REPUBLIC OF NAMIBIA
MINISTRY OF EDUCATION
JUNIOR PRIMARY PHASE
MATHEMATICS SYLLABUS
GRADE 1 – 3
RUMANYO VERSION
FOR IMPLEMENTATION: 2015
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
LIKUKWAMO LYAUKALIMO (TABLE OF CONTENTS)
1. LITWAROMO ................................................................................................................. 1
2. Konda ............................................................................................................................. 1
3. Vitambo .......................................................................................................................... 1
4. Makushongoshetakano .................................................................................................. 2
5. Magwanikilito vishongwa peke nandjendititoshongo yakwatakanito vishongwa navintje. 2
6. . Ndjenditito yakushonga nakukushonga ........................................................................ 3
7. Vitundwamo vyantatekotomporwa kuuhura wamwaka. .................................................. 4
8. Uyivi vitundwamo kutwara moomo vyakukwamena ........................................................ 6
9. Vashongwa vantambondunge yakutanga vana hepa tanko kuvawapaika naviviyauka
vyalikushongo lyapantateko ure wavivike vitano (5) .............................................................13
10. Mulyowaneko .............................................................................................................32
11. USHWINKANGO ( GLOSSARY ) ..............................................................................35
1 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
1. LITWAROMO
Yino ndjendititoshongo kuna kushingonona ovyo vyawapero kukushonga nakuwaneka mulyo
wamatematika kutamekera mushurentateko dogoro muntambondunge ya 3.Matematika
kwakara shishongwa shamaruha ghamakushongo kutwara mundjendititoshongo
yamatematika.Mwakara nka navitimwitira vyagwanikito navishongwa vyapeke kutwara
mundjendititoshongo yavishongwa navintje.Mushishongwa shino shamatematika,
vashongwa kukwata lighano nakuwaneka ukonentu wakukushuvashuva wamanongontjo
ghamatematika.
Vino kuvatera vashongwa vakulite maghano ghavo
mukughayara,kukonakona,nakugharughanita kumaruha ghapeke ghamakushongo muliparu
nalintje.Mukutikitamo shishongwa shino, vashongwa vana hepa ntani ruvede rwashishongwa
8 shaperiode muntambondunge 1-2, ano 9 muntambondunge 3 mushivike,kutwara
mundjendititoshongo yatulitapo NIED mushurentateko yino ndjendititoshongo NIED
kwavitambura ashi litjindjo lyayo ngalikakarakonka mumwaka wa 2021.
2. Konda
Shishongwa shino shamatematika, ntjoshirughanito shahepero mukukulika uyivi namaruha
ghapeke munkarapamwe.Matematika kwakaranka ruha rwa mpo yetu.Matematika kuvhura
kurughanitako mukutapa mapukururo ghakutikiliramo.
Tuna hepa kuwana shishongwa shino shamatematika mukuwaneka
ukonentu,uyivi,mukughupapo vitughana vyavingi vyakeheyuva.Matematika kutapa uwa
nalihuguvaro kuvashongwa mukughupapo maudito nakuhafera vidanauka
vyanomora.Mushuredidi kwakaramo hepero ashi vashongwa vana hepa tanko kuwana
ntateko mwene yamatematika kuntamekero.
Uyivi muvaru ndjo ntjimantjima yaukaro mwene mumakushongo ghapantateko.Likushongo
lino kwalitulitapo navitomporwa,kuvara,kushetekera,ruvede navimaliva muukaro
wavashongwa wakeheyuva.Mushishongwa shamatematika kwakaramo uyivi
wavishwintateko wavashongwa mumukunda wavo.Vitambo vyakuupapo maudito,likukwamo
lyanomora namapukururo,kwatapa virugho kuvashongwa vayive nawa matematika muukaro
wavo wakeheyuva.
3. Vitambo
Kukulika kurughana nomora nakughayara vyamatematika.
Kukulika ukaro wakuhafera matematika.
Kurenka vashongwa vayive ntateko danomora nantjangito danomora.
Kurenka vashongwa vakwate lighano kudemenena kumatematika nandughanito
yamatematika.
Kurenka vashongwa vatikitemo kurughanita matematika muliparu lyakehe liyuva.
2 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
4. Makushongoshetakano
Makushongoshetakano, kwa tapa unankondo kukehe mushongwa dakuhamena
mumakushongo ghakutikiliramo.Vino kuna hameneno ndjenditito yakuvatera vashongwa
navantje mukuvashonga kushetakana nakughupapo mapiyaghano ghavashongwa
navantje.Makushongontateko,kuwapeka nkarapamwe navitambo vyashikengamantjo
muNamibia mukukulika vighayarera vyamwaka wa 2030. Vashongwa kwakara namaudito
ghakukushonga ghakukushuvashuva ghapamundinda wavashongwa.Mpo ngoli shi
makushongo ghavo ghana hepa kuwana vishongitito vyahepero nantjongitito
yakukushuvashuva kutwara muvihepwa vyavo.
Ntjongitito yakukushonga vashongwa vene navavene mutumbunga twavo,yiwa unene
mbyovyoshi mushongi kukenga kovyo vayiva kare vene,navyo vahepa kurughana pavavene
makura mushongi kuvavatera tupu mposhi vawaneko mauyivi namaunongo
ghamape.Ndjendititoshongo yamakushongoshetakano kwanegheda vitomporwa ovyo
vahepa kuyiva vashongwa vakaro namaudito ghakukushonga mposhi vaviyive
navo.Ndjenditito yambatero yapamundinda ( lLSP ) yina hepa kukarapo mposhi yineghede
nakukengurura makushongo ghapamundinda ghavashongwa vakaro namaudito mposhi
vawane mbatero kumushongi.
Maghano ghamwe ghantjongititoshetakano munkondashongero kugha wana
mundjendititoshongo yamumwaka wa 2012.Ntjongititoshongo yino, kukulika kehe uno
mushongwa maghano ghendi nauyivi wendi mukuvatera muundjuni uno,mukunkondopeka
mapukururo nauyivi walikugwanekero.
Ntambondunge yapantateko kutikitamo makushongo ghanavantje vamati
navakadona.Vashongi vana hepa kuyivashi weni mukutekura vashongwa vano
palikushetakano,vishongitito navintje vivatere rudivharwa naruntje mwamuwa.Vashongi vana
hepa kushayikitapo makutondoghoro munkondashongero kumwe nakunomenashi kushonga
kukulike rudivharwa palishetakano.Makonakono kwa negheda ashi navantje vamati
navakadona kwakara namauyivi mukutompora muvivarero,mposhi vashongi vahepa
kukorangeda navantje vamati navakadona varughane nawa.Mulyo unene ashi
pantambondunge yantateko kutulitapo makorangedo ghalikuturomo nalikuyuvho kuvamati
navakadona mukurughana nawa muvivarero.
5. Magwanikilito vishongwa peke nandjendititoshongo yakwatakanito vishongwa
navintje.
Viparatjangwa vyavishongwa vakwatakanita mundjendititoshongo yavishongwa navintje
mbyo vino: Likushongomukunda, HIV/AIDS, Makushongomuhoko< Makushongo
ghauntuwamuntu naudemokoli, Makushongo ghamapukururo nalihangakanito naUtakamiti
ndjira.Vino kwavinkondopeka mundjendititoshongo yankarapamwe yamuNamibia,mpongoli
shi vashongwa vetu navantje vana hepa ntani vino:
Kuyiva nkalito namaudito
Kuyiva viyititapo vyavyo munkarapamwe detu
3 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
Kuyiva ashi weni mukughupapo oyo nkalito namaudito nakukukundako
munkarapamwe yavo.
Ano nkalito namaudito kwaghadimburura ngoli weno:
Kukunga nakuyendita marunone ghantjitwe yetu.
Likugho kumwe nalikukwamo lyaHIV/AIDS
Maudito ghaundjewandjewa nalinyateko,ukashu waukanguki nalidjonauro
undjewandjewa.
Vishintashinta vyamumpongatani nalipangero lyakuncenuna unankondo naulimburuki
kuyita umbondo.
Ukashu walikushongo mukushetakanita undjewandjewa wandjira.
Maudito ghavirongo muundjuni.
Mpovili vihoninita vyavingi vagwanikilita nandjendititoshongo yino,ngoli mbyo tupu
va tapako shihoninita shimwe mukehe ndjendititoshongo yino vatapa pano:
Likushongomukunda
HIV / AIDS Makushongompong
atani Undjewandjewa
wandjira
Ntambondunge 1- 3 Mapukururo ndjenditito: Pikitogarafika yina kuneghedo lirughanito mema mushivike.
Ntambondunge 2 Ruvede
Ntambondunge 3 Mapukururo ndjenditito: Pikitogarafika yavamati navakadona
Ntambondunge 1 Kuvara : Kuvara shivaro shavihauto mushitaura,muntambondunge 1 na 2 vishwiyivito vyandjira
6. Ndjenditito yakushonga nakukushonga
Likukwamo lyakushonga nakukushongita kwahamena mulikukwamo lyamakushongo
ghapamwanuke mwene (LCE) kwalitjangurura mudokumente yapolisi daministeli (
mumatjangwa ghalikukwamo lyaumpititi ) namu (LCE) . Ndjendito yino kuhuguvalita uwa
wamakushongo nange veta ava di tura mushirughana .kuweda ko nkedi yakurughanita
shiparatjangwa kukara shitambo shakudemenena kukushonga nakushonga pantambo
yapalivhu.
Shitambo ne kukulita makushongo ghakuyiva nakuyuvha, ndughanito naukaro naukonentu
kushure ogho a wana kulikoro nambunga, namaugwanekero mumukunda. Makushongo
ghamushure ghanakona kukaramo, lidikopo, kuwederera nakuranya vashongwa kutwara
uyivi naukonentu.
Vashongwa kukushonga unene nange ava kuturamo mumakushongo kupitira mulikuturomo
lyalinene, likwatitoko naviyeramo , kehe mushongwa kwakara panaumwendi navihepwa
vyendi , nkedi yakukushonga , uyivi naukaro . Mushongi ana kona kupakere mbili vihepwa
4 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
vyavashongwa nakuwapeka uyivi wamakushongo ghavo momo vyawapera.Nkedi
damakushongodina kona kukushuva ngoli vikuwe namunda yamakukwamo ghavishongwa.
Nampiri maruha ghaliraka vaghahangura mundjendititoshongo, mushongi ana kona
kutakamita ashi odo ndjenditito anakona kudishonga munkedi damunda.
Mushongi ana kona kutokora, kutwara vitambo navitomporwa vyamakushongo
namanongontjo ovyo vyakutikitamo, nange ruvede rwaruwa kushonga vikaramo
vyamatematika, paruvede rwaruwa vadimburure mbudi naumwavo , pakushana mbatero
yakukushonga, nange mpoyiri nkedi yimwe mwakuwederera ko ndi liwederero lina hepa
kulikwama, ndinange vashongwa vana kona kuvakorangeda vawane nkedi davavene
kupitira mushishongwa ndi mulivango lya vikaramo .
Kurughana mumbunga, vaviri, pantjendi, ndi navantje mukondashongero muruvede rwa
matematika, lina kona, kuliwapaika nawa nakulikenga nawa. Liruwaneno kumwe
namakushongo ghakurughana kumwe vana kona kughakorangeda kehe pano.shihonena
,mumatematika kuvhura dikare nkedi dadingi dakughupapo udito ntani vanuke vakurughana
mumbunga ngavakushonga kumwe. Vyamulyoko, virughana vina kona kukara mulyo mposhi
vashongwa vakengemo mulyo wamo. Momo vana kutanga vashongwa manongontjo
ghanaumwavo ghambunga namakugwanekero kuvhura kuvapa vitambo vahamene
mumaghano nakukengurura virughana vyavo mulikengero lyamushongi.
Matematika kuna hepa kukara likukwamo lyakutikiliramo nakukuhamitiramo muliparu
lyavo.Shihoninita; shivaro shanomora mbiri, shivaro shanomora ntatu navishwi kuviwana
mumukunda.Mpiri ngoli matematika kwakara shihanganita liraka lyanavantje mukutikitamo
vashongwaghona varughanite matematika.Nka kapishi mumbapira tupu mwakuwana
matematika, mushongi ana hepa kurughanita vishongitito vyakumona yira mawe, tutondo,
vidukito vyamabwitiri,nkandi navimweya ngoli.
7. Vitundwamo vyantatekotomporwa kuuhura wamwaka.
Mukuwana mpito nakutameka ntambondunge 1 vashongwa navantje kuna kuvataterera
vinakugwanita vino; likuyuvho, kughayara, kukara mumpongatano, kukanguka parutu
mukukushonga matematika.Pakumana ntambondunge yautatu (3) muvivarero
vyapantambondunge yantateko, kuna kuvataterera vaneghede ashi kuvhura vitomporwa vino
vina kukakwamoko:
Shivaroghanokuliko
5 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
Vashongwa vadimburure, vashingonone, vaghambe nomora, omo dakutundakanena,
kutokora uyivi wavivaroghanokuliko pakanwa,pakutjanga namukurughanita nawa likukwamo
nomora mukumahurapo maudito ghamareru ghakeheyuva muliparu lyavo.
Kumahura udito
Vashongwa vatikitemo uyivi washivaroghanokuliko mukughupapo maudito ghamareru
muukalimo wakeheyuva pakuvara, kushinganyeka, kushetakanita nakurughanita ndjenditito
yaumwavo.
Kuvaraura
Vashongwa vana hepa kutikitamo ndughanito ne (4) dantateko yira; kupakapo, kuupapo,
muyarovhukito nakugaununa/kutapera.
Kushetakanita
Vashongwa vana hepa kudimburura, vavhuruke nakuyiva maumwe ghakushetakanita
navishetakanito ( unaure, mukumo, liyarararo, ruvede navimaliva ) mukuvirughanita kehe
liyuva muliparu lyavo.
Vimaliva
Vashongwa vavhuruke vimaliva vyavitenda (vikuvo ) navivyamafo ( vyambapira).Vaghambe
uyivi wavo wavimaliva pakanwa, kutjanga nakurughanita vimaliva mukughupapo maudito
ghamaukalimo ghakeheyuva.
Vishwifanikito
Vashongwa vavhuruke nakushingonona vishwi nakutanta ukaro wavyo namo
vyakutundakana pakatji kavishwi nanomora mbiri 2D nashishwi shashivaro vyanomora ntatu
3D muliparu lyene lyene.
Mapukururo nandjendititorughanito
Vashongwa vaghongere, vakwatakanite, vaneghede, vatoroke nakumpompeka mapukururo
mukurughanita pikitogarafiki nabargarafiki kutwara muvifaneka vya ngoweyo nakututa konda
yavishinganyeka ( pumba ).
6 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
8. Uyivi vitundwamo kutwara moomo vyakukwamena
Uyivi vitundwamo moomo vyakukwamena kwatundiliranga muntambo yashurentateko nange
muntambondunge 3. Vino kuna kunegheda uyivi,maghano, ukaro, vino kwapitiranga
mumatematika muntambondunge dashure dapantateko.Mpiri ndi ngoweyo, makushongo
ukalimo wamushurentateko kapi vaghahamitiramo muno mumakushongo
ghapantateko.Ghagho ghano makushongo kugha wana tupu mundjendititoshongo
yashurentateko.
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
SHIVARO SHALIKWATOGHANOKULIKO
KUVARAURA,NOMORA,KUVIRIPITA NAKUKAHEPITA,MAPI GHANOMORA,
NOMORA DAUMURONGO, MULYOVANGO,NONGONONA NAKUSHINGANYEKA,
GHONGORA,MPUNGIKURURO, KUMPOMPEKA NAKUFANIKITA,NOMORA
DAVIVARODIROSHETAKANO NAVIVAROSHETAKANO, SHINGONONA.
Vara nawa
nomora nange
ku 20
Vara nawa nomora
nange ku 100
Vara nawa nomora
nange ku 500
Vara nawa nomora
nange ku 1000
Dimburura
nomora nange
ku 10
Tjanga nomora
nange ku 9
Varura,ghamba
nakudimburura
nomora nange ku 100
Tjanga nomora nange
ku 20
Varura,ghamba
nakudimburura nomora
nange ku 500
Tjanga nomora nange
ku 100
Varura,ghamba
nakudimburura
nomora nange ku
1000
Tjanga nomora nange
ku 500
Vara navininke
vyakumona
nange ku 4
Vara navininke
vyakumona nange ku
6
Shinganyeka vininke
vyakumona nange ku
10
Shinganyeka vininke
vyakumona nange ku
20
Tjangurura
nomora
nakutotapo
mapi ghaureru
Totapo mapi
ghanomora kutundilira
1 nange 10
Totapo mapi
ghanomora kutundilira
1 nange 20
Totapo mapi
ghanomora kutundilira
1 nange 50
Kupakapo nakuupapo
nomora daumurongo
nange ku 100
Kupakapo nakuupapo
nomora daumurongo
nange ku 500
Dimburura mulyo
wanomora
Dimburura shi
shivaronomora
Dimburura shi
shivaronomora ntatu
7 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
yashivaronomora
mbiri kutunda 1 nange
20
kwakara nanomora
mbiri.
Nongonona nomora
yamulivango
lyamurongo ntani
nayiyalivango
lyaumwe.
dashivaronomora.
Nongonona nomora
yamulivango
lyalifere,murongo
nayiyalivango
lyaumwe.
Tura nawa
vininke
vyakumona
mumpundi
yimwe
Tura vininke
mumpopa kutundilira
1 nange 10
Tura vininke mumpopa
kutundilira 1 nange 50
Tura vininke
mumpopa kutundilira
1 nange 100
Mpungika
nawa vininke
nakuvishetaka
nita
Tura nawa vininke
nakuvishetakanita
nanomora kutunda ku
1 nange 20
Twenyaura
nakuvarura nomora
Tura nawa vininke
nakuvishetakanita
nanomora kutunda ku 1
nange 100
Twenyaura nakuvarura
nomora
Tura nawa vininke
nakuvishetakanita
nanomora kutunda ku
1 nange 500
Twenyaura
nakuvarura nomora
Twenyaura muyaro
wanomora kutundilira
1st – 10th
Twenyaura muyaro
wanomora kutundilira
1st –20th
Twenyaura muyaro
wanomora kutundilira
1st –100th
Negheda
likugho kumwe
mpungi
linakuneghedo
kushetakana
nakudira
kushetakana
Negheda likugho
kumwe mpungi
linakuneghedo
kushetakana nakudira
kushetakana
pakurughanita
nomora 0 – 10
Dimburura
vivarodiroshetakano
navivaroshetakano
kutundilira 0 - 99
Dimburura
vivarodiroshetakano
navivaroshetakano
kutundilira 0 - 500
Waneka nomora
dakukufana ndi
dakukuwa kutunda 1-
Koshonona/gaununa
shivaro shanomora
mbiri nange ku 100
Koshonona/gaununa
shivaro shanomora
ntatu nange ku 500
8 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
10
KUKOSHONONA UDITO
Koshonona
maudito
ghashitimwitira
shaureru
Koshonona maudito
ghashitimwitira
shaureru mumpompa
kutunda 0 - 10
Koshonona maudito
ghashitimwitira
shaureru mumpompa
kutunda 0 - 50
Koshonona maudito
ghashitimwitira
shaureru mumpompa
kutunda 0 - 100
KUVARAURA
KUPAKAPO,KUUPAPO,MUYAROVHUKITO,KUGAUNUNA/KUTAPERA,MAUDITO
GHANTAMBOVHUKITO,VIVAROVHONGO
SHURENTAT
EKO
NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Yiva nawa shivaro
shakupakapo
kutundilira 0 – 10
Wedako nomora mbiri
ndi ntatu mushivaro
shapakatji ka 1- 20
Yiva nawa shivaro
shakupakapo
kutundilira 0 – 20
Wedako nomora mbiri
ndi ntatu mushivaro
shapakatji ka 1-100
Yiva nawa shivaro
shakupakapo
kutundilira 0 –20
Wedako nomora mbiri
ndi ntatu mushivaro
shapakatji ka 1- 500
Ghupamo nomora
yimwe kwaunyayo
mukatji kanomora 1-
10
Yiva nawa shivaro
shakughupamo
kutundilira 1- 10
Ghupamo nomora
yimwe ndi mbiri
munomora dambiri
kutunda 11- 99
Yiva nawa shivaro
shakughupamo
kutundilira 1- 20
Ghupamo nomora
mbiri ndi ntatu
munomora dantatu
kutunda 100- 500
Faneka mpungi
davininke nakuvara
shivaro shodo mpungi
Yiva mumutwe
vivarovhukito vya 1, 2,
5 na 10
Vhukita kehe nomora
nange ku 20 nanom
ora dapakatji ka 1
nange 10
Yiva mumutwe
vivarovhukito vya
1,2,3,4,5 na 10
Vhukita kehe nomora
nange ku 50
nanomora dapakatji
ka 1 nange 10
Pampakana nomora 5
ntani pampakana
nomora 10
Pampakana nomora
nange ku 50
Pampakana nomora
nange ku 100
9 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Kahepita
nomorashetakano
nange ku 10 ntani
kahepita nomora 20
Kahepita nomora
nange ku 50 ano
nomoradiroshetakano
nange ku 20
Kahepita nomora
nange ku 100
Yiva mumutwe
ligaununo lyaureru
nalivhukito
linakukugho
nanomora 2, 3, 5 na
10
Kutepakanenu
vininke
kushetakana
mumbunga
pakurughanita
vininke
vyakumona
Kutepakanenu vininke
10 mumbunga mu 2s,
3s, 4s na 5s
Kugaunwinenu vininke
vyakumona mumbunga
ya 2s,3s,4s, 5s na 10s
Gaununa nomora
mbiri kutundilira 10
nange 100
pakurughanita nomora
dino 1- 5
Koshonona maudito
ghantambo
dakuvhukita
mulikukwamo 0- 10
kurughanita kupakapo
nakuupapo
Koshonona maudito
ghantambo
dakuvhukita
mulikukwamo 0- 100
kurughanita kupakapo
nakuupapo
Koshonona maudito
ghantambo
dakuvhukita
mulikukwamo 0- 500
kurughanita kupakapo
nakuupapo
Kugaunwinenu
vininke
mugwaneke
Kugaunwinenu
vininke mugwaneke
nakudimburura
shivaro “ nashintje “
ndi “ ukahe “
Kugaunwinenu vininke
mugwaneke
nakudimburura shivaro
“ nashintje “ ndi “ ukahe
“ ndi ¼
Kugaunwinenu vininke
mushetakane
mumaruha
nakudimburura : 1, ½,
¼, ⅓, ¾
KUMETA
UNAURE, MUKUMO, UKALIMO, LIYARARARO, RUVEDE, MALIVA
Shetakanita
vininke
munaure hana
kurughanita
umwe
wavimetito.
Shetakanita,meta
nakudidilika unaure
wavininke hana
kurughanita umwe
wavimetito
Shetakanita,meta
nakudidilika unaure
wavininke hana
kurughanita umwe
wavimetito ntani
nakurughanita cm
Shetakanita,meta
nakudidilika unaure
wavininke hana
kurughanita umwe
wavimetito ntani
nakurughanita (m) na
(cm)
10 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Rughanita lifupipiko lya
cm
Rughanita lifupipiko
lya m na cm
Shetakanita
mukumo
davininke viviri
hana
kurughanita
umwe
wamukumo
Shinganyeka,shiviha
nakushetakanita
mukumo wavikalimo
muvyuma hana
kurughanita umwe
wamukumo
Shinganyenga shiviha
nakumeta mukumo
daukalimo
wavininke,rughanita
kilogarama
Rughanita lifupipiko lya
kg.
Shinganyeka shiviha
nakumeta mukumo
wavininke hana
kurughanita vimwe
vya kilogarama
nagarama
Rughanita lifupipiko
lya kg, g
Shetakanita
ukalimo
wavininke viviri
hana
kurughanita
umwe
waukalimo
Shinganyeka
,mpompeka nakumeta
ukalimo
wavininke/vyuma
hana kurughanita
umwe waukalimo
Shinganyeka,mpompek
a nakumeta ukalimo
wavininke/vyuma hana
kurughanita litera
Kurughanita lifupipiko
lya ( l )
Shinganyeka
nakumpompeka,sheta
kanita ukalimo
navyuma hana
kurughanita mukumo
waumwe
nakurughanita
litera,lifupipiko, ml, l
Meta nakushetakanita
liyarararo muvishwi
hana kurughanita
umwe
wamuvikwambando.
Meta nakushetakanita
liyarararo muvishwi
hana kurughanita
umwe
wamuvikwambando.
Hangura
likushuvo
lyapakatji
kamaruvede
ghaliyuva.
Tundakanita
likushuvo lyaviviyauka
lyaumwe
navivyamunkarapamw
e mwayendo mayuva
ghakukushuva shuva.
Tundakanita
vishorauka vyakehe
yuva namuvivike
namwedi
Tundakanita
vishoroka
vyamuliyuva,muvivike
namwedi.
Twenyaura
mayuva
ghamushivike
Twenyaura mayuva
ghamushivike
namwedi
damwaka.shetakanita
shinema shashire
nashishashifupi
Twenyaura mayuva
ghashivike namwedi
damwaka rughanita
kalendeli
nakudimburura
mapukururo.vara
Twenyaura mayuva
ghashivike,mwedi
damwaka rughanita
kalendeli mukuwana
mapukururo.vara
ruvede rwaviri,ukahe
11 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
ruvede rwaviri naukahe
waviri.
waviri,kupititako,kuhu
pitako,namunute.
Twenyaura
nakudimburura
vimaliva
vyavitenda
vyaNamibia,
5c, 10c, 50c.
Danauka
shidana
shavimaliva
kuyombilite
kuura
nakuulita.
Twenyaura
nakudimburura
vimaliva vyavitenda
vyaNamibia, 5c, 10c,
50c, N$1, na N$5
Kuyombilite kuura
nakuulita vininke
kuvara vimaliva
muuhunga,kuyiva
tjindji yamu N$5
Twenyaura
nakudimburura
vimaliva, vitenda
navivyamafo yira;
N$10, N$20.
Kuyombilite kuura
nakuulita
vininke,kuvara vimaliva
muuhunga,kuyiva tjindji
yamu N$10
Twenyaura
nakudimburura
vimaliva
vyaNamibia,vyavitend
a navivyamafo N$10,
N$20 na N$50.
Kuyombilite kuura
nakuulita
vininke.kuvara
vimaliva
muuhunga.kuyiva
tjindji yamu N$20
SHISHWISHONGITO
VISHWISHONGITO,SHIVAROVANGOTUMBUKIRO NASHIVAROKARERO
Dimburura
nakufaneka
vishwishongo
vyamaruha
maviri 2D
Dimburura,twenya,ha
ngura vishwishongo
vyamaruha maviri
2D,matatu 3D, vishwi
vyavikwambando,nkat
a,shikwalitjaro,shikovh
utatu,mbumbe,kapun
di nashikwampakero
Dimburura,twenya,han
gura vishwishongo
vyamaruha maviri
2D,matatu 3D, vishwi
vyavikwambando,nkata
,shikwalitjaro,shikovhut
atu,mbumbe,kapundi
nashikwampakero
Dimburura,twenya,ha
ngura vishwishongo
vyamaruha maviri
2D,matatu 3D, vishwi
vyavikwambando,nkat
a,shikwalitjaro,shikovh
utatu,mbumbe,kapund
i nashikwampakero
Waneka shishwi
shamaruha maviri 2D,
matatu 3D dimbuura
ruha rwauhunga.
Negheda
nakutontonona
vininke ovyo
vyakaro narutu
mumukunda.
Shingonona vininke
ovyo vyakaro narutu
mumukunda.
Tontonona nkalito
yavininke ovyo una
faneke palikarata.
Fwaturura ukaro
wavininke vafaneka
vyakukufana
palikarata.
12 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHURENTAT
EKO NTAMBONDUNGE 1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
NDJENDITITOGHANO NANDUGHANITO
NTJANGITOFANO, MAFANORONDAKANO
Hangura
nakushetakanit
a vininke
vyakumona
Pongaika, wapaika
nakunegheda lifano
pantjongitofano.
Kunegheda viwaneka
pantjongitofano
Pongaika, wapaika
nakunegheda lifano
pantjongitofano.
Kunegheda viwaneka
pantjongitofano
Pongaika, wapaika
nakunegheda lifano
pantjongitofano.
Kunegheda viwaneka
pantjongitofano
13 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
9. Vashongwa vantambondunge yakutanga vana hepa tanko kuvawapaika naviviyauka vyalikushongo lyapantateko ure wavivike
vitano (5)
mushinema shakutanga kuuto wakutameka nalikushongo lyenelyene nakuviyiva nawanawa.Kwama ndjenditito yakaropo yakuNIED
yamumwaka wa 2011.
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
SHIVAROKWATOGHANOKULIKO
KUVARAURA Likukwamo nomora 0-100 Likukwamo nomora 0-500 Likukwamo nomora 0-1000
Shitamboshongwa Vashongwa vavhure kuvara vininke vyakumona navi vyakudira kumona nakuwaneka lighano lyakuvara kehe yuva muliparu lyavo.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kuvara vininke vyakumona nange 20 ntani shingaranyima kutunda 20-0
Va vare nawa nange ku 100,mu 2s nange 30,mu 5s na 10s nange ku 100
Kuvara vininke vyakumona nange ku 50, mu 2s nange 50, mu 3s nange 30, mu 4s nange 40, mu 5s na 10s nange 100.
Mpungikurura vininke mukuvivara pankedi yaureru yira mumpungi da 2s,3s na 5s.
Vavare nawa nange ku 500,mu 2s nange ku 100,mu 3s nange ku 30,mu 4s nange ku 40, mu 5s na 10s nange ku 500.
Vavare nawa nakushinganyeka munyima kutunda 20 nange 0, 30 nange 0,mu 2s kutunda 20 nange 0
Kuvara vininke vyakumona nange ku 100, mu 2s nange 100, mu 3s nange 60, mu 4s nange 80, mu 5s na 10s to 150.
Mpungikurura vininke mukuvivara pankedi yaureru yira mumpungi da 2,5;10
Vavare nawa nange ku 1000 nakuvara munyima nakumeho pankehe dino nomora: 1s nange 1000, mu 2s nange 500, mu 3s nange 60, mu 4s nange 80, mu 5s na 10s nange 1000, mu 20s nange 500, mu 30s nange 180, 50s na 100s nange 1000.
Dimburura shivaro shavininke vana tapa hana kuvivara.
Shitamboshongwa Vashongwa vadimburure, kushinganyeka nakutikitamo liwapukururo lyauyivi mukurughanita likufano namapi.
14 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Dimburura nomora yavininke nange ku 6 hana kuvivara, ntani vavi vare ngoli.
Dimburura nomora yavininke nange ku 10 ovyo vana mpungiki nawa,ntani vavivare ngoli
Dimburura ashi vininke vyakukushuvashuva mumpungi kunegheda shivaro shakukufana yira:
2 ntatu ndi 3 mbiri ndi 5+1
Shinganyekera vininke vyakumona nange ku 20 mukuvimpungika, ntani vavivare ngoli.
Dimburura ashi vininke vyakukushuvashuva mumpungi kunegheda shivaro shakukufana.
Shinganyekera vininke vyakumona nange ku 30 mukuvimpungika, ntani vavivare ngoli.
Dimburura ashi vininke vyakukushuvashuva mumpungi kunegheda shivaro shakukufana.
Tura mulikwamo nawa nakushetakanita
Shitamboshongwa Vashongwa ngava vhura kurughanita ushwinkango muvivarero mukutura nawa nakushetakanita nomora mulikukwamo.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Tura nawa vininke nakushetakanita shivaro (nomora dakutamekera 1-20) rughanita ushwinkango: unene,udidi,vyashetakana.< ,> ,= yira ;> unene, < udidi, = vyashetakana
Tura nawa nomora kutamekera 1-20 ( nomora didi nange nomora nene),ntani nomora nene nange nomora didi, ditjange kutamekera kunomora
Tura nawa vininke nakushetakanita shivaro (nomora dakutamekera 1-100) rughanita ushwinkango: unene, udidi, vyashetakana. <,>, = yira ;> unene, < udidi, = vyashetakana.
Tura nawa nomora kutamekera 1-100 ( nomora didi nange nomora nene),ntani nomora nene nange nomora didi, ditjange kutamekera
Tura nawa vininke nakushetakanita shivaro (nomora nange 500) rughanita ushwinkankango: unene,udidi,vyashetakana.< ,> ,= yira ;> unene, < udidi, = vyashetakana
Tura nawa nomora kutamekera 1-500 ( nomora didi nange nomora nene),ntani nomora nene nange nomora didi, ditjange
15 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
didi nange nomora nene ndi nomora nene nange nomora didi: 11, 5, 12 na 3
Dimburura livango nomora yavininke vyakumona kutunda 1st nange 10th ndi 1st nange kuuhura.
Twenya,varura nakurughana nanomora 1st, 2nd, ,3rd , nange 10th munomora didi nange nene, ntani nene nange didi yira; 10th , 9th , 8th ngongo
kunomora didi nange nomora nene ndi nomora nene nange nomora didi: 48, 16, 92 na 61
Dimburura livango nomora yavininke vyakumona kutunda 1st nange 20th
Twenya,varura nakurughana nanomora 11th , 12th , 13th ngongo; munomora didi nange nene, ntani nene nange didi yira; 20th ,1 9th ,1 8th ngongo
kutamekera kunomora didi nange nomora nene ndi nomora nene nange nomora didi: 402, 284, 361 na 68
Dimburura livango nomora yavininke vyakumona kutunda 1st nange 30th
Twenya,varura nakurughana nanomora 20th, 21th , 22nd ngongo; munomora didi nange nene, ntani nene nange didi yira; 27th ,26th ,25th ngongo
Litulitopo nomora Shitamboshongwa Vashongwa vavhuruke,kuvarura nakutjanga nomora
Vitomporwa Vashongwa ngava vhuru ku:
Vitomporwa Vashongwa ngava vhuru ku:
Vitomporwa Vashongwa ngava vhuru ku:
Kuvarura, kutwenyaura nakudimburura nomora nange ku 100, palikarata nomora omo da kukwama.
Vatjangurure nomora kutundilira 0-20
Vavare madina ghanomora munkango nange 10 yira; mwe, viri, tatu.....
Vakengurure nakudimburura nomora davihauto nadidandjugho mumukunda wavo.
Kuvarura, kutwenyaura nakudimburura nomora nange ku 500, palikarata nomora omo da kukwama, nakutontonona livango karerera lya nomora.
Tjanga nomora kutamekera 0-100
Vavare madina ghanomora munkango nange 10 yira; ntantatu,ntane,murongo
Vakengurure nakudimburura nomora davihauto, nomora dandjugho, mwaka davanuke.
Kuvarura, kutwenyaura nakudimburura nomora nange ku 1000, nakutontonona livango karerera lyanomora.
Tjanga nomora kutamekera 0-500
Vakengurure nakudimburura nomora dakukarerera mumukunda wavo yira; vinema, mukosho wavininke, mukumo wavininke, ukalimo wamumakende.
Kupampakana Shitamboshongwa
16 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
nakukahepita Vashongwa vayive ndjenditito yakupampakana nakukahepita.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku
Pampakana nomora dino; 1, 2,3,4,5 na 10 navininke ndi hana vininke.
Kahepita nomora dino navininke ndi hana vininke 2,4,6,8,10....20
Pampakana nomora nange ku 50 hana kutulika nakutulika yira;23+23=46; ntani 9+9= 18
Kahepita vivaroshetakano nange ku 50.kahepita nomora vivarodiroshetakano nange ku 19 navininke ndi hana vininke.
Pampakana nomora nange ku 100 navininke yira;24 = 40 + 8 =48 hana kurundurura ntani 36 = 60 + 12 = 72
Kahepita nomora nange ku 100 dahana vihupwa nadi dakaro navihupwa yira; 36 = 15 +3 = 18 hana vihupwa.ntani 87 = 40 +3 r 1 = 43 r 1 navihupwa.
Tontonona vivare nakuviturapo
Shitamboshongwa Vashongwa vayive shi weni mukutontonona nakutura vivaro nakuvhuruka vivaro nange 20.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhuru ku:
Vhuruka nomora nange ku 10 yira; 9= 1+8, 9= 8+1 =, 9 – 8 = 1, 9 – 1 = 8, 9 = 2 + 7; ngogngo
Vhuruka nomora nange ku 10 udiwapukurure;
Vhuruka nomora nange ku 20
Gaununa nakuturapo vivarero vyanomora mbiri nange ku 99 navininke vyakudira kumona yira; 25 = 20 +5 ndi 15 + 10, ngongo 20 + 17 = 37; 30 +7 = 37
Vhuruka nomora nange ku20 udiwapukurure
Gaununa vivarero nakuvitura munomora dantatu,mundjendito dakukushuvashuva nange ku 500 navininke vyakumona ndi vyakupira kumona yira; 154 = 100 + 50 + 4 154 = 150 + 4 154 = 100 + 54
Mulyovango Shitamboshongwa Vashongwa vavhuruke vivaro vyanomora dalivangotumbukiro namulyovango.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Dimburura nomora damavango maviri nange ku 99 shi kwakara nalikushuvo mulyovango yira; 12 yakukushuva ku 21
Dimburura mulyovango wamavango matatu nange ku 500 yira mavango 3, 2 na 4, kutamekera kwa Kunene
Dimburura vivarero vyamulyovango vitatu nange ku 1000 kutamekera kwa Kunene nange kwakudidi 1, 8,
17 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
mulyovango washivaro shamavango 3 na 4,kutamekera kumulyo vhango waudidi ( 34 na 43)
nange kwakudidi (234 ndi 432)
Dimburura mulyovango wanomora walifere,murongo mu 347 yira; 3 = 300, 4 = 40, 7 = 7
4 yira ( 841 na 148 )
Dimburura mulyovango walifere, murongo mumulyovango wanomora ntatu. 958, 9 = 900, 5 = 50, 8 = 8
Nungura/ghonora Dimburura kughongora ndi kungura muvarovhukito wamurongo (10) nange ku 100. Rughanita nomora dapalikarata yira; 33→30; 38→40
Ghongora nomora nange ku 10; ntani ghongora kunyima nanomora dino 1, 2, 3 ,4 ntani ghongora kumeho nanomora dino 5, 6 ,7 ,8, 9 yira ; 62 = 60, 75 = 80
Likukwamonomora
Shitamboshongwa Vashongwa vayive vivarodiroshetakano navivaroshetakano nakutwikira kushingonona nomora mulikukwamo.
Vitomporwa Vitomporwa Vitomporwa
Vashongwa ngava vhura ku: Vashongwa ngava vhura ku: Vashongwa ngava vhura ku:
Vadimburure nomora dakuvhura kugaununa paviri kutamekera 1—20
Vatamunune nomora daureru 1—20 yira; 1, 3, 5, 7........
Shingonona likukwamo nomora 3, 6, 9 , 12, 15
Manita nakushingonona likukwamo nomora odo dinapiromo; 1—50 yira mu 20;...;...;23...;...;26
Wedapo viviri pa kehe nomora kutunda 21—31 yira; 21; 23 ; 25; 27; 29; 31
Rughanita likukwamonomora mukupakapo nakuupamo yira; 8 +9 = 17; 28 +9 = 37; 80 +90 =170
Vamanite nakushingonona nalikukwamonomora kutunda 1—100 yira; kutjanga nomora dina piromo; 3, 6, 9, 12......
Manite likukwamonomora kutunda 1—100 mukuyudamo odo dina piromo yira 50;...;...;...;58;...;...;...; 66
Shingonona likukwamonomora yira; 3, 6; 9,12,18,21... mukuturangapo tatu.
Kurughanita likukwanomora pakupapo nakuupamo.
Nomoradiroshetakano nanomorashetakano
Shitamboshongwa Vashongwa kudimburura nomoradiroshetakano nanomorashetakano.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
18 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Kudimburura nomora pakuditura yimwe nayimwe kutunda 1—10 mukuyuvhako lishetakano lyanomora mumpungi (kutura nomorashetakano mumpungi dakukufana ntani nomoradiroshetakano mumpungi dakukushuva).
Kudimburura nomoradiroshetakano nanomorashetakano nange ku 99
Vayive ashi nomoradiroshetakano kuhura na 1, 3, 5, 7, 9( 57 ) ano nomorashetakano kuhura na 0, 2, 4, 6, 8 yira ( 38 )
Kudimburura nomoradiroshetakano nanomorashetakano kutunda 0 - 500
Vayive ashi nomoradiroshetakano kuhura na 1, 3, 5, 7, 9 ( 857 ) ano nomorashetakano kuhura na 0, 2, 4, 6, 8 yira ( 638 )
LIVARADARO
Kupakapo Shitamboshongwa Vashongwa vakwate lighano lyavivarontateko mukunkondopeka kupakapo nantjangito.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kupakapo nomora dambiri ndi kupitakanapo mushivaro shapakatji kanomora 0- 20 mukurughanita ndjenditito dino
- Kurughanita vifanayika ndi vininke vyakumona
- Kuvaraura navintje
- Kuvara mukurughanita makarata ghanomora yira kutura mulighano nomora yamuhovo ntani kutwikira kuvara nanyara
- Kutura nomora yayinene pamuhovo
- Kupampakana nakukahepita
- Kutwikira nakugaununa nomora vihonena vyaviviyauka
- Manita vifaneka nanomora odo dinapiromo
Pakapo nomora daumurongo nange ku 100 yira; 20 + 30
Pakapo nomora yimwe kunomora dambiri mumutwe ( nakuvitjangashi)
Pakapo nomora mbiri ndi kupitakanapo pakatji kanomora 0 – 100 mumutwe ndi kutjanga pakurughanita ndjenditito dino
- Kuvara kumeho yira; 28 +3
- Pampakana nakukahepita yira; 30 + 40 = 30 +30 +10
- Kurughanita nomora vayiva
- Kurughanita shihonena shakupakapo yira; 58 +23 = 58 +20 +3 = 78 +3 =81
- Kugaununa nakutamununa nomora yira; 58 +23 = ( 50 +
Pakapo nomora daumurongo nange ku 500 yira; 120 + 30
Pakapo nomora dambiri-mbiri dogoro ku 100 mumutwe (nakuvitjangashi)
Pakapo nomora mbiri ndi kupitakanapo pakatji kanomora 0 – 500 mumutwe ndi kutjanga pakurughanita ndjenditito dino
- Kuvara kumeho yira;328+3
- Pampakana nakukahepita
- Kurughanita nomora vayiva
- Kurughanita shihonena shakupakapo yira;
- Kugaununa nakutamununa nomora
- Kurughanita mulyovango yira;342+185=(300+100)+(40
19 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
- Yudamo shivaro osho shina piromo mulivango lyamuporongwa nange ku 20 yira; 5 + = 12
- Muvaro wamayoka
- Shivaro shaviyungu(piramide)
20 ) + ( 8 + 3 ) = 70 + 11 = 81 Vihonena vyavininke naviviyauka;
- Ruha rumwe nafifanikita mudima
- Nomora dapamutunda
- Mutunda hana nomora
- Nomora dapalikarata
- Yuda nomora odo dina piropo nange ku 100 yira; 75 – = 68
+80)+(2+5) Vihonena vyavininke naviviyauka;
- Ruha rumwe navifanikito mudima
- Nomora dapamutunda
- Mutunda hana nomora
- Nomora dapalikarata
- Yuda nomora odo dina piropo nange ku 200 yira; 130 + =167
Kughupamo Shitamboshongwa Vashongwa vayive lighano lyavivaro ntateko mukunkondopeka kughupamo
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Upamo nomora yimwe 1 – 20 rughanita ndjenditito dino
- Upamo shivaro kumwe nakuvara vininke ndi vifanayika
- Vara shingaranyima
- Vara kumeho yira 19 – 17 ,kuvara viviri kutamekera 17 nange 19
- Kurughanita ndjenditito vayiva yira; 3 – 1 = 2
- Gaununa nakuwedako nomora Vihonena vininke naviviyauka
- Nomora dapamutunda
- Makarata nomora
- Manita mutunda hana nomora
- Yudamo nomora dina piropo Yira; dogoro ku 20; 16 - ... = 12
- Muvaru wamayoka
Kughupamo nomora daumurongo nange ku 100 yira; 60 – 50
Kughupamo nomora yimwe kunomora peke kutamekera nomora 0 – 99 mukurughanita ndjenditito dino
- Kuvara shingaranyima
- Kuvara kumeho nalikushuvo lyanomora yayididi yira; 72 – 68
- Kurughanita ndjetito vayiva
- Kugaununa nakuwedako nomora
- Kurughanita ndjenditito yira; 62 – 48 = 62 -40 -8 = 22 – 8 =14 Vihonena vininke naviviyauka
Kughupamo kehe shivaro shanomora mbiri, ndi ntatu pakatji kanomora dino; 100 na 500 mukurughanita ndjenditito dino
- Kuupamo nomora daumurongo nange ku 500 yira ; 260 – 50
- Kuvara shingaranyima
- Kuvara kumeho opo vina wapere yira ; 410 – 296
- Kugaununa nakuwedako nomora
- Kurughanita ndjenditito dino dakughupamo
- Kurughanita mulyovango
Kurughanita nomora yimwe kunomora yadantatu
20 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
- Muvaru waviungu
Shetakanita kuupamo kukupakapo yira; 18 -2 = 16 ndi 16 + 2 = 18
- Nomora dapamutunda
- Makarata nomora
- Manita mutunda hana nomora
- Mutunda hana nomora Muvaru wamayoka
- Muvaru waviungu
Kughupamo nomora yimwe kunomora dambiri mumutwe
Shetakanita kuupamo kukupakapo.
mumutwe.
Kurughanita likukwamo nomora yira ; 100 – 37 = 63 200 – 37 = 163
Muyarovhukito Shitamboshongwa Vashongwa vakwate nawa lighano lyamuvaru wamuyarovhukito nantjangitito yanomora.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kuvara mu 2s nange ku 20, mu 5s nange ku 50, mu 10s nange ku 100.
Kuvara navininke vyakumona mumpungi da 2, 5, na 10 kumwe nakughamba yira ; “ 5 +5 +5 tupundi tu tatu twavihamena 5 kukara 15”
Faneka mpungi davininke uvyukuruke kupakapo hana kurughanita muyarovhukito yira;
2 + 2 + 2= 6
Kuvara mu 2s nange ku 20, mu 3s nange ku 30, mu 4s nange ku 40, mu 5s nange ku 50, namu 10s nange ku 100
Negheda muyarovhukito ashi livyukuruko lyakupakapo mu 2s, 3s, 4s, 5s, 10s yira; Maria kwa wananga mushivike N$ 5. 00 Maliva mangapi a wananga muvivike 6? N$ 5+ N$ 5 +N$ 5 +N$ 5 + N$ 5 +N$ 5 = N$ 30, 00
Vhukita kehe nomora mbiri nange ku 20 mukurughanita nomora kutamekera 1 nange 10 mukuvyukuruka kupakapo nakupampakana.
Vhuruka nakutikitamo muyarovhukito wa 1x, 2x, 5x
Kurughanita muyarovhukito washivaro shanomora mbiri; 2, 3, 4, 5, na 10 mukuwaneka lilimbururo lyapakatji ka 100 – 500 mukurughanita litontonono vivarero nakuviturapo yira ; 73 x 4 = ( 70 x 4 ) + ( 3 x 4 ) ndi 7 3 X 4 280 12 292
Rughanita muyarovhukito wanomora mbiri nange ku 50 washivaro nomora pakatji ka 1 – 10 rughanita kupakapo ndi kupampakana yira; 43 x 6 =
21 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
na 10x.
43 +43 +43 +43 +43 +43
Vhuruka wangu muhuunga muyarovhukito wanomora dino 1x, 2x, 5x na 10x
Tameka nakuvhuruka kurughanita muyarovhukito wanomora 3x na 4x.
Kugaununa/kutapera Shitamboshongwa Vashongwa vavhure kukwata lighano mukugaununa/kutapera muvaru nakutjanga.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Tura vininke vyakukushetakana mumpungi navininke vyakumona vavare shivaro shavyo.
Vawaneke ndjenditito yanaumwavo mukutapera vininke mumbunga vishetakane
- Kulimburura kuukaro
- Kurughanita vininke vyakumona ( shishwi ÷ nakushirughanitashi paruvede runo )
- Kurughanita tufano
- Kurughanita vitimwitira vyaudito yira; Kativa ana kara na apere 9 vakugaunwine vashetakane navaunyendi va 3.Ngapi apulesi a wana kehe uno?
- Negheda shi kutapera ne livyukuruko lya kuupamo morwa yira; 2 kuyi upamo rukando ru 3 mu 6 (rughanita vininke vyakumona )
Tura ndi mpungika mpungi
Vawaneke ndjenditito yavavene mukugawinina vininke mumpungi da 2,3,4,5 na 10 vakugaunune vininke vashetakane mumpungi da 2,3,4,5 kurughanita vininke vyakumona kufaneka nakupingatanita nomora (washarughanita ÷ pashirugho shino) rughanita weno; mawe 16 kughatura yira weno; 16 mumuyaro wa 8 wa 2, 2 = 16.muyaro wa 4 = 16
Fanikita kugaununa namuyarovhukito wa 1, 2, 5 na 10.
Tura vininke mumpungi nange ku 50 mu 2s, 3s, 4s, 5s namu 10s nashivaro hupito ntani nashivaro dirohupito vyakudira kugaununa.
Rughanita shishwi shino ÷ nashivaro shapakatji ka 10 – 100 kehe nomora yapakatji ka 1 – 10 navihupwa ndi hana vihupwa pakurughanita ndjenditio yakuupamo.
Dimburura vihupwa kutwara muudito washivarero nandjenditito dimwe dampungi.
Vhuruka nakutikitamo vivarerogaununo vyaureru mukurughanita muyarovhukito wa nomora dino 2, 3, 5 na 10 yira; 20 ÷ 2 = 10→ 2 x 10 = 20
22 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
davininke 10 mu 2s, 3s, 4s namu 5s vyashivaro hupito ndi vyashivarodiro hupito.
Kumahura maudito ghantambo davivaro vyamuyarovhukito
Shitamboshongwa Vashongwa vaupepo maudito mukurughanita ndjenditito dakukushuvashuva namaghano vanatura mulikukwamo.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kukoshonona likukwamo lyamuvaru kutamekera 0 – 10 mukupakapo nakuupamo yira;
7 + 3 – 4 =
Kukoshonona likukwamo lyamuvaru kutamekera 0 – 100 mukupakapo nakuupamo yira; 23 + 45 – 31 =
Kukoshonona likukwamo lyamuvaru kutamekera 0 – 500 mukupakapo nakuupamo yira;
123 + 245 -131 =
Vivaro vhongavhongo Shitamboshongwa Vashongwa vakwate lighano nakudimburura vivaro vhongavhongo
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vakutapere vininke vashetakane yira;kuteta apere mumaruha maviri ghakushetakana yira; kurughanita shihonena shino:
Nkinda yakuyura nkindayau- kahe
Kutwenyaura maruha gha vivarovhongavhongo yira;
Nashintje Ukahe Shiune pakanwa ½ ,¼
Kutwenyaura maruha ghavivarero vhongavhongo yira; shiune
¼ shiutatu ⅓ Ukahe ½ Nashintje
23 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Tjanga vivarerovhongavhongo ½, ¼, ⅓ negheda maruha ghakushetakana, naruntje.
KUMAHURA UDITO
Kumahura udito Shitamboshongwa Vashongwa vamahure maudito ghakuhamena vikaramo vyakehe liyuva pakurughanita kupakapo, kuupamo, kumpungika, kukutepatana nakurughanita ndjenditito wapero.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kumahura nakughamba maudito ghavitimwitira, vishoroka vya kehe liyuva mulikukwamo 1 – 10.
Didilika ndjenditito mukuwaneka likoshonono pakurughanita vininke vyakumona, kukuyonga, kukupa maghano, waneka likukwamo, kuhamena muvidana, nakuvhongavhonga vifaneka navifanaika nanomora.
Tikitamo ndjenditito yayiwa mukumahura maudito ghanomora 1 – 10 mukurughanita kupakapo, kuupamo, kumpungika nakutapatana kumwe yira; kuna kara namaguni mbyo nalipo matatu, mbyo pana hupu matano. Maguni mangashi naghantje Ghana karopo?
Vashingonone ndjenditito oyo varughanita nakutegherera
Kumahura nakughamba maudito ghavitimwitira, vishoroka vya kehe liyuva mulikukwamo 1 – 50.
Didilika ndjenditito mukuwaneka likoshonono pakurughanita vininke vyakumona,kukuyonga,kukupa maghano,waneka likukwamo,kuhamena muvidana,nakuvhongavhonga vifaneka navifanaika
Rughanita ndjenditito dakukushuvashuva mukukoshonona maudito ghalikukwamo nomora 1 – 50 mukutikitamo ndughanito “ ne “ ( + , - ,x , ÷ ) yira ;kuna kara vanuke 30 kushipito ano 16 mo vakadona. Vamati vangapi mo ngoli?
Vashingonone ndjenditito oyo vana rughanita nakutegherera
Kumahura nakughamba maudito ghavitimwitira, vishoroka vya kehe liyuva mulikukwamo 1 – 100.
Didilika ndjenditito mukuwaneka likoshonono pakurughanita vininke vyakumona, kukuyonga, kukupa maghano, waneka likukwamo, kuhamena muvidana, vyakuvhongavhonga nadiagrama nanomora.
Rughanita ndjenditito dakukushuvashuva mukukoshonona maudito nakutjanga maudito ghashitimwitira kukwama likukwamo nomora 1 – 100 tikitamo ndughanito “ ne “ ( + , - , x , ÷ ) tjanga shitimwitira shaudito nakushetakanita Nomora yira; 18 - =
24 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
kumashingonono ghavaunyavo. kumashingonono ghavaunyavo.
Kukuyonga maudito ghakukushuvashuva ghakuhamena kuudito wakukufana.
Dimburura nakuwapukurura mapuko.
15
Limburura: Maria karekere vaunyendi 18 kushipito shendi ano 15 mbo vayiro, vangapi vadiliro kuya?
Shingonona ndjenditito una rughanita.
Kukuyonga maudito ghakukushuvashuva ghakuhamena kuudito wakukufana.
Dimburura nakuwapukurura mapuko.
LIMETO
Unaure Shitamboshongwa Vashongwa kuvhura: Vayive mulyo wakukushetakanita unaure navyovyawapero muliparu lyavo lyakehe liyuva. Kuwaneka maruvede nankondo, kughamba nakutikitamo vishetakanita. Kuwaneka lighano lyakushetakanita. Kukulika lighano lyakehe liyuva mukutikitamo kushetakanita vininke.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kushetakanita unaure wavininke vyakukushuvashuva mukurughanita ushwinkanga; ure, ufupi, ure ngudu, ufupi ngudu, kupitakana/ una ure wakukufana.
Kushetakanita unaure, washarughanita vikalimo vyakukukarerera yira; shikandeko, mpadi mukushetakanita likushuvo lyaunaure wavashongwa.
Kutura nawa nakushetakanita vininke mukurughanita ushwinkango, kukufana, ure ngudu, ufupi ngudu.
Washarughanita yira vininke vyakudira kuwapera yira; rughodi, shimbapira mukushetakanita unaure naghuyaghayu washikovhune.
Rughanita shishetekilito shakuwapera, shasentimetera (cm), rughanita lifupipito
Shetakanita nakughoneka nawa vininke.
Rughanita muuhunga ushwinkango; kukufana, ure/ureunene, ufupi/ufupiunene nashinema.
Rughanita shishetekilito shakuwapera mukushetakanita unaure, naunaufupi wavininke, rughanita lifupipito lya nkango m, cm.
25 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Shinganyeka unaure wambapira nantishe kumwe nakuvitjanga musentimetera (cm)
nkango, rughanita shitaulitondjira, shetakanita nawanawa unaure wambapira navitafura (ntishe) nakudidilika sentimetera davyo.
Faneka ndjira yakuvyukilira uyiture munaure wayo nasentimetera.
Rughanita kupakapo nakuupamo maure namaufupi ghavininke.
Shetakanita nawa unaure nauyaghayu wankondashongero, rughanita m, cm tupu.
Shinganyeka unaure nauyaghayu wankondashongero kumwe nakuvitjanga mu cm, m.
Faneka ndjira yakuvyukilira nakushetakanita munaure cm na m.
Mukumo Shitamboshongwa Vashongwa kuvhura: Vayive mulyo wakushetakanita mukumo mukuwapera kehe liyuva muliparu lyavo. Kuwaneka maruvede ghakonda, kughamba nakutikitamo vishetakanita. Kuwaneka lighano lyakushetakanita vininke. Kukulika lighano lya kehe liyuva mukutikitamo vishetakanita vyavininke.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kushetakanita nawanawa mukumo davininke pakuvikwata namavoko nakushetakanita mukumo davyo.
Rughanita ushwinkango muuhunga yira; ure, udito, udito ngudu, ure ngudu.
Kushetakanita nawanawa mukumo davininke pakuvikwata namavoko nakurughanita ½ (ukahe) wakiligarama na 1kg yashiviha.
Rughanita nawa ushwinkango mukushetakanita vininke; udito, udito ngudu, ure, ure ngudu.
Tura nawa nakushetakanita vininke vitatu (3) mukumo wavyo.
Rughanita shiviha mu (kg)
Kushetakanita vininke kehe liyuva, rughanita ‘garama’ (g).
Shinganyeka mukumo wavininke kehe liyuva rughanita (g).
Rughanita nawa liraka mukushetakanita mukumo yira; udito, udito ngudu, udito ngudu ngudu, ure, ure ngudu, ure ngudu ngudu.
Tura nawa nakushetakanita vininke 5 dimukumo davyo.
Rughanita lifupipito; g- garama, kg- kilogarama.
26 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
mukumeta mukumo nakutjanga limeto muuhunga pakurughanita mfupipiko yavyo (g, kg).
Ukalimo Shitamboshongwa Vashongwa kuvhura: Vayive mulyo wakushetakanita ukalimo kehe liyuva muliparu lyavo. Kuwaneka maruvede nakonda, mukughamba nakutikitamo kushetakanita. Kuwaneka nawa lighano mukushetakanita. Kukulika lighano nakuvitikitamo kushetakanita vininke.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kutura nawa nakushetakanita vyuma vya kukushuvashuva kutwara mukuyura, ukahe wa ukalimo yira; mabwitiri, vimbangu, navitoromani.
rughanita ushwinkango yira; kuyura, ukahe, vingi, kupitakana
Shetakanita ukalimo wavyuma vyakukushuvashuva.
Shetekera nakushetakanita ukalimo.
Tura nakushetakanita kehe liyuva ukalimo wavininke.
Rughanita ushwinkango muuhunga yira; vingi, usheshu.
Shetekera nakonda kehe liyuva vininke maukalimo nalitera.
Shinganyeka ukalimo wavininke kehe liyuva (litera).
Shetekera nakudidilika ukalimo rughanita lifupipito (l) litera.
Tura nawa nakushetakanita vininke kehe liyuva kutwara ukalimo wavininke.
Rughanita ushwinkango muuhunga yira; ungi, usheshu, kungipa nakusheshupa navikando viviri, vikando vitatu.
Shetakanita vininke kehe liyuva, rughanita litera, mililitera (l.ml).
Shinganyeka kehe liyuva ukalimo wavininke rughanita litera, mililitera.
Shetekera nakudidilika ukalimo wavininke, rughanita (l, ml).
Liyarararo Shitamboshongwa Vashongwa va: Kwata lighano lyaliyarararo nakutikitamo kehe liyuva muliparu lyavo. Kuwaneka maruvede nakonda, mukughamba nakutikitamo kushetakanita. Kuwaneka nawa lighano mukushetakanita. Kukulika lighano nakuvitikitamo kushetakanita vininke
27 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kundika liyarararo munda nauhura mukushetekera vishwi, rughanita maukalimo, shetekera vidukito vyamabwitiri vigwaneke.
Shetakanita liharango lyavishwi vyakukushuvashuva rughanita vyawapero yira; vikandeko vyamaghoko, mpadi namapepa.
Kundameka liyarararo pantunda, munda, nauhura, meta shikungu pantunda rughanita lipepa lyanomora A4 mukuvara maruha ghamapepa.
Shetakanita maruha ghavishwi vyakukushuvashuva shinene shikwambando mukuwaneka shivaro shaliyarararo yalivango.
Ruvede Shitamboshongwa Vashongwa vayive nakurughanita ruvede muuhunga. Vayive shi shirugho shakutika kuni vyashorokanga vishoroka vya kehe liyuva nawa muliparu.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kukuyonga viviyauka vyakehe liyuva mumundi, vyamunkarapamwe muliro nakuvishetakanita navishorokwa vya mwi, matiku, ngurangura, shitenguko nangurova.
Twenyaura mayuva ghashivike namadina ghamwedi damwaka muuhunga.
Shetakanita ure, ufupi yira; kuupa shirugho mukudika ndjugho, ano lipwiyumuko lyapapause lifupi.
Rughanita ushwinkango muuhunga; ure, ufupi, mwi,
Hamitira vishoroka vya kehe liyuva vya ntantani mumundi, nkarapamwe mumaruvede, mayuva vivike namwedi.
Twenyaura mayuva ghashivike namadina ghamwedi damwaka muuhunga.
Rughanita kalindeli mukuwaneka mapukururo kuhamena mayuva naliyuva.waneka liyuva lyashivike lyalishampuruko lyaumwe.
Dimburura nawa shirugho shashishoroka shashinene
Hamitira vishoroka vya kehe liyuva vya ntantani mumundi, nkarapamwe mumaruvede, mayuva vivike namwedi.
Twenyaura mayuva ghashivike namadina ghamwedi damwaka muuhunga.
Rughanita kalindeli mukuwaneka mapukururo kuhamena mayuva naliyuva.waneka liyuva lyashivike lyalishampuruko lyaumwe.
Waneka nawa shirugho shavishoroka muviri,
28 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
matiku, yona lyo kalipito, namuntji yona ngurangura, shitengeyuva ngurova.
yira; kukara viri ne (4) pashure kehe liyuva, mayuva 7 ghashivike.
Tanta ruvede nawa paviri dapampo (danomora 1 – 12).
mumayuva, mumwaka rughanita ruvede.
Tanta nawa ruvede paviri,ukahe waviri,kupita munute,munute dakuhupako.negheda nalivoko paviri da kare 4.15
Vimaliva vyashikantani Shitamboshongwa Vashongwa vayive shi weni kurughanita vimaliva vyaNamibia.
Vitomporwa Vitomporwa Vitomporwa
Vashongwa ngava vhura ku: Vashongwa ngava vhura ku: Vashongwa ngava vhura ku:
Twenyaura nakudimburura likushuvo lyamulyo wavimaliva vyavitenda (vikuvo) vyaNamibia; 5c, 10c, 50c, N$1, N$5.Kuyonge unene wavyo, viyivito vyavyo, ruvara rwavyo namulyo wavyo.
Pongaika vimaliva vyamulyo wakukufana wavitenda (vikuvo) nange ku 50c yira; 10c = 5c +5c, 20c = 10c +10c.
Negheda kughura nakughulita vininke pakudana navimaliva nakutapa tjindji yitunde mu N$5.00 tjindji yikare musenda ndi mudola.
Twenyaura nakudimburura vimaliva vyavitenda (vikuvo) navintje navivyamapepa yira; N$10, N$20 .kuyonge mulyo wavyo.
Renka senda dikare dora; 200c = N$2.00.
Pongayika vimaliva vyavitenda (vikuvo) nange ku N$10.00, pakuvipaka kumwe yira; N$ 1, 10 = 50c +50c +10c ndi N$ 1.10 = N$1 +10c.
Negheda kughura nakughulita pakudana navimaliva nange ku N$20.00.vara nawa tjindji muuhunga.
Rughana tjindji yavimaliva vyavikuvo nange ku N$10.00 yira; mukosho wanyango N$11,50 ana ghuru shuma sha N$20 yamafo, rughana weno; N$11,50 +N$5 +N$2 +N$1 +50c = N$20.00.
Faneka likukwamo lyakughura vininke shinganyeka mukosho
Twenyaura nakudimburura vimaliva vyavitenda (vikuvo) navintje navivyamapepa yira; N$10, N$20 .kuyonge mulyo wavyo.
Tura senda dikare dora yira; 265c = N$2,65 125c = N$ 1, 25.
Pongayika vimaliva vyavitenda (vikuvo) nange ku N$50.00, pakuvipaka kumwe yira; N$ 23.50 = N$10 +N$10 +N$1 +N$1 +50c.
Negheda kughura nakughulita pakudana navimaliva nange ku N$50.00.vara nawa tjindji muuhunga.
Rughana tjindji yavimaliva vyavikuvo nange ku N$20.00 yira; Paulus ana uru ndya da N$37.00.Ana tapa N$50.00 yamafo, kurughana weno; N$ 37 + N$ 10 N$ 2+ N$ 1 = N$ 50.00.
Faneka likukwamo lyakughura
29 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
wavininke. vininke, shinganyekera ndando yavininke, konakona mukosho muvitora.
Tura mukosho wakukwateramo wavininke viviri.shinganyeka mukosho wa N$6.90 +N$ 4.20: N$7.00 +N$4.00 = N$11.00
VISHWISHONGOFANIKITO
Vishwishongofano Shitamboshongwa Vashongwa vadimburure, vatwenyaure, nakushingonona vifanayika vyamaruha maviri (2D) namatatu (3D).
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kudimburura nakutwenyaura vishwi vyamaruha maviri 2D yira; shikwambando, nkata, shikovhune, shikovhutatu.
Waneka nakudimburura vininke mumukunda.
Tura nakuhangura vishwi ovyo unatwenyaura pamuhovo kutwara muntjingononi yaruvara, unene, shishwi naunene wavyo.
Faneka nakurughana vishwishingononi: kukughudungura, maruha, vinkotye, twenya kuvyukilira yira; faneka/rughana shikovhune shamaruha maviri ghamafupi ghakuvyukilira, shamaruha maviri ghakuvyukilira kukunungakana.
Tota mafano namapi ghavishwi.
Dimburura nakutwenyaura vishwi vyamaruha matatu 3D,
Kudimburura nakutwenyaura vishwi vyamaruha maviri 2D yira; shikwambando, nkata, shikovhune, shikovhutatu vitetwa vyakukufana nalighuta.
Waneka nakudimburura vininke mumukunda.
Tura nakuhangura vishwi: shikwambando, nkata, shikovhutatu, vitetwa vyakukufana nakuyiva maruha navinkotye ashi ngapi.
Faneka,rughana vishwi vinakuneghedo lighutaC,rughanita shitetwa shashikovhutatu shakuvyukilira yira;
Tota mafano namapi ghavishwi
Dimburura nakutwenyaura vishwi vyamaruha matatu 3D, mbumbe, shinampakero.
Tura nakuhangura rudi
Kudimburura vishwi vyamaryha maviri (2D) yira; shikwambando,nkata,shikovhune,vintetwa vyakukufana,lighuta
Tura nakuhangura vishwi kutwara munaure, munaufupi, unene.
Rughana vishwi vina kuneghedo shishwi shangandi yira; gwanikitira tutondo tutano twakushetakana munaure tuneghede lifano lyashishwi.
Dimburura rulyo rwashikovhutatu (shipepa, shinkotye, lipi) mukuhangura unene, kushetakana, udidi washishwi.
Shingonona vishwi ntateko vyamaruha maviri 2D yira; shikwambando, shikovhune yira;
30 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
shikovhune, kapundi nashikwampakero.
Tura nakuhangura vininke vyamaruha matatu 3D, vimwe vyakukuvhundungura, vimwe vyakukugaunuka.
Shingonona vininke vyavindambo wayiva yira; vikondo, vinkotye, vipara, kuvyukilira nakushetakana.
Totapo vishwi vyaumoye.
rwavishwi vyamaruha matatu 3D kutwara mukukufana, vipara, shivaro shavipara.
Shingonona vininke yira; vikondo, vinkotye, vipara, kukughudungura, shikovhune, shikovhutatu.
Totapo vishwi vyamaruha matatu 3D ovyo una kuvhuruka vyavimbapira, nkata.
Totapo mafano namapi ghavishwi omo muna hamo vishwi ntateko.
Dimburura nakutwenyaura vishwi vyamaruha matatu 3D yira; mbumbe, shikwampakero, shikovhune, ntjoka, shikovhutatu.Kengurura vipara vyavyo, ndopi ne shikovhune, mbumbe kuvhura kuyighandumuna.
Tura nakuhangura vininke vyamaruha matatu 3D kutwara muvikondo, vipara, shivaro shavipara.
Shingonona vininke vyayiviko yira; vinkotye, vipara, kuvyukilira, kugetauka, shikovhune, shikovhutatu nankata.
Totapo vifanikita vyambapira vyavininke vyakukughumba yira; vimbangu, vipirangi navipurashitika.
Vhuruka vininke vyavikwamakovhu kehe liyuva yira; vibono vyashimbangu, likungu, mbapira.
Ntjongititofanikito,mafano ghakukurondanga
Shitamboshongwa Vashongwa vapongaike, kuwapaika, kunegheda nakughamba mapukururo.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Kuhangura vininke mudimutinga nakutwenyaura kehe mpungi yira; vihauto,
Kupongaika, kuwapeka nakunegheda mapukururo ghashighamba yira; nyango,
Kupongaika, kuwapeka nakunegheda mapukururo kushighamba yira; shivaro
31 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
SHIPARATJANGWA NTAMBONDUNGE1 NTAMBONDUNGE 2 NTAMBONDUNGE 3
maroli.
Kupongaika mapukururo ghashighamba yira; shivaro shavashongwa, vidanauka, kukuwapaika nakunegheda pantjangito fanikito.
Kughamba mukuwaneka mapukurura yira; kukenga pantjangito fanikito “shi vashongwa vangashi vahoro kudana mbara.
Rughanita vidukito vyamakende mukumeta vininke nakudidilika vitundwamo pantjongitofanikito.
vikwalividi, pashineghedo ntjangitofanikito.
Kughamba nakutura maghano mukuwaneka mapukururo gheneghene, kukuyonga yira; kukenga kuntjangitofanikito ashi vangashi vashongwa kavalyo shiapura shivike sho.
narudi rwavidira mumukunda, rughanita mafano ghakukurondanga, ntjangitofanikito.
Ghamba nakutura pamwe maghano mukuwaneka mapukururo gheneghene nakukuyonga ovyo vanawaneke yira; kukenga pagarafika shi marudi ghavidira mangapi tuna wana?
Rughanita ushwinkango wakuwapera pamapukururo ruvede rwakuwapaika garafika yira; usheshu, ungi, kehe pano kumoneka undambo, kuvhuka, kusheshupa shakudira kurunduruka.
Livango nkarera, livangotumbukira navininke vyakurundurura
Shitamboshongwa Vashongwa vadimburure, livangonkarera, livangotumbukira navininke vyakurundurura.
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Vitomporwa Vashongwa ngava vhura ku:
Shingonone undambo walivangonkarera lyavininke navantu varughanite maruha ghamavango tumbukira muliraka lyauhunga yira; kushelikunya, munda, pandje, kuwiru, konda, kumeho, kushikondo, pepi namukatji.
Shingonone livango tumbukira lyavininke vanafaneke palikarata yira; palikarata lyamunkondashongero.Shikungu shande kurumontjo.
Tura nakushingonona maruha ghamavangotumbukiro ghavininke vafaneka palikarata lyaliharango yira; shitondo shashinene kwakara kushelikunya yarunone rwa mema. Nkondashongero kwakara kurumontjo kutunda kushitondo.
32 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
10. Mulyowaneko
Mukuwaneka ntambo dakutikiliramo davitomporwa mulyowanekoyenderero
dakukushuvashuva hepero muntambondunge yapantateko mposhi ditape lifano
lyavashongwa omo vana kurughana na omo vana kutompora.Mulyowanekoyenderero( CA )
dina hepa kukena,ureru nakuvhura kulirughanita,lidemeneno likare pandunge damwanuke
nauyivi omo ana kuvikuyombilita.
Vitomporwa vyamundjendititoshongo kuna kutapa liyuvhoko namanongontjo ghamushongwa
omo ana kughanegheda mposhi ngo vakonakona.Ano ngoli ndjendititoshongo yina hepa
kukara yakukushonga kapishi yamakonakono ghamulyowaneko tupu.
10.1 Shitambo shamulyowaneko
Shitambo shamulyowaneko ne mukuwana mbudi daushiri damakushongo ghamushongwa
mumanongontjo.Mbudi yino vana hepa kuiyrughanita mukutapa vitundwamo vyakuhamena
nkondo naudwa wavo,oko vana kurughana nawa,ntani kuni na weni
mwakuwapukurura.Vakondi vana hepa kuvakorangeda nakuvapa ndjapo kovyo vana
rughana nawa nakuvavatera mumakushongo ghavo.
Mulyowanekoyenderero kuvatera nka mushongi a wapukurure rushongito rwendi nakutapa
uyivi mwene wamakushongo ghavashongwa.Lidemeneno valimone ashi lyamulyowaneko
wakukushonga kapishi lyamulyowaneko wakushonga.
Atwe kukengera mukuwana ukenu wakehe vitundwamo vyamushongwa vyamaghanoteto
mukutantera makushongo kumeho,kuyendita likwatitoko lyakukushonga nakukengurura
ndjenditito detu dakushonga.
10.2 Nkedi damulyowaneko
Mulyowaneko lyakupira paveta
Mushongi ana hepa kukengurura nawa kehe mushongwa ashi ana yiva nawa matetoghano
vatjangurura mundjenditoshongo yamatematika ,kuwana lifano lyaliyendo kumeho
lyavitundwamo vyamushongwa.Vino kuvirughana munkedi yakupira paveta mukukengera
kehe mushongwa vitundwamo vyendi mumakushongo navirughana vyendi ruvede oro vana
kughamba , maghano, uyivi,likuturomo nalikugwanekero lyavo mposhi mushongi a tape
vitwa muushiri kwavyo vanakurughana.
Vino kuna kutantashi, ruvede ndoro ana kushonga mushongi kuno ghuye kuna kutapa vitwa
kovyo ana kuyuva ndi ovyo ana kumona,shi are wakutegherera, are wakudira kuteghera,are
wakuhova kumana virughana vyamatematika nalikuturomo lyavo mumpungi
davo.Mulyowaneko lina hepa kudemenena pamaghanoteto vayiva ntani vikuwe nashitambo
shakehe shishongwa ntani kuturamo umwe,vaviri ndi viviyauka vyambunga.likuturomo
lyavashongwa nalihamenomo kuvirughana vyambunga navyo kuvikenga ntani pakehe
ntambo yamakushongo,mushongi ana hepa kukara naushiri ashi vashongwa kuna kuwana
maghanoteto ghauhunga.
33 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
Mulyowaneko wapapaveta
Omo kukarapo lituropo lyalikengururo yira mapuro ghambunga,makonakono
ghamafupi.Makonakono ghapangambo nakupepa twakurughanena.Tupepa twakurughanena
tuwa unene ntani kuvhura kuturughanita nampiri pashitafuratjango ndi palipepa.Mulyo unene
ashi mushongi a wapeke nakughayara mukukenga vashongwa nakuvapa vitwa pashifaneko
shashitwa 5.
Kurughanita vitjangwa namakonakono ghapangambo kuvhura tupu kukengera paruvede
rwarufupi rwamaghanoteto ntani kapishi vi ghupe shirugho shashire.Makonakono ghamafupi
kuvhura kughatapa muruha rwashirugho shavivarero, ntani mushongi a kwame ruvede rwa
karopo kutwara muviviyauka vyamatematika.
10.3 Litjangururo vitwa
Ukaro wavashongwa vaviwaneka kutwara mumaghanoteto ghandjendititoshongo
yamatematika vana ghanegheda kuntji pakutapa vitwa hepero unene ashi vineghede uyivi
wamushongwa kutwara kumaghanoteto.Muntambondunge dino 1dogoro 3, vitwa kuvi tura ku
10. Likuhamo lyapakatji kavitwa vyakutapa namaghanoteto vana gha negheda kuntji.
Ndanda
%
Shinema(gr
4-12)
Vitjangurura vyamaghanoteto
A 80%+ Kuna wana maghanoteto nawa kupitakanena.Mushongwa
muwawa mumaruha naghantje ghamaghanoteto.
B 70-79%
Kuna wana maghanoteto nawa.Vitundwamo vyamushongwa
kuna karapawiru unene ntani mumaruha naghantje muwalika.
C 60-69% Kuna wana maghanoteto nawa.Mushongwa ana wana
maghanoteto nawa mumavango ghamwe ghakupira kuyiviva.
D 50-59%
Kuna wana maghanoteto hashako.Vitundwamo
vyamushongwa kuna kukuwa nandunge
dadisheshu.Mushongwa ana hepa mbatero mumaruha
ghamwe.
E 40-49%
Kuna wana pakatji tupu kamaghanoteto ogho vana
kumona ashi hashako.Mushongwa kapi ana wana uyivi wene
wene mushongwa ana pumbwa mbatero mumakushongo
ghendi.
U 0-39%
Kuna wana maghanoteto ghapalivhu unene
ghakuurumuka.Mushongwa kapi ana wana ungi
wamaghanoteto,mwanuke ghuno ana pumbwa mbatero
yamakushongo.
34 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
10.4 Neghidito yalikengeroyenderero
Likengero lina hepa kukara ruha rwashishongwa ntani nkedi yalikengero vana hepa
kuyiturapo pavishongwa ntani pakurughana vashongwa vyavyo,mushongi ana hepa
kurughana likengero lyapaveta nalyakupira paveta mumaghanoteto naghantje nauyivi
washishongwa.Muntambo yapantanteko,likengero ndyo lyamulyopo,vino kuna kutantashi
vitwa,kuna hepa kukenga omo a tomporanga mushongwa kutwara kumaghanoteto.
10.4.1 Likengeroyenderero lyakupira paveta
Likengeroyenderero lyakupira paveta kwaliturangapo mukukengera nawa navitjangwa (
kenga shitwa 10.4.3 ) vino kuna kuntantashi,ruvedero vana kurughana vishongwa
vyavo,mushongi ana hepa kughupa vitwa avi tjange pambapira yamadina kutwara
muviwanamo ndi maudito.Vimbapira vino ndi vitantera vino ngavinegheda litjango shirongwa
shakumeho,mbatero makushongo ndi weni mwakutapa vitwa vyalikengeroyenderero
lyapaveta kapishi hepero uvitjange.
10.4.2 Likengeroyenderero lyapaveta
Likengeroyenderero lyapaveta lyakaropo,lyalyo naruntje kwa shwa kulirughana kunyima
yahulito yantjimantjima ndi mpopo lighano lyayiviko lya hepa likengururo lyakumeho
yakuyivita lighano lyalipe.Vashongi kuvhura kutapa vitjangwa vyavifupi ndi
vyalikengeroyenderero lyapakanwa ndi mapuraghero ogho vatamwinina mushinema. Konda
yevhi, mushongi kutapa vitwa kukwama 10
Mumakengeroyenderero ghamangi vatapa mushinema,likengeroyenderero limwe tupu ndyo
lyakutjangapo.Likengeroyenderero lino kulirughana paruvede rwaperiode momo
munkondarongero.Evi kuna kutanta ashi kundereko mushongwa wapantambo yantanteko
yantambondunge 1 dogoro 3 wakuvhura kutjanga makonakono ghamushivike ndi a kare
naruvede rwalikukwamo lyamakonakono muruvede omo mushongwa a kuwapayikira ndi
kukushonga ashi kwayatjanga likonakono.Vitwa vyalikengeroyenderero vyakaropo kuvitjanga
paforomu dakutjanga likengeroyenderero.Kuuhura washinema vitwa vyakehe shirongwa
kuvipakerera kumwe mumuyaro.
35 NIED Syllabus: Mathematics Juniorr Primary Phase 2014
11. USHWINKANGO ( GLOSSARY )
NB: Lifwatururo vana tapa pano kuna lirughanita tupu kuukalimo wamundjendititoshongo
yino ngoli kapishi kukehe ukalimo wapeke.
Liyarararo livango lyakushetakana
Pauruvi vyakurughanita pauruvi
Vitomporwa manongontjo ghamulyo ghakaroshi kugharuna ndi
kuughatikitamo Mukuwaneka mutompo wangandi.
Likwatoghan lighano lyenelyenepo lyashininke shakaropo
Mulyowanekoyenderero lishetakanito lyavitundwamo vyamushongwa kutwara
muvirughana ana rughana munkondashongero
mutukonakonoghona varughana mushinema ndi
mumwaka,hanashi mumakonakono ghakuuhura wamwaka
tupu.
Kuwapera nkarero yarenkitango virerupe mukurughana shintu.
Kushinganyeka kuvara kwakughayarera mukuwaneka shivaro shangandi
Lyanavantje makushongo ghakuhamitiramo kehe uno
Kuvandja kukengurura nakunongonona
Kuvara nauhaya kuvara nauyivi
Ghongora shuweda pepi
Makushongotwalilikido makushongo ghakutwikira/makushongo ghakuyenderera
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