MINISTRY OF EDUCATION JUNIOR PRIMARY PHASE …

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

http://www.nied.edu.na/

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


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.


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.


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.


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.


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




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




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




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




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




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,




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


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:



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:



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




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



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:



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



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




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:



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



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




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



Nopatorona dononomora Sitamborongo Varongwa va hepa kudimburura nonomora dokupira kuhetakana nedi dokuhetakana/depando kutamununa nokusingonono elikwamo lyononomora




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



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




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



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




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



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




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



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




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



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




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




Kugaununa yininke momaruha gokuhetakan ngwendi; Teta siapura momaruha gavali gokuhetakana


po kuruganesa sihonena sa ngesi; Kutumbura maruha goyintau Kutumbura maruha goyi ntau



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




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



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




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



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






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




Kupompeka no kuhetakanesa Kupompeka no kuhetakanesa Kupompeka nokuhetakanesa



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



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




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


Kuruganesa kalinda pokudimburura mauzera aga va tamba gokuhamena mazuva ngwendi kupapara ezuva lyehampuruko lyaguwme mosivike

Kuhamesera yihorokwa yemembo neyi yomomukunda komaruveze, mazuva nomakwendi


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



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




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



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)




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



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



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



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




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



kositji

Grafikafano sitafura grafika zokulironda

Sitamborongo Varongwa va hepa; kupongeka, kuwapayika, kulikida nokutara mauzera

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


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


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.


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


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


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


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.

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