathwe emugqeni wezinombolo kuqalqwq kashumi kufinyelel emumva kokungama-30 kuya kokuyi-100 noma kuqala kokuyi-100 kuya kokungama-50. koku 10x10 Thola amakhadi ahambisana ngamabili ukwakha i-100. • Umuqga wezinombolo Amaqhinga okubala Beka izinombolo emabhokisini ukwakha i-100. • Ukuphinda kabili sebenzisa lamaqhinga ngokulinganayo  + 70 = 100 okubala alandelayo: nokuhlukanisa kabili 20 +  = 100 • Beka inombolo enkulu ngokulinganayo kuqala ukuze ubala 100 –  = 90 • Ukwakha nokuhlakaza 100 – 40 =  uqhubeke noma uye izinombolo emumva Amaqhinga okubala: • Sebenzisa ubudlelwano phakathi Bheka amanothi kaThemu 1 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola kokuhlanganisa nokususa

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI CAPS THEMU1 nemizuzu engu KONYAKA 24) 1.16 • Umuqga wezinombolo Izibalo zekhanda. • Ukuphinda kabili ngokulinganayo nokuhlukanisa kabili ngokulinganayo • Ukwakha nokuhlakaza izinombolo • Sebenzisa ubudlelwano phakathi kokuhlanganisa nokususa • Sebenzisa ubudlelwano phakathi kokuphindaphinda nokuhlukanisa 1.17 • sebenzisa uphinde ngaleThemu abafundi baqhubeka noku: usho amagama Amaqhezu • Funda amagama ezingxenye zamaqhezu; ajwayelekile amaqhezu ezimweni ezijwayelekile • Sebenzisa amagama ezimweni ezehlukene; okufaka uhhafu, ikota, • Bona ingxenye yeqhezu; okwesishiyagalombili, okwesithathu, • Qala ukuqonda ubudlelwano bobungako bamaqhezu; okwesithupha, okwesihlanu. • Thola amaqhezu ezinto; bese • Bona amaqhezu • Funda ngokufana/ngokuhambelana kwamaqhezu; emdwebeni Ngalethemu abafundi bazoqhathanisa amaqhezu. • Qala ukubona ukuthi • Ukusebenzisa imicu yamaqhezu noma izinti zikaCuisenaire. ohhafu aba-2 noma okwesithathu oku-3 kwenza into eyodwa ephelele nokuthi uhhafu o-1 kanye namakota ama-2 kuyalingana 465 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO NAMAKHONO 466 ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI   nemizuzu engu THEMU1 KONYAKA 24) • Bhala amaqhezu Isibonelo: anjengo hhafu o-1 Lemifanekiso ingasebenza kangcono ekufundiseni abafundi ukthi basho noku-2 amagama amaqhezu nokuwaqhathanisa. Isibonelo: orange   red     Izibalo IBANGA 1-3 dark  green   dark  green   purple   purple   purple   purple   red   red   red   red   red   red   W   W   W   W   W   W   W   W   W   W   W   W   Veza ukuqonda amaqhezu ukukhombisa oku-1 okuphelele, ohhafu, okokuthathu, orange   red   amakota, okokuhlanu, okwesithupha, okwesishiyagalombili, okweshumi. dark  green   dark  green   Kuhle kakhulu nukthi abafundi ngezinto eziphathekayo futhi bangaqhathanisi purple   purple   purple   purple   amaqhezu besebenzisa udonga lwamaqhezu asezithombeni. Abafundi badinga red   red   red   red   red   red   ukuyithinta into ngo kuyilinganisa nenye. W   W   W   W   W   W   W   W   W   W   W   W   • Bangaki ohhafu abalingana nokuphelele? • Mangaki amakota alingana nokuphelel? • Mangaki amakota akha uhhafu owodwa? Yenza abafundi babeke imicu yamaqhezu eduze kweminye ukuthola izimpendulo. • Kungaki okokuthathu okulingana nokuphelele? • Kungaki okokwiyisithupha okulingana nokokuthathu? • Kungaki okokwiyisithupha okulingana nokuwuhhafu? • Yikuphi okukhulu, okokuthathu oku-1 noma oku-1 okuhhafu? • Yikuphi okukhulu oku- 2 kokuthathu noma amakota ama- 3 ? Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI- 2 YEBANGA LESI-3 2. AMAPHETHINI, UBUDLELWANE NE ALJEBHRA UKUQONDA Isikhathi CAPS UKUQONGA OKUFUNDWAYO esinqunyiwe OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO se hora eli ABHEKWA NGOKUPHELA -1 nemizuzu NGETHEMU 2 KONYAKA engama-24) 2.1 Ukubukela, Ukubukela ukuqhubeka Qhubeka nokunikeza abafundi uhla olufanayo lamaphethini nolukaThemu 1, 1 isifundo ukuqhubeka nokuchaza nokuchaza ngamagama kodwa ufake zonke izimo nezinto ezintsha kumaphethini njengoba kwenziwe Amaphethini eZimweni neSikhundla okusazibalo-md- Ukubukela, ukuqhubeka Ukubukela, uku- webo nokuchaza ngamagama qhubekanamaphethini Bheka amanothi amaphethini kaThemu 1 noma nmanothi eSikhundla neZimo alula eThemu yesi-2. • amaphethini alula akhiwe ngezinto • amaphethini alula Vumela abafundi bakopishe kuqala, bese beyaqhubeka bagcine ngokuwachaza eziphathekayo ngezinto eziphathek- amaphethini. Njengamanje bafanele ukuwachaza amaphethini ngaphandle kosizo ayo lwemibuzo ebaholayo. Qhubeka nokugxila ekuthuthukiseni ulimi abaludingayo • amaphethini alula ukuchaza amaphethini. akhiwe ngukudweba • amaphethini alula imigqa, izimo noma akhiwe ngemidwebo Amanye amaphethini enziwe esukela ohlotsheni olulodwa lwesimo, kodwa izinto isibonelo ngasinye sesimo siyenyuka noma sinciphe isib. Uhla lwamaphethini: Ukwakha amaphethini Amanye amaphethini enziwe ngamaqoqo lapho khona izimo zezinto ezifanayo Amaphethini alula asez- angawakho zenzeka, kodwa inombolo yesimo kanye neyento ngayinye ikhula noma incipha imweni noma emaqoq- ngendlela ejwayelekile. Isib. Ukwakha amaphethini weni aphindwe ngendlela angawakho asejiyometri efana nse. Ukukopisha amaphethini kusiza abafundi ukubona ukulandelana ukuthi amaphethini akheke kanjani. • Ngezinto Amaphethi lapho khona eziphathekayo inombolo noma ubun- Ukuqhubeka namaphethini kusiza abafundi ukubheka ukuthi bezwisise kahle gako bezinto esiga- ukulandelana kwephethini. • Ngokudweba imigqa, beni ngasinye eshintsha izimo nezinto Ukuchaza iphethini ukusiza abafundi ukuthuthukisa ulimi namakhono ngengendlela engaqage- okukhuluma. Iyakusiza ukubona ukuthi abafundi bayihumusha kanjani iphethini. Amaphethini leka, okungukuthi Kuvame ukuba lula kubafundi ukukhuluma ngamaphethini emva kokuba asizungezile amaphethini akhula bewenzile. Njengamanje abafundi bayakwazi ukuchaza amaphethini ngaphandle ngendlela elindelekile. Ukukhomba,ukuchaza kosizo lokulekelelwa imibuzo. Qhubeka nokugxila ekuthuthukiseni ulimi ngamagama nokubukela Ukwakaha amaphethini abulidingayo ukuchaza amaphethini. amaphethini asejiyometri angawakho • ngokwemvelo Ukwakha amaphethini angawakho asejiyometri • empilweni yesimanje yansukuzonke • Ngezinto eziphathek- ayo 467 • emasikweni ethu ayigugu • Ngokudweba imigqa, izimo nezinto Izibalo IBANGA 1-3

UKUQONDA Isikhathi UKUQONGA OKUFUNDWAYO esinqunyiwe OKUFUNDWAYO NAMAKHONO (esifundweni 468 IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO se hora eli ABHEKWA NGOKUPHELA -1 nemizuzu NGETHEMU 2 KONYAKA engama-24) 2.2 Ukubukela, Ukubukela, Bheka amanothi eThemu yoku-1, 3 izifundo ukuqhubeka nokuchaza ukuqhubeka nokuchaza Amaphethini Qhubeka nohla lwezinombolo nokubala ngokulandelanisa ngendlela elandelayo: ezinombolo Ukubukela,ukuqhubeka Ukubukela,ukuqhubeka • Ngoku-1 kusukela kunoma iyiphi inombolo ephakathi kwe 0 nama 500 nokuchaza izinombolo nokuchaza izinombolo Izibalo IBANGA 1-3 ezilula ngokulandelana ezilula ngokulandelana • Ngokuyi-10 kusukela kunoma iyiphi inombolo kubalwa ngokuyi 10 phakathi kwe kufinyelele e- 1000 kufinyelele e- 150 0 nnama 500 Ukwakaha amaphethini • Ngoku 5 kusukela kunoma iyiphi inombolo kubalwa ngoku 5 phakathi kwe 0 ne angawakho 500 Ukulandelanisa Ukwakha amaphethini makukhombise ukubala • Ngoku 2 kusukela kunoma iyiphi inombolo kubalwa ngaku 2 phakathi kwe 0 ne angawakho ezinombolo. kuyiwe phambili 500 nasemuva ngo: • Ngokuyi 100 kusukela kunoma iyiphi inombolo kubalwa ngama-100 kufinyelele • Ngoku-1 kusukela okungenani e-1000 kunoma iyiphi • Ngokungama 50 kusukela kunoma iyiphi inombolo kubalwa ngama-50 inombolo ephakathi kufinyelele okungenani e-1000 kwe 0 nama 500 • Ngoku 3 kusukela kunoma iyiphi inombolo kubalwa ngaku 3 phakathi kwe 0 ne • Ngokuyi-10 kusukela 500 kunoma iyiphi inombolo kubalwa • Ngoku 4 kusukela kunoma iyiphi inombolo kubalwa ngaku 4 phakathi kwe 0 ne ngokuyi 10 phakathi 500 kwe 0 nnama 500 Sebenzisa izinto, izithombe, amathebula nemidwebo yokuqhubeka nezinombolo • Ngoku 5 kusukela ukulekelela abafundi ekushintsheni ekubaleni ngokweqa nokulandelanisa ukuya kunoma iyiphi ekuphindaphindeni ngako-10, 5, 2, 4. inombolo kubalwa ngoku 5 phakathi kwe Siza abafundi ukuba basebenzise amaphetrhini abawaziyo njengesisekelo 0 ne 500 sokuzilungiselela nokufunda amanye amaphethini isib. • Ngoku 2 kusukela • Ukulandelana ngaku-2 ukwendlalela ukulandelana ngaku-4; kanye kunoma iyiphi • Ukulandelana ngaku-5 ukwendlalela ukulandelana ngama-50. inombolo kubalwa Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ngaku 2 phakathi kwe 0 ne 500

UKUQONDA Isikhathi UKUQONGA OKUFUNDWAYO esinqunyiwe OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO se hora eli CAPS ABHEKWA NGOKUPHELA -1 nemizuzu NGETHEMU 2 KONYAKA engama-24) • Ngoku 3 kusukela kunoma iyiphi inombolo kubalwa ngaku 3 phakathi kwe 0 ne 500 • Ngoku 4 kusukela kunoma iyiphi inombolo kubalwa ngaku 4 phakathi kwe 0 ne 500 Ngokungama 50, 100 okungenani kokuyi 1000 469 Izibalo IBANGA 1-3

ITHEMU YESI-2 YEBANGA LESI- 3 3. INDAWO NESIMO (IJIYOMETRI) 470 IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI THEMU 2 nemizuzu engu KONYAKA 24) 3.1 Isikhundla nokubukeka Isikhundla nokubukeka Yini eyahlukile ebangeni lesi 2? 2 izifundo kwento kwento Isikhundla, • Akukho kugxila okubaluliwe kokuthuthukisa ulimi lwesikhundla, njengoba lokhu Izibalo IBANGA 1-3 inkomba • Qondanisa ukubukeka • Qondanisa ukubukeka kwenziwa emabangeni 1 nele-2. nokubukeka kwento okwahlukene kwento okwahlukene • Landela izinkomba ezichaza kabanzi okungukuthi. Ukuzungeza isikole, kwento kwento efanayo yansu- kwento efanayo ukunokuzungeza ikilasi kuphela kuzonke yansukuzonke • Nika izinkomba zezindawo ezisekilasini nasesikoleni • Yisho into yansu- • Yisho into kuzonke nendlela yansukuzonke nendlela • Imibhalomdwebo nokubukeka kweqoqo lezinto zibukwa ngaphezulu. Ilapho ebukeka ngayo uma ebukeka ngayo uma kugxilwa khona ngethemu yesi-3 ikhonjiswa ngendlela ikhonjiswa ngendlela Isikhundla nezinkomba engajwayelekile engajwayelekile • Landela izinkomba • Funda, uhumushe futhi Isikhundla nezinkomba udwebe imibhalomd- lokhu kungenziwa ngemisebenzi engenziwa abafundi ngokunyakaza belandela • Landela izinkomba webo engahlelekile, imiyalelo. eBangeni lesi- 3 abafundi banganikezwa imiyalelo ngomlomo noma ukuhamba uzungeze noma ukukubukeka babhalelwe ikilasi, nesikole kwezintonto eziqo- qelwe ndawonye uma - Ukunyakaza bezungeza ikilasi isib. “ woza phambili nekilasi”; “ima eduze • Nikiza izinkomba zibukwa ngaphezulu kwesitulo sakho”; “ gxuma weqe umgqomo wezibi”; kanye ukuhamba kuzungezwa ikilasi, - Nokunyakaza bezungeza ekilasini noma esikoleli okusho ukuthi noma • Thola izinto emibhal- nesikole izinkomba ezinde ngokuthe xaxa, “ Hamba uphumele phandle jikela wenimdwebo kwesobunxele, qhubeka wehle nephasiji, nqamula inkundla, ukuphi manje.” Isikhundla nezinkomba • Nikeza izinkomba • Landela izinkomba ukuhamba uzungeze Abanye abafundi bangakuthola kulula ukunikeza izinkomba ngokwenza ikilasi, nesikole abakushoyo okumayelana nezinkomba ozinikezile. Kwabanye abafundi kuyasiza ukubanika inkombandlela yezinto ezigqamile zezinkomba. • Nikiza izinkomba uku- - Yisho noma uyaqhubeka noma ubheke enkombeni noma jika Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola hamba kuzungezwa ikilasi, nesikole - Yisho noma uyaqonda, jikela ngakwesobunxele noma jikela ngakwesokudla. • Landela izinkomba - Nikeza izimpawu lapho kufanele ujike khona isib. uma ufika ehhovisi ukusuka endaweni likamabhalane jikela kwesobunxele bese uya kwenye indawo es- emubhalwenimidwebo engahlelekile

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGASEKUPHELENI THEMU 2 nemizuzu engu KONYAKA 24) 3.1 - Ubona ukuthi kusafanele uhambe kangakanani. Kunezindlela ezehlukene zokusho ukuthi kusamele uhambe kangakanani, isib. Isikhundla, inkomba o Hamba izinyathelo 30 noma 10 amamitha; nokubukeka o Hamba udlule amakilasi ama- 3,noma hamba uze udlule ikilasi lika mnu kwento Radebe noma o Hamba okungaba umzuzu o- 1. Isikhundla nokubukeka kwento Ebangeni lesi- 3 abafundi kumele banikezwe umisebenzi lapho bengakwazi uku- qondanisa ukubukeka okwahlukene (ukubuka kuqhamuka ngaphezulu, ukubuka kuqhamuka emaceleleni, ukubuka kuqhamuka ngaphambili) kweezito ezihlukahl- ukane zansukuzonke. Lokhu kuzosiza abafundi ukuba bakwazi ukuhumusha imidwebo yezinto ezise- jiyometri eyenziwe ngezindlela ezahlukene zokubuka. Abafundi kumele banikezwe imisebenzi lapho bengakwazi ukubona into ethile esithombeni esidwetshiwe, isithombe esithathwe ngendlela engajwayelekile, isib. Ukubukeka kwengaphezulu lenkomo, ukubukeka kwengaphambili lesixubho. 471 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 472 IZIHLOKO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI THEMU 2 nemizuzu engu KONYAKA 24) 3.2 Uhla lwezinto Uhla lwezinto Yini eyahlukile ebangeni lesi- 2? 3 izifundo Izinto ezinhlang- Bona usho izinto ezi 3-D Bona usho izinto ezi 3-D • Abafundi abasabheki ukuthi into ingagingqika noma ingashibilika, babheka othintathu ekilasini nasezithombeni. ekilasini nasezithombeni. ukuthi indawo engaphezulu iyisicaba noma igobile. 3-D • izimo eziyindilinga • izimo eziyindilinga • Lapho izinto zinengaphezulu eliyisicaba, abafundi babheka ukuthi Izibalo IBANGA 1-3 (izimbulunga) (izimbulunga) lelongaphezulu liyisikwele, lingunxantathu, lingunxantathu noma liyindilonga. • izimo ezingamabhokisi • izimo ezingamabhokisi • Amakhoni namaphiramidi ayethulwa (lokhu kungagxilwa kukho ngeThemu yesi (amaphrizimu) (amaphrizimu) 3 neye 4). • amasilinda • amasilinda Okunconywe ukuba kugxilwe kuko ngoThemu 2 • amaphiramidi Izimpawu zezinto Abafundi basebenza ngezinto ezifanayo nalezo ababezisebenzisa eBangeni lesi- 2 • amakhoni chaza, uhlele bese uqhathanisa izinto ezi- • Amabhola nezinto ezinezimo zamabhola; Izimpawu zezinto 3-D ngokwe: • Amasilinda nezinto ezinezimo zamasilinda; kanye chaza, uhlele bese • izimo ezi 2-D, ezakha uqhathanisa izinto ezi- • Izinhlobonhlobo zamabhokisi nezinye izinto ezinzimo zamaphrizimu ubuso bezinto ezi 3-D 3-D ngokwe: angonxande namakhiyubhi. • izimo ezi 2-D, ezakha Abafundi bangagxila ezintweni ezintsha (amaphiramidi namakhoni) ngeThemu ubuso bezinto ezi 3-D yesi 3 neye 4 • ingaphezulu lezinto Ukubona nokusho amabhola (izimbulunga) namabhokisi (amaphrizimu) eliyisicaba noma kanye namasilinda ligobile • Abafundi baqhubeka nokusho, ukuhlela nokwenza amaqoqo ezinto. Abafundi kumele banikezwe uhla lwezinto abazosebenza ngazo: • Izimo ezinjengendilinga, isib. amabhola anobungako obungalingani, izimabula, amawolintshinjll. • Izimo ezinjengamaprisimu,isib. amabhuloki, izitini, amabhokisi anobungako okwahlukene isib. amabhokisi kamentshisi, amabhokisi amasiriyeli, amabhokisi etiye, amabhokisi omuthi wokuxubha; kanye Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Izimo ezinjengamasilinda, okufaka omabili amasilinda amade nazacile, isib. amaphayiphi awumbhobho, nemibhobho yephepha lasendlini yangasese ezakhiwe ngokhadibhodi ezimfishane, kanye namasilinda abanzi isib. Ithini likapholishi wezicathulo, amathiniesinefu njl.

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGASEKUPHELENI THEMU 2 nemizuzu engu KONYAKA 24) 3.2 Imisebenzi okugxilwa Imisebenzi okugxilwa Abafundi bangathola izinto ezibunjiwe ngengebhola (nokuyimbulunga) noma Izinto ezinhlang- kuyo kuyo njengebhokisi, (iprisimu) noma okusandilinga noma uhlobo oluthile lwezinto othintathu • buka wakhe • buka wakhe ezibunjwe njengendilinga. Abafundi bangathola noma babonise izinto usebenzisa izinto usebenzisa izinto ezibunjwe njengamabhokisi (iprisimu) ekilasini isib.lelithini likatamatisi libunjwe 3-D ezi 3-D ozinikeziwe ezi 3-D ozinikeziwe njengembulunga. usebenzisa izinto usebenzisa izinto Ngesikhathi sokufunda ngokuzimela abafundi bangaqhubeka ngokweza eziphathekayo eziphathekayo amabhola besebenzisa izimbulunga, namabhokisi besebenzisa (amaprisimu) usebenzisa izimo ezi usebenzisa izimo ezi ngobumba noma ubumba yokudlala. 2-D ezisikiwe ubumba, 2-D ezisikiwe ubumba, Ukugxila ezimpawini zezinto ezingama 3-D: indawo ephezulu eyisicaba izinti zokuvungula,izinti izinti zokuvungula,izinti noma egobile. zokumunca zokumunca • Ukwakha into eyi 3-D ehamba iyodwa isiphuzo,nazinye izinto isiphuzo,nazinye izinto ezi3-D ezisejiyometri ezi3-D ezisejiyometri Abafundi basebenzisa amabhokisi asikiwe abazikwele, noma onxande ukwenza ibhokisi.lokhu kugxila esmweni esiyisicaba sebhokisi. Abafundi bazobe sebebuka Uhla lwezimo izimo eziyizicaba zeprisimu nesilinda bazichaze ukuthi ziyiyindinga, isikwele, • izindilinga unxande. • onxantathu eziyizimo eziyizicaba nezigobile • izikwele Ukwakha ibhokisi kusiza abafundi ukuthi bagxile ezimweni eziyicaba zezinto. • onxantathu Abafundi bangabheka ukuthi zonke izimo ezisejiyometri zinezimo eziyizicaba Izimpawu zezimo kuphela. Ebangeni 1 no 2 abafundi bahlukanisa izinto ezinezimo ezisejiyometri kulezozinto ezigingqikayo nezishibilikayo. Lokhu kulekelela abafundi ukuba Chaza, uhlele bese bagxile ekutheni izimo zezinto zizyizicaba noma zigobile noma ziyagingqika. uqhathanisa izimo ezi Amanye amasilinda anzimo eziyizicaba, anye anezimo ezigobile. Lokhu 2-D ngokwe: kulungisela abafundi ukuba bagxile ezimweni zezinto eziyisicaba(izinto ezinga • isimo shibilika) noma ezigobile or curved (izinto ezingagingqika) Amasilinda amanye • izinhlangothi eziqondile anezicaba amanye agobile • izinhlangothi Umsebenzi obhalwayo ezindilinga Noma umsebenzi omningi wokusebenza ngezinto ezingaman 3-D uyimisebenzi wezinto eziphathekayo, umsebenzi kufanele uhlanganiswe njengomsebenzi wokubhala. Kulelibanga kufanele kugxilwe ekubizeni izinto nasekukhulumeni ngezimo zezindawo. Abafundi abalindelekile ukubala noma ukwazi inombolo yesikwele, unxande, unxantathu, noma indawo eyindilinga izinto ezinazo. Ulimi Ikhono lolimi olubalulekile lokukhuluma ngezinto ezingama 3-D: Ingaphezulu lendawo, isicaba, okugobile, amabhokisi, amabhola, osilinda 473 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 474 IZIHLOKO ALINDELEKILE AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGASEKUPHELENI THEMU 2 nemizuzu engu KONYAKA 24) 3.3 Izinhlobo zezimo ezahl- Akukho ukugxila okuthile kwezimo ezi 2-D okunconyelwe uThemu 2.Noma kunjalo, abafundi bangahlanganisa lokhu osekufundiwe ukene ngokubona nokubiza ama 2-D shapes kuthemu 2,ngokwenza umsebenzi obhalwayo ngesikhathi sokufunda ngokukhululeka. Izimo eziyi 2-D • izindilinga • onxantathu Izibalo IBANGA 1-3 • izikwele • onxande Isimo samaphethini Ukuchaza, ukuhlela, nokuqhathanisa ngokub- heka • isimo • amacala aqondile • amacala ayimbulunga Ukudweba izimo • izindilinga • onxantathu • izikwele • onxande 3.4 Ukufana nse nhlangothi Ukufana nse nhlangothi Yini okusha ebangeni lesi 3? 2 izifundo zombili zombili Okufana nse Ukubona nokubhala umugqa ohlukanisakablili kufane nse nhlangothi zombili • Ukubona nokubhala Ukubona nokubhala Ngokugoqa iphepha nokubuyiswa kombiko umugqa ohlukanisa umugqa ohlukanisakablili kablili kufane nse kufane nse Imisebenzi yokugoqwa kwamaphepha okukhululisa ukuqonda ukufananse kuzimoezingu 2-D nhlangothi zombili kufaka: Ngokugoqa iphepha ezisazibalomidwebo • Imsebenzi lapho upende omanzi ubekwe ephepheni ngaphambi kokuba nokubuyiswa kombiko Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola nalezo ezingesizo ligoqwe nemi izibalomidwebo • Sebenzi lapho iphepha lisikiwe noma lihleluliwe kulayini eligoqwe kulo. • Ukubona nokubhala umugqa Lemisebenzi ingenziwa uma kwenziwa izifundozezizibalo noma zamakhono ohlukanisakablili empilo kufane nse Cela abafundi ukuba baqagele ukuthi kuzophuma ziphi izimo uma sebevula Ngokugoqa iphepha lamaphepha abawasikile. Lokhu kusiza ukulolonga indlela ababona ngayo izimo nokubuyiswa ezifana nse. kombiko

ITHEMU YESI- 2 YEBANGA LESI-3 4. ISILINGANISO ISIKHATHI CAPS UKUQONDA UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.1 Ukusho isikhathi Ukusho isikhathi Abafundi bayaqhubeka nokwenza bekhuluma ngobude besikhathi nokulandelana 2 izifundo kwaso. isikhathi • ukufunda izinsuku • ukufunda izinsuku ekhalendeni ekhalendeni Ngeskhathi sokufundisa ikilasi lonke nokugxila emaqenjini,abafundi abaqhubeke bakhulume ngezinsuku zeviki,ngezinyanga zonyaka nosuku namhlanje, • bheka izinsuku • bheka izinsuku kanjalo nezinsuku ezdlule nezizayo.Abafundi baqhubeke ukubeka izigameko zokuzalwa, zokuzalwa, ezilandelayo ekhalendeni; imigubho yezenkolo, imigubho yezenkolo, amaholide,izigameko amaholide,izigameko • izinsuku zokuzalwa; zomlando izehlakalo zomlando izehlakalo • imigubho yezenkolo; zekilasi ekhalendeni. zekilasi ekhalendeni. • izigameko zomlando; • Ukusho isikhathi • Ukusho isikhathi ngamahora ayi -12 ngamahora ayi -12 • izehlakalo zesikole - amahora - amahora • amaholide. - uhhafu/isigamu - uhhafu/isigamu Qhubeka ucele abafundi bakhulume ngesikhathi, ngezikhawu ezejwayelekile sehora sehora nsukuzonke; - ikota yehora - ikota yehora • ngamahora namaminithi ewashini lezinombolo,noma - imizuzu - imizuzu • ngamahora,uhhafu wamahora, kanye nekota yamahora usebenzisa amawashi anezinti. ewashini elinezinti ewashini elinezinti nelinezinombolo nokunye nelinezinombolo nokunye Isibonelo; abafundi.bangacelwa ukuba bakhulume ngesikhathi uma isikole okungamathuluzi okungamathuluzi siqala,ngezikhathi sekhefu nasemakhaya noma beshintsha izifundo.Khetha angatshengisa isikhathi angatshengisa isikhathi izikhathi lapho iwashi litshengisa ihora noma uhhafu wehora noma ikota isib. Iselulafoni. isib. Iselulafoni. yehora. Kuyasiza ukuba newashi elikhulu lokubukisa ekilasini,yilapho abafundi bezokhomba khona isikhathi.Abafundi bangenza eyabo imifanekiso yamawashi ukubala ubude ukubala ubude Angacela abafundi batshengise izikhathi ezehlukene kuhlangene nokubala isib. besikhathi nokudlula besikhathi nokudlula Ngitshengise ihora le10. Ubani isikhathi ikota nohhafu ngaphambi kuka10? kwaso kwaso Ngesikhathi sokufunda ngokuzimela abafundi abaqhubeke bazijwayeze sebenzisa ikhalenda sebenzisa ikhalenda ukukhuluma ngesikhathi. ubala nokuchaza ubude ukubala nokuchaza besikhathi ngezinsuku ubude besikhathi • ngamahora nohhafu wehora,nekota yehora, ewashini elinezinti noma ngamasonto noma bezinsuku noma • ngamahora nangaminithi ewashini lezinombolo. 475 ngezinyanga ufake bamasonto noma nalokhu izinyanga kuhlangene Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO 476 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) • shintsha iznsuku • ukusebenzisa iwashi Abafundi benza izibalo ngamaviki noma izinsuku uma benikwe ikhalenda noma namasonto ukubala ubude ingxenye yekhalenda isib.ukuthola izinsuku, nokubala isikhathi nokubona beskhathi ngamahora umehluko phakathi kwazo • shintsha phakathi noma uhhafu wehora kwamasonto Izibalo IBANGA 1-3 nezinyanga ukusebenzisa iwashi ubala ubude besikhathi ngamahora noma ngohhafu bamahora. ukubala ubude besikhathi nokudlula kwaso sebenzisa ikhalenda ubala nokuchaza ubude besikhathi ngezinsuku noma ngamamasonto noma ngezinyanga ufake nalokhu • shintsha iznsuku namasonto • shintsha phakathi kwamasonto nezinyanga ukusebenzisa iwashi ubala ubude besikhathi ngamahora /ngohhafu noma amakota Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.2 Isilinganiso Isilinganiso Yini umahluko eBangeni 2? Izifundo 2 esingahlelekile esingahlelekile ubude eBangeni 2 abafundi ba- • ukuhlawumbisela • ukuhlawumbisela • Kugxiliswa ubude ngesilinganiso esingahlelekile nangamayunithi angenasilin- ulinganise, ulinganise, ganiso uqhathanise, uqhathanise, • Isilinganiso ngamamtha sasethuliwe uhlele bese ubhala uhlele bese ubhala ubude usebenzisa ubude usebenzisa kuThemu 2 eBangeni 3abafundi bangaqhubeka ukwenza isilinganiso esingahlele- isilinganiso isilinganiso kile ngokusebenzisa amayunithi angenasilinganiso nokulinganisa ngamamitha. esingalinganisiwe isib, esingalinganisiwe isib, kuThemu 3 bazoqala balinganise ngamasentimitha besebenzisa irula. isandla,amanyathelo, isandla,amanyathelo, ubudebepensela, ubude bepensela, Ukuqagela,isilinganiso, ukuqhathanisa, nokubhala ubude nobubanzi use- ikokubala.njll. ikokubala.njll. benzisa amayunithi angenasilinganiso sobude • ukuchaza ubude • ukuchaza ubude Abafundi bangafunda yonke inqubo yokwenza isilinganiso ngokusebenzisa ama- bezinto ngokubala bezinto ngokubala yunithi angenasilinganiso.isilinganiso ngamayunithi angenasilinganiso akumele uqala ngokuqagela uqala ngokuqagela abukelwe phansi kunokulinganisa ngamayunithi anesilinganiso. ukuthi bungakanani ukuthi bungakanani ubude bamayunithi ubude bamayunithi isilinganiso ubude ngamayunithi angenasilinganiso kuhlanganisa ukubala ukuthi angahleliwe angahleliwe mangaki amayunithi akhethiwe afana nobude baleyonto elinganisiwe.isib. ubude bedesiki buyizandla eziyi-8. • ukusebenzisa • ukusebenzisa ulimi ukhuluma ulimi ukhuluma Abafundi abalinganise izinto eziningi ezehlukene besebenzisa uhla lwezinto njen- ngokuqhathanisa isib, ngokuqhathanisa isib, gamayunithi angahleliwe. kude xaxa, kufishane kude xaxa, kufishane Zintathu izindlela zokusebenzisa amayunithi angahleliwe: xaxa, kuphakeme xaxa, kuphakeme xaxa, kubanzi xaxa njll. xaxa, kubanzi xaxa njll. • Ukupakisha izinto eziifanayo nezlnobude obulinganayo phezu kwentambo lapho uzobona ukuthi zingaki izinto ezingangalobobude njengo-ibhokisi likametshisi,izivalo zamabhodlela afanayo noma izinto zokubala,amapensela amasha apakishiwe kusuka ekuqaleni uya ekugcineni kwedesiki. Okusemqoka yilokhu- • Zonke izinto ziinobude obulinganayo.Ngeke ushosho ukuthi incwadi inobu- banzi obuzivalo zamabhodlela ezyi-12 uma izivalo zambhodlela zinobungako obungalingani.isib,izivalo zamabhodlela obisi amalitha ayi-12 nezamabhodlela zophuzo olubandayo,namaninkela njll. 477 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO 478 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.2 Ukwethula isinganiso • • Azikho izikhala ezishiywayo phakathi nezinto: zidinga ukupakishwa ngendlela esihleliwe yokuthi zithintane. ubude Ukwethula isinganiso • Ukuhlawumbisela esihleliwe • Ukusebenzisa izinto ezifanayo njengngamayunithi angenasilinganiso.Beka ulinganise, intoeduze kwenye,susa eyokuqala uyibeke endaweni yalena yesibili.Lokhu Izibalo IBANGA 1-3 • Ukuhlawumbisela uqagele,uhlele kwenzeka uma usebenzisa isandla,ubude unyawo,noma amanyathelo. ulinganise, bese ubhala ubude uqagele,uhlele • Ukusebenzisa into eyodwa njengesilinganiso esingenasilinganiso ulokhu ngamamitha (kungaba bese ubhala ubude uyiphenqa noma ubeke uphawu lapho uzoqala khona nalapho uzogcina khona amamtha ngezinduku ngamamitha (kungaba ngaphambi kokushelela. noma ubude bentambo amamtha ngezinduku ngamamitha) Abafundi mabafundiswe ukusho amayunithi. Isib. Incwadi inobude bezivalo zama- noma ubude bentambo ngesilinganiso bhodlela ayi-12 ububanzi, ikilasi linobude obungamanyathelo angama-38. ngamamitha) esihleliwe sobude ngesilinganiso Uma abafundi sebeke balinganisa ngeyunithi izikhathi eziningana, banga • Ukuhlawumbisela esihleliwe sobude hhawumbisela basho ukuthi ubude obungakanani bento obunalingana naleyo nokulinganisa ubude yunithi.Kusemqoka kuhlawumbisela ngaphambi kokulinganisa kodwa kungenziwa ngamasentimitha uma abafundi sebeke bayisebenzisa leyo yunithi.. usebenzisa irula Abafundi kumele bafundiswe ukuze bakwazi ukuqhathanisa ubude,ukuphakama, Alukho uguquko noma ububanzi ngokusebenzisa iyunithi efanayo.isib.Uma isilinganiso sobubanzi olungenziwa phakathi bomnyango kuyizandla nobubanzi bedesiki bungamapeni ayi 8 ubude,angeke kwamamitha usho ukuthi umnyango ubanzi ngokuthe xaxa kunedesiki. Abafundi kumele balinganise ngohla lwamayunithi angahleliwe,ukuze bakwazi- • bayaqala ukuqonda ukusebenzisa amayunithi amancane,kusho ukukhula kwesikhathi isib.ububanzi bekilasi bungamanyathelo angama-20 kodwa ubude obungama-48 bezinyawo • bayaqala ukusebenzisa amayunithi lawo afanele lokho okulinganiswayo.isib. isilinganiso ububanzi bekilasi ngezivalo zamabhodlela kuwukuchitha isikhathi. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.2 Ukuhlawumbisela,isilinganiso,ukuqhathanisa nokubhala ubude,ukuphakama nobubanzi ngokusebenzisa amamitha ubude Abafundi bahlanganisa ulwazi lwabo lokuqonda ubude nge-1-imitha, nokuseben- zisa ubude bemitha isilinganiso.Lokhu kwenzakala kahle uma abafundi sebelin- ganisa ngethulusi lemitha(njengerula lemitha;induku enqanyulwe yenza imitha noma intambo enobude obuyimitha).Ukukubona ubude bemitha kwenza abafundi babe nesithombe sokwazi ukuthi imitha lide kangkanani.Kuyenzeka isilinganiso amamitha ngokusebenzisa isondo lokukala, kodwa ubude bemitha bungabon- akali. Abafundi abathole izinto ezinobude bemitha.Kuyasiza ukuthi nsukuzonke kube nezinto eziqhathaniswayo.isib.ububanzi bomnyango nokuphakama kwefasitela kuvamise ukuba imtha-1.Yikho lokhu okusiza abafundi bakwazi ukusebenzisa imi- tha ekulinganiseni ubude noma ububanzi nokuhlawumbisela ubude bezinye izinto ngaphandle kokulinganisa.. Abafundi kumele bahlawumbisele ngaphambi kokulinganisa.Bathola izinto ezinde ngokuthe xaxa nezifishanyana kunemitha-1.Bangalinganisa izinto eziningi nga- mamitha. Qhathanisa ubude ngezinto ezehlukene. Ukurekhoda isilinganiso Nanxa isilinganiso kulikhono eliphathekayo, kwezinye ikhathi abafundi kumele barekhode izilinganiso abazitholile (ngamayunithi angahleliwe namamitha) Ukulinnganisa ubude ngokuxazulula izinkinga nokubala ezimeni ezijwayele- kile Ngesikhathi esinikeziwe sezinombolo,ukusebenza kanye nobudlelwano kwazo abafundi baxazulula izinkinga besebenzisa isimo esijwayelekile njenge- • isilinganiso esingahlelekile sobude • isilinganiso ubude ngamamitha Qikelela ubheke uhla lwezinombolo eziqondene neThemu, bese ubheka uhla lwezinhlobo zezinkinga eziqondene naleyo themu. Qikelela ubheke uhla lwezinombolo eziqondene neThemu, bese ubheka uhla 479 lwezinhlobo zezinkinga eziqondene naleyo themu Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO 480 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.3 Isilinganiso Isilinganiso Yini okuhlukile eBangeni 2? esingahlelekile esingahlelekile isisindo EBangeni 2 abafundi bagxile esilinganisweni esingahlelekile sesisindo. Abafiindi • Ukuhlawumbisela • Ukuhlawumbisela bakujwale isilinganiso ukuzimelela uma benza loku. Sebeqalile futhi ukusebenza ulinganise, ulinganise, ngama kilograms. Bahlela imikhiqizo yansukuzonke enesisindo esibhalwe ama Izibalo IBANGA 1-3 uqhathanise uhlele uqhathanise uhlele kilograms. Bafunda isisindo sabo esikalweni sasendlini yangasese. bese ubhala isisindo bese ubhala isisindo Isilinganiso esingalinganisiwe sesisindo kesebenza isilinganiso usubenzisa isilnganisa usubenzisa isilnganisa sokuzimelela nezingalinganisiwe esingalinganisiwe. esingalinganisiwe. Nokuzimelela isib, Nokuzimelela isib, Abafundi bangafunda imithetho nokwenziwa kwesilinganiso kusebenza amabhuloki, izitini njll, amabhuloki, izitini njll, izilinganiso ezingalinganisiwe. Ukukala ngezilinganiso ezingalinganisiwe akufanele zibukelwe phansi ukunalezi ezinesilinganiso. Abafundi kumele • Ukusebenzisa • Ukusebenzisa bahlanganise amkhono abo okulinganisa ngokwenza izilinganiso ezingahleliwe ulimi ukhuluma ulimi ukhuluma isilinganiso isisindo ngesilinganiso esingahlelekile. ngokuqhathanisa, isib, ngokuqhathanisa, isib, kulula, kuyasinda, kulula, kuyasinda, Izisindo ezenzelwe isilinganiso izinto ezithengiswayo. Uma singekho isilinganiso kulula xaxa, kuyasinda kulula xaxa, kuyasinda esihleIelwe izinto ezithengisayo, ungasenza ngokuhlanganisa okuhamba xaxa xaxa ngakubili njengalokhu okulandelayo ikhothenga: inkomishi kayogathi, ingezansi lebhodlela lamalitha ama 2, ingezansi lebhodlela lobisi elingamalitha ama 2, • Ukwethula • Ukwethula isinganiso (izitsha ezifanayo zibekwa ngokulengisa ezinhlangothini zombili zekhothenga). isilinganiso esingahlelekile esingahlelekile Isilinganiso isisindo ngezilinganiso ezingenasilingasilinganiso, isilinganiso • ukuqhathanisa ngesisindo samayunithi esingenasilinganiso esifaka ukubala ukuthi mangaki • ukuqhathanisa uhlele bese ubhala amayunithi anesisindo esifana nento ekaliwe. Isibonelo. Irula linesisindo uhlele bese ubhala ukukhangisa esilinganayo namabhuloki ayi 9. ukukhangisa ngesisindo sazosibe ngesisindo sazosibe siveziwe ephaketheni Abafundi kumele balinganise izinhlobonhlobo zezinto ngamayunithi angahlelekile. siveziwe ephaketheni ngokwama kilogramu Abafundi kumele bafundiswe njalo ukubhala iyunithi uma benikeza isisindo, isib. ngokwamakilogramu isib amakilogramu ama Incwadi inesisindo esifanayo nomabula abangama 34. isib amakilogramu ama 2 erayisi,ne1 kilogramu 2 erayisi,ne1 kilogramu likafulawanoma Uma abafundi bekale iyunithi kaningi, kufanele bahlawumbisele ukuthi mangaki likafulawanoma ngamagramu isib. amayunithi azoba nesisindo esifanayo naleyonto abayikalile. Ukuqagela ngamagramu isib. Amagramu eswayi ngaphambi kokuthi bakale kubalulekile, kodwa kungenziwa kuphela uma Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Amagramu eswayi ang-500 abafundi sebelinganisile naleyo yunithi ang-500 Abafundi badinga ukufundiswa ukuze bakwazi ukuqhathanisa isisindo sezinto ezehlukene kusetshenziswa iyunithi efanayo. Isibonelo uma irula linesisindo esingangamabhuloki 20 nesikele sinesisindo somabula abanga20, ngeke usho ukuthi kunesisindo esilinganayo noma cha, noma ikuphi okusinda kakhudlwana.

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.3 • ISILINGANISO izisindo • lapho kunesikali Ukubhala izilinganiso zabo ngokusebenzisa sasendlini isisindo Yize isilinganiso kuyikhono lokwenza, abafundi kumele babhale loko isikali sasendlini yokugeza abafundi abakulinganisile ngazozonke izikhathi. yokugeza. bangazilinganisa izisindo zabo Ukusebenza ngama grams Akukho zinguquko besebenzisa ezilindekile phakathi • ukuhlela umkhiqizo ngokwesisindo amakilogramu. kwamagramu Okulindelekile yikuthi abafundi bengasebenza ngegilosa ethengiwe ngama grams, lapho khona namakilogramu abafundi bazofunda inombolo yama grams ibhaliwe ephaketheni. Abafundi bangaqhathanisa inombolo eseduze isisndo samaphakethe anezinto ezingafani (njenge, ushukela, impuphu, irayisi nolayini esikalini nensipho eyimpuphu yokuwasha) adayisa ngama grams. Bazochaza izisindo njenge cishe/maduze/ Abafundi banganikezwa uhla lezinto ezipakishwe ngezindlela ezingefani ngaphezulu/ngaphansi/ ukuze kulandelaniswe kuqale kokusinda kakhulu kuye kokulula, lapho khona yiso nqo inombolo kulandelaniswa ngokwesisindo esibhalwe ephaketheni ngalinye isib. 2 g iraysi, (yamakilogramu) 1 g ushukela, 5 g impuphu, 10 g istambu. bazofunda izinombolo Abafundi badinga ukwazi ukubhala ngokufingqiwe “g” okumele grams. zesikali. Ukusebenza ngama kilograms • Lapho isikali sokuzimelela esinezi • ukuhlela umkhiqizo ngokwesisindo ngcezu zesisindo abafundi bengasebenza ngegilosa ethengiwe ngama grams, lapho khona ngamagabelo inombolo yama grams ibhaliwe ephaketheni. Abafundi bangaqhathanisa angamagramu, isisndo samaphakethe anezinto ezingafani (njenge siriyeli, itiye, ikhofi, usawoti, abafundi ubhontshisi, amaphakethe kashukela amancane, amaphakethe amancane bangalinganisa izisindo obisi oluyimpuphu, amaphakethe kajeli, amaphakethe amancane erayisi) zezinto ezehlukene adayisa ngama grams. Akukho zinguquko Abafundi banganikezwa uhla lezinto ezipakishwe ngezindlela ezingefani ezilindekile phakathi ukuze kulandelaniswe kuqale kokusinda kakhulu kuye kokulula, lapho khona kwamagramu kulandelaniswa ngokwesisindo esibhalwe ephaketheni ngalinye isib. 2 kg iraysi, namakilogramu 1 kg ushukela, 5 kg impuphu, 10 kg istambu. 481 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO 482 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.3 Kubalulekile ukuthi abafundi bakhonjiswe okuncane, ukusindayo okupakishiwe njengo sawoti nalezo namaphakethe amakhulu kodwa alula njengama rice isisindo crispies noma amacorn flakes. Loku kubenza babone ukuthi akusho ukuthi ubukhulu bephakethe kusho ukuthi liyasinda ukenelincane, ngaphandle uma Izibalo IBANGA 1-3 kulinganiswa ngokuqhathanisa into ephakathi ephaketheni efanayo. Ungaba nesiqiniseko sokuthi uma iphakethe lilikhulu linesisindo esikhulu uma • kuqhathaniswa into ephakathi efanayo; kanye • uma uhlola isisndo esikalini (okungadingeki emabangeni aphansi). Abafundi badinga ukwazi ukubhala ngokufingqiwe “kg” okumele kilograms Abafundi akudingekile ukuthi bafunde isikali sasekhishini ngama grams. Loku kwenziwa emazingeni aphakathi emfundo. Ukufunda isikali sasendlini yokugezela Lapho khona kunezikali zasendlini yangasese abafundi bangazisebenzisa ukufunda isisndo sabo. Kunezinhlobo ezimbili zezikali zasendlini yangasese: esezinombolo nesiluthi. Isikali sezinombolo kulula ukusisebenzisa ngoba isisindo sibhalwa ngezinombolo. Uma unesikali sasendlini yangasese sezinombolo, bheka ukuthi isisindo sikalwa kuphela ngama kilograms. Ungazihlela kabusha izinye izikali ukuze zikhombise ama kilograms. Uma ungakwazi ukusihlela ukuba sikhombise ama kilograms, bafundise abafundi ukuba bangawanaki amakilograms okwamanje. Eziningi izikali zasendlini yokugezela ezinothi zibhalwe izinombolo ngama 10 kg igabela ngalinye, zibe nomugqa omude ukeminye ekhombisa ama 5 kg. Imigqa ye 1 kg ngalinye ayinazo izinombolo. Loku kufana nendlela imigqa esebenza ngayo eruleni. Yenza abafundi baqale ngokubala ukuze babone ukuthi kunezikhala eziyi 10ngaphambi kophawu la 10 kg, ukuze isikhala ngasinye sizomela 5 kg. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi bangafunda isillinganiso ngaphandle kwesikali sangampela sasendlini yangasese kanye nezithombe zesikali zesikali sasendlini yangasese. Kulula okufunda isisindo kusetshenziswa isithombe ukunokusebenzisa isikali sangampela.

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.3 Ukubhala okulinganisiwe 4 izifundo isisindo Yize isilinganiso kuyikhono lokwenza, abafundi kumele babhale izilinganiso zabo ngasosonke isikhayhi. Isilinganiso isisindo esimweni esejwayelekile sokuxazulula izinkinga nokubala Ngesikhathi esibekelwe ukusebenza kwezinombolo nobudlelwane, kungaxazululwa izinkinga ezisebenzisa isimo esejwayelekile se: • Isilinganiso esingahlelekile sesisindo; kanye • Isilinganiso isisindo ngama kilograms. Qaphela ukuthi uhla lwezinombolo luba lisezingeni lethemu, kanye nezinga lezinhlobo zezinkinga. Abafundi abalindelekile • ukwazi ukuthi 1 000 g = 1 kg; noma • ukushintsha phakathi kwama grams nama kilograms. Ukubala ngama grams zingakhethwa ukuba zingeqi 1 000 g. 483 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO 484 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.4 Isilinganiso Ngesikha somsebenzi wokuzimela abafundi kumele baqhubeke ukuqagela nokulinganisa, ukuqhathanisa, ukuhlela nokubhala esingahlelekile umthamo wesitsha noma okumumethwe esitsheni kusetshenziswa isilinganiso esingahlelekile. Ukulandela izindlela zokupheka, Umthamo okufaka nokubhaka, kuyasebenza esimweni esejwayelekile lapho khona abafundi bezozijwayeza isilinganiso. Ukhetha izindlela • Uhlawumbisela zokupheka lapho izithako zinikezwe ngezikalo zezinkomishi, amathesipuni, noma amayunithi ezingahlelekile. nokulinganisa, Izibalo IBANGA 1-3 ukuqhathanisa • Qhathanisa uhlele umthamo wezinhlobonhlobo zamabhodlela nezinto zegilosa lapho khona umthamo ochazwe khona nokuhlela ephaketheni. umthamo wesitsha • Sebenzisa noma ibhodlela eliyilitha e-1 noma ojeke abayilitha e- 1ukuqagela nokulinganisa, ukuqhathanisa, ukuhlela kubhalwe esingawumumatha umthamo wezitsha noma okumumethwe ezitsheni ngamalitha. (isitsha esngakumumatha Bheka amanothi kathemu 3. uma sigcwalisiwe) Abafundi kumele banikezwe imisebenzi ebhalwayo ukuhlanganisa okulandelayo,okufaka ukufunda izithombe ze noma okumumethwe isitsha ngokusebenzisa • Imikhiqizo ezinomthamo obhaliwe ukuze kulandelane ngendlela ehlelekile; kanye isilinganiso esingalinganisiwe isib. • Izithombe zojeke lapho umthamo usondele enombolweni ethi ilitha e- 1 noma amalitha ama-2 ngokulandelana kobukhulu. isipuni namankomishi Okulindelekile ukuthi abafundi bafunda kuphela inombolo yomugqa olandelayo ngobukhulu noma uhla. Bachaza umthamo wabo • Ukuchaza umthamo ngokuthi cishe/eduze kwa ngaphezudlwana / ngaphezulu ngaphansi kulingana nenombolo(yamalitha) bafunda ujeke. wesitsha ngokubala Isilinganiso umthamo njengesimo esejwayelekile sokuxazulula izinkinga nezibalo ukuthi mangaki amayunithi angahleliwe Ngesikhathi esibekelwe ukusebenza kwezinombolo nobudlelwane, kungaxazululwa izinkinga ezisebenzisa isimo esejwayelekile se: angagcwaliswa, • Isilinganiso esingahlelekile somthamo; kulesositsha isib. ibhodlela lingagcwala • Isib. Ugogo usebenzisa izinkomishi ezi- 2 zobisi ukwenza uphudingi. Uma ephinda kabili izithako, uzodinga ubisi olungakanani? izinkomishi ezi-4. • amlitha Ukwethula isilinganiso Qaphela ukuthi uhla lwezinombolo luba lisezingeni lethemu, kanye nezinga lezinhlobo zezinkinga. esingahlelekile • Ukuhlawumbisela ulinganisa, uqhathanisa, Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola uhlele bese ubhala lowomthamo waleyonto ngokulinganisa ngamalitha,uhhafu welitha nekota yelitha.

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.4 • Ukuqhathanisa nokuhlela, nokubhala Umthamo ngokukhangisa umthamo waso siveziwe ephaketheni ngokwamalitha isib. Amalitha ama-2l obisi, ilitha 1yobisi, amalitha ayi-5l kapende,noma ngamamililitha. isib.amamililitha anga-500ml obisi,amamililitha anga-340ml wesiphuzo esibandayo, amamililitha anga- 750ml kawoyela. • Ukwazi ukuthi inkomishi elingene ingamililitha anga- 250ml. • Ukwazi ukuthi ithisipuni ingamamililitha angu- 5ml Alukho uguquko oludingakalayo phakathi kwamamililitha namalitha 485 Izibalo IBANGA 1-3

ITHEMU YESI-2 YEBANGA LESI-3 5. ULWAZI OLUQOKELELWE 486 UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIW OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 5.4 Ukuqoqa nokuhlela Izibalo IBANGA 1-3 Ukuqoqa • ukuqokelelwa kol- nokuhlela ulwazi wazi ngekilasi noma ngesikole ukuphen- dula imibuzo ezobuzwa uthisha. • Ukuhlela ulwazi olu- nikwe uthisha noma incwadi. • Ukuhlela ulwazi; - uhla - amathali - amathebula 5.5 Ukubhala okumele ulwazi Ukubhala okumele ulwazi Ukubhala okumele ulwazi ngoku- • igrafu yezithombe • i bhagrafu 5.6 Ukuhlaziya nokuhumu- Ukuhlaziya ulwazi Uma abafundi sebesebenze kulolonke ulwazi oluphelele ngethemu 1,baye bahl- 1 isifundo sha ulwazi kulokho okumele ulwazi aziye izimo ezehlukene zokubhala okumele ulwazi kumele ikunike umqondo. Ukuhlaziya okunikiwe. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola nokuhumusha Ukuphendula imibuzo Kuyancomeka ukuthi kuthemu 2unika abafundi ulwazi ukuba baluhlaziya kanje; ulwazi ngolwazi olunikiwe • igrafu yezithombe • igrafu yezithombe • Amathebula • ibhagrafu Abafundi baphendula imibuzo leyo ebuzwa uthisha mayelana negrafu nethebula,bheka uthemu 1 nemibuzo efanele nehlukene.

ITHEMU YESI-3 YEBANGA LESI-3 1. IZINOMBOLO, IZIMPAWU NOBUDLELWANO BAZO UMQONDO KANYE UMQONDO CAPS NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 1.1 Ukubala izinto Yenza iqoqo lezinto Yimuphi umehluko eThemu 2? Bala izinto eziphathekayo eziphayhekayo Uhla lwezinombolo luyanda / khula abafundi kufanele banikwe ithuba lokuthinta, eziphathekayo zansukuzonke nyakaziza babale izinto ezingama-700 ezingamaqoqo enziwe ngokuhlukene. Hlawumbisela ubale ezingama-750 izinto eziphathekayo ukuhlawumbisela ubale Bheka amanothi kwThemu 1 kanye neye 2 okungenani eziyi-1000 ngokuthembekile. nsuku zonke Hlawumbisela ngokuthembeka. Isu ngokuzwakalayo lokwenza amaqoqo inombolo yezinto liyagqugquzelwa. eziphathekayo ezingabalwa. 1.2 Bala uyephambili Bala uyephambili Yimuphi umehluko eThemu 2? Bala uyephambili ubuye uhlehle kanje: ubuye uhlehle kanje: Uhla lwezinombolo luyakhula kufinyelela ezi- 700. ubuye uhlehle • Nga-1 kusukela • Nga-1 kusukela Bheka amanothi eThemu yoku-1 kanye neye 2 kunoma iyiphi kunoma iyiphi inombolo ephakathi inombolo ephakathi kuka -0 ne -1000 kuka -0 ne -700 • Ngokuyi -10 kusukela • Ngokuyi -10 kusukela kunoma iyiphi inombolo kunoma iyiphi inombolo uphindaphinda uphindaphinda phakathi kuka-0 ne phakathi kuka-0 ne 700 -1000 • Noku - 5 kusukela • Ngoku - 5 kusukela kunoma iyiphi inombolo kunoma iyiphi inombolo uphindaphinda uphindaphinda phakathi kuka -0 ne phakathi kuka -0 ne 700 1000 • Ngaku-2 kusukela • Ngaku-2 kusukela kunoma iyiphi inombolo kunoma iyiphi inombolo uphindaphinda uphindaphinda phakathi kuka -0 kuya phakathi kuka -0 kuya koku 700 koku 1000 • Ngoku-3 usukela • Ngoku-3 usukela kunoma iyiphi inombolo kunoma iyiphi inombolo uphindaphinda 487 uphindaphinda phakathi kuka -0 kuya phakathi kuka -0 kuya koku 700 koku 1000 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 488 KUPHELA UNYAKA NGETHEMU YE-3 1.2 • Ngoku-4 kusukela • Ngoku-4 kusukela Bala uyephambili kunoma iyiphi inombolo kunoma iyiphi inombolo ubuye uhlehle uphindaphinda uphindaphinda phakathi kuka -0 kuya phakathi kuka -0 kuya koku 1000 koku 700 • 20s, 25s, 50s,100s • 20s, 25s, 50s,100s Izibalo IBANGA 1-3 kufinyelela okungenani kufinyelela okungenani e- 1 000 e- 1 000 1.3 Ukwazi nokufunda Ukwazi nokufunda Yimuphi umehluko eThemu 2? izinombolo izinombolo Izimpawu Abafundi bayakhomba, bafunde babhale: namagama • Khomba, ubone, • Khomba, ubone, ezinombolo • Izimpawu zezinombolo kufinyelela e-1000; kanye ufunde izimpawu ufunde izimpawu zezinombolo kusukela zezinombolo kusukela • Amagama ezinombolo kufinyelela ema- 500. ku 0 kuya e- 1000 ku 0 kuya e- 1000 Bheka amanothi eThemu 2 • Bhala uphawu • Bhala uphawu lenombolo kusukela ku lenombolo kusukela ku 0 kuya e -1000 0 kuya e- 1000 • Khomba, ubone, • Khomba, ubone, ufunde amagama ufunde amagama ezinombolo kusuka ku ezinombolo kusuka ku 0 kuye ema 1000 0 kuye ema -500 • Bhala amagama • Bhala amagama ezinombolo kusuka ku ezinombolo kusuka ku 0 kuye ema 1000 0 kuye ema- 500 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.4 Hlela, uqhathanise Hlela, uqhathanise Yimuphi umehluko eThemu 2? izinombolo kufinyelele izinombolo kufinyelele Chaza, qhathanisa, Abafundi bayahlela baqhathanise izinombolo kufinyelela ema-500 baqhubeke ema-999 ema-500 nokusebenzisa izindlela ezifingqiwe ukubhala izinombolo ezijwayelekile. bese uhlela izinombolo • Hlela izinombolo • Hlela izinombolo Bheka amanothi eThemu 2 eziphelele kufinyelele eziphelele kufinyelele ema-999 kusukela ema-500 kusukela kokuncane kakhulu kokuncane kakhulu kuye kokukhulu kuye kokukhulu kakhulu, okukhulu kakhulu, okukhulu kakhulu kuye kakhulu kuye kokuncane kakhulu. kokuncane kakhulu. • Qhathanisa izinombolo • Qhathanisa izinombolo eziphelele kufinyelele eziphelele kufinyelele ema-999 usebenzisa ema-500 usebenzisa okuncane kuna, okuncane kuna, okukhulu kuna, okukhulu kuna, okuningi kunokunye, okuningi kunokunye, okumbalwa kunokunye okumbalwa kunokunye kanye nokulingana. kanye nokulingana. Sebenzisa izinambolo Sebenzisa izinambolo ezijwayelekile ezijwayelekile ukukhombisa ukukhombisa ukuhleleka kwezinamba ukuhleleka kwezinamba ngokwesikhundla ngokwesikhundla • Sebenzisa, • Sebenzisa, ufunde, ubuye ufunde, ubuye ubhale izinombolo ubhale izinombolo ezijwayelekile kufaka ezijwayelekile kufaka indlela efingqiwe indlela efingqiwe kufinyelela ema- 31. kufinyelela ema- 31. 489 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 490 KUPHELA UNYAKA NGETHEMU YE-3 1.5 Bona ubungako Bona ubungako Yikuphi okuhlukile eThemu 3 Ubungako benani benani lenombolo benani lenombolo Inhlobo efanayo yemibuzo nemiyalelo inikeziwe eThemu 3.uhla lwezinombolo lenombolo kwizinombolo kwizinombolo lwengeziwe kepha abafundi basasebenza ngezinombolo ezihamba ngantathu. ezihamba ngantathu ezihamba ngantathu kuleThemu kufanele kuqhutshekwe nokugxila e: kufinyelela ema- 999 kufinyelela ema- 999 • Ubungako benombolo; • Ukwazi ukuthi • Ukwazi ukuthi • Ukuhlakaza izinombolo ngamakhulu, amashumi, ngakunye usebenzisa inombolo ngayinye inombolo ngayinye Izibalo IBANGA 1-3 amakhadi ezimeli bungako bezinombolo kanye nezinye izinsiza ekwenzeni imeleni. imeleni. ubungako bezinombolo; • Ukuhlakaza izinombolo • Ukuhlakaza izinombolo • Ukubhala ngendlela yokwandisa izinombolo. ezihamba ngantathu ezihamba ngantathu kufinyelela ema - 999 kufinyelela ema - 999 Bheka amanothi eThemu yesi- 2 ngokuphindaphinda ngokuphindaphinda ngokuyi- ngokuyi- 100,ngokuyishumi 100,ngokuyishumi kanye nokukodwa / kanye nokukodwa / imivo. imivo. • Khomba ubuye usho • Khomba ubuye usho ubungako benombolo ubungako benombolo ngayinye. ngayinye. Izinkinga zezibalo zezinombolo 1.6 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Abafundi kulindeleke baxazulule izinkinga zezibalo zamagama besebenzisa Amaqhinga alandelayo ukuxazulula alandelayo uma lamaqhinga alandelayo: izinkinga zezibalo bese uxazulula izinkinga: • Ukwakha nokuhlakaza izinombolo okuxazulula uchaza isixazululo • Ukwakha nokuhlakaza izinkinga zezibalo • Ukphinda kabili nokuhlukanisa kabili sakho: izinombolo • Umugqa wezinombolo • Ukwakha • Ukphinda kabili nokuhlakaza nokuhlukanisa kabili • Ukusondezela emashumini izinombolo Bheka amanothi eThemu 2 • Umugqa wezinombolo • Ukphinda kabili • Ukusondezela nokuhlukanisa kabili emashumini • Umugqa Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola wezinombolo • Ukusondezela emashumini

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.7 Xazulula izinkinga Xazulula izinkinga Izibonelo zezinhlobo zezinkinga ezingenziwa kuleThemu zezibalo zamagama zezibalo zamagama Ukuhlanganisa esimweni esjwayelekile esimweni esjwayelekile - Izinkinga zezibolo zokuhlanganisa nokususa nokususa bese uchaza bese uchaza - UPamela uqoqe izivalo zamabhodlela ezingama- 413. Uma uSipho emnika isisombululo okufaka isisombululo okufaka izivalo zamabhodlela ezingama-29, uzoba nenombolo efanayo noPamela. ukuhlanganisa ukuhlanganisa nokususa okuholela nokususa okuholela - Zingaki izivalo zamabhodlela abazoba nazo bobabili? ezimpendulweni ezimpendulweni ezifinyelela ema-999. ezifinyelela ema-800. - Ubenezingaki izivalo zamabhodlela uSipho ? • IBANGA LESI-2 lineqoqo lomabuli abangama-500. IBANGA LESI-3 linomabuli abambalwa nge-170 kuneBanga 2.bangaki omabuli bebangaBanga 3 bebonke? • uJabulani noZanele baqoqe ubuhlalu obungama-250.uJabulani wathola obungama-160, bungaki ubuhlalu uZanele abutholile. 1.8 Xazulula izinkinga Xazulula izinkinga Izibonelo zezinhlobo zezinkinga ezingenziwa kuleThemu zezibalo zamagama zezibalo zamagama Ukuhlanganisa esimweni esjwayelekile esimweni esjwayelekile Uhlobo lwezinkinga: uhlelo ngononina ngokuphindelela uchaze isisombululo uchaze isisombululo okuholela • Ingadi yemifino inemigqa eyi-12 yezitshalo, umugqa ngamunye unezitshalo ufaka ukuphindaphinda ufaka ukuphindaphinda eziyisi-7, zingaki izitshalo izitshalo ezisengadini zizonke? ezibalweni okunezimpendulo okunezimpendulo zokuphindaphinda ezifinyelela ema-99. ezifinyelela ema-75. • Ingadi yemifino inemigqa eyi-12 yezitshalo, umugqa ngamunye unenombolo elinganayo yezitshalo, uma zizonke zingama-48, zingaki izitshalo kumugqa ngamunye? • Ingadi yemifino inezitshalo ezingama-48 ezitshalwe emigqeni, kunezitshalo eziyisi-7 kumugqa ngamunye, mingaki imigqa esengadini ? Ukuqhathanisa /ubukhulu bokulinganiselwa UThemba unoswidi abayi-6, uThemba unokuphidwe kathathu ngokuningi kuno Senzo, bangaki oswidi uSenzo anobo? UZodwa unoswidi abayi-18, lokhu kuphindwe kathathu ngobuningi kunoThemba, bangaki oswidi uThemba anabo? isilinganiso Amapetshisi athengisa ngama- R8 ikhilogremu. Uma ngithenga amakhilogremu ama-4, kuzoba yimalini? 491 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI 492 ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 1.8 Amapetshisi athengisa ngama- R8 ikhilogremu. Uma nginama- R32, mangaki amakhilogremu engingawathenga? Ukuhlanganisa ngokuphindelela Ngithenga amakhilogremu ama-4 amapetshisi ngama- R32. Libiza malini okuholela ikhilogremu elilodwa? ezibalweni zokuphindaphinda Usebenzisa ukusondezela Itekisi ithatha abagibeli abayi-15, ingabe abantu abayi-73 bangalingana Izibalo IBANGA 1-3 ematekisini ama-5? 1.9 Xazulula izinkinga Xazulula izinkinga Izibonelo zezinhlobo zezinkinga ezingenziwa kuleThemu zezibalo eziphathekayo zezibalo eziphathekayo Ukwenza amaqoqo uchaze isisombululo uchaze isisombululo • UNksz Tshongwe uqoqela ndawonye amakhekhe ayi-66 emaphaketheni ayi-6, nokuhlukaniselana okufaka ukuhlukanisa okufaka ukuhlukanisa mangaki amaphakethe okuyisi-6 anawo? okuholela ngokulinganayo kanye ngokulinganayo kanye ezibalweni • UThobo uthola ama- R72 ngokuthengisa amathikithi omdlalo ngama- R9,00. namaqoqo kufinyelela namaqoqo kufinyelela zokuhlukanisa mangaki amathikithi awathengisilel? kuma -100 okungafaka kuma -75 okungafaka izinsalela izinsalela • Umphakathi usiza imindeni eyi-9 elahlekelwe izimpahla emlilweni.kunezingubo eziyi-75 imindeni ezozihlukanisa ngokulinganayo. a) Umndeni ngamunye uzothola izingubo ezingaki? b) Zingakhi ezisele? silinganiso • Amapetshisi athengisa ngama- R8 ikhilogremu. Uma nginama- R32, mangaki amakhilogremu engingawathenga? • Ngithenga amakhilogremu ama-4 amapetshisi ngama- R32. Libiza malini ikhilogremu elilodwa? Izinkinga zesilinganiso izinhlobo ezintsha zezinkinga eThemu 3. Abafundi bangadinga isikhathi esengeziwe uma bexazulula lezizinkinga. Bheka amanothi eThemu 2 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.10 Xazulula izinkinga Xazulula izinkinga Izibonelo zezinhlobo zezinkinga ezingenziwa kuleThemu zezibalo bese uchaza zezibalo bese uchaza Ukuhlukanisa oku- Ukuhlukanisa okuholela emaqhezwini holela emaqhezwi- isisombululo okfaka isisombululo okfaka ni ukwabelana okuholela ukwabelana okuholela • Hlukanisela abangane abathathu oshokoledi abayi-7 bathole okulinganayo kuzisombululo ezifaka kuzisombululo ezifaka kungasali lutho. ingxenye eyodwa ingxenye eyodwa • Hlukanisela izingane ezi-4 ngokulinganayo oshokoledi abayi-13,ingane yeqhezu namaqhezu yeqhezu namaqhezu ngayinye izothola abangaki? anezingxenye anezingxenye ezingaphezu kolulodwa. ezingaphezu kolulodwa. Iqoqo lamaqhezu 1 1 3 2 1 1 3 2 2 4 4 Isibonelo , , , , njll5 2 4 4 5 Isibonelo , , , , njllnjll • Ugogo unika uZola ama- R12. uZola ufuna ukulondoloza okuthathu kwemali, yimalini okufanele ayilondoloze? • Kunamakhekhe ayi-12 epuletini.u Nomonde uthatha ikota eyodwa yekhekhe kungakanani okusele? ukubhala Abafundi akudingekile babhale uphawu lweqhezu, abafundi bafunda ukubhala okukodwa kokuhlanu, amakota amathathu, noma okuthathu kokuyisithupha. Lokhu kubasiza kuqala ukuqonda ukuthi amagama amaqhezu achaza ukuthi zingaki izingxenye ezilinganayo okuphelele okuhlukaniswe kwayizo, Isib. Uhhafu, okuthathu, ikota njll.okwesibili zingaki ezalezo zingxenye ezithathwayo, Isib. Okubili kokuthathu. Okumele izinkinga zamagama zamaqhezu Abafundi kufanele badwebe izimphendulo zabo ukukhombisa ukuthi bayayiqonda inking. Lindela ukuthi abanye abafundi bangadweba ngendlela kepha bangayibizi ngendlela ingxenye yeqhezu. Abafundi kufanele basho izingxenye ezihlukanisiwe ngokuzibhala njengo: kubili kokuthathu. 493 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI 494 ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 1.11 • Bona, ukhombe imali • Bona, ukhombe imali Izibonelo zezinkinga ezingenziwa kuleThemu yaseNingizimu Afrika yaseNingizimu Afrika Imali Inani lemali nokwenza isamba Isib. uhlweza namaphepha uhlweza namaphepha Bhala 325c ngamarandi nohlweza. • Xazulula izinkinga • Xazulula izinkinga zezimali kufaka isamba zezimali kufaka isamba Zingaki izindlela ezihlukene ongenza ngazo ama-R400 usebenzisa imali noshintshi amarandi noshintshi amarandi yamaphepha kuphela? Wazi kanjani noma unazo zonke izixazululo? Izibalo IBANGA 1-3 noma uhlweza. noma uhlweza. UMnu Zungu umakhi uthola ibhonasi ngokuqeda umsebenzi ngesikhathi.unquma • Guqula bakathi • Guqula bakathi ukuhlukanisa ibhonasi phakathi kwakhe nombazi. kwamarandi nohlweza. kwamarandi nohlweza. Bathola ama- R400 ngamunye. Liyini inani lebhonasi? UNina nabangane bakhe abathathu bahlukaniselana ama-R20,60. Eyedwa kubo uthola malini? UKUBALA ESIMWENI ESIKHULULEKILE 1.12 Sebenzisa lamaqhinga Sebenzisa lamaqhinga Abafundi balindeleke ukuthi babale izinkinga zezibalo zamagama besebenzisa alandelayo uma wenza alandelayo uma wenza lamaqhinga: Amaqhinga izibalo: izibalo: • Ukukha nokuhlakaza izinombolo (izindlela noma • Ukwakha nokuhlakaza • Ukwakha nokuhlakaza amasu) • Ukuphinda nokuhlukanisa kabili ngokulinganayo izinombolo izinombolo • Umugqa wezinombolo • Ukphinda kabili nokuh- • Ukphinda kabili nokuh- lukanisa kabili lukanisa kabili • Ukuhlanganisa ishumi • Umugqa wezinombolo • Umugqa wezinombolo Bheka amanothi ethemu yoku-1. • Ukusondezela • Ukusondezela emashumini emashumini Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.13 • Izibalo zokuhlanganisa • Izibalo zokuhlanganisa KuleThemu abafundi baqhubeka nokubala ngezinombolo ezihamba ngantathu ukuyofika ema 999 ukuyofika ema 800 kufike ema-800. Ukuze bakwazi ukubala ngezinombolo ezihamba ngantathu Ukuhlanganisa abafundi kufanele bakwazi uku: nokususa • Izibalo zokususa besu- • Izibalo zokususa besu- kela kuma 999 kela kuma 800 • Ukufunda nokubhala izimpawu zezinombolo kufinyelela ema-800 ngokuzethemba; • Sebenzisa izimpawu • Sebenzisa izimpawu ezifanele (+, –, =, ) ezifanele(+, –, =, ) • Ukuhlela nokuqhathanisa izinombolo kufinyelela okungenani ema-800 ngokuzethemba; • Phindaphinda wenze • Phindaphinda wenze amabhondi ezinombolo amabhondi ezinombolo • Ukubala ngamaqoqo kufinyelela ema-800; kanye kuyofika e - 30 kuyofika e - 30 • Nokubala ngezikhawu zoku- 2, 3, 4, 5, 10, 50 kanye ne- 100 kufinyelela ema- 800 ngokuzethemba. Izindlela okungenziwa ngazo izibalo zokuhlanganisa nokususa. • Ukuhlanganisa ngokuhlakaza zombili izinombolo Ukuhlanganisa izinombolo ezihamba ngantathu ngezihamba ngambili 524 + 82 =  = (500 + 20 + 4) + (80 + 2) = 500 + (20 + 80+ (4 + 2) = (500 + 100) + 6 = 600 + 6 = 606 Ukuhlanganisa izinombolo ezihamba ngantathu ngezihamba ngantathu 323 + 436 =  323 + 436 = = (300 + 20 + 3) + (400 + 30 + 6) = (300 + 400) + (20 + 30) + (3 + 6) = 700 + 50 + 9 = 759 • ukuhlanganisa (ngokuhlakaza inombolo ezohlanganiswa) Abafundi bazohlakaza inombolo ngendlela ezovumelana nabo, Lokhu kukhomba ukuthi bazokwenza ngezindlela ezihlukene. 524 + 82 =  495 524 + (40 + 40 + 2) 524 + 40 → 564 + 40 → 604 + 2 = 606 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 496 KUPHELA UNYAKA NGETHEMU YE-3 1.13 Ukubala uqhubeka kusukela ema-40 kufike ema-524 kungenziwa ngokubala ngamashumi. Ukuhlanganisa nokususa Ukuhlanganisa izinombolo ezihamba ngantathu kanye nezihamba ngantathu 323 + 436 =  = 323 + (400 + 20 + 6) Izibalo IBANGA 1-3 = (323 + 400) + 20 + 6 = (723 + 20) + 6 = 743 + 6 = 749 • ukususa ngokuhlakaza zombili izinombolo izinombolo ezihamba ngantathu ususa ezihamba ngambili 889 - 137 =  889 - 137 = (800 + 80 + 9) - (100 + 30 + 7) = (800 - 100) + (80 - 30) + (9 - 7) = 700 + 50 + 2 = 752 • susa ngokuhlakaza inombolo eyodwa 889 - 137 =  889 - (100 + 30 + 7) 889 - 100 789 - 30 759 - 7 = 752 · sebenzisa ukuhlukanisa ngokulingana ukuhlakaza inombolo 525 + 16 = 525 + 8 + 8 = (525 + 8) + 8 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola = 533 + 8 = 541 • bala uqhubeka kanye nokubala uhlehle 805 = 798 =  Ukubala ngakunye kusuka ema-798 kuyisu elifanele ngoba ngoba izinomblo zisondelene.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.13 • Khomba izinombolo eziseduze kweziphindwe kabili Ukuhlanganisa 245 + 246 nokususa Ungasho ukuthi lesibalo ngokuphinda kabili ama-245 + 1 phinda kabili 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 = 491 • Shintsha inombolo iphindaphinde ngamashumi ususe noma uhlanganise ngokukodwa. Bala uqhubeke noma uhlehle kusondezele eshumini 588 + 9 588 + 10 = 598 598 - 1 = 597 588 + 19 588 + 20 = 608 608 - 1 = 607 Thuthukisa wenze ngokuphindaphinda amakhono okuhlanganisa nokususa. Abafundi badinga ukuzilungiselela ngokwenza ngokuphindaphinda izinhlobo ezithize zamakhono okuhlanganisa nokususa. Abafundi kufanele bathole ithuba lokwenza lezinhlobo ezilandelayo zezibalo ngezinombolo ezifinyelela ema-800: Hlanganisa noma susa okuhamba ngakubili ngokuphindaphinda ngama-10, weqe e-100 40 + 70 70 + 80 497 120 - 30 150 - 60 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 498 KUPHELA UNYAKA NGETHEMU YE-3 1.13 Isibonelo: Ukuhlanganisa 65 + 10 nokususa 124 + 10 326 - 10 358 - 10 Izibalo IBANGA 1-3 Hlanganisa noma ususe inombolo ehamba yodwa kuya noma kusuka kwinom- bolo ehamba ngantathu ungeqi amashumi Isibonelo 634 +5 775 +  = 779 768 - 4 Hlanganisa ususe inombolo ehamba yodwa kuya kanye nokusuka ekuphin- daphindeni nge-100 Isibonelo: 600 + 4 500 + 3 700 - 6 800 - 5 Qala ukuhlanganisa kanye nokususa okuhamba ngakubili uphindaphinda nge- 100 100 + 100 100 + 200 200 + 200 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 300 + 400 Abafundi kufanele banikwe ithuba lokwenza ngokuphindaphinda amaphethini ngokuhlanganisa nokususa Uma ngazi ukuthi 1+ 1 = 2

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.13 Kanti kuyini loku: Ukuhlanganisa 10 + 10 nokususa 100 + 100 Qala ukuhlanganisa noma ukususa okuhamba ngakubili kokuphindaphinda ku- suka kunoma iyiphi inombolo enezinombolo ezintathu Isibonelo: 675 + 100 762 - 100 Ukubheka iziphumo zezibalo Ngokubheka ukufaneleka kwesiphumo / isiphumo esifanele Abafundi kufanele baqeqeshwe ukubona isiphumo / isixazululo esifanele. One way to do this is to estimate their answers before calculating. When adding two numbers that are close to each other, e.g. 145 and 146, learners can use doubling as a way of estimating their answers. Ukubheka iziphumo / izixazululo Abafundi kufanele bazi ukuthi banga: • Bheka izibalo zokuhlanganisa ngokususa. Isibonelo: If 436 + 118 = 454; then 454 - 118 = 436 • Bheka izibalo zokususa ngokuhlanganisa. Isibonelo 684 - 248 = 436, then 436 + 248 = 684 Ukusebenzisa uhlelo lokuphambana ukubheka iziphumo / izigxazululo esinye sezizathu sokufundisa ukuhlanganisa nokususa ndawonye. 499 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 500 KUPHELA UNYAKA NGETHEMU YE-3 1.14 • Phindaphinda • Phindaphinda kuleThemu abafundi baqhubeka noku: izinombolo ngo 2, 3, izinombolo ngo 2, 3, Ukuhlanganisa • Sebenzisa baqonde ulimi lokuphindaphinda; ngokuphindelela 4,, 10 kuya kwisamba 4,, 10 kuya kwisamba okuholela sama-99 sama-99 • Ukumela ukuphindaphinda kuhlelo ngononina; ezibalweni • Sebenzisa izimpawu • Sebenzisa izimpawu • Ukusebenzisa izimpawu ezifanele ukuhumusha imisho yezinombolo; zokuphindaphinda ezifanele ezifanele • Ukuqonda ukuthi ukuhlanganisa ngokuphindaphinda kungamelwa usebenzisa Izibalo IBANGA 1-3 (x, =, ) (x, =, ) uphawu lokuphindaphinda; • Ukwenza ngokuphindaphinda kanye nokuqonda ukuthi ukuphindaphinda kungenziwa nangayiphi indlela (umthetho wokuguquguqula indlela izinombolo ezimi ngayo); • Sebenzisa umugqa wezinombolo ukhombise izibalo ukuphindaphinda ukwazi ukuchaza okumelwe (indlela ukugxuma okukhombisa ukuhlanganisa ngngokuphindelela); • Baqala ukuqonda indlela yokwehlukanisa uma kuphindaphindwa. • Abafundi baqhubeka nokusebenzisa imifanekiso enhlobonhlobo ukuze baqonde ukuphindaphinda. Bheka amanothi eThemu 2. Amasu asizayo ukuphindaphinda • Sebenzisa ukuphindaphinda Isibonelo: Gcwalisa umugqa uphindaphinda ngokuhlanu, iyiphi iphethini oyibonayo? 1 2 3 4 5 6 7 8 9 10 ×5 × 10 Phinda kabili inombolo ekumugqa wokuphindaphinda ngokuhlanu ukuthola izinombolo kumugqa wokuphinda ngama -10. Yimaphi amaphethini owabonayo? Gcwalisa umugqa wokuphinda ngokubili. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 1 2 3 4 5 6 7 8 9 10 ×2 ×4 Phinda kabili izinombolo emugqeni wokuphinda kabili ukuthola izinombollo kumugqa wokuphinda ngokune.eyiphi iphethini oyibonayo?

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.14 • Sebenzisa ukuhlukanisa kabili ngokulingana Ukuhlanganisa Amaqoqo amathathu okuyi- 8 kwenza-24 ngokuphindelela okuholela ezibal- Amaqoqo ayisithupha oku- 4 enza- 24 weni zokuphin- daphinda   4         +      4       +      4       +      4       +      4       +      4   ngakho:            8                   +                    8                     +                    8         Amaqoqo ayisithupha oku-4 ayafana namaqoqo amathathu okuyi-8. 1.15 • Hlukanisa izinombolo • Hlukanisa izinombolo Yimuphi umehluko eThemu 2? kufinyelele ema-99 kufinyelele ema-99 ukuhlukanisa KuleThemu uhla lwezinombolo abafundi abazosebenza ngalo lukhulile kufinyelela ngoku 2, 3, 4, 5, 10 ngoku 2, 3, 4, 5, 10 ema-99.ukusebenza gohla lwezinombolo olukhulile kusho ukuthi abafundi ku- • Sebenzisa izimpawu • Sebenzisa izimpawu fanele baqale ukusebenza ngamasu afanele ukubala kanye nabakubhale phansi ezifanele (÷, =, ) ezifanele (÷, =, ) ukufinyelela esiphumeni. Amasu okubhala phansi ngeThemu 3 kanye 4 abafundi bazokwenza bephindaphinda ukubhala ukuhlu- kanisa besebenzisa izinombolo banganciki emidwebeni.amasu okubhala ngekhe afinyeleleke kubafundi uma bengakwazi ukubala.imizamo yokuzama indlela abangayiqondi ingaba neziphumo ezinezimpazamo abafundi abangeze bak- wazi ukuzibona.kubalulekile ukuthi abafundi bakwazi ukukhomba ukuxhumana phakathi kokuphindaphinda kanye nokuhlukanisa.inhloso yokubhala phansi kufanele kube ukuthuthukisa ukuqonda ubudlelwano bezinombolo. Ukusebenzisa ukuphindaphinda Bafundi kufanele bakwazi ukusebenzisa ulwazi lwabo lokuphindaphinda, kufanele baqale ukuthi: “Kuyini engikwaziyo ngokuphindaphinda ukuze ngithole imphendulo?” 96 ÷ 3 =  Ngiyazi: 10 x 3 = 30 Manjalo: 96 - 30 = 66 Ngiyazi 10 x 3 = 30 Manjalo: 66 - 30 = 36 Ngiyazi 10 x 3 = 30 501 Manjalo: 36 - 30 = 6 6÷3=2 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI 502 ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 1.15 Kulendlela engenhla, abafundi basebenzisa ukuphindaphinda manjalo basuse ngokuphindelela ema-96.bahlanganise ukuthi basuse kangaki: 2 + 10 + 10 + 10 ukuhlukanisa = 32 Ukuhlakaza izinombolo Abafundi banga ‘hlakaza’ 96 kube izinombolo ezihamsisana no- 3.abafundi baphinde basebenzise ulwazi lwabo lokuphindaphinda benze izibalo zokuhlukanisa. Izibalo IBANGA 1-3 96 ÷ 3 =  96 = 30 + 30 + 30 + 6 10 amaqoqo 10 amaqoqo 10 amaqoqo 2 amaqoqo oku - 3 oku - 3 oku - 3 oku - 3 Okwenziwa abafundi kuzo zombili izibonelo ukusebenzisa ukuhlukanisa ngokuphindaphinda ‘uhlakaza’. Njengoba ukuphindaphinda ‘ukwakha’ izinombolo, ukuhlukanisa kungabonwa njengoku ‘hlakaza’ izinombolo’. Ngalendlela ukuqonda ukuhlukanisa kuqinisa ukuphambana nokuphindaphinda. Abafundi bangasebenzisa ukuhlukanisa ngokuphindaphinda ngokuhlakaza,babhale phansi ngendlela efanayo nalokhu okukhonjiswe ngezansi.96 ÷ 3 =    10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 96 ÷ 3 = 32 Ukusebenza ngezinsalela Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi basebenzile ngezinsalela uma benza izinkinga zezibalo zamagama zokwenza amaqoqo nokuhlukanisa. Kubalulekile ukuthi banikwe imisho yezinombolo zokuhlukanisa (esimweni esikhululekile) lokho kuvumela izinsalela. Isibonelo: Chazela abafundi ukuthi: Uma bazi ukuthi 28 ÷ 7 = 4. Bangathini ngalokhu 29 ÷ 7 = 4 be? Kulindeleke ukuthi abafundi babhale phansi izimpendulo zabo ngalendlela: 29 ÷ 7 = 4 insalela 1. Sifuna abafundi bakwazi ukusho ukuthi amaphi amaphuzu lokuhlukanisa abawaziyo; Isib. ngiyazi 25 ÷ 5 = 5 ngakho ke 26 ÷ 5 = 5 insalela 1

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.16 Ulwazi Lwezinombolo: Ulwazi Lwezinombolo: Izibolo zekhanda Uhla kufinyelela ku 999 Uhla kufinyelela ku 700 Izibalo Zekhanda Bheka amanothi weThemu 2, kepha sebenzisa uhla lwezinombolo oluphezulu • Hlela iqoqo • Hlela iqoqo olubekelwe iThemu 3. lezinombolo lezinombolo ezikhethiwe ezikhethiwe ozinikeziwe. ozinikeziwe. • Qhathanisa izinombolo • Qhathanisa izinombolo kufike ema-999 kufike ema-200 usho okuningi noma usho okuningi noma okumbalwa okumbalwa • Yazi ukuthi • Yazi ukuthi iyiphi inombolo iyiphi inombolo engaphezu ngoku-1 engaphezu ngoku-1 noma okumbalwa noma okumbalwa ngokukodwa. ngokukodwa. • Yazi ukuthi iyiphi • Yazi ukuthi iyiphi inombolo engaphezu inombolo engaphezu ngoku-2 noma ngoku-2 noma okumbalwa ngokubili okumbalwa ngokubili • Yazi ukuthi • Yazi ukuthi iyiphi inombolo iyiphi inombolo engaphezu ngoku-3 engaphezu ngoku-3 noma okumbalwa noma okumbalwa ngokuthathui ngokuthathui • Yazi ukuthi iyiphi • Yazi ukuthi iyiphi inombolo engaphezu inombolo engaphezu ngoku-4 noma ngoku-4 noma okumbalwa ngokunei okumbalwa ngokunei • Yazi ukuthi • Yazi ukuthi iyiphi inombolo iyiphi inombolo engaphezu ngoku-5 engaphezu ngoku-5 noma okumbalwa noma okumbalwa ngokuhlanu ngokuhlanu • Yazi ukuthi iyiphi • Yazi ukuthi iyiphi inombolo engaphezu inombolo engaphezu 503 ngokuyi-10 noma ngokuyi-10 noma okumbalwa ngokuyi-10 okumbalwa ngokuyi-10 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 504 KUPHELA UNYAKA NGETHEMU YE-3 1.16 Khumbula Khumbula ngokushesha: ngokushesha: Izibalo Zekhanda • Amaqiniso • Khumbula amaqiniso ngokuhlanganisa okuhlanganisa nokususa kufike ema- nokususa kufike- 20 20 • hlanganisa Izibalo IBANGA 1-3 • Hlanganisa noma ususe noma ususe okuphindaphindwa ukuphindaphinda nge-10 kusuka koku-0 ngamashumi kusuka kufike e-100 koku-0 kufike e-100 Amasu okubala • Amaqiniso ngekhanda okuphindaphinda Sebenzisa lamasu nokususa woku: alandelayo okubala: • Ithebula • Beka inombolo enkulu lokuphindaphinda kabili kuqala ukuze ubale kufike- 2 x 10 uqhubeka noma ubale • Ithebula uhlehla lokuphindaphinda • Umugqa wezinombolo ngamashumi kufike- 10 x 10 • Ukuhlanganisa kabili nokuhlukanisa kabili Amasu okubala ngokulingana Sebenzisa lamasu • Ukwakha nokuhlakaza alandelayo okubala: • Sebenzisa • Beka inombolo enkulu ubudlelwano phakathi kuqala ukuze ubale kokuhlanganisa uqhubeka noma ubale nokususa uhlehla • Sebenzisa • Umugqa wezinombolo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ubudlelwano phakathi • Ukuhlanganisa kabili kokuphindaphinda nokuhlukanisa kabili nokuhlukanisa ngokulingana • Ukwakha nokuhlakaza

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-3 CAPS 1.16 • Sebenzisa ubudlelwano phakathi Izibalo Zekhanda kokuhlanganisa nokususa • Sebenzisa ubudlelwano phakathi kokuphindaphinda nokuhlukanisa 1.17 • Sebenzisa ubuye kuleThemu abafundi baqhubeka noku: unike amagama Amaqhezu • Funda amagama ezingxenye zamaqhezu; ajwayelekile amaqhezu ezimweni ezijwayelekile • Sebenzisa amagama ezimweni ezihlukene; njengo: uhhafu, • Khomba ingxenye yeqhezut; ikota, okukodwa kokuthathu, okukodwa • Baqala ukuqonda ubungakho beqhezu. kokuyisithupha, nokukodwa kokuhlanu • Ukuthola amaqhezu ezinto; • Bona amaqhezu • Bafunda ngamaqhezu alinganayo kanye asemidwebeni • Nokuqhathanisa amaqhezu. • Baqala ukubona ukuthi KuleThemu abafundi bangaqala ukubala izingxenye zamaqhezu bafunde ohhafu ababili noma namagama amasha amaqhezu. okuthathu kokuthathu Ukubala izingxenye zamaqhezu kuvumela abafundi ukubona izingxenye kwenza okuphelele eziphindaphindayo kubanike ulimi lweqhezu elixubile kanye neqhezu mbumbulu. kanye nokuthi uhhafu izindilinga zamaqhezu kufanele zisetshenziswe kulomqondo. Gqugquzela owodwa kanye abafundi ukubala njenga bezobala izinto eziqoqiwe Isib.okukodwa kokune, namakota amabili okubili kokune, okuthathu kokune, okune kokune, okuhlanu kokune... kuyalingana. ungacela abafundi benze okukodwa okuphelele besebenzisa okune kokune • Bhala amaqhezu ubabuze: “uma sinokuhlanu kokune, ingabe loko kungaphezu kokukodwa njenge okukodwa okuphelele, kungaphansi kokokodwa okuphelele, noma kuyafana nokukodwa kokubili, okubili okuphelele?”Thatha lelithuba ukwendlalela amaqhezu axubile ngokubuza: “thatha kokuthathu okuthathu kokuyisikhombisa.kungaki okuphelele ongakwenza? Zingaki izingcezu ezisele?” sifuna abafundi bathi kuno: “kubili okuphelele kanye nokukodwa kokuthathu okusele.” Loluhlobo lomsebenzi lukhuthaza: • Ukuqonda inombolo yohhafu kokuphelele 505 • Izindlela ezihlukile zokukhuluma ngezinombolo eziphindaphindiwengohhafu. Izibalo IBANGA 1-3

IBANGA LESI-3 ITHEMU 3 2. AMAPHETHINI, UBUDLELWANE NE - ALJEBHRA 506 UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 2.1 Kopisha, uqhubezele Amaphethini atholakala Qhubeka unikeze abafundi uhla lwamaphethini afanayo njengaeThemu yoku - 1, 1 isifundo 3 isi- uchaze lapho siphila khona kodwa faka zonke izimo ezintsha nezinto kwiphethini njengoba zenziwe kwisimo fundos Amaphethini nendawo. Bheka amanothi amaphethini eThemu loku - 1 kanye namanothi esimo ejiyometri Kopisha, qhubezela Bona, chaza nendawo aeThemu yesi - 2. Izibalo IBANGA 1-3 ubuye uchaze ngamagama ubuye ngamagama ukopishe amaphethini Vumela abafundi ukuthi bakopishe kuqala, bese beqhubezela ekugcineni ejiyometri bachaze amaphethini. Kulindekeukuthi babe sebekwazi ukuchaza amaphethini • Amaphethini alula ngaphandle kokusizwa. Qhubeka ugxile ekuthuthkiseni uLimi abaludingayo enziwe ngezinto • Ngokwemvelo ukuchaza amaphethini. eziphathekayo;abuye • Kwimpilo yesimanje • Amaphethini alula yansukuzonke enziwe ngokudweba • Amasiko angamagugu imigqa, izimo noma izinto Qala uchaze amaphethini akho Qala amaphethini akho ejiyometri • Ngezinto eziphathekayo • Ngokudweba imigqa, izimo noma izinto Amaphethini atholakala lapho siphila khona Bona, chaza ngamagama ubuye ukopishe amaphethini ejiyometri Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Ngokwemvelo • Kwimpilo yesimanje yansukuzonke • Amasiko angamagugu

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 2.2 Kopisha, uqhubezele, Kopisha, uqhubezele, Bheka amanothi eThemu yoku - 1 uchaze uchaze Amaphethini Qhubezela ukulandelana ukuze ufake lokhu: ezinombolo Kopisha, uqhubezele Kopisha, uqhubezele • Ngokukodwa kusuela kunoma iyiphi inombolo phakathi kwe - 0 nama - 750 ubuye uchaze uhla uchaze ukulandelana olulula lwezinombolo kwezinombolo olulula • Ngamashumi kusukela kunoma iyiphi inombolo phakathi kwe - 0 nama - 750 kufinyelele okungenani kufinyelele okungenani • Ngakuhlanu kusukela kunoma iyiphi inomnolo phakathi kwe - 0 nama - 750 ema - 200. e - 180. • Ngakubili kusukela kunoma iyiphi inombolo phakathi kwe - 0 nama - 750 Qamba awakho Ukulandelana kufanele amaphethini kukhombise ukubala uya • Ngamakhulu kusukela kunoma iyiphi inombolo eyisiphindaphindi se - 100 emuva naphambili nga: kufinyelele okungenani e - 1 000 Qamba awakho amaphethini ezinombolo. • Ngakunye kusukela • Ngamashumi ama - 50 okungenani kufinyelele e - 1 000 kunoma iyiphi inombolo phakathi kwe • Ngamashumi angama - 25s kusukela kunoma iyiphi inombolo eyisiphindaphindi - 0 nama - 750 sama - 25 kufinyelele okunganani e - 1 000 • Ngokuyishumi • Ngamashumi ama - 20s kusukela ema - 20s kufinyelele okungenani e - 1 000 kusukela kunoma iyiphi • Ngakuthathu kusukela kunoma iyiphi inombolo phakathi kwe - 0 kufinyelela inombolo phakathi kwe okunganai ema - 750 - 0 nama - 750 • Ngakune kusukela kunoma iyiphi inombolo kufinyelela okunganani ema - 750 • Ngakuhlanu kusukela kunoma iyiphi Sebenzisa izinto, izithombe, amatafula kanye imidwebo exhumayo ukweseka inombolo phakathi kwe abafundi uma besuka ekubaleni ngokweqa nokulandelanisa kufinyelele - 0 kya ema - 750 ekuphindaphindeni ngo: 10, 5, 2, 4, 3. • Ngakubili kusukela Siza abafundi ngokusebenzisa amaphethini abawaziyo okuyisisekelo ekwenzeni kunoma iyiphi ngokuphindelela nasekufundeni amanye amaphethini. Isib. inombolo phakathi kwe • Landelanisa ngakubili ukwenza isisekelo ngokulandelana ngama - 20s - 0 kuya ema - 750 • Ngakuthathu kusukela kunoma iyiphi inombolo phakathi kwe - nama - 750 • Ngakune kusukela kunoma iyiphi inombolo eyikuphindaphinda ngakune phakathi kwe - 0 kufinyelela ema - 507 750 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 508 KUPHELA UNYAKA NGETHEMU YE-2 • Ngamashumi ama - 20s,25s, 50s, nge - 100s kuze ku- finyelele okunganai e - 1000 Qamba uchaze Izibalo IBANGA 1-3 amaphethini akho Qamba uchaze amaphethini akho ezinombolo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI-3 YEBANGA LESI-3 3. INDAWO NESIMO (IJIYOMETRI) UMQONDO KANYE UMQONDO CAPS NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 3.1 Isikhandla nokubonisa Isikhundla nokubonisa Yini entsha eBangeni lesi - 3 3 izifundo Isikhundla, • Linganisa imibono • Funda, uhumushe • Amabalazwe, amapulani, nemibono ephezulu yezinto ukubuka eyahlukene yezinto ubuye udwebe • Ukuthola izinto kumabalazwe nokubonisa zansukuzonke amabalazwe ezifanayo angahlelekile noma • Ukulandela izinkombandleala kwibalazwe ukubukeaka kwezinto • Shono izinto • Dweba amabalazwe angahlelkile, amapulani noma nemibono yezinto zansukuzonke • Thola izinto eziqoqekile uma usukhonjiswe kumabalazwe Ukufunda, ukuhunyushwa kwamabalazwe icala elingajwayele Isikhundla ukubonakala Amabalazwe indlela esezingeni eliphezulu lokubuka indawo. EBangeni lesi nezinkombandlela - 3, abafundi basebenza kuphela ngamabalazwe angahleliwe, lokhu akufaki • Funda, uhumushe Landela izinkombandlela amabalazwe asetshenziswa emigaqweni noma amabalazwe ezifundo zezwe. ubuye udwebe kusukela endaweni amabalazwe Ingasiza abafundi ukuqala izinhlelo noma ukubukeka kwendawo encane, eyodwa kuya kwenye angahlelekile, noma isib. Ithileyi elinezinto noma uhlaka lwepulani lwekilasi, ngaphambi kokubuka ngebalazwe elingahleliwe ukubukeka kwezinto. amabalazwe ezindawo ezinkulu. • Thola izinto NgeThemu yesi - 2 qondanisa ukubukeka kwezinto uzibuka ngaphezulu. Uma kumabalazwe ubuka into uyiqhamukela ngaphezulu iba nokutsheka kance. Abantwana babona icala elitshekile lomhlaba esikhathini esiningi kunalelo lokuwubuka ngaphezulu. Isikhundla Ingabasiza abafundi ukuthi baqale ngokuqondanisa lezondawo abzibona nezinkombandlela zitshekile. Uma izindlela ezimbili zokubuka zinikeziwe, abafundi bangaqondanisa • Landela lokho abakubonayo nalokho okubonwa ngabanye ngakwelinye icala.. izinkombandlela Qala usize abafundi ukuthi baqonde amabalazwe namapulani, bese beqoqa ukuze ukwazi izinto ezindaweni ezikwibalazwe. isib.“thola iklikini, yini esduze kwayo?” ukuhambahamba ekilasini Uma abafundi sebekwazi ukuthola izindawo ezahlukene kwibalazwe, qala ubanikeze izinkombandlela kusukela endweni eyodwa kuya kwenye kwibalazwe. • Nikeza izinkombandlela Dweba ukubukeka kwezinto eziqoqiwe uzibuka ngaphezulu namabalazwe zekilasi nesikole angahlelkile • Landela Kulula kubafundi ukudweba indlela izinto ezibukeka ngayo uma uzibuka izinkombandlela ngaphezulu kunokudweba ibalazwe ngengqondo noma belisusela engqondweni. kusukela endaweni Indlela elula yokudweba ukubukeka kwento uyibuka ngaphezulu ukwenza eyodwa kuya abafundi ukuthi babuke izinto eziqoqene ndawonye, isib. Izinto ezisetafuleni kwenye ngebalazwe likathisha, noma izinto ezikwithileyi elibekwe phansi. Abafundi bangaqhubeka 509 elingahleliwe ngokudweba amapulani angahlelekile kanye namabalazwe ezindawo ezincane. isib.ikilasi. Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 510 KUPHELA UNYAKA NGETHEMU YE-2 3.2 Uhla lwezinto Uhla lwezinto Izincomo zokugxilwa kuhko eThemu ye - 3 5 izifundo Izinto ezinhlang- Bona usho izinto Bona usho izinto • Abafundi bangagxila ezintweni ezintsha eBangeni lesi - 3, okuyiphiramidi, othintathu ezinhlangothintathu ezinhlangothintathu amakhoni. ekilasini nasezithombeni ekilasini nasezithombeni • Abafundi bakha izinto besebenzisa izitro noma izinto zokugeza amaphayiphi • Okunesimo esisabhola • Okunesimo esisabhola noma izinti zokuvungula noma ishubhu elenziwe ngephepha. (spheres) (spheres) Izibalo IBANGA 1-3 Yethula amakhoni namaphiramidi kubafundi • Okumise okwebhokisi • Okumise okwebhokisi Kugxilwa kwizimpawu zezinto ezinhlangothintathu: ubuso obuyisicaba, (prisms) (prisms) izimo eziyisicaba • Isilinda • Isilinda • Ubuso obuyisicaba • Iphiramidi • Iphiramidi NgeThemu yesi - 2 • Amakhoni • Amakhoni • Abafundi bagxila ekutheni babheke ukuthi izinto zinobuso obuyisicaba. Izimpawu zezinto Izimpawu zezinto • Abafundi bachaza izimo zobuso obuyisicaba ngokuthi basho ukuthi Chaza, hlela, Chaza, hlela, kuyindilinga, isikwele, noma unxande. uqhathanise izinto uqhathanise izinto Abafundi bayaqhubeka bakwenze lokhu ngeThemu yesi - 3, kodwa manje ezinhlangothintathu: ezinhlangothintathu: sebebheka nephiramidi kanye nekhoni. • Izimo zezinto • Izimo zezinto • Ukwakhiwa kwezinto ngazodwa ezinhlangothintathu ezinhlangothimbili ezinhlangothimbili zenza ubuso bezinto zenza ubuso bezinto Abafundi basebenzisa izinti zokuvungula, amashubhu amaphepha agingqiwe, ezinhlangothi ntathu ezinhlangothi ntathu izinto zokuhlamba amapayipi ukwenza iphiramidi. Kulokhu abafundi bagxila onqenqemeni lwephiramidi. Abafundi akulindelekile ukuthi babale inani • Ubuso noma • Ubuso noma lonqenqema noma amakhoni (lokhu kwenziwa eBangeni lesi - 6). ingaphezulu eliyisicaba ingaphezulu eliyisicaba Ukubona nokusho izinto Imisebenzi okugxilwa Imisebenzi okugxilwa kuyo kuyo Abafundi kufanele banikezwe uhla lwezinto abazosebenza ngazo: Buka wakhe izinto Buka wakhe izinto • Izimo ezisambulunga njenge: bhola, omabuli, amawolintshi, njll; onikezwe zona onikezwe zona • Izimo eziyiprizimu, njengamabhuloki, izitini, amabhokisi ezinto ezahlukene,, ezinhlangothintathu ezinhlangothintathu nokunye; usebenzisa izinto usebenzisa izinto Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola eziphathekayo eziphathekayo • Izimo eziyisilinda, kufaka ezinde neziwumncingo, isib. izingcezu ezimise ezifana nezimo ezifana nezimo okwamaphayiphi, umbhobho wephepha lasendlini yangasese, isilinda ebanzi ezinhlangothimbili, ezinhlangothimbili, nokunye. ubumba/udongo, ubumba/udongo, ezinye izinto zejometri ezinye izinto zejometri • Izimo ezingamakhoni;kanye ezinhlangaothintathu. ezinhlangaothintathu • Nezimo eziyiphiramidi

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 3.2 Abafundi kufanele bathole babuye bakhombise izinto ezise okwebhola (sphere), Izinto ezinhlang- noma ezimise okwebhokisi (prisms) noma ezimise okwesilinda (cylinder), ezimise othintathu okwe phiramidi noma ikhoni. • Uma benikezwe izinto eziqoqiwe; • Ekilasini, Isib. Lesitini simise okwebhokisi noma leliwolintshi limise okwebhola. Ngesikhathi sokufunda ngokuzimela abafundi bangenza amabhola kanye nama- silinda namabhokisi (prisms) Imisebenzi ebhalwayo Nakuba imisebenzi eminingi yezimo ezinxantathu yenziwa ngokubhala, um- sebenzi uhlanganiswa ngokwenza imisebenzi ebhalwayo. EBangeni lesi - 3 kufanele kugxilwe ekushiweni kwamagama ezinto kubuye kukhulunywe ngobuso bazo. Akulindelekile ukuthi abafundi babale noma bazi inani lezikwele, unxande, unxande noma into enobuso obuyindilinga, ungqengqema lwento. ULimi Ukukwazi ukusebenzisa uLimi ukukhuluma nezinto ezinezimo ezinhlangothin- tathu: Ubuso, isicaba, ibhokisi, isilinda, ikhoni 3.3 Uhla lwezimo Uhla lwezimo Bheka amanothi eThemu yoku - 1. 2 izifundo Izimo ezinhlang- • indilinga • indilinga Abafundi kufanele bagxile kulokho abagxile kukho, kodwa futhi benzeimisebenzi othimbili • unxantathu • unxantathu eyahlukene. • isikwele • isikwele Abafundi basebenza ngezindilinga nezikwele ezinobungako obahlukene kanye nonxantathu nonxande onobungako obuhlukene. Abafundi bazihlela ngokwama- • unxande • unxande cala azo ukuthi ayindilinga noma aqondile. Izimpawu zezimo Izimpawu zezimo Abafundi bahlela baqoqelendawonye izimo ngokonxantathu, izikwele, unxande Chaza, hlela uqhananise Chaza, hlela uqhananise noma indilinga. izimo ezinhlangothimbili izimo ezinhlangothimbili Umsebenzi uhlanganiswa ngemisebenzi ebhalwayo okufanele ifake imidwebo (2-D) ngokwe: (2-D) ngokwe: yonke edingekayo kwimo. • simo • simo • amacala aqondile • amacala aqondile • amacala awulawondi • amacala awulawondi Dweba izimo Dweba izimo • indilinga • indilinga 511 • unxantathu • unxantathu • isikwele • isikwele Izibalo IBANGA 1-3 • unxande • unxande

ITHEMU YESI- 3 YEBANGA LESI-3 4. ISILINGANISO 512 UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 4.1 Ukusho isikhathi Ukusho isikhathi Abafundi bayaqhubeka ukwenza ngokuphindelela bekhuluma ngesikhathi nokulandelana kwaso. Isikhathi • funda izinsuku • funda izinsuku kwikhalenda kwikhalenda Ngesikhathi sokufunda kwekilasi lonke nangesikhathi samaqoqo okugxilwa kulo, Izibalo IBANGA 1-3 abafundi bayaqhubeka bakhulume ngezinsuku zesonto, zezinyanga zonyaka • faka izinsuku • faka izinsuku nosuku abakulona, nezinsuku ezizayo nezangaphambili. Abafundi bayaqhubeka zokuzalwa, imigubho zokuzalwa, imigubho bafake lezigameko ezilandelayo kwikhalenda: yezenkolo, izehlakalo yezenkolo, izehlakalo eziwumlando, eziwumlando, • izinsuku zokuzalwa; izehlakalo zesikole izehlakalo zesikole • imigubho yezenkolo; kwikhalenda kwikhalenda • izehlakalo eziwumlando; • shono isikhathi • shono isikhathi esingamahora ayi - 12 esingamahora ayi - 12 • izehlakalo zesikole; ngama: ngama: • amaholidi - hora - hora qhubeka ugqugquzele abafundi ukuthi bakhulume ngesikhathi njalo - isigamu sehora - isigamu sehora nansukuzonke - ikota lehora - ikota lehora • ngamahora nangamaminithi ewashini lezinombolo; - amaminithi - amaminithi • ngamahora, ngesigamu sehora nangekota lehora besbenzisa iwashi lezinti Ewashini lezinti Ewashini lezinti isib. abafundi bangacelwa ukuthi basho isikhathi sokuqala kwesikole, isikhathi nelezinombolo nezinye nelezinombolo nezinye sekhefu nesokuya ekhaya, noma uma beshintsha izifundo. Khetha isikhathi izinsimbi ezikhombisa izinsimbi ezikhombisa lapho iwashi lisho isikhathi siwungqo ezimpondweni noma ligamenxe noma isikhathi isib. isikhathi isib. kuyikota lehora. Kuyasiza ukuba newashi elikhulu elisebenzayo ekilasini ukuze umakhalekhukhwini umakhalekhukhwini abafundi bakwazi ukubheka kulona. Abafundi bangabuye benze umfanekiso wewashi. Ungabe usubacela ukuti bakhombise izikhathi ezahlukene ezifaka Bala ubude besikhathi Bala ubude besikhathi ukubala ewashini. Isib. “Ngikhombise ihora leshumi. Ngabe isikhathi besiyimizuzu nokuhamba kwaso nokuhamba kwaso eyishumi nanhlanu ngaphambi kwehora leshumi10?” Sebenzisa ikhalenda Sebenzisa ikhalenda See notes for Term 1. ukubala nokuchaza ukubala nokuchaza Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ubude besikhathi ubude besikhathi Ngesikhathi somsebenzi wokuzimela, abafundi bayaqhubeka benze imisebenzi ngezinsuku noma ngezinsuku noma ehambelana nokushiwo kwesikhathi: ngamasonto noma ngamasonto noma • ngamahora,ngesigamu samahora nangekota lehora kusetshenziswa iwashi ngezinyanga kufaka: ngezinyanga kufaka: lezinti • ukuguqula phakathi • ukuguqula phakathi • ngamahora nangamaminithi kusetshenziswa iwashi lezinombolo kwezinsuku namasonto kwezinsuku namasonto Abafundi bangabala ngamasonto noma ngezinsuku uma benayo noma • ukuguqula phakathi • ukuguqula phakathi benikezwe ikhalenda noma ingxenye yekhalenda ukuthi bayisebenzise. Isib. kwamasonto kwamasonto Ukuthola izinsuku nokubala umehluko phakathi kwezinsuku nesikhathi. nezinyanga nezinyanga

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO CAPS KUPHELA UNYAKA NGETHEMU YE-2 4.1 sebenzisa amawashi sebenzisa amawashi Ukufunda iwashi lezinti ngamaminithi Izifundo eziyi - 6 ukubala ubude besikhathi ukubala ubude besikhathi Isikhathi Chitha okungenani izifundo ezintathu ugxile ekufundweni kwamakhono ngamahora noma ngamahora noma adingekayo okufunda iwashi lezinti ngesigamu sehora ngesigamu sehora nekota lehora nekota lehora • Khumbuza abafundi ukuthi kusho ukuthini ukuthi ekuseni nantambama (a.m. and p.m.) • Khumbuza abafundi ukuthi amaminithi angama - 60 ngehora, ngakhoke amaminithi angama - 30 anguhhafu wehora, nokuthi amaminithi ayi - 15 ayikota lehora. Abafundi babala ngakuhlanu uthisha ekhomba ewashini lezinti. • Chaza ukubalwa kwesikhathi uma kusayoshaya ihora nokubalwa kwesikhathi selishayile ihora (“past” and “to”) • Nikeza abafundi isikhathi sokwenza bephindelela isikhathi besebenzisa iwashi lezinti. Abafundi abanikeze isikhathi njalo ngosuku kuze kuphele unyaka. Abafundi bangahlola isikhathi basebenzise iwashi lezinti ukubona ukuthi banikeze isikhathi esifanele na uma besibheka ewashini lezinti. Abafundi benza umfanekiso wamawashi abangawasebenzisa ukusho isikhathi babuye babale umehluko phakathi kwesikhathi. 4.2 Ukulinganisa Ukwethulwa Yini eyahlukile eThemu yesi - 2? okungahlelekile kokulinganisa Ubude ngeThemu yesi - 2 abafundi bagxila kulokhu: okuhlelekile • Hlawumbisela, • Ukulinganisa ngokungahlelekile kusetshenziswa isikali esingenasilinganiso linganisa, qhathanisa, • Sela, linganisa, sobude hlela ubhale qhathanisa, hlela phansi ubude ubhale phansi • Ukulinganisa ngamaitha. usebenzise isikali usebenzise amamitha NgeThemu yesi - 3 abafundi baqala ukulinganisa ngamasentimitha besebenzisa esingenasilinganiso, (kungaba izinduku irula. Lokhu kuzoba ukulinganisa kokuqala kesetshenziswa into ethile isib: amagxthu enziwe zamamitha noma engasetshenziswa abafundi uma befunda ngaphandle kokulinganisa imigqa eya ngezandla, amagxathu, ubude bentanmbo) ngokukhula. ubude bepensela, njll. njengobude beyunithi obejwayelekile. Ukuhlawumbisela, ukulinganisa, ukuqhathanisa, nokubhala phansi ubude, • Chaza ubude ukuphakama nobubanzi kusetshenziswa amamitha. bezinto ngokuzibala • Hlawumbisela usebenzisa isikali ulinganise • Abafundi kufanele bahlanganise ukuqonda kwabo kobude obuyimitha elilodwa esingenasilinganiso ngamasentimitha besebenzisa ubude bemitha ukukala. Bheka amanothi eThemu yesi - 2. usebenzisa irula. Ukuhlawumbisela, ukulinganisa, ukuqhathanisa, nokubhala phansi ubude, 513 ukuphakama nobubanzi ngamasentimitha kusetshenziswa irula • Sebenzisa irula Izibalo IBANGA 1-3 Khombisa abafundi ukuthi kuqalwa kanjani ukukala kusukela e - 0.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI 514 ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 4.2 • Sebenzisa uLimi Akukho ukuguquka Uma abafundi besebenzise amayunithi bahlele lapho kuqala khona izinto ukukhuluma okwenzekalayo njengeba zisetshenziswe ekukaleni kokuqalwa kwezinto. Uma ulinganisa Ubude ngokuqhathanisa, phakathi kwamamitha ngamasentimitha, awuhleli lapho kuqala khona irula kanye nokuqala lapho kuqala isib. okude kakhulu, namasentimitha. khona izinto ezizokalwa. Uhlela izinto esezikaliwe kusukela ku 0 kwirula. okufishane kakhulu, Okudingakalayo okubanzi kakhulu, okuwumncingo Izibalo IBANGA 1-3 kakhulu. Ukwethulwa kokulinganisa okuhlelekile Irabha iwu - 2cm ubude • Sela, linganisa, qhathanisa, hlela Kungalinganiswa lapho kuqala khona into elinganiswayo nenye inombolo ubhale phansi ekwirula bese kususwa inombolo eskuqaleni kwento ngasekugcineni kwento. usebenzise amamitha (kungaba izinduku zamamitha noma ubude bentanmbo) njengobude beyunithi obejwayelekile. • Hlawumbisela ulinganise Irabha iwu (3 cm - 1 cm) = 2 cm ubude ngamasentimitha Ngaphandle uma abafundi bebuza ngalokhu, noma bazitholele bona, usebenzisa irula. kungayekelelwa iBanga le - 4. Akukho ukuguquka • Ukuhlawumbisela ngamasentimitha okwenzekalayo phakathi kwamamitha Abafundi kufanele bathole izinto eziyisentimitha elilodwa ngqo ubude. namasentimitha. Mhlawumbe umunwe wabo ungaba yisentimitha elilodwa. Lokhu Okudingakalayo. kungasetshenziswa njengokuhlawumbisela ubude, ububanzi, ukuphakama ngamasentimitha. Uma abfundi sebenolwazi ngokulinganisa ngamasentimitha, kufanele bahlwumbisele ngaphambi kokulinganisa. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Imigqa, imidwebo nezinto Yenza abafundi baqale ngokulinganisa ngemigqa. Kulula ISILINGANISO ubude bemigqa, ukuphakama, noma ububanzi bezinto eziphathekayo kusetshenziswa irula. EBangeni le - 4, abafundi balinganisa ngamasentimitha nangamamilimitha. EBangeni le - 3 akulindelekile ukuthi basebenzise amamilimitha.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 4.2 • Qhathanisa ukulinganisa ngamasentimitha. Ubude Abafundi kufanele baqhathanise ubude, ububanzi nokuphakama kwezinto ezilinganisiwe ngamasentimitha. • Ukubhala phansi isilinganiso Nakuba ISILINGANISO kuyikhono, abafundi kufanele babhale phansi ISILINGANISO (ngokukala okunesilinganiso nokungenaso) ngasosonke isikhathi. Ukulinganisa ubude njengesimo esejwayelekile ukuxazulula izinkinga kanye nokubala Ngesikhathi esinikezwe izinombolo, ukusebenza, nobudlelwano bezinombolo abafundi bangaxazulula izinkinga ezisebenzisa isimo esi: • Ukulinganisa okungahlelekile kobude; • Ukulinganisa ubude ngamamitha; • Ukulinganisa ubude ngamasentimitha. Bheka uhla lwezinombolo lweThemu, kanye nohla lwezinkinga ezifanele iThemu. Abafundi abalindelekile ukuthi: • Bazi ukuthi u - 100 cm = 1 m; • Ukwenza izinguquko eziphakathi kwamasentimitha namamitha; • Ukufunda ubude ngamamilimitha (lokhu kwenziwa eBangeni le - 4); • Ukwazi ukuthi u - 10 mm = 1 cm; noma • Ukwenza izinguquko phakathi kwamasentimitha namamilimitha. Ukubala ngamasentimitha kungakhethwa ukuze bangeqeli ngaphezulu kwama - 100 cm. 515 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI 516 ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 4.3 Isilinganiso Ngesikhathi semisebenzi yokuzimela abafundi bangenza lokhu: Isisindo esingahlelekile • Hlawumbisela, linganisa, qhathanisa, ubhale phansi isisndo sezinto esebenzisa • Hlawumbisela, isilinganiso sokuzimelela ngamayunithi angahlelekile ukukala. uqhathanise, • baqhathanisa, bahlele, babhale phansi abakutholile ulinganise, hlela - igilosa nesisindo ngokwamakhilogramu ubhale phansi isisindo, usebenzisa isikali - igilosa nesisindo ngokwamagremu Izibalo IBANGA 1-3 esingenasilinganiso bona amanothi eThe - 2 nesikali sokuzimelela ukulinganisa ubude njengesimo esejwayelekile ukuxazulula izinkinga kanye isib. Amabhuloki, izitini, nokubala nokunye. Ngesikhathi esinikezwe izinombolo, ukusebenza, nobudlelwano bezinombolo • Sebenzisa uLimi abafundi bangaxazulula izinkinga ezisebenzisa isimo esi: ukukhuluma • ukulinganisa ngokwesisindo; ngokuqhathanisa, isib. kulula, kuyasinda, • isindo ngokwamakhilogramu; kulula kakhulu, kusinda • isisndo ngokwamagremu kakhulu. Bheka uhla lwezinombolo lweThemu, kanye nohla lwezinkinga ezifanele iThemu. Ukwethulwa kokulinganisa okuhlelekile • Qhathanis, hlela, ubhale phansi isisindo sezinto zokuthengisa ezihleliwe zabhalwa nesisindo sazo ngokwamakhilogramu, isib. ikhilogramu lerayisi, ikhilogramu likafulawa, noma ngamagremu, isib. amagremu angama - 500 g oswayi. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Balinganisa isisindo sabo ngama khilogramu besebnzisa isikali sokuzimelela sasendlini yokugezela. Azikho izinguquko eziphakathi kwamamililitha namalitha adingekayo.

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 4.4 Ukulingasanisa Ngesikhathi semisebenzi yokuzimela abafundi bayaqhubeka ngalokhu: okungahlelekile Umthamo Hlawumbisela ubye ulinganise, qhathanisa, hlela, bhala phansi umthamo • Hlawumbisela wezitsha usebenzisa isilinganisi esingenasilinganiso. Uma ulandela uhla ubuye ulinganise, lwendlela yokwenza into ethile, kufaka ukubhaka, yilona lolohlu oluyisimo qhathanisa ubye uhlele esejwayelekile okufanele ukuthi abafundi balwenze ngokuphindelela. Khetha umthamo wezitsha uhla lokwenza izinto olunezithako olunezikali ngezinkomishi, amathisipuni noma (gcwalisa umthamo amayunithi angahlelekile. ongathathwa izitsha) • Qhathanisa uhlele umthamo wohla lwamabhodlela negilosa lapho umthamo ngokusebenzisa isikali ukhonjisiwe ngaphandle kwephakethe. esingenasilinganiso isib. izinkezo • Sebenzisa ilitha elilodwa lebhodlela noma ilitha likajeke ukuhlawumbisela nezinkomishi nokulinganisa, ukuqhathanisa, ukuhlela nokubhala phansi umthamo wezitsha ngokwamalitha. • Chaza umthamo wezitsha ngokubala • Sebenzisa izitsha ezimakiwe ngokwamalitha. Isib. 200 ml, 330 ml, 500 ml, 750 ubuye usho ukuthi ml, noma 250 ml kulinganiswa izinkomishi, noma 5 ml izipuni zokukala, noma mangaki amayunithi ujeke onemigqa yamamililitha emakiwe ngokomteliwuthathayo angahlelekile Bheka amanothi eThemu ye - 1. agcwalise isitsha, isib. ibhodlela linomthamo Abafundi kufanele banikezwe umsebenzi obhalwayo ukuhlanganisa lokhu wezinkomishi e - 4. okulandelayo, kufaka iukufundwa kwezithombe: Ukwethulwa • Zomkhiqizo onomthamo obhalwe ngamlitha ukuze kulandelane. kokulinganisa okuhlelekile • Izithombe zojeke ezinomthamo osendelene nelitha elilodwa noma amabili. • Hlawumbisela, • Okulindelekile ukuthi abafundi bafunda kuphela okusondelene nolayini linganisa, qhathanisa wokulinganisa (gradation line). Bachaza umthamo wabo nokucishe, sondelene/ hlela ubhale phansi duze, kungaphezulu kancane, kungaphansi kancane, inombolo eqondile umthamo wezinto (yamalitha) abawufunda kujeke. ngokwamalitha, • Imikhiqizo nemithamo yakhona ebhalwe ngokwamamililitha ukuze ilandelane. isigamu selitha, ikota yelitha • Izithombe zojeke lapho umthamo isondelene nomugqa wokulinganisa (gradation line) Okulindelekile ukuthi abafundi bafunda kuphela inombolo esondele emugqeni wokulinganisa 517 Izibalo IBANGA 1-3

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO 518 KUPHELA UNYAKA NGETHEMU YE-2 4.4 • Qhathanisa, uhlele Umthamo wokulinganisa ngokwesimo esejwayelekile ukuxazulula izinkinga ubhale phansi nokubala Umthamo umthamo wezinto Ngesikhathi esinikezwe izinombolo, ukusebenza, nobudlelwano bezinombolo zokuthengisa abafundi bangaxazulula izinkinga ezisebenzisa isimo esi: eziqoqelwe ndawonye omthamo • Ukulinganisa okungahlekile komthamo, isib. ugogo usebenzise izinkomishi wazo ubhaliwe ezimbili zobisi ukwenza ikhekhe. Uma engaphinda kabili uhla lwakhe lokubhaka Izibalo IBANGA 1-3 ngokwamalitha. Isib. uzodinga ubisi olungakanani? amalitha amabili • Amalitha obisi, ilitha lesiphuzo esiqandayo, amalitha • Amamililitha amahlanu kapende noma ngamamililitha, Qaphela ukuthi uhla lwezinombolo olufanele lweThemu luyalandlelwa, kanye isib. 2 amalitha obisi, nohla lwenhlobo yezinkinga. 5 amalitha esiphuzo esiqandayo, 750 amalitha kawoyela. • Yazi ukuthi inkomishi eyejwayelekile iwu - 250 amalmililitha • Yazi ukuthi ithisipuni iwu 5 amamililitha Azikho izinguquko eziphakathi kwamamililitha namalitha adingekayo. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 CAPS 4.5 Ubungako Ubungako Ukulinganisa okuzungeza izinto noma ukulinganisa ubungako bento 1 isifundo bangaphandle bento bangaphandle bento bangaphandle kusha eBangeni lesi - 3. Ubungako bangaphandle • Phenya ubude Phenya ubude Ubungako bangaphandle bento kulinganiswa ngokungahlelkile kuphela eBangeni nobungako bebanga obuzungeza bebanga obuzungeza le - 3 bangaphezulu izinto eziyizimo izinto eziyizimo Nikeza abafundi isikhathi sokwenza ngokuphindelela kusetshenziswa intambo bento ethile ezinhlangothintathu ezinhlangothintathu ISILINGANISO uzungeza izinto ezahlukene ezifana: nekhanda, ibhodlela (kufaka nezinhlangothimbili nezinhlangothimbili amabhodlela amade abukeka ewumncingo, namabhodlela amafishanekakhulu kusetshenziswa kusetshenziswa intambo abukeka ebanzi) amathini, izinkomishi, amabhokisi, nokunye. Yenza ukuthi intambo. abafundi baqale ngokuhlawumbisela ukuthi yiziphi izinto ezinobungako Ubungako bangaphandle obuthe xaxa babuye bahlole ngokuzimaka ngobude bebanga bangaphezulu ngaphandle kwentambo babuye baziqhathanise. • Phenya ubungako Abafundi bangalinganisa ubungako bangaphandle bento bezimo bengaphezulu ezinhlangothimbili kusetshenziswa intambo. bendawo usebenzisa Abafundi bangenza ukulinganisa okungahlelkile kobungako bangaphandle intambo. usebenzisa amayunithi anesikali esingenasilinganiso esifana nezivalo zamabhodlela, amabhokisi kametshisi, nokunye. 519 Izibalo IBANGA 1-3

IBANGA LESI-3 ITHEMU YESI- 3 5. ULWAZI OLUQOKELELWE 520 UMQONDO KANYE UMQONDO NAMAKHONO NAMAKHONO IZIHLOKO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ISIKHATHI ADINGEKAYO UMA OKUGXILWA KUKHO KUPHELA UNYAKA NGETHEMU YE-2 5.4 Qoqa ubuye uhlele Qoqa ubuye uhlele Kwaphakanyiswa ukuthi ngeThemu yoku - 1 abafundi benza ibha grafu yekilasi, 3 izifundo ulwazi ulwazi nokuthi ngeThemu ye - 2 bahlaziya amagrafu ezithombe namathebula anikeziwe. Qoqa ubuye uhlele NgeThemu ye - 3 abafundi bangasebenza ngolwazi lonke (bheka amanothi ulwazi • Qoqa ulwazi ngekilasi Qoqa ulwazi ngekilasi eThemu yoku - 1) noma uqale ngolwazi olwethuliwe ohleni noma amathali noma noma yesikole noma yesikole amathebula babuye bahlele kabusha lokhu kwibha grafu. Izibalo IBANGA 1-3 ukuphendula imibuzo ukuphendula imibuzo ebuzwe nguthisha ebuzwe nguthisha Kulula kubafundi ukuthi badwebe ibha grafu ngokusebenzisa amabhuloki amaphepha. • Hlela ulwazi olunikezwe Bhala okumele ulwazi nguthisha noma incwadi. Kuzodinga ukuthi ubakhumbuze abafundi ukuthi izimpawu ezibalulekile zebha Bhala okumele ulwazi grafu (bheka amanothi iThemu yoku - 1). • Hlela ulwazi kwibha (bar) Abafundi kufanele baphendule imibuzo ekwibha grafu; bheka iThemu yoku - 1 - uhla Hlaziya ubuye ukuze uthole izinhlobo zemibuzo ezifanele. uhumushe ulwazi - amathalisi Phendula imibuzo - amatafula ngolwazi olukwibha (bar) 5.5 Bhala okumele ulwazi Bhala okumelele Bhala okumele ulwazi ulwazi • igrafu yezithombe • igrafu eyibha (bar graph) 5.6 Hlaziya ubye uhumushe ulwazi Hlaziya ubuye uhumushe ulwazi Phendula imibuzo ngolwazi olumelwe kulokhu: • igrafu yezithombe • igrafu eyibha (bar graph) Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

ITHEMU YESI-4 YEBANGA LESI-3 1. IZINOMBOLO, IMISEBENZI NOBUDLELWANO BAZO IMIQONDO ISIKHATHI CAPS NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.1 Ukubala izinto Ngasemaphethelweni alethemu abafundi kumele ukuba sebeke babona, eziphathekayo baphatha, futhi benyakazise izinto ezi1 000. Kufanele babe nomqondo Izinto zokubala wobuningi obu 1 000. Isu lokuhleka ngokwezinyanda ligqugquzeliwe. Ukuqagela nokubala ngokuyiko ukufika okungenani1 000 lezinto ezisetshenziswa njalo. Isu lokuhlela ngokwamaqoqo lugqugquzeliwe 521 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 522 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.1 Izinto zokubala Izibalo IBANGA 1-3 Ngasemaphethellweni ethemu abafundi kumele bakwazi ukuphendula lelzinhlobo ezilandelayo zemibuzo kanye nemiyalelo: • Bala iziinto zokubala ngokamaqoqo/ izinyanda ezingakuhlanu,ngamashumi • Phinda uhllele ubale futhi. Ingabe usanesibalo esifanayo sezinto zokubala? • Nazi izinto zokubala ezingama- 200. Zibale ngokuthi uzenze amaqoqo/ izinyanda ezihamba ngamashumi. • Ukuzibala zonke lezizinto zokubala ezingama- 200 ungakhetha ukuzibala ngamaqoqo ahamba ngama- 20 noma ama- 25? Kungani? • Nquma ukuthi kungaba iyiphi indlela engcono yokubala iqoqo lamapensela/ amapeni omsizi. • Nazi izinto zokubala izingama- 80 Uma sibala ngakubili noma ngamashumi, ingabe isamba sezinto zokubala sizohlala sinjalo? • Bala izinto zokubala ezingama- 46 ngokuzibeka ngamaqoqo/izinyanda ezihamba ngakubili. Ingabe kuyashesha ukubala ngakubili kunokubala Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ngakodwana?

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.2 Bala ukuyaphambili noma Bala ukuyaphambili noma Ngasemaphethelweni ethemu abafundi kumele bakwazi: uhlehal/ ubuyela emumva uhlehal/ ubuyela emumva Ukubala Ukubala ngokuzethemba, bephimisa ngakunye, ngamashumi, ngakuhlanu, ngamashumi amabili, nga nga ngamashumi amabili ananhlanu, ngamashumi amahlanu, ngamakhulu ukuya e- 1000 uyaphambili nasemuva • 1 ukusuka kunoma iyiphi • 1 ukusuka kunoma Ukuphendula imibuzo efana: inombolo ephakathi kwe iyiphi inombolo 0 na 1000 ephakathi kwe 0 na Bala ngamashumi usuka 400 ukuya 500. Manje bala uhlehla/ ubuyela emumva futhi. 1000 Bala ngaku 2 usuka 564 ukuya 580. Manje bala uhlehla/ ubuyela emumva futhi • bephindaphinda ngama 10 phakathi kuka 0 • bephindaphinda Bala ngamashumi amahlanu kusukela ema - 600 kufinyelela ema - 800. Mangaki ama - 50 nama 1000 ngama 10 phakathi owabalilie? kuka 0 nama 1000 • bephindaphinda ngaku5 Bala uye emuva ngama - 100s kusukela ema - 620. Mangaki ama - 100s owabalile? phakathi kuka 0 nama • bephindaphinda 1000 ngaku5 phakathi kuka 0 Bala uye emuva ngakunye kusukela - ema - 876 kufinyelela ema - 866. Kungaki okukodwa nama 1000 okubalile? Ungaqiniseka kanjani ukuthi wenza ngakho? • bephindaphinda nga 2 phakathi kuka 0 nama • bephindaphinda nga 2 Bala ngokuyi - 15 uye phambili kusukela ema - 305. 1000 phakathi kuka 0 nama 1000 Uma ubala ngama - 25 kusukela ema - 525 kufinyelela ema - 850 ungayisebenzisa lenombolo 725? • bephindaphinda nga 3 phakathi kuka 0 nama • bephindaphinda nga 3 Bala uhlole 1000 phakathi kuka 0 nama Iyiphi inombolo elandelayo? 1000 • bephindaphinda nga 4 467, 468, 469, phakathi kuka 0 nama • bephindaphinda nga 4 1000 phakathi kuka 0 nama 725, 750, 775, 1000 420, 440, 460 • ngama 20, 25, 50, 100 ukufika okungennani • ngama 20, 25, 50, 100 820, 800, 780 1 000 ukufika okungennani 1 000 Bala usebenzisa umugqa wezinombolo Dweba umugqa wezinombolo ongenalutho ukhombise lezinombolo kuwo: 602, 604, 610. Manje-ke ungawabeka kuphi 606? Bala usebenzisa umugqa wakho wezinombolo usuka 602 ukuya 610. Bala ngamashumi usuka 314 ukuya 344.Yimaphi amadijithi asguqukayo? Yimaphi amadijithiangaguquki? Kungani amakhulu angaguquki? Kwenzakalani uma ubala uhlehla, ubuyela emumva? 523 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 524 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.3 ukukhomba, ukubona ukukhomba, ukubona Ngasemaphethellweni ethemu abafundi kumele bakwazi: kanye nokufunda kanye nokufunda Izimpawu Ukufunda nokubhala izinombolo ukufika okungenani 1 000 zezinombolo izinombolo izinombolo kanye namagama Ukuphendula imibuzo efana nokuthi: • ukukhomba, ukubona • ukukhomba, ukubona ezinombolo kanye nokufunda kanye nokufunda Iyiphi inombolo ebhalwe kulelikhadi? Izibalo IBANGA 1-3 izimpawu zezinombolo 0 izimpawu zezinombolo ukuya1 000 0 ukuya1 000   642 • Ukubhala izimpawu • Ukubhala izimpawu Thola ikhadi elina 738 noma amakhulu ayisikhombisa amashumi amathathu nesishiyagalombil zezinombolo 0 -1 000 zezinombolo 0 -1 000 Funda lezinombolo ezilandelayo kuzwakale: 534, 947, 974, 345 • ukukhomba, ukubona • ukukhomba, ukubona kanye nokubhala kanye nokubhala Funda lamagama: amagama ezinombolo 0 amagama ezinombolo • Amakhulu amathathu,amashumi amane anambili ukuya1 000 0 ukuya1 000 • Amakhulu ayisishiyagalombili namashumi amabli ananye • Ukubhala amagama • Ukubhala amagama ezinombolo 0 -1 000 ezinombolo • Amakhulu amane, amashumi ayisithupha nanye. 0-1 000 • Inkulungwane • Amashuma amabili anesishiyagalolunye Bhala ngokwezimpawu zezinombolo • Amakhulu amahlanu namashumi ayisikhombisa • Amakhulu amahlanu • Amakhulu ayisithupha namashumi ayisishiyagalombili ananhlanu Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.4 Ukuchaza, Ukuchaza Ngasemaphethellweni ethemu abafundi kumele bakwazi: ukuqhathanisa ukuhlela nokuqhathanisa Ukuchaza, Ukuhlela izinombolo ukufika okungenani 1000 izinombolo ukufika 999 izinombolo ukuqhathanisa Ukuphendula imibuzo ebuzwe ngezindlela ezahlukene: uhlele izinombolo • Ukuchaza eziphelele ukufika 999 nokuqhathanisa Ukufunda umugqa wezinombolo. • Chaza bese izinombolo eziphelele uqhathanisa izinombolo ukufika 999 usebenzisa- eziphelele kufinyelele kuncane ku- kukhulu ema- 999 usebenzisa ku- kungaphezulu ku-, okuncane okunokunye, more than, kulidlanzana okukhulu okunokunye, Avela kuphi 450? ku- futhi kulingana na- okungaphezulu • Ukuchaza okunokunye, Avela kuphi 700? nokuqhathanisa okumbalwa Avela kuphi 350? izinombolo eziphelele okunokunye Manje-ke gcwalisa zonke izinombolo. ukufika 999 ukusuka nokulingana nokunye. kokuncane ukuya Ukubhala izinombolo ukusuka kwenkulu ukuya kwencane • Ukuchaza kokukhulu, nokukhulu nokuqhathanisa 345, 428, 389, 561, 600, 739, 620, 824 ukuya kokuncane izinombolo eziphelele Ukuqhathanisa izinombolo ukufika 999 Ukusebenzisa ukufika 999 ukusuka izinombolo ezimele kokuncane ukuya Izibonelo isikhudla ukukhombisa kokukhulu, nokukhulu • Iyiphi inombolo enkulu ngoku-1 kuma-563 ukuhleleka, isikhundla ukuya kokuncane noma ukuma • Iyiphi inombolo eza ngemuva kwama-768 Ukusebenzisa • Ukusebenzisa, ukufunda izinombolo ezimele • Iyiphi inombolo engaphansi ngoku-1 kuma- 431 nokubhala izinombolo isikhudla ukukhombisa • Iyiphi inombolo enkulu ngoku-10 kuma-620 ezimele isikhundla, ukuhleleka, isikhundla umbandakanya indlela noma ukuma • Iyiphi inombolo engaphansi ngoku-10 kuma- 650 efingqiwe ukufika 31 • Iyiphi inombolo enkulu ngoku-20 kuma -480 • Ukusebenzisa, ukufunda nokubhala • Iyiphi inombolo engaphansi ngoku-20 kuma- 740 izinombolo ezimele isikhundla, • Iyiphi inombolo enkulu ngoku-25 kuma -625 umbandakanya indlela • Iyiphi inombolo enkulu ngoku-50 kuma 250 efingqiwe ukufika 31 • Iyiphi inombolo engaphansi ngoku-50 kuma- 700 525 • Iyiphi inombolo enkulu ngoku-300 kuma -300 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 526 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) Phendula amanga noma iqiniso. Nikeza isizathu sempendulo oyinikile/ oyishilo 220 asondele kakhulu 200 ku 250 403 awasondele kakhulu 400 ku 420 15 lisondele kakhulu 0 ku 30 Izibalo IBANGA 1-3 Gcwalisa ngokuthi kuningi/ ngaphezulu kuno kuncane noma kungaphansi kuno 145 mu _________ 154 823 mu_________ 789 466 mu_________ 664 Sebenzisa amadijithi 9, 0, 6 ukwenza inombolo enkulu kunazo zonke ongase uyenze. Iyiphi inombolo encane kunazo zonke ongase uyenze? 1.5 Ukubona ukuthi Maphakathi nalethemu ukuhlanganiswa kwalemiqondo elandelayo kufanele izinombolo kugcizelelwe futhi kugqugquzelwe: Ukubona isikhundla sobungako ezingamadijithi • Izinombolo zingahlukaniswa ngokwamakhulu, amashumi nangakunye benombolo amathathu ezitholakala 999 zimele okungaki • Ukuqonda ukuthi 51 makhulu ku 15 ngoba 51 anamaqoqo/ izinyanda 5 ezihlukaniswe ngamaqoqo/ izinyanda ezihamba ngamashumi, 15 bese kuthi • Ukubona ukuthi iqoqo/ inyada 1 lihambe ngamashumi inombolo ngayinye imeleni • Uma bebala ngaku shumi, uma abafundi befika 40 sebayazi ukuthi sebebala amashumi 4 • Ukuhlakaza izinombolo ezinamadijithi Ngasemaphethellweni ethemu abafundi kumele bakwazi: 3 ukufika 999 Ukusebenzisa, ukufunda kanye nokubhala lolulimi lokusebenza ngngokuphindelela okwe ngesimelabungako baluqondisise. 100, ngokuphindelela kweshumi, kanye Izinhlamvu noma okuhamba ngakunye, ngamashumi, ngamakhulu, idijithi, nangakunye (HTU) idijithi elilodwa, inomboolo yamadijithi amabili …, inombolo yamadijithi amathathu, isimelabungako…. • Ukubona nokusho Ukubona 0 njengesimeleli (as place holder) uma sikhuluma Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola isimeIabungako sedijithi ngezinombolo ezinamadijithi amabilii- noma amathathu afana ngayinye 60 305 720

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.5 Ukuhlukanisa inombolo ukukhombisa inani ledijithi ngayinye Ukubona isikhundla 637 = 600 + 30 + 7 sobungako benombolo Ukusebenzisa amakhadi amafuladi khadi (flard cards) ukukhombisa lokhu   600   30   7   Ukusebenzisa amabhuloki Dienes (dienes blocks) ukukhombisa isimelabungako senombolo Ukuphendula imibuzo efana nalela: Shano ukuthi idijithi 7 e127 limeleni kanjalo no 2? Kanye no 1? Kunamakhulu amangaki kulezi zinombolo ezilandelayo 300, 500, 700, 412, 568 Kunamaqoqo amangaki amashumi kuleyo naleyo nombolo kulezinombolo ezilandelayo? 50, 80, 100, 200, 700, 120 Bhala izinombolo: Ikhulu nanhlanu Amakhulu ayisithupha nashumi amabili nanhlanu Amakhulu amane nashumi ayisishiyagalombili nesishiyagalolunye Amakhulu amathathu anantathu Bhala izinombolo: 1 ikhulu + 2 amashumi Amakhuku amabili + 3 amashumi + 7 imivo Amakhulu amane + 9 amashumi + 3 imivo Chaza ukuthi iyiphi inombolo efanele ukungena ebhokisini ngalinye 872 =  + 70 + 2 129 = 100 +  + 20 + 9 527 346 = 300 + 40 +  Bhala ubungako bedijithi ngayinye kulenombolo 762 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 528 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) UKUXAZULULA IZINKINGA ESIMWENI ESEJWAYEKILE 1.6 Ukusebenzisa amasu Abafundi balindeleke ukuxazulula izibalo zamagama besebenzisa lamasu alandelayo uma uxazulula alandelayo: Amasu okuxazulula izinkinga izinkinga, nokuchaza • Ukwakha kanye nokubhidliza izinombolo isixazululo sezinkinga: Izibalo IBANGA 1-3 • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo • Ukwakha kanye nokubhidliza izinombolo • Imigqa yezinombolo • Ukuphinda kabili • nokusondezela emashumini nokuhlukanisa kabili Buka amanothi ethemu ye 2 mayelana namasu alandelayo ngokulinganayo • Ukwakha kanye nokubhidliza izinombolo • Imigqa yezinombolo • Ukuphinda kabili nokuhlukanisa kabili ngokulinganayo • nokusondezela emashumini • Imigqa yezinombolo nokusondezela emashumini Maphakathi kwalethemu abafundi bangasebenzisa amasu okusondezela eshumini uma bexazulula izibalo zamagama Isibonelo: UNoah una R48,00. Iphakethe lamakhadi alithathayo libiza R5, 00. Angathenga amaphakethe amangaki? Abafundi bangasondezela R48 eshumini, okuzoba R50.00. Lokhu kuchaza ukuthi angathenga cishe amaphakethe 10. Abafundi kuzofanele babale baphinde babalisise ukuze bathole ukuthi ingabe sebesondele ngokwenele eshumini. Vumela abafundi ukuba bakhethe amasu abakwazi ukuwasebenzisa bekhululekile. Noma kunjalo, uma abafundi besebenzisa amasu angavamile lapho-ke badinga ukucetshiswa ukuba bakhethe amasu avamile. Abafundi akudingekile ukuba bangenzi amaphutha ngamasu abo. Bazokwazi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ukubuye bawasebenzise futhi uma sebefunda emabangeni aphakathi.

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.7 Ukuxazulula izibalo Ngasemaphethellweni ethemu abafundi kumele bakwazi: ukwenza izibalo zamagama esimweni zamagama ezilandelayo Ukuhlanganisa esjwayelekile nokususa nkuchaza isixazululo Ukuhlanganisa nokususa esimbandakanya Kunezinhlobo okungenani ezintathu zokuhlanganisa nokususa There are at ukuhlanganisa, ukususa, least three basic types of addition and subtraction problems and each type can okuholela ngezimpendulo be posed in different ways. The basic types are: ezifika 99. Shitsha uNoluthando uqoqe amaphepha okudlala anamathelayo/amastikha a 234. USilo wabuye wamupha amanye amastikha 80. Usenamastikha amangaki manje? Kunabagibeli 500 esitimeleni. 176 labagibeli lehla.Bangaki abagibeli abebesele esitimeleni? Hlanganisa UNosisi uqoqa izinto ezizosetshenziswa kumaprojekthi ezikole okuguqula izinto kabusha.Ucoshe amabhodlela kaplastiki 124 kanye namathini 268. Zingaki izinto asezicoshile? Isitolo sinamaphakethe amashibusi 368; 82 angama chippos kanti asele angama ziksnacks.Mangaki amaphakethe noma amaZicksnacks asele? Qhathanisa IBANGA LESI-2 liqokelele R446. IBANGA LESI-3 laqokelela R729. Ingabe IBANGA LESI-3 liqokelele malini ngaphuzulu? Ukubuza isibalo samagama ngasinye ngezindlela ezehlukile zsibalo zamagama kufanele zibuzwe ngezindlela ezahlukile. Ngokwesibonelo, zozibili lezibalo zimayelana noshintshi, kodwa “izinombolo ezicashile” zisezindaweni ezahlukene esibalweni Isitolo besinamaphakethe emphuphu; kwafakwa enye i oda 55. Manje kunamaphakethe emphuphu a 170. Mangaki amaphakethe abekade ekhona kwasekuqaleni? Isitolo besinamaphakethe kashukela 500. Ngemuva kokudayisa amanye alamaphakethe, bekunamaphakethe kashukela 324 asele. Bathengise amaphakethe amangangaki? 529 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 530 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.8 Ukuxazulula izinkinga Izibonelo zezibalo ezingenziwa kulethemu esimweni esejwayelekile, Ukuhlanganisa nokuchaza izixazululo Ukuhlanganisa ngokuphindaphinda ngokuphindelela zezinkinga ukusebenzisa kuhelela Izimoto 36zinamasondo amangaki? ukuphinda ekuphindaphindeni Isilinganiso Izibalo IBANGA 1-3 UThami ugcina 35c ngeviki. Imalini ayigcinayo emasontweni a 8? Amagridi UMnu Khumalo utshala izinhla e 20 zezihlahla zikawolintshi. Kunezihlahla e 12 ohleni ngalunye. Zingaki izihlahla ezitshaliwe uma seziphelele? Izibalo ezixhumene ngemisebenzi eyahlukene UHeila uthengisa amasosiji ewabiza R4 lilinye. Yaka ithebula umsize ukuba akwazi ukuthola inani lamaoda amakhulu. Isibalo samasosiji 1 2 3 4 5 10 20 Intengo ngokwama R 4 8 Sebenzisa ithebula ukuthola intengo yamasosiji a 7 na 23 amasosiji. USedick ubheka izingane. Ubiza R20 yokugibela, kany R5 ukubheka ingane ihora ngalinye. Mugcwalisa lelithebula. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.9 Ukuxazulula izinkinga Izibonelo zezibalo ezingenziwa kulethemu nokuchaza izixazululo Ukwenza amaqoqo Ukuhlela ngamaqoqo nokuhlukaniselana ezibalweni eziphathekayo okuholela ezimbandakanya Ukuhlela ngamaqoqo, ngokulahla insalela the ekuhlukaniseni ukwahlula ngokulinganayo Isitolo esithengisa izinkwa, sithengisa izikhwanyana zamakhekhe a 12. nokuhlela ngamaqoqo Banamakhekhe 118. Kungaphuma izikhwanyana ezingaki zamakhekhe awu ukufika 100 nezimpendulo 12 isikhwama ngasinye? ezingase zibe nensalela. Ukuhlela ngamaqoqo ngokufaka inselela empendulweni Umlimi unamaqanda 227. Udinga amabhokisi amangaki aphatha amaqanda 6 lilodwa ukuze akwazi ukupakisha amaqanda? Ukwahlula Ukwahlula, ulahla insalela Abangane abahlanu bahlula ibhokisi likaswidi o 84 ukuze bakwazi ukuthola inani lamaswidi alinganayo. 531 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 532 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.10 Ukuxazulula izinkinga Izibonelo zezibalo ezingenziwa kulethemu nokuchaza izixazululo Ukuhlukaniselana Ukwahlula okuholela ezingcezwini okuholela ezibalweni eziphathekayo emaqhezwini ezimbandakanya Yahlula amagabelo kashokoledi 15 phakathi kwabangane, ngendlela yokuthi ukwahlula ngokulinganayo bonke bathola inani elifanayo lamagabelo kashokoledi kungasali lutho. Izibalo IBANGA 1-3 okuholela kwizixazululo Yahlula amagabelo kashokoledi 7 phakathi kwabangane 3, ngendlela yokuthi ezimbandakanya bonke bathola inani elifanayo lamagabelo kashokoledi kungasali lutho. amaqhezu anezingcezu ezingaphezu kolulodwa Iqhezu lohlobo oluthile kanye nalawo ayiqhezu elilodwa kokuphelele isib. Ugogo upha uKiki R12.u Kiki ufuna ukulondoloza iqhezu lokuthathu lwalemali. 1 1 3 2 Kufanele alondoloze malini? 2 ,4 ,4 ,5 , Loluhlobo lwesibalo kufanele abafundi basenze umanje sebake benza izibalo zokwahlula okungenani amahlandla amane nma amahlanu, okuyikhona okuzobaholela ekutheni bazi namagama ezingcezu lweziqhezu. Ukuhlanganisa iziqhezu Umlolongi webhola lezandla upha abadlali ingxenye yewolintshi ngamunye.. Kunabadlali aba 14. Udinga amawolintshi amangaki? Loluhlobo lwesibalo kufanele abafundi basenze umanje sebake benza izibalo zokwahlula okungenani amahlandla amane noma amahlanu, okuyikhona okuzobaholela ekutheni bazi namagama ezingcezu lweziqhezu. Ukubhala iziqhezu Abafundi abadingekile ukubhala izimpawu zeziqhezu. Abafundi bafunda ukulebula izingxenye njengokuthi iqhezu kokuhlanu, 1 fifth, okuthathu koqhezu lokwesine noma okuthathu koqhezu lokwesithupha 3. Lokhu kubasiza okuqala ukuba baqonde ukuthi igama leziqhezu lichaza ukuthi zingaki izinhla zokugcwele ezahluliwe isib. Ingxenye, okunye kokuthathu, okunye kokune njl. Nokuthi zingaki izinhla ezithathwa njengokubili kokuthu. Ukumela iziqhezu zezibalo zamagama Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Abafundi kufanele badwebe izimpendulo zabo ukubonakalisa ukuthi bayasiqonda isibalo. Ukulindele ukuthi abanye abafundi bangase badwebe kahle kodwa balubizi kahle uhla lweqhezu. Abafundi kufanele basho izingxenye abazibhale ngokuhlanganyela, izingxenye ezi 2 kwezintathu.

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.11 • Ukubona nokukhomba Izibonelo zezibalo ezingenziwa kulethemu uhlwweza lwase Imali • INani lemali kanye nokwakha isamba isib. Ningizimu Afrika kanye namanoyhi asebhange/ - Bhala 325c ngokwamarandi namasenti. imaliyephepha. - Zingaki izindlela ongazisebenzisa ukwakha R400 usebenzisa kuphela • Ukuxazulula izibalo amanothi asebhange/ imali engamaphepha? Wazi kanjani ukuthi ingabe zemali nokuhlanganisa unazo zonke izixazululo? ushintshi - UTravis unocezu oluyi 50c kanye nezinye ezi 20c ezine. Amatofi abiza R1, ngokwamarandi noma 20. Uzothola ushintshi kamalini? amasenti. • uMandla ubhadala R5,50 ethekisini uma eya esikoleni. • Uguquko phakathi kwamarandi namasenti - Ingabe usebenzisa malini nsuku zonke ukuya nokubuya esikoleni? Izibalo zokuthenga nokudayisa • UPedro uphiwe wugogo R5. Yimaphi amaswidi amathathu angawathenga? ushokoledi R2,70; uswidi R1,80; izibungu ezimuncu R1,40; uswidi kapentshisi R1,60; uminti R2,20; utofi R1,20. • UDamon uthenge izincwadi ezintathu R80 eyodwa; Kuzobuya ushitshi kamalini uma ebhadala R300? • Amaphakethe kaminti 5 abiza 44c lilodwa. UMnu King ufuna ominti 88. Angathenga amaphakethe amangaki? Uzobhadala malini? IZIBALO 1.12 • Ukusebenzisa amasu Buka amanothi eThemu ye - 3 uma bebala Amasu (izindlela noma amaqhinga) • Ukwakha nokubhidliza izinombolo • Ukuphindaphinda nokuhlukanisa kabili ngokulingana • Umugqa wezinombolo • Ukusondezela eshumini 533 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 534 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 • Ukuhlanganisa ukufika Maphakathi nalethemu abafundi baqhubeka nokwehlakaza izinombolo ukuze 999 bakwazi ukubala. Ukuhlanganisa nokususa • Ukususa usuka 999 Izindlela ezingasetshenziswa ukukhombisa izibalo zokuhlanganisa nokususa • Ukusebenzisa izimpawu Ukwehlakaza izinombolo zibe yizingcezu ezincane ukuze ukubala kubelula Izibalo IBANGA 1-3 ezifanele (+, -, =, ) Ukusebenzisa ulwazi lwesimelibungako ukuhlakaza izinombolo ngamakhulu, ngamashumi kanye nemivo • Ukuzilolongela amabhondi ezinombolo • Ukuhlanganisa ngokuhlakaza zombili izinombolo ukufika 30 Ukuhlanganisa amadijithi ehamba ngamatathu nalawo ahamba ngambili 524 + 82 =  = (500 + 20 + 4) + (80 + 2) = 500 + (20 + 80+ (4 + 2) = (500 + 100) + 6 = 600 + 6 = 606 Ukuhlangaisa amadijithi amathathu namanye amadijithi amathathu 323 + 436 =  323 + 436 = = (300 + 20 + 3) + (400 + 30 + 6) = (300 + 400) + (20 + 30) + (3 + 6) = 700 + 50 + 9 = 759 • Ukuhlanganisa (ngokuhlakaza izinombolo okufanele zihlanganiswe) Abafundi bazokwehlakaza izinombolo ngendlela ezoba lula kubona. Lokhu kuchaza ukuthi bazokwenza ngezindlela ezahlukene. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 524 + 82 =  524 + (40 + 40 + 2) 524 + 40 → 564 + 40 → 604 + 2 = 606

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 Ukuhlangaisa amadijithi amathathu namanye amadijithi amathathu Ukuhlanganisa 323 + 436 =  nokususa = 323 + (400 + 30 + 6) = (323 + 400) + 30 + 6 = (723 + 30) + 6 = 753 + 6 = 759 • Ukususa ngokuhlakaza izinombolo zombili Three-digit subtract three-digit 889 - 137 =  889 - 137 = (800 + 80 + 9) - (100 + 30 + 7) = (800 - 100) + (80 - 30) + (9 - 7) = 700 + 50 + 2 = 752 • Ukususa ngokuhlakaza inombolo eyodwa Three-digit subtract three-digit 889 - 137 =  889 - (100 + 30 + 7) 889 - 100 → 789 - 30 → 759 - 7 = 752 • Ukusebenzisa ukuhlukanisa inombolongoukuhlakaza inombolo kabili 525 + 16 = 525 + 8 + 8 = (525 + 8) + 8 = 533 + 8 = 541 • Qhubeka ubale ubuyela emumva 535 805 = 798 =  ukubala uya phezulul ngakunye uqale 798 kuyiqhinga elifanele ngoba Izibalo IBANGA 1-3 izinombolozisondelene.

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 536 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 • Ukukhomba okusondele ekuphindaphindeni kabiliI Ukuhlanganisa 245 + 246 nokususa Lesibalo esngenhla singabizwa ngokuphindaphinda 245 + 1 phindaphinda 246 -1 Izibalo IBANGA 1-3 245 + 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 = 491 Ukuthuthukisa nokulzilolongela amakhono okuhlanganisa nokususa. Abafundi kumele bazilolongele amakhono ezinhlobo zokuhlanganisa kanye nokususa Ukubala uya phezulu naphansi ukusondezela 10 588 + 9 588 + 10 = 598 598 - 1 = 597 588 + 19 588 + 20 = 608 608 - 1 = 607 Abafundi kumele babenamathuba okwenza lezizinhlobo zokubala ngezinombolo ezifika 800: Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukuhlanganisa noma ukususa izinombolo ezibhanqiwe ngokuphindaphinda ngaku 10,unqamula 100 40 + 70 70 + 80 120 - 30 150 - 60

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 Ukuhlanganisa noma ukususa 10 ukuya noma ukusuka kunoma yimaphiamadijithi ezinombolo ezimbili noma ezintathu kanye nokunqamula Ukuhlanganisa ama 100 nokususa Isibonelo: 65 + 10 124 + 10 326 - 10 358 - 10 Ukuhlangansisa noma ukususa idijithi eyodwa noma inombolo enamadijithi amathathu ngaphandle kokunqamula amashumi. Isibonelo: 634 +5 775 +  = 779 768 - 4 Ukuhlangansisa noma ukususa idijithi eyodwa ukusuka noma ukuya kngokuphindelela kwe 100 Isibonelo: 600 + 4 500 + 3 700 - 6 800 - 5 Ukuqala ukuhlanganisa nokususa okubhanqiwe kokuphindaphinda kwe 100 100 + 100 100 + 200 200 + 200 300 + 400 537 Abafundi kumele baphiwe ithuba lokuzilolongela amaphethini atholakala ekuhlanganiseni nasekususeni. Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 538 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 Uma ngazi ukuthi 1+ 1 = 2 Ukuhlanganisa Manjeke yini: nokususa 10 + 10 100 + 100 Izibalo IBANGA 1-3 Ukuqala ukuhlanganisa nokususa okubhanqiwe kokuphindaphinda ukusuka kunoma iyiphi inombolo enamadijithi amathathu Isibonelo: 675 + 100 762 - 100 Ukuqonda ukuhlanganisa ekupheleni konyakande Ekupheleni konyaka abafundi kufanele bakwazi: Ukusebenzisa nokuqonda ulimi lokuhlanganisa: Ubunigi,,hlanganisa, isibalo,isamba, sekukonke,kulungana, uphawu…. nokufunda nokubhala uphawu lokuhlanganisa(+) kanye nophawu lokuninganisa (=) Qhubeka uthuthukisa ukuqonda kokuhlanganisa njengokubala uqhubeka kanye nezinyathelo kumugqa wezinomblo. Isib. Phendula lokhu okulandelayo. Kungaki ekudingeka ukuba ngikungeze 67 ukuze ngenze 85? Nasi isbbalo esiwumusho engingasisebenzisa embuzweni wami: 67 +  = 85. Ukuphendula izinhlobo zemibuzo elandelayo: • Hlanganisa ndawonye 43 ne 19 • Ngeza ishumi kwi 167 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • 51 hlaganisa 83 • Ngeza 70 ema- 50 • 280 = 120 + 80 +  • Yini 30 ngaphezukwe 160 • Thola inani le 156 ne 14 • Ngeza ishumi nambili ekhulwini namashumi ayisikhombisa nanhlanu

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 • Iyiphi inmbolo uma wengeza ishumi ku 483? Ukuhlanganisa • Kufanele wengeze yiphi inombolo ema- 45 ukuthola i-178? nokususa • Kufanele wengeze yiphi inombolo e ma-25 ukuthola i-178? • Kufanele ngongeze yiphi inombolo e ma-56 ukuthola i-170? • Yini okumele ngiyihlanganise ema- 56 ukuthola i- 170? • Amashumi 12 hlanganisa 8 imivo • 245 + 10 =  245 + 20 =  245 + 30 =  Yazi ukuthi  limele inombolo efihliwe 45 + 81 =  67 +  = 125 47 + 32 + 8 =  31 +  + 20 = 160  + r = 100  + r = 120  + r = 450 Ukuqonda nokusebenzisa ulwazi lokuthi ukuhlanganisa kungenziwa nganoma iyiphi indlela.noma izinombolo zingahleleka nanoma iyiphi indlela 178 + 12 = 190 ngakho-ke 12 + 178 = 190 Ukuqonda ukususa ekupheleni konyaka Ukusebenzisa nokuqonda ulimi lokususa: Thatha, susa, kusele mangaki,kuncana kangakanani lokhu.. kuna..., umehluko phakathi, kuningi kangakanani lokhu ……kuna…..okungakanani ukwenza…… nokufunda nokubhala uphawu lokususa(-) Qhubeka uthuthukise ukuqonda kokususa njengo: • thatha; noku 539 • thola umehluko phakathi. Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 540 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 Ukuqonda ukuthi ukususa iqanda akuyishintshi inombolo: Ukuhlanganisa 192 - 0 = 192 192 = 192 - 0 nokususa Ukuphendula imibuzo ebhaliwe ebekwe ngezindlela ezahlukahlukene kanje: 37 thatha 13 Izibalo IBANGA 1-3 Thatha 40 e 280 162 susa 42 Subtract 45 from 390 Yini umehluko phakathi kwa 738 ne 157? 117angaphansi kanganani ku 449? Iyiphi inombolo okufanele uyisuse ku 56 ukuze uthole 122? Iyiphi inombolo okufanele uyisuse ku 56 ukuze uthole 132? Iyiphi inombolo okufanele uyisuse ku 56 ukuze uthole 142? Thola izinombolo ezibhangqiwe ezinomahluko we10 Kunamapeni omsizi a 45 kwi shalofu elidonswa likathisha. Ukhipha amapeni a 17. Mangaki asele? Thola izinombolo ezibhangqiwe ezinomahluko wa 20. Yazi ukuthi  limele inombolo efihliwe. 557 - 134 =  800 - 530 =  762 -  = 448 598 - 42 =  Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola 687 -  = 375 13 - 6 = 15 -   - 18 = 24 174 - 14 =  199 -  = 25

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 Ukuqala ukuqonda ukuthi Ukuhlanganisa 125 - 10 wahlukile kuno10 - 125 nokususa Ukuqonda ubudlelwano phakathi kokuhlanganisa nokususa. Ukusebenzisa ubudlelwano phakathi kokuhlanganisa nokususa. Ukusho nokubhala iphuzu lokususa elinikiwe ephuzwini lokuhlanganisa nangokuphambanayo (vice versa). Isib: 25 + 68 = 93 implies that 93 - 68 = 25 68 + 25 = 93 implies that 93 - 25 = 68 122 - 104 = 18 implies that 18 + 104 = 122 Ngaphandle kokusebenzisa izinsiza phendula lokhu okulandelayo: Uyazi ukuthi 145 + 120 = 265 Kuyini: 120 + 145 265 - 120 265 - 145 154 - 38 = 116 Uyazi ukuthi 154 - 116 116 + 38 38 + 116 Bhala uphendule lokhu okulandelayo: 64 - 37 =  ngakhoke 37 +  = 64 137 - 17 =  ngakhoke  + r = 137 200 - 100 =  ngakhoke  + 100 = 200 541 89 - 38 = 51; 51 umehluko ngoba  + r = 89 Bhala izibalo zamagama ezine usebenzisa lezizinombolo.160, 35, 125 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 542 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.13 Ukuhlola imiphumela yezibalo Ukuhlanganisa Ukwahlulela ukuba nezizathu khwezixazululi nokususa Abafundi kumele balolongwe ukwahlulela ukuba nezizathu khwezixazululi Enye indlela yokwenza lokhu ukuqagela izimpendulo zabo ngaphambi Izibalo IBANGA 1-3 kokubala. Uma behlanganisa izinombolo ezimbili ezisondelene isib. 45 46, abafundi bangasebezisa ukuphinda kabili njengendlela yokuqagela izimpendulo zabo. Ukuhlola izixazululo Abafundi kumele bazi ukuthi banga • sihlola isibalo sokuhlanganisa ngokususa.Isibonelo: uma 36 + 18 = 54; ngakho 54 - 18 = 36 • sihlola isibalo sokususa ngokuhlanganisa isibonelo: 84 - 48 = 36, bese 36 + 48 = 84 Ukusebenzisa ukusebenza ngokuhlanekezela ukuhlola izixazululo ngesinye sezizathu zokufundisa ukulhanganisa nokususa kanye kanye. 1.14 • Ukuphindaphinda Maphakathi nalethemu abafundi baqhubeka: izinombolo 1 ukuya 10 Ukuhlanganisa • Ukusebenzisa nokuqonda ulimi lokuphindaphinda, ngokuphindelela nga 1, 2, 3, 4, 5, 10 okuholela • Ukumela ukuhlela ukuphindaphinda ngononina; • Ukusebenzisase ekuphindaphindeni izimpawu ezifanele • Ukusebenzisa izimpawu ezifanele ukuchaza iizibalo eziyimisho; (x, =, ) • Ukuqonda ukuthi ukuhlanganisa ngokuphindaphinda kungavezwa ngokusebenzisa uphawu lokuphindaphinda; • Ukuzuzilolonga nokuqonda ukuthi ukuphindaphinda kungenziwa nanganoma iyiphi indlela. (umthetho wokumiswa kwezinombolo); • Ukusebenzisa umugqa wezinombolo ukubonisa izibalo zokuphindaphinda Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola babuye bakwazi ukuchaza okumelwe (ukuthi imeqo ikubonisa kanjani ikuhlanganisa ngokuphindaphinda); no • Nokuhuba ithebula lokuphindaphinda Ekupheleni kwethemu abafundi kumele bakwazi: Ukusebenzisa ulimi lokuphindaphinda ngendlela ephathekayo:

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.14 Ukuphindaphinda, izikhathi, phindaphinda, phindaphinda ngo,isiphindaphindi se..,okuningi, amaqoqo e.., isikhathis njengo (enkulu, ende, okubanzi..), kabili, Ukuhlanganisa ngokuphindelela kathathu,kangango, ukufunda nokubhala uphawu lokuphindaphinda (x) okuholela Ukusebenzisa ulimi ukwenza izibalo zokuphindaphinda ekuphindaphindeni Ukuqonda ukuphindaphinda njengokuhlanganisa ngokuphindelela 6 kuhlanganiswe ndawonye izikhathi 3 kuyafana nokuthi: 6 + 6 + 6 = 18 3 nokuningi o 6 = 18 3 izikhathi 6 = 18 6 x 3 = 18 3 x 6 = 18 Ukuqonda ukuphindaphinda njengoba kuchaza izinhlelo ngononina Ukuqala ukubona ukuthi ukuphindaphinda kungenziwa nanganoma iyiphi indlela / uhlelo Ukuphendula imibuzo ebuzwe ngezindlela ezahlukene Izihlanu ezimbili Phindaphinda 5 3 phinda 5 UlhIa lwezinto zokubala ezintathu.Kunezinhla 4. Zingaki izinto zokubala sezizonke? 2 phindaphinda 7 543 16 phinda izikhathi 2 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 544 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.14 Ukuqonda umthetho wokumiswa kwezinombolo wokuphinda Ukuhlanganisa 3 x 4 = 12 kufana nokuthi 4 x 3 = 12 ngokuphindelela okuholela Ukubona ukusetshenziswa kwesimeleli  ukumela inombolo efihliwe. ekuphindaphindeni 2+2+2= Izibalo IBANGA 1-3 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 4x8=x4 8 + 8 + 8 = 3 koku yisishiyagalombili = 8 x  = 24 Ukuqonda ubudlelwano phakathi kokuphindaphinda nokuphinda kabili Kopisha ithebula elingezansi. Gcwalisa uhla lokuphindaphinda izikhathi 4 (‘Umugqa wokuphindaphinda ‘ 4 ‘) 1 2 3 4 5 6 7 8 9 10 4s 2s Kusetshenziswe izifanekiso ezahlukene ukuphindaphinda • Ophahla bokuphiphinda • Amaflowu shadi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • Amathebula

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 • Ukwahlukanisa ukufika Yini okuhlukile kwethemu 3? 99 nga 1, 2, 3, 4, 5, 10 Ukwahlukanisa Ekupheleni kwethemu kufana uqunisekise ukuthibakwazi: • Ukusebenzisa izimpawu ezifanele (÷, =, ) • Ukuqonda ukuthi ukuhlukanisa kabili ukuhlanekezela kokuphinda kabili nokukhumbula ukuphindwa kabili kwazozonke izinombolo ukufika 20 kanye nengxenye ehambisana nayo; • Ukubona ukuhlukanisa njengokuhlela ngamaqoqo; • Ukuqonda nokuthokozela ubudlelwano phakathi kokuphindaphinda nokwahlukanisa nokuthi zisebenza ngokuhlanekezela; • Ukusebenzisa izindlela ezibhaliwe eziphathekayo nezingahlelekile ukwahlukanisa amadijithi amabili ngezinombolo one zamadijithi; • Ukusebenzisa ulwazi lwabo lwesimelabungako ukwenza izibalo zokuphindaphinda nokwahlukanisa; • Ukuchaza ukuthi basebenzise ziphi izibalo nokuthi kungani; • Ukuxoxa ngezimpendulo nokuchaza imicabango ba • Sebenzise ulwazi lokusebenza kwezinombolo nokuhlanekezela okuhambisanayo kanye nokuphindaphinda nokuhlukanisa kabili; ukuqagela nokuhlola izibalo. Amaqhinga okurekhoda Kunamaqhinga athile okurekhoda angasetshenziswa ngabafundi may use eBangeni 3. Abafundi bangeke bangabi nokunqikaza kuwo wonke lamaqhinga. Badinga ukuholwa uma bebheka izibalo zamagama zokwahlukanisa bazokwazi ukukhetha amaqhinga afanele abazowasebenzisa. Kulindelekile ukuthi abafundi angeke basathembela kakhulu ekudwebeni izithombe kanti bazosebenzisa izinombolo ukuchaza imicabango yabo. 545 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 546 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 Ukususa ngokuphindelela Ukwahlukanisa Leliqhinga kuzofanele lisetshenziswe uma kuxazululwa izibalo zamagama kant abafundi kumele baholelwe ekufuneni ukwahlukana kwezinombolo bakhethe ukuthi izibalo zingenziwa yini ngokusebenzisa ukususa ngokuphindaphinda. Izibalo IBANGA 1-3 40 ÷ 8 =  40 - 8 → 32 - 8 → 24 - 8 → 16 - 8 → 8 - 8 = 0 Abafundi babala ukuthi bakususe kangaki oku 8 ukufika 0. Ukuhlanganisa ngokuphindaphinda Abanye abafundi bangase basebenzise leliqhinga ukuqonda ubudlelwano phakathi kokuphindaphinda nokwahukanisa. Nakhona ke lapha umehluko wezinombolo uzothola ukuthi ingabe iqhinga lilungile noma cha. 40 ÷ 8 =  8 + 8 → 16 + 8 → 24+ 8 → 32 + 8 → 40 Abafundi babala ukuthi bahlanganise okukangaki oku 8 ukufika40. Ukusebenzisa ukuphindaphinda Abafundi kumele bakwazi ukusho ukuthi: “Yini engiyaziyo ngkuphindaphinda engangisiza ngikwazi ukubala ukwahlukanisa? Abafundi bangabhala phansi amaphuzu okuphindaphinda abawaziyo ebhodini lemikhondo, ukubasiza ukuthi bakwazi ukwahlukanisa Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 Ukwahlukanisa Ibhodi lemikhondo 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 10 + 10 + 4 = 24 Ngakhoke 72 ÷ 3 = 24 Ukuhlukanisa Ngamaqoqo Ukuhlukanisa ngamaqoqo kokwahlukanisa ngaphezu kokuhlanganisa kuchaza ukuthi inomblolo ingaphulwa ibe yizinhla ekuzoba lula ukuzibala. 39 ÷ 3 =  = (30 + 9) ÷ 3 = (30 ÷ 3) + (9 ÷ 3) = 10 + 3 = 13 547 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 548 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 Ukwahlakaza izinombolo zibe yizingxenye: 60 enziwe ingxenye Ukwahlukanisa Abafundi kumele bakwazi ukusho ukuthi: “Yini engiyaziyo ngokwahlukanisa nge 5?” Abafundi bayazi 30 ayahlukaniseka ka 5 kungasali insalela. 60 ÷ 5 =  Izibalo IBANGA 1-3 30 ÷ 5 = 6 30 ÷ 5 = 6 6 + 6 = 12 Ukusebenzisa izingxenye ukwahlula ngo 4 Abafundi bebelokhu bephindaphinda, behlukanisa ngokwezingxenye iminyaka emithathu yonke. Kumele basebenzise lamakhono njengamaqhinga okubala. Ulwazi lokuphindaphinda nokuhlukanisa ngokwezingxenye lungasetshenziswa uma sekwahlukaniswa: 96 ÷ 4 =  96 ÷ 2 = 48 48 ÷ 2 = 24 Ekupheleni kwethemu kumele bakwazi: Ukuqonda, ukusebenzisa nokuqala ukufunda: Okukodwa ngamunye, okubili, ngamunye … hlukanisa ngokulingana, ingxenye, hlukanisa kabili,okuphelele,yahlula, yahlula ngo 3 yahlula ngo 4, yahlula ka 2 yahlula ka 3, insalela,, yahlula ngo … amaqoqo alinganayo Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola oku...,insalela Ukufunda, ukubhala nokusebenzisa uphawu lokwahlukanisa (÷) Ukusebenzisa lolulimi ukwenza izibalo zokwahlukanisa Ukuqonda ukwahlukanisa njengokwakha amaqoqo noma ukususa ngokuphindaphinda

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 Ukuphendula imibuzo ebhaliwe ebuzwe ngezindlela ezahlukane: Ukwahlukanisa hlukanisa 16 nga 2 Yahlula 20 nga 5 Zingaki izihlanu ezenza 50? Mangaki ama 10c ohlweza enza 50c? Kungaki okune e 20, e 28, e 36? Kungaki okuhlanu e 20, e 40, e 50, e 60? UAnnina uthi ufunda amagama 5 amasha nsukuzonken. Uthatha amalanga  ukufunda amagama a 40. 6 amashumi ÷ 3 =  amashumi Ukubona ukusetshenziswa kwezimpawu ezifana  ezenzelwe izinombolo ezifihliwe Buka izinto izinto zokubala ezingezansi ugcwalise imusho eyizibalo                  Kunamaqembu a  oku 3 15 - 3 - 3 -  -  -  = 0 15 ÷ 3 =  Buka imidwebo ugcwalise umusho wezibalo:                       549 Kunamadothi a  esewonke kanti kunamaqoqo a r amadothi a 3 iqoqo ngalinye. Ngakhoke:  ÷ 3 = r Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 550 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 Kunamadothi a  sewewonke, kanti kunezinyanda/ amaqoqo 4 ezinamadothi Ukwahlukanisa ngayinye/ngalinye. Ngakhoke:  ÷ 4 = r Izibalo IBANGA 1-3 Kopisha uqedele: 20 ÷ 2 =  20 ÷  = 10 20 ÷  = 2 21 ÷ 3 =  21 ÷  = 7 21 ÷ 7 =  Ukuqonda imigomo yokwahlukanisa nga 1 ne 0 6 ÷1 =  8÷1= 12 ÷  = 12 6÷0= ÷4=0 1÷1= 0÷7= Ukusebenzisa,ukufunda nokuqala ukubhala: Okusele, insalela.... Ukubala izinsalela uma benza izibalo zokwahlula: 12 ÷ 5 noku- 2 insalela 2 23 ÷ 7 noku- 3 insalela 2 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Ukuqonda ubudlelwano phakathi kokuphindaphinda nokuhlukanisa phakathi Ukuphendula izinhlobo zemibuzo elandelayo: Kopisha lelithebula elilandelayo.

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.15 Gcwalisa uhla lokuphindanga - 4. Ubona yiphi iphetheni? Ukwahlukanisa 1 2 3 4 5 6 7 8 9 10 4s 2s Ukuhlukanisa kabili ohleni ‘lokuphindwe 4 ukuthola izinombolo zohla oluphindwe ka 2. Ubona yiphi iphethini? Ukuqonda ukuthi ukwahlula kuphendulela ukuphindaphinda. Ukubonisa lezizibalo zemisho ngemidwebo 4 x 5 =  20 ÷ 5 =  12 x 4 =  48 ÷ 4 =  551 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 552 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.16 Umqondo wezinombolo: Izibonelo zemibuzo engase ibuzwe: Uhlu 999 Izibalo zekhanda Umqondo wezinombolot: • Ukuhlela iqoqo Amagama ezinombolo kanye nezimpawu elinikiwe lezinombolo ezikhethekile. Phakamisa ikhadi noma bhalaphansi igama lenombolo. Khetha umfundi ukuba Izibalo IBANGA 1-3 abhale uphawu olumele inombolo oluhambisana nayo. • Ukuqhathanisa izinombolo ukufika e 999 Okuningi noma kuncane kuno nokusho ukuthi yikuphi Okungaphansi ngoku-1 kokwa- 900 1,2,3,4,5 noku 10 noma okumbalwa Okuningi ngoku-1kokwa-899 Ukukhumbula Okuningi ngoku-2kokwa-702 Ngokushesha: Okuningi ngoku-2 kokwa- 405 • Ukuhlanganisa namaphuzu okususa Okuningi ngku-3kokwa- 477 ukuya 20 Okuncane ngoku-3kokwa- 251 • Ukuhlanganisa noma Okuningi ngoku-4 koklwa-868 ukususa usebenzisa isiphindaphindi se10 Okuningi ngoku-4 kokwa- 967 ukusuka 0 ukuya 100 Okuningi ngoku-5 kokwa- 729 • Iziqinisekiso Okuncane ngoku-5 kokwa- 685 zokuphindaphinda nokwahlulwa kwe: Okuningi ngoku-10 kokwa- 490 - Ithebula Okuncane ngoku-10 kokwa- 660 lokuphindaphinda Lubizwani uhlamvu lwesihlanu lwe Alfabethi? kabili ukufika 2 x 10 Ibizwani inyanga ye 9 yonyaka? - Ithebula lokuphindaphinda Ukulandelanisa nokuqhathanisa kashumi ukufika10 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola Yikuphi okuningi: 621noma 671? x 10 Ngiphe noma iyiphi inombolo ephakathi kwe - 154 kanye 159.

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.16 Amaqhinga okubala Iziqinisekiso zokususa nokuhlanganisa: Izibalo zekhanda Ukusebenzisa amaqhinga • Ukwazi ngekhanda onke ambhondi ezinombolo okuhlanganisa nokususa alandelayo okubala: ukufika 20. • Ukubeka inombolo  + r = 20 enkulu kuqala ukuze  + r = 16 ubale uqhubeka noma ubuyela emumva 20 =  - r • Umugqa wezinombolo Isiqinisekiso sokuhlanganisa nokususa zonke izinombolo ukufika kanye nokufaka 20. • Ukuphindaphinda nokuhlukanisa kabili 1 + 11 = 12 11 + 1 = 12 • Ukwakha nokuhlakaza 2 + 10 = 12 10 + 2 = 12 • Ukusebenzisa 3 + 9 = 12 9 + 9 = 12 ubudlelwano phakathi 18 - 4 = 14 18 - 14 = 4 kokuhlanganisa nokususa 18 - 5 = 13 18 - 13 = 5 • Ukusebenzisa 18 - 6 = 12 18 - 12 = 6 ubudlelwano phakathi Ukukhumbula masishane ukuphindaphinda kokuhlanganisa ukufika e 20. kokuphindapkhinda Lokhu kufanele kufake iziqinisekiso ezihambela nokususa nokwahlula • 1+1=2 • 2+2=4 • 3+3=6 • 4+4=8 • 5 + 5 = 10 • 6 + 6 = 12 • 7 + 7 = 14 • 8 + 8 = 16 • 9 + 9 = 18 • 10 + 10 = 20 553 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 554 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.16 Ngibonise inonmbolo engingayengeza ukuze ngenze ama-20. (ukubhala phansi noma ukusebenzisa isimelabungako kumafuladi khadi). Izibalo zekhanda • 8 • 2 Izibalo IBANGA 1-3 • 9 • 15 • 3 Ngokhombise inombolo esele uma oku....kususwa ema-20 (bhala usebenzisa isimelibungako noma amafuladi khadi) • 5 • 18 • 0 • 14 • 7 Amaqhinga okubala: Ukusebenzisa amasu okubala ukuhlanganisa nokususa ngokufanelekile. Ukuhlanganisa izinombolo ezithile usebenzisa amaqhinga afana nalawa alandelayo: • Funa izinombolo ezihamba ngambili ezenza okuyi 10 uqale usebenzise lezi 2+7+8 2 + 8 kwenza 10 bese wengeza 7. Fakainombolo enkulu kuqala ngendlela efanele yokuqhubeka ubala ngokuya phambili noma uya emumva Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.16 • Qala ngenombolo enkulu kakhulu Izibalo zekhanda 5 + 15 Phinda uchaze isibalo esiwumusho: 15 + 5 uqhubeke ubala ukufika 20 • Ukushintsha inombolo bese uyahlanganisa noma ususe 10 bese uyahlanganisa noma ususe oku-1 Isibonelo: 8 + 9 = 17 uchaze ukuthi umumuntu angase enze 8 + 9 = 8 + 10 - 1 6 + 11 = 17 uchaze ukuthi umumuntu angase enze 6 + 10 + 1 17 - 9 = 8 uchaze ukuthi umumuntu angase enze 17 - 10 + 1 • Ukwehlakaza inombolo ibe yizingxenye ezithile bese uyahlanganisa Ukwehlakaza nokwakha izinombolo: Isibonelo bala ngengqondo uchaze: Qhubeka wephule izinombolo zibe izicucu ezincane’ 8 + 12 = 8 hlanganisa (10 + 2) = 8 + 2 + 10 = 10 + 10 = 20 • Ukusebenzisa ukuphindaphinda njengesu lokubala ngengqondo Ukubona okusondele kuzinombolo eziphindwe kabili isib. 8 + 7 = 15 Ukuchaza ukuthi iyinombolo ephindwe kabili kwi-7 hlanganisa 1 noma okuphindwe kabili kwi-8 ususe oku-1 Ukubona ukuthi uma izinombolo ezimbili zisondelene ngobungako bazo kulula ukuthola umehluko ngokuqhubeka ubala uya phabili ungayi emumva. 17- 13 = 4 nokuchaza ukuthi ukubala uqhubeka usuka e-13 uya e-17 kukunika oku- 4 555 Izibalo IBANGA 1-3

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo 556 IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) 1.16 Ezinye izibalo zekhanda zingenziwa ngaphandle kwezinsiza, kodwa kuvalme ukuba wusizo ukwenza izibalo zengqondo ngokusebenzisa izinsiza. Izibalo zekhanda Izinsiza ezinconyiwe/ ezingase zisetshenziswe • Umungqa wezinombolo (ohleliwe nongenalutho) Izibalo IBANGA 1-3 • Uphahla lwezinombolo • Isimelabungako (amafladi khadi) • Ubuhlalu bokubala 1.17 • Ukusebenzisa nokubiza Ekupheleni kwethemu abafundi kumelele bakwazi: amaqhezu esimweni es- Amaqhezu • Ukubona amaqhezu emifanekiso nokugcizelela ukuqonda kwabo ukuthi ejwayelekilese nokum- izingxenye kufanele zilingane ngobungako bazo. bandakanya izingxenye, iqhezu kokune, iqhezu • Ukwazi ukuthi amaqhezu amane enza okuphelele nokuthi iqhezu kokune kokuyisishiyagalom- ngalinye kufanele lilingane; bili iqhezu kokuthathu, • Ukuthola amaqhezu amaqoqo ezinsiza; iqhezu kokuyisithu, iqhezu kokuhlanu • Ukufunda nokubhala amagama amaqhezu; • Ukubona iziqhezu ngen- • Nokuhlela; ukuchaza; nokuqhathaniswa kwamaqhezu. lela yemibhalomidwebo Ekupheleni kwethemu abafundikumele baqonde amaqhezu njengengxenye • Ukuqala ukubona ukuthi izingxenye ezimbili yokuphele, futhi bakwazi ukupphendula imibuzo efanayo nale: noma iqhezu kokuthathu • izingxenye = okukodwa okuphelele kwenza okukodwa okuphelele nokuthi in- • ingxenye kokunequarters = okukodwa okuphelele gxenye eyodwa nokubili • ingxenye kokuthathu = okukodwa okuphelele kokune kuyalingana • izingxenye = okukodwa okuphelele • Ukubhala amaqhezu njengengxenye, noma • okukodwa kokuhlanu = okukodwa okuphelele Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola amaqhezu amabili • okukodwa kokuyisithupha = okukodwa okuphelele kwamathathu. Ukuphendula imibuzo efana nalena elandelayo: Uma umfanekiso wahlukaniswe ngezingxenye ezi 2 ezilinganayo, lezingxenye sizibiza___ Uma umfanekiso wahlukaniswe ngezingxenye ezi 3 ezilinganayo, lezingxenye sizibiza ___

IMIQONDO ISIKHATHI NAMAKHONO IMIQONDO NAMAKHONO (ngokwesifundo IZIHLOKO OKUDINGEKAYO AMANOTHI ACACISAYO NOMA UMHLAHLANDLELA WOKUFUNDISA esingangehora CAPS OKUGXILWE KUWO KU NGOKUPHELA THEMU 1 nemizuzu engu KONYAKA 24) Uma umfanekiso wahlukaniswe ngezingxenye ezi ____ ezilinganayo, lezingx- enye sizibiza amaqhezu kokune. Ukukwazi ukuqhathanisa ubungako bamaqhezu   Ingabe ingxenye eyodwa yinkulu noma incane kunamaqhezu amathathu kokune? Amaqhezu amangaki kokune afana nokukodwa okuphelele? Amaqhezu amangaki kokuyisishiyalombili afana nokukodwa okuphelele? Ingabe okubili kokune kuyalingana nengxenye eyodwa kokubili? Thola amaqhezu ezinto ezithile ezifanayo. Kunobuhlalu o 12. 8 obupinki no 4 obumhlophe. Yingxenye engakanani yobuhlalu emhlophe? 557 Izibalo IBANGA 1-3

ITHEMU YESI-4 YEBANGA LESI-3 2 AMAPHETHINI, UBUDLELWANE NE-ALJEBHRA 558 UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 2.1 Ukopisha,ukwandisa Amaphethini asi- Abafundi bazosebenza ngamaphethini kusukela kwimvelo, isikhathi samanje isifundo 1 l Izibalo IBANGA 1-3 nokuchaza zungezile esiphila kuso nangamagugu namasiko ethu kusuka eBangeni 1 kuya eBan- Amaphethini ez- geni 6.Lokhu kusho ukuthi asho isidingo sokuchtha isikhathi esiningi wenza isambalomdwebo Ukukopisha, wandise • imvelo lesisihloko.Kumele uthisha akhethe imisebenzi namaphethini afanele lelobanga. beseuchaza ngamagama • kusukela esikhathini Enye yamaphethini okumele bawabone yiwo umgqa ohlukanisa into kabili ilin- • amaphethini alula samanje esiphila kuso gane, isib, amaqabunga amaningi nezilwane kunobuso obuhlukaniseka kabili ob- enziwe ngezinto • kusukela kumagugu ufana nse.Kanjalo nezinambuzane eziningi uma uzibuka ngaphezulu, namaphet- eziphathekayo namasiko hini ezinyoni eziningi uma uzibuka ngaphansi. • amaphethini alula EBangeni -3 kunokugxila ekutholeni umugqa ohlukanisa into kabili ilingane enziwe ngokudweba nse ngokugoqa iphepha bese besho ukuthi bayithole kanjani.Abafundi benza imigqa,izimo noma amaphethini besika izimo ngephepha eligoqiwe.Kungaqhutshekwa kwenziwe izinto onodoli, izimoto, izikebhe namakhathoni ngamaphethini askiwe asenamathis- Bayenza bachaze elwa.Abafundi sebengakubuka bakhulume ngamaphethini abawathole konodoli amaphethini nasezithombeni. Ezinamaphethini bese ziyasikwa kwakhiwe kuhlotshiswe ngawo. Bayenza bachaze Abafundi babuka amaphethini kulokhu- amaphethini abo asejiyo- • uthango (ucingo,izingodo noma udonga); metri • umsebenzi wezitini namathayizi aphansi; • ngezinto eziphathek- ayo • ukufulela; • ukudweba imigqa,izimo • okokugqoka nezindwangu; noma izinto. • amapuleti,izinkomishi, namasosi; Amaphethini asi- • amabholaa okudlala; zungezile • izilwane njengezinkomo uvemvane,idube, indlulamithi,ingwe,izinyoni.izinambu- Ukukhomba,uchaze nga- zane njll. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola magama nokukopisha amaphethini asejiyometri • Izimbali namacembe; • imvelo • Amaphepha odonga,amaphepha odonga enziwe ngokubhaliwe okutholakala ngaphakathi ezindlini nasemkhukhwini • kusukela esikhathini samanje esiphila kuso • Okwamasiko okwesikhathi samanje • kusukela kumagugu • Amabhodwe enziwe ngobumba noma obhasikidi abalukwayo. namasiko

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 2.1 Bangawachaza kanjani amaphethini abawabona lapho behlala khona? Amaphethini ez- Kunezindlela ezehlukene zokuchaza amaphethini abawabonayo lapho behlala isambalomdwebo khona.Amaphethini amaningi asizungezile akhiwe ngemigqa,izimo noma izinto.Izinto noma izimo akudingi ukuba kufaniswe nezimo ezisejiyometri konhlangothimbili -2-D.noma izinto ezingonhlangothintathu 3-D uma usebenza neBanga 2.Bonke abafundi ababone lapho • Iphindeka kanjani isib.. • Imigqa eqondile enquma komunye (njengendwangu yetafula),imigqa lehamba ngezansi kwendwangu noma inqume eshethini,imigqa le ehamba iye phezulu ebhulukweni’ • Imigqa egobile njjengemigqa esandilinga ebonakalayo uma usika u-anyanisi; • Imigqa engaqondile njengemigqa emunweni wakho nedube elimthende, nend- lovu, imvubu nabantu asebegugile. • imigqa emazombezombe oyithola ngesikhathi usika iklabishi noma uyithola esihlabathini ekade sipheshulwa umoya.; • amadothi anobungako obulinganayo, amadothi asakazeke yonke indawo; • izimo ezinobungako obulinganayo; • izimo ezinemibala efanayo • amaphethini akhiwe izimo ezehlukene,izimo ezakha amaphethini ngokwemi- bala ezisesikhumbeni sendlulamithi 559 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO 560 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 2.2 Ukopisha,wandise bese Ukopisha,wandise bese Bheka amanothi kathemu 1. 3 izifundo uyachaza uyachaza Amaphethini Yandisa ukulandelana ufake lokhu ezinombolo Ukukopisha wandise Ukukopisha,wandise • bala nga-1 usuka kunoma yiyiphi inombolo ephakathi kuka 0 no 1 000 bese uchaza nokuchaza ukulandelana Izibalo IBANGA 1-3 ukulandelana okulula kwezinombolo ezilula • bala nga-10 phakathi kuka 0 no 1 000 kwezinombolo okungenani 1000 • bala nga-5 phakathi kuka 0 no 1 000 okungenani 200 Ukulandelana kumele • bala nga-2 phakathi kuka 0 no 1 000 Bayenza bachaze kutshengise lokhu amaphethini abo • bala nga-100 phakathi kuka100 no 1 000 • bala nga-1-usuka ku- Bayenza bachaze noma yiyiphi inombolo • bala nga-50 phakathi kuka 50 no 1 000 amaphethini ezinombolo ephakathi -kuka-0 zabo ne-1 000 • bala nga-25 phakathi kuka 25 no 1 000 • bala nga-10-kusuka • bala nga-20 phakathi kuka 20 no 1 000 kunoma yiyiphi inom- Sebenzisa izinto,izithombe, amathebula nomdwebo oxhumanayo ukulekelela bolo ephinda nge-10 abafundi ukudlulela ekubaleni ngokweqa izinombolo nokulandelanisa okuholela phakathi -kuka-0 ukuphindaphinda kwezinombolo-10, 5, 2, 4, 3. ne-1 000 • bala nga-5-kusuka kunoma yiyiphi inom- bolo ephinda nge-5 phakathi kuka-0 ne-1 000 • bala nga-2-usuka ku- noma yiyiphi inombolo ephakathi -kuka-0 kuya ku-1 000 • bala nga-100 usuka Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola ku-100 uya1 000 • bala nga-50 usuka ku- 50 uya 1 000 • bala nga-25 usuka ku- 25 uya 1 000 • bala nga-20 usuka ku 20 uya 1 000

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 2.2 Ukwenza nokuchaza amaphethini abo Amaphethini ezinombolo Ukwenza nokuchaza amaphethini abo • izikhawu ezinikiwe eBangeni 2 kwengeza izinhla zezinombolo • bala ngo- 20,25, 50,100 uze ufike ku- 1000 561 Izibalo IBANGA 1-3

ITHEMU YESI-4 YEBANGA LESI-3 3. INDAWO NESIMO (IJIYOMETRI) 562 UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 3.2 Uhla lwezinto Uhla lwezinto Bheka amanothi kaThemu 2. isifundo1 Izibalo IBANGA 1-3 3-D izinto ezinhlan- Bona usho ngamagama Bona usho izinto Kulethemu bangenza, babukeze, nokuhlanganisa nomsebenzi wezinto ezingonh- gothintathu izinto ezinhlangothintathu ngamagama ezinhlang- langothintathu 3-D-ngokomsebenzi obhalwayo. 3-D ezilapha ekilasini othintathu 3-D ezilapha Ukugxila nokubuka bese uzibiza ngamagama nezithombe ekilasini nezithombe • Isimo sebhola (Okusambulunga,) • Isimo sebhola • Isimo sebhola • Izimo ezisabhokisi (iprizimu) • (Okusambulunga,) • (Okusambulunga,) • Amasilinda (cylinder) • Izimo ezisabhokisi • Izimo ezisabhokisi (iprizimu) (iprizimu) • Amaphiramidi (pyramids) • Amasilinda • Amasilinda • amakhoni; (cones) • amakhoni • amakhoni Uma zivezwe esithombeni sombalomdwebo noma ezintweni nsukuzonke. izimpawu zalezozinto izimpawu zalezozinto Imibuzo okufanele abafundi bagxile kuyona: ukuchaza,uhlele, ukuchaza,uhlele, • ukuthi ingaphezulu blezinto ligoqene noma liyisicaba; noma nokuqhathanisa izinto nokuqhathanisa izinto • ukuthi ingaphezulu eliyisicaba lezinto lingonxantathu, nxande, isikwele, izindil- ezinhlangothintathu-3-D ezinhlangothintathu-3-D inga. kanje;: kanje: • izimo ezinhlangothim- • izimo ezinhlangothim- bili-2-D lezo ezenza bili-2-D lezo ezenza ubuso bezinto ezin- ubuso bezinto ezin- gonhlangothintathu- gonhlangothintathu- 3-D 3-D • ingaphezulu lendawo • ingaphezulu lendawo eyisicaba negobile eyisicaba noma ego- Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola bile

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 3.2 imisebenzi okugxilwe kuyo 3-D izinto ezinhlan- gothintathu • Ukubuka nokwakha izinto ezinhlangothintathu- 3-D usebenzisa izinto eziphathekayo njengo okusikwe izimeni ezinhlangothimbili- 2-,D,ubumba, izinti zokuvungula,izinti zokumunca, nozinye izinto ezinhlangothintathu -3-D 3.4 okufana nse nxazombili okufana nse nxazombili Umsebenzi womugqa ohlukanisa into kabili ilingane ngokugoqa iphepha wenziwa Isifundo 1 kuthemu 2, kuzosiza abafundi bakhombe umugqa ohlukanisa izinti zilingane okufana nse • Bona udwebe umugqa • Bona udwebe umugqa emidwebeni yezinto ezisambalomdwebo nokungezona ezisambalomdwebo. nxazombili ohlukanisa into kabili ohlukanisa into kabili ilingane ezimweni ilingane ezimweni Umsebenzi obhalwayo mawube nalezizibonelo lapho- ezisambalomdwebo ezisambalomdwebo • Umugqa ohlukanisa into kabili mawungabi wosuka phezulu noya phansi nezingezona nezingezona kuphela izibalomdwebo izibalomdwebo konhlangothimbili -2-D konhlangothimbili-2-D • Kunemigqa eminingi ehlukanisa into kabili esmeni nasezintweni. 563 Izibalo IBANGA 1-3

ITHEMU YESI-4 YEBANGA LESI-3 4. ISILINGANISO 564 UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.1 Ukukhuluma Ukukhuluma Abafundi bayaqhubeka nokwenza bekhuluma ngobude besikhathi nokulandelana Izifundo2 Izibalo IBANGA 1-3 ngesikhathi ngesikhathi kwaso ISIKHATHI • ukufunda izinsuku • ukufunda izinsuku . ekhalendeni ekhalendeni Ngeskhathi sokufundisa ikilasi lonke nokugxila emaqenjini,abafundi abaqhubeke • beka izinsuku • beka izinsuku bakhulume ngezinsuku zeviki,ngezinyanga zonyaka nosuku namhlanje, izokuzalwa, izokuzalwa, kanjalo nezinsuku ezdlule nezizayo.Abafundi baqhubeke ukubeka izigameko imigubho yezenkolo, imigubho yezenkolo, ezilandelayo ekhalendeni; amaholide,izigameko amaholide,izigameko • izinsuku zokuzalwa; zomlando izehlakalo zomlando izehlakalo zekilasi ekhalendeni. zekilasi ekhalendeni. • imigubho yezenkolo; • Ukukhuluma • Ukukhuluma • izigameko zomlando; ngesikhathi ngamahora ngesikhathi ngamahora • izehlakalo zesikole angu -12 angu -12 • amaholide. - amahora - amahora Qhubeka ucele abafundi bakhulume ngesikhathi, ngezikhawu ezejwayelekile - uhhafu wehora - uhhafu wehora nsukuzonke; - ikota yehora - ikota yehora • ngamahora namaminithi ewashini lezinombolo,noma - amaminithi - amaminithi • ngamahora, uhhafu wamahora, kanye nekota yamahora usebenzisa amawashi ewashini elinezinti ewashini elinezinti anezinti. nelinezinombolo nokunye nelinezinombolo nokunye Isibonelo; abafundi.bangacelwa ukuba bakhulume ngesikhathi uma isikole siqala, okungamathulusi okungamathulusi ngezikhathi sekhefu nasemakhaya noma beshintsha izifundo.Khetha izikhathi angatshengisa isikhathi angatshengisa isikhathi lapho iwashi litshengisa ihora noma uhhafu wehora noma ikota yehora. Kuyasiza isib. Iselifoni. isib. Iselifoni. ukuba newashi elikhulu lokubukisa ekilasini, yilapho abafundi bezokhomba khona ukubala ubude ukubala ubude isikhathi.Abafundi bangenza eyabo imifanekiso yamawashi Angacela abafundi Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola besikhathi nokudlula besikhathi nokudlula batshengise izikhathi ezehlukene kuhlangene nokubala isib. Ngitshengise ihora kwaso kwaso le10. Ubani isikhathi ikota nohhafu ngaphambi kuka10? sebenzisa ikhalenda sebenzisa ikhalenda Ngesikhathi sokufunda ngokuzimela abafyndi abaqhubeke bazijwayeze ubala nokuchaza ubude ubala nokuchaza ubude ukukhuluma ngesikhathi. besikhathi ngezinsuku besikhathi ngezinsuku • ngamahora iuhhafu wehora,nekota yehora, ewashini elinezinti noma ngamasonto noma noma ngamasonto noma ngezinyanga ufake ngezinyanga ufake • ngamahora nangaminithi ewashini lezinombolo. nalokhu nalokhu

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 CAPS ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.1 • shintsha iznsuku • shintsha iznsuku Abafundi benza izibalo ngamasontonoma izinsuku uma benikiwe ikhalenda noma namasonto namasonto ingxenye yekhalenda isib.thola izinsuku nokubala isikhathi nokubona umehluko ISIKHATHI phakathi kwazo. • shintsha phakathi • shintsha phakathi kwamasonto kwamasonto Bafunda imizuzu ewashini lezinti nezinyanga nezinyanga Chitha isikhathi ngezifundo ezi-2 ugxilisa ngokuhlanganisa amakhono okufunda ukusebenzisa iwashi ukusebenzisa iwashi imizuzu ewashini lezinti ubala ubude besikhathi ubala ubude besikhathi Bheka amanothi kathemu 3. ngamahora /ngohhafu ngamahora /ngohhafu noma amakota noma amakota 4.2 Isilinganiso Zonke izinhlobo zokulinganisa ubude ezisohlweni zingenziwa ngesikhathi esingahlelekile sokuzmela ngethemu yonke.Umsebenzi wonke mawubhalwe. UBUDE • Hlawumbisela ulinganise, uqhathanise, uhlele bese ubhala ubude usebenzisa isilinganiso esingalinganisiwe isib, isandla, amanyathelo, ubudebepensela, ikokubala.njll. • Chaza ubude bezinto ngokubala uqala ngokuqagela ukuthi bungakanani ubude bamayunithi angahleliwe • Sebenzisa ulimi ukhuluma ngokuqhathanisa isib, kude xaxa, kufishane xaxa, kuphakeme xaxa, kubanzi xaxa njll. 565 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO 566 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.2 Ukwethula isinganiso esihleliwe UBUDE • Ukuhlawumbisela ulinganise, Izibalo IBANGA 1-3 uqagele,uhlele bese ubhala ubude ngamamitha (kungaba amamtha ngezinduku noma ubude bentambo ngamamitha) ngesilinganiso esihleliwe sobude • Ukuhlawumbisela nokulinganisa ubude ngamasentimitha usebenzisa irula Alukho uguquko olungenziwa phakathi kwamamitha namasentimitha. Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 CAPS ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.3 Isilinganiso Ukwethula isilinganiso Ukuhlanganisa umsebenzi owenziwe ngesisindo unyaka wonke, ababfundi isifundo1 esingahlelekile esihleliwe abenze umsebenzi obhalwayo lapho - ISISINDO • Ukuhlawumbisela Abafundi benza To consolidate the work done on mass throughout the year, learners should do ulinganise, umsebenzi obbhalwayo written exercises in which they uqhathanise uhlele bewuhlanganisa • Bezofunda izithombe ezizovumela ukuba baqhathanise izisindo zezinto lapho bese ubhala isisindo nokufunda izithombe - kuvezwe khona kusilinganiso esizimelele; usubenzisa isilnganisa • Imiphumela yesisindo esingalinganisiwe. • Bezofunda izithombe lezo ezizovumela izisindo ezibhalwe kulezozinto ebhalwe kuyo Nokuzimelela isib, kusilinganiso esizimelele, ngokusebenzisa amayunithi angenasilinganiso amabhuloki, izitini njll, • Iisisindo ukuqhathanisa; sezithombusebenzisa • Ukusebenzisa • ukuqhathanisa;uhlele,bese ubhala lokho okutholile isikali sasendlini ulimi ukhuluma yokugeza, lapho uthi - izithombe zegilosa ezinesisindo esibhalwe ngamakilogramu; ngokuqhathanisa, isib, lukhomba inombolo kulula, kuyasinda, - izithombe zegilosa ezinesisindo esibhalwe ngamagramu eseduze kolayini. kulula xaxa, kuyasinda xaxa - ukufunda izithombe zesikali sasendlini yokugeza sitshengisa okusondelene nekilogramu liphelele Ukwethula isinganiso esingahlelekile Bheka amanothi kathemu 2. • Qhathanisa uhlele Isilinganiso somthamo njengesimo esejwayelekile sokuxazulula izinkinga bese ubhala nokubala ukukhangisa Esikhathini esimiselwe iziNombolo ukuSebenza noBudlelwano bazo abafundi ngesisindo sazosibe sebengaxazulula izinkinga besebenzisa isimo esjwayelekile ngoku; siveziwe ephaketheni ngokwamakilogramu • Isilinganiso esingahlelekile sesisindo isib amakilogramu ama • Isisindo ngamakilogramu 2 erayisi,ne1 kilogramu likafulawa • Isisindo ngamagramu • ISILINGANISO izisindo Bhekisisa ukuthi ithemu inohlelo lwezinombolo ezifanele lona;kanjalo nohlobo zabo ngokusebenzisa lwezinkinga oluhlukene kwaleyo themu isikali sasendlini yokugeza. 567 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO 568 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.4 Isilinganiso Ukwethula isilinganiso Ngeskhathi sokusebenza ngokuzimela abafundi bangaqhubeka ngoku- isifundo1 esingahlelekile esihleliwe UMTHAMO • Ukuhlawumbisela nokulinganisa, baqhathanise, bahlele bese bebhala • Uhlawumbisela Abafundi babhala umthamo wesitsha noma okumumethwe yisitsha leso usebenzisa isilinganiso nokulinganisa, imisebenzi esingalinganisiwe. Izibalo IBANGA 1-3 ukuqhathanisa ngokuhlanganyela • Ukuqhathanisa nokuhlela umthamo wamabhodlela ahlukene nohla lwezinto nokuhlela nokufunda izithombe; ozozithenga lapho umthamo azokhangisa ngawo ephaketheni lelo. umthamo wesitsha • Imiphumela esingawumumatha • Ukusebenzisa i-1litha lamabhodlela, noma 1ilitha lojeke ukuqagela ngomthamo obhaliwe (isitsha nokulinganisa uqhathanisa ubhala kuwo ngokuhlela esngakumumatha ngokulandelana umthamo wezitsha noma okumumethwe yilezo zitsha ngamalitha. uma sigcwalisiwe) okuhleliwe noma okumumethwe Bheka amanothi kuthemu 3 isitsha ngokusebenzisa • Izithombe zojeke isilinganiso Abafundi kumele banikwe umsebenzi obhaliwe ohlanganisa nokufunda izithombe lapho umthamo esingalinganisiwe isib. nge- usondezelayo isipuni namankomishi kumalitha noma • Imiphumela yomthamo obhaliwe kuwona ukuze kuhlelwe ngokulandelana amalitha amabili kwayo • Ukuchaza umthamo kulayini obhaliwe noma wesitsha ngokubala • Izithombe zojeke lapho umthamo usondelene nenombolo 1 yelitha noma 2 uhhafu wamalitha ukuthi mangaki wamalitha kulayini obhaliwe noma ikota yamalitha amayunithi angahleliwe angagcwaliswa, • Izithombe zojeke Okulindelekile ukuba abafundi bodwa bafunde inombolo eseduze kolayini.Lokho kulesositsha isib. lapho umthamo kuchaza ukuthi umthamoo (cishe ugcwale.ngaphezulu ngaphansi.kancane, noma ibhodlela lingagcwala useduze kwenombulo kuyalingana ngamalitha) befunda ojekeni. izinkomishi ezi-4. yamamililitha kulayini Isilinganiso somthamo njengesimo esejwayelekile sokuxazulula izinkinga obhaliwe.. nokubala Ukwethula isilinganiso esingahlelekile Okulindelekile ukuthi Esikhathini esimiselwe iziNombolo ukuSebenza noBudlelwano bazo abafundi abafundi bazofunda sebengaxazulula izinkinga besebenzisa isimo esjwayelekile ngoku; • Ukuhlawumbisela inombolo leyo ebhaliwe ulinganisa, • Isilinganiso esinahleliwe somthamo nokumumethwe isib. Ugogo usebenzisa uqhathanisa, Ukuchaza umthamo izinkomishi ezi 2 zobisi ukwenza uphudingi uma engaziphinda kabili izinlto Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola uhlele bese ubhala njengokuthi cishe ku... azisebenzisile, angadinga ubisi olungakanani? lowomthamo waleyonto (gcwale,ngaphansi, ngokulinganisa ngaphezulu njll) befunda • Amalitha ngamalitha,uhhafu inombolo ebhaliwe • amamililitha welitha nekota yelitha. kujeke. Bhekisisa ukuthi ithemu inohlelo lwezinombolo ezifanele lona;kanjalo nohlobo Alukho uguquko phakathi lwezinkinga oluhlukene kwamamililitha namalitha

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO CAPS ABHEKWA sehora eli 1 NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.4 • Ukuqhathanisa nokuhlela, nokubhala UMTHAMO ngokukhangisa umthamo waso siveziwe ephaketheni ngokwamalitha isib. Amalitha ama-2l obisi, ilitha 1yobisi, amalitha ayi-5l kapende,noma ngamamililitha. isib.amamililitha anga-500ml obisi,amamililitha anga-340ml wesiphuzo esibandayo, amamililitha anga- 750ml kawoyela. • Ukwazi ukuthi inkomishi elingene ingamililitha anga- 250ml. • Ukwazi ukuthi ithisipuni ingamamililitha angu- 5ml Alukho uguquko oludingakalayo phakathi kwamamililitha namalitha 569 Izibalo IBANGA 1-3

UKUQONDA ISIKHATHI UKUQONDA ESINQUNYIWE OFUNDWAYO OKUFUNDWAYO 570 NAMAKHONO (esifundweni IZIHLOKO NAMAKHONO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA ADINGEKAYO sehora eli 1 ABHEKWA NGOKUPHELA nemizuzu engama NGETHEMU 1 KONYAKA 24) 4.5 iPerimitha Isizinda Abafundi bayethulwa okokuqala ekulinganiseni ingaphezulu lendawo eBangeni izifundo2 3.EBangeni 3 naseZingeni eliphakathi yilapho kuphela isizinda silinganiswa IPerimitha nenga- • Ukucwaninga ngobude Ukucwaninga ngokungahlelekile. phezulu lendawo bezinto ezingaba- ingaphezulu lendawo onhlangothimbili- 2-D usebenzisa amathayela. Abafundi bathola ukuthi zingaki izimo noma izinto ezingavala ingaphezulu Izibalo IBANGA 1-3 nonhlangothintathu lendawo.Bapakisha izimo noma izinto ngaphandle kokushiya izikhala usebenzisa intambo. phakathi kwezimo nezinto.Sebezobala basho ukuthi zingaki izimo ezivale lelingaphezulu lendawo. Isib. Abafundi bangapakisha izikwele noma onxande Ingaphezulu lendawo phezu kwekhasi,bese beyabala ukuthi zingaki izimo ezivale ikhasi.Abafundi • Ukucwaninga bazosho ukuthi ingaphezulu lendawo yekhasi ithathe izimo ezingako isib.ikhasi ingaphezulu linengaphezulu lendawo enonxande aba-16 lendawo usebenzisa Kunokwenzeka ukuthi izimo zingakwazi ukugcwalisa ikhasi lonke njengoba amathayela. kwenziwe ngezansi   Abafundi sebengasho ukuthi ubungako bekhasi ngokunakisisa.isib.Ingaphezulu lendawo yekhasi inonxande abayi-18 ngaphezulu kodwa bancane ngabangu-28. Yenza abafundi bafake amathayela kulelingaphezulu lendawo besebenzisa izimo ezehlukene nangezimo ezifanyo ezehluke ubungako.Lokhu kuzokwenza abafundi babone ukuthi- • Isimo esincane,uma ziziningi zingalingana ukuvala kulelongaphezulu lendawo. Uma isimo sisincane kakhulu, maningi amathuba wokuthi kungene izimo eziningi phezulu kwendawo; Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola • isimo osikhethile singayshintsha indlela obubale ngayo Akulindelekile ukuthi abafundi bakale ingaphezulu lendawo ngokubala ngezikwele phezu kwegrid yesikwele; lokhu kuyokwenziwa emaZingeni aPhakathi

ITHEMU YESI-4 YEBANGA LESI-3 5. ULWAZI OLUQOKELELWE UKUQONDA OFUND- ISIKHATHI ESIN- CAPS UKUQONDA OKU- QUNYIWE WAYO NAMAKHONO FUNDWAYO NAMA- IZIHLOKO ADINGEKAYO AMANOTHI ACHAZAYO NOMA UMHLAHLANDLELA WOKUFUNDISA (esifundweni KHONO ABHEKWA NGOKUPHELA KON- sehora eli 1 nemi- NGETHEMU 1 YAKA zuzu engama 24) 5.4 Ukuqoqa nokuhlela Ukuqoqa • ukuqokelelwa kolwazi nokuhlela ulwazi ngkilasi noma ngesikole ukuphendula imibuzo ezobuzwa uthisha. • Ukuhlela ulwazi olunikwe uthisha noma incwadi. • Ukuhlela ulwazi; - uhla - amathali - amathebula 5.5 Ukubhala okumele ulwazi Ukubhala okumele ulwazi Ukubhala okumele ulwazi • igrafu yezithombe • ibhagrafu 5.6 Ukuhlaziya Ukuhlaziya ulwazi Kulelizinga abafundi kumele ngabe sebebonisiwe zonke izimo zolwazi Isifundo 1 nokuhumusha ulwazi ngokubhala okumele oludingakalayo eBangeni 3 (uhla, amathali, igrafu yezithombe, ibhagrafu) Ukuhlaziya ulwazi okunikiwe kuyancomeka ukuba ngethemu 4 kugxiliswe ekuhlaziyeni ulwazi. Ubanika ulwazi nokuhumusha Ukuphendula imibuzo lokuhlaziya okungenani- ulwazi ngolwazi olunikiwe • igrafu yezithombe e-1 • igrafu yezithombe • nethebula elilodwa. • ibhagrafu Abafundi baphendula imibuzo leyo ebuzwa uthisha mayelana negrafu nethebula,bheka uthemu 1 nemibuzo efanele 571 Izibalo IBANGA 1-3

Izibalo IBANGA 1-3 INGXENYE YE - 4: UKUHLOLA 4.1 Isingeniso Umsebenzi wokuhlola uwuhlelo oluhleliwe oluqhubekayo lokukhomba, ukuqoqa, kanye nokuhumusha ulwazi ngokusebenza kwabafundi, usebenzisa izindlela ezahlukene okubandakanya izinhlobonhlobo zokuhlola.inezinyath- elo ezine: • ukulungiselela nokuqoqa ubufakazi bomphumela, • ukuhlolwa kobufakazi, • ukubhala okutholiwe kanye • Nokusebenzisa lolulwazi ukuqonda okusiza ekuthuthukiseni abafundi ukuze benze kangcono ohlelweni lokufunda nokufundisa. Ukuhlola kufanele kubengezindlela ezimbili ngokuhleliwe (kuhlolwa ukufunda) kanye nokungahlelekile (kuhlolwa ukufunda).kuko kokubili kufanele abafundi baziswe ngokutholiwe ukwandisa ulwazi lokufunda izibalo. Kumabanga aphansi amaqhinga asemqoka okuhlola ngokuhlelekile kanye nokungahlelekile ukuhlola ngokubhekwa kwabafundi nguthisha, izingxoxo, ukubonisa ngokwenza kanye nokubhaliwe. EBangeni R ukuhlolwa kufanele kube ngezingxoxo kanye nokubonisa ngokwenza. 4.2 Uhlola ngongakuhlelekile /ukuhlola kwansukuzonke Ukuhlolwa kokufunda kuwuhlelo oluqhubekayo lokuqoqa ulwazi ngokuphumelela komfundi.Ukuqhapha inqubeke- laphambili yabafundi nsukuzonke kungukuhlola okungahlelekile,lokhu kwenzeka ngokubhekwa kwabafundi nguthisha,izingxoxo,ukubonisa ngokwenza kanye nokuxhumana okungahlelekile kwasekilasinil.lokhu akufanele kubonwe njengohlelo olwahlukile emisebenzini efundwayo ekilasini.ukuhlola okungahlelekile kwenza uthisha akwazi ukuqapha inqubekelaphambili yabafundi kanye nezinhlelo zokufundisa zosuku.Ukuhlola okungahlelekile kusetshen- ziswa: • ukwaziswa kwabafundi ngokutholiwe • ukukwazi ukuhlelela ukufundisa Ngezinye inkathi uthisha angagcina uhla lokubheka abafundi (checklist) azobhala kulo akuthola ngesikhathi ehlola inqubekelaphambili yabafundi, uthisha nabafundi bangamaka umsebenzi owenziwe.ukuhlola okungahlelekile akuyona ingxenye yokuhlola okuhleliwe.imiphumela yokuhlola okungahlekile okwenziwa nsukuzonke akusetshenziselwa ukuphumelela komfundi. 4.3 Ukuhlola okuhlelekile Yonke imisebenzi yokuhlola kuhlelo lonyaka ithathwa njengokuhlola okuhlelekile.umsebenzi wokuhlola ohlelekile umakwa uphinde ubhalwe ngokuhlelekile nguthisha.lusetshenziselwa ukuphumelela nokudluliselwa kwabafundi eBangeni elilandelayo. 572 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Ukuhlola okuhlelekile kunika othisha ulwazi oluzokwenza akwazi ukubona inqubekelaphambili yabafundi eBangeni kanye nasesifundweni. Uthisha angabheka abafundi abayishumi ngesikhathi ngakho ke umsebenzi wokuhlola okuhlelekile ungenziwa ngamaqoqo amancane, kungathatha izinsuku ezimbalwa ukuhlola ikilasi lonke.zonke izinto zokusebenza eziphathekayo kufanele zibekhona njengokujwayelikele,(izinto zokubala eziphathekayo,ishadi lezinombolo njll.) Ukuhlola okusetshenziswayo kufanele kuhambisane neminyaka kanye nokukhula komfundi. Ukuhlola kufanele kubhekelele ukukhula kwamazinga okucabanga namakhono abafundi.ukwakhiwa kwalomsebenzi wokuhlola kufanele kufake ulwazi olufundiwe ngezindlela ezahlukene. Izinhlobo ezahlukene zokuhlola (ukubhekwa kwabafundi, izingxoxo, okwenziwayo kanye nokubhalwayo) kufanele inike umfundi ithuba lokukhombisa angakwazi ukukwenza, abanye abafundi bakhombisa ukwazi ngezindlela ezahlukene.Isib. • abanye abafundi abakuthola kulukhuni ukufunda bayazazi izibalo • Abanye abafundi bangaba ngaphansi kwezinga elilindelekile lokukhula ngolimi lokufunda nokufundisa. Umsebenzi wokuhlowa awube izibalo ezingancikile olimini nasekufundeni. Uthisha makaqonde ukuthi yini okuhlolwayo.ulwazi lwezibalo namakhono angahlolwa ngezindlela ezahlukene. izinhlobo ezahlukene zokuhlola zilungele ulwazi namakhono kwizihloko ezahlukene ngokweminyaka ehlukene yabafundi.kuyasiza ukusebenzisa uhlu lokubheka ukusebenza kwabafundi ukubona ukukhula kwabo olwazini lwezibalo emabangeni aphansi.iRubric ingasetshenziswa ukuhlola amakhono abafundi ekuxazululeni izinkinga zezibalo. 4.4 Uhlelo lokuhlola ukuhlola okuhlelekile Ngezansi kunezindlela ezihleliwe zokuhlola okuhlelekile kwezibalo kumaBanga 1 - 3: IBANGA ITHEMU1 ITHEMU2 ITHEMU3 ITHEMU4 ISAMBA 1 2 2 2 1 7 2 2 2 2 2 8 3 2 3 3 2 10 Othisha bayagqugquzelwa ukwenza ukuhlola kokuqala okuyisisekelo kweThemu yoku-1. Imiphumela yabafundi yokuhlola kokuqala ingasetshenziselwa ukubekwa kwabafundi ezingeni labafundi, makusetshenziselwe ukukala izinga lomsebenzi ekungaqala ngawo ukufundiswa nezingxenye zomsebenzi ezidinga isikhathi esiningi.abafundi bakhula ngokwamazinga ahlukene abanye abafundi bathatha kancane ekuqaleni kodwa ngokuqhubeka kwesikhathi bayakwazi ukuba sezingeni elilindelekile ezibalweni. Ukuhlola okuhlelekile kwezibalo kufaka ngaphezu kwesihloko esisodwa ezibalweni;kufanele onyakeni kufanele ufake lonke ulwazi lwezibalo nezihloko,akuyikho konke okufakiwe kuhlelo lwezifundo okuhlolwa ngokuhlelekile noma kubhalwe ngokuhlelekile.Izonombolo ukusebenza nobudlelwano kuthatha ama-60% wezibalo emaBangeni 1-3.ama-60% ukuhlolwa okuhlelekile eThemu ngayinye kunyaka wonke kufanele ugxile kwi-zinombolo ukusebenza nobudlelwano. Ingxenye ngayinye yokuhlola okuhlelekile ayizimeli emsebenzini ohlolwayo.ezinye izingxenye zihlolwa kanyekanye CAPS 573

Izibalo IBANGA 1-3 kanti ezinye zingahlolwa ngezikhathi ezihlukene Isib. amakhono okubala ngokweqa izinombolo angenziwa kanye nokunye kulomsebenzi: • Ukuqedelela ukubala ngokulandelana • Ukufunda nokubhala izimpawu zezinombolo • ukubala Ukuhlola okuhlelekile okunezibalo zokuxazulula izinkinga ngokwenza amaqoqo noma ngokwabelana nokuhlola ukukwazi ukukala umthamo kungenziwa ngezikhathi ezihlukene. 4.5 Ukubhala nokubika ngokusebenza kwabafundi Ukubhala ngokusebenza kwabafundi kuyindlela uthisha agcina ngayo ulwazi lwezinga umfundi akulo kulowo msebenzi ohleliwe.lolulwazi luveza ulwazi lokusebenza komfundi ukufika ezingeni olubekwe kwi CAPS.ulwazi ngokusebenza komfundi malunike ubufakazi bokukhula komfundi kuleloBanga akulo nokuholela ekudluleleni eBangeni elilandelayo. ulwazi olubhalwe ngokusebenza komfundi lungasiza ukuveza inqubekelaphambili ekufundeni nasekufundiseni. Ukubika ngokusebenza komfundi kuwuhlelo olwazisa abafundi,abazali,isikole nabaxhasi ngenqubekelaphambili yokusebenza kwabafundi,lokhu kungabikwa ngezindleal ezahlukene ezingafaka irephothi lokusebenza komfundi,imihlangano yabazali,njll.othisha kumaBanga onke parephotha ngama-% kuzozonke izifundo.ithebhula elingezansi libonisa ubungako bama-%,amazinga kanye nezincazelo zawo: AMAZINGA NAMAPHESENTI ABHALWAYO UKUBIKA UKUSEBENZA KOMFUNDI UPHAWU LOKULINGANISA INCAZELOYOKUQHUBA KOMFUNDI IPHESENTI 7 Umphumela ovelele 80 - 100 6 Umphumela oncomekayo 70 - 79 5 Umphumela owanele 60 - 69 4 Umphumela ogculisayo 50 - 59 3 Umphumela olingene 40 - 49 2 Umphumela ongagculisi 30 - 39 1 Umphumela ongalungile 0 - 29 4.6 Ukuqinisekisa ukuhlola okuhleliwe Ukuqinisekisa ukuhlola okuhleliwe kuwumsebenzi wokuqinisekisa ukuthi umsebenzi wokuhlola mawube ngofanele, ngosemthethweni, ngothembekile. ukuqinesikisa ukuhlola kwenziwa ezikoleni, ehhovisi lesifunda, elesifundazwe nakuzwelonke. 4.7 Jikelele Losomqulu mawufundwe uhlanganiswe nalokhu okulandelayo: 4.7.1 National policy pertaining to the progrmme and promotion requirements of national Curriculam statement Grades R-12; and 4.7.2 The policy document, National Protocol for Assessment Grades R-12 574 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 4.8 Izibonelo zezinhla zokuhlola zamabanga 1-3 Ngezansi izibonelo zezinhla zokubheka ukuhlola aphansi. Lokhu kusiza othisha ukuba bakwazi ukulungiselela nokwenza ukuhlola okuhlelekile ngendlela eqhubekayo. IBANGA R Uhla lokubheka abafundi ezibelweni zomthamo √ noma Ulwazi lwezibalo Ulwazi Izinqumo ukuphawula x Izinombolo, Izimpawu Ukubala Qagela uphinde ubale ngekhanda nobudlelwane bazo kufinyelela esi-5(amaculo ezinombolo,kanye nemilolozelo ukuthuthukisa ulwazi lwezinombolo) Ukubona izinombolo Bona izinombolo esimweni esijwayelekile- Isib.iminyaka yabafundi,irejista njll. Qonda izinombolo ezijwayelekile(Isib. ngesikhathi sokuzikhulula) Ulwazi lwezinombolo Qonda okukodwa-nokukodwa okuqondanayo Khomba bese uchaza Khomba izithombe zezinombolo kanye izinamba eziphelele namakhadi amachashaza afaka inombolo ku-1 Yazi uphawu lwenombolo ku-1 Bona igama lenombolo ku-1 Ukuxazulula izinkinga Sebenzisa izinto eziphathekayo zezibalo Chaza ukucabanga kwakho ngamagama nangemidwebo noma ngezinto eziphathekayo Amaphethini Kopela,wandise Bona amaphethini akuzungezile. nobudlelwane ubuye wenze awakho amaphethini. Kopela,wandise,wakhe amaphethini Indawo nezimo Bona,ukhombe,usho Bona,ukhombe bese usho amagama amagama ezinto amabhola ezinhlangothintathu Bona,ukhombe bese usho amagama amabhokisi Bona,ukhombe,usho Bona, khomba bese usho amagama amagama ezinto ezimpawu zamaqoqo abo, nabanye ezinhlangothimbili abafundi. Yakha iphazili yezingcezu eziyi-6 Khombisa ikhono lokuhlukanisa phakathi kwesthombe esiphambili nesisemuva. CAPS 575

Izibalo IBANGA 1-3 Izimo ezisejiyometri Khomba,ubone indilinga. Khomba,ubone unxantathu Khomba,ubone isikwele Chaza, uhlele, Qhathanisa,amaqoqo amabili usho ukuthi uqhathanise izinto iliphi elinokuningi,okuncane,okuningi ezinhlangothintathu kunokunye,nokuncane kunokunye ngokwe: Hlela izinto eziphathekayo: Ubungako-okukhulu nokuncane Umbala-imibala yendalo- (obomvu,oliphuzi,oluhlaza) Isimo-indilinga,unxantathu kanye nesikwele Izinto eziphathekayo eziginqikayo Izinto eziphathekayo ezishelelayo Bona umugqa Bona umugqa ohlukanisa phakathi okufana ohlukanisa kabili kufane nse nxazombili nse nhlangothi zombili: Ukuqonda indawo: Ukwazi ingaphambili nengemuva Ubudlelwano phakathi Ukwazi ngaphezulu kwe, okungaphansi, komfundi nezinto okungezansi. ezimbili noma ngaphezulu Ukwazi phakathi nangaphandle Ukwazi phezulu naphansi Izinkomba Ukwazi ulwazi lwamagama afana ngaphambili,ngemuva, Isilinganiso Isikhathi Sebenzisa amgama ubusuku nemini,ukukhanya nobumnyama,ekuseni nantambama,ukuchaza isikhathi sosuku. Hlela zosuku ngokulandelana kwazo. Ukukwazi ukubona izinsuku seveki,izikhathi zonyaka kanye nesimo sezulu. Ukwazi usuku lwakhe lokuzalwa Ubude Ukuhlukanisa ubude nobufishane,okude ngokuthe xaxa nokufishane kakhulu.(ishadi lobude) Ukuqokelwa Qoqa,hlela,dweba,funda Ukukwazi ukuqoqa,uhle,udwebe,ufunde,uhla nokuhlelwa kolwazi bese ubhala okumele ziye izinto ngokwesakhiwo esisodwa. lwezinombolo ulwazi oluqoqiwe ISILINGANISO SOKUGCINA: 576 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBANGA R UHLA LOKUHLOLA ITHEMU 2 Ulwazi √ noma Ulwazi Izinqumo Ukuphawula Lwezinombolo x IZINOMBOLO, Ukubala Qagela, ubale ngekhanda kuyofika ku 7 IZIMPAWU (clula, isho imilolozelo) NOBUDLELWANE BAZO Bala uya phambili ubuye uhlehle (1 - 4) Ukwazi ulwazi lwamagama njenga okuningi / okungconywana. Ukubona Izinombolo Ukubona izinombolo ezimweni ezejwayelekile njenge nombolo yendlu, ikheli. Ukubona bese Uchaza Khomba, izithombe zezinombolo namakhadi Izinombolo amachashaza Ukwazi izimpawu zezinombolo 1, 2, 3,4 Bona amagama ezinombolo Ulwazi Lwezinombolo Uyakwazi ukbeka okunye nokunye ngokuqondana Hlukanisa phakathi kokuningi, okuncane okuyingcosana Ukubona umehluko kwimali ewuhlweza Ukuxazulula Izinkinga Sebenzisa izinto eziphathekayo Zezinombolo Chaza ngamagama noma ngemidwebo Xazulula izinkinga zezibalo ngokukhuluma ezokuhlanganisa nokususa kufika kunombolo 4. AMAPHETHINI Ukukopisha, uqhube, Kopela, qhuba bese wakha amaphethini NOBUDLELWANE wakhe amaphethini usebsnzisa izinto, izimo nemali. INDAWO NEZIMO Ukubona, Akha iphazili elinezingcezu eziyi 12 ukhombe, bes unika igama lezimo Khombisa ikhono lokuhlukanisa phakathi ezinhlangothimbili kwezinto eziphambili nezingemuva esithombeni. Izimo ezibalombhalo Bona, khomba bese usho igama likanxantathu Ubona umumo kanxantathu Ukuchaza, uhlele bese Qhathanisa amaqoqo ezinto amabili usho uqhathanisa izinto ukuthi yiziphi ezinde noma ezimfushane ezinhlangothintathu: Hlela izinto ngezimo - yinde/imfushane imibala izimo Akha izimo Sebenzisa amabhuloki ezinhlangothintathu Bona umugqa Bona umugqa ohlukanisa kabili kulingane ohlukanisa kabili futhi kufane ezintweni eziseduze nawe kulingane kufane Uyakwazi ukusebenza kwizinhlangothi zombili Ubudlelwano nendawo Ukuqonda ubudlelwano phakathi komfundi okuyo nezinto ezimbili noma ezintathu CAPS 577

Izibalo IBANGA 1-3 Isilinganiso Isikhathi Uyazi izinsuku zeviki,izikhayhi zonyaka njll. imilolozelo namaculo Wazi usuku lwakhe lokuzalwa (phinda hlola) Ubude Uyazi umehluko kokkude nokufushane Ukuqokelela Qoqa, Qoqa,hlela, dweba, funda beseudweba nokuhlela ulwazi hlela,dweba,funda okumele ulwazi bese ubhla izinto ezimela ulwazi ISILINGANISO SOKUGCINA: IBANGA R-UHLA LOKUHLOLA 578 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 ITHEMU 3 ULWAZI √ Noma ULWAZI IZINQUMO PHAWULA LWEZBALO x IZINOMBOLO, ukubala Qagela bese ubala ngekhanda ufike ku- 7 IZIMPAWU (amaculo ezinombolo nemilolozelo) ukuze NOBUDLELWANE athuthuise ulwazi lwezinombolo BAZO Bala uya emuva naphambili (1-7) Bazi ukuthi ihlombe ulishaye kangaki kakhulu / kancane Ukubona izinombolo Babona izinombolo esimeni esijwayelekile isib. iminyaka, irejista (uhlole njalo) Thola bese uzichaza Thola izithombe zezinombolo namakhadi izinombolo anamachashaza ufike ku- 7 Yazi izimpawu zezinombolo - 5, 6, 7 Bona amagama ezinombolo -kuhlanu, isithupha,isikhombisa Ulwazi lwezinombolo Hlukanisa phakathi kokuningi,okuyimbijana,nokul inganayo,okuningi nokumbalwa ufike- 7 Bona imibala nezinhlobo zezilwane emalini engamaphepha yase Mzansi. Ukuxazulula Sebenzisa izinto eziphathekayo izinkinga Chaza ngendlela ocabanga ngayo ngamagama,nangokudweba noma ngezinto eziphathekayo. Xazulula izinkinga zokuhlanganisa nokususa ngomlomo ufike ku- 7 AMAPHETHINI Kopisha qhuba bese Kopisha,uqhube bese uzakhela awakho NOBUDLELWANE uzakhela awakho amaphethini usebenzisa izithombe amaphethini INDAWO NEZIMO Buka uthole Yakha okungenani izingcezu eziyi-18 zephazili bese ubize onhlangothimbili-2-D izimo/izithombe Izimo ezisazibalo Bona,uthole bese usho izimo eziyisikwele. mdwebo Qonda isimo sezimo ezejwayelekile esezifundiwe kuze kube manje (ukugcina ismo singashintshile) Yakha izinto Yakha izimo ezintweni nangezibonelo ozinikiwe ezinhlangothintathu 3-D usebenzisa izinto Kopisha isakhiwoemdwebeni osekhadini eziphathekayo Ubudlelwano Bona ubudlelwano phakathi kwezinto ezimbili bendawo noma eziningi nokuthi zihlobene kanjani - Ngaphambili,ngemuva, ngaphezulu, phe zulu,phansi,ngaphansi,ecelelni phakathi kwesokudla kwesokunxele Yenza ngokulandela imiyalo ebhodini lokugaxa Izinkomba Yazi izindlela ezehlukene ngokulandela ishadi lemicibisholo CAPS 579

Izibalo IBANGA 1-3 Izilinganiso Ubude Qagela bese ukala ubude bezinto ezehlukene Isisindo Qonda ngalolulwazi okulula,okunzima, kusinda kakhulu kusinda kancane, kulula kancane kulula kakhulu Umthamo Qonda lolulwazi kugcwele,akukho,kugcwele kuno, kuncane kune” Ukuqokelela Qoqa uhlele, Bakwazi ukuqoqa bahlele, badwebe, bafunde nokuhlela ulwazi udwebe, ufunde bese bethula lololwazi ngokulihlaziya uyayithula ngokwesihloko leso ISILINGANISO SOKUGCINA: 580 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBANGA R UHLA LOKUHLOLA ITHEMU 4 ULWAZI ULWAZI IZINQUMO √ nomax Ukuphawula LWEZIBALO Izinombolo,izimpawu Ukubala Qagela uphinde ubale ngekhanda kufinyelela nobudlelwane bazo eziyi-5(amaculo ezinombolo,kanye nemilolozelo ukuthuthukisa ulwazi lwezinombolo)) Bala uye emuva kanye naphambili (1-10) Bala ngakubili (imilolozelo kanye namaculo ezinombolo) Ukuqonda amagama afana:nokuningi kanye nokuncane(kushaywa izandla) Ukuqonda izinombolo kushaywa izandla kaningana nakancane kakhulu. Ukubona izinombolo Ukubona bese ukhomba izinombol ezimweni ezijwayelekile.Isib.iminyaka yabafundi njll. Ulwazi Khomba izithombe zezinombolo kanye lwezinombolo namakhadi amachashaza afaka inombolo kusuka ke-0-10 Khomba bese uchaza izinamba Yazi uphawu lwenombolo eyesi-8,9,10 kanye eziphelele no-0 Bona igama lenombolo eyesi-8,9,10 kanye no-0 Qedela ukulandelana kwezinombolo ezilula kusuka kweyo-1-10 Ulwazi Hlukanisa phakathi kokuningi,okuncane,okulin lwezinombolo ganayo,okuningi kakhulu,nokuncane kakhulu kuyofika kokuyi-10 Ukukwazi ukulandelana kwezinombolo ezijwayelekile okokuqala,okwesibili,okwesithathu kuyofika kokuyisithupha. Ukuxazulula Sebenzisa izinto eziphathekayo izinkinga zezibalo Chaza ukucabanga kwakho ngamagama nangemidwebo noma ngezinto eziphathekayo Xazulula izinginkinga zokuhlanganisa nokususa ubebenzisa izinombol kufinyelela e-10 Amaphethini Kopela, Kopela,wandise wenze amaphethini alalelwayo nobudlelwane wandise ubuye wenze awakho Ukwazi ukudlala umdlalo (gxa) amaphethini. CAPS 581

Izibalo IBANGA 1-3 Indawo nezimo Bona, ukhombe, Ukukwazi ukwenza okungenani ngezingcezu usho amagama ezingama-24 ezinto ezinhlangothimbili Izimo ezisejiyometri Ukubona akhombe indilinga,unxantathu,isikwele nonxande. Bona umugqa Bona umugqa ohlukanisa phakathi okufana nse ohlukanisa kabili nxazombili ezintweni kufane nse nhlangothi zombili: Ukwazi ulwazi lwamagama eduze kwe,phakathi namaphakathi,kwesokunxele kanye nesokudla. Ubudlelwano phakathi kwezinto Ukukwazi ukwenza umsebenzi oseqophelweni eliphezulu kwibhodi lokugaxa. Izinkomba Ukwazi ulwazi lwamagama afana ngaphambili,ngemuva,phezulu naphansi,kwesokunxele kanye nesokudla. Isilinganiso Ubude Ukuqonda ukuthi izinto ziyakalwa kusetshenziswa ibhande lokukala. Ukuqokelwa Qoqa, hlela, dweba, Ukukwazi ukuqoqa, nokuhlelwa kolwazi funda bese ubhala uhle,udwebe,ufunde,uhlaziye izinto lwezinombolo okumele ulwazi ngokwesakhiwo esisodwa. oluqoqiwe ISILINGANISO SOKUGCINA: 582 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Izibonelo zezinto zokusebenza uma kuhlolwa Isiphakamiso sohla lohlelo lokuhlolwa oluhlelekile Isibonelo sohla lohlelo lokuhlolwa samabanga R kuya ku 3 sinikiwe ngenzansi. Lokhu kuzosiza othisha ukuba bahlele futhi benze uhlelo lokuhlolwa oluhlelekile ngendlela eqhubekayo. Isibonelo sezinto zokusebenza uma kuhlolwa Ukusebenzisa Uhla lokuhlola isilinganiso Ibanga 1 Uhlalo lokubheka Abafundi ezibalweni zomthamo Ulwazi Isihloko Izinqumo  noma  Ukuphawula Lwezibalo Qhathanisa bese uyahlela umthamo woketshezi ezitsheni ezimbili ezibekwe ezibekwe eduze kwesinye. Qhathanisa umthamo woketshezi olusezitsheni ezimbili ezinomumo ongafani ngokuwuthela esiy- ISILINGANISO sheni sesithathu. Umthamo Bhala umthamo wezitsha usebsnzisa isikalo esin- galinganisiwe njenge izipuni, izinkomishi njll. Phendula imibuzo ngkuthi yisiphi isitsha esin- omthamo omningi. Usebenzisa amagama okuqhathanisa njn- gokuthi kuningi kuno, kuncane kuno, kugcwele, akugcwele. Ibanga 1 Ithemu 4: Umsebenzi wokuhlola Ulwazi Isihloko Izinqumo  noma  Ukuphawula Lwezibalo Hlela bese uqhathanisa isisindo sezinto ezintathu noma ngaphezulu ngokuzibeka ezimbili kanyakan- ye esikalini bese ezilandelanisa ngesisindo sazo. ISILINGANISO Isisindo Yisho isiso sezinto usebenzisa isikali esingalin- ganisiwe. Sebenzisa amagama okuqhathanisa isisindo njenga kulula, kuyasinda kulula kakhulu. Ukukwazi ukubhala izilinganiso ezithathiwe CAPS 583

Izibalo IBANGA 1-3 Ukusebenzisa izinto zokusebnza (rubric) ukuhlola izinkinga zezibalo Izinkinga zezibalo zingahlolwa ngokusebenzisa ithuluzi lokuhlola. Okuthathwa njengendlela efanele yokuxazulula izinkinga zezibalo: • Ushintsho kubafundi lapho bekhula olwazini lokusebenza ngezinombolo nasekwazini ukukhulisa ulwazi lwezinombolo, • Kuncike olwazini lokukhula kwezinombolo nasezinkingeni zezinhlobo zezinombolo. eBangeni 1 Ukusebenzisa ithuluzi lokuhlola ekuxazululeni izinkinga zezinombolo Akazi uzoqalaphi noma wenza okungafanele. 1 Uyayiqonda inkinga yezibalo, aqale bese engakwazi ukuqeda ngendlela efanele. 2-3 Uyayiqonda inkinga yezibalo, asebenzise imidwebo noma izinto zokubala Uyakwazi ukuchaza abe namaphutha 4-5 ambalwa. Uyasenza asiqede isibalo ngendlela efanele. Uyakwazi ukuchaza indlela enze ngayo nokucabanga kwabanye. 6-7 eBangeni 2 Ukusebenzisa ithuluzi lokuhlola ekuxazululeni izinkinga zezinombolo Akazi uzoqalaphi noma wenza okungafanele. 1 Uyayiqonda inkinga yezibalo, aqale bese engakwazi ukuqeda ngendlela efanele. noma 2-3 Uyayiqonda inking yezibalo, asebenzise imidwebo noma izinto zokubala. Uyayiqonda inking yezibalo, asebenzise imidwebo noma izinto zokubala Uyakwazi ukuchaza abe namaphutha 4-5 ambalwa. Uyasenza asiqede isibalo esebenzisa ulwazi lwezinombolo namaqhinga afana nokuhlakaza nokuhlanganisa 6-7 izinombolo, ukuziphinda kabili, ukuzihlukanisa kabili, umugqa wezinombolo njll. Uyakwazi ukuchaza indlela enze ngayo nokucabanga kwabanye. eBangeni 3 Ukusebenzisa ithuluzi lokuhlola ekuxazululeni izinkinga zezinombolo Akazi uzoqalaphi noma wenza okungafanele. 1 Uyayiqonda inkinga yezibalo, aqale bese engakwazi ukuqeda ngendlela efanele esebenzisa imidwebo neinto 2-3 zokubala. Uyayiqonda inkinga yezibalo ayixazulule esebenzisa izinombolo.Uyakwazi ukuchaza isixazululo sakhe. 4-5 Wenza izibalo aziqede ngendlela efanele esebenzisa ulwazi lwezinombolo ngendlela efanele namaqhinga okuhlakaza izinombolo abuye azihlanganise, ukuhlukanisa kabili, ukusondezela eshumini, umugqa wezinombolo 6-7 ngokufanele. 584 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Izibonelo: Ukusebenzisa ithuluzi lokuhlola ekuxazululeni izinkinga zezinombolo eBangeni 1 kuya ku 3 Inja inemilenze emine. Mingaki imilenze yezinja eziyi 12? Ibanga 1: Isilinganiso: 1. Umfundi akayiqondi inking yezibalo, bese esbenzisa amasi okungewona. Ibanga 1: Isilinganiso 6 Umfundi uyayiqonda inkinga yezibalo, bese eyixazulula ngen- dlela efaneleinkinga. Uyakwazi ukuchaza inkinga. Ibanga 2: Isilinganiso 4 Umfundi uyayiqonda inkinga yezibalo. Umfundi webanga 2 kufanele asebenzise izinombolo nezimpawu zokuhlanganisa uphindaphinda. Umlimi utshale izihlahla emigqeni eyisithupha. Umugqa ngamunye unezihlahla eziyi 13. Zingaki izihlahla azitshalile sezizonke? Ibanga: Isilinganiso 6 Umfundi uyayiqonda inkinga yezibalo bese eyixazulula ngendlela efanele esebenzisa izinombolo nezimpawu zokusebenza izibalo zebanga 2. Ibanga 3: Isilinganiso 4 Umfundi uyayiqonda inkinga yezibalo bese eyixazulula ngendlela efanele. Kodwa akasebenzisi amaqhinga nzindlela zokubala eziseBangeni 3, njengoku phindaphinda inombolo usebenzisa ukuhlakaza nokuyihlanganisa inombolo. Ibanga 3: Isilinganiso 5 Uyasebenza asiqede isibalo esebenzisa izinombolo nezimpawu zokusebenza ngezinombolo namaqhinga afana nokuhlakaza abuya ache inombolo. Uyakwazi ukuchaza indlela enze ngayo nokucabanga kwabanye. UGcina unezimabuli ezingama 258 bese uJabu eba nezingama 384. Banezimabuli ezingaki sezizonke? Ibanga 3: Isilinganiso: 5 Uyasebenza asiqede isibalo esebenzisa izinombolo namaqhinga afana nokuhlakaza nokwakha izinombolo,ukuziphinda kabili, ukuzisondeza eshumini, umgqa wezinombolo njll. Uyakwazi ukuchaza indlela enze ngayo nokucabanga kwabanye. CAPS 585

Izibalo IBANGA 1-3 Ubani uhafu wama- 237? Ibanga 3. Isilinganiso: 5 Uyakwazi ukuxazulula izinkinga zezibalo esebenzisa ulwazi lwezinombolo, namaqhinga okuhlakaza abuye ache izinombolo, ukuziphinda kabili, azihlukanise kabili,azisondeze eshumini nomugqa wezinombolo. Uyakwazi ukuchaza indlela enze ngayo nokucabanga kwabanye. Ibanga 1 ithemu 1: Isibonelo somsebenzi wokuhlola kokuqala Uhlobo Uhla lwezinto ezihlolwayo Pnoma  Ukuphawula Lomsebenzi Okukhulunywayo Umfundi uyakwazi uku: • Izinto eziphathekayo kuyofika kweziyishumi? • Iliphi iqoqo elincane/ eliningi? • Ukufunda izimpawu zezinombolo kuyofika koku 5? Okwenziwayo Umfundi uyakwazi uku: • Ukulandelanisa izinto? • Ukukopisha iphethini? • Ukubeka izinto phambili kwakhe? • Ukubeka izinto ngemuva kwakhe? • Ukuhlela izinto ngokophawu olulodwa? • Ukusebenza ngenkinga uke uthole isisombu- lulo? 586 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Ibanga 1: Isibonelo Somsebenzi Wokuhlola Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Izimpawu Ulwazi lwezinom- Bala ngokuzethemba iznto kufinyelele kweziyi 10. Isho amagama azo nobudlelwane bazo bolo ngokulandelana. Bhala bese ufunda izimpawu zezinombolo kusuka kweyodwa uya kweyesihlanu Hlela izinombolo kusukela kweyokuqala kukya kweyesihlanu; kusukela kwencane kuya kwenkulu. Sebenzisa amagama ukuchaza isikhundla senombolo uma uqhathanisa nezinye njengo engaphambi, engemuva Ukuxazulula Xazulula izinkinga zezibalo zamagama ezifaka ukuhlanganisa, ukususa izinkinga zezibalo izinombolo ezifika kweziyisi 5. Esebenzisa imidwebo nezinye izinto. Uyakwazi ukuchaza izixazululo zakhe. Uxazulula izinkinga zokwenziwayo kufaka ukuhlukaniselana ngokulingana nokwenza amaqoqo ngezinombolo kufinyelela ku 5 okunezimpendulo ezin- ezinsalela. Uyakwazi ukuchaza izimpendulo zakhe. Ukubala Uyakwazi ukuhlanganisa kuze kufinyelele ku 5 esebenzisa imidwebo nez- inye izinto. Uyakwazi ukususa kunoma iyiphi inombolo kuze kufike ku 5. Esebenzisa imidwebo nezinye izinto. Amaphethini, Ubudlel- Amaphethini Uyakwazi ukuqedela ukulandelana kwezinombolo ebala ngakunye kuze wane ne-Aljibhra Ezinombolo kuyifika e 10. Isibonelo 1, 2, 3, 4, __, __, __, __, 9, 10 Indawo nezimo Izikhundla Uyakwazi ukulandela imiyalelo abeke into ngayinye ngokomyalelo kathisha Isibonelo: Beka inkmishi phezulu kwetafula. Izimo ezinhlang- Ukubona nokunika amagama: othintathu • Izimo zamabhola • Izimo zamabhokisi Isilinganiso Isikhathi Chaza izikhathi zosuku. Isibonelo: ekuseni, ntambama, ebusuku ubude Ukwazi ukukala ubude, ububanzi esebenzisaizikali ezingahlelekile. Isisindo Ukwazi ukukalaaqhathanise isisindosezinto ezintathu esbenzisa isikali esin- gahlelekile. Abesehlela izinto ngesisindo sazo. Achaze isisindo esebenzisa amagama afana -kulula kuna, kuyasinda kuna. Ukuqokelela nokuhlelwa Ukuhlela amaqo- Qoqa bese ehlela izinto ezejwayelekile ngokwemiyalelo enikwe uthisha. kolwazi lwezinombolo qo ezinto Dweba isithombe sezinto ezihleliwe. CAPS 587

Izibalo IBANGA 1-3 Ibanga 1 Ithemu yesi-2: Umsebenzi Wokuhlola woku- 1 ULWAZI LWEZIBALO ISIHLOKO UHLA LWEZINTO EZIHLOLWAYO Izinombolo, Izimpawu Ulwazi Lwezinombolo Bala ngokuzethemba iznto kufinyelele kweziyi 20. Isho amagama azo nobudlelwane ngokulandelana bezinombolo Asho ukuthi iliqoqo lezinto eziningi noma ezincane, lapho amaqoqo enezinto ezingengaphansi kuka 10 Ufunda izimpawu zezinombolo kuye kufinyelele ema- 30 Ubhala izimpawu zezinombolo kuya ku10 Ukuxazulula Uxazulula izinkinga zezibalo zamagama lapho kuhlanganiswa kubuye Izinkinga Zezibalo kususwe kunezimpendulo ezifika. Kusebenzisa: • izinto • imidwebo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili Uyakwazi ukuchaza izixazululo zakhe Izibalo Wenza izibalo zokuhlanganisa kuye kfike ku 10 esbenzisa: • izinto • imidwebo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili Ubhala umusho wezinimbolo onophawu + Wenza izibalo zokususa kusukela e- 10 noma ngaphansi esebenzisa: • izinto eziphathekayo • imidwebo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili Ubhala umusho wezinimbolo onophawu - Amaphethini, Amaphethini Uqedela ukulandelana kwezinombolo ebala kufinyelela ku 30. ubudlelwane ne-Aljibhra Ezinombolo • Ngakunye: 20, 21, 22, 23, __, __, __, __, 28; __; 30. • Ngakuhlanu:.5, 10, 15, __, __, 30, Amaphethini Kopela aqhube iphethini; Okusejiyometri • Esebenzisa uhlobo olulodwa lwento kodwa olushintsha umbala. • Esbenzisa izinto ezifanayo ezinobungako obungafani Indawo nezimo Izimo Khomba bese usho igama: Ezinhlangothimbili indilinga isikwele unxantathu 588 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga 1 Ithemu yesi- 2: Umsebenzi Wokuhlola wesi- 2 ULWAZI LWEZIBALO ISIHLOKO UHLA LWEZINTO EZIHLOLWAYO Izinombolo, Izimpawu Ulwazi Lwezinombolo Bala uye phambili ubuye uhlehle ngakunye kusukela ku 1 kuya ku 20 nobudlelwane bazo Bala uye phambili ngo 5, ngo 2, kusukela ku 0 kuya ku 50 Usebenzisa amagama ukuchaza isikhundla senombolo esebenzisa - ngapphambi kuka, emuva kuka Qhathanisa ubungako bezinombolo kuyofika ku 10 esebenzisa amagama afana no kuningi kuna, kuncane kuna Hlela izinombolo kusukela ki 1 kuya ku 10 kusukela kwencane kuya kwenkulu Ufunda izimpawu zezinombolo kusukela ema- 50 Ukuxazulula Izinkinga Uxazulula izinkinga zokwenziwayo esebenzisa ukuhlukaniselana Zezibalo ngokulingana, nokwenza amaqoqo ngezinombolo kuyofinyelela ku 10 okunezimpendulo ezinezinsalela. Esebenzisa lokhu okulandelayo: • izinto eziphathekayo • imidwebo • umugqa wezinombolo Uyachaza izimpendulo. Ukuxazulula Izinkinga Uxazulula izinkinga zezibalo zamagama ezifaka ukuhlanganisa Zezibalo ngokuphindelelakunezimpendulo ezigcina e-10. Besebenzisa lokhu: • izinto • imidwebo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili Uyachaza izimpendulo. Imali Ukubona imali ewuhlweza neyamaphepha yaseNingizimu Afrika 5c, 10c,, 50c, R1, R2; R5 Uxazulula izinkinga zezimali ezifaka isamba noshintshi okuye kuyofika kuR10 naku 20c Ukubala Wenza ukuhlanganisa ngokuphindelela kuyofika ku 10 esebenzisa: • izinto • imidwebo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili Ubhala umusho wezinombolo Amaphethini, Ulwazi Lwezinombolo Uqedela ukulandelana kwezinombolo uma ebala:Completes number ubudlelwane ne-Aljibhra sequences of counting • ngankunye ehlehla esuka ku 50: 50, 49, 48, __, __, 45, __, __, 42; __; 40. • Ngamashumi eya phambili kuyofika ku 50:.10, 20, 30, __, __, Isilinganiso Umthamo Uqagela, akale aqhathanise ahlele bese ebhala umthamo esebenzisa izikali ezingalinganisiwe njenge zipuni nezinkomishi. Ukuqokelela Hlela amaqoqo ezinto Uqoqa, ahlele izintoeziphayhekayo ngokwezinqumo ezinikwe uthisha. nokuhlelwa kolwazi Udweba isithombesezinto ezihleliwe noma achaze iqoqo lezinto lwezinombolo ezihleliwe. CAPS 589

Izibalo IBANGA 1-3 IBanga 1 Ithemu yesi- 3 Somsebenzi Wokuhlola woku- 1 ULWAZI LWEZIBALO ISIHLOKO UHLA LWEZINTO EZIHLOLWAYO Izinombolo, Izimpawu Ulwazi Lezinombolo Bala izinto ezingama 40 ngokuyikho. nobudlelwane bazo Asho ukuthi iliqoqo lezinto eziningi noma ezincane, lapho amaqoqo enezinto ezingengaphansi kuka 15 Ufunda izimpawu zezinombolo kuyofinyelela ku 70. Ubhala izimpawu zezinombolo kuya ku20 Ukuxazulula Uxazulula izinkinga zezibalo zamagama ezisezimweni ezijwajyelekile Izinkinga Zezibalo ezifaka izimpendulo ezinizinombolo ezifika ku 15. Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili Uyakwazi ukuchaza izimpendulo. Izibalo Wenza izibalo zokuhlanganisa kuye kufike kunombolo 15. Usebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili ubhala umusho wezinombolo esebenzisa +, = Wenza izibalo zokususa kusukela e-15 nangaphansi esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili ubhala umusho wezinombolo esebenzisa -, = Amaphethini, Amaphethini Qedela ukulandelana kwezinombolo ubala: ubudlelwane ne- ezinombolo Aljibhra • ngakunye uya emuva usuka kunoma iyiphi inombolo: 60, 59, 58, __, __, __, 54, __, __, 51. • Ngakubili uya phambili usuka kunoma iyiphi inombolo.44, 46, 48, __, __, __,56; __, 60 Amaphethini Uyakopela, aqhube bese echaza amaphethini lapho kusethsenziswe Okusejiyometri izimo ezahlukene eziyiqoqo, kodwa amaqoqo aphindwe ngendlela efanayo. Indawo nezimo Izimo Ubona bese esho amagama: • Okuyisimo sebhola • Okuyisimi sebhokisi Ahlele izinto ngokuthi ziyagingqika noma ziyashelelela. 590 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga 1 Ithemu yesi- 3: Somsebenzi Wokuhlola wesi- 2 ULWAZI LEZIBALO ISIHLOKO UHLA LWEZINTO EZIHLOLWAYO Izinombolo, izimpawu Ulwazi Bala uya phambili ngama 10, ngama 5, ngokubili kuya ku 80 nobudlelwane bazo Lwezinombolo Sebenzisa amagama ukusho ubungako benombolo Qhathanisa ubungako benombolo kufike ku 15: kuning kuna, kuyingcosana Uhlakaza izinombolo: 11 kuya 15 kanje: 10 nokukodwa, 12 = 10 + 2 Ukuxazulula Uxazulula izinkinga zezibalo zamagama ezisezimweni ezijwajyelekile ezifaka kwezinkinga izimpendulo ezinizinombolo ezifika ku 15. Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili Uyakwazi ukuchaza izimpendulo Uxazulula izinkinga zezibalo ezifaka ukwabelana nokwenza amaqoqo kuyifika ku15 okunezimpendulo ezinezinsalela. Esbenzisa: • izinto • imidwebo • umugqa wezinombolo Uyakwazi ukuchaza izimpendulo Imali Ukubona imali ewuhlweza neyamaphepha yaseNingizimu Afrik 20a 5c, 10c,, 50c, R1, R2; R5 Uxazulula izinkinga zezimali ezifaka isamba noshintshi okuye kuyofika kuR10 naku 20c Ukubala Wenza izibalo zokuhlanganisa ezphindaphindayo kufika ku 15. Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili ubhala umusho wezinombolo esebenzisa +, = Amaphethini, Amaphethini Qedela ukulandelana kwezinombolo ebala: ubudlelwane ne- Ezinombolo Aljibhra • ngakunye ehlehla kusuka ku 80;. 80, 79, 78, __, __, __, __, 73, ___; __; 70. • Ngamashumi kya ku 80:.10, 20, 30, __, __,__, __, __, • Ngakuhlanu:.5, 10, 15, __, __, 30, __, __.45, __, __, 60, __, __, __, 80 Indawo nezimo Okufana nse Bona bese uyadweba umugqa ohlukanisa kabili kufane nse kwisimo nxazombili esinhlangothmbili Isilinganiso Ubude Qagela, ukale, uqhathanise, uhlele bese ubhala ubde usebenzisa izikalo ezingalinganisiwe. Ukuqokelela Ulwazi Uphendula imibuzo ngolwazi lwegrafu yezithombe. nokuhlelwa kolwazi lwezinombolo CAPS 591

Izibalo IBANGA 1-3 IBanga 1 Ithemu yesi- 4: Somsebenzi Wokuhlola woku-1 ULWAZI LWEZIBALO ISIHLOKO UHLA LWEZINTO EZIHLOLWAYO Izinombolo, Izimpawu Ulwazi Bala izinto ezingama 50 ngokuyikho. nobudlelwane bazo lwezinombolo Isho ukuthiyiliphi iqoqo elinezinto eziningi kunelinye lapho iqoqo linezinto ezingengaphansi kuka 20 Funda izimpawu zezinombolo kuya ku 80. Ukuxazulula Uxazulula izinkinga zezibalozokuhlanganisa nokususa ezinezimpendulo kwezinkinga ezifika ku 20 Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili Izibalo Wenza izibalo zokuhlanganisa kufika ku 20. Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili ubhala umusho wezinombolo esebenzisa +, = Wenza izibalo zokususa kusukela ema- 20 nangaphansi. Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili ubhala umusho wezinombolo esebenzisa -, = Amaphethini, Amaphethini Qedela ukulandelana kwezinombolo ebala: ubudlelwane ne-Aljibhra Ezinombolo • ngakunye ehlehla esuka 80: 80, 79, 78, __, __, __, 74, __, __, 71. Ngambili:.64, 66, 68, __, __, __,76; __, 80 Indawo nezimo Izimo Bona bese usho amagama: Ezinhlangothimbili • Izindilinga • Unxande • Isikwele Hlela ngukuthi izimo inmacala ayindilinga noma aqondile Isilinganiso Isisindo • Qagela, ukale, uqhathanise, uhlele bese ubhala isisindo useben- zisa izikali ezingalinganisiwe kanye nesikali. • Sebenzisa amagama ukkhuluma ngokuqhathanisa isisindo njen- gokuthi kulula, kuyasinda 592 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga 1 Ithemu yesi- 4: Somsebenzi Wokuhlola wesi- 2 ULWAZI LWEZIBALO ISIHLOKO UHLA LWEZINTO EZIHLOLWAYO zinombolo, Izimpawu Ulwazi Bala uya phambili ngama 10, ngama 5, ngokubili kuya ku 100 nobudlelwane bazo Lwezimbolo Usebenzisa amagama ukuchaza ubungako bezinombolo. Qhathanisa ubungako benombolo kufika ku20 usebenzisaamagama afana ingcosana, kuningi kuna Hlela izinombolo kusuka ku1 kuya ku 20 kusukela kwenkulu kya kwencane Uhlakaza izinombolo: 11 kuya 20 kanje: 10 nokukodwa, 12 = 10 + 2 Funda izimpawu zezinombolo kufinyelele e- 100 Bhala izimpawu zezinombolo kufinyelele ema- 20 Ukuxazulula Uxazulula izinkinga zokwenziwayo esebenzisa ukuhlukaniselana nokwenza kwezinkinga amaqoqo kuya ku 20 okunezimpendulo ezinezinsalela. Esebenzisa lokhu oku- Zezibalo landelayo: • izinto eziphathekayo • imidwebo • umugqa wezinombolo Uyachaza izimpendulo. Imali Ukubona imali ewuhlweza neyamaphepha yaseNingizimu Afrik 20a 5c, 10c,, 50c, R1, R2; R5 Uxazulula izinkinga zezimali ezifaka isamba noshintshi okuye kuyofika kuR20 naku 50c Ukubala Wenza izibalo zokuhlanganisa ezphindaphindayo kufika ku 20. Esebenzisa: • Izinto eziphathekayo • imidwebo • ukwakha nokuhlukanisa izinombolo • umugqa wezinoombolo • ukuphinda kabili ukkhlunisa kaibili ubhala umusho wezinombolo esebenzisa +, = Amaphethini, ubudlelwane Amaphethini Qedela ukulandelana kwezinombolo ebala: ne-Aljibhra ezinombolo 99: 99, 98, 97, __, __, __, 93, __, __, 89. Ngamashumii:.10, 20, 30, __, __, __,70; __, 90 Indawo nezimo Indawo Sebenzisa amagama asho izinkomba lapho enyakaza ekilasini Qondanisa izingxenye ezihlukene zezinto. Isilinganiso Isikhathi Uyazi izinsuku zeviki Uyazi izinyanga zonyaka Ukuqokelela nokuhlelwa Ulwazi Uphendula imibuzo ngegrafu yezithombe kolwazi lwezinombolo CAPS 593

Izibalo IBANGA 1-3 IBanga 2 Ithemu yoku-1: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo,ubudlelwane Ulwazi Amamqoqo nokubala kufinyelela ezintweni eziyi-100 nokusebenza kwazo lwezinombolo Ukuqhathanisa nokuhlela izinombolo eziphelele kufinyelele kuma-25 Ukucaza izinombolo ezingambili kufinyelela ema-25 ngamashumi nangakunye isib. 23=20+3 Ukufunda nokubhala izimpawu zezinombolo kusukela ku 0 kuya ku 100 Ukuxazulula Ukuxazulula izinkinga zezibalo zamagama ohlwini olufaka izinkinga ukuhlanganisa, ukususa okunezimpendulo ezifinyelela kuma-20 kusetshenziswa loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bese uchaza izixazululo zakho ezinkingeni Imali Ukubona imali awuhlweza yaseSouth Africa 5c,10c, 20c, 50c, R1, R2, R5 nengamaphepha R10, R20, R50 Ukuxazulula izinkinga zemali ufake isamba noshintshi R20 nohlweza kufinyelela ku 50c c Ukubala Ukuhlanganisa kufinyelela kuma-20 Usebenzise loku okulandelayo • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala izibalo zezinombolo usebenzisa +, = Ukususa kufinyelela kuma-20 Usebenzise loku okulandelayo • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala umusho wezinombolo usebenzisa -, = Amaphethini, ubudlelwane ne- Amaphethini Qedela ukulandelana kwezinombolo uma kubalwa uqhubeka noma aljibhra ezinombolo uhlehla • ngakunye kusuka 0 - 100 e.g. 99, 98, 97, __, __, __, 93, __, 91, 90 • ngamashumi kusuka ku 0 - 100 e.g. 10, 20, 30, __, __, __, 70__, __, 100 • ngakubili kusuka ku 0 - 100 e.g. 80, 82, 84, __, __, 90, _, __, __, ___, 100 594 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 Indawo nezimo zezakhiwo 3-D Ukubona amagama ezinombolo • isakhiwo sebhola: imbulunga (spheres) • isakhiwo sebhokisi (prisms) 2-D izimo Ukuzibona namagama Izindilinga, onxantathu, izikwele, nonxande Isilinganiso Isikhathi Isho isikhathi sewashi lezinti ngamahora ubude Qagela, kala, qhathanisa,hlela, ubhale ubude,ububanzi, udude ngamamitha Ibanga 2 Ithemu 2: Ukuhlola 1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu nobudlel- Ulwazi lwezi- Bala izithombe zezinto ezingamaqoqo kufinyelele e-150 wane bazo nombolo Qhathanisa izinombolo kufinyelele e-50 Funda ubhale inombolo kusukela ku 0 - 50 Bala uqhubeke uphinde uhlehle ngama - 10, 2, 5, kufinyelele e-150 Ukuxazulula Xazulula izinkinga ezibonakalayo ngokusebenzisa ukuthi kuyalingana, izinkinga ukucaza, namaqoqo ngezinombolo eziphelele kufinyelele ema-50 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bese uchaza izixazululo zakho ezinkingeni Amaphethini, ubudlelwane ne- Amaphethini Qedela ukulandelana kwezinombolo uma kubalwa uqhubeka noma aljibhra ezinombolo uhlehla kusukela ku 0 - 150 isib.131, 132, 133, __, __, __, 137, __, ___, ___, 141 • ngamashumi phakathi kuka 0 & 200 isib.150, 140, 130, __, __, 100, __, __.70, __, __, 40 • bala ngakubili isib. 150, 148, 146, 144, __, __, 138, __, __, 132. • Bala ngokuhlanu kusuka ku 0 - 150 e.g. 105, 110, 115, __, __, __, 135, __, __, 150 Kopela, uqedele futhi uchaze amaphethini lapho izimo zeza- khiwo zisetshenziswe ukwakha amaqoqo. Kodwa amaqoqo ezimo ayaphindwa ngendlela efanayo. Isilinganiso isikhathi Yisho isikhathi sewashi lezinti ngamahora, nangohhafu CAPS 595

Izibalo IBANGA 1-3 Ibanga-2 Ithemu 2: Ukuhlola 2 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi lwezi- Bala uqhubeka ngo 3,4 nobudlelwane bazo nombolo Ukuxazulula Xazulula uchaze indlela oxazulile ngayo inkinga emayelana nokuhlukanisa izinkinga ngokulinganayo okuholela ekutholakaleni kwamaqhezu. Amaqhezu Ukubona nokusebenzisa uhhafu, ingxenye eyodwa kokuthathu, ingxenye eyodwa kokune, ingxenye eyodwa kokuhlanu, esimweni esejwayelekile Ukubona amaqhezu entweni esamdwebo Bhala amaqhezu asho uhhafu, nengxenye eyodwa kokuthathu Ukubala Ukuhlanganisa kufinyelela kokungama-50 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala umusho wezinombolo usebenzisa +, = Ukususa kufinyelela kuma-50 Usebenzise loku okulandelayo • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala umusho wezinombolo usebenzisa -, = Amaphethini, ubudlelwane Amaphethini Qedela ukulandelana kwezinombolo ngendlela efanele eziphakathi kuka 0 ne ne- aljibhra ezinombolo 150 • ukubala ngakunye • ukubala ngakune isib.4, 8, 12 __, __, 24, __, 32, __, __, __, 48 • ukubala ngantathu isib. 3, 6, 9, __, __,21, __, __,__, 33, 36. Isilinganiso Isisindo Qagela, kala, qhathanisa,hlela, ubhale isisindo usebenzisa ukukala okungahl- elekile nesikalo sokuzimelela isib. Amabhuloki, azitini njll. Landelanisa izinto ngesisindo samakiligram ngokulandelana 596 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga- 2 Ithemu yesi- 3: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi Bala ufinyelele e-180 lezithombe zezinto ezingamaqoqo nobudlelwane bazo lwezinombolo Qhathanisa uhlele izinombolo kufinyelela ema- 75 Ukufunda nokubhala uphawu lenombolo ukufinyelela e 180 Bala uqhubeka noma uhlehla ngo 2, 10, 5phakathi kuka 0 & 180 Hlakaza izinombolo ezihamba ngambili kufinyelele ema-75 ngamashumi nangakunye isib. 48 = 40 + 8 Ukuxazulula Xazulula izinkinga zezibalo zamagama esimweni esejwayelekile kungena izinkinga ukuhlanganisa ngokuphindelela kufinyelela kuma-40 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bese uchaza izixazululo zakho ezinkingeni ukubala Phindaphinda izinombolo 1 - 10 ngo 5, 4 Usebenzisa loku okulandelayo: • Izinto eziphathekayo • imidwebo • umugqa wezinombolo bhala umusho wezinombolo usebenzisa x, = Amaphethini, ubudlelwane Amaphethini Qedela ukulandelana kwezinombolo kwa: ne- aljibhra ezinombolo • ukubala uqhubeka noma uhlehla ngakunye phakathi kuka 0 & 180 isib. 180, 170, 160, __, __, 120, __,__ 90, • ukubala ngakubili isib. 150, 152, 154, __, 156, __, 160, __, __, 166 • ukubala ngakuhlanu kusuka ku 0 - 150 e.g.120, 125, 130, 135, __, __, __, 155, __, __, 170, __, 180 Indawo nezimo zezakhiwo indawo Sebenzisa ulimi olufanele ukuchaza indawo kulandelwa izinkomba ukuzungeza ekilasini CAPS 597

Izibalo IBANGA 1-3 IBanga-2 Ithemu yesi- 3: ukuhlola kwesi- 2 Ulwazi lwezibalo Isihloko Izinqumo Izinombolo, izimpawu nobudlelwane Ulwazi Bala uqhubeke ngoku-4,3 bazo lwezinombolo Ukuxazulula Xazulula uchaze izixazululo ezinkingeni ezifaka ukulingana izinkinga nokuhlukaniselana. Amaqhezu Ukubona usebenzise uhhafu,okokuthathu,okokune,okokuhlanu esimweni esejwayelekile Ukubona amaqhezu mudwebeni Bhala amaqhezu ngendlela yengxenye yokukodwa kokubili, yokukodwa kokuthathu njll Amaphethini,ubudlelwane ne- Amaphethini Qedela ukulandelana kwezinombolo 0 & 180 aljibhra ezinombolo • ukubala ngakunye • ukubala ngakubili isib. 104,108, 112 __, __, 124, __, 132, __, __, __, 148 • ukubala ngakuthathu isib. 103, 106, 109, __, __,121, __, __,__, 133, 136. Amaphethini Kopela, uqhubeke nokuchaza amaphethini okusejiyometri lapho okusazibalo kunezimo ezifanayo, kodwa inombolo yesimo ngasinye ikhuphuka mdwebo noma incipha ngendlela ekahle Indawo nezimo zezakhiwo indawo Hlanganisa ukubonakala kwezinto ezifanayo 2-D shapes Bona usho Indilinga, unxantathu, isikwele, unxantathu nonxande Hlela izakhiwo ngokuba nezinhlangothi eziqondile neziyindilinga Isilinganiso Isisindo Qagela, kala, qhathanisa, hlela, ubhale isilinganiso sezitsha usebenzisa izikalo ezingahlelekile isib. Izipuni, nezinkomishi Isikhathi Funda iwashi lezinti ngamahora, isigamu, nengxenye yehora Sebenzisa ikhalenda ukubala ubude besikhathi bezinsuku namasonto Ukuqokelela nokuhlelwa kolwazi Ukuqokelela Akha igrafu yezithombe ephepheni elinezikwele uma usunikezwe lwezibalo okuqokeleliwe 598 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga-2 Ithemu yesi- 3: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi Counts pictures of grouped objects up to 200 nobudlelwane bazo lwezinombolo Orders and compares numbers to 99 Ukuxazulula Xazulula izinkinga zezibalo zamagama esimweni esejwayelekile izinkinga kungene ukuhlukanisa namaqoqo kufinyelela ku 99 nezimpendulo eziba nezinsalela uma usebenzisa loku okulandelayo usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bese uchaza izixazululo zakho ezinkingeni Imali Ukubona imali yase South Africa 5c, 10c, 20, 50c, R1, R2; R5 neyamaphepha R10, R20, R50 Xazulula inkinga yezimali efaka izimpendulo noshintshi kufinyelela ku R99 namasenti afinyelela ku 95c Amaphethini, ubudlelwane ne- Amaphethini Qedela ukulandelana kwezinombolo ubala uqhubeka noma uhlehla aljibhra ezinombolo • ngakunye phakathi ku 0 no 200 • ngamashumi phakathi ku 0 no 200 isib. 130, 140, 150, -__, ___, ___, __, 200 Indawo nezimo zezakhiwo 2-D Ukubona usho • indilinga • unxantathu • isikwele • unxande hlela ngokwakheka kwamacala ayindilinga noma aqondile Isilinganiso Isikhathi Sebenzisa iwashi lezinti ukubala ubude besikhathi esedlule ngamahora, isigamu, nengxenye yehora CAPS 599

Izibalo IBANGA 1-3 IBanga-2 Ithemu yesi- 4: Ukuhlola kwesi- 2 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi Ukubala kuqhubeka noma kuhlehla ngo 2, 5 to 200 nobudlelwane bazo lwezinombolo Ukufunda nokubhala izinombolo kufinyelela ema-200 Izibalo Bhala ukuhlanganisa kufinyelele kuma 99 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala imisho yezibalo usebenzisa +,= Bhala ukususa kusukela kunoma iyiphi inombolo kufinyelele ema- 99 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebophansi • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala imisho yezibalo usebenzisa -,= Amaphethini, ubudlelwane ne- Amaphethini Qedela ukulandelana kwezinombolo eziphakati kuka 0 & 200 aljibhra ezinombolo • ukubala ngakubili kusuka ku- 160, 162, 164, __, 166, __, 170, __, __, 176, __, 180 • ukubala ngakuhlanu kusuka ku 0 - 200 e.g.160, 165, 170, __, __, __, 190__, 200 Ukuqokelela nokuhlelwa kolwazi Ukuqokelela Ukuphendula imibuzo emayelana negrafu yezithombe lwezibalo 600 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga-2 Ithemu yesi- 4: Ukuhlola kwesi-3 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi Bala uqhubeke ngaku-4,3 nobudlelwane bazo lwezinombolo Ukuxazulula Ukuxazulula izinkinga zezibalo zamagama esimweni esejwayelekile izinkinga kufakwa ukuhlanganisa ngokuphindaphinda ukoholela ekuphandaphindeni okwakha izimpendulo ezifinyelela ema- 50 Bhala ukuhlanganisa kufinyelele kuma 99 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili uchaze indlela oxazulule ngayo inkinga Ukubala Ukuphindaphinda izinombolo 1 - 10 ngo 3 usebenzise loku okulandelayo: • Izinto eziphathekayo • imidwebo • ukwakha nokubhidlisa • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili bhala imisho yezibalo usebenzisa x,= Amaphethini, ubudlelwane ne- Amaphethini Qedela ukulandelana kwezinombolo aljibhra ezinombolo • ukubala ngakunye • ukubala uhlehla ngakune isib.. 48,44, 40 __, __, 28, __, __, 16, __, __, 0 • ukubala uhlehla ngakutathu isib. 36, 33, 30, __, __, 21, 18, __,__, 9, __, __, 0. Indawo nezimo zezakhiwo 3-D Ukubona usho • izimo ezingamabhola (spheres) • izimo ezingamabhokisi (prisms) • izimbulunga (cylinders) Sorts objects into those that roll and those that slide Izinhlangothi Ukubona udwebe umugqa wokulinganisa izinhlangothi ezilinganayo ubona izinhlangothi ezilinganayo nezifana ns kokusejiyometri nezifana ezinhlangothimbili Isilinganiso Umthamo Landelila ngendlela izinto ezinesisindo esilinganiswe ngamalitha Funda umthamo ngamalitha esithombeni sojeke bokulinganisa CAPS 601

Izibalo IBANGA 1-3 IBanga-2 Ithemu yoku- 1: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Ulwazi Hlela ngamaqoqo ezinto bese ubala ugcine ezintweni ezingama-200 lwezinombolo Izimpawu nobudlelwano Qhathanisa bese ulandelanisa izinombolo eziphelele ufike kuma-99 bazo Funda ubhale izimpawu zezinombolo kusuka ku-okuya kuma- 500 Hlakaza izinombolo ezihamba ngazimbili ufike kuma-99 ngamashumi nangakunye isib. 78 = 70 + 8 Ukuxazulula Xazulula izinkinga zamagama esimweni esijwayelekile ufaka ukuhlanganisa, izinkinga ukususa nezimpendulo zifike kuma-99 usebenzise okukodwa okulandelayo; • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili • ukusondezela eshumini 10 • bese uchaza ukuthi uyixazulule kanjani lezozinkinga Imali Xazulula izinkinga zezimali ufake isamba noshintshi wamarandi namasenti ukubala Yenza izibalo zokuhlanganisa uze ufike ema-99 usebenzisa okukodwa okulandalelayo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili • ukusondezela emashumini • Bhala umusho wezinombolo usebenzisa +, = Yenza izibalo zokususa uze ufike ema-99 usebenzisa okukodwa okulandelayo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili • ukusondezela emashumini • Bhala umusho wezinombolo usebenzisa + = Amaphethini Izinombolo Qedela ukubala izinombolo ngokulandelana ubala uya phambili nasemuva ubudlelwane zamaphethini kanje; Ne-algebra • ngakunye phakathi kuka-0 no 200 isib. 199,1 98, 197, __, __, __, 13, __, 191, 190 • ngamashumi phakathi kuka 0 no 200 isib. 110, 120, 130, __, __, __, 170__, __, 200 • ngamakhulu phakathi kuka 0 no 500 isib. 100, 200, 300, __, __, • ngakuhlanu phakathi kuka 0 no 200 isib. 150, 155, 160, __, __, __, 180, __, __, 195, __ • ngakubili phakathi kuka 0 no 200 isib. 180,182, 184, __, __, 190, _, __, __, ___, 200 Indawo nezimo Unhlangothi- Zibone uzisho ngamagama izimo mbili 2-D indilinga,unxantathu isikwele kanye nonxande Hlela izimo ezinamacala aqondile nalezo ezinamacala ayizindilinga Isilinganiso Isikhathi Funda izinsuku ekhalendeni Batshele isikhathi ewashini lezinti ngamahora,uhhafu wehora nekota yehora Umthamo Qagela,ulinganise,uqathanise ulandelanise bese urekhoda umthamo wesitsha ngokusebenzisa izikali ezingalihlelekile isib.izipuni nezinkomishi. Hlela nsukuzonke izinto ezinomthamo obhalwe kuzo amamilimitha 602 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga- 3 Ithemu yesi-2: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi Bala izithombe zamaqoqo ezinto eziphathekayo (isib.ngamaqoqo 10s, 25s, nobudlelwano lwezinombolo 50s or 100s) uze ufike ku-500 Bazo Hlela uqhathanise izinombolo uze ufike ema-500 Funda ubhale izinombolo kusuka 0 - 1 000 Ukuxazulula Xazulula izinkinga eziphathekayo ufake ukwabelana kwamaqoqo izinkinga alinganayo kwinombolo ephelele uze ufike ema-75 usebenzisa okukodwa kokulandelayo • yakha ubuye uhlakaze izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa kabili • ukusondezela eshumini-10 Bese uchaza ukuthi uyixazulule kanjani leyonkinga ukubala Hlukanisa izinombolo kuya ku 50 nga 2, 5, 10 Amaphethini Amaphathini Qedela ukubala lezizinombolo ngokulandelana bese ubala uya phambili ubudlelwane ezinombolo nasemuva Ne-algebra • ngakunye ngakathi kuka- 0 no 500 isib. 389, 399, 400,, __, __, __, 404, __, ___, ___, 40 • ngamashumi phakathi kuka- 0 no 500 no 300, 310, 320, __, __, 350, __, __.370, __, __, 400 • amakhulu phakathi kuka- 0 no 1 000 isib. 1000, 900, 800, __, __, 500, __, __.200, __, 0 Indawo nezimo Unhlangothi- Zibone usho amagama azo ntathu 3-D • izimo eziyibhola (spheres) • izimo eziyibhokisi (prisms) • amasilinda Hlela izinto eziphathekayo kulezo ezimagwincigwinci nakulezo eziyizicaba Izilinganiso Ubude Qagela,kala, landelanisa bese uqhathanisa ubude nobubanzi nokuphakama usebenzisa izikali ezingahlelekile Ukuqagela, ukukala,ukuhlela nokuqhathanisa ubude usebenzisa amamitha CAPS 603

Izibalo IBANGA 1-3 IBanga- 3 Ithemu yesi-2: Ukuhlola kwesi-2 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo izimpawu Ulwazi Ukubala uye phambili nasemuva nga- 2s, 4s noma 3s kuya ku 500 nobudlelwano lwezinombolo Bazo Ukubala Yenza ukuhlanganisa kufike ku 400 usebenzisa okukodwa okulandelayo • ukwakha nokuhlakaza izinombolo • Umugqa wezinombolo • Ukuphinda ngakubili nokuhlukanisa ngakubili • Ukusondezela eshumini 10 Bhala umusho wezinombolo usebenzise +, = Yenza izibalo zokususa usuka ema- 400 noma okungaphansi usebenzisa okukodwa okulandelayo • Ukwakha nokuhlakaza izinombolo • Umugqa wezinombolo • Ukuphinda ngakubili nokuhlukanisa kabili • Ukusodezela eshumini 10 Bhala umusho wezinombolo usebenzisa _, = Amaphethini, Amamphethini Qedela lezi zinombolo ngokulandelana nobudlelwane ne-aljebra ezinombolo • Ukubala ngakubili phakathi kuka -0 no 500 isib. 450, 448, 446, 444, __, __, 438, __, __, 432. • Ukubala ngakune phakathi kuka-0 no 500 isib. 404, 408, 412 __, __, 424, __, 432, __, __, __, 448 • Ukubala ngakuthathu phakathi kuka- 0 no 500 isib. 403,406, 409, __, __,421, __, __,__, 433, 436. Amaphethini Kopisha,uqhubeke bese uchaza amaphethini lapho izimo ezehlukene okusazibalo zisetshenziswa khona ukwenza amaqoqo,kodwa izimo zamaqoqo mdwebo ziyaphindeka ngokufanayo. 604 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga- 3 Ithemu yesi-2: Ukuhlola kwesi-3 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Uwazi Bala uye phambili ngaku- 5s, 50s, 100s naphakathi kuka 0 no 500 lwezinombolo Nobudlelwano Hlakaza izinombolo ezinezinombolo ezintathu ngamakhulu,ngamashumi Bazo nangakunye isib. 247 = 200 + 40 + 7 Ukuxazulula Xazulula bese uchaza umphumela wenkinga efaka ukwabelana izinombolo ngokulinangana okuholela ezibalweni zamaqhezu Izibalo Ukubona bese usebenzisa ohhafu, amakota,ingxenye eyodwa zamaqhezu kweziyisishagalombili,ingxenye eyodwa kweziyisithupha, ingxenye eyodwa kokuthathu, ingxenye eyodwa kwezinhlanu esimweni esijwayelekile, Bona uthole amaqhezu esimweni somdwebo Bhala amaqhezu esimweni sika hhafu,izingxenye ezimbili kokuthathu njll etc Amaphethini, Amaphethini Qedela izinombolo ngokulandelana nobudlelwane ezinombolo Ne-algebra • Bala ngakuhlanu phakathi kuka-0 - 500 isib. 105, 110, 115, __, __, __, 135, __, __, 150 • Bala ngamashumi amahlanu phakathi kuka-0 - 1000 isib. 550, 600, 650, __, __, 800, __, __, __, 1 000, Indawo nezimo Isikhundla Landela izinkomba unyakaze ujikeleze isikole nenkomba Nika izinkomba zokunyakaza ujikeleza isikole Isilinganiso Isisindo Qagela, kala.qhathanisa uhlele bese urekhoda isisindo ngokusebenzisa isikali esihlelekile isib.amabhuloki.izitini njll. Hlela izinto eziphathekayo ezibhalwe ama-gremu. CAPS 605

Izibalo IBANGA 1-3 IBanga 3 Ithemu yesi-3: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, izimpawu Ulwazi Bala ufike kuma- 750 izithombe ezihlelwe ngamaqoqo (isib: hlela ngamaqoqo nobudlelwano bazo lwezinombolo angama- 20, 25,50 noma nge- 100) Qhathanisa bese ulandelanisa izinombolo uze ufike kuma- 750 Funda ubhale izimpawu zezinombolo uze ufike ku- 100 Ukuxazulula Xazulula izinkinga zamagama esimweni esijwayelekile okufaka ukuphindaphinda izinkinga kuze kufike kuma- 75 usebenzisa okukodwa kwalokhu: • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo number lines • ukuphinda kabili nokuhlukanisa phakathi • ukusondezela emashumini bese uchaza ukuthi uyicazulule kanjani lezo zinkinga Ukubala Ungaphindaphinda oku-2, 5, 10 ufike kusamba esingama- 99 Usebenzisa loku okulandelayo • ama-apharatha • ukudweba • umugqa wezinombolo bhala umugqa wezinombolo usebenzisa u-X, = Amaphethini, Izinombolo Qedela izinamba ngokulandelana ubala uya phambili nasemuva. ubudlelwane ne- zamaphethini Aljebra • ngakunye phakathi kuka- 0 no 750 isib: 665, 666, 667, __, __, __, 671, __, ___, ___, 675__, __, 678 • ngamashumi phakathi kuka- ono 751 isib: 650, 660, 670, __, __, 700, __, __.730, __, __, 760 • ngamakhulu phakathi kuka- 0 no 1000 isib: 0, 100, 200, __, __, 500, __, __.800, __, 1 000 606 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga- 3 Ithemu yesi-3: Ukuhlola kwesi-2 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Ulwazi Bala uye phambili nasemuva koku- 2s, 20s, 4s, 3s uze ufike kuma- 750 izimpawu lwezinombolo nobudlelwane Hlakaza izinombolo ezinhlangothi ntathu (3-D) ukufika kuma-750 emakhulwini, bazo emashumini nokukodwa isib: 648 = 600 + 40 + 8 Ukubala Ungaphindaphinda ngoku - 3, 4 ufike kusamba esingama 99 usebenzisa okukodwa kwalokhu: • ama-apharathas • ukudweba • umugqa wezinombolo • ukuphinda kabili bhala umugqa wezinombolo usebenzisa u-X, = Amaphethini, Izinombolo Qedela izinombolo ngokulandelana ubudlelwane ne- zamaphethini aljebra • bala ngakubili phakathi kuka- 0 naa- 750 isib: 750, 749, 748, __, __, 445, __, __, 742. • bala ngamshumi ababili phakathi kuka - 0 ne - 1000 isib: 800, 820, 840, 860, __, __, 920, __, __, 980 • bala ngokune phakathi kuka- 0 nama- 750 isib: 704, 708, 712 __, __, 724, __, 732, __, __, __, 748 • bala ngokuthathu phakathi kuka - 0 nama- 750 isib:. 630,633, 639, 641, __, __,650, __, __,__, 661 Amaphethini Kopela, andise aphinde achaze amaphethini ejiyometri ukuthi kwenzeke izimo okusazibalo ezifanayo, kodwa izinombolo zohlobo lwezimo luyandiswa noma luncishiswe mdwebo ngendlela ejwayelekile. Indawo nezimo Unhlangothi Uwabone namagama mbili 2-D Indilinga, unxantathu, isikwele kanye nonxande Dweba indilinga, isikwele, unxande, unxantathu Ukuqokelelwa Ulwazi akha ibagrafu ephepheni elinezikwele uma unikwe ukuqokelewa nokuhlelwa kolwazi nokuhlelwa lwezinombolo kolwazi lwezibalo CAPS 607

Izibalo IBANGA 1-3 IBanga-3 Ithemu yesi-3: Ukuhlola kwesi-3 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Ulwazi Bala uye phambili ku- 5s, 50s, 25s ufike kuma - 750 izimpawu lwezinombolo nobudlelwane bazo Ukuxazulula Xazulula uphinde uchaze isombululo sezinkinga ezibandakanya ukwahlukaniselana izinkinga okulinganayo okuholela kumaqhezu Amaqhezu Ukubona nokuhlukanisa izingxenye ezimbili ezahlukanisiwe, ikota, okuyisishiyagalombili, okuthathu, okuyisithupha, okuyisihlanu Chaza indlela yemidwebo yamaqhezu Khomba ukuthi ukuhlukana phakathi kuphelele Bhala amaqhezu ngendlela eyodwa ehlukana phakathi, oku-1 okuhlukaniswe kathathu njll. Amaphethini, Izinombolo Qedela izinombolo ngokulandelana Completes number sequences ubudlelwane ne- zamaphethini aljebra • bala ngakuhlanu phakathi kuka - 0 nama- 750 isib: 705, 710, 715, __, __, __, 735, __, __, 750 • bala ngamashumi amahlanu phakathi kuka- 0 kuya kwi -1000 isib: 1 000, 950, 800, __, __, 650, __, __, __, 450, • bala ngamashumi amabili nanhlanu phakathi kuka- 0 kuya kwi-1000 isib: 525, 550, 575, __, __, 650, __, __, __, 750 Indawo nezimo Isikhundla Landela unkomba unyakaze usuka endaweni uya kwenye indawo ekubalazwe elingahlelekile Isilinganiso Isikhathi Shono isikhathi esikuwashi lezinombolo ngamahora nemizuzu Sebenzisa ikhalenda ukubala ubude besikhathi ezinsukwini nasemavikini. 608 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga lesi-3 Ithemu yesi-4: Ukuhlola koku-1 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Ulwazi Bala izithombe zezinto eziliqembu ukufika ku- 1 000 izimpawu lwezinombolo Hlela uphinde uqhathanise izinombolo kuya ku- 999 nobudlelwane Ulwazi Xazulula izinkinga zamagama esimweni esijwayelekile okufaka ukuphindaphinda kuze bazo lwezinombolo kufike kuma- 75 usebenzisa okukodwa kwalokhu: • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo number lines • ukuphinda kabili nokuhlukanisa phakathi • ukusondezela emashumini bese uchaza ukuthi uzicazulule kanjani lezo zinkinga Ukubala Hlukanisa izinombolo kuya kuma- 9 ngo- 2, 4, 5, 10, 3 Imali Money Xazulula inking yezimali ufake isamba noshintshi wamarandi noma amasenti. Amaphethini, Izinombolo Qedela izinamba ngokulandelana ubala uya phambili nasemuva ubudlelwane ne- zamaphethini • kokukodwa okuphakathi kuka - 0 ne - 1000 isib: 889, 890, 891,, __, __, __, aljebra 895 __, ___, ___, 889__, __, 892 • kokuyishumu okuphakathi kuka - 0 ne 1000 isib: 1000, 990, 980 __, __, 950, __, __.920, __, __, 890 Isilinganiso Isikhathi Sebenzisa isikhathi ukubala ubude besikhathi ngamahora namaminithi CAPS 609

Izibalo IBANGA 1-3 IBanga lesi- 3 Ithemu yesi-4: Ukuhlola kwesi-2 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Ulwazi Bala uye phambili nasemuva koku-2s, 4s, 3s uze ufike ku- 1 000 izimpawu lwezinombolo nobudlelwane Funda uphinde ubhale uphawu lwezinombolo ukufinyelela e- 1 000 bazo Ukubala Yenza ukuhlanganisa kusukela ema- 99 nangaphansi usebenzisa okukodwa kwalokhu okulandelayo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo number lines • ukuphinda kabili nokuhlukanisa phakathi • ukusondezela emashumini bhala umugqa wezinombolo usebenzisa u- +, =, Ingabe ukukhipha okukwezinye izinombolo eziyi- 999 noma zingaphansi zisebenzisa lokhu: • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo number lines • ukuphinda kabili nokuhlukanisa phakathi • ukusondezela emashumini bhala umugqa wezinombolo usebenzisa u-X, = Amaphethini, Izinombolo Qedela izinamba ngokulandelana ubudlelwane ne- zamaphethini aljebra • ubala ngakubili phakathi kuka- 0 ne 1000 isib: 1000, 998, 996, __, __, 990, __, __, 984 • ubala ngakune phakathi kuka -0 ne 1000 isib: 840, 844, 852 __, __, 864, __, 872, __, __, __, 894 • bala ngakuthathu phakathi kuka- 0 ne - 1 000 isib: 960,963, 966, 969, 971, __, __,980, __, __,__, 691 Indawo nezimo Okufana nse Buka bese udweba ulayini wokufana nse nxazombili kunhlangothi mbili izimo nxazombili ezisazibalo mdwebo nokungezona ezisazibalo mdwebo Ukuqokelelwa Ulwazi Phendula imibuzo ngolwazi kugrafu yezithombe nokuhlelwa kolwazi lwezibalo 610 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola

Izibalo IBANGA 1-3 IBanga- 3 Ithemu 4: Ukuhlola 3 Ulwazi lwezibalo Isihloko Uhla lwezinto ezihlolwayo Izinombolo, Ulwazi Bala uye phambili koku- 5s, 50s, 25s phakathi kuka - 0 kanye ne - 1 000 izimpawu lwezinombolo nobudlelwane bazo Solve Xazulula izinkinga zamagama esimweni esijwayelekile okufaka ukuphindaphinda kuze Problems kufike kuma- 50 usebenzisa okukodwa kwalokhu: • ama-apharathasi • imidwebo • ukwakha nokuhlakaza izinombolo • umugqa wezinombolo • ukuphinda kabili nokuhlukanisa phakathi bese uchaza ukuthi uzicazulule kanjani lezo zinkinga Ukubala Ungaphindaphinda ngoku- 3 ukufika kuma- 99 usebenzisa okukodwa kwalokhu • ama-apharathas • ukudweba • umugqa wezinombolo • ukuphinda kabili bhala umugqa wezinombolo usebenzisa u-X, = Amaphethini, Izinombolo Qedela izinamba ngokulandelana ubudlelwane ne- zamaphethini aljebra • bala ngokuhlanu phakathi kuka - 0 ne- 1000 isib: 1 000, 995, 990, 985, __, __, __, 965, __, __, 950 • bala ngamashumi amahlanu phakathi kuka- 0 ne- 1000 isib: 600, 650, 700, __, __, 850, __, __, __, • bala ngamashumi amabili nanhlanu phakathi kuka- 0 ne- 1000 isib: 1 000, 975, 950, __, __, 875, __, __, __, 775 Indawo nezimo Inhlangothi Uwabone namagama ntathu (3-D) • izimo ezingamabhola (spheres) • izimo eziyibhokisi (prisms) • amasilinda • ipyramidi • ama-cone Ukuhlela izinto eziphathekayo kulezo ezimagwincigwinci nakulezo eziyisicaba Chaza izimo ezinhlangothi mbili (2-D) ezenza isicaba kwizomo ezinhlangothi ntathu (3-D) Isilinganiso Umthamo Funda umthamo wamalitha ezithombeni ezilinganisa Funda umthamo kumamililitha ezithombeni ezilinganisa ijagi CAPS 611

Izibalo IBANGA 1-3 612 Isitatimende Senqubomgomo Yohlelo Lwezifundo Nokuhlola