Republic of Namibia
MINISTRY OF EDUCATION
JUNIOR PRIMARY PHASE
FOR IMPLEMENTATION: 2015
MATHEMATICS SYLLABUS
GRADES 1-3
RWAKWANGALI VERSION
Ministry of Education
National Institute for Educational Development (NIED)
Private Bag 2034
Okahandja
Namibia
© Copyright NIED, Ministry of Education, 2014
Mathematics Syllabus Grades 1 - 3
ISBN 978-99945-2-050-3
Printed by NIED
Website: http://www.nied.edu.na
Publication date: 2014
Yikaramo
1. Etwaromo ....................................................................................................................... 1
2. Madinkango .................................................................................................................... 1
3. Yitamo ............................................................................................................................ 1
4. Erongopakerero ............................................................................................................. 1
5. Elikwatakano noyirongwa peke noyuma yongendesorongo – tavakano ......................... 3
6. Ngendeso zoKuronga noKulironga ................................................................................. 3
7. Matomporo gokouhura welima ....................................................................................... 5
8. Ekulikositumbwiso lyononomora ..................................................................................... 6
9. Yikaramo yokulironga ....................................................................................................12
10. Ngendesokonakono ...................................................................................................35
11. Muzaro gonoNkango .................................................................................................38
1 NIED Syllabus: Mathmatics Junior Primary Phase 2014
1. Etwaromo
Elikwamo lyoyironwa eli kwa tamba elirongo nekonakono lyomuvaru mo-harade 1 dogoro
moruha lyelirongo lyomuvaru, varongwa kukwategano nokufunda maukonentu, nondunge,
magano nonongendeso dokulisiga-siga dopamuvaru, dokukonakona nokutoroka
pananomora nomalitundukano gononomora nonopatorona edi da kara po mouzuni.
Ngo sirongwa, muvaru kwa kara monda zoruha rwelirongo ropamuvaru
mongendesesorongo, nye kwa kara nosumagwanekero noyirongwa peke mo
ngendesorongo nazinye. Yitambo, yitamborongo nomatomporo gokulirambakana pokatji
koyirongwa nayinye oyo kuna kara mulyo gelirongo mongendesorongo nazinye.
Kutwara omu ya wapera, sirongwa esi kwa hepa noperiode – 8 (mo Harade 1 no2) ntani
noperiod 9 (moharade 3) mosivike.
NIED kwa li gwa newapukuro lyomukunduruko tarururo gongendesesorongo. Mvhura vana
kundindira kuka tura moyirugana etarururo lyelikukwamo lyopo- Ntambo zoPilimere zePevhu
kuna kara 2021.
2. Madinkango
Muvaru kuna kara siruganeso somulyo melirongoukonentu nomounongononigano
nomomaruha gamwe meparu monkarapamwe. Ago kugava mbatero kekuliko lyonondunge
nopagazaro lyediwo-ukonentu ediwo lyomuvaru nalyo kuna kara ruha rompo zetu ntani
kuvhura kuliruganesa mokutuntura magano nelizuvho nawa-nawa lyomauzera. Tuna hepa
ediwo lyopamuvaru nomaukonentu gokuvhura kurugana yirugana yoyinzi yankenyezuva
yimo tupu hena nokukohonona maudigu. Ago kugava ruhafo nepando ntene varongwa tava
kohonona maudigu nezuvho uwaawa momaudano gononomora mulyo unenepo asi
varongwa va kwate ntateko zomuvaru, morwa ekwategano lyomagano gomuvaru
gopazeruko kwa hamena pontambo zetateko ezi.
Ediwo nonomora yizo ntjima-tjima zefano lyerongo lyoPilimere, ntani alyo kuna kara mulyo
unene koNtambo zePilimere zePevhu. Elikwamo lyoyirongwa kwa li tungira poyiha
yomatomporo goyivara, mahetayiko, ruveze noyimaliva eyi ava yiruganesa vanona nkenye
siruwo. Erongoheteko alyo kuna kara ekwategano lyomuvaru gevega ntani montambo ezi
kwa kara mo ekwategano lyontateko zoyihwi yo momukunda govarongwa yuma kuna kara
ekohonono udigu, nopatorona dononomora ntani eruganeso mapukururo kugava siruwo
sokukwategano nkarero zankenyezuva zomuvaru. Efundo lyovanona momuvaru nga li kura
moomu vana kumona no patarona domuvaru nokulironga eruganeso mapukururo.
3. Yitamo
Yitambo yomuvaru kuna kara:
Kukulika eruganeso nonomora negazadaro pamuvaru
Kukulika nkareso zongwa kombinga zomuvaru
Kurerupika varongwa ku gwana ntateko zegano lyoyidimbwiliso lyononomora
Kurerupikira varongwa kukwategano nokufunda magano gopamuvaru no yiruganeso
Kurerupika varongwa kuruganesa muvaru meparu lyawo lyankenye ezuva
4. Erongopakerero
Erongopakerero kuna kara unankondo wankenye murongwa mokukulika elihameseromo, ndi
kugwana mpito zonene zemelikwamo lyerongo yimo tupu noyirugana azi gava ngendeso
2 NIED Syllabus: Mathmatics Junior Primary Phase 2014
zerongo zomonosure dakarapo. Alyo kwa demenena ponompango devatero nepemburo
malisigo ga kara mokatji kovarongwa navenye nokugusa po yilimbikwa nayinye yelirongo.
Erongo lyopantateko kuwapayikira nkarapamwe yitambo yokomeho monzodi zaNamibia
zomo 2030 mokukulika elipakerero kumwe. Varongwa kugwanekera noyilimbikwa yelirongo
noyihepa yimwe youumwe ngava yi gweda mo mosure za ngesi noyihepwa yawo ngava yi
fira sinka monongendeso dokulisiga-siga moomu ya fira. Varongwa nye womaudigu
gomanene wokupira ku gwanena mo mauwa mokukara monosure da ngesi awo ngava vapa
yihepwa kutwara moyihepwa yawo youumwe, norunone rwevatero ndi nosure dorunone,
dogoro ngasi sike siruwo sokulipakerera mongendesorongo, ndongeso noyiruganeso kwa yi
hetekera povarongwa wonosure edi.
Ngendeso zelirongo lyomunona pwamwene ngo ndongeso yizo za liza noyihepwa varongwa
velirongo lyokulikarera, morwa kutamekera kweyi va diva neyi ava rugana nare noku va
vatera va gwane ediwo nomaukonentu. Mutungorugano gongendesorongo gerongopakerero
kwa vyukilira matomporo aga nava vhura kudiva varongwa woyihepwa yokulikarera.
Erongofanayiko lyevatero lyankenye gumwe lya hepa kukara po yipo li pitisire nokukonakona
ngendeseso zelirongo lyankenye gumwe lyovarongwa woyihepwa yelirongo lyokulikarera.
Mavyukiso gamwe gomafanayiko gokulironga nokuronga gomosure zelirongo pakerera
kuvhura kugagwana momutungorugano gondesorongo zelirongopakerero lyomo (2012)
Mavyukiso ga ngesi ngaga vatera kugava kovarongwa navenye nondunge, maukonentu
nonkareso dokuva vatera kupita mouzuni womaudigu gomanzi, ganakugenderera kulisinta
nokuzura mauzera nelirong konentu lyomagwanekero.
Ntambo zoPilimere zePevhu kugava siruwo sokuhetakana sokulironga kwa navenye vagara
novakadi. Varongi va hepa kudiva nokukwategano omu nava tekura varongwa navenye
pakuhetakana, ntani yiruganeso nayinye ya hepa kuvatera marudi pauhunga. Varongi va
hageke “ehamo kumwe tupu mononkondwarongero nokutakamesa asi erongo lyawo li kulike
ehetakano lyopomarudi. Ekonakono kwa likida asi navenye vakadona novamati va kara
nononkondo dokutompora momuvaru yiponye asi varongi va gave mukumo kovarongwa
navenye vamati novakadona yipo va rugane nawa. Yina kara nomulyo asi ntambo
zoPilimere zePevhu zi gave mukumo nelihuguvaro lyomomuvaru mwa navenye vamati
novakadona.
3 NIED Syllabus: Mathmatics Junior Primary Phase 2014
5. Elikwatakano noyirongwa peke noyuma yongendesorongo – tavakano
Yiparatjangwa yopangendesorongo – tavakano kwa gwederera mo elirongo mukunda, HIV
no AIDs, Elirongo lyoUnankondo womuntu noUdemokoli, Mapukururo noMagwanekero,
Elirongoukonetu neKungonzira. Eyi kwa yi tura mongendesorongo zakarapo morwa nkenye
siparatjangwa kwa hama unenepo koyiponga nomahomono monkarapamwe zetu
zaNamibia.
Varongwa vetu navenye va hepa:
Kukwategano nkareso zosiponga nehomono
Kukwategano ekundamo lyoyuma eli monkarapamwe zetu
Ku kwategano asi ngapi mokuvhura kugusapo yiponga nomahomo mo nkarapamwe zawo
Yiponga noMahomono gomanene kwa ga dimburura ngesi asi;
Efirosinka netakameso runone nonsitwe
Ehamo lyoyikwamoko yoHIV AIDs
Ma udigu goukanguki nelipakerero kumwe nenyateko, ruhepo roukarokanguki noyihando
Epiro kulimburukwa komahetayiko gepoperonzira Yirongwa yimwe ya zira mo mokuyiruganesa kumwe noyuma yongendesorongo - tava kano
zokulikarera. Melikwamo lyoyirongwa eli kuna kara mo yihonena yoyinzi yoma likwatakano peke
koyuma yongendeso rongo-tavakano, nye sihone nasimwe tupu soyuma yongendesorongo
tavakano yiso va gava oko konhi.
ELIRONGO MUKUNDA HIV NO AIDS ELIRONGO LYO
VATUNGIMO EPOPERO NZIRA
Harade 1-3
Eruganeso
mapukururo Elikido
lyografika zomafano
Eruganeso lyomema
mosivike
Harade 2
Ruveze
Harade 3
Eruganeso
Mapukururo
Grafika zo mafano zo
vamati no vakadona
Harade 1
Kuvara nonomora
domatuwa mositaura
Harade 1 no 2 yifano
yoyi dimbwiliso nzira
6. Ngendeso zoKuronga noKulironga
Ngendeso zokuronga nokulironga kwa demenena ponkedi zelirongo lyomurongwa pwa mwene moomu va li singonona momatjangwa goveta zouministeli nomomutungorugano gopafano gelirongo lyomurongwa pwamwene, ngendeso zangesi kuhuguvaresa erongo lyewa lyomulyo lyelirongo ntene nompango tava di tura mosirugana. Simpe hena ngendeso zosumahangakano kuna kara erwameno lyedi lyerongo nelirongo lyoNtambo zoPilimere zePevhu. Yitambo kuna kara yokukulika elirongo nekwategano ntani nekuliko lyediwo, maukonentu nonkareso zina, kugwederera kekuliko lyopankarapamwe. Nkenye murongwa kuwiza nediwo lyenene lyonondunge noyihorokwa yopankarapamwe eyi ga gwana mekoro nomomukunda megwanekero neyi yomomukunda. Elirongo monosure lya hepa kuhameseramo etungo, etamununo nehomono lyeyi ga diva nare murongwa ntani noyihorokwa.
4 NIED Syllabus: Mathmatics Junior Primary Phase 2014
Varongwa kulironga nawa ntene kuna li hamesera mo sankondonkondo mongendeso zelirongo mokulitura mo unene mokugava makwafo noyigwana mo. Nkenye murongwa kwa kara pwamwene noyihepwa yamwene, sinano selirongo yihorokwa nevhuro, murongi ga hepa kusikisamo yihepwa yovarongwa nokuwapayika ehoroko lye lirongo kutwara moyihepwa yawo. Nduganeso zomurongi zi kare zokulisiga-siga nye za gomoka va zi tunga nawa melikwamo lyoyirongwa. Murongi ga hepa kutokora kutwara mo yitamborongo nomomatomporo aga nava vhura kusikisamo, ntene yikara mo yomuvaru tava yi rongo nawa nopazuvhoko usimbu, oku yina wapere, varongwa kuva siga va gwane ndi va papare mauzera gavene, ntene vana pumbwa elirongo pankondopeko ndi pangawopeko, ndi ntene pana kara erunduruko lyoukonentu ndi momauzera aga nava vhura kusikura, ndi ntene varongwa tava gwana mukumo mokugwana nonzira davene mosiparatjangwa ndi moruha royikaramo. Yirugana yankenye gumwe, monombunga, vavali-vavali ndi ngonkondwarongero mudima mosiruwo somuvaru sa hepa kusiwapayika nokusididilika. Eruganeno kumwe lyelirongo muvaru va hepa kulipa mukumo nkenye apa yina wapere, sihonena, momuvaru kuvhura mukare nonduganeso dononzi dokukohonono udigu, erugano lyovarongwa monombunga kuvhura va lirongereko kovakwawo. Yina kara hepero asi yirugana yi tante yuma, yipo varongwa va mone mo elikwatakano lyankenye sirugana. Moomu vana kukulika paumwene, pankarapamwe nomaukonentu gopamukunda, kuvhura nye mepitisiro lyomurongi, pazeruko kuvapa yitumbukira yokulihamesera momafanayiko nemekonakono lyoyirugana yavene. Muvaru gu kare kuna li zi ago hena gutante yuma kovarongwa, ntene gu hamena keparu lyawo. Sihonena ngwendi yifanovali ndi yifanotatu kuvhura kuyigwana momukunda gwawo ogu va kara. Nampili moomu ya kara ngoso muvaru kwa kara eraka lyanavenye, ayo ntudi yi hamene pomukunda neruganeso lyokuvhura kukwategano varongwa nokuhafera eruganeso lyomuvaru. Ntene nobuke ado kwapakerera, murongi situmbukira sendi soku ruganesa yihonena noyiruganeso yopamukunda yokumoneka ngwendi mamanya, yitji nomaruswiko gomakende ngoso.
5 NIED Syllabus: Mathmatics Junior Primary Phase 2014
7. Matomporo gokouhura welima
Mokuhwilira moHarade 1 montambo zoPilimere zePevhu, varongwa navenye kuna kuvandindira valiwapayikire pankarapwamwe, palizuvho panandunge noparutu yipova tameke nelirongo lyakarapo lyomuvaru. Pokumana muvaru goHarade gomoNtambo zoPilimere zePevhu, varongwa kuna kara ndindira va vhure kulikida oyo yina kukwama ko; Yitumbwiso yoNonomora Varongwa kuvhura kudimburura, kusingonona nokugava nonomora nomalihameno gado kupwagesa ekwategano lyawo lyomagano gononomora pakana nokutjanga ntani nokuruganesa nonomora melikwamo moomu vana di hepere mokugusapo maudigu gankenyezuva meparu. Kukohonona Maudigu Varongwa kuvhura kuruganesa ekwategano lyawo lyomagano gononomora mokagusapo maudigu goureru melihameno lyankenye zuva mokuvara, mokungungunyika nomomahetayiko, pokuruganesa nongendeseso davene nononduganeso, nokuruganesa nonomora kutwara mehetekero eli vana hepa. Kuvara Varongwa kuvhura kuruganesa nonduganeso ngwe.a. kuturako, kugusomo, kuvhukisa nokugavero pokuruganesa nongendeseso nononduganeso, nokuruganesa nonomora mehekero eli vana hepa. Kumeta Varongwa kuvhura kudimburura, kunongonona nokukwategano uumwe wokumeta pauhunga noporuganeso yo (unaure, mukumo, unzi, ruha, ruveze noyimaliva) ntani kuruganesa uumwe owu meparu lyankenyezuva Yimaliva Varongwa kuvhura kudimburura yimaliva yaNamibia yoyitenda nomafano nokukutuntura ekwategano lyawo lyoyimaliva pakana nopakutjanga ntani kuruganesa yimaliva mokukohonona maudigu gankenyezuva. Erongoheteko Varongwa kuvhura kudimburura nokusingonona erongoheteko lyoyifano nokukarerapo mukaro nomalitundakano pokatji koyifanovali noyifanotatu meparu lyene-lyene. Eruganeso lyo Mapukururo Varongwa kuvhura kupongayika, kukama, kulikida, kutoroka nokuhangura mauzera pokuruganesa nogarafikafano nonogarafika dokulironda yipo di tulisepo ehagero nokurugana mapumbo gouhunga.
6 NIED Syllabus: Mathmatics Junior Primary Phase 2014
8. Ekulikositumbwiso lyononomora
NTAMBO ZOPAPILIMERE ZEPEVHUVU
HARADE 1 HARADE 2 HARADE 3
Kuvara, nonomora, kuvalipika nokutura Harufa, nopatorona dononomora, nonomora
donoMurongo donoro, mulyo gomavega, kungungunika nokuyereka kuudinga,
kupongeka, kupompeka nokuhetakanesa, yivaro ya hana mapando
noyihetakanovaro, ezungururo lyononomora.
Kuvara pamahina dogoro 20
Kuvara pamahina dogoro 100
Kuvara pamahina dogoro 500
Kuvara pamahina dogoro 1000
Kudimburura nonomora dogoro 10 Kutjanga nonomora dogoro 9
Kuresa, kutumbura ntani kudimburura nonomora dogoro 100 Kutjanga nonmora dogoro 20
Kuresa, kutumbura ntani kudimburura nonomora dogoro 500 Kutjanga nonomora dogoro 100
Kuresa, kutumbura ntani kudimburura nonomora dogoro 1000 Kutjanga nonomora dogoro 500
Kungungunyika dogoro koyininke 4
Kungungunyika dogoro koyininke 6
Kuyereka yininke dogoro ko 10
Kuyereka yininke dogoro 20
Kurundurura nokutunga no patorona doureru
Kunongonona nopatorona donomora melikwamo lyononomora 1 dogoro 10
Kunongonona nopatorona melikwano lyononomora 1 dogoro 20
Kunongonona nopatorona dononomora melikwamo lyononomora do 1 dogoro 50
Kuturako no kugusamo nonomora donomurongo donoro dogoro 100
Kuturako nokugusamo nonomora donomurong donoro dogoro 500
Kudimburura mulyo gevega lyankenye nomora mono nomora kutunda 1 dogoro 20
Kudmburura mulyo gomavega gwa nkenye nomora mononomora mbali kulikida unzi Kudimburura unamurongo nouumwe
Kudimburura mavega ga nkenye nomora mononomora ntatu kulikida unzi Kudimburura unamafere unanomurongo nouumwe
Kutura yininke monomuzumo
Kutura yininke kutunda ko-1 dogoro ko-10 mo mono mpungi
Kutura yininke 1 dogoro 50 monompungi
Kutura yininke kutunda ko - 1 dogoro ko-100 mo nompungi
Kupompeka nokuhetakanesa nompungi do yininke
Kupompeka nokuhetakanesa nompungi doyininke nononomora 1-20
Kupompeka nokuhetakanesa nompungi doyininke nonomora 1-100
Kupompeka nokuhetakanesa nompungi nononomora 1-500
Kudimburura unamurongo
Kudimburura unamafere
7 NIED Syllabus: Mathmatics Junior Primary Phase 2014
NTAMBO ZOPAPILIMERE ZEPEVHUVU
HARADE 1 HARADE 2 HARADE 3
nouumwe unanomurongo nounauumwe
Kutura yininke mono muzumo
Kutura yininke kutunda ko- 1 dogoro ko-10 mo monompungi
Kutura yininke kutunda ko -1 dogoro ko-50 monompungi
Kutura yininke kutunda ko -1 dogoro ko -100 mo nompungi
Kupompeka nokuhetakanesa nompungi do yininke
Kupompeka nokuhetakanesa nompungi doyininke nononomora 1-20 Kutumbura nokuresa
Kupompeka nokuhetakanesa nompungi doyininke nononomora 1-100 Kutumbura nokuresa
Kupompeka nokuhetakanesa nompungi nononomora 1-500 Kutumbura nokuresa
Kupompeka nonomora doku likarera kutunda ko-1 dogoro 10
Kupompeka nonomora dokulikarera kutunda ko-1 dogoro ko-20
Kupompeka nonomora do kulikarera kutunda 1 dogoro 100
Kulikida eligwo lyazimwe nazimwe yi likide ehetakano nepiro ehetakano lyonompungi
Kulikida eligwo lyazimwe nazimwe kumwe nonomora 0-10 yilikide ehetakano nepiro ehetakano lyonomuzoro
Kudimburura nonomora da hana mapando nononomora domapando 0-99
Kudimburura nonomora dahana mapando nononomora domapando 0-500
Kugwana vakwa wo wononomora mononomora mononomora 1-9
Kuzungurura nonomora dombali dogoro 99
Kuzungurura nonomora dontatu dogoro 500
Ekohonono maudigu
Kukohonona maudigu gesanseko lyo ureru
Kukohonona maudigu gemesanseko lyoureru kutwara melikwamo 0-10
Kukohonona maudigu gemesanseko kukwama melikwamo 0-10
Kukohonona maudigu gemesanseko kutwara melikwamo 0-100
Kuvara
Kutura kumwe, kugusamo, kuvhukisa, kugavera, maudigu, gonontambo dononzi, yintau
Kukoneka kutura kumwe usili wononomora 0-10 Tura nonomora mbali nantatu kumwe nosivarero
Kukoneka kutura kumwe usili wononomora 0-20 Kutura nonomora mbali nantatu kumwe dopokatji ko 1-100 kumwe nosivarero
Kukoneka kutura kumwe usili wononomora 0-20 Kutura nonomora mbali nontatu kumwe dopokatji ko 1-100 kumwe nosivarero
Kugusamo nomora zimwe monomora
Kukoneka egusamo lyousili lyononomora 1-10 Kugusamo nomora zimwendi mbali
Kukoneka egusomo lyousili lyononomora 1-20 Kugusamo nonomora mbali ndi
8 NIED Syllabus: Mathmatics Junior Primary Phase 2014
NTAMBO ZOPAPILIMERE ZEPEVHUVU
HARADE 1 HARADE 2 HARADE 3
nonkwawo dopokatji ko 1-10
mononomora mbali dopakatji ko 11-99
ntatu mononomora ntatu dopokatji ko 100-500
Kufaneka no mpungi doyininke nokudihetakanesa kononomora dokuligwa kumwe
Kukoneka yi mpungu yo 1,2,5 ntani 10 Kuvhukisa nkenye tupu nonomora mbali dogoro ko 20 dankenye nomora pokatji ko 1-9
Kukoneka yi mpungu yo 1,2, 3,4,5 ntani 10 Kuvhukisa nkenye tupu nonomora mbali dogoro ko 50- da nkenye tupu nomora pokatji ko 1-10
Kuvalipika nonomora dogoro kwa 5 ntani ku valipika dogoro ko-10 Kuteta pokatji nonomora depando dokuhetakana dogoro ko 10 ntani kuteta pokatji 20
Kuvalipika no nomora dogoro ko 50 Kuteta pokatji nonomora dogoro ko 50 ntani nonomora dokudira ku hetakana dogoro ko 20
Kuvalipika nonomora dogoro ko 100 Kuteta pokatji nonomora dogoro ko 100 Kukoneka usili we gavero lyoureru lyokulitundakana nousili we vhukiso lyo 2,3,5 ntani 20
Kuligaununa yininke pa kuhetakan novahameni womombunga pokuruganesa yininke yokumoneka
Kugaununa dogoro ko 10 yininke mono mbunga da 2, 3, 4 ntani da 5
Kugavera yininke mono mbunga da 2, 3, 4, 5 ntani do-10
Kugavera nkenye tupu nonomora mbali kutunda ko 10 dogoro ko 100 pokuruganesa nonomora do kutunda kwa 1-5
Kukohonona maudigu go nontambo dononzi gokutunda ko 0-10 kumwe neturoko negusomo
Kukohonona maudigu go nontambo dononzi gokutunda ko 0-100 kumwe neturoko negusomo
Kukohonona maudigu gonontambo donzi gokutunda ko 0-500 kumwe neturoko negusomo
Kuligavera yininke pa kuhetakana
Kugavera yininke pa kuhetakana nopakulifana “nasinye” ntani “ukahe”
Kugavera yininke momaruha go kuhetakana ntani “nasinye” “ukahe” ntani “siune”
Kugavera yininke momaruha ntani pokulifana “nasinye” “ukahe” “siune”, “siutatu” ntani yitatu moyiune kuruganesa yidimbwiliso yomuvaru ngwe
, , ,
Kumeta
9 NIED Syllabus: Mathmatics Junior Primary Phase 2014
NTAMBO ZOPAPILIMERE ZEPEVHUVU
HARADE 1 HARADE 2 HARADE 3
Unaure, Mukumo, Unzi, Ruha, Ruveze, Yimaliva
Kuhetakanesa nokumeta unaure woyi ninke pokuruganesa
Kuhetakanesa nokumeta unaure wosininke pokuruganesa uumwe wokukwateramo
Kuhetakanesa, kumeta nokutura nokutjanga unaure wosininke pokuruganesa uumwe
Kuhetakanesa kuhemeta nokutjanga ure wosininke pokuruganesa
Ruumwe woyi ruganeso yokukwatera mo
wokukwateramo ntani uumwe owu kara po monosentimeta Kuruganesa esupipiko: cm
siruganeso soku kwateramo ntani uumwe owu wa karapo monosentimeta Kuruganesa esupipiko: cm
Kuhetakanesa nomukumo doyininke yivali pokuruganesa uumwe woyininke yokukwateramo
Kungungunyika, kuhetakanesa nokumeta mukumo goyininke pokuruganesa uumwe woyininke yokukwateramo
Kungungunyika, kumeta no mukumo goyininke pokuruganesa uumwe wokukwateramo no uumwe owu wa karapo Kuruganes: Kg
Kungungunyika, kumeta no kuhetakanesa nomukumo doyininke pokuruganesa uumwe wo yinke yokukwateramo ntani uumwe woyinke ya karapo Kuruganesa: Kg
Kuhetakanesa unauzi woyininke yivali pokuruganesa uumwe wokukwateramo
Kungungunyika, kupompeka, kuhetakanesa nokumeta unzi woyipako pokuruganesa uumwe woku kwateramo
Kukungungunyika, kupompeka nokumeta unzi woyipako pokuruganesa uumwe wokukwateramo ntani uumwe owu wa karapo womono litera Kuruganesa esupipiko: (l)
Kungungunyika, kuhetakanesa ntanti kumeta unzi woyipako pokuruganesa uumwe woku kwateramo nowu wakarapo mono lita nomo nomililita Kuruganesa masupipiko: l, ml
Kuheteka nokuhetakananesa maruha monda zoyifano/yihwi pokuruganesa uumwe wokukwateramo
Kuheteka nokuhetakanesa maruha monda zoyifano ndi yihwi pokuruganesa uumwe wokukwateramo ntani nosikwambando
kuhangura pokatji komaruveze gokulisiga-siga
Kuhamesera mambo noyiviyauka yopomukunda
Kuhamesera yihoroka yankenye zuva komazuva,
Kuhamesera yihoroka ya nkenyezuva
10 NIED Syllabus: Mathmatics Junior Primary Phase 2014
NTAMBO ZOPAPILIMERE ZEPEVHUVU
HARADE 1 HARADE 2 HARADE 3
gemezuva yokulisiga-siga koruveze rwemezuva
yivike nonomwedi komazuva, yivike nonomwedi
Kutumbura mazuva gomosivike
Kutumbura mazuva go mosivike nomakwedi gomomvhura/melima
Kutumbura mazuva go mosivike nomakwedi gomomvhura/melima pokuruganesa kalinda nokudimburura mauzera aga vana tamba
Kutumbura mazuva gomosivike nomakwedi gomomvhura/melima pokuruganesa kalinda nokudimburura mauzera aga vana
Kuhetakanesa sinano/siruwo “sosire” nesi “sosisupi”
Kutanta ruveze monovili ntani monoharufa vili
Tamba Kutanta ruveze mono vili, monoharufa vili, nomunute ronantano zina kupitisa vili, nomunute ronantano dina hupuko zi tone vili ntani nonomunute
Kutumbura no kudimburura yimaliva yoyitenda yaNamibia 5c, 10c, 50c Kuruganesa yimaliva yokudanesa mokuliyomberesa mokuranda nokulirandesa randesa
Kutumbura nokudimburura yimaliva yoyitenda yaNamibia 5c, 10c, 50c, N$1, no N$1 no N$5 Kuliyomberesa kuranda nokulirandesa-randesa yininke, kuvara yimaliva nokugava tjindji zouhunga zo ko N$5
Kutumbura nokudimburura yimaliva yaNamibia yoyitenda nayinye ntani yomafo nayinye ngwendi N$10, no N$20 Kuliyomberesa kuranda nokulirandesa randesa yininke, kuvara yimaliva nokugava tjindji zouhunga zo ko N$10
Kutumbura nokudimburura yimaliva yaNamibia nayinye: Yimaliva yoyitenda nayinye neyi yomafo nayinye ngwendi; N$10, N$20 no N$850 Kuliyomberesa kuranda nokulirandesa-randesa yininke, kuvara yimaliva nokugava tjindji zouhunga zoko N$20
Erongoheteko yifano, Evega noMukaro
Kudimburura nokusikura yifano yoyina yivali
Kudimburura, kutumbura, kuhangura nokugaununa yifano yoyiha yivali nayitatu sikwambando sikwamusere, sikwarwarwa ekovhutatu
Kudimburura, kutumbura kuhangura, kugaununa yifano yoyiha yivali nayitatu sikwambando sikwamusere, sikwarwarwa, ekovhutatu,
Kudimburura, kutumbura, kuhangura, nokugaununa yifano yoyiha yivali nayitatu; sikwambando, sikwamusere, sikwarwarwa,
11 NIED Syllabus: Mathmatics Junior Primary Phase 2014
NTAMBO ZOPAPILIMERE ZEPEVHUVU
HARADE 1 HARADE 2 HARADE 3
sikwaguni kapundi ntani kone
salyalyakana, sikwampakero, sikwa-euta, sikweguni, kapundi, kone, sikwatenga
ekovhutatu, salyalyakana, sikwampakero, sikwa-euta, sikweguni, kapundi, kone, sikwetenga, sipentagone, siprisima nosipiramide Kugwana makovhu mo yifano yoyiha yivali nayitatu nokudimburura ekovhu lyouhunga
Kulikida nokusingonona evega lyorutu koyininke yomukunda
Kusingonona evega, lyorutu noyininke yomomukunda
Kusingonona mukaro goyininke eyi vafaneka ponokarata dokulituntika
Kusingonona mukaro goyininke eyi vafaneka ponokarata dokulitunkika
Kuhangura nokugaununa yininke
Kupongeka, kuwapayika nokulikida mauzera pografikafano Kutoroka nokuhangura mauzera
Kupongeka kuwapaika nokulikida mauzera pografikafano Kutoroka nokuhangura mauzera
Kupongeka kuwapayika nokulikida mauzera pografikafano, yitafura ndi grafika Kutoroka nokuhangura mauzera
12 NIED Syllabus: Mathmatics Junior Primary Phase 2014
9. Yikaramo yokulironga
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kuvara Sitamborongo Varongwa va hepa kuvara pokuruganesa yininke yokumoneka ntani pokudira kuruganesa yinike yokumoneka ntani kukwategano yihepwa neziromo lyokuvara kwankenyezuva
Matomporo: Murongwa kuvhura:
Matomporo: Murongwa kuvhura:
Matomporo: Murongwa kuvhura:
Kuvara yininke yokumoneka dogoro ko 20 ntani sinderenyima kutunda ko 20-0
Kuvara pamahina dogoro ko 100, mono 2 dogoro ko 30, mono 5 no 10 dogoro 100
Kuvara yininke yokumoneka dogoro ko 50 ntani mono 2 dogoro 50, mono 3 dogoro 30, mono 4 dogoro 40 mono 10 dogoro 100
Kuwapukurura epongeko lyoyininke moku ninkisa va vare noureru ngwendi, epongeko mono 2, 3, na 5
Kuvara pamahina dogoro ko 500, mono 4 dogoro ko 40, mono 5 no 10 dogoro ko 500
Kuvara sinderenyima kutunda ko 20 dogoro ko 0, 30 dogoro ko 0, mono 2 kutunda ko 20 dogoro ko 0
Kuvara yininke yokumoneka dogoro ko 100 ntani mono 2 dogoro 100, mono 3 dogoro ko 60, mono 4 dogoro ko 80, mono 5 no 10 dogoro 100
Kuwapukurura epongeko lyo yinike moku ninkisa va vare noureru ngwendi epongeko mono 2, 3, na 5
Kuvara pamahina dogoro ko 1000, ntani sinderenyima nokomeho kutundilira pwa nkenye nomora; mono 1 dogoro ko 1000, mono 2 dogoro ko 500 mono 3 dogoro ko 60, mono 4 dogoro ko 80, mono 5 no 10 dogoro ko 1000 mono 20 dogoro ko 500, mono 30 dogoro ko 180, mono 50 nono 100 dogoro ko 1000
Kungungunyika (kudimburura nonomora doyininke vana gava va hana kuyivara
Sitamborongo Varongwa vahepa kungungunyika, kuyereka nokuruganesa maukonentu gewapukururo malitundakano gonopatorona
Matomporo: Matomporo: Matomporo:
13 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Murongwa kuvhura: Murongwa kuvhura: Murongwa kuvhura:
Kungungunyika sivaro soyininke dogoro ko 6 yahana kuyivara ntako kuyikona kona ntani kuyivara
kungungunyika sivara soyininke dogoro ko 10 po kuyitura mono mpungi
kudimburura mawapayiko/gonopatorona do kulisiga-siga doyininke kuvhura kukarerapo nomora zimwe tupu ngwendi;
□□□ □□ □□ □□□ □□ □ □ □□ □ □ Nombali 3, nontatu 2 ndi 5+1
Kungungunyika sivaro soyininke dogoro ko 20 po kuyitura mono mpungi douhunga, kuyikonakona ntani kuyivara
Kundimburura mawapayiko/ gonopatorona do nokulisiga-siga doyininke kuvhura kukarerapo nomora zimwe tupu
Kungungunyika sivaro soyininke dogoro ko 30 pokuyitura monompungi, kuyikonakona ntani kuyivara
Kudimburura mawapayiko/gonopatorona dokulisiga-siga doyininke kuvhura kukarerapo nomora zimwe tupu
Kupompeka
nokuhetakanesa
Simborongo Varongwa va hepa kuruganesa nonkango domuvaru dokupompeka nokuhetakanesa nonomora pagano nopahanguro lyewa
Matomporo: Murongwa kuvhura:
Matomporo: Murongwa kuvhura:
Matomporo: Murongwa kuvhura:
Kupompeka nokuhetakanesa yininke nononomora (elikwamo lyononomora) pokuruganesa nonkango: sinene kupita opo, sinunu kupita opo ntani sasa hetakana ko (sidimbwiliso ‘>’soyinzi kupita opo’<’ sinunu kupita opo kapi va si gweda mo
Kupompeka nokuhetakanesa nonomora kutunda 1-100 pokuruganesa nonkango; 4 yinzi-yinunu yahetakana yingapi, yinzi/ yinunu, sinene/sinunu ntani kulikida yidimbwiliso yinzi kupita opo yinunu kupita opo
Kupompeka nokuhetakanesa nonomora dogoro ko 500 pokuruganesa nonkango pauhunga; yinzi/unene sinene kupita opo sinunu kupita opo, sa hetakana ko demenena yidimbwiliso >sinene kupita < sinunu kupita opo
Kupompeka nonomora kutunda ko 1-20 kutunda kwezi zonunu
Kupompeka no kuhetakanesa kutunda kwa 1-100 pokuza
Kupompeka nonomora melikwamo kutunda kwa 1-500
14 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
dogoro zonene ntani pokuza komeho kutunda zonene yi ze kwezi zonunu ntani mokutunda komeho yi ze konyima, kutunda kwezi zonene yi ze zonunu ngwendi; tjanga nonomora edi kutunda kwezi zonunu yize kwezi zonene ntani kutunda kwezi zonene yi ze kwezi zonunu 11, 5, 12, no3
Kudimburura mavega goyininke kutunda kwesi “sokuhova (1) dogoro kwesi “soumurongo (10) ndi “sokuhova (10) dogoro soku “hulilira”
Kutumbura, kuresa nokuruganesa nonomora dokulikida mavega kutunda ko 1-20 melikwamo lyokuza komeho nokonyima ngwendi; komeho gokuhova (1) gouvali (2) goutatu (3) nangoso konyima gourozimwe (10) gouro nane (9)
komeho nokonyima ngwendi; tjanga nonomora edi melikwamo lyokuza komeho nokutengura konyima 48, 16, 92 ntani 61
Kudimburura mavega kutudna 1-20 kutumbura nokuresa nonomora dokulikida mavega melikwamo lyokuza komeho nokutengura konyima ngwendi; kuza komeho gouronazimwe, gouronambali, gouronantantu, nangoso kuza konyima 20, 19, 18
ngwendi; Tjanga nonomora edi melikwamo lyokuza komeho nokonyima 402, 284, 361 ntani 68
Kudimburura mavega kutunda 1-30 kutumbura nokuresa nonomora dokulikida mavega kuza komeho nokutengura konyima ngwendi; 20, 21, 22, nangoso 27, 26, 25
Kulikida nonomora Sitamborongo: Varongwa va heap kudimburura, kuresa nokutjanga nonomora
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Kuresa, kutumbura nokudimburura nonomora dogoro ko 100, pekarata lyononomora nopomusunda gononomora
Kusikura, kurundurura nokutjanga nonomora 0-20
Kuresa, kutumbura nokudimburura nonomora pekarata lyononomora nopomusunda gononomora dogoro ko 500 nokufwaturura konda zomavega gonomora
kutjanga nonomora 0-100
kuresa, kutumbura nokudimburura nonomora dogoro 1000 pekarata lyononomora nokufwaturura konda zomavega gononomora
Kutjanga nonomora 0-500
15 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kuresa madina gononomora dogoro komurongo (10) mononkango ngwendi; zimwe, mbali
Kunomena, kugwana nokudimburura yononomora momukunda gwawo, ngwendi; nonomora domatuwa, nonomora domambo
Kutjanga madina gononomora dogoro 10 mononkango ngwendi; ntantatu ntane rozimwe
Kunomena, kugwana nokudimburura yononomora domomukunda gwawo ngwendi; kusesupika mugenda, sivaro somatuwa nonomora do matuwa nomvhura dovanona
Kunomena, kugwana nokudimburura yononomora momukunda gwawo ngwendi; sinano, simbapira somukoso, siviha soyininke younzi weyi yemekende
Kuvalipika
nokuturaharufa
Sitamborongo Varongwa va heap kukwategano nompango dokuvalipika nokutura harufa nonomora
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Kuvalipika nonomora 1,2,3,4,5 no 10 pokuruganesa ndi pokupira kuruganesa yininke
Kuvalipika nonomora dogoro ko-50 ntani nonomora dapira epando dogoro ko 19 pokuruganesa ndi pokupira kuruganesa yininke ngwendi: tura harufa 44 ta zi kara 22 ntani tura harufa 19 tra zi kara 9 nosihupwe
Kuvalipika nonomora dogoro ko-100 kumwe noyihupwe ndi kwato yihupwe ngwendi; Harufa zo 36=15+3=18 )kwahana yihupwe) harufa 20-87= 40+3 nosihupwe 1=43 nosihupwe 1
Ezungururo (kuteza
nokutunga nonomora)
Sitamborongo Varongwa va hepa kukwategano mokuteta nokutunga nonomora nokudiworoka malikwatakano gonomora dogoro ko 20
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kutameka kudiworoka elikwatakano lyononomora dogoro ko 10 ngwedi
9=1+8;9=8+1,9-8= 1;9-1=8;9=2+7; nangoso
Kudiworoka elikwatakano lyononomora dogoro ko-10 usimbu ntani pauhunga
kutameka kudiworoka elikwatakano lyononomora dogoro ko 20
kudiworoka elikwatakano lyononomora dogoro ko-20 usimbu ntani pauhunga
Kuteta nokutunga nonomora mbali ndi ntatu mononzira dokulisiga-siga dogoro ko 500 pokuruganesa ndi kupira
16 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kuteta nokutunga nonomora mbali dogoro ko 99 pokuruganesa ndi pokupira kuruganesa yininke yokumoneka ngwendi; 25=20+5 ndi 15 +10 nangoso
27+6=33, 65-21=44
pokuruganesa yininke yokumonesa ngwendi;
154=100+50+4 154= 150+4 154= 100+54
Mulyo goMavega Sitamborongo Varongwa va heap kudimburura evega lyonomora nomulyo gevega
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kudimburura mononmora dombali dogoro ko 99 asi evega lyonomora kureta malisigo kounene wonomora ngwendi; 12 za lisiga no 21; pokugava nonomora 3 no 4 kuforoma nonomora mbali dononene unene ntani nomora
Kudimburura monomora dantatu dogoro ko 500, asi mavega gononomora kulikida unene wononomora ngwendi: Pokugava nonomora 3, 5 no 4 kuforoma nomora zantatu zonene unene nezi zonunu unene (543 ntani 345)
Kudimburura mononomora dantatu dogoro ko 1000, asi mavega gononomora mononomora kulikida unene wonomora ngwendi; pokugava nonomora 1, 8, no 4 kuforoma nomora zonene unene nezi zonunu unene
Zonunu unene (34 no 43)
Kudimburura mulyo gevega lyomafere, lyouro zimwe ntani lyozimwe mononomora dantatu ngwendi; Monomora 958 mulyo go -9 = 900, go 5 =50 go 8 =8
zononomora ntatu (841 no 148)
Kudimburura mulyo gevega lyefere, lyorozimwe ntani lyozimwe nonomora dantatu
Ehamesero ko Kuhorowora ndi kudimburura evhukiso lyopopepi noumurongo konomora vagava dogoro ko 100, pokuruganesa musunda gononomora ndi ekarata lyononomora ngwendi;
3330 38 40
Kuhamesera kopepi noumurongo hamesera kononomora adi haga no 1,2,3,4 ntani hamesera ko nonomora adi haga no 5, 6, 7, 8, 9 ngwendi;
62 kuzihamesera ko 60 75 kuzihamesera ko 80
17 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Nopatorona dononomora Sitamborongo Varongwa va hepa kudimburura nonomora dokupira kuhetakana nedi dokuhetakana/depando kutamununa nokusingonono elikwamo lyononomora
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kudimburura nonomora dokuvhura kuhangura momaruha gavali pahetakano, nonomora dokupira kuhangura momaruha gavali pahetakano melikwamo lyo 1-20
Kutamununa nokusingonona elikwamo lyonono kutunda 1-20 ngwendi:
Manesa 1, 3, 5….,….,…..,
Kumanesa nokusingonona elikwamo lyo ureru lyononomora kutunda 1-50 ngwendi; zwida mo nononomora di napili mo 20;……;….;23……;…….;26
Kumanesa nokusingonona elikwamo lyononomora melikwamo kutunda 1-100 ngwendi; tjanga nonomora dina pili mo 3, 6, 9, 12…..;…….;…..
Kumanesa nokusingonona elikwamogona lyononomora kutunda 1-100 ngwendi; zwida mo nonomora dina pili mo 50…..;….;….. 54;……;…….;…..;58
Kusingonona elikwamo ngwendi; Gweda kontantu (3) nkenye siruwo
Kusingonona elikwamo ngwendi; gava nonomora dokupira kuhetakana kutunda ko 21 dogoro 31 ndi tameka no-21 makura kutura turako 2 nkenye siruwo
Kupakerera nopatorona dononomora dokutunda kokutura kumwe nokugusamo malikwatakano gononomora ngwendi;
8+9=17 80+90=170
Kusingonona elikwamo lyevhukiso nantatu dogoro ko 66 ngwendi; (22 kugweda ko 3)
Kupakerera nopatorona donomora dokutunda ko kutura kumwe nokugusamo malikwatakano gononomora
Nonomora dokuhetakana/depando nedi dokupira
Sitamborongo Varongwa va hepa kudimburura nonomora dokuhetakana/depando nedi dokupira kuhetakana
Matomporo Matomporo Matomporo
18 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
kuhetakana Varongwa Kuvhura: Varongwa kuvhura: Varongwa Kuvhura:
Kulikida elihameno lyazimwe-nazimwe lyononomora kutunda 1 dogoro 10 mokukwategano mapongeko gokuhetakana (nondanda dokuhetakana kuninka nomuzumo dokuhetakana ano nonomora dokupira kuhetakana kuninka nomuzumo do kupira hetakana
Kudimburura nonomora dokupira kuhetakana nedi dokuhetakana kutunda ko 0 dogoro ko 99
Kudimburura nonomora asi nonomora dokupira kuhetakana kuhageka mo 1, 3, 6, 7, 9 (ngwendi; 57) ano nonomora dokuhetakan kuhagera mo 2, 4, 6, 8 (ngwendi 38)
Kudimburura nonomora dokupira kuhetakana nedi dokupira kuhetakan kutunda kutunda ko 0 dogoro 500
Kudimburura asi nonomora nonomora dokupira kuhetakana kuhagera mo 1, 3, 6, 7, ndi 9 (ngwendi 857) ano dokuhetakana kuhagera mo 0, 2, 4, 8 (ngwendi 638)
Kutura kumwe Sitamborongo Varongwa va hepa kukwategano magano gontateko zomuvaru mokufunda eturo kumwe zo ngendeso zonomora
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kutura kumwe nonomora mbali ndi ntatu no sigwanamo so pokatji ko0-20, pokuruganesa nonduganeso odo dina kukwama ko;
- Kuruganesa mafanondi yiruganeso yokumoneka
- Kuvara nayinye - Kuvara kutwikida pokuruganesa
ekarata lyonononora ndi pomusunda gononomorwa ndi
Kutura kumwe nonomora donomurongo dogoro ko 100
- kutura kumwe nomora zimwe
kononomora mbali momutwe (kapisi kutjanga)
Kutura kumwe nonomora mbali ndi kupita opo donokatji ko 0-100 momutwe ndi pokugenderera kutjanga pokuruganesa nonduganeso odo dina ku kwamako;
- Kutwikira kuvara (koyivaruro yeeyi ya liza yelike ngwendi; 28+3
- Kuvalipika nokutura harufa ngwendi; 30+40 = 30+30+10
- Kuruganesa no nomora dousili
Kutura kuwme nonomora do nomurongo dogoro ko 500 ngwendi; 120+30
- Kutura kumwe nonomora mbali dogoro ko 100 momutwe (kapisi kutjanga)
Kutura kumwe nonomora mbali ndi kupita opo dokulisiga-siga dopokatji ko 0-500
- Kutwikida ku vara (koyivaruro ya liza yelike ngwendi; (328+3)
- Kuvalipika nokutura harufa - Kuruganesa usili wononomora
dokudivikwa - Kuruganesa nontambo dokutura
kuwme do kulisiga-siga - Kuzungurura no kutunga
19 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
nkenye tupu nkedi ruganeso ngwendi; kutura nomora zo kuhova momutwe ntani kuruganesa nonyara mokutwikira kuvara
- Kutura nomora zonene zi kare zokuhova
- Kuvalipika nokutura harufa
Kutunga nokuzungurura nonomora sihonena;
- Manesa diagarama zokupupa no nomora dina pili mo
dokudivikwa - Kuruganesa no ntambo dokutura
kuwme dokulisiga-siga ngwendi 58+23=58+20+3=
78+3=81 - Kuzungurura nonomora
nokutunga nonomora ngwendi; 58+23=(50+20) + (8+3)=70+11=81 Sihonena so yiruganesa
nonomora - Kuruganesa mulyo gomavega
ngwendi; 342+185=(300+100) +(40+80) + (2+5) Sihonena soyiruganeso noyiviyauka
- Diagarama zoruha rwanavenye - Musunda gono nomora - musunda gononomora gokupira
nonomora sihonena; - Zwida mo nomora dina pili
Zwida mo nonomora dina pili mo moavega gosiporangwa gonontanto dononomora dogoro ko 20 ngwendi; 5+….=12
Ezoka lyononomora
Piramide zononomora
Noyiviyauka - Diagrama zo zoruha rwanarunye - Musunda gononomora gokupira
yuma - Ekarata lyononomora sihonena; - Zwida mo nonomora dina pili
momavega gosiporangwa gontanto zononomora dogoro ko 100 ngwendi; 15+…..=3
Momavega gosiporongwa gonontanto dononomora ngwendi; 130+…..=167
Kugusamo restitution Sitamborongo Varongwa va hepa kukwategano ntateko zomagano mokufunda eturokumwe nongendeso zonomora
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kugusamo nomora zimwe monomora nkwawo melikwamo lyo kutunda ko 1-20 pokuruganesa nonduganeso dina kukwamo
- Pakumana kugusapo yimwe makura kuvara yokuhupapo pokuruganesa yiruganeso yokumona ndi yipandayika
- Kuvara sinderenyima 19-17 - Kuvara kukandwisa pokuturako 2
Kugusamo nonomora dono murongo dogoro ko 100 ngwendi a 60-50
- Kugusamo nomora zimwe monomora nkwawo melikwawo kutunda 0-99 pokuruganesa nonduganeso dina kukwamako;
- Kuvara sinderenyima - kuvara kukandwisa nondanda
nomalisigo gomanunu ngwendi;
Kugusamo nkenye tupu nonomora mbali ndi nonomora ntatu monomora ntatu dopokatji ko 100-500
- Pakumona kugusa po makura kuvara yokuhupapo
- kuruganesa nonomora dousili dokudivikwa ngwendi; 3-2=1
- Kumanesa diagarama zo kupupa kuwme nonomora dina
20 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
kutunda 17-19 - Kuvara kukandwisa ngwendi a
yoyo 19-17, kuvara kukandwisa na mbali kutunda ko 17 dogoro 19
- Kuruganesa usili wononomora dokudivikwa ngwendi; 3-1=2
72-68 - Kuruganesa nonomora do usili
dokudivikwa - kuzungurura nokutunga
nonomora - Kuruganesa nontambo dokulisiga-
siga dokugusamo
pili mo - Kutwikakana mafano nonomora - Kuruganesa malikwatakano
gononomora - Musunda gononomora
gomawokowoko - Kugusamo nonomora ntatu ntani
nomora zimwe momutwe
Kuzungurura nokutunga sihonena soyiruganeso noyiviyauka
- Musunda gononomora - Ekarata lyononomora sihonena; - Manesa diagarama zokupupa
nonomora dina pili - Zwida mo nonomora dina pili
momavega go siporangwa gonontanto dononomora dogoro ko 20 ngwendi 16- ….=12
- Ezoka lyononomora - Piramide zono nomora
Hamesera egusomo kokutura kumwe ngwendi; 18-2=16 ntani 16+2=18
Ngwendi; 62-48=62-40-8 =22-8=14 Sihonena; soyi ruganeso noyi viyauka
- Kumanesa diagarama zokupupupa kumwe nonomora dinapili mo
- Ekarata lyononomora - Musunda gononomora - Musunda gononomora gokupira
nonomora - Ezoka lyononomora - Piramide zononomora
Kugusamo nomora zimwe tupu monomora mbali momutwe
Hamesera egusomo ko kuturako
- Kukonakona nopatorona donomora ngwendi; 100-37=63 200-37=163
Kukoneka nokuruganesa eturo kumwe lyoureru lyousili wokulihamena egusomo ngwendi; 20-2=18 16+2=20
Kugusamo nonomora donomurongo dogoro ko 500 ngwendi a 260-50
Evhukiso Sitamborongo Varongwa va hepa kukwategano ntateko zegano lyomuvaru mokufunda evhukiso kumwe nongendeso zonomora
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kuvara mono 2 dogoro ko 20 ano mono 5 dogoro ko 50, ntani mono 10 dogoro ko 100
Kuvara mono 2 dogoro ko 30, mono 4 dogoro ko 40, mono 5 dogoro ko 50, mono 10 dogoro ko 100
Kuvhukisa nkenye tupu nonomora da mbali na 2, 3, 4, 5 ntani 10 kumwe siretwapo sopokatji ko 100-500 pokuruganesa ezungururo ngwendi; 73÷4=(70x4) + 3x4
73 ÷ 4
21 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kuvara yininke yokumoneka mo nompungi da 2, 5 ntani no 10 ngwendi; 5+5+5 kugwana no 3 donozi ado kuna hetakana po 15
Kulikida asi evhukiso erugururo lyeturo kumwe lyono 2, 3, 4, 5, ntani no 10 ngwendi; maliya kugwana N$5.00 nkenye sivike, yingapi nga kara nayo konyima zoyivike 6? N$5+N$5+N$5+N$5+N$5+N$5 = 30
Kuvhukisa nkenye tupu nonomora dambali nankenye tupu nomora pokatji ko 1 dogoro 10 pokuruguruka eturo kumwe
Kufaneka nompungi doyininke nokuyereka sigwano pokuruguruka eturo kumwe (sidiviso sevhuki so nokusiruganesasi pontambo ezi) nani kuruganesa unzi wono 3 ndi no 2
Kutameka kudiworoka nokuruganesa yimpungu yo 1x, 2x, 5x ntani 10 pokuruganesa yidiviso yevhukiso
Ndi kuvalipika ngwendi; 73x6= 73+73+73+73+73+73
Kudiworoka usimbu ntani pauhunga yi mpungu yo 1, 2, 5 ntani 10
Kutameka kudiworoka nokuruganesa yimpungu yo 3 no 5
Egavero Sitamborongo Varongwa va hepa kukwategano ntateko magano gomuvaru mokufunda egavero nongendeso zonomora
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kuwapayika yininke monompungi dokuhetakana pokuruganesa yiruganeso yokumoneka nokuvara sivaro sonompungi
Kugwana ngendeseso zavene zokugaununa pahetakano pokatji kovahameni womombunga
- Kudana sidana sonkareso - Kurugana maudigu gosanseko - Kuruganesa mafano (sidiviso
segavero simpe nokusiruganesa
Kugwana ngendeseso zokuzegavero yininke monompungi da 2, 3, 4, 5, ntani 10 ndi kuligaununa yininke pahetakano pokatji kovahameni va 2, 3, 4, 5, ntani 10 pokudanauka sidana somaudigu, po kuruganesa
Kuruganesa sidiviso so (÷) nokurugana egaununo lyononomora dopokatji ko 10 no 100 nankenye nomora zopokatji ko 1-5 dokukara ndi do kupira kukara noyihupe pokurugurura egavero ndi ngendeseso zo peke
Kudimburura yihupe nokupira kuyipakera mbili ndi kuyigavera simpe kutwara moudigu pokuruganesa ngendeso
22 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
si pontambo ezi) ngwendi Martina kuna kara noyiapura 9 yiyo vana yi li gaununa nova kwawo va 3 pa hetakano yiapura yingapi ana gwana nkenye mukwawo zendi?
yiruganeso yokumonek, mafano ntani kutwikakano nonomoro (sidiviso segavero simpe nokusiruganesasi
zepongeko
Kuwapayika ndi kupongeka yininke dogoro ko 10 mono 2, 3, 4 ntani 5 noyihupe no kupira yihupe
Kuwapayika ndi kupongeka yininke mono 2, 3, 4, 5 ntani 10 noyihupe ntani nokupira yihupe yokupira kugaununa hena simpe (mamanya mabeli, nangoso ntani yihupe yokuvhura kugavera hena simpe (chokorade yikuki nangoso) kutwara mehano lyoudigu
Kudiworoka nokuruganesa usili wegavero lyoureru
Maudigu gonontambo donozi
Sitamborongo Varongwa va hepa kukohonona maudigu gonontambo donzi pokuruganesa ngendeseso, nduganeso, magano nongendeso panandunge
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kukohonona yivarero youketanga melikwamo lyo 0-100 kumwe neturoko negusomo ngwendi; 7+3-4 = □
Kukohonona yivarero youketanga melikwamo lyo 0-100 kumwe neturoko negusomo ngwendi a 23+45-31=□
Kukohonona yivarero yo uketanga melikwamo lyo 0-500pokuruganesa eturokumwe negusomo ngwendi 123+245-131=□
Yintau Sitamborongo Varongwa va hepa kukwtegano magano gomuvaru mokudimburura yintau
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kugaununa yininke momaruha gokuhetakan ngwendi; Teta siapura momaruha gavali gokuhetakana
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
po kuruganesa sihonena sa ngesi; Kutumbura maruha goyintau Kutumbura maruha goyi ntau
23 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
yanasinye (harufa, sosiune selike ngwendi Nasinye
Harufa Siune
Kudimburura noharufa noyiune pakana ntani moyidiviso yomuvaru
,
yanayinye ndi mpungi harufa, siune, siutatu, siutatu kosiune, nosiutatu selike)
Kutjanga yidiviso yoyintau mwanayinye nonoharufa yiune noyiutatu ngo unziwokuhamena mwnasinye nokulikida maruha gokuhetakana omu va si gavera sinaunye
Ekohononolyo Maudigu Sitamborongo Varongwa va hepa kukohonona maudigu gemesanseko gokuhamena nkenyezuva pokuruganesa eturo kumwe, egusomo, epongeko egavero nokuruganesa nduganeso panondunge
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kukohonona nokufwaturura maudigu gankenye ezuva melikwamo lyononomora 1-10
Kutjanga nonzira douhunga dokugwana ekohonono pokuruganesa yininke yokumoneka, kuliyonga/kuligaunwina magano, kugwana no patorone, kudana sidana nokutwikakana mafano, nodiagarama nonomora
Kukohonona nokufwaturura maudigu goyihorokwa yankenye zuva melikwamo lyononomora 1-50
Kutjanga nonzira douhunga dokugwana ekohonono pokuruganesa yininke yokumoneka, Kuliyonga/kuligaunwina magano, kugwana nopatorone, kudana sidana nokutwikakanamafano, nodiagrama nonomora
Kukohonona nokufwaturura maudigu goyihorokwa yankenye ezuva melikwamo lyononomora 1-100
Kutjanga nonzira douhunga dokugwana ekohonono pokuruganesa yininke yokumoneka, kuliyonga/kuligaunwina magano, kugwna nopatarone, kudana sidana nokutwikakana mafano, no diagrame nonomora
Kuruganesa ngendeseso nonduganeso zongwa zokukoho
Kuruganesa nonduganeso dokulisiga-siga dokukohonona
Kuruganesa nonduganeso dokulisiga-siga dokukohonona
24 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
nona maudigu melikwamo lyo 1-10 pokuruganesa eturo kumwe, egusomo, epongeko ndi egavero ngwendi; ame kani kere noyistrwaberi nokulyapo yitatu, makura yiyo kayi hupirepo yitano. Yingapi ka yi kere petameko
Kufwaturura ngendeseso vana ruganesa nokupurakena komafwatururo govarongwa va kwawo
maudigu melikwamo 1-50 pokuruganesa nonduganeso ne ngwendi; Kapa kere vanona ronantatu pokapitogona, ava ntazimwe kava kere vakadona Vamati va ngapi kava kere?
Kufutwatura ngendeseso vana ruganesa nokupurakena komafwatururo govarongwa vakwawo
Kuliyonga nongendeseso dokulisiga-siga domaudigu gokulifana
Kudimburura nokuwapeka mapuko
maudigu nokutjanga maudigu gemesanseko pokuruganesa nontanto melikwamo lyonono mora 1-100 pokuruganesa no nduganeso ne ngwendi; Tjanga maudigu gemesanseko yipo yi hetakane nonontanto dononomora
18-□=15
Elimbururo: Maliya kazigidire vakwawo 18 kokapitogona kendi ano 15 yiwokava wizire ko. Va
ngapi kava pilire kuwizako?
Kufwaturura nduganeso na ruganesa nokupurakena komafwatururo govarongwa vakwawo
Kuliyonga nongendeseso dokulisiga-siga do maudigu gokulifana
Kudimburura nokuwapeka mapuko
Unaure Sitamborongo
Varongwa va hepa kukwategano mulyo gokumeta maure ntani neturo lyalyo moyirugana yankenyezuva
Kugwana siruwo sokuteda, kufwaturura nokuruganesa emeto
Kugwana nondunge dokudimburura ehetekaneso
Kukulika egano neturo moyirugana emeto lyoyininke yankenyezuva
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kuhetakanesa yininke unaure gokulisiga-siga pokuruganesa nonkango douhunga sihonena;
Kupompeka no kuhetakanesa yininke pokuruganesa nonkango douhunga sihonena; kwa
Kuhetakanesa nokupompeka yininke pokuruganesa nonkango douhunga kwa
25 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
ure/usupi; ure unene kupita opo/usupi unene kupita opo; ure unene sili/ usupi unene sili; ure wokuhetakana/ ure ngwendi
Kumeta ure pokuruganesa uumwe wa hana kusingonona ngwendi; sinano sosikandeko, sikandeko, mulyato gompadi, sinano-ntambo nemeto lyokulisiga-siga tunda munona zende munona
hetakana, ure unene/ usupi unene; ure unene sili/usupi unene sili
Kuruganesa uumwe wokupira kusingonona ngwendi; ngodi ndi darate zokugotauka zokumetesa ure nounene wosikwarwarwa
Kuruganesa uumwe wonkarero wonosentimeta nokutjanga emeto pokuruganesa masupipiko; cm (pokuruganesa sitawiso sokukwateramo sonomereka do 1cm dokukulina pa da hana nonomora)
Kumeta nokuteda pauhunga ure wonobuke, yitafura nokutjanga (mono centimeta mwelike)
Kufaneka musunda gokuvhukilira momaure gonosentimeta vagava
hetakana ngwendi; ure unene/usupi unene kupita; ure unene sili/usupi unene sili (sinano pokatji)
Kuruganesa uumwe wonkarero wonometa nonosentimeta wokumetesa ure (sitawiso yiso simeteso somontenta nawa-nawa) no kutjanga emeto pokuruganesa masupipiko gouhunga; m, cm
Kuruganesa eturo kumwe negusomo lyoureru
Kumeta nokuteda pauhunga maure nomaunene nonomusika monda, nokomukunduruko gonkondwarongero nokutjanga (monosentimeta, nomonometa mwelike)
Kufaneka musunda gokuvhukilira momaure gonosentimeta va gava
Mukumo Sitamborongo Varongwa va hepa: Kukwategano mulyo gemeto lyomukumo nomu ava li ruganesa nkenyezuva Kugwana ruveze rokuteda, kufwaturura nokurugana emeto Kugwana egano lyewa nawa lyonondunge dokuhetakanesa
Kugwana egano neturo moyirugana emeto lyoyininke
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
26 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Pakumona kehetakaneso nomukumo doyininke pokukwaterera yininke nankenye kuwoko nokutara sosidigu po nesi sosirerupo ndi kuruganesa siviha sokukwatera mo ngwendi (kapstok)
Kuruganesa nonkango pauhunga ntene kuna kupompeka nokuhetakanesa ngwendi; ureru/udigu; ureru unene/udigu unene ntani; udigu wokulifana; udigu ngwendi
Pakumona kuhetakanesa mukumo goyininke yomukumo gono kirograma ½ neyi yomukumo gokirograma 1 pokukwaterera yininke ndi kuruganesa siviha sokukwateramo ngwendi siviha sehetakaneso
Kuruganesa nonkango pauhunga nokupompeka nokuhetakanesa yininke ngwendi; yokulifana; udigu/ureru; udigu unene/ureru unene; udigu unene sili/ureru unene sili
Kupompeka nokuhetakanesa yininke yitatu, kutwara mo-mukumo gevhuko nesesupo pokuruganesa siruganeso sokukwateramo ngwendi; kapstok
Kumeta yininke yankenye ezuva nokuteda pauhunga pokuruganesa nograma (g)
Kungungunyika yininke yankenye zuva pokuteda uhunga nopokuruganesa nongrama
Kuruganesa eraka lyonomukumo mouhunga pokupompeka nopokuhetakanesa ngwendi; udigu/ureru; udigu unene/ureru unene; udigu unene sili/ ureru unene sili
Kupompeka nokuhetakanesa yininke yitano kutwara mo mukumo gokuvhuka nogu gokusesupa
Kuruganesa uumwe wonkarero mokumeta nomukumo (grama, kirograma) nokutjanga mameto pokuruganesa masupipiko gouhunga (g/kg)
Unzi Sitamborongo Varongwa va hepa: Kukwategano mulyo gemeto lyoyiunzi neturo lyayo moyirugana yankenyezuva Kugwana siruwo sokuteda, kufwaturura nokuruganesa emeto Kugwana nondunge dokudimburura ehetakaneso Kukulika egano neturo moyirugana emeto lyoyinke yankenyezuva
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kupompeka no kuhetakanesa Kupompeka no kuhetakanesa Kupompeka nokuhetakanesa
27 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
yuma yokulisiga-siga (makende yipakote, yindorohwa nangoso) ku twara mevhuko nemesesupo
Kuruganesa nonkango douhunga ngwendi; kuzura/mwato; harufa zokuzura/harufa mwato; sivaro sokulifana unzi ngwendi yinzi/yinunu kupita opo
kuhetakanesa unzi woyipako yokulisiga-siga noyihwi nonoheteko dokulisiga-siga nokuditjanga
Kumeta nokuhetakanesa unzi wonomuzaro douumwe wokupira kusingonona
yininke yankenyezuva kutwara mounzi wayo
Kuruganesa nonkango douhunga ngwendi; yinzi; yinunuunzi ngwendi
Kumeta netedo pauhunga unzi woyininke yankenyezuva po kuruganesa uumwe wonkarero mokumeta (monolita)
Kungungunyika pakuteda pauhunga unzi woyininke ya nkenye ezuva pokuruganesa uumwe wonkarero mokumeta (momolita)
Kumeta nokutjanga unzi po kuruganesa esupipiko (l)
yininke yankenyezuva kutwara mo unzi wayo
Kuruganes nonkango douhunga ngwendi a yinzi/yinunu, yinzi ngwendi ruvali, ngwendi unzi ngwendi unzi pwarutatu, ngwendi harufa zoko
Kumeta netedo pauhunga unzi woyininke yankenyezuva pokuruganesa uumwe wonkarero mokumeta (monomililita)
Kungungunyika pokuteda pauhunga unzi woyininke yankenyezuva pokuruganesa uumwe wonkarero wokumeta (monolita nonomililita)
Kumeta nokutjanga unzi pokuruganesa esupipiko (l)
Ruha Sitamborongo Varongwa va hepa: Kukwategano negano lyoruha neturo moyirugana rwalyo yankenyezuva Kugwana siruwo sokuteda, kufwaturura nokuruganesa emeto Kugwana nondunge dokudimburura ehetakaneso
Kukulika egano neturo moyirugana emeto lyoyininke
Kuhamesera ruha kontunda monda zomurudi pokumeta hararasi yihwi pokuruganesa uumwe va pira kusingonona ngwendi; Gava sivaro
Hamesera ruha kontunda monda zomurudi pokumeta hararasi yihwi pokuruganesa uumwe va pira kusingonona ngwendi; kumeta pontunda zombanga
28 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
somaruswiko gekendegona fire monda zosihwi
Kuhetakanesa hararasi maruha goyihwi pokuruganesa uumwe va pira kusingonona ngwendi; sikandeko, nomulyato donompadi, kuteta mapepa
nepepa lyo A4 pokuvara sivaro somapepa
Kuhetakanesa maruha goyihwi yokulisiga-siga pokuruganesa yikwambando nokuvara sivaro soyikwambando mokugwana ruha
Ruveze Sitamborongo Varongwa va hepa kukwategano nokuruganesa ruveze pauhunga
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kulyonga yiviyauka yemembo neyi yomomukunda yankenyezuva kutwara moruveze rwemezuva, mokuhetakanesa noyihorokwa yemezuva, yomasiku, yongurangura neyiyongurova neyi yomasiku
Kutumbura mazuva gomosivike nomakwedi gomomvhura melikwamo lyouhunga
kuhetakanesa yiruwo yo”yire” ntani yoyi “supi” ngwendi; Kuna kwata siruwo sosire mo kudika embo, ruveze ropause rusupi
Kuhamesera yihorokwa yankenyezuva yembo neyi yomomukundakomaruveze, mazuva nonkwedi
Kutumbura mazuva gomosivike nomakwedi gomomvhura melikwamo lyouhunga
Kuruganesa kalinda pokudimburura mauzera aga va tamba gokuhamena mazuva ngwendi kupapara ezuva lyehampuruko lyaguwme mosivike
Kuhamesera yihorokwa yemembo neyi yomomukunda komaruveze, mazuva nomakwendi
Kutumbura mazuva gomosivike nomakwedi gomomvhura melikwamo lyouhunga
Kuyereka ure woyihorokwa monovili, momazuva ntani monomvhura pokuruganesa musunda go ruveze
Kuruganesa nonkango mouhunga ngwendi; ruveze rorure/rorusupi, mutenya/masiku, nkera/naina/mungura/ngurangura/ ngurova / masiku
Kudimburura woyihorokwa ya divikwa nawa ngwendi; ose kukara novili ne kosure nkenyezuva, sivike kupwa momazuva 7
Kuyereka woyihorokwa monovili, mazuva, mvhura pokuruganesa musunda goruveze
29 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kutanta ruveze nawa-nawa monovili nomo noharufa donovili dopampo
Kutanta ruveze monovili nomonoharufa donovili, (nomunute ronantanto dina pitiko kovili ntani nomunute ronantano dina hupuko zi toone vili) ntani nomunute dopavili zopampo ngwendi faneka kuwoko povili zi likide 4:15
Yimaliva Sitamborongo Varongwa va hepa kukwategano omu noruganesa yimaliva yaNamibia
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kutumbura nokudimburura mulyo gokulisiga-siga goyimaliva yoyitenda pokudimburura 5c, 10c, 50c, N$1 ntani N$5 nokuliyonga yimoneka yayo ngwendi; nomora, yidiviso, ruvara nomulyo
Kuhorowora muzumo goyimaliva yoyitenda yokuhetakana mulyo koyimaliva yikwawo yoyitenda
Kutumbura nokudimburura yimaliva nayinye yoyitenda ntani mafo go N$10 naga go N$20 nokuliyonga mulyo gwayo noyidiviso yokuyihamena
Kutura nosenda monodora ndi kusinta ngwendi 200c = N$2 (evhukiso lyo 100c lyelike)
Kuhorowora muzumo goyimaliva yoyitenda yokulisiga-siga yokusika ko N$5 eyi nava tura kumwe dogoro komukoso ogo vana tumbura ngwendi;
N$1,10 = 50c +50c+10c ndi
Kutumbura nokudimburura yimaliva yoyitenda nayinye ntani nomafo go N$10 no N$20 nokuliyonga mulyo gwayo noyidiviso yokuyihamena
Kutura nosenda monodora ndi kusinta ngwendi 265c = N$2.65
Kuhorowora muzumo goyimaliva yoyitenda yokulisiga-siga yokusika ko N$5 eyi nava tura kumwe dogoro komukoso vana tumbura ngwendi; N$1.10 = 50c + 50c + 10c
Ndi N$1.10= N$1+10
Kulikida erando nelirandeso lyo yininke noyimaliva yokudanesa, kuvara yimaliva nokugava tjindji zoko N$5 (tjindji zi kare
N$1.10 = 1+10c
Kulikida erando nelirandeso lyo yininke dogoro N$20 noyimailva yokudanesa nokuvara yimaliva notjindji mo uhunga
Kulikida erando nelirandeso lyo yininke yokusika ko N$50 zoyimaliva yokudanesa nokuvara yimaliva notjindji
30 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
monosenda ndi monodora, kapisi nayinye)
Kuruganesa tjindji zoyitenda dogoro koN$10. Ngwendi; Estera kuna mukosere N$11.50 pokuranda yikwa enyango. Age kuna yi futu nefo lyonodora N$20 age kuna rugana tjindji pokutura kumwe N$11.50 dogoro kugwana N$20: N$11.50+N$5+N$250c = N$20
Kutura elikwamo lyoyininke yokukaranda no kulikida mukoso gokungungunyika, nokukonakona mukoso moyitora
mouhunga
Kurugana tjindji zomafo nezi zoyi tenda dogoro ko N$20 ngwendi; Paurusa kuna kuranda nondya do N$837 yiyo ana di futu no N$50 zomafo. Ta rugana nye sivaro sotjindji pokugwederera ko N$37 dogoro yi sike ko N$50: N$37 + N$10+N$2+N$1 = N$50
Kutura elikwamo lyoyininke yokukaranda no kulikida mukoso gokungungunyika, nokukakonakono mukoso moyitora
Pausimbu kungungunyika mukoso goyininke yivali ngwendi; Sivaro sokungungunyika so N$6.90+N$4.20+7.00+4.00 = N$ 11.00
Yifano Yerongo heteko Sitamborongo: Varongwa va hepa: kudimburura, kutumbura nokupapara maukaro goyifano yoyiha yivali (2D) ney yayitatu (3D)
Matomporo Varongwa Kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa Kuvhura:
Kudimburura nokutumbura yifano yoyiha yivali nayinye: Sikwambando, sikwamusere, ikwarwarwa ne kovhutatu
Kudimburura nokutumbura yifano yoyiha yivali; sikwamusere, ekovhutatu ekovhutatu lyoku lyakana sikwa-euta
Kudimburura nokutumbura yifano yoyiha yayivali, sikwambando, sikwamusere, sikwarwarwa, ekovhutatu, ekovhutatu lyokulyalyakana, sikwa-euta pedagoni
31 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kugwana nokudimburura yininke yomomukunda
Kuhangura no kugaununa yifano/yihwi (ngwendi keguru) Kutwara momaukaro gayo; ruvara, nomora, sihwi nomaruha gomanzi
Kufaneka /kurugana yifano nonomukaro dayo pokuruganesa no nkango ngwe.a kufaneka/kurugana sikwarwarwa kumwe nomaruha gavali gomasupi ntani gavali gomare nomaruha gavali gokuvyukulira va twikira yikare yibono yine
Kugwana nokudimburura yininke yomo mukunda
Kuhangura nokugaununa yifano/yihwi yokulisiga-siga (yikwambando, yikwamusere, makovhutatu quadilaterale, patagoni, hexagoni octagoni kutwara moyimoneka yayo yerongoheteko; sivaro somaruha sivaro soyibono (momaure) ntumbwiso kapi zina kara hepero va zi dive varongwa ntumbwiso; pedagoni, hexagoni no octogoni
Kufaneka/ kurugana yifano pokulikida mulyo gokuhamena yidiviso ngwendi; kufaneka sikwa euta sokuvhura kudimburura sokufana ngwendi euta sokuvhura kudimburura ngwendi, kufaneka/kurugana ekovhutatu lyalyakana lyokuvhura kudimburura kumwe nonomusunda ntatu dokuvyuka dokulifana hambara moure, nomora zokulifana moyibono/makovhuntatu gokuvhuka gokulifana hambara moure,nonomora dokulifana moyibono/makovhu
Kuhangura nokugaununa yifano, yihwi yokulisiga-siga (quadrilateral, pedagoni, hexagoni, octogoni kutwara moyimonekwa yoyifano/yihwi yayo; sivaro somaruha, sivaro somaure, sivaro somusika, sivaro soyibono, sivaro soyibono youhunga kapi yina kara hepero varongwa va dive nontumbwiso, hexagon na octagoni
Kufaneka/kurugana yifano pokulikida mulyo gokuhamena yi diviso ngwendi.a. Nungakana tutji/tuhatji tokulifana moure yipo yifane pentangoni, zokuvhura kudimburura
Kudimburura makovhu gouhunga, nokuruganesa yiruganeso eyi va likida (sibono somapepa, sitika sonopatorona) mokudimburura makovhu moyifano ngwendi sinene kupitapo, kwa hetakana ndi sinunu kupita ekovhu lyouhunga
32 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
Kupapara ntateko zoyifano yoyiha yivali ngwendi sikwambando ntani sikwamarwarwa, kutwara moyimoneka yayo yokulifana
Kutota mafano nonopatorona kumwe noyifano
Kudimburura no kutumbura yifano yoyiha yitatu nayinye; sikweguni, sikwarwarwa soprisima kapundi nokone
Kuhangura nokugaununa yifano yoyiha yitatu (moomu ya kara keguru) kutwara monomukaro dayo ngwendi; yokusindumuka ndi kuseneta yokupongeka nokudira kusigamo ndi kusigamo evega mokatji
Kusingonona yininke nayinye pokuruganesa nonkango ngwendi
Kutota mafano nonopatorona kumwe noyifano
Kudimburura nokutumbura yifano yoyiha yitatu; sikweguni, kapundi, kone, sikwetenga, cuboid, (sikwarwarwa soprisima)
kuhangura no kugaununa (ngwendi: keguru) kutwara moyimonekwa yemerongo heteko lyoyifano ngwendi; kupenga ndi yipara yokuzaramo; yihwi yoyipapara ntani ntene yipara yokuzarama, sivaro soyi para
kusingonona yininke nayinye pokuruganesa nonkango ngwendi
(Pokugonya yifano yokulifana gosikwarwarwa kwa lifana
Kutota mafano nonopatorona kumwe noyifano rambangako nontateko zoyifano yoyiha yivali
Kudimburura nokutumbura yifano yoyiha yitatu nayinye; sikweguni, kone, sikwarwarwa soprisima, sipiramide, ekovhu tatu lyoprisima ntani kukonakona yimonekwalyayo ngwendi; sipara sondopi kwafana sikwarwarwa, sikweguni, kuvhura kusindumuka
Kuhangura nokugaununa (ngwendi keguru) kutwara moyimonekwa yemerongoheteko lyoyifano ngwendi; kouhura, somusika sokupenga ndi sipara sokuzarama, sivaro soyipara
Musunda getetokatji
33 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
mauhura, yibono, yipara kuvyuka, kupenga ntani kuzarama
mauhura, yibono, yipara, kuvyuka, kupenga, kuzarama, kuliudinga, sikwarwarwa, sikwayihatatu, hambara sikwamusere
kusingonona yininke nayinye pokuruganesa nonkango ngwendi; mauhura, yibono, yipara, kuvyuka, kupenga, kuzarama, hambara sikwarwarwa, hambara sikwamuse
Kutota yihoneneso yamwene
Kutota yihoneneso yamwene
Kutota yifano yoyihayitatu yokutunda komapepa ntani keruguruko lyoyiruganeso
Kutota yifano yoyihatayitatu yokutunda komapepa ntani
keruguruko lyoyiruganeso
Kusingonona yininke nayinye pokuruganesa nonkango ngwendi; mauhura, yibono, yipara, kuvyuka, kupenga, kuzarama, hambara sikwarwarwa, hambara sikwamusere
Kutotapo yihoneso neyokutunda komapepa ntani keruguruko lyoyiruganeso ngwendi; yipakote,
Yitji no yiplastika
Evega mukaro neLigumaguro lyoyinke
Sitamborongo Varongwa va hepa kudimburura evega, mukaro ntani maligumaguro goyininke
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Kusingonona elitundakano lyo yininke novantu pokuruganesa eraka lyomavega nomavyukiso ngwendi: keguru, pevhu, kontunda, konhi, konyima, ponze, monda, kwama ko, pokatji
Kusingonona evega lyoyininke eyi va faneka ponokarata dokulituntika ngwendi: pokarata zomosure zetu, Mbanga zange kwa karera korumoho
Kutura nokusingonona mavyukiso gokulisiga-siga malitundakano gonomukaro doyininke va faneka ponokarata domavega gadivikwa ngwendi; pokarata Sokudanena; sitji sosinene kwa kara konyima zorunone romema; Nkondwarongerero kwa karera korumoho kutunda
34 NIED Syllabus: Mathmatics Junior Primary Phase 2014
SIPARATJANGWA HARADE 1 HARADE 2 HARADE 3
kositji
Grafikafano sitafura grafika zokulironda
Sitamborongo Varongwa va hepa; kupongeka, kuwapayika, kulikida nokutara mauzera
Matomporo: Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Matomporo Varongwa kuvhura:
Kugaununa yininke mono muhanguro nokutumbura nkenye muzumo ngwendi; matuwa, matoroka nangoso
Kupongayika mauzera gosuma pauhunga ngwendi; sivaro ntani marudi goyiligusisomukuma yokulisiga-siga yovarongwa, kuyiwapayika nokuyitura po grafikafano
Kutoroka yigava nokugwana mauzera nokuliyonga yigwana ngwendi; kutara kografikafano, varongwa vangapi vana kudana mbara zokusanga
Kuruganesa uumwe wokupira kusingonona ngwendi; maruswiko gomakende nokutjanga yitundwamo pografikafano
Kupongayika kuwapayika nokulikida mauzera pauhunga ngwendi; marudi genyango noyikwehidi pografikafano
Kutokoroka no kuhangura yigwana mokugwana mauzera aga vana tamba ngwendi; kutara kografikafano nokutanta asi varongwa va ngapi ka va lire siapura?
Kupongayika, kuwapayika nokulikida mauzera gosuma pauhunga ngwendi; sivaro nomarudi goyidira atu gwana momukunda pokuruganesa, yitafura, nografikafano nonografika dokulirondanga
Kutoroka nokuhangura yigwana mokugwana mauzera aga vana tamba nokuliyonga yitundwamo ngwendi; kutara kongrafika zokulironda nokutanta asi yidira yi ngapi katu gwene?
Kuruganesa nonkango dokugava mauzera ntene tava hangura nografika ngwendi; yinunu, yinzi, nkenyepa, kumoneka, nayinye, kuvhura, esesupo, pakarerero
35 NIED Syllabus: Mathmatics Junior Primary Phase 2014
10. Ngendesokonakono
Mokugwana nawa-nawa elikwamo lyelirongo lyokusikiliramo pantambo zomatomporo gokulisiga-siga gomukaro gekonakono-twikido kuna kara nohepero moNtambo zoPilimere zepevhu, mokugava efano lyokusikuliramo lyerunduruko nesikisomo lyomurongwa. Ekonakono-twikido li kare ta zuvhika nawa, ure ntani kuliruganesa noureru, alyo lya demenena ponompango neliyombereso lyomurongwa pwamwene. Matomporo gomelikwamo lyelirongo kulikida ekwategano nomaukonentu aga murongwa na vhura kulikida, ago yigo hena nava vhura kumukonakona. Nampili ngoso, egano lyelikwamo lyelirongo lyokutwaredera kelirongo kapisi lyokutwaredera kekonakono.
10.1 Yitambo yeKonakono
Sitambo somakonakono sokugwana mauzera gousili nomauzera gomulyo goyirugana yo murongwa momatomporo. Mauzera ga ngesi ngava ga ruganesa pokugava yitundwamo yovarongwa komasikisomo noku vana kupira kusikisamo, oku vana kurugana nawa, noku vana hepa mbatero zewapukururo. Va kurona va hepa kugwana mauzera nkenyapa kezo komeho lyovana wawo kupitira momatjangwa goposure. Kuva korangeda va gave nomfeto nevatero kovarongwa merongo Ekonakono-twikido kuvatera hena varongi va wapukurure ndongeseso zawo nokugava ehorokorongo lyewa kovarongwa. Edemeneno li kare ekonakono lyelirongo kapisi ekonakono morwa elirongo. Ose kukonakona tugwane efano lyousili lyomasikisomo lyankenye murongwa lyomatomporo yipo li gave mbatero kerongo nelirongo lyokomeho pokurugana erongovatero nokukonakona ezokomeho lyongendesorongo zanyamwetu.
10.2 Marudi goNgendesokonakono
Murongi ga hepa kukonakona nkenye murongwa omu ana fundu nawa matomporo vasingonona melikwamo lyelirongo ya ngesi kugava efano lyomurongwa lyerunduruko momunene hena, ya ngesi kuvhura kuyirugana ponkendi zokuwiza po tupu, pokunomena erunduruko lyomurongwa melirongo nopoyiruwo yokuliyomberesa awo kuna kukonakona kufwaturura yininke ya kara po noku noyigwana, pokuruganesa nondunge, magwanekero, nompanguro domulyo, yimo tupu nomomalihamesero vene mwanayinye. Eyi kuna kutanta asi ose kunomena yirugana yomurongwa nositambo sekonakono moomu tuna kuronga, yimonokutura patjangwa eyi tuna kumona. Varongi, kunomena varongwa navenye moyiruwo yoyirongwa yomuvaru. Apa yipo ava dimbwilire asi yilye ogu ana kufirasinka na yilye ana kupira kuyipakera sinka, yilye ana kuvhura kurugana pwamwene gelike, na yilye ana kukondjangana pokurugana gelike. Pokupura mapuro awo kudidilika ogu ana kwategano magano gomuvaru na yilye ana pili kuyikwategano. Pokutarera yiviyauka, awo kunomena ogu ana kutjiura yirugana nokuruganesa nondunge domuvaru, na yilye ana pili kuyininka ngoso. Kutarera hena ekaramo, hamesero mo negwederereko koyirugana yomombunga. Ngendeso zekonakono lyakarapo: Eyi kuna tamba etulisopo siruwo sekonakono ngwendi mapuragero, makonakono gomasupi noyipeparuganeno (pakara mapuro noyiruganoyombereso). Yipepa ruganeno mulyo unene morwa kuvhura kuyiruganesa kositafuratjango ndi posipepa. Kuna kara mulyo unene asi varongi va wapayike nokutura mafanayiko yipo va konakone varongwa nokugava yitwa 10. Eruganeso lyomakonakono gokutjanga nopakana aga ga kara po kuga konakona melikwamo va yereka lyomatomporo, makura nokuvhurasi ga guse siruwo sosire. Va hepa
36 NIED Syllabus: Mathmatics Junior Primary Phase 2014
kurugana makonakono gomasupi gomuvaru moruha ronoperiode domuvaru ntani va ga mone asi yirugana yomoperiode domomuvaru
10.3 Masingonono goHarade
Ntambo zomasikisomo zomurongwa momalitundakano nomatomporo gemelikwamo lyelirongo lyomuvaru kwa ga likida monoHarade donondanda Ntene vana gava noHarade donondanda yina kara, mulyo asi yi likide ntambo zousili zomasikisomo gomurongwa zomalitundakano nomatomporo. Mo Harade 1 dogoro 3, noHarade dononda nda kwa di hamesera ko sihetekeso so yirugana yoyitwa ntazimwe malitundakano pokatji konoHarade nomatomporo aga va gava va galikida konhi.
Harade % Kutunda
(etwikiromo) 1-12
Esingonono lyetomporo
A 80%+ Kwa sikisamo matomporo nawa mokupitakanena. Murongwa kwa manamo unene momaruha nagenye goamtomporo
B 70-79 %
Kwa sikisamo matomporo nawa unene. Murongwa kwa sikisamo momu nene keguru lyoyihepwa younakatji ntani kwa sikisamo peguru lyosinzi somaruha getompororo
C 60-69 Kwa sikisamo matomporo nawa. Murongwa kwa sikisamo matomporo pakupanda moukaro wahana kudivikwa nokuya hamena
D 50-59%
Kwa sikisamo matomporo pakupanda. Murongwa kwa sikisamo mokuliza noyihepwa youkatji. Murongwa kuvhura a kare nohepero zombatero zelirongo momaruha gamwe
E 40-49%
Kwa sikisamo mousesu wounzi womatomporo pagazaro asi kuvhura kurugana yirugana yoyiwa. Murongwa kuvhura a pire kusikisamo matomporo nagenye, nye esikisomo lyo murongwa yina gwanene kupita ntambo zousesu zomatomporo. Murongwa kuna hepa mbatero zelirongo momaruha nagenye
U 0-39%
Kwato harade, murongwa nokuvhurasi kusika pontambo zopausesu zetomporo, nampili a gwane mbatero zelirongo lyenene komurongi. Murorongwa kuna manamo mokugwana mbatero zelirongo
10.4 Mavyukiso momunene gekonakono-twikido (yoyinzi kuyigwana moNtamo
zoPilimere zePevhu Mpango zeVyukiso zoSirongo)
Ekonakono lya hepa kukara moruha romafanayiko gosirongwa ntani lya hepa ku kara nomukaro guna zere. Mosiruwo soyirongwa, ntani ntene varongwa kuna kurugana yirugana yomonkondwarongero, murongi ta rugana ekonakono – twikido lyokulituntika neli lya kara po momatomporo nagenye gokulisiga-siga momaukonentu goyirongwa nayinye. Montambo zoPilimere zepevhu ekonakono kwa kara nonzira zelikido egawo yitwa komasikisomo. Eyi kuna kutanta asi ntene yitwa ndi noharade donononda tava di gava, ya kara mulyo asi di likide ntambo zousili zomasikisomo gomurongwa momalitundakano nomatomporo.
37 NIED Syllabus: Mathmatics Junior Primary Phase 2014
10.4.1 Ekonakono Twikido lyeLituntiko
Ekonakono – twikido lyelituntiko kulirugana menomeno, pakotoko nokudidilika patjangwa (tara sihonena po 10.4.3). Eyi kuna kutanta ntene varongwa kuna kurugana yirugana yomosirongwa, murongi kudidilika pomukweyo gomadina gomosure yokuhamena masikisomo ndi maudigu. Madidiliko ndi makumbururo ga ngesi nga ga vyukisa mafanayiko goyirongwa yokomeho, noyi hepwa yevatero elirongo, ntani mokugava yitwa yekonakono-twikido lya karapo kapi yina kiara nomulyo gokutjanga makumbururo ndi madidiliko gankenye etomporo, nye kandomo tupu vana hepako ka likide asi murongwa ana sikisamo ukonentu. Nampili ngoso umbangi wopatjanga simpe una kara nohepero ntene murongwa kuna kukondjagana oku age ana hepa mbatero simpe.
10.4.2 Ekonakono –twikido lyakarapo
Ekonakono-twikido lyakarapo unene po kulirugana ntene kuna gozo suma ndi unene po ntene egano lina hepa ekonakono komeho vaka tameke negano lyepe. Varongi kuvhura pamwe kugava makonakono gomasupi ndi gopakana ndi mapuragero va hanesa mwaza sinano. Makonda zeyi murongi ta gava yitwa 10. Kutwara momakonakono gomanzi va rugana mosinano, limwe tupu lyomakonakono aga karapo yilyo, lyokutura patjangwa. Ekonakono lyangesi kulirugana mosiruwo sonoperiode da karapo. Kuna kutanta asi kutupu varongwa wontambo zoPilimere zePevhu woHarade 1 dorogro 3 ngava vhura kara sivike nasinye nomakonakono ndi elikwamo lyomakonakono omu ngava kara tava lirongere makonakono. Yitwa yomakonakono ga karapo kuyitura patjangwa po nontjango foroma dekonakono –twikido. Kouhura wosinano, yitwa yankenye sirongwa kuyi tura kumwe momukweyo gosigwano. Unakatji kuna kara sivaruro soyigwanamo yoyitwa va gavere nounzi wo makonokono ga kara po aga va gava, sintau sodesimare naso kusilikida ngwendi 3.2. Yitwa younakatji kuyi hamesera nokuyisinta monoHarade ngwendi moomu vana yi likida mo 10.3
38 NIED Syllabus: Mathmatics Junior Primary Phase 2014
Muzaro gonoNkango
(Mulyo unene): Etanto lyononkango edi vana gava omu ku rugana tupu kononkango
domoyikara mo yomongendeseso ezi mwelike kapisi hepero koyikaramo yopeke.
Ehanguro: Kukwata egano suma po kusigaununa momaruha Ekovhu: Sihwi esi ava ninki nsene no musunda mbali dokuvyuka
tadi ligwanekere ndi tadi ligwanekere ndi tadi livindakana pokudiheteka momavaru.
Ruha: Unene wosivaro sevega ou wakudumika rumbandingwa
rwe vega ndi sihwi Unandunge: Kwa hamena koundunge (ukonentu) Matomporo: Mahetaiko gomaunongo aga ava pakere po mbili asi yigo
po gohepero yipo va rugane sirugana ndi vasikisemo nkarero zosirugana
Egano: Egano lyo panayinye lyosuma esi sakara po Kusupipika nonkango: Pausupi hena pavhuliko kugava mapukururo gomanzi
mononkango dononsupi Ekonakono twikido: Mahetaiko gezokomeho lyovarongwa kukwama
koyirugana yawo, eyi ava rugana monda zonkondwa rongero ndi ekonakonogona ndi mapuragero aga ava rugana mwaza sinema ndi elima, kupitakana yemekonakono lyoparumwe tupu.
Mulyo gonkarero wapero: Yuma yahamena kediwo maunongo, magano no mulyo ogu
nava vhura kuruganesa moyirongwa yokupita pasimwe ndi komaruha gelirongo
Malisiga-sigo (gopamuhoko): Malisigo gopamuhoko nahena nopo yikweparu
pankarapamwe nomalisigo goparudivarwa, mombunga, monkarapamwe ndi mevegarongero
Sihwi sokuhetakana: Sihwi sokuhetakan esi somakovhutatu maruha gaso
nagenye gahetakan monaure Engunguniko: Kugazara nawa papumbo ndi evaruro lyopangederera lyo
unzi Sevhumudima: Ezarararo lyouzuni lyo kuliza kumwe nekuliko ngo
yitundwamo yewapukururo ediwo yirugana youkonentu nomagwanekero pamwe ayo kukahagera mezumbaneso yidimbwililiso yopampo pamundinda
Makovhu Ntanzimwe: Sihwi sokuhetakana so maruha ntazimwe aga
gahetakana moure Erongo pakerero: Sirugana sokuhamesera mo nkenye gumwe
39 NIED Syllabus: Mathmatics Junior Primary Phase 2014
Mulyo Gwelirongo: Esingonono lyeyi va tjanga eyi varongwa nava vhura
kudiva neyi nava vhura kurugana ngo yitundwamo yerongo lyawo kehagero lyosinano soruveze sihonena; kehagero lyoPilimere zepevhu. Ayo kuyitumbura hena asi “Mulyo goyikaramo”. Mulyo gwelirongo kusingonona eyi varongi nava vhura kuronga neyi varongwa nava vhura kulironga.
No sure dakarapo: Nosure edi momunene adi sikisa mo yihepwa
yovarongawa ava vapira kukara noyihepwa yerongo lyosipesiyare (lyokulikerera). Nkenye sure ezi za pira kukara asi sure zokulikerera (sipesiyare)
Elitjangero lyopagwanekero gumwe nagumwe: Ehetakaneso lyozimwe ntani nomora zimwe tupu
mononkango kwa nkenye suma semepongeko. Makovhu Ntantatu: Sihwi somaruha ntantatu gohetakana (sihwi sankenye
apa) kana mo naure) Nonomora dondikido evega: Nomora ngamoomu ngwendi zokuhova ndi zauvali ezi azi
likida mukaro gonomora melikameno Mulyo gwevega: Mulyo gonomora agu va yerekera komukaro gwazo mono
nomora sihonena; monomora 567, ezi nomora 7 kuna kara sidiviso sono zimwe 5 ezi 6 sidiviso sonomurongo ano ezi 5 sidiviso somafere
Makovhugatano: Sihwi somakovhu (maruha) gatano omu
gahetakan makovhu aga nagenye sikwarwarwa ga hetakana monaure wago.
Ngendeseso Nkondopeko: Ngendeseso zoku nkondopeka elirongo Ekovhu: Ekovhu lyonompani 90 Elikwamo lyelirongikidoLyewapayikiro: Elikwamo va tulirapo po varongwa woHarade 1
womoNamibia medimbururo lyousili asi varongwa wovanzi kapi va gwana eliwapayikiro sure komeho zokutameka sure. Alyo kwa liyereka li vatere varongwa va kara nekwato egano lyomaunongo aga ga kara nohepero momunene/kelirongo lyakara po
Elikwamo lyo yihorokwa (nonomora) Omu ayi likwama tunda simwe zende simwe monkedi
zelikwatakano Malikaro goyininke: Kuhamena kevega Sihwi sokuliudinga: Sininke ndi sihwi so maruha ga 3 esi sa kara noyimoneka
ngwendi mbara (mulyo unene sihwi kwa lifana kumwe napa)
Kangungunika: Kudimburura sivaro soyininke mepongeko ya hana
kuyivara
40 NIED Syllabus: Mathmatics Junior Primary Phase 2014
Ngendeseso gwanekedeso: Egwanekero egano lyokulifana ndi suma momaruha gosirongwa peke
Sihwi soyihatatu: Sininke esi sakara no musika, sazara-rara nosinko nga
moomu nkenye sininke omu mouzuni Sihwi soyihatatu (gatatu 3) Sininke esi sa kara nomusika nosinko ngamoomu nkenye
sininke mouzuni omu Vili zopampo: Vili zakara nonomora nokuwoko Sihwi soyihavali (ga 2): Sihwi esi sakara nomaruha gavali tupu (nga moomu
kuzararara no musika) nye sahana karampu. Nondung gwanekero: Nondungu apa daligwanekerera nonzira mbali di tunge
ekovhu.
The National Institute for Educational Development
Private Bag 2034
Okahandja
NAMIBIA
Telephone: +64 62 509000
Facsimile: +64 62 509033
E-mail: [email protected]
Website: http://www.nied.edu.na
© NIED 2014