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INGABULA-ZIGCAWU Ukuphumeza umgaqo-nkqubo asinto ilula ukuyenza. Yinkqubo yokutolika izinto nokusebenzisana nabanye okuthi kuthathe ithuba elithile. Sithi sifunde kule nkqubo size sizame ukuhlenga-hlengisa iindlela zokungenelela ngoncedo ukwenzela ukuba zifaneleke yaye zilungele iimeko ezahluka-hlukeneyo. Into esiyifundileyo kule minyaka ilishumi nangaphezulu edlulileyo kukuba sonke kufuneka sithethe, simamele size sifumane izisombululo kwimingeni esijongene nayo. Ezi shedyuli zomsebenzi zisisiphumo somgaqo-nkqubo nenkqubo yokufunda elolu hlobo. ULwazi lokuFunda nokuBhala kunye noLwazi lokuBala nezinye iinkalo zomsebenzi kwiSigaba seSiseko neSigaba esiPhakathi zizinto ezibalulekileyo elijolise kuzo iSebe leMfundo eNtshona Koloni. Sifuna ukomeleza izikolo zaseprayimari size sidale amathuba esiseko esomeleleyo ukwenzela ukuba sibe nokuphucula amathuba abanawo abafundi kwimisebenzi yabo yokufunda. Sikholelwa ukuba esi siseko sinako ukuphucula iziphumo zolwazi lokufunda nokubhala nolwazi lokubala, izinga lokupasa kwabafundi ngokubanzi nezinga labafundi abagqibayo ukufunda. UMzantsi Afrika lilizwe elisakhulayo yaye sivile ukuba, kweli xesha loqhagamshelwano lwehlabathi jikelele, amazwe asazama ukuleqa umgangatho kumele avelise izakhono eziyimfuneko. Ngako oko ke amazwe afana neli lethu anawo amandla okwazi ukukhuphisana namanye kunye nokuzinza. Into ebaluleke kakhulu kukuba nabafundi abakwaziyo ukufunda, ukubhala nabakuvuyelayo ukuya esikolweni. Ukuxabiseka kwesikolo kwezentlalo kungaphuculwa ukuba kwenziwa iinzame mpela zokufunda. Iishedyuli zomsebenzi ziza kuthathwa njengenxalenye yomqulu ophathelele kwiPhulo leZiseko zokuFunda. Lo mqulu uthathwa njengesixhobo sokuxhasa nokunika intsingiselo kweli phulo. Ngenxa yoluvo lokuba amaphulo aba yintetho nje yomlomo engenaziphumo, iishedyuli zomsebenzi ziza kusebenza njengentsika yokuxhasa ukwakhiwa kweziseko zolwazi lokufunda nokubhala kunye nokubala. Lilinge lokubonelela ootitshala ngezikhokelo zokufundisa usuku ngalunye lwesikolo. Ezi shedyuli zomsebenzi ziza kuthunyelwa ezikolweni ngenjongo yokufumana ingxelo ngokuqhubekayo (feedback). Ziza kuvavanywa kwakhona kwizikolo ezithile ezikhethiweyo. La maxwebhu aza kusasazwa njengezikhokelo ngoJanuwari 2009 kuze kucelwe izimvo ngoJulayi 2009. Ziya kuphindwa zivavanywa kwakhona ezi shedyuli zomsebenzi ngoJulayi 2009. Zonke izimvo ezifunyenweyo ziya kusetyenziswa ekuphuculeni ngakumbi iishedyuli zomsebenzi. ISebe leMfundo eNtshona Koloni liziko elithanda ukufunda izinto yaye lizama ukuqonda iimeko elisebenza phantsi kwazo ngamaxesha onke. Le nkqubo yokufunda yinkqubo ehlala iqhubeka okokoko, njengoko sineemeko ezingahlali zimi ndawonye neziguquka ngokukhawuleza. Lo gama sihlala sikukhumbula oku, ukucelwa kwezimvo novavanyo lilinge lokwamkela ingcamango yeziko elithanda ukufunda izinto ngokuvelisa iingcinga ezisekelwe kwiimbono zootitshala, kwakunye nezo zabo bakwiimeko ezahlukeneyo kwiphondo lethu. Siyazi ukuba ukunyanzelisa indlela enye yokwenza izinto kwiimeko ezahlukeneyo asiyondlela esa empumelelweni. Siyazi kwakhona ukuba kufuneka simamele, sithethe size sifumane iimpendulo zokukhawulelana nemingeni ephambi kwethu. Ukwenza uvavanyo nokucela iikhomenti kuza kusinika ithuba lokuthetha, lokumamela nokufumana izisombululo njengoko siqhubela phambili nenkqubo yemfundo es emgangathweni elungiselelwe bonke abafundi bethu.

uGqr. S. Naicker, uMlawuli oyiNtloko woPhuhliso lweKharityhulam

ISHEDYULI YOMSEBENZI

ULWAZI LOKUBALA

IBAKALA 3

NCEDA UQAPHELE: Ishedyuli yomsebenzi yoLwazi lokuBala iqulunqelwe ukunceda nokukhokela ootitshala kwisiGaba sesiSeko ekufundiseni iinqobo zekharityhulam ekufuneka kufundiswe malunga nazo yonke imihla. Ukuqulunqwa kwale shedyuli yomsebenzi kucwangciswe ngobunono ukwenzela ukuba ukusetyenziswa kwe-NCS ngokunjalo nakwiziPhumo zeziFundo kunye nemiGangatho yoVavanyo kuLwazi lokuBala kugxininiswa ngaphezulu ekwenzeni ukuze utitshala akwazi ukufundisa. Le shedyuli yomsebenzi ke ngoko inokusetyenziswa ngokuqiniseka njengoko ibandakanya zonke iziPhumo zeziFundo nemiGangatho yoVavanyo umfundi afuna ukuyazi ukuze afumane iikhonsepthi zokubala ezingundoqo kunye nezakhono ekupheleni kwebakala nesigaba. Ishedyuli yomsebenzi ke ngoko icacisa ukuba YINTONI ekufuneka ifundiswe ize ikhatshwe sisikhokelo sikatitshala esicebisa malunga nokuba ungenziwa NJANI lo msebenzi. Kubalulekile ukuba la maxwebhu alandelayo afundwe kunye ukulungiselela ingqiqo engaphezulu yoLwazi lokuBala, o.k.t.

• The NCS Policy Statement (INkcazelo yePolisi ye-NCS) • Assessment Policy 2007 (IPolisi yoVavanyo yowe-2007) • The Numeracy Work schedule (IShedyuli yoMsebenzi yoLwazi lokuBala) • The Numeracy Teacher Guide (IsiKhokelo sikaTitshala soLwazi lokuBala)

Ishedyuli yomsebenzi yahlulwe ngaphezulu yayimisebenzi yemihla ngemihla ebandakanya iikota ezine ngokungqinelanayo. Ukwabiwa kwexesha loLwazi lokuBala koku kulandelayo: AmaBakala 1 no-2: 1 iyure 30 imizuzu ngosuku IBakala 3: 1 iyure 45 imizuzu ngosuku Ukufumana isikhokelo esimalunga nendlela yokusebenzisa eli xesha uyacelwa ukuba ufunde isiKhokelo sikaTitshala esibandakanya imisebenzi yokufunda nokufundisa eqingqiweyo ukuxhasa ishedyuli yomsebenzi. Kwiiveki ezimbini zekota 1 uvavanyo olwandlalelayo (baseline assessment) kufuneka lwenziwe ngaxeshanye nokufundiswa kweekhonsepthi ezintsha njengoko kubonisiweyo kule shedyuli yomsebenzi.

- 1 -

ISHEDYULI YOMSEBENZI YOLWAZI LOKUBALA

IBAKALA 3

IKOTA 1

IVE-KI

IZIPHUMO ZESIFUNDO

UVAVANYO LWEMIGANGATHO NOKUFUNDISA OKUNGUNDOQO

ISIKHOKELO SIKATITSHALA

1- 2

LO 1 Amanani, ukusetyenziswakwamanani nolwalamano

Uvavanyo olwandlalelayo (baseline

assessment) luzaliswa ngokungqamene nokufundisa okwenzeka kwiveki 1 neyesi-2

Ukubala okwenziwa imihla ngemihla

o Bala ukusuka ku-1 ukuya ku-200 kwitshathi yamanani

o Bala izinto ukuya ku-100 o ngophinda-phindo lwezibini, izithathu, izine,

izihlanu, amashumi ukusuka kulo naliphi inani ukuya ku-250

o sebenzisa umgca-manani (osenokuba yikhalenda, umgca-manani ome nkqo (vertical number line), itshathi yamanani, isixhobo sokubala (abacus)

Izibalo zentloko

o Yenza izibalo zentloko +, -, ×, ÷ ukuya ku-50

IKhonsepti yeNani neXabiso

• Hlaziya • iisimboli zamanani namagama amanani

abhalwe ngamazwi ukusuka ku-1-100 baze baphonononge unxibelelwano lwawo

• iibhondi ukuya ku-20

o Yazisa • amanani 101-150 uzibhale ngamazwi. • cwangcisa, chaza uthelekise la manani

angasentla • amanani alumelo (place values)

lwamanani amalungu ma-3 kuMakhulu kuMashumi nakwiMivo (Hundreds Tens Units) (HTU))

• Inyumerali, isimboli noNye kwisinye noBini obhalwe ngamazwi ngoLwimi lokuQala oLongezelelweyo (First Additional Language) (FAL)

o Iisethi, ukudibanisa nokuthabatha

• ukudityaniswa nokuthatyathwa kwamanani alungu linye namalungu mabini ukuya ku-20

i) sebenzisa izinto zokusebenza eziphathekayo

ii) umgca-manani

Isahluko 2

Isahluko 3

- 2 -

LO 2 Iiphatheni, iifankshini ne-aljebra

iii) iingxaki zokubala ezibhalwe

ngamazwi • ukucazulula amanani angamalungu

ama-2 njengobhalo olunabileyo, o.k.t. 87 = 80 + 7, sebenzisa oonotsheluza

• yalatha iisethi zomelo ukwenza ukuba izibalo zezivakalisi ezivulekileyo zibe yinyaniso, umz. □ + Δ = 47

• bhala iingxaki zokubala ngamazwi o Amaqhezu: a) ukwenza iihafu neekota ngokusonga

nokusika iimilo zamaphepha b) bhala amaqhezu ½; ¼ kumacandelo

onxulumano lwamanani (relative sections)

c) iihafu namanani angambini nangumnqakathi (even and odd numbers) ukuya ku-10.

o Ukuphinda-phinda nokwahlula-hlula

a) Hlaziya ulwazi malunga nokulandelayo: ukuphinda-phinda njengophinda-phindo olushunqelelweyo, umz. 3 + 3 + 3 = (3 × 3 = 9) kwisinye

b) Nokuhlaziya ulwazi malunga nokulandelayo: ukwahlula-hlula ngentsalela ukuya ku-10 ngokuphathekayo nangomlomo

c) bhala ngamazwi iingxaki zokubala

AmaCebo okuSombulula iiNgxaki Fundisa ngezibalo zokusombulula iingxaki;

o ukudityaniswa nokuthatyathwa konye no-2 – kokubhalwe ngamanani ukuya ku-100, umz. 35 + 4, 67 – 43,

o cwangcisa, chaza uthelekise amanani anamalungu ama-2

o ukuphinda-phinda kusetyenziswa njengokudibanisa okuphinda-phindwayo kwenani elifanayo

o ukwahlula-hlula njengokuthabatha okuphinda-phindwayo kwenani elifanayo

o ukuphinda-phindwa nokwahlulwa-hlulwa kwamanani anamalungu amabini nenani elinelungu elinye, umz. 4 × 5 = 20 20 ÷ 5 = 4

o qwalasela ukucazululeka (numerosity) kwamanani ukuya ku-34

Sebenzisa amacebo: • ukuqikelela • sebenzisa umgca-manani, itshathi

yamanani, izinto zokubala • ukwakhiwa nokucazululwa kwamanani:

ukwakha u-10

Isahluko 4

- 3 -

LO 3 ISithuba esiVulekileyo neMilo (IJometri) LO 4 Umlinganiselo

• ukuphinda kabini nokuhafisha

okukhokelela ekubhalweni ngamaqela nasekwabeni apho kusetyenziswa nalapho kungasetyenziswa zintsalela (remainders)

• wachaze ngomlomo amacebo owasebenzisileyo oko ukubhale ebhodini

• tshekisha izisombululo zabalingane kwiingxaki zokubala

Iiphatheni

o Khuphela uze wandise amanani aqhelekileyo usebenzisa uphinda-phindo luka-10, 5, 2, ukuya ku-200

o khuphela uze wandise iiphatheni usebenzisa izinto ezifumaneka kwindawo okuyo okanye iiphatheni eziqwalaselwe kwiimagazini

ISithuba esiVulekileyo neMilo

o qaphela uze walathe izinto ezingu-2-D, 3-D, izinto nemifanekiso efumaneka kwindawo okuyo, iibhokisi, iibhola, neesilinda; izangqa, oonxa-ntathu (triangles), izikwere, iingxande (rectangles); ezimbhuntshuntshu (cones), iiphiramidi

o chaza iimpawu zezi milo nezinto ezingasentla

Imali

o Fumana ixabiso elilinganayo lemali eziinkozo ukuya kwi-R5, umz. i-R1 = 10c+10c+10c+10c+10c+10c+10c+10c+10c+10c) ikwayiyo kwakhona i-(50c+50c)

o Fundisa malunga neengxaki zezibalo ezibhalwe ngamazwi ezinxulumene nemali

o Thenga evenkileni usebenzisa imali etshintshekileyo

o Fundisa malunga nendlela elula yokugcina iincwadi ezimalunga nezinto ezithengiweyo.

Ixesha

o funda uze ubhale ixesha ngokwamanani nangedijithali ngokweeyure, iihafu zeeyure

o bhekiselela kubude bezifundo, usuku lwesikolo, iintsuku neenyanga

Ubunzima

o qikelela, linganisa uze uthelekise ngokusebenzisa isikali uthelekise ubunzima babafundi ngeekhilogram

o isigama: bungaphezulu kuneli, bunganeno kuneli; bunzima kuneli, bukhaphukhaphu kuneli

Isahluko 5

Isahluko 6

Isahluko 7

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LO 5 UkuSebenzisa iDatha

Idatha

o Qokelela idatha eklasini malunga nobunzima babafundi obebulinganiswe kwiveki egqithileyo

o qokelela ngokungqamene nokuba bangaphi abafundi abanobunzima obungaphezulu kweekhilogram ezingama-30, ezinganeno kwe-30 kg,

Isahluko 7

3- 4

LO 1 Amanani, izibalo, ukusetyenziswa kwamanani nolwalamano

UMSEBENZI 1 WOVAVANYO OLUQINGQIWEYO



o Bala ukusuka ku-200 ukuya ku-400 o Bala izinto ukuya ku-100 o Bala ngoo-2,4,5,10 ukusuka nakweliphi

inani, umz. 25, 35, 45, 55, njl. njl. ukuya ku-100

o Bala ngoo-2 ubheka phambili uze ubuyele umva ku-20

o Bala ngoo-3 ukubheka phambili nokubuyela umva ku-30

Izibalo zentloko

o Yenza izibalo zentloko, +, -, ×, ÷ ukuya ku-50


o Hlaziya • iisimboli zamanani namanani abhalwa

ngamazwi ukusuka ku-1-100 • cwangcisa, chaza uze uthelekise

amanani anamalungu ama-2 ukuya ku-99

• ukuphinda-phinda njengokudibanisa okuphindwayo kwenani elinye

• Ukwahlula-hlula njengokuthabatha okuphindwayo kwenani elinye

• Ukudibanisa nokuthabatha amanani angamalungu ayi-2 ukuya ku-20

o Yazisa

• amanani 151-200 uze uwabhale phantsi ngokwamazwi.

• cwangcisa, chaza uze uthelekise amanani

• amanani alumelo ala manani angasentla kuMakhulu kuMashumi nakwiMivo (HTU) abandakanya u-‘0’ njengenani elilumelo, umz. ku-100-200 no-200…

• inani, isimboli nenani elibhalwe ngamazwi uThathu noNe ngoLwimi lokuQala oLongezelelweyo (First Additional Language (FAL)

Isahluko 2

Isahluko 3

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• ukudityaniswa nokuthatyathwa kwamanani alungu linye nangamalungu mabini ukuya ku-20


ii) umgca-manani iii) iingxaki zokubala ezibhalwe

ngamazwi • ukudityaniswa nokuthatyathwa

kwamashumi, umz. 20+60; 80+20; 90-50 • ukunatyiswa kweekhomponenti

ezingundoqo esebenzisa u-+ kwisinye – umz. 7+3, 17+3, 27+3 njl. njl. 7-3, 17-3, 27-3 njl. njl.

• Bhala phantsi izibalo ezibhalwe ngamazwi usebenzisa imali

o Amaqhezu:

a) ukwenza iihafu neekota ngokusonga nokusika iimilo zamaphepha

b) bhala phantsi amaqhezu ½; ¼ kumacandelo angqameneyo (relative sections)

c) bhala phantsi izibalo ezibhalwayo, umz. ihafu enye ka-13=7½

ize ikota enye ka-8=2

o Ukuphinda-phinda nokwahlula-hlula a) Fundisa malunga nophawu u-’x‘

njengokuphinda-phinda nofundwa njengo-‘phinda-phinda ngeli nani’ kwisinye nophawu u-‘÷’ njengokwahlula-hlula olufundwa ‘njengokwahlula-hlula ngeli nani’

b) ukuphinda-phinda nokwahlula-hlula ukuya ku-20 ukuphinda-phinda nokwahlula-hlula ukuya ku-20 njengezibalo eziphendulelweyo (inverse operations), umz. 4x5 = (20÷5=4)

c) ukwahlula-hlula ngentsalela ukuya ku-10 ngokuphathekayo nangomlomo

d) bhala phantsi iingxaki zokubala ezibhalwa ngamazwi

e) ukuphinda kabini nokuhafisha kwifomathi yethebhile kusetyenziswa iiprophathi ezisetyenziswa ngokutshintshiselanayo nokubala ngokuphendulelayo (inverse), umz. iThebhile ka-2 ukuya ku-20:

Ukuphinda kabini Ukuhafisha/ukuphendulela 1x2 2÷2 2x2 4÷2 3x2 6÷2 4x2 8÷2

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LO 2 Iiphatheni, iifankshini ne-aljebra LO 3 ISithuba esiVulekileyo neMilo (iJometri) LO 4 Umlinganiselo

AmaCebo okuSombulula iiNgxaki

o Fundisa malunga neengxaki zokubala uze usebenzise amacebo wakho ukusombulula izibalo, umz. • ukuqikelela • umgca-manani, itshathi yamanani,

ukubalwa kwezinto • Ukwakha nokucazulula amanani:

ukwakha u-10 • ukuphinda kabini nokuhafisha

okukhokelela ekubhalweni ngokwamaqela nasekwabeni kusetyenziswa nalapho kungasetyenziswa ntsalela

• chaza ngomlomo amacebo asetyenzisiweyo uze ucacise malunga nawo ebhodini


Iiphatheni

o yalatha, uchaze uze ukhuphele iiphatheni eziqatshelwe eklasini

o yenza uze wandise iiphatheni ezilula zejometri

ISithuba esiVulekileyo neMilo

o Thelekisa iimilo zika-2-D nezezinto ezingu-3-D emifanekisweni nakwindawo ohlala kuyo.

o sota iintlobo ngeentlobo zeemilo zika-2-D kwisinye nezinto ezingu-3-D

Imali

o Phonononga amanani alumelo olulinganayo lwemali eziinkozo e-R5

o Ukuthenga evenkileni: ngemali etshintshekileyo engagqithangalu kwi-R2, izixa ezikhulu kufuneka zenziwe yimali engaphezulu kwemali enye eyingqekembe, umz. R5 =R2,+R2+R1

o Bhala phantsi izibalo ezisekelwe kwibali

Ixesha o Hlaziya ulwazi malunga nokulandelayo: o Iiwotshi zamanani nezexesha ledijithali

kwiziqingatha zeeyure, imizuzu o ukubhekiselela kubude bosuku lokufunda,

ubude bekhefu lokufunda (interval), iintsuku, iiveki neenyanga

Ubude o linganisa umgama ngokujikeleze iimilo zika-

2D ngentambo o qikelela ukuba yeyiphi imilo apho

sisebenzisa khona intambo eninzi/ encinane

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

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Idatha

o uqokelela idatha ephathelele kumlinganiselo weemilo zika-2-D

o zoba iphikthografi ukubonisa idatha yeemilo zika-2-D esenza owona mlinganiselo mninzi/mncinane wentambo

5- 6

LO 1 Amanani, izibalo, ukusetyenziswa kwamanani nolwalamano


Ukubala okwenziwa imihla ngemihla o Bala ukusuka ku-1 ukuya ku-200 kwitshathi

yamanani o ukwandisa ukubala ukusuka ku-200 ukuya

ku-400 o Bala izinto ukuya ku-100 o Bala ngoo-2,4,5,10 ukuso nakweliphi inani,

umz. u-25, 30, 35, 40, njl. njl. ukuya ku-100. Bala ngoo-2 uye phambili uphinde ubuyele umva ukuya ku-20

o Bala ngoo-3 uye phambili uphinde ubuyele umva ukuya ku-30

Izibalo zentloko


IKhonsepthi yeNani neXabiso

o Hlaziya • Iisimboli ezingamanani namanani

abhalwe ngamazwi ukusuka ku-1-100 uze uphonononge unxibelelwano lwawo

• Iibhondi ukuya ku-20 • ukucazulula amanani amalungu ma-2

njengobhalo olunatyisiweyo, o.k.t. 87 = 80 + 7, usebenzisa oonotsheluza

• qaphela isethi yamanani alumelo (values) ukwenza izibalo ezibhalwe ngezivakalisi ezivulekileyo zibe yinyaniso, umz. □ + Δ = 56

• bhala phantsi izibalo ezibhalwe ngamazwi

o Yazisa

• amanani 201-250 uze uzibhale phantsi ngamazwi.

• ucwangcisa, achaze aze athelekise la manani angasentla.

• umelo lwamanani angasentla kuMakhulu kuMashumi nakwiMivo (HTU) lubandakanya u-‘0’ njengenani elimeleyo (place holder), umz. ku-100-200 kwisinye no-200…

Isahluko 2

Isahluko 3

- 8 -

• inani, isimboli kwisinye negama

elinguHlanu noThandathu ngoLwimi lokuQala oLongezelweyo (First Additional Langauge) (FAL))


• ukudibanisa nokuthabatha ngamashumi nangemivo ukuya ku-30 ngaphandle kokusebenzisa kucazulula okanye kuthwalwa kwamanani asiwe kwamanye)

• yenza iingxaki zokubala ezibhalwe ngamagama ubandakanya kwakhona iingxaki ezinxulumene nemali

• sondeza la manani koyena 10 ukufutshane, umz. 76 →80; 43→40

o Amaqhezu:

a) Hlaziya ulwazi malunga namaqhezu ½; ¼ uze uwabhale kwizibalo.

b) Fundisa malunga nekhonsepthi yeekota ezintathu kwezine ¾ ngokwahlula into enye epheleleyo ibe ziziqwengana/ziikota ezi-4 uze ufakele imibala ezi-3 zezi kota.

c) bhala i-¼ ibe yimibala ziziqwengana eziyimibala emi-3 ukubonisa i-¾ yenani elipheleleyo.


a) ukuhlaziya ngomlomo nangokubhaliweyo ukuya ku-20 kugxilwa kwizibalo eziphendulelweyo (inverse sums), umz. 6x3 =18 ke ngoko u-18÷3=6 b) bethelela ngentloko ithebhile ukusuka ku-2 ukuya ku-24

c) bhala iingxaki zokubala ngamazwi d) Fundisa malunga nokuphinda kabini

nokuhafisha kwifomathi yethebhile kusetyenziswa iiprophathi ezisetyenziswa ngokutshintshiselanayo (commutative properties) nokubala ngokuphendulelayo (inverse), umz. iThebhile ka-3 ukuya ku-36:

Ukuphinda kabini izibalo zokuhafisha/ eziphendulelweyo 1x3 3÷3 2x3 6÷3 3x3 9÷3 4x3 12÷3 e) ukwahlula-hlula ngentsalela ukuya ku-20

ngokuphathekayo nangomlomo f) iingxaki zokubala ezibhalwe ngamazwi

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LO 2 Iiphatheni, iifankshini ne-aljebra LO 3 ISithuba neMilo (iJometri) LO 4 Umlinganiselo


Fundisa ngeengxaki zokusombulula izibalo: o ukudityaniswa nokuthatyathwa kwamanani

anelungu elinye namanani anamalungu ama-2 ukuya, umz. 35 + 4, 28 – 7,

o hlanganisa kwakhona uze uphinde uwacazulule amanani


o ukwahlula-hlula kusetyenziswa njengokuthabatha okuphinda-phindwayo kwenani elinye

o ukuphinda-phindwa nokwahlulwa-hlulwa kwamanani anamalungu amabini nenani elinelungu elinye, umz.

4 × 5 = 20 20 ÷ 5 = 4 o qwalasela ukucazululeka (numerosity)

kwamanani ukuya ku-40


yamanani, izinto zokubala • ukwakha nokucazulula amanani:


okukhokelela ekwabelaneni ikhona naxa ingekho intsalela

• thetha ngomlomo malunga namacebo asetyenziswayo uze ucacise malunga nawo ebhodini


Iiphatheni

o Yandisa iiphatheni zamanani alula ukuya ku-300

o qonda iiphatheni zamanani ezilula kwiifankshini yokubala yangasentla uze uphonononge ngaphezulu kulo naliphi na inani ngokophinda-phindo luka-10, 5, 2 ukuya ku-500

ISithuba neMilo

o sebenzisa ukuphindwa kwephepha nokwetyisa ingcamango ukuqaphela imigca elingana macala onke (symmetry) kwiimilo ezingu-2-D

Imali

o Phonononga umelo olulinganayo lwemali eziinkozo ukuya kwi-R5

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 10 -


o ukuthenga evenkileni: imali etshintshekileyo

engagqithangalu kwi-R2, izixa ezikhulu ekufuneka zibe ngaphezulu kwengqekembe enye, umz. i-R5 =R2,+R2+R1

o bhala phantsi izibalo ezisekelwe kwibali

Ixesha o Hlaziya ulwazi malunga nexesha elibhalwe

ngamanani neledijithali o ukubhekiselela kubude bosuku lokufunda,

ubude bekhefu lokuphumla kwizifundo (interval), iintsuku neenyanga

o cwangcisa iminyhadala yezenkolo yekota kwikhalenda

Ubude o thelekisa ubude babafundi ngeesentimitha

nangeemitha o linganisa ubude babafundi ngee-cm

neemitha

Umthamo o qikelela, linganisa umthamo/ ivolyum

usebenzisa imilinganiselo eqingqiweyo nengaqingqwanga

o linganisa umahluko ngevolyume phakathi kwezikhongozeli ezahlukeneyo

Idatha

o qokelela le datha ingasentla ngokobude – eyona inde kakhulu, eyona imfutshane kakhulu

7- 8

LO 1 Amanani, ukusetyenziswa kwamanani nolwalamano




o Nabisa ukubala ukusuka ku-200 ukuya ku-400

o Bala izinto ukuya ku-100 o Bala ngoo-2, 4, 5,10 ukusuka nakweliphi

inani, umz. 25, 30, 35, 40 ukuya ku-100 o Bala ngoo-2 uye phambili uphinde ubuyele

umva ukuya ku-20 o Bala ngoo-3 uye phambili uphinde ubuyele

umva ukuya ku-30

Izibalo zentloko o Yenza izibalo zentloko +, -, ×, ÷ ukuya ku-

50

IKhonsepti yeNani neXabiso • Hlaziya

Isahluko 2

Isahluko 3

- 11 -

• Iisimboli ezingamanani namanani



njengobhalo olunatyisiweyo, o.k.t. 37 = 30 + 7, usebenzisa oonotsheluza

• qaphela iisethi zamanani alumelo (values) ukwenza izibalo ezibhalwe ngezivakalisi ezivulekileyo zibe yinyaniso, umz. □ + Δ = 56

• bhala phantsi ngamazwi iingxaki zokubala

• Yazisa • Amanani 251-300 uze uwabhale phantsi

ngamazwi. • ucwangcisa, achaze aze athelekise la

manani angasentla. • Ubhala umelo lwamanani angasentla

kuMakhulu kuMashumi nakwiMivo (HTU) lubandakanya u-‘0’ njengenani lomelo (place holder), umz. ku-100-200 kwisinye no-200…

• inyumerali, isimboli kwisinye negama elinguXhenxe nesiBhozo ngoLwimi lokuQala oLongezelweyo (First Additional Langauge) (FAL)


• Ukudityaniswa nokuthatyathwa kwamanani alungu linye namanani angamalungu amabini ukuya ku-20


ii) umgca-manani iii) iingxaki zokubala ezibhalwe ngamazwi

• Ukucazulula amanani amalungu ma-2 njengobhalo olunatyisiweyo, o.k.t.

87 = 80 + 7, sebenzisa oonotsheluza • Qaphela iisethi zamanani alumelo

ukwenza ukuba izibalo zezivakalisi ezivulekileyo zibe yinyaniso, umz.

□ + Δ = 47 • Bhala iingxaki zokubala ngokwamazwi

o Amaqhezu:

• Fakela umbala kwiikota ezintathu zeqhezu elipheleleyo uze ubhale iqhezu elihlangeneyo (unitary fraction) ‘¾’


• uhlaziyo lolwazi ngomlomo nangokubhaliweyo ukuya ku-20 kugxilwe koku

- 12 -


• kwizibalo eziphendulelweyo (inverse

sums), umz. 6x3 =18 ke ngoko 8÷3=6 • gcina ngentloko ithebhile ka-2 ukuya ku-

24 • bhala phantsi iingxaki zokubala

ngokwamazwi • Fundisa ngokuphinda kabini nokuhafisha

kwifomathi yethebhile kusetyenziswa iiprophathi ezisetyenziswa ngokutshintshiselanayo (commutative properties) nokubala ngokuguqulelweyo (inverse), umz.

iThebhile ka-3 ukuya ku-36: Ukuphinda kabini Ukuhafisha/izibalo eziphendulelweyo 1x3 3÷3 2x3 6÷3 3x3 9÷3 4x3 12÷3 Ukwahlula-hlula okunentsalela efikelela

ku-20 yezinto eziphathekayo kwisinye neengxaki zezibalo ezenziwa ngamazwi omlomon


Fundisa ngeengxaki zokubala: o ukudityaniswa nokuthatyathwa kwamanani

anelungu elinye namanani anamalungu ama-2 ukuya ku-100, umz. 35 + 4, 67 – 43,

o cwangcisa, chaza uze uthelekise amanani angamalungu ama-2



o ukuphinda-phindwa nokwahlulwa-hlulwa kwamanani anamalungu amabini nenani elinelungu elinye, umz. 4 × 5 = 20

20 ÷ 5 = 4 o qwalasela ukucazululeka (numerosity)

kwamanani ukuya ku-50





• thetha ngomlomo malunga namacebo asetyenziswayo uze ucacise malunga nawo ebhodini

Isahluko 4

- 13 -

LO 3 ISithuba neMilo (iJometri) LO 4 Umlinganiselo


• tshekisha izisombululo zabalingane

kwiingxaki zokubala

Iiphatheni o khuphela uze wandise iiphatheni zamanani

ezilula ukuya ku-500 o uphinda-phindo loo-2, 4 phakathi ko-0 no-40 o Amanani amnqakathi nangambini ukusuka

ku-A no-□

ISithuba neMilo o Sebenzisa ukusongwa kwephepha

nokwetyisa ingcamango ukuqaphela imigca yokulingana kwamacala onke (symmetry) kwiimilo ezingu-2-D

Imali

o Phinda kwakhona okwenziwe kwiiveki 5-6

Ixesha o ukusombulula iingxaki ezibandakanya

ukubala nokuphendulelwa kwamanani phakathi: • kwemizuzu neeyure • kweentsuku neeveki • kweentsuku neenyanga

Umthamo

o Phinda kwakhona iifankshini yeeveki 5-6.

Idatha o Shwankathela uze uphonononge idatha

eqokelelwe kwiiveki 5-6

Isahluko 5

Isahluko 6

Isahluko 7

9-10





o Bala izinto ukuya ku-100 o Bala ngoo-2, 4, 5,10 ukusuka nakweliphi



umva ukuya ku-30


50

IKhonsepti yeNani neXabiso o Hlaziya :

• Iisimboli ezingamanani namanani abhalwe ngamazwi ukusuka ku-1-100 uze uphonononge unxibelelwano lwawo

Isahluko 2

Isahluko 3

- 14 -


njengobhalo olunatyisiweyo, o.k.t. 87 = 80 + 7, sebenzisa oonotsheluza • qaphela iisethi zamanani alumelo

(values) ukwenza izibalo ezibhalwe ngezivakalisi ezivulekileyo zibe yinyaniso, umz. □ + Δ = 56


o Yazisa

• amanani 301-350 uze uzibhale phantsi ngamazwi.


• Ubhala umelo lwamanani angasentla kuMakhulu kuMashumi nakwiMivo (HTU) lubandakanya u-‘0’ njengenani elimeleyo (place holder), umz. ku-100-200 kwisinye no-200…

• inani, isimboli kwisinye negama elinguThoba noShumi ngoLwimi lokuQala oLongezelweyo (First Additional Langauge) (FAL)



Hlaziya • ukudityaniswa nokuthatyathwa

kwamanani alungu linye namanani amalungu mabini ukuya ku-20

• ukucazulula amanani amalungu ma-2 njengobhalo olunatyisiweyo, o.k.t.

87 = 80 + 7, sebenzisa oonotsheluza

o Amaqhezu: • Hlaziya ulwazi ngokufakela umbala

kwiikota ezintathu zeqhezu elipheleleyo uze ubhale iqhezu elihlanganisayo (unitary fraction) u-‘¾’


• Hlaziya ulwazi ngomlomo nangokubhaliweyo ukuya ku-20 ugxile kwizibalo eziphendulelweyo (inverse sums), umz. 6x3 =18 ke ngoko u-8÷3=6

• Ithebhile 3 ukuya ku-36 • Ukwahlula-hlula nentsalela ukuya ku-20

yeengxaki eziphathekayo zokubala zomlomo nezibhalwayo

o Amaqhezu:

Phinda kwakhona okwenziwe kwiiveki 7-8

- 15 -




Phinda kwakhona okwenziwe kwiiveki 7-8

AmaCebo okuSombulula iiNgxaki Fundisa ngeengxaki zokubala:;

Iiphatheni


ISithuba neMilo o qaphela uze uchaze izinto ezimilo yazo ingu-

3-D ezikwiindawo ezahlukeneyo

Ixesha o Phinda kwakhona izibalo nezibalo

eziguquliweyo (conversions) phakathi: • Kwemizuzu neeyure • Iintsuku neeveki • Iintsuku neenyanga

Ubude

o qikelela, linganisa uze uthelekise ubude bezinto ngokweemitha

Ubunzima

o Qikelela, linganisa uze uthelekise ubunzima bezinto ngokweekhilogram neegram.

Idatha

o zoba imifanekiso uze wakhe iphikthografi yezinto ezilinganiswe ngokweekhilogram neegram ezingasentla.

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 16 -


IBAKALA 3

IKOTA 2

IVE- KI

IZIPHUMO ZESIFUNDO



11-12

LO 1 Amanani, ukusetyenziswa kwamananinolwalamano



o ukwandisa ukubala ukusuka ku-200 ukuya ku-400

o Bala izinto ukuya ku-100 o Bala ngoo-2,4,5,10 ukuso nakweliphi inani,

umz. u-25, 30, 35, 40, njl. njl. ukuya ku-200 Bala ngoo-2 uye phambili uze uphinde ubuyele umva ukuya ku-20

o Bala ngoo-3 uye phambili uze uphinde ubuyele umva ukuya ku-30

o Bala ngoo-4 uye phambili uze uphinde ubuyele umva ukuya ku-40

Izibalo zentloko


IKhonsepti yNani neXabiso

o Hlaziya • Iisimboli ezingamanani namanani


• Iinyumerali 301-350 uze uzibhale ngokwamazwi.

• Iibhondi ukuya ku-39 • Amanani alumelo (ordinal value)

amanani ukusuka ekuqaleni ukuya kwelamashumi amathathu anethoba

• ukucazulula amanani amalungu ma-2 njengobhalo olunatyisiweyo, o.k.t.

87 = 80 + 7, sebenzisa oonotsheluza • qaphela iisethi zamanani alumelo

(values) ukwenza izibalo ezibhalwe ngezivakalisi ezivulekileyo zibe yinyaniso, umz. □ + Δ = 56


o Fundisa malunga nokulandelayo:

• Iinyumerali 351-400 uze uzibhale phantsi ngamazwi.


• Ubhala umelo lwamanani angasentla kuMakhulu kuMashumi nakwiMivo (HTU) lubandakanya u-‘0’ njengenani elimeleyo

Isahluko 2

Isahluko 3

- 17 -

(place holder), umz. ku-100-200 kwisinye

no-200… • inyumerali, isimboli kwisinye negama

elinguNye ukuya kwiShumi ngoLwimi lokuQala oLongezelweyo (First Additional Language) (FAL)

• Bhala phantsi iingxaki zokubala ngamazwi

• Iibhondi zika-40 • Umelo lwamanani (ordinal value)

ukusuka ekuqaleni ukuya kumashumi amane

o Iisethi, ukudibanisa nokuthabatha • ukudibanisa nokuthabatha ngamashumi

kusetyenziswa ukuthwala kwamanani ayokudityaniswa kwamanye (carrying) nokucazululwa kuka-10

• Fundisa malunga nokubala unyukela phezulu kwizibalo usebenzisa ukunatyiswa kweekhomponenti ezingundoqo, umz. .

5 15 25 +6 +6 +6 ─ ─ ─ • Bhala iingxaki zokubala ngokwamazwi • Ukusondeza inani ku-10 ongoyena

ukufutshane, umz. 76 →80; 43→40; 94→90, njl. njl.

o Amaqhezu:

a) bhala phantsi i-½ ne-¼ yamanani 4,8,12,16 kwisinye no-20

b) Fundisa ngekhonsepthi yesinye esithathwini ngokwahlula umcwe wephepha ube bubude obuziisentimitha ezili-9 libe ngamalungu ama-3 alinganayo.

c) Bhala phantsi iqhezu elihlanganisayo (unitary fraction) u-⅓ kwiziqwengana.


• Cacisa malunga neepropathi etshintshiselanayo (commutative property) ngokuphinda-phinda, umz. 8x2=2x8

• Cacisa ngokwahlula-hlula njengokwaba nokudibanisa izinto ndawonye, umz. yahlulela (yabela) amaqela ama-4 iilekese ezili-12

• Gcina ngentloko ithebhile ka-2 ukuya ku-24

• Gcina ngentloko ithebhile ka-3 ukuya ku-36

• Bhala iingxaki zokubala ngokwamazwi

- 18 -





o fumana izisombululo usebenzisa amanani aphindeke kabini (doubles) namanani aphantse ukuphindeka kabini (near doubles), umz. 13 + 16 = (13 +13) + 3 +140 + 154 = (140 + 140) + 14

o ukudityaniswa ngokuphindwayo nokuthatyathwa kwamanani angamalungu ama-3 ukuya ku-500, umz. 150 + 50 + 50 + 50 + 50 =

o ukuphinda-phinda njengokudibanisa okuphindwayo kwenani elinye






• thetha ngomlomo ngamacebo asetyenziswayo uze ucacise malunga nawo ebhodini


Iiphatheni

o Qaphela iiphatheni zamanani usebenzisa u-+, - ukuya ku-500

o Yenza uze wandise iinyaniso zamanani angundoqo, umz. 6 + 2 = 8, 60 + 20 = 80, 600 + 200 = 800

ISithuba neMilo

o Qaphela imigca elingana macala onke kwiimilo ezingu-2-D usebenzisa ukusongwa kwamaphepha nokwetyisa ingcamango

Imali o Phinda kwakhona umsebenzi wekota

edlulileyo

Ixesha o Hlaziya ulwazi ngewotshi yamanani

neyedijithali ebonisa iiyure, iihafu yeeyure nekota yeyure

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 19 -


o ukuguqulwa (conversion) kwemizuzu

neeyure, iintsuku neeyure, iintsuku neenyanga

o amagama eenyanga zonyaka

Ubunzima o qikelela, linganisa, thelekisa ucwangcise

izinto, ukuze ukwazi ukuqinisekisa ukuba zeziphi ezizezona zinzima, izeziphi ezizezona zikhaphukhaphu kakhulu

o yenjenjalo nakwiimilo zika-3-D

Idatha o qokelela uze ushwankathele idatha yezinto

ezilinganisiweyo uze uzidweliswe kwimo yethebhile

13-14

LO 1 Amanani, izibalo, nonxibelelwano lwamanani




o Bala izinto ukuya ku-100 o Bala ngoo-2,4,5,10 ukusuka nakweliphi




umva ukuya ku-40


50

IKhonsepthi yeNani neXabiso • Hlaziya • achazwa ngomlomo, abhaliweyo

eenyumeral 300-400 • Ucwangcisa, achaze aze athelekise la

manani angasentla. • Ubhala umelo lwamanani angasentla

kuMakhulu kuMashumi nakwiMivo (HTU) lubandakanya u-‘0’ njengenani elimeleyo (place holder), umz. ku-100-200 kwisinye no-200…

• inyumerali, isimboli kwisinye negama elinguNye ukuya kwiShumi ngoLwimi lokuQala oLongezelweyo (First Additional Language) (FAL)


• Iibhondi zika-40

Isahluko 2

Isahluko 3

- 20 -


• Umelo lwamanani (ordinal value)

ukusuka ekuqaleni ukuya kumashumi amane

o Yazisa

• amananii 401-450 uze uwabhale ngamazwi.

• Iibhondi zika-41 • Umelo lwamanani (ordinal numbers)

ukusuka kwelokuqala ukuya kumashumi amane ananye


• ukudibanisa nokuthabatha ngamashumi kusetyenziswa ukuthwala kwamanani ayokudityaniswa kwamanye (carrying) nokucazululwa kuka-10 ukuya ku-‘99’

• Fundisa ngokusetyenziswa kwezibalo ukuya phezulu (vertical application of sums) usebenzisa iikhomponenti ezingundoqo, umz.

5 15 25 +6 +6 +6 ─ ─ ─ • Bhala iingxaki zokubala ngokwamazwi

o Amaqhezu:

• Fumana u-⅓ wamanani 3, 6, 9, 12, 15 • Ngqamanisa ukusombulula iingxaki

ngokwahlula-hlula ngethebhile ka-3x

o Ukuphinda-phinda nokwahlula-hlula • Fundisa uze ucacise ukwahlula-hlula

nentsalela ngale fomathi ilandelayo, umz.

Amanani angundoqo

Zingaphi izithathu?

intsalela

20 34

6 11

2

1

o Yandisa ukuya kutsho kulwahlulo-hlulo lukane nontlanu nentsalela

o Bhala iingxaki zokubala ngokwamazwi

AmaCebo okuSombulula iiNgxaki Fundisa ngeengxaki zokubala: o ukudityaniswa nokuthatyathwa kwamanani


o cwangcisa, chaza uze uthelekise amanani angamalungu ama-2


Isahluko 4

- 21 -


o ukwahlula-hlula njengokuthabatha

okuphindwayo kwenani elinye o fumana izisombululo usebenzisa amanani

aphindeke kabini (doubles) namanani aphantse ukuphindeka kabini (near doubles), umz. 13 + 16 = (13 +13) + 3 +140 + 154 = (140 + 140) + 14

o ukuphinda-phinda nokwahlula-hlula kwamanani alungu amalungu mabini namanani alungu linye, umz. 4 × 5 = 20

20 ÷ 5 = 4 o qaphela ukucazululeka kwamanani

(numerosity) ukuya ku-34 o Sebenzisa amacebo akho uze wabelane

nabalingane

Iiphatheni o Bhala phantsi amanani aphindiweyo

wamanani angumnqakathi ukuya ku-49 o Bhala phantsi iiphatheni zamanani

usebenzisa ukudibanisa nokuthabatha amanani amalungu ma-2 namanani amalungu ma-3

ISithuba neMilo

o qaphela uze uqwalasele iimpawu ezahlukileyo zeemilo ezingu-2-D (oonxa-ntathu (triangles), izikwere, iingxande (rectangles), izangqa) nezinto ezingu-3-D (iibhokisi, iiprizim, iiphiramidi, izangqa (spheres), ezimbhuntshuntshu (cones)

Imali

o Qwalasela amanani alumelo olulinganayo lwemali eziinkozo ukuya ku-R5 umz.

5c = 1c+1c+1c+1c+1c or 2c+2c+1 o Thenga evenkileni usebenzisa imali

etshintshekileyo engagqithanga kwi-R2 o Bhala phantsi iingxaki zokubala ngamazwi

uze ubhale indlela yokusetyenziswa koku kungasentla.

Ixesha

o sombulula iingxaki ezibandakanya ukubala ngamanani aguquliweyo (conversions) phakathi: kwemizuzu neeyure, iintsuku neeyure, iintsuku neenyanga

Ubude

o qikelela ubude bezinto uze uzilinganise ngeemitha nangeesentimitha

o rekhoda izinto ezifunyanisiweyo

Isahluko 5

Isahluko 6

Isahluko 7

- 22 -


Idatha

o phinda kwakhona okwenziwe kwiiveki 11 neye-12, qokelela idatha yenyanga yekhalenda: abafundi benza ingcaciso-ntetho, abafundi abenza ingcaciso-ntetho yomsebenzi wasekhaya wesikolo yonke imihla

o Idatha irekhodwa kuluhlu lokutshekisha (checklist), bonisa uze uthelekise idatha

15-16

LO 1 Amanani, ukuestyenziswa kwamanani nolwalamano





o Nabisa ukubala ngaphezulu ukusuka ku-400 ukuya ku-600

o Bala izinto ukuya ku-200 o Bala ngoo-2, 5,10 ukusuka nakweliphi inani,

umz. 25, 30, 35, 40 ukuya ku-200 o Bala ngoo-2 uye phambili uphinde ubuyele



umva ukuya ku-40 o Ngophinda-phindo luka-100 ukuya ku-500

Izibalo zentloko


IKhonsepti yNani neXabiso

o Hlaziya • amanani 401-450 uze uwabhale

ngamazwi. • Iibhondi zika-41 • Amanani alumelo (ordinal numbers)

ukusuka ekuqaleni ukuya kumashumi amane ananye


• amanani451-500 uze uwabhale ngamazwi.

• Ubhala umelo lwala manani angasentla ku-HTU

• Iibhondi zika-42 • Amanani alumelo (ordinal numbers)

ukusuka ekuqaleni ukuya kumashumi amane anesibini

Isahluko 2

Isahluko 3

- 23 -



• ukudibanisa nokuthabatha ngamashumi kusetyenziswa ukuthwala kwamanani ayokudityaniswa kwamanye (carrying) nokucazululwa kuka-10 ukuya ku-‘99’

• Fundisa malunga nokubala usenyukela phezulu usebenzisa ukunatyiswa kweekhomponenti ezingundoqo, umz.

29 39 49 +7 +7 +7 ─ ─ ─


o Amaqhezu:

• Phinda kwakhona okwenziwe kwiiveki 13-14

• Ngohlobo olubhaliweyo: ½ ka-30 = ¼ ka-40 = ⅓ ka-33 = njl. njl.


a) Hlaziya ulwazi malunga nokuphinda-phinda njengokudibanisa okufinyeziweyo, umz.

3 + 3 + 3 = (3 × 3 = 9) kwisinye b) Nokuhlaziya ulwazi ngokwahlula-hlula nentsalela ukuya ku-10 ngokuphathekayo nangomlomo c) Bhala phantsi iingxaki zokubala ngamazwi


Fundisa malunga neengxaki zokubala: o bonisa amacebo ahlukeneyo

anokusetyenziswa o ukuthatyathwa kwamanani anamalungu

amabini, anamalungu ama-3, umz. 344-122 (cazulula inani elo lithatyathwayo)

344 – 122 = (344 – 100 = 244 – 20 = 224 – 2 = 222 o okanye ukongeza amalungu amanani ama-

2/ amalungu amanani ama-3,





• thetha ngomlomo ngamacebo asetyenziswayo uze ucacise malunga nawo ebhodini

Isahluko 4

- 24 -



• tshekisha izisombululo zabalingane

kwiingxaki zokubala

Iiphatheni o Bhala amanani aphindwayo amanani

angumnqakathi ukuya ku-49 o bhala iiphatheni yamanani usebenzisa

ukudityaniswa nokuthatyathwa kwamanani amalungu ma-2 namanani amalungu ma-3

ISithuba neMilo

o Phinda kwakhona okwenziweyo kwiiveki 15 -16

Imali

o Qwalasela amanani alumelo alinganayo email ezinkozo ukuya kwi-R5 umz.

5c = 1c+1c+1c+1c+1c or 2c+2c+1 o Thenga evenkileni ngemali etshintshekileyo

engagqithangalu kwi-R2 o Bhala iingxaki zokubala ngamazwi uze

ubhale malunga nokusetyenziswa koku kungasentla.

Ixesha

o ukusombulula iingxaki kubandakanywa ukubala nokuguqulela phakathi kwemizuzu neeyure, iintsuku neeyure, iintsuku neenyanga

Ubunzima

o qikelela ubunzima o linganisa nge-kg ne-g o dwelisa uluhlu lwezinto ezilinganiswayo

Idatha

o Phinda kwakhona okwenziwe kwiiveki 11 neye-12

o xoxa uze uthelekise idatha erekhodelwe inyanga yekhalenda

Isahluko 5

Isahluko 6

Isahluko 7

17-18








umz. 25, 30, 35, 40, njl. njl. ukuya ku-200 o Bala ngoo-2 uye phambili uphinde ubuyele

umva ukuya ku-20

Isahluko 2

- 25 -

o Bala ngoo-2 uye phambili uphinde ubuyele




Izibalo zentloko


IKhonsepthi yeNani neXabiso


ngamazwi. • Iibhondi zika-42 • Amanani alumelo ukusuka ekuqaleni

ukuya kumashumi amane anesibini

o Yazisa • amanani 501-550 uze uwabhale

ngamazwi. • Bhala amanani alumelo ala manani

angasentla kwi-HTU • Iibhondi zika-43 • Amanani alumelo ukusuka ekuqaleni

ukuya kumashumi amane anantathu

o Iisethi, ukudibanisa nokuthabatha • ukudibanisa nokuthabatha ngamashumi

kusetyenziswa ukuthwala kwamanani ayokudityaniswa kwamanye (carrying) nokucazululwa kuka-10 ukuya ku-‘99’

• Fundisa malunga nokubala uye phezulu usebenzisa ukunatyiswa kweekhomponenti ezingundoqo, umz.

59 69 79 +3 +3 +3 ─ ─ ─ • Bhala phantsi iingxaki zokubala

ngamazwi

o Zalisa izibalo zezivakalisi ezivulekileyo uze uqinisekise iimpawu, umz. 13+□+6=30 no- 20*7=13 36-□- 6 =20 no- 48*2= 50

o Amaqhezu:

• Hlaziya ulwazi malunga neehafu zamanani angamabini nayiminqakathi (even and odd numbers) ukuya ku-20

• Hlaziya ulwazi malunga nezithathu zamanani ukuya ku-30

• Hlaziya ulwazi malunga neekota zamanani ukuya ku-40

Isahluko 3

- 26 -

LO 2 Iiphatheni, amanani ne-aljebra LO 3 ISithuba o neMilo (iJometri) LO 4 Umlinganiselo


• Hlaziya ulwazi ngawo wonke umsebenzi wexesha elidlulileyo

• Fundisa malunga nethebhile ka-5 (ngeeprophathi ezitshintshisekayo kwisinye nezibalo eziphendulelweyo (commutative properties and inversion) umz. iThebhile ka-5 ukuya ku-50:

• Ukuphinda kabini izibalo zokuhafisha/ eziphendulelweyo 1x5 5÷5 2x5 10÷5 3x5 15÷5 4x5 20÷5 • Bhala phantsi iingxaki zokubala

ngamazwi

AmaCebo okuSombulula iiNgxaki Fundisa ngeengxaki zokubala:

• bonisa amacebo ahlukeneyo anokusetyenziselwa oku;

• ukuthatyathwa kwamanani amalungu mabini, amanani amalungu ma-3, umz. 344 - 122 (cazulula inani elo lithatyathwayo) 344 – 122 =

(344 – 100 = 244 – 20 = 224 – 2 = 222 • ukudibanisa amanani anamalungu ama-

2/ anamalungu ama-3, • Sebenzisa amacebo akho uze

utshekishe izisombululo zabalingane kwiingxaki

Iiphatheni

o qwalasela iiphatheni zamanani usebenzisa ukudibanisa, ukuthabatha nokuphinda-phinda ukuya ku-500

ISithuba neMilo

o beka iliso, yenza iimilo ezingu-2-D nezinto ezingu-3-D usebenzisa izinto eziphathekayo, umz. iibloko zokwakha, iisethi zokwakha, imicinga yokusela isiselo, njl. njl.

Imali Phinda kwakhona okwenziwe kwiiveki 15-16

Ixesha


Ubude o Qikelela ubude, linganisa ngeemitha nee-cm

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 27 -


Idatha

o qokelela idatha eklasini ukuphendula imibuzo ebuzwa ngutitshala: umz. Bangaphi abafundi abayonwabelayo iMathematika? Bangaphi abafundi abakonwabelayo ukuFunda? Bangaphi abafundi abazonwabelayo ezeMidlalo?

19-20











Izibalo zentloko



o Hlaziya ulwazi malunga nokulandelayo: • Iinyumerali 501-550 uze uzibhalwe

ngamazwi. • Iibhondi zika-43 • Amanani alumelo (ordinal numbers)

ukusuka ekuqaleni ukuya kumashumi amane anantathu


• Iinyumerali 551-600 uze uzibhale ngamazwi.

• Bhala amanani alumelo ala manani angasentla ku-HTU


ukusuka ekuqaleni ukuya kumashumi amane anesine


• Phinda kwakhona okwenziwa kwiiveki 17-18

Isahluko 2

Isahluko 3

- 28 -


o Amaqhezu:





o Fundisa ngeengxaki zokubala: • bonisa amacebo ahlukeneyo

anokusetyenziselwa oku; • ukuthatyathwa kwamanani amalungu

mabini, amalungu ma-3, umz. 344 - 122 (cazulula inani elithatyathwayo) 344 – 122 =

344 – 100 = 244 – 20 = 224 – 2 = 222 • ukudibanisa, amanani amalungu-2,

amanani amalungu ma-3 • sebenzisa amacebo akho wabelane

ngawo nabalingane bakho

Iiphatheni o onke amanani apheleleyo namaqhezu

(iihafu) akumgca-manani: phakathi ko-1 onehafu kwisinye no-10 onehafu

o chaza uze ukhuphele iiphatheni eziqwalaselweyo kwiimagazini

ISithuba neMilo o Phinda kwakhona okwenziwe kwiiveki 17-18

Imali o Qwalasela amanani alumelo olulinganayo

lwemali eziinkozo ukuya ku-R5 umz. 5c = 1c+1c+1c+1c+1c okanye 2c+2c+1 o Thenga evenkileni usebenzisa imali

etshintshekileyo engagqithanga kwi-R2 o Bhala phantsi iingxaki zokubala ngamazwi

uze ubhale indlela yokusetyenziswa koku kungasentla.

Ixesha

o Qwalasela imihla ebalulekileyo kwikhalenda: imihla yeminyhadala yezembela neyezenkolo

Ubude

o qikelela ubude ubulinganise ngeemitha nangee-cm

o rekhoda uluhlu lwezinto nemilinganiselo yazo

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 29 -


Idatha o qokelela idatha eklasini ukuphendula

imibuzo ebuzwe ngutitshala: Bangaphi abafundi abanezikhaftina zelantshi? Bangaphi abafundi abaza neziqhamo esikolweni? njl. njl.

- 30 -


IBAKALA 3

IKOTA 3

IVE-KI

IZIPHUMO ZESIFUNDO



21-22




o Yandisa ukubala ukusuka ku-200 ukuya ku-400






umva ukuya ku-40 o Ngophinda-phindo luka-100 ukuya ku-500 o Ngophinda-phindo luka-50 ukuya ku-500

Izibalo zentloko

o Yenza izibalo zentloko +, -, ×, ÷ ukuya ku- 50



ngamazwi. • Ubhala umelo lwala manani angasentla

nge-HTU • Iibhondi zika-44 • Amanani alumelo (ordinal numbers)

ukusuka kwisinye ukuya kumashumi amane anesine

o Yazisa

• amanani 601-650 uze uwabhale ngamazwi.

• Ubhala umelo lwala manani angasentla nge-HTU


ukusuka kwisinye ukuya kumashumi amane anesihlanu


• Hlaziya ulwazi malunga nokwenziwe kwiiveki 17-18

Isahluko 2

Isahluko 3

- 31 -

LO 2 Iiphatheni, iifankshini ne-aljebra LO 3 ISithuba neMilo (iJometri)

o Amaqhezu:

• Hlaziya ulwazi malunga neehafu namanani angambini nangumnqakathi (odd and even numbers) ukuya ku-20

• Hlaziya ulwazi ngamanani abala ngezithathu ukuya-30

• Hlaziya ulwazi malunga neekota zamanani ukuya ku-40


• Hlaziya ulwazi ngomsebenzi wexesha elidlulileyo

• Fundisa ngethebhile ka-5 (eneeprophathi ezitshintshiselanayo nezibalo eziphendulelweyo (commutative properties and inversion) umz. ithebhile ka-5 ukuya ku-50

• Bhala phantsi iingxaki zezibalo ngamazwi

• Hlaziya ulwazi malunga nokwahlula-hlula nentsalela yeethebhile ezingu-2,3,4 no-5




o ucwangcisa, achaze aze athelekise amanani amalungu ma-2



o ukuphinda-phinda nokwahlula-hlula amanani anamalungu amabini nanelungu elinye, umz. 4 × 5 = 20 20 ÷ 5 = 4

o qwalasela ukucazululeka kwamanani (numerosity) ukuya ku-34

utshekisha izisombululo zabalingane kwizibalo

Iiphatheni

o onke amanani apheleleyo namaqhezu (iihafu) kumgca-manani: phakathi ko-3 nehafu kwisinye no-10 nehafu

o khuphela uze wandise ulandelelwano lwamanani ukuya kutsho ubuncinane ku-750

ISithuba neMilo

o qwalasela uze wenze iimilo ezingu-2-D kwisinye nezinto ezingu-3-D kwindawo okuyo nakwimifanekiso

Isahluko 4

Isahluko 5

Isahluko 6

- 32 -

LO 4 Umlinganiselo


Ixesha

o qaphela uze uchaze iikhalenda ezahlukeneyo ezisetyenziswa kwiinkcubeko ezahlukeneyo

o qwalasela imihla ebalulekileyo kwikhalenda: imihla yezembali neyeminyhadala yezenkolo

Idatha

o funda uze utolike idatha kwiithebhile nakwizintlu ezilula

Isahluko 7

23-24












Izibalo zentloko



o Hlaziya • amanani 601-650 uze uwabhalwe

ngamazwi. • Ubhala umelo lwala manani angasentla

ku-HTU • Iibhondi zika-45 • Amanani alumelo (ordinal numbers)

ukusuka ekuqaleni ukuya kumashumi amane anesihlanu

o Yazisa

• amanani 651-700 uze uwabhalwe ngamazwi.

• Ubhala umelo lwala manani angasentla ku-HTU


ukusuka kwisinye ukuya kumashumi amane anesihlanu

Isahluko 2

Isahluko 3

- 33 -



• Hlaziya ulwazi lomsebenzi wexesha elidlulileyo

• Fundisa malunga nesigama: dibanisa, thabatha, umahluko, izibalo xa zidityanisiwe (sum of), dibanisa kwinani/kumanani, lahlekelwa, zuza, ukudibanisa, ndishotelwa kangaka, zingaphi …ngaphezulu/nganeno kunoku, njl. njl.

o Amaqhezu:


• Fundisa ngekhonsepthi kwisinye kwisihlanu (one fifth) ngokwahlula isiqwenga sephepha esibude buyi-15 cm, libe ngamalungu amahlanu alinganayo.

• Cacisa ngokubhaliweyo okuthethwa ngu-1/5 (isinye kwisihlanu)


• Hlaziya ulwazi lomsebenzi wexesha elidlulileyo

• Fundisa ngethebhile ka-5 (eneeprophathi ezitshintshiselanayo (commutative properties and inversion) umz. ithebhile ka-5 ukuya ku-50

• Bhala phantsi iingxaki zezibalo ngamazwi

• Hlaziya ulwazi malunga nokwahlula nentsalela kuluhlu lweethebhile zika-2,3,4 and 5


o bonisa amacebo ahlukeneyo anokusetyenziswa

o ukuthatyathwa kwamanani amalungu mabini, amalungu ma-3, umz. 344 -122 (cazulula inani elo lithatyathwayo) 344 – 122 = (344 – 100 = 244 – 20 = 224 – 2 = 222

udibanise amananani amalungu ma-2/ ma-3, o zalisa isivakalisi sezibalo ezivulekileyo uze

ungqinisise iimpawu zokubala, umz. 8x□ =24 15*7=8 12÷□=2 24*26=50 o tshekisha izisombululo zokubala

zabalingane

Iiphatheni o khuphela amanani apheleleyo namaqhezu

(iihafu) kumgca-manani: phakathi ko-3½ no-and 10 ½


Isahluko 4

Isahluko 5

- 34 -



ISithuba neMilo

o qwalasela uze wenza iimilo ezingu-2-D nezinto ezingu-3-D kwindawo okuyo nakwimifanekiso

Imali

o Fundisa malunga namanani alumelo alinganayo email eziinkozo ukuya kwi-R5 usebenzisa + no-x umz.. R1 =50c+50c okanye 10cx10c

o Thenga evenkileni; ngemali etshintshekileyo enikiweyo engekho ngaphezu kwe-R2

o funda ngeengxaki zokubala ngokunxulumene nokuphinda-phinda nokwahlula-hlula ngoo-2, 3 no-4

Ixesha o Phinda kwakhona okwenziwe kwiiveki 21

neye-22

Ubunzima o qikelela, linganisa, thelekisa uze ucwangcise

izinto ezingu-3-D usebenzisa imilinganiselo eqingqiweyo nengaqingqwanga (umz. iipakethe, kg)

Idatha

o funda uze utolike idatha ebhalwe kwiithebhile nakwizintlu ezilula

Isahluko 6

Isahluko 7

25-26












Izibalo zentloko


Isahluko 2

- 35 -



ngamazwi. • Ubhala phantsi amanani alumelo (place

value) ala manani angasentla kwi-HTU • Iibhondi zika-46 • Amanani alumelo (ordinal number) unye

ukuya kumashumi amane anesithandathu



• Ubhala phantsi amanani alumelo (place value) ala manani angasentla kwi-HTU

• Iibhondi zika-47 • Amanani alumelo (ordinal number) unye

ukuya kumashumi amane anesixhenxe

o Iisethi, ukudibanisa nokuthabatha • Hlaziya ulwazi malunga nesi sigama:

dibanisa, thabatha, umahluko, izibalo xa zidityanisiwe (sum of), dibanisa kwinani/kumanani, lahlekelwa, zuza, ukudibanisa, ndishotelwa kangaka, zingaphi …ngaphezulu/nganeno kunoku, njl. njl.

• Bethelela amanani alumelo (place values) lwamanani ukuya ku-999 kugxininiswa ngokukodwa inyaniso yokuba inani lomelo lwenani kwishumi lifana ngokuphindwe kalishumi nelo lenani elinye elifumaneka kanye kwicala lalo lasekunene.

o Amaqhezu:





• Hlaziya ulwazi malunga nokwenziwe kwixesha elidlulileyo

• Fundisa malunga nethebhile ka-5 (eneeprophathi ezintshintshiselanayo nezibalo eziphendulelweyo (commutative properties and inversion) umz. ithebhile ka-5 ukuya ku-50

Isahluko 3

- 36 -


• Bhala phantsi iingxaki zokubala

ngamazwi • Hlaziya ulwazi malunga nokwahlula

enentsalela kuluhlu lweethebhile zoo-2,3,4 no-5


Fundisa ngeengxaki zokubala: o Bonisa amacebo ahlukeneyo

anokusetyenziswa o Ukuthabatha amanani amalungu ama-2,

amanani amalungu ama-3, umz. 344 -122 (cazulula inani elo lithatyathwayo) 344 – 122 = 344 – 100 = 244 – 20 = 224 – 2 = 222

o Okanye ukudibanisa amanani amalungu ma-2/ amanani amalungu ama-3,

o zalisa izibalo zezivakalisi ezivulekileyo uze ungqinisise iimpawu zokubala, umz.

8x□ =24 15*7=8 12÷□=2 24*26=50 o Tshekisha izisombululo zokubala

zabalingane

Iiphatheni o onke amanani apheleleyo namaqhezu

(iihafu) kumgca-manani: phakathi ko-3 ½ no-10½


ISithuba neMilo

o qwalasela uze wenze iimilo ezingu-2-D nezinto ezingu-3-D kwindawo okuyo nakwimifanekiso

Imali

o Bethelela amanani alumelo alinganayo email eziinkozo ukuya kwi-R5 usebenzisa + no-x, umz. R1 =50c+50c okanye 10cx10c

o Thenga evenkileni; sebenzisa imali etshintshekileyo engekho ngaphezu kwe-R2

o Sombulula iingxaki zokubala zamanani abhalwe ngamazwi ngokungqamene nokuphinda-phinda nokwahlula-hlula ngo-2, 3 no-4

Ixesha


Ubunzima o qikelela, linganisa, uthelekise uze

ucwangcise izinto ezingu-3-D usebenzisa imilinganiselo engaqingqwanga neqingqiweyo (iipakethe, kg)

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 37 -


Idatha

o Funda uze utolike idatha ebhalwe kwiithebhile nezintlu ezilula

27-28












Izibalo zentloko




ngamazwi. • Bhala phantsi amanani alumelo ala

manani angasentla ku-HTU • Iibhondi zika-47 • Amanani alumelo (ordinal numbers)

unye ukuya kumashumi amane anesixhenxe

o Yandisa


• Bhala phantsi amanani alumelo ala manani angasentla ku-HTU


unye ukuya kumashumi amane anesibhozo


• Hlaziya ulwazi malunga nesi sigama: dibanisa, thabatha, umahluko, izibalo xa zidityanisiwe (sum of), dibanisa kwinani/kumanani, lahlekelwa, zuza,

Isahluko 2

Isahluko 3

- 38 -


ukudibanisa, ndishotelwa kangaka, zingaphi …ngaphezulu/nganeno kunoku, njl. njl. • Bethelela amanani alumelo (place

values) lwamanani ukuya ku-999 kugxininiswa ngokukodwa inyaniso yokuba inani lomelo lwenani kwishumi lifana ngokuphindwe kalishumi nelo lenani elinye elifumaneka kanye kwicala lalo lasekunene.

o Amaqhezu:


• Hlaziya ulwazi malunga nekhonsepthi yesinye kwisihlanu ngokwahlula isiqwenga sephepha elibude buyi-15 cm, sibe ngamalungu amahlanu alinganayo.

• Cacisa malunga negama elibhaliweyo u-1/5 (isinye kwisihlanu)


• Phinda kwakhona iifankshini yeeveki 23-24

• Yandisa ukuphinda-phindwa kwezibalo zibe ngamanani amakhulu, umz. 34x2 NGAPHANDLE KOKUTHWALA INANI UYOLIDIBANISA KWAMANYE (WITHOUT CARRYING)


Fundisa malunga nokulandelayo: Problem sums; o Bonisa amacebo ahlukeneyo

anokusetyenziswa o Ukuthatyathwa kwamanani amalungu

mabini, amanani amalungu ma-3, umz. 344-122 (cazulula inani elo lithatyathwayo) 344 – 122 = (344 – 100 = 244 – 20 = 224 – 2 = 222

o Okanye udibanise amanani amalungu ma-2/ amalungu ma-3 or adding 2/ 3 digit numbers,

o zalisa izibalo zezivakalisi ezivulekileyo uze ungqinisise iimpawu zokubala, umz.

8x□ =24 15*7=8 12÷□=2 24*26=50 o Tshekisa izisombululo zabalingane

kwiingxaki zokubala

Iiphatheni o Khuphela amanani apheleleyo namaqhezu

(iihafu) kumgca-manani: phakathi ko-3 ½ no-10 ½

o Khuphela uze wandise ulandelelwano lweziphindi zoo-3, 4 ukuya ubuncinane ku- 1000

Isahluko 4

Isahluko 5

- 39 -



ISithuba neMilo

o qaphela uchaze izinto ezingu-3-D uzijonge kwiinkalo ngeenkalo

Imali

o Fundisa malunga namanani alumelo alinganayo nemali eziinkozo ye-R5 usebenzisa + no- x umz. R1 =50c+50c okanye 10cx10c

o ukuthenga evenkileni; imali etshintshekileyo enikiweyo engagqithanga kwi-R2

o iingxaki zokubala ezibhalwe ngamazwi ngokungqamene nokuphinda-phinda nokwahlula-hlula ngoo-2,3 no-4

Ixesha

o cwangcisa iminyhadala neziganeko zembali ukulungiselela isiqingatha sesibini sonyaka kwikhalenda yeklasi

Umthamo

o qikelela, linganisa, thelekisa uze ucwangcise izinto ezingu-3-D usebenzisa imilinganiselo engaqingqwanga neqingqiweyo (umz. iibhotile neelitha)

Idatha

o Funda uze utolike idatha ebhalwe ngeethebhile nezintlu ezilula

o sota ucwangcise idatha ngokweempawu ezichaziweyo ngezizathu ezithile

Isahluko 6

Isahluko 7

29-30












50

Isahluko 2

- 40 -

IKhonsepthi yaManani naManani aluMelo

o Hlaziya ulwazi malunga nokulandelayo: • Iinyumerali 751-800 uze uzibhale

ngamazwi. • Bhala amanani alumelo (place values)

ala manani angasentla kwi-HTU • Iibhondi zika-48 • Amanani alumelo (ordinal number) unye

ukuya kumashumi amane anesibhozo

o Yandisa • amanani 801-850 uze uwabhale

ngamazwi. • Bhala amanani alumelo (place values)

ala manani angasentla kwi-HTU • Iibhondi zika-49 • Amanani alumelo (ordinal number) unye

ukuya kumashumi amane anethoba



• Bethelela amanani alumelo (place values) lwamanani ukuya ku-999 kugxininiswa ngokukodwa inyaniso yokuba inani lomelo lwenani kwishumi lifana ngokuphindwe kalishumi nelo lenani elinye elifumaneka kanye kwicala lalo lasekunene.

o Amaqhezu:





• Phinda kwakhona iifankshini yeeveki 27-28

• Yandisa ukuphinda-phindwa kwezibalo zibe ngamanani amakhulu, umz. 34x2 NGAPHANDLE KWAKUTHWALA MANANI UWADIBANISE NAMANYE (WITHOUT CARRYING)

Isahluko 3

- 41 -




Fundisa ngeengxaki zokubala: o bonisa amacebo ahlukeneyo

anokusetyenziswa o ukuthatyathwa kwamanani amalungu

mabini, amalungu ma-3, umz. 344-122 (cazulula inani elithatyathwayo) 344 – 122 = (344 – 100 = 244 – 20 = 224 – 2 = 222

o okanye udibanisa amanani amalungu ma-2/ amanani amalungu ma-3,

o Zalisa izibalo zezivakalisi ezivulekileyo ungqinisise malunga neempawu zokubala , umz.

8x□ =24 15*7=8 12÷□=2 24*26=50 o Tshekisha izisombululo zabalingane

kwiingxaki zokubala

ISithuba neMilo o Funda, tolika uzobe iimaphu

ezingaqingqwanga zesikolo uze ukhombe izinto ezithile emaphini

Imali

o Fundisa malunga namanani alumelo alinganayo email eziinkozo ukuya kwi-R5 usebenzisa + no-x umz. R1 =50c+50c okanye 10cx10c

o ukuthenga evenkileni; imali etshintshekileyo enikiweyo engekho ngaphezulu kwe-R2

o iingxaki zokubala ezibhalwe ngamazwi ngokungqamene nokuphinda-phinda nokwahlula-hlula ngoo-2,3 and 4

Ixesha

o ukusombulula iingxaki ezibandakanya ukubala kubandakanywa imizuzu neeyure, iintsuku neeveki

Ubude

o qikelela, linganisa, thelekisa uze ucwangcise izinto ezingu-3-D usebenzisa imilinganiselo engaqingqwanga neqingqiweyo (umz. ubude berula neemitha)

Idatha

o Funda utolike idatha ebhalwe kwithebhile nakwizintlu ezilula

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 42 -


IBAKALA 3

IKOTA 4

IVE-KI

IZIPHUMO ZESIFUNDO



31-32



o Bala ukusuka kulo naliphi inani elikwitshathi yamanani ukuya ku-1000





umva ukuya ku-40 o Bala ngophinda-phindo luka-100 ukuya ku-

500 o Bala ngamanani ayiminqakathi nangambini

(odd and even numbers) ukuya ku-300


50

IKhonsepthi yeNani nExabiso o Hlaziya


• Bhala amanani alumelo (place values) ala manani angasentla ku-HTU

• Iibhondi zika-49 • Amanani alumelo (ordinals): unye ukuya

kumashumi amane anethoba o Yazisa


• Bhala amanani omelo (place values) zala manani angasentla ku-HTU

• Iibhondi zika-50 • Amanani alumelo (ordinal numberi) unye

ukuya kwelamashumi amahlanu



Isahluko 2

Isahluko 3

- 43 -


• Bethelela amanani alumelo (place

values) lwamanani ukuya ku-999 kugxininiswa ngokukodwa inyaniso yokuba inani lomelo lwenani kwishumi lifana ngokuphindwe kalishumi nelo lenani elinye elifumaneka kanye kwicala lalo lasekunene.

o Amaqhezu:

• Fumana amaqhezu azizihlanu (fifths) zamanani ukuya ku-50, o.k.t. wangqamanise nokwahlula-hlula ngo-5


• yandisa ukuphinda-phindwa kwezibalo asiwe kumanani amakhulu, umz. 34x2 NGAPHANDLE KOKUWATHWALA AMANANI ADITYANISWE NAMANYE (WITHOUT CARRYING)


Fundisa neengxaki zokubala:; • +, - ngamanani anamalungu amabini,

nanamalungu ama-3 ukuya ku-1000 • × wobuncinane bamanani amalungu ma-

2 ngalungu li-1 ukuya kutsho ubuncinane ku-100

• ÷ wobuncinane bamanani amalungu ma-2 ngamanani alungu li-1 ukuya kutsho ubuncinane ku-100

• cazulula amanani anamalungu ama-3, sebenzisa ubhalo oluxandileyo (expanded notation) ukuya ku-1000; sebenzisa oonotsheluza

• cwangcisa amanani ukusuka kwelona lincinane kakhulu ukuya kwelona likhulu uphinde ukutshintshe oko ngenye indlela (vice versa)

• qonda ixabiso lamanani ngamanye afumaneka kwinani elipheleleyo ukuya kutsho ubuncinane kumanani amalungu ma-3, umz. 734: ixabiso lika-7 no-3. Buza okufanayo malunga no-4; liyintoni ixabiso lala manani manye ku-473

• Yakha iithebhile zokuphinda-phinda ngoo-2, 3, 4, 5, 7, 9, 10, 11 ukuya ku-100

• Yandisa ulandelelwano lwamanani ukuya ku-1000.

o Sebenzisa amaCebo: • ukwakha nokucazulula amanani • Ukuphinda kabini nokuhafisha amanani • Ukuqikelela

Isahluko 4

- 44 -



• ukusa amanani kwinani elincinane

(rounding off) ukuwasa kwelona likufutshane lilishumi

• ukubala izinto ezisetyenziswa ekubaleni • umgca-manani, itshathi yamanani • chaza malunga nezisombululo zokubala

kwiingxaki

Iiphatheni o amanani apheleleyo namaqhezu (iihafu)

kumgca-manani: phakathi ko-1 onehafu no-10 onehafu

o khuphela uze wandise ulandelelwano lwamamanani ukuya kutsho ubuncinane ku-1000

ISithuba

o zoba iimaphu ezingaqingqwanga zesikolo okanye indlela izinto ezimacala ma-3 alinganayo nezimacala amathathu angalinganiyo (3-dimensional objects) uze ukhangele izintoe ezo kwimaphu

Imali

o Hlaziya ulwazi malunga nomsebenzi wexesha elidlulileyo

o Fundisa malunga ne-R10 eliphepha iphethwe ngesandla

Ixesha

o qonda uze uchaze iindidi ezahlukeneyo zeekhalenda ezisetyenziswa kwiinkcubeko ezahlukeneyo

o qaphela imihla ebalulekileyo kwikhalenda: imihla eyimbali neyeminyhadala yezenkolo

Ubude

o phicotha indawo leyo ingumphezulu, umz. kwimethi, ukusebenzisa ukuthayilisha

Umthamo

o qikelela uze ulinganise ngeelitha nangeemililitha

Idatha

o qokelela idatha kwibala lesikolo ngokweempawu ezinikwe ngutitshala

o cwangcisa idatha kwibhagrafu o nika ingxelo ngeengqokelela

ezicwangcisiweyo

Isahluko 5

Isahluko 6

Isahluko 7

- 45 -

33- 34


UMSEBENZI 1 UVAVANYO OLUQINGQIWEYO

Ukubala okwenziwa imihla ngemihla o Bala ukusuka kulo naliphi inani elikwitshathi

yamanani ukuya ku-1000 o Bala izinto ukuya ku-200 o Bala ngoo-2, 5,10 ukusuka nakweliphi inani,








50

IKhonsepti yeNani neXabiso o Hlaziya



• Iibhondi zika-50 • Amanani alumelo (ordinal number)

ukusuka kwisinye ukuya kumashumi amahlanu

o Yandisa




ukusuka kwisinye ukuya kumashumi amathandathu


• Hlaziya ulwazi malunga nesi sigama: inkulu kunale, incinane kunale, oko ukwenza ngeempawu

• Qaphela izinto ezihamba kwisinye, umz. ibhedi, ikhabhathi, isihlangu, ilokhe noo-2,13,4,15,6,17, njl. njl.

• Cacisa unxibelelwano phakathi kokudibanisa nokuphinda-phinda ngezibalo kokulandelayo, umz. 45x3 = 45+45+45

Isahluko 2

Isahluko 3

- 46 -


o Amaqhezu:

• Fumana amaqhezu azizihlanu zamanani ukuya ku-50, o.k.t. kungqamanise nokwahlula-hlulwa.


• Hlaziya ulwazi ngeethebhile zoo-2,3,4 no-5 nezibalo eziphendulelweyo (inverse operations)

• Fundisa ngethebhile ka-10 ezineeprophathi ezitshintshiselanayo (commutative properties and inversion) (Funda okwenziwe kwiiveki 7-8)


Fundisa ngeengxaki zokubala: • +, - ngamanani anamalungu amabini,

nanamalungu ama-3 ukuya ku-1000 • x wobuncinane bamanani amalungu ma-








Sebenzisa awakho amacebo • Thetha ngamacebo asetyenzisiweyo uze

ukucacise oko ebhodini • Tshekisa izisombululo zabalingane

kwiingxaki zokubala

Iiphatheni o Amanani apheleleyo namaqhezu (iihafu)

kumgca-manani: phakathi ko-3 ½ no-10 ½ o khuphela uze uwandise ulandelelwano

lwamanani ukuya kutsho ubuncinane ku-1000

Isahluko 4

Isahluko 5

- 47 -



ISithuba neMilo

o Phinda kwakhona okwnziwe kwiiveki 31 neye-32

Imali o Hlaziya ulwazi malunga nomsebenzi

wexesha elidlulileyo o Fundisa malunga ne-R10 eyimali eliphela

uyiphethe ngesandla

Ixesha o Phinda kwakhona okwenziwe kwiiveki 31

neye-32

Ubunzima o qikelela, linganisa, thelekisa uze ucwangcise

izinto ezingu-3-D usebenzisa imilinganiselo engaqingqwanga neqingqiweyo (umz. iipakethe, kg)

Idatha

o Phinda kwakhona okwenziwe kwiiveki 31 neye-32

Isahluko 6

Isahluko 7

35- 36










500 o Bala ngophinda-phindo luka-50 ukuya ku-




50

IKhonsepthi yaManani naManani aluMelo o Hlaziya ulwazi malunga nokulandelayo:



Isahluko 2

Isahluko 3

- 48 -







ukusuka kwisinye ukuya kumashumi asixhenxe


• Hlaziya ulwazi malunga namanani alumelo (place values) ukuya ku-99

• Ukuqwalaselwa kweesethi nezinto ezingekhoyo kwisethi enikiweyo ethile, umz. {12, 14, 16,-;-;-;-26, 28, 30}, njl. njl. Uze uyinike igama lo sethi njengesethi yamanani aphinda-phinda ngambini (even numbers), njl. njl.

• Phinda kwakhona ucacise ngonxibelelwano phakathi kokudibanisa nokuphinda-phinda kwizibalo, umz. . 45x3 = 45+45+45

• Ukudibanisa kumanani amane athi xa edityaniswa ewonke angabi ngaphezulu ko-99 oyitotali, umz. 13+10+60+7=

o Amaqhezu:

• Hlaziya ulwazi lwamaqhezu ezihlanu (fifths) zamanani ukuya ku-50, o.k.t. wangqamanise nokwahlula-hlula.

• Fundisa malunga ngamaqhezu angamashumi ngokwahlula isiqwenga sephepha esiyi-20 cm ubude sibe ngamalungu ali-10 alinganayo

• Bhala igama 1/10 iqhezu elilishumi elinye


• Hlaziya ulwazi ngeethebhile ngoo-2,3,4 no-5 nezibalo eziphendulelweyo (inverse operations)

• Hlaziya ulwazi ngethebhile ka-10 ezineeprophathi ezitshintshiselanayo nezibalo eziphendulelweyo (commutative properties and inversion) (Funda okwenziwe kwiiveki 7-8)

• Ukuphinda-phinda amanani amalungu ma-2 ngoo-2,3,4,5, kwisinye nokuthwala amanani adityaniswe kwamanye amanani (carrying), umz. 25x3

- 49 -

LO 2 Iiphatheni, iifankshini ne-aljebra LO 3 ISithuba esiVulekileyo neMilo (iJometri) LO 4 Umlinganiselo

AManani okuSombulula iiNgxaki

Fundisa ngeengxaki zokubala: ; • +, - ngamanani anamalungu amabini,









o Sebenzisa amacebo akho • Thetha malunga namacebo

asetyenzisiweyo aze uwabhale ebhodini • Tshekisha izisombululo zabalingane

kwiingxaki zokubala

Iiphatheni o Phinda kwakhona okwenziwe kwiiveki 31

no-32 o Chaza iiphatheni eziqatshelweyo

ISithuba esiVulekileyo neMilo o Zoba iimaphu ezingaqingqwanga zesikolo

okanye zokuma kwezinto ezinamacala ama-3 alinganayo namanye angalinganiyo uze uzikhangele kwimaphu

Imali

o Hlaziya ulwazi malunga nomsebenzi odlulileyo

o Fundisa malunga ne-R20 eliphepha uyiphethe esandleni

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 50 -


Ixesha

o Sombulula iingxaki ezibandakanya ukubala ubandakanya nezibalo eziphendulelweyo (conversions) phakathi: kwemizuzu neeyure; iiyure neentsuku; iintsuku neenyanga

Ubude o Phicotha umphezulu wendawo ethe

gabalala, umz. imethi, idesika usebenzisa ukuthayilisha

Idatha o Qokelela idatha kwibala lokudlala

ngokweempawu ezinikwe ngutitshala o Cwangcisa idatha kwibhagrafu o Nika ingxelo ngeengqokelela

ezicwangcisiweyo

37- 38














50

IKhonsepthi yaManani naManani aluMelo o Hlaziya ulwazi malunga nokulandelayo:





Isahluko 2

Isahluko 3

- 51 -





ukusuka kwisinye ukuya kumashumi asixhenxe ananye ukuya kwikhulu


• Hlaziya ulwazi malunga nokulandelayo: place values to 99

• Ukuqaphela iisethi namalungu angekhoyo kwisethi enikiweyo, umz. {12, 14, 16,;-;-;-;-26,28, 30} , njl. njl. etc uze uchaze isethi, umz. isethi yophinda-phindo lwamanani ngambini (even numbers) uze unike igama lesethi leyo, umz. isethi yamanani ngambini, njl. njl.

• Phinda kwakhona ucacise malunga nonxibelelwano phakathi kokudibanisa nokuphinda-phinda kwizibalo, umz. 45x3 = 45+45+45

• Cacisa malunga nonxibelelwano phakathi kokuthabatha nokwahlula-hlula, umz. 55÷11= (55-11-11-11-11-11)

• Udibanisa kumanani amane ufumane itotali engekho ngaphezu ko-99, umz. 13+10+60+7=

o Amaqhezu:

• Hlaziya ulwazi malunga namaqhezu azizihlanu (fifths) ukuya ku-50, o.k.t. angqamane nokwahlula-hlula.

• Fundisa ngamaqhezu angamashumi (tenths) ngokwahlula-hlula ngesiqwenga sephepha esiyi-20 cm ubude sibe ngamalungu ayi-10 alinganayo

• Bhala igama 1⁄ 10 iqhezu leshumi elinye

o Ukuphinda-phinda nokwahlula-hlula • Hlaziya ulwazi malunga nokulandelayo:

iithebhile 2,3,4 no-5 ngokusebenzisa izibalo eziphendulelweyo (inverse operations)

• Hlaziya ulwazi ngethebhile ka-10 kwisinye neeprophathi ezitshintshiselanayo nezibalo eziphendulelweyo ( commutative properties and inversion) (Funda iiveki 7-8)

- 52 -


• Ukuphinda-phindwa kwamanani

amalungu ma-2 ngo-2,3,4,5, kusetyenziswa nokuthwala kwamanani adityaniswe namanye (carrying), umz. 25x3

• Ukwahlulwa-hlulwa kwamanani amalungu ma-2 kusetyenziswa okanye ngaphandle kokusebenzisa ukucazululwa kwamanani ikhona okanye ingekho intsalela, umz. 67÷3; 54÷5


Fundisa malunga neengxaki zokubala:; • +, - ngamanani anamalungu amabini,









o Sebenzisa amacebo akho • Thetha ngamacebo asetyenzisiwayo uze

uwabhale ebhodini • Tshekisha izisombululo zabalingane

kwiingxaki zokubala

ISithuba neMilo o Hlaziya ulwazi

Imali

o Hlaziya ulwazi malunga nomsebenzi odlulileyo

o Fundisa malunga ne-R50 eliphepha uyiphethe ngesandla

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

- 53 -


Ixesha

o Sombulula iingxaki ezibandakanya ukubala kwisinye nezibalo eziphendulelweyo (conversions) phakathi: kwemizuzu neeyure; iiyure neentsuku; iintsuku neenyanga

Ubude o Phicotha umphezulu wendawo, umz, imethi,

idesika usebenzisa ukuthayilisha

Idatha o Qokelela idatha kwibala lokudlala esikolweni

ngokweempawu ezinikwe ngutitshala o Cwangcisa idatha kwibhagrafu o Nika ingxelo ngeengqokelela

ezicwangcisiweyo

39- 40













50

IKhonsepti yeNani neXabiso o Hlaziya







Isahluko 2

Isahluko 3

- 54 -



• Bhala amanani alumelo (place values)

ala manani angasentla ku-HTU • Iibhondi zika-50 • Amanani alumelo (ordinal number)



Hlaziya ulwazi malunga nomsebenzi wexesha elidlulileyo

o Amaqhezu:





o Fundisa malunga neengxaki zokubala ezizezakho uze usebenzise amacebo wakho ekufumaneni izisombululo;

o Tshekisha izisombululo zabalingane kwiingxaki zokubala

ISithuba neMilo

o Ukuhlaziya ulwazi

Imali o Ukuhlaziya ulwazi

Ixesha

o Ukuhlaziya ulwazi

Ubunzima o Ukuhlaziya ulwazi

Ubude

o Ukuhlaziya ulwazi

Idatha o Ukuhlaziya ulwazi

Isahluko 4

Isahluko 5

Isahluko 6

Isahluko 7

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