CAPS MATHS ISIXHOSA GR R FS

National Curriculum Statement (NCS) ISIXHOSA MATHEMATICS Curriculum and Assessment Policy Statement Foundation Phase Grade R    

INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA IBANGA LABAQALAYO (R) MATHEMATIKA CAPS

MATHEMATIKA IBANGA LABAQALAYO (R) 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: 978-1-4315-0438-1 Design and Layout by: Ndabase Printing Solution Printed by: Government Printing Works INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) 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

MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) IZIQULATHO ISAHLUKO SOKU- 1: INTSHAYELELO NEMVELAPHI............................................................................ 3 1.1 IMvelaphi ....................................................................................................................................................... 3 1.2 AmaGqabantshintshi....................................................................................................................................... 3 1.3 IiNjongo eziPhangaleleyo zeKharityhulam yoMzantsi Afrika. ..................................................................... 4 1.4 UKwabiwa kweXesha................................................................................................................................. 6 1.4.1 IsiGaba esisisiSeko. ................................................................................................................................ 6 1.4.2 IsiGaba esiPhakathi................................................................................................................................. 6 1.4.3 IsiGaba esiPhezulu.................................................................................................................................. 7 1.4.4 IBanga 10 - 12......................................................................................................................................... 7 ISAHLUKO SESI- 2: INKCAZELO, IINJONGO, IZAKHONO NOMXHOLO.............................................. 8 2.1 Intshayelelo...................................................................................................................................................... 8 2.2 Yintoni iMathematika?..................................................................................................................................... 8 2.3 Iinjongo ezingundoqo ..................................................................................................................................... 8 2.4 Izakhono ezingundoqo ................................................................................................................................... 9 2.5 Iinkalo zemixholo ekugqalwe kuyo ............................................................................................................... 9 2.6 Ulwabiwo lweenkalo zemixholo.................................................................................................................... 11 2.7 IMathematika kwisiGaba esisisiSeko........................................................................................................... 11 2.7.1.. Izikhokelo zolawulo lweklasi.................................................................................................................. 12 2.7.2.. Abafundi abaneengxaki zokufunda kwiMathematika............................................................................. 13 2.7.3.. Imisebenzi yokubala ngentloko............................................................................................................. 13 2.8 IBanga labaQalayo(R).................................................................................................................................... 14 2.9 Izixhobo ezicetyiswayo: igumbi lesiGaba esisisiSeko............................................................................... 17 ISAHLUKO SESI- 3: INKCAZELO YOMXHOLO .................................................................................... 18 3.1 Intshayelelo.................................................................................................................................................... 18 3.2 Inkcazelo yomxholo ukubonisa inkqubela-phambili.................................................................................. 18 • Amanani, ii-opareyshini nolwalamamo........................................................................................................ 19 • Iipateni, isiphumo sentsebenziswamo yamanani / ifankshini ne-aljibra...................................................... 26 • Isithuba nemilo (ijiyometri).......................................................................................................................... 27 • Umlinganiselo. ............................................................................................................................................ 30 • Indlela yokusebenza ngolwazi oluqokelelweyo. ......................................................................................... 35 CAPS 1

MATHEMATIKA IBANGA LABAQALAYO (R) 3.3 Inkcazelo ngomxholo. ................................................................................................................................... 37 3.4 Ukulandelelanisa nesantya somxholo ........................................................................................................ 38 3.5 Amanqaku angcaciso.................................................................................................................................... 60 ISAHLUKO 4: UHLOLO......................................................................................................................... 262 4.1 Intshayelelo ................................................................................................................................................. 262 4.2 Ukuhlola okungekho seSikweni okanye kwemihla ngemihla ................................................................. 262 4.3 Ukuhlola okuSesikweni .............................................................................................................................. 262 4.4 Inkqubo yokuHlola okuSesikweni.............................................................................................................. 263 4.5 UkuRekhodisha nokunika Ingxelo ngomsebenzi. .................................................................................... 263 4.6 Ulwazi gabalala. ........................................................................................................................................... 264 4.7 Imizekelo yeetshekilisti zohlolo olusesikweni ezicetyiswayo ................................................................ 264 2 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) ISAHLUKO SOKU-1: INTSHAYELELO NEMVELAPHI 1.1 IMvelaphi INkcazelo yeKharityhulam yeSizwe yeBanga R - 12 (NKS) icacisa ipolisi yekharityhulam nokuhlola ezikolweni. Ukuphucula ukusetyenziswa kwayo, iNkcazelo yeKharityhulam yeSizwe ihlaziyiwe, yaye uhlaziyo luya kuqala ukusebenza ngeyoMqungu/ngoJanyuwari 2012. Isifundo ngasinye senzelwe uxwebhu olunye lwePolisi yeKharityhulam nokuHlola endaweni yala maxwebhu madala angala: INkcazelo yeKharityhulam yeSizwe, iziKhokelo zeNkqubo yokuFunda kunye neziKhokelo zokuHlola zesiFundo kwiBanga R - 12. 1.2 AmaGqabantshintshi (a) INkcazelo yeKharityhulam yeSizwe (NKS) yeBanga R - 12 (EyoMqungu/Janyuwari 2012) imele inkcazelo yepolisi yokufunda nokufundisa kwizikolo zoMzantsi Afrika yaye iquka oku kulandelayo: (i) INkcazelo yePolisi yeSizwe yeKharityhulam nokuHlola yesifundo ngasinye kwezo zifundo zivunyiweyo zesikolo; (ii) Uxwebhu lwepolisi oluthi, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R - 12.; kunye (iii) Noxwebhu lwepolisi oluthi, National Protocol for Assessment Grades R - 12 (EyoMqungu/Janyuwari 2010). (b) Uxwebhu oluthi, National Curriculum Statement Grades R - 12 (eyoMqungu/Janyuwari 2012) lungena endaweni yala maxwebhu eNkcazelo yeKharityhulam yeSizwe mabini alandelayo: (i) iRevised National Curriculum Statement Grades R - 9, Government Gazette No. 23406 of 31 May 2002, kunye (ii) neNational Curriculum Statement Grade 10 - 12 Government Gazettes, No 25545 of 6 October 2003 and No. 27594 of 17 May 2005. (c) Amaxwebhu enkcazelo yekharityhulam yesizwe ekuthethwe ngawo kwimihlathana (a) no(b) aquka la maxwebhu epolisi alandelayo, aza kuthi aye eyekiswa ngokuyekiswa, engenelewa yiNational Curriculum Statement Grades R - 12 (eyoMqungu/Janyuwari 2012) ngo2012 - 2014: (i) INkcazelo yeKharityhulam yeSizwe yezifundo ngezifundo, isiKhokelo seNkqubo yokuFundisa kunye nesiKhokelo sokuHlola sesiFundo yeBanga R - 9 neyeBanga 10 - 12; (ii) Uxwebhu lwepolisi oluthi, National Policy on assessment and qualifications for schools in the General Education and Training Band, olubhengezwe kwiGovernment Notice No. 124 ekwiGovernment Gazette No. 29626 of 12 February 2007; (iii) Uxwebhu lwepolisi oluthi, the National Senior Certificate: A qualification at Level 4 on the National Qualifications Framework (NQF), olubhengezwe kwiGovernment Gazette No.27819 of 20 July 2005; CAPS 3

MATHEMATIKA IBANGA LABAQALAYO (R) (iv) Uxwebhu lwepolisi oluthi, An addendum to the policy document, the National Senior Certificate: A qualification at Level 4 on the National Qualifications Framework (NQF), regarding learners with special needs, olupapashwe kwiGovernment Gazette, No.29466 of 11 December 2006, lufakwe kuxwebhu lwepolisi oluthi, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R - 12; kunye (v) Uxwebhu lwepolisi oluthi, An addendum to the policy document, the National Senior Certificate: A qualification at Level 4 on the National Qualifications Framework (NQF), regarding the National Protocol for Assessment (Grades R - 12), olubhengezwe kwiGovernment Notice No.1267 in Government Gazette No. 29467 of 11 December 2006. (d) Uxwebhu lwepolisi oluthi, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R - 12; kunye namacandelo akwiPolisi yeKharityhulam nokuHlola njengoko ebonisiwe kwisahluko sesi-2, 3 nesesi-4 solu xwebhu aqulethe izithethe nemigangatho yeNkcazelo yeKharityhulam yeSizwe yeBanga R - 12. Ngoko ke, olu xwebhu luya kuthi, ngokwecandelo 6A leSouth African Schools Act (uMthetho oLawula iZikolo zaseMzantsi Afrika), ka1996 (uMthetho wama-84 ka1996,) lwenze isiseko sokuxhobisa umPhathiswa weMfundo esisisiSeko ukuba akwazi ukubeka awona manqanaba aphantsi eziphumo nemigangatho, ngokunjalo neenkqubo nemigaqo yokuhlola inkqubela phambili yabafundi, manqanaba lawo za kusebenza kwizikolo zikaRhulumente nezabucala. 1.3 IiNjongo eziPhangaleleyo zeKharityhulam yoMzantsi Afrika (a) INkcazelo yeKharityhulam yeSizwe yeBanga R - 12 inika isikhokelo kulwazi, izakhono nezithethe ezinokufundwa ezikolweni zaseMzantsi Afrika. Le kharityhulam ijonge ukuqinisekisa ukuba abafundi bafumana ulwazi nezakhono ngeendlela ezihambelana nobomi babo bemihla ngemihla. Kungoko ke le kharityhulam ikhuthaza uluvo lokusebenzisa kakhulu iimeko zalapha, kodwa ibe ikwayise iso nemiba ebalulekileyo yehlabathi jikelele. (b) INkcazelo yeKharityhulam yeSizwe yeBanga R - 12 yenza oku kulandelayo: -- Ixhobisa abafundi ngolwazi, izakhono nezithethe eziya kubanceda ukuba bakwazi ukuzimela nokuthabatha inxaxheba ekuhlaleni njengabemi belizwe elikhululekileyo; nokuba bavela kweyiphi imo yezentlalo, uhlanga, isini, bekhangeleka njani ngokomzimba okanye bekuliphi inqanaba lengqiqo; -- Ivulela abafundi amathuba okuya kwimfundo ephakamileyo; -- Incedisa abafundi ukuba bakwazi ukuphuma kumaziko emfundo baye kumaziko omsebenzi; yaye -- Inika abaqeshi umfanekiso ocacileyo ngobuchule nolwazi abanalo abafundi. (c) INkcazelo yeKharityhulam yeSizwe yeBanga R - 12 isekelwe phezu kwale mithetho-siseko ilandelayo: - Ukuphuculwa kwezentlalo: ukuqinisekisa ukuba kuyalungiswa ukungalingani kwezemfundo okwabangelwa lixesha lobandlululo, nokuba bonke abemi banikwa amathuba emfundo alinganayo; - Ukufunda ngokubandakanyeka kusetyenziswa ingqiqo: ukukhuthaza indlela yokufundisa efuna abafundi ukuba bathathe inxaxheba bebonakalisa ingqiqo, endaweni yokufunda ngokubethelela izimvo nokufunda nje bengaziqiqisisi iinyaniso okanye izimvo abazinikwayo; - Ulwazi nezakhono ezikumgangatho ophakamileyo: ukubekwa kweyona migangatho isezantsi yolwazi nezakhono ekufuneka abafundi bezibonakalise kwibanga ngalinye, kananjalo nokumiselwa imigangatho ephezulu enokufikelelwa kuzo zonke izifundo; 4 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) - Ukuqhubela phambili: umxholo wokufundwayo neemeko ekufundwa phantsi kwazo kwibanga ngalinye ubonisa ukuqhubela phambili, ukususela kokulula ukuya koko kuntsonkothileyo; - Amalungelo oluntu, uqukaniso, ukukhathalelwa kokusingqongileyo nobulungisa bezentlalo: ukufakwa kwemithetho-siseko neendlela zokwenza ubulungisa kwezentlalo nokukhathalela indalo esingqongileyo kwanamalungelo oluntu, njengoko ebekiwe kuMgaqo-siseko weRiphablikhi yoMzantsi Afrika. INkcazelo yeKharityhulam yeSizwe yeBanga 10 - 12 ibonakalisa uvakalelo kwimiba yeyantlukwano enjengendlala, ukungalingani, uhlanga, isini, ulwimi, ubudala, ukuba nenkubazeko neminye imiba; - Ukuxatyiswa kolwazi lwemveli: ukuthathela ingqalelo ubutyebi bembali kunye nelifa lemveli leli lizwe njengeentsika zokuxhasa izithethe eziqulethwe nguMgaqo-siseko; kunye - Nentembeko, umgangatho ophezulu, kunye negalelo elibonakalayo: ukunika imfundo enokuthelekiseka neyamanye amazwe ngokomgangatho, ukunatyiswa kwanokungena nzulu kwayo kwimiba efundiswayo. (d) INkcazelo yeKharityhulam yeSizwe yeBanga R - 12 ijonge ukuphuhlisa abafundi abakwaziyo: -- ukuchonga nokusombulula iingxaki bathabathe izigqibo besebenzisa ingqiqo nokucinga okubonakalisa ubugcisa; -- ukusebenza ngempumelelo bebodwa naxa bekunye nabanye njengamalungu eqela; -- ukuzicwangcisa nokuzilawula bona buqu kunye nemisebenzi yabo ngentembeko nangempumelelo; -- ukuqokelela, ukuhlalutya, ukucwangcisa nokuhlaba amadlala ulwazi; -- ukunxibelelana nabanye ngempumelelo besebenzisa ubuchule bokubonwayo, bemiqondiso kunye/okanye nezinye izakhono zolwimi ngeendlela ezahlukileyo; -- ukusebenzisa inzululwazi nobuchwepheshe ngempumelelo nangokubonakalisa ukuba noxanduva ngokunengqiqo ekukhathaleleni indalo esingqongileyo nempilo yabanye; kunye -- nokubonisa ukuliqonda ihlabathi ukuba liyiseti yezinto ngezinto ezizalanayo ngokuqaphela ukuba iimeko ezisonjululwa phantsi kwazo iingxaki azizimelanga zodwa geqe. (e) Ukuqukaniswa kwemfundo kufuneka kube ngundoqo ekulungiseleleni, ekucwangciseni nasekufundiseni kwisikolo ngasinye. Oku kunokwenzeka kuphela xa bonke ootitshala benolwazi oluphangaleleyo malunga nendlela yokuqonda nokusombulula izidingo zokufunda kunye nendlela yokucwangcisela abafundi abangafaniyo. Undoqo ekulawuleni ukuqukaniswa kwemfundo kukuqinisekisa ukuba izidingo ziyachongwa zize zisonjululwe ngawo onke amaqela enkxaso efanelekileyo asesikolweni, aquka ootitshala, amagosa esithili, amaQela eNkxaso amaZiko athile, abazali neZikolo zabaFundi abaneeMfuno eZizodwa njengamaZiko aXhobisa ngoLwazi. Ukusombulula izidingo eklasini, ootitshala mabasebenzise iindlela ngeendlela zokujongana neyantlukwano kwikharityhulam ezifana nezo zikuxwebhu lweSebe leMfundo esisisiSeko oluthi Guidelines for Inclusive Teaching and Learning (2010). CAPS 5

MATHEMATIKA IBANGA LABAQALAYO (R) 1.4 UKwabiwa kweXesha 1.4.1 IsiGaba esisisiSeko (a) Ixesha elabelwe ukufundisa kwisiGaba esisisiSeko limi ngolu hlobo: IBANGA 1-2 IBANGA 3 ISIFUNDO IBANGA R (IIYURE) (IIYURE) (IIYURE) ULwimi lwaseKhaya 10 7/8 7/8 ULwimi lokuQala 2/3 3/4 oloNgezelelweyo Izibalo 7 7 7 IzaKhono zoBomi 6 6 6 • ULwazi lokuQala (1) (1) (1) • UbuGcisa beZandla (2) (2) (2) • EzemiThambo (2) (2) (2) • UkuziPhatha neNtlalo (1) (1) (1) LILONKE 23 23 25 (b) Ixesha elabelwe ukufundisa leBanga R, 1 nelesi-2 ziiyure ezingama-23. IBanga lesi-3 ziiyure ezingama-25. (c) IBanga R - 2 labelwe iiyure ezilishumi, zize zibe li-11 kwiBanga lesi-3. ULwimi lwaseKhaya lwabelwe ezona lwimi zininzi ezisi-8 nezona zimbalwa ezisi-7; luze uLwmi oLongezelelweyo lwabelwe ezona zimbalwa zibe 2 zize ezona zininzi zibe 3 kwiBanga R - 2. KwiBanga lesi-3 ezona yure zininzi zisi-8, zize zibe si-7 ezona zimbalwa kuLwimi lwaseKhaya; kanti kuLwimi oloNgezelelweyo ezona zimbalwa zi-3, zize ezona zininzi zibe 4. (d) IMathematika yabelwe iiyure ezisi -7. (e) KwizaKhono zoBomi, uLwazi lokuQala lwabelwe iyure e-1 kwiBanga R - 2, zi-2 kwiBanga lesi-3, njengoko kubonisiwe kwizibiyeli kwiBanga. 1.4.2 IsiGaba esiPhakathi (a) Ixesha elabelwe ukufundisa kwisiGaba esiPhakathi limi ngolu hlobo: ISIFUNDO IIYURE ULwimi lwaseKhaya 6 ULwimi lokuQala oloNgezelelweyo 5 IMathematika 6 INzululwazi nobuChwepheshe (neTeknoloji) beNdalo 3,5 INzululwazi yezeNtlalo 3 IzaKhono zoBomi 4 • UbuGcisa beZandla (1,5) • EzemiThambo (1) • UkuziPhatha neNtlalo (1,5) ZIZONKE 27,5 6 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) 1.4.3 IsiGaba esiPhezulu (a) Ixesha elabelwe ukufundisa kwisiGaba esiPhezulu limi ngolu hlobo: ISIFUNDO IIYURE ULwimi lwaseKhaya 5 ULwimi lokuQala oloNgezelelweyo 4 IMathematika 4,5 IiNzululwazi zezeNdalo 3 INzululwazi yezeNtlalo 3 UbuChwepheshe (iTeknoloji) 2 INzululwazi yoLawulo lwezoQoqosho 2 IziFundo ngezoBomi 2 UbuGcisa neNkcubeko 2 ZIZONKE 27,5 1.4.4 IBanga 10 - 12 (a) Ixesha elabelwe ukufundisa iBanga 10 - 12 limi ngolu hlobo: IZIFUNDO IIYURE 1. ULwimi lwaseKhaya 4.5 2. ULwimi lokuQala oloNgezelelweyo 4.5 4.5 3. IMathematika 2 4. IziFundo ngezoBomi 12 (3x4yr) 5. Ubuncinane bazo naziphi izifundo ezithathu ezikhethwe kwiQela B isiHlomelo B, iiTheyibhile B1 – B8 zoxwebhu lwepolisi oluthi, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R – 12, ngokuxhomekeke kwimigaqo ebekwe kumhlathi wama-28 wolu xwebhu lwepolisi. ZIZONKE 27,5 Ixesha elabelwe ukufundisa ngeveki malisetyenziselwe ukufundisa izifundo ngokweemfuno zezifundo zeNkcazelo yeKharityhulam yeSizwe yeBanga R - 12 (NKS) ezichatshazelwe apha ngasentla, hayi ezinye izifundo ezongezelelweyo. Ukuba umfundi ufuna ukongeza izifundo, makongezelwe elinye ixesha lezo zifundo azongezileyo. CAPS 7

MATHEMATIKA IBANGA LABAQALAYO (R) ISAHLUKO SESI- 2: INKCAZELO, IINJONGO, IZAKHONO NOMXHOLO 2.1 Intshayelelo KwisiGaba esisisiSeko, izakhono eziphambili kwiKharityhulam yoLwimi lwaseKhaya zezi: Kwicandelo lesibini, isiGaba sesiSeko seMathematika iNkcazelo yePolisi yeKharityhulam nokuHlola inika ootitshala ingcaciso yeMathematika, iziphumo ezingundoqo, izakhono ezingundoqo, ugxininiso kumxholo, umthamo weenkalo zemixholo, izixhobo zokufunda ezinokusetyenziswa kwisifundo seMathematika kwisiGaba esisiSeko, izikhokelo ezinokusetyenziswa ukuxhasa abafundi abaneengxaki ekufundeni iMathematika, ukubala ngentloko nokomeleza ukufundisa izakhono zokubala kwabaqalayo kwiBanga labaQalayo. 2.2 Yintoni iMathematika? IMathematika lulwimi olusenza ukuba sisebenzise iisimboli namanani ukuchaza ulwalamano lwamanani lwejiyometri nolweegrafu. Ngumsebenzi owenziwa ngabantu oquka iipateni zokuqaphela, zokumela nezokuphanda nezolwalwamano ngokomgangatho ophathekayo nezokuhlala naphakathi kwezinto ngokokwazo. Incedisa ukwakha inkqubo yokubala ngentloko eqinisa ukusebenzisa ukucinga nzulu, ngokuchanekileyo nokwenza izisombululo eziza kukhokelela ekuthatheni izigqibo ezizizo. 2.3 Iinjongo ezingundoqo Iinjongo zokufunda nokufundisa iMathematika kukuphuhlisa ezi zinto zilandelayo kumfundi: • Izinto ezingundoqo kunxibelelwano lweMathematika zisetyenziswa kwezentlalo, kwezisingqongileyo, kwezenkcubeko nezobudlelwano ngezoqoqosho; • Ukuzithemba nokukwazi ukumelana nayo nayiphi imeko yeMathematika ngaphandle koloyiko lwayo; • Ukufuna ukwazi nokuthanda iMathematika; • Ukuncoma, ukuyonwabela, ubuhle nondiliseko lweMathematika; • Ukuqaphela ukuba iMathematika inecandelo lobugcisa obenziwa ngabantu; • Ulwazi olunzulu lweengqiqo ukunika intsingiselo yeMathematika; kunye • Nokufumana ulwazi olungundoqo nezakhono ezifunekayo: -- Ukusebenzisa iMathematika kwizinto ezibonwayo, kwezentlalo nezokusombulula iingxaki zeMathematika; -- Ukufunda izifundo ezinxulumeneyo; kunye -- Nokufunda banzi ngeMathematika. 8 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) 2.4 Izakhono ezingundoqo • Ukwakha izakhono ezingundoqo zeMathematika, umfundi kufuneka: • Akhe isigama esichanekileyo seMathematika; • Akhe isigama samanani, ingqiqo yamanani, ukubala nokusebenzisa izakhono; • Afunde ukumamela, ukuthetha, ukucinga, nokuqiqa usebenzisa ulwazi olufumeneyo; • Afunde ukuphanda, ukuhlalutya, ukumela ukutolika ulwazi; • Afunde ukubuza imibuzo nokusombulula iingxaki; kunye • Nokwakha ulwazi nokubaluleka kweMathematika nendima eyidlalayo ebomini, nakuphuhliso lobume bomfundi. 2.5 Iinkalo zemixholo ekugqalwe kuyo IMathematika kwisiGaba esisisiSeko siquka iinkalo ezintlanu. Inkalo nganye yongeza kulwazi lwezakhono ezingundoqo. Le theyibhile ingezantsi ibonisa ugxininiso jikelele lweenkalo zemixholo kunye nezakhono eziziinkalo kwisiGaba esisisiSeko. Itheyibhile 2.1 Umxholo ekugqalwe kuyo kwiMathematika yesiGaba esisisiSeko Ulwazi lomxholo lweMathematika Iinkalo Umxholo ekugqalwe kuyo jikelele Umxholo ekugqalwekuyo kwisiGaba esisisiSeko zemixholo Ulwazi/ uphuhliso lwamanani luquka: Uluhlu lwamanani oluphuhliswa kwiBanga lesi-3 luquka amanani azeleyo ukuya kwi-1000 namaqhezu aqhelekileyo. • Intsingiselo yeendidi zamanani Kwesi sigaba, ingqiqo ngamanani yabafundi iphuhliswa ahlukeneyo; ngezinto eziphathwayo ukubala ingqokelela yezinto, • Ukuzalana phakathi kweendidi ipatishini, ukudibanisa iikhwantithi, ukubala ngokuqakatha zamanani ahlukeneyo; ngeendlela ezahlukeneyo, ukusombulula izibalo zamazwi, nokwakha nokwahlula amanani. • Ukuzalana ngobukhulu beendidi zamanani ezahlukeneyo; • Ukubala kunceda abafundi ekuphuhliseni ingqiqo ngamanani, ukubala ngentloko, uqikelelo, izakhono • Ukuboniswa kwamanani ngeendlela zokubala nokunakana iipateni. ezahlukeneyo; kunye • Ingqiqo yamanani ikhulisa abafundi ngeemilo zamanani • Nefuthe lokusebenza ngamanani. ikwaphuhlisa iindlela ezinokwenza kube lula ukubala. Amanani, • Ukusombulula iingxaki kunceda abafundi ekuchazeni IiOpareyshini iindlela abacinga ngayo ngokuthetha nangokubhala nolwalamano ngokuba bazobe benze neesimboli. • Abafundi bakhulisa ulwazi lwabo lwabasaqala ukubala ngokudibanisa, ngokuthabatha ngokuphindaphinda nangokwahlulahlula. • Abafundi baphuhlisa ulwazi lwabo lwamaqhezu ngokubala basombulule izibalo kuquka nokwaba izinto eziphathekayo nangokusebenzisa imizobo.Iingxaki zezibalo maziquke nezisombululo eziza kunikwa nemazisekelwe kumanani apheleleyo okanye amaqhezu, ukwehlulelana makungaquki ukufumana amanani apheleleyo qha, makuquke nokufumana ukuqokelelwa kwengqokelela yezinto. Kweli nqanaba, abafundi abalindelekanga ukuba bafunde nokuba babhale iisimboli zamaqhezu. CAPS 9

MATHEMATIKA IBANGA LABAQALAYO (R) Ulwazi lomxholo lweMathematika Iinkalo Umxholo ekugqalwe kuyo jikelele Umxholo ekugqalwekuyo kwisiGaba esisisiSeko zemixholo I-Aljibra lulwimi lokufunda nokuthetha Kwesi sigaba, abafundi basebenzisa zombini: ngoninzi lweMathematika yaye • Iipateni zamanani (umzekelo: ukubala ngokuqakatha); lungagqithiselwa nasekufundweni kunye kwemisebenzi nokunye ukuzalana kwezinto. Esona siseko sale nkalo • Neepateni zejiyometri (umzekelo: imizobo). yomxholo kukuba abafundi bafumane Abafundi mabasebenzise izinto eziphathekayo, imizobo izakhono ezaneleyo ekusebenziseni neesimboli xa bekhuphela, besongeza, bechaza naxa IiPateni, iAljibra. Kukwagqalwe: besenza iipateni. iiFankshini • ukucaciswa kweepateni nokuzalana Ukukhuphela iipateni kunceda abafundi ukubona indlela neAljibra kwazo kusetyenziswa ukubonisa eyiyo ezenziwe ngazo iipateni. ulwazi lweesimboli, iigrafu, neetheyibhile, kunye Ukongeza iipateni kunceda abafundi ukuba bakhangele ukuba bazilandele kakuhle na iipateni. • ukufuna uchaze ukungatshintshi nokutshintsha kweepateni, kunye Ukuchaza iipateni kunceda abafundi ukuba baphuhlise nokuzalana okwenza abafundi ukuba izakhono zabo zolwimi. benze uqikelelo nokusombulula iingxaki. Ukubethelela kulandelelwano lweepateni kwenza isiseko sokuphuhlisa izakhono zokucinga ngeAljibra. Iipateni zamanani zincedisana nophuhliso lokwazi nokwakha amanani, ukusebenzisa nolwalamano lwamanani. Iipateni zejiyometri ziquka ulandelelwano lwemigca, inkangeleko, nezinto kunye neepateni zelizwe jikelele, kwiipateni zejiyometri abafundi basebenzisa ulwazi lwabo lwesimo nobume. Ukufunda isiThuba neMilo kunceda Kwesi sigaba abafundi babethelela kwizinto ezinokwakheka ekulandeleni nasekuthandeni kuka 2-D no 3-D, iimo, iindawo nezalathiso. ipateni, ekulandeleni, ukuphumelela • Abafundi bafunda ngezinto ezinembonakalo yamacala nasekuboneni ubuhle kwizinto zendalo amathathu neemo ezinembonakalo yamacala amabini, nenkcubeko. Ibethelela: ukwahlula, ukwahlula ngakwamaqela, ukuchaza nokubiza • kwiimpawu, ulwalamano; agama azo. IsiThuba neMilo(ijiyometri) • ukuziqhelanisa, iindawo; kunye • Abafundi bazoba iimilo bakhe ngezinto. • nenguqulelo yezinto ezinokwakheka • Abafundi bayazitshintsha bazichaze iimilo nezinto kuka 2-D no 3-D. ezikwiindawo ezibangqongileyo ezifana nezinto neemilo zeMathematika. • Abafundi bachaza indawo ezikuyo izinto, bona nabanye besebenzisa isigama. • Abafundi balandela benika izalathiso. Umlinganiselo ubethelela • Kwesi sigaba, ulwazi lwabafundi kumlinganiso luphuhliswa ekukhetheni nasekusebenziseni ngokwenza izinto ezahlukeneyo besebenzisa izinto imivo ngokufanelekileyo, izixhobo, eziphathekayo, iimilo, befunda iimpawu zobude, umthamo, neefomyula ukuqikelela ubungakanani ubunzima, ieriya nexesha. beempawu zeziganeko, iimo, izinto • Abafundi balinganisa umthamo weemilo zezinto nokusingqongileyo. Ijongene ngqo besebenzisa iiyunithi ezingamiselekanga apho Imilinganiselo nolwazi lwenzululwazi, iteknoloji kufanelekileyo, ezinjengezandla, izantya, nezikhongozeli, nezezimali kwilizwe jikelele, inceda njalo njalo. umfundi ukuba: • Abafundi bathelekisa ubuninzi ngokwahlukeneyo • Enze uqikelelo olwenza besebenzisa isigama sokuthelekisa esinje ngobude/ okuvakalalyo; yaye ubufutshane, ubunzima/ ubukhaphukhaphu, njalo njalo. • Aqonde ulwazi lwemilinganiselo • Abafundi baziswa kwiiyunithi ezinjengeegrem, iikhilogrem, neziphumo zazo. iimililitha, iilitha, iisentimitha neemitha. Imisetyenzana yexesha kufuneka ibekelelwe abafundi baqhelaniswe ukwazi ixesha elidlulayo phambi kokuba bakwazi ukulifunda. 10 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) Ulwazi lomxholo lweMathematika Iinkalo Umxholo ekugqalwe kuyo jikelele Umxholo ekugqalwekuyo kwisiGaba esisisiSeko zemixholo Kwindlela yokusebenza ngolwazi Ugxininiso kumaBanga asisiseko ekufundiseni oluqokelelweyo, abafundi babonisa nasekufundeni indlela yokusebenza ngolwazi oluqokelweyo izakhono: ukuhlela izinto nedatha ngeendlela ezahlukeneyo, zixhomekeke kubomi bezinto nedatha. • zokuqokelela; Ukusebenzangowazi • Abafundi kulindeleke ukuba batolike ze bakhe iigrafu oluqokelelweyo • ukucwangcisa; zemifanekiso neegrafu zezitena ngongqamaniso • ukubonisa; kunye lwamanani nedatha abayinikiweyo. • nokuhlalutya ucacise ulwazi olunikiweyo. 2.6 Ulwabiwo lweenkalo zemixholo Ulwabiwo lweenkalo zeMathematika lunceda iinkalo ezimbini: ulwabiwo lunika isikhokelo ngexesha emalinikwe nokufundisa kwinkalo yomxholo ngokufanelekileyo; okwesibini ulwabiwo lunika isikhokelo ngendlela umxholo omawuhlolwe ngayo. Ulwabiwo lweenkalo zemixholo alufani kumaBanga esiGaba esisisiSeko. Itheyibhile 2.2 Ulwabiwo lweenkalo zemixholo kwisiGaba esisisiSeko ULWABIWO LWEENKALO ZEMIXHOLO Ummandla womxholo IsiGaba 1 IsiGaba 2 IsiGaba 3 Amanani, ii-Opareyshini noLwalamano* 65% 60% 58% Ipateni, iiFankshini neAljibra 10% 10% 10% Isithuba nesimo (Ijiyometri) 11% 13% 13% Imilinganiselo 9% 12% 14% Ukusebenzisa nolwazi oluqokelelweyo 5% 5% 5% 100% 100% 100% *KwisiGaba sabaQalayo (R - 3), kubalulekile ukuba kugxininiswe ekufundiseni amanani, ukusebenza nolandelelwano kwiMathematika. Kubalulekile ukuba abafundi baphume bewazi kakuhle amanani bekwazi nokubala. Injongo kukuba abafundi baqiniseke bazithembe kumanani nasekubaleni. Ngenxa yesi sizathu ixesha lokufundisa amanani, ukusebenza nolandelelwano longeziwe. Uninzi lomsebenzi kwipateni malenziwe kwiipateni zamanani ukubethelela ulwazi lwabafundi ngamanani. 2.7 IMathematika kwisiGaba esisisiSeko IMathematika yesiGaba esisisiSeko iqinisa uqhagamshelwano phakathi kobomi babafundi abasaqalayo naBangaphandle esikolweni, neMathematika enzima kwiizigaba ezingaphambili kwelinye icala. KwisiGaba sabaQalayo, abafundi mabakrotyiswe kwimiba yeMathematika ebanika amathuba okuba bathethe baze barekhodishe iingcinga zabo zeMathematika. Ixesha elichithwa ekufundiseni iMathematika linegalelo ekuphuhliseni ulwazi lwengqiqo nezakhono kubafundi. Imisetyenzana ekufuneka abafundi beyenzisiwe kukuba akufunekanga ibe ngxaka-ngxaka koko kufuneka igxininiswe kwingqiqo yeKharityhulum yeMathematika. CAPS 11

MATHEMATIKA IBANGA LABAQALAYO (R) 2.7.1 Izikhokelo zolawulo lweklasi Ixesha elisikelwe ukufundisa iMathematika kusuku ngalunye kufuneka luthathwe njengepiriyodi. Ngepiriyodi yeMathematika ezi zinto zilandelayo kufuneka zenzeke: • Imisebenzi yeklasi yonke -- IMathematika ebalwa ngentloko -- Ukuqukunjelwa kwemisebenzi yengqiqo -- Ukulawula iklasi (ukunika imisebenzi yomfundi ngamnye, njalo njalo.) • Ukufundisa amaqela amancinci -- Ukubala -- Uphuhliso lwamanani engqiqo (imisebenzi yokuthetha neyenziwa ngezandla) -- Ukusombulula iingxaki (imisebenzi yokuthetha neyenziwe ngezandla) -- Ukurekhodisha okubhaliweyo -- Ukuphuhlisa iindlela zokubala (imisebenzi yokuthetha neyenziwe ngezandla) -- Iipateni -- Isithuba nesimo -- Imilinganiselo -- Indlela yokusebenza ngolwazi oluqokelelweyo • Ukusebenza wedwa Abafundi bayaziqhelanisa baqukumbele iingqiqo eziphuhliswe ekufundisweni kwiklasi yonke nakumaqela amancinci. Imisebenzi yeklasi yonke: apho kugxininiswa kubalo lwentloko, makubekho uqukumbelo lwengqiqo nokunikwa imisebenzi kangangemizuzu engama-20 ngosuku ekuqaleni kwesifundo seMathematika. Ngeli xesha utitshala uza kusebenza neqela lonke leklasi eqwalasela ekwarekhodisha, apho kufanelekileyo, amagama eentsuku zeveki, umhla, abafundi abakhoyo nabangekhoyo esikolweni nokuba injani imo yezulu. Ukubala ngentloko kuquka ukubala ngentloko okukhawulezileyo okunje ngokuthi “inani phambi nasemva kwesi-8 ngu-2 ngaphezu/ ngaphantsi ko-8 ngu: 4+2; 5+2; 6+2” njalo njalo. Ngeli thuba utitshala makaqukumbele iingqiqo ezinobunzima. Enye into ebalulekileyo utitshala amakayenze kukuba anike iklasi yakhe imisebenzi ephangaleleyo nemisebenzi abayenza bodwa ngokwabo ngelixa ancedisana namaqela amancinci. Imisebenzi yamaqela amancinci: olona hlobo lusebenzayo kuxa utitshala esebenza ngamaqela amancinci (8 ukuya kwi-12) anabafundi abalingana ngokucinga emethini okanye ezitafileni, ngelixa abanye besebenza bodwa. Utitshala usebenza ngokuthetha nangokwenza nabafundi, besebenza imisebenzi enjengokubala, uku- qikelela, uphuhliso lwengqiqo lwamanani nokusombulula iingxaki, nemisebenzi yeepateni, izithuba neemilo, imilinganiso, indlela yokusebenza ngolwazi oluqikelelweyo, ekufuneka icwangciswe ngobunono. Ukwenzela ukubethelela ukufunda, ukubhala makube yinxalenye yemisebenzi yamaqela apho kunokwenzeka. Abafundi mababe nezinto zokubhala (umzekelo: iincwadi zokubhala) zemisebenzi yokusombulula iingxaki. Imisebenzi yamaqela mayibe nonxibelelwano, abafundi mabakhuthazwe ukuba “benze, bathethe baze barek- 12 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) hodishe” iingcinga zabo ngeMathematika. Ootitshala mabazame ukungabajongeli phantsi abafundi abaqonda kade; nabo kufuneka banikwe imisety- enzana enzima. Kuba lula ukuxuba imisebenzi kwiqela labantwana abakwinqanaba elilinganayo lokucinga. Kodwa amaqela axubeneyo asebenza kakuhle ukwakha, ukulinganisa iipateni nokuhlela okanye imidlalo. Imisebenzi eyenziwa ngabanye: ngeli lixa utitshala asebenza ngeqela elincinci, amanye amaqela makenze imisebenzi yeMathematika eyahlukeneyo ebethelela nequkumbela iingqiqo nezakhono ebezifundisiwe ku- maqela amancinci. Imisebenzi eyenziwa ngabanye mayohlula-hlulwe ukulungiselela amaqela ahlukeneyo ngokucinga. Imisebenzi yamaqela azimeleyo aquka: -- Iincwadi zemisebenzi; -- Incwadi zemisebenzi yokubhala/ amakhadi okubala, ukudlala ngamanani, imisebenzi elula ngokusemxholweni, njalo njalo; -- Imidlalo yeMathematika enjengeLudo, dominos, iiphazili ; kunye -- Nemisebenzi equka ukwakha, ukuHlola, iipateni okanye imilinganiselo. Iphiriyodi yeMathematika kufuneka incede abafundi abaneengxaki zokufunda, nemisebenzi yabantwana abakrele-krele nemisebenzi yokuHlola, njalo njalo. Imisebenzi yamaqela amancinci nazimeleyo mayijongwe, ikorekishwe ngutitshala njengemisebenzi yohlaziyo ecwangcisiweyo nengacwangciswayo. Ukujongwa kwendlela abafundi abafunda nabafundiswa ngayo incedisa utitshala ukuba enze uhlaziyo oluqhubekayo, alandele ukujonga inkqubo yabo aze acwangcise imisebenzi yokuncedisana nabafundi abafu- mana iingxaki. 2.7.2 Abafundi abaneengxaki zokufunda kwiMathematika Kubalulekile ukuba abafundi abaneengxaki zokufunda kwiMathematiki bakrotyiswe kwimisebenzi eyenzelwe ukufunda. Ixesha elininzi malisetyenziswe kwimizekelo nemisebenzi yezandla neyenziwayo kunabanye abafundi, umzekelo, ukusetyenziswa kwemisebenzi enzima msinyane kungadodobalisa ukuqhubeka kwaba bafundi. Aba bafundi mabanikwe ithuba elongezelelweyo: • Lokugqibezela imisebenzi; • Ukufumana izakhono zokucinga (belandela iindlela ezithile); kunye • Nemisebenzi yokuHlola. Inani lemisebenzi emayenziwe malilungiselelwe abafundi kodwa kungasileli izakhono ekufuneka zifundisiwe. 2.7.3 Imisebenzi yokubala ngentloko Ukubala ngentloko kunendima enkulu kwikharityhulam. Iibhondi zamanani neetheyibhuli zokuphinda-phinda zithatha ngokuba abafundi bayazi okanye bamele ukukhumbula uluhlu lwesigaba ngasinye. Kwakhona, ukubala ngentloko kwenzelwa ukubala ukuya kufika kumanani amakhulu ubala ngokuqakatha nokwenza imisebenzi enjengo“kubala phantsi naphezulu kwileli yamanani”, umzekelo, utitshala unokubuza le mibuzo ilandelayo “imibuzo ethungelanayo” “qala kuma-796 yongenza ngesi-7. Ewe, ngama-803 nciphisa isi-5. Ewe, ngama-798. Yandisa nge-10…wandise ngesi-2… kuma-90…unciphise ngesi-5…” njl. Le misebenzi incedisa abafundi ekwakheni imigca-manani yokubala ngentloko. CAPS 13

MATHEMATIKA IBANGA LABAQALAYO (R) Ukubala ngentloko kubonakala kakhulu xa kubalwa naxa kuphuhliswa icandelo lamanani ngokunxulumene nesihloko samanani neepateni, kunokuphinda kuvele kwimisebenzi yolinganiselo nakwindlela yokusebenza ngolwazi oluqokelelweyo. Xa besebenzisa imisebenzi yokubala ngentloko, utitshala makangabanyanzeli abafundi ukuba benze imisebenzi abangenakho ukuyenza — izixhobo zokubhala nezokubala mazisoloko zifumaneka kubafundi abazifunayo. 2.8 IBanga labaQalayo(R) Indlela yokufunda iMathematika mayisetyenziswe ngokunxulumanisa nangokufunda ngokudlala. Utitshala makasoloko ezixhobisa, abe nomcebisi kunomququzeleli. Umcebisi usebenzisa amathuba okufunda okungacwangciswanga xa abafundi besenza imidlalo ngokukhululekileyo kwikona yokudlala ngokuzikhethela okanye kweyeebhloko zokwakha, zesanti, nemidlalo yamanzi nemisebenzi, encediswa ngutitshala kwizibalo ezijongene nengqiqo ezinjengokubala, uphuhliso lwengqiqo yamanani, nesithuba nesimo, iipateni, ixesha neminye imisebenzi eqalayo yeMathematiki. Imibala yodwa asiyongqiqo yeMathematika, kodwa ingasetyenziswa ekuphuhliseni iingqiqo zeMathematika ezinjengokuhlenga-hlengisa, ukwahlula-hlula nokuchaza. Yonke imiba yeBanga labaQalayo, iquka ubume beklasi, ukufundisa nokufunda makukhokelele ekuphuhlisweni kokufunda komfundi ngokupheleleyo. Uphuhliso olunxulunyaniswe nokufunda kwabaqalayo, inyumerasi luquka nokuphuhliswa kwengqondo (ukusombulula iingxaki, ukucinga ngolandelelwano nokuqiqa), uphuhliso lolwimi (ulwimi lweMathematika kunye nokuphuhlisa izakhono zokushukuma kunye nemvakalelo yobume. Zonke ezi meko zingaphuhliswa ngamabali, iingoma, imidlalo yeminwe, izicengcelelzo, imidlalo yamanzi, iithoyi zokufundisa kunye nemidlalo yeebhodi, ngokwakha nemisebenzi yokuzungeza, imidlalo yemibono, imidlalo yangaphandle neyaseyadini yokudlala. Imidlalo emininzi mayiquke izakhono zenyumeresi, umzekelo, ukulinganisa izixhobo zokupheka okanye ukubala xa uyokuthenga. Ngamanye amazwi, ukufumana izakhono zeMathematika yabaqalayo nezinye izakhono ezinxulumene neMathematika ezinjengezootitshala abaphum’ izandla, kulandela le migaqo yamanqanaba okufunda ilandelayo: • Kwinqanaba lezinto ezibanjwayo (esebenzisa umzimba nemizwa); • Kwinqanaba lezinto eziphathekayo (3-D, usebenzisa izinto ezinje ngeebhloko, iziciko zeebhotile, amasebe, neezinye izinto ezisekuhlaleni); kunye • Besebenzisa/ bebonisa iphepha nepensile (ezemizobo, amakhadi okuthelekisa njl.) KwiBanga labaQalayo ithayimtheyibhile ibizwa ngokuba yinkqubo yemihla ngemihla, iquka la macandelo alandelayo: • Imisebenzi ekhokelwa ngutitshala; • Izinto ezenziwa rhoqo; kunye • Imisebenzi ekhokelwa ngabafundi okanye imidlalo ekhululekileyo. Ugxininiso malube sekusetyenzisweni kwezi zakhono kwisicwangciso semihla ngemihla ukukhuthaza ulwazi lwenyumeresi yabaqalalyo ngokuyonwabela nangokufunda. Umzekelo, ekufundeni okukhokelwa ngutitshala inyumeresi ifunyanwa ngexesha lesangqa. Uninzi lwezangqa lunokunikwa ukuphuhlisa iMathematika kwisangqa sakusasa xa abafundi bebuliswa kujongwa abakhoyo nabangekhoyo; lithuba lokufundisa amanani nokubala. Kwezinye izangqa, ezinjengezangqa zeMathematika, izangqa zamalungu asetyenziswa ukubona , ukushukuma, umculo nezangqa zobugqi zinokuncedisa ukufundisa iMathematika. Imisebenzi yobugcisa bokuyila inokubethelela kwiMathematika, umzekelo, kusetyenziswe iimilo zejiyometri njengezangqa nezikwere ukwenza ikholaji okanye ukuyila iipateni zokwenza ifreyimi yemifanekiso. Itshati yemozulu, 14 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) ikhalenda neengoma zeentsuku zokuzalwa zinika ixesha lokufundisa izakhono zeMathematika. Lulwazi lukatitshala olunokuphuhlisa imfundo yabafundi. • Indlela zokwenza izinto, apho abafundi bathatha inxaxheba, njengexesha lokutya, ukufika, ixesha lokugoduka, ixesha lokuya ezimfanelweni (ngasese), zonke ezo zinto zinokusetyenziswa ukufundisa iMathematika. Abafundi abanxibe bomvu, umzekelo, yiya ezimfanelweni (ngasese) (imibala kunye namanani aqhelekileyo), umfundi ngamnye ufumana ipleyiti kunye nesonka (ungqamaniso lwamanani), uThandi ufuna isonka sesibini, uMandla yena wanele. Le nto ikhokelela kumathuba okufundisa, ngamanye amazwi, ukuba ngumcebisi wokufundisa. • Ngexesha lokudlala utitshala angakhuthaza ukufundiswa kweMathematika yabaqalayo kwiindawo ezilungiselelwe ukudlala. Imidlalo yangaphandle enjengokugwencela (ukukhwela) emaplangeni okanye ukuqhuba ibhayisekile kunokukhuthaza isigama esinjengokunyuka/ ukwehla, ezantsi/ phezulu, ukukhawuleza/ ukucotha, phezulu/ ezantsi, njl. Imidlalo yesanti namanzi iza kuqinisa ulwazi lwezakhono ezinjengobunzima, nomthamo. Yonke le misebenzi ikhuthaza izakhono zamalungu omzimba, ikhuthaza ukufundisa esikolweni ilitheresi nenyumeresi. Nantsi imizekelo yezi zakhono: -- Ukuphuhlisa ulwazi lwendawo yesithuba, umzekelo emva, phambili, ngaphantsi, emva kwento (umzekelo, le nto ingayanyaniswa nendawo yenani kwiMathemathika); kunye -- Nezalathiso kunye namacala (zinganxulumaniswa namanani nokubhala iileta nasekufundeni ukunene nasekhohlo). Le nto sithetha ngayo apha ngentla ibonisa indlela iBanga labaQalayo eliphuhlisa ukusombulula iingxaki, ukucinga ngengqiqo nemfundo yokuba ngabemi ngenxa yokubethelela ukuba ngabafundi abasebenzisanayo nabaxoxisanayo. Ngokusebenzisa amathuba afundisekayo, utitshala makakhuthaze abafundi ukuba bajonge izigqibo abazithathayo baqikelele okunokwenzeka, umzekelo, ukuba isikhongozeli esisetyenziswe ngexesha ebesesisetyenziswe kumdlalo wamanzi singathatha amanzi angaphezu kwesinye isikhongozeli. Ngokunika ingcebiso aze acele umngeni kubantwana ukuba bacinge ngezinye iindlela zokusombulula iingxaki, aphinde abakhuthaze ukuba bacinge nzulu ngezizathu nangezigqibo abathi bazithathe. NgaIe ndlela yokucinga awuncedi iMathematika kuphela, koko uphuhlisa ulwazi ngokupheleleyo yaye izizathu zikaCAPS ziyaphuhliseka kakhulu. Iindlela zokuhlaziya kwiBanga labaQalayo mazibe zezinganyanzelisi ukubhala uvavanyo yaye abantwana maBangafakwa kuxinzelelo lokubhala uvavanyo. Ngenxa yesi sizathu, imisebenzi yokuHlola ayifakwanga kulo mqulu kaCAPS. Umsebenzi ngamnye wovavanyo mawulungiswe ngobunono ukwenzela ukuba unxulumanise izakhono ezininzi. KwiBanga labaQalayo uvavanyo lwenziwa ngokujonga, utitshala erekhodisha esebenzisa itshekhilisti. Loo nto inika indlela aqhuba ngayo umfundi ngamnye wonyaka wonke, ubunzima abufumeneyo neendawo ebegqwese kuzo. Olu hlobo lunceda ukukhawulelana neengxaki nendawo agqwesa kuzo ukuba ziqhubele phambili. Indlela yakudala, yokufundisa abafundi bevaleleke kwigumbi lokufundela engenakudlala mayingasetyenziswa, nanjengoko ingakukhuthazi ukufunda inyumeresi ngokugqibeleleyo komfundi okwisiGaba sabaQalayo. IBanga labaQalayo malingenziwa iBanga loku-1. Eli Banga linezalo iimpawu ezibonisa indlela abantwana abakule minyaka abazifumanela ngayo ubomi jikelele, ulwazi, izakhono, nendlela yokuziphatha eza kubanika amathuba kwiminyaka ezayo yokufunda okuseSikweni. CAPS 15

MATHEMATIKA IBANGA LABAQALAYO (R) INKQUBO YEMIHLA-NGEMIHLA: IBANGA LABAQALAYO (R) (Ukusaka ± 7:30 – 13:00) UKUFIKA NEMIDLALO Izibalo • Imisebenzi Esekelwe Ukubulisa Iimini Zokuzalwa IiLwimi Kwikharithyulam (Caps) Irejista Iindaba IziBalo (Izibalo) Ama- 36 Izakhono zoBomi IMISEBENZI Iilwimi • Iingoma Nomculo emiz EKHOKELWAYO Izibalo • Imisebenzi Efuna Ucinge NGUTITSHALA Izakhono zobomi • Izicengcelezo Zokubala • Imidlalo yelizwe • Iingxoxo Ngezihloko lokuzakhela • IMISEBENZI YOBUGCISA • Umfuniselo Wezenzululwazi (yonke imihla: undoqo -1 +2/3 • Imidlalo yokulinganisa Ama- 50 • Imidlalo Yokuzikhethela imisebenzana exhasayo) • Ukwakha emiz • Okwenziwa Imihla Ngemihla • UKUDLALA IMIDLALO • Ukudlala ngeebhloko YOKUZIKHETHELA EKLASINI • Iithoyi zokufunda Ulwimi • Imidlalo yokusebenzisa Ama- 30 IMISEBENZI Iilwimi ukucinga • Imisebenzi esekelwe kwi- EKHOKELWA Izibalo kharityhulam (caps) emiz NGUTITSHALA Izakhono zoomi • Iiphazili • (Ulwimi lwasekhaya) • Ikona yeencwadi • Amabali IXESHA LOKUYA KUZIKHULULA I-10 lemiz (NGASESE) uLwimi, IziBalo, IzaKhono • Ixesha lokuthula • Ukudlala eqongeni zoBomi • Iincwadi/imifanekiso • Ukufunda imifanekiso • Iingxoxo • Imisebenzi efuna ucinge Ama- 20 IXESHA LOKUTYA • Ipowusta yomzali emiz uLwimi, IziBalo, izaKhono zoBomi • Umdlalo Ngamanzi • Ileta yomzali • Umdlalo Ngesanti • Iindaba • Umdlalo • Imibongo nezicengcelezo Ukudlala Imidlalo Ngokulinganisa Ama- 60 • Umculo/iingoma Yokuzikhethela Eklasini • Iibhola • Izikali/ iiteyiphu emiz Ze Kucocwe. • Oojingi • Iingxoxo ngezihloko • Iithoyi Zamavili • Imisebenzi yoluntu • Iithoyi Zokufunda • Ezenziwa imihla ngemihla • Ijangili jim • Imidlalo yokuzikhethela • Amatayara IXESHA LOKUYA KUZIKHULULA uLwimi, I-10 lemiz • Imithambo Izakhono zoBomi IziBalo, izaKhono zoBomi • Imidlalo • Imisebenzi ethathelwe IMISEBENZI IiLwimi kwipolisi yekharityhulum Ama- 30 EKHOKELWAYO IziBalo nokuhlola (Izakhono zobomi) emiz NGUTITSHALA Izakhono zobom • Iingoma nomculo • Imibongo nezicengcelezo Ama- 30 • Ukuxoxwa kwemixholo IBALI Yonke imihla emiz • Imihla yokuzalwa • Imisebenzi yesiqhelo Ixesha lokuphumla/ lokuthula ze kugodukwe • Ukudlala okukhululekileyo 16 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) 2.9 Izixhobo ezicetyswayo: igumbi lesiGaba esisisiSeko • Izinto zokubala • idayisi elikhulu • ifreyim enkulu yokubala • itshati yobude • iposta enkulu ka-1 – 100 neka-101 – 200 (itshati ye-100) • iintlobo ezahlukeneyo zomgca-manani • iseti yefladi-khadi(Flard cards) • imali yokudlala — umwangalala nengamaphepha • ikhalenda yonyaka esikuwo • iwotshi yosiba enkulu yodonga • isikali • iibhloko zokwakha • udongwe • iintlobo zeebhokisi ngokweemilo nobungakanani obuvela emakhaya • iintlobo zeebhotile zeplastiki nezikhongozeli zokubonisa ubungakanani • imizekelo yesifiye/ingqukumba (sphere) (ibhola), amaxande, ityhubhu, ikhowuni, ipiramidi kunye nesilinda. Utitshala angazenzela ezakhe izixhobo. • Iiplastiki, amakhalibhodi azizikwere, amaxande ahlukeneyo, izangqa, oonxantathu beendidi zobukhulu • Imidlalo yeMathematika, umzekelo, iLudo, inyoka neleli, iiphazili ezijiko-jiko, idomino, iiTangram, njl. • Ezifunekayo kwiBanga labaQalayo (R) neloku-1: • Iindawo zesanti nokudlala ngamanzi -- Izixhobo zokugwencela, zokuncekelela, zooswingi nezoogqaphu -- Ivenkile yomdlalo nezinto zokuthengwa ngemali yokudlala -- Imidlalo exutyiweyo enjengothi ‘yintoni esesikwereni’? -- iibhloko CAPS 17

MATHEMATIKA IBANGA LABAQALAYO (R) ISAHLUKO SESI- 3: INKCAZELO YOMXHOLO 3.1 Intshayelelo KuMjikelo weMfundo noQeqesho Jikelele kukho iinkalo ezintlanu zemixholo yeMathematika: • Amanani, ii-Opareyshini noLwalamano. • Iipateni, iiFankshini/ifankshini i ne-aljibra. • Isithuba nemilo (Ijiyometri). • Umlinganiselo. • Ukusebenza ngolwazi oluqokelekweyo. Umxholo wenkalo nganye uyacazululwa ube zizihloko zeMathematika, umzekelo, kwisiThuba neMilo kwisiGaba esisisiSeko isihloko esinye sineemilo ezinokwakheka kuka (2-D). Iingqiqo nezakhono zixeliweyo kwisihloko ngasinye. ICandelo lesi-3 leNkcazelo yePolisi kaZwelonke yeKharityhulam nokuHlola linika lize licacise ngomxholo weMathematika ofunekayo. 3.2 Inkcazelo yomxholo ukubonisa inkqubela-phambili Iitheyibhile zesigaba ezingamagqabantshintshi zibonisa inkcazelo yeengqiqo nezakhono nenkqubela-phambili ukusuka kwiBanga labaQalayo ukuya kwelesi-3. Nangona kunjalo, kwizihloko ezithile, iingqiqo nezakhono ziyafana kumaBanga amabini okanye amathathu alandelelanayo. Ingcaciso ngomxholo iza kukunika izikhokelo ngendlela inkqubela-phambili efanele ukuba imiliselwe ngayo. Okufumaneka kumxholo othile makufundwe kunye nangcaciso ngomxholo lowo. Amagqabantshintshi ngesiGaba esisisiSeko abonisa inkqubela-phambili ngeenkalo zomxholo; Ukubala ngamanani nolwalamano, iipateni, imisebenzi ne-aljibra, umlinganiselo nokusetyenziswa kolwazi/ datha kwiBanga labasaQalayo – ukuya kwelesi-3 njengoko kuxeliwe kule theyibhile ingasezantsi: 18 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

AMAGQABANTSHINTSHI ESIGABA ESISISEKO 1. AMANANI, II-OPAREYSHINI NOLWALAMAMO Inkqubela-phambili yamanani, ukubala nolwalamano. CAPS • Inkqubela-phambili engundoqo kumanani, ukubala nolwalamano yenzeka ngeendlela ezintathu: -- Uluhlu lwamanani luyanda. -- Iindidi ezahlukeneyo zamanani ziyafundiswa. -- Iindlela zokubala ziyaguquka. • Njengokuba ummandla wamanani owenza izibalo usanda ukuya kwiBanga lesi-3, abafundi kufanele babe neendlela ezichanekileyo zokubala. • Imeko-bume mayithathelwe ingqalelo uluhlu lwamanani lweBanga kunye nokukwazi ukubala kwabafundi. ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 UKUPHUHLISA INGQIQO YAMANANI: Bala ngamanani apheleleyo. 1.1 Bala izinto eziphathekayo. Bala izinto eziphathekayo. Bala izinto eziphathekayo. Bala izinto eziphathekayo. Bala izinto. Qikelela uze ubale uye kufika kwi- Qikelela uze ubale uye kufika Qikelela uze ubale uye kufika Qikelela uze ubale uye kufika kwi- 10 lezinto ezisetyenziswa imihla kuma-50 ezinto ezisetyenziswayo kuma-200 ezinto ezisetyenziswayo 1 000 lezinto ezisetyenziswayo ngemihla ngokuzithemba. imihla ngemihla ngokuzithemba. imihla ngemihla ngokuzithemba. imihla ngemihla ngokuzithemba. Kukhuthazwa ukubala ngokuqukanisa. Kukhuthazwa ukubala ngokuqukanisa. Kukhuthazwa ukubala ngokuqukanisa. 1.2 Bala uye phambili nasemva ngezinye Bala uye emva naphambili ngezinye Bala uye phambili nasemva: Bala uye phambili nasemva: ukusuka kwisi-1 ukuya kwi-10; ukusukela kulo naliphi inani phakathi Bala usiya • Ngoo-1 ukusukela kulo naliphi inani • Ngoo-1 ukusukela kulo naliphi inani kwe-0 ukuya kwi-100. phambili, ubale Sebenzisa izingqisho neengoma eliphakathi kwe-0 nama-200. eliphakathi kwe-0 ne-1000. ubuya umva. zamanani. • Bala uye phambili: • Ngama-10 ukusukela kwisininzi • Ngama-10 ukusukela kwisininzi • Ngama-10 ukusukela kwisininzi sama-10 phakathi kwe-0 nama-200. sezi-10 phakathi kwe-0 ne-1000. sama-10 phakathi ko-0 ne-100. • Ngezi-5 ukusukela kwisininzi sezi-5 • Ngezi-5 ukusukela kwisininzi sezi-5 • Ngezi-5 ukusukela kwisininzi sezi-5 phakathi kwe-0 nama-200. phakathi kwe-0 ne-1000. phakathi kwe-0 ne-100. • Ngezi-2 ukusukela kwisininzi sezi-5 • Ngezi-2 ukusukela kwisininzi sezi-2 • Ngezi-2 ukusukela kwisininzi sezi-2 phakathi kwe-0 nama-200. phakathi kwe-0 ne-1000. phakathi kwe-0 ne-100. • Ngezi-3 ukusukela kwisininzi sezi-3 • Ngezi-3 ukusukela kwisininzi sezi-3 phakathi ko-0 nama-200. phakathi kwe-0 ne-1000. • Ngezi-4 ukusukela kwisininzi sezi-4 • Ngezi-4 ukusukela kwisininzi sezi-4 phakathi kwe-0 nama-200. phakathi kwe-0 ne-1000. • Ngama-20, ngama-25, ngama-50 ne-100 ukuya kwi-1000. 19 MATHEMATIKA IBANGA LABAQALAYO (R)

ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 UKUPHUHLISA INGQIQO YAMANANI: Ukumela amanani azeleyo. 20 1.3 Qaphela, gqala uze ufunde Qaphela, gqala uze ufunde Qaphela, gqala uze ufunde Qaphela, gqala uze ufunde amanani. amanani. amanani. amanani. Iisimboli zamanani • Qaphela, gqala uze ufunde iisimboli • Qaphela, gqala uze ufunde iisimboli • Qaphela, gqala uze ufunde iisimboli • Qaphela, gqala uze ufunde iisimboli namagama zamanani ukusuka ku-1 ukuya zamanani ukusuka ku-1 ukuya kwi- zamanani ukusuka kwi-0 ukuya zamanani ukusuka kwi-0 ukuya amanani kwi-10. 100. kuma-200. kwi-1 000. • Bhala iisimboli zamanani ukusuka • Bhala iisimboli zamanani ukusuka • Bhala iisimboli zamanani ukusuka ku-1 ukuya kuma-20. kwi-0 ukuya kwi-100. kwi-0 ukuya kwi-1 000. • Qaphela, gqala uze ufunde • Qaphela, gqala uze ufunde • Qaphela, gqala uze ufunde • Qaphela, gqala uze ufunde amagama amanani ukusuka ku-1 amagama amanani ukusuka ku-1 amagama amanani ukusuka kwi-0 amagama amanani ukusuka kwi-0 ukuya kwi-10. ukuya kwi-10. ukuya kwi-100. ukuya kwi-1 000. • Bhala amagama amanani ukusuka • Bhala amagama amanani ukusuka • Bhala amagama amanani ukusuka ku-1 ukuya kwi-10. kwi-0 ukuya ku-100. kwi-0 ukuya kwi-1 000. UKUPHUHLISA INGQIQO YAMANANI: Chaza, thelekisa uze ucwangcise amanani azeleyo. 1.4 Chaza, thelekisa uze ucwangcise Chaza, thelekisa uze ucwangcise ingqokelela yezinto ukuya kwi-10. ingqokelela yezinto ukuya kuma-20. Chaza, thelekisa uze ucwangcise • Chaza amanani azeleyo ukuya • Chaza uze uthelekise ingqokelela amanani azeleyo. ku-10. yezinto ngokobuninzi, MATHEMATIKA IBANGA LABAQALAYO (R) ngokobuncinane nangokufanayo. • Thelekisa ukuba kwezi ngqokelela zimbini zinikiweyo zezinto ziziphi • Chaza uze ucwangcise ingqokelela ezinkulu, ezincinane, ezincinane yezinto ukusukela kweyona ininzi kunenye, ezinkulu kunezinye, ukuya kweyona incinane nokusuka ezingaphezu kwenye, ezingaphantsi kweyona incinane ukuya kweyona kwezinye, ezilingana nenye, inkulu. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA ezininzi, ezimbalwa ukuya kutsho ku-10. • Cwangcisa ngaphezu kweengqokelela ezimbini ezinikiweyo zezinto ukusukela kweyona incinane ukuya kweyona inkulu ukuya kutsho kwi-10.

ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 1.4 Chaza, thelekisa uze ucwangcise Chaza, thelekisa uze ucwangcise Chaza, thelekisa uze ucwangcise amanani ukuya kutsho kuma-20. amanani ukuya kutsho kuma-99. amanani ukuya kutsho kuma-999. Chaza, thelekisa CAPS uze ucwangcise • Chaza uze uthelekise amanani • Chaza uze uthelekise amanani • Chaza uze uthelekise amanani amanani azeleyo. azeleyo ngokobuncinane kunelinye, azeleyo ukuya kuma-99 azeleyo ukuya kuma-999 ubukhulu kunelinye nokuba ngokobuncinane kunelinye, ngokobuncinane kunelinye, ngaphezulu kwelinye, ngokuba ubukhulu kunelinye nokuba ubukhulu kunelinye nokuba ngaphantsi kwelinye, nokulingana ngaphezulu kwelinye, ngokuba ngaphezulu kwelinye, ngokuba nelinye. ngaphantsi kwelinye, nokulingana ngaphantsi kwelinye, nokulingana nenye. nelinye. • Chaza uze ucwangcise amanani • Chaza uze uthelekise amanani • Chaza uze uthelekise amanani ukusukela kwelona lincinane ukuya azeleyo ukuya kuma-99 ukusukela azeleyo ukuya kuma-99 ukusukela kwelona likhulu nokusukela kwelona kwelona lincinane ukuya kwelona kwelona lincinane ukuya kwelona likhulu ukuya kwelona lincinane. likhulu nokusukela kwelona likhulu likhulu nokusukela kweyona likhulu ukuya kwelona lincinane. ukuya kwelona lincinane. Sebenzisa amanani aqhelekileyo Sebenzisa amanani aqhelekileyo Sebenzisa amanani aqhelekileyo Sebenzisa amanani aqhelekileyo ukubonisa ucwangciso, indawo ukubonisa ucwangciso, indawo ukubonisa ucwangciso, indawo ukubonisa ucwangciso, indawo okanye ubume. okanye ubume. okanye ubume. okanye ubume. Phuhlisa ulwazi ngamanani Beka izinto emgceni ukusukela Beka izinto emgceni ukusukela Sebenzisa, funda uze ubhale amanani aqhelekileyo, umzekelo, okokuqala, kweyokuqala ukuya kweyeshumi kweyokuqala ukuya kweyeshumi aqhelekileyo, kuquka ukushunqulela okwesibini, okwesithathu ukuya okanye eyokuqala ukuya okanye eyokuqala ukuya (okokuqala, okwesibini, okwesithathu kweyesithandathu neyokugqibela. kweyokugqibela, umzekelo, kweyokugqibela, umzekelo, ukuya kweyama-31). eyokuqala, eyesibini, eyesithathu....... eyokuqala, eyesibini, eyesithathu....... kweyeshumi. kweyamashumi amabini. UKUPHUHLISA INGQIQO YAMANANI: Ixabiso lendawo elimi kuyo inani 1.5 Qalisa ukuqonda ixabiso lendawo Qalisa ukuqonda ixabiso lendawo Qaphela ixabiso lendawo ame kuyo elimi kuyo inani ubuncinane elimi kuyo inani ubuncinane amanani amivo mi-3 ukuya ku-999. Ixabiso lendawo amanani amivo mi-2 ukuya kuma-20. amanani amivo mi-2 ukuya kwi-99. elimi kuyo inani. • Cazulula amanani amivo mi-2 • Cazulula amanani amivo mi-2 • Cazulula amanani amivo mi-3 abe zizininzi ze-10 kunye nemivo ukuya kwi-99 abe zizininzi ze-10 ukuya kwi-999 abe zizininzi ze-100, (neeyunithi). kunye nemivo. zibe zizininzi ze-10 kunye nemivo. • Chonga uze uxele ixabiso lendawo • Chonga uze uxele ixabiso lendawo lomvo ngamnye. lomvo ngamnye. SOMBULULA IINGXAKI ZOKUBALA KWIMEKO ETHILE 1.6 Sebenzisa iindlela ngeendlela Sebenzisa iindlela ngeendlela Sebenzisa iindlela ngeendlela Sebenzisa iindlela ngeendlela ezilandelayo ukuya kutsho kwi-10: ezilandelayo xa usombulula iingxaki ezilandelayo xa usombulula iingxaki ezilandelayo xa usombulula iingxaki Iindlela zezibalo nokuchaza izisombululo zezibalo nokuchaza izisombululo zezibalo nokuchaza izisombululo 21 ngeendlela • Izixhobo eziphathekayo, umzekelo, kwiingxaki zezibalo: kwiingxaki zezibalo: kwiingxaki zezibalo: kusombulula iikhawunta / izixhobo zokubala. iingxaki zezibalo MATHEMATIKA IBANGA LABAQALAYO (R)

ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 1.6 • Ileli yamanani aphathekayo. • Izixhobo eziphathekayo, umzekelo, • Imizobo okanye izixhobo • Ukwakha nokucazulula amanani. 22 iikhawunta / izixhobo zokubala. eziphathekayo, umzekelo, Iindlela • Ukuphindaphinda nokwahlulahlula iikhawunta / izixhobo zokubala. ngeendlela • Imifanekiso yokuzoba ibali • amanani. zokusombulula ngezibalo. • Ukwakha nokucazulula amanani. iingxaki zezibalo • Imigca-manani. • Ukwakha nokucazulula amanani. • Ukuphindaphinda nokwahlulahlula amanani. • Ukuwelisela inani kumashumi. • Ukuphindaphinda nokwahlulahlula amanani. • Imigca-manani. • Imigca-manani. 1.7 Sombulula iingxaki zokubala Sombulula iingxaki zokubala Sombulula iingxaki zokubala Sombulula iingxaki zokubala izibalo (amabali ngezibalo) izibalo (amabali ngezibalo) izibalo (amabali ngezibalo) izibalo (amabali ngezibalo) Ukudibanisa ngokusemxholweni ucacisa ngokusemxholweni ucacisa ngokusemxholweni ucacisa ngokusemxholweni ucacisa okuthabatha. isisombululo sakho kwiingxaki isisombululo sakho kwiingxaki isisombululo sakho kwiingxaki isisombululo sakho kwiingxaki zezibalo kuquka ukudibanisa zezibalo kuquka ukudibanisa zezibalo kuquka ukudibanisa zezibalo kuquka ukudibanisa nokuthabatha ngeempendulo ukuya nokuthabatha ngeempendulo ukuya nokuthabatha ngeempendulo ukuya nokuthabatha ngeempendulo ukuya kutsho kwi-10. kutsho kuma-20. kutsho kuma-99. kutsho kuma-999. 1.8 Sombulula iingxaki zokubala Sombulula iingxaki zokubala Sombulula iingxaki zokubala izibalo (amabali ngezibalo) izibalo (amabali ngezibalo) izibalo (amabali ngezibalo) Ukudibanisa ngokusemxholweni ucacisa ngokusemxholweni ucacisa ngokusemxholweni ucacisa okuphindiweyo isisombululo sakho kwiingxaki isisombululo sakho kwiingxaki isisombululo sakho kwiingxaki okukhokelela MATHEMATIKA IBANGA LABAQALAYO (R) zezibalo kuquka ukudibanisa zezibalo usebenzisa ukudibanisa zezibalo kuquka ukudibanisa kuphindaphindo nokuthabatha ngeempendulo ukuya ngokuphindaphindeneyo nokuthabatha ngeempendulo ukuya lwamanani. kutsho kuma-20. nophindaphindo oluneempendulo kutsho kwi-100. ukuya kuma-50. 1.9 Sombulula uze ucacise Sombulula uze ucacise izisombululo Sombulula uze ucacise izisombululo Sombulula uze ucacise izisombululo izisombululo kwizibalo zamagama kwiingxaki zezibalo abazenza kwiingxaki zezibalo abazenza kwiingxaki zezibalo abazenza INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukwahlula ngokusemxholweni (izibalo zamazwi) ngokwabo abafundi kuquka ukwaba ngokwabo abafundi kuquka ukwaba ngokwabo abafundi kuquka ukwaba ngokwamaqela eziquka ukwaba ngokulinganayo, ngokulinganayo nokwahlula ngokulinganayo nokwahlula ngokulinganayo nokwahlula nokwaba ukwahlula ngokwamaqela ngamanani ngokwamaqela amanani azeleyo ngokwamaqela amanani azeleyo ngokwamaqela ukuya kutsho kwi-100 ngokulinga azeleyo ukuya kutsho kwi-10 kunye ukuya kutsho kuma-20 kunye ukuya kutsho kuma-50 kunye kunye neempendulo ezinokuquka okukhokelela neempendulo ezinokuquka iintsalela. neempendulo eziquka iintsalela. neempendulo eziquka iintsalela. iintsalela. kulwahlulwa- hlulo. 1.10 Sombulula uze ucacise izisombululo Sombulula uze ucacise izisombululo kwiingxaki eziprekthikhali zezibalo kwiingxaki eziprekthikhali zezibalo Ukwaba eziquka ukwaba ngokulinganayo eziquka ukwaba ngokulinganayo ngokulinganayo kukhokelele kwizisombululo eziquka kukhokelele kwizisombululo eziquka okukhokelela amaqhezu amanyeneyo. amaqhezu angamanyananga kumaqhezu. namanyeneyo.

ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 1.11 Phuhlisa ulwazi ngemali eziinkozo/ • Qaphela uze ufundise ngemali • Qaphela uze ufundise ngemali • Qaphela uze ufundise ngemali engumwangalala nengamaphepha eziinkozo yaseMzantsi Afrika (i-5c, eziinkozo yaseMzantsi Afrika (i-5c, eziinkozo yaseMzantsi Afrika kunye Imali CAPS yebhanki yaseMzantsi Afrika. i-10c, i-20c, i-50c, i-R1, i-R2, i-R5) i-10c, i-20c, i-50c, i-R1, i-R2, i-R5) nemali engamaphepha. kunye nemali engamaphepha kunye nemali engamaphepha eyi-R10 nama-R20. eyi-R10, i-R20 nama-R50. • Sombulula iingxaki zemali eziquka • Sombulula iingxaki zezemali • Sombulula iingxaki ezingemali iitotali netshintshi ye-R20 kunye eziquka iitotali netshintshi ye-R99 eziquka iitotali netshintshi neesenti ukuya kuma-20c. kunye neesenti ukuya kuma-90c. ngokweerandi okanye iisenti. • Guqula phakathi kweerandi neesenti. IZIBALO EZINGALAWULWA-MEKO 1.12 Sebenzisa iindlela ngeendlela Sebenzisa iindlela ngeendlela Sebenzisa iindlela ngeendlela ezilandelayo zokubala xa usenza ezilandelayo zokubala xa usenza ezilandelayo zokubala xa usenza Ubuchule izibalo: izibalo: izibalo: bokubala • Imizobo okanye izixhobo • Imizobo okanye izixhobo (Iindela) eziphathekayo, umzekelo, eziphathekayo, umzekelo, iikhawunta / izixhobo zokubala. iikhawunta / izixhobo zokubala. • Ukwakha nokucazulula amanani. • Ukwakha nokucazulula amanani. • Ukwakha nokucazulula amanani. • Ukuphindaphinda nokwahlulahlula • Ukuphindaphinda nokwahlulahlula • Ukuphindaphinda nokwahlulahlula amanani. amanani. amanani. • Imigca-manani. • Imigca-manani. • Imigca-manani. • Ukuwelisa inani kumashumi. 1.13 Sombulula iingxaki zokudibanisa • Dibanisa ukuya kuma-20. • Dibanisa ukuya kuma-99. • Dibanisa ukuya kuma-999. nokuthabatha ngomlomo Ukudibanisa • Thabatha ukusuka kuma-20. • Thabatha ukusuka kuma-99. • Thabatha ukusuka kuma-999. nezisombululo ukuya kutsho kwi-10. nokuthabatha. • Sebenzisa iisimboli ezifanelekileyo • Sebenzisa iisimboli ezifanelekileyo • Sebenzisa iisimboli ezifanelekileyo (+, –, =, ) (+, –, =, ). (+, –, =, ). • Qhelanisa iibhondi zamanani ukuya • Qhelanisa iibhondi zamanani ukuya • Qhelanisa iibhondi zamanani ukuya kwi-10. kuma-20. kuma-30. 1.14 • Dibanisa inani elinye ngokuphinda • Phindaphinda amanani ngo-1 ukuya • Phindaphinda ngalo naliphi inani Ukudibanisa phindiweyo ukuya kutsho kuma-20. kwi-10 ngo-2, 5, 3 kunye no-4 ngo-2, 3, 4, 5, 10 ukuya kwitotali ngokuphinda kwitotali engama-50. eli-100. phindiweyo • Sebenzisa iisimboli ezifanelekileyo • Sebenzisa iisimboli ezifanelekileyo • Sebenzisa iisimboli ezifanelekileyo okukhokelela (+, =, ). (+, –, =, ). (x, ). 23 kuphindaphindo lwamanani. MATHEMATIKA IBANGA LABAQALAYO (R)

ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 1.15 • Hlulahlula amanani ukuya kuma-99 24 ngo-2, 3, 4, 5, 10. Ukwahlulahlula. • Sebenzisa iisimboli ezifanelekileyo (÷, =, ). 1.16 Ingqiqo ngamanani: Uluhlu Ingqiqo ngamanani: Uluhlu Ingqiqo ngamanani: Uluhlu lwama-20. lwama-99. lwama-999. Izibalo zentloko. • Xela inani phambi nasemva kwenani elinikiweyo. • Cwangcisa iseti enikiweyo • Cwangcisa iseti enikiweyo • Cwangcisa iseti enikiweyo yamanani akhethiweyo. yamanani akhethiweyo. yamanani akhethiweyo. • Thelekisa amanani ukuya kutsho • Thelekisa amanani ukuya kutsho • Thelekisa amanani ukuya kutsho kuma-20 uze uxele ukuba u-1 kuma-99 uze uxele ukuba u-1, 2, kuma-999 uze uxele ukuba u-1, 2, kunye no-2 ungaphantsi okanye 3, 4, 5 kunye no-10 ungaphantsi 3, 4, 5 kunye ne-10 ungaphantsi ungaphezulu. okanye ungaphezulu. okanye ungaphezulu. Ukukhumbula ngokukhawuleza: Ukukhumbula ngokukhawuleza: Ukukhumbula ngokukhawuleza: • Izinto eziyinyaniso ngokudibanisa • Izinto eziyinyaniso ngokudibanisa • Khumbuza ngezinto eziyinyaniso nokuthabatha ukuya kwi-10 nokuthabatha ukuya kuma-20. ngokudibanisa nokuthabatha ukuya MATHEMATIKA IBANGA LABAQALAYO (R) kuma-20. • Dibanisa okanye uthabathe izininzi • Dibanisa okanye uthabathe izininzi ze-10 ukusuka kwi-0 ukuya kwi-100. zika-10 ukusuka kwi-0 ukuya kwi- 100. • Izinto eziyinyaniso ngophindaphindo: INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- 2 Iithaymtheyibhile ka-2 eneempendulo ukuya kutsho kuma-20. -- 10 iithayimtheyibhile ze-10 eneempendulo ukuya kutsho • kwi-100 • Izinto eziyinyaniso ngokwahlulahlula amanani: -- Ukuya kutsho kuma-20 kohlulwe ngo-2 -- Ukuya kutsho kwi-100 kohlulwe • nge-10

ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 Iindlela zokubala Iindlela zokubala Iindlela zokubala • Sebenzisa iindlela zokubala • Sebenzisa iindlela zokubala • Sebenzisa iindlela zokubala CAPS ukudibanisa nokuthabatha ukudibanisa nokuthabatha ezilandelayo: ngokukuko: ngokukuko: • Beka inani elikhudlwana kuqala • Beka inani elikhudlwana kuqala • Beka inani elikhudlwana kuqala ukuze ubale ukuya phambili okanye ukuze ubale ukuya phambili okanye ukuze ubale ukuya phambili okanye ngasemva. ngasemva. ubuya umva. • Umgca-manani. • Umgca-manani. • Umgca-manani. • Ukuphindaphinda nokwahlulahlula • Ukuphindaphinda nokwahlulahlula • Ukuphindaphinda nokwahlulahlula amanani. amanani. amanani. • Ukwakha nokucazulula amanani. • Ukwakha nokucazulula amanani. • Ukwakha nokucazulula amanani. • Sebenzisa ulwalamano phakathi • Sebenzisa ulwalamano phakathi kokudibanisa nokuthabatha. kokudibanisa nokuthabatha. • Sebenzisa ulwalamano phakathi kokuphindaphinda nokwahlulahlula. 1.17 • Sebenzisa uze uxele amaqhezu • Sebenzisa uze uxele amaqhezu e-unitary (unitary fractions) e-unitary (unitary fractions) Amaqhezu. ngokwemixholo eqhelekileyo ngokwemixholo eqhelekileyo kuquka iziqingatha, iikota, izithathu kuquka iziqingatha, iikota, izibhozo, nezine. izithandathu, izihlanu, izithathu nezine. • Qaphela amaqhezu ngokodidi • Qaphela amaqhezu ngokodidi lomzobi. lomzobo. • Qala ukuqaphela ukuba iziqingatha ezibini okanye ezithathu zezithathu zenza enye epheleleyo kunye nesiqingatha esinye kunye neekota ezimbini ziyalingana. • Bhala amaqhezu njengesiqingatha • Bhala amaqhezu njengesiqingatha esi-1. esi-1, nezithathu ezi-2. 25 MATHEMATIKA IBANGA LABAQALAYO (R)

AMAGQABANTSHINTSHI ESIGABA ESISISEKO 2. IIPATENI, ISIPHUMO SENTSEBENZISWAMO YAMANANI / IFANKSHINI NE-ALJIBRA 26 Inkqubela-phambili kwiipateni, iifankshini/ ifankshini ne-aljibra. • Kwiipateni, kwiifankshini ne-aljibra, sinika abafundi amathuba: -- Okugqibezela nokwandisa iipateni ezimelwe ziimo ezahlukeneyo. -- ukukhetha nokuchaza iipateni. • Ukuchaza iipateni sisiseko sabafundi kwisiGaba esiPhakathi ukuchaza imithetho ngeepateni. Oku kwenziwa ngokuseSikweni kumsebenzi we-aljibra kwisiGaba esiPhezulu. ISIHLOKO IBANGA LABAQALAYO IBANGA LOKU-1 IBANGA LESI-2 IBANGA LESI-3 2.1 Ukukhuphela nokwandisa Ukukhuphela, ukwandisa Ukukhuphela, ukwandisa Ukukhuphela, ukwandisa nokuchaza. nokuchaza. nokuchaza. Iipateni zejiyometri • Ukukhuphela nokwandisa iipateni • Ukukhuphela, ukwandisa • Ukukhuphela, ukwandisa • Ukukhuphela, ukwandisa ezilula usebenzisa izinto nemizobo nokuchaza amagama. nokuchaza amagama. nokuchaza amagama. (umzekelo, ukusebenzisa imibala • Iipateni ezilula ezenziwe ngezinto • Iipateni ezinzima ezenziwe ngezinto • Iipateni ezinzima ezenziwe ngezinto neemilo). eziphathekayo. eziphathekayo. eziphathekayo. • Iipateni ezilula ezenziwa ngemizobo • Iipateni ezinzima ezenziwa • Iipateni ezinzima ezenziwa yemigca, iimilo okanye izinto. ngemizobo yemigca, iimilo okanye ngemizobo yemigca, iimilo okanye izinto. izinto. Ukuyila iipateni zakho. Ukuyila nokuchaza iipateni zakho. Ukuyila nokuchaza iipateni zakho. MATHEMATIKA IBANGA LABAQALAYO (R) • Ukuyila iipateni zakho zejiyometri. • Ngezinto eziphathekayo. • Ngezinto eziphathekayo. • Ngezinto eziphathekayo. • Ngokuzoba imigca, iimilo okanye • Ngokuzoba imigca, iimilo okanye izinto. izinto. • Ngokuzoba imigca, iimilo okanye izinto. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Iipateni ezisirhangqileyo Iipateni ezisirhangqileyo Iipateni ezisirhangqileyo Ukukhetha, ukuchaza ngamagama Ukukhetha, ukuchaza ngamagama Ukukhetha, ukuchaza ngamagama nokukhuphela iipateni zejiyometri nokukhuphela iipateni zejiyometri nokukhuphela iipateni zejiyometri. • Kwindalo, • Kwindalo, • Kwindalo, • Kubomi bemihla ngemihla, • Kubomi bemihla ngemihla, • Kubomi bemihla ngemihla, • Kwimveli yethu yenkcubeko. • Kwimveli yethu yenkcubeko. • Kwimveli yethu yenkcubeko. 2.2 Ukukopa, ukwandisa nokuchaza. Ukukopa, ukwandisa nokuchaza. Ukukopa, ukwandisa nokuchaza. Iipateni Ukukopa, ukwandisa nokuchaza Ukukopa, ukwandisa nokuchaza Ukuopa, ukwandisa nokuchaza zamanani ulandelelwano lwamanani olulula ulandelelwano lwamanani olulula ulandelelwano lwamanani olulula ukuya kutsho kwi-100. ukuya kutsho kuma-200. ukuya kutsho kuma-999. Ukuyila nokuchaza iipateni zakho. Ukuyila nokuchaza iipateni zakho. Ukuyila nokuchaza iipateni zakho.

AMAGQABANTSHINTSHI ESIGABA ESISISEKO 3. ISITHUBA NEMILO (ijiyometri) Ukuqhubeka kwindawo nemo CAPS Undoqo wokuqhubeka kwindawo nemo kungaphunyezwa ngoku: • bethelela kwiipropati neempawu zemo nezinto kwiBanga ngalinye; kunye • nokusuka efundeni kolwimi lwendawo nokudityaniswa kwezimvo ezahlukeneyo kwangalaa nto ekufundeni nasekulandeni indlela kwiimephu ezingekho seSikweni. ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 3.1 Ulwimi lwendawo Ulwimi lwendawo Ulwimi lwendawo Indawo-bume, Chaza indawo yento malunga Chaza indawo yento malunga Chaza indawo yento malunga ukufumana nenye umz. ngaphezulu kwenye, nenye umz. ngaphezulu kwenye, nenye umz. ngaphezulu kwenye, indawo ngaphambili, ngasemva, ekunene, ngaphambili, ngasemva, ekuneene, ngaphambili, ngasemva, ekunene, nembonakalo ekhohlo, phantsi, phezulu, ecaleni ekhohlo, phantsi, phezulu, ecaleni ekhohlo, phantsi, phezulu, ecaleni Indawo-bume nembonakalo Indawo-bume nembonakalo Indawo-bume nembonakalo • Qonda ze udibanise iimbonakalo • Qonda ze udibanise iimbonkalo • Qonda ze udibanise izimvo ezahlukeneyo ngezinto ezifanayo ezahlukeneyo ngezinto ezifanayo ezahlukeneyo ngezinto ezifanayo yonke imihla yonke imihla yonke imihla • Xela into yemihla ngemihla njengoko kuboniswe ubume bayo obungaqhelekanga • Funda, tolika, ze uzobe iimephu ezingekho seSikweni okanye izimvo eziphezulu zengqokelela yezinto. • Khangela izinto kwimephu Indawo -bume nesalathiso Indawo nesalathiso Indawo nesalathiso Indawo nesalathiso Landela izalathiso ukuhamba-hamba • Landela izalathiso ukuhamba- • Landela izalathiso ukuhamba- • Landela izalathiso ukuhamba- eklasini hamba eklasini hamba eklasini hamba eklasini nasesikolweni . • Landela imiyalelo ukubeka into • Nika izalathiso zokuhamba-hamba enye ngokuhambelana nenye umz. eklasini nasesikolweni. ukubeka ipensile emva kwebhokisi • Landela izalathiso ukusuka kwenye indawo uye kwenye kwimephu engekho seSikweni 27 MATHEMATIKA IBANGA LABAQALAYO (R)

ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 3.2 Uludwe/ uluhlu lwezinto Uludwe/ uluhlu lwezinto Uludwe/ uluhlu lwezinto Uludwe/ uluhlu lwezinto 28 Izinto Khumbula ze uxele izinto Khumbula ze uxele izinto Khumbula ze uxele izinto Khumbula ze uxele izinto ezinokwakheka ezinokwakheka kuka 3-D eklasini ezinokwakheka kuka 3-D eklasini ezinokwakheka kuka 3-D eklasini ezinokwakheka kuka 3-D eklasini kuka 3-D nasemifanekisweni nasemifanekisweni nasemifanekisweni • Iimilo ezibubhola, • Iimilo ezibubhola (into engqukuva • Iimilo ezibubhola (into engqukuva • Imilo ezibubhola (into engqukuva eqinileyo eqinileyo eqinileyo • Iimilo ezibubhokisi • Iimilo ezibubhokisi • Iimilo ezibubhokisi (into ebonakala • Iimilo ezibhokisi (into ebonakala ngokufanayo) ngokufanayo) • Iisilinda / imibhobho • Iisilinda / imibhobho • iiphiramidi • iikhowuni impawu zezinto Iimpawu zezinto Iimpawu zezinto Iimpawu zezinto Chaza, hlela uze uthelekise izinto Chaza,hlela uze uthelekise izinto Chaza,hlela uze uthelekise izinto Chaza, hlela uze uthelekise izinto eznokwakheka kuka 3-D malunga: ezinokwakheka kuka 3-D malunga: ezinokwakheka kuka 3-D malunga: ezinokwakheka kuka 3-D malunga • nobungakanani • nobungakanani • nobungakanani • Iimilo ezinokwakheka kuka 2-D ezenza iimbuso zezinto • izinto eziqengqelekayo MATHEMATIKA IBANGA LABAQALAYO (R) • umbala • umbala ezinokwakheka kuka 3-D • izinto eziqengqelekayo • izinto eziqengqelekayo • izinto ezitshibilikayo • Izinto ezisicaba nezigosogoso • izinto ezitshibilikayo • izinto ezitshibilikayo Imisebenzi yokubethelela Imisebenzi yokubethelela Imisebenzi yokubethelela Imisebenzi egxininiswayo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA • sebenzisa izinto ezinokwakheka • Qaphela ze wakhe izinto • Qaphela ze wakhe izinto eziyi • Qaphela ze wakhe izinto kuka 3-D ezifana neebhloko ezinokwakheka kuka 3-D -3-D ozinikiweyo usebenzisa ezinokwakheka kuka 3-D zokwakha, ukuvuselela ngokutsha, ozinikiweyo usebenzisa imathiriyeli imathiriyeli ephathekayo efana ozinikiweyo usebenzisa imathiriyeli njalo njalo ukwakha amalungu ephathekayo efana neebhloko nemisikwa ezinokwakheka ephathekayo efana nemisikwa ezinto umz iithawa, iibhulorho, njalo zokwakha, ukuvuselela neekiti kuka 2-D, iibhloko zokwakha, ezinokwakheka kuka 2-D , njalo. zokwakha ukuvuselela, iikiti zokwakha nezinye udongwe, micinga yokuvungula, izinto ezinokwakheka kuka 3-D imicinga yokusela (izitro) nezinye ezinemigca neembombo - izinto ze 3-D ezinemigca nembobo

ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 3.3 Uluhlu lweemilo Uluhlu lweemilo Uluhlu lweemilo Uluhlu lweemilo Imilo Chaza, hlela ze uthelekise iimilo Qonda/khumbula ze uxele iimilo Qonda/khumbula ze uxele iimilo Qonda/khumbula ze uxele iimilo CAPS enokwakheka ezinokwakheka kuka 2-D/ imifanekiso ezinokwakheka kuka 2-D ezinokwakheka kuka 2-D ezinokwakheka kuka 2-D kuka ngokwezi zinto: • Izangqa • Izangqa • Izangqa 2-D • Ubungakanani • oonxantathu • oonxantathu • oonxantathu • Umbala • izikwere • izikwere • izikwere • Imilo eyimigca nembombo • iingxande • iingxande Iimpawu zemilo Iimpawu zemilo Iimpawu zemilo Chaza, hlela ze uthelekise iimilo Chaza, hlela ze uthelekise iimilo ei Chaza, hlela ze uthelekise iimilo eyi ezinokwakheka kuka 2-D malunga: 2-D malunga: 2-D malunga: • nobungakanani • nobungakanani • nemilo • umbala • milo • amacala athe ngqo • amacala athe ngqo • amacala athe ngqo • izangqa • izangqa • izangqa Ukuzoba imilo • Izangqa • oonxantathu • izikwere • iingxande 3.4 Ulingano-macala (Isimetri) Ulingano-macala (Isimetri) Ulingano-macala (Isimetri) Ulingano-macala (Isimetri) Ulingano-macala • Ukukhumbula isimetri emzimbeni • khumbula isimetri emzimbeni wakho • khumbula ze wakhe umgca • khumbula ze wakhe umgca (isimetri) wakho wesimetri kwimilo ezinokwakheka wesimetri kwiimilo ezinokwakheka • khumbula ze wakhe umgca kuka 2-D enemigca neembombo kuka 2-D enemigca neembombo wesimetri kwiimilo ezinokwakheka nengenayo nengenayo kuka 2-D enemigca neembombo nengenayo • Yenza umgca wesimetri ngephepha elisongiweyo 29 MATHEMATIKA IBANGA LABAQALAYO (R)

AMAGQABANTSHINTSHI ESIGABA ESISISEKO 4. UMLINGANISELO 30 Ukuqhuba noMlinganiselo • Undoqo wokuqhuba nomlinganiselo kumaBanga jikelele ungaphunyezwa ngokuqalwa kwe: -- Milo/ iifomu ezintsha zomlinganiselo -- Izixhobo ezitsha zomlinganiselo, ukuqala ngezixhobo ezingekho seSikweni ze udlulele kwezo ziseSikweni kubaBanga lesi- 2 nelesi-3 -- Iiyunithi ezintsha zomlinganiselo ngakumbi kumaBanga elesi -2 nelesi-3. • Ubalo nokusombulula iingxaki ngomlinganiselo makuthabathele ingqalelo ubungakanani bomsebenzi osele wenziwe. ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 4.1 Ukuqingqa ixesha Ukuqingqa ixesha Ixesha Ukuthetha malunga nokudlula Ukuthetha malunga nokudlula kwexesha kwexesha • Ukuthetha ngezinto ezenzeke emini • Ukulandelelanisa iziganeko nezo zenzeka ebusuku ezenzeka rhoqo ebomini babo. • Abafundi balandelelanisa iziganeko • Ukuthelekisa ubude bexesha ezenzeke ngexesha lasemini usebenzisa ulwimi umz. ende, emifutshane, ekhawulezayo • Ukulandelelanisa iziganeko necothayo. MATHEMATIKA IBANGA LABAQALAYO (R) ezenzeka rhoqo ebomini babo. • Ukulandelelanisa iziganeko usebenzisa ulwimi umz. izolo, namhlanje, ngomso. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 4.1 Ukuxela ixesha Ukuxela ixesha Ukuxela ixesha Ixesha • Chaza ukuba into yenzeke xesha • Funda imihla yekhalenda CAPS nini umz. kusasa, emva kwemini, • Bhala iintsuku zokuzalwa, ebusuku, kwangoko/ngethuba, kade iminyhadala yenkolo, iintsuku zeholide, iziganeko zembali, iziganeko zesikolo ngokwekhalenda • Xela ze ulandelelanise iintsuku • Xela ze ulandelelanise iintsuku zeveki neenyanga zonyaka zeveki neenyanga zonyaka • Bhala iintsuku zokuzalwa • Bhala iintsuku zokuzalwa, kwikhalenda iminyhadala yenkolo, iintsuku zeholide, iziganeko zembali, iziganeko zesikolo ngokwekhalenda • Ixesha ngosuku, ngeziqendu • Xela ixesha ngokosuku zeeyure, umkhono weyure -- Iiyure -- Iziqendu zeyure -- Umkhono weyure -- Imizuzu • iwotshi yosiba newotshi edanyazayo, umz. Ixesha leselula Bala ubude bexeha nokuhamba Bala ubude bexeha nokuhamba kwalo kwalo • Sebenzisa ikhalenda ukubala • Sebenzisa ikhalenda ukubala nokuchaza ixesha: nokuchaza ixesha: -- ngosuku, -- ngosuku, -- ngeeveki -- ngeeveki -- neenyanga • Ukusebenzisa iwotshi ukubala • Sebenzisa iwotshi ukubala ubude ubude bexesha: bexesha: -- Iiyure -- Iiyure -- Iziqendu zeyure -- Iziqendu zeyure -- Umkhono weeyure. 31 MATHEMATIKA IBANGA LABAQALAYO (R)

ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 4.2 Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni 32 Ubude • Thelekisa ze ulandelelanise ubude, • Thelekisa ze ulandelelanise ubude, umphakamo okanye ububanzi umphakamo okanye ububanzi bezinto ezimbini nangaphezulu bezinto ezimbini nangaphezulu ngokuzibeka zibe calanye. ngokuzibeka zibe calanye. Sebenzisa ulwimi ukuthetha Sebenzisa ulwimi ukuthetha malunga nokuthelekisa umz ende, malunga nokuthelekisa umz ende, emfutshane, nebanzi emfutshane, nebanzi • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, thelekelela, landelelanisa ze thelekisa, landelelanisa, ze thelekelela, landelelanisa ze urekhodishe ubude usebenzisa urekhodishe ubude usebenizisa urekhode ubude usebenzisa imilinganiselo engekho seSikweni imilinganiselo engekho seSikweni imilinganiselo engekho seSikweni umz umlinganiselo ngesandla, umz umlinganiselo ngesandla, umz umlinganiselo ngesandla, izantya, ubude bepensile izantya, ubude bepensile izantya, ubude bepensile nekhawunta. nekhawunta. nekhawunta • Chaza ubude bezinto ngokubala • Chaza ubude bezinto ngokubala • Chaza ubude bezinto ngokubala nokuxela ubude beeyunithi nokuxela ubude beeyunithi nokuxela ukuba zingaphi iiyunithi ezingekho seSikweni ezingekho seSikweni ezingekho seSikweni nobude bazo Ukwazisa umlinganiselo Ukwazisa umlinganiselo oseSikweni oseSikweni MATHEMATIKA IBANGA LABAQALAYO (R) • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, thelekisa, landelelanisa ze thelekisa, landelelanisa ze urekhode ubude usebenzisa iimitha urekhodishe ubude usebenzisa (usenokusebenzisa izinti okanye iimitha (usenokusebenzisa izinti imisonto) njengeeyunithi zobude okanye imisonto) njengeeyunithi eziseSikweni. zobude eziseSikweni. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA • Qikelela ze ulinganisele ubude ngeesentimitha usebenzisa irula. Akukho nguqulelo zifunekayo phakathi kweemitha neesentimitha

ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 4.3 Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umthamo • Thelekisa ze ulandelelanise ubude • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, CAPS bezinto ezimbini nangaphezulu thelekisa, landelelanisa, ze thelekisa, landelelanisa, ze thelekisa, landelelanisa ze ngokuziva ngesandla okanye urekhodishe ubuninzi usebenzisa urekhodishe ubuninzi usebenzisa urekhodishe ubuninzi usebenzisa usebenzise isikali sokulungelelanisa isikali nemilinganiselo engekho isikali nemilinganiselo engekho isikali nemilinganiselo engekho seSikweni umz iibloksi, izitena seSikweni umz iibloksi, izitena seSikweni umz iibloksi, izitena. • Chaza ubude bezinto ngokubala • Chaza ubude bezinto ngokubala • Chaza ubude bezinto ngokubala nokuxela ubude beeyunithi nokuxela ubude beeyunithi nokuxela ubude beeyunithi ezingekho seSikweni ezingekho seSikweni ezingekho seSikweni • Sebenzisa ulwimi ukuthetha • Sebenzisa ulwimi ukuthetha • Sebenzisa ulwimi ukuthetha • Sebenzisa ulwimi ukuthetha malunga nothelekiso umz ilula, malunga nothelekiso umz ilula, malunga nothelekiso umz ilula, malunga nothelekiso umz ilula, inzima, ilulana, inzinyana inzima, ilulana, inzinyana inzima, ilulana, inzinyana inzima, ilulana, inzinyana Ukwazisa umlinganiselo • Ukwazisa umlinganiselo oseSikweni oseSikweni • Thelekisa, ulandelelanise ze • Thelekisa, landelelanisa, ze urekhodishe ubuninzi bezinto urekhodishe ubuninzi bezinto ezilungiselelwe intengiso ezilungiselelwe iintengiso ezinobunzima obuxelwe ezinobunzima obuxewe ngekhilogrem kuphela umz u2 kg ngeekhilogrem: werayisi no1kg womgubo • u2 kg werayisi no1kg womgubo • Thatha umlinganiselo umlinganiselo wobubanzi babo ngeekhilogram • Iigrem umz. 500 grems yetyuwa usebenzisa isikali sendlu • Thatha umlinganiselo umlinganiselo yokuhlambela wobubanzi babo ngeekhilogram usebenzisa isikali sendlu yokuhlambela • Akukho nguqulelo phakathi kweegrem nekhilogrem Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni Umlinganiselo ongekho seSikweni • Thelekisa ze ulandelelanise • Thelekisa ze ulandelelanise umlinganiselo wobubanzi umlinganiselo wokubanzi (ubuninzi ngokomthamo) (ubuninzi ngokomthamo) kwizikhongozeli ezibini kwizikhongozeli ezimbini ezibekwe ngokusondeleleneyo. ezibekwe ngokusondeleneyo. Abafunda bajonga ngokugalela Abafundi bajonga ngokugalela kwisikhongozeli sesithathu xa kwisikhongozeli sesithathu xa kuyimfuneko. kuyimfuneko. • Thelekisa ze ulandelelanise • Thelekisa ze ulandelelanise 33 umlinganiselo wokubanzi umlinganiselo wokubanzi onokuthwalwa zizikhongozeli onokuthwalwa zizikhongozeli ezimbini xa zigcwalisiwe. (ubuninzi) ezimbini xa zigcwalisiwe. (ubuninzi) MATHEMATIKA IBANGA LABAQALAYO (R)

ISIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 4.4 • Sebenzisa ulwimi ukuthetha • Sebenzisa ulwimi ukuthetha 34 malunga nokuthelekisa izinto malunga nokuthelekisa izinto Umthamo/ umz ngaphezulu, kancinci, izele, umz ngaphezulu, kancinci, izele, Ivolumu ayinanto ayinanto • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, thelekisa, landelelanisa, ze thelekisa, landelelanisa, ze thelekisa, landelelanisa, ze urekhodishe ubude usebenzisa urekhodishe ubuninzi bomthamo urekhodlshe ubuninzi bomthamo imilinganiselo engekho seSikweni wezikhongozeli (ubuninzi wezikhongozeli (ubuninzi umz amacephe neekomityi bomthamo wesikhongozeli xa bomthamo wesikhongozeli xa ugcwalisiwe) ngokusebenzisa ugcwalisiwe) ngokusebenzisa imilinganiselo engekho seSikweni imilinganiselo engekho seSikweni umz amacephe neekomityi umz amacephe neekomityi • Chaza ubuninzi besikhongozeli • Chaza ubuninzi besikhongozeli • Chaza ubuninzi besikhongozeli ngokubala nokuxela ukuba zingaphi ngokubala nokuxela ukuba zingaphi ngokubala nokuxela ukuba zingaphi iiyunithi ezingekho seSikweni iiyunithi ezingekho seSikweni iiyunithi ezingekho seSikweni ukugcwalisa isikhongozeli umz ukugcwalisa isikhongozeli, umz. ukugcwalisa isikhongozeli umz ibhotile inobuninzi beekomityi ezine ibhotile inobuninzi beekomityi ezine. ibhotile inobuninzi beekomityi ezine. • Umlinganiselo ongekhoseSikweni • Umlinganiselo ongekhoseSikweni • Qikelela, thatha umlinganiselo, • Qikelela, thatha umlinganiselo, thelekisa, landelelanisa, ze thelekisa, landelelanisa, ze urekhodishe ubuninzi bezinto urekhodishe ubuninzi bezinto MATHEMATIKA IBANGA LABAQALAYO (R) ngomlinganiselo weelitha ngomlinganiselo weelitha • Iihafu zelitha neekota zelitha • Thelekisa, ulandelelanise ze • Thelekisa, ulandelelanise ze urekhodishe ubuninzi bezinto urekhodishe ubuninzi bezinto ezilungiselelwe iintengiso ezilungiselelwe iintengiso INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA ezinobunziba obuxelwe ngeelitha ezinobunziba obuxelwe ngeelitha umz iilitha ezimbini zobisi, ilitha enye yesiselo esibandayo, iilitha Akukho nguqulelo phakathi kweegrem ezintlanu zepeyinti nekhilogrem, iimililitha neelitha 4.5 Umjikelezo nommandla Umjikelezo Phanda ngomgama ophakathi nommandla kweemilo ezinokwakheka kuka 2-D neyi-3-D usebenzisa uthelekiso okanye iiyunithi ezingekho seSikweni. Ummandla Phanda i-eriya usebenzisa uthayilisho

AMAGQABANTSHINTSHI ESIGABA ESISISEKO 5. INDLELA YOKUSEBENZA NGOLWAZI OLUQOKELELWEYO Ukuqhubeka kwindlela yokusebenza ngolwazi oluqokelelweyo CAPS • Undoqo wokuqhubeka kwendlela yokusebenza ngolwazi oluqokelelweyo kumaBanga jikelele lungaphunyezwa ngoku: • Ukuqhubela phambili ngokuSebenza ngoLwazi oluQokeleleweyo (ulwazi) kuwo onke amaBanga okufezekiswa ngolu hlobo: -- Ukusuka ekusebenziseni kwento uye kusebenzisa ulwazi / ulwazi; kunye -- Nokusebenza neefom ezintsha zomelo-lwazi lwedatha. • Abafundi mabasebenze umjikelo opheleleyo wedatha ubuncinane kanye ngonyaka – oku kuquka ukuqokelelwa nokulungisa ulwazi, ukumela ulwazi, ukuhlahlela/ukucalula, ukutolika nokunika ingxelo ngedatha. • Ezinye zezi nkangeleko zingentla zedatha zingenziwa njengemisebenzi ekhethekileyo. IsIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 5.1 Ukuqokelela nokulungisa izinto Ukuqokelela nokulungisa izinto Qokelela ze Qokelela ze uhlele izinto Qokelela ze uhlele izinto uhlele izinto eziphathekayo zemihla ngemihla eziphathekayo zemihla ngemihla 5.2 Ukumela/ukubonakalisa Ukumela/ukubonakalisa ingqokelela ehleliweyo yezinto ingqokelela ehleliweyo yezinto Ukumela/ Zoba umfanekiso wengqokelela Zoba umfanekiso wengqokelela ukubonakalisa yezinto (ipictograph) yezinto ingqokelela ehleliweyo yezinto 5.3 Ukuxoxa nokunika ingxelo Ukuxoxa nokunika ingxelo ngengqokelela ehleliweyo yezinto ngengqokelela ehleliweyo yezinto Ukuxoxa nokunika ingxelo Ukuphendula imibuzo emalunga: • Nika izizathu zokuba ingqokelela ngengqokelela ihlelwe njani • Nokuba ingqokelela ihlelwe njani ehleliweyo • Ukuphendula imibuzo emalunga yezinto • Ukuzoba ingqokelela -- Nokuba uhlelo lwenziwe njani (inkqubo) -- Ibonakala njani le ngqokelela ihleliweyo(imveliso) • Chaza ingqokelela okanye/ umzobo • Cacisa ukuba le ngqokelela ihlelwe 35 njani MATHEMATIKA IBANGA LABAQALAYO (R)

IsIHLOKO IBANGA R IBANGA 1 IBANGA 2 IBANGA 3 5.4 Ukuqokelelo nokulungisa ulwazi Ukuqokelelo nokulungisa ulwazi Ukuqokelelo nokulungisa ulwazi 36 Ukuqokelela • Qokelela ulwazi emalunga neklasi • Qokelela ulwazi emalunga neklasi • Qokelela ulwazi emalunga neklasi nokulungisa okanye isikolo ukuphendula imibuzo okanye isikolo ukuphendula imibuzo okanye isikolo ukuphendula imibuzo ulwazi ebuzwa ngutitshala ebuzwa ngutitshala ebuzwa ngutitshala • Lungiselela ulwazi ngokungqinelana • Lungiselela ulwazi enikezelwe kwazo ngutitshala okanye incwadi yomfundi • Lungiselela ulwazi ngoko -- Uluhlu -- Ngokungqinelana -- kwetheyibhile 5.5 Ukubonakalisa ulwazi Ukubonakalisa ulwazi Ukubonakalisa ulwazi Ukubonakalisa Ukubonakalisa igrafu yemifanekiso Ukubonakalisa igrafu yemifanekiso, • Lungiselela ulwazi ngokwe ulwazi (picto graph) ejongene no-1 ukuya ejongene no-1 ukuya ku-1 kuphela -- igrafu yemifanekiso, ejongene ku-1 kuphela no-1 ukuya ku-1 kuphela -- igrafu yezitena(bar graph) 5.6 Ukucalula nokutolika ulwazi Ukucalula nokutolika ulwazi Ukucalula nokutolika ulwazi MATHEMATIKA IBANGA LABAQALAYO (R) Ukucalula Phendula imibuzo emalunga nedatha Phendula imibuzo emalunga nedatha Phendula imibuzo emalunga nolwazi nokutolika yegrafu yemifanekiso ejongene no-1 yegrafu yemifanekiso ejongene no-1 enikezelweyo ulwazi ukuya ku-1 kuphela ukuya ku-1 kuphela • igrafu yemifanekiso ejongene no-1 ukuya ku-1 kuphela INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA • igrafu yezitena

MATHEMATIKA IBANGA LABAQALAYO (R) 3.3 Inkcazelo ngomxholo Kweli candela lenkcazelo ngomxholo utitshala unikwe oku kulandelayo: • Amagqabantshintshi ekota eBanga labaQalayo ukuya kwiBanga lesi- 3. • Ingcebiso ngendlela yokulandelelelanisa izihloko ngokweekota: ayiyiyo yonke imiba yezihloko emayifundiswe kwikota nganye. Eminye imiba yezihloko kufuneka ifundisiwe kuqala phambi kokuba kufundiswe eminye. • Ingcebiso ngexesha emalithathwe ukufundisa izihloko ezithile apha enyakeni. Ixesha emalithathwe ukufundisa umxholo othile liyohluka - omnye umxholo ufuna ixesha elininzi kunomnye. • Ingcaciso nemigaqo yokufundisa enemizekelo apho kuyimfuneko. Ummandla womxholo ngamnye wohlulwe wazizihloko. Yonke imimandla yomxholo kufuneka ifundiswe kwikota nganye. Ukulandelelaniswa kwezihloko ngokweekota kunika uluvo lokuba izihloko zingasasazwa njani kwaye zingahlaziywa njani apha enyakeni. Akuyomfuneko ukuba zifundiswe kwikota nganye zonke izihloko zezithuba, iimilo nomlinganiselo wokusebenza ngolwazi oluqokelelwayo. Kodwa ke zonke ezinye izihloko mazifundiswe unyaka wonke. Kwisahluko sesi-2 (umhlathi 2.6) indlela yokuthatha umlinganiselo umxholo inikiwe. Xa oku kudityaniswe neeyure zonyaka (jonga kumhlathi we-3.5 ngasezantsi) unokuthi ukwazi ukubala iiyure eziqingqiweyo zommandla womxholo ngamnye. Ootitshala banokukhetha indlela yokulandelelanisa nexesha emalithathwe kumxholo ngamnye ngendlela eyahlukileyo, oko bekwenza ngokweengcebiso abazifumene kwesi sahluko. Oko kukuthi ootitshala Bangalitshintsha kancinci ixesha ebelicetyisiwe elabelwe isihloko eso kodwa ke makuqatshelwe umlinganiselo neeyure ezimiselweyo zommandla womxholo weMathematika wesiGaba esisisiSeko. • IMathematika yeBanga labaQalayo yimilo yeMathematika yabaQalayo kwaye ke ayohlulwanga ngokwamaxesha esifundo. Utitshala weBanga labaQalayo makadibanise iMathematika kwizifundo zemihla ngemihla kodwa ke ixesha malibekwe bucala apho utitshala aqwalasela ngokukodwa kwimisebenzi yeMathematika. Ukuba akakwenzi oku abafundi abasayi kuye bazazi kwaye bavelise iingqiqo nezakhono ezinqwenelekayo. • Ixesha lamaBanga oku-1 - 3 labiwe ngolu hlobo: -- Iiyure ezisixhenxe ngeveki (10 iiveki x 4 iikota x 7 iiyure = 280 iiyure ngonyaka) kufuneka iiyure ezisixhenxe ngeveki zisetyenziselwe iMathematika) -- Isifundo ngasinye seMathematika kufuneka sibe yiyure e-1, imizuzu engama-24 ngosuku kwiBanga loku-1 ukuya kwelesi-3 -- Oku kuthetha ukuba kukho iikota ezine ezineeveki ezilishumi ezinezifundo ezintlanu (Ukusuka ngomvulo ukuya kutsho ngolwesihlanu) ngeveki. -- Vumela ithuba elingangeveki ukulungiselela ukuqhelanisa nokuqinisa ukuqala kwekota nganye kuba abantwana abancinci bayakulibala oko bakufundisiweyo ngakumbi ngexesha leholide kwaye bayaphuma kwisingqi sesikolo. Vumela iveki ekupheleni kwekota ukuqinisa iingqiqo. Oku kunika 8 x 4 x 5 = 160 zezifundo. CAPS 37

MATHEMATIKA IBANGA LABAQALAYO (R) 3.4 Ukulandelelanisa nesantya somxholo Ezi theybhile zilandelayo zinikiwe kwiBanga ngalinye kwiBanga labaqalayo ukuya kwelesithathu (R-3): • Isantya sezihloko zonyaka (zibonisa ukusasazwa kwezihloko ngokweekota kwaye zicebisa ngokomlinganiselo wexesha emalichithwe kummandla womxholo. • Ukulandelelana kwezihloko zonyaka (bonisa ukuba izihloko zabiwe ngokweekota kwaye kukho inkqubela phambili yomxholoi nezakhono kwiikota zonke) • Ukucaciswa kwamanqaku ngokwesihloko –ezi theyibhile zinika ingcaciso ngomxholo nesikhokelo sokufundisa sesihloko ngasinye njengoko silandelelanisiwe ngokweekota. Iiplani zezifundo – Ukwabiwa kwexesha ngokwekota Inani sesona sihloko sibalulekileyo kwimathematika yamaBanga asisiseko. Amaxesha amaninzi kwiveki nganye, kwikota kunye nonyaka kugqaliselwa kumanani,izibalo nolwalamano.Iavareji kukuba nezifundo zeMathematika ezintathu okanye ezininzi kunoku ezigqale kuManani,Izibalo,noLalwamano.Ixesha elishiyekileyo malahlulwe kweminye imimandla yomxholo.Isithuba neSimo noMlinganiselo zifuna ixesha nengqwalaselo kunolwazi olusetyenziselwa ukuhlalutya iiPateni,Iifankshini ne-Aljibra.Itheybhile engezantsi ibonisa inani lezifundo ezabelwe umxholo nezihloko zeBanga ngalinye kwiiPateni,Isiphumo sentsebebnziswano yamanani ne-Aljibra,Isithuba neSimo.uMlinganiselo, ukusebenza ngoLwazi olusetyenziselwa ukuhlalutya: Ukwabiwa kommandla womxholo nezihloko kwizifundo zeBanga labaqalayo Njengoko kwiBanga labaqalayo imathematiki ikwimo yemathematika yabaqalayo iingcebiso ezilandelayo zokwabiwa kwexesha zinika ugqaliselo kwiziqendu zemathematika nemisebenzi engekho seSikweni ehambelanayo. Oku kukuqinisekisa ukuba zonke iinkalo zomxholo zikhona. Imisebenzi yemathematiki yabaqalayo inokuba kukubala inani lezitya neekomityi zokugalela izimuncumuncu,ukubala imidlalo edlalwa naphandle ,imidlalo edlalwa ngaphakathi endlwini umz. Idomino neephazili.Utitshala kufuneka alungise yonke imisebenzi ngokweemfuno zabafundi kunye nezixhobo zokufundisa ezikhoyo egumbini lokufunda. ISithuba neMilo yimiba ebalulekileyo ekukhuleni kwemathematika kubafundi abancinci kwaye kufuneka isasazwe evekini,kugqalwe kwiziqendu ezithile phantsi kwenkxaso katitshala kunikwe namathuba amaninzi okuba abafundi bakhe izinto,badlale ngesanti namanzi. Umlinganiselo mawufakwe kwimisebenzi yokubala,umz ukuthelekelela nokubala xa bethatha umlinganiselo umgama ngezandla,ngeenyawo namanqwanqwa. Irejista yokubhalisa abafundi netshati yemozulu zinika ithuba elininzi lokusebenza ngolwazi olusetyenziselwa ukuhlalutya. 38 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) Itheyibhile 3.1: Ulwabiwo lwexesha ngeveki ngokommandala womxholo Ixesha Ummandla womxholo Isihloko elinokusetyenziswa Amanani, Ii-Opareyshini Ukubala Imizuzu eli -120 noLwalamano Ukuqaphela amanani Chonga aze achaze amanani azeleyo Ulwazi ngamanani Ukusombulula iingxaki zezibalo IiPateni , iiFankshini ne-Aljibra Kopa,andise aze ayile iipateni zakhe Imizuzu engama- 80 Isithuba nemilo (Ijiyomeri) Nakana, chonga uze axele ukwakheka kweemilo zejiyometri / Imizuzu engama- 80 imifanekiso enokwakheka kuka 2-D. Yakha izinto ezinokwakheka kuka 3-D besebenzisa izixhobo eziphathekayo. Ukuzalana ngokwesithuba Izalathiso Umlinganiselo Ixesha Imizuzu engama- 80 Ubude Ubunzima Umthamo Ukusebenza ngolwazi Qokelela, hlela, zoba, funda uze abonakalise ulwazi Imizuzu engama- 60 oluqokelelweyo Imizuzu engama- 420 IIYURE ZIZONKE Iiyure ezisi -7 ngeveki • Ukwabiwa kwenkalo nezihloko kwizifundo zebanga loku-1 ukuya kwelesi-3 Izifundo ezintathu ubuncicnci ngeveki mazichithwe kufundiswa Amanani,Izibalo,Ukuzalana (umz phakathi kwe 4 ne 4 1 1 4 seeyure). Izifundo ezibini ezishiyekileyo (umz.phakathi 2 2 ne 3 seeyure) mazahlulwe phakathi kwezihloko zeminye imimmandla yomxholo njengoko kucetyisiwe ngasezantsi. Itheyibhile 3.2: Inani lezifundo ezicetyiswayo zebanga loku-1 ngekota Inani lezifundo UMMANDLA IZIHLOKO Ikota Ikota Ikota yei Ikota IIyure WOMXHOLO yoku- 1 yesi- 2 -3 yesi -4 zizonke Zonke izihloko zaManani,ii-Opareyshini Amanani, ii-Opareyshini noLwalamano. 22 30 28 25 105 noLwalamano IiPateni , iiFankshini ne- Iipateni yamanani 3 3 3 3 12 Aljibra Iipateni zejiyometri 1 1 1 1 4 Iimilo zokwakheka kwe 2-D 3 3 6 Isithuba nemilo Ukwakheka kwezinto kuka 3-D 3 2 1 6 Indawo, fumana indawo apho ikhoyo (IJiyometri)) 2 1 3 nembonakalo Ulingano macala 1 1 2 Ixesha 2 2 Umlinganiselo Ubude 2 2 4 Ubunzima 2 2 4 Umthamo 1 2 1 4 Ukuqokelela, ukuhlela, abonakalise aze 2 1 3 Ukusebenza ngolwazi acalule izinto oluqokelelweyo Umjikelo opheleleyo wolwazi 3 3 Izintlu zomjikelo wolwazi 2 2 Izifundo zizonke 40 40 40 40 160 CAPS 39

MATHEMATIKA IBANGA LABAQALAYO (R) Itheyibhile 3.3: Inani lezifundo ezicetyiswayo zebanga lesi-2 ngekota Inani lezifundo UMMANDLA IZIHLOKO Ikota Ikota Ikota yei Ikota IIyure WOMXHOLO yoku- 1 yesi- 2 -3 yesi -4 zizonke Amanani, ii-Opareyshini Zonke izihloko zaManani, ii-Opareyshini 24 25 24 26 99 noLwalamano noLwalamano IPateni , iiFankshini Iipateni yamanani 3 3 3 3 12 neAljibra Iipateni zejiyometri 1 1 1 1 4 Iimilo zokwakheka kuka 2-D 3 3 6 Ukwakheka kwezinto kuka 3-D 3 2 1 6 Isithuba nemilo Indawo, fumana indawo apho ikhoyo (IJiyometri) 2 1 3 nembonakalo Ulingano-macala 1 1 2 Ixesha 3 1 3 1 8 Ubude 3 1 4 Umlinganiselo Ubunzima 3 1 4 Umthamo 3 1 4 Ukusebenza ngolwazi Umjikelo opheleleyo wolwazi 3 3 6 oluqokelelweyo Izintlu zomjikelo wolwazi 1 1 2 Izifundo zizonke 40 40 40 40 160 Itheyibhile 3.4: Inani lezifundo ezicetyiswayo zebanga lesi-3 ngekota Inani lezifundo UMMANDLA IZIHLOKO Ikota Ikota Ikota yei Ikota IIyure WOMXHOLO yoku- 1 yesi- 2 -3 yesi -4 zizonke Amanani, ii-Opareyshini Zonke izihloko zaManani, ii-Opareyshini 26 22 19 27 94 noLwalamano noLwalamano IiPateni , iiFankshini Iipateni yamanani 3 3 3 3 12 ne-Aljibra Iipateni zejiyometri 1 1 1 1 4 Iimilo zokwakheka kuka 2-D 2 2 4 Iimilo zokwakheka kuka 3-D 3 3 1 7 Isithuba nemilo Indawo, fumana indawo apho ikhoyo (IJiyometri) 2 3 5 nembonakalo Ulingano-macala 2 1 3 Ixesha 3 2 3 2 10 Ubude 2 2 4 Ubunzima 2 1 3 Umlinganiselo Umthamo 2 1 3 Umjikelo 1 1 I-eriya 2 2 Ukusebenza ngolwazi Umjikelo opheleleyo wolwazi 3 3 6 oluqokelelweyo Izintlu zomjikelo wolwazi 1 1 2 Izifundo zizonke 40 40 40 40 160 40 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

AMAGQABANTSHINTSHI EBANGA LABAQALAYO 1. AMANANI,II-OPAREYSHINI NOKUZALANA UKUBALA CAPS IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 1.1 Ukubala izinto Uluhlu lwanani: 1-5 Uluhlu lwamanani: 1-7 Uluhlu lwamanani: 1 - 10 Uluhlu lwamanani: 0 - 10 Qikelela uze • Uhambelwano lwamanani • Uhambelwano lwamanani • Uhambelwano lwamanani • Uhambelwano lwamanani ubale izinto Yazisa itshati yoncedo uze Bethelela itshati yoncedo imihla Bethelela itshati yoncedo imihla Bethelela itshati yoncedo imihla ukuvelisa ulwazi ulandelelanise indlela izimuncumuncu ngemihla ngemihla ngemihla ngamanani. ezinikezelwa ngayo • Bala ngoononye • Bala ngoononye • Bala ngoononye • Bala ngoononye -- Izixhobo eziphathekayo -- Izixhobo eziphathekayo -- Izixhobo eziphathekayo -- Izixhobo eziphathekayo -- Amalungu omzimba -- Amalungu omzimba -- Amalungu omzimba -- Amalungu omzimba -- Ukuqhwaba izandla -- Ukuqhwaba izandla -- Ukuqhwaba izandla -- Ukuqhwaba izandla -- Ukungqisha -- Ukungqisha -- Ukungqisha -- Ukungqisha -- Ukunyuka ngamanqwanqwa -- Ukunyuka ngamanqwanqwa -- Ukunyuka ngamanqwanqwa -- Ukunyuka ngamanqwanqwa • Bala ngokucengceleza • Bala ngokucengceleza • Bala ngokucengceleza • Bala ngokucengceleza -izicengcelezo zamanani neengoma izicengcelezo zamanani neengoma izicengcelezo zamanani neengoma iziicengcelezo zamanani neengoma • Qhwaba izandla amaxesha • Qhwaba izandla:amaxesha • Qhwaba izandla: amaxesha amaninzi/ambalwa amaninzi/ambalwa amaninzi/ambalwa zininzi/zimbalwa, ezona zininzi/ezona zimbalwa Leliphi inani lokuqhwaba elimbalwa/ elininzi zininzi/zimbalwa, ezona zininzi/ezona zimbalwa 1.2 Bala usiya Uluhlu lwamanani: 1 Uluhlu lwamanani: 1 ukuya ku- 4 Uluhlu lwamanani: 1 ukuya ku -7 Uluhlu lwamanani: 0 ukuya ku -10 phambili ubale Ukubala okungacwangciswanga Ukubala okungacwangciswanga Ukubala okungacwangciswanga Ukubala okungacwangciswanga ubuya umva. kusetyenziswa izicengcelezo kusetyenziswa izicengcelezo kusetyenziswa izicengcelezo kusetyenziswa izicengcelezo zamanani neengoma, zokubala,izinto zamanani neengoma, izinto zamanani neengoma, izinto zamanani neengoma, izinto ezinokwakheka kuka 3-D,ukubala zokubala, izinto ezinokwakheka kuka zokubala, izinto ezinokwakheka kuka zokubala,izinto ezinokwakheka kuka usebenzisa iintshukumo zomzimba. 3-D,ukubala usebenzisa iintshukumo 3-D,ukubala usebenzisa iintshukumo 3-D,ukubala usebenzisa iintshukumo zomzimba neleli yamanani. zomzimba neleli yamanani. zomzimba neleli yamanani. Bala: Bala Bala: Bala: • ngoononye • ngoononye • ngoononye • ngoononye • ngonombini 41 MATHEMATIKA IBANGA LABAQALAYO (R)

IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 1.3 Uluhlu lwamanani: Uluhlu lwamanani: Uluhlu lwamanani: Uluhlu lwamanani: 42 Iisimboli • Iisimboli zamanani:1 • Iisimboli zamanani: 2 ukuya kwi - 4 • Iisimboli zamanani: 5 ukuya kwi -7 • Iisimboli zamanani: 0 ukuya kwi - 10 zamanani • Amagama amanani: nye • Amagama amanani: nye , mbini , • Amagama amanani: ntlanu, • Amagama amanani: qanda, namagama ne. ntandathu, sixhenxe sibhozo, lithoba, lishumi amanani. -- Ukufunda usebenzisa umzimba -- Ukufunda usebenzisa umzimba -- Ukufunda usebenzisa umzimba -- Ukufunda usebenzisa umzimba. -- Eziphathekayo elinokwakheka ka -- Eziphathekayo ezinokwakheka -- Eziphathekayo ezinokwakheka -- Eziphathekayo elinokwakhekaku (Nakana uze 3 –D ezinenani elingu -1. kuka kuka 3 –D ezinamanani 5, 6 no- ka 3 –D ezinamanani 0,8,9 no 10 uchonge iisimboli 7. zamanani baze -- 3 –D ezinamanani 2, 3 no- 4. baqaphele -- Ezibubambeka ezinamakhadi -- Ezibubambeka ezinamakhadi -- Ezibubambeka ezinamakhadi -- Ezibubambeka ezinamakhadi amagama emifanekiso equka inani u- 1. emifanekiso equka amanani 2,3 emifanekiso equka amanani 5,6 emifanekiso equka amanani 0,8,9 amanani) no- 4. no- 7. no- 10. -- Ezibubambeka ezinamakhadi -- Ezibubambeka ezinamakhadi -- Ezibubambeka ezinamakhadi -- Ezibubambeka ezinamakhadi anamachaphaza aquka inani u- 1. anamachaphaza aquka amanani anamachaphaza aquka amanani anamachaphaza aquka amanani 2,3 no- 4. 5,6 no- 7. 0,8,9 no- 10. • Bethelela ulwazi alufumeneyo • Bethelela ulwazi alufumeneyo • Bethelela ulwazi alufumeneyo • Bethelela ulwazi alufumeneyo olunenani elingu -1 olunenani elingu -1 ukuya kwisi-4 olunenani elingu -1 ukuya kwisi-7 olunenani eli-0 ukuya kwi-10 MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 NAKANA AMANANI 1.4 Sebenzisa amanani kwiimeko Sebenzisa amanani kwiimeko Sebenzisa amanani kwiimeko Sebenzisa amanani kwiimeko CAPS eziqhelekileyo eziqhelekileyo eziqhelekileyo eziqhelekileyo Chaza, thelekisa uze ucwangcise • Abafundi kufuneka bayazi iminyaka • Abafundi kufuneka bazazi iinombolo • Abafundi kufuneka bawazi • Bethelela ulwazi malunga amanani azeleyo. yabo zezindlu zakumawabo needilesi amagama abo neenombolo neminyaka,inombolo zabo zeminxeba zakumawabo/okanye yendlu,idilesi,inombolo yomnxeba • Ukugqityezelwa kwerejista inombolo yeselula (inombolo yasekhaya/inombolo yeselula. yabafundi yabazali babo) Sebenzisa iindlela ezininzi (Ukusebenzisa • Bethelela ukusetyenziswa • Bethelela ukusetyenziswa • Bethelela ukusetyenziswa zokuthatha irejista Umz. amanani kwiimeko kwamanani ngokugqibezela irejista kwamanani ngokugqibezela irejista kwamanani ngokugqibezela irejista eziqhelekileyo) njengakwikota yokuqala. umz. njengakwikota yokuqala. njengakwikota yokuqala umz -- Ingaba umfundi onesimboli/ -- Ingaba umfundi ohlala kwindlu • umz.ingaba umfundi ubhiyozela -- Bangaphi abafundi abangekhoyo umzobo we- ayisi-khrim ukhona enenombolo ye- 123 ukhona umhla wakhe wokuzalwa ngomhla esikolweni namhlanje ? esikolweni namhlanje? esikolweni namhalnje we 16 Matshi ukhona namhlanje? Singakwazi njani oku Abantwana baxoxa ngoku phakathi kwabo. -- Ingaba umfundi ogama -- Ingaba umfundi ohlala linguSipho ukhona esikolweni kwinombolo ye 123 Wendy • Qashisa; namhlanje ? sitalato ukhona namhlanje ? • Bala iikhabathi ezingenanto -- Ingaba umfundi ogama -- Ingaba umfundi onenombolo • Bala izitulo ezingahlalanga bantu linguSipho onefani engu Mathole yomnxeba engu 082234567 ukhona esikolweni namhlanje ? ukhona esikolweni namhalnje? • Chonga amanani asemfanekisweni • Chonga amanani emfanekisweni • Chonga amanani asemfanekisweni • Chonga amanani asemfanekisweni nakumaqweqwe anamachaphaza nakwiqweqwe elinamachaphaza nakumaqweqwe anamachaphaza nakumaqweqwe anamachaphaza • Dlala umdlalo wamakhadi amanani • Dlala umdlalo wamakhadi amanani • Dlala umdlalo wamakhadi amanani • Dlala umdlalo wamakhadi amanani • Chonga amanani kwisibhengezo/ • Chonga amanani kwisibhengezo/ • Chonga amanani kwisibhengezo/ ucwecwe lolwazi,kwicwecwe elidala ucwecwe lolwazi,kwicwecwe elidala ucwecwe lolwazi,kwicwecwe elidala lomhla wokuzalwa lomhla wokuzalwa lomhla wokuzalwa 43 MATHEMATIKA IBANGA LABAQALAYO (R)

IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 INGQIQO NGAMANANI (UKUZALANA) 44 Chaza, thelekisa Uluhlu lwamanani: 1 Uluhlu lwamanani: 1 ukuya kwi- 5 Uluhlu lwamanani: 1 ukuya kwi- 7 Uluhlu lwamanani: 0 ukuya - 10 uze ucwangcise • Chonga uze uchaze amanani • Chonga uze uchaze amanani • Chonga uze uchaze amanani • Chonga uze uchaze amanani amanani apheleleyo ukuya kwi-1 apheleleyo apheleleyo apheleleyo (Chonga uze • Amanani apheleleyo 2, 3 nesi-4 • Amanani apheleleyo 5, 6 ne -7 • 8, 9, 10 ne 0 uchaze amanani apheleleyo) • Bethelela amanani -1ukuya kwi-4 • Bethelela amanani -1 ukuya kwi -7 • Bethelela amanani- 0 ukuya kwi -10 Thelekisa ukuba zeziphi ezona kwezi zimbini kwingqokelela yezinto ezi: Thelekisa ukuba zeziphi ezona • Nkulu nencinci kwezi zimbini kwingqokelela • Nkudlwana nencinanana yezinto ezi: • Eyona inkulu neyona incinci a) Nkulu nencinci • (Yazis*a ingqiqo) b) Nkudlwana • Lungisa ezingaphezulu kwesibini nencinanana kwingqokelela yezinto ozinikiweyo c) Eyona incinci ukusuka kweyona incinci ukuya neyona inkulu kweyona inkulu kunye nokusuka kweyona inkulu ukuya kweyona MATHEMATIKA IBANGA LABAQALAYO (R) incinci Thelekisa ukuba • Nkulu kune-, ncinci kune- lingana • Nkulu kune-, ncinci kune- lingana • Nkulu kune-, ncinci kune- lingana zeziphi e zimbini ne- ne- ne- kwingqokelela yezinto ezi • Ninzi nencinane Umz. Ukuqhwaba • Ninzi nencinane Umz. ukuqhwaba • Ninzi nencinane umz. ukuqhwaba • Ninzi nencinane umz. ukuqhwaba ngokungalindelekanga ngokungaliindelekanga ngokungaliindelekanga ngokungalindelekanga a) Nkulu kune- INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA • Ukubuza umbuzo ongowona • Ukubuza umbuzo ongowona b) Ncinci kune- c) Lingana ne-

IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 Inani Ukwakha ukuqwalasela Ukwakha ukuqwalasela Ukwakha ukuqwalasela Ukwakha ukuqwalasela amanani CAPS lolandelelwano/ amanani olandelelwano amanani olandelelwano amanani olandelelwano olandelelano ngokusaphuhliswayo, lesingaphi ngokusaphuhliswayo, umzekelo, ngokusaphuhliswayo, umzekelo, ngokusaphuhliswayo, umzekelo, umzekelo, eyokuqala, eyesibini, eyokuqala, eyesibini, eyesithathu.... eyokuqala, eyesibini, eyesithathu.... eyokuqala, eyesibini, eyesithathu.... eyesithathu....eyokugqibela, eyokugqibela, elandelayo. eyokugqibela, elandelayo. eyokugqibela, elandelayo. elandelayo. • Ukutshayelela ngexesha lokutya • Ukomeleza amanani olandelelano • Ukomeleza amanani olandelelano • Ukutshayelela amanani lemihla ngemihla nangexesha ngokusaphuhliswayo ngexesha ngokusaphuhliswayo ngexesha olandelelano – okokuqala, lokuzikhulula – eyokuqala, lokuzikhulula lemihla nemihla lokuzikhulula lemihla nemihla okwesibini, ukwesithathu, ukuya eyesibini, eyokugqibela nelandelayo kokwesithandathu • Ukuwasebenzisa nangexesha • Ukuzisebenzisa nangexesha lemisetyenzana yezakhono zobomi. lemisetyenzana yezakhono zobomi • Ukomeleza amanani olandelelano ngokusaphuhliswayo ngexesha • Nangexesha lemisetyenzana lokuzikhulula lemihla nemihla yobuchwepheshe bokuyila (xa kukho imfuneko) • Ukuwasebenzisa nangexesha lemisetyenzana yezakhono zobomi. UKUSOMBULULA IINGXAKI NGOKWEMEKO USEBENZISA EZI NDLELA ZILANDELAYO: 1.6 Ukusebenzisa ezi ndlela Ukusebenzisa ezi ndlela Ukusebenzisa ezindlela zilandelayo Ukusebenzisa ezindlela zilandelayo zilandelayo zilandelayo Ubuchule bokusombulula • Izixhobo ezibonwayo umzekelo, • Izixhobo eziphathekayo umzekelo, , • Izixhobo eziphathekayo umzekelo, , • Izixhobo eziphathekayo umzekelo, , iingxaki zezibalo izinto zokubala izinto zokubala izinto zokubala izinto zokubala • Ileli yamanani • Ileli yamanani (Ukusebenzisa obu buchule bulandelayo) 45 MATHEMATIKA IBANGA LABAQALAYO (R)

IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 1.7 • Ukusebenzisa izixhobo zokubala • Ukusebenzisa izixhobo zokubala • Ukusebenzisa izixhobo zokubala 46 nokusombulula izibalo eziquka u-1,- nokusombulula izibalo eziquka u-5,- nokusombulula izibalo eziquka u-8,- Ukudibanisa 2,-3 no -4 ngokuthetha. 6, no -7 ngokuthetha. 9, -10 no 0 ngokuthetha. nokuthabatha • Ukubethelela ukusonjululwa • Ukubethelela ukusombululwa • Ukubethelela ukusombululwa kwezibalo eziquka amanani kwezibalo eziquka amanani kwezibalo eziquka amanani Ukusombulula ukusuka kwelo- 1 - 4 ukusuka kwelo-1 - 7 ukusuka kwelo-1 – 10. izibalo zomlomo nokucacisa isisombululo efakela okulandelayo: a) Ukudibanisa nokuthabatha ngeempendulo ezifikelela kwi -10 1.9 Ukwahlula ngokwamaqela nokwaba MATHEMATIKA IBANGA LABAQALAYO (R) ngokulinganayo okukhokelela kulwahlulwa- hlulo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA b) Ukwaba ngokulinganayo nangamaqela kumanani apheleleyo ukuya kwi-10 ngeempendulo eziquka intsalela.

IsIHLOKO IKOTA YOKU-1 IKOTA YESI-2 IKOTA YESI-3 IKOTA YESI-4 1.11 Imali Imali Imali Imali • Velisa ukwazi imali yaseMzantsi • Velisa ukwazi imali yaseMzantsi CAPS Afrika engumwangalala. Afrika engamaphepha • 20c, 50c, R1, R2, R5 • R10, R20, R50, R100, R200, • Chonga imibala kunye nezilwanyana ezibonakala kwezi nkozo. • Chonga ukufana nomahluko okhoyo • Chonga ukufana nomahluko okhoyo kwezi nkozo umz. hlela imali phakathi kwemali engamaphepha ngokombala nangobukhulu umz. hlela imali ngokombala nangobukhulu • Banike imali yokudlala kwikona • Banike imali yokudlala kwikona • Banike imali yokudlala kwikona yasekhaya. yasekhaya. yasekhaya BALA NGOKUSEBENZISA: 1.13 Ukusombulula izibalo zokudibanisa Ukusombulula izibalo zokudibanisa Ukusombulula izibalo zokudibanisa nokuthabatha ukuya ku -4 nokuthabatha ukuya ku -7 nokuthabatha ukuya ku -10 Ukudibanisa ngokuthetha ngokuthetha. ngokuthetha. nokuthabatha. Ukusombulula izibalo zokudibanisa nokuthabatha ngokuchaziweyo nezisombululo ukuya kwi- 10 ngokuthetha 47 MATHEMATIKA IBANGA LABAQALAYO (R)

MATHEMATIKA IBANGA LABAQALAYO (R) Iintlobo Zezibalo kwiSigaba sabaQalayo(R) Izibalo ezimiswayo kubafundi beSigaba sabaQalayo kufuneka kuquke izinto ezisegumbini lokufundela kuphela, umzekelo, izinto zokubala, abantwana, izihlangu, kodwa ingabi ziilekese, imivundla iityatyambo, njalo-njalo. Ayingabo bonke abantwana abancinci abanokuzikhohlisa ngokuthi izibali okanye iminwe yimivundla – badinga izinto ngokwazo. Utishala angasebenzisa imifanekiso kwisiqendu sesibini sonyaka kuphela. Izinto eziphathekayo mazigcinwe – imifanekiso kukongeza, ayithathi indawo yezinto ezibonwayo. Amasetyana angasetyenziswa xa utitshala engenazo izixhobo. Izibalo ezilandelayo zizekelisa iintlobo zezibalo emazilungelelaniselwe utitshala ukulungela umngangatho wokuqonda wabafundi bakhe. Ukwahlula ngamaqela Nanga amaqebengwana a – 8. (Utitshala ukhupha iznto zokubala ezi – 8, okanye ubonisa umfanekiso wamaqebengwana a – 8). UThemba ufumana amaqebengwana a - 2 yonk’imihla. Uza kufumana amaqebengwana ngeentsuku ezingaphi ? Ukwaba ngokulinganayo Amaqebengwana ama – 6. (Utitshala ukhupha izibali ezi – 6, okanye ubonisa imifanekiso yamaqebengwana ama – 6.) Kufuneka oothedi abathathu babelane ngawo onke amaqebengwana bafumane inani elilinganayo lamaqebengwana. Uthedi ngamnye uza kufumana amaqebengwana amangaphi ? Ukudibanisa, ukuthabatha, ukudibanisa okuphinda phindiweyo Abantwana ababini (2) banamehlo amangaphi? Abantwana abane (4) baneendlebe ezingaphi? Mingaphi iminwe esandleni esinye (1)? Mingaphi iminwe kwizandla ezibini (2)? ULinda unezibali ezintandathu (6). Unika uBandile izibali ezibini (2). Unezibali ezingaphi ngoku? Ootitshala mabaxube iintlobo zezibalo imihla ngemihla. Mabandise ubukhulu bamanani abawasebenzisayo ngokuthe chu, Bangathathi ngokungathi abafundi abanakho ukusebenza ngamanani amakhulu. 48 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

AMAGQABANTSHNTSHI ESIGABA SABAQALAYO (R) 2.IIPATENI, IIFANKSHINI NOLWALAMANO IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 CAPS 2.1 • Chonga iipateni empahleni, • Kopa, wandise uyile ezakho • Kopa, wandise uyile ipateni yakho • Kopa, wandise uyile iipateni zakho kwizinto nakokusingqongileyo iipateni ngemifanekiso ozimameleyo Iipateni zejiyometri • Kopa ugqibezele iipateni • Kopa ipateni yengxolo Kopa wandise iipateni ezilula • Kopa iipateni usebenzisa • Kopa iipateni ozinikiweyo • Ipateni yomdlalo wokungciloza eziphindaphindwayo ukubethana komzimba usebenzisa imali eziinkozo/ usebenzisa izinto engumwangalala • Kopa,gcwalisa uyile ezakho ezibonwayo nemizobo. iipateni (Yila iipateni zakho eziphindaphindwayo) 49 MATHEMATIKA IBANGA LABAQALAYO (R)

AMAGQABANTSHINTSHI KWISIGABA SABAQALAYO(R) 3. ISITHUBA NEMILO (IJIYOMETRI) 50 IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 3.1 Ulwalamano ngokobume Ulwalamano ngokobume Ulwalamano ngokobume Ulwalamano ngokobume Indawo-bumilo, Indawo yezinto ezimbini okanye Indawo yezinto ezimbini okanye Indawo yezinto ezimbini okanye Indawo yezinto ezimbini okanye ukufumana indawo ezininzi ngokunxulumene ezininzi ngokunxulumene ezininzi ngokunxulumene ezininzi ngokunxulumene apho ikhoyo nomfundi nemfundo nemfundo nemfundo nembonakalo • Ngaphambili nangasemva • Ngaphezulu nangaphantsi • Ngaphambili nangasemva • Ngaphambili nangasemva Ukuchaza into enye • Phezulu,phezu kwe, ngaphantsi • Phezulu, phezu kwe, ngaphantsi • Phezulu, phezu kwe, ngaphantsi enokwakheka kuka 3-D nangezantsi nangezantsi nangezantsi uyinxulumanisa nenye (umzekelo, ngaphambili • Ngaphakathi nangaphandle • Ecaleni kwe • Ecaleni kwe nangasemva) • Phantsi naphezulu • Phakathi • Phakathi • Ecaleni kwe naphakathi kwe • Ekhohlo nasekunene • Ekhohlo nasekunene • Umsebenzi wephegibhodi Imidlalo yangaphandle ibalulekile. Chaza izinto uzivelela kumacala Indawo yezinto ezimbini okanye isixhobo sokugwencela ngamacala bezibona ngeendlela ezininzi ngokunxulumene singasetyenziswa ukubethelela, ezahlukileyo , umzekelo, unodoli, nemfundo umzekelo: indlu ngaphambili, ngasemva, • Ngaphambili nangasemva MATHEMATIKA IBANGA LABAQALAYO (R) emacaleni kuxhomekeke ukuba • Ingqiqo zeMathematika ume ndawoni • Phezulu, phezu kwe, ngaphantsi • Ubugcisa bokuyila nangezantsi • Ukwakheka komzimba • Ecaleni kwe • Phakathi INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA • Ekhohlo nasekunene • Umsebenzi wephegibhodi • Phambili nasemva Ulandela izalathiso • Izalathiso -phambili / emva • Phambili/ emva • Phambili nasemva (eyedwa no/okanye • Imidlalo enje ngokulandela uloliwe • Itshati yeentolo • Phantsi naphezulu nomnye weqela) ukuzibeka kwisithuba • Imiqobo xa ulandela isalathiso • Ngentla nangezantsi esithile (Ingqiqo • Ukufunda ngemithambo yomzimba • Ekhohlo nasekunene yokwalathisa) nemisetyenzana ngomculo • Siphuma phi isandi?

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 3.2 Izinto ezinokwakheka CAPS kuka -3-D Qonda, uchonga nokuthiya izinto ezinokwakheka kuka 3-D egumbini lokufundela: • Iibhola: Fundisa unike ithuba a) Iibhola lokusebenza ngeebhola b) Iibhokisi • Iibhokisi: Fundisa unike ithuba lokusebenza neebhokisi 3.2 • Ukufundisa Itshati Yoqoqosho • Hlela ngokufana nangokwahluka (ukuhlela izinto zokudlala) Izinto ezinokwakheka kuka -3-D • Ubungakanani: Hlela izinto • Ubungakanani:hlela izinto • Ubungakanani: hlela izinto • Ubungakanani: hlela izinto ezinokwakheka kuka 3-D ezinokwakheka kuka 3-D ezinokwakheka kuka 3-D ezinokwakheka kuka 3-D Chaza, uhlele ngobukhulu ngobukhulu ngobukhulu ngobukhulu nokuthelekisa izinto ezinokwakheka kuka • Umbala: hlela izinto • Umbala: chonga uhlele izinto • Umbala: hlela izinto • Umbala: hlela izinto 3-D no – 2-D ngo: ezinokwakheka kuka 3-D no – 2-D zokubala ngemibala ebomvu, ezinokwakheka kuka 3-D ezinokwakheka kuka 3-D ngokwemibala yokuqala ebhlowu, emthubi neluhlaza nezimacala-mabini ngokwemibala nezimacala-mabini ngokwemibala a) Ubungakanani (nkulu/ncinci) • Imilo: hlela izinto ezinokwakheka • Imilo: hlela izinto ezinokwakheka • Imilo: hlela izinto ezinokwakheka • Imilo: hlela izinto ezinokwakheka kuka 3-D no 2-D ngokwemilo kuka 3-D no 2- D ngokwemilo kuka -3-D no 2-D ngokweemilo kuka 3-D no 2-D ngokwemibala b) Mbala (bomvu, zazo bhlowu, • Izinto eziqengqelekayo mthubi,hlaza) -- Chonga uphonononge izinto c) Imilo (isangqa, eziqengqelekayo unxa-ntathu, -- Ukomeleza izinto isikwere, uxande) eziqengqelekayo d) Izinto • Izinto ezitshebelezayo eziqengqelekayo -- Chonga uphonononge izinto e) Izinto ezitshebelezayo ezitshebelezayo -- Qonda uphonononge izinto ezitshebelezayo 51 MATHEMATIKA IBANGA LABAQALAYO (R)

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 Ukwakha izinto Iyaqhubekeka Iyaqhubekeka Iyaqhubekeka Iyaqhubekeka 52 ezinokwakheka kuka • Bonelela ngeebhloko zokwakha • Bonelela ngeebhloko zokwakha • Bonelela ngeebhloko zokwakha • Bonelela ngeebhloko zokwakha 3-D ngokusebenzisa nemathiriyeli yokwakha ngexesha neemathiriyeli yokwakha nemathiriyeli yokwakha ngexesha nemathiriyeli yokwakha ngexesha imathiriyeli ephathekayo lokudlala ngaphakathi yonke ngexesha lokudlala ngaphakathi lokudlala ngaphakathi yonke lokudlala ngaphakathi yonke (umzekelo, iibhloko imihla yonke imihla imihla imihla zokwakha) • Phonononga ngeebhloko • Phonononga ngeebhloko • Abafundi mabazakhele esabo • Iyaqhubekeka ngexesha lokudlala zokwakha zokwakha isakhiwo bekopa kumzekelo ngaphakathi onikiweyo • Khuphela isakhiwo esifanayo kuyilo okanye ikhadi lomfanekiso • Ukomeleza ukukhuphela isakhiwo esifanayo kuyilo okanye ikhadi lomfanekiso 3.3 • Vumela umfundi ngamnye akhethe ikhadi lakhe lesimboli ngosuku Iimilo ezinokwakheka lokuqala kuka-2-D. • Bonisa isimboli/ifoto kwiinyanga • Bonisa iisimboli/iifoto zomfundi • Bonakalisa igama lomfundi • Bonakalisa igama lomfundi Qonda, uchonga ezintathu zokuqala negama lomfundi kwiinyanga kuphela kuphela nokuthiya iimilo ezintathu ezilandelayo. ezinokwakheka • Yazisa igama leklasi, umzekelo, • kwiinyanga ezintandathu • Kwiinyanga ezintandathu MATHEMATIKA IBANGA LABAQALAYO (R) kuka 2-D egumbini ngokusebenzisa umfanekiso . • Iyaqhubekeka zokugqibela zonyaka zokugqibela zonyaka lokufunda • Leyibhelisha ucango ngegama • Iyaqhubekeka • Iyaqhubekeka nasemifanekisweni , likatitshala . kuquka: • Ileyibhile ebonisa iBanga a) Iisimboli zabafundi labaQalayo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA b) Igama leklasi Ukwakha iiphazili Iiphazili Iiphazili (Iyaqhubekeka) Iiphazili (Iyaqhubekeka) Iiphazili (Iyaqhubekeka) a) Ubuncinane: • Qalisa ukufundisa iiphazili • Nika iintlobo ngeentlobo zeephazili • Nika iintlobo ngeentlobo zeephazili • Nika iintlobo ngeentlobo zeephazili unike isikhokelo sokwakha iiphazili ngexesha lokudlala ngaphakathi ngexesha lokudlala ngaphakathi ngexesha lokudlala ngaphakathi b) Iikota 1: 6 izijungqe imihla ngemihla imihla ngemihla imihla ngemihla. • Xoxa umfanekiso wephazili c) Ikota 2: 12 izijungqe • Abafundi mabagqibe ubuncinane • Abafundi mabagqibe ubuncinane ngohoyo olulodwa kwiinkcukacha • Abafundi mabagqibe ubuncinane d) Ikota 3: 18 izijungqe ezifana nombala, abantu/ iphazili yezijungqe ezi-12 iphazili yezijungqe ezi-18 iphazili yezijungqe ezingama -24 izilwanyana, izinto, ukuma ekupheleni kwekota yesi- 2. ekupheleni kwekota yesi- 3 ekupheleni kwekota yesi- 4. e) Ikota 4: 24 izijungqe kwabantu/izilwanyana nezinto • Yila bagcwalise eyabo iphazili • Yila bagcwalise eyabo iphazili • Abafundi mabagqibe ubuncinane yezijungqe ezi – 4 yezijungqe ezi – 5 iphazili enezijungqe ezi-6 ekupheleni kwekota yoku-1.

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 3.3 • Tshayelela ukuqwalasela kokuthile • Ukomeleza ukuqwalasela • Ukomeleza ukuqwalasela • Ukomeleza ukuqwalasela kokuthile ngokuhlela kokuthile ngokuhlela kokuthile ngokuhlela Iimilo ezinokwakheka (chonga izinto –“ndibona ngamehlo CAPS imisetyenzana, ukutshatisa imisetyenzana, ukutshatisa imisetyenzana, ukutshatisa kuka-2-D. am amancinane”) nemisetyenzana yamaqela nemisetyenzana yamaqela nemisetyenzana yamaqela Ukuqwalasela okuthile nexesha lokuqoqosha lemihla nexesha lokuqoqosha lemihla nexesha lokuqoqosha lemihla ngemihla. ngemihla. ngemihla. Iimilo zejiyometri • Ukubethelela isangqa • Ukubethelela unxa-ntathu • Ukubethelela isikwere • Ukubethelela isangqa, unxa- a) Isangqa ntathu, isikwere noxande • Ukufundisa isangqa • Ukukwazi ukuqaphela iimilo • Ukukwazi ukuqaphela iimilo b) Unxantathu kwiimo zonke ezifumaneka kuzo kwiimo zonke ezifumaneka kuzo • Ukomeleza uxande • Ukufundisa unxa-ntathu (ukuqinisekisa isimo sikanxa- (ukuqinisekisa isimo semilo c) Isikwere • Ukukwazi ukuqaphela iimilo • Ukubethelela isikwere ntathu) efundiweyo) d) Uxande kwiimo zonke ezifumaneka kuzo (ukuqinisekisa isimo semilo e) Ulwazi ngemilo esifundisiweyo) (ukuqinisekisa isimo) 3.4 • Chonga amalungu omzimba • Ukuwela umngca ophakathi- • Ukuwela umngca ophakathi– • Ukwakha uqwalaselo lokuba (phantsi kokubala) ukwenza intshukumo imisetyenzana yebhodi kukho ulingano-macala kwizinto Ulingano macala • Intloko, amehlo, impumlo, • Sebenzisa ukuwela umgca • Sebenzisa ukuwela umgca • Sebenzisa ukuwela umgca Unakana umgca umlomo, isilevu, intamo, amagxa, osembindini ngexesha leZakhono osembindini ngexesha leZakhono osembindini ngexesha leZakhono wolingano –macala ingalo, isandla, iminwe, isifuba, Zobomi (uKwakheka Komzimba) Zobomi (uKwakheka Komzimba) Zobomi (uKwakheka Komzimba) kunye noko umlenze, idolo, unyawo, iinzwane. kumngqongileyo • izicengcelezo neengoma • Umzimba womntu unamacala • Imisetyenzana yobugcisa bokuyila amabini • bethelela ukuqwalasela ukuba umzimba unamacala amabini , umzekelo, “icala elinye” “nelinye icala” nto leyo ikhokela “kwicala lasekunene necala lasekhohlo” • Ukuwela umgca osembindini okubandakanywa kwizibalo. • Okungasentla makwenziwe ngexesha lokwakheka komzimba. • Ukusebenzisa izicengcelezo neengoma • Ngexesha lobugcisa bokuyila 53 MATHEMATIKA IBANGA LABAQALAYO (R)

amagqabantshintshi kwisigaba sabaqalayo(R) 4.umlinganiselo 54 IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 4.1 • Fundisa isigama “imini no-busuku” ne “ukukhanya/ubumnyama “’ Ixesha: • Ekuseni, emva kwemini, ebusuku Chaza ixesha losuku ngokwe- imini okanye (ukufunda ngokungekho seSikweni ubusuku . ngexesha lenkqubo yemihla ngemihla netshati yemozulu) Ukulandelelanisa • Ukuqalisa inkqubo Yemihla • Inkqubo Yemihla ngemihla • Inkqubo Yemihla ngemihla • Inkqubo Yemihla ngemihla iziganeko ezenzeka ngemihla (iyaqhubekeka) (iyaqhubekeka) (iyaqhubekeka) rhoqo ebomini bakho -- abafundi banikwa ithuba -- Ukubethelela ukulandelelanisa -- Ukubethelela ukulandelelanisa -- Ukubethelela ukulandelelanisa bemihla ngemihla. lokulandelelanisa iziganeko iziganeko ezenzeka ngosuku iziganeko ezenzeka ngosuku iziganeko ezenzeka ngosuku ezenzeka emini . kwinkqubo yemihla ngemihla kwinkqubo yemihla ngemihla kwinkqubo yemihla ngemihla a) Inkqubo Yemihla -- Imifanekiso iboniswa ukusuka ngemihla ngasekhohlo ukuya ekunene b) Itshati Yemozulu ukwakha icala uqala kulo xa ufunda -- Inkokheli yosuku ihambisa utolo olushukunyiswayo MATHEMATIKA IBANGA LABAQALAYO (R) ngokwemisetyenzana ekwinkqubo yemihla ngemihla . • Ukufundisa Itshati Yemozulu • Itshati yemozulu (yonke imihla) • Itshati yemozulu (yonke imihla) • Itshati yemozulu (yonke imihla) (yonke imihla) -- Utitshala ukhokela abafundi -- Utitshala ukhokela abafundi -- Utitshala ukhokela abafundi -- Abafundi bazi usuku , umhla INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA ukwazi igama losuku, ukwazi igama losuku, ukwazi igama losuku, nenyanga ngoonotsheluza umhla nenyanga ngengoma umhla nenyanga ngengoma umhla nenyanga ngengoma babonise iileyibhile neesimboli nangemvano-siphelo, nangemvano-siphelo, nangemvano-siphelo, kwikhalenda yeveki . oonotsheluza nokubonisa oonotsheluza nokubonisa oonotsheluza nokubonisa iileyibhile neesimboli iileyibhile neesimboli iileyibhile kwikhalenda ebonisa iveki kwikhalenda ebonisa iveki . -- Ukwakha uqwalaselo lwesigama sexesha . -- Ukubonisa iintsuku zokuzalwa, ukuphuma, iintsuku ezibalulekileyo, iintsuku zokuphumla phakathi evekini . -- Ukulandelelanisa iinyanga zonyaka ngengoma.

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 4.1 • Iintsuku zeveki • Iintsuku zeveki (iyaqhubekeka) • Iintsuku zeveki (iyaqhubeka) • Iintsuku zeveki (iyaqhubeka) Ixesha: -- Utitshala ufundisa abafundi -- Utitshala ufundisa abafundi CAPS ingoma okanye imvano-siphelo ingoma okanye imvano-siphelo Ukulandelelanisa ngeentsuku zeveki. Phinda ngeentsuku zeveki. Phinda iziganeko ezenzeka yonke imihla xa ku xoxwa yonke imihla xa ku xoxwa rhoqo ebomini bakho ngetshati yemozulu ngetshati yemozulu bemihla ngemihla. c) Iintsuku zeveki -- Ukulandelelanisa iintsuku zeveki ngengoma d) Itshati yamaxesha onyaka • Itshati yamaxesha onyaka • Itshati yamaxesha onyaka • Itshati yamaxesha onyaka • Itshati yamaxesha onyaka -- Ukutshayelela itshati ebonisa -- Usiba olubonisa ixesha lonyaka -- Usiba olubonisa ixesha lonyaka -- Usiba olubonisa ixesha lonyaka amaxesha amane onyaka liyahanjiswa xa kutshintsha liyahanjiswa xa kutshintsha liyahanjiswa xa kutshintsha ngokubonisa: amaxesha onyaka amaxesha onyaka amaxesha onyaka o IHlobo -- Ngosuku lokuqala emva -- Ngosuku lokuqala emva -- Ngosuku lokuqala emva o UKwindla kweeholide z esikolo utitshala kweeholide zesikolo utitshala kweeholide zesikolo utitshala makabuze abafundi ukuba makabuze abafundi ukuba makabuze abafundi ukuba o Ubusika bebesenza ntoni ngexesha bebesenza ntoni ngexesha bebesenza ntoni ngexesha o Intwasa-hlobo leeholide leeholide leeholide -- Ukwakha uqwalaselo lokwenziwayo ngumfundi ukusukela xa evuka ukuya xa esiya esikolweni . -- Ukwakha uqwalaselo ngokwenzekileyo phakathi kwexesha lesidlo sasebusuku nelokulala . • Ukufundisa itshati yeentsuku • Kuyaqhubekeka qho xa kulusuku • Kuyaqhubekeka qho xa kulusuku • Kuyaqhubekeka qho xa kulusuku zokuzalwa lomfundi lokuzalwa lomfundi lokuzalwa Ukufundisa itshati lomfundi lokuzalwa ngokweentsuku • Abafundi mabazi iminyaka yabo • Iyaqhubekeka • Iyaqhubekeka • Iyaqhubekeka zokuzalwa • Ukwakha uqwalaselo lwecala ekubhekiswa ngakulo xa kufundwa. • Abafundi mabazi iintsuku zabo zokuzalwa (usuku nenyanga) 55 MATHEMATIKA IBANGA LABAQALAYO (R)

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 4.2 Ubude Ubude Ubude Ubude 56 Ubude • Ubude nobufutshane, • Ende kakhulu nemfutshane • Qikelela ubude bezinto • Linganisa ubude bomfundi ukuba mdana nokuba mde kakhulu, endana, emfutshanana ezahlukileyo. ngetheyipi yokulinganisa Ukuthelekisa (ngokubonwayo). (ukuphicotha ubude). (sebenzisa izandla endaweni nokulandelelanisa • Qikelela ulinganise izinto yetheyipi yokulinganisa). izinto ngokuziphatha • Ukutshayelela isigama sobude. • Ukubethelela isigama sobude . ezahlukileyo usebenzisa iinyawo, usebenzisa isigama izandla, umsonto, uluthi, njalo- • Itshati yobude ngezandla/iinyawo • Abafundi bakhangela ukuba esisiso sokuchaza njalo. bakhulile na oko kwikota ubude. ephelileyo • Baqalise itshati (abafundi bangathelekisa ubude yobude babo kwinto ekhoyo eklasini, -- Linganisa umzekelo, ikhabhathi) ngezandla (ngokubonwayo nangokumayana) -- Ukulinganisa ngemizila yeenyawo (ngokubonwayo nangokumayana) -- Ukulinganisa MATHEMATIKA IBANGA LABAQALAYO (R) ngetheyipi yukulinganisa (ngokubonwayo nangokumayana) -- De, futshane INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Ndana, futshanana -- Mde,mdana (ngokubonwayo) -- Qikelela.

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 4.3 Ubunzima Ubunzima • Fundisa isigama sobunzima CAPS ngokuthelekisa ubunzima bezinto Thelekisa, ezahlukahlukileyo, umzekelo, ulandelelanise izinto ngokuziphatha -- Lula/nzima usebenzisa isigama -- Lulana/nzinyana ukuchaza okulandelayo: • Ukubethelela ubunzima a) Lula, nzima (lulanyana/nzima) b) Lulana, nzinyana c) Iyaqhubekeka ngexesha lokudlala ngamanzi nesanti 4.4 Umthamo Umthamo Umthamo • Fundisa isigama somlinganiso • Thelekisa ulandelelanise izinto womthamo ngokuthelekisa ngokuphathekayo usebenzisa Thelekisa umthamo wezikhongozeli isigama ukuchaza okulandelayo: ulandelelanise izinto ezahlukahlukileyo, umzekelo, ngokuziphatha -- Ayinanto/izele usebenzisa -- “ayinanto/izele -- Kakhulu/kancinci isigama ukuchaza -- “ninzi kune/ncinci kune okulandelayo: -- Ncinci kune/ninzi kune • Ukomeleza umthamo a) Ayinanto, izele -- Ninzi /ncinci b) Kakhulu, kancinci -- Iyaqhubekeka ngexesha lokudlala ngamanzi nesanti . c) Phantsi kune, phezulu kune d) Iyaqhubekeka ngexesha lokudlala ngamanzi nesanti. 57 MATHEMATIKA IBANGA LABAQALAYO (R)

AMAGQABANTSHINTSHI KWISIGABA SABAQALAYO(R) 5.UKUSEBENZA NGOLWAZI OLUQOKELELWEYO 58 IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 5.1 • Fundisa isigama solwazi • Qokelela izinto (izinti • Buza umbuzo: “Ingaba amagama • Sebenzisa itshati yokuzalwa olusetyenziselwa ukuhlalutya ezahlukeneyo ngobukhulu) anonoobumba abathandathu ukwazi ukuba lusuku lukabani Ukuqokelela ngokuqokelela ulwazi lwenani ngawo axhaphakileyo?” lokuzalwa olukweyiphi inyanga. nokuhlela izinto. lamakhwenkwe nenani • Qokelela ulwazi ukuphendula • Qokelela ulwazi kubafundi ukwazi Qokelela ulwazi lamantombazana abaseklasini usebenzisa oonotsheluza umbala wodongwe lokudlala Qokelela izinto bamagama. lweveki ezayo, umzekelo, bhlowu, eziphathekayo zodidi mthubi, luhlaza olufanayo (emnye Qokelela ulwazi (abafundi okanye/elilungu leqela) basebenzisa oluphi uhlobo umzekelo, amagqabi lwesithuthi xa besiza esikolweni) alishumi, iimilo ezilishumi Ukuhlela • Hlela ulwazi ngokumisa abafundi • Hlela izinto eziqokelelweyo (izinti • Hlela oonetsheluza bamagama • Hlela ulwazi ngokweentsuku nokurekhodisha ngokwemigca yamakhwenkwe ngobukhulu bazo. ngokwenani kwigama ngalinye. zokuzalwa zabafundi. ulwazi namantombazana. • Umntwana ngamnye ukhetha Hlela izinto ibhloko emela umbala eziphathekayo awukhethileyo aza kudlala ngawo ngobunjani,umzekelo, evekini MATHEMATIKA IBANGA LABAQALAYO (R) ubungakanani • Hlela ulwazi oluqokelelweyo bamagqabi. (abahamba ngenyawo, ngemoto yabazali, iteksi, okanye ibhasi). 5.2 • Sebenzisa igrafu ngebhloko • Zoba igrafu yengqokelela yezinto • Zoba igrafu ngokuncamathisela • Zoba igrafu ebonisa iintsuku okanye imilo ukubonisa ulwazi. (izinti ngobukhulu bazo). unotsheluza wegama phantsi zabafundi kwinyanga nganye. Ukubonisa ingqokelela INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA kwekholamu efanelekileyo. ehleliweyo yezinto. • Sebenzisa izinto zokwenyani ukwenza igrafu njengebhloko, (Zoba igrafu ukubonisa • Yenza igrafu ukubonisa ulwazi iityhubhu ezipakishiweyo, iibhokisi ulwazi Zoba umfanekiso oluqokelelweyo usebenzisa izitena zeLego ezimela imibala yodongwe nje ngerekhodi yolwazi okanye iimilo oluza kusetyenziswa, umzekelo, eqokelelweyo). bhlowu, mthubi noluhlaza. • Zoba igrafu yemifanekiso ukubonisa abafundi abahamba ngenyawo, abeza ngeteksi,ngeemoto zabazali nabeza ngebhazi.

IsIHLOKO IKOTA YOKU -1 IKOTA YESI -2 IKOTA YESI -3 IKOTA YESI -4 5.3 • Funda utolike ulwazi • Funda utolike iigrafu usebenzisa • Funda utolike ulwazi • Funda utolike iigrafu usebenzisa ngokusebenzisa udongwe imibuzo ngokubala oonotsheluza imibuzo ukwazi inyanga Ukuxoxa nokunika CAPS ukubonisa inani la makhwenkwe bamagama kwikholamu nganye eneentsuku ezininzi zokuzalwa . ingxelo ngengqokelela nelamantombazana aseklasini. nokufikelela kwisigqibo. ehleliweyo ye-zinto. • Ngokukhethwa ngabafundi umbala wodongwe lokudlala uzakuba Funda uze mthubi ,umzekelo. utolikeutolike igrafu • Funda utolike iigrafu(Bangaphi Ukuphendula imibuzo abahamba ngeenyawo, abeza esekelwe kumfanekiso ngeteksi, ngebhasi, njalo njalo) . wakho okanye izinto ezihleliweyo, umzekelo, “Uzobe amagqabi amangaphi amakhulu ? Ngawaphi amakhulu kakhulu okanye amancinci? 59 MATHEMATIKA IBANGA LABAQALAYO (R)

3.5 AMANQAKU Angcaciso 60 IBANGA LABAQALAYO(R) IKOTA YOKU- 1 Umyinge wexesha lokufundisa: Iveki 1 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelaniso engekho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 4.1 Ukulandelelanisa iziganeko eziqhubekayo ebomini babo bemihla ngemihla Inkqubo yemihla ngemihla inikezelwa Imihla ngemihla, ngemo yomfanekiso emva kokwaziswa Ixesha • Qala ukufundisa inkqubo yemihla ngemihla Ukulandelelaniswa -- Yakha ukulandelelana kweziganeko zosuku olunye. kweziganeko -- Imifanekiso mayixhonywe ukusuka ekunene kuye ekhohlo. ezilandelelanayo kubomi bemihla -- Inkokeli yosuku ihambisa isikhombisi ukusuka ekhohlo ukuya ekunene njengoko ngemihla imisebenzi yenkqubo yosuku iqhubeka. Inkqubo yemihla -- Abafundi bafumana amava okulandelelanisa iziganeko ngosuku. ngemihla INKQUBO YEMIHLA NGEMIHLA ECETYISWAYO MATHEMATIKA IBANGA LABAQALAYO (R) Umsebenzi weklasi okhokelwa Irejista, imihla ngutitshala (ucwangciswe kwiCAPS), Umsebenzi weklasi okhokelwa Amathuba INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukufika yokuzalwa, imozulu, Ithuba lokucoca ubugcisa obubonwayo, umdlalo ngutitshala (ucwangciswe kwiCAPS) okuya ngasese iindaba wangaphakathi okhululekileyo umdlalo Umsebenzi weklasi wangaphandle Amathuba okhokelwa ngutitshala Ixesha Ixesha Ixesha lokutya okhululekileyo okuya ngasese (ucwangciswe lokuphumla lokugoduka nokucoca kwiCAPS)

Umyinge wexesha lokufundisa: Iveki 1 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelaniso CAPS engekho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo Amanqaku: • Ukunikezelwa/ukufundiswa komxholo kuxhomekeke kwixesha elikwinkqubo yemihla ngemihla. • Inkqubo yemihla ngemihla iyaguqu-guquka, umz amathuba okuya ngasese angasuswa asiwe kwenye inkqubo kuxhomekeke kw imeko yesikolo. • Bonakalisa imisebenzi yetshati kuphela emva kokuba yazisiwe. • IIKHOLAMU ZAMANQAKU Angcaciso AZIBHALWA NGOKULANDELELANA, KOKO ZIBHALWA MALUNGA NOMXHOLO. Ngako oko kufuneka wenze isigqibo sokuba ngowuphi umsebenzi omawenziwe. • Kwezinye iiveki imisebenzi ingaphezulu kwesihlanu. Oku kukuqinisekisa ukuba unemisebenzi eyaneleyo oza kukhetha kuyo, loo nto ayithethi ukuba kufuneka wenze yonke imisebenzi efakiweyo. 1.4 • Ukuqalisa izifundo ngamathuba okuya ngasese (sebenzisa amanani olandelelwano isepha, itaweli yobuso, izindlu zangasese, Emva kokuba ukubonisa idawo-bume) amanzi abalekayo amathuba angasese Chaza, thelekisa azisiwe, lo msebenzi uze ulandelelanise -- Khulisa ukuqonda kokulandelelana kwamathuba okuya ngasese, umz amanani mawenzeke yonke amanani olandelwano umz. (qala uye kwindlu yangasese, emva koko hlamba izandla, vala imihla. itephu, ze wosule /womise izandla, njalo njalo.) -- Yenza uqhelaniso lwamanani aqhelekileyo umz. uNandi ngowokuqala, uNamhla ngowesibini, njalo njalo 61 MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 1 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 62 Uqhelaniso engekho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 3.2 • Ukwazisa itshati yokucoca Itshati yokucoca Emva kokuba amathuba okucoca Izinto -- Misela amaqela amancinci okusebenza. Hlamba azisiwe, lo msebenzi ezinokwakheka izikhongozelo -- Khuthaza ukulandelelaniswa nokuhlelwa kwezixhobo mawenziwe yonke kuka 3-D zepeyinti imihla. Yahlula inani labafundi eklasini yakho babengamaqela asibhozo okucoca. Iqela ngalinye neebrashi malithabathe inxaxheba ekucoceni indawo betshintshisana ngeveki Incwadi Chaza, hlela uze uthelekise izinto ezinokwakheka kuka 3-D ngoko: yokucoca ikona • Bungakanani Ukubuyisela • Umbala iiblhoko • Izinto eziqengqelekayo endaweni yazo • Izinto ezitshebelezayo Tshayela umgangatho Ukuqoqosha MATHEMATIKA IBANGA LABAQALAYO (R) ikona yendlu Pakisha/ buyisela iiphazili endaweni yazo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Coca iitafile zobugcisa Coca i itafile

Umyinge wexesha lokufundisa: Iveki 1 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelaniso CAPS engekho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 1.1 • Ukwazisa Itshati Yomncedisi nendlela ekuza kuhanjiswa ngayo ukutya/ ekuza kutyiwa Itshati yomncedisi Emva kokuba ngayo. Itshati Yomncedisi Bala izinto Qikelela uze ubale izinto ukukhulisa ingqiqo yamanani Itshati Yomncedisi yazisiwe, izidlo mazityiwe yonke -- Itshati yomncedisi isetyenziselwa ukuchonga umncedisi wosuku oza kulungisa itafile imihla. ngexesha lokutya. -- Izangqa ezihlanu kwitshati yabancedisi zimele amaqela amahlanu abafundi abahluliweyo, umz iqela elibomvu, iqela elibhlowu, iqela elityheli, iqela eliluhlaza kunye neqela eli-orenji. Angasebenzisa iindidi zeziqhamo/ izilwanyana/ izithuthi njalo njalo. -- Isimboli yomfundi ngamnye mayibekwe ngaphakathi kwesangqa seqela angena kulo. -- Ukujika iintolo ezidityaniswe phakathi kwisangqa sichaza inkokeli yeqela. Inkokeli yeqela iyajikeleza yonke imihla ukuqinisekisa ukuba umfundi ngamnye ufumana ithuba lokuba yinkokeli. -- Inkokeli yeqela ibala inani labafundi neepleyiti malunga nenani labafundi abakhoyo kwiqela laloo mini. (ukuhambelana kwepleyiti nomfundi) 3.3 Ukunakana , ukuchonga nokuxela imilo/imifanekiso enokwakheka kuka- 2-D eklasini. Amakhadi aneesimboli ezizodwa Njengokuba -- Iisimboli zabafundi zabafundi. abafundi befika Izinto Yenza amakhadi enziwe ngemifanekiso ngosuku lokuqala. ezinokwakheka • Nika umfundi ngamnye ithuba lokuzikhethela isimboli yakhe yekhadi. kuka -2-D yeesimboli. -- Yenza amalungiselelo ebhloko yobuchule ngesimboli yomfundi ngamnye (umfanekiso okanye ifoto). Iilokha, iibhokisi okanye iihuku ezixhonywe eludongeni zineesimboli -- Ncamathisela isimboli kwilokhari yomfundi ngamnye. eziphawuliweyo. -- Yeka umfundi achonge ilokhari yakhe edibana nesimboli yakhe. Ileyibheli yeBanga labaQalayo (R) -- Ncamathisela isimboli negama ezimpahleni zomfundi. Umfanekiso wegama leklasi oxhonywa -- Abafundi bachonga iisimboli zabo nezabahlobo babo ngokudlala imidlalo ukukhuthaza elucangweni. abafundi ekuchongeni amakhadi esimboli ahlukileyo umz abafundi benza isangqa Mawube neleyibheli yegama nefani notitshala bebonisa zonke iisimboli ze bafuze abafundi ukuba bachonge ezabo. yetitshala. -- Iifoto ezincinci zabafundi zingasetyenziswa njengamakhadi esimboli ukuba zikhona. -- Amagama eklasi • Bethelela into yokuba abafundi Bangamalungu eqela elinye elikhulu ngokuba iklasi uyinike igama elinye, umz ngokusebenzisa imifanekiso yeklasi. 63 Abafundi mabalazi igama likatitshala wabo MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 1 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 64 Uqhelaniso engekho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo Amanqaku: • Bonisa kuphela isimboli yomfundi/ifoto kwiinyanga ezintathu zokuqala. • Bonisa isimboli yomfundi/ifoto kunye negama lomfundi kwiinyanga ezintathu ezizayo. • Bonisa kuphela igama lomfundi kwileyibheli kwiinyanga ezintandathu zokugqibela enyakeni • Gcina ucango unyaka wonke. • Leyibhelisha igama likatitshala • Leyibhelisha ubonisa iklasi yeBanga R Umyinge wexesha lokufundisa: Iveki 2 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelwaniso engekho ngaphantsi kwesihlanu, umsebenzi wemathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso MATHEMATIKA IBANGA LABAQALAYO (R) ezinokusetyenziswa eliqikelelweyo 1.1 Qikelela ze ubale ngokuthemebekileyo izinto zemihla ngemihla Inani lamaculo nezicengcelezo Imihla ngemihla Bala izinto Ukubala kwemihla ngemihla • Ukubala ngentloko/ ngesingqi ukusuka kwisinye ukuya kwisihlanu. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA • Cula amaculo ngamanani nezicengcelezo Noxa abafundi bengenalwazi ngamanani xa beqala iBanga R, mabakhuthazwe ukuba benze izicengcelezo zamanani amaculo ze babale ngentloko yonke imihla.

Umyinge wexesha lokufundisa: Iveki 2 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelwaniso CAPS engekho ngaphantsi kwesihlanu, umsebenzi wemathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 1.4 Thelekisa ukuba phakathi kwezinto ezimbini ozinikiweyo yeyiphi enkulu nencinci Usuku olu-1 Chaza, hlela, ze Bafundise ngokhulu noncinci ulandelelanise Ukufunda usebenzisa intshukumo yomzimba amanani -- Abafundi bafumana amava ngokhulu noncinci, baqotha imizimba bazenze bancinci ze bazolule kangangoko banako bezenza bakhulu. Abafundi -- Xelela abafundi badibanise izandla zabo nezabahlobo bejonga ukuba zezikabani ezikhulu okanye ezincinci. -- Thelekisa izandla zikatitshala nezomfundi -- Thelekisa ingalo katitshala neyomfundi. Chaza ,uhlele uze uthelekise izinto ezinokwakheka kuka 3-D no 2-D ngokobungakanani Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Yenza iibhola ezinkulu nezincinci. -- Fumana izinto ezinkulu nezincinci -- Phawula izinto ezinkulu ngesitikha esibomvu ze ezincinci uziphawule ngesityheli. Udongwe lokudlala Thetha malunga nobungakanani obahlukeneyo bezinto . Izinto ezinkulu nezincinci -- Hlela izinto ezinkulu nezincinci ngokobungakanani. Ukusebenzisa izinto okanye iimilo ezokwakheka kuka 2-D okanye imifanekiso Sebenzisa amagama ‘ubukhulu’ no‘buncinci’ xa usenza imisebenzi yobugcisa: -- Ngokukhangela imifanekiso yezinto ezinkulu nezincinci uze uyisike. -- Abafundi mababhale ngokucinezela/mabathreyise izandla zabo ze basike umtrheyiso. Iimagazini, amaphepha-ndaba, Mababeke umthreyiso omnye phezu komnye. Jonga ukuba sisandla sikabani esikhulu izibhengezo, izikere nesincinci. -- Yahlula iphepha kabini. Iphepha i-A3, iikhrayoni -- Ncamathisela zonke izinto ezincinci kwelinye icala lephepha ze uncamathisele izinto ezinkulu kwelinye. 65 MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 2 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 66 Uqhelwaniso engekho ngaphantsi kwesihlanu, umsebenzi wemathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 3.1 Chaza idawo bume yezinto ezi-2 okanye ezi-3 ezinokwakheka kuka 3-D Usuku olu-1 ngokunxulumene nomfundi: ngaphandle nangaphakathi Indawo-bume, ukufumana Ukufunda usebenzisa intshukumo yomzimba indawo apho hoyo, -- Nika umfundi ngamnye uHula-hupu (Hoops). (Utitshala ubonisa abafundi ngokuthi nembonakalo UHula-hupu (Hoops) enze nabo ebiza abagama “ngaphakathi nangaphandle”). Mabatsibatsibe ngaphakathi nangaphandle uhula-hupu belinganisa imiyalelo katitshala. -- Yima ngomlenze omnye kuhula-hupu ze omnye umlenze ube ngaphandle. -- Thabatha ibhokisi ze umfundi atsibatsibe ngaphakathi nangaphandle emva koko abafundi baxoxe ngokuba umfundi ungaphandle na okanye ungaphakathi. -- Tsibela ngaphandle nangaphakathi kwamavili njengomsebenzi wokuthamba. -- Tsibela ngaphakathi nangaphandle kuhula-hupu uvale amehlo. Ukusebenzisa izinto eziphathekayo ezinekwakheka kuka 3-D Yeka abafundi: MATHEMATIKA IBANGA LABAQALAYO (R) -- Batsale unodoli (umntwana) ngaphakathi bafake unodoli phakathi ze bamkhuphele ngaphandle kwekhothi (ibhedi) -- Jula ibhola /ibhinbhegi (bhinbhegi) kuhula-hupu/evilini -- Sebenzisa udongwe ze ulubumbe lube ziibhola izisicaba (indlu yentaka); bumba ngaphezu kwebhola enye (amaqanda) ze uwabeke ngaphakathi/ ngaphandle INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA kwendlwana yentaka ngokomyalelo katitshala. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Yalela abafundi ukuba: -- Bajonge umfanekiso ze bakhangele ukuba Bangazifumana na izinto ezibonisa izinto ezingaphakathi nezingaphandle. -- Mabazobe zona ngaphandle / ngaphakathi kukahula-hupu/ ibhafu, njalo njalo.

Umyinge wexesha lokufundisa: Iveki 2 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelwaniso CAPS engekho ngaphantsi kwesihlanu, umsebenzi wemathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 3.2 Ukwakha izinto ezinokwakheka kuka- 3-D usebenzisa izinto eziphathekayo Iibhloko mazipakishwe kwishelfu, Imini e-1 uze ngokoyilo olunikiweyo olungasemva ukuphinde oku Izinto • Phonononga amathuba okwakha iibhloko ngexesha kusenziwa umdlalo kweshelfu . ngexesha lokudlala ezinokwakheka okhululekileyo wangaphakathi ngokukhululekileyo kuka 3-D -- Inxaxheba ethathwa ngutitshala ekujongeni lo mdlalo yonke imihla Izixhobo ezongezelelweyo ezifana -- Phonononga amathuba okwakha ibhloko ngokuncedisa abafundi ukuba bakhe neminwe emifutshane, (imifanekiso/ ngokunqamlezileyo (ezisicaba), ngokwehlayo (sicaba), izakhiwo ezide nezifutshane. iimbuso ezincanyathiselwe ezimpahleni -- Hlela ze ulandelelanise iibhloko ezahlukeneyo ngokudibanisa ezineemilo ezifanayo. ngeephegi), iimoto zokudlala, izilwanyana zasezifama, iimpawu zendlela, njalo njalo -- Hlela ze ulandelelanise iimilo ezahlukeneyo ngokuzidibanisa ngokobungakanani. mazenziwe zifumaneke. -- Hlela iibhloko ngokobukhulu nobuncinci. -- Umfundi ngamnye makafumane ibhloko enamacala anokwakheka kuka 3-D, ebuxande ze azilungise ngeendlela ezininzi, ukuba kunokwenzeka, umz zidwelise ze uziqokelele ngeendlela ngeendlela. Abafundi Bangathelekisa ze bakope /bakhuphele ezabanye. Basenokwabelana ngeebhloko bengamaqela ukubenza baqonde ngeendlela ezimi ngayo. -- Nyusela ukupakishwa kweebhloko zokwakha ngokoyilo olunikiweyo olungasemva kweshelfu ngokuzidibanisa ngokolu yilo lunye. 67 MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 2 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 68 Uqhelwaniso engekho ngaphantsi kwesihlanu, umsebenzi wemathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 3.2 Chaza, hlela ze uthelekise izinto ezinokwakheka kuka 3-D no 2-D ngokwemibala Izinto/imifanekiso eyahlukeneyo Usuku olu-1 engundoqo, oluhlaza okwesibhakabhaka, obomvu, otyheli/oqanda enokwakheka kuka 3-D no -2-D/ Izinto imifanekiso eklasini umz imintla ezinokwakheka Bonisa umbala ube mnye ngexesha. Sukudibanisa umbala omnye nesimo esinye yeebhotile, iibhloko zeLego, iilogu kuka 3-D Yahlula abafundi babe ngamaqela amahlanu. ezimibala-bala, njalo njalo. amakhadi ayimibala: obhlowu, obomvu, oqanda. Nika iqela ngalinye izinto ezinemibala emininzi ezinokwakheka kuka 3-D no -2-D ngokweemilo. -- Bafundise umbala ngamnye ngokubabonisa ikhadi elinalo mbala ufuna abantwana Izinto ezahlukeneyo ezikwimo bawazi, umz obhlowu. Wuphinda-phinde nomnye umbala. ezinokwakheka kuka 2-D nezi 3-D -- Abafundi mabahlele izinto ngokokwakheka kuka 3-D no -2-D ngokwamakhadi awohlukeneyo abonisiweyo. Ukufunda usebenzisa intshukumo yomzimba Izangqa ezibomvu, eziqanda nezibhlowu -- Ncamathisela izangqa ezinemibala eyahlukeneyo (bomvu, qanda, bhlowu), nqunqa ngutitshala ezisikwe kwikhalibhothi. ikhalibhodi esifubeni somfundi ngamnye. MATHEMATIKA IBANGA LABAQALAYO (R) -- Abafundi mabazicwangcise ngokwemibala eyahlukileyo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Utitshala ubiza abafundi abahlanu beze ngaphambili ze anike umfundi ngamnye into Izinto ezahlukeneyo ezikwiimo eyahlukileyo enokwakheka kuka 3-D ukuba ayibambe ngesandla sakhe. ezinokwakheka kuka 3-D eziqokelelwe -- Abafundi abashiyekileyo mabahlale phantsi ngokwamaqela benengqokelela yezinto phambi kwexesha ze zabekwa kumbindi INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA ezinokwakheka kuka 3-D kumbindi wetafile. weqela ngalinye. -- Umfundi wokuqala ngaphambili makaphakamise into yakhe enokwakheka kuka 3-D umz. ibhloko yeyunifiksi ebhlowu okanye isangqa esiqanda, iimilo zelogu okanye iiphazili, njalo njalo Iresiphi yokupeyinta ngeminwe: -- Abafundi, ngokwetafile, bahlela izinto ezahlukeneyo ezinokwakheka kuka 3-D njengoko abafundi beziphethe. ikomotyi yomgubo ibe nye 3.3 Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso ikomityi yeswekile ibe nye Izinto -- Utitshala ulungisa ipeyinti yeminwe kwangethuba amathontsi amathathu esijiki-bala ezinokwakheka sokutya/iphawuda yepeyinti kuka 2-D -- Abafundi bazoba imilo ngepeyinti besebenzisa iminwe. iikomityi ezintlanu zamanzi abilileyo -- Batrheyisa imilo ezinokwakheka kuka -2-D ze bayifake umbala. (zamisa amanzi ngokucothayo)

Umyinge wexesha lokufundisa: Iveki 2 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelwaniso CAPS engekho ngaphantsi kwesihlanu, umsebenzi wemathematika ngeveki (± 5) Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angcaciso ezinokusetyenziswa eliqikelelweyo 4.1 Ukulandelelanisa iziganeko ezenzeka rhoqo kubomi babo bemihla ngemihla Ixesha • Iinyanga zonyaka • Ixesha Bafundise itshati yemihla yokuzalwa -- Yila / yenza itshati yemihla yokuzalwa emibalabala umz. uloliwe onamakhareji alishumi elinambini (inyanga nganye) – iinyanga mazilandelelane ukusuka ekunene ukuya ekhohlo emakharejini. Beka igama nesimboli /ifoto yomfundi kwinyanga azalwa ngayo. -- Benze baqonde ngokufundwa kwexesha umz. iinyanga zonyaka ngokuthi bacengceleze amagama eenyanga bezikhomba ngamagaba eenyanga. -- Khulisa ukukwazi ukufunda izalathiso. Umz. Bonisa ileyibheli yenyanga nganye yonyaka kumqolo omnye ukusuka ngasekhohlo ukuya ngasekunene. -- Yalela abafundi bachonge iisimboli/iifoto zabo ze babethelele entloko (bankqaye) ukuba usuku lwakhe lokuzalwa lukweyiphi inyanga. -- Bakhuthaze ukuba bazi iminyaka yabo. -- Phinda–phinda lo msebenzi ngokuzingisileyo(amaxesha ngamaxesha) Itshati yomhla/yosuku wokuzalwa eneenyanga ezilishumi elinambini zonyaka zibonisiwe ukusuka ekhohlo ukuya ekunene Isithsaba okanye umfanekiso wekeyiki yosuku lokuzalwa lubonakalisa ukuba usuku lokuzalwa ludlule. Ingoma: Qamba eyakho ingoma “EYOMQUNGU (JANYUWARI), EYOMDUMBA (FEBRUWARI), EYOKWINDLA (MATSHI), UTSHAZIMPUZI (EPRELI), UCANZIBE (MEYI), ISILIMELA (JUNI), EYEKHALA (JUNI), EYETHUPHA (AGASTI), EYOMSINTSI (SEPTEMBA), EYEDWARHA (OKTOBHA), EYENKANGA (NOVEMBA), EYOMNGA (DISEMBA). Januwari Februwari Unyaka wonke xa kukho usuku lokuzalwa. Qaphela: • Usuku lokuzalwa komfundi lubaluleke kakhulu kwaye malubekwe bucala njengomjikelo weemini zokuzalwa apho abafundi baza kucula u“Min’ eMnandi Kuwe!” beqhwaba izandla ngokweminyaka yokuzalwa kwamakhwenkwe/amantombazana. • Umfundi ngamnye eklasini angazoba umfanekiso ze utitshala aqokelele/adibanise yonke imifanekiso kwincwadi yosuku lokuzalwa komntwana, lowo ubhiyozela usuku lwakhe lokuzalwa. 69 • Utitshala angenza imbasa yosuku lwemini yokuzalwa kwenkwenkwe okanye intombazana ze abafundi bayihombise ngezixhobo zekholaji. • Lo msebenzi mawuphindaphindwe ngosuku lokuzalwa komfundi ngamnye apha eklasini. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki 3 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 70 Uqhelaniso engakho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Amanqaku Isihloko Amanqaku angcaciso Isihloko angcaciso 1.1 Qikelela ze ubale izinto zemihla ngemihla ezithembekileyo Inani lamaculo nezicengcelezo Imihla ngemihla Bala izinto • Ukubala ngomlomo kwemihla ngemihla -- Ukubala ngentloko/ ngesingqi ukusuka kwisinye ukuya kwisihlanu. -- Cula amaculo ngamanani nezicengcelezo Noxa abafundi bengenalwazi ngamanani xa beqala iBanga R, mabakhuthazwe ekuculeni izicengcelezo zamanani amaculo ze babale ngentloko yonke imihla. Chonga uze ubale amalungu omzimba awohlukileyo (Umfanekiso womzimba) Chonga/khetha ze ubale iindawo ezahlukenleyo zomzimba Amaculo aneentshukumo nezicengcelezo Usuku olu-1 Ukubala kwemihla ngemihla komlomo ukusuka kwisinye ukuya kwisihlanu. IUkufunda usebenzisa intshukumo yomzimba (Ziqukwe nezakhono zobomi – ubume ubububo bomntu) -- Benze baqonde ngokufundwa kwamalungu omzimba ngokuthi babale amalungu Iphazili/ imidlalo ebonakalisa abantu omzimba. nemizobo yomzimba -- Ndibonise impumlo ze uyibale. Zingaphi iimpumlo zakho? Amakhadi emidlalo MATHEMATIKA IBANGA LABAQALAYO (R) -- Ndibonise iindlebe zakho uzibale.,Zingaphi? Ingaba ikho eyongeziweyo? Masibale ngokwengeza. Abafundi -- Ndibonise izandla zakho. Zingaphi? Masizibale.Ubona ntoni ezandleni zakho? Iminwe? Ungayibala? Masibale izandla neminwe: 1,2,3,4,5. -- Mangaphi amehlo? Bala iindlebe zakho namehlo akho. Bamba amehlo neendlebe zakho ngeli xesha ubalayo, uqale ngeendlebe zakho. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Hlala ujongane nomhlobo wakho ze ubale amalungu akhe omzimba kodwa qala uwabambe ze uwabale. Utitshala makakhokele le nkqubo, umz bamba indlebe yomhlobo wakho ibe nye; bamba enye indlebe yakhe; yibale/zibale; inye, zimbini. Ingaba ziyafana nezakho. Qhuba nalo msebenzi. -- Chonga / khetha amalungu omzimba apho lifumaneka lilinye emntwini umz impumlo inye, umlomo mnye, isilevu sinye, njalo njalo. Ukusebenzisa iimilo ezinokwakheka kuka- 2-D okanye imifanekiso Yalela abafundi: -- Bajonge isipili ze bazithreyise/ bazizobe. -- Mabenze uyilo lwemizimba yabo kwiphephandaba ze bawuhombise kakuhle. Zoba umgca embindini. Isipili esipheleleyo ngobude -- Nqunqa / sika imifanekiso yamalungu omzimba ahlukeneyo kwimagazini okanye Iphepha i-A4 , iikhrayoni isibhengezo ze ugqibezele ubuso. Imagazini, Izibhengezo, iiflaya, izikere. -- Nqunqa/ sika ubuso kwiimagazini ze uzobe amanye amalungu omzimba ashiyekileyo.

Ixesha lokufundisa elicetyiswayo: Iveki 3 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelaniso CAPS engakho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Amanqaku Isihloko Amanqaku angcaciso Isihloko angcaciso 3.3 Ukuqonda/ukunakana umgca wolingano-macala wakho Abafundi Usuka olunye Ulingano - macala Benze baqonde ukuba umzimba womntu unamacala amabini Ukusebenza ngentshukumo yomzimba Bethelela kwicala elinye / kwelinye icala Utitshala uthetha nabantwana malunga nomphambili womzimba nomva kwakunye nomntla nomzantsi womzimba. Yenza abafundi: -- Bazijonge esipilini apho banokuthi babone yonke imizimba yabo. -- Bachonge /bakhethe okokuba ngawaphi amalungu akwelinye icala aphinde abe kwelinye icala lomzimba. -- Babambe amalungu omzimba njengoko kufuneka umz ‘bamba iinzwane zakho, bamba iinyawo zakho, bamba imilenze yakho” Abafundi bangenza imithambo bevale amehlo. Isipili esipheleleyo ngobude -- Babambe ilungu elinye lomzimba nelinye ilungu lomzimba umz. chukumisa amaqatha utitshala angabeka esebenzisa akho ngempumlo njalo njalo. (ikwangumsebenzi womgca ogqitha embindini) imilinganiselo yeminwe/umzobo osikwe ekhadibhodini 3.2 Ukuqonda/ ukunakana, ukuchonga nokuxela izinto ezinokwakheka kuka- 3-D eklasini. izinto ezingqukuva umz ii-orenji, ii Usuku olu-1 -apile, iibhola, iinkonkxa ezingqukuva Izinto iibhola ezingenanto. (Yenza iibhola usebenzisa ezinokwakheka Benze baqonde, bachonge baze bathiye iibhola amagama izinto esele zisebenzile umz. iibhola kuka 3-D zamaphephandaba abotshwe ngekawusi -- Abafundi badlala ngeebhola ze babonakalise, baxele zonke izinto abanokuzenza endala) ngebhola. Utitshala ukhokela ingxoxo ngokubuza imibuzo. izinto ezisisikweri -- Chonga zonke izinto ezinokuqengqeleka umz. bonisa iibhokisi ze ubuze imibuzo: ucinga ukuba ibhloko ingaqengqeleka? Masibone”. umz iibhloko -- Qengqa zonke izinto ze ubukele ukuba ziqengqeleka njani umz iinkonkxa ukudlala iresiphi yodongwe: ziqengqelekela kwicala elinye kuphela. ikomityi yomgubo     -- Sebenzisa udongwe ukubumba iibhola ezinokuqengqeleka xa kusenziwa imidlalo ihafu yekomityi yetyuwa, Xuba zonke (umdlalo wokuzikhethela ngaphakathi). izithako ikomityi enye yamanzi, -- Ngexesha lentshukumo abafundi Bangazama ukuyeka imizimba yabo iqengqeleke, 71 iqengqwa ngexesha becambalele ngemizimba yabo njengebhola neengqukumba. iitispuni ezimbini ze-oyile yokupheka amathontsi ambalwa okujika umbala ukutya MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki 3 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 72 Uqhelaniso engakho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Amanqaku Isihloko Amanqaku angcaciso Isihloko angcaciso 3.3 Ukuqonda/ ukunakana, ukuchonga nokuxela iimilo ezinokwakheka kuka 2-D eklasini Makusetyenziswe ingoma ehambelana Usuku olu-1 okanye imifanekiso nesangqa. Izinto ezinok- wakheka kuka 2-D - izangqa • Ukufundisa izangqa Umdlalo, “inkukhw’ ibek’ iqanda. Intoni? Iqanda” Xa ufundisa izangqa okokuqala izinto ezisetyenziswayo mazifane ncakasana ngento yonke umz. ubungakanani obunye, umbala omnye, imvakalo enye). Imisebenzi eyenziwa ngentshukumo yomzimba Utitshala uzoba isangqa phantsi /emgangathweni. Yeka abantwana bahamba-hambe bejikeleza isangqa ngexesha bethetha, “ ndihamba ecaleni kwesangqa…jikelele jikelele” Yenza abafundi: -- Babambane ngezandla benze isangqa. -- Benze isangqa ngemizimba yabo. -- Bajikeleze isangqa ngaxeshanye becula ingoma. MATHEMATIKA IBANGA LABAQALAYO (R) -- Bahlale phantsi esangqeni bephoselana ngento ukusuka komnye ukuya komnye ngexesha becula “mbongolo, mbongolo, ibigqith’ aph’ imbongolo”. Umfundi osenento ngexesha kuyekwa ukucula, makahambe aye kuhlala embindini wesangqa. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Hula-hupu Usuku olu -1 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Utitshala ubonisa abantwana isangqa sokudlala ze abacacisele ukuba xa sibizwa kuthiwa sisangqa. Isangqa asinazikona. Yenza abafundi: -- Baphathe isangqa sokudlala esinokwakheka kuka 3-D ngeli xa bejikeleza isangqa. Izinto eziziindidi ngeendidi -- Fumane izinto eklasini ezifana ncakasana nesangqa. ezinokwakheka kuka 3-D ezifana nebhola yentenetya, amaqam, iibhaloni njalo Ukuhlela ze bathelekise izinto ezinokwakheka kuka 3-D ngokobungakanani nombala njalo. Utitshala unika abafundi iintlobo ngeentlobo zezinto ezimilo zinokwakheka kuka 3-D no -2-D imilo ezinokwakheka kuka 2-D ezifana ngokobungakanani obahlukeneyo (khulu kunye noncinci) kunye nemibala bomvu, qanda, nokusika isangqa seplastikhi. bhlowu) ezifana nebhola yentenetya, amaqam, iibhaloni njalo njalo. Yenza abafundi: -- Hlela izinto ngokobukhulu nobuncinci. -- Hlanganisa izinto ngokwemibala eyahlukeneyo.

Ixesha lokufundisa elicetyiswayo: Iveki 3 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu Uqhelaniso CAPS engakho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Amanqaku Isihloko Amanqaku angcaciso Isihloko angcaciso 4.1 • Ukwazisa itshati yemozulu nekhalenda Itshati yemozulu kufuneka ibonise iiveki, Emva kokuba itshati umz iintsuku zeveki ngokulandelelana ifundisiwe yemozulu Ixesha a) Ixesha kwazo ukusuka ekhohlo ukuya ekunene lo msebenzi b) Iintsuku zeveki kwiinyanga zokuqala ezintandathu ze mawenziwe yonke yenziwe yonke imihla. imihla. c) Ukulandelelanisa iziganeko Oonotsheluza: d) Ukubala -- BeeNtsuku zeveki -- Imozulu imele iveki enye (iintsuku ezintlanu) usebenzisa iisimboli zamakhadi. umz iintsuku ezintathu ngeveki zilandelelana ukusuka ekhohlo ukuya ekunene (jonga -- Bamanani ukusuka kwisinye ukuya umzekelo apha ngezantsi) kumashumi amathathu ananye -- Imozulu mayenziwe yonke imihla -- Amagama eenyanga ezilishumi elinambini -- Utitshala ukhokela abafundi ukuqonda amagama eentsuku, imihla, iinyanga ngokoonotsheluza abanemifanekiso (ekugqibeleni abafundi Bangachonga ze babonise -- Unyaka umz. 2012 oonotsheluza ngokwabo). -- Amakhadi anemozulu umz -- Inkokeli yosuku iqwalasela imozulu phandle ze yabelane ngaloo nto iyifumeneyo namalungu eqela xa ewonke umz kuyana, kukho amafu, yimini eshushu. -- Utitshala ubonisa abafundi izinto azifumeneyo ngokusebenzisa oonotsheluza Fundisa abantwana njengemifanekiso (ekugqibeleni abafundi Bangabonisa ababo oonotsheluza). kukho umoya ingoma yeentsuku -- Ngokwenza oku abafundi Bangafunda ngeentsuku zeveki neempelaveki. zeveki abaza kuyazi ngentloko (abaza -- Bafunda ngo‘namhlanje, izolo, ngomso’ njalo njalo, ngokungalindelekanga. kushushu kuyinkqaya) -- Abafundi banikwa amathuba okubala ukuya kuma kwisihlanu. Babala iintsuku ezishushu, ezibandayo, ezinomoya, njalo njalo. kuyana -- Babonisa iisimboli zabafundi ukuba ngaba kukho iintsuku zokuzalwa kuloo veki. -- Babonisa nawuphi na umsebenzi owenzeka evekini umz. ukuya kumzi wezilwanyana kukho amafu (ibonakaliswe ngomfanekiso wezilwanyana) 73 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki 3 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala imizuzu engekho ngaphantsi kwamashumi amathathu ngosuku (± 30), imizuzu 74 Uqhelaniso engakho ngaphantsi kwesihlanu umsebenzi weMathematika ngeveki (± 5) Amanqaku Isihloko Amanqaku angcaciso Isihloko angcaciso Umzekelo wetshati Itshati yemozulu yemozulu Juni 2012 Cawa Mvulo Lwesibini Lwesithathu lwesine Lwesihlanu Mgqibelo 12 13 14 15 16 17 18 4.1 Ukulandelelanisa iziganeko ezenzeka rhoqo kwimihla ngemihla ebomoni babo Ixesha • Iintsuku zeveki Iculo: Iintsuku zeveki okanye baqambe Utitshala ufundisa abafundi amaculo nezicengcelezo ezimalunga neentsuku zeveki. awabo amaculo eentsuku zeveki. Phinda-phinda ukuxoxa ngetshati yemozulu yonke imihla. Iculo: MATHEMATIKA IBANGA LABAQALAYO (R) “Zisixhenxe iintsuku zeveki, zisixhenxe iintsuku zeveki”. “Cawe, Mvulo, Lwesibini, Lwesithathu, Lwesine, Lwesihlanu, Mgqibelo.” (phinda-phinda kabini) • Ukufundisa itshati ebonisa amaxesha onyaka omane uwabonisa ngotolo: Amakhadi amane awohlukeneyo Litshintshe elo anomfanekiso wexesha elinye lonyaka. xesha lixhonyiweyo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Sikweliphi ixesha lonyaka ngoku? xa kutshintsha -- Liliphi ixesha lonyaka esele lidlulile? Amaxesha ixesha lonyaka Amaxesha onyaka -- Liliphi ixesha lonyaka elizayo/elilandelayo? -- Bonisa umfanekiso wexesha lonyaka esikulo neenyanga zalo, umz ngoJanyuwari (Ixesha) ukuya kuMatshi ungabonisa umfanekiso waseHlotyeni. IHlobo UKwindla INtwasahlobo UBusika Qaphela: Yonke imiba emitsha mayaziswe ngokwamaqondo alandelayo • Iqondo lemisebenzi eyenziwa ngentshukumo yomzimba (amava ngemiba yomzimba novakalelo) • Iqondo lezinto eziphathekayo(ukusetyenziswa kwezinto ezinokwakheka kuka 3-D) • Iqondo lezinto ezIsemifanekisweni (ukubonakaliswa kwezinto ezinokwakheka kuka 3-D ephepheni umz.ukuzoba, ukudibanisa imifanekiso, amakhadi emidlalo, amaphepha okusebenzela njalo njalo) zonke iimilo ezibizwa ngokuba zimacala mabini.

Iveki 4 Umyinge wexesha lokufundisa: Ukuqala Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu ukufundisa engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) CAPS amanani Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 1.1 Chonga ze uchaze amanani apheleleyo Usuku olu- 1 Ukubala izinto Ukufundisa intsingiselo yenani u-1 Ukubala komlomo okuqala kwisinye ukuya kwisihlanu Inani lamaculo nezicengcelezo Ukufunda usebenzisa intshukumo yomzimba Yenza abafundi: -- Bachonge amalungu omzimba umz impumlo enye. -- Banqwale intloko kanye, ukungqisha kanye, ukutsiba kanye. -- Babambe umnwe omnye, isandla esinye, unyawo olunye njalo njalo -- Benze inani isinye ngemizimba yabo -- Babhale inani isinye emoyeni/phantsi. -- Baqhwabe izandla kanye Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka- 3-D Yenza abafundi: Izinto eklasini nokusingqongileyo -- Bachonge nayiphina into ezimeleyo eklasini umz. ibhloko eyakhiweyo ibenye. -- Benze inani, u-nye ngodongwe. Ukusebenzisa iimilo ezinokwakheka kuka- 2-D okanye imifanekiso Umfanekiso Yenza abafundi: wento enye -- Bachonge imifanekiso ngento enye kumakhadi awahlukeneyo. -- Badibanise/babophe amakhadi anemifanekiso ngento enye nemakhadi anechaphaza. Isixhobo sokubala sibe sinye kumfundi -- Badibanise rhoqo amakhadi anemifanekiso namakhadi anedothi nenani elinye ngamnye lesixhobo sokubala umz. dibanisa inani elinye lesixhobo sokubala kwedothi nganye. Iindidi ngeendidi zemifanekiso -- Emva kokuba ufundise inani u-inye bonisa, ncamathelisa unotsheluza eludongeni ekoonotsheluza. Oonotsheluza ukuze abafundi bambone yonke imihla. abanamachaphaza 75 MATHEMATIKA IBANGA LABAQALAYO (R)

Iveki 4 Umyinge wexesha lokufundisa: Ukuqala 76 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu ukufundisa engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) amanani Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 2.1 • Chonga iipateni zokusingqongileyo neempahla zabafundi Usuku olu- 1 Iipateni zejiyometri Yenza abafundi: -- Bathethe ngeepateni ebebeziqwalasele kokusingqongileyo nasezimpahleni zabo: -- Ziziphi iipateni ezinemigca, iibhloko? -- Ingaba iipateni ziyafana zonke, yintoni umahluko, zifana ngantoni? -- Yenziwe ngantoni ipateni? -- Ipateni iphindaphindiwe – imigca/ ibhloko/imilo Ukusebenza ngentshukumo yomzimba Iiribhoni ezibomvu nezibhlowu Utitshala ubopha iribhoni ebomvu nebhlowu kwiingalo ezine zabafundi. Wakha ipateni ngokubeka umfundi oneribhoni ebomvu ngaphambili eklasini kulandele oneribhoni ebhlowu ze kugqibele oneribhoni ebomvu. Yeka abantwana bagqibezele le pateni. MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka- 3-D Iziciko zeebhotile ezibomvu nezibhlowu kumfundi ngamnye -- Utitshala wenza ipateni ngeziciko ezithathu ezibhlowu nezintathu ezibomvu. -- Yenza abafundi bakhuphele ipateni katitshala. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Iveki 4 Umyinge wexesha lokufundisa: Ukuqala Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu ukufundisa engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) CAPS amanani Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.2 Ukuqonda/ ukunakana, ukuchonga nokuxela imilo ezinokwakheka kuka 3-D no 2-D Iindidi zezinto eziseklasini Usuku olunye eklasini nemifanekiso nezokungqongileyo Izinto ezinokwakheka Ukwenza bakwazi ukwahlula phakathi kwezinto ezifotwe zankulu ngaphambili nezo kuka 3-D zincinci ngasemva. 3.3 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iimilo Utitshala ubeka izinto ezahlukeneyo ekalsini naphandle kwibala lokudlalela: ezinokwakheka Yenza abafundi: kuka 2-D -- Babonise izinto ezahlukeneyo eklasini umz izinto ezenziwe ngemithi, izinto ezibomvu, izinto ezenziwe ngeplastikhi njalo njalo -- Jonga izinto ezithile eklasini ngokomyalelo katitshala umz ibhola kwisikhongozeli sebhloko ye Lego, ithoyi yemoto esekhabhathini, epensile esenkonkxeni njalo njalo.. -- Jonga izinto ezifanayo umz amaqhosha angqukuva kulawo ambhoxo, iqamza elibomvu phakathi kwalawo anemibala, njalo njalo. -- Hlela izinto ngokweentlobo zazo umz. ubungakanani, umbala, imvakalo okanye imilo. -- Dlala umdlalo, “Ndiyalonda ngamehlo am amancinci, into engqukuva........” -- Jonga izinto ezifanayo ngokomyalelo katitshala umz. intaka emthini, iribhoni esemthini, iintyatyambo ezintle,imbovane ihamba emagqabini njalo njalo. -- Emakhaya abafundi mabakhuthazwe ukuba bakhuphe amacephe/ iimela/ iifolokhwe Ukusebenzisa iimilo ezinokwakheka kuka 2-D/ imifanekiso Nawuphina umfanekiso omkhulu oxoxwayo (ipowusta) Bonisa abantwana umfanekiso ze ubabuze imibuzo ehambelana nomfanekiso. Umz: Iiphazili -- “Iphethe ntoni intombi encinci esandleni sayo.? -- “Bangaphi abantu abakhwele iinqanawe? -- Yakha iiphazili ze udlale imifanekiso yedomino elungele ukukhulisa ulwazi labafundi olkuchonga izinto phakathi kwezinye nokuqaphela iinkcukacha . 77 MATHEMATIKA IBANGA LABAQALAYO (R)

Iveki 4 Umyinge wexesha lokufundisa: Ukuqala 78 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu ukufundisa engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) amanani Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.2 Ukuqonda/ ukunakana, ukuchonga nokuxela izinto ezinokwakheka kuka- 3-D Usuku olu- 1 ngokuphonononga imilo nobungakanani beebhokisi Izinto ezinokwakheka Ukufunda usebenzisa intshukumo yomzimba kuka 3-D Yenza abafundi: -- Ukugwencela ngaphakathi nangaphandle kwebhokisi. Iindidi zeebhokisi ezinkulu nezincinci (ifriji -- Hlola ibhokisi ngaphakathi ngokuthetha ngokuthi uxele ukuba yintoni engaphakathi. engenanto neebhokisi zesitovu) Umz. ibhokisi inomgangatho/ umphantsi, amacala amane/ amacala nesiciko. -- Songa ibhokisi evuliweyo ukujonga imilo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Sebenzisa iibhokisi ukwakha isakhiwo umz. indlu, igaraji (kwenze xa usebenzisa ubuchule obubonwayo ngeebhokisi ezinobungakanani obungafaniyo) -- Nika abafundi izinto ezahlukeneyo ezifana namaqhosha, iibhloko Iibhloko ezingangcitywanga (unifix MATHEMATIKA IBANGA LABAQALAYO (R) ezingangcitywanga,iziciko zeebhotile, iiklipu zesonka zeplastikhi. blocks) ,iziciko zebhotile, iiklipu zesonka zeplastikhi. Yenza abafundi: (abafundi bangeza nazo emakhaya) -- Hlela izinto ngokwamaqela ohlobo olunye -- Jonga umahluko phakathi kwezinto -- Jonga ukuba ziziphi izinto ezisisikwere nezingqukuva INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Hlela izinto ezimbala mnye

Iveki 4 Umyinge wexesha lokufundisa: Ukuqala Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu ukufundisa engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) CAPS amanani Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.3 Ukuqonda/ ukunakana, ukuchonga nokuxela izinto ezinemilo ezinokwakheka kuka- Amakhadi emidlalo akhumbuza ngemilo Usuku olunye 2-D eklasini nemifanekiso. Izinto ezinokwakheka -- unxantathu kuka 2-D Ukufundisa unxantathu Xa ufundisa unxantathu okokuqala izinto emazisetyenziswe mazifane ncakasana ngandlela Uboya okanye udongwe. zonke (ubungakanani obunye, umbala omnye, inkangeleko enye) Unxantathu unamacala amathathu angqalileyo. Loo nto ibizwa ngokuba ngunxantathu. Ukufunda usebenzisa intshukumo yomzimba “ibhegi” (ibhegi yelaphu ene-elastikhi emantla) enemilo yejiyometri. Yenza abafundi: -- Benza imilo ngemizimba yabo umz. abafundi benza unxantathu ngemizimba yabo. -- Benza unxantathu besebenzisa iminwe yabo. -- Benza unxantathu besebenzisa izicwili zoboya okanye udongwe. Isethi yamakhadi adityanisiweyo anemilo -- Hamba emdeni wemilo kanxantathu. Ngexesha uhamba thetha, ‘ ndihamba ecaleni lika ezotyiweyo. nxantathu, icala,linye, mabini, mathathu, okanye inye,zimbini,zintathu iikona. -- Bamba imilo. Sebenzisa ubungakanani obukhulu bemilo okanye beka imilo eyahlukeneyo ebhegini. Umfundi makabambe imilo esebhegini ze azidibanise zibe yisethi yamakhadi, amakhadi amilo yenziwe kuzo). -- Zoba imilo engunxantathu emoyeni, phantsi/emgangathweni nge- (itshokhwe) nasephepheni. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ukuchaza, Iphepha i-A4 nekhrayoni Yenza abafundi: ukuhlela nokuthelekisa -- Hlela imilo eLogi ngokwemilo (isangqa nonxantathu), ubungakanani (enkulu nencinci) izinto kunye nombala (ibomvu,iqanda,ibhlowu) Imilo ze-Logi (logi shapes) ezinokwakheka -- Khangela iimilo ezingoonxantathu eklasini nakokusingqongileyo. Izinto eklasini nakokusingqongileyo. kuka 3-D no- 2-D. 79 MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 5 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu 80 engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 1.1 Chaza ze uchonge amanani apheleleyo Usuku olu- 1 Ukubala izinto Ukubethelela ulwazi olufumene kwiveki yesi -4 oluquka inani -1. Inani lamaculo nezicengcelezo Ngomlomo: ukubala ngokucengceleza ukusuka kwisinye ukuya kwisihlanu. Ukufunda usebenzisa intshukumo yomzimba Umfanekiso Yenza abafundi: we-nto enye 1 Inye -- Yenza izandi zomzimba umz ukuqhwaba izandla kanye. -- Utitshala uveza/ ubonisa unotsheluza obonisa inani: inye ze abantwana baphakamise umnwe omnye, isandla esinye, ngonyawo olunye njalo njalo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Yenza abafundi: into enye -- Fumana into ibenye eklasini Isixhobo esinye sokubhala -- Bala isixhobo sokubala kanye. MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa iimilo ezinokwakheka kuka 2-D/ imifanekiso Iindidi zonotsheluza ezinomfanekiso omnye kunye nedothi enye -- Tshatisa iindidi zomfanekiso omnye, kunye nonotsheluza omnye wedothi. -- Tshatisa iindidi zemifanekiso kunye nonotsheluza wedoti nesimboli yenani elinye INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Tshatisa isimboli yenani nenani legama likanotsheluza. -- Yenza iphazili yenani ze uyeke abantwana bazidibanise umz. Unotsheluza onesimboli elinani negama lenani 1 1 Umfanekiso Inye wento enye 1 Inye

Umyinge wexesha lokufundisa: Iveki 5 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu CAPS engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.4 Ukomeleza/ukuqinisa ukuqonda ukuba umzimba omnye unamcala amabini umz icala Usuku olu- 1 elinye, elinye icala, ukuya ekhohlo nasekunene Ulingano -macala Ukufunda usebenzisa intshukumo yomzimba Utitshala ucacisa ngamacala amabini omzimba omnye. Yenza abafundi Isihlukuhli senziwa ekhaya – isikhongozeli -- Yima ngomlenze omnye ze uphinde ume ngomnye. nesiciko, sizaliswe ngamatye. -- Hamba ngesingqi usebenzisa isingqi sesihlukuhli ukuya kwicala elinye leklasi. Xa isihlukuhli siyekile abantwana mabaye kwelinye icala leklasi. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Umfundi ngamnye unikwe ibhin bhegi(bhinbhegi) Yenza abafundi -- Beka ibhinbhegi phantsi ecaleni kwabo. -- Beka ibhinbhagi iinzwane nezandla njalo njalo. ibhinbhegi yomntwana ngamnye -- Beka ibhinbhegi phantsi kwelinye icala lemizimba ze baphinde baye kwelinye icala. -- Ukomeleza lo mba unxulumaniso nobuchule obubonwayo ngokuyeka abantwana benze umfanekiso webhabhathane. (Songa iphepha libe yihafu/isiqingatha, galela am./aqabaza epeyinti emigceni esongiweyo; songa esiphakathini ze usasaze ipeyinti ngokukhuhla umfanekiso; vula ujonge ibhabhathane; sika umgca ongumda – ibhabhathane linamacala amabini alinganayo. 3.2 Ukuqonda, ukuchonga ze uxele izinto ezinokwakheka kuka 3-D “ingxowa yokuphampatha” (ibhegi Usuku olunye eyenziwe ngelaphu eneplastikhi emantla) Izinto Ukufundisa nokuphonononga izinto eziqengqelekayo ezinokwakheka Ngaphakathi ebhegini kukho: -- Xoxa ngobungqukuva bezinto. Faka izinto ezingqukuva zibe ninzi ebhegini (ibhegi kuka 3-D yelaphu). Abafundi bathatha izinto ebhegini baze bachaze ubungqukuva bazo. Iibhola ezinesayizi ezahlukeneyo,amaqam, iinkonkxa -- Abafundi babonisa ukuba izinto ezahlukeneyo ziqengqeleka njani ukuhla zinyuka zesiselo ezingenanto, iisilinda, imilo etafileni nezitena ezibini. yeplastikhi okanye imilo yesiciko sebhotile seplastikhi. 81 MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 5 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu 82 engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.1 Indawo-bume yezinto ezimbini okanye ezininzi ngokunxulumene nomfundiChaza Izitulo Usuku olu- 1 izinto enye enokwakheka kuka 3-D ngokunxulumene nenye Indawo-bume, uku- Abafundi fumana indawo, -- Ngaphambili / ngasemva nembonakalo Ukufunda usebenzisa intshukumo yomzimba Oonotsheluza ababonisa isenzo eso Utitshala ukhetha abafundi ababini nesicengcelezo esibalayo: ngaphambili nangasemva -- Beka izitulo ezibini ngaphambili eklasini. -- Abantwana ababini babonisa ngalo mba ngaphambili nangasemva ngokwemiyalelo katitshala. Umz o Sipho yima ngaphambili kwesitulo o Carl yima emva kesitulo -- Xa sele iphumelele utitshala uphakamisa unotsheluza ze abafundi babonakalise isenzo besebenzisa izitulo zabo. o ”oku kungabonakaliswa kwakhona ngokusebenzisa abantwana abathathu. MATHEMATIKA IBANGA LABAQALAYO (R) -- Amy uma emva kuka Sipho, ze uCarl ame ngaphambili kuka Amy. -- Utitshala unika abafundi idayisi elikhulu elinemifanekiso eyahlukileyo ebonisa “ umphambili nomva” ubhale emacaleni umz yima ngaphambili komnye onenwele ezinde, yima ngasemva kwalo mntu unxibe ibhulukhwe; hlala phambi komnye.njalo njalo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Yenza badlale umdlalo bengamaqela bephoselana ngedayisi ze benze ude uye kuphela.

Umyinge wexesha lokufundisa: Iveki 5 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu CAPS engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.2 Thelekisa ukuba ziziphi izinto ezimbini ozinikiweyo ezi: Usuku olu-1 Izinto nkulu kunenye ze ibe ncinci kunenye ezinokwakheka • Ukubethelela ingqiqo - inkulu (inkulwana)kunenye ze ibe ncinci kunenye kuka-3-D (incinanana) Ukufunda usebenzisa intshukumo yomzimba Umfanekiso wempuku nowenja (qiniseka Yenza abafundi: ukuba umfanekiso wenja mkhulu kunomfanekiso wekati) -- Benza imizimba yabo ibe mikhulu ngokutweza iingalo zabo ngaphezu kweentloko zabo. -- Benza imizimba yabo ibe mincinane ngokugoba ze baziqothe. -- Xela ukuba ingaba inja inkulu na kunempuku. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Sebenzisa rhoqo ubuncinane izinto ezimbini xa uthelekisa. Izinto eklasini umz iibhloko, iibhola, -- Thelekisa ubungakanani obahlukeneyo bebhloko efanayo umz iibhola, amaqhosha, iipleyiti, amaqhosha, amaso, izinti, itafile, iipleyiti, izitulo njalo njalo ukufumana ukuba yeyiphi into enkulu/incinci, iiphegi, iibhokisi, iinkonkxa, amabhastile, enkudlwana/ encinanana, enkulu kakhulu/nencinci kakhulu.” iziciko, amaqokobhe, iziciko zeebhotile, -- Yaba izakhiwo ngeebhloko ze abafundi bathelekise ezo zakhiwo zikhulu kakhulu nezo njalo njalo. zincinci kakhulu. Ukusebenzisa iimilo enzinokwakheka kuka 2-D okanye imifanekiso -- Thelekisa imifanekiso ebonisa izinto ezinkulu nezincinci nezinkudlwana nezincinanana. Imifanekiso ebonisa ubukhulu nobuncinci -- Sebenzisa ukuqonda ubukhulu / nobuncinci kubugcisa boyilo. 83 MATHEMATIKA IBANGA LABAQALAYO (R)

Umyinge wexesha lokufundisa: Iveki 5 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu 84 engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.2 Thelekisa ukuba kwezi zinto zimbini uzinikiweyo yeyiphi: izangqa ezikhulu nezincinci ezizotywe Usuku olu-1 esantini okanye phantsi. Izinto -- Enkulu nencinci ezinokwakheka -- Enkulu kunenye nencinci kunenye kuka-3-D -- Enkulu kakhulu ze ibe ncinci kakhulu Ukufunda usebenzisa intshukumo yomzimba Utitshala uzoba isangqa esantini, phantsi. -- Abafundi bahamba emdeni wesangqa. Utitshala uzoba isangqa esikhulu kunesinye kumphandle kwesangqa -- Abafundi bahamba emdeni wesangqa esikhulu kunesinye. -- Utitshala ubuza imibuzo enje ngale: o “Sesiphi isangqa esincinici kakhulu?” o “Sesiphi isangqa esikhulu kakhulu?” MATHEMATIKA IBANGA LABAQALAYO (R) o “Hamba kwisangqa esincinci” o “Hamba kwisangqa esikhulu” Utitshala uzoba isangqa esikhulu kakhulu ngaphandle kwesangqa. -- Abafundi bahamba emdeni wesangqa esikhulu kakhulu, kananjalo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Utitshala ubuza imibuzo enje ngokuthi: o Sesiphi isangqa esikhulu kakhulu?” o “Sesiphi isangqa esincinci kakhulu?

Umyinge wexesha lokufundisa: Iveki 5 Umsebenzi omnye weklasi ocwangcisiweyo okhokhelwa ngutitshala imizuzu engekho ngaphantsi kwabashumi abathathu ngosuku (± 30), imizuzu CAPS engakho ngaphantsi kwesihlanu umsebenzi webathebatika ngeveki (± 5) Abanqaku Isihloko Abanqaku angcaciso Isihloko angcaciso 3.2 Ukusebenzisa izinto eziphathekayo esinokwakheka kuka 3-D Iibhloko zokwakha neebhola zobungakanani obahlukeneyo. Izinto Abafundi bahlela ze bathelekise izinto ezinobungakanani obahlukeneyo umz (inkulu ezinokwakheka kakhulu, incinci kakhulu) umz. Amaqhosha, amacephe, iibhokisi kuka-3-D zamayeza, iibhokisi zezihlangu, -- Isiciko esikhulu ukusuka kwesincinici. amakhathoni obisi angenanto, iibhotile -- Amacephe ukusuka kwamancinci zamayeza ezingenanto, njalo njalo -- Iibhokisi ezinkulu ukusuka kwezincinci Lo msebenzi ungadluliselwa kwimidlalo yangaphandle (umdlalo wesanti nomdlalo wamanzi) apho abafundi Bangathelekisa izinto ze bathethe okokuba yeyiphi encinici kunenye/enkulu kunenye, enkulu nencinci Oku kunganxulunyaniswa nobugcisa bokubonwayo – mabenze umfanekiso owenziwe ngamaphepha besebenzisa izinto ezinkulu nezincinci. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Yenza abafundi: -- Badlale imidlalo yamakhadi ze bachonge imifanekiso emincinci/ emikhulu/ emikhulu kakhulu. -- Buza imibuzo enje: “Yeyiphi intlanzi yokuqala okanye yeyiphi intlanzi yokugqibela?” “Yeyiphi intlanzi ephakathi?” -- Gqithela koonobumba ukuze abafundi bakhumbule ukuba imifanekiso imele amagama. Akunyanzelekanga ukuba abafundi mabafunde oonobumba. 85 MATHEMATIKA IBANGA LABAQALAYO (R)

Iveki 6 Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 86 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.1 Qikelela uze ubale izinto zemihla ngemihla ngokuzithemba. Iingoma nezicengcelezo zamanani. Rhoqo ngosuku. Bala izinto Ukubala kwemihla ngemihla -- Ngomlomo: Ukubala ngokucengceleza ukusuka kwisi-1 ukuya kwisi-5. -- Cula iingoma nezicengcelezo zamanani. 2.1 Ukukopa nokwandisa iipateni usebenzisa ipateni yokubetha amalungu omzimba Abafundi. Usuku olu-1. Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba: -- Utitshala ubonisa ngepateni yokubetha amalungu omzimba kwaye abafundi kufuneka bakope ipateni, umzekelo, qhwaba qhwaba, ngxishi; qhwaba qhwaba, ngxishi;.......... njalo njalo........... Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Kopa ipateni enezinto, umzekelo: -- Ukusebenzisa iindidi ezahlukeneyo zamagqabi. -- Ukusebenzisa iimilo, umzekelo, isangqa, isangqa, unxantathu, isangqa, Iimilo zeLogi. MATHEMATIKA IBANGA LABAQALAYO (R) -- Ukusebenzisa izinto, umzekelo, iphegi ebomvu, iphegi ebhlowu, iphegi etyheli, iphegi Iphegi -bhodi yazo. ebomvu,…………… Ukusebenzisa imifanekiso /iimilo ezinokwakheka kuka 2-D. Yalela abafundi: INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Ukuyila iipateni zabo ngamakhadi anemifanekiso, umzekelo, iintyatyambo, igqabi, Nika abafundi amakhadi anemifanekiso. igqabi, intyatyambo……… Amakhadi amibala-bala. -- Ukuyila iipateni zabo ngamakhadi anemibala, umzekelo, ubomvu, ubhlowu, ubomvu, Utitshala unokusika iimilo kwisponji. ubomvu……… -- Ngexesha lobugcisa boyilo yalela abafundi bashicilele iipateni basebenzise imisiko yeemilo.

Iveki 6 Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.3 Qaphela, chonga uze uthiye isikwere. Usuku olu-1. Izinto Fundisa ngesikwere. ezinokwakheka Xa ufundisa ngesikwere okokuqala, izinto ezisetyenzisiweyo mazifane twatse Abafundi. kuka 2-D (ngobungakanani, ngombala nemvakalo/noburhabaxa). Isikwere sinamacala amane. Oku Intambo. kubizwa ngokuba sisikwere. Ukufunda usebenzisa intshukumo yomzimba: -- Iklasi yonke ima ibe sisikwere. -- Yalela abafundi beseso sikwere basenzileyo ngentambo bahambe kwikhaphethi besithi, “Ndihamba kwisikwere – kwicala elinye, kumacala amabini, amacala amathathu, amacala amane – onke amacala ayafana?” -- Yalela amaqela abafundi benze izikwere ezincinane. Isiciko senkonkxa. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Ithayile esisikwere. -- Utitshala ubonisa umahluko phakathi kwesangqa nesikwere ngokuphakamisa isiciko Iindidi ezahlukeneyo zeziciko nezinto senkonkxa nethayile esisikwere. ezimile ngokwesikwere. -- Isiciko singqukuva ize ithayile ibe neencam neekona. Amaphepha okubhalela. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Iikhrayoni. -- Utitshala uzoba erhangqele isiciko nethayile. -- Isiciko simele isangqa nethayile imele isikwere. -- Yalela abafundi bathreyise berhangqele isiciko nethayile besebenzisa iikhrayoni. Hlela izinto ezinokwakheka kuka 3-D kunye neemilo enokwakheka kuka 2-D okanye Amakhadi eemilo. imifanekiso izinto ezinokwakheka kuka 3-D no2-D Yahlulahlula abafundi babe ngamaqela. ezinjengeebhloko, iibhloko zeLego Yalela abafundi: ezinjengemidlalo yokubakhumbuza -- Hlela iindidi ngeendidi zezinto ezinokwakheka kuka -3-D no2-D ezinikwe ngutitshala ngeemilo ezifana nokuba “Yintoni ngobungakanani nebala. ekwisikwere?” -- Bakhumbuze ngeemilo ngokubadlalisa imidlalo namakhadi emidlalo ngexesha lokudlala ngaphakathi. 3.2 Qaphela, khetha uze uxele Iibhloko. Usuku olu-1 Izinto • izinto ezinokwakheka kuka 3-D ezitshebelezayo Iibhola. ezinokwakheka Fundisa ngezinto ezitshebelezayo. Iibhokisi. kuka 3-D -- Nika abafundi iindidi ezahlukeneyo zezinto ezahlukeneyo ezinokwakheka kuka 3-D Isilayidi / itheyibhile eneebhloko. 87 kunye no -2-D njengeebhloko, iibhokisi, iibhola, njalo njalo. -- Yalela abafundi balinganise ngokudlala ngokubonisa ukuba ziziphi izinto ezitshibilizayo nokuba ziziphi eziqengqelekayo. MATHEMATIKA IBANGA LABAQALAYO (R)

Iveki 6 Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 88 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo -- Abafundi banokusebenzisa isitshebelezi kwindawo yokudlala okanye utitshala unokusebenzisa itafile ukwenza indawo ehlayo ngokubeka iibhloko ezi-2 ngaphantsi kwazo. -- Ingaba zikho ezinye izinto ezitshibilika ngokunyukayo? -- Ziziphi izinto ezitshibilikela ngasezantsi? -- Kutheni ezi zinto zikwazi ukutshibilika? 3-1 Chaza izinto ezinokwakheka kuka 3-D ngokunxulumene nenye Usuku olu-1 Indawo-bume, • Fundisa la magama: ngaphakathi / ngaphantsi, ngasezantsi / ngaphezulu. ukufumana indawo Ukufunda usebenzisa intshukumo yomzimba: nembonakalo. -- Umfundi ngamnye uhlala esitulweni sakhe. Isitulo somfundi ngamnye -- Abafundi bamamela imiyalelo katitshala baze balandele eli xa imisebenzi eyenziwayo, umzekelo, hlala esitulweni, lala phantsi kwesitulo. ngaphezu kwetafile. -- Chopha phezu kwesitulo. Hlala phantsi kwetafile. -- Beka izandla zakho entloko. MATHEMATIKA IBANGA LABAQALAYO (R) -- Beka izandla zakho phantsi kweenyawo. -- Beka ibhinbhegi phantsi kwekhwapha. -- Chopha phezu kwebhinbhegi. ngaphantsi / ngasezantsi -- Beka ihupu phantsi kwamadolo akho. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Yalela abafundi ababini babambe intambo yokutsiba baze abanye beklasi barhubuluze phantsi kwentambo. -- Khangela into phantsi kwekhaphethi / kwetafile / ibhokisi njalo njalo. Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Utitshala unika abafundi iindidi zemifanekiso engamagama angala: ngaphantsi, ngaphakathi nangaphezulu abonisiweyo, umzekelo, umntu okhwele ihashe, usana olulele phantsi kwengubo, njalo njalo. Yalela abafundi: -- Chonga amagama angala: ngaphantsi, ngaphezulu, nangaphakathi emifanekisweni.

Iveki 6 Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 4.1 Chaza ixesha losuku ngokosuku nobusuku / ukukhanya nobumnyama. Izitulo neengubo. Usuku olu-1 Ixesha • Fundisa ngamagama angala: “usuku / ubusuku”, “ukukhanya / ubumnyama”. Ithotshi. Nxulumanisa oku nezihloko zoLwazi olusisiSeko kwiZakhono zoBomi. Ukufunda usebenzisa intshukumo yomzimba: -- Ziqhelanise nobumnyama ngokuhlala phantsi kwetafile nezitulo ezogqunywe ngengubo. -- Yenza mnyama iklasi ngokuvala imikhusane nokucima izibane. -- Abafundi bathetha ngamava abo kumnyama eklasini naxa kukhanya. Ipowusta yemini nobusuku. -- Khupha ithotshi ukhanyise phantsi kwengubo. Imifanekiso engemisebenzi yexesha -- Thetha ngemisebenzi eyenzekayo ebusuku nasemini. lasemini nexesha lasebusuku. Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Utitshala wenza iphowusta yelanga nenyanga aze akhuphe imifanekiso ebonisa okwenzekayo ngexesha lasemini nasebusuku. -- Abafundi mababeke imifanekiso phantsi kwelanga kunye / okanye kwenyanga. 89 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 7 90 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.3 Nakana, khetha uze uxele iimilo ezinokwakheka kuka 2-D eklasini Iindidi zeephazili – ubuncinane izicwili Usuku olu-1 ezi-6. Izinto • Fundisa ngeephazili uze unike isikhokelo ngendlela yokuzenza. ezinokwakheka -- Xoxa ngephazili yemifanekiso unike ingqwalasela eyodwa kumbala, abantu / kuka 2-D izilwanyana, izinto, indawo yokuma kwabantu / kwezilwanyana nezinto. -- Ukwalatha, ukuqaphela nokutshatisa iindidi ezahlukeneyo zezicwili zeephazili, umzekelo o izicwili zeekona. o izicwili ezinecala elinye elingqalileyo. Uyakha njani ipazili -- Pakisha zonke izicwili zeepazili ngokuzijongisa phezulu -- Chonga iikona zezicwili zeepazili uze utshatise umbala,into njl-njl nazo ngeekona zepazili -- Yakha isakhelo esinekona ezi-4 usebenzisa zonke izcwili ezinecala elinye MATHEMATIKA IBANGA LABAQALAYO (R) -- Ukuba umfundi uyasokola unokwakha ipazili phezu komfanekiso abawunikiweyo -- Zonke iipazili kufuneka zigqityiwe phambi kokuba uzipakishe INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 7 CAPS Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.1 Chaza into enye enokwakheka kuka 3-D ngokunxulumene nomfundi. Usuku olu-1 Indawo- -- ngaphakathi / ngaphandle bume,ukufumana • Indawo ezimi kuyo izinto ezimbini okanye ngaphezulu ngokunxulumene nomfundi. Umdlalo: Emlanjeni (phakathi kwemigca indawo emibini), ngaphandle komlambo nembonakalo -- ngaphakathi / ngaphandle (ngaphandle kwemigca emibini). Ukufunda usebenzisa intshukumo yomzimba: -- Utitshala usebenzisa iteyiphu yephepha okanye intambo yokutsiba ukwenza imigca Iintambo ezi-2 zokutsiba. emibini emgangathweni. -- Abafundi bema bonke kwicala elinye aze utitshala akhwaze, “emlanjeni (Bonke abafundi kufuneka batsibele phakathi kwemigca emibini, baze bakhwaze “ngaphandle komlambo.” Abafundi mabatsibele bonke kwicala ngalinye lemigca emibini. -- Abafundi aBangawulandeliyo umyalelo ngokuchanekileyo bayaphuma kwaye abaqhubeki nokudlala. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Yalela abafundi: -- Beme qelele kancinane nebhaskithi / ibhakethi. Iemerana okanye ibhaskithi. -- Baphose ibhinbhegi (bhinbhegi) ebhaskithini. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Abafundi bazoba umfanekiso obonisa ngongaphakathi nongaphandle. Iphepha neekhrayoni. 91 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 7 92 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.1 • Indawo ezime kuyo izinto ezimbini okanye ngaphezulu ngokunxulumene nomfundi. Usuku olu-1. Indawo- Ngaphezulu / ngaphakathi / ngaphantsi bume,ukufumana Ukufunda usebenzisa intshukumo yomzimba: indawo kunye nembonakalo Yalela abafundi balandele imiyalelo: -- Beka ibhloko ebomvu ngaphezu kwentloko yomhlobo wakho. -- Beka ibhloko etyheli ngaphantsi / ngasezantsi kwetafile. -- Thwala ibhloko entloko uze ukhwele etafileni. Iibhloko zokwakha / iibhloko zeyunifiksi (unifix blocks). -- Rhubuluza phantsi kwetafile uvale amehlo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Yalela abafundi: Iimilo zeLogi (logi shapes). -- Pakisha oonxantathu ngaphezu kwabanye. MATHEMATIKA IBANGA LABAQALAYO (R) -- Pakisha izikwere ezibhlowu ngaphezu kwezinye. Imifanekiso eyahlukeneyo. -- Beka isangqa esibomvu ngaphantsi kwesikwere esityheli. -- Beka isangqa esityheli nonxantathu obomvu ngaphantsi / ngasezantsi kwesikwere esibhlowu. Ukusebenzisa izinto ezinokwakheka kuka 2-D okanye imifanekiso. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Utitshala wenza amakhadi anemifanekiso kunye namakhadi aneemilo. Amakhadi eemilo. -- Abafundi mababeke iimilo ngaphezu / ngaphantsi / ngasezantsi komfanekiso ngokuyalelwa ngutitshala. Umzekelo, beka isikwere esibhlowu ngaphezu kwebhaskithi yeziqhamo.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 7 CAPS Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.1 • Bethelela kulwazi ngamacala alinganayo omzimba wakhe. Usuku olu-1. Ulingano-macala Ukufunda usebenzisa intshukumo yomzimba: Yalela abafundi: -- Baxela amalungu emizimba yabo. -- Mabacule nayiphi ingoma malunga nomzimba. Ingoma: Intloko namagxa, sifuba nesinqe, madolo nenzwane.” Utitshala ubonisa abafundi ulingano macala (isimetri) ngokuxhoma intambo phambi komfundi. -- Abafundi kufanele bazi ukuba imizimba yabo yahlulwe yangamacala amabini. Intambo yokubonisa. Imizimba yabafundi. Utitshala ucacisa ngendlela umzimba owahlulwe ngayo ube ngamacala amabini kuze kubekho umgca ophakathi. -- Yonke into anayo umntu inezinto ezimbini kumacala amabini omzimba, umzekelo, amehlo, iindlebe, iingalo, imilenze, njalo njalo. -- Yonke into anayo umntu inento enye ebekwe kumgca ophakathi, umzekelo, impumlo, umlomo, umbhono. Ukuqhuba nokufundisa ngolingano-macala (ngesimetri), yalela abafundi: -- Matsha, uphakamise amadolo phezulu. -- Matsha ‘okwejoni elomeleleyo lenkonkxa.’ -- Nqumleza iingalo, nqumleza imilenze elixa umatshayo. Imifanekiso engagqitywanga. -- Nxulumanisa oku nobuGcisa baseqongeni beZakhono zoBomi. 93 Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Zoba imifanekiso engagqibelelanga ephepheni uze uyalele abafundi bagqibezele umfanekiso. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 7 94 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.1 • Iindawo ezimi kuyo izinto ezimbini okanye ngaphezulu ngokunxulumene nomfundi. Usuku olu-1. Indawo- -- Phezulu nangasezantsi. bume,ukufumana Ukufunda usebenzisa intshukumo yomzimba: Cula ingoma. indawo nembonakalo Yalela abafundi: -- Babonise ngamagama “phezulu” “phantsi” ngokushukumisa imizimba yabo iye phantsi Sebenzisa izitephsi ezikhoyo esikolweni. naphantsi ngokomyalelo katitshala. Ijungle gym (isixhobo sokugwencela). -- Bakhwele kwizitephsi ezibini eli xa ubala inani lazo. Ileli yentambo yokukhwela. -- Mabehle kwizitephsi ezibini bebala. -- Bakhwela “phezulu” “phantsi” kwisixhobo sokukhwela esiphandle. Imifanekiso ebonisa uphezulu nophantsi, -- Bakhwela “phezulu” “phantsi” kwintambo yokukhwela ileli xa isikolo sinayo. umzekelo izitephsi. -- Bajonga phezulu naphantsi. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. MATHEMATIKA IBANGA LABAQALAYO (R) -- Utitshala unika abafundi iindidi ezahlukeneyo zemifanekiso malunga nophezulu nophantsi njengoko kubonisiwe, umzekelo, umntu ukhwela phezulu entabeni, ibhaloni yomoya iya phezulu emoyeni ize ihle iye ezantsi, umntu uhla kwizitephsi, njalo njalo. Yalela abafundi: o Balathe uphezulu naphantsi kwimifanekiso. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 8 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.4 • Ukunqumla umgca ophakathi oqukwe ekubaleni. Usuku olu-1. Ulingano - macala Ukufunda usebenzisa intshukumo yomzimba: Yalela abafundi: Abafundi. -- Bayadanisa baze baxhume ngokwesingqisho elixa bebala. Iingoma nezicengcelezo zamanani. -- Bamise bajongane baze bamane benqamleza beqhwaba (ngasekhohlo kubafundi abasekhohlo) becula ingoma engamanani / isingqisho. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Yalela abafundi: -- Baphosela ugxa wabo ibhola xa bebala. -- Bahamba kwintambo egosogoso becula ingoma, umzekelo, “Indlovu enye encinane encikeleleyo.” -- Bakhabelana ibhola. Ibhola, intambo. Umsebenzi ongasentla unokunxulunyaniswa neZakhono zoBomi. 2.1 • Wenza iipateni zakhe. Usuku olu-1. Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba: Iimilo zeplastikhi eziBomvu neziBhlowu. Yalela abafundi bayile ipateni besebenzisa: -- Imizimba yabo, umzekelo, intombazana enye enelokhwe, amakhwenkwe amabini aneebhulukhwe. Usebenzisa iziciko zeebhotile nepeyinti Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: ebomvu nebhlowu. -- Usebenzisa iimilo ezibomvu nezibhlowu, umzekelo, izikwere ezibhlowu ezi-2, oonxantathu ababomvu aba-2, izikwere ezibhlowu ezi-2….. -- Sebenzisa ipateni kwimisebenzi yobugcisa ngokusebenzisa ipeyinti ebomvu nebhlowu eneziciko zebhotile. bomvu luhlaza bomvu luhlaza bomvu luhlaza Sebenzisa iimilo ezinokwakheka kuka 2-D usebenzisa imibala ephambili. Yalela abafundi: -- Basebenzise oobhontsi ukushicilela umbala ngepeyinti, umzekelo, luhlaza, orenji, U-A4 Paper. 95 luhlaza…………kunye nencam yamaphepha. (Umsebenzi unokwenziwa ngobuGcisa Ipeyinti eluhlaza ne-orenji okanye nayiphi obubonwayo). eminye imibala onayo. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 8 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 96 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.2 Qaphela, khetha uze uxele izinto ezinokwakheka kuka 3-D. Usuku olu-1. Izinto • Bethelela kwizinto eziqengqelekayo. ezinokwakheka Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: kuka 3-D Yalela abafundi: -- Badlala ngeebhotile zeplastikhi, iinkonkxa, iibhola, i-orenji, njalo njalo baze Iibhotile zeplastikhi. baqwalasele okwenzekayo xa beziqengqa. Utitshala uyabuza: -- Ziziphi iibhloko kwikona yeebhloko ezinokuqengqeleka? Iibhloko. Iibhloko zeLego. -- Iibhloko azikwazi kuqengqeleka kuba zinamacala amathandathu angqalileyo kuphela. Iinkonkxa, iikomityi zeplastikhi, -- Qengqa izinto ezahlukeneyo uze ubone ukuba yeyiphi enokuqengqeleka ikwa yeyiphi iingqukumba zamaphepha angasese, engakwaziyo. amakhandlela, i-orenji, iibhola, njalo njalo. -- Abafundi kufanele bazi ukuba izinto ezingqukuva zinokuqengqeleka. 3.1 • Phuhlisa ulwazi ngezalathiso ngokufundisa amagama okwalatha “ngaphambili / Usuku olu-1. MATHEMATIKA IBANGA LABAQALAYO (R) ngasemva”, “umphambili / umva”. Indawo-bume, ukufumana indawo Ukufunda usebenzisa intshukumo yomzimba: nembonakalo Yalela abafundi: Balandela izalathiso zikatitshala (uzimele kunye / okanye njengelungu leqela) nokuzibeka kwabo eklasini umzekelo, INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Abafundi. -- Mabeme “ngaphambili” eklasini. (thathela ingqalelo ngomphambili waseklasini apho ucango lukhoyo). -- Mabeme “ngasemva” eklasini. -- Mabaye phambili nasemva. -- Mabarhubuluze baye phambili nasemva. -- Mabaye phambili nasemva.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 8 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.1 Utitshala uzoba ipateni emgangathweni ngetshokhwe okanye emgangathweni, umzekelo, Usuku olu-1. Indawo-bume, Izotywe phantsi. ukufumana indawo nembonakalo okanye Yalela abafundi: -- Bayahamba / okanye barhubuluze emigceni yepateni. -- Beka isicwili sephepha elibomvu kwiikona zimele irobhothi. Xa abafundi besezikoneni zabo kufuneka baguqule umzimba wonke ukubaqhelanisa nezalathiso. Iphepha elibomvu. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Yalela abafundi: -- Mabenze indledlana ngeebhloko zokwakha. -- Mabatyhale ithoyi yemoto iye phambili nasemva ibe “kwindlela” eyakhiwe ngeebhloko. Iibhloko zokwakha. -- Mabatyhale ithoyi yemoto ngokuyisa kwelinye icala nokuyisa kwelinye icala “lendlela” eyakhiwe ngokweebhloko. 97 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 8 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 98 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 5.1 • Fundisa ngokuSetyenziswa kolwazi (besebenzisa imizimba yabo) ngokuqokelela Usuku olu-1. izinto eklasini okanye kummandla wokusingqongileyo ngokweempawu Qokelela ,uhlele ezixeliweyo, umzekelo: izinto Ukufunda usebenzisa intshukumo yomzimba: Yahlulahlula abafundi babe ngamaqela. Abafundi abeme kwimiqolo emibini. -- Kwiqela ngalinye yalela onke amakhwenkwe eme emgceni uze uyalele onke 5.2 amantombazana eme emgceni kufutshane nasemakhwenkweni. Bonisa ingqokelela -- Yalela abafundi babale inani lamakhwenkwe nenani lamantombazana kwiqela ngalinye. yezinto ezihleliweyo. -- Ngoku ungakwazi ukugqibezela “igrafu yomzimba” yamakhwenkwe namantombazana ngokweqela ngalinye. Into ephathekayo usebenzisa izinto ezinokwakheka kuka 3-D: -- Abafundi banokusebenzisa ulwazi olungasentla ukuphuhlisa igrafu yezinto 5.3 ezinokwakheka kuka 3-D ngokusebenzisa iibhloko / iimilo, njalo njalo olumele umfundi Iintombi Amakhwenkwe MATHEMATIKA IBANGA LABAQALAYO (R) Ukuxoxa ngamnye. □ nokunika ingxelo Ukufunda nokubonisa igrafu. □ □ ngengqokelela ehleliweyo yezinto Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. □ □ 2 3 -- Abafundi benza igrafu ngokusebenzisa udongwe ukwenza ibholana encinane emele indlela abatolika ngayo umsebenzi wangaphambili. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Nika abafundi iphepha elinomfanekiso wentombazana nenkwenkwe ngaphezu Udongwe. kwephepha ngalinye lomfundi. U-A4 Paper. -- Yalela abafundi baqengqe iibhola ezimele inani lamantombazana namakhwenkwe kwiqela labo. -- Abafundi babeka inani leebhola ngaphantsi komfanekiso ochongiweyo.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki ye- 9 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa CAPS elithelekelelwayo 3.2 • Ukunakana nokunokuphonononga izinto ezitshebelezayo neziqengqelekayo. Usuku olu-1. Izinto Utitshala ubamba ibhola aze ayibhampise emgangathweni. Uyayiqengqa emgangathweni. ezinokwakheka Emva koko utitshala uthabatha ibhokisi enze kwangolo hlobo lwangaphambili. kuka 3-D Utitshala uyabuza: Ibhola -- Yeyiphi into enokuqengqeleka? -- Kutheni ibhokisi ingakwazi ukuqengqeleka? -- Yeyiphi into enokutshebeleza? Utitshala ubonisa abafundi ukuba ibhokisi inamacala amane (iikona) kwaye ayikwazi kuqengqeleka, kodwa ibhola ayinazo iikona kwaye iyakwazi ukuqengqeleka. -- Bakhuthaze abafundi bakhangele izinto eklasini ezinokuqengqeleka nokutshebeleza. Ibhokisi -- Qonda ukuba abafundi bayakwazi ukukhangela izinto ezinokuqengqeleka nezinokutshebeleza. 99 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki ye- 9 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 100 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.3 Ukunakana, ukuchonga nokuxela iimilo ezinokwakheka kuka 2-D eklasini Usuku olu-1. nakwimifanekiso. Izinto ezinokwakheka -- Isangqa kuka 2-D Ukufunda usebenzisa intshukumo yomzimba: Yalela abafundi: Abafundi. -- Benza isangqa besebenzisa iminwe. -- Benza isangqa besebenzisa izandla zozibini. Umtya. -- Bahlala ekhaphethini, benze isangqa eli xa bebambene ngezandla. -- Bahamba kwisangqa esikhulu, esenziwe ngomsonto ekhaphethini. -- Badlala umdlalo apho abafundi bahlala kwisangqa baze bacule ingoma. o Umfundi omnye uma ngaphandle kwesangqa aze abaleke esijikeleza ephethe ibhola ngezandla zakhe. o Umfundi ukhetha ukubeka ibhola ngasemva kwaye nabaphi abafundi abahleli kwisangqa. MATHEMATIKA IBANGA LABAQALAYO (R) o Umfundi okhethiweyo kufuneka aphakamise ibhola aze ayiphose komnye umfundi, eli xa abalekayo ejikeleza isangqa kwakhona andule ahlale kwisikhewu esikhoyo. o Xa ngaba ibhola ibethe umfundi obalekayo, kufuneka ahambe aye kuhlala phakathi esangqeni uze umdlalo uqhubeke. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Ibhola ekhatywayo, ibhola yentenetya, INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Yalela abafundi: ibhola yegalufa, i-apile, i-orenji, iihupu, njalo njalo. -- Bakhangela izinto ezingqukuva eklasini. -- Bakhangela iimilo ezimele isangqa. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. I-orenji, i-apile, itafile, ibhola, imayibhile, -- Utitshala uxela izinto baze abafundi bakhethe ukuba ziziphi na izinto ezingqukuva, incwadi, ibhokisi. umzekelo, i-orenji, i-apile, itafile, ibhola, imayibhile, incwadi, ibhokisi, njalo njalo.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki ye- 9 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa CAPS elithelekelelwayo 3.1 Indawo yento enye okanye ezimbini ngokunxulumene Ukufundisa ukufutshane / Usuku olu-1. ngaphakathi – ngokudibene nombala. Indawo –bume, ukufumana indawo • Ingqiqo – ecaleni kwe/phakathi: dibanisa nombala nembonakalo. Utitshala ubiza abafundi abathathu. Ucacisa ngo-kufutshane no-ngaphakathi ngokubeka abafundi ngokwahlukeneyo ngokuthi: -- UCraig ume ecaleni kukaSoso. -- UMelinda umi phakathi kukaCraig noSoso. Umsebenzi unokwenziwa kwakhona nabanye abafundi. Utitshala unika abafundi iibhloko zokwakha ezimibala yahlukeneyo aze abanike imiyalelo: -- Babeka ibhloko ebomvu kufutshane nebhloko etyheli. Iibhloko ezimibala-bala. -- Babeka ibhloko ebhlowu phakathi kwebomvu nebhloko etyheli. Into ephathekayo usebenzisa izinto ezi-3: Ukusebenzisa iibhinbhegi kwimibala eyahlukeneyo (ebomvu, ebhlowu, etyheli, eluhlaza), nika abafundi umyalelo: -- Mababeke ibhinbhegi ebhlowu kufutshane nebhinbhegi etyheli. -- Mababeke ibhinbhegi ebomvu phakathi kwebhinbhegi etyheli nebhlowu. Iibhinbhegi ezimibala-bala. Lo msebenzi unokudityaniswa neZakhono zoBomi. 101 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki ye- 9 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 102 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.2 • Cwangcisa nokuba yeyiphi ingqokelela yezinto ezimbini ozinikiweyo ukusukela Usuku olu-1. kweyona incinane ukuya kweyona inkulu. Izinto ezinokwakheka Ukufunda usebenzisa intshukumo yomzimba kuka 3-D Nika abafundi udongwe uze ubayalele benze iibhola ngodongwe. Udongwe lokudlala. -- Kumaqela abo babeka iibhola zabo zodongwe ukusukela kweyona incinane ukuya kweyona inkulu kakhulu. Into ephathekayo usebenzisa izinto ezinokwakheka kuka 3-D: -- Ilungu leqela ngalinye kufuneka lifumane into eklasini. Naziphi izinto eziseklasini. -- Bayalele abafundi bacwangcise izinto ngokobuncinane ukuya kwenkulu ngokwamaqela abo ohlukeneyo. Utitshala unika iqela ngalinye iidayrektri zeefowuni ezindala. Yalela abafundi: -- Mabakrazule iphepha kwidayrektri baze balishwabanise iphepha libe yibhola kumaqela abo. Idayrektri yefowni. MATHEMATIKA IBANGA LABAQALAYO (R) -- Abafundi mabathelekise ukuba yeyiphi na ibhola enkulu kakhulu kwaye iyeyiphi encinane kakhulu. Iphepha elingu-A4 elinemifanekiso. Izinto ezimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Nika abafundi iphepha elinemifanekiso yezinto ezinkulu nezincinane. -- Abafundi banokufakela imibala kwizinto ezinkulu barhangqele izinto ezincinane. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki ye- 9 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa CAPS elithelekelelwayo 4.2 • Thelekisa uze ucwangcise izinto ngokuziphathekayo usebenzisa isigama Usuku olu-1. esifanelekileyo ukuchaza ubude. Ubude -- Ende / emfutshane kakhulu -- Eyona inde / eyona imfutshane Ukufunda usebenzisa intshukumo yomzimba: -- Utitshala ubiza abafundi aba-4 aze abuze iklasi ukuba imncedise ukucwangcisa abafundi ukusukela koyena mde ukuya koyena mfutshane. -- Bayalele abafundi bazicwangcise ngokwabo kumaqela abo ukusukela koyena mde ukuya koyena mfundi mfutshane. -- Umfundi omnye woyame eludongeni ngelixa elinye ilungu leqela lithatha umlinganiselo wobude esebenzisa izandla zabo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iirula, iikhrayoni, iipensile, irabha, njalo njalo. Utitshala ubeka iindidi zezinto kwitheyibhile nganye yeqela njengeerula, iipensile, iikhrayoni, iirabha, njalo njalo. -- Hlela zonke izinto ezinde kunye nazo zonke ezimfutshane kunye. Itshati yobude -- Abafundi mabahlele izinto ukusuka kweyona inde ukuya kweyona imfutshane USipho unobude Itshati yobude. obuzizandla ezi-6. -- Utitshala unetshati yobude exhonywe eludongweni ukuze akwazi ukubonisa ubude bomntwana ngamnye. U-Abby unobude -- Sebenzisa amakhadi aneesimboli zabafundi ukubonisa ubude bomfundi ngamnye obuzizandla ezi-5. kwitshati yobude. -- Utitshala kunye nabafundi bafikelela kwisigqibo sokuba uSipho uzizandla ezintandathu ubude aze uAbby abe zizandla ezintlanu kuphela kuba mfutshane. 103 MATHEMATIKA IBANGA LABAQALAYO (R)

IVEKI YE-10 Sebenzisa iveki 10 ukuqwalasela ubuthathaka kunye / okanye nezithintelo ekufundeni. Inkalo yomxholo Isihloko Imilinganiselo yokuHlola 104 Amanani, ii- 1.1 Ukuqikelela nokubala ngokucengceleza ukuya kutsho kwisi-5 (Iingoma nezingqisho zamanani eziqukwe opareyshini ukuphuhlisa amanani). Bala izinto noLwalamano. Nakana amanani kwimeko oqhelekileyo, umzekelo, ubudala, irejista. Qonda amanani ahambelanayo (Itshati ngexesha lokutya). Khetha imifanekiso yamanani kunye namakhadi anamachokoza abandakanya inani unye Yazi isimboli yenani u-1. Nakana igama lenani unye. 1.6 Sebenzisa izixhobo eziphathekayo. Ubuchule/iindlela zokusombulula iingxaki Cacisa indlela ocinga ngayo ngamagama kunye nemizobo okanye izinto eziphathekayo. Iipateni nee- 2.1 Chonga iipateni kwizinto ezisingqongileyo. fankshini ne-Aljibra Kopa, yandisa, yenza iipateni zakho. Iipateni zejiyometri Isithuba nemilo 3.1.Indawo-bume,ukufumana indawo Yazi: ngaphambili kwe/nasemva kwe (Ijiyometri). nembonakalo Yazi: phezulu kwe,ngaphantsi kwe Yazi: ngaphakathi,ngaphandle Yazi:phezulu,phantsi 3.2 Izinto ezinokwakheka kuka 3-D ne 3.3 iimilo Qonda iingqiqo: ngaphambili,ngasemva MATHEMATIKA IBANGA LABAQALAYO (R) ezinokwakheka kuka 2-D Nakana, khetha,uxele iibhola. Nakana, khetha,uxele iibhola iibhokisi. Nakana, khetha,uxele isimboli yakhe, isimboli yogxa wakhe negama leklasi. Yakha iphazili ezi-6. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukubonisa isakhono sokukwazi ukwahlula phakathi kwezinto “ezisemva” “neziphambili”. Chonga unakane isangqa. Chonga unakane unxantathu. Chonga unakane isikwere. Thelekisa ukuba yeyiphi ingqokelela enikiweyo yezinto ezimbini ezinkudlwana, ezincinanana, ezinkulu kakhulu nezincinane kakhulu. Hlela izinto: Ubungakanani – inkulu nencinci. Umbala – imibala engundoqo (obomvu, otyheli, obhlowu). Imilo – isangqa, unxantathu nesikwere. Izinto eziqengqelekayo. Izinto ezitshebelezayo.

Inkalo yomxholo Isihloko Imilinganiselo yokuHlola Isithuba nemilo 3.4 Qaphela umgca wesimetri kuye. (Ijiyometri). CAPS Ulingano-macala Umlinganiselo. 4.1 Ukusebenzisa amagama afana nala: imini, ubusuku, ukukhanya nobumnyama, kusasa, emva kwemini, ngokuhlwa ukuchaza ixesha losuku. Ixesha Cwangcisa iziganeko eziphindelelayo ebomini bakhe bemihla ngemihla (inkqubo yemihla ngemihla). Bonisa nokuqonda iintsuku zeveki, amaxesha onyaka nemo-zulu. Yazi usuku lwakho lokuzalwa. 4.2 Yahlula phakathi kobude, ubudana, ubude kakhulu, futshane, futshanana, futshane kakhulu (itshati yobude). Ubude Ukusebenza 5.1. Akwazi ukuqokelela, ukuhlela, ukuzoba, ukufunda nokuhlalutya izinto ngokophawu olunye. ngolwazi Qokelela uhlele izinto oluqokelelweyo. 5.2 . Bonisa ingqokelela yezinto ezihleliweyo 5.3. Xoxa uze unike ingxelo ngengqokelela yezinto ezihleliweyo 105 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 106 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.1 • Fundisa intsingiselo yenani elingu-2. Imifanekiso emibini yeentaka yengoma Usuku olu-1. yokubala - Bala izinto Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kutsho kwi -2. “Iintaka ezimbini………” Ukubala ukuya phambili nasemva ukuya kutsho kwi -2. Ukubala ngokucengceleza ku -1 ukuya kwi- 7. Bethelela “ubuninzi” “nombalwa”. Qhwaba izandla kaninzi…..YIMA. Qhwaba izandla amatyeli amafutshane. Utitshala uqhwaba amaxesha ama- 2. Ukufunda usebenzisa intshukumo yomzimba: Yalela abafundi: -- Biza abafundi aba- 2 ngaphambili. Babale. -- Bala izitulo ezi- 2, iitafile, njalo njalo. -- Ukwalatha izibini zamalungu omzimba njengamehlo, iindlebe, izandla, iinyawo, amadolo, amagxa, njalo njalo. MATHEMATIKA IBANGA LABAQALAYO (R) -- Sebenzisa umzimba, umzekelo, baqhwaba izandla kabini, bashukumisa iintloko kabini, Imizimba yabafundi. ukunyathela emgangathweni kabini okanye batsibe kabini, njalo njalo. -- Phakamisa iminwe emi- 2, izandla ezi- 2, iinyawo ezi-2. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.1 Sebenzisa izinto ezinokwakheka kuka 3-D: Bala izinto Yalela abafundi: -- Ukwalatha isibini sezinto ezifanayo eklasini, umzekelo, izihlangu ezibini, iikhrayoni, njalo njalo. -- Ukuphuhlisa ulwazi ngolondolozo lwamanani ngokuyalela abafundi bapakishe izinto zokubala ezimbini okanye naziphi izinto ngeendlela ezahlukeneyo, umzekelo, Izinto zokubala ezi- 2 okanye izinto ezi- 2 okanye okanye zomfundi ngamnye. Xa ubala, inani lezinto alichatshazelwa bubungakanani, okanye indawo elimi kuyo, okanye nokuba zezodidi olufanayo. Umzekelo: -- Ukucwangcisa amaqhosha ama- 2, iipensile ezi- 2, iihupu ezi- 2, abafundi aba- 2, njalo njalo. -- Zibale ngendlela eyahlukileyo, umzekelo, zibale uzisakaze, ziqumbanise, zibe semgceni. 107 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 108 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.3 • Ukwazi ngesimboli yenani nokunakana igama lenani elibandakanya inani elingu- 2. Usuku olu-1. Iisimboli zamanani Sebenzisa Iimilo enokwakheka kuka 2-D. Beka ngokwamanani oonotsheluza namagama bamakhadi ngezinto ezimbini. Yalela abafundi: amanani -- Ukutshatisa amakhadi emifanekiso anemifanekiso emi-2 kuwo namakhadi anamachokoza amabini kuwo. Izinto eklasini nakummandla osingqongileyo. -- Bonisa oonotsheluza nomfanekiso wenani lezinto ezikhethiweyo , umzekelo, ipere yezihlangu, iikhrayoni ezimbini, njalo njalo. -- Yalela abafundi bakhangele inani elifanayo lezinto eklasini. -- Ukuchonga oonotsheluza abanamanani emifanekiso awohlukileyo. Ifoto -- Ukuchonga oonotsheluza abanesimboli yenani elingu- 2. yezinto -- Ukunakana oonotsheluza abanegama lenani e-2 -- Ukunxibelelanisa isimboli yeanani elingu-2 kunye nenani lezinto nenani lamachokoza. -- Ukunxibelelanisa igama lenani kunye nekhadi lesimboli yenani elingu- 2 inani lezinto kunye nenani lamachokoza. MATHEMATIKA IBANGA LABAQALAYO (R) -- Dibanisa unotsheluza onenani elingu -1 uze uyalele abafundi bachonge amanani u- 1 Unotsheluza onemifanekiso emibini, no- 2. amachokoza, isimboli yenani negama lenani. -- Yenza iiphazili zamanani uze uyalele abafundi bazitshatise, umzekelo, INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ifoto yezinto ezi- 2 2 isibini 2 isibini

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.2 • Chaza, hlela uze uthelekise izinto ezinokwakheka kuka 3-D no2-D ngokokufana Usuku olu-1. nokwahluka kwazo Izinto ezinokwakheka Izinto ezifanayo nezahlukeneyo. kuka 3-D kunye Ukufunda usebenzisa intshukumo yomzimba: -- Khetha amantombazana amabini usebenzisa isingqisho sokubala. -- Abanye abafundi balatha indlela afana ngayo amantombazana amabini? -- Khetha inkwenkwe nentombazana usebenzisa isingqisho sokubala. -- Abanye abafundi balatha indlela intombazana nenkwenkwe eyahluke ngayo. -- Bengababini omnye umfundi “uma” ngendlela ethile aze omnye akope le ndlela “eme” ngayo, umzekelo, -- omnye umfundi uma ubeka izandla entloko yakhe esinye emlenzeni. Omnye ukopa “indawo yokuma.” -- Ukuhlela abafundi ngokwesini, abo banezihlangu, nabo baneembadada, kunye nabo bahamba ngeenyawo. -- Biza abafundi abalandelayo beze ngaphambili. Amantombazana namakhwenkwe aneebhulukhwe, intombazana enelokhwe. o Bonke abantwana abanxibe izihlangu, omnye akanxiBanga zihlangu. -- Buza umbuzo othi: “Ngowuphi umfundi ongangqamaniyo? “Ngowuphi umfundi owahlukileyo?” 109 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 110 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 3.2 • Chaza ,hlela uze uthelekise izinto ezinokwakheka kuka 3-D kunye neemilo Yenza imidlalo yamakhadi okutshatisa Usuku olu-1. ezinokwakheka kuka 2-D ngokwendlela ezifana ngayo nangendlela ezohluke ngayo njengoko kuxeliwe kumzekelo Izinto ongasezantsi. ezinokwakheka -- Abafundi ababini babhampisa iibhola: ibhola enkulu nebhola encinane. kuka 3-D kunye -- Abanye abafundi balatha iindlela iibhola ezifana ngayo nezahluke ngayo. -- Omnye umfundi uqengqa i-orenji, omnye uqengqa ibhola. -- Abanye abafundi balatha iindlela ibhola ne-orenji ezifana ngayo nezahluke ngayo. -- Abafundi baqaphela izihlangu zamakhwenkwe neembadada zamantombazana. -- Abanye abafundi balatha iindlela izihlangu ezifana ngayo nezahluke ngayo. -- Abafundi bakhangela izinto ezifanayo eklasini. 3.3 Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. Nezinto -- Ukunika imidlalo yamakhadi yokutshatisa ukukhuthaza okufanayo nokwahlukileyo, ezinokwakheka umzekelo, kuka 2-D Ukutshatiisa imidlalo ngamakhadi. MATHEMATIKA IBANGA LABAQALAYO (R) -- Inkqubela-phambili engamakhadi anzima ngaphezulu ekuhambeni konyaka. Abafundi akunyanzelekanga ukuba bafunde oonobumba, umzekelo, INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.4 • Ukucwangcisa nokuthelekisa iingqokela yezinto esebenzisa “iyalingana ne” okanye Usuku olu-1. “iyafana”. Chaza,thelekisa uze ucwangcise Ukufunda usebenzisa intshukumo yomzimba: amanani Yalela abafundi: -- Baphuhlisa amagama:efanayo neyahlukileyo. -- Ukuthelekisa iminwe yabo neenzwane zabo. Nangona inenani elifanayo ikhangeleka yohlukile. -- Ukuthelekisa iminwe, iinzwane namehlo. Zibonakala zohlukile kodw Sinenani elifanayo leminwe neenzwane, umzekelo, i- 10 kodwa sinamehlo amabini kuphela. -- Ukuthelekisa iindlebe, iingalo, imilenze neenyawo. Zibonakala zohlukile kodwa zinenani elifanayo, oko kukuthi sinezibini zezi zinto. -- Utitshala uzoba izangqa ezibini phantsi okanye wenza izangqa ezibini ngomsonto. Yalela abafundi bazohlule ukwenzela ukuba inani labafundi lilingane kwisangqa ngasinye. Bala inani labafundi. Khomba amaqela alinganayo kwafanayo. 111 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 112 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.4 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Usuku olu-1. Chaza,thelekisa -- Baphuhlisa amagama okufanayo nokwahlukileyo. uze ucwangcise -- Beka iseti yeesimboli zomfundi phakathi kwikhaphethi. amanani -- Nika umfundi ngamnye ikhadi lesimboli. Abafundi bazama ukutshatisa iisimboli zabo nefanayo ekhaphethini. -- Beka iqela lezinto etafileni uze uzohlule zibe ngamaqela alinganayo (enye yeyakho, enye yeyam). Imizekelo: 1. Beka izinto ezimbini zodidi olufanayo, umzekelo, iikhrayoni, emqolweni wetafile. Buza umfundi omnye ukuba atshatise ikhrayoni nganye katitshala neyakhe. (Umfundi kufuneka athathe iikhrayoni ezimbini zokutshatisa inani leekhrayoni zikatitshala. “Ngoku umntu ngamnye unenani elinye / elifanayo leekhrayoni.” 2. Phinda lo msebenzi mnye njengasentla ku- 4 kunye nezinto ezi- 6 zabafundi zokuqonda ulwazi ngamagama athi “okufanayo / okulinganayo.” 3. Utitshala ubeka iibhloko ezi- 2 kumqolo wetafile. Unika ngamnye abafundi ababini MATHEMATIKA IBANGA LABAQALAYO (R) ibhloko. Yalela utitshala ukuba atshatise ibhloko nganye kwiibhloko zakhe. (Abafundi ngabanye kufuneka beze nenye ibhloko yokutshatisa neebhloko ezimbini zikatitshala). “Ngoku umntu ngamnye uneebhloko ezi- 2. Sinenani elifanayo neebhloko.” Iibloko zikatitshala INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Yalela abafundi bathelekise umfanekiso noonotsheluza abanamachaphaza. Mabachonge amakhadi afanayo. Iibhloko. -- Banike umdlalo wokumetshisa amakhadi ngexesha lokudlala ngaphakathi apho abafundi banokwahlula phakathi kokufanayo nokwahlukileyo.

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.4 • Ukucwangcisa nokuthelekisa iingqokelela zezinto usebenzisa “ngaphezulu kwe ”. Usuku olu-1. Chaza,thelekisa, Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kutsho ku- 2. ucwangcise Bethelela “u-ninzi” “no -mbalwa”. amanani Qhwaba izandla zakho kanininzi........YIMA Qhwaba izandla amatyeli ambalwa. Utitshala uqhwaba amaxesha ukuya kuma kuma- 2. Ukufunda usebenzisa intshukumo yomzimba: Umfundi uyazixela iingqokelela ezinikiweyo ezimbini zezinto: “ngaphezulu” Yalela abafundi: -- Bala amehlo abo neminwe yabo. Buza umbuzo: “Zeziphi ezininzi abanazo?” -- Bonisa iminwe emibini kwesinye isandla nomnwe omnye kwesinye isandla. “Sesiphi isandla esinezingaphezulu?” -- Khetha abafundi abathathu usebenzisa isingqisho sokubala xa usenza oko. Zahlula ngokwamaqela esi- 2 nesi- 1. -- Bala inani labafundi kwiqela ngalinye. Thelekisa amaqela amabini uze ubuze imibuzo enje ngale: “Leliphi iqela elinabafundi abaninzi?”. “Leliphi iqela elinezingaphezu kwesinye?” 113 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswa ukuba lisetyenziswe: Iveki ye- 11 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama-± 30 ngosuku (imisebenzi yeMathematika emi-± 5 ngeveki) 114 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.4 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Chaza,thelekisa, -- Beka izibini ezi- 2 zezikere, izinto zokubala ezi- 3 neekhrayoni ezi- 4 kwitheyibhile. Bala Naziphi izinto eziseklasini. ucwangcise izinto zeqela ngalinye. amanani -- Buza umbuzo othi: “Ngawaphi amaqela anezinto ezininzi. Leliphi iqela elinezinto ezininzi”. “Leliphi iqela elinezikere ezininzi? “Leliphi iqela elinezingaphezu kwezintathu?” -- Beka iindidi ezahlukeneyo zezinto eziphathekayo (amakhohlombe, izitya, iziciko, njalo- njalo). Zihlele ngokwamaqela (zonke iziciko kunye), ubala inani lazo kwiqela ngalinye uze ubonise ukuba leliphi na iqela elingaphezulu, elingaphantsi, elilinganayo. Banike ithuba lokusebenza ngezinto zokubala zabo. Qala ngamanani amancinane. -- Unxulumaniso: Izikhongozeli mazinikwe xa kudlalwa ngamanzi nesanti ukunika amathuba okulingisa ngeengqiqo ezinjengo-ngaphezulu, ngaphantsi no-lingana. MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso. -- Yalela abafundi bathelekise umfanekiso noonotsheluza abanamachaphaza. Khetha amakhadi angaphezu kwenani elinikiweyo ngutitshala, umzekelo, Umfanekiso noonotsheluza -- Utitshala uthi: Khangela ikhadi elinemifanekiso yamachaphaza angaphezu kwesi- 2? abanamachaphaza. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Ukutshatisa amakhadi anenani elifanayo lezinto izixhobo zokubala. (ipakethi yesixhobo Iikhawunta / izixhobo zokubala. sokubala / ikhawunta yechokoza ngalinye okanye umfanekiso ngamnye).

Ixesha lokufundisa elicetyiswayo: Iveki ye -12 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama ±30 ngosuku (±5 ezemisebenzi ye mathematika ngeveki) Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Nakana uze uchonge isimboli yenani kunye negama lenani elibandakanya u- 2 Usuku olu-1. Bala izinto Ngomlomo: Bala yonke imihla izinto ukuya kwi- 2 Bala ubhekisa phambili nangasemva uye kwi- 2 Ukubala ngokungenantsingiselo u- 1 ukuya kwi- 7 Iingoma zamanani neezicengcelezo Bethelela ingqiqo ka “ninzi no mbalwa” Qhwaba kaninzi …… YIMA Qhwaba izandla zakho amaxesha ambalwa.Utitshala uqhwaba ukuya kwi- 2 Ukufunda usebenzisa intshukumo yomzimba Vumela abafundi ba: -- Bhampise ibhola kanye ,ngamanye amagama ixesha eli-1 Ibhola -- Bhampise ibhola kabini,ngamanye amagama amaxesha ama- 2 emhlabeni baze Intlama yokudlala abafundi bahambe phezu kwenani elingu- 2 -- Zobe isimbolli engu- 2 esantini,emoyeni ,ekhaphethini njl-njl -- Benze inani elungu- 2 -- Khangele abahlobo bakho aba- 2 abanxibe izihlangu Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi mabenze oku: Izinto zokubala -- Thatha izinto zokubala -- Thatha izinto zokubala ezimbini 115 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki ye -12 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama ±30 ngosuku (±5 ezemisebenzi ye mathematika ngeveki) 116 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Oonotsheluza abanemifanekiso emibini, Usuku olu-1. amachaphaza, iisimboli zamanani Bala izinto Abafundi mabenze oku: negama lenani. -- Chonga oonotsheluza abanemifanekiso uze ubadibanise nenani lezinto . -- Chonga oonotsheluza abaphawulwe ngamachokoza amabini baze bawadibanise nenani eIilingana nezinto ezo. Umfanekiso -- Chonga isimboli yenani nonotsheluza onegama lenani uze uyidibanise nenani yezinto elilingana nezinto ezo. ezezi-2 2 bini -- Chonga isimboli yenani elingu- 2 emfanekisweni oyinikwe ngutitshala. -- Khangela apha egumbini utsho ukuba ulibona phi inani elingu-2. Izinto zokubala -- Hlula iklasi ibe ngamaqela amabini.Nika ithuba lokudlala ngeedomino ngokwamaqela. Imifanekiso enesimboli yenani eli - 2 MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswayo: Iveki ye -12 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama ±30 ngosuku (±5 ezemisebenzi ye mathematika ngeveki) Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.7 • Sombulula ngomlomo uze ucacise izisombululo zezibalo zamazwi (izibalo Iingoma zamanani nezicengcelezo Usuku olu-1. ezingamabali) ezibandakanya u-2 Ukudibanisa nokuthabatha Ukufunda usebenzisa intshukumo yomzimba Imizekelo: 1. Utitshala ubiza umfundi omnye ukuba eze ngapahambili.Umfundi uyazibala.Utitshala uphinda abize omnye umfundi aze abuze: Bangaphi abafundi bebonke 1kunye no 1→2.(Utitshala uthi u 1no 1 benza u 2) 2. Utitshala uthabatha isitulo esi-1 .Uthi athathe nesinye aze abuze ukuba zingaphi izitulo zizonke? U -1 no 1  2. 3. Utitshala uphakamisa uminwe emi-2 aze athi:“bala iminwe yam”.Ukuba ndifihla ubemnye ,ndibona iminwe emingaphi ? 2 thabatha 1  1. 4. Utitshala uphakamisa uminwe emi-2 aze athi: bala iminwe yam”.Ukuba andiyisusi iminwe yam,ubona iminwe emingaphi ?2 thabatha 0  2. 5. Kukho umntwana omnye ekhaya.Kufika omnye eze kudlala.Bangaphi bebonke abantwana ngoku? 6. Kukho abantwana ababini etafileni.Umntwana ngamnye ufuna isitulo sakhe.Ingaba sifuna izitulo zibe ngaphi? Ukusebenzisa izinto eziphathekayo ezinokwakheka okungu 3-D Umz: Izixhobo zokubala 1. Ukuba uneqebengwana elinye aze umama akunike elinye,uya kuba namaqebengwana Izinto zokubala (izixhobo zokubala ukuba amangaphi ? awunawo amaqebengwana) 2. Utitshala unekhawuntari ezimbini, kwisandla sakhe esinye, akanazo kwesinye .Ingaba Izinto zokubala (Izixhobo zokubala) zingaphi izixhobo zokubala zakhe zizonke ? Ibhola 3. UCay uneebhola ezimbini.Ibhola enye kwezi zimbini iyaqengqeleka.Ingaba uCay Iibhloko ushiyeke neebhola ezingaphi? 4. Ukuba uneebhloko ezimbini uze unike umhlobo wakho ibhloko enye, ingaba umntu emnye uza kuba neebhloko ezingaphi? 117 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki ye -12 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama ±30 ngosuku (±5 ezemisebenzi ye mathematika ngeveki) 118 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 • Landelelanisa/cwangcisa uze uthelekise ingqokelela yezinto usebenzisa Usuku olu-1. “ingaphantsi kune” Chaza,thelekisa ucwangcise, Ngomlomo: Bala izinto yonke imihla uye kuma kwinani eli-2 Iingoma zamanani nezicengcelezo amanani Bethelela ingqiqo engu “ninzi” no “mbalwa” Qhwaba izandla zkho amaxesha ama……YIMA Qhwaba izandla zakho amaxesha ambalwa.Utitshala uqhwaba aye kuma ku -2. Ukufunda usebenzisa intshukumo yomzimba (Dibanisa ubugcisa bokwenza eqongeni nezakhono zobomi-umdaniso) Iingoma: Intloko ,”amagxa ,sifuba -- Cula ingoma:” Intloko ,”amagxa ,sifuba nesinqe“.Cula onke amagama kumjikelo nesinqe“ yokuqala” si -- Kumjikelo olandelayo phungula igama ambalwa- libe linye. Umz.Intloko,amagxa,sifuba ne......Sifuba ne...... -- Cula ingoma ube namagama ambalwa owashiyayo Intloko namagxa ne....... ne..........” -- Utitshala uyalatha ngalo lonke ixesha beshiyelela igama ambalwa kude kungashiyeki MATHEMATIKA IBANGA LABAQALAYO (R) magama Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Imitya emine ezinamanani amaso awohlukileyo. Utitshala wenza imitya yamaso. Faka amaso amathathu kumtya wokuqala ,amaso amabini kumtya wesibini,iliso elinye INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA kumtya wesithathu namaso amathathu kumtya wesine. -- Abafundi mabachonge oku:Let learners identify: -- Ngowuphi owona mtya onawona maso ambalwa ? -- Ngowuphi umtya wamaso oneliso elinye elingaphezulu komtya onamaso amathathu?

Ixesha lokufundisa elicetyiswayo: Iveki ye -12 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama ±30 ngosuku (±5 ezemisebenzi ye mathematika ngeveki) Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 Ukusebenzisa iimilo ezinokwakheka kuka- 2-D okanye imifanekiso Usuku olu-1. Chaza, thelekisa -- Abafundi mabathelekise umfanekiso nonotsheluza onamachaphazChonga unotsheluza Yenza imifanekiso nonootsheluza ucwangcise, onenani elingaphezulu okanye ongaphantsi kulawo anikwe ngutitshala. Umz.Ngowuphi bamachaphaza. amanani unotsheluza onezinto ezingaphezu kwesibini? -- Ngowuphi unotsheluza onezinto ezimbalwa kune-4? • Bethelela ukuthelekiswa kwezinto eziyingqokelela usebenzisa: Usuku olu-1 -- ngaphezulu kune -- ngaphantsi kune (mbalwa) Ukubala ngomlomo: Bala izinto yonke imihla uye kuma kwinani elingu-2 Iingoma zamanani nezicengcelezo Cengceleza ngokubala ukusuka ku -1 -7 Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kwisi-2 Utitshala wenza umtya onamaso.Faka amaso amathathu kumtya wokuqala,abe-2 kumtya Imitya emine ezinamanani amaso wesibini awohlukileyo. Abafundi bachonga: -- Ngowuphi umtya wamaso onawona maso ambalwa? -- Ngowuphi umtya wamaso onawona maso maninzi? -- Ngowuphi umtya wamaso onamaso amabini ngaphezulu kunomnye umtya? -- Ngowuphi umtya wamaso onamaso amathathu ngaphantsi kunomnye umtya? Nxulumanisa nobugcisa bokubonwayo apho abafundi boluka istro,sika imilo ezinemingxuma phakathi,amagqabi njl-njl 119 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki ye -12 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama ±30 ngosuku (±5 ezemisebenzi ye mathematika ngeveki) 120 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 Ukusebenzisa imifanekiso/iimilo ezinokwakheka kuka 2-D Imitya emine ezinamanani amaso Usuku olu-1 awohlukileyo. Chaza, thelekisa Beka iqela lezinto etafileni uze uzahlule ngolu hlobo: ucwangcise, -- Amaqela alinganayo ((enye yeyakho, enye yeyam) amanani -- Amamqela angalinganiyo(thelekisa ubone ukuba leliphi iqela elizinto ezinzi kunelinye/ leliphi iqela elinezinto ezimbalwa/ngawaphi alinganayo) -- Ukuba kukho amqela amabini angalinganiyo kufuneka senze ntoni ukuze alingane?) 3.2 • Chaza,hlela uze uthelekise izinto ezinikwakheka kuka 2-D kunye no 3-D Usuku olu-1 Izinto Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D ezinokwakheka Abafundi maba: kua 3-D kunye -- Hlele iintlobo ngeentlobo zezinto ngokobukhulu. -- Hlele uze uthelekise iibhloko zokwakha ngokobukhulu (inkulu,incincic) Izinto ezinkulu nezincinci ezahlukileyo 3.3 apha egumbini lokufunda umz ibhola, -- Hlele ibhloko ngokwe sakheko esifanayo Nezinto unodoli, imoto yokudlala, iibhloko. ezinokwakheka Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso MATHEMATIKA IBANGA LABAQALAYO (R) kuka 2-D Hlula abantwana babe ngamaqela amahlanu.Nika iqela ngalinye izinto ezineemilo Iibhloko zokwakha neebhola ezahlukileyo. ezinobukhulu obungalinganiyo -- Abafundi mabahlele imilo ngoko o Mbala INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA o Imilo (nokuba abafundi abazazi izakheko) Iimilo nokuba zeziphi imilo (logi shapes) o Ubukhulu ezinemibala eqaqambileyo. -- Sebenzisa amakhadi anemidlalo abonakalisa umbala,ubukhulu nemilo

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Fundisa intsingiselo yenani u – 3 Usuku olu-1 Bala izinto Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi-3 Bala usiya phambili ubale ubuya umva uye kuma kwisi- 3 Iingoma zamanani nezicengcelezo Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kwisi- 3 Ukufunda usebenzisa intshukumo yomzimba Abafundi ngokwabo -- Utitshala ubetha igubu okanye udlala umculo.Xa umculo ucimile abafundi bohlulwa Izinto zokubala (izixhobo zokubala) babengamaqela amathathu. -- Buza abantwana ukuba ngubani onamalungu osapho amathathu kuphela. -- Abafundi bema emgceni.Utitshala ubuza ukuba ngubani owesithathu emgceni?’ -- Yohlula abafundi babe ngamaqela ama ±5 -- Abafundi maba: -- Krazule amaphepha amathathu kwincwadi esisalathiso seenombolo zomnxeba endala. Incwadi yeenombolo zomnxeba endala. -- Shwabanise amaphepha amathathu abe ziibhola ezintathu bawaqinise kangangoko. Ukuphucula ubucala sebenzisa esona sandla umntwana asisebenzisayo.Abantwana banokuhlala phezu kwesandla angasisebenzisi rhoqo. -- Vule iibhola uze uzishwabanise kwakhona. -- Bale iibhola emveni kokuba uzishwabanise zontathu. -- Njengokuba ubala phosa iibhola zontathu ebhaskithini uze uzibeke embindini weqela. Lo msebenzi unokunxulunyaniswa neMithambo kwiziFundo Zobomi. 121 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 122 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Usuku olu-1 Bala izinto Abafundi maba: -- Chonge izinto ezi- 3 egumbini lokufunda -- Phakamisa iminwe emithathu -- Beka izinto ezi- 3 etafileni.Umfundi ngamnye makeze etafileni eze kubala into nganye. Izinto zokubala/izixhobo zokubala okanye Abafundi babamba into nganye lo gama bebala.Phinda phinda nagezinye izinto. izinto -- Phuhlisa ulwazi lwamanani ngokuthi ubayeke abafundi bapakishe izixhobo zokubala ezintathu okanye nokuba yintoni ngendlela ezahlukileyo. Umz. Xa ebala, inani lezinto malingachatshazelwa bubukhulu okanye indawo okanye ukufana. MATHEMATIKA IBANGA LABAQALAYO (R) Umz. -- Cwangcisa amaqhosha ama-3, iipensile ezi-3, izangqa ezi-3, abafundi aba-3 njl-njl. -- Bala ezi zinto ngeendlela ezininzi umz. Zibale zither saa, ziqokelelene, zisemgceni okanye zibekwe enye phezu kwenye. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye umfanekiso Oonotsheluza abanemifanekiso INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Bonisa umfanekiso wembiza yesiXhosa enemilenze emithathu. Oonotsheluza abanamachaphaza -- Bala imilenze. Izixhobo zokubala -- Abantwana mabacinge ngayo yonke into enemilenze emithathu. -- Bonisa ikhadi elinomfanekiso onezinto ezintathu.Abafundi babala izixhobo zokubala Umfanekiso ezihambelana nenani. wezinto ezintathu -- Yenza njalo ngoonotsheluza abanamachokoza. -- Abafundi batshatisa oonotsheluza abanamachaphaza nonotsheluza onomfanekiso.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.3 • Zazi iisimboli zamanani uze unakane amagama amanani abandakanya inani elingu- 3 Iityhubhu Usuku olu-1 Iisimboli zamanani Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi- 3 Oonotsheluza abanamanani ano -1 ukuya namagama kwi- 3 Bala ubhekisa phambili nangasemva uye kuma kwisi- 3 amanani Bethelela u –“ ninzi “no “mbalwa” Umfanekiso Qhwaba izandla amaxesha amaninzi……YIMA onezinto ezint 3 ntathu Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kwisi- 3 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Nika umfundi ngamnye iityhubhu ezi- 3 -- Utitshala ubonisa abantwana ichaphaza,umfanekiso,isimboli okanye unotsheluza onamanani u-1 ukuya ku- 3 -- Abafundi babhala inani elithile baze bathathe iityhubhu ezilingana nelo nani. Ukusebenzisa iimilo ezinokwakheka kuka- 2 D okanye imifanekiso Oonotsheluza abanamanani emifanekiso awohlukileyo. Abafundi ba: Unotsheluza onesimboli yenani engu-3 -- Chonga ononotsheluza onamani emifanekiso awohlukileyo Unotsheluza ophawulwe ngamachaphaza -- Chonga unotsheluza onenani elingu-3 ama-3 -- Tshatisa isimboli yenani elisisi-3 kunye nenani lezinto nenani lamachaphaza. -- Tshatisa igama lenani kunye nonotsheluza onesimboli yenani lamachokoza. Umfanekiso onezinto -- Nika umfundi ngamnye ikhadi elinamanani u -1 ukuya kutsho kwi -3. Utitshala ezint 3 ntathu uphakamisa ichaphaza okanye umfanekiso. Umfundi makaphakamise ikhadi elinenani elihambelana nechaphaza okanye umfanekiso. 123 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 124 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.7 • Sombulula ngomlomo iingxaki ezixeliweyo zokudibanisa nokuthabatha Usuku olu- 1 ezinezisombululo ukuya kwi- 3. Ukudibanisa nokuthabatha Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi-3 Bala ubhekisa phambili nangasemva uye kuma kwisi-3 Iingoma zamanani nezicengcelezo Ukufunda usebenzisa intshukumo yomzimba Imizekelo: -- Utitshala ubiza abafundi ababini ukuba beze ngapahambili.Abafundi baya babala. Utitshala uphinda abize omnye umfundi aze abuze: Bangaphi abafundi bebonke:2 kunye no 1→3.(Utitshala uthi 2 no 1 benza isi- 3) -- Utitshala uthabatha izitulo ezi-3. Akongezi situlo.Zingaphi izitulo ngoku? 3 no 0® 3 -- Utitshala uthabatha izitulo ezi-3 .Uthatha sibe sinye aze abuze ukuba zingaphi izitulo Izitulo ngoku? 3 no 1→ 2.(2 no 1 bakunika isi -3) -- Utitshala ubiza abantwana aba-3 beze ngaphambili.Babale.Uthumela ababini ukuba baye kuhlala phantsi.Bangaphi abafundi abashiyekileyo? 3 thabatha 2 →1 MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Nika abafundi abathathu izixhobo zokubala.Utitshala ubalisa ibali baze abantwana babeke into yokubala. Imizekelo: 1. U-Anelisiwe unee-orenji ezi -2.UPopo umnika i-orenji e-1.Ingaba uAnelisiwe unee- INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA orenji ezi ngaphi ngoku? 2 no 1→3 (Utitshala uthi: 2 no 1 ukunika 3). 2. Umthi unesebe elinye.Kukhula amanye amasebe ama-2.Umthi unamasebe amangaphi ngoku? 1 no 2→3. Imizekelo: Izinto zokubala ezi-3 zomfundi ngamnye 1. Inkawu ineebhanana ezi -3.Itya ibhanana ibe -1.Ingaba ishiyekelwe ziibhanana ezingaphi? 3 thabatha 2→1. 2. Kukho ii-apile ezi-2 emthini.I-apile e-1 iyawa.Kushiyeke ii-apile ezingaphi emthini? 2 thabatha 1 →1.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 2.1 • Yila iipateni zakhe esebenzisa izinto ezimbini Usuku olu-1 Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba Abafundi benza isangqa.Bacula besebenzisa amagama ngokukhawulezayo Umzekelo: Imvula,imvula Chapha,chapha Imanz’ ilokhwe yam Imanz’ lokhwe yam Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi ba: -- Qokelela apha egumbini lokufunda izinto ezi-3 ezifanayo. Umz iikhrayoni ezi-3 Ikhrayoni -- Qokelela ezinye izinto ezi-3 ezifanayo umz.iibhloko ezi- 3 Into yokuncamathisela -- Abafundi bayila iipateni zabo besebenzisa izinto ezimbini.umz Ingqokelela yezinto nokuba ziintoni -- Ikhrayoni enye, ibhloko enye, ikhrayoni enye….. -- Iikhrayoni ezimbini, ibhloko enye, iikhrayoni ezimbini, ibhloko enye….. -- Vumela abafundi ukuba bayile iipateni ngeendlela ezahlukileyo. -- Batshintshiselana nabahlobo babo ngezinto.Makuphinda phindwe oku. 125 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 126 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 3.3 Nakana,chonga uze uxele iimilo ezinokwakheka kuka- 2-D ezilapha egumbini Usuku olu-1 lokufunda eziquka imifanekiso. Izinto ezinokwakheka -- unxantathu kuka 2-D • Bethelela ulwazi olufundwe kwiveki yesine ukuze anakane, achonge, axele unxantathu. Ukufunda usebenzisa intshukumo yomzimba Zoba, okanye usebenzise intambo ukuyila umphandle weemilo ezinkulu zikanxantathu. Abafundi maba: -- Hamba kumacala emilo onke aze aqwalasele iimpawu zika nxantathu. Njengokuba behamba abafundi mabathi: Ndihamba kunxantathu.Nye, mbini, ntathu amacala. Umdongwe okanye intlama yokudlala Okanye nye,mbini, ntathu iikona (ii-engile) -- Utitshala uxelela abafundi ukuba unxathathu uneekona ezintathu namacala ama-3. -- Zoba unxantathu emoyeni okanye esantini. Izinto ezinemilo kanxantathu egumbini -- Bumba unxantathu ngomdongwe. lokufunda naphandle. MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi maba: Yenza amakhadi abenezanqga,oonxantathu nezikwere -- Nakane baze bachonge izinto egumbini lokufunda ezinemilo kanxantathu. ezahlukileyo ezi-5. -- Nakana baze bachonge izinto endalweni ezinemilo kanxantathu. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Faka iintlobo ngeentlobo zezangqa noonxantathu abanobukhulu obahlukenenyo kwibhegi.Chonga unxantathu phakathi kwezo milo.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE 13 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 3.3 Hlela izinto ezinokwakheka kuka 3-D neemilo ezinokwakheka kuka 2-D Usuku olu-1 Izinto Hlela izinto ngokwemilo nombala. ezinokwakheka kuka 2-D Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Abafundi maba: Imifanekiso apho unxantathu anokuchongwa khona. -- Chonga unxantathu emifanekisweni. -- Zoba unxantathu ephepheni. Amakhadi anemidlalo ephuhlisa -- Kopa unxantathu kwikhadi olinikiweyo ukuqatshelwa kweemilo ezifana -- Rhangqa izangqa ezikwiphepha lomsebenzi olinikiweyo nezikwere efana nale “Yintoni ekwisikwere”. -- Yenza imifanekiso usebenzisa unxantathu ngexesha lokuzoba Iimilo zelogi (logi shapes) -- Dlala umdlalo wamakhadi ophucula uze ubethelele iimilo. 127 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 14 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 128 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Bethelela ulwazi alufumeneyo lwenani u-3 Usuku olu-1 Bala izinto Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi-3 Bala usiya phambili, ubale ubuya umva uye kuma kwisi-3 Bala ngentloko ngokungenantsingiselo ukuqala ku-1-7 Iingoma zamanani nezicengcelezo. Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kwisi-3 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi ba: -- Funa izinto ezibomvu zibe -3 egumbini lokufunda. Izinto ezibomvu. -- Yenza inani elingu-3 besebenzisa umdongwe. Umdongwe. -- Bumba iibhola ezi-3 ezinkulu ngomdongwe. MATHEMATIKA IBANGA LABAQALAYO (R) -- Bumba ibhola ezi-3 ezincinci ngomdongwe. -- Khangela egumbini lokufunda abafundi aba-3 abanxibe umbala omnye. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 14 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku ngangcaciso ukuba zisetyenziswe elisondeleyo 1.7 • Sombulula ngomlomo uze ucacise isisombululo kwizibalo zamazwi (izibalo Usuku olu-1 ezingamabali) ezinenani elingu-3 Ukudibanisa nokuthabatha Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi-3 Bala usiya phambili ubale ubuya umva uye kuma kwisi-3 Ukufunda usebenzisa intshukumo yomzimba Imizekelo: 1. Utitshala ubiza abafundi aba- 2 ukuba beze kuhlala ekhaphethini.Utitshala ubiza Abafundi umfundi omnye ukuba aze kuhlala ekhaphethini.Utitshala ubize abantwana aBangaphi ukuba beze kuhlala ekhaphethini.Utitshala uthi: 2 no 1 bakunika u 3. 2. Kukho abantwana abathathu.Umntwana ngamnye ufuna ikhrayoni yakhe.Zingaphi ikhrayoni esizifunayo? 3. Abantwana abathathu bame bonke.Omnye uyaphuma egumbini.Bangaphi abantwana abashiyekileyo? Izinto eziphathekayo ezinokwakheka kuka- 3-D Imizekelo: 1. Utitshala ubeka izinto zokubala ezi -3 etafileni.Uthatha izixhobo zokubala ezi-2. Zingaphi izixhobo zokubala ezishiyekileyo etafileni? Utitshala uthi 3 thabatha 1 kushiyeka 2. 2. UPat uneekati ezimbini.Uphiwa nguBusi ikati e-1.Zingaphi iikati zikaPat zizonke? 1 no 2→3. Utitshala uthi 1 no 2 zikunika 3. Izixhobo zokubala 3. Ukuba ikati enye inomsila omnye, mingaphi imisila yeekati ezi- 3 iyonke? 1 and 1 and 1→3 129 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 14 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 130 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku ngangcaciso ukuba zisetyenziswe elisondeleyo 2.1 • Gqibezela iipateni azinikiweyo enezinto ezi- 2 Usuku olu-1 Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba -- Abafundi mabakope ipateni yentshukumo. Umz. Xhuma, xhuma, tsiba, tsiba, xhuma, xhuma, tsiba........ -- Abafundi bagqibezela ipateni besebenzisa imizimba yabo umz. e.g. Bama ecaleni komnye baze bemana betshintsha izandla zabo bezibeka entloko,izandla emahlezeni,izandla entloko…… Izinto eziphathekayo ezisebenzisa ukwakheka kuka 3-D -- Abantwana mabakope ipateni yento umz. iliso, iliso(bead), uluthi, uluthi, iliso, iliso, Nokuba yintoni uluthi, uluthi ..... Iimilo ezinokwakheka kuka 2-D okanye umfanekiso -- Utitshala unika abantwana imifanekiso yento enye esele isikwe kakuhle eziindidi ezininzi.(Sika imifanekiso ngexesha lemisebenzi yobugcisa bokubonwayo). Imifanekiso eneentengiso. -- Utitshala wenza ipateni baze abafundi bayikope umz.umfanekiso wekofu; iti, iswekile…. MATHEMATIKA IBANGA LABAQALAYO (R) -- Abafundi mabagqibezele ipateni ngokuzoba: -- Intyatyambo, igqabi, intyatyambo..... Iphepha elingu A4 neekhrayoni -- Isangqa esi bhlowu, isekile ebomvu, isangqa esi bhlowu...... njl-njl. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 14 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku ngangcaciso ukuba zisetyenziswe elisondeleyo 3.2 • Hlela uze uthelekise izinto ezinokwakheka kuka 3-D neemilo ezinokwakheka Izinto ezifana nezi: Usuku olu-1 kuka2-D ngokweempawu ezithile Izinto Iimpahla zokunxiba ezahlukileyo ezinokwakheka Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iintlobo ngeentlobo zeziqhamo kuka 3-D Hlula abantwana babe ngamaqela ama-5. Iindidi ngeendidi zezilwanyana zasefama -- Utitshala uqokelela izinto ezaneleyo ukuze iqela ngalinye libe nakho ukuzihlela zokudlala ngokweempawu ezimbini. (Zinokuba ninzi kunoku). Iimilo ezahlukileyo ze- jiyometri -- Nika iqela lezinto ezineempawu ezimbini ukuze lizihlele. Iindidi ngeendidi zeebhloko zokwakha Abantwana mabenze oku: Iindidi ngeendidi zeebhloko zelogi (logi -- Hlela izinto ezifanayo nezahlukileyo. blocks) Ukusebenzisa iimilo ezinokwakheka kuka- 2 D okanye imifanekiso Iindidi ngeendidi zezinto ezifana namagqabi,amakhuni,amatye nj-njl Abantwana mabahlale kula maqela bebekuwo. Iindidi ngeendidi zamaqhosha. -- Thelekisa uze uhlele imifanekiso eyahlukileyo ebiqokelelwe ngutitshala.umz.Iindidi ngeendidi zemifanekiso yeelokhwe, ukutya, izithuthi njl-njl. Iindidi ngeendidi zemibala yeziciko zeebhotile. -- Abafundi bagqibezela amaphepha okusebenza apho batshatisa khona imifanekiso emibini umz. Intlama yamazinyo nebrashi yamazinyo, ilaphu lokuhlamba ubuso Iindidi ngeendidi zeekhrayoni. nesepha. Qokelela imifanekiso kwiimagazini neencwadana zolwazi. Sika uze uncamathisele emakhadini. 131 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 14 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 132 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku ngangcaciso ukuba zisetyenziswe elisondeleyo 3.1 • Indawo yezinto ezimbinio kanye ezininzi ngokunxulumene nomfundi Abantwana Usuku olu-1 Indawo –bume, -- Bethelela u-ngaphezulu/ngaphantsi Ibhokisi ukufumana indawo Ukufunda usebenzisa intshukumo yomzimba nembonakalo. Umfundi ngamnye uhlala esitulweni. -- Abantwana babonisa oku: ngaphezulu,ngaphantsi ngokulandela imiyalelo katishala. umz hlala phezu kwebhokisi,lala phantsi kwebhokisi/kwetafile. -- Hlala phantsi kwetafile.Zisonge ube mncinci ukuze ube nakho ukungena phantsi kwetafile. phezu kwe phantsi kwe -- Yima ngeenyawo phezu kwesitulo uze uzolule kangangoko unakho. -- Ngena etafileni yakho uze ujiwule iingalo zakho wenze izangqa ezinkulu/ezincinci. -- Beka iibhloko entloko uze ukhwele etafileni. -- Khetha abafundi abahlanu usebenzise isicengcelezo samanani -- Sebenza le miyalelo kumfundi ngamnye: MATHEMATIKA IBANGA LABAQALAYO (R) o Hlala phantsi izandla zakho zibe phantsi kwemilenze yakho. o Yima ngeenyawo izandla zakho zibe semahlezeni akho. o Yima ngeenyawo izandla zakho zibe ngasemva. o Hlala phantsi izandla zakho zibe semagxeni akho. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA o Yima ngeenyawo uphothe izandla zakho ngaphambili. Abafundi bama ngaphambili logama elinye iqela lihleli ekhaphethini. -- Wenza ntoni umfundi wokuqala?(Uhleli phantsi) -- Ziphi izandla zakho ?(Izandla zakhe ziphantsi kwemilenze) -- Phinda nelinye iqela labafundi usebenzisa la magama okwesibini, okwesithathu, okwesine, okokugqibela. -- Khupha phandle iqela elitsha lize libonise ngokwalo oku -ngaphezulu, ngaphantsi,ngaphezulu kwe-

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE - 15 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Bethelela ulwazi alufumeneyo lwamanani u-1,2 no 3 Usuku olu-1 Bala izinto Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi-3 Bala usiya phambili ubale ubuya umva uye kuma kwisi-3 Iingoma zamanani nezicengcelezo Bala nngentloko gokungenantsingiselo ukuqala ku-1-7 Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kwisi-3 Ukufunda usebenzisa intshukumo yomzimba Imizimba yabafundi. Khuthaza abantwana ukuba bafumanise oku: Ukucula balinganise ingoma umz. “ amahotyazana mahlanu emthini, -- Ilungu lomzimba eli-1 elikwaziyo ukushukuma libheke phezulu okanye libheke phantsi, kwabhabha lalinye kwasala liye emacaleni umz. ulwimi amane…………… -- Amalungu ama-2 asetyenziselwa ukutsiba umz.imilenze Izicengcelezo zamanani Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iibhloko Abafundi bakhulisa ingqiqo ngamanani ngoku-: Izinto ezibomvu -- Sebenzisa iibhloko ezi-3 wakhe ithawa -- Khangela izinto ezi-3 ezibomvu apha egumbini lokufunda. Ukusebenzisa imilo ezinokwakheka kuka- 2 D okanye umfanekiso Utitshala uzoba umfanekiso olula -- Utitshala ubuza imibuzo engqamene nenani lezinto ezisemfanekisweni. umz. Zingaphi iifestile ozibonayo? njl-njl 1.2 • Sebenzisa amanani u 1, 2 and 3 kwiimeko eziqhelekileyo Usuku olu-1 Ukubala usiya Ngomlomo: Bala izinto yonke imihla uye kuma kwinani elisisi-3 Ingoma zamanani nezicengcelezo phambili nokubala Bala usiya phambili, ubale ubuya umva uye kuma kwisi-3 ubuya umva Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kwisi-3 133 -- Khuthaza abafundi ukuba bafunde ngentloko iinombolo zakumawabo kwakunye nesitalato ahlala kuso. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE - 15 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 134 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.2 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iimagazini, iintengiso Usuku olu-1 Ukubala usiya Abafundi maba: Oonotsheluza abanamachaphaza phambili nokubala -- Khangele imifanekiso yamanani angu 1,2, no 3 kwimagazini neflaya baze ubuya umva bayincamathisele ephepheni.(nxulumanisa nobugcisa bokubonwayo) -- Tshatisa inani lezinto neenani lamachaphaza kunotsheluza. -- Bonisa ikhadi lamachaphaza.Abantwana baphosa inani elilinganayo neebhibhegi Iibhinbhegi kwibhokisi. Umdlalo weenyoka neeleli -- Dlala umdlalo weenyoka neeleli needomino. IiDomino AMANQAKU: Singqongwe ngamanani: -- Yonke indlu inenani -- Sonke sinamanani awahlukileyo kwiinombolo zethu zomnxeba MATHEMATIKA IBANGA LABAQALAYO (R) -- Sibona amanani ezifestileni zeevenkile -- Sibona amanani kwizinto esizithengayo ezivenkileni -- Sibona amanani ezimotweni 1.4 • Cwangcisa uze uthelekise ingqokelela yezinto usebenzisa u- ngaphezulu kune, Usuku olu-1 ngaphantsi kune, lingana ne ukuya kwinani elingu-3. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Chaza,uthelekise uze ucwangcise Ukufunda usebenzisa intshukumo yomzimba amanani Biza abafundi beze ngaphambili.Mabenze isangqa Ababini mabeme ngenyawo. -- Bangaphi abahleli phantsi. Babale. Leliphi inani elingaphezulu/elona lingaphezulu, leliphi elingaphantsi/elona lingaphantsi. -- Abafundi abathathu mabeme ngenyawo.Babale.Leliphi elona nani lingaphezulu/ lingaphantsi? Biza omnye umfundi eme. Babale. Ingaba abafundi abahleli phantsi Bangaphezulu kunabo bahleli phantsi? -- Phinda usebenzisa amanani ukusuka ku- 1ukuya kwisi 3.. -- Bala amantombazana.Bala amakhwenkwe.Ingaba amakhwenkwe angaphezulu kunamantombazana?

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE - 15 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Usuku olu-1 Chaza,uthelekise Hlula abafundi babe ngamaqela amahlanu. uze ucwangcise Nika iqela ngalinye isijungqe somtya/sewulu kunye nezinto ezintlanu(zingangaphezulu/ amanani ngaphantsi). Abafundi benza inesi ngewulu. -- Utitshala usebezela iqela ngalinye,eliyalela ukuba lenze iqela lezinto ezi- 3 okanye ezi- 2 okanye e-1 kwiinesi zabo. Umtya -- Abafundi mabachonge iqela elinezinto ezingaphezulu kwe -1. Izinto ezi- 5 kwiqela ngalinye -- Leliphi iqela elinezinto ezingaphantsi kwe-3? -- Leliphi iqela elinezinto ezilinganayo? 2.1 • Kopa uze ugqibezele ipateni ngokwale mibala: bomvu, bhlowu, tyheli. Usuku olu-1 Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba -- Utitshala ulinganisa ipateni.Uyayiphinda phinda aze agcine isingqisho.umz o Qhwaba, snepa(iminwe), qhwaba, snepa o Nqokra iminwe (snap), qhwaba, Nqokra iminwe (snap), qhwaba, ngqisha o Qhwaba, snepa, snepa, qhwaba, Nqokra iminwe (snap), snepa Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Utitshala unika abafundi izixhobo zokubala/iziciko zeebhotile ezi-3 ezibomvu, ezi-3 ezibhlowu kunye nezi-3 ezityheli. Abafundi maba: -- Kope ipateni abayinikiweyo kwiipateni zikatitshala umz.bomvu,bhlowu,tyheli(phinda Umfundi ngamnye makafumane phinda amaxesha amaninzi ngepateni eyahlukileyo) ezintathu ezibomvu, ezintathu eziluhlaza -- Gqibezele ipateni enikiweyo umz bhlowu,tyheli,bomvu…………. (phinda phinda okwesibhakabhaka nezintathu ezityheli amaxesha ngepateni eyahlukileyo) izixhobo zokubala okanye iziciko zeebhotile. -- Abafundi mabahlele izixhobo zokubala ngokwemibala emithathu eyahlukileyo. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Iphepha elingu A4 -- Nika abafundi iphetshana elincinci. Iikhrayoni -- Abafundi mabagqibezela iimilo ezinezakhiwo ezinokwakheka kuka- 2-D njengesiphelo -- Gqibezela umfanekiso ngexesha lobugcisa obubonwayo ngokuthi uzobe umfanekiso phakathi. Karabo Siya 135 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE - 15 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 136 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 Thelekisa uze uhlele izinto ngokuzibamba esebenzisa isigama esifanelekileyo Usuku olu-1 ukuchaza ubude Ubude -- inde, imfutshane, -- indana, imfutshanana, Iibhloko zokwakha -- eyona inde eyona imfutshane Ukufunda usebenzisa intshukumo yomzimba -- Umfundi omnye ulala phantsi.Abanye abafundi babeka iibhloko ngokomgca emacaleni omzimba wakhe. -- Utitshala uyalela iklasi ukuba bakhe into emfutshane kunabahlobo babo nendana kunabahlobo babo. Abafundi mabaqiniseke ukuba: -- Sesiphi isakhiwo esidana? -- Sesiphi esona sakhiwo side? -- Sesiphi isakhiwo esifutshanana? MATHEMATIKA IBANGA LABAQALAYO (R) -- Sesiphi esona sakhiwo sifutshane? Abantwana mabalungise iindidi zezixhobo zokwenza izinto: Umtya -- Ukusuka kweyona inde ukuya kutsho kweyona imfutshane. Intambo -- Ukusuka kweyona imfutshane ukuya kutsho kweyona inde. Imicwe yelaphu INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Abafundi mabathelekise ubude bezinto ezahlukileyo. Iikhrayoni ezinobude obahlukileyo Utitshala unika abantwana izijungqe zewulu okanye umtya.Bakhuthaze ukuba baqikelele phambi kokuba benze imilinganiselo. Abantwana mabathathe imilinganiselo: -- Iintloko zabo. -- Iinyawo zabo. -- Amaqatha abo. Iwulu okanye umtya -- Izihlahla zabo. Abafundi -- Abafundi mabathelekise ubude obahlukileyo ngokubona ukuba zeziphi izijungqe zemitya ezidana okanye ezifutshanana umz.umlinganiselo womtya wentloko yam umdana kunalowo wesihlahla sam. -- Abafundi mabaqiniseke ukuba uqikelelo lwabo lulungile kusini na.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE-16 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Fundisa intsingiselo yenani elingu -4 Usuku olu-1 Bala izinto Ngomlomo: Bala izinto yonke imihla uye kuma ku-4 Bala usiya phambili ubale ubuya umva uye kuma ku- 4 Izicengcelezo zokubala neengoma Bala ngentloko ngokungenantsingiselo ukuqala ku-1-7 Imizimba yabafundi Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye kui- 4 Ukufunda usebenzisa intshukumo yomzimba Abafundi mabenze oku: -- Nqwala intloko amaxesha ama- 4. -- Abafundi mababonakalise u- 4 besebenzisa imizimba yabo. Mabaqiniseke ukuba bafuna abafundi aBangaphi. -- Abafundi bavala amehlo abo.Utitshala ubetha etafileni amaxesha ama- 4.Abafundi bavula amehlo abo baxele ukuba bave izithonga ezingaphi.Phinda phinda ngamanani u-1 ukuya kwi- 4. 137 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE-16 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 138 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Usuku olu-1 Bala izinto Abafundi mabenze oku: Intlama yokudlala -- Yenza u- 4 usebenzisa intlama yokudlala. Izinto ezingqukuva -- Khangela abahlobo bakhe aba- 4 abanxibe izihlangu. Yenza ikhadi lamanani eliviwayo ngokusika amanani kwiphepha -- Khangela izinto ezi- 4 ezingqukuva. lokukhuhla(sand paper) uze -- Gquma amehlo abafundi baze bachonge la manani: 1 ukuya kwi- 4 ngokuva/ uwancamathisele kwikhadi-bhodi ngokukhuphela ikhadi lamanani eliviwayo. encinci.Ungawagquma ngeplastiki encamathelayo ukuze abafundi bakwazi -- Bonakalisa ukuqonda amanani ngokuthi abafundi babeke izixhobo zokubala/izinto ukwenza amanani omdongwe kula ezine ngeendlela ezahlukileyo.umz. makhadi. Izinto zokubala ezi-4 okanye izinto ezine zomfundi ngamnye. Iimagazini,iiflaya,iintengiso Iphepha le A4 neglu MATHEMATIKA IBANGA LABAQALAYO (R) Xa ubala inani lezinto alichatshazelwa bubukhulu,indawo okanye uhlobo olunye.Umz: -- Lungisa amaqhosha ama- 4, iipensile ezi- 4, izangqa ezi- 4, abafundi aba- 4 njl-njl. Umfanekiso -- Zibale ezi zinto ngeendlela ezahlukileyo umz. Zibale zithe saa, sisondelelene, wezinto INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA zisemgceni okanye zibekwe enye phezu kwenye. ezi-4 Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Abafundi mabenze oku: -- Khangela imifanekiso emi- 4 uze uyincamathisele ephepheni. -- Tshatisa inani lezinto namanani amachaphaza akunotsheluza. -- Chonga unotsheluza onamachaphaza amane.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE-16 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 • Sebenzisa inani elingu-4 kwiimeko eziqhelekileyo Usuku olu-1-1 Chaza,thelekisa -- Ingaba inani elingu -4 likwenza ucinge ntoni? uze ucwangcise Imoto - amavili amane Iidilesi zamakhaya abafundi amanani Isitulo- imilenze emine Inja - iintupha Itafile - imilenze emine Abafundi -- Ukukhulisa ukukhumbula,khuthaza abafundi ukuba bafunde ngentloko iinombolo zakumawabo negama lesitalato. 4 Izinto eziphathekayo ezinokwakheka kuka- 3-D -- Nika ithuba lokudlalwa kwemidlalo yamakhadi amanani yiklasi yonke. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Bonisa ikhadi elinesimboli yenani u- 4 Imidlalo yamakhadi amanani nokuba Dlala imimdlalo efana nale: yeyiphi na. -- Ukuba inombolo yendlu yakokweni unenani elingu-4, qhwaba ka-4. -- Khangela umhlobo wakho onenombolo yendlu efanayo neyakokwenu. (Abafundi Umfanekiso mababuzane iinombolo zamakhaya abo) wezinto -- Ngubani onenombolo yakokwabo enamanani angaphezulu kwe-4? ezi-4 -- Bonisa abafundi unotsheluza onamachaphaza amane. Oonotsheluza abanemifanekiso -- Chonga unotsheluza onemifanekiso emine. namachaphaza ama -4 139 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE-16 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 140 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 3.2 • Ukuphononnga amathuba okwakha ngeebhloko Usuku olu-1 Izinto Abantwana mabenze oku: Iibhloko zokwakha umz. ezinokwakheka -- Sebenzisa iibhloko ezi-4 ukwakha isakhiwo sakho. kuka 3-D -- Yakha isakhiwo esineebhloko ezintathu ukunyuka neebhloko ezi-5 ukunqamleza. -- Sebenzisa iibhloko kangokuba befuna ukwakha uloliwe. -- Chonga ukuba ngowuphi umntu owakhe oyena loliwe mde. -- Yakha isakhiwo esiphakamileyo. -- Yakha isakhiwo esithe tyaba umz .indlela okanye indlu. -- Chonga ukuba ngubani owakhe esona sakhiwo siphakamileyo. -- Nika abafundi iibhloko zokwakha ngexesha lokudlala ukuze bakwazi ukuqhubekeka beHlola iibhloko zokwakha. 3.2 • Khulisa ukukwazi ukohlula phakathi kweemilo kwizinto ezisingqongileyo, Usuku olu-1 ngaphandle kobukhulu, okanye ubungakanani be-eengile. Izinto MATHEMATIKA IBANGA LABAQALAYO (R) ezinokwakheka Ukufunda usebenzisa intshukumo yomzimba kuka 2-D Yahlula abafundi babe ngamaqela ama-3: Khetha umsebenzi -- Lalani phantsi nize nenze unxantathu ngemizimba yenu. Yalatha ukuba noxa ube mnye unxantathu weqela unemilo eyahlukileyo kwelinye yelinye iqela, imilo iseyileyo osebenzisa kanxantathu. ukufunda INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA usebenzisa -- Utitshala uzoba oonxantathu abohlukileyo phantsi/emhlabeni umz. intshukumo yomzimba, eziphathekayo Abafundi nemifanekiso -- Abafundi bahamba ecaleni kwamacala emilo baze babe namava ee-engile ezahlukileyo ngemizimba yabo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Sebenzisa amasebe asi-7 uze uwabeke emgceni   Amasebe asi-7 omfundi ngamnye

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE-16 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 3.2 -- Sebenzisa amasebe ukwenza umgca ogoso. Izinto   ezinokwakheka kuka 2-D -- Sebenzisa amasebe ukwenza uzigizegi.   -- Sebenzisa amasebe ukwenza unxantathu.   -- Yalatha ukuba oonxantathu babamntwana abafani kodwa ke imilo iseyileyo kanxantathu. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye iimifanekiso Amakhadi anezangqa,oonxantathu nezikwere ezi-5 ezahlukileyo. Utitshala uzoba kunotsheluza izangqa,oonxantathu nezikwere ezi-5 ezahlukileyo.umz   Utitshala wohlula abafundi babe ngamaqela. Abafundi maba: -- Nakana oonotsheluza bakanxantathu phakathi kwezinye iimlo. 141 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE-16 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 142 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 4.2 Thelekisa ngokwenza uze ucwangcise izinto usebenzisa isigama esifanelekileyo Usuku olu-1 ukuchaza ubude. Ubude Ipensile,intambo, -- de, futshane, Umtya,ipegi -- ndana, mfutshanana, Itshati yezandla -- eyona inde, eyona imfutshane,   Itshati Heightyobude Chart -- futshane, mfutshanana, eyona imfutshane, Term Ikota 1 Yoku1 Ikota 2 Termyesi2 -- de, ndana, eyona inde -- inde, imfutshane, -- indana, imfutshanana, -- eyona inde eyona imfutshane Bethelela ubude Ukufunda usebenzisa intshukumo yomzimba Ema kwenziwe ngabafundi: MATHEMATIKA IBANGA LABAQALAYO (R) -- Hlola ubude ngokuthi uthelekise ubude bezinto, kwenye. -- Qonda ukuba yeyiphi eyona nto iyeyona inde okanye eyona imfutshane. -- Thelekisa ubude babafundi ababini uze uchonge ukuba ngowuphi umfundi omfutshane ingowuphi omde. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Thelekisa ubude babafundi abaninzi kunesibini uze ubuze le mibuzo “ngowuphi oyena mfundi mfutshane, ngowuphi oyena mfundi mde. -- Utitshala uthatha umlinganiselo wabafundi esebenzisa itshati yobude ebeyisebenzisa kwikota yoku- 1. -- Utitshala ushiya imibhalo yekota edlulileyo apho abhale khona imilinganiselo yabantwana (izandla /iisimboli zabantwana) ukuze bakwazi ukuthelekisa imilinganiselo emibini. -- Abafundi bafumanisa ukuba ingaba bakhulile ukusuka kwikota yoku- 1. -- Ngubani ongakhange akhule? -- Ngubani okhule kakhulu ukusuka kwikota yoku- 1? umz o USipho ukhule ngesandla esinye o Ubude buka Abby buyinto enye.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 17 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Bethelela ulwazi alufumeneyo ngentsingiselo yenani u-4 Usuku olu-1 Bala izinto Ngomlomo: Bala izinto yonke imihla uye kuma ku-4 Bala usiya phambili, ubale ubuya umva uye kuma ku-4 Bethelela u –“ ninzi “no “mbalwa” Iingoma zamanani nezicengcelezo Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye ku-4 Ukufunda usebenzisa intshukumo yomzimba Abafundi: -- Bhala u- 4 emoyeni usebenzisa umnwe -- Cula ingoma umz. “amahotyazana mane emthini..... -- Jikajika amaxesha ama- 4 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Itreyi yokubhaka emcaba/ibhokisi yesanti Abafundi mabakhulise ulwazi lwabo lwamanani ngoku: Izinto ezinokwakheka kuka 3-D ezikwazi ukuqengqeleka. -- Zoba u-4 esantini. Izicwili zepazili ezi- 4 -- Khangela izinto ezinokwakheka kuka 3-D ezikwazi ukuqengqeleka. -- Yakha iipazili usebenzisa izicwili zephazili ezi- 4. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Utitshala ukhetha amagama ama- 4 konootsheluza.Utitshala ubonisa igama ngokukhawuleza aze enze njalo abonise umfanekiso wesilwanyana okanye into yokudlala. Amakhadi anemifanekiso ezinto -- Umfundi obekhethiwe ngokuthi kuboniswe igama lakhe ngokukhawuleza uyalelwa zokudlala. ukuba enze ingxolo eyenziwa yiloo nto yokudlala. Amakhadi anemifanekiso ezilwanyana -- Phinda phinda ude ubonise onke loo magama. -- Buza ukuba mangaphi amagama abafundi abonisiweyo.Zingaphi izinto zokudlala// izilwanyana abazibonileyo. 143 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 17 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 144 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.3 • Yazi iisimboli zamanani uze uqaphele igama lenani elingu-4 Usuku olu-1 Iisimboli zamanani Ngomlomo: Bala izinto yonke imihla uye kuma ku-4 kunye namagama Bala usiya phambili, ubale ubuya umva uye kuma ku-4 Iingoma zamanani nezicengcelezo amanani Bethelela u –“ ninzi “no “mbalwa” Qhwaba izandla amaxesha amaninzi……YIMA Qhwaba izandla amaxesha ambalwa.Utitshala uqhwaba aye ku -4 Ukufunda usebenzisa intshukumo yomzimba -- Bhala inani u-4 emoyeni, phantsi, emqolo kumhlobo wakhe. -- Phakamisa iminwe emi-4. -- Utitshala ubetha igubu.Xa igubu liyeka abafundi bazahlula ngokwamaqela amane. Ukusebenzisa imilo ezinokwakheka kuka 2-D okanye imifanekiso Oonotsheluza abanesimboli yenani. -- Bonisa abafundi unotsheluza onesimboli ka-4. Unotsheluza onegama lenani elingu-4 MATHEMATIKA IBANGA LABAQALAYO (R) -- Chonga igama lenani kunotsheluza. Izinto ezinokwakheka kuka 3-D -- Tshatisa igama lenani nenani elilinganayo lezinto. 4 ne INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 17 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.7 • Sombulula ngomlomo izibalo zamazwi (izibalo ezingamabali) aze anike Usuku olu- 1 isisombululo kwiingxaki ezinenani elingu-4. Ukudibanisa nokuthabatha Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Imizekelo: 1. Utitshala ukunika iibhloko ezi-2 ube wena uneebhloko ezi-2.Zingaphi iibhloko onazo ngoku? 2. Ukuba unezangqa ezibhlowu ezi-2 nezangqa ezi-2 ezibomvu, zingaphi izangqa zakho zizonke? 3. USipho uneekhrayoni ezi-4, uJoy unekhrayoni e-1. Ngubani onekhrayoni ezininzi? Iibhloko 4. Ukuba uJonga unoonodoli aba-4 aze alahlekelwe ngunodoli o-1.Bangaphi oonodoli abashiyekileyo? Ikhrayoni Hlula abafundi babe ngamaqela. Izangqa ezibhlowu nezibomvu -- Nika iqela ngalinye izinto ezininzi.umz iipensile,ikhrayoni,iikomityi,iimilo.Abafundi Oonodoli mababelane ngezinto kumaqela onke (ungqinelwano lwamanani) -- Buza imibuzo efana nale: “Ingaba zikhona izinto ezishiyekileyo?” Izinto ezaneleyo zomfundi ngamnye -- (Utitshala uqinisekisa ukuba kukho inani elininzi lezinto kunenani labafundi) Susa ezifana neepensile, iikhrayoni, iikomityi, ezinye izinto ukubonisa ukwabelana ngokulinganayo) iimilo. 145 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 17 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki 146 Izixhobo zokufundisa ekucetyiswa Ixesha ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 • Cwangcisa uze uthelekise ingqokelela yezinto usebenzisa u ngaphezulu kune, Usuku olu-1 ngaphantsi kune, lingana ne ukuya kwinani elingu-4. Chaza,thelekisa uze uhlele amanani Hlula abafundi ngokwamaqela: -- Utitshala unika iqela ngalinye izixhobo zokubala ezi-4 nezijungqe zewulu ezi-2. Amaqela mawenze oku: Iwulu/umtya -- Yila izangqa ezibini (iiseti) ngewulu. Izixhobo zokubala ezi- 4 -- Ngokomyalelo katitshala babeka izixhobo zokubala kwiseti nganye. -- Amalungu eqela achonga iseti enezinto zokubala ezininzi kunye (ngaphezulu kune) -- Sesiphi isangqa esinezinto zokubala ezingaphantsi kunesinye.(ngaphantsi kune) -- Sesiphi isangqa esinenani elilinganayo nesinye isangqa? (lingana ne) Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Lungisa iseti yamakhadi emifanekiso ngendlela efanelekileyo.umz MATHEMATIKA IBANGA LABAQALAYO (R) Umfanekiso Umfanekiso Umfanekiso Umfanekiso wento e-1 wezinto ezi-2 wezinto-3 wezinto-4 Lungisa iseti yamakhadi amachaphaza ngendlela efanelekileyo umz. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Buza imibuzo efana nale “Leliphi ikhadi elinezinto/amachaphaza amaninzi? -- Leliphi inani elingaphezulu kwe -2 njl-njl.

Ixesha lokufundisa ekucetyiswa into yokuba lisetyenziswe: IVEKI YE- 17 Iplani ekhokelwa ngutitshala enemisebenzi yeklasi eyimizuzu engama 30 ngosuku (5 ezemisebenzi ye mathematika ngeveki Izixhobo zokufundisa ekucetyiswa Ixesha CAPS ISIHLOKO Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 5.1 • Khulisa indlela yokusebenza ngolwazi oluqokelelweyo Usuku olu-1 Qokelela uze Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D uhlele izinto -- Abafundi mabaqokelele amasebe ali-9. -- Hlela amasebe ngokobuncinci nobukhulu. Abafundi baqokelela amasebe 5.2 Zoba igrafu ukubonisa ulwazi Bonisa ingqokelela Iimilo ezinokwakheka kuka 2-D okanye imifanekiso yezinto ezihleliweyo -- Yenza igrafu yemifanekiso enamasebe. -- Abafundi babeka amasebe kwigrafu yemifanekiso ngokobungakanani-ncinci/nkulu.   Amasebe Small amancinci twigs Amasebe twigs Largeamakhulu Iphepha lokufunda legrafu yemifanekiso. Utitshala uyilela abafundi iphepha lika A4 elinemiqolo efanelekileyo. 5 3 5.3 Xoxa uze unikezele Funda uze utolike igrafu ingxelo ngezinto Thetha ngeziphumo ngokubuza imibuzo umz.Mangaphi amasebe amancinci? Mangaphi ezihleliweyo amasebe amakhulu? Ngawaphi awona maninzi/mbala? 147 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha Lokufundisa Elicetyisiweyo : Iveki ye- 18 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isangqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) 148 Izixhobo zokufundis aekucetyiswa Ixesha Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Bethelela ulwazi olufunyenwe kuqukwa amanani 1, 2, 3 no -4 Usuku olu- 1 Bala izinto Ngomlomo: bala izinto zemihla ngemihla ukuya ku-4 Bala usiya phambili, ubale ubuya umva ukuya ku-4 Iingoma zamanani neemvano-siphelo Ukubala ngentloko ngokungena ntsingiselo 1-7 Bethelela isigama ‘ninzi” no “mbalwa” Qhwaba izandla kaninzi …….YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ka- 4. Ukufunda usebenzisa intshukumo yomzimba Abafundi maba: -- Cinezele inani-1 esibhakabhakeni besebenzisa iminwe. Itreyi /ibhokisi enesanti -- Abafundi mababambe iintloko zabo kabini. -- Babambe izandla nabanye abafundi abane. MATHEMATIKA IBANGA LABAQALAYO (R) -- Vala amehlo abafundi uthi mabachonge amanani 1-4 ngokulandela abakuvayo xa Iseti yonootsheluza bamagama (Iikhadi becinezela koonetsheluza bamagama zamanani) Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi maba: INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Zobe inani lokuqala esantini. Neziphi izinto -- Fumane u-3 kwizinto ezifanayo. Abafundi -- Xhuma-xhuma endaweninye kabini. Iiphazili zezijungqe ezi-4 -- Yakha iiphazili ngezijungqe ezi-4 nangaphezulu. 1.11 • Ukunakana nokuchonga imali eziinkozo/umwangalala yaseMzantsi Afrika Usuku olu- 1 Imali Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Yenza abafundi baqonde imifanekiso eyahlukileyo yezilwanyana nezityalo emalini 5c,10c,20c,50c,R1,00,R2,00 and R5,00 ezinkozo. imali ezinkozo (imali yokudlala okanye imali yakwenyani) -- Ukubekeleleka kwemali kungasetyenziswa kwikona yeZakhono zoBomi apho abafundi banokudlala khona ivenkile. Ngomdlalo abafundi baphicothe iindidi zemali eziinkozo.

Ixesha Lokufundisa Elicetyisiweyo : Iveki ye- 18 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isangqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) Izixhobo zokufundis aekucetyiswa Ixesha CAPS Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.7 Ukusombulula izibalo zokudibanisa nezokuthabatha ezichazwe ngomlomo ukuya Usuku olu- 1 ku-4 Ukudibanisa nokuthabatha Ngomlomo: bala izinto zemihla ngemihla ukuya ku-4 . Bala ukuya phambili, ubale ukubuya umva ukuya ku-4 . Iingoma zamanani neemvano-siphelo Ukubala ngentloko ngokungenantsingiselo 1-7 Bethelela isigama ‘ninzi” no “mbalwa” Qhwaba izandla kaninzi …….YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ka- 4.Ukufunda usebenzisa intshukumo Abafundi yomzimba Izinto zokubala Imizekelo: Iipensile -- Utitshala ubizela umfundi phambi kwekasi. Aphinde abize abanye abathathu. Ubize abafundi aBangaphi xa bebonke? -- Utitshala upakisha izinto zokubala ezithathu. Wongeza enye. Zingaphi izinto zokubala Sebenzisa iindidi ngeendidi zezixhobo eziphezu kwetafile? ukukunika amacebo okusebenzisa iindlela ezahlukileyo zokufundisa. -- Abafundi bama phambi kweklasi. Utitshala ucela umfundi omnye ahlale phantsi. Bangaphi abafundi abaphambi kweklasi ngoku? -- UBusi uneepensile ezi- 4. Unika uWelile iipensile ezi-2.UBusi ushiyeke neepensile ezingaphi? 149 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha Lokufundisa Elicetyisiweyo : Iveki ye- 18 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isangqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) 150 Izixhobo zokufundis aekucetyiswa Ixesha Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 • Landelelanisa uthelekise ingqokelela zezinto ngokusebenzisa “ninzi kune, mbalwa Usuku olu- 1 kune” no”lingana ne” ukuya kwinani lesi-4 Chaza,thelekisa uze ulandelelanise Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D amanani -- Utitshala unika ilungu ngalinye leqela inani elithile leekhrayoni. -- Amalungu eqela makachonge oyena mfundi oneekhrayoni ezininzi kwezabanye. -- Ngowuphi umfundi oneekhrayoni ezimbalwa kunezabanye ? -- Ngabaphi abafundi abanamanani alinganayo eekhrayoni ? iikhrayoni Ukusebenzisa iimilo ezinokwakheka kuka 2-D/imifanekiso -- Cwangcisa iiseti zoonotsheluza bamanani aquka amanani 1-5 ngokulandelelana, umzekelo, MATHEMATIKA IBANGA LABAQALAYO (R) 1 2 3 4 5 Oonotsheluza bamanani namachaphaza -- Buza imbuzo efana noku “ ngabaphi oonotsheluza abanezinto ezininzi ?” INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Leliphi inani elikhulu kune-2 ? njalo njalo,

Ixesha Lokufundisa Elicetyisiweyo : Iveki ye- 18 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isangqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) Izixhobo zokufundis aekucetyiswa Ixesha CAPS Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 2.1 • Khuphela ugqibezele ipateni enikiweyo ngemali eziinkozo/mwangalala. Imali yokudlala okanye imali yokwenyani Usuku olu- 1 (5c,10c,20c) Iipateni zejiyometri Khuphela ipateni enikiweyo -- Utitshala useta ipateni esebenzisa “ imali yokudlala” , umzekelo, 5c, 5c, 5c, 10c, 10c,10c,20c, 20c, 20c Abafundi maba: -- Khuphele iipateni ezininzi eziyilwe ngutitshala. Gqibezela ipateni enikiweyo Abafundi maba: -- Gqibezele iipateni ezininzi eziyilwe ngutitshala, umzekelo, o 5c, 5c, 10c, 10c,………… o 5c, 10c,……… o 10c, ,20c……….njalo njalo 151 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki ye- 19 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isanqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) 152 Izixhobo zokufundis aekucetyiswa Isihloko Amanqaku angcaciso Ixesha elisondeleyo ukuba zisetyenziswe 1.1 • Bethelela ulwazi olufunyenweyo oluquka amanani 1, 2, 3 no 4. Usuku olu- 1 Bala izinto Ngomlomo l: bala izibali zemihla ngemihla ukuya ku-4. Bala ukuya phambili, ubale ukubuya ukubuya umva ukuya ku-4. Ukubala ngentloko okungenantsingiselo 1-7 Iingoma zamanani neemvano-siphelo. Bethelela “ninzi” no “mbalwa” . Qhwaba izandla amaxesha amaninzi …….YIMA . Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba amatyeli ama- 4 Ukufunda usebenzisa intshukumo yomzimba Unotsheluza wesimboli yamanani enamanani 1-4 Utitshala uphakamisa unotsheluza wamanani onenani elingu-3 athi kubafundi: Umzekelo, -- Ndidinga amakhwenke alinani elithile. -- Ephakamise inani- 2 esithi, ndidinga inani lamantombazana alinani elithile. -- Yakhani amaqela (ephakamise inani-2). -- Phinda umsetyenzana ngoonotsheluza abanenani ku-1-4 3 MATHEMATIKA IBANGA LABAQALAYO (R) 1.16 Izibalo zentloko Iseti yoonotsheluza bemifanekiso namachaphaza ukusuka ku1-4 Izibalo zentloko Utitshala uphakamisa unotsheluza wenani -3 abuze abafundi: -- Leliphi eli nani? INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Leliphi inani eliza phambi kuka-3? -- Leliphi inani elilandela emva kuka-3? -- Phinda ngamanani u1-4 . -- Ungandibonisa na unotsheluza onenani elifana nenani lamachaphaza akulo unotsheluza?

Ixesha lokufundisa elicetyisiweyo: Iveki ye- 19 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isanqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) Izixhobo zokufundis aekucetyiswa Isihloko Amanqaku angcaciso Ixesha elisondeleyo CAPS ukuba zisetyenziswe 1.16 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Izibalo zentloko -- Utitshala uqhwaba ngesingqisho ngokucotha ukubonakalisa inani. Abafundi mabakhuphe amaso alingana nelo nani bawabonise, umzekelo, amaso a-4. Amaso ama-4 kumfundi ngamnye -- Abafundi mababeke amaso a-1, 2, 3 okanye 4 phambi kwabo. -- Abafundi mababonise ukuba mangaphi amaso abanayo ngokuwathelekisa nonotsheluza, umzekelo, amaso a-4 nenani -4. Oonotsheluza bamanani 1,2,3 no 4 -- Mabakhangele omnye umfundi onenani elifanayo lamaso. Oonotsheluza bamachaphaza Ukusebenzisa iimilo ezinokwakheka kuka 2-D/imifanekiso Utitshala uphakamisa unotsheluza wamanani enziwe ngamachaphaza wenani - 2 abuze kubafundi: 1 2 -- Mangaphi amachaphaza kulo notsheluza? -- La machaphaza amele eliphi inani? 3 4 -- Leliphi inani elilandela eli? -- Mababale elonani lamachaphaza emaphepheni abo. 153 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki ye- 19 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isanqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) 154 Izixhobo zokufundis aekucetyiswa Isihloko Amanqaku angcaciso Ixesha elisondeleyo ukuba zisetyenziswe 1.7 • Ukusombulula izibalo zokudibanisa nokuthabatha ngomlomo nezisombululo ukuya Usuku olu- 1 ku-4 Ukudibanisa nokuthabatha Ukufunda usebenzisa intshukumo yomzimba -- Bizela abafundi abathathu ngaphambili. Babale. -- Biza omnye umfundi. Bangaphi xa bebonke? 3 no 14 (untathu nonye banika 4) -- Buyisela abafundi aba -3 emva ekhapethni. Bangaphi abafundi abakhoyo ngoku? 4 thabatha 3→1 Yohlula abafundi ngokwamaqela. Izinto zokubala Buza imibuzo efana nale: -- Zingaphi iimpumlo ozibonayo eqeleni lakho? Sebenzisa iindidi zezixhobo ukwazi ukuba -- Mingaphi imilomo? namava okusebenzisa iindlela ezininzi -- Mingaphi imizimba: zokufundisa. -- Kubafundi ababini, mangaphi amehlo? -- Kubafundi ababini, mingaphi imilenze? MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: 1. Utata kaLindiwe unemoto. Mangaphi amavili akulo moto? 2. Xa kuphantshe ivili elinye lakhutshwa emotweni, kushiyeke amavili amangaphi? Izinto zokubala 3. Inkukhu inamantshontsho ama- 4. Ama- 2 alahleka. Mangaphi akhoyo enkukhwini? INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 4. Isikhukukazi sifumana amantshontsho aso ebelahlekile. Sinamantshontsho amangaphi ngoku?

Ixesha lokufundisa elicetyisiweyo: Iveki ye- 19 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isanqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) Izixhobo zokufundis aekucetyiswa Isihloko Amanqaku angcaciso Ixesha elisondeleyo CAPS ukuba zisetyenziswe 1.4 • Landelelanisa uthelekise iingqokelela zezinto ngokusebenzisa “ninzi kune, ncinci Usuku olu- 1 kune” ne “lingana ne” kwinani -4 Chaza,thelekisa uze ulandelelanise Ukufunda usebenzisa intshukumo yomzimba amanani -- Utitshala ubeka iindidi zeezinto phezu kwetafile, umzekelo, iikhrayoni ezimbini, iibhloko ezi-4 ezifanayo, iinkonkxa ezi-3, iincwadi ezi-2. Iikhrayoni, iibloko, iinkonkxa, iincwadi. Abafundi maba: -- Bale inani leekhrayoni neenkonkxa. Ingaba iikhrayoni zininzi kuneenkonkxa? -- Bale inani leebloko neleencwadi. Ingaba iibhloko zimbalwa kuneencwadi? Ingaba iibhloko zininzi kuneencwadi? -- Bale inani leencwadi neleekhrayoni. Ingaba ayalingana amanani ezinto okanye hayi? Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Abafundi mabahlale ekhaphethini banikwe inani lezinto zokubala umfundi ngamnye. -- Umfundi ngamnye makabe nenani elahlukileyo lezinto zokubala. Izinto zokubala -- Abafundi mababeke izinto zokubala phambi kwabo. Utitshala ubuza abafundi: Utitshala unika umfundi ngamnye izinto zokubala zamanani ahlukileyo ukuya ku-4 o Ngoobani abanezinto zokubala ezininzi? o Ngoobani abanezinto zokubala ezimbalwa? o Ngoobani abanezinto zokubala ezilinganayo? 3.3 Nakana, chonga, uchaze imilo ezinokwakheka kuka 2-D eklasini nakwimifanekiso imizobo yabafundi Usuku olu- 1 Izinto • Yila ugqibe iphazili yezijungqe ezi- 4 ezinokwakheka (Nxibelelanisa noBuchule boKubonwayo) kuka 2-D Abafundi maba: -- Zobe umfanekiso ephepheni le A4. -- Utitshala uzoba imigca emva komzobo womfundi. -- Umfundi usika umfanekiso kwimigca ebonisiweyo. -- Umfundi ugqibezela/wakha eyakhe iphazili. 155 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki ye- 19 Umsetyenzana omnye weplani ekhokelwe ngutitshala (isanqa) owe ± 30 imizuzu ngosuku (± 5 imisetyenzana yeMathematika ngeveki) 156 Izixhobo zokufundis aekucetyiswa Isihloko Amanqaku angcaciso Ixesha elisondeleyo ukuba zisetyenziswe 4.1 • Yakha ukuqwalasela okwenzekayo phakathi kwesidlo sasebusuku nexesha lokulala Imifanekiso ebonisa okwenzekayo Usuku olu- 1 ukusuka ngexesha lesidlo sasebusuku Ixesha (Nxulumanisa nezihloko zoLwazi olusisiseko kwiZakhono zoBomi) ukuya kwixesha lokulala. Abafundi maba:   -- Thethe ngabakwenzayo emva kwesidlo sasebusuku. -- Thethe ngokwenzekayo emakhaya emva kwesidlo sasebusuku. Utitshala ubuza: -- ‘’ uza esikolweni ekuseni okanye ebusuku?” -- Ukuba uNcedo ufika esikolweni emva kokukhala kwentsimbi, ufike emva kwexesha okanye phambi kwexesha? -- Ilanga libaphi ebusuku?” Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Iphepha neekhrayoni -- Abafundi bazoba umfanekiso ukubonisa nayiphi into eyenzeka emva kwesidlo sasebusuku. -- Nika iiphazili ezibonisa ukulandelelana kweziganeko/imisebenzi. MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Iveki yama- 20 Sebenzisa iveki yama- 20 ukuhoya izithinteli kufunda Umxholo Isihloko Iindlela zokuHlola Amanani, ii- 1.1 Qikelela nokubala ngentloko ngokungenantsingiselo ukuya ku-7 (iingoma zamanani nezicengcelezo CAPS opareyishini eziquka ukukhulisa ingqiqo yamanani) Bala izinto noLwalamano Bala ubuya umva nokubala usiya phambili (1-4) Qonda iingqiqo “ninzi no mbalwa” (ukuqhwaba) Nakana amanani kwiimeko eziqhelekileyo,umzekelo, inani lendlu, idilesi Chonga imifanekiso yamanani namakhadi anamachaphaza Zazi iisimboli zamanani 1, 2, 3 ,4 Nakana amagama amanani u-bini, ntathu kunye no-ne Qonda ukuhambelana kwamanani (Itshati yabancedisi ngexesha lokutya) Yahlula phakathi kuka ninzi, ncinci, linganayo, ninzi nombalwa ukuya ku-4 Nakana iindidi zemali eziinkozo zaseMzantsi Afrika 1.6. Sebenzisa izixhobo ezibonakalayo Ubuchule/iindlela zokusombulula iingxaki Chaza iingcinga zakho ngamagama nangemizobo okanye izinto ezibonakalayo zezibalo 1.7. Sombulula iingxazi zokudibanisa nokuthabatha ngomlomo Ukudibanisa nokuthabatha IiPateni 2.1. Kopa, yandisa, uze uyile iipateni zakho (izinto, iimilo nemali yenkozo) neeFankshini Iipateni zejiyometri 157 MATHEMATIKA IBANGA LABAQALAYO (R)

Iveki yama- 20 Sebenzisa iveki yama- 20 ukuhoya izithinteli kufunda Umxholo Isihloko Iindlela zokuHlola 158 Isithuba nemilo 3.1. Qonda indawo-bume yenzinto ezimbini nangaphezulu ngokunxulumene nomfundi (Ijiyometri) Indawo-bume,ukufumana indawo nembonakalo ngaphezulu ,ngaphantsi 3.2. Yakha iphazili ubuncinane ezili-12 Iimilo enokwakheka kuka 2-D Bonakalisa ulwazi lokwahlula phakathi kwezinto ezingaphambili nezingasemva (phinda uhlole) Nakana, chonga uxele oonxantathu Qonda imilo kanxantathu (ukuqonda iimilo) 3.2 Thelekisa yeyiphi kwezimbini ezinikiweyo iingqokelela yezinto ezinde,ezindana; mfutshane/ mfutshanana .Izinto ezinokwakheka kuka 3-D Hlela izinto ngokobukhulu- ubude nobufutshane Imibala –(bomvu, mthumbi, bhlowu noluhlaza) Imilo Sebenza ngobuchule ngeebhloko ezakhayo 3.4 Nakana umgca wolingano- macala kuye nakokumngqongileyo MATHEMATIKA IBANGA LABAQALAYO (R) Ulingano- macala Ukukwazi ukuwela umgca ophakathi Umlinganiso 4.1 Qonda iintsuku zeveki, amaxesha onyaka netshati yemozulu (iingoma nezicengcelezo – phinda uhlole) Ixesha Yazi usuku lwakhe lokuzalwa (phinda uhlole) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 4.2 Ukwahlula phakathi kweyona inde, eyona imfutshane, endana, emfutshanana (itshati yobude) Ubude Ukusebenza 5.1 Ukwazi ukuqokelela, ukuhlela, ukuzoba, ukufunda nokubonisa (calula) izinto ngongophawu oluye ngolwazi Qokelela uze uhlele izinto oluqokelelweyo. 5.2 Bonisa ingqokelela yezinto ezihleliweyo 5.3 Xoxa uze unike ingxelo ngengqokelela yezinto ezihleliweyo

IKOTA YESI- 3 IMATHEMATIKA ISIGABA SABAQALAYO Ixesha lokufundisa elicetyisiweyo: Iveki yama - 21 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) CAPS Izixhobo zokufundisaekucetyiswa Ixesha Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.1 • Fundisa intsingiselo yenani 5 usuku olu- 1 Ukubala izinto Ngomlomo: Bala izinto zemihla ngemihla ukuya ku -5. Iingoma zamanani nezicengcelelzo Bala ukuya phambili nokuya emva ukuya ku -5. Ukubala imvano-siphelo neengoma, umzekelo, ”Iimfenana ezintathu Bala ngentloko ngokungenantsingiselo 1-10 zixhumaxhuma phezu kwebhedi”. Bethelela ukubala ngolandelelwano: Utitshala ubala izinto ezi- 3 ngokulandelelana. Khomba kwizinto nganye ubala eyokuqala, Izinto ezi-3 eyesibini, eyesithathu. Bethelela isigama “ninzi” no”mbalwa”. Qhwabani izandla kaninzi…..YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba izandla ka- 5. Buza inani eliqhwatywe kaninzi okanye kambalwa Ukufunda usebenzisa intshukumo yomzimba Khuthaza abafundi ukufumana inani -5 ngoku: -- Qhwaba izandla ka -5. -- Fumana ukuba bangaphi abafundi eklasini abane minyaka e -5. 159 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki yama - 21 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 160 Izixhobo zokufundisaekucetyiswa Ixesha Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.16 Ukubala ngentloko usuku olu- 1 Izibalo zentloko -- Utitshala uqhwaba izandla zakhe ngesingqi engangxamanga kahlanu ukubonisa inani Izikhongozeli ezinezinto zokubala -5. Abafundi mabakhuphe inani lezinto zokubala ezi - 5 bazibonise. -- Abafundi bapakisha izinto zokubala ezi- 5 ngokulandelelanayo bazibale. -- Utitshala uyabuza: -- Leliphi inani eliza phambi kwenani -5? -- Leliphi eliza emva ko-4, njalo njalo? -- Xa unee- apile ezi-5 waphisa ngezi -2,zingaphi ezishiyekileyo? -- Bonisa ngeminwe. -- Uneenzwane ezingaphi kunyawo olu-1? Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi bakha ulwazi lwamanani ngo: -- Kwakha inani -5 besebenzisa udongwe lokudlala. MATHEMATIKA IBANGA LABAQALAYO (R) -- Chola amagqabi a-5. -- Bala izinto bezitshatisa nezinto zokubala. -- Yakha uqwalaselo lokulondoloza amanani ngokuthi abafundi maba -- Pakishe izinto zokubala ezi- 5 okanye ezinye izinto ngeendlela ezahlukileyo,umzekelo, INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Udongwe okanye udongwe lokudlala Amagqabi Xa kubalwa inani lezinto alichatshazelwa bubukhulu balo, okanye indawo, okanye luhlobo olunye, umzekelo, -- Cwangcisa amaqhosha a-5, iipensile ezi-5, iihula-hupu ezi-5, abafundi aba-5, njalo njalo. -- Zibale ngendlela eyahlukileyo,umzekelo, zibale zisasazekile, zidibene, zisemgceni okanye zipakishiwe

Ixesha lokufundisa elicetyisiweyo: Iveki yama - 21 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Izixhobo zokufundisaekucetyiswa Ixesha CAPS Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.4 • Khulisa ukukhumbula uze ukhuthaze abafundi ukukhumbula ngentloko amanani usuku olu- 1 ezindlu, iidilesi neenombolo zefowuni. Chaza,uthelekise uze ulandelelanise Dlala imidlalo enje ngale ilandelayo: amanani -- Utitshala ubiza inani lendlu, idilesi okanye inombolo yefowuni yomfundi. Umfundi elilelakhe inani lendlu okanye idilesi kufuneka aphendule. -- Xa utitshala esenza irejista yabafundi abakhoyo makabuze imibuzo efana nale: “ Ifowuni makube yeyomzali yaye ingaba umfundi oneli nani lefowuni ukhona namhlanje: 435-6256?” “ ingaba umfundi isenokuba yinombolo yecell phone ohlala eMandela Drive 123 ukhona namhlanje?” Irejista yobukho . -- Abafundi basebenzisa oonotsheluza beesimboli zamanani ukupakisha amanani abo ezindlu okanye awefowuni ngokulandelelana nokuba ayichanekanga. Unotsheluza weesimboli zamanani okanye iisimboli zamanani ezinkulu -- Linganisa iincoko kwifowuni yokudlala. Abafundi bafowunela umntu obalulekileyo. ezenziwe ngekhadibhodi. Nxulumanisa nobuchule bokwenza(idrama) kwiZakhono zoBomi Ifowuni yokudlala Ukusebenzisa iimilo enokwakheka kuka 2-D/imifanekiso Amakhadi eentsuku zokuzalwa Utitshala ubonisa abafundi: Amaphephandaba, iimagazini -- Iindidi zemidiya apho kufumaneka inani -5,umzekelo, oonotsheluza beentsuku Oonotsheluza abanamachaphaza ama-5 zokuzalwa, amaphepha –ndaba, iimagazini, iiflaya, umzekelo, njalo njalo. Oonotsheluza abanemifanekiso emi- 5 -- Unotsheluza onamachaphaza ama -5 nonotsheluza wemifanekiso emi-5. ezinto -- Abafundi mabahlanganise unotsheluza wemifanekiso nowamachaphaza ngamanani Izinto zokubala alinganayo ezibali okanye izinto. -- Yakha iiphazili zamanani ezinenani -5,umzekelo Umfanekiso   wezinto Picture ezi-5 of 5   objects 5   161 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki yama - 21 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 162 Izixhobo zokufundisaekucetyiswa Ixesha Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 1.3 • Zazi iisimboli zamanani namagama amanani eziquka inani -5 Usuku olu- 1 Iisimbolo Ngomlomo: Bala ukuya phambili nokubuya umva ukuya ku-5 zamanani kunye Ukubala ngentloko ngokungenantsingiselo 1-10 namagama amanani Ukufunda usebenzisa intshukumo yomzimba Iingoma zamanani neemvano-siphelo -- Iklasi yonke mayihlale kwisangqa. -- Nombola abafundi ngokwepateni. 1, 2, 3, 4, 5 1, 2, 3, 4, 5 -- 1, 2, 3, 4, 5 . -- Buza imibuzo enje ngale; “ ngubani ozakuba yinombolo-5 elandelayo ? “ ngubani ozakuba yinombolo-4 elandelayo? -- Uyisombulule njani le ngxaki? -- (Abafundi basombulula ingxaki ngendlela yokucingela inani elilandelayo ngokuqhubekeka ngokubala) Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D MATHEMATIKA IBANGA LABAQALAYO (R) -- Sebenzisa amakhadi amanani aviwa ngesandla (itactile number cards) eziquka Amakhadi amanani aviwa ngesandla amanani 1-5. (Tactile number cards) ngenani -5 -- Abafundi bavala amehlo beve inani- 5 ngokusebenzisa iminwe kwiisimboli zamanani. Nika abafundi izinto zokubala ezi-5 umfundi ngamnye neekomityi ezimbini okanye izikhongozeli ezibini zamaqanda. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Buza abafundi: “ ungazicwangcisa njani ezi zinto zokubala kwizikhongozeli ezibini?   okanye njl njl.

Ixesha lokufundisa elicetyisiweyo: Iveki yama - 21 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Izixhobo zokufundisaekucetyiswa Ixesha CAPS Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo Ukusebenzisa iimilo okanye imifanekiso enokwakheka kuka 2-D Yenza abafundi ba: Oonotsheluza bemifanekiso, amachaphaza, iisimboli zamanani -- Chonga oonotsheluza abanemifanekiso emi-5 . nezamagama amanani -- Chonga oonotsheluza abanamachaphaza ama-5. Izibali ezi-5 -- Chonga isimboli -5 apho ibonakala khona eklasini. Um- -- Chonga isimboli yenani kunotsheluza. fanekiso Nakana igama lenani kunotsheluza. wezinto Ntlanu ezi-5 -- Hlanganisa inani lesibali negama lenani nesimboli yenani ngokupakisha into yokubala kunotsheluza ngamnye womfanekiso nowamachaphaza . 3.4 • Ukubethelela umgca wolingano- macala kuye ngokwenza izinto ezikhuthazela Usuku olu- 1 ukuwelwa komgca ophakathi Ulingano-macala Ukufunda usebenzisa intshukumo yomzimba Emva koko, Abafundi maba: ngokuqhubekayo ngexesha lokudlala -- Dlala umdlalo wokulandela inkokheli apho abafundi balinganisa ubume kwitshati. nangexesha -- Dlala umdlalo wokulandela inkokheli apho utitshala abonisa ubume nabafundi lemisebenzi bamlinganise. (iquka ukuwela umgca ophakathi, umzekelo, phatha idolo lasekhohlo yokukhulisa ngesandla sasekunene) umzimba -- Dlala umdlalo wokulandela inkokheli apho umfundi abonisa ubume abanye bamlinganise. -- Utitshala ubonisa ukutsiba-tsiba nabafundi bakhuthazwe ukulinganisa utitshala. Ukusebenzisa zinto eziphathakayo ezinokwakheka kuka 3-D Abafundi maba: -- Beke ibhinbhegi ekhohlo, ekunene,ngaphambili nangasemva komzimba. -- Sebenzise isandla sasekhohlo ubeke ibhinbhegi ngasekunene komzimba wakhe. -- Zolule ukwela umgca ophakathi. -- Phinda enze ngesandla sasekunene. Nxulumanisa nemiThambo kwiZakhono zoBomi 163 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki yama - 21 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 164 Izixhobo zokufundisaekucetyiswa Ixesha Isihloko Amanqaku angcaciso ukuba zisetyenziswe elisondeleyo 4.2 • Qikelela ulinganise ubude bezinto ezahlukileyo usebetyenzisa iinyawo, izandla, Usuku olu- 1 umtya, amakhuni, njl njl. Ubude Ukufunda usebenzisa intshukumo yomzimba Abafundi maba: -- Thelekise ubude beenyawo nezandla zabo . -- Abafundi mabaqikelele yeyiphi izinto ende yeyiphi emfutshane ngokulinganisa iinyawo Izinto ezinobude obuhlukeneyo okanye izandla zabo,umzekelo, itafile okanye isijungqe sethumbu lasekhaya. ezinokulinganiswa ngesandla okanye -- Qikelele ukuba yeyiphi into ende kakhulu okanye emfutshane kakhulu, umzekelo, ngeenyawo,umzekelo, irula, itafile, indlela yeenyawo okanye umgca wezitena. ucango, izitena, ipali yeempondozebhola, iklasi, ilayibhrari, njl. njl. -- Abafundi mabaqikelele ukuba yeyiphi ende kunenye, umzekelo, iklasi okanye igumbi lootitshala. -- Buza imbuzo enje nge: “yeyiphi endana/ende kakhulu, ipensile okanye umtya? MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyisiweyo Iveki yama- 22 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Ixesha CAPS Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 1.1 • Ukubethelela ulwazi olufumanekayo oluquka inana u- 5 usuku olu- 1 Bala izinto Ngomlomo: Bala izinto zemihla ngemihla ukuya ku -5 Bala ukuya phambili nokubuya umva ukuya ku -5 Iingoma zamanani nezicengcelezo umzekelo, Ukubala ngentloko okungenantsingiselo 1-10 Bethelela isigama “ninzi” no “mbalwa ”. Izicengcelezo neengoma zokubala Qhwaba izandla amatyeli amaninzi........YIMA. “1,2,3,4,5 ” Qhwaba izandla kambalwa. Utitshala uqhwaba kahlanu Buza umbuzo:” Leliphi inani elibe lininzi/elibe mbalwa lokuqhwaba?” Ukufunda usebenzisa intshukumo yomzimba Khuthaza abafundi ukufumana inani -5 ngoku: -- Bonisa iminwe emihlanu emoyeni. Izinto zokubala -- Fumana izinto ezi-5 ezibomvu, bhlowu, mthubi, luhlaza. -- Fumana izinto ezi -5 ezibonakala okwesangqa, isikwere, unxantathu. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi mabakhe ulwazi lwamanani ngoku: Iincwadi -- Landa iincwadi ezi-5 kwikona yeencwadi Iibhoko zokwakha okanye iityhubhu zeyunifekisi (unifix tubes) -- Ukwakha iincochoyi ngeebhloko ezi-5. 165 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo Iveki yama- 22 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 166 Ixesha Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 1.7 • Ukusombulula iingxaki zezibalo ngomlomo (izibalo zamazwi)nokucacisa usuku olu- 1 izisombululo kwiingxaki eziquka inani -5 Ukudibanisa nokuthabatha Ukufunda usebenzisa intshukumo yomzimba: -- Bizela abafundi aba-5 ngaphambili. -- Yabela abafundi aba-5 izitulo ezi-5 ngokulinganayo. -- Thatha isitulo esinye. Yaba izitulo ezishiyekileyo kubafundi abahlanu. Umfundi omnye ushiyeka engena situlo. -- Qala ku-5. Bala ubuya umva. Qala ku -3. Balela ku -5. Qala ku-1. Balela ku-4 , njl njl. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Imizekelo: 1. Bonisa umnwe omnye kwisandla esinye neminwe e-4 kwesinye isandla. Yiminwe emingaphi xa iphelele? 2. USandla unamaqebengwane ama- 4. UMpho umnika eli-1 kwakhona.USandla Izinto zokubala unamaqebengwane amangaphi xa ewonke? MATHEMATIKA IBANGA LABAQALAYO (R) Iimabhule (marbles) 3. UTini unamatye ama -5 wawanika uMiya onke. UMiya unamatye amangaphi ? Ingoma 4. UJama uneemabhule ezi- 5 walahla ezi- 2. Ushiyeke neemabhule ezingaphi? 5. Ikati enye ineendlebe ezimbini. Iikati ezimbini zineendlebe ezingaphi? 6. Ingoma, “Amahotyazana mahlanu emthini ” (cacisa ukuba amahobe ayehla ngenani). INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyisiweyo Iveki yama- 22 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Ixesha CAPS Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 1.4 • Thelekisa ukuba yeyiphi ingqokelela yezinto ezinikiweyo ezininzi kune, ezimbalwa Usuku olu- 1 kune, ezilinganayo ukuya ku-5 Chaza,uthelekise uze ulandelelanise Ngomlomo: Bala izinto zemihla ngemihla ukuya ku-5 amanani Bala ukuya phambili, ubale ubuya umva ukuya ku- 5 Bala ngentloko okungenantsingiselo 1-10 Iingoma zamanani nemvano-siphelo Bethelela isigama “ninzi” no-“mbalwa ”. Qhwaba izandla amatyeli amaninzi........YIMA. Qhwaba izandla kambalwa. Utitshala uqhwaba kahlanu Buza umbuzo:” Leliphi inani elibe lininzi/elibe mbalwa lokuqhwaba?” Ukufunda usebenzisa intshukumo yomzimba -- Utitshala ubeka izinto ezininzi phezu kwetafile, umzekelo, ziimagi ezi-2, iibhloko ezi-5 ezifanayo, izikhongozeli ezi-4, iincwadi ezi -2. Abafundi maba: -- Bala inani leemagi nezikhongozeli. Ziimagi okanye zizikhongozeli ezininzi? Imagi ezi-2, iiblokhi ezifanayo ezi-5, -- Bala inani leebhloko neleencwadi. Zimbalwa iibhoko kuneencwadi? Zininzi iibhoko izikhonkozeli ezi-4, incwadi ezi-2. kunencwadi? -- Bala iincwadi neemagi. Ziyalingana izinto okanye hayi? Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Izijungqe ezibini zewulu zomfundi -- Abafundi bahlala ekhaphethini benze iinesi ezimbini ngewulu. ngamnye -- Utitshala unika umyalelo, umzekelo, abafundi bafake izinto zokubala ezibini Izinto zokubala ezi-6 zomfundi ngamnye kwenye inesi, baphinde bafake ezintathu kwenye. Yeyiphi inesi enezininzi? Yeyiphi   enezimbalwa? -- Utitshala ubizela abafundi aba-5 phambi kweklasi. Ufaka inani elahlukileyo lamaso ezandleni zomfundi ngamnye. -- Sesiphi isandla esinamaso amaninzi? -- Sesiphi isandla esinamaso ambalwa? Amaso Izinto ezikwimilo enokwakheka kuka 2-D/imifanekiso -- Utitshala ubonisa amakhadi amabini anamanani ahlukileyo amachaphaza Oonotsheluza bemifanekiso nemifanekiso. nabamachaphaza abaquka amanani 1 - 5 167 -- Abafundi bathelekisa amakhadi anemifanekiso namachaphaza achonge ukuba nkulu kune, mbalwa kune nokulingana. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo Iveki yama- 22 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 168 Ixesha Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 2.1 • Bethelela ukukhuphela ipateni enikiweyo Usuku olu- 1 Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba -- Ukusebenza ngamaqela bakhuphele ipateni enikiweyo, umzekelo, umfundi, isitulo, umfundi, isitulo. -- Abafundi ababini, isitulo esinye, abafundi ababini, isitulo esinye. Abafundi -- Ngqisha ngonyawo olunye, ngqisha ngolunye unyawo, xhuma-xhumela phambili, Izitulo xhuma-xhumela emva Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Utitshala uyila ipateni esebenzisa izinto zokubala neziciko zeebhotile, umzekelo, isibali, Izinto zokubala isibali, isiciko sebhotile, isibali, isibali, isiciko sebhotile. Abafundi bakhuphela ipateni. Iziciko zeebhotile -- Hamba kancinci, kancinci, msinya, msinya. (utitshala uthetha ehamba) Abafundi bakhuphela ipateni. Ukusebenzisa iimilo enokwakheka kuka 2-D/imifanekiso -- Yohlula abafundi kumaqela amahlanu. Nika iqela ngalinye imifanekiso yokwenza MATHEMATIKA IBANGA LABAQALAYO (R) ipateni. -- Abafundi bayila iipateni zabo zemifanekiso usebenzisa imifanekiso enikiweyo, Imifanekiso nayiphi efumanekayo, umzekelo, umzekelo, iintengiso. o Iorenji iapile, iapile, iorenji Phinda phinda imifanekiso ukuqinisekisa o Ibhabhathane, ibhabhathane, inyozi, inyozi. ukuba zanele. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Lo msebenzi unganxulumaniswa noBugcisa bokubonwayo kwiZakhono zoBomi

Ixesha lokufundisa elicetyisiweyo Iveki yama- 22 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Ixesha CAPS Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 3.3 Qwalasela, chonga uxele iimilo ezinokwakheka kuka 2-D eklasini nasemifanekisweni. isikwere emgangathweni/phantsi Usuku olu- 1 Iimilo • Bethelela ulwazi olufunyenwe kwiveki yesi-6 equka isikwere ezinokwakheka Nxulumanisa neMithambo kwiZakhono zoBomi kuka 2-D Ukufunda usebenzisa intshukumo yomzimba -- Zoba isikwere phantsi uvumele abafundi batsiba-tsibe kuso. Abafundi mabathi: “ nditsiba-tsiba eskwerini – icala elinye, amacala amabini, amacala amathathu, amacala amane, onke amacala ayafana ” -- Abafundi mabalale engceni/ ekhaphethini intloko yomnye ibe sezinyaweni zomnye benze isikwere. -- Amaqela abafundi mabalale ekhaphethini ukwenza izikwere ezincinci. Ukusebenzisa izinto ezinokwakheka kuka 3-D -- Utitshala uzoba igridi phantsi. -- Vaka imilo yokwenyani, umzekelo, iimilo zeLogi, okanye imifanekiso yemilo kwibhoko nganye. -- Utitshala ubiza imilo. Ibhinbhegi -- Abafundi balahlela ibhinbhegi phakathi kwebhoko ehambelana nemilo ebiziweyo . Ukusebenzisa iimilo okanye imifanekiso enokwakheka kuka- 2-D Iikhadibhodi ezimbini zezikwere esinye Abafundi mabahlulahlule indidi zezikwere ezilungiswe ngutitshala ngobukhulu nangemibala. sibhlowu esinye siluhlaza. -- Abafundi maba: Ikhadibhodi eziphakathi -- Chonge izikwere ngobukhulu bazo ngokuchaza izikwere ezikhulu, ezincinci ngokobungakanani zezikwere ezi-2 neziphakathi. esinye sibhlowu esinye siluhlaza. -- Chonge imibala yeendidi zezikwere . Iikhadibhodi ezincinci kakhulu zezikwere ezi-2 esinye sibhlowu esinye siluhlaza. Hlela izinto ngokwemilo, ubungakanani nombala • Hlela iindidi zezinto ngokombala nangemilo 169 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki yama- 23 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 170 Ixesha Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 1.1 • Ukubethelela ulwazi abalufumanekayo olubandakanya amanani u-1 ukuya kwi -5 usuku olu- 1 Bala izinto Ngomlomo: Bala izinto zemihla ngemihla ukuya ku -5 Bala ukuya phambili, ukubala ubuya umva ukuya ku -5 Khetha imsebenzi embalwa Bala ngentloko okungenantsingiselo 1-10 Iingoma zamanani nezicengcelezo Bethelela isigama “ninzi” no “mbalwa ”. Qhwaba izandla amatyeli amaninzi........YIMA. Qhwaba izandla kambalwa. Utitshala uqhwaba ka- 5 Buza umbuzo:” Leliphi inani elibe lininzi/elibe mbalwa lokuqhwaba?” Ukufunda usebenzisa intshukumo yomzimba Abafundi maba: -- Utitshala udlala igubu . -- Abafundi bayahambahamba. Igubu MATHEMATIKA IBANGA LABAQALAYO (R) -- Xa igubu liyeka ukubetha, utitshala ukhwaza inani eliphakathi kuka- 1 no- 5. -- Abafundi bazicwangcisa ngokwamaqelana, umzekelo, utitshala ukhwaza inani -3 abafundi bazicwangcise kumaqela esi-3. Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Utitshala ubeka izinto phezu kwetafile ziyimfumba. Abafundi mabaqikelele ukuba INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA zingaphi izinto ezikwimfumba. -- Mabazibale emva koko.

Ixesha lokufundisa elicetyisiweyo: Iveki yama- 23 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Ixesha CAPS Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 1.6 Masidlale: Ubuchule Utitshala uyila ileli yamanani phantsi. Inani eliselelini limela inani lendlu umfundi ahlala bokusombula kuyo. iingxaki zezibalo 0 1 2 3 4 5 Utitshala ukhetha abafundi abasebenzisa imvano-siphelo wanika umyalelo: -- Qala eqandeni. Cacisa ukuba iqanda lithetha ukuba “akukho nto” yaye ukubala kuqala ku -1 . -- Bala ngeli xesha uhambayo. -- Utitshala uthi kumfundi: “ ukwindlu yesi-2, yeyiphi indlu elandela indlu yesi-2? Isicengcelezo sokubala: -- Imiyalelo egqithayo ingathi: “ yiya kwindlu yesi-3. Buyela emva kwindlu yesibini. Yiya phambili kwindlu yesi-4. 1, 2, 3, 4, 5, -- Utitshala uthi: “ ndikwindlu yesi- 3, yeyiphi elandelayo?” Xa ndibambise intlanzi -- Yiya kwindlu yesi- 4. Hambisa inani elinye phambili. Hambisa amanani amabini emva. 6, 7, 8, 9, 10 -- Yima phambi kwendlu yesithathu neyesi-5. Ndayikhulula kwakhona 1.4 • Sebenzisa inani -5 kwimeko eqhelekileyo Usuku olu- 1 Chaza,thelekisa Ukuphuhlisa inkumbulo, khuthaza abafundi uku: uze ulandelelanise -- Khumbula iifowuni zikamama nootata babo. Ifowuni kamama okanye ekatata nedilesi amanani yasekhaya -- Khumbula iidilesi zamakhaya abo. -- Iifowuni maziphindaphindwe ngexesha lerejista yobukho yemihla ngemihla. 3.2 • Yakha izinto ezikwakheka kuka 3-D kusetyenziswa imatheriyali ephathekayo Usuku olu- 1 Izinto -- Abafundi basebenzisa umzekelo katitshala. Utitshala unika imiyalelo elandelayo: Ibhloko ezakhayo/ Iibhloko zeLego Iyaqhubekeka ezinokwakheka -- Yakha incochoyi elingana neyam ngokuphakama. Nasiphina isixhobo sokwakha kuka -3-D -- Yakha incochoyi engaphantsi kweyam. -- Yakha incochoyi ephakame kuneyam. -- Abafundi mabakhe esabo isakhiwo ngokukopa kumzekelo onikiweyo. 171 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyisiweyo: Iveki yama- 23 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) 172 Ixesha Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 3.1 Ukulandela izalathiso ukuhamba okanye ukuzibeka kwisithuba esithile Usuku olu- 1 Indawo-bume • Phuhlisa ulwazi lwezalathiso ngokufundisa isigama “phambili “ “nasemva” ukufumana indawo Ukufunda usebenzisa intshukumo yomzimba nembonakalo -- Njengentshayelelo, bethelela ulwazi olufunyenweyo kwiiveki ezisibhozo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Zoba isangqa esikhulu, unxantathu okanye isikwere ephetshaneni ulibeke phantsi. -- Abafundi maba: Imilo emikhulu ezotywe ephetshaneni -- Qhube imoto yokudlala kwimigca yesikwere abafundi baxele icala eya ngakulo imoto Imoto yokudlala (phambili nasemva ,ukhohlo nasekunene usebenzisa ingalo ukubonisa ukhohlo nokunene) Iimilo ezinokwakheka kuka 2-D okanye imifanekiso Imifanekiso ebonisa amacala ngokucacileyo, umzekelo, icala imoto eya -- Abafundi mabaqhele isigama Sika- phambili nesika- emva ngokubonisa amacala ngakulo, icala umntu ahambela ngakulo. emifanekisweni, umzekelo, icala imoto eya ngakulo, icala umntu ahambela ngakulo. MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyisiweyo: Iveki yama- 23 Iplani enye yomsebenzi weklasi okhokelwe yititshala (isanqa) ye ± 30 imizuzu ngosuku (± 5 imisebenzi yeMathematika ngeveki) Ixesha CAPS Isihloko Amangqaku angangcaciso Izixhobo ezicetyisiweyo elisondeleyo 4.2 Ukuthelekisa nokulandelelanisa izinto eziphathekayo esebenzisa isigama i intsuku ezi- 2 esifanelekileyo ukuchaza ubude Ubude • Ukuqikelela ubude bezinto ezahlukileyo okanye Ukufunda usebenzisa intshukumo yomzimba -- Abafundi bazicwangcisa ngobude ukusuka komfutshane ukuya komde. Thelekisa khetha kuphela ubude babo nabanye abafundi. imisetyenzana -- Dlala umdlalo wokulandela inkokheli. Oyena mde wenza isenzo abanye bamlinganise embalwa bengasemva kwakhe. Jika umgca ukuze omfutshane ibe nguye ongaphambili. -- Abafundi mabathelekise izandla neenyawo zabo ukuze babone ukuba zezoobani ezinde kakhulu nezimfutshane kakhulu. Qikelela uthathe umlinganiselo: Izinto zobude obahlukeneyo njenge: -- Abafundi baqikelela izinto- ende kwemfutshane, umzekelo, ubude betafile okanye Ipensile, ikhrayoni, izijungqe zomtya isijungqe somtya. (omnye ube usongiwe), itafile, iincwadi, -- Qikelela izinto - ende nemfutshane,umzekelo, ipensile, ikhrayoni . imicinga, Ipaperclips (ezisongiweyo, ezivuliweyo nezijijeneyo)njl njl. -- Abafundi mabathelekelele, yeyiphi into enokuba nde kwenye, umzekelo, imicinga emibini edityaniswe ngobude okanye ikliphu zemali ezintathu ezidityanisiweyo. -- Buza le mibuzo: “ yeyiphi endana/ende, ipensile okanye isijungqe somtya? ” njl njl. -- Sesiphi isitulo esikude kakhulu ukusuka edesikeni katitshala ? -- Zingaphi iipensile ezinokungena kwicala elide ledesika katitshala ? -- Mangaphi amanyathelo owathathayo ukuya emnyango ? -- Zingaphi iibhokisi zematshisi ezinesanti ezinokungena kule bhokisi? -- Zingapihi iikomityi zamaqanda ezinamanzi ezinokuzalisa le glasi? -- Naba abafundi abathathu nezitulo ezine. -- Zingaphi izitulo esizidingayo? 173 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 24 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 174 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.1 • Fundisa intsingiselo yenani u- 6 Usuku olu-1 Bala izinto Ngomolomo: Bala izinto zangemihla ngemihla uye kuma ku- 6. Bala usiya phambili ubale ubuya umva uyokuma ku-6. Amaculo nezicengcelezo zamanani. Ukubala ngentloko ngokungenantsingiselo 1-10 Ukubethelela indawo yenani/into kwiseti: ootitshala bapakisha izinto ezi- 3 emgceni. Khomba kwinto nganye eli xa ubalayo ;eyokuqala, eyesibini, eyesithathu Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Zenzele awakho amakhadi amakhulu Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 6 eesimboli zamanani, abafundi abakwazi ukuwabamba. Banokufunda iminyaka Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? yabo, iiflethi/ inombolo zasemakhayeni Ukufunda usebenzisa intshukumo yomzimba abo/ iinombolo zemfono- mfono/ inombolo zoonomyayi zabazali babo, nezinye. Abafundi maba: Le seti inye ingaphinda isetyenziswe -- Bala ukuya ku-6 logama unyuka amanqwanqwa. MATHEMATIKA IBANGA LABAQALAYO (R) ukukhangela amanani bawapakishe -- Bala ubuya umva logama usihla usihla ngamanqwanqwa ngokulandelelana kwawo. -- Zoba u -6 esantini uze uhambe/ uxhume/utsibe ngomlenze omnye ecaleni kwayo. -- Qhwaba izandla ka- 6. -- Nakana amanani -1 uye ku- 6 usebenzisa iisimboli zamanani amakhulu. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Makapakishe inombolo yendlu yakowabo okanye inombolo yemfono -mfono esebenzisa amakhadi eenombolo amakhulu.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 24 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Usuku olu-1 Bala izinto Bala izinto eklasini. Abafundi mabenze ezi zinto zilandelayo: Buza imibuzo enje ngale: -- Leliphi inani eliza emva ko- 3, leliphi inani eliza emva ko -5, njl.?” Izinto ezise klasini nakummandla osingqongileyo. -- Utitshala upakisha izinto phezu kwetafile. Abafundi mabaqikelele ukuba zingaphi ezi zinto bazibonayo. Mabazibale emveni koko. -- Phuhlisa ulwazi lwamanani ngokwenzisa abafundi ukuba bapakishe izinto Sebenzisa izixhobo ezahlukeneyo zokubala(iikhawuntara) okanye izinto ngeendlela ezahlukeneyo, umzekelo ezikunika iintlobo ezahlukeneyo ukufundisa izicwangciso- qhinga. Xa sibala, inani lezinto azichaphazeli ubungakanani okanye indawo ezikuyo okanye ziyafana. imizekelo: -- lungelelanisa amaqhosha ama -6, iipensile ezi -6,iihupu ezi- 6, abafundi aba- 6 njl. Njl. -- zibale ngeendlela ezahlukeneyo, imizekelo, zibale uzisakazile, zigcine zidibene, zisemgceni okanye zicukene. Yohlula abafundi ngabathandathu,banike iibhloko zokwakha ezi- 6. Amaqela maba: -- bale iibhloko zabo -- khe ithawa ngeebhloko ezi- 6, bakhuthaze abafundi ukuba babale iibhloko xa besakha Iibhloko zokwakha ezi- 6 kumfundi ithawa. nganye. -- Utitshala uyazula zula eleyibhelisha iithawa zabafundi ngamakhadi amanani. Abafundi babala iibhloko. Maba phinda phinde ukubala. 175 -- Khetha umfundi aphose idayisi. Qinisekisa ukuba abafundi bayalibona bonke idayisi. Abafundi mababale amachokoza bakhombe kwithawa ehambelana namachokoza. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 24 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 176 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.3 • Yazi iisimboli zamanani uze unakane amagama amanani abandakanya isi-6. Usuku 1 Iisimboli zamanani Ngomlomo: Bala izinto zemihla ngemihla uye kuma ku-- 6. namagama Bala usiya phambili, ubale ubuye umva uyokuma ku- 6. Iingoma nezicengcelezo zamanani. amanani Bethelela u “ zininzi/ zimbalwa”. Qhwaba izandla kaninzi …YIMA. Qhwaba izandla amaxesha ambalwa. . Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba -- Zoba inani u -6 emhlabeni/ emgangathweni uze uyalele abafundi ukuba bahambe ecaleni kwamanani. -- Zoba inani u -6 esantini nasemoyeni. -- Bumba inani u-6 ngodongwe. -- Abafundi mabaqashele ukuba Bangaphi abafundi abafunekayo ukwenza inani u -6 besebenzisa imizimba yabo.Mabakhe inani u- 6 ngemizimba yabo. Izinto eziyi -6. MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa izinto ezipathekayo ezinokwakheka kuka- 3-D -- Beka induli yezinto etafileni. Dlala ngamanani aphakathi ko- 1 uye ku- 6. -- Abafundi mabaqikelele ukuba zingaphi izinto abazibonayo. -- Bala izinto. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukusebenzsia iimilo ezinokwakheka kuka 2-D okanye imifanekiso Yenza imifanekiso ufakele amachokoza kumakhadi anenani u - imizekelo ; -- Khetha koonotsheluza abaxutyiweyo kwezinemifanekiso ezino -6 uzidibanise nezilingana twatse nezinto zokubala. Umfanekiso -- Bonisa oonotsheluza abanemifanekiso ano-6 ubadibanise namachokoza nezinto wezinto ezi-6 zokubala ezino -6. -- Bonisa oootsheluza abanamachokoza ano-6 uwadibanise nesimboli u -6 nezinto Izinto zokubala okanye izinto zokubala ezi- 6. ezinokwakheka kuka 3-D -- Jonga koonotsheluza abaxutyiweyo abanegama lenani u -6 ulidibanise nesimboli u- 6 kunye nezinto zokubala. Umfanekiso onezinto ntandathu ezi-6

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 24 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.13 • Sombulula iingxaki zokudibanisa nokuthabatha ngomlomo ezineempendulo ukuya ku -6 . Ukudibanisa nokuthabatha Ngomlomo: Bala izinto zemihla ngemihla uyo kuma ku- 6. Bala usiya phambili, ubale ubuya umva uyokuma ku -6. Iingoma nezicengcelelzo zamanani. Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Imizekelo 1. Utitshala ubiza abafundi abathathu ngaphambili. Abafundi mabababale.Utitshala ubiza abanye ababini abuze: Bangaphi abafundi bebonke? 3 no 2  5. (utitshala uthi: 3 no 2 benza 5) 2. Utitshala upakisha izitulo ezi- 2. Yongeza ezinye ezi 2. Zingaphi ngoku zizonke? 2 no 2  4. Abafundi 3. Utitshala uphakamisa isandla esinye. Uthi “bala iminwe yam. Ukuba ndifihle ubhontsi Izitulo wam, mingaphi iminwe oyibonayo? 5 uthabathe u 1 4. 4. Abafundi mababale iminwe yabo kwisandla esinye. Fihla ubhontsi wakho, mingaphi iminwe oyibonayo? 5 uthabathe u 1 ® 4 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi mabapakishe izinto zokubala eziyi- 6 benze ezi zinto zilandelayo: Amaso nezinto zokubala. • Utitshala makanike abafundi izinto zokubala ezi- 6. • Utitshala unika imiyalelo abafundi baphendule, imizekelo, pakisha izinto zokubala zibe- 2, yongeza ezinye ezi- 3. • Zingaphi zizonke? 2 no 3  5. • Bala izinto zokubala ezi -4. Yongeza ezi -2 kwezi-4. zingaphi zizonke ngoku? 4 no 2  6. • Bala onke amaso onawo. Ukuba ugquma amaso amabini ngesandla sakho ubona amaso amangapphi ngoku? 6 uthabathe u 2  4. 177 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 24 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 178 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.13 • Ngomlomo, sombulula izibalo zamazwi ezibandakanya u- 6 Usuku olu- 1 Ukudibanisa Ngomlomo: Bala izinto zemihla ngemihla uyokuma ku -6. nokuthabatha Bala ukuya phambili, ubale ubuya umva uye kuma ku -6. Bethelela u “ zininzi/ zimbalwa”. Iingoma nezicengcelelzo zamanani. Qhwaba izandla kaninzi …YIMA. Qhwaba izandla amaxesha ambalwa. . Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukusebenzisa zinto eziphathekayo ezinokwakheka kuka 3-D Imizekelo: 1. UMpho unamaqebengwana ama- 4. UPeter umnika amanye ama- 2 ngaphezulu. Izinto zokubala Mangaphi amaqebengwana kaMpho ewonke? 2. UNontle unoonodoli aba -3 noMandisa unoonodoli aba- 2. Ngowuphi onoonodoli Sebenzisa iindidi zezixhobo abaninzi? Bangaphi oonodoli baka Nontle ngaphezu kwabaka Mandisa? ezahlukeneyo ezinokunika iindidi MATHEMATIKA IBANGA LABAQALAYO (R) 3. Kukho iintaka ezi- 5 elucingweni. Ezi -2 zibhabhile. Zingaphi iintaka ezishiyekileyo? zokusebenzisa izicwangiso -qhinga. 4. UPat uneemoto zokudlala ezi -6. UThina unezi- 4. Zingaphi iimoto zokudlala uThina anazo ngaphantsi kunezika Pat? 5. Umntwana ngamnye unempumlo enye. Abantwana abathathu bane …… INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 6. Umntwana ngamnye uneenyawo ezimbini. Abantwana abathathu bane……. 7. Umntwana ngamnye uneengalo ezimbini. Abantwana ababini bane….. 8. Umntwana ngamnye unomlomo omnye.Abantwana abathathu bane….. 3.2 • Yakha izinto esinokwakheka kuka 3-D kuyilo okanye ikhadi lelinofanekiso. “Iimilo yeLogi” izakhono ngebhloko Izinto -- Abafundi mabenze: Nasiphi isixhobo sokwakha ezinokwakheka -- Yakha isakhiwo usebenzisa umfanekiso Amaso, umtya wesihlangu kuka 3-D -- Abafundi bahlohla amaso belandela abakubona emfanekisweni. Amakhadi ahlukeneyo abonisa iindlela ezahlukeneyo zamaso.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 25 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.1 • Bethelela ulwazi olufunyenwe kwiveki yama- 24 olubandakanya inani u-6. usuku olu- 1 Bala izinto Ngomlomo: bala izinto yonke imihla uyo kuma ku -6. Bala usiya phambili, ubale ubuya umva uyokuma ku -6. Bala ngentloko ngokungenantsingiselo 1-10 Iingoma nezicengcelezo zamanani. Bethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Iseti yamakhadibhodi enkulu eneesimboli zamanani. Masidlale umdlalo: Ungawapeyinta kwiplastiki eqinileyo Utitshala ubeka ikhadibhodi enkulu enamanani okanye amakhadi anamanani ukuqala ku- 1 okanye kwikhadibhodi. ukuya ku -6 ngokokulandelelana kwawo phantsi. Utitshala unika abantwana imiyalelo enje nge: -- Hlala kwinani u- 6. 1 6 -- Beka umnwe wakho kwinani u -3. 3 2 -- Baleka ujikeleze kwinani u- 2 kathathu. 4 5 -- Xhuma phezu kwenani u -1. -- Utitshala makasasaze amakhadi anamanani abanike le miyalelo ingentla. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi maba: -- Bala izinto eklasini ezibandakanya amanani u-1 ukuya kwi-6. -- Utitshala upakisha izinto phezu kwetafile. Abafundi mabaqikelele ukuba zingaphi ezi zinto bazibonayo. Mabazibale emveni koko. 179 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 25 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa 180 elithelekelelwayo 1.3 • Nakana uze uchonge iisimboli zamanani namagama amanani abandakanya inani u -6 usuku olu- 1 Iisimboli zamanani Ngomlomo: bala izinto ezisetyenziswa yonke imihla uyo kuma ku -6. kunye namagama Bala usiya phambili, ubale ubuya umva uyokuma ku-6. amanani Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Iingoma nezicengcelelzo zamanani. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Bonisa oonotsheluza abanemifanekiso ano- 6 ubadibanise namachokoza nezinto zokubala ezino-6. -- Dlala umdlalo ukhethe inani eliyisimboli elifana ngqo, kwamanye ulithelekise nezinto Izinto zokubala zokubala ezifanayo. Oonotsheluza abaneesimboli zamanani -- Dlala umdlalo ukhethe igama lenani elifana ngqo, kwamanye ulithelekise nezinto namagama amanani, umzekelo zokubala ezifanayo. -- Dlala umdlalo ukhethe inani lezinto zokubala elifana ngqo, kwamanye ulithelekise MATHEMATIKA IBANGA LABAQALAYO (R) nezinto zokubala ezifanayo. Umfanekiso wezinto Thandathu -- Cinezela(threyisa) inani u- 6 usebenzise ikhrayoni. ezi-6 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 25 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 1.4 • Landelelanisa uze uthelekise ingqokelela yezinto usebenzisa “ ngaphezu kuna/ Usuku olu- 1 ngaphantsi kuna” uyokuma ku -6. Chaza,thelekisa uze ulandelelanise Ngomlomo: bala izinto uyokuma ku -6. amanani Bala usiya phambili, ubale ubuya umva uyokuma ku- 6. Iingoma nezicengcelezo zamanani. Khetha uphela Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” imisebenzi embalwa. Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Iihupu (hoops)ezimbini -- Utitshala ubeka ihupu ezimbini phantsi       -- Ubiza abafundi abathathu beme kwindlu yentaka yokuqala aze abize abanye ababini baye kuma kwenye indlu yeentaka. -- Yeyiphi indlu yeentaka enabafundi abaninzi kunenye? Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Izijungqe ezimbini zewulu kumfundi ngamnye. -- Abafundi mabahlale emethini benze iindlwana zeentaka ezimbini ngewulu. Izinto zokubala -- Utitshala unika imiyalelo, umzekelo, abafundi babeka izinto zokubala zibe mbini kwindlu yeentaka nezine kwenye indlu yeentaka, yeyiphi indlu yentaka enezinto zokubala ezininzi? Yeyiphi enezingaphantsi? Phinda phinda usebenzise amanani   uyokuma ku -6. -- Utitshala usebenzisa isiciko sesikhongozeli seayisi krim. Uxhoma iiphegi ezintathu phezu kwesiciko nezinye ezintathu ekunene kwesiciko. Zeziphi iiphegi ezininzi kunezinye okanye ziyalingana?   -- Abafundi bangenza umdlalo ngalo msebenzi bengamaqela besebenzisa iziciko neempahla zabo. Clothes Impahla Lid of a Isiciko pegs sesikhongozeli iphegi container 181 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 25 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 182 Ixesha Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Utitshala ubonisa amakhadi anamachokoza anamanani anemifanekiso kuyo Imifanekiso kunye namakhadi anamachokoza.                   -- Abafundi mabathelekise amakhadi anemifanekiso namachokoza bakhangele “amaninzi kunamanye” ambalwa kunamanye” “alinganayo”. Abafundi bazoba izindlu zeentaka ezimbini ephepheni. Kumyalelo, mabapakishe izinto zokubala bazitshatise nezindlu zeentaka ngekhrayoni. Phuhlisa ingqiqo u” yahlula ngokulinganayo” umzekelo     Iphepha eliyi A4 neekhrayoni zamafutha     Izinto zokubala MATHEMATIKA IBANGA LABAQALAYO (R) Yenza amaqela amanani azeleyo iimpendulo zibe nentsalela, umzekelo     INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 3.3 Nakana,uchonge uze uxele amagama eemilo ezinokwakheka kuka 2-D eklasini Iikhrayoni Usuku olu- 1 nasemifanekisweni Iimilo iphepha le A4 ezinokwakheka • Yenza ugqibezele iphazili enezicwili ezintlanu izikere kuka 2-D Abafundi maba: • Zoba umfanekiso kwiphepha le A4. Imvulopu okanye ibhegi ozenzeleyo • Utitshala uzoba imigca emva kwemizobo yabafundi. ukufaka iphazili kwi (goba iphepha ufake • Umfundi usika umfanekiso phezu kwemigca. iglu emacaleni). • Umfundi ugqibezela iphazili yakhe.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 25 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Ixesha CAPS Isihloko Amanqaku angangcaciso Izixhobo ezinokusetyenziswa elithelekelelwayo 5.1 • Inani loonobumba kumagama abafundi Qokelela uze Ukusombulula iingxaki: Buza abafundi ingxaki yezibalo: uhlele izinto “Ingaba amagama anoonobumba abathandathu ngawona athandwayo? Singenza njani siyifumane impendulo? Loluphi ulwazi ekufuneka siluqokelele? Qokelela ulwazi -- Abafundi mababale oonobumba kumagama abo, kwiileyibhile zamagama ebezenziwe ngutitshala. -- Utitshala uphakamisa ikhadi elinenani elingqamana nenani loonobumba begama lomfundi, abuze: ngubani umfundi onegama elinoonobumba aba- 4, uphakamisa ikhadi eline nani u -4. qhuba ngawo onke amanani. Zoba igrafu -- Utitshala uzoba le grafu elandelayo ephakamise amanani: 5.2 Iileta ezi 3 Iileta ezi 4 Iileta ezi 5 Iileta ezi 6 Bonisa ingqokelela yezinto Tom Solo Phiko Unathi ezihleliweyo Pam Miya Nathi Phumla Nobe Sipho Ludwe Naila 2 3 5 2 5.3 Funda uze utolike igrafu Xoxa uze -- Leliphi inani elifumaneka rhoqo koonobumba bamagama? unikezele ingxelo yengqokelela -- Ngawaphi amagama anoonobumba abangaphezu kwe -5?. yezinto -- Ngawaphi amagama anoonobumba abangaphantsi kuno -5?. ezihleliweyo 183 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 26 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 184 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.1 • Bethelela ulwazi olufunyenwe kwiveki yama- 24 equka amanani u-1 ukuya kwi -6 Usuku olu- 1 Ukubala amanani Ngomlomo: bala izinto yonke imihla uyokuma ku -6. Bala usiya phambili, ubale ubuya umva uyokuma ku -6. Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Iingoma nezicengcelezo zamanani. Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Abafundi ba: Iiseti ezimbini zemilo zamanani zekhadibhodi “kwisingxobo sokuva”. -- kha isimboli yamanani ngemizimba yabo. -- Bonisa inani leminwe yabo ngokomyalelo katitshala. -- kha iisimboli zamanani ngomtya okanye ngentlama yokudlala. MATHEMATIKA IBANGA LABAQALAYO (R) -- va imilo yenani esingxobeni bachaze inani ngalinye. -- Bhala isimboli yenani ukuqala ku -1 uyokuma ku -6 phantsi nasemoyeni, njl. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 26 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ukubala amanani Abafundi maba: -- Bale izinto eklasini eziquka e-1 ukuya kwezi- 6 Izinto eklasini -- Bale izinto zokubala uyokuma ku -6. -- Beke iityhubhu okanye izinto zokubala ezinemibala ngomgca phezu kwetafile. Izinto zokubala ezinemibala okanye -- Tshatise iityhubhu ngemibala besebenzisa iityhubhu zeyunifeksi okanye izinto iityhubhu zeyunifiksi (unifix tubes). zokubala. Imizekelo: bomvu bhlowu luhlaza -- Yenza amaqela obude ahlukeneyo. Abafundi mabatshatise ngokobungakanani. 1.3 • Azi iisimboli zamanani aze anakane amagama amanani abandakanya u -1 ukuya ku -6. usuku olu- 1 Iisimboli zamanani Ngomlomo: bala izinto yonke imihla uyokuma ku -6. namagama Bala usiya phambili, ubale ubuya umva uyokuma ku- 6. amanani Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Umphambili Umva Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi- 6. wekhadi wekhadi Ukusebenzisa imilo ezinokwakheka kuka 2-D okanye imifanekiso Masenze umdlalo: Thandathu 6 -- Utitshala wenza amakhadi anamanani ano 1-6 anamagama amanani ecaleni nesimboli kwelinye icala. Amakhadi anamanani u 1-6 anamagama -- Abafundi bafunda amagama amanani baqikelele iisimboli zamanani. amanani ecaleni nesimboli kwelinye icala. -- Baguqula amakhadi bazilungise apho benze kakubi khona. (yenza iiseti ezimbalwa ukwenzela ukuba 185 umfundi ngamnye abe neseti yakhe). MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 26 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 186 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.7 • Sombulula izibalo zamazwi ngomlomo (izibalo zamazwi) kwimeko ethile uze Usuku olu- 1 ucacise isisombululo kwiingxaki yezibalo ezibandakanya inani- 6. Ukudibanisa nokuthabatha Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Iingoma nezicengcelezo zamanani. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukusebenzisa zinto eziphathekayo ezinokwakheka kuka 3-D 1. Nika umfundi ngamnye iphepha I A4 elinemigca enyukileyo nezinto zokubala ezi- 6, imizekelo   Umfundi unikwa izinto zokubala ezi- 6 Iphepha elinemigca enyukileyo embindini eyi A4 2. Yenza abafundi baziphose izinto zokubala ngobunono ephepheni bacacise ukuba ziwe njani, imizekelo MATHEMATIKA IBANGA LABAQALAYO (R) u 4 no 2 6 (u 4 no 2 zenza 6) u 3 no 3  6 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 3. Phinda ngamanani u 1 ukuya 5. u 5 no 1  6 4. Ukusombulula iingxaki: Cacisa izisombululo zengxaki. 5. Yenza ngokufanayo nakwiingxaki zokuthabatha.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 26 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 4.4 • Fundisa umlinganiselo womthamo ngokuthelekisa ukuba izikhongozeli zithatha Usuku olu-1 kangakanani, imizekelo Umthamo/Ivolumu -- “ayinanto/ izele” Khetha umsebenzi omnye okanye -- “ungaphezu kune/ ingaphantsi kune” emibini. -- Kakhulu, kancinci Fundisa umthamo kubafundi ngokubuza ukuba sesiphi isikhongozeli ezithatha kakhulu. Amanzi nesanti zezona zixhobo Abafundi bathanda ukwenza uthelekiso kubude ngaphezu komthamo. ukuphuhlisa umthamo(ngexesha lomdlalo wamanzi) nange (ngexesha lomdlalo Umzekelo, xa bebuzwa ukuba yeyiphi ethatha umthamo omkhulu, isikhongozeli eside wesanti) nesifutshane, abafundi abaninzi baya kukhetha isikhongozeli eside nokuba esifutshane sithatha umthamo omkhulu wamanzi. Ukufunda usebenzisa intshukumo yomzimba “enkulu kune/ ngaphantsi kune” Iindidi zezikhongozeli ngokwe milo nobungakanani. -- Sebenzisa isikhongozeli esinye njengomlinganiselo omiselekileyo, umzekelo, ikomityi yeyogathi.Nika abafundi iindidi ezahlukeneyo zezikhongozeli. -- Abafundi mabenze: -- Khangela ukuba zeziphi izikhongozeli ezithatha umthamo omkhulu, zeziphi ezithatha Ikomityi yeyogathi ngaphantsi, umzekelo ikomityi yeyogathi. “Sesiphi isikhongongozeli esikhulu? Sesiphi iskhongozeli esithatha kancincit?” Nika abafundi icephe nebhakethi enesanti ukugalela isanti ekomityini ngecephe. Abafundi mabenze ezi zinto zilandelayo: -- Bala ukuba mangaphi amacephe afunekayo ukuzalisa ikomityi. Ufuniselo lungenziwa Ibhaskithi yesanti nzima ngokubanika izikhongozeli ezininzi, imizekelo, ikomityi, iglasi yeplastiki,nejagi Ikomityi encinci. Icephe -- Phinda lo msebenzi usebenzise iikomityi. 187 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 26 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 188 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 3.1 Ukuchaza into enye okanye ngaphezulu ezinokwakheka kuka- 3-D ngokunxulumene Iphegi bhodi yomfundi ngamnye okanye usuku olu- 1 nenye ngokwammaqela. Indawo- bume,ukufumana • Indawo-bume yezinto ezi-2 okanye ngaphezulu ngokunxulumene nenye Amakhadi azotywe iipateni. indawo Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D nembonakalo Ibhodi yephegi (Pegboard work) Abafundi mabasebenzise isandla sasekhohlo nesasekunene, emveni koko mabazisebenzise zombini ukufaka iiphegi ebhodini. -- Utitshala uxelela abafundi ukuba bazifake phi iphegi,imizekelo Kumqolo ongaphambili Ikumqolo ongezantsi Ngasekhohlo ngasekunene Iphegi bhodi yomfundi ngamnye okanye Embindini ngokwamaqela. MATHEMATIKA IBANGA LABAQALAYO (R) Abafundi mabenze ezi zinto zilandelayo: Amakhadi azotywe iipateni. -- Yenza iimilo kwiphegi bhodi usebenzisa iiphezi zemibala. -- Utitshala wenza ipateni elula ngeephegi kwi phegibhodi abafundi bakope kwezabo iibhodi. -- Abafundi bakopa ipateni kumakhadi anemizobo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 27 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.1 • Fundisa intsingiselo yenani u- 7 Usuku olu- 1 Ukubala izinto Ngomlomo: Bala izinto yonke imihla uyo kuma kwi- 7. Bala usiya phambili, ubale ubuya umva uyokuma kuwi-7. Ukubala ngentloko ngokungenantsingiselo usuka ku-1 uyokuma kwi- 10. Ukubethelela amanani aqhelekileyo: Iingoma nezicengcelezo zamanani. Utitshala upakisha izinto ezi -3 ngomgca. Khomba kwinto ngeli xesha ubalayo eyokuqala, eyesibini, eyesithathu, eyesine. Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Iibhola zamaphephandaba -- Utitshala wahlula abafundi ngokwamaqela. Nika iqela ngalinye iibhola ezisi- 7 ezenziwe Iibhaskithi ngamaphephandaba. -- Abafundi mabaphose iibhola ebhaskithini. Abafundi mababale ngokukhwaza xa bephosa iibhola. -- Bala amaxesha utitshala angqisha etafileni umkope. -- Bala usebenzisa ibhithi esetyenziswa rhoqo lo mzuzu abafundi behamba ngamanyathelo, betsibela ngaphakathi nangaphandle. -- Ngqisha iinyawo ngexesha usebenzisa isingqisho esisetyenziswa rhoqo. 189 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 27 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 190 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ukubala izinto Utitshala upakisha iibhloko zokwakha embindini womgangatho. Iibhloko zokwakha okanye iibhloko zelego Unika imiyalelo enjengale: -- Thatha iibhloko ezintathu kwezipakishiweyo. -- Thatha iibhloko ezine kwezipakishiweyo uzibuyisele ezimbini njl. -- Utitshala upakisha izinto phezu kwetafile. Abafundi mabaqikelele ukuba zingaphi izinto ezipakishiweyo.zibaleni emva koko. -- Ukuphuhlisa ulwazi ngogcino lwamanani ngokuba abafundi bapakishe izinto zokubala ezisixhenxe okanye izinto ngeendlela ezahlukeneyo, imizekelo Xa ubala , inani lezinto alichaphazeli ubungakanani, okanye indawo, okanye ngokufana. imizekelo: MATHEMATIKA IBANGA LABAQALAYO (R) -- Cwangcia amaqhosha asi- 7, iipensile ezisi -7,iihupu (hoops) ezisi -7 , abafundi abasi -7, njl. -- Zibale ngeendlela ezahlukeneyo, imizekelo, zibale uzisasazile, zindawonye,zisemgceni okanye zicukene. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Masidlale umdlalo: Iiseti ezimbalwa zemifanekiso -- Utitshala uyazoba okanye ancamathisele imfanekiso kwelinye icala lekhadi, azobe noonotsheluza beesimboli ezino -1 ukuya amachokoza kwelinye, aquka amanani aqala ku -1 ukuya ku -7, (yenza iiseti ku 7. ezimbalwa). -- Ukhupha iseti yamakhadi kumfundi ngamnye. -- Abafundi babala imifanekiso esekhadini. -- Guqula ikhadi uze ubale amachaphaza. Umzobo -- Utitshala uphakamisa ikhadi elinamachaphaza. onezinto 7 ezi si- 7 -- Abafundi batshatisa awabo amakhadi kwelikatitshala. -- Utitshala uphakamisa iseti yamakhadi anesimboli kuwo. -- Abafundi batshatisa awabo amakhadi kulawo katitshala anesimboli. -- Umfundi onekhadi elichanekileyo makaphakame, abale inani lemifanekiso ngokukhwaza.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 27 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.13 • Sombulula ngomlomo iingxaki zokudibanisa nokuthabatha eziquka inani u-7 Usuku olu-1 Ukudibanisa Ngomlomo: Bala izinto yonke imihla uyo kuma ku- 7. Iingoma nezicengcelezo zamanani. nokuthabatha Bala usiya phambili, ubale ubuya umva uyokuma ku -7. Bethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? 1.6 Ukufunda usebenzisa intshukumo yomzimba 0 1 2 3 4 5 6 7 Ubuchule -- Sebenzisa ileli yamanani ilele ncwaba (ngokuxwesa) bokusombulula -- Qala ngo -0 rhoqo. Bala rhoqo xa ushukuma. iingxaki Utitshala uyabuza: -- Leliphi inani eliphakathi kwe- 4 nesi- 6? Umfundi uba nolwazi xa esebenzisa ileli yamanani. -- Ngawaphi amanani aphakathi ko- 2 nesi- 5? -- Sebenzisa ezakho iimbono ukwenza abafundi ukuba bazi inani u-7 ngokubamba izinto besebenzisa imizimba yabo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka- 3-D Amaso okanye izinto zokubala Nika umfundi ngamnye amaso okanye izinto zokubala ezisi- 7. Buza imibuzo enjengale: -- Susa into yokubala ibe- 1 kwelinye icala (ekhohlo). Xa sifakela enye into yokubala ekhohlo, zingaphi ke ngoku? -- U- 1 no -1→2 (utitshala uthi: 1 no 1 zenza 2) -- Yisa izinto zokubala ezi- 4 ngasekunene. Xa sifakela ezimbini ngaphezulu ngasekunene, zingaphi ngoku? Izinto zokubala -- kunye no- 26 -- unezinto ezi- 5 zokubala uthathe ezi-2, zingaphi ezishiyekileyo? 191 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 27 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 192 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.11 • Nakana uze uchonge imali yaseMzantsi Afrika Usuku olu- 1 Imali Imali engamaphepha -- Sebenzisa imali yamaphepha, imizekelo R10, R20, R50, R100, R200 -- Yazisa abafundi ngemifanekiso yezilwanyana ezahlukeneyo kwimali yamaphepha Imizekelo yenyani yemali yamaphepha R10, R20 ne R50 (okanye imali -- Mabenze imidlalo yemali kwizindlu zokudlala. yamaphepha okudlala) 1.9 • Ngomlomo, sombulula uze ucacise iingxaki zezibalo zamazwi eziquka: Usuku olu- 1 Ukwahlula -- Ukwaba ngokulinganayo, ngokwamaqela -- Ukwahlula ngokwamaqela amanani apheleleyo kunye Khetha omnye nokwaba okanye emibini ngokulinganayo -- nezisombululo ezinentsalela yamanani ukuya ku -7 imisebenzi okukhokelela Ngomlomo: Bala izinto yonke imihla uye kuma kwi- 7. ebandakanya kulwahlula-hlulo ukufunda usebenzisa Bala ukuya phambili, ubale ubuya umva uye kuma kwi -7. intshukumo Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Iingoma nezicengcelezo zamanani. yomzimba MATHEMATIKA IBANGA LABAQALAYO (R) Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 27 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.9 Ukufunda usebenzisa intshukumo yomzimba Ukwahlula Yakha iiseti usebenzisa abafundi: ngokwamaqela Imizekelo: Sebenzisa izixhobo ezahlukeneyo ukunika nokwaba ezinye iindlela zokufundisa. ngokulinganayo 1. Abafundi mabakhe amaqela ngaba 2, 3, 4, 5 nangaba- 6.Bala ukuba bangaphi abafundi okukhokelela kwiqela. kulwahlula-hlulo 2. Zoba iimilo ezinkulu kwikonkriti okanye esantini. Abafundi benza amaqela, imizekelo, Izixhobo zokunyuka okanye iitafile abafundi aba- 4 phakathi kwemilo. nezitulo. 3. Ngexesha lokutya utitshala uthi: “ungaya kwiqela labafundi abane ukuyohlamba izandla”okanye uthi: “ abafundi abane mabaye kuhlamba izandla”.   4. Khetha abafundi abasi-7 usebenzisa izicengcelezo zokubala. 5. Abafundi abasi -7 mabalinganise babeziintaka benze ngathi kukho umithi besebenzisa izinto zokudlala zokugwencela zaphandle okanye izitulo neetafile ngaphakathi. 6. Utitshala wenza umdlalo wokuthumela iintaka ezimbini emithi (abafundi ababini bagwencela kwisixhobo). Intaka nganye ngexesha ibhabhela emthini. “Ziingaphi iintaka emthini ngoku? Zingaphi emhlabeni? 7. Pinda wenze amaqela abafundi usebenzisa amanani ukusuka ku-1 ukuya kwi-7. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Izinto zokubala Imizekelo: Nika abafundi iphepha nekhrayoni 1. Utitshala unika abafundi izinto zokubala. Abafundi mabenze iiseti ezi- 4 ngezinto izinto zokubala zokubala. Yenza enye iseti yoonontathu. “zingaphi izinto zokubala kule seti intsha?     2. Abafundi mabazobe izangqa ezimbini ephepheni. Utitshala makanike imiyalelo, abafundi mabapakishe izinto zokubala besenza iiseti ezimbini ukwenzela kubekho iseti enezinto zokubala ezingaphezulu kunezinye iiseti. Buza imibuzo enje ngo”yeyiphi iseti enezinto zokubala ngaphezulu/ ngaphantsi? 193 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 27 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 194 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 4.4 Thelekisa uze ulandelanise ngokwenza izinto ngezinto usebenzisa isigama amanzi (ngexesha lomdlalo wamanzi) iintsuku ezi- 2 esicacisayo: nesanti (ngexesha lomdlalo wesanti) Umthamo/Ivolumu zikulungele ukuphuhlisa umthamo. a) umthamo Okanye imisebenzi b) ayinanto, izele,incinci kune, zininzi kune, kakhulu, kancinci) ekhethiweyo emibini Iingoma nezicengcelezo zamanani. okanye emithathu Ngomlomo: bala izinto yonke imihla uyo kuma ku- 7. Bala usiya phambili, ubale ubuya umva uyokuma ku -7. Bethelela ulwazi olufunyenwe kwiveki yama- 26 equka umthamo Iindidi zezikhongozeli zeendidi Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” ezahlukeneyo zeemilo nobungakanani. Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi- 6 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Abafundi maba: MATHEMATIKA IBANGA LABAQALAYO (R) -- Cwangcisa izikhongozeli ezibini okanye ezintathu ngokwemithamo, ngamanye amazwi, ikomityi sesiphi isikhongozeli esinokuthatha ezininzi okanye ezimbalwa?abafundi BangaHlola ukuqashisa kwabo ngokugalela amanzi kwizikhongozeli ezingenanto babale ukuba sesiphi esithatha ezona komityi ezininzi.Yongeza inani lezikhongozeli ukuyenza nzima ikomityi ngakumbi. irayisi INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Abafundi Bangasebenzisa ikomityi ukulinganisa ukuba zingaphi iikomityi zerayisi, iimbotyi imbotyi okanye isanti ukugcwalisa. Iindidi zobungakanani zamabhakethi -- Funa izikhongozeli eziyeleleneyo (imiz.ibhakethi kwipitsi yesanti) ukuqala kuncinci kwipitsi lwesanti. ukuya ku- nkulu. -- Nika abafundi iindidi zezikhongozeli (iindidi zobungakanani neemilo)uze ubuze imibuzo: o “Zeziphi izikhongozeli ezinokuthatha awona manzi okanye isanti? o Xa ugalela amanzi kwisikhongozeli ukusa kwesinye, ingaba uzakusigcwalisa?” Iindidi zezikhongozeli zeendidi ezahlukeneyo zeemilo nobungakanani. -- Abafundi mabazikhangelele ukuba kwenzeka ntoni xa isikhongozeli singagcwaliswanga ncam xa kuphinde kwagalelwa amanye, imizekelo- yongeza amabhastile/iimabhile amanzi ezicocekileyo, iibhloko zeLego, iibhloko zeplastiki, imizekelo, abafundi bayiyatha imidlalo Isanti yokuqashela xa beqashela ukuba sesiphi isikhongozeli esithatha umthamo omkhulu, bakhangele iimpendulo zabo ukuba baphumelele na.(utitshala uyacacisa ukuba izito Izinto ezinje ngamabhastile acocekileyo, ezidadayo azichaphazeli ubungakanani bamanzi). iibhloko ze Lego, iibhloko zeplastiki.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 28 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.1 • Bethelela ulwazi abalufumeneyo kuquka inani- 7 Usuku olu- 1 Ukubala izinto NGomlomo: bala izinto yonke imihla uyo kuma kwi -7. Bala usiya phambili, ubale ubuya umva uyokuma kwi- 7. Bethelela iingqiqo ezingu “zininzi/ zimbalwa” Iingoma nezicengcelezo zamanani. Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi -7 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba Amakhadi eesimboli aquka u- 1 ukuya ku- 7. -- Abafundi ababini babizwa ngaphambili. Abanye abafundi bayababala.Abafundi ababini aBangaphambili baphakamisa iisimboli ezinamanani. -- Yongeza omnye umfundi ngaphambili. Abanye abafundi bayababala. Umfundi omnye makaphakamise isimboli enenani u -3. -- Qhuba kude kube nabafundi abasi- 7 ngaphambili. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Beka iinkonkxa ezisi- 7 ngomgca umz. Iinkonkxa ezisi 7ezinesimboli   zamananiezincanyathiselwe kuzo 1 2 3 4 5 6 7 o Iimbewu okanye amatye -- Abafundi mababeke nimbewu/ ilitye kwinkonkxa yokuqala, ezimbini kweyesibini, ezintathu kweyesithathu, c baqhubekeke zide iinkonkxa zosi- 7 zibe nnembewu/ namatye njengokuba kubonisiwe ngaphandle. r -- Thatha iikhrayoni (phakathi kwe- 10 ne- 15) bazifake ekomityini. Abafundi mabaqashele e Iikhrayon neemagi ukuba zingaphi ezisekomityini. Mabaxoxe impendulo. t -- Bonisa ukuba zibalwa njani ngokukhupha ibenye ngexesha bazibeke ngomgca. e   u s 195 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 28 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 196 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.3 • Nakana isimboli yenani negama lenani elibandakanya u- 7. Usuku olu- 1 Iisimboli zamanani Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso . namagama Masenze umdlalo: amanani . -- Abafundi mabahlale kwisangqa.Beka ikhadi elinenani liqubudiwe phambi komfundi ngamnye. (inokuba yisimboli, igama, amachaphaza okanye umfanekiso equka amanani u- 1 ukuya kwi- 7) -- Fundisa abafundi ukugqithisa amakhadi kumfundi olandelayo ngokuwatshibiliza Umfanekiso ngobuso phantsi emethini. wezinto IsiXhenxe ezisiXhenxe -- Abafundi bayacengceleza: “Inani eliyimfihlo, inani eliyimfihlo, linoba lithini? Mandikrobe” -- Abafundi baya kroba emakhadini. -- Utitshala uphakamisa ikhadi lakhe lenani. -- Abafundi abanamakhadi afana nakatitshala baphakamisa awabo, bathi: “ndizakuliphakamisa ikhadi lam phezulu, ukwenzela wonke ubani abone”. 3.2 • Yakha izinto ezinokwakheka kuka-3-D usebenzisa izinto eziphathekayo “Iimilo zeLogi” izakhono zebhloko Usuku olu- 1 MATHEMATIKA IBANGA LABAQALAYO (R) Izinto • Kopa isakhiwo kwikhadi eliyiliweyo okanye elinomfanekiso “iibhloko zengqondo” Iyaqhubeka ezinokwakheka Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Nokuba zeziphi (pegboard) izixhobo kuka- 3-D zokwakha -- Umfundi wakha isakhiwo esifana nesakhiwo esisemfanekisweni. Iphegibhodi -- Kopa uyilo olusemfanekisweni usebenzise iphegibhodi. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Wandise lo msebenzi kubuGcisa obubonwayo. -- Nika umfundi ngamnye iphepha elinezangqa ezikhulu nezincinci, oonxantathu nezikwere. Izangqa ezinkulu nezincinci, nxantathu nezikwere ephepheni. Abafundi maba: Izikere, iglu -- Sike iimilo bakhe izakhiwo ezinokwakheka kuka 2-D ephepheni bazincamathisele. -- Hombise imifanekiso ngemizobo.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 28 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 3.4 • Phuhlisa ukukwazi ukubona umgca ophakathi kubo Mabanakane umgca wolingano- Ulingano-macala Ukufunda usebenzisa intshukumo yomzimba macala kubo na- Abafundi maba: kokubangqongileyo. -- Khumbule ulwazi obunalo; bamba amalungu omzimba ngemiyalelo. Dlala “uSimoni • Bawela umgca uthi: bamba....” ophakathi kubo Umdlalo: “USimoni uthi, bamba.......” -- Nika eminye imiyalelo apho abafundi bawela umgca ophakathi njenge: “bamba idolo lakho ngempumlo, bamba igxalaba lakho ngendlebe.Bamba idolo lakho lasekhohlo ngonyawo lwasekunene. Bamba ingqiniba yakho ngesandla sakho, njl. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Abafundi bazoba ebhodini Abafundi maba: -- Zobe izangqa ebhodini. -- Zobe imigca ebhodini. Qinisekisa ukuba abafundi bawela umgca ophakathi. -- Zobe umgca ebhodini udibanisa ichokoza kwelinye elikude kwelinye. -- Zobe umzobo osisi- 8 oleleyo ebhodini. Sebenzisa iintshukumo ezinkulu ukuqinisekisa ukuba abafundi bawela umgca ophakathi. (Abafundi basebenzisa izandla zasekunene nasekhohlo.) Ukusebenzisa imilo enokwakheka kuka 2-D okanye imifanekiso Nxulumanisa nobuGcisa Bokubona Amaphephandaba amabini kumfundi ngamnye Abafundi maba: Ipeyinti nebhrashi -- Peyinte kwiphephandaba ukusuka ekunene nasekhohlo. 197 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki yama- 28 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 198 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 4.3 Thelekisa, ulandelelanise izinto eziphathekayo ngokwenza usebenzisa isigama Usuku olu- 1 esifanelekileyo esicacisayo: Ubunzima -- ubunzima imizekelo, ikhaphu khaphu, inzima,ikhaphu khaphana,inzinyana • Fundisa ingqiqo- “ubunzima” imizekelo - ukuthatha umlinganiselo wobunzima (ukuveyisha) kuthetha ukuba into inobunzima obungakanani Khetha imisebenzi -- ikhaphu khaphana/ inzinyana emibini okanye Izinto ezinokwakheka kuka 3-D eziziindidi Ukuthatha umlinganiselo wobunzima kuthetha ukuba into inzima kangakanani. emithathu. zobunzima, umzekelo, iibhloko zeLego, Ukufunda usebenzisa intshukumo yomzimba iithoyi, iibhloko zokwakha, iinkonkxa, izikhongozeli, njl. Abafundi mabaqikelele ubunzima bezinto: -- Bamba ezi zinto zilandelayo, enye kwisandla ngasinye ukwenzela ukuba baqikelele ukuba yeyiphi enzima okanye ekhaphu khaphu, imizekelo o Ilitye nebhloko yokwakha. o Ikari yokudlala yeplastiki nemoto yokudlala yentsimbi. o Inkonkxa/ itoti yekofu nebhotile yesiselo. MATHEMATIKA IBANGA LABAQALAYO (R) Isikali o Ibhola enkulu yerabha neyekhilikithi. Ungazenzela isikali esilula: Abafundi badla ngokucinga ukuba izinto ezinkulu zezona zisindayo xa kuthiwa -- Uzakufuna ihengari yeplastiki mabaqashele phakathi kwee obhjekthi ezimbini. ebhijelweyo, -- Fundisa isikali, umzekelo- weyisha izinto ukubonisa impendulo echanekileyo. -- Iithabhu ezimbini zemajerini INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Buza imibuzo enje nge“yeyiphi into enzima/ ekhaphu khaphu? Abafundi mabakhangele okanyeibhotile yecoke nee ziitringi. izinto ezinzima nezikhaphu khaphu eklasini kunezi bebeziweyishile. -- Gqobhoza imingxuma emibini -- Qinisekisa ukuba zikhona izikali zokuweyisha ngexesha labo lokudlala ukwenzela echaseneyo kwithabhu yemajerini/ ukuba baqhube umsebenzi wokuweyisha. iibhotile zecoke. -- Makubekho isikali kwikona yendlu yokudlala ukwenzela ukuba baweyishe ukuba -- Ncamathisela iithabhu/ iibhotile zingaphi iibhloko eziweyisha ngokufanayo, umzekelo, iapile. ekugqibeleni kwehengari. – Uzakuba nesikali. -- Xhoma ihengari esikhonkwaneni okanye kwihuku abafundi mabaqalise ukuveyisha – -- Bonisa abafundi ukuba ihengari kufuneka ilingane rhoqo xa bezakuveyisha.

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 29 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.1 • Ukubethelela ulwazi olifundiweyo ngamanani ukuqala ku- 1 ukuya ku -7 Usuku olu- 1 Ukubala izinto Ngomlomo: Bala izinto yonke imihla uyo kuma kwi -7. Bala phambili nasemmva uyokuma kwi -7. Ukubala ngokungenantsingiselo ukuqala ku-1 uyokuma kwi-10. Iingoma nezicengcelezo zamanani. Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 7 Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukusebenzisa izinto eziphathekayo eziokwakheka kuka 3-D Abafundi maba: -- Qokelele amasebe. Wagcine eklasini ukwenzela xa befuna ukuwasebenzisa kwakhona. -- Sebenzisa awakho amasebe, imizekelo ukubala isimboli u -5 Amasebe   okanye okanye njl-njl. Abafundi maba: Umfanekiso nonotsheluza abanamachokoza ano 1 ukuya kwi -7 • Sebenzise iiseti zamakhadi abo anamanani u -1 ukuya ku -7.. Isimboli yamanani nonotsheluza abano -1 • Mabazobe izinto zamanani ngokomyalelo katitshala, umzekelo zoba izangqa ezibini. ukuya ku -7. • Mababale ukuya kwinani abalinikiweyo, umzekelo utitshala ubiza inani u-3. Abafundi mabaqhubeke ukubala... ne, ntlanu, ntandathu. Umfanekiso wezinto IsiXhenxe • Ngexesha lokutya utitshala makabuze: “Bangaphi abafundi abanezonka ezimdaka? ezisiXhenxe Bangaphi abanezonka ezimhlophe? Ingaba ngabafundi abanezonka ezimhlophe aBangaphezulu kunabanye? Zeziphi ezininzi/ ezimbalwa?” Iphepha nekhrayoni • Utitshala upakisha izinto etafileni. Abafundi mabaqikelele ukuba zingaphi izinto ezipakishiweyo.Mabazibale emva koko. 199 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 29 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 200 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.3 • Nakana iisimboli zamanani namagama amanani ezibandakanya u -1 ukuya kwi- 7 usuku olu- 1 Iisimboli zamanani Ngomlomo: Bala izinto yonke imihla uyo kuma kwi-7. Iingoma nezicengcelezo zamanani. namagama Bala ukuya phambili, ubale ukubuya umva uyokuma kwi -7. amanani Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” 3 5 2 Qhwaba kaninzi…YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma kwi -7 Amakhadi amakhulu amanani Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? aneesimboli Ukufunda usebenzisa intshukumo yomzimba -- Beka amakhadi esimboli amakhulu eklasini okanye ngaphandle kwindawo yokudlala. Izithsaba ezaneleyo zabafundi ezenziwe -- Biza le ndawo ngokuba li “ Lilizwe lamanani’ abafundi bona zii “nkosi namakhosazana ngamakhadibhodi, ezinamanani amanani” beka isithsaba kumfundi ngamnye ezenziwe ngamakhadibhodi, zinamanani abhaliweyo. abhaliweyo ngokucacileyo.. -- Nika abafundi imiyalelo enje ngo: 1 6 o Bonke abafundi abanxibe bomvu mabatsibe kabini. 4 MATHEMATIKA IBANGA LABAQALAYO (R) o Bonke abafundi abaneenwele ezinde , mabachwechwe ukuya kuma ku- 6. Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Abafundi maba: Iphepha nekhrayoni INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Zoba amachaphaza ngokwenani elinikwe ngutitshala, umzekelo zoba amachaphaza amabini. Phinda ude uye kuma ku- 7 Iseti yamakhadi yamanani ano - 1 ukuya -- Yiba neeseti zeesimboli zamanani ezininzi namakhadi amagama amanani.Nika ku -7 umfundi ngamnye ikhadi. Utitshala uphakamisa ikhadi abafundi abanamakhadi afana nelakhe mabaphakise awabo. -- Ingcebiso: quka abafundi ukwenza awabo amakhadi. -- Dlala imidlalo yokutshatisa isimboli yamanani namagama amanani. Umfanekiso wezinto IsiXhenxe ezisiXhenxe

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 29 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 1.7 • Sombulula ngomlomo iingxaki zokudibanisa nokuthabatha ezineempendulo ukuya Usuku olu- 1 Ukudibanisa ku -7. nokuthabatha Ukuthetha: bala izinto yonke imihla uyo kuma ku -7. Bala phambili nasemva uyokuma ku -7. Ukubethelela iingqiqo ezingu “zininzi/ zimbalwa” Qhwaba kaninzi…YIMA. Iingoma nezicengcelezo zamanani. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla aye kuma ku- 7. Buza imibuzo, ngabaphi abaqhwabe kakhulul/ kancinci? Ukufunda usebenzisa intshukumo yomzimba -- Jonga kwiveki yama- 24 nama- 27 ngemisebenzi. -- Sebenzisa ezakho iimbono ukunika abafundi olunye ulwazi ngenani u -7 besebenzisa Izinto zokubala imizimba yabo. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Jonga kwiveki yama- 24 nama- 27 ngemisebenzi. -- Sebenzisa ezakho iimbono ukunika abafundi olunye ulwazi ngenani u -7 besebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D. 201 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 29 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) 202 Izixhobo ezicetyiswayo/ Ixesha Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 3.1 Ukulandela izalathiso ukuhamba okanye ufumana indawo ethile kwisithuba esithile Usuku olu- 1 Indwo-bume, • Phuhlisa ulwazi lokwalathisa ngokusebenzisa amakhadi oonotsheluza beentolo ukufumana netshati yeentolo. indawo kunye Ukufunda usebenzisa intshukumo yomzimba nembonakalo Abafundi mabahambe ngeendlela ezahlukeneyo: -- ukuya emnyango, Ibhodi -- ukuya efestileni, -- ukuya ekoneni yencwadi, njl-njl. Ukusebenzisa zinto eziphathekayo ezinokwakheka kuka 3-D Abafundi maba: -- Zobe isi- 8 esithe tyaba ebhodini. Qinisekisa ukuba abafundi bawela imigca yabo ephakathi.   MATHEMATIKA IBANGA LABAQALAYO (R) Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Unotsheluza onotolo olunye. Guqula oonotsheluza bajonge kwiindlela Abafundi mabenze ngokwamaqela amancinci okanye bodwa: ezahlukeneyo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Beka amehlo konootsheluza uze use ingalo yakho kweli cala ekhonjwe lutolo uthethe eli xa usenzayo, umzekelo- xa umfundi ekhupha ingalo yakhe, kufuneka athi” kunene”. Itshati yotolo (iphowusta yotolo -- Ukwenza intshukuma ya phezulu nasezantsi umfundi angasebenzisa nokuba yeyiphi ngokweendlela ezahlukeneyo.) ingalo. -- Bonisa isalathiso kwitshati yentolo. -- Ncamathisela imizila yeenyawo yalathe ngasemnyango.     Isigama: Phezulu/ ezantsi;phakathi/ phandle; ngaphezulu/ ngaphantsi; phambili/ emva; phambi ko/ emva; kwicala elinye/ kwelinye icala; emva ko; ekhohlo/ ekunene

Ixesha lokufundisa ekucetyiswa ukuba lisetyenziswe: Iveki 29 Umsebenzi weklasi omnye ofundiswa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (imisebenzi yeMathematika emi ± 5 ngeveki) Izixhobo ezicetyiswayo/ Ixesha CAPS Isihloko Amanqaku angangcaciso ezinokusetyenziswa eliqikelelweyo 4.3 • Bethelela ulwazi olufunyenwe kwiveki yama- 28 ebandakanya ubunzima: “eyona usuku olu- 1 ikhaphu-khaphu / eyona inzima” Ubunzima Ukufunda usebenzisa intshukumo yomzimba Abafundi maba: -- Thelekise ubunzima bezikhongozeli ezintathu ukuya kwezintlanu (umzekelo 400g kwiinkonkxa ezingenanto) zibe nesanti enobunzima obuhlukeneyo, ukwenzela zibe nobunzina obahlukeneyo. Iinkonkxa ezingenanto ezinomlinganiselo olinganayo -- Zibeke ngokobukhaphu khaphu nobunzima ngokuva umlinganiselo. Emva koko, mabasebenzise isikali ukuqonda ukuba abafundi bajonge ukuba iimpendulo zabo bezichanekile na. -- Iingcebiso: Linga ukuba zingaphi iintsinjana ezingqukuva zokukala okanye izikhonkwane Isikali ezinobunzima obufanayo.Kungasetyenziswa ezinye izinto. Utitshala ubeka izinto ezinobunzima obahlukeneyo kwizikhongozeli ezifana ngqo, umzekelo, izikhongozeli zesonka samasi; ibhloko nebhola yetenesi. Izinto ezinje ngebhloko zeLego Bafundi maba: -- Ve umohluko wobunzima phakathi kweeobhjekthi ezimbini, qajela ukuba yeyiphi Izinto ezahlukeneyo ngobunzima ezinje ekhaphu khaphu okanye enzima. ngeentsinjana zokukala nezikhonkwane. -- Sebenzisa isikali ukufumana impendulo echanekileyo. Izikhongozeli zesonka samasi, enye ibe nebhloko enye inebhola yetenesi. -- Cel’umngeni kubafundi bafumane izinto eklasini ezinobunzima obulinganayo. Ipitsi lesanti nendawo yokudlala yamanzi mayibe ziindawo ezibethelela ezinje ngo ikhaphu khaphu/ inzima/ inzima ngakumbi esebenzisa izikhongozeli ezahlukenenyo, isikali, isanti emanzi neyomileyo. Ipitsi lesanti NB: Hlala nabafundi ngeli xa bathethayo, baxoxayo, naxa bacacisayo. Isitya somdlalo wamanzi, isikhongozeli okanye isikhongozeli esivulekileyo sokusela iinkomo. 203 MATHEMATIKA IBANGA LABAQALAYO (R)

Iveki yama-30 Ukusebenzisa iveki yama-30 ukuqwalasela imiba abangekayibambi nezinto ezichongwe njengeziyimiqobo (izidingo) ekufundeni Inkalo yomxholo Isihloko Imilinganiselo yoHlolo 204 Amanani, ukuBala 1.1 Qikelela nokubala ngokucengceleza ukuya kwi-7 (amaculo nezicengcelezo ngamanani zidityanisiwe noLwalamano ukuphuhlisa ingqiqo ngamanani) ukubala izinto Bala ubuya umva nokubala usiya phambili (1-7) Yazi ukuba ngawaphi amaxesha okuqhwaba angaphezulu/ angaphantsi Nakana amanani kwiimeko eziqhqelekileyo umz. Ubudala ,irejista (isigama esisetyenziswa xa kufundwa ngamanani) (UkuHlola kwakhona) Chonga imifanekiso yamanani namakhadi anamachaphaza ukuya kwinani lesi-7 Zazi iisimboli zenani 5, 6, 7 Nakana amagama amanani u-ntlanu, ntandathu, sixhenxe Yahlula phakathi kuka ngaphezulu, ngaphantsi nozilingana, ninzi nombalwa ukuya kwi-7 Nakana imibala kwakunye neentlobo zezilwanyana kwimali engamaphepha yaseMzantsi Afrika. 1.6 Sebenzisa izixhobo eziphathekayo Ubuchule bokusombulula iingxaki zezibalo Cacisa ingcinga yakho ngamazwi nangemizobo okanye izinto eziphathwayo 1.7 no 1.13 Ukudibanisa nokuthabatha Ukusombulula ngomlomo iingxaki zokudibanisa nokuthabatha ukuya kwisi-7 Iipateni, neefankshini 2.1 Iipateni zejiyometri K opa, ukwandisa nokuyila ezakho iipateni usebenzisa imifanekiso ISithuba 3.1 Yazi indawo-bume yezinto ezi-2 nangaphezulu ngokunxulumeneyo-ngaphambili kwe,ngasemva,ngaphezulu MATHEMATIKA IBANGA LABAQALAYO (R) neMilo(Ijiyometri) kwe,phezu,ngaphantsi,ezantsi,ecaleni kwe,embindini,ekhohlo,ekunene Indawo-bume,ukufumana indwawo nembonakalao Landela imiyalelo kwibhodi yeepegi Zazi izalathiso kwitshathi yezalathiso 3.2 Yakha usebenzisa umzekelo wesakhiwo Izinto ezinokwakheka kuka 3-D Kopa isakhiwo kwikhadi eliyiliweyo okanye lomfanekiso INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 3.3 Yakha iipazili ubuncinci izicwili ezinga-18 Izinto ezinokwakheka kuka 2-D Nakana ,ukuchonga nokuxela isikwere Qonda iimilo azifundileyo (ulwazi lweemilo) Umlinganiselo 4.2 Ubude Qikelela nokuthatha umlinganiselo wobude bezinto ezahlukileyo 4.3 Ubunzima Qonda amagama abonakalisa ubunzima “lula,nzima; lula kunenye, nzima kunenye; lula kuzo zonke, nzima kuzo zonke” 4.4 Umthamo/Ivolumu Qonda amagama abonakalisa umthamo “engenanto, egcweleyo, ngaphezulu kune, ngaphantsi kune” Ukusebenzisa ulwazi 5.1 Ukuqokelela, nokuhlela izinto Yazi ukuqokelela, ukuhlela, ukuzoba, ukufunda nokubonisa izinto (ukucalula) ngokophawu oluthile oluqokelelwayo 5.2 Ukubonisa 5.3 Ukuxoxa nokunikezela ingxelo yengqokelela yezinto ezihleliweyo

IKOTA YESI- 4 IMATHEMATIKA IBANGA LABAQALAYO(R) Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 31 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.1 • Ukwazisa intsingiselo yenani i- 8 Usuku olu- 1 Ukubala Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-8 Bala usiya phambili nokubuya umva ukuya kwi-8 Iingoma zamanani nezicengcelezo. Bala ngokucengceleza 1-10 Yazisa ukubala ngoonombini usebenzisa isicengcelezo samanani Bini,ne,thandathu,bhozo Bethelela ukubala ngolandelelwano: utitshala ubeka izinto ezine emgceni. Ukhomba Indoda enye esangweni kwinto nganye ngeli xa abalayo, eyokuqala, eyesibini, eyesithathu, eyesine. Uthi ungxamile Bethelela ingqiqo ka “uninzi nombalwa” Bini, ne, thandathu, bhozo Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla kasi-8 Utitshala makasebenzise eyakhe ingoma Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi. yamanani nesicengcelezo Ukufunda usebenzisa intshukumo yomzimba Yenza abafundi: -- Babale izinyathelo ezisibhozo ngoku ngeli xa bajikeleza iklasi. -- Babonise iminwe esibhozo. 0 1 2 3 4 5 6 7 8 -- Yenza abafundi: -- Basebenzise ileli yenani elele phantsi (xwesileyo) -- Ukuqinisekisa ukuba abafundi basoloko beqala kwi-0 (qanda). Ingqokolela yoonotsheluza besimboli yamanani -- Bachonge iisimboli zamanani ngeli xa bahamba kumgca- manani u-1 ukuya kwi- 8. -- Bahambe kwilungu ngalinye ngoku babala ngokucengceleza(counting rhythmically) 205 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 31 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 206 mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.3 • Ukunakana iisimboli zamanani namagama amanani Ingqokelela yezinto ezi-8 eziseklasini Usuku olu- 1 Iisimboli zamanani Ukusebenzisa izinto ezinokwakheka kuka 3-D Izinto okanye izixhobo zokubala namagama Yenza abafundi: amanani -- Babale izinto eziseklasini ezibandakanya amanani u-1 ukuya kwi-8. -- Babale ngezinto zokubala ukuya kwi-8. -- Ukukhulisa ulwazi ngogcino-manani ngengqondo ngokwenza abafundi bapakishe Izixhobo zokubala ezi-8 okanye izinto izixhobo zokubala ezisi- 8 okanye naziphi na izinto ngeendlela ezahukeneyo umz. ezisi-8 Unotsheluza onesimboli yenani negama MATHEMATIKA IBANGA LABAQALAYO (R) Xa kubalwa, inani lezinto malingachatshazelwa bubungakanani, okanye ubume lenani, amachaphaza kunye nemifanekiso bendawo,okanye nokuba zezohlobo olunye.Umzekelo: umz. -- Cwangcisa amaqhosha a-8, iipensile ezi- 8, oohupu aba- 8, abafundi aba-8, njl. Umfanekiso -- Bala izinto ngokulandelelana okwahlukileyo umz. zibale ziqaqelene, zisondelelene, wezinto isibhozo ezisi -8 zisemgceni okanye zipakishiwe. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Yenza abafundi: -- Badlale imidlalo ngokunxulumanisa inani lezixhobo zokubala kunye namagama amanani, isimboli yenani, amakhadi amachaphaza nemifanekiso ebandakanya inani iikhrayoni i1-8. izixhobo zokubala -- Bakhuphele inani usi-8 ngekhrayoni.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 31 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.4 • Ukusebenzisa inani usi-8 kwimeko eqhelekileyo Usuku olu- 1 Ukuchaza, Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-8. ukuthelekisa Ukubala usiya phambili nokubuya umva ukuya kwi-8. Iingoma zamanani nezicengcelezo nokuhlela amanani Ukubethelela ukubala ngezi- 2 usebenzisa izicengcelezo zamanani Ukubethelela ingqiqo ngo “uninzi nombalwa” Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla ka-8. Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi. Ukufunda usebenzisa intshukumo yomzimba Yenza abafundi: -- Benze inani usi-8 ngeminwe yabo. Umtya/ iwulu okanye udongwe. -- Bakhe inani ngomtya okanye udongwe. Isithebe esinentlabathi -- Babhale iisimboli zamanani kwisithebe(tray) sentlabathi -- Beka amakhadi esimboli yamanani amakhulu ngokulandelelanayo kumgangatho ukuya Ingqokolela yamakhadi amakhulu kwi-8. aneesimboli zamanani Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iimbotyi ezisibhozo kumfundi ngamnye Utitshala unika umfundi ngamnye iimbotyi ezi- 8, unotsheluza onamachaphaza, unotsheluza onegama,nezixhobo noonotsheluza abanamachaphaza asi- 8. zokubala Yenza abafundi: -- Bapakishe ukhozo lwembotyi kwichaphaza ngalinye elikunotsheluza. isibhozo -- Babale iimbotyi. -- Banxulumanise unotsheluza wechaphaza kwigama lenani nakwizixhobo zokubala. 207 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 31 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 208 mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.3 Ukunakana, ukuchonga nokuxela izinto ezinokwakheka kuka 2-D eklasini Usuku olu- 1 nasemfanekisweni Izinto ezinokwakheka -- Ukufundisa uxande Amakhadi emidlalo akhulisa unakano kuka-2-D Ukufunda usebenzisa intshukumo lweemilo. Yenza abafundi: -- Benze uxande olunamacala amane angqalileyo. -- Bakhe iimilo ngemizimba yabo umz. Abafundi aba- 6 bakha uxande ngemizimba yabo. Uboya okanye udongwe -- Bakhe uxande besebenzisa iminwe yabo . -- Benze/ bakhe uxande nezijungqe zewulu okanye udongwe. “Ingxowa empampathwayo” (Feely bag) eneentlobo zemilo zejiyometri. -- Bahambe ngaphandle kungqameko lwemilo yoxande.Njengokuba behamba abafundi bathi “ndihamba ecaleni koxande- linye icala elide, linye icala elifutshane, elinye icala Ukutshatisa amakhadi neemilo ezizotywe elide, elinye icala elifutshane. kuwo. -- Beva iimilo ngezandla.Basebenzisa iimilo zobungakanani obukhulu okanye babeka MATHEMATIKA IBANGA LABAQALAYO (R) iintlobo zeemilo kwingxowa empampathwayo (feely bag).Yiba nengqokolela yamakhadi aneemilo ezizotywe kuwo.Umfundi uva imilo engxoweni aze ayitshatise namakhadi. Iphepha elibukhulu buyi A4 nekhrayoni -- Bazoba imilo yoxande emoyeni, emhlabeni/ kumgangatho (ngetshokhwe) ekugqibeleni bazobe ephepheni. Ukusebenzisa iimilo ezinokwakheka kuka 2-D ngokobungakanani,umbala nemilo Izinto ezibuxande eklasini. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Yenza abafundi bakhangele izinto eziziingxande eklasini. Zonke iimilo ezifundiweyo ukuza kuthi ga ngoku: Ukusebenzisa iimilo/imifanekiso ezinokwakheka kuka 2-D iintlobo zemifanekiso ezineemilo kuzo. -- Ukuchonga imilo eluxande kwimifanekiso -- Ukuchonga zonke iimilo ezazisiweyo ukuza kuthi ga ngoku kwimifanekiso. Ukuhlela izinto ezinokwakheka kuka -3-D no- 2-D ngokobungakanani, umbala nemilo. -- Ukuhlela ingqokolela yezinto ngokobungakanani, umbala nemilo.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 31 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 5.1 • Ukubethelela ingqiqo yokusebenza ngolwazi oluqokelelweyo ngokuqokelela izinto Itshati yomhla wokuzalwa eklasini okanye kokusingqongileyo ngokweempawu ezinikiweyo, umzekelo, imihla Ukuqokelela yokuzalwa yabafundi . nokuhlela izinto Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ukuqokelela nokuhlela ulwazi Januwari Februwari -- Ukusebenzisa itshati yemihla yokuzalwa, ukuchaza imihla nenyanga yokuzalwa.. -- Abafundi bancedisa ekwenzeni igrafu ukubona ukuba yeyiphi inyanga yonyaka ebonakala inemihla yokuzalwa emininzi. -- Utitshala uzoba igrafu yeenyanga ezili-12 zonyaka. -- Ngoncedo lukatitshala abafundi babeka amagama abo belandela inyanga yomhla wokuzalwa komfundi ngamnye . Janyuwari Februwari Matshi Aprili Meyi Juni Julayi Sipho Dali Noni Kabelo Selina Thabo Mavi Bongi Bongi Pat Lizo Jabu 5.2 Ikhadi elinamagama abafundi . Hlubi Celiwe Tim Thandi Titi Ukubonisa ulwazi Dolly lwengqokelela 4 3 0 3 3 3 2 Zoba imiqolo eli-12 kumcu omkhulu wephepha.Bonisa yezinto -- Abafundi babala amagama babhale inani lilonke lemihla yokuzalwa phantsi kwenyanga ngekhadi lamagama iinyanga abafundi abakhumbula ezihleliweyo nganye.. ngazo imihla yokuzalwa.Sebenzisa iishiti ezi± 3 -- Abafundi bathelekisa inani lemihla yokuzalwa kwiinyanga ezohlukeneyo. zephepha elibukhulu bungama A2 elizotywe imiqolo. Utitshala ubuza imibuzo enjengale: -- “Yeyiphi inyanga enemihla yokuzalwa emininzi?” -- “Yeyiphi inyanga enemihla yokuzalwa emincinane?” -- “Ziziphi iinyanga ezinenani elifanayo lemihla yokuzalwa? Ziyalinganal.” 5.3 -- “Ziziphi iinyanga ezinamakhwenkwe amaninzi akhumbula imihla yawo yokuzalwa”? Ukuxoxa -- “Ziziphi iinyanga ezinamantombazana amaninzi akhumbula imihla yawo yokuzalwa”? nokunika ingxelo Abafundi baxoxa ngezigqibo ezilandelayo: ngengqokelela yezinto -- UJanyuwari uneyona mihla yokuzalwa mininzi. Abafundi abane bakhumbula imihla ezihleliweyop yabo yokuzalwa ngoJanyuwari. -- Akukho zikhumbuzo zamihla yakuzalwa ngoMatshi.Inye inyanga apho kungekho bafundi bakhumbula imihla yabo yokuzalwa. 209 -- Ezinye iinyanga zinemihla yokuzalwa elinganayo njl. Ziziphi ezi nyanga? MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 210 mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.1 • Ukubethelela a ulwazi olufunyenwe kwiveki yama-31 oluquka inani elingusi- 8. Usuku olu- 1 Ukubala izinto Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-8 Ukubala usiya phambili nokubuya umva ukuya kwi-8 Iingoma nezicengcelezo zamanani Ukubala ngokucengceleza u-1 ukuya kwi-10 Ukubethelela ukubala ngezi- 2 usebenzisa izicengcelezo zamanani Ukubethelela “uninzi nombalwa” Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla ka-8 Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi Ukufunda usebenzisa intshukumo yomzimba Makudlalwe umdlalo: Igubu -- Utitshala udlala ngesixhobo- umz. Igubu MATHEMATIKA IBANGA LABAQALAYO (R) -- Abafundi bayajikeleza . -- Xa igubu liyeka ukukhala, utitshala ubiza inani eliphakathi kuka- 1 ne-8 ze abafundi bazilungise ngamaqela amancinane umz. Utitshala ubiza inani eli-8 baze abafundi bazilungise ngamaqela anabafundi aba-8 -- Bonisa iminwe e-8 kwizandla zakho zozibini. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Yakha ingqokelela nabafundi.Zoba isangqa esikhulu entlabathini.Yenza abafundi bakhe amaqela abafundi aba-8 ngaphakathi kwesangqa.Amaqela abafundi abasi-8 bangenza umsebenzi kunye ngemini umz. Badlale kwikona yebhloko, baye kwindawo yomsebenzi wobuGcisa (art area) njl.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ukubala izinto Yenza abafundi: -- Basebenzise izixhobo zokubala ukunakana ukuba ngawaphi amanani eza ngaphambi Izixhobo zokubala kwesi-8 nasemva kwesi- 5? Liliphi inani eliphakathi kwesi- 6 nosi-8 ? -- Babale izinto ngambini: izibini zezihlangu, zeekawusi, zamacicic o Izibini zezihlangu o Izibini zeekawusi o Izibini zamehlo amabini, o Izibini zamacici, o Izibini zeendlebe Amakhadi aneenombolo zomnxeba o Izibini zemilenze needilesi Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Xa kuthathwa irejista yobukho utitshala ubuza:“Ingaba umfundi onenombolo yendlu okanye idilesi …… ulapha?” umfundi makaphendule ngokubonisa ukuba “ulapha”. -- Phinda ngemini elandelayo ngeenombolo zemfono-mfono neenombolo zeseli(cell). 211 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 212 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.7 • Ukusombulula ngomlomo izibalo zamanani zamazwi ezibandakanya inani eli- 8 Usuku olu- 1 Ukudibanisa Ukufunda usebenzisa intshukumo yamalungu omzimba nokuthabatha -- Utitshala uncedisa abafundi ukwenza iqela labafundi aba-6 nelinye iqela elinabafundi aba- 2. -- Dibanisa amaqela ama- 2 ukwenza iqela eli- 1. Amaqela abafundi -- Buza abafundi ukuba Bangaphi abafundi kwiqela elidityanisiweyo? 6 no- 28.(utitshala uthi: u- 6 no zi- 2 benza i- 8) -- Yenza iqela labafundi aba- 8. Thatha abafundi aba- 3 benze iqela elincinci. Bangaphi abafundi abashiyeke kwiqela elikhulu? Ba-8 uthabathe aba- 3 5. -- Khetha abafundi ababini usebenzisa isicengcelezo sokubala. -- Beka amasebe ama-4 kwisandla esinye somfundi namasebe ama-4 kwesinye isandla somfundi. Mangaphi ewonke amasebe ngoku? U-4 no 4  8. Amasebe Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Isicengcelezo sokubala: MATHEMATIKA IBANGA LABAQALAYO (R) Nika umfundi ngamnye amasebe a-8 . Amasebe -- UTshidi unamasebe ama-6 umhlobo wakhe unamasebe ama-2. Mangaphi amasebe Isicengcelezo: Yenza esakho abanawo ewonke? u - 6 no - 2  8. (1, 2, 3, 4, 5 -- UMonica unamasebe asi-8. Ulahle amasebe ama-2.Ushiye amasebe amangaphi uMonica? Asi- 8 uthabathe 2  6. Ndakha ndabambisa intlazi iphila INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukusebenzisa imilo ezinokwakheka kuka 2-D okanye imifanekiso 6, 7, 8, 9, 10 -- Utitshala ubeka imifanekiso emi-2 kwibhodi yeflaneli .Wongeza eminye imifanekiso Ndabuya ndayiyeka yahamba) emi-5. Mingaphi imifanekiso ekwibhodi yeflaneli ngoku? Uzi-2 nozi 5  7. Amasebe -- Beka iimilo ezisi-8 kwibhodi yeflaneli. Thabatha iimilo ezi-5 kwibhodi yeflaneli. Kushiyeke zingaphi? .zisi-8 uthabathe 5→3. Imifanekiso/neemilo zebhodi yeflaneli.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 2.1 • Ukukopa nokwandisa iipateni eziviwayo Usuku olu- 1 Iipateni zejiyometri Ukufunda usebenzisa intshukumo yomzimba Abantwana bahamba nesingqi somculo ngemizimba yabo umz.. -- ngqisha, ngqisha, ngciloza,ngciloza........ Isidlali mculo (CD) -- Tsiba ngomlenze omnye, tsiba ngemilenze emibini,tsiba ngemilenze emibini....... Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D . Nxulumanisa nobuGcisa beQonga, umculo kwiZakhono zoBomi Abafundi bahamba nesingqi somculo ngezandla zabo baphathe amathanga abo umz. -- Qhwaba, qhwaba, betha,betha (qhwaba ngezandla ubethe amathanga ngezandla. -- Utitshala wenza amakhadi esingqi abafundi bawaphinde ngokuqhwaba isingqi (basebenzise izandla ukuqhwaba neenyawo ukungqisha) Ukubethana kwamalungu omzimba Umz..     π π   π π  -- qhwaba,qhwaba, ngqisha, ngqisha, ……… -- qhwaba ukhwaze, qhwaba, khwaza……. 213 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 214 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.3 Ukunakana, ukuchonga nokuchaza iimilo ezinokwakheka kuka 2-D eklasini Amakhadi emidlalo akhulisa unakano usuku olu- 1 lweemilo. Izinto • ukubethelela ulwazi ngoxande ezinokwakheka Izinti zematshisi Ukufunda usebenzisa intshukumo yomzimba kuka-2-D Yenza abafundi: Iwulu okanye udongwe. -- Benze/bakhe iimilo ngemizimba yabo umz.abafundi aba-4 bakha uxande ngemizimba yabo. Ingxowa empampathwayo (“Feely bag”) eneemilo zejiyometri ezahlukileyo. -- Bakha uxande besebenzisa iminwe yabo. -- Benza uxande besebenzisa izinti ezi-6 zematshisi. Quka iimilo ezinkulu nezincinane -- Benza/bakha uxande ngezijungqe zewulu okanye udongwe. kunye noonxantathu bee-engile (angles)ezahlukeneyo kwingxowa MATHEMATIKA IBANGA LABAQALAYO (R) -- Bahamba ngaphandle kwemilo yoxande. empampathwayo umz. -- Beva iimilo ngezandla. Beka iimilo ezahlukeneyo kwingxowa empampathwayo(“feely bag”)Yiba nengqokolela yamakhadi okutshatisa azotywe iimilo. Abafundi beva imilo engxoweni baze bayitshatise namakhadi. -- Bazoba imilo yoxande emoyeni, entlabathini, kumgangatho/emhlabeni bagqibele INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA ngokuzoba emoyeni. Tshatisa ingqokelela yamakhadi ekuzotywe kuwo iimilo Iphepha elibukhulu buyi-A4 nekhrayoni

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.3 Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Izinto -- Yenza abafundi bajonge izinto ezimile okoxande eklasini Izinto ezibuxande eklasini. ezinokwakheka Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso kuka 2-D Ukudlala umdlalo: “Yeyiphi elahlekileyo?” Iindidi zeemilo umz. Iimilo zelogi -- Ukubeka iimilo ezinokwakheka kuka 2-D (zingabingaphezulu kweemilo ezi- 5) kwiphetshana embindini wekhaphethi umz.iimilo ezikumdlalo we-Logi . -- Xoxa ngemilo nganye nabafundi. -- Nika abafundi ithuba lokufunda ngentloko iintlobo zeemilo ezikwiphetshana. -- Abafundi bavala amehlo abo. -- Utitshala ususa enye yeemilo. -- Abafundi mabavule amehlo abo batsho imilo elahlekileyo. -- Phinda inkqubo. -- Ukukhuthaza ukukhuliswa kweemilo zejiyometri ngokunika iintlobo zamakhadi zemidlalo enjenge “yintoni esesikwereni?” okanye nokuba nguwuphi umdlalo. 215 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama- 32 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 216 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.1 Indawo bume yezinto ezimbini okanye nangaphezulu ngokunxulumene nenye usuku olu- 1 Indawo- Ukufunda usebenzisa intshukumo yomzimba bume,ukufumana Yenza abafundi: indawo -- Beme phakathi kwezinto ezimbini okanye abafundi ababini nembonakalo -- Beme ngasecaleni kwentombazana enxibe ilokhwe ebhlowu -- Beme ngasecaleni kwenkwenkwe eneembadada ezimbala umdaka (brown). Izitulo ezi - 2. -- Bahambe phakathi kweebhokisi. -- Bagaqe bejikeleza itafile. -- Bagaqe phantsi kwesitulo. -- Babeke isitulo phambi kwabo. -- Babeke isitulo emva kwabo. -- Beme kwizitulo zabo. -- Bahlale kumgangatho. -- Babeke izitulo ngaphezu kwabo. MATHEMATIKA IBANGA LABAQALAYO (R) -- Babeke izitulo emacaleni abo. -- Babeke izitulo kwicala labo lasekhohlo/ lasekunene. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Yenza abafundi bagqibezele iphazili enemifanekiso yabantu okanye izilwanyana. Iiphazili -- Bahlohla amaso ngokomyalelo katitshala umz.hlohla amaso abomvu. Beka iliso Amaso aza kuhlohlwa INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA eliluhlaza ecaleni kweli bomvu njl. Iiphegibhodi neephegi -- Hlohla amaso ngokokulandelelana kwemifanekiso oyinikiweyo. Ukusebenza kumaqela amancinane. Utitshala unika abafundi iphegibhodi kunye neephegi ezigcwele isandla. Nika le miyalelo ilandelayo: -- Beka iiphegi ezimbini ezibomvu kumphezulu wekona esekhohlo. -- Beka iphegi eluhlaza ngasekunene kwephegi ebomvu. -- Beka iphegi enye ebhlowu ngaphantsi kwephegi eluhlaza njl. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Amaphepha okusebenzela (Worksheets) -- Zoba abantu okanye izilwanyana ezingenangalo okanye imilenze okanye anemizobo ezingenamikhono ucele abafundi bagqibezele umzobo.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.3 Ukubethelela ulwazi olufunyenwe kwiveki yama-31 neyama-32 eziquka amanani u-1 Usuku olu- 1 ukuya kusi-8 Ukubala izinto Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-8 Bala usiya phambili nokubuya umva ukuya kwi-8 Iingoma nezicengcelezo zamanani Bala ngokucengceleza u-1ukuya kwi-10 Bethelela ukubala ngezibini usebenzisa isicengcelezo samanani Bethelela ukubala ngolandelelwano Utitshala ubeka izinto ezi-8 emgceni. Ukhomba kwinto nganye ngeli xa abalayo,eykuqala, eyesibini, eyesithathu, eyesine, eyesihlanu. Bethelela ingqiqo “uninzi nombalwa” Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla ka-8 Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi. Ukufunda usebenzisa intshukumo yomzimba -- Abafundi basebenzisa imizimba yabo ukwakha isimboli yenani. Iisimboli zamanani amakhulu awenziwe -- Utitshala wenza amanani kwimathiriyeli eyahlukeneyo enokuviwa ngabantwana umz. ngephepha lokukhuhla Iphepha lokukhuhla (sandpaper)/ udongwe/umtya. -- Benza izicengcelezo/iingoma zamanani. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Ukusebenzisa izinto eziphathekayo ezinjenge bhloko nezilwanyana ezenziwe Iibhloko nezilwanyana zokudlala ngeplastikii. zasefama zeplastiki -- Ukuzibala, ukuzihlela, ukubeka ezisibhozo emgceni njl. Yahlula abafundi ngokwamaqela. Beka imfumba yezilwanyana zasekhaya embindini weqela ngalinye Izilwanyana zasekhaya zeplastiki ezili-9 Yenza abafundi: -- Basebenze ngababini eqeleni beqikelela ukuba zingaphi izilwanyana ezikwimfumba. Iiseti zamakhadi eesimboli zamanani ezimbalwa. -- Isibini nganye sithatha ikhadi lenani ukutshatisa ingqikelelo yabo. -- Babale elona nani lezilwanyana. 217 -- Isibini singafumana inkwenkwezi ibekwe kumabunzi abo. Iinkwenkwezi zokuvuza -- Phinda ngokubeka inani elahlukileyo lezilwanyana embindini wekhaphethi. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 218 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.3 Ukunakana nokuchonga iisimboli zamanani namagama amanani abandakanya amanani u-1 ukuya kwi-8 Iisimbolo Umfanekiso noonotsheluza beesimboli zamanani kunye Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso zamanani namagama -- Tshatisa isimboli yenani kumfanekiso ochanekileyo. amanani -- Umfundi makaqonde ukuba iqela lezinto linganenani elifanayo lezinto. Izixhobo zokubala Umfanekiso wezinto isiBhozo ezisibhozo -- Abafundi mabakhombe kwinto nganye njengoko bebala. Ingqokolela yamakhadi amanani equka amanana u-1 ukuya kwi-8 MATHEMATIKA IBANGA LABAQALAYO (R) -- Abafundi mabakwazi ukutshatisa into nenye umz.intliziyo enye nelanga. -- Batshatise umfanekiso okunotsheluza, unotsheluza wamachaphaza, isimboli yenani, unotsheluza wegama lenani, inani lezixhobo zokubala ezifanayo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.4 • Ukulandelelanisa nokuthelekisa ingqokelela yezinto kusetyenziswa “ungaphezulu Usuku olu- 1 kune/ngaphantsi kwe” no “zilingana” ukuya kwi-8 Chaza,uthelekie uze ulandelelanise Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-8 Bala usiya phambili nokubuya umva ukuya kwi-8 Bethelela ukubala ngezi- 2 usebenzisa izicengcelezo zamanani Iingoma nezicengcelezo zamanani Ukubethelela ingqiqo ka “ninzi no-mbalwa” iibhloko Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla kasi-8 Ukufunda usebenzisa intshukumo yomzimba -- Utitshala ubeka iibhloko ezisi-8 etafileni. Abafundi mabaqikelela inani leebhloko ngaphandle kokuzibala. -- Utitshala ubuza: o “ingaba iibhloko zingaphezu kwesithathu?” Izixhobo zokubala o Abafundi bajonga impendulo yabo ngokubala iibhloko o “belusondele kangakanani uqikelelo lwakho? Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Yakha iqela labafundi aba- 4.Nika iqela ngalinye izixhobo zokubala ezi-8 nephepha Iphepha elibukhulu buyi A4 elineendlwana elizotywe izangqa ezibini ezikhulu.Biza izangqa ngeendlwane. ezimbini ezizotyiweyo. -- Abafundi babeka izixhobo zokubala kwindlwana nganye ngokomyalelo katitshala batsho ukuba zingaphi     -- Abafundi bathelekisa “iindlwana” baxele ukuba yeyiphi indlwana “engaphezulu kunenye”, “engaphantsi kunenye”, “efanayo” okanye enezixhobo zokubala “ezilinganayo”. 219 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 220 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.4 Yahlula abafundi ngokwamaqela Iibhokisi ezizizikwere ezincamathelanayo Usuku olu- 1 (Unifix cubes) Chaza,uthelekie -- Nika iqela ngalinye iityhubhu zeyunifekisi ezincamathelanayo (unifix cubes) ezininzi uze ulandelelanise nengqokelela yamakhadi eesimboli zamanani aquka amanani u-1 ukuya kwisi-8 Amakhadi eesimboli zamanani u-1ukuya kusi-8 -- Yenza iqela lenze incochoyi (ithawa) uze uliphawule ngelebheli incochoyi nganye ngenani leetyhubhu ezisetyenzisiweyo umz. Oonotsheluza bamachaphaza Iimilo ezinokwakheka kuka 2-D okanye imifanekiso nemifanekiso -- Utitshala ubonisa amakhadi amabini anamachaphaza amanani ahlukileyo MATHEMATIKA IBANGA LABAQALAYO (R) nemifanekiso. Imifanekiso yezinto ezisi-8 -- Yenza abafundi bathelekise amakhathi anemifanekiso namachaphaza ukuchonga e”ngaphezulu kunenye”,”ngaphantsi kunenye” no”zilingana”. 1.13 • Ukusombulula ngomlomo iingxaki zokudibanisa nokuthabatha ukuya kwi-8 usuku olu- 1 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukudibanisa Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-8 nokuthabatha Ukubala usiya phambili nokubuya umva ukuya kwi-8 Kubethelela ukubala ngezi- 2 usebenzisa izicengcelezo Iingoma nezicengcelezo zamanani Ukubethelela ingqiqo ngo “ninzi no-mbalwa” Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla ka-8 Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.13 Ukufunda usebenzisa intshukumo yomzimba Ukudibanisa Imizekelo: nokuthabatha 1. Utitshala ubiza abafundi aba-3 ukuba beze ngaphambili.Abafundi bayababala. Utitshala ubiza abanye abafundi aba-2 abuze ukuba: “Bangaphi abafundi bebonke?” 2  5. (utitshala uthi: u-3 no- 2 benza u- 5) 2. Utitshala upakisha izitulo ezibini. Ongeze ezimbini ngaphezulu. Zingaphi izitulo eziphaya ngoku? Uzi- 2 nozi- 2 →uzi- 4. 3. Utitshala uphakamisa isandla esinye.aze athi: “bala iminwe yam. Ukuba ndifihla umnwe omnye, mingaphi iminwe oyibonayo? Zi- 5 uthabathe ibe- 1  4. 4. Yenza abafundi babale iminwe kwesinye sezandla zabo. Fihla umnwe wakho omnye; mingaphi iminwe oyibonayo? Zi-5 uthabathe ibe-1 →zi- 4. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Yenza abafundi bapakishe izixhobo zokubala ezi-6 uze wenze oku kulandelayo: -- Utitshala unika umfundi ngamnye izixhobo zokubala ezi-6. Utitshala unika imiyalelo ze abantwana baphendule umz.pakisha izixhobo zokubala ezi-2, yongeza esinye, yongeza ezinye ezi-3.Zingaphi zizonke. U- 2no-1 no-3→isi-6. -- Bala izixhobo zokubala ezi-4. Bala ezi-2 ukusuka kuzi-4.Zingaphi onazo ngoku? U- 4 no- 2 →isi- 6. -- Bala onke amaso onawo. Ukuba wogquma amaso amabini ngesandla sakho, Izinto okanye izixhobo zokubala mangaphi amaso owabonayo? Isi-6 uthabathe zibe-2 →zi- 4. Ukusebenzisa iimilo okanye imifanekiso ephathekayo enokwakheka kuka 2-D Yenza iphazili yamanani uze uvumele abafundi baphicothe ngephazili   6 Iphazili yamanani 3 9 7                                2                      9   221 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 222 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.3 Ukunakana,ukuchonga nokuchaza izinto ezinokwakheka kuka 3-D Usuku olu-1 Izinto • Ukuzakhela ingqinqo yento engqondweni ezinokwakheka • Ukufunda usebenzisa intshukumo yomzimba kuka 2-D Utitshala uchaza into abuze abafundi ukuba iyintoni umz. -- ‘ndicinga ngento ebomvu, enamavili amane, iingcango ezine neefestile ezivulekayo yenze isandi “vuum”.lo msebenzi ungenziwa ngamaqela ujikwe ubelukhuphiswano – elinye iqela kufuneka lichaze, elinye iqela liqikelele ukuba iyintoni na le kuthethwa ngayo Nokuba ngowuphi umfanekiso -- Chaza umntu uze ucele abafundi ukuba bamchonge umntu lowo . Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso umfanekiso oneenxenye ezisikiweyo -- Bonisa umfundi umfanekiso umenze awujonge.Wuthathe ucele umfundi ukuba achaze iinkcukacha ngokokuzikhumbula kwakhe. umzobo ongagqitywanga -- Thatha umfanekiso ube mnye usike iinxenye zawo.Beka umfanekiso osikiweyo MATHEMATIKA IBANGA LABAQALAYO (R) neenxenye zawo ebhokisini uze ucele abafundi ukuba bakhangele iinxenye ezilahlakileyo zomfanekiso ngamnye abawukhethayo. -- Zoba umfanekiso ongaphelelanga kwihetshana ucele abafundi bagqibezele umfanekiso INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-33 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.4 • Ukukhulisa ulwazi lokuba umzimba womntu unecala lasekhohlo nelasekunene usuku olu- 1 elinokushukuma ngokuzimeleyo Ulingano- macala Ukufunda usebenzisa intshukumo yomzimba -- Beka ibhanti elinwebekayo (elastic band) kwisihlahla sasekunene somfundi ngamnye. Iingoma/ izicengclezo zentshukumo -- Cula iculo elinentshukumo: “ndibeka unyawo lwam lwasekhohlo phakathi” umz. “Ndibeka unyawo lwasekhohlo Yenza abafundi: ngaphakathi” -- Babeke izandla zabo zasekunene kwiintloko zabo. Yenza ezakho izicengcelezo -- Baphathe amadolo abo asekhohlo ngeengqiniba zabo zasekunene. -- Baphathe amagxa abo asekunene ngezandla zabo zasekhohlo njl. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D 3.1 Nika umfundi ngamnye iibhloko zokwakha Ibhloko yomfundi ngamnye Indawo- bume,ukufumana Yenza abafundi ukuba bahlale kwikhaphethi: indawo -- Mababeke iibhloko kumacala abo asekunene/ amacala asekhohlo nembonakalo -- Ngamagxa abo asekhohlo/ amagxa asekunene -- Ngamadolo abo asekhohlo/ amadolo asekunene njl. -- Ngonyawo lwasekhohlo /kunene njl-njl. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Iphepha -- Umfundi ngamnye ufumana iphepha nekhrayoni. -- Yenza abafundi bazobe umgca kumbindi wephepha ukusuka phezulu kuye ezantsi nomnye umgca embindini ukusuka ekhohlo kuye ekunene. -- Utitshala unika imiyalelo: o Beka umnwe wakho kumbindi womnqamlezo .     o Zoba isangqa kwibhloko ekumphezulu osekhohlo. o Zoba unxantathu kwibhloko ekumzantsi osekunene . o Zoba isikwere kwibhloko ekumphezulu osekunene. o Zoba uxande kwibhloko ekumzantsi osekhohlo 223 -- Xoxa ngephowusta yomfanekiso. Abafundi baphendula imibuzo ebenza bacacise (ngaphandle kokubonisa) indawo bumilo yezinto emfanekisweni. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-34 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 224 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.1 • Fundisa intsingiselo yenani isi- 9 iintsuku ezi- 2 Bala izinto Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwi-9 Ukubala usiya phambili nokubuya umva ukuya kwi-9 Iingoma nezicengcelezo zamanani Ukukhumbuza ukubala ngezi- 2 usebenzisa izicengcelezo zamanani Ukubethelela ukubala ngolandelelwano: Utitshala ubeka izinto ezine emgceni. Ukhomba kwinto nganye ngeli xa abalayo,eyokuqala, eyesibini, eyesithathu, eyesine. Ukubethelela ingqiqo ka “ninzi no -mbalwa” Qhwaba izandla amaxesha amaninzi……..YIMA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla kali-9 Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi. Ukufunda usebenzisa intshukumo yomzimba MATHEMATIKA IBANGA LABAQALAYO (R) Yenza abafundi: -- Babale ukuya kwi-9 ngoku banyuka izitephu. Iingqokelela zeesimboli zamanani -- Bazoba inani uli-9 esantini/ phantsi/emhlabeni bahambe phezu kwalo. amakhulu -- Baqhwaba izandla amaxesha ali-9. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Banakana amanani u-1 ukuya kwi-9 ngengqokelela yeesimboli zamanani amakhulu. -- Sebenzisa ezakho iingcinga ukwenza abafundi babonakalise amava ngentsingiselo yenani uli-9 ngemizimba yabo/ ngamalungu emizimba yabo.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-34 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.6 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ileli yamanani Ubuchule Utitshala uyila umgca manani okanye ileli phantsi okanye emhlabeni: bokusombulula -- Utitshala unika imiyalelo enjenga le: iingxaki 0 1 2 3 4 5 6 7 8 9 -- Yima kwiqanda okanye qala kwiqanda. -- Bala njengoko ushukuma. -- Shenxa uye kwinani uzi-5. Buya umva uye kwinani u-2. Shenxela ngaphambili uye kwinani si-8. -- Shenxela kwinani usi-8.Shenxa inani libe li-1 ngaphambili. Shenxa amanani ama-2 ukuya emva . -- Liliphi inani eliza emva kwe-3 ? -- Liliphi inani eliza ngaphambi kwe-7? -- Ukukhulisa ulwazi logcino manani ngokwenza abafundi bapakishe izixhobo zokubala okanye nayiphi na into ngeendlela ezahlukeneyo umz. Xa kubalwa, inani lezinto malingachatshazelwa bubungakanani, okanye ubume bendawo,okanye nokuba zezohlobo olunye.Umzekelo: -- Cwangcisa amaqhosha ali-9, iipensile ezili- 9, oohupu abali- 9, abafundi abali-9, njl. -- Bala izinto ngokulandelelana okwahlukileyo umz. zibale ziqaqelene, zisondelelene, zisemgceni okanye zipakishiwe ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Ukusebenzisa inani uli-9 kwimeko eqhelekileyo Yenza abafundi: 225 -- Batshatise unotsheluza wemifanekiso nenani lamachaphaza afanayo. Pakisha inani lezixhobo zokubala ezifanayo MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-34 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 226 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.3 • Ukunakana iisimboli zamanani namagama amanani Iisimboli zamanani Ukufunda usebenzisa intshukumo yomzimba Izinto ezi-5 (ukukhumbula ngokubona) kunye namagama -- Beka izinto ezi-5 emgceni. amanani -- Yenza abafundi bazijongisise -- Abafundi mabajonge kude aze utitshala asuse enye into. Izixhobo zokubala -- Ubafundi kufuneka batsho ukuba yeyiphi into esusiweyo. Imifanekiso -- yibuyisele uphinde amaxesha amaninzi uqhubeke ekususeni izinto ezimbini yezinto nezingaphezulu. eziliThoba Yenza abafundi: Iingqokelela zamakhadi ezimbalwa -- bakhethe isimboli yenani uli-9 negama lenani phakathi kwabanye oonotsheluza. eziquka inani u-1 ukuya kwi-9 -- Beka unotsheluza wesimboli yenani phantsi ngokokulandelelana kwamanani. -- Beka oonotsheluza beesimboli zamanani ngokulandelelana okusabalakileyo iThoba MATHEMATIKA IBANGA LABAQALAYO (R) Yahlula abafundi ngokwamaqela amancinane. Utitshala unika iqela ngalinye ingqokelela yamakhadi eesimboli zamanani. Oonotsheluza abanesimboli Nika abafundi imiyalelo umz. yenani,igama lesimboli, amachaphaza nemifanekiso umz. -- Phathani inani uzi-4, beka ingqiniba yakho kwinani usi-8, hlala kwinani uzi-3, baleka ujikeleze inani uzi-5 amaxesha amahlanu njl. Umfanekiso INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA wezinto iThoba -- Badlala imidlalo beqhakamshela izixhobo zokubala amanani namagama amanani , eziliThoba isimboli yenani, amakhadi amachaphaza kunye nemifanekiso. -- Qinisekisa ukuba isimboli yenani negama lenani lisoloko liqhakamshelene nenani Izinto zokubala lezinto ezifanayo.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-34 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.1 Ukulandela izalathiso ,ukufumana indawo nembonakalo Usuku olu- 1 Indawo- • Ukukhulisa ingqiqo yezalathiso bume,ukufumana Ukuzoba unxantathu omkhulu, okanye isikwere phantsi . indawo nembonakalo -- Abafundi bahamba ecaleni kwemilo bebonisa ngokukhwaza ukuba bajika ekhohlo Iimilo ezinkulu ezizotywe ephepheni okanye ekunene ngezandla zabo -- Ukufundisa usebenzisa intshukumo yomzimba Zoba unxantathu omkhulu, okanye isikwere ephepheni uwubeke phantsi umzobo lowo. Imoto yokudlala Yenza umfundi omnye: -- Atyhale imoto yokudlala ecaleni kwemigca. -- Intsalela yabafundi yolula izandla zayo zasekhohlo okanye ekunene kwicala elingqinelanayo bathi ekhohlo okanye ekunene. Yenza abafundi: Unodoli -- Bachaze izinto kwimbonakalo ezahlukeneyo umz. Unodoli (umphambili/umva), indlu (umphambili/umva), umphambili/ umva wesikolo, imoto (umphambili/umva) Indlu kuxhomekeke apho ume khona. Imoto -- Abafundi bachaza abakubonayo umz. Ukuba kukhona umthi ngaphambi kwendlu bachaza indawo ome kuyo umthi. Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Imifanekiso ebonisa icala ngokucacileyo -- Vumela abafundi ukuba bakwenze ngokwabo ukuya phambili/ emva ngokwalatha icala umz. Icala eya kulo imoto, icala aya kulo emfanekisweni. umntu 227 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-34 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 228 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.3 Ukunakana,ukuchonga nokuxela iimilo ezinokwakheka kuka 2-D eklasini, Usuku olu- 1 kwimifanekiso nokuzihlela Iimilo ezinokwakheka • Bethelela ulwazi ngesangqa, unxantathu, isikwere noxande kuka2-D Ukufunda usebenzisa intshukumo yomzimba Yenza abafundi babe ngababini. Iintlobo ngeentlobo zeemilo -- Makazobe imilo kumqolo womhlobo wakhe ngeminwe yakhe. Omnye umfundi makachaze imilo leyo Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Iphepha elinezangqa, oonxantathu , Nika iimilo zejiyometri zobungakanani nobungqingqwa obahlukeneyo. izikwere kunye neengxande umz. Yenza abafundi: -- Bahlele iimilo zejiyometri ngokwe: zangqa, oonxantathu,izikwere neengxande . -- Bahlele iimilo zejiyometri ngokobungakanani. MATHEMATIKA IBANGA LABAQALAYO (R) -- Bahlele iimilo zejiyometri ngokombala Ukusebenzisa imilo ezinokwakheka kuka 2-D okanye imifanekiso Dibanisa iimilo ezinkulu nezincinane Yenza abafundi: kunye noonxantathu bee-engile ezohlukeneyo umz.. -- basike ezi milo zibalwe ngasentla ephepheni. Dibanisa iimilo ezinkulu nezincinane kunye noonxantathu bee-engile ezahlukeneyo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Bahlele iimilo ezahlukeneyo bebonke. -- Cwangcisa umfanekiso oneemilo ezisikiweyo uwusebenzise ngexesha lomsebenzi wobuGcisa.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-34 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.4 • Ukukhulisa ulwazi lokuba lukhona ulingano-macala kwizinto Usuku olu- 1   Ulingano-macala Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Khangela izinto eziyinyani ezizakubonisa ulingano-macala.(icala elinye lifana nelinye icala)umz.ibhabhathane, igqabi lentyantyambo. -- Utitshala nabafundi baqokelela imifanekiso eyiliweyo ngokolingano-macala umz. Imifanekiso epeyintwe ezindlwini, imifanekiso ekwiithayile, imifanekiso ekwiivazi nakwizambuleni zokuhla (parachutes). Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Abafundi basika iimilo zentliziyo okanye ivazi yentyantyambo kwiphepha eliqotywe kubini baze balihombise ngexesha lobuGcisa obuBonwayo     Iphetshana eliqotywe kubini 229 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-35 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 230 mayibe ± 5) Ubude bexesha Isihloko Amanqaku (notes) angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 1.1 • Ukubethelela ulwazi olufumaneke kwiveki yama-34 equka inani i-9 Usuku olu- 1 Bala izinto Ngomlomo: Ukubala izinto zemihla ngemihla ukuya kwisi-9 Bala usiya phambili nokubuya umva ukuya kwisi-9 Izicengcelezo neengoma zamanani Bala ngokucengceleza u-1 ukuya kwi-10 Bethelela ukubala ngezi- 2 usebenzisa izicengcelezo zamanani Ukubethelela ingqiqo ka “ninzi no-mbalwa” Qhwaba izandla amaxesha amaninzi……..YEKA. Qhwaba izandla amaxesha ambalwa. Utitshala uqhwaba izandla kali-9 Buza umbuzo ukuba kukuphi okona kuqhwaba kungaphezulu / kungaphantsi. Ukufunda usebenzisa intshukumo yomzimba Ingqokelela yamakhadibhodi amakhulu amakhadi eesimboli zamanani. Masidlale umdlalo: ungazipeyinta kwizijungqe ezingqingqwa Utitshala ubeka phantsi iimilo zeekhadibhodi ezinkulu zamanani okanye amakhadi aquka MATHEMATIKA IBANGA LABAQALAYO (R) zeplasitiki okanye ibhodi eqinileyo amanani u-1 ukuya kwi-9 ngokulandelelana. Utitshala unika abafundi imiyalelo enjenga le:   7 1 8 -- Hlala kwinani uzi-6 6 3 -- Beka uzwane lwakho kuzi-3 4 5 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Jikeleza inani uzi-2 kathathu. 9 2 -- Tsiba ngaphezu kwenani u-1. -- Utitshala angathi ekugqibeleni asasaze amakhadi eesimboli zamanani. 1.4 • Sebenzisa amanani kwimeko eqhelekileyo usuku olu- 1 Chaza,uthelekise Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D ulandelelanise Yenza abafundi: Izixhobo zokubala amanani -- Babale izinto eklasini Izinto eziseklasini -- Babale ngezinto zokubala -- Utitshala ubeka imfumba yezinto phezu kwetafile.Yenza abafundi baqikelele ukuba zingaphi izinto ezikwimfumba. Bayazibala emva koko.

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-35 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso Unotsheluza onesimboli yenani negama lenani, amakhadi amachaphaza Yenza abafundi: nemifanekiso umz.. -- Badlale imidlalo ngokuqhakamshela izixhobo zokubala amanani namagama amanani, iisimboli zamanani, amakhadi amachaphaza nemifanekiso. Umfanekiso wezinto iThobanine -- Baqinisekisa ukuba isimboli yenani negama lenani zisoloko ziqhakamshelene nenani eziliThoba lezinto ezifanayo -- Bakhuphela inani uli-9 ngeekhrayoni Izixhobo zokubala, iikhrayoni 1.7 • Sombulula izibalo zamanani zamazwi ngomlomo kwimeko equka amanani u-1 ukuya Usuku olu- 1 kwi-9 Ukudibanisa nokuthabatha Ukufunda usebenzisa intshukumo yomzimba -- Balisa ibali ngomthi onentaka enye. Enye iyangenelela.Zingaphi iintaka ngoku?Abafundi Umfanekiso womthi omkhulu balinganisa ibali bezogqume ubuso. U-1 no-1 wenza isi-2. -- Phinda ibali kuze kushiyeke iintaka ezisi-9 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Umhlobo omnye unezixhobo zokubala ezisi-8 umz.izilwanyana zeplastiki omnye une-1 Izixhobo zokubala ezili-9 ngaphezulu. Zingaphi izilwanyana zeplastiki abanazo zizonke? Isi-8 ne-1 9 Ukusebenzisa imilo ezinokwakheka kuka 2-D okanye imifanekiso -- Nika umfundi ngamnye iphepha lokusebenzela elinomfanekiso womthi. Abafundi Iphepha lokusebenzela kunye nezixhobo babeka isixhobo sokubala esinye emthini. Baqhubeka besongeza isixhobo sokubala zokubala esinye ngexesha 231 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-35 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 232 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.1 • Chaza indawo yezinto ezimbini ,enye ngokunxulumene nenye Usuku olu- 1 Chaza izinto Ukufunda usebenzisa intshukumo yomzimba ezimbini enye -- Umfundi ucela umhlobo ukuba eme phakathi kwezinto ezimbini/ abafundi ngokunxulumene nenye -- Umfundi ucela umhlobo ukuba eme ecaleni kwentombazana enxibe ilokhwe ebhlowu. -- Umfundi ucela umhlobo ukuba eme ecaleni kwenkwenkwe enembadada ezibhrawuni. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D • Xhoma intambo phakathi kwezinto ezimbini. • Abafundi baxhoma iimpahla zokunxiba ngokomyalelo umz. -- “xhoma ihempe kwicala elisekhohlo kwintambo yokwaneka kwimpahla” -- “xhoma ilokhwe ngasekunene kwehempe “ Iphepha -- Xhoma itshefu ecaleni kwe .....njl.” Iikhrayoni -- Xhoma ibhulukhwe phakathi kwe …. njl.” MATHEMATIKA IBANGA LABAQALAYO (R) Ukusebenzisa iimilo ezinokwakeka kuka 2-D okanye imifanekiso • Zoba umfanekiso wendlu ngokwemiyalelo umz. -- Zoba uphahla kumantla ephepha -- Zoba iindonga zendlu kumbindi wephepha. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Zoba inja kwisandla sasekhohlo sendlu Iphepha malingabi likhulu kakhulu ukuqinisekisa ukuba iintlobo zeemilo zoyama kwenye ukwakha indlu

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-35 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki CAPS mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo 3.3 Ukunakana, ukuchonga nokubiza iimilo ezinokwakheka kuka 2-D eklasini Usuku olu- 1 nasemifanekisweni: Izinto ezinokwakheka -- Ukukwazi ukuqaphela iimilo Ukheta eminye kuka 3-D • Ukubethelela ulwazi olufunyenweyo ngoxande imisebenzi Ulwazi-ngemilo bubulumko bokwahlula phakathi kweemilo kokusingqongileyo, ngaphandle kobungakanani okanye ubungakanani be-engile Iqela ngalinye lifumana iibhloko Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D ezingalinganiyo zokwakha ezilu-9 ezimile Yahlula abafundi ngamaqela . njengoxande -- Nika iqela ngalinye iibhloko ezingalinganiyo zokwakha ezilu-9 ezimile njengoxande. Yenza abafundi: -- Bahlele iibhloko zokwakha ezimile njengoxande ngokwamaqela obungakanani. -- Babale inani leebhloko zokwakha Utitshala unika le miyalelo ilandelayo: -- Beka ibhloko yokwakha emile okoxande kumgca ongqalileyo. Umtya wewulu   -- Beka ibhloko yokwakha emile okoxande ngokume nkqo.   -- Beka ibhloko yokwakha emile okoxande kumgca ogoso-goso.   -- Utitshala unika umfundi ngamnye umsonto wewulu.abafundi bakha uxande ngewulu.   233 Utitshala uyabaxelela ukuba amacala esikwere somfundi ngamnye awafani kodwa imilo ise luxande MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha elicetyiswayo lokufunda nokufundisa: Iveki yama-35 Umsebenzi omnye weklasi ocwangcisiweyo okhokelwa ngutitshala (isangqa) wemizuzu engama ± 30 ngosuku (Imisebenzi yeMathematika ngeveki 234 mayibe ± 5) Ubude bexesha Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo obuqikelelwayo Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso -- Utitshala uzoba oonotsheluza abahlukileyo abangama-20, umnye uneendidi Amakhadi aneentlobo zoonotsheluza ezahlukileyo zoonxantathu, izangqa, izikwere kunye neengxande umz.. aBangama-20, ikhadi lilinye lineentlobo ezintlanu zoonxantathu, zesangqa,   isikwere kunye noxande. MATHEMATIKA IBANGA LABAQALAYO (R) Utitshala wahlula abafundi ngokwamaqela . Yenza abafundi: -- Khetha unotsheluza woxande kwezinye iimilo INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Yenza abafundi: -- Khetha yonke imifanekiso eneentyantyambo phakathi kwemifanekiso yemithi namagqabi.

Ixesha lokufundisa elicetyiswayo: Iveki yama- 36 Umsebenzi katitshala ocwangcisiweyo (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.1 Bethelela ulwazi olufunyenweyo olubandakanya amanani ukusuka ku- 1 ukuya kwi- 9 usuku olu-1 Bala izinto Ngomlomo: Ukubala izinto ezisetyenziswa yonke imihla ukuya kwi-9 Amaculo nezicengcelezo zamanani Bala usiya phambili nokubuya umva ukuya kwi-9. Bethelela ukubala ngezi- 2 besebenzisa izicengcelezo zamanani Bethelela ingqiqo ka “zininzi” no “zimbalwa”. Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba izandla kasi-9. Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Beka izinto ngokwamaqela aquka amanani -1 ukuya ku-9, abale izinto ngokuvakalayo. Izixhobo zokufundisa eklasini. -- Dlala iidomino Amanani edomino Sebenzisa iimilo eziphathekayo ezinokwakheka kuka 2-D okanye imifanekiso Nika umfundi ngamnye umfanekiso, ichaphaza, isimboli yamanani okanye amakhadi anamagama amanani. Amakhadi aziintlobo-ntlobo abandakanya Abafundi balandela imiyalelo katitshala amanani ukusuka ku-1 ukuya ku-9, umfundi ngamnye eklasini makafumane -- Abafundi bahlala kwisangqa. oonotsheluza -- Utitshala ubiza inani, umz. -9. Abafundi abanomfanekiso, ichaphaza, iisimboli zamanani namakhadi anamagama amanani u-9, hamba-hamba apho kwisangqa, usithi “Ndinethoba” -- Yenjenjalo nakwamanye amanani. -- Xa bonke befumene ithuba lokuba linani, biza amanani ngokulandelelana kwawo. -- Abafundi bayema, baphakamise amakhadi abo xa inani elo lekhadi libiziwe ngutitshala -- Qaphela ukuba bayakwazi ukuzimisa ngokulandelelana ukusuka ku-1 ukuya kwi -9. -- Qaphela ukuba bayakwazi ukumisa amakhadi amele la manani 1, 2, no 3 ukuya kwi-9 ndawonye 235 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 36 Umsebenzi katitshala ocwangcisiweyo (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 236 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.4 • Thelekisa ukuba yeyiphi enengqokelela e-: usuku olu-1 Chaza,thelekisa -- ngaphezu kwenye ulandelelanise -- ngaphantsi kwenye(mbalwa) amanani -- lingana nenye (fanayo Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Utitshala unika iintlobo ngeentlobo zezinto ezinjengamagqabi, amatye, iziciko zeebhotile, iikhrayoni, iibhloko njl. -- Bavumele abafundi ba: -- zihlele ngokwamaqela azo, umz. amatye odwa. -- bale inani lezinto kwiqela ngalinye. -- bonise iqela elinezingaphezu kwezinye, ngaphantsi kwezinye nezilinganayo njl. IiSeti zamanani ukuya kwi- 9 -- Abafundi bahlala emethini benze iindlwane zeentaka ngewulu. MATHEMATIKA IBANGA LABAQALAYO (R) -- Utitshala uyalela abafundi babeke amaqanda ama- 2 kwindlwane yokuqala, ama- 4 Imicu emibini yewulu kumfundi ngamnye, kwindlwane yesibini. amaqanda ali- 9 kumfundi ngamnye -- Ubabuza imibuzo enjengale: “Yeyiphi indlwane enamaninzi/enangaphezulu kunenye”, “enangaphantsi kunenye” “enalinganayo/ afanayo” mangaphi la maqanda ewonke?” umz. “indlwane” enamaqanda ama-2 ingaphantsi “kwindlwane” enamaqanda ama- 4 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA   -- Bayalele abafundi benze iiseti zabo ezibonisa “ngaphezulu kune”, “ngaphantsi kune” ne ‘lingana / efana ne” basebenzise amanani ukuya kwi-9.

Ixesha lokufundisa elicetyiswayo: Iveki yama- 36 Umsebenzi katitshala ocwangcisiweyo (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.13 • Ukusombulula izibalo zomlomo zokudibanisa nokuthabatha ezibandakanya usuku olu-1 amanani ukusuka ku-1 ukuya kwi-9 Ukudubanisa nokuthabatha Ngomlomo: Ukubala izixhobo zemihla-ngemihla ukuya kwi-9. Amaculo nezicengcelezo zamanani Bala usiya phambili nasemva ukuya kwi-9. Bethelela ukubala ngezibini usebenzisa izicengcelezo zamanani Bethelela ulandelelwano lokubala: Utitshala ubeka izinto ezi- 6 emgceni. Ukhomba into nganye xa ezibala, umz. eyokuqala, eyesibini, eyesithathu, eyesine, eyesihlanu, eyesithandathu Bethelela iingqiqo ezinje ngezi “zininzi” no “zimbalwa” Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-9. Buza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye. Intshukumo yamalungu omzimba -- Utitshala ubiza umfundi eze ngaphambi kweklasi. -- Ubeka amanani amaso ohlukeneyo ukuya kwi-9, kwisandla somfundi ngamnye, umz. Amaso nezinto zokubala ama-4 kwisandla esinye nama-5 kwesinye -- Utitshala ubeka abafundi ngamaqela abo ali-9. -- Abafundi bahlala emgangathweni -- Utitshala ucela ababini beme ngeenyawo. -- Utitshala uyabuza: “Bangaphi abafundi abahleli emgangathweni?” 237 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 36 Umsebenzi katitshala ocwangcisiweyo (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 238 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.13 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Ukudubanisa -- Abafundi bahlala emethini. Xa ungenazo iikomityi neesosi zama nokuthabatha ukuzenza. -- Umfundi ngamnye ufumana amaso ali-9 akwikomityi yeplastiki enesosi. -- Bayalelwa ukuba bathathe amaso ama-6 ekomityini yeplastiki bawabeke esosini. Bayalelwa ukuba bongeze amathathu apho esosini. Mangaphi amaso asekomotyini? 6 no 39. -- Thatha amaso ama- 4 kwisosi uwabeke ekomtyini yeplastiki. Thatha amanye ama-5 uwadibanise kumaso asekomityini yeplastiki. Mangaphi amaso asesosini? 9 thabatha 4 uphinde uthabathe 5→0. -- Thabatha amaso ama- 4 ekomityni yeplastikii uwabeke esosini. Mangaphi ashiyeke ekomityini yeplastiki? 9 thabatha 4 →5. -- Thabatha amaso ama-5 ekomityini uwabeke esosini. Mangaphi ashiyeke ekomityini? 5 thabatha 5 →0. Ukusebenzisa iimilo eziphathekayo ezinokwakheka kuka 2-D okanye imifanekiso Yohlula abafundi ngamaqela. Nika iqela ngalinye iseti yemifanekiso yoonotsheluza MATHEMATIKA IBANGA LABAQALAYO (R) -- Bala imifanekiso emi- 6 kunotsheluza. Xa usongeza unotsheluza nemifanekiso emi- 2, mingaphi oya kuba nayo ngoku? 6 no 2  8. -- Bala izinto ezisi- 8 kwikhadi lomfanekiso. Xa usogquma imifanekiso emi- 3, mingaphi Iiseti ezimbalwa zemifanekiso oyibonayo? 8 thabatha 3  5. yoonotsheluza -- Beka izixhobo zokubala ezilelo nani. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA 2.1 • Ukukopa ipateni yengxolo Usuku olu-1 Iipateni zejiyometri Intshukumo yamalungu omzimba -- Utitshala wohlula abafundi ngamaqela amathathu. Sebeza ubonakalise eqeleni ngalinye ingxolo yohlobo lwemoto abazakuyilinganisa. Imifanekiso yeendidi zeemoto/zezithuthi -- Iqela ngalinye lenza ingxolo yemoto abayinikiweyo xa liceliwe ngutitshala, umz. Woosh, okanye iimatshini ezintathu. brrrm, zonk / Woosh, brrrm, zonk.

Ixesha lokufundisa elicetyiswayo: Iveki yama- 36 Umsebenzi katitshala ocwangcisiweyo (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 5.1 • Bethelela ingqiqo yokusebenza ngolwazi oluqokelelweyo usuku olu-1 Qokelela uze Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: uhlele izinto Masidlale umdlalo Hlela nokubeka ngamaqela umbala okhethiweyo wodongwe lwale veki ilandelayo, umz. -- Izibalo ema zisombululwe ukubonisa umbala wodongwe weveki. Qokelela ulwazi uze ulihlele -- Sebenzisa izinto eziphathekayo ukwenza igrafu esinjengeebhloko, iityhubhu, iLego Luhlaza, mthubi, luhlaza, bomvu, iLego ezimele imibala yomdongwe owucwangcisele ukuwenza, umz. mthubi, luhlaza, bhlowu, (kusetyenziswa uhlobo olunye kuphela) bomvu njl. -- Umfundi ngamnye ukhetha ibhloko enye emele umbala awukhethileyo womdongwe aza kudlala ngawo evekini. 5.2 Bonisa ingqokelela Zoba igrafu yezinto ezihleliweyo -- Iibhloko ziyabekwa ngokwemibala ekwiphowusta. 5.3 Xoxa uze Funda nokutolika igrafu unikezele ingxelo -- Ngendlela abafundi abazikhethele ngayo imibala yomdongwe weveki iyakuba ngengqokelela ngumthubi. yezinto ezihleliweyo   Bhlowu Blue Mthubi Yellow Luhlaza Green 2 4 2 239   MATHEMATIKA IBANGA LABAQALAYO (R)

240 Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.1 • Fundisa intsingiselo yenani i-0 (iqanda) usuku olu-1 Bala izinto Ngomlomo: Ukubala izinto zemihla-ngemihla uqala ku-0 ukuya kwi-10. Bala usiya phambili nokubuya umva, uqala ku-0 ukuya kwi-10. Amaculo nezicengcelezo zamanani Bethelela ukubala ngezibini esebenzisa izicengcelezo zamanani Bethelela ubala ngokulandelelanisa amanani: Utitshala ubeka izinto ezi- 6 emgceni. Ukhomba into nganye xa ezibala, umz. eyokuqala, eyesibini, eyesithathu, eyesine, eyesihlanu, eyesithandathu Bethelela iingqiqo ezinje ngezi “zininzi” no “zimbalwa” Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. Buza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye Utitshala uchaza ukuba i-0 yinto engekhoyo, ukubala izinto ezikhoyo kuqala ku-1. MATHEMATIKA IBANGA LABAQALAYO (R) Intshukumo yamalungu omzimba -- Utitshala ubonisa abafundi igama lenani i-0. -- Abafundi mabachonge amalungu omzimba enza u-0, umz. o Umlomo womfundi INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA o Iminwe yomfundi  1.1 Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Bala izinto -- Utitshala ubeka izixhobo zokubala esandleni sakhe, esinye singabi nanto tu. Izinto zokubala -- Uvula isandla esinye abonise abafundi izixhobo zokubala, avule esinye abonise abafundi ukuba asinanto. 0 -- Lo msebenzi ungenziwa kusetyenziswa abafundi. Sebenzisa izinto ezibubonakalayo ezinokwakheka kuka 2-D nemifanekiso -- Utitshala ubonisa abafundi oonotsheluza abangenamifanekiso, nesimboli yenani u-0.

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.1 • Ukwazisa intsingiselo yenani i-10 Usuku olu- 1 Bala izinto Ngomlomo: Ukubala izinto zemihla-ngemihla ukuya kwi-10. Ukubala usiya phambili nokubuya umva, ukuya kwi-10 Amaculo nezicengcelezo zamanani Khetha imisebenzi embalwa Ukubala ngokucengceleza 0-10 Ukubethelela ukubala ngezi- 2 esebenzisa izicengcelezo zamanani Ukubethelela ulandelelwano lokubala: Utitshala ubeka izinto ezi- 6 emgceni. Ukhomba into nganye xa ezibala, umz. eyokuqala, eyesibini, eyesithathu, eyesine, eyesihlanu, eyesithandathu Ukubethelela iingqiqo ezinje ngezi “zininzi” no “zimbalwa” Ukuqhwaba izandla kaninzi.......YIMA Ukuqhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. Ukubuza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye Ukufunda usebenzisa intshukumo yamalungu omzimba Bavumele abafundi ba: -- bengababini benze inani i-10 ngemizimba yabo (abafundi aba-4). Sika amanani ekhadibhodi -- bale ukuya kwi-10 ushukuma ngesingqi segubu. -- bambe iminwe eli-10. -- zobe inani i-10 esantini, emgangathweni bahambe nakuyo. -- tsibe amaxesha ali-10 -- beke amanani abawasike kumakhadibhodi kwi”ngxowa empampathwayo” -- thathe iseti yoonotsheluza abanemifanekiso emele inani, umz. iibhola ezimbini ekhadini Isimboli enkulu yoonotsheluza bamanani elibhalwe inani u-2. Umfundi umpampatha amanani ebhegini awatshatise namakhadi 241 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 242 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo Ukusebenzisa izinto ezibonakalayo ezinokwakheka kuka 3-D: Bavumele abafundi ba: -- beke iinombolo zeefowuni zabo besebenzisa iisimboli ezinkulu zamakhadi amanani. Amakhadi aneenombolo zeefoni Baxelele ngo-0 omele i-10. zabafundi -- Qaphele amanani ngokuwabeka ngezinto ezintlanu ngeendlela ezahlukeneyo, umz. 1 7 8 0 4 3 5 6 9 2 Xa bebala inani lezinto alitshintshwa bubungakanani, ubume, ukuzalana, umz.: MATHEMATIKA IBANGA LABAQALAYO (R) -- Beka amaqhosha ali-10, iipensile ezili-10, iihulahupu ezili-10, abafundi abali-10 njl. -- Zibale ngolunye uhlobo lolandelelwano, umz.zibale zithe saa, zidibene, zisemgceni njl. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS Ukusebenzisa iimilo ezinokwamheka kuka 2-D okanye imifanekiso Bayalele abafundi ba: -- beke izinto ngokwamaqela azo abandakanya amanani ukusuka ku-1 ukuya kwi-10 Izinto eklasini babale ngokuvakalayo izinto ezo. Utitshala wohlula abafundi ngamaqela ama-5 Bayalele abafundi ba: -- landelelanise, batshatise amakhadi emifanekiso, oonotsheluza bamachaphaza, Iseti yamakhadi emifanekiso ukuya kwi- iisimboli zamanani kunye namagama amanani ukuya kwi-10, umz. 10 Into e-1 Izinto ezi-2 Izinto ezi-3 inye zimbbini zintathu 0 njl-njl. Izinto zokubala Pakisha izixhobo zokubala kwikhadi lamachaphaza ngalinye 243 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 244 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 2.1 • Dlala umdlalo wepateni- “usikhoji” njl. Usuku olu-1 Iipateni zejiyometri Nxulumanisa nezeMithambo kwiZakhono zoBomi Funda usebenzisa intshukumo yamalungu omzimba -- Hamba-hamba apho eklasini. Ngesingqi somculo naxa umculo uphela, biza Umzekelo wepateni ezotywe igama lemilo, abafundi mabayenze imilo leyo ngeminwe yabo. Emaqeleni abo emgangathweni okanye everanda. Bangazilinganisa iimilo ngemizimba yabo. -- Zoba le pateni ilandelayo emgangathweni okanye everanda, abafundi mabahamba- hambe kwiindlela okanye iimilo ezilapho kuloo pateni.   Xoxa ngale pateni, umz. -- Buza imibuzo elandelayo: MATHEMATIKA IBANGA LABAQALAYO (R) -- ”Yeyiphi imlo elandela uxande lokuqala?” -- “Yeyiphi imilo ephambi kwesangqa sokuqala? Abafundi balandela ipateni ngolu hlobo: -- Utitshala uthi: ”Zintle, tsiba phambi kukaMilisa”, “Neli ungatsiba emva kukaSindi” INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Tsiba ngeenyawo zombini kuxande. -- Tsiba ngonyawo lwasekhohlo kunxantathu. -- Tsiba ngonyawo lwasekunene kwisikwere. -- Tsiba ngeenyawo zombini kwisangqa, jika-jika umzimba wakho ume kwisangqa. -- Gqibezela ipateni.

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 2.1 Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Umfundi ngamnye ufumana ezi milo zilandelayo: Iipateni zejiyometri -- Umfundi ngamnye ufumana ezi milo zilandelayo: Utitshala wenza ipateni ngeemilo zakhe. Bavumele abafundi ba: -- Kope iipateni zikatitshala besebenzisa ezi milo zingentla. -- Velisa ezabo iipateni ngeemilo abazinikiweyo. 3.1 Landela izalathiso ukuhamba okanye ukufumana indawo kwisithuba esithile Imiyalelo katitshala. usuku olu-1 Indawo- • Ukhulisa ingqiqo yezalathiso, ngokulandela imiyalelo kuquka ikhohlo nekunene Isigama: bume kunye Funda usebenzisa intshukumo yamalungu omzimba phezulu/phantsi nembonakalo Bayalele abafundi balandele imiyalelo katitshala: phakathi/phandle -- Jonga phezulu/phantsi/ecaleni. phezu/ezantsi -- Goba/ekhohlo/ekunene. ngaphezulu/emva/ngaphantsi -- Phakamisa umlenze wasekhohlo/wasekunene. phambi kwe-/emva kwe- -- Gaqa ujikeleze itafile. kweli cala/kwela cala -- Yiya phambili/ecaleni/ngasemva ekhohlo/ekunene -- Faka isandla sakho/ sikhuphe -- Yima ekunene ecaleni kwesitulo/yima ekhohlo ecaleni kwesitulo. -- Yima phambi/ emva kwesitulo sakho. -- Yima phakathi kwezitulo ezibini. -- Jonga ekhohlo/ekunene. -- Jika unyawo ulise ekhohlo. Jika unyawo ulise ekunene 245 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 246 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo Ukusebenzisa izinto ezibonakalayo ezinokwakheka kuka 3-D: ibhodi Bayalele abafundi benze oku kulandelayo ebhodini, ba: -- zobe izangqa bejikeleza   -- zobe imigca engqalileyo esuka ekhohlo ukuya ekunene   -- zobe imigca eya phezulu neya ezantsi.   MATHEMATIKA IBANGA LABAQALAYO (R) -- utitshala uzoba amachaphaza amabini, abafundi bayidibanise ngomgca.   INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswayo: Iveki yama- 37 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 5.1 • Bethelela ukusebenza ngolwazi oluqokelelweyo Usuku olu-1 Qokelela uze uhlel Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: eizinto -- Xoxa nabafundi iindlela abeza ngazo esikolweni. -- Zoba imifanekiso ebonisa izithuthi ezo zabo ndawonye nabo besiza esikolweni okanye bekhatshwa ngabazali babo, umz.   5.2 Bonisa ingqokelela yezinto ezihleliweyo Imifanekiso yezithuthi kwiimagazini,umz. itekisi, ibhasi, imoto kunye nabafundi 4 2 3 1 bekhwele kuzo. Zoba xa ungenazo iimagazini. 5.3 -- Hlalutya iziphumo ngemibuzo Xoxa uze unikezelo ingxelo ngengqokelelo yezinto ezihleliweyo 247 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 38 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 248 Isihloko Amanqaku ngangcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.1 • Bethelela ulwazi olufunyenwe kwiiveki ezingama-37 olubandakanya i-0 ukuya kwi-10 Usuku olu-1 Bala izinto Ngomlomo: Ukubala izinto zemihla-ngemihla uqala kwi-0 ukuya kwi-10. Bala usiya phambili nokubuya umva, uqala kwi-0 ukuya kwi-10. Bala ngentloko ngokungenantsingiselo uqala kwi-0 ukuya kwi-10 okanye Bethelela ukubala ngezi- 2 esebenzisa izicengcelezo zamanani Bethelela ukubala ngokulandelelanisa amanani: khetha imisebenzi embalwa Utitshala ubeka izinto ezi- 6 emgceni. Ukhomba into nganye xa ezibala, umz. eyokuqala, eyesibini, eyesithathu, eyesine, eyesihlanu, eyesithandathu Bethelela iingqiqo ezinje ngezi “zininzi” no “zimbalwa” Amaculo nezicengcelezo zamanani Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. Buza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye. Funda usebenzisa intshukumo yomzimba MATHEMATIKA IBANGA LABAQALAYO (R) -- Utitshala uzoba izangqa ezili-11 (0 to 10) emgangathweni okanye usebenzise ihulahuphu. Bhala amanani ukusuka ku-0 ukuya kwi- 10 ngaphandle kwesangqa Iingxowa zeembotyi ezi-10 ngasinye. Biza inani abafundi bagibisele ingxowa yembotyi kweso sangqa sibiziweyo. Zoba izangqa esantini/emgangathweni -- Khumbuza abafundi ukuba u-0 yinto engekhoyo. Xa umfundi egibisele ingxowa okanye sebenzisa iihulahuphusi. yembotyi kwisangqa esingenanto uzakuphuma kulo mdlalo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Umfundi ugibisela ingxowa yembotyi kwisangqa esihambelana nechaphaza okanye nekhadi lomfanekiso eliboniswe ngutitshala. -- Umfundi ugibisela ingxowa yembotyi kwisangqa esiboniswe kwisimboli yamanani ngutitshala. -- Yenjenjalo usebenzisa amakhadi amagama amanani

Ixesha lokufundisa elicetyiswayo: Iveki yama- 38 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku ngangcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.3 Nakana, uze chonga iisimboli zamanani kunye namagama amanani Iseti yamakhadi amanani eqala ku- 0 ukuya kwi-10 Iisimboli zamanani Sebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso kunye namagama Bavumele badlale umdlalo: amanani Amakhadi abandakanya amanani, -- Bhala igama lenani kwicala elinye lekhadi, isimboli yamanani kwelinye icala ukuqala ku- -- qala ku-0 ukuya kwi-10.(sebenzisa iiseti ezimbalwa). 1 ukuya kwi-10 namagama amanani -- Mabafunde igama lenani baqikelele isimboli yenani. kwicala elinye nesimboli yenani kwelinye icala. (Yenza iiseti ezimbalwa ukuze -- Mabalijonge ikhadi elo , balungise iziphoso zabo. abafundi babe nawabo amakhadi). 1.4 • Fundisa ulandelelwano lwamanani, umz. eyokuqala, eyesibini, eyesithathu, usuku olu-1 eyesine, eyesihlanu, eyesithandathu ... eyokugqibela. Ukuchaza, ukuthelekisa Le ngqiqo ikhuliswa emva kwethuba nangokuleyibhelisha iimeko ezizenzekelayo apha nokulandelelanisa eklasini, umz. yimani emgceni siya phandle, “USiya ngowokuqala, uHelen ngowesibini amanani .......” Funda usebenzisa intshukumo yomzimba -- Mabadlale ugqatso. Ngowuphi ofike kuqala/ owesibini/owokugqibela? Dlala umdlalo – “Yeyiphi eyona”? -- Cela abafundi abahlanu bahlale ezitulweni zabo, benze umgca. -- Utitshala uthi: “Ndicinga omnye waba bafundi. Umfundi unxibe ijezi ebomvu.” -- Qala ngomfundi ongaphambili, bajikeleze bonke ubabamba, ubabuze: “Ingaba ungumfundi wokuqala, wesibini, wesithathu ... njl.? Abafundi aba-5 mabeme phandle kumanqwanqwa .Utitshala makabeke ikhadi lesimboli yamanani efanelekileyo ezantsi komfundi ngamnye kumanqwanqwa. Izitulo ezihlanu Bonisa umfundi kwinqwanqwa: Iseti yamakhadi eesimboli zamanani -- sokuqala. aqala ku-1 ukuya kwi-10 -- sesibini. Zenzele xa kungekho zixhobo -- sesithathu njl’. zolandelelwano Umfundi okwinqwanqwa lokuqala uveza ikhadi lesimboli yamanani emva kokuba ibiziwe njengempendulo ngumhlobo wakhe. 249 Yenjenjalo ude uye kumfundi wesi- 6. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 38 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 250 Isihloko Amanqaku ngangcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.7 • Sombulula ngomlomo izibalo zamazwi (izibalo ezingamabali) ezibandakanya i-10 usuku olu-1 Ukuthabatha noku Ngomlomo: Ukubala izinto zemihla-ngemihla uqala kwi -0 ukuya kwi-10. dibanisa Ukubala usiya phambili nokubuya umva, uqala kwi-0 ukuya kwi-10. Ukubethelela iingqiqo ezinje ngezi “zininzi” no “zimbalwa” Ukuqhwaba izandla kaninzi.......YIMA Ukuqhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. Ukubuza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye Imizekelo: 1. Kwaye kukho iintombi ezi- 5 endlwini. Kwafika za-5 kwakhona iintombi kule ndlu. Zingaphi zizonke ngoku? 5 no 5 → 10. 2. Bala izixhobo zokubala ezi- 7. Bala ezibini ngaphezulu. Bala esinye ngaphezulu. Zingaphi zizonke? 7 no 2 no 1 → 10. 3. Kukho izixhobo zokubala ezili-10 phezu kwetafile. Kushiyeke za-4.Zingaphi ezisusiweyo? 10 thabatha 6 → 4. MATHEMATIKA IBANGA LABAQALAYO (R) 4. Uneemabhile ezili- 10. Thabatha ezi- 3. Zingaphi ozishiyileyo? 10 thabatha 3→7 izixhobo zokubala 5. Wenze iikeyiki ezili-10. Wathengisa ezi-2 iikeyiki.Ushiye zangaphi? 3.1 • Ukulandela izalathiso uhamba-hamba okanye ukufumana indawo kwisithuba usuku olu-1 esithile eklasini Indawo- INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA bume,ukufumana Ukufunda usebenzisa intshukumo yomzimba indawo -- Bacele beme emva eklasini nembonakalo -- Bacele beme ecaleni eklasini/ nakwelinye icala ngokunjalo. -- Bacele beme ngaphambili eklasini. Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Ingxolo inentsingiselo. intsimbi Abafundi bamamela i-: impempe -- intsimbi nasiphina isixhobo sokucula -- impempe iibhloko zomthi ezi-2 -- nasiphina isixhobo sokucula. -- Bangqubanisa iibhloko ezimbini zomthi.

Ixesha lokufundisa elicetyiswayo: Iveki yama- 38 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku ngangcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 3.1 Abafundi bayacimela, bachonge ingxolo yentsimbi/yempempe/nasiphina isixhobo sokucula. Intsimbi Indawo- -- Abafundi bayacimela, bachonge ingxolo ukuba isuka phina.Bangagibisela ibhibhegi Impempe bume,ukufumana kwicala evakala ngakulo ingxolo, bayichaze ukuba isuka kweliphi na icala, umz. phambi Isixhobo somculo nokuba sesiphina indawo kweklasi,ngakwikona yokufunda njl. nembonakalo Iibloko ezimbini -- Utitshala uyala aba- 4 ukuba beme ngasedongeni apho eklasini. Abafundi aba-4 kumacala amane eklasi,umfundi ngamnye abe nesakhe isixhobo somculo sahluke kwesomnye: (intsimbi, impempe, nasiphina isixhobo sokucula, iibhloko zomthi zokucula ezi-2). -- Utitshala ukhomba umfundi ngamnye, asebenzise isixhobo sakhe enze ingxolo, lowo ukhonjiweyo, umz. intsimbi -- Abanye bayachaza ukuba ingxolo isukaphi, ngokukhomba ngesalathiso icala elo isuka kulo. -- Bethelela ulwazi lwekhohlo nelokunene, ngokuyalela abafundi beme ngaphambi/ ngasemva eklasini, mabenze ingxolo, abanye abafundi bayichaze ukuba isuka ngaphi, ekhohlo/ekunene -- Phinda oku ugqale kwisandi esivela ekhohlo nasekunene eklasini. Abafundi bathi “ekhohlo” xa isandi sisuka kwicala lasekhohlo baze bathi “ekunene” xa isandi sisuka kwicala lasekunene. Sebenzisa iimilo ezinokwakheka kuka 2-D nemifanekiso Mabagqibezele iphepha lokusebenzela, bazobe umgca ngekhrayoni phakathi kwemigca, Iphepha lokusebenzela kunye umz. neekhrayoni 251 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 38 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 252 Isihloko Amanqaku ngangcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 4.2 • Thelekisa uze uhlele izinto ngokwenza usebenzisa isigama esifanelekileyo ukuhaza Itshati yobude ubude Ubude iteyiphu yokuthatha umlinganiselo • Thatha umlinganiselo wobude wabafundi ngeteyiphu yokuthatha umlinganiselo   Chart Heightyobude Itshati Funda usebenzisa intshukumo yomzimba -- Zekelisa kwikota yokuqala neyesibini apho bebesenza imilinganiselo yomphakamo wetshati ngezandla. -- Yenza umlinganiselo wobude bomfundi. -- Beka iteyiphu ngakwimifanekiso yezandla ezibonakalisa umphakamo wetshati. -- Mabulinganiswe ubude babafundi kwakhona. -- Baxelele ukuba sisebenzisa isixhobo somlinganiselo omiselekileyo kway umama usebenzisa oku xa esenza ilokhwe. -- Ngoku abasezozandla ezilishumi ubude kodwa bazisentimitha ezilishumi ubude -- Mabathelekise imiphakamo yabo. Ngowuphi oyena mde/ mfutshane eklasini? Sebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: MATHEMATIKA IBANGA LABAQALAYO (R) -- Umfundi ungqengqa emgangathweni,abanye babeke iibhloko zokwakha ezilinganayo emgceni ecaleni komfundi lowo ungqengqileyo. -- Bayalele benze into ende/emfutshane kunomhlobo wakho INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.1 • Ukubethelela intsingiselo yenani i-10 Amaculo nezicengcelezo zamanani usuku olu-1 Bala izinto Ngomlomo: Ukubala izinto zemihla-ngemihla uqala kwi-0 ukuya kwi-10. Bala usiya phambili nokubuya umva, uqala kwi-0 ukuya kwi-10. Bala ngentloko ngokungenantsingiselo uqala kwi-0 ukuya kwi-10 Bethelela ukubala ulandelelanisa amanani: Utitshala ubeka izinto ezi- 6 emgceni. Ukhomba into nganye xa ezibala, umz. eyokuqala, eyesibini, eyesithathu, eyesine, eyesihlanu, eyesithandathu Bethelela iingqiqo ezinje ngezi “zininzi” ne “zimbalwa” Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. Buza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye Funda usebenzisa intshukumo yomzimba Bavumele abafundi ba/be: -- nze isicengcelezo samanani besebenzisa iminwe yabo elishumi. -- bale amanani amaxesha utitshala ebetha itafile -- qhwabe izandla kali-10. -- bale izitepusi ezihamba abafundi xa bephuma eklasini okanye bedlala ihulahupu. -- ngqishe iinyawo zabo ngesingqi esinye. Iibhinbhegi nebhasikithi -- Beme beli-10 kwisangqa esinebhaskithi esizikithini umfundi ngamnye enengxowa yembotyi baziphose ebhaskithini zibeli-10. Mababale ngokuvakalayo xa bephosa iibhinbhegi .Qiniseka ukuba bonke abafundi baphose ebhaskithini 253 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 254 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.1 Ukusebenzisa izinto ezibonakalayo ezinokwakheka kuka 2-D okanye imifanekiso Bala izinto Yohlula abafundi babengamaqela amancinci. -- Banike iiphazili zamanani. -- Mabadlale iphazili yamanani. Yenza iphazili yamanani ebendakanya amanani ukuqala ku-1 ukuya kwi-10 -- Mabaphose idayisi ukubonisa iphazili yamanani ema yakhiwe. imifanekiso e-6 mbini Izinto ntlanu ezi-5 MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.13 • Bethelela ukusombulula izibalo zokudibanisa nezokuthabatha ukuya kwi- 10 Usuku olu-1 Ukudibanisa Ngomlomo: Ukubala izinto zemihla-ngemihla uqala ku-0 ukuya kwi-10. nokuthabatha Bala usiya phambili nokubuya umva, uqala ku-0 ukuya kwi-10. Amaculo nezicengcelezo zamanani Bethelela ukubala ngezibini esebenzisa izicengcelezo zamanani Bethelela iingqiqo ezinje ngezi “zininzi” ne “zimbalwa” Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. ngokubuza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye Ukufunda usebenzisa intshukumo yomzimba -- Utitshala ubiza abafundi aba-5 bezengaphambili, ongeze omnye de aye kwi-10. -- Babala ngokuvakalayo. 5 no 1  6. (ithi: ntlanu dibanisa inye, yenza ntandathu) 6 no 1 7. 7 no 1  8. 8 no 1  9. 9 no 1→10. -- Utitshala ubayalela ukuba babale bebuya umva 10 thabatha 1  9 9 thabatha 1  8 10 thabatha 2  8 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D: Izixhobo zokubala ezili-10 kumfundi ngamnye Abafundi bahlala emethini. Umfundi ngamnye unezixhobo zokubala ezili-10 neziciko zeplastiki. Bayalele balandele imiyalelo: Iziciko zeplastiki, umz. iziciko ze-ayisi krim -- Pakisha izixhobo zokubala ezi- 4 esicikweni sakho. Dibanisa ezi- 4 ngaphezulu. Zingaphi zizonke? 6 no 4  10 255 -- Pakisha izixhobo zokubala ezili- 10. Thabatha zibe - 5. Kushiyeke zangaphi? njl-njl. MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 256 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 1.13 Ukusebenzisa iimilo eziphathekayo ezinokwakheka kuka 2-D okanye imifanekiso Imifanekiso yonotsheluzaebandakanya amanani ukuqala ku- 1 ukuya kwi- 10 Ukudibanisa -- Bala izinto ezisi-8 ekhadini lomfanekiso. Xa udibanisa amakhadi omfanekiso ama-2 nokuthabatha ngaphezulu, zingaphi onazo ngoku? -- 8 no 2 →10. Pakisha kwalamanani ezixhobo zokubala. Izixhobo zokubala -- Bala izinto ezili-10 ekhadini lomfanekiso. Xa uthabatha ezi- 3, zingaphi ezishiyekileyo? 10 thabatha 3  7. Pakishakwalamanani ezixhobo zokubala. 1.4 • Ukuthelekisa ukuba yeyiphi enengqokelela e-: Usuku olu-1 Chaza,thelekisa -- ngaphezu kwenye uze ulandelelanise -- ngaphantsi kwenye(mbalwa) amanani -- lingana nenye (fanayo Ngomlomo: Ukubala izinto zemihla-ngemihla uqala ku-0 ukuya kwi-10. Bala usiya phambili nasemva, uqala ku-0 ukuya kwi-10. Bethelela ukubala ngezi- 2 esebenzisa izicengcelezo zamanani MATHEMATIKA IBANGA LABAQALAYO (R) Bethelela iingqiqo ezinje ngezi “zininzi” no “zimbalwa” Qhwaba izandla kaninzi.......YIMA Qhwaba izandla kambalwa. Utitshala uqhwaba ukuya kumaxesha ali-10. Buza umbuzo ngokona kuqhwaba kungaphezulu/kungaphantsi kunezinye INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA Ukufunda usebenzisa intshukumo yomzimba -- Beka abafundi aba-6 ndawonye kuhulahupu nabanye aba-4 komnye uhulahupu. iihulahupu ezi-2 -- ” ingaba kukho abafundi abongezelekileyo, umfundi oyedwa, aBangaphantsi okanye abalinganayo kuhulahupu -- Abafundi mabachonge ihulahupu enezingaphezu/ngaphantsi/ezilinganayo nenye

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 1.4 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Chaza,thelekisa -- Beka izixhobo zokubala ezili-10. ezi- 6 nezi- 4 etafileni. Izixhobo zokubala uze ulandelelanise -- Nika inani lezixhobo zokubala eziphezu kwetafile amanani -- Buza le mibuzo: “Ingaba zingaphezu kwesi- 7?” “ingaba ziyalingana, zingaphantsi, zimbalwa, zonele, azonelanga?” -- Bayalele ba: “qonde iimpendulo zabo ngokubala izixhobo zokubala.” “ingaba uqikelele kangakanani?” Ukusebenzisa iimilo eziphathekayo ezinokwakheka kuka 2-D okanye imifanekiso Amakhadi amabini anamanani ohluka-hlukeneyo ngamachaphaza -- Utitshala ubonisa amakhadi amabini anamachaphaza amanani ohluka-hlukeneyo nangemifanekiso kwanemifanekiso kuwo. -- Bavumele bathelekise amakhadi anemifanekiso namachaphaza kuwo, bachonge angaphezulu/ angaphantsi/nalinganayo 257 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 258 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 3.1 • Chaza izinto ezimbini okanye ngaphezulu ezinokwakheka kuka 3-D Usuku olu-1 ngokunxulumene nenye. Indawo- bume,ukufumana • Bethelela ulwazi ngokhohlo nokunene indawo Ukufunda usebenzisa intshukumo yomzimba nembonakalo Imizila yeenyawo esephepheni, ebonisa -- Utitshala ubeka imizila yeenyawo ekhohlo nasekunene emacaleni onke eklasi. ekhohlo/ekunene -- Abafundi bagaqa ngengalo nedolo elinye lasekhohlo nelasekunene ngaxesha linye. -- Benjenjalo besiya apho kukho isitya sokuhlambela MATHEMATIKA IBANGA LABAQALAYO (R) Utitshala uqhina iwulu ebomvu kwisihlahla somfundi ngomnye sasekunene. Utitshala unika imiyalelo. -- Phakamisa unyawo lwakho lwasekhohlo. INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA -- Beka unyawo lwakho lwasekunene esitulweni. -- Bamba idolo lakho lasekhohlo ngengqiniba yakho yasekunene.. -- Tsala indlebe yakho yasekhohlo ngesandla sasekunene. Isijungqe sewulu ebomvu -- Beka isandla sakho sasekunene kwigxalaba lakho lasekhohlo, isandla sakho sasekhohlo kwigxalaba lasekunene. -- Zigone.(isandla ngasinye sinqumle umbindi ukuya kwigxalaba lenye ingalo)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo CAPS 3.1 Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D Indawo- -- Utitshala ubeka iinkonkxa ezisi-7 phezu kwetafile bume,ukufumana -- Abafundi mabachaze inani elisekhohlo ku-3, elisekunene ku-6, eliphakathi ko- 3 no- 6. indawo nembonakalo -- Leliphi inani lokuqala nelokugqibela.   1 2 3 4 5 6 7 Iinkonkxa ezibhalwe amanani. o 1 n -- Utitshala ubeka iimoto/oonodoli aba-3 abanxibe imibala egqamileyo phezu kwetafile. c -- Ubuza imibuzo enjenje: r o Ngowuphi unodoli/ e imoto esekhohlo? o Ngowuphi unodoli/ t imoto esekunene? e   Iimoto/onodoli aba-3. o Ngowuphi unodoli/ imoto ephakathi? u o Yeyiphi imoto/unodoli wokuqala/wokugqibela? s Ukusebenzisa iimilo ezinokwakheka kuka 2-D okanye imifanekiso i -- Ngexesha lokuyila okubonwayo abafundi benza imizila yepeyinti besebenzisa izandla zasekhohlo nesasekunene. -- Bayasika bancamathelise emaphepheni bebonisa unyawo lwasekhohlo nolwasekunene. 2.1 • Yila ipateni yakhe Amakhadi emilo nepateni. Usuku olu-1 Iipateni zejiyometri Ukusebenzisa izinto eziphathekayo ezinokwakheka kuka 3-D -- Abafundi bakopa iipateni kwezo bazinikiweyo. -- Bazenzela ezabo iipateni baze bazichaze. 259 MATHEMATIKA IBANGA LABAQALAYO (R)

Ixesha lokufundisa elicetyiswayo: Iveki yama- 39 Umsebenzi ocwangcisiweyo okhokelwa ngutitshala (isangqa) imizuzu engama- ± 30 ngemini (imisebenzi emi-± 5 yeMathematika ngeveki) 260 Isihloko Amanqaku angcaciso Izixhobo ezicetyiswayo Ixesha elimisiweyo 2.1 Umsebenzi wePhegibhodi (peg board): Iphegibhodi neephegi. Iipateni zejiyometri Bayalele basebenzise izandla zasekunene kuqala, zasekhohlo, zozibini ukubeka iiphegi iiPateni ekukotshwa kuzo ngabafundi. kwiphegibhodi. -- Utitshala uxelela abafundi apho kubekwa khona iiphegi, umz. o Kumgca ophezulu. o Kumgca osezantsi. o kwicala ekhohlo. o ekunene. o phakathi. Bavumele be/ba: -- nze iimilo kwiphegibhodi ngeephegi ezimibala-bala. -- Utitshala uhlula-hlula ipateni elula ngeepegi kwiphegibhodi yakhe baze abafundi bakope ipateni bayibeke kwiiphegibhodi zabo. MATHEMATIKA IBANGA LABAQALAYO (R) INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

Iveki yama- 40 Sebenzisa iveki 40 ukwenza izisombululo ezikhankanyiweyo okanye izithintelo kufundo. Umxholo Isihloko Umlinganiselo woHlolo CAPS Inani nee- 1.1 Qikelela nokucengceleza ukubala ukuya kwi - 10 (iingoma zamanani nezicengcelezo) Opareyishini Bala ukuya phambili nokubala ubuya umva (0-10) Bala izinto Bala ngezi- 2 (iingoma zamanani nezicengcelezo) Qonda ingqiqo ngo: “zininzi” no “zimbalwa” (uqhwaba) Qonda ukuqhwaba okuninzi/nokumbalwa 1.4 Nakana nokuqaphela amanani kwiimeko eziqhelekileyo, umz. ubudala,irejista Chaza,thelekisa uze ulandelelanise amanani Hlula phakathi ko-ngaphezulu kune-, ngaphantsi kune- eyona i -, ilingana ne – ukuya kwi - 10 Qonda amanani olandelelwano - elokuqala, elesibini, elesithathu, elesine,njl. 1.6 Sebenzisa izixhobo ezibonwayo Ubuchule bokusombulula iingxaki zezibalo Chaza into oyicingayo ngamagama ,ngokuzoba nangezinto eziphathekayo 1.7 no 1.13 Sombulula udibaniso nothabatho ngomlomo ubandakanya amanani ukuya kwi - 10 Ukudibanisa nokuthabatha Iipateni ne fankshini 2.1 Kopa, yandisa nokuyila iipateni eziviwayo Iipateni zejiyometri landela umdlalo ka”sikhoji” Isithuba 3.1 Yazi iingqiqo:ecaleni kwe,phakathi nasembindini,ekhohlo nasekunene nemilo(Ijiyometri) Qonda iingqiqo: ngaphambili,ngasemva,phezulu,ezantsi,ekhohlo ekunene Indawo-bume,ukufumana indawo nembonakalo 3.2 yazi ukwakha ubuncinane iphazili ezingama- 24 izinto ezinokwakheka kuka 3-D no 3.3 Izinto nakana nokuchonga isangqa, unxantathu, isikwere, nexande ezinokwakheka kuka 2-D 3.4 nakana umgca wolingano -macala kwizinto Ulingano -macala Umlinganiselo 4.2 Qonda ukuba izinto zinokuthathwa umlinganiselo kusetyenziswa iteyipu Ubude Ukusebenza 5.1 Kwazi ukuqokelela, ukuhlela, ukuzoba, ukufunda, nokubonisa izinto ngokophawu olunye. ngolwazi Qokelela uze uhlele izinto oluqokelelweyo 5.2 Bonisa ingqokelela yezinto ezihleliweyo 5.3 Xoxa uze unukezele ingxelo ngengqokelela 261 yezinto ezihleliweyo MATHEMATIKA IBANGA LABAQALAYO (R)

MATHEMATIKA IBANGA LABAQALAYO (R) ISAHLUKO 4: uhlolo 4.1 INTSHAYELELO UkuHlola yinkqubo eqhubekayo yokufunda ecwangcisiweyo yokuchonga, ukuqokelela nokutolika ulwazi malunga nendlela abaqhuba ngayo abafundi, usebenzisa iindlela ezahlukeneyo zokuHlola. Oku kubandakanya amanyathelo amane: • Ukuqokelela ubungqina bokusebenza komfundi • ukuphonononga obu bungqina • ukurekhoda okufunyanisiweyo noku • sebenzisa olo lwazi ukuqondisisa nokuncedisa uphuhliso lwabafundi ukuphuhlisa ukufunda nokufundisa. UkuHlola kufanela kusekwe kokungekho sikweni (ukuHlola kokufunda nokuseSikweni (ukuHlola kokufunda). Kwi- imeko zombini kunikwa ingxelo ekufanele abafundi bayazi ngokufunda kwabo. Kwinqanaba elisisiseko, obona buchule bungundoqo kuHlolo oluseSikweni nolungekho seSikweni kukujongwa baqatshelwe ngutitshala, iingxoxo zomlomo, imiboniso eyenziwayo nokurekhodisha ephepheni. UkuHlola kwiBanga labaqalayo malwenziwe ngNgomlomo nezenziwayo. 4.2 UKUHLOLA OKUngekho SESIKWENI OKANYE KWEMIHLA NGEMIHLA UkuHlola kokufunda kunenjongo yokuthi gqolo ukuqokelela ulwazi malunga nokusebenza komfundi . Oku kubi- zwa ngokuba kukuHlola okungekho seSikweni. Oku kukubeka esweni rhoqo kwenkqubo yomfundi. Oku kwenziwa ngokubonisa, ngokuxoxa, ngokwenza imisebenzi yeprekthikhali, imiboniso,ukusebenzisana okungekho seSikweni eklasini, njalo njalo. Makungabonwa oku njengokwahlukileyo koko kwaseklasini. UkuHlola okungekho seSikweni kunceda ukuba utitshala abeke esweni inkqubo yomfundi nokwenza izigqibo ezisekelwe kokufunyaniswe yonke imihla. UkuHlola okungekho seSikweni kusetyenziswa uku: • Ukunika ingxelo kubafundi • Ukuncedisa kwisicwangciso sokufundisa. Ngamanye amaxesha utitshala unokugcina itshekhilisti okanye asebenzise uludwe lwenkqubo yokukhangela njen- gendlela yokurekhoda inkqubo yabafundi. Ngamanye amaxesha abafundi okanye ootitshala banokumakisha le misebenzi yokuHlola. Noko kunjalo, ukuHlola okungekho seSikweni aluyiyo inxalenye yokurekhodishwa njengoHlolo oluseSikweni. Iziphumo zemisebenzi yokuHlola zemihla ngemihla azithathelwa ngqalelo ekunyuselweni nasekukhut- shelweni isatifikethi. 4.3 UKUHLOLA OKUSESIKWENI Yonke imisebenzi yokuHlola iyinxalenye yenkqubo eseSikweni yokuHlola yonyaka kwaye ithatyathwa njengokuHlola okuSeSikweni. Imisebenzi yokuHlola okuseSikweni iyamakishwa ize irekhodishwe ngokuseSikweni ngutitshala elun- giselela ukuqhubela phambili nokukhutshwa kwesatifikethi. Imisebenzi yokuHlola okuseSikweni iyinxalenye yeN- kqubo yokuHlola yonyaka eseSikweni kwiBanga ngalinye nakwisifundo ngasinye. Utitshala unokujonga abafundi abali-10 ngexesha, ngoko imisebenzi yokuHlola okuseSikweni yenziwa ngokukodwa kwumatyeli ogxininiso emaqeleni amancinane, yaye kuthabatha iintsuku ezimbalwa ukuHlola iklasi yonke. Zonke izixhobo abaqhele ukuzisebenzisa abafundi, mazibe khona njengesiqhelo (izixhobo zokubala, iitshati zamanani njalo njalo). Iindlela zokuHlola ezisetyenziswayo mazibe kwizinga neminyaka efanelekileyo, zibe nokukhulisa kubafundi. Uku- Hlola okuseSikweni makulungiselele onke amanqanaba anengqiqo nabanako ukukwenza abafundi. Indlela eyilwe ngayo le misebenzi ma iquke umxholo wesifundo ngeendlela ezahlukeneyo. 262 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) Iindlela ezahlukeneyo zokuHlola (ukukhangela, Ngomlomo, ezenziwayo nezibhalwayo) mazisetyenziswe ukunika umfundi ngamnye ithuba lokubonisa akwaziyo ukukwenza. Oku kwenziwa kuba abanye abafundi babonisa abakwa- ziyo ukukwenza ngohlobo oluthile lwendlela yokuHlola. Umzekelo, • Abanye abafundi abafumana kunzima ukufunda, benza kakuhle kwiMathematika. • Abanye abafundi Bangangabikho kwizinga elamkelekileyo kulwimi lokufunda nokufundisa. Imisebenzi yokuHlola kwiMathematiki mayibandakanye imisebenzi engaxhomekekanga kulwimi, engaxhomekekan- ga kukwazi ukufunda, ukubonisa eyona nto banako ukuyenza abafundi. Noko kunjalo, mayiqondakale eyona nto eHlolwayo. Ulwazi nezakhono ezithile ziHlolwa ngokukuko ngeendlela ez- ithile zokuHlola. Iintlobo ezahlukeneyo zokuHlola zilungele izakhono neengqiqo ezidingekayo kwiintlobo ngeentlobo zezihloko ngokweminyaka yabafundi. Kuluncedo ukusebenzisa itshekhlisti yokukhangela ukuHlola abafundi besen- za imilinganiso kumaBanga abaqalayo. IiRubhriki zingasetyenziswa ukuvavanya izakhono zabafundi zokusombulula iingxaki. 4.4 INkqubo yokuHlola OKUSESIKWENI Imisebenzi yokuHlola okuseSikweni yeMathematiki ibandakanya ngaphezu kwesihloko esinye kwiMathematiki. Im- isebenzi yokuHlola ngonyaka kufuneka iquke zonke iinkalo zomxholo nezihloko, kodwa asiyiyo yonke into kwiimfuno zekharityhulam ema ihlolwe kwenziwe ingxelo ngayo ngokuseSikweni. Amanani, ukusebenza nolwalamano kwenza ipesenti engama- 60% yeMathematiki kwiBanga labaqalayo . Le nto ithetha ukuthi ipesenti engama - 60% yokuHlola okuseSikweni iKota nganye ngonyaka ma igxininise kumanani, imisebenzi nolwalamano. Umsebenzi wokuHlola okuseSikweni ma ungabonwa njengesiganeko esinye okanye uvavanyo olunye. Eminye im- ilinganiso yokuHlola ingasetyenziswa ngexesha elinye, kodwa eminye ingaHlolwa ngamaxesha ohlukeneyo. Umze- kelo, ukuba isakhono sokubala ngokuqakatha siyaHlolwa , ukukwazi ukwenza oku kulandelayo kungaHlolwa kuwo lo msebenzi umnye: • Ukugqibezela ukubala ngokulandelelanisa • Ukufunda nokubhala iisimboli zamanani • Ukubala Nangona kunjalo, ukuba umsebenzi wokuHlola uquka ukusombulula izibalo zamanani zamazwi ngokwenza amaqela okanye ukwahlula ngokulinganayo, nokuHlola abantwana ukukwazi ukwenza umlinganiselo womthamo; Kungen- zeka ukuba le miba yeMathematiki iHlolwe ngamaxesha angafaniyo nangeendlela ezahlukeneyo. 4.5 UKUREKHODisha NOKUNIKA INGXELO NGOMSEBENZI) Ukurekhoda yinkqubo apho utitshala abhala phantsi izinga lokusebenza lomfundi ngamnye kumsebenzi othile ohlolwayo. Kubonisa inkqubela-phambili yomfundi ekuzixhobiseni ngolwazi oluxeliweyo ngokweeNkcazelo zePolisi yeKharityhulam nokuHlola. Iirekhodi zomsebenzi womfundi kufanele zinike ubungqina ngenkqubela-phambili yom- fundi ngokweBanga kunye nokulungela kwakhe ukuqhubela phambili xa epasile ukuya kwiBanga elilandelayo. Iirekhodi zomsebenzi womfundi kufanele zisetyenziswe ukungqinisisa inkqubela-phambili eyenziwe ngootitshala nabafundi kwinkqubo yokufundisa nokufunda. Ukukhupha iripoti okanye ingxelo yinkqubo yokwazisa abafundi, abazali babo, isikolo nabanye abathathi-nxaxheba malunga nendlela asebenza ngayo umfundi ezifundweni zakhe gabalala. Zininzi iindlela ezisetyenziswayo ukunika iripoti okanye ingxelo ngomsebenzi womfundi. Ziquka amakhadi eripoti okanye engxelo, ukubiza iintlanganiso naba- zali, iintsuku zokutyelela esikolweni, iinkomfa zabazali nootitshala, ukufownela abazali, ukuthumela iileta kubazali, ukuthumela oolindixesha besikolo okanye beklasi kubazali, njalo njalo. Ootitshala kumaBanga onke banika iripoti CAPS 263

MATHEMATIKA IBANGA LABAQALAYO (R) okanye ingxelo ngokweepesenti ngesifundo ngasinye. Amazinga ohlukeneyo okusebenza kunye neepesenti aham- belana nazo adweliswe kwiTheyibhile engasezantsi. IIKHOWUDI NEEPESENTI ZOKUREKHODA NOKURIPOTA (NOKUNIKA INGXELO NGOMSEBENZI INKCAZELO NGENDLELA AQHUBE NGAYO KUMSEBENZI KHOWUDI IPESENTI WAKHE UMFUNDI 7 Uphumelele emagqabini 80 – 100 6 Ugqwesile 70 – 79 5 Uphumelele ngokuqaqambileyo 60 – 69 4 Uphumelele ngokwanelisayo 50 – 59 3 Uphumelele ngokufanelekileyo 40 – 49 2 Uphumelele ngokuyinxalenye 30 – 39 1 Akaphumelelanga 0 - 29 4.6 ULWAZI GABALALA Le dotyhumenti kufanele isetyenziswe nezi zilandelayo 4.6.1 National policy pertaining to the progrmme and promotion requirements of national Curriculam statement Grades R-12; and 4.6.2 The policy document, National Protocol for Assessment Grades R-12 4.7 Imizekelo YEETSHEKILISTI ZOHlolo OLUSeSikweni eziCETYISWAYO Imizekelo yeetshekilisti zokuHlola inikiwe kwiBanga labaQalayo (R) ngezantsi: Injongo kukuncedisa ootitshala bacwangcise baze benze uHlolo oluseSikweni ngendlela eqhubekayo. IMIZEKEKLO YEETSHEKILISTI ZEBANGA LABAQALAYO (R) IKOTA YOKU - 1 Inkalo Umxholo Umlinganiselo wokuHlola √ okanye x Ukuphawula yomxholo Amanani,ii- Ukubala Ukuqikelela aze abale ngokucengceleza ukuya kuzi- 5 Opareyshini (Iingoma nezicengcelezo zamanani zibandakanywe noLwalamano ukukhulisa ingqiqo yamanani) Unakano Ukunakana amanani kwiimeko eziqhelekileyo umzekelo: lwamanani iminyaka yokuzalwa, rejista(isigama esisetyenziswa xa kufundwa amanani) Ukuqonda amanani ngokulandelelana (umzekelo ngexesha lesiqhelo lokuya ngasese) Ingqiqo ngamanani Ukuqondana phakathi komnye nomnye/ukungqamanisa (Itshati yomncedisi ngexesha lesidlo) Ukuchonga Ukuchonga imifanekiso yamanani namakhadi nokuchaza amachaphaza equka inani u-1 amanani Ukwazi isimboli yenani u-1 apheleleyo Ukunakana igama lenani u-1 Ukusombulula Ukusebenzisa izixhobo eziphathekayo izibalo zamanani Ukuchaza iingcinga zakhe ngamazwi nangemizobo zamazwi okanye izinto eziphathekayo Iipateni Ukukopa, wandise, Ukuchonga iipateni kokusingqongileyo neFankshini uze uyile iipateni Ukukopa, andise aze ayile iipateni ezizezakhe zakho 264 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) IMIZEKEKLO YEETSHEKILISTI ZEBANGA LABAQALAYO (R) IKOTA YOKU - 1 Inkalo Umxholo Umlinganiselo wokuHlola √ okanye x Ukuphawula yomxholo Isithuba Ukunakana, Ukunakana, achonge aze abize iibhola nemilo achonge aze Ukunakana, achonge aze abize iibhokisi axele izinto ezinokwakheka kuka 3-D Ukunakana, Ukunakana, achonge aze abize iisimboli zakhe, iisimboli achonge aze zabahlobo kunye negama leklasi axele izinto Ukwakha ebuncinaneni iphazili emaqhekeza ma- 6 ezinokwakheka Ukubonisa ukukwazi ukohlula phakathi kwezinto kuka 2-D ezifotwe zankulu ngaphambili nezo zifotwe zancinci ngemva(foreground and background) Iimilo zejiyometri Ukuchonga nokunakana isangqa Ukuchonga nokunakana unxantathu Ukuchonga nokunakana uxande Ukuchaza, Ukuthelekisa ukuba kwizinto eziqokelelweyo ezimbini, ahlele aze yeyiphi enkulu kunenye, encinane kunenye, enkulu kuzo athelekise izinto zonke, eyona incinane kuzo zonke ezinokwakheka Ukuhlela izinto ngokobungakanani – enkulu nencinane kuka 3-D ngokwe:: Umbala – Imibala engundoqo (bomvu, qanda, bhlowu) Imilo – isangqa, unxantathu noxande Izinto eziqengqelekayo Izinto ezitshebelezayo Ukunakana umgca Ukunakana umgca wolingano-macala kwisiqu sakhe wolingano-macala: Ulwalamano ngok- Ukwazi phambi kwe-/ ngemva kwe- wezithuba: Ukwazi phezu kwe-, phantsi kwe- Indawo-bumilo Ukwazi ngaphakathi, ngaphandle yezinto ezimbini Ukwazi phezulu, phantsi ngokunxulumene nomfundi Ingqiqo Ukuqonda la magama: ukuya phambili, emva, phambili yokwalathisa nasemva Umlinganiselo Ixesha Ukusebenzisa amagama anjengo: usuku, ubusuku, ubumhlophe nobumnyama, kusasa, emalanga, ngobusuku, ukuchaza ixesha losuku Ukulandelelanisa izinto ezenzekayo ngosuku (Inkqubo yosuku) Ukubonisa nokwazi iintsuku zeveki, amaxesha onyaka nemozulu Ukwazi iintsuku zokuzalwa zabo Ubude Ukwahlula phakathi ko: inde, inde kunenye, inde kuzo zonke, imfutshane, imfutshane kunenye, imfutshane kuzo zonke (Itshati yobude) Ukusebenza Ukuqokelela, Ukukwazi ukuqokelela, ahlele, azobe, afunde aze abonise ngolwazi ahlele, azobe, (atolike) izinto ngokophawu olunye. oluqokelelw- afunde aze eyo abonise ulwazi UHLELO LUKUGQIBELA: CAPS 265

MATHEMATIKA IBANGA LABAQALAYO (R) IMIZEKELO YEETSHEKHILISTI ZEBANGA LABAQALAYO(GRADE R) IKOTA YESI- 2 Inkalo Umxholo Umlinganiselo wokuHlola √ okanye x Ukuphawula yomxholo Amanani,ii- Ukubala Qikelela aze abale ngokucengceleza ukuya ku- 5 Opareyshini (Iingoma nezicengcelezo zamanani zibandakanywe noLwalamano ukukhulisa ingqiqo yamanani) Bala ukubuya umva nokuya phambili (1-4) Qonda amagama “ninzi no mbalwa” (uqhwaba) Unakano Nakana amanani kwiimeko eziqhelekileyo umzekelo: lwamanani inombolo yendlu, irejista yedilesi Ukuchonga Chonga imifanekiso yamanani namakhadi amachaphaza nokuchaza Zazi iisimboli zamanani 1, 2, 3, 4 amanani apheleleyo Nakana amagama amanani - mbini, ntathu, ne Ingqiqo ngamanani Qondana phakathi komnye nomnye/ukungqamanisa (Itshati yomncedisi ngexesha lesidlo) Hlula phakathi kwamagama: ngaphezu, ngaphantsi nokulingana, ninzi nezimbalwa ukuya kuzi-4 Nakana iintlobo zemali ezinkozo/mwangalala yoMzantsi Afrika Ukusombulula Sebenzisa izixhobo eziphathekayo izibalo zamanani Chaza iingcinga zakhe ngamazwi nangemizobo okanye zamazwi izinto eziphathekayo. Sombulula izibalo zamanani zomlomo ngokudibanisa nokuthabatha ukuya ku- 4 Iipateni Ukukopa, wandise, Kopa, wandise, uze uyile iipateni zakho (izinto, iimilo neFankshini uze uyile iipateni nemali ezinkozo) zakho Isithuba nemilo Ukunakana, Yakha iphazili emaqhekeza ali -12 ubuncinane. achonge aze Bonisa ukukwazi ukohlula phakathi kwezinto ezifotwe axele izinto zankulu ngaphambili nezo zifotwe zancinci ngemva ezinokwakheka (foreground and background) (Hlola kwakhona) kuka 2-D Iimilo zejiyometri Nakana nokuchonga unxantathu Qonda agcine ulwazi luka nxantathu (ugcino-lwazi lwemilo) Ukunakana, Thelekisa ukuba kwizinto eziqokelelweyo ezimbini, achonge aze yeyiphi enkulu kunenye, encinane kunenye, enkulu kuzo axele izinto zonke, eyona incinane kuzo zonke ezinokwakheka Hlela izinto ngokobungakanani– ende nemfutshane kuka 3-D ngokwe: Imibala – (bomvu, qanda, bhlowu noluhlaza) Iimilo Ukwakha izinto Phicotha ukwakha ngeebhloko ezinokwakheka kuka 3-D esebenzisa izinto eziphathekayo Ukunakana umgca Ukunakana umgca wolingano-macala kwisiqu sakhe wolingano-macala: nokumngqongileyo Ulwalamano Ukuqonda indawo-bumilo yezinto ezimbini nangaphezulu ngokwezithuba ngokungqamene nomfundi Phezu kwe, phantsi kwe 266 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) IMIZEKELO YEETSHEKHILISTI ZEBANGA LABAQALAYO(GRADE R) IKOTA YESI- 2 Inkalo Umxholo Umlinganiselo wokuHlola √ okanye x Ukuphawula yomxholo Umlinganiselo Ixesha Qonda iintsuku zeveki, amaxesha onyaka netshati yemozulu (iingoma nezicengcelezo – Hlola kwakhona) Lazi usuku lwakhe lokuzalwa (Hlola kwakhona) Ubude Hlula phakathi kwe; eyona inde, eyona imfutshane, (Itshati yobude) Ukusebenza Ukuqokelela, Kwazi ukuqokelela, ahlele, azobe, afunde aze abonise ngo lwazi ahlele, azobe, (atolike) izinto ngokophawu olunye. oluqokelelweyo afunde aze abonise ulwazi UHLELO LUKUGQIBELA: IMIZEKELO YEETSHEKHILISI ZEBANGA LABAQALAYO(GRADE R) IKOTA YESI - 3 Inkalo Amagqa- Umxholo Imilinganiselo yoHlolo √ okanye x yomxholo bantshintshi Amanani,ii- Ukubala Qikelela nokubala ngokucengceleza ukuya kwi - 7 Opareyshini (iingoma nezicengcelezo zamanani zibandakanywa noLwalamano ukukhulisa ingqiqo ngamanani) Bala ubuya umva nokuya phambili (1 -7) Ukwazi ukuba kuqhwatywa kangaphi ngaphezulu/ ngaphantsi Ukunakana Nakana amanani kwiimeko eziqhelekileyo - umzekelo: amanani iminyaka yokuzalwa, irejista (Hlola kwakhona) Ukuchonga Chonga imifanekiso yamanani namakhadi amachaphaza nokuchaza ukuya kwinani i - 7 amanani Ukwazi iisimboli zamanani 5, 6, 7 apheleleyo Nakana amagama amanani ; hlanu, ntandathu, sixhenxe Ingqiqo ngamanani Ukwahlula phakathi ko: ngaphezulu, ngaphantsi nezilingana, zininzi nezimbalwa ukuya kwi -7 Nakana umbala neentlobo zezilwanyana kokubhaliweyo eMzantsi Afrika Ukusombulula Sebenzisa izixhobo eziphathekayo izibalo Chaza iingcinga zakhe ngamazwi nangemizobo okanye izinto eziphathekayo Ngomlomo usombulula izibalo ukuya kwi-7 ngokudibanisa nokuthabatha Iipateni Ukukopa, wandise Kopa, andise aze ayile iipateni zakhe esebenzisa neFankshini aze ayile iipateni imifanekiso zakhe CAPS 267

MATHEMATIKA IBANGA LABAQALAYO (R) Isithuba nemilo Nakana, achonge Yakha iphazili enezicwili/izijungqe ezili- 18 ubuncinane (Ijiyometri) aze axele iimilo/ imifanekiso enokwakheka kuka 2-D Iimilo zejiyometri Nakana, achonge aze axele uxande Qonda ugcino- milo olufundiweyo (shape conservation) Ukwakha izinto Yakhela kumzekelo wokwakha onikiweyo ezinokwakheka Kopa isakhiwo kuyilo nekhadi lomfanekiso kuka 3-D esebenzisa izixhobo eziphathekayo Uzalwano yazi imeko -bume yezinto ezimbini nangaphezulu lwesithuba ngokuzalana kwazo Phambi kwe-, emva kwe-, ngaphezu kwe-, phantsi kwe-,ezantsi kwe-, kufuphi ne-,ecaleni kwe-, phakathi, ekhohlo nasekunene UYenza ngokwemiyalelo kwi phegi-bhodi Ingqiqo Yazi izalathiso kwitshati yokukhomba yokwalathisa Umlinganiselo Ubude Qikelela nokwenza umlinganiselo kubude bezinto ezahlukeneyo Ubunzima Qonda amagama anjengo: “ubulula, ubunzima, ilula kunenye, inzima kunenye, eyona ilula kuzo zonke, eyona inzima kuzo zonke” Umthamo Landela amagama ajengo: ize, izele, ngaphezu kwe-, ngaphantsi kwe- Ukusebenza Ukuqokelela, Kwazi ukuqokelela, ahlele, azobe, afunde aze atolike ngolwazi ahlele, azobe, izinto ngokophawu olunye oluqokelelweyo afunde aze abonise ulwazi UHLELO LOKUGQIBELA 268 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA

MATHEMATIKA IBANGA LABAQALAYO (R) IMIZEKELO YEETSHEKHILISI ZEBANGA LABAQALAYO (GRADE R) IKOTA YESI - 4 Inkalo Amagqa- Umxholo Imilinganiselo yoHlolo √ okanye x yomxholo bantshintshi Amanani,Ii- Ukubala Qikelela nokubala ngokucengceleza ukuya kuzi - 10 opareyshini (iingoma nezicengcelezo zamanani zibandakanywa noLwalamano ukukhulisa ingqiqo ngamanani) Bala ukuya emva nokuya phambili (0 -10) Bala ngezi- 2 (Iingoma nezicengcelezo zamanani) Qonda amagama anjengo: “ninzi no mbalwa” (ngokuqhwaba) Qonda ukuba uqhwabe kangaphi ngaphezu/ ngaphantsi, elona lininzi/ elona lincinane Chonga umfanekiso wenani kunye namakhadi anamachaphaza ukusuka kwi-0 ukuya kwi-10 Zazi iisimboli zala manani 8,9,10 ne-0 kwaye: Anakane amagama ala manani- isibhozo, isithoba, ishumi neqanda Gqibezela ulandelelwano lwamanani alula ukusuka kwinani u-1 ukuya kwi-10 Ukunakana Nakana aze achonge amanani kwiimeko eziqhelekileyo - amanani umzekelo iminyaka yokuzalwa, irejista yamanani Ukuchonga Chonga imifanekiso yamanani namakhadi amachaphaza nokuchaza amanani ukusuka 0 – 10 apheleleyo Zazi iisimboli zamanani 8, 9, 10 Nakana amagama amanani - isibhozo, ithoba neshumi kunye ne – 0 Gqibezela ulandelelwano olulula lwamanani ukusuka ku 1-10 Ingqiqo ngamanani Hlula phakathi ko: ngaphezulu, ngaphantsi, ilingana, ezona zininzi nezona zimbalwa ukuya kwi nani i-10 Qonda amanani alandelelanayo - eyokuqala, eyesibini, eyesithathu, eyesine, eyesihlanu neyesithandathu Ukusombulula Sebenzisa izixhobo eziphathekayo izibalo Chaza iingcinga zakhe ngamazwi nangemizobo okanye izinto eziphathekayo Ngomlomo usombulula izibalo zamanani ngokudibanisa nokuthabatha amanani ukuya kwi – 10 IiPateni Ukukopa, wandise Kopa, andise aze ayile iipateni ezimanyelweyo zakhe neFankshini aze ayile iipateni Qonda umdlalo “ uSkhotshi/ uGuni / uNochelesi / zakhe uNochelu” Isithuba nemilo Ukunakana, Kwazi ukwakha iphazili emaqhekeza engama- 24 (ijiyometri) achonge aze ubuncinane axele iimilo ezinokwakheka kuka 2-D Iimilo zejiyometri Nakana aze achonge isangqa, unxantathu, uxande nesikwere Ukunakana umgca Nakana umgca wolingano-macala kwizinto wolingano-macala Uzalwano Yazi amagama anjengo: kufuphi ne-, phakathi, lwesithuba embindini, ekhohlo nasekunene Kwazi ukwenza umsebenzi wephegi-bhodi ophambili Ingqiqo Qonda amagama anjengo: phambili nasemva, phezulu yokwalathisa naphantsi, entla nasezantsi, ekhohlo nasekunene CAPS 269

MATHEMATIKA IBANGA LABAQALAYO (R) Umlinganiselo Ubude Qonda ukuba izinto ziyalinganiswa nangokusebenzisa itheyiphu yokulinganisa Ukusebenza Ukuqokelela, ahlele, Kwazi ukuqokelela, ahlele, azobe, afunde aze atolike ngolwazi azobe, afunde aze izinto ngokophawu olunye oluqokelelweyo abonise ulwazi UHLELO LOKUGQIBELA 270 INKCAZELO YEPOLISI YEKHARITYHULAM NOKUHLOLA