## Topic outline

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• 0. Imyitozo yo kwiyibutsa

Igikorwa cya 1

Musome, maze mwuzuze imibare ibura muri iyi mbonerahamwe.

Igikorwa cya 2

Soma, wuzuze imibare ibura muri iyi mbonerahamwe.

Igikorwa cya 3

Mugereranye mukoresheje ibimenyetso <, > na =.

Igikorwa cya 4

Mutondeke muhereye ku mubare muto mujya ku munini.

Igikorwa cya 5

Mutondeke muhereye ku mubare munini mujya ku muto.

Igikorwa cya 6

Sesengura imibare ikurikira:

Igikorwa cya 7

Andika umubare wasesenguwe.

Igikorwa cya 8

Andika imibare yasesenguwe.

Igikorwa cya 9

Sesengura imibare mo ibinyacumi n’ibinyabumwe.

Igikorwa cya 10

Andika umubare wasesenguwe wifashishije urugero.

Urugero: c 9 b 0 = 90

Igikorwa cya 11

Koresha imbonerahamwe y’ibara, uteranye.

Igikorwa cya 12

Koresha imbonerahamwe y’ibara, ukuremo.

Igikorwa cya 13

Ifashishe utubarisho, wuzurishe imibare ibura.

Igikorwa cya 14

Koresha utubarisho, uteranye cyangwa ukuremo.

Igikorwa cya 15

Koresha utubarisho, utahure intera idahinduka yakoreshejwe.

Igikorwa cya 16

Ifashishe utubarisho mu kubara, wuzuze imibare ibura ahari utudomo.

Igikorwa cya 17

Mukore amahurizo akurikira:

a) Gasaro afite imineke 35 musaza we Gatari afite imineke 42. Bombi bafite imineke ingahe?

b) Muhoza yaguze ikaramu ya F50 n’umugati wa F40. Byombi yabyishyuye amafaranga angahe?

c) Rugira afite imyaka 45 naho umugore we afite imyaka 32. Shaka igiteranyo k’imyaka yabo.

Igikorwa cya 18

Uzuza imbonerahamwe zikurikira:

Igikorwa cya 19

Igikorwa cya 20

Andika umugabane ungana n’igice gisize ibara.

Igikorwa cya 21

1. Kubara, gusoma no kwandika imibare kuva kuri 0 kugera kuri 200

Igikorwa cya 1

Itegereze amashusho, uvuge ibiri gukorwa.

Igikorwa cya 2

Igikorwa cya 3

Igikorwa cya 4

Mukore akarundo k'udushyimbo 200 mubare musubira inyuma, mukore akandi karundo k'udushyimbo 128.

Igikorwa cya 5

Mwitegereze uru rutonde, murusome muranguruye ijwi.

Igikorwa cya 6

Bara mu macumi, wuzuze umurongo w’ibara ukurikira.

Igikorwa cya 7

Mutombore udupapuro  twanditseho imibare: 138,117, 136,186 na 174 mu gaseke, buri wese abwire  bagenzi be umubare yatomboye.

Igikorwa cya 8

Mwitegereze ishusho, namwe mukore urutonde rw’imibare kuva ku 100 kugera kuri 200.

Igikorwa cya 9

Uzuza imirongo y’ibara ikurikira:

Igikorwa cya 10

Mwuzuze iyi mirongo y’ibara, musome imibare iriho.

Igikorwa cya 11

Mwandike mu magambo imibare yose iri hagati  y'iyo mwahawe.

Igikorwa cya 12

Musome, mwandike mu magambo no mu mibare.

Igikorwa cya 13

Babiri babiri, mwuzuze imbonerahamwe ikurikira:

2. Gusesengura imibare kuva kuri 0 kugera kuri 200

Igikorwa cya 1

Andika iyi mibare mu mbonerahamwe ukurikiza urugero rwatanzwe.

Igikorwa cya 2

Mukoreshe imbonerahamwe y’isesengura mwuzuze buri mubare mu mwanya wawo.

Igikorwa cya 3

Andika umubare wasesenguwemo ibinyajana , ibinyacumi n' ibinyabumwe.

3. Kugereranya imibare kuva kuri 0 kugera kuri 200

Igikorwa cya 1

Mutombore udupapuro turiho imibare n’uturiho ibimenyetso (<,>,=). Mugereranye imibare musobanure igisubizo mwabonye.

Igikorwa cya 2

Mufate amakarita yanditseho imibare n’ibimenyetso by’igereranya: < , > na = mugereranye.

Igikorwa cya 3

Musome, mugereranye amanota y'abanyeshuri.

Mu gusoza igihembwe abanyeshuri babonye amanota atandukanye kuri 200. Kagabo afite 190, Yohani afite 151, Marita afite 173, Kalisa afite 180, Uwera afite 190. Mugereranye amanota ya babiri babiri muvuge uko arutana. Mu gusoza igihembwe abanyeshuri babonye amanota atandukanye kuri 200.

a) Kagabo na Marita

b) Yohani na Marita

c) Kagabo na Uwera

d) Kalisa na Marita

e) Kagabo na Yohani

f) Kagabo na Kalisa

g) Yohani na Kalisa

h) Uwera na Marita

Igikorwa cya 4

Itegereze iyi shusho, ugereranye amashu abanyeshuri basaruye.

Umwaka wa mbere wasaruye:                          amashu 125

Umwaka wa kabiri wasaruye:                           amashu 105

Umwaka wa gatatu wasaruye:                          amashu 156

Umwaka wa kane wasaruye:                            amashu 140

Umwaka wa gatanu wasaruye:                        amashu 162

Umwaka wa gatandatu wasaruye:                   amashu 158

Mugereranye umusaruro:

a) w'umwaka wa 1 n'uw'umwaka wa 2.

b) w'umwaka wa 2 n'uw'umwaka wa 3.

c) w'umwaka wa 1 n'uw'umwaka wa 3.

d) w'umwaka wa 4 n'uw'umwaka wa 5.

e) w'umwaka wa 6 n'uw'umwaka wa 5.

f) w'umwaka wa 2 n'uw'umwaka wa 5.

g) w'umwaka wa 1 n'uw'umwaka wa 5.

h) w'umwaka wa 2 n'uw'umwaka wa 4.

i) w'umwaka wa 6 n'uw'umwaka wa 3.

Reka ngereranye imibare nkoreshe <, > na =

4. Gutondeka imibare kuva kuri 0  kugera kuri 200

1. Gutondeka imibare uva ku muto ujya ku  munini

Igikorwa cya 1

Mukore uturundo tw’utubarisho 100, 150, 170, 180, 200  mutubare maze mutondeke imibare yatwo muhereye ku muto mujya ku munini.

Igikorwa cya 2

Mwitegereze ishusho, mutondeke amakarita y’imibare muhereye ku mubare muto mujya ku munini.

Reka ntondeke imibare mva ku muto njya ku munini

2. Gutondeka uva ku munini ujya ku muto

Igikorwa cya 3

Mukore uturundo tw’utubarisho 115, 155, 195, 100, 170 mutubare, maze mutondeke imibare yatwo muhereye ku munini mujya ku muto.

Igikorwa cya 4

Mutondeke amakarita y’imibare muhereye ku mubare munini mujya ku muto.

Igikorwa cya 5

Mutondeke imibare ikurikira muhereye ku munini mujya ku muto.

Reka nkore

1. Tondeka uhereye ku mubare muto ujya ku munini.

2. Tondeka uhereye ku mubare munini ujya ku muto.

5. Guteranya imibare kuva kuri 0 kugera kuri 200

1. Guteranya imibare mu mutwe

Igikorwa cya 1

Babiri babiri mukoreshe amakarita, muteranye mu mutwe.

Igikorwa cya 2

Bara maze wandike igisubizo mu kazu

Igikorwa cya 3

Hera ku mubare urimo ibara ritukura, uteranye wandike igisubizo ahabugenewe.

2. Iteranya ritabitsa

Igikorwa cya 4

Mukoreshe uturundo 2, kamwe mugashyiremo utubarisho 95, akandi mugashyiremo utubarisho 104. Mufate utubarisho two mu karundo ka mbere mutwongere mu karundo ka kabiri, muvuge umubare mubonye.

Igikorwa cya 5

Ifashishe utubarisho mu kubara wuzuze.

Igikorwa cya 6

Mwifashishe amakarita yanditseho imibare n'ariho ibimenyetso byo + na =

Igikorwa cya 7

Kora iyi myitozo ukurikije urugero wahawe.

Reka nteranye

3. Iteranya ribitsa

Igikorwa cya 8

Itegereze, ubare, maze uteranye imibare iri mu mbonerahamwe

Reka nkore

Nsobanukiwe ko:

• Iyo uteranya imibare uhera ku binyabumwe.

• Iyo igiteranyo k’ibinyabumwe kingana cyangwa kiruta icumi (10) urabitsa.

• Wandika ibinyabumwe by’icyo giteranyo, 10 rigize ikinyacumi 1 ukaryongera ku binyacumi, ugakomeza utyo.

Reka nkore

6. Amahurizo yo guteranya imibare kuva kuri 0 kugera kuri 200

Reka dukore amahurizo dukurikiza urugero twahawe

Urugero:

Ikigo cyacu cyakiriye abanyeshuri bashya 123 mu cyumweru cya mbere naho mu cyumweru cya kabiri bakira abanyeshuri 54. Shaka umubare w'abanyeshuri baje muri ibyo byumweru byombi?

Igisubizo:

Umubare w'abanyeshuri 123 + 54= 177

Abanyeshuri baje mu byumweru byombi ni 177

1.  Uwase yari afite amanota 120. Uyu munsi yabonye amanota 40 ubwo amaze kugira amanota angahe?

2. Hirwa yaguze ibigori 100 ageze mu rugo ahasanga ibindi bigori 12 bamuzaniye ubwo yagize ibigori bingahe?

3. Kangabe yaguze ibitabo 65 by’imibare n'ibitabo 95 by’Ikinyarwanda. Ubwo yaguze ibitabo bingahe?

4. Umudugudu wa Kabeza wateye ibiti 112  ku muganda. Naho uwa Kigabiro utera ibiti 88. Shaka igiteranyo k’ibiti byatewe n’iyo Midugudu yombi ?

5.  Amashuri y'umwaka  wa kabiri  afite abanyeshuri 111 b’abahungu n’abakobwa 89. Shaka umubare w'abanyeshuri biga muri ayo mashuri.?

6. Uwamahoro afite inkoko 142 naho musaza we Nkusi afite inkoko 32. Ubwo bombi bafite inkoko zingahe?

7. Sogokuru afite imyaka 74 naho nyogokuru akagira imyaka 69. Bombi bafite imyaka ingahe yose hamwe?

8. Mugabo yaranguje amagi 108 ku wa Mbere. Ku wa Kabiri  aranguza amagi 87. Yaranguje amagi angahe muri iyo minsi ibiri ?

9.  Kaneza   afite   inka  137 z'imbyeyi n'inka 46 z'ibimasa. Shaka umubare w'inka atunze zose hamwe?

7. Gukuramo imibare kuva kuri 0 kugera kuri 200

1. Gukuramo imibare mu mutwe

Igikorwa cya 1

Itegereze imbonerahamwe ukurikize urugero ukore umwitozo wo gukuramo 10.

2. Ikuramo ridatira

Igikorwa cya 2

Mwifashishe utubarisho 125. Mukuremo utubarisho 23. Mubare utubarisho dusigaye muvuge umubare w'utubarisho dusigaye.

Igikorwa cya 3

Mukoreshe utubarisho mwuzuze umubare ubura.

Igikorwa cya 4

Mwifashishe amakarita yanditeho imibare n'ariho ibimenyetso bya - , =

•Mufate ikarita imwe yo muri

•Mukurikizeho ikarita iriho ikimenyetso cya  -

•Mukurikizeho ikarita yo muri B

•Mukurikizeho ikarita iriho ikimenyetso cya =

•Muhitemo igisubizo mu makarita yo muri

Igikorwa cya 5

Mukoreshe imbonerahamwe y’ibara,  mukore iyi myitozo mukurikije urugero mwahawe.

3. Ikuramo ritira

Igikorwa cya 6

Mwitegereze urugero, muganira ku byakozwe.

Uburyo bwa mbere

Igikorwa cya 7

Mukoreshe imbonerahamwe y’ibara, mukuremo imibare mukurikije urugero mwahawe.

Nsobanukiwe ko:

Iyo ukuramo imibare uhera ku binyabumwe. Wasanga ibinyabumwe ari bike ku bikurwamo, ugatira ikinyacumi kimwe kingana n’ibinyabumwe icumi, ukabyongera kuri bya binyabumwe byari bike maze ugakuramo. Ukandika igisubizo. Ukomeza utyo, ukuramo ibinyacumi n’ibinyajana.

Reka nkore

8. Amahurizo yo gukuramo imibare kuva kuri 0 kugera  kuri 200

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Ku munsi w'inama y'ababyeyi hitabiriye ababyeyi 197. Muri bo 88 bari abagore. Ubwo abagabo bitabiriye inama ni bangahe?

Igisubizo:

Abagabo bitabiriye inama                197 – 88=109

Abagabo bitabiriye inama ni            109

1. Ku ishuri dufite inkoko 200 nibatekamo inkoko 50 hazasigara inkoko zingahe?

2. Uwera yaguze amagi 170 ageze ku iduka rye acuruzaho amagi 60 ubwo yasigaranye amagi angahe?

3. Mugisha yabonye amanota 156. Ubwo yabuze amanota angahe ngo agire amanota 200.

4. Shimwa yasaruye imifuka 166 y’umuceri naho Shema asarura imifuka 187 y'umuceri. Ni nde wasaruye umuceri mwinshi? Yamurushije imifuka y'umuceri ingahe?

5. Keza yaguze ibigori 178 maze ibigori 69 babitekera abashyitsi. Ubwo yasigaranye ibigori bingahe?

6. Kayiranga yasaruye inanasi 195, azijanye ku isoko acuruza inanasi 139 izindi zirasigara. Yasigaranye inanasi zingahe ?

7. Umudugudu wacu urimo ingo 187. Niba ingo 149 muri zo zoroye inka,ubwo Umudugudu wacu urimo ingo zingahe zitoroye inka?

8. Muhizi afite imifuka 187 ya sima. Niba yarakuyemo imifuka 139 ya sima akayubakisha inzu yasigaranye imifuka ya sima ingahe ?

9. Mu Mudugudu wa Bwiza harimo ingo 172. Niba ingo 148 muri zo zarafashe mituweli, hasigaye ingo zingahe zitabonye mituweli?

9. Mara ya 2 n’ibikubo bya 2

Igikorwa cya 1

Mukore uturundo tw'utubarisho tubiri tubiri ku buryo bukurikira: akarundo 1; uturundo 2, 3, 4, 5 ,6 , 7, 8, 9, 10  muvuge umubare mwabonye muri buri karundo.

Igikorwa cya 2

Uzurisha imibare ibura.

Reka nkore

1. Uzuza umubare ubura

2. Uzuza iyi mbonerahamwe

3. Gereranya

10. Gukubisha 2 imibare y’imibarwa ibiri

Igikorwa cya 3

Mukoreshe imbonerahamwe y’ibara, mukore imyitozo ikurikira mukurikiza urugero mwahawe:

Nsobanukiwe ko:

Iyo ukuba imibare, uhera ku binyabumwe ujya ku binyacumi.

11. Amahurizo yo gukuba imibare na 2

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Mu cyumba k'inama harimo intebe 42. Intebe imwe yicayeho abantu 2. Shaka umubare w'abantu bari muri icyo cyumba.

Igisubizo:

Umubare w'abantu 2 × 42 =  84

Umubare w'abantu bari mu cyumba ni 84.

1. Abanyeshuri 30 buri umwe yavomye utujerikani 2. Ubwo bose hamwe bavomye utujerikani tungahe?

2. Mu banyeshuri 34 buri wese yasaruye amashu 2. Shaka umubare w’amashu yose hamwe yasaruwe.

3. Umuhanda ufite amatara 33 kuri buri ruhande. Ufite amatara angahe ku mpande zombi?

12. Igabanya ridasagura ry'imibare y'imibarwa ibiri cyangwa itatu na 2

Igikorwa cya 1

Mubare umubare w’ibintu biri mu kirundo mufite muwandike ahabugenewe. Mubigabanyemo uturundo 2 tungana maze muvuge ibyo mubonye muri buri karundo; mwandike umubare  ahabugenewe.

Igikorwa cya 2

Uzuza iyi mbonerahamwe ukurikije urugero wahawe.

Reka nkore

Nsobanukiwe ko:

Kugabanya bidufasha gusangira n'abandi, kugabana turinganiza tudacura abandi. Ni umuco mwiza ugaragaza urukundo no  kutabera.

Igikorwa cya 4

Mugabanye imibare ikurikira mukurikije urugero mwahawe:

Reka nandike mu mahembe ngabanye

Reka ndebere ku rugero nkore

Nsobanukiwe ko:

Iyo umubarwa wa 1 utagabanyika na 2, ufata ukurikiyeho, ukagira imibarwa ibiri ukagabanya.

13. Amahurizo yo kugabanya imibare na 2

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Gabanya ku buryo bungana ibitabo 148 ibigo by'amashuri 2. Buri kigo uzagiha ibitabo bingahe?

Igisubizo:

Buri kigo nzagiha ibitabo 148 : 2 = 74

Buri kigo kizabona ibitabo 74

1. Gabanya ku buryo bungana amakayi 48 abanyeshuri 2. Buri wese azamuha amakaye angahe?

2. Ku munsi w’ibirori twateye intebe 100 mu mahema abiri. Buri hema ryagiyemo intebe zingahe?

14. Mara ya 3 n’ibikubo bya 3

Igikorwa cya 1

Mukore uturundo tw'utubarisho dutatu dutatu ku buryo bukurikira: akarundo 1; uturundo 2, 3, 4, 5, 6 ,7, 8, 9,10. Muvuge umubare mwabonye kuri buri nshuro.

Igikorwa cya 2

Uzurisha umubare ubura.

Reka nkore

1. Uzuza umubare ubura.

2. Uzuza iyi mbonerahamwe.

3. Gereranya

15. Gukubisha 3 imibare y’imibarwa ibiri

Igikorwa cya 1

Mukoreshe imbonerahamwe y’ibara, mukore iyi myitozo mukurikije urugero mwahawe.

Nsobanukiwe ko:

Iyo ukuba imibare uhera ku binyabumwe ujya ku binyacumi.

Igikorwa cya 2

Mukube mukurikije urugero mwahawe.

16. Amahurizo yo gukuba imibare na 3

Reka dukore amahurizo dukurikije urugero twahawe

1. Mu mashuri 3, buri shuri ririmo abakobwa 33 n’abahungu 32. Shaka umubare w’abanyeshuri bose.

2. Nagize amanota 60 adahinduka mu bihembwe

3. Narangije umwaka mfite amanota angahe? 3. Butera yaguze amakarito 3 y’isabune. Shaka umubare w’amasabune yaguze niba buri karito irimo amasabune 32.

4. Shaka umubare w’ibisheke biteye ku mirongo 3 niba buri murongo uriho ibisheke 23.

5. Inkoko za Kamariza zitera amagi 40 buri munsi. Shaka umubare w’amagi zitera mu minsi itatu.

6.  Mu rusengero rwacu harimo ibihande 3 kandi buri ruhande kirimo intebe 43. Shaka umubare w’intebe ziri mu rusengero.

17. Igabanya ridasagura ry'imibare y'imibarwa  2 cyangwa 3 na 3

Igikorwa cya 1

Mubare ibintu biri mu kirundo, mwandike umubare ahabigenewe. Mugabanyemo uturundo dutatu tungana, muvuge umubare w'ibyo mubonye kandi mwandike ahabugenewe.

Igikorwa cya 2

Mwuzuze imbonerahamwe zikurikira:

Igikorwa cya 3

Kora imyitozo ukurikije urugero wahawe.

Reka nkore

Nsobanukiwe ko:

Iyo ugabanya na 3: Umubarwa wa mbere utagabanyika na 3, ufata umubarwa uwukurikiye ukagira imibarwa 2 ukagabanya.

18. Amahurizo yo kugabanya imibare na 3

Reka dukore amahurizo  dukurikije urugero twahawe

Urugero:

Gabanya ku buryo bungana mudasobwa 189, ibigo nderabuzima 3. Buri kigo nderabuzima uzagiha mudasobwa zingahe?

Igisubizo:

Buri kigo nzagiha mudasobwa 189:3= 63 Buri kigo kizabona mudasobwa 63

1. Ku munsi w’amanota ikigo cyacu kizahemba abana 3 ba mbere muri buri shuri. Niba haguzwe ibihembo 36. Ubwo ikigo cyacu kigizwe n’amashuri angahe?

2. Abanyeshuri bashaka gutera indabo 69 ku mirongo itatu ku buryo bungana. Kuri buri murongo bazahatera indabo zingahe?

3. Umuyobozi w’ishuri ryacu bamuhaye ibitabo 186 abigabanya amashuri 3 ku buryo bungana. Buri shuri  yarihaye ibitabo bingahe?

4. Ikigo nderabuzima gifite inzitiramubu 159. Nibazigabanya ku buryo bungana Imidugudu 3. Buri Mudugudu uzabona  inzitiramubu zingahe ?

5. Inkoko za Butera zitera amagi 180 mu minsi itatu, ubwo ku munsi zitera amagi angahe?

• 1. Kubara, gusoma no kwandika imibare kuva kuri 0 kugera kuri 500

Igikorwa cya 1

Itegereze ishusho, uvuge imibare abariho bafite.

Igikorwa cya 2

Soma uranguruye ijwi imibare iri kuri a, b, c na d.

Igikorwa cya 3

Musome imibare yanditse ku byapa.

Igikorwa cya 4

Mwitegereze urutonde rw'imibare musome muranguruye ijwi.

Igikorwa cya 5

Koresha amajana, wuzuze uyu murongo w’ibara.

Igikorwa cya 6

Mwuzuze imbonerahamwe ikurikira:

Igikorwa cya 7

Uzuza imibare ibura mu mbonerahamwe.

Igikorwa cya 8

Mutombore udupapuro twanditseho imibare 242, 318, 425, 499, 384, buri wese avuge umubare yatomboye.

Igikorwa cya 9

Mufate amakarita 10 yanditseho imibare kuva kuri 200 kugera kuri 500 maze muyatondeke ku meza mukurikiza uko iyo mibare ikurikirana.

Igikorwa cya 10

Mwitegereze ishusho  namwe mukore urutonde rw’imibare kuva ku 200 kugera kuri 500.

Igikorwa cya 11

Mwuzuze iyi mirongo y’ibara imibare iburamo.

Igikorwa cya 12

Mwuzuze iyi mirongo y’ibara imibare iburamo.

Igikorwa cya 13

Mwandike mu magambo imibare iri hagati y'iyo mwahawe.

a) Kuva kuri 200 kugera kuri 205

b) Kuva kuri 265 kugera kuri 270

c) Kuva kuri 295 kugera kuri 300

d) Kuva kuri 345 kugera kuri 350

e) Kuva kuri 360 kugera kuri 365

Igikorwa cya 14

Soma, wandike mu mibare.

a) Magana abiri mirongo inani:

b) Magana ane na mirongo itatu:

c) Magana atatu na gatanu:

Igikorwa cya 15

Soma, wandike mu magambo iyi mibare:

a) 325:          b) 175:           c) 298:

Igikorwa cya 16

Mwuzuze iyi mbonerahamwe.

2. Gusesengura imibare kuva kuri 0 kugera kuri 500

Igikorwa cya 1

Andika iyi mibare mu mbonerahamwe y’ibara ukurikiza urugero.

Igikorwa cya 2

Mukoreshe imbonerahamwe y’isesengura mwuzuze umubare mu mwanya wawo.

Igikorwa cya 3

Mwandike umubare wasesenguwemo ibinyajana, ibinyacumi n’ibinyabumwe.

3. Kugereranya imibare kuva kuri 0 kugera kuri 500

Igikorwa cya 1

Mufate amakarita ariho imibare muyagereranye mukoresheje ibimenyetso :  <  , > na = kandi  musobanura uko mwabikoze.

Igikorwa cya 2

Mutombore udupapuro turiho imibare muyigereranye mukoresheje(<,>, na =).

Igikorwa cya 3

Musome, mugereranye amanota y'abanyeshuri.

Mu gusoza igihembwe abanyeshuri babonye amanota atandukanye kuri 500. Butera afite 351, Mutoni afite 473, Kabarisa afite 380, Uwase afite 390, naho Mukayiranga akagira 429.

Mugereranye amanota ya:

a) Kabarisa na Mutoni

b) Butera na Kabarisa

c) Uwase na Mutoni

d) Butera na Mutoni

e) Uwase na Kabarisa

f)  Uwase na Butera

g) Kabarisa na Mukayiranga

h) Mukayiranga na Butera

i)  Uwase na Mukayiranga

j)  Mukayiranga na Mutoni

Igikorwa 4

Itegereze iyi shusho, ugereranye Karoti abanyeshuri basaruye.

Umwaka wa mbere            :  Karoti 158

Umwaka wa kabiri             :  Karoti 261

Umwaka wa gatatu            :  Karoti 356

Umwaka wa kane              :  Karoti 398

Umwaka wa gatanu           :  Karoti 434

Umwaka wa gatandatu      :  Karoti 497

Mugereranye umusaruro.

a) w'umwaka wa 1 n’uw'umwaka wa 3.

b) w'umwaka wa 2 n’uw'umwaka wa 3.

c) w'umwaka wa 3 n’uw'umwaka wa 4.

d) w'umwaka wa 4 n’uw'umwaka wa 5.

e) w'umwaka wa 5 n’uw'umwaka wa 6.

f) w'umwaka wa 2 n’uw'umwaka wa 5.

g) w'umwaka wa 6 n’uw'umwaka wa 1.

h) w'umwaka wa 4 n’uw'umwaka wa 2.

i) w'umwaka wa 5 n’uw'umwaka wa 3.

Reka ngereranye nkoreshe <, > na =

4. Gutondeka imibare kuva kuri 0 kugera kuri 500

1. Gutondeka uva ku mubare muto ujya ku munini

Igikorwa cya 1

Mukore uturundo tw’utubarisho, 200, 230, 300, 350, 400 na 499. Mutubare, maze mutondeke imibare yatwo muhereye ku muto mujya ku munini. Mwerekane uko mwabikoze.

Igikorwa cya 2

Mufate amakarita y’imibare, muyatondeke muhereye ku yanditseho umubare muto mujya ku yanditseho umubare  munini.

Igikorwa cya 3

Tondeka uhereye ku mubare muto ujya ku munini.

2. Gutondeka uva ku mubare munini ujya ku  muto

Igikorwa cya 4

Mukore uturundo tw’utubarisho, 235, 274, 315, 472, 499 mutubare maze mutondeke imibare yatwo  muhereye ku munini mujya ku muto.

Igikorwa cya 5

Mwitegereze iyi shusho, mutondeke amakarita y’imibare muhereye ku mubare munini mujya ku muto.

Reka nkore

Mutondeke muhereye ku mubare munini mujya ku muto.

a) 252, 475, 330

b) 453, 248, 500

c) 479, 500, 315

d) 254, 328, 432

e) 424, 256, 337

f) 390, 299, 473

5. Guteranya imibare kuva kuri 0 kugera kuri 500

1. Guteranya imibare mu mutwe.

Igikorwa cya 1

Teranya mu mutwe.

a) 200 + 50 =      b) 200 + 20 =        c) 220 + 30 =

d) 250 + 50 =      e) 300 + 50 =        f) 350 + 50 =

g) 400 + 50 =      h) 450 + 50 =        i) 300 + 80 =

Igikorwa cya 2

Muteranye mwandike igiteranyo ahabugenewe.

2. Iteranya ritabitsa

Igikorwa cya 3

Mwitegereze iyi shusho muvuge ibiri gukorwa.

Igikorwa cya 4

Mukoreshe uturundo 2 tw’utubarisho, kamwe mugashyiremo utubarisho 225 akandi mugashyiremo 163. Mufate utubarisho two mu karundo ka mbere mutwongere mu karundo ka kabiri muvuge umubare mubonye.

Igikorwa cya 5

Mukoreshe utubarisho mukore iyi myitozo.

Igikorwa cya 6

Mwifashije amakarita yanditseho iyi imibare n'ibimenyetso: + , =

•Mufate ikarita imwe yo muri A

•Mukurikizeho ikarita iriho ikimenyetso cyo guteranya +

•Mukurikizeho ikarita yo muri B

•Hakurikireho ikarita iriho ikimenyetso cya =

•Igisubizo kibe imwe mu makarita yo muri C.

Igikorwa cya 7

Koresha imbonerahamwe y’ibara ukore iyi myitozo ukurikije urugero wahawe.

3. Iteranya ribitsa

Igikorwa cya 8

Mwitegereze urugero, mukoreshe imbonerahamwe y’ibara muteranye.

Nsobanukiwe ko:

• Iyo uteranya imibare uhera ku binyabumwe.

1. Iyo igiteranyo kingana cyangwa kiruta 10, urabitsa.

2. Wandika ikinyabumwe k’icyo giteranyo,

3. Ikinyacumi 1 ukacyongera ku binyacumi

4. Ugakomeza utyo.

Reka nkore

a) 205 + 258 =               b) 277+ 196 =                    c) 339 +1 43 =

d) 285+146 =                 e) 337 + 126 =                   f) 288 + 145 =

g) 149 + 336 =               h) 273 + 149 =                   i) 189 +227 =

6. Amahurizo yo guteranya imibare itarenga 500

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Nahimana yagize amanota 225 mu gihembwe cya mbere, mu cya kabiri agira amanota  215. Yabonye amanota angahe muri ibyo bihembwe byombi?

Igisubizo:

Yabonye amanota 225+215= 440 Yabonye amanota 440

1. Umuyobozi w’ikigo yaguze ibitabo 265 by’imibare n'ibitabo 195 by’Ikinyarwanda. Yaguze ibitabo bingahe byose hamwe?.

2. Umudugudu wa Kanyinya wateye ibiti 312 ku munsi w’umuganda. Uwa Kinyinya wateye ibiti 188.  Iyo Midugudu yombi yateye ibiti bingahe?

7. Gukuramo imibare kuva kuri 0 kugera kuri 500

1. Gukuramo imibare mu mutwe.

Igikorwa cya 1

Kuramo mu mutwe.

a) 500 - 50 =             b) 400 - 50 =            c) 300 - 50 = d) 200 - 50 =

e) 100 - 50 =             f) 50 - 50 =               g) 450- 50 = h) 350 - 50 =

i) 250 - 50 =              j) 150 - 50 =             k) 500 - 100 = l) 400 - 100 =

2. Ikuramo ridatira

Igikorwa cya 2

Mwitegereze iyi shusho, muvuge ibiri gukorwa.

Igikorwa cya 3

Mwifashishe utubarisho 345 mukuremo utubarisho 132 mubare utubarisho dusigaye muvuge umubare mubonye.

Igikorwa cya 4

Mwifashije amakarita yanditseho iyi imibare n'ibimenyetso: - , =

•Mufate ikarita imwe yo muri A

•Mukurikizeho ikarita iriho ikimenyetso cyo gukuramo -

•Mukurikizeho ikarita yo muri B

•Hakurikireho ikarita iriho ikimenyetso cya =

•Igisubizo kibe imwe mu makarita yo muri C.

Igikorwa cya 5

Mukoreshe imbonerahamwe y’ibara, mukore iyi myitozo mukurikije urugero mwahawe.

Reka dukore mu matsinda

Mwifashishe utubarisho mwuzuze umubare ubura.

3. Ikuramo ritira

Igikorwa cya 6

Mukuremo imibare ikurikira mukurikije urugero mwahawe:

Reka nkuremo ntira nkurikije urugero nahawe

a) 452 - 247 =              b) 343 - 148 =            c) 264 - 139 =

d) 471 - 357 =             e) 345 - 228 =             f) 465 - 258 =

g) 372 - 228 =             h) 482 - 357 =             i) 495 - 389 =

Nsobanukiwe ko:

Iyo ukuramo imibare uhera ku binyabumwe. Wasanga ibinyabumwe ari bike ku bikurwamo, ugatira ikinyacumi kimwe kingana n’ibinyabumwe icumi, ukabyongera kuri bya binyabumwe byari bike maze ugakuramo. Ukandika igisubizo. Ukomeza utyo, ukuramo ibinyacumi n’ibinyajana.

Reka nkuremo

a) 400 - 358 =                      b) 397- 268 =

c) 493 - 334 =                      d) 485 - 346 =

e) 336 - 327 =                      f) 485 - 248 =

8. Amahurizo yo gukuramo imibare itarenga 500.

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Ikigo cyacu gifite abanyeshuri 378. Abanyeshuri 132 biga mu mwaka wa 6. Nibarangiza hazasigara abanyeshuri  bangahe?

Igisubizo:

Hazasigara abanyeshuri    378 - 132 = 246

Hazasigara abanyeshuri    246

1. Inkoko za Tito zateye amagi 370. Amagi 87 arameneka. Yasigaranye amagi angahe?

2. Makuza yasaruye imifuka 466 y’ibishyimbo mushiki we asarura imifuka 387 y'ibishyimbo. Ni nde wasaruye byinshi? Yamurushije imifuka ingahe yibishyimbo?

9. Mara ya 4 n’ibikubo bya 4

Igikorwa cya 1

Mwitegereze namwe mukore nk’ibi.

Igikorwa cya 2

Mwuzuzemo umubare ubura .

Reka nuzuze imibare ibura

Reka ngereranye nkoreshe <, > na =

10.Gukubisha imibare y’imibarwa ibiri na 4

Igikorwa cya 1

Mukoreshe imbonerahamwe y’ibara mukore imyitozo ikurikira mukurikiza urugero mwahawe.

Nsobanukiwe ko:

Iyo ukubisha imibare y'imibarwa 2 na 4 uhera ku binyabumwe ujya ku binyacumi.

Igikorwa cya 2

Kuba ukurikije urugero wahawe.

11. Amahurizo yo gukuba imibare na 4

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Mu ishuri turi abanyeshuri 42, buri munyeshuri afite ibitabo 4 byo gusoma. Shaka umubare w’ibitabo byose biri mu ishuri ryacu.

Igisubizo:

Umubare w'ibitabo byose  4 × 42 = 168.

Umubare w'ibitabo byose ni  168.

1. Mu muganda w’ukwezi abaturage 82 bateye ibiti 4 buri wese. Shaka umubare w’ibiti byatewe n’abo baturage bose.

2. Imbere y’ishuri hari imirongo 4 y’abanyeshuri. Shaka umubare w’abanyeshuri bari kuri iyo mirongo niba buri murongo uriho abanyeshuri 22.

12. Kugabanya imibare na 4gikorwa

Igikorwa cya 1

Bara umubare w’ibintu biri mu kirundo, bigabanyemo uturundo 4 tungana, bara ibyo ubonye muri buri karundo. Kurikiza urugero rwatanzwe.

13. Igabanya ridasagura ry'umubare w'imibarwa 2 cyangwa 3 na 4

Igikorwa cya 1

Mugabanye mukurikije urugero mwahawe .

Igikorwa cya 2

Andika mu mahembe ugabanye.

a) 80 : 4 =         b) 64 : 4 =        e) 96: 4 =

c) 88  : 4 =        d) 92 : 4 =         f)  72: 4 =

Igikorwa cya 3

Andika mu mahembe ugabanye ukurikije urugero wahawe.

a) 500 : 4 =           b) 296 : 4 =             c) 492 : 4 =             d) 388 : 4 =

e) 284 : 4 =           f) 480 : 4 =              g) 376 : 4 =             h) 472 : 4 =

i) 368 : 4 =            j) 464 : 4 =              k) 260 : 4 =              l) 456: 4 =

m) 252 : 4 =         n) 448 : 4 =             o) 344 : 4 =              p) 440 : 4 =

Nsobanukiwe ko:

Iyo ugabanya umubare ufite imibarwa irenze umwe na 4, umubarwa wa mbere mu binyajana utagabanyika na 4 ufata umubarwa uwukurikiye w'ibinyacumi ukagira imibarwa ibiri ukagabanya.

14. Amahurizo yo kugabanya imibare na 4

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Umuyobozi w’ishuri yaguze ibitabo 488 abigabanya amashuri 4 ku buryo bungana. Buri shuri ryabonye ibitabo bingahe?

Igisubizo:

Buri shuri ryabonye ibitabo 488 : 4 = 122

Buri shuri ryabonye ibitabo 122

1. Umubyeyi yagabanyije abana be 4 amakayi 144 ku buryo bungana. Buri mwana yahawe amakayi angahe?

2. Mu cyumba k'inama hari abaturage 368. Bicaye mu bihande 4 kandi buri ruhande rurimo intebe zingana. Ubwo muri buri ruhande hicaye abaturage bangahe?

15. Mara ya 5 n’ibikubo bya 5

Igikorwa cya 1

Mwitegereze namwe mukore nk’ibi.

Igikorwa cya 2

Uzurisha umubare ubura.

Reka nuzuze umubare ubura

Reka ngereranye nkoreshe <, > na =

16. Gukubisha 5 imibare y’imibarwa ibiri

Igikorwa cya 1

Mukoreshe imbonerahamwe y’ibara mukore imyitozo

Nsobanukiwe ko:

Iyo ukuba umubare w'imibarwa 2 na 5, uhera ku binyabumwe ugakurikizaho ibinyacumi.

Igikorwa cya 2

Kuba ukurikije urugero wahawe

17. Amahurizo yo gukuba umubare w'imibarwa 2 na 5

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Mu cyumba cyabereyemo ubukwe hari imirongo 5 y’intebe, kuri buri murongo hariho intebe 91. Shaka umubare w’intebe ziri muri icyo cyumba cy’ubukwe.

Igisubizo:

Umubare w'intebe     91 x 5 = 455

Umubare w'intebe ni  455

1. Umujyanama w’ubuzima yatanze inzitiramubu 5 kuri buri muryango. Shaka umubare w’inzitiramubu zatanzwe ku miryango 81.

2. Mu ishuri ryacu hari abanyeshuri 41. Shaka umubare w’imyitozo ikorwa n’abanyeshuri bose buri munsi niba buri munyeshuri akora imyitozo 5 ku munsi.

3. Icyumba k'inama  kirimo intebe 61. Shaka umubare w'abantu bashobora gukwirwa muri icyo cyumba niba buri ntebe yicarwaho n'abantu 5.

4. Amatsinda 31 agizwe n'abantu 5 buri tsinda. Shaka umubare w'abantu bose bari muri ayo matsinda.

5. Mu gakarito k'amazi harimo uducupa 40. Shaka umubare w'uducupa tw'amazi turi mu dukarito 5.

18. Igabanya ridasagura ry'umubare w'imibarwa 2 cyangwa 3 na 5

Igikorwa cya 1

Bara umubare w’ibintu biri mu kirundo, bigabanyemo uturundo 5 tungana, bara ibyo ubonye muri buri karundo. Andika imibare ubonye ahabigenewe ukurikiza urugero rwatanzwe.

Reka nuzuze imibare ibura

Igikorwa cya 2

Mugabanye mukurikije urugero mwahawe.

Igikorwa cya 3

Andika mu mahembe ugabanye.

a) 105 : 5 =         b) 210 : 5 =        e) 330 : 5 =          g) 440 : 5 =

c) 315 : 5 =         d) 220 : 5 =        f) 135: 5 =            h) 145 : 5 =

Nsobanukiwe ko:

Iyo ugabanya umubare ufite imibarwa ibiri cyangwa itatu, umubarwa wa mbere (ibinyajana) utagabanyika na 5, ufata umubarwa uwukurikiye (ibinyacumi)  ukagira imibarwa ibiri hanyuma ukagabanya.

Reka nuzuze iyi mbonerahamwe

19. Amahurizo yo kugabanya umubare w'imibarwa 2 cyangwa 3 na 5

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Nugabanya ku buryo bungana amacunga 65 abanyeshuri 5. Buri wese azabona amacunga angahe?

Igisubizo:

Buri wese azabona amacunga 65 : 5 = 13

Buri munyeshuri azabona amacunga 13

1. Ishyirahamwe ry’aborozi 5 ryagabanye inka 495 ku buryo bungana. Buri mworozi yatwaye inka zingahe?

2. Ikigo nderabuzima kigiye gutanga inzitiramubu 385 ku midugudu 5. Buri mudugudu uzahabwa inzitiramubu zingahe?

• 1. Kubara, gusoma no kwandika imibare kuva kuri 0 kugera ku 1000

Igikorwa cya 1

Mwitegereze ishusho, muvuge ibyo mubonaho, muganire ku nshuro imibare y’amajana yagaragajwe.

Igikorwa cya 2

Soma uranguruye ijwi imibare iri kuri a, b, c, d na e

Igikorwa cya 3

Mwitegereze ishusho, musome imibare yanditse kuri izi modoka.

Igikorwa cya 4

Mwitegereze uru rutonde rw'imibare, musome muranguruye ijwi.

Igikorwa cya 5

Uzuza uyu murongo w’ibara ukoresha amajana.

Igikorwa cya 6

Mwuzuze iyi imbonerahamwe hanyuma musome imibare mwujujemo.

Igikorwa cya 7

Mutombore udupapuro twanditseho imibare

Buri wese abwire bagenzi be umubare yatomboye.

Igikorwa cya  8

Muge mu mashuri y'umwaka wa mbere, ay'umwaka wa kabiri n'ay'umwaka wa gatatu. Maze mubaze umubare  w'abanyeshuri biga muri buri  shuri. Muwandike nimusubira mu ishuri buri wese asome imibare yanditse.

Igikorwa cya 9

Mwitegereze ishusho namwe mukore urutonde rw'imibare kuva kuri 500 kugera ku 1000.

Igikorwa cya 10

Mwuzuze imirongo y’ibara nimurangiza musome imibare iri kuri buri murongo.

Igikorwa cya 11

Mwandike mu magambo imibare yose iri hagati y'iyo mwahawe.

a) Kuva kuri 500 kugera kuri 510

b) Kuva kuri 665 kugera kuri 675

c) Kuva kuri 595 kugera kuri 605

d) Kuva kuri 846 kugera kuri 856

e) Kuva kuri 968 kugera kuri 978

Igikorwa cya 12

Andika iyi mibare mu magambo.

a) 725

b) 875

c) 998

d) 693

Igikorwa cya 13

Andika aya magambo mu mibare.

a) Magana atandatu mirongo inani:

b) Magana inani  na mirongo itatu:

c) Magana atanu na gatanu:

Igikorwa cya 14

Mwuzuze imibare ibura mu mbonerahamwe. Nimurangiza musome imibare mwujujemo.

2. Gusesengura imibare kuva kuri 0 kugera kuri 999

Igikorwa cya 1

Andika iyi mibare mu mbonerahamwe ukurikiza urugero wahawe.

Igikorwa cya 2

Koresha imbonerahamwe y’isesengura, wuzuze buri mubare, mu mwanya wawo. Kurikiza urugero rwatanzwe.

Igikorwa cya 3

Mukoreshe imbonerahamwe y’isesengura, mwandike umubare wasesenguwemo ibinyajana (j),ibinyacumi (c) n'ibinyabumwe (b).

a) c 7 b 3 j 1 =              b) b 5 j 8 c 2 =                c) j 9 b 6 c 5 =

d) c 8 b 2 j 3 =              e)  b 5 c 7 j 2 =               f)  c 7 j 2 b 6   =

g) j 6 b 5 c 4   =            h) b 8 j 4 c 0 =                i)  j 5 b 9 c 1 =

3. Kugereranya imibare kuva kuri 0 kugera kuri 999

Igikorwa cya 1

Mufate amakarita yanditseho imibare 325 na 253  n'ibimenyetso by'igereranya  <  ,  >  na  = mugereranye mwerekana uko mwabikoze.

Igikorwa cya 2

Mufate amakarita yanditseho imibare. mugereranye abiri abiri mukoresheje ibimenyetso:      <> na = .

Igikorwa cya 3

Mutombore udupapuro turiho imibare 565 na 935 n’uturiho ibimenyetso by’igereranya  < ,  >  na  =. Mugereranye imibare mwatomboye musobanure igisubizo mwabonye.

Igikorwa cya 4

Itegereze iyi shusho ugereranye ibisheke abanyeshuri basaruye.

Reka ngereranye nkoreshe <, > na =

4. Gutondeka imibare kuva kuri 0 kugera kuri 999

1. Gutondeka uva ku mubare muto ujya ku munini

Igikorwa cya 1

Mukoreshe ikibarisho, mubare imibare 515, 650, 720, 847 na 905  maze mutondeke imibare muhereye ku muto mujya ku munini.

Igikorwa cya 2

Mwitegereze iyi shusho, mutondeke amakarita y'imibare muhereye ku mubare muto mujya ku munini.

Igikorwa cya 3

Tondeka imibare ikurikira uhereye ku muto ujya ku munini:

a) 542, 745, 603            b) 835, 784, 910

c) 947, 598, 612            d) 756, 882, 623

e) 777, 658, 831            f ) 771, 717, 177

2. Gutondeka uva ku mubare munini ujya ku muto

Igikorwa cya 4

Mukoresheje ikibarisho, mubare iyi mibare: 475, 649, 728, 694 na 823. Maze mutondeke imibare muhereye ku munini  mujya ku muto mwerekane uko mwabikoze.

Igikorwa cya 5

Mwitegereze iyi shusho mutondeke amakarita y'imibare muhereye ku mubare munini mujya ku muto.

Igikorwa cya 6

Mutondeke muhereye ku mubare munini mujya ku mubare muto.

a) 522, 745, 830        b) 953, 848, 600        c) 779, 500, 615          d) 854, 728, 932

e) 524, 556, 637        f) 990, 799, 673         g) 612,621,672            h) 836,806,863

i) 924,908,942           j) 739,709, 793          k) 672,607,627             l)  549,509,594

5. Guteranya imibare igiteranyo kitarenga 999

1. Guteranya imibare mu mutwe

Igikorwa cya 1

Musome imibare muyiteranye mu mutwe maze mwandike igisubizo

a) 500 + 50 =            b) 500 + 20 =            c) 720 + 30 =

d) 650 + 50 =            e) 800 + 50 =            f) 750 + 50 =

g) 600 + 50 =            h) 850 + 50 =            i) 900 + 80 =

Igikorwa cya 2

Musome imibare, muyiteranye mu mutwe mwandike igisubizo.

2. Iteranya ritabitsa

Igikorwa cya 3

Mwifashishe amakarita yanditeho imibare n'ariho ibimenyetso bya + , =

•Mufate ikarita imwe yo muri

•Mukurikizeho ikarita iriho ikimenyetso cyo +

•Mukurikizeho ikarita yo muri

•Mukurikizeho ikarita iriho ikimenyetso cya =

•Muhitemo igisubizo mu makarita yo muri

Igikorwa 4

Mukoreshe imbonerahamwe y’ibara mukore imyitozo ikurikira mukurikije urugero mwahawe:

a) 523 + 475 =                  b) 635 + 262 =                    c) 712 + 277 =

d) 347 + 551 =                  e) 752 + 245 =                    f) 664 + 325 =

g)682 + 216 =                   h) 591+ 406 =                     i) 615 + 381 =

Igikorwa cya 5

Ifashishe ibibarisho mu kubara wuzuza umubare ubura.

3. Iteranya ribitsa

Igikorwa cya 6

Mukoreshe imbonerahamwe y’ibara muteranye iyi mibare mukurikije urugero mwahawe.

a)625 + 167 =             b)534 + 148 =               c)446 + 229 =

d)617 + 175 =             e)415 + 228 =               f)523 + 228 =

g)376+ 128 =              h)518+ 315 =                i)392+ 278 =

Nsobanukiwe ko:

Iyo uteranya imibare uhera ku binyabumwe.

Reka nkoreshe imbonerahamwe y'ibara nteranye

a) 520 + 258 =              b) 277 + 496 =          c) 539 + 143 =           d) 685 + 146 =

e) 737 + 126 =              f) 588 + 145 =           g) 449 + 336 =           h) 673 + 149 =

i) 489 + 227 =               j) 565 + 208 =            k) 834 + 128 =           l) 798 + 186 =

6. Amahurizo yo guteranya imibare igiteranyo kitarenga 999

Reka dukore amahurizo dukurikije urugero twahawe

Urugero:

Mu kigega harimo ibigori 567, nibongeramo ibindi 312 ubwo haraba harimo ibigori bingahe byose hamwe?

Igisubizo:

Umubare w'ibigori 567 + 312 = 879

Ibigori byose hamwe ni 879

1. Abanyeshuri bakoresheje impapuro 534 mu kizamini k’imibare. Mu kinyarwanda bakoresha impapuro 365. Bakoresheje impapuro zingahe zose hamwe?

2. Mu bukwe bakoresheje impapuro 450 zo kwihanaguza intoki mbere yo gufungura. Nyuma bakoresha izindi mpapuro 539. Bakoresheje impapuro zingahe zose hamwe?

3. Mu isoko harimo abacuruzi 723 bacuruza. Hiyongeraho abandi bacuruzi 276. Ubwo harimo abacuruzi bangahe?

7. Gukuramo imibare ikinyuranyo kitarenga 999

1. Gukuramo imibare mu mutwe

Igikorwa cya 1

Musome, mukuremo mu mutwe mwandike igisubizo.

a) 800 - 50 =              b) 900 - 50 =               c) 700 - 50 =

d) 600 - 50 =              e) 500 - 50 =               f) 950 - 150 =

g) 850 - 150 =            h) 650 - 150 =             i) 450 - 50 =

2. Ikuramo ridatira

Igikorwa cya 2

Mwitegereze iyi shusho muvuge ibiri gukorwa.

Igikorwa cya 3

Mwifashishe amakarita yanditseho imibare n'ariho ibimenyetso bya - , =

•Mufate ikarita imwe yo muri A

•Mukurikizeho ikarita iriho ikimenyetso cya  -

•Mukurikizeho ikarita yo muri B

•Mukurikizeho ikarita iriho ikimenyetso cya =

•Muhitemo igisubizo mu makarita yo muri C

Igikorwa cya 4

Mukoreshe imbonerahamwe y’ibara mukore imyitozo mukurikije urugero mwahawe.

3. Ikuramo ritira

Igikorwa cya 5

Mukoreshe imbonerahamwe  y'ibara mukuremo imibare ikurikira mukurikije urugero mwahawe.

a) 651 - 246 =                      b) 542 - 147 =                           c) 463 - 138 =

d) 774 - 359=                       e) 845 - 226 =                            f) 966 - 257 =

g) 577 - 228 =                      h) 783 - 357 =                            i) 694 - 389 =

Reka nkore

1. Koresha imbonerahamwe y’ibara ukore iyi myitozo:

a) 785 - 356 =                   b) 937 - 268 =                 c) 693 -  339 =

d) 785 - 348 =                   e) 836 - 327 =                 f) 985 - 246 =

g) 721 - 272 =                   h) 832 - 149 =                 i) 642 - 247 =

j) 438 -  399  =                  k) 934 - 288 =                 l) 296 - 199 =

m) 634 - 277 =                   n) 731 - 292 =                o) 543 - 247 =

p) 732 - 163 =                    r) 296 - 199 =                 s) 634 - 277 =

t) 731 - 292 =                    u) 543 - 247 =                 v) 732 - 163 =

2. Uzuza umubare ubura.

8. Amahurizo yo gukuramo imibare iri munsi ya 999

Reka dukore amahurizo dukurikije urugero twahawe

Urugero

Ikigo cyacu bagihaye ibitabo byo gusoma 850 niba 615 byarahawe abanyeshuri, hasigaye ibitabo bingahe?

Igisubizo

Hasigaye ibitabo  850- 615 = 235

Hasigaye ibitabo 235

1. Mwarimu yaguze amakaramu 500, aduha  amakaramu 342. Yasigaranye amakaramu angahe?

2. Butera yasaruye imifuka 646 y’ibirayi, mushiki we  asarura imifuka 837 y'ibirayi. Ni nde wasaruye imifuka myinshi? Yamurushije imifuka ingahe?

3. Umwaka ushize Zigama yaranguye amashati 954, acuruza amashati 719 . Shaka umubare w’amashati yasigaranye?

4. Mu busabane ku Murenge wacu baguze  amacupa 960 ya fanta. Abitabiriye ubusabane bari 756 kandi buri wese yahawe icupa1 rya fanta. Ubwo hasigaye Fanta  zingahe?

5. Uyu mwaka Leta yaguze imodoka 942 zose hamwe. Niba 749 muri zo ari imodoka ntoya shaka umubare w'imodoka nini yaguze?

9. Mara ya 6 n’ibikubo bya 6

Igikorwa cya 1

Mukore uturundo tw'utubarisho dutandatu dutandatu,  ku buryo bukurikira: Akarundo 1; uturundo 2; 3; 4; 5; 6; 7; 8; 9; 10. Muvuge kandi mwandike umubare mwabonye kuri buri nshuro.

Igikorwa cya 2

Uzurisha imibare ibura.

Reka nuzuze imibare ibura

Gereranya

10. Gukubisha 6 imibare y’imibarwa 2 cyangwa 3

Igikorwa cya 1

Mukoreshe imbonerahamwe y’ibara mukore imyitozo.

Nsobanukiwe ko:

Iyo ukuba imibare uhera ku binyabumwe.

Igikorwa cya 2

Mukube mukurikije urugero mwahawe.

11. Amahurizo yo gukuba imibare na 6

Reka dukore amahurizo dukurikije urugero twahawe

1. Intebe 51 zicarwaho n'abantu bangahe niba buri ntebe ifite ibyicaro 6.

2. Abanyeshuri 41 bahawe amakayi 6 buri wese. Shaka umubare w'amakayi bahawe yose hamwe.

3. Inyubako ifite amagorofa 31, buri gorofa rifite ibyumba 6. Shaka umubare w'ibyumba biri muri iyo nyubako.

4. Imbere y’ibendera hari imirongo 6 y’abanyeshuri. Vuga umubare w’abanyeshuri bari kuri iyo mirongo niba buri murongo uriho abanyeshuri 61.

5. Mu cyumba cy’ubukwe hari imirongo 6 y’intebe, kuri buri murongo hari intebe 95. Shaka umubare w’intebe ziri muri icyo cyumba.

6. Umubaji afite ibiti 6. shaka umubare w'imbaho zizavamo niba buri giti azagisaturamo imbaho 50.

12. Kugabanya imibare na 6 badasagura

Igikorwa cya 1

Mubare umubare w’ibintu biri mu kirundo mubigabanyemo uturundo 6 tungana maze mwandike igisubizo ahabugenewe.

Reka nuzuze imibare ibura

13.  Igabanya ridasagura ry'imibare y'imibarwa 2 cyangwa 3 na 6

Igikorwa cya 1

Mugabanye imibare ikurikira mukurikije urugero mwahawe:

Nsobanukiwe ko:

Iyo ugabanya umubare ufite imibarwa ibiri cyangwa itatu, umubarwa w'ibinyajana (j) utagabanyika na 6 uhita ufata umubarwa uwukurikiye w'ibinyacumi (c) ukagira ibiri hanyuma ukagabanya.

Reka nandike mu mahembe ngabanye

14. Amahurizo yo kugabanya imibare na 6

Reka dukore amahurizo dukurikije urugero twahawe

1. Umucuruzi yagabanyije abanyeshuri 6 amakayi 246 ku buryo bungana. Ubwo buri munyeshuri azafata amakayi angahe?

2. Inka za Musoni zikamwa litiro 486 mu minsi 6. Ubwo ku munsi zikamwa litiro zingahe ?

3. Gabanya ku buryo bungana imipira yo gukina 864 mu bigo 6. Buri kigo uzagiha imipira ingahe?

15. Gukubisha imibare 10 na 100

Igikorwa cya 1

Mufate utubarisho 10 inshuro  1, 2, 3 , 4 , 5 ,6 , 7, 8, ,9 na 10. Muvuge umubare w’utubarisho mubonye kuri buri nshuro.

Nsobanukiwe ko:

• Iyo ukubisha umubare 10  n'undi mubare wandika uwo mubare ukongeraho zeru imwe.

• Iyo ukubisha umubare 100 n'undi mubare wandika uwo mubare ukongeraho amazeru 2.

Igikorwa cya  2

Mukube na 10 cyangwa 100 mukurikije urugero mwahawe.

Reka nkore

1. Uzurisha 10 cyangwa 100

2. Uzuza izi mbonerahamwe

3. Kuba imibare ikurikira

URL: 1
• 1. Kimwe cya kabiri (1/2)

(a) Gusoma no kwandika umugabane 1/2

Igikorwa cya 1

Fata urupapuro uruhinemo ibice bibiri bingana. Ubitandukanye ubyereke bagenzi bawe, muganire ku bice mubonye.

Igikorwa cya 2

Fata urupapuro uruhinemo ibice bibiri bingana. Igice kimwe ugisige ibara. Ugereranye igice gisize. ibara n'ikidasize.

Igikorwa cya 3

Itegereze amashusho, uvuge izina ry’igice cyakuwe ku kizima.

Nsobanukiwe ko:

•Icunga ryose, ipapayi yose n'inanasi yose, ari ikizima. Igice kimwe cya kabiri ( 1/2 ) ni umugabane.

• 1/2 (kimwe cya kabiri) k’ikintu ari cya kintu ugabanyamo ibice bibiri bingana.

• 1/2 (kimwe cya kabiri) inshuro ebyiri ari ikizima kimwe.

Igikorwa cya 4

Mwitegereze,mwigane uko bandika 1/2.

(b) Gushushanya no gusiga ibara umugabane 1/2

Igikorwa cya 5

Itegereze usige ibara kimwe cya kabiri (1/2) cya buri shusho.

Igikorwa cya 5

Shushanya uruziga ku rupapuro, 1/2 cyarwo ugisige ibara.

2. Kimwe cya kane 1/4

(a) Gusoma no kwandika umugabane 1/4

Igikorwa cya 1

Fata urupapuro uruhinemo ibice bine bingana. Bitandukanye ubyereke bagenzi bawe muganire ku bice mubonye.

Igikorwa cya 2

Mufate urupapuro muruhinemo ibice bine bingana ariko ntimubitandukanye. Mufate igice kimwe mugisige ibara, nimugereranye igice gisize ibara n'ibidasize.

Igikorwa cya 3

Itegereze, uvuge izina ry’igice cyakuwe mu kizima.

Nsobanukiwe ko:

• Icunga ryose n'isabune yose ari ikizima

• Igice kimwe cya kane ( 1/4 ) ni umugabane

• 1/4 (kimwe cya kane) k’ikintu ari cya kintu ugabanyamo ibice bine bingana.

• 1/4 (kimwe cya kane) inshuro enye ari ikizima kimwe.

Igikorwa cya 4

Itegereze, wigane uko bandika 1/4 ubyereke abandi.

(b) Gushushanya no gusiga ibara umugabane 1/4

Igikorwa cya 5

Itegereze amashusho, usige ibara kimwe cya kane (1/4) cyaburi shusho.

Igikorwa cya 6

Shushanya uruziga ku rupapuro, usige ibara kimwe cya kane (1/4) cyarwo wereke bagenzi bawe.

3. Kimwe cya munani  ( 1/8 )

(a) Gusoma no kwandika umugabane 1/8

Igikorwa cya 1

Mufate urupapuro muruhinemo ibice umunani bingana. Mubitandukanye mubyereke bagenzi banyu, muganire ku bice mubonye.

Igikorwa cya 2

Mufate urupapuro muruhinemo ibice umunani bingana, igice kimwe mugisige ibara. Nimurangiza mugereranye igice gisize ibara n'ibidasize.

Igikorwa cya 3

Itegereze, uvuge izina ry’igice cyakuwe mu kizima.

Nsobanukiwe ko:

•Icunga ryose n'igisheke cyose ari ikizima

•Igice kimwe cya munani ( 1/8 ) ni umugabane

• 1/8 (kimwe cya munani) k’ikintu kizima ari cya kintu ugabanyamo ibice umunani bingana.

• 1/8 (kimwe cya munani)inshuro umunani ari ikizima kimwe.

Igikorwa cya 4

Itegereze wigane uko bandika 1/8

(b) Gushushanya no gusiga ibara umugabane 1/8

Igikorwa cya 5

Mwitegereze, musige ibara kimwe cya munani ( 1/8 ) cya buri shusho.

Igikorwa cya 6

Shushanya uruziga ku rupapuro usige ibara kimwe cya munani (1/8) cyarwo.

4. Ibice bigize umugabane

Igikorwa

Itegereze umugabane ukurikira, uvuge ibice bigize umugabane:

Nsobanukiwe ko:

Umubare wo hejuru bawita ikibara naho uwo hasi ukitwa ikita. Ikita n’ikibara bitandukanwa n’umurongo utambitse bita umurongo w’umugabane

5. Kugereranya imigabane

Igikorwa cya 1

Mwitegereze imigabane ikurikira maze mugereranye:

Igikorwa cya 2

Itegereze wandike imigabane yashushanyijwe maze uyigereranye ukoresheje >,< na =

Igikorwa cya 3

Ukurikije urugero wahawe, gereranya imigabane ukoresheje >,< na =

Nsobanukiwe ko:

Iyo bagereranya imigabane ihuje ikibara bagendera kuri aya mategeko:

• Umugabane munini uba ufite ikita gito.

• Umugabane muto uba ufite ikita kinini

6. Guhuza imigabane ugakora ikizima

Igikorwa

Mwitegereze ishusho maze namwe mukore ibisa na byo mwifashishije ipapayi, icunga, inanasi, indimu, n’ibindi.

7. Akamaro k’imigabane

Igikorwa

Mwitegereze ishusho ikurikira maze musobanurire bagenzi banyu akamaro k’imigabane:

Nsobanukiwe ko:

Imigabane idufasha kugabana na bagenzi bacu tukaringaniza.

• 0. Imyitozo yo kwiyibutsa ingero

Igikorwa cya 1

Muganire ku bintu mushobora gupima uburebure bwabyo, mukore urutonde rwabyo.

Igikorwa cya 2

uzuza ukoresheje ibimenyetso <, > na

Igikorwa cya 3

Tondeka ingero z’uburebure zikurikira uhereye ku ruto ujya ku runini.

Igikorwa cya 4

Teranya cyangwa ukuremo.

Igikorwa cya 5

Amahurizo

1. Ikibaho cyo mu ishuri ryacu gifite m 8 z'uburebure naho icyo mu ishuri rya barumuna bacu gifite m 6. Vuga igiteranyo cy’uburebure bw’ibyo bibaho byombi.

2. Kaneza afite umurima wa karoti ufite m 20 z'uburebure, Mitari afite upima m 18. Shaka uburebure bw’iyo mirima yombi.

3. Mariza yaguze m 14 z’umwenda ku wa mbere, kuwa kabiri agura m 13. Ku wa gatatu agura  m 12. Shaka igiteranyo cy’uburebure bw’umwenda yaguze.

4. Mayira yaguze umugozi wa m 10 naho murumuna we agura umugozi wa dm 19, Vuga uburebure bw'umugozi bombi bafite.

5. Nshuti yaboshye umusambi wa dm 20 naho murumuna we aboha uwa dm 17. Ubwo amurusha metero zingahe?

6. Naboshye umugozi ureshya na m 72, nkataho m 12 bazizirikisha igitoki cyari kigiye kugwa. Nasigaranye umugozi ureshya na metero zingahe?

7. Munezero afite urubaho rwa m 12 naho murumuna we kagabo akagira urupima m 8. Ubwo izo mbaho zombi zireshya na m zingahe?

1. Gupima uburebure ukoresheje imetero

Igikorwa

Mwitegereze amashusho, maze mukore ibikorwa bikurikira:

1.  Mukoreshe imetero mupime:

(a) Uburebure bw’intebe mwandikiraho.

(b) Uburebure bw’ameza ya mwarimu.

2. Mukoreshe imetero mupime:

(a) Ubutambike bw’akabati k’ibitabo ka  mwarimu.

(b) Ubutambike bw’ikibaho mwandikaho.

3. Mukoreshe imetero mupime:  Umuzenguruko w'ishuri mwigamo.

4. Mukoreshe imetero mupime:

(a) Ubutambike bw’urugi rw’ishuri ryanyu.

(b) Uburebure bw'inkuta ebyiri zikurikiranye.

5. Mukoreshe agacamurongo mupime uburebure  bw’amakayi yanyu n’ubw’ibitabo by’imibare.

2. Guca metero mo ibice 10 bingana

Igikorwa

Mwitegereze ishusho, maze mukore ibikorwa bikurikira mugendeye ku rugero mwahawe:

1. Mufate igisheke gipima metero imwe mugicemo   uduce icumi (10) tungana.

2. Mufate umugozi upima metero imwe muwucemo   uduce icumi (10) tungana.

3. Mufate urudodo rupima metero imwe murucemo   uduce icumi (10) tungana .

4. Mufate igitambaro badodamo imyenda (ijyora)  gipima metero imwe mugicemo uduce icumi (10)  tungana.

Nsobanukiwe ko:

Metero 1 (m1) ivamo uduce 10 tungana buri gace gapima desimetero1 (dm1). Metero 1 ingana na desimetero 10.  m1= dm 10

3. Guca desimetero mo ibice 10 bingana

Igikorwa

Mwitegereze ishusho mukore ibikorwa bikurikira mugendeye ku rugero mwahawe.

1. Mufate umugozi upima desimetero imwe maze   muwucemo uduce icumi (10)tungana.

2. Mufate agati kumye gapima desimetero imwe    maze mugacemo uduce icumi (10)tungana.

Nsobanukiwe ko:

• Desimetero 1 (dm1) ivamo uduce 10 tungana buri gace gapima santimetero 1 (cm 1).

• m1 uyigabanyamo uduce 10 tungana. Buri gace gapima dm1. m1 = dm10

• m1 uyigabanyamo uduce 100. Buri gace gapima cm1. m1= cm100

• dm1 uyigabanyamo uduce 10 tungana. Buri gace gapima cm1. 1dm = 10 cm

Ingero z’uburebure zirutana inshuro 10

m1 = dm10       1dm = 10 cm

4. Guhindura ingero z’uburebure

Igikorwa

Mwitegereze imbonerahamwe yo guhindura ingero z’uburebure maze muyigane mukore imyitozo

Nsobanukiwe ko:

• Iyo uhindura ingero z’uburebure ubanza gukora   imbonerahamwe yo guhindura ukandikamo    imibare wahawe.

• Iyo uva ku rugero runini ujya ku ruto wongeraho   zeru(0).

• Iyo uva ku ruto ujya ku runini ugakuraho zeru (0).

Reka mpindure mu rugero bambajije

a) m 6  = cm...            c) dm 75 = cm .....

b) dm 40= m....          d) cm 990 = dm ......

5. Kugereranya ingero z’uburebure

Igikorwa

Hindura ingero z’uburebure mu rugero ruto, ugereranye ukoresheje >, < na =

Nsobanukiwe ko:

• Iyo ugereranya ingero z’uburebure, ubanza kuzihindura mu rugero ruto, hanyuma ukagereranya imibare ugashyiramo ikimenyetso cyo kugereranya ( <,>, = ).

6. Gupima uburebure bw’ahantu hatandukanye

Igikorwa

Mukore ibikorwa bikurikira mwerekane uko mwabikoze n'igisubizo byatanze:

1. Mukoreshe imetero mupime umuzenguruko w'ishuri mwigiramo.

2. Mukoreshe imetero mupime uburebure bwa m 10  mu kibuga.

3. Mukoreshe imetero mupime  umuzenguruko    w'ubusitani

4. Mukoreshe akagozi gapima metero10 maze mupime uburebure bw’ikibuga cy’umupira w’amaguru.

7. Gutondeka ingero z’uburebure

Igikorwa cya 1

Mutondeke ingero z’uburebure muhereye ku rugero ruto mujya ku runini mukurikije urugero mwahawe.

a) dm 45, m 7, cm 350               e) cm 125, dm 45, m 9

b) dm 79, m 130, m 4                 f) cm 76, m 4, cm 576

c) 345 cm, m 8, dm 65               g) cm 127, dm 45, m 9

d) m 7, cm 985, dm 75               h) dm 65, m 9, cm 456

Igikorwa cya 2

Tondeka ingero z’uburebure uhereye ku rugero runini ujya ku ruto ukurikije urugero wahawe.

a) cm 245, m 7, dm 35                  e) cm 5, dm 54, cm 915

b) cm 79, m 3, dm 49                    f) cm 768, dm 49, m 5

c) dm 45, cm 814, m 6                  g) dm 27, cm 458, m 9

d) dm 78, cm 895, m 7                  h) dm 69, dm 978, 6 m

Nsobanukiwe ko:

• Iyo utondeka ingero z’uburebure ubanza guhindura ingero zose wahawe mu rugero ruto.

• Utondeka uva ku rugero ruto ujya ku runini cyangwa uva ku runini ujya ku ruto.

8. Guteranya ingero z’uburebure

Igikorwa

Hindura mu rugero wabajijwe mbere yo guteranya, ukurikije urugero wahawe.

Nsobanukiwe ko:

Iyo uteranya ingero z’uburebure ubanza guhindura ingero zose wahawe mu rugero wabajijwe ugateranya.

9. Gukuramo ingero z’uburebure

Igikorwa

Hindura mu rugero wabajijwe mbere yo gukuramo ukurikije urugero wahawe.

Nsobanukiwe ko:

Iyo ukuramo ingero z’uburebure ubanza guhindura ingero zose wahawe mu rugero wabajijwe, ugakuramo.

10. Gukuba ingero z’uburebure n'umubare ushyitse

Igikorwa

Kuba nyuma uhindure mu rugero wabajijwe.

Nsobanukiwe ko:

Iyo ukuba ingero z’uburebure n'umubare ushyitse ubanza gukuba ingero wahawe igisubizo ubonye ukagihindura mu rugero wabajijwe.

11.Kugabanya ingero z’uburebure n'umubare ushyitse

Igikorwa

Gabanya wandike igisubizo ukurikije urugero wahawe.

Nsobanukiwe ko:

Iyo ugabanya ingero z’uburebure n'umubare ushyitse ubanza kugabanya ingero wahawe icyo ubonye ukagihindura mu rugero wabajijwe.

12. Amahurizo ku ngero z’uburebure

Reka dukore amahurizo dukurikije urugero twahawe

1. Umwaka ushize nateye igiti gifite dm 50, z'uburebure ubu gifite dm 80 ubwo kimaze kwiyongeraho dm zingahe?

2. Umubaji yaguze urubaho rwa cm 100 arucamo uduce 5 tungana. Buri gace kareshya gate?

3. Gatari yaguze ikizingo cy’umugozi ureshya na m 60 arashaka gucamo uduce 3. Shaka uburebure bwa buri gace muri dm.

4. Gatera yahinze amashu mu murima upima m 89 z'uburebure. Naho Munezero yayahinze mu murima ufite m 97.

(a) Ni nde wahinze amashu mu murima muremure?

(b) Yamurushije guhinga m zingahe?

5. Kuva mu rugo ujya ku ishuri hari dm 420. Ubwo kuva mu rugo ujya ku ishuri nkoresha m zingahe?

13. Akamaro k’ingero z’uburebure

Igikorwa cya 1

Muganire ku bikorwa birimo gukorwa n'ibikoresho biri gukoreshwa.

Nsobanukiwe ko:

• Ingero z'uburebure zikoreshwa iyo bapima  uburebure bw'ibintu bitandukanye nk'ikibanza, umurima,umuhanda,inzu n'ibindi.

• Iyo upima uburebure ukoresha imetero,metero bushumi cyangwa metero buhine

Igikorwa cya 2

Muganire ku kamaro k’ingero z’uburebure mu  buzima bwa buri munsi.

Igikorwa cya 3

Muganire ku hantu h’ingenzi ingero z’uburebure zikoreshwa.

URL: 1
• 1. Urugero fatizo rw’ingero z'ibitembabuzi litiro (l)

Igikorwa

Mwitegereze amashusho, muvuge izina ry’ibintu biri mu macupa n'utujerekani n'ingano yabyo.

2. Gupima ibitembabuzi

Igikorwa cya 1

Mwitegereze amashusho maze mukore nk’ibiri gukorwa.

Igikorwa cya 2

Mwifashishe amacupa (utujerekani) apima L5 mubyuzuzemo amazi muyashyire mu macupa (utujerikani) ya L1 hanyuma muvuge umubare w'amacupa ya  L1 uvuye muri L5.

Igikorwa cya 3

Mufate akajerikani gatwara  L2, mukuzuzemo amazi mukoresheje icupa rya L1. Nimuvuge umubare w'amacupa mwasutsemo. Mubikore mutyo no ku kajerikani gatwara L5 n'aka L10.

3. Kugereranya ibitwarwamo ibitembabuzi

Igikorwa cya 1

Mufate utujerekani, amacupa, amajagi n'ibikombe. Mushyire hamwe ibihuje itwara maze musobanurire bagenzi banyu itwara ryabyo n'impamvu mwabivanguye. Mugereranye mukoresha <, >, =

Igikorwa cya 2

Igikorwa cya 3

Tondeka uva ku rugero ruto ujya ku runini

Igikorwa cya 4

Tondeka uva ku rugero runini ujya ku ruto.

4. Guteranya ingero z’ibitembabuzi muri litiro

Igikorwa 1

Mukore imyitozo ikurikira mukurikije urugero

5. Amahurizo yo guteranya ingero z'ibitembabuzi muri litiro

Reka dukore amahurizo dukurikije urugero twahawe

1. Mvomesha ikivomesho gitwara  L15 naho mukuru wange avomesha igitwara L 24.Twese hamwe tuvoma L zingahe?

2. Twashigishe L300 z'ubushera bwo kwakira abashyitsi mu bukwe, abaturanyi bacu badutwerera L175 z'ubushera. Ubwo twagize L zingahe zose hamwe?

3. Mutabazi afite imashini itanga umuriro. Mu gitondo ashyiramo L 195 z'amavuta na L 205 ku mugoroba. Ubwo ku munsi ashyiramo L zingahe?

6. Gukuramo ingero z'ibitembabuzi

Igikorwa

Mukore imyitozo ikurikira mukurikije urugero mwahawe.

7. Amahurizo yo gukuramo no guteranya ingero z'ibitembabuzi

Reka dukore amahurizo dukurikije urugero twahawe

1. Twaretse L225 z'amazi y’imvura. Bukeye tuyameshesha imyenda hasigara L24.Twamesheje L zingahe?

2. Umucuruzi yaranguye L100 z’amavuta agurisha L35 akiva kurangura.Yasigaranye  L zingahe?

8. Gukuba ingero z'ibitembabuzi n'umubare ushyitse

Igikorwa  cya 1

Mukore imyitozo ikurikira muhereye ku rugero

9. Amahurizo yo gukuba ingero z'ibitembabuzi

Reka dukore mu matsinda

1. Ku munsi dukenera L 61 z'amazi dukora isuku Ubwo dukenera L zingahe mu minsi itanu?

2.  Umuturanyi yagabanyije ku buryo bungana L 72 z'amavuta imiryango 3. Ubwo buri muryango wahawe L zingahe?

10. Kugabanya ingero z'ibitembabuzi n'umubare ushyitse

Igikorwa

Mukore imyitozo ikurikira mwifashishije urugero rwatanzwe

11. Amahurizo yo kugabanya ingero z'ibitembabuzi n'umubare ushyitse

Reka dukore amahurizo dukurikije urugero twahawe

1. Abana 5 bahuje isabukuru yabo y’amavuko maze ababyeyi babo babagurira L50 z’umutobe, ngo bazigabane banganye bityo buri wese azimanire abo yatumiye. Buri mwana yabonye L zingahe?

2. Gabanya ku buryo bungana L 186 z’amata abacuruzi 6. Buri mucuruzi azahabwa  L zingahe?

3. Mugabo afite L155 za mazutu ashaka gushyira mu modoka 5 ku buryo bungana.Shaka umubare wa L azashyira muri buri modoka.

12. Akamaro k’ingero z'ibitembabuzi

Igikorwa cya 1

Mwitegereze amashusho muvuge ahantu litiro ikoreshwa mu buzima bwa buri munsi.

Igikorwa cya 2

Muganire ku kamaro ko gukoresha litiro mu gupima ibitembabuzi.

Igikorwa cya 3

Muganire bimwe mu bikoresho mukoresha mu rugo iwanyu. Buri wese avuge izina ry’igikoresho na litiro gitwara n’icyo gikoreshwa.

Nsobanukiwe ko:

• Litiro ari urugero fatizo rw’ingero z’ibitembabuzi

• Litiro ikoreshwa bapima ibitembabuzi nk’amata, amazi, amavuta, umutobe, peterori.

URL: 1
• 1. Urugero fatizo mu ngero z’uburemere (kg)

Igikorwa

Mwitegereze muvuge ibyo mubona ku mashusho n’igipimo cyabyo.

Nsobanukiwe ko:

Kg ari rwo rugero bapimamo  uburemere bw'ibintu bitandukanye.

2. Amoko atandukanye y’iminzani

Igikorwa

Mwitegereze amashusho y’iminzani ikurikira, muvuge ubwoko mukunze kubona mu iduka no mu isoko:

Nsobanukiwe ko:

Iyo upima uburemere bw’ibintu ukoresha umunzani. Hari amoko menshi y’iminzani akoreshwa. Ariko imenyerewe ni umunzani wa gakwege, umunzani w’amabuye n’umunzani w’isaha.

3. Gupima uburemere muri kg

Igikorwa cya 1

Muterure ibintu bitandukanye buri wese   agenekereze avuge ibiro ibyo bintu byapima.

Igikorwa cya 2

Mwitegereze ishusho, muvuge ibirimo gukorwa namwe mubikore.

Igikorwa cya 3

Mwitegereze amashusho, muvuge ibirimo gukorwa.

Igikorwa cya 4

Mwifashishije umunzani, mupime ibintu bifite uburemere butarengeje kg 10. Hanyuma muge mwandika uburemere bwa buri kintu mwapimye.

4. Akamaro ka kilogarama (kg)

Igikorwa cya 1

Mwitegereze amashusho, muvuge ahantu bapima uburemere bakoresheje umunzani.

Igikorwa cya 2

Muvuge akamaro ko gukoresha kg mu gupima uburemere.

Nsobanukiwe ko:

• Kilogarama(kg) ari urugero fatizo rw’ingero, z’uburemere.

Kg ikoreshwa iyo bapima uburemere bw’ibintu.

Igikorwa cya 3

Muganire ku bibi byo kudakoresha umunzani ngo umenye umubare wa kg z’ibintu ugiye gukoresha cyangwa ugiye kugura.

Twiyemeje ko:

Tuzajya tugura ibintu badutumye tubanje kubasaba gupima tukareba ko byuzuye mbere yo kubigura.

5. Kugereranya ingero z’uburemere

Igikorwa 1

Muganire ku nkuru ikurikira. Maze buri wese aze kubwira bagenzi be inkuru ivuga ibyo yakoze birimo ingero z’uburemere.

Keza na Gisa barushanyijwe gutonora amashaza, barangije bapima ayo buri wese yatonoye. Hanyuma basanga Keza yatonoye Kg 3 naho Gisa yatonoye Kg 2. Gisa yiyemeza ko ubutaha ari we uzatonora amashaza menshi.

Igikorwa cya 2

Muterure ibintu bitandukanye, muvuga ikiremereye cyane kurusha ikindi n’icyoroshye kurusha ikindi.

Igikorwa cya 3

Mugereranye mukoresheje <, >, =

Igikorwa cya 4

Tondeka uva kuri kg nkeya ujya kuri kg nyinshi

a) Kg 51, kg 26, kg 21         d) Kg 42, kg 25, kg 27

b) Kg 21, kg 12, kg 81         e) Kg 28, kg 40, kg 52

c) Kg 31, kg 24, kg 47          f) Kg 32, kg 51, kg 57

Igikorwa cya 5

Tondeka uva kuri kg nyinshi ujya kuri kg nkeya

a) Kg15, kg 27, kg  12         d) Kg 24, kg 52, kg 29

b) Kg 21, kg 82, kg 18         e) Kg 27, kg 37, kg 25

c) Kg 31, kg 28, kg 75          f) Kg 23, kg 15, kg 72

Nsobanukiwe ko:

Iyo ugereranya cyangwa utondeka ingero z'uburemere ugereranya cyangwa ugatondeka urebeye ku mibare ikurikira kg. Umubare muto ugaragaza ibiro bike naho umubare munini ukagaragaza ibiro byinshi.

6. Guteranya ingero z’uburemere muri kg

Reka dukore dukurikije urugero  twahawe

7. Amahurizo yo guteranya ingero z’uburemere muri "kg"

Reka dukore amahurizo dukurikije urugero

1. Kamanzi yazigamye kg 12 z'imyumbati mu kwezi gushize. Mukuru we azigama kg 15 z'imyumbati. Bose hamwe bazigamye kg zingahe?

2. Rukundo yacuruje kg 50 z'umuceri mu gitondo arongera acuruza kg 25 z'umuceri ku mugoroba. Ubwo Rukundo yacuruje kg zingahe zose hamwe?

3. Mu rugo duteka kg 5 z’ibirayi ku manywa, nijoro tugateka kg 4 z'ibitoki. Shaka umubare wa kg turya ku munsi.

4. Mbabazi acuruza kg 15 z’isukari na kg 25 z'ifu y'igikoma buri munsi. Ubwo ku munsi acuruza kg zingahe zose hamwe?

8. Gukuramo ingero z’uburemere muri "kg"

Reka nkore nkurikije urugero

9. Amahurizo yo gukuramo ingero z’uburemere

Reka dukore dukurikije urugero twahawe

1. Umucuruzi yaranguye kg 150 z’ibishyimbo agurisha kg 75 z'ibishyimbo. Yasigaranye kg zingahe?

2.  Gisa yasaruye kg 247 z'umuceri ahaho abaturanyi be kg 130. Yasigaranye kg zingahe z'umuceri?

10. Gukuba ingero z’uburemere n'umubare ushyitse

Reka dukore dukurikije  urugero twahawe

11. Amahurizo yo gukuba ingero z’uburemere

Reka dukore dukurikije urugero twahawe

1. Mu rugo duteka kg 6 z’ibirayi ku munsi. Ubwo mu minsi 3 duteka kg zingahe?

2. Murengezi atwara kg 61 z'ibitoki ku ngorofani. Azatwara kg zingahe z'ingahe nagenda inshuro 3?

3. Muhizi ateka amandazi.Ku munsi akoresha kg 31 z’ifarini. Azakoresha Kg zingahe z’ifarini mu gihe k’iminsi 10?

12. Kugabanya ingero z'uburemere n'umubare ushyitse

Reka dukore dukurikije urugero twahawe

13. Amahurizo yo kugabanya ingero z’uburemere

Reka dukore dukurikije urugero twahawe.

1. Gabanya ku buryo bungana kg 450 z'umuceri abantu 5. Buri wese azatwara kg zingahe?

2. Abacuruzi ba 4 bafatanyije kugura kg 328 z'isukari bazigabana ku buryo bungana buri wese yatwaye kg zingahe?

3. Ibishyimbo bipima kg 284 bigabanyirize mu mifuka 4 ku buryo bungana. Buri mufuka uzajyamo kg zingahe?

4. Mu gihe k'isarura ry'ibishyimbo, umubyeyi yasaruye kg 48 azigabanya abana be 4 ku buryo bungana ngo babijyane ku isoko. Buri wese yatwaye kg zingahe?

5. Mu rugo duteka kg 30 z'ibirayi mu minsi 5.Ubwo duteka kg zingahe buri munsi?

• 0. Imyitozo yo kwiyibutsa amafaranga

Igikorwa cya 1

Mukoreshe <, > na = mugereranye

Igikorwa cya 2

Mutondeke aya mafaranga muhereye ku make mujya ku menshi.

a) F 75, F 50, F 90             d) F 60, F 100, F 70

b) F 90, F 80, F 50              e) F 60, F 30, F 80

c) F 100, F 20, F 60              f) F 40, F 70, F 20

Igikorwa cya 3

Mutondeke aya mafaranga akurikira muhereye ku menshi mujya ku make.

a) F 75, F 50, F 90                    f) F 60, F 100, F 70

b) F 90, F 80, F 50                   g) F 60, F 30, F 80

c) F 100, F 20, F 60                  h) F 40, F 70, F 20

d)  F 45, F 15, F 50                   i) F 25, F 100,F 65

e) F 60, F 75, F 35                    j) F 70, F 35, F 90

Igikorwa cya 4

Mukoreshe ibiceri mushake igisubizo

a) F 35 + F 25 =               d) F 85 – F 45 =

b) F 25 + F 45 =               e) F 45 – F 35 =

c) F 55 + F 35 =                 f) F 35 + F 45 =

d) F 75 - F 25  =                h) F 95 -  F 65 =

Igikorwa cya 5

Amahurizo: 1. Kariza afite F 100 arashaka kugura ibisuguti bigura F 50. Bazamugarurira angahe?

2. Keza bamuhaye F 80 bongeraho andi F 20 Yagize F angahe yose hamwe ?

3. Kayitare bamuhembye F 100 ayaguramo ikaramu ya F 50 n’umuneke wa F 40. Vuga F Kayitare yasigaranye.

4. Kanamugire bamutumye ikibiriti cya F 20 n'umwembe wa F 50. Ubwo Yakoresheje  F angahe?

5. Kuzwa yatoye F 100 aguraho ikaramu y'amafaranga 50. Ubwo yasigaranye F angahe?

1. Ibiranga amafaranga y’u Rwanda

Igikorwa cya 1

Mufate amafaranga mushyire hamwe asa kandi afite agaciro kangana, hanyuma mubwirane uko mwabikoze?

Igikorwa cya 2

Muganire ku itandukanirizo riri hagati y’inoti n’ibiceri mugendeye k'uko bikoze n’ibibiranga.

2. Akamaro k’amafaranga

Igikorwa cya 1:

Mwitegereze amashusho muvuge ibyo muyabonaho.

Nsobanukiwe ko:

Amafaranga atuma tugura ibyo dukeneye.

Igikorwa cya 2

Muganire ku bibazo bikurikira, muze kubwira   bagenzi banyu ibyo mwaganiriye.

1. Ufite F 100 wayagura iki?

2. Ufite F 500 wayagura iki?

3. Ufite F 1000 wayagura inzu?

Igikorwa cya 3

Muganire ku kamaro k'amafaranga nimurangiza mugasobanurire bagenzi banyu mutari kumwe mu itsinda

3. Uko amafaranga aboneka

Igikorwa cya 1

Mwitegereze amashusho muyaganireho muvuge ibyo muyabonaho.

Nsobanukiwe ko:

Amafaranga tuyavana mu mirimo dukora.

Twiyemeje ko:

Tugiye kujya dukoresha amafaranga  neza twirinda kuyakoresha ibitateganyijwe.

Igikorwa cya 2

Buri wese abwire bagenzi be aho umuryango we uvana amafaranga ukoresha. Mubiganireho.

Igikorwa cya 3

Musome urutonde rw'ahantu abantu bashobora kuvana amafaranga. Maze muvangure aho ashobora kuboneka biciye mu nzira nziza n'aho yaboneka biciye mu nzira mbi:

4. Kugura no kugurisha

Igikorwa cya 1

Mwitegereze amashusho musubize ibibazo bikurikira.

a)  Mutoni arashaka kugura icunga n'umwembe. Azabigura F angahe?

b)  Gisa yaguze umutobe w'imbuto n'ikigori. yishyuye  F angahe?

c)  Kangabe yatumye Uwase urupapuro rw'isuku , umuneke n'umugati.Yamuhaye F angahe?

d) Mahame yantumye Butera ikigori n'umugati.Ubwo yamuhaye F angahe?

Igikorwa cya 2

Mwitegereze amashusho, musubize ibibazo bikurikira.

a) Muhizi afite F 750 nagura ikayi n'ikaramu  bazamugarurira F angahe ?

b)  Ingabire afite inoti ya F 500 nagura ipapayi    na bombo bazamusubiza F angahe?

5. Kuvunjisha amafaranga y’u Rwanda

Igikorwa cya 1

Mukore iyi myitozo.

Igikorwa cya 2

Mwuzuzemo imibare ibura.

6. Gukora urutonde rw’ibintu mbere yo kubigura

Igikorwa cya 1

Mwitegereze ishusho, muvuge icyo mubonaho.

Nsobanukiwe ko:

Gukora urutonde rw’ibyo ugiye kugura bituma: utibeshya, udatakaza umwanya, ugahitamo iby’ingenzi, bituma kandi ucunga neza Nsobanukiwe.

Igikorwa cya 2

Kora urutonde rw'ibyo wagura uramutse ufite F 1000

Twiyemeje ko:

Igihe cyose bazajya badutuma guhaha tuzajya dukora urutonde rw’ibyo badutumye ndetse n’igiciro  cyabyo.

Igikorwa cya 3

Soma urutonde rw'ibyo Gahima ashaka kujya kugura ku isoko maze ushake umubare wa F azakoresha.

1. Ibitunguru =F200                  2. Isabune= F200

3. Ubunyobwa= F200               4. Ibirayi= F 300

7. Gukoresha no gufata neza amafaranga

Igikorwa cya 1

Muhitemo iby’ingenzi mwatangaho amafaranga kurusha ibindi, musobanure impamvu.

Igikorwa cya 2

Itegereze amashusho, uvuge ibyo uyabonaho.

Nsobanukiwe ko:

Amafaranga agura ibintu bikenewe kurusha ibindi. Tugomba gufata neza amafaranga

Twiyemeje ko:

Tuzajya dukoresha amafaranga neza, twirinda kwandika ku mafaranga no kuyaca. Twiyemeje kubika neza amafaranga.

8. Umuco wo kuzigama

Igikorwa

Itegereze amashusho, uvuge ibyo uyabonaho.

Nsobanukiwe ko:

Kuzigama ari umuco mwiza. Ibyo uzigamye birakugoboka.

Twiyemeje ko: Tuzajya tuzigama amafaranga.

9. Uburyo bwo gukora umushinga uciriritse

Igikorwa

Muganire ku mashusho akurikira, namwe mutange urugero rw'agashinga mwakora kakababyarira inyungu mu gihe gito.

Nsobanukiwe ko:

Dufite ubushobozi bwo gukora udushinga duto.

Twiyemeje ko:

Tugiye kujya dukora udushinga duto.

10. Kugereranya amafaranga atarenze F1000

Igikorwa cya 1

Mugereranye amafaranga mukoresheje ibimenyetso  bya >,< na

Igikorwa cya 2

Tondeka amafaranga uhereye ku make ujya ku menshi.

Igikorwa cya 3

Tondeke amafaranga uhereye ku menshi ujya ku make.

11. Guteranya no gukuramo amafaranga atarenga F1000

Igikorwa

Muteranye cyangwa mukuremo amafaranga akurikira:

12. Gukuba no kugabanya F atarenga F1000 n'umubare ushyitse

Igikorwa

Mukore imyitozo ikurikira yo gukuba no kugabanya:

13. Amahurizo yo guteranya no gukuramo amafaranga

Reka dukore dukurikije urugero twahawe

1. Mahoro yaguze ikayi ku F 350, n’ikaramu ya F 200. Byose hamwe yabiguze F angahe?

2. Shema yagiye kugura icupa ry’amazi rigura F 300 afite inoti ya F 500. Bamugaruriye F angahe?

3. Manirakiza bamuhembye F 900. Ayaguramo umutobe w'imbuto bamugarurira F 200. uwo   mutobe w'imbuto yawuguze F angahe?

4. Gasore bamutumye kugura umugati bamuha F    900 agezeyo barawumuha bamugarurira F 250 Umugati yawuguze F angahe?

5. Uwamahoro yaguze imineke ku F 600, agura n'ishu rya F 300. Ubwo byose yabiguze F angahe?

14. Amahurizo yo gukuba no kugabanya amafaranga n'umubare ushyitse

Reka dukore dukurikije urugero twahawe

1. Mukuru wange afite F 800 arashaka kuyatugabanya ku buryo bungana uko turi 4.  Buri wese azamuha F angahe?

2. Gabanya ku buryo bungana F 900 abana 3. Buri wese uzamuha F angahe?

3. Ningura amakayi 2 nzishyura F angahe niba ikaye imwe igura F 200.

4. Isambusa imwe igura F 100. Nguriye bagenzi bange isambusa 10, nakwishyura F angahe?

5. Ishimwe arashaka kugura amakayi 6 kandi buri kayi igura F 100. Ubwo yose azayagura F angahe?

• 1. Kuvuga igihe kerekanwa n’isaha

(a) Isaha yuzuye

Igikorwa cya 1

Mwitegereze amashusho akurikira, muvuge amazina y’ibiri ku mashusho n’akamaro kabyo.

Igikorwa cya 2

Mwitegereze amasaha, muvuge igihe.

Nsobanukiwe ko:

(a) Isaha y’inshinge

• Igira inshinge ebyiri cyangwa eshatu.  Urushinge rurerure rubara iminota.

Urushinge rugufi rubara amasaha.  Agashinge gato karekare kabara amasegonda.

• Mu isaha y’urushinge :

- Handitsemo imibare kuva kuri 1 kugera kuri 12 bivuga amasaha.

- Kuva ku mubare umwe ujya ku wundi harimo isaha 1.

(b) Isaha y’imibare:

- Umubare ubanza ugaragaza amasaha

- Umubare uza inyuma y’utudomo tubiri  ugaragaza iminota.

- Isaha igira iminota 60

- Umunsi ugira amasaha 24

(c) Umunsi

ugizwe n’ibice 2:

- Mbere ya saa sita

-  Nyuma ya saa sita.

-  Buri gice cy’umunsi kigira amasaha 12.

Igikorwa cya 3

Subiza ibi bikurikira:

1. Ibice bigize umunsi ni bingahe?

2. Umunsi utangira ryari ukarangira ryari?

3. Isaha imwe igira iminota ingahe?

Igikorwa cya 4

Itegereze amasaha uvuge igihe.

Bandika kandi bagasoma isaha ku buryo bukurikira

Igikorwa cya 5

Mwitegereze, muvuge igihe.

Nsobanukiwe ko:

ku isaha y'urushinge:

Niba urushinge rubara amasaha ruri ku mubare   runaka urubara iminota ruri kuri 12 ni isaha iba yuzuye.

ku isaha y'imibare:

Iyo imibare ibanza ikurikiwe n'amazeru 2 isaha iba yuzuye urugero: (7:00)

Imyitozo

(b) Isaha irengaho iminota 30

Igikorwa cya 6

Mwitegereze amasaha, muvuge igihe

Nsobanukiwe ko:

Ku isaha y'urushinge:

Iyo urushinge rubara amasaha ruri hagati y'imibare  ibiri naho urubara iminota ruri ku mubare 6 basoma isaha irengaho iminota mirongo itatu.

Ku isaha y'imibare

Iyo isaha y'imibare harimo umubare ukurikirwa n'utudomo tubiri na 30, iba ari isaha irengaho iminota mirongo itatu.

Urugero: 9 : 30 saa tatu n' iminota 30.

Itegereze amasaha akurikira maze uvuge igihe:

Igikorwa cya 7

Mushushanye amasaha y’inshinge abara:

a) 11 : 00         c) 10 : 30         e) 2 : 30

b)   8 : 30        d) 3 : 00            f) 5 : 00

2. Indangaminsi

Igikorwa 1

Mwitegereze indangaminsi hanyuma musubize ibibazo biri munsi yayo.

Ibibazo:

a) Icyumweru kigira iminsi ingahe? yivuge.

b) Icyumweru gitangira ku wa kangahe?

c) Icyumweru kirangira ku wa kangahe?

d) Icyumweru kigira iminsi ingahe y’imibyizi? Yivuge.

e) Icyumweru kigira iminsi ingahe y’ikiruhuko? Yivuge.

Nsobanukiwe ko:

Icyumweru kigira iminsi 7.

Icyumweru gitangira ku munsi wa mbere kikarangira ku munsi wa karindwi. Kuri uwo munsi, bamwe bavuga ko ari ku cyumweru abandi bakavuga ku isabato.

Reka nkore

1. Uza ku ishuri iminsi ingahe mu cyumweru? Yivuge.

2. Iwanyu mujya gusenga ku wa kangahe?

3. Ni uwuhe munsi ukunze kuberaho ubukwe?

4. Kuki habaho iminsi y’imibyizi n’iminsi y’ikiruhuko?

Igikorwa cya 2

Mwitegereze indangaminsi musubize.

Ibibazo

(a) Umwaka ugira amezi angahe?

(b) Ese amezi yose agira iminsi ingana?

(c) Vuga amazina y’amezi agira iminsi 30?

(d) Ni ukuhe kwezi kugira iminsi mike?

(e) Ukwezi kugira ibyumweru bingahe?

(f) Umwaka ugira ibyumweru bingahe?

Nsobanukiwe ko:

Umwaka ugira amezi 12

- Ukwezi kwa Gashyantare ni ko kugira  iminsi 28 cyangwa 29.

- Ukwezi kugira ibyumweru 4.

- Umwaka ukagira ibyumweru 52.

- Umwaka usanzwe ugira iminsi 365 naho umwaka ufite ukwezi kwa kabiri gufite iminsi 29       ugira iminsi 366.

Igikorwa cya 3

Mukore indangaminsi y’ukwezi murimo muyimanike mu ishuri.

3. Ibikorerwa ku ishuri n’isaha bikorwamo

Igikorwa cya 1

Mwitegereze amashusho, mukore urutonde rw’ibintu by’ingenzi mukora ku ishuri ndetse n’isaha mubikoreraho.

Nsobanukiwe ko:

Ibikorwa by’ingenzi bikorerwa ku ishuri ari ibi bikurikira:

4. Gukora gahunda y’ibikorwa by’icyumweru

Igikorwa cya 1

Itegereze gahunda y’ibikorwa bya Kagabo bya buri cyumweru nawe ukore gahunda y'ibyo ukora mu cyumweru.

Nsobanukiwe ko:

Iyo umuntu ateguye gahunda y’ibyo akora bituma yubahiriza igihe.

Twiyemeje ko:

- Tuzajya twubahiriza igihe twirinda gukererwa.

- Tuzajya dukorera igikorwa icyo ari cyo cyose ku   gihe.

Igikorwa cya 2

Muganire ku bibi byo kutubahiriza igihe.

Reka nkore

1. Ni gihe ki?

2. Uzuza interuro zikurikira:

3. Andika amezi y'umwaka agira:

a) Iminsi 31                      b) iminsi 30

• 0. Imyitozo yo kwiyibutsa

Igikorwa  cya 1

Garagaza amazina y'imirongo ikurikira:

Igikorwa cya 2

Garagaza amazina y'amashusho akurikira:

Igikorwa  cya 3

Vuga izina ry'imfuruka zikurikira:

1. Imirongo igororotse

(a) Imirongo igororotse

Igikorwa cya 1

Mwitegereze imirongo ikurikira, muvuge ibiyiranga:

Igikorwa cya 2

1. Koresha agacamurongo ushushanye iyi mirongo:

(a) Umurongo ugororotse uberamiye iburyo.

(b) Umurongo utambitse.

(c) Imirongo ibiri igororotse ihagaze.

Nsobanukiwe ko:

Imirongo igororotse irimo amoko ane ari yo:

Umurongo ugororotse utambitse.

Umurongo ugororotse uhagaze.

Umurongo ugororotse uberamiye iburyo.

Umurongo ugororotse uberamiye ibumoso.

Igikorwa cya 3

Vuga amazina y'imirongo ikurikira:

(b) Imirongo ifunze

Igikorwa cya 4

Mwitegereze imirongo ikurikira, muvuge uko iteye.

Igikorwa cya 5

Koresha agacamurongo ushushanye imirongo ikurikira:

a) umurongo unyuranamo ufunze

b) umurongo ufunze

Nsobanukiwe ko:

Umurongo ufunze ni umurongo ufunze ku buryo nta kanya na gato kinjira cyangwa gasohoka imbere.

(c) Imirongo ifunguye

Igikorwa cya 6

Mwitegereze imirongo ikurikira, muvuge uko iteye.

Igikorwa cya 7

Shushanya:

a) Umurongo ufunguye ibumoso

b) umurongo ufunguye hejuru

Nsobanukiwe ko:

Imirongo ifunguye ari imirongo idafunze.

Vuga amazina y'imirongo ikurikira

(c) Imirongo ivunaguye

Igikorwa cya 8

Mwitegereze imirongo ikurikira muvuge uko iteye.

Igikorwa cya 9

Shushanya:

a) Umurongo uvunaguye

b) Umurongo uhese ufunguye hasi

Nsobanukiwe ko:

Imirongo ihese ari imirongo itagororotse.

Imirongo ivunaguye ari imirongo ikozwe n’uduce tw’umurongo.

Igikorwa cya 10

Andika amazina y'imirongo ikurikira

2. Amoko y’imfuruka

(a) Imfuruka igororotse

Igikorwa cya 1

Mwitegereze amashusho, muvuge ibyo muyabonaho.

Igikorwa cya 2

Shushanya  imfuruka igororotse

Nsobanukiwe ko:

Imfuruka igororotse igizwe n’imirongo ibiri igororotse, umwe utambitse undi uhagaze.

Igikorwa cya 3

Mwitegereze ibintu biri mu ishuri, mwerekane ibifite  imfuruka igororotse

(b) Imfuruka ifunganye

Igikorwa cya 4

Mwitegereze amashusho, muyaganireho.

Nsobanukiwe ko:

Imfuruka ifunganye igizwe n’imirongo ibiri: umwe utambitse cyangwa uhagaze n’undi uberamiye iburyo.

Igikorwa cya 5

Mwifashishije uduti cyangwa uducamurongo mukore imfuruka ifunganye.

(c) Imfuruka yagutse

Igikorwa cya 6

Mwitegereze amashusho, muyaganireho.

Igikorwa  cya 7:

Shushanya imfuruka yagutse igizwe:

a) Imirongo ibiri iberamye

b) Umurongo utambitse n'uberamye

Nsobanukiwe ko:

Imfuruka yagutse igizwe:

- Imirongo 2 iberamiye

- Umurongo uhagaze n'uberamye

- Umurongo utambitse n'uberamiye ibumoso

Igikorwa  cya 8:

Mwifashishe uduti mukore imfuruka yagutse.

Vuga amazina y'imfuruka zikurikira

(d) Kugereranya imfuruka igororotse, imfuruka yagutse n'imfuruka ifunganye

Igikorwa cya 9

Mwitegereze amashusho, mugereranye imfuruka.

Nsobanukiwe ko:

- Imfuruka igororotse iruta imfuruka ifunganye

- Imfuruka yagutse iruta imfuruka igororotse

- Imfuruka yagutse iruta imfuruka ifunganye

- Imfuruka ifunganye irutwa n'imfuruka igororotse

- Imfuruka ifunganye irutwa n'imfuruka yagutse

• 0. Imyitozo yo kwiyibutsa ikinyatuzu

a) Huza A na B, B na C uvuge izina ry’imfuruka ubonye

b) Huza A na C, C na B uvuge izina ry’imfuruka ubonye

a) Huza A na B, B na C uvuge izina ry’imfuruka ubonye

b) Huza D na E, E na F uvuge izina ry’imfuruka ubonye

1. Ibiranga ikinyatuzu

Igikorwa cya 1

Mwitegereze amashusho, muyaganireho.

Nsobanukiwe ko:

Ikinyatuzu kigizwe n'imirongo ihagaze yitwa inkingi hamwe n'imirongo itambitse yitwa imbariro.

2. Uko bubaka ikinyatuzu

Igikorwa cya 1

Ubaka ikinyatuzu kigizwe na:

a) Inkingi 6             b) Imbariro 6

3. Uko bashyira akadomo ku kinyatuzu

Igikorwa cya 3

Mwitegereze uko bashyira akadomo mu kinyatuzu, mubiganireho.

Igikorwa cya 4

a) Akadomo A ku ihuriro ry'inkingi ya 2 n'urubariro rwa 4

b) Akadomo B ku ihuriro ry'inkingi ya 5 n'urubariro rwa 3

Igikorwa

Mukore ibi bikurikira:

– Mubare inkingi uko zikurikirana 1, 2, 3, 4, 5, 6

– Mubare imbariro uko zikurikirana 1, 2, 3, 4, 5, 6

Urugero:

•Erekana akadomo ku ihuriro ry'inkingi ya 4 n'urubariro rwa 3. Ako kadomo kite A

•Erekana akadomo ku ihuriro ry'inkingi ya 5 n'urubariro rwa 6. Ako kadomo kite B.

Nsobanukiwe ko:

Iyo baranga akadomo kari mu kinyatuzu bahera ku nkingi bajya ku rubariro.

Urugero:

Akadomo A kari ku nkingi ya 4 n'urubariro rwa 3

Igikorwa

Mukore ibi bikurikira

1. Mushushanye ikinyatuzu k’inkingi 5 n’imbariro 5

a) ku nkingi ya 3 n'urubariro rwa 4

b) ku nkingi ya 4 n'urubariro rwa 5

c) ku nkingi ya 2 n'urubariro rwa 3

3. Mushushanye ikinyatuzu k’inkingi 7 n’imbariro 7

4. Mushushanye ikinyatuzu k'inkingi 8 n'imbariro 8 Mwerekane akadomo ku ihuriro ry'inkingi ya 5 n'urubariro rwa 4. Ako kadomo kite A

Mwerekane akadomo ku ihuriro ry'inkingi ya 7 n'urubariro rwa 6. Ako kadomo kite B

• 1. Kare

(a) Ibiranga kare

Igikorwa cya 1

Mwitegereze aya mashusho, mupime uburebure bw'impande, maze muvuge uko impande n’imfuruka zayo zimeze.

Nsobanukiwe ko:

Kare igira impande 4 zingana n’imfuruka 4 zigororotse.

Igikorwa cya 2

Mu mashusho akurikira mugaragaze Kare, muvuge impamvu ari yo mwahisemo:

Igikorwa cya 3

Mwifashishije urupapuro, mukore ishuho ya  kare ifite cm 10 z'uruhande muyikate hanyuma muyereke bagenzi banyu.

(b) Umuzenguruko wa kare

Igikorwa cya 4

Mwitegereze ishusho,7 muvuge ibiri gukorwa :

Igikorwa cya 5

Mukore ibi bikurikira hanyuma muvuge ibyo mubonye:

– Mushushanye kare ifite cm 20 z’uruhande.

– Muyizengurutseho akagozi mugakate.

– Mupime buri ruhande mukoresheje agacamurongo muteranya ku rundi kugeza murangije impande 4

– Muteranye uburebure bw’impande enye.

– Mupime n’uburebure bwa wa mugozi maze mubigereranye.

Nsobanukiwe ko:

Umuzenguruko wa Kare ungana n’igiteranyo cy’uburebure bw’impande 4

Urugero:

Shaka umuzenguruko wa kare ifite cm 23 z'uruhande.

Igisubizo:

Uburyo bwa 1 :

Umuzenguruko = cm23 + cm23 + cm23 + cm23 = cm 92.

Uburyo bwa 2:

Umuzenguruko = cm23 × 4 = cm 92.

Igikorwa cya 6

Mukore ibi bikurikira mukurikije urugero mwahawe:

1. Shaka umuzenguruko wa kare ifite:

(a) cm 40 z’uruhande                (c) dm 50 z’uruhande

(b) m 60 z’uruhande

2. Shaka umuzenguruko w’ikibanza cya kare gifite uruhande rupima m30

3. Mushake umuzenguruko w’idirishya rya kare rifite uruhande rwa cm 72.

2. Urukiramende

(a) Ibiranga urukiramende

Igikorwa cya 1

Mwitegereze amashusho, mupime uburebure bw'impande, maze muvuge uko mubona impande n’imfuruka zayo zimeze.

Igikorwa cya 2

Mu mashusho akurikira mwerekane urukiramende:

Nsobanukiwe ko:

Urukiramende rufite impande 4, ebyiri ebyiri ziteganye zirangana. Rufite imfuruka enye zigororotse. Impande ndende zitwa uburebure. Impande ngufi zitwa ubugari

Igikorwa cya 3

Mwifashishije urupapuro, mukore ishusho  y’urukiramende, muyikate muyereke bagenzi banyu.

(b) Gushaka umuzenguruko w’urukiramende

Igikorwa cya 4

Mwitegereze ishusho, muvuge ibiri gukorwa :

Igikorwa cya 5

Mukore ibi bikurikira, hanyuma muvuge ibyo mubonye:

- Mushushanye urukiramende rufite cm 30 z'uburebure na cm 25 z'ubugari.

- Muruzengurutseho akagozi mugakate.

- Noneho mupime buri ruhande mukoresheje agacamurongo.

-  Muteranye ibipimo by'izo mpande uko ari 4. maze  mugereranye uburebure bw'umugozi n'ubw'impande mwapimye.

Igikorwa cya 6

1 Shaka umuzenguruko w’urukiramende ukurikije urugero wahawe.

Urugero:

Shaka umuzenguruko w'urukiramende rufite: Uburebure bwa  cm8 n'ubugari bwa  cm4 .

Igisubizo:

Uburyo bwa 1:

Umuzenguruko = cm 8 + cm 8 + cm 4 + cm 4  = cm 24

Uburyo bwa 2:

Umuzenguruko = (cm 8 + cm 4 ) x 2 = cm 24

a) Uburebure: cm 12 ubugari: cm 7

b) Uburebure: cm 40 ubugari: cm 25

c) Uburebure: cm 30 ubugari: cm 12

2. Shaka umuzenguruko w’umurima ufite ishusho y’urukiramende rwa m 60 z’uburebure na m 30 z’ubugari.

Nsobanukiwe ko:

Tubonye ko umuzenguruko ungana n’igiteranyo k’impande zose, Uburebure inshuro 2 n'ubugari inshuro 2. Bivuze ko ushobora guteranya uburebure (L) n’ubugari (l) ugakuba kabiri. Mu mpine, umuzenguruko = L + L + l + l = (L + l) × 2

3. Mpandeshatu

(a) Ibiranga mpandeshatu

Igikorwa cya 1

Mwitegereze amashusho, muvuge ibyo mubona.

Igikorwa cya 2

1. Mu mashusho akurikira, mugaragaze mpandeshatu.

2 Mushake ibintu bifite ishusho ya mpandeshatu   biri mu ishuri ryanyu.

Nsobanukiwe ko:

Mpandeshatu ari ishusho ifite impande 3 n’imfuruka eshatu

Igikorwa cya 3

Mukore amashusho ya mpandeshatu, mu rupapuro muyakate, muyereke bagenzi banyu.

Igikorwa cya 4

Mukore ibi bikurikira, hanyuma muvuge ibyo  mubonye:

– Mupime buri ruhande

– Muteranye ibyo mubonye

Nsobanukiwe ko:

Umuzenguruko wa mpandeshatu ugizwe  n'igiteranyo k'impande zose.

Urugero:

Shaka umuzenguruko wa mpandeshatu ifite impande:  cm 30,  cm 25 na cm 35

Igisubizo:

Umuzenguruko:  cm 30 + cm 25 + cm 35 = cm 90

Igikorwa cya 5

Mushake umuzenguruko wa mpandeshatu zifite impande zikurikira:

a) cm 15, cm 15, cm 15

b) dm 27,dm 60, dm 30

c) cm 42, cm 24 na cm 38

• 1. Guteranya no gukuramo utahura umubare ubura

Igikorwa cya 1

Mwitegereze ishusho, mwuzuze umubare ubura muvuge uko mwawubonye.

Igikorwa cya 2

Mutahure umubare ubura.

Nsobanukiwe ko:

Iyo ushaka umubare ubura mu iteranya ry'imibare  ibiri, ufata igisubizo ugakuramo umubare baguhaye.

Igikorwa cya 3

Mwitegereze ishusho mwuzuze umubare ubura, muvuge uko mwawubonye.

Igikorwa cya 4

Mutahure umubare ubura.

Nsobanukiwe ko:

Iyo ushaka umubare ubura mu ikuramo ry'imibare ibiri, ufata umubare baguhaye ugakuramo igisubizo baguhaye.

Igikorwa cya 5

Mwitegereze ishusho, mwuzuze umubare ubura, muvuge uko mwawubonye.

Igikorwa cya 6

Mutahure umubare ubura.

Nsobanukiwe ko:

Iyo ushaka umubare ubura ari wo ubanza, uteranya igisubizo n'umubare baguhaye.

Igikorwa cya 7

Mutahure imibare ibura muhereye ku rugero mwahawe.

2. Gukuba no kugabanya utahura umubare ubura

Igikorwa

Tahura umubare ubura ukurikije urugero wahawe.

Nsobanukiwe ko:

- Iyo utahura umubare ubura harimo ikimenyetso cyo (x) ufata igisubizo ukakigabanya n'umubare   baguhaye.

-  Iyo utahura umubare ubura harimo ikimenyetso cyo kugabanya (:) ufata igisubizo ukagikuba    n'umubare baguhaye.

Reka  nkore

3. Urukurikirane rw’imibare

(a) Gushaka intera idahinduka yakoreshejwe

Igikorwa cya 1

Mushake intera idahinduka yakoreshejwe mu rukurikirane rw’imibare muhereye kuri uru rugero.

a) 18, 20, 22               b) 75, 55, 35                  c) 12, 20, 28             d) 100, 70, 40

e) 999, 892, 785          f) 400, 250, 100            g) 105, 100, 95         h) 23, 30, 37

i) 15, 30, 45                 j) 900, 700, 500            k) 600, 450, 300        l) 150, 200, 250

Nsobanukiwe ko:

1. Iyo imibare ikurikiranye ihereye ku muto ijya ku munini intera idahinduka iri hagati y'imibare, uyibona ufata imibare ibiri ya mbere, umubare munini ukawukuramo umuto, ukabona umubare bagiye bongeraho

2. Iyo imibare ikurikiranye uhereye ku munini ujya ku muto kandi intera iri hagati y'imibare idahinduka, ufata imibare ibiri ya mbere ugafata umubare munini ukawukuramo umuto ukabona umubare bagiye bakuraho

(b) Gushaka umubare ubura mu rukurikirane rw’imibare

Igikorwa cya 2

Mwuzuze uru rukurikirane rw’imibare

Reka  nkore

1. Shaka imibare  ibura

2. Shaka intera idahinduka yakoreshejwe mu ruhererekane rw’imibare ikurikira:

a) 100, 85, 70, 55. Intera idahinduka ni ....

b) 22, 40, 58, 76. Intera idahinduka ni ....

c) 93, 80, 67, 54 Intera idahinduka ni ....

• 1. Gukora amatsinda y'ibintu ukoresheje igishushanyo

Igikorwa

Mwitegereze amashusho, mubare ibisa maze mubiganireho.

2. Gusesengura ibishushanyo byifashishwa mu mibare

Igikorwa

Mwitegereze, muvuge umubare uringaniye na buri gashusho.

Nsobanukiwe ko:

- Utubabi 2 turinganiye n'umubare 2

- Ibitabo 9 Biringaniye n'umubare 9

- Imodoka 4 ziringaniye n'umubare 4

- Bombo 9 ziringaniye n'umubare 9

- Amacunga 10 aringaniye n'umubare 10

Reka  nkore

1. Mwitegereze ibishushanyo bikurikira, mushyire    hamwe ibisa, mwerekane umubare wabyo, kandi   mubitondeke mu buryo buhagaze.

2. Mukore igishushanyo kifashishwa mu kubara mushyireho:

a) Amakaramu 6

b) Imineke 9

c) Amacunga 5

d) Ibiti 3

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