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Topic outline
- General
- Umutwe wa 1: Imibare kuva kuri 0 1 kugera ku 2 000Umutwe wa 1: Imibare kuva kuri 0 1 kugera ku 2 000
1.1 Gusoma imibare kuva kuri 0 kugera ku 2 000
Igikorwa cya 1
Mwitegereze ishusho maze mwigane ibiri gukorwa.
Igikorwa cya 2
Mufate amakarita yanditseho iyi mibare:
Mukore imibare itandukanye iri hagati ya:
1) 1 000 na 1 030
2) 1 040 na 1 05
3) 1 060 na 1 070
4) 1 080 na 1 090
Buri mubarwa ukora inshuro imwe.
Igikorwa cya 3
Musome imibare muhereye ku muto mujya ku munini
Koresha amakarita y’imibare wahawe ukore imibare 3 iri hagati ya 1 000 na 2 000. Nurangiza uyisomere bagenzi bawe.
Mu gakarito karimo udupapuro twanditseho imibare 1234; 1908; 1567; 1324; 1110. Buri wese atombore agapapuro kamwe asome aranguruye ijwi umubare wanditseho.
1.2 Kwandika imibare kuva kuri 0 kugera ku 2 000
Igikorwa
Mukoreshe aya makarita y’imibare. Mukore imibare 4 iri hagati ya 1 000 na 2 000
Muyandike mu magambo hanyuma muyisomere bagenzi banyu. Buri mubarwa ukoreshwe inshuro imwe mu mubare.
Umwitozo
Shaka imibare ibura kuri uyu murongo w’ibara, uyisome unayandike mu magambo.
Shaka imibare iri hagati ya:
a) 1 990 na 2 000
b) 1 240 na 1 250
c) 1 590 na 1 600
d) 1 920 na 1 930
Uyandike mu mibare no mu magambo
Mukoresheje amakarita y’imibare:
Nimukore imibare 4 iri hagati ya 1 000 na 2 000. Nimurangiza muyandike mu magambo hanyuma muyisomere bagenzi banyu. Itegeko: Buri mubarwa ukora inshuro imwe mu mubare
1) Andika mu mibare cyangwa mu magambo
a) 1 924
b) Igihumbi magana atatu na cumi n’ikenda:
c) Igihumbi magana inani mirongo irindwi na kane:
d) 1 499
2) Koresha amakarita y’imibare akurikira
ukore imibare 6 iri hagati ya 1 000 na 2 000 uyisome, uyandike mu ikayi yawe y’imyitozo, mu mibare no mu magambo.
3) Soma imibare iri mu mbonerahamwe ikurikira
– Iyanditse mu magambo uyandike mu mibare
– Iyanditse mu mibare uyandike mu magambo
1.3 Gusesengura imibare kuva kuri 0 kugera ku 2 000
Igikorwa cya 1
Itegereze imbonerahamwe ikurikira usobanure ibyakozwe
Umubare 1 456 ugizwe n’ikinyagihumbi ---- ibinyajana---- ,
ibinyacumi---- n’ibinyabumwe -----
Igikorwa cya 2
Mwandike imibare ikurikira mu mbonerahamwe mukurikiza urugero rw’ibyakozwe mu gikorwa cya 1. Mugaragaze ibinyagihumbi, ibinyacumi, n’ibinyabumwe.
a) 1 456 b) 1 239
c) 1 699 d) 1 479
e) 1 953 f) 1 974
Reka nisuzume
Itegereze ibinyagihumbi (h), ibinyajana(j), ibinyacumi (c) n’ibinyabumwe(b) maze wandike umubare wasesenguwe.
a) h 1 c 9 b 5 j 7 c) j 6 b 9 c 4 h 1 e) b 7 c 5 h 1 j 9
b) b 9 j 9 h 1 c 9 d) c 9 j 3 h 1 b 5 f) c 9 h 1 b 5 j 2
Koresha imbonerahamwe y’ibara ushyire umubare mu mwanya wawo.
a) 1 456 = h _ j _ c _ b _ d) 1 239 = b _ j _ c _ h _
b) 1 996 = c _ h _ b _ j _ e) 1 197 = c _ j _ h _ b _
c) 1 759 = j _ b _ h _ c _ f) 1 597 = j _ b _ h _ c _
Nsobanukiwe ko:
– Agaciro k’ibinyagihumbi (h) ari umubare wabyo gukuba na 1 000
– Agaciro k’ibinyajana (j) ari umubare wabyo gukuba na 100
– Agaciro k’ibinyacumi (c) ari umubare wabyo gukuba na 10
– Agaciro k’ibinyabumwe (b) ari umubare wabyo gukuba na 1
Igikorwa cya 3
a) Itegereze usobanure ibyakozwe
1 675 = 1 000 + 600 + 70 + 5
1 675 = (1 × 1 000) + (6 × 100) + (7 × 10) + (1 × 5)
1 675 = Ikinyagihumbi , Ibinyajana , Ibinyacumi , Ibinyabumwe
b) Kora nk’ibyakozwe hejuru muri a)
1 874
Igikorwa cya 4
Musesengure imibare ikurikira mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b) musobanure uburyo byakozwemo.
a) 1 265 = c) 1 645 = e) 1 997 =
b) 1 799 = d) 1 436 = f) 1 956 =
Mutahure kandi mwandike imibare yasesenguwe
a) (1 × 1 000) + (9 × 100) + (4 × 10) + (5 × 1) =
b) 1 000 + 900 + 50 + 9 bingana-----
c) Ikinyagihumbi 1 + Ibinyajana 9 + Ibinyacumi 7 + Ibinyabumwe 3 bingana---
1) Koresha imbonerahamwe y’ibara uvuge umwanya n’agaciro k’imibarwa iciyeho akarongo
a) 1 456 c) 1 324 e) 1 179
b) 1 795 d) 1 299 f) 1 975
2) Shaka umubare wasesenguwemo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) b 6 h 1 c 9 j 9 = c) c 9 h 1 b 9 j 7 =
b) b 7 c 9 h 1 j 9 = d) j 5 b 4 c 8 h 1 =
3) Sesengura imibare ikurikira mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) 1 765 = c) 1 956 = e) 1 564 =
b) 1 672 = d) 1 254 = f) 1 713 =
4) Shaka umubare wasesenguwe
a) (1 × 1 000) + (2 × 100) + (3 × 10)+ (4 × 1) =
b) 1 000 + 300 + 70 + 1 =
c) h 1 + j 7 + c 9 + b 6 =
1.4 Kugereranya imibare 2 itarenze 2 000
Igikorwa cya 1
Itegereze iyi shusho uvuge ibiri gukorwa:
Igikorwa cya 2
Mukurikize urugero mwahawe mugereranye imibare ikurikira mukoresha <, > na =
Igikorwa cya 3
Mukurikize urugero mwahawe mugereranye imibare ikurikira mukoresha <, > na =
Nsobanukiwe ko:
Iyo ugereranya imibare ibiri wita kuri ibi bikurikira:
1. Uhera ku binyagihumbi ujya ku binyabumwe ukagenda ugereranya buri mubarwa
2. Iyo ibinyagihumbi bingana uhita ugereranya ibinyajana
3. Iyo ibinyajana bingana uhita ugereranya ibinyacumi
4. Iyo ibinyacumi bingana ugereranya ibinyabumwe
5. Ibyo byose iyo birangiye wamenye umubare munini n’umuto cyangwa wabonye ko imibare ingana
ukoresha ibimenyetso by’igereranya ari byo: < (Birutwa), > (Biruta) na = (Bihwanye)
Ikitonderwa:
Ibimenyetso by’igereranya bya < na > bigomba kuba bireba buri gihe ahari umubare munini.
Igikorwa cya 4
Mukoreshe amakarita ariho imibare mugereranye imibare mushyiramo ikimenyetso k’igereranya gikwiye.
Gereranya abantu babarurirwa mu kagari kacu bari muri iyi mbonerahamwe
a) Umubare w’abagore n’uw’abagabo
b) Umubare w’abana n’uw’abagabo
c) Umubare w’abagore n’uw’abana
d) Umubare w’abagabo n’uw’urubyiruko
e) Umubare w’abagore n’uw’urubyiruko
f) Umubare w’abana n’uw’urubyiruko
Igikorwa cya 5
Mwitegereze iyi shusho maze mugereranye amajwi y’abana batorewe guhagararira abandi mu Kagari.
a) Muhizi afite amajwi--------
b) Mutesi afite amajwi--------
c) Kayitesi afite amajwi--------
d) Mutayomba afite amajwi----
e) Muri aba bakandida ni nde ufite amajwi make?
f) Muri aba bakandida ni nde ufite amajwi menshi?
g) Gereranya amajwi y’abakandida ukoresheje <, > na =
– Kayitesi na Mutayomba
– Kayitesi na Muhizi
– Kayitesi na Mutesi
– Mutayomba na Muhizi
– Mutayomba na Mutesi
– Muhizi na Mutesi
Mukoreshe <, > na = mugereranye imibare ikurikira:
1.5 Gutondeka imibare kuva kuri 0 kugera ku 2 000
A. Gutondeka imibare kuva ku muto ujya ku munini
Igikorwa
Kurikiza urugero utondeke imibare yo kuri (a) na (b) uva ku muto ujya ku munini.
Urugero: Tondeka imibare uhereye ku muto ujya ku munini,
1 649, 1 836, 1 598, 1 752
Igisubizo: 1 598, 1 649, 1 752, 1 836
a) 1 953, 1 395, 1 593 b) 1 613, 1 136, 1 479
Reka nisuzume
Ifashishe impapuro, wandike imibare 10, iri hagati ya 1 000 na 2 000 uyitondeke uva ku muto ujya ku munini.
Nsuzuma ngusuzume
Mukoreshe amakarita mwigane ibiri gukorwa ku ishusho mutondeke imibare iriho muhereye ku muto mujya ku munini
B. Gutondeka imibare uva ku mubare munini ujya ku mubare muto
Igikorwa
Mukurikize ingero mwahawe maze mutondeke imibare yo muri (a) n’iyo muri (b) muva ku munini mujya ku muto.
Urugero: Tondeka iyi mibare uva ku munini ujya ku mu
1 987, 1 897, 1 789
Igisubizo: 1 987, 1 897, 1 789
a) 1 048, 1 840, 1 084 b) 1 613, 1 136, 1 479
Reka nisuzume
Tondeka imibare iri ku makarita uva ku munini ujya ku muto
Nsuzuma ngusuzume
Mwifashishe impapuro, mwandike imibare 10, iri hagati ya 1 000 na 2 000 muyitondeke muva ku munini mujya ku muto.
Nsobanukiwe ko:
Iyo utondeka imibare ukoresha imbonerahamwe y’ibara.
– Ukabanza kugereranya ibinyagihumbi ureba uko birutana
– Ibinyajana na byo ukareba uko birutana
– Ibinyacumi na byo ukareba uko birutana
– Ibinyabumwe na byo ukareba uko birutana
– Ugatondeka ukurikije uko wabisabwe.
1.6 Guteranya imibare igiteranyo cyayo kitarenze 2 000
A. Iteranya ritabitsa ry’imibare ibiri igiteranyo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 1 324 + 675 =
1 324 + 675 = 1 999
a) 1 156 + 823 = d) 972 + 1 017 =
b) 1 543 + 456 = e) 675 + 1 323 =
c) 1 235 + 704= f) 794 + 1 002 =
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo + na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo +
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo uteranya imibare ibiri ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara
2. Umubare munini ukajya hejuru, umuto ukajya hasi.
3. Uteranya uhereye ku binyabumwe ugaherukira ku binyagihumbi.
4. Ukandukura igiteranyo
Reka nisuzume
Muteranye imibare ikurikira:
a) 1 234 + 763 =
b) 567 + 134 =
c) 990 + 1 009 =
d) 1 099 + 900 =
e) 765 + 1 213 =
f) 1 002 + 691 =
B. Iteranya ribitsa ry’imibare igiteranyo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe:
Urugero: 1 425 + 575 = 2 000
a) 934 + 799 =
b) 967 + 999 =
c) 999 + 1 001 =
d) 1 099 + 897 =
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo + na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo +
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo uteranya imibare ibiri:
1. Wifashisha imbonerahamwe y’ibara
2. Uteranya uhereye ku binyabumwe ugana ku binyagihumbi.
3. Umubare munini ujya hejuru, umuto ukajya hasi.
4. Iyo igiteranyo k’ibinyabumwe kigizwe n’imibarwa ibiri, wandika ikinyabumwe k’icyo giteranyo, ukabitsa
ikinyacumi hejuru y’ibinyacumi, ukabiteranya, ugakomeza utyo kugera ku binyagihumbi.
5. Ukandukura igiteranyo.
Reka nisuzume
Teranya imibare ikurikira:
a) 1 056 + 899 =
b) 797 + 1 197 =
c) 1 235 + 757 =
d) 972 + 969 =
e) 675 + 979 =
f) 1 239 + 476 =
1.7 Amahurizo yo guteranya imibare igiteranyo cyayo kitarenze 2 000
Urugero:
Umwaka ushize Muhizi yasaruye inanasi 799, uyu mwaka
asarura 967. Shaka igiteranyo k’inanasi yasaruye mu myaka
ibiri.
Nsuzuma ngusuzume
1) Mu Mujyi wa Kigali hubatse amagorofa 754 n’andi mazu y’ikitegererezo 969. Shaka umubare w’amazu yose yubatswe mu Mujyi wa Kigali?
2) Mu isoko hacururizamo abagore 1 006 n’abagabo 979. Shaka umubare w’abacuruzi bose hamwe.
3) Ishuri ryigamo abakobwa 997 n’abahungu 967. Shaka umubare w’abanyeshuri biga muri iryo shuri.
4) Mu bitaro byivurizamo abarwayi batandukanye, mu kwezi kumwe haje abagore 799, abana 356 n’abagabo 795.
Shaka umubare w’abivurije muri ibyo bitaro bose hamwe.
Reka nisuzume
1) Mu nzu y’imyidagaduro hari abagore 976 n’abagabo 779.
Muri iyo nzu harimo abantu bangahe?
2) Akagari kacu gatuwemo n’abagore 357, abana 656, abagabo 337 n’urubyiruko 731. Akagari kacu gatuwe n’abaturage bangahe?
3) Muri banki habikuza abantu batandukanye. Mu cyumweru kimwe habikuje abagore 969, abagabo 656 n’urubyiruko 245. Shaka umubare w’ababikuje muri icyo cyumweru.
4) Mu murenge wa Kicukiro harimo amazu y’ikitegererezo 675, amagorofa 199 n’amazu aciriritse 992. Muri uwo murenge harimo amazu angahe?
1.8 Gukuramo imibare itarenze 2 000
A. Ikuramo ridatira ry’imibare itarenze 2 000
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe
Urugero: 1 999 – 1 675 = 324
Igikorwa cya 2
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo – na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya –
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuramo imibare ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara
2. Wandika imibare mu mbonerahamwe y’ibara uhereye ku munini.
3. Uhera ku binyabumwe ukuramo ugaheruka ibinyagihumbi.
4. Wandukura ikinyuranyo ubonye.
Reka nisuzume
Kuramo imibare ikurikira:
a) 1 995 – 763 =
b) 1 567 – 1 341 =
c) 1 990 – 1 090 =
d) 1 999 – 979 =
e) 1 765 – 1 213 =
f) 1 956 – 923 =
B. Ikuramo ritira ry’imibare itarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 1 282 – 967 = 315
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo – na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo –
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuramo imibare isaba gutira ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara.
2. Wandika umubare munini hejuru y’umubare muto mu mbonerahamwe y’ibara.
3. Ukuramo uhereye ku binyabumwe ugana ku binyagihumbi.
4. Iyo gukuramo ibinyabumwe bidashoboka, utira ikinyacumi kimwe ukongera ku binyabumwe umubare
10 ugakuramo.
5. Ukomeza utyo aho bidashoboka hose, kugeza ukuyemo ibinyagihumbi.
Reka nisuzume
Kuramo imibare ikurikira
a) 1 034 – 799 =
b) 1 123 – 979 =
c) 1 234 – 1 196 =
d) 1 345 – 997 =
e) 1 456 – 1 299 =
f) 1 789 – 1 236 =
1.9 Amahurizo yo gukuramo imibare itarenze 2 000
Urugero:
Mu kigo cyacu higa abanyeshuri 1 791. Niba abahungu ari 999, shaka umubare w’abakobwa biga mu kigo cyacu
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuramo imibare:
1. Ugaragaza ibyo baguhaye mu ihurizo.
2. Ugaragaza ibyo bagusaba mu ihurizo.
3. Wandika umubare munini wahawe mu ihurizo ukawuvanamo umubare muto, ukandika ikinyuranyo.
Nsuzuma ngusuzume
1) Kaneza yateye ibiti 1 917. Hashize iminsi hava izuba
ryinshi 769 muri byo biruma. Yasigaranye ibiti bingahe?
2) Mutoni yari afite inka 1 231, inka 523 muri zo yazigabiye abavandimwe n’inshuti. Yasigaranye inka zingahe?
3) Umurenge wacu utuwe n’abaturage 1 163. Niba abaturage 999 muri bo ari abagore n’abana, shaka umubare w’abagabo n’urubyiruko batuye mu murenge wacu.
4) Uruganda rukora imifuka rwakoze imifuka 1 721, imifuka 179 muri yo igurwa na Rukundo. Shaka umubare w’imifuka uruganda rwasigaranye.
Reka nisuzume
1) Ishuri ryacu ryahize kuzatera ibiti 2 000 uyu mwaka kugeza ubu tumaze gutera 1 099. Harabura ibiti bingahe ngo twese umuhigo?
2) Mu bitaro by’Akarere hari harwariye abarwayi 1 532
none hasezerewe abarwayi 799 bamaze gukira neza.
Hasigayemo abarwayi bangahe?
3) Abanyamuryango ba koperative babumbye amatafari
1 911, amatafari 975 muri yo bayubakisha ikiraro k’inkoko.
Shaka umubare w’amatafari yasigaye.
4) Mu kigo cyacu harimo abantu 1 921, muri bo 124 ni abakozi b’ikigo. Shaka umubare w’abanyeshuri biga muri iryo shuri.
1) Itegereze neza ibiri mu mbonerahamwe maze ukore ibyo wabajijwe
Shaka igiteranyo k’imibare ikurikira:
a) A 1 + B 1 =
b) A 1 + C 1 =
c) A 1 + D 1 =
d) A 2 + B 2 =
e) A 2 + C 2 =
f) A 2 + D 2 =
Shaka ikinyuranyo k’imibare ikurikira:
a) A 1 – B 1 =
b) A 1 – C 1 =
c) A 1 – D 1 =
d) A 2 – B 2 =
e) A 2 – C 2 =
f) A 2 – D 2 =
2) Mu kagari kacu harimo abantu 996 bemerewe gutora. Mu Kari duturanye, harimo abantu bemerewe gutora 999. Ubwo abantu bemerewe gutora muri utwo tugari twombi ni bangahe?
3) Mu ibarura riheruka, Akagari kacu kari gatuwe n’abantu 1 964 bose hamwe. Niba 1 324 muri bo ari abana, ubwo Akagari kacu kari gatuwe n’abantu bakuru bangahe?
1.10 Mara ya 7 n’ibikubo bya 7 bitarenze 70
Igikorwa
a) Mukore uturundo tw’utubarisho 7, 14, 21, 28, 35, 42,
49, 56, 63, 70.
b) Mubare ibiri muri buri karundo maze mwandike inshuro
uwo mubare ugaruka kuri buri murongo.
c) Ese witegereje ibikurikira hari isano iri hagati yo guteranya
no gukuba na 7?
3) Uzurisha umubare ukwiye
1.11 Mara ya 8 n’ibikubo bya 8 bitarenze 80
Igikorwa
a) Mukore uturundo tw’utubarisho 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
b) Mubare ibiri muri buri karundo maze mwandike inshuro
uwo mubare ugaruka kuri buri murongo.
c) Ese witegereje ibikurikira hari isano iri hagati yo guteranya no gukuba na 8?
1) Uzurisha imibare ikwiye
1.12 Mara ya 9 n’ibikubo bya 9 bitarenze 90
Igikorwa
a) Mukore uturundo tw’utubarisho 9, 18 , 27, 36, 45, 54, 63, 72, 91, 90.
b) Mubare ibiri muri buri karundo maze mwandike inshuro
uwo mubare ugaruka kuri buri murongo.
c) Ese witegereje, ibikurikira hari isano iri hagati yo guteranya
no gukuba na 9?
1) Uzurisha imibare ikwiye
1.13 Gukuba imibare y’imibarwa ibiri cyangwa itatu na 7, 8 na 9 igikubo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 237 × 7 = 1 659
7 × 7 = 49 Twandika 9 mu binyabumwe tukabitsa 4 mu binyacumi.
7 × 3 = 21 Twandika 1 + 4 mu binyacumi tukabitsa 2 mu binyajana.
7 × 2 = 14 Twandika 4 + 2 mu binyajana tukabitsa 1 mu binyagihumbi.
Nsobanukiwe ko:
Iyo ukuba imibare uhera ku binyabumwe. Iyo usanze
igikubo kigizwe n’imibarwa ibiri wandika ikinyabumwe
k’icyo gikubo hanyuma ukabitsa ikinyacumi mu binyacumi.
Ukomeza utyo kugeza ku binyagihumbi.
Nsuzuma ngusuzume
Shaka umubare ubura
Reka nisuzume
Igana urugero wahawe ushake ibikubo by’iyi mibare
Urugero:
1.14 Ikuba ry’umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe.
Urugero:
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo × na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo ×
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuba umubare w’imibarwa 3 n’undi w’imibarwa 2:
1. Wandika imibare mu mbonerahamwe y’ibara
2. Ukubisha ikinyabumwe kugeza urangije imibarwa yose
3. Ukubisha ikinyacumi k’igikuba ukandika ikinyabumwe k’igikubo munsi y’inyacumi k’igikubo wabonye.
4. Uteranya ibikubo byose uhereye ku binyabumwe ujya ku binyagihumbi.
Itegereze neza imbonerahamwe ushake igikubo wabajijwe
1.15 Amahurizo yo gukuba umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo kitarenze 2 000
Urugero:
Mu cyumba k’inama harimo imirongo 19 y’intebe kandi kuri buri murongo hariho intebe 105. Shaka umubare w’intebe ziri mu cyumba k’inama.
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuba imibare:
1. Ugaragaza ibyo baguhaye mu ihurizo
2. Ugaragaza ibyo bakubaza mu ihurizo
3. Wandika imibare wahawe mu ihurizo mu buryo
buhagaze maze ukayikuba hanyuma ukandika igikubo.
Nsuzuma ngusuzume
1) Data yatemye ibitoki abipakira imodoka 17 ziruzura. Shaka umubare w’ibitoki yatemye niba buri modoka
yaratwaye ibitoki 117.
2) Ibitaro by’Akarere kacu bifite ibyumba by’abarwayi 19. Muri buri cyumba harimo abarwayi 105. Shaka umubare w’abarwayi bari muri ibyo bitaro.
3) Mu gasanduku k’itora hajyamo amajwi 148. Shaka umubare w’amajwi ajya mu dusanduku tw’itora 13.
4) Mubumbyi abumba amatafari 165 buri munsi. Shaka umubare w’amatafari abumba mu minsi 12.
Reka nisuzume
1) Abanyeshuri bateye ibiti ku mirongo. Buri murongo bawuteyeho ibiti 162 batera imirongo 12. Bateye ibiti
bingahe muri rusange?
2) Butera yaguriye abana 135 bo mu Kagari amakayi. Buri mwana yamuguriye amakayi 14. Ubwo Butera yaguze amakayi angahe yose hamwe?
3) Umucuruzi acuruza isabune 124 buri munsi. Shaka umubare w’isabune acuruza mu minsi 16.
4) Mu kigo k’ishuri hari ibyumba by’amashuri 18 kandi muri buri shuri harimo intebe 15. Icyo kigo k’ishuri kirimo intebe zingahe?
1.16 Ikuba ry’imibare na 100 na 1 000 igikubo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mwifashishije urugero mwahawe.
Urugero:
a) 19 × 100 = 1 900 c) 1 × 1 000 = 1 000
b) 13 × 100 = 1 300 d) 2 × 1 000 = 2 000
a) 12 × 100 = c) 1 × 1 000 = e) 19 × 100 =
b) 17 × 100 = d) 10 × 100 = f) 2 × 1 000 =
Nsobanukiwe ko:
– Iyo ukuba umubare na 100 wandika uwo mubare ukandika amazeru abiri (00) inyuma y’uwo mubare.
– Iyo ukuba umubare na 1 000 wandika uwo mubare ukandika amazeru atatu (000) inyuma y’uwo mubare.
Uzurisha 100 cyangwa 1 000
1.17 Igabanya ridasagura ry’umubare w’imibarwa 4 n’umubare w’umubarwa 1 imibare
itarenze 2 000
Igikorwa cya 1
Mwuzuze iyi mbonerahamwe
Igikorwa cya 2
Musubize ibibazo bikurikira mukurikije ingero mwahawe
Urugero:
a) 1 236 : 4 =
b) 1 575 : 5 =
c) 1 648 : 8 =
d) 1 989 : 9 =
e) 1 768 : 2 =
f) 1 326 : 6 =
Nsuzuma ngusuzume
1) Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo : na = .
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo :
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
2) Mukore amakarita ariho imibare mwihitiyemo iri hagati ya 1 000 na 2 000 n’andi ariho ibimenyetso – na : .Mukore nk’ibyakozwe hejuru.
Nsobanukiwe ko:
Iyo ugabanya imibare ukora ibi bikurikira:
1. Wandika imibare mu mahembe
2. Uhera ku binyagihumbi ugabanya, ugakurikizaho
ibinyajana, ibinyacumi, ugaherukira ku binyabumwe.
3. Iyo ibinyagihumbi ari bike ugereranyije n’ikigabanya ufatira hamwe ibinyagihumbi n’ibinyajana.
4. Iyo ibyasigaye ku binyagihumbi n’ibinyajana hiyongereyeho n’ibinyacumi ari bike ugereranyije n’ikigabanya ushyiramo 0 ugakuramo hanyuma ukamanura ibinyabumwe.
Itegereze neza imbonerahamwe maze ukore ibyo wabajijwe
Shaka ikigabanyo k’imibare ikurikira
a) A 1 na B 2
b) A 2 na B 1
c) A 3 na B 5
d) A 4 na B 4
e) A 5 na B 3
f) A 4 na B 8
1.18 Amahurizo yo kugabanya
Urugero:
Abanyeshuri 96 bashyizwe mu matsinda 8 ku buryo bungana. Buri tsinda ririmo abanyeshuri bangahe?
Nsuzuma ngusuzume
1) Abanyeshuri 378 bashyizwe mu mashuri 9 ku buryo bungana. Buri shuri ryagiyemo abanyeshuri bangahe?
2) Akarere gafite ibitabo 894 gashaka gusaranganya ku buryo bungana amashuri 6. Buri shuri rizahabwa ibitabo bingahe?
3) Umurenge wacu ufite inzitiramibu 1 985 ushaka kugabanya ku buryo bungana utugari 5 tuwugize. Buri kagari kazabona inzitiramibu zingahe?
4) Umuhinzi yasaruye imifuka y’ibirayi 1 359 ayipakira amafuso 9 ku buryo bungana. Buri fuso yatwaye imifuka ingahe y’ibirayi?
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo kugabanya imibare,
1. Ugaragaza ibyo baguhaye mu ihurizo
2. Ugaragaza ibyo bakubaza.
3. Wandika imibare wahawe mu ihurizo mu mahembe maze ukayigabanya hanyuma ukandika ikigabanyo.
Reka nisuzume
1) Keza afite amagi 1 768 ashaka gushyira mu makarito 8 ku buryo bungana. Buri karito izajyamo amagi angahe?
2) Abaterankunga bafite imipira yo gukina 1 484 bashaka gusaranganya ku buryo bungana uturere 7. Buri karere kazahabwa imipira ingahe?
3) Mubumbyi yabumbye amatafari 1 888 mu minsi 8. Shaka umubare w’amatafari abumba ku munsi umwe niba abumba amatafari angana buri munsi.
4) Gabanya ku buryo bungana ibitabo 1 845 ibigo by’amashuri
5. Buri kigo kizahabwa ibitabo bingahe?
Umutwe wa 1: Imibare kuva kuri 0 1 kugera ku 2 000 - Umutwe wa 2: Imibare kuva kuri 0 kugera ku 5 000Umutwe wa 2: Imibare kuva kuri 0 kugera ku 5 000
2.1 Gusoma imibare kuva kuri 0 kugera ku 5 000 Igikorwa cya 1
a) Mwitegereze maze musome imibare iri ku ishusho.
b) Imibare iri ku ishusho igizwe n’imibarwa ingahe?
Igikorwa cya 2
a) Musome imibare iri kuri uru ruziga muhereye ku muto mujya ku munini.
b) Ni iyihe mibare igizwe n’imibarwa ine?
c) Vuga imibare igizwe n’imibarwa itatu.
Reka nisuzume
Fata amakarita yanditseho iyi mibare:
Ukore imibare 3 wishakiye iri hagati ya
a) 2 000 na 2 500
b) 2 500 na 3 000
c) 3 000 na 3 500
d) 3 500 na 4 000
e) 4 000 na 4 500
f) 4 500 na 5 000
Mu gakarito karimo udupapuro twanditseho imibare 1 251; 2 437; 3 317. Tombora agapapuro kamwe usome umubare wanditseho uranguruye ijwi.
2.2 Kwandika imibare kuva kuri 0 kugera ku 5 000
Igikorwa cya 1
Mukoreshe amakarita y’imibare mwahawe mukore imibare 5 iri hagati ya 2 000 na 5 000. Muyandike mu magambo hanyuma muyisomere bagenzi banyu.
Itegeko: Buri mubarwa ukora inshuro imwe mu mubare
Igikorwa cya 2
Mushake imibare ibura kuri uyu murongo w’ibara, muyandike muyisome, munayandike mu magambo.
Igikorwa cya 3
Mukoreshe amakarita y’imibare akurikira mukore imibare 5 iri hagati ya 2 000 na 5 000. Muyandike mu magambo.
Muyisomere bagenzi banyu. Buri mubarwa ukora inshuro imwe mu mubare
Reka nisuzume
Shaka imibare wabajijwe maze uyandike mu mibare no mu magambo: Imibare iri hagati ya:
a) 2 015 na 2 020 b) 2 070 na 2 075 c) 4 065 na 4 070
1) Andika imibare ikurikira mu mibare cyangwa mu magambo
a) 4 924
b) Ibihumbi bitatu na cumi n’umunani
c) Ibihumbi bine magana inani na mirongo irindwi
d) 2 949
e) 4 157
f) Ibihumbi bibiri magana arindwi na mirongo itanu na kane
2) Koresha amakarita y’imibare akurikira:
ukore imibare 6 iri hagati ya 1 000 na 5 000 uyisome kandi uyandike mu ikayi yawe y’imyitozo, mu mibare no mu magambo.
3) Soma imibare iri mu mbonerahamwe ikurikira:
a) Iyanditse mu magambo uyandike mu mibare
b) Iyanditse mu mibare uyandike mu magambo
2.3 Gusesengura imibare kuva kuri 0 kugera ku 5 000
Igikorwa cya 1
Mwandike iyi mibare mu mbonerahamwe mukurikiza urugero mwahawe. Mugaragaze ibinyagihumbi, ibinyajana, ibinyacumi, n’ibinyabumwe.
Urugero: Umubare 2 456 ugizwe n’ibinyagihumbi 2, ibinyajana 4, ibinyacumi 5 n’ibinyabumwe 6
a) 3 546
b) 2 932
c) 4 969
d) 2 794
e) 4 935
f) 3 794
Igikorwa cya 2
Mukoreshe imbonerahamwe y’ibara mushyire buri mubare mu mwanya wawo.
a) 2 564 = h_ j_ c_ b_
b) 3 968 = c_ h_ b_ j_
c) 4 975 = j_ b_ h_ c_
d) 2 936 = b_ j_ c_ h_
e) 3 917 = c_ j_ h_ b_
f) 4 795 = j_ b_ h_ c_
Igikorwa cya 3
Mwitegereze ibinyagihumbi (h), ibinyajana(j), ibinyacumi (c) n’ibinyabumwe(b) maze mwandike umubare wasesenguwe.
a) h 2 c 7 b 5 j 9 =
b) b 9 j 8 h 4 c 1 =
c) j 6 b 4 c 6 h 2 =
d) c5 j 3 h 2 b 9 =
e) b 7 c 9 h 3 j5 =
f) c 9 h 4 b 4 j 1 =
Nsobanukiwe ko:
– Agaciro k’ibinyagihumbi (h) ari umubare wabyo × 1 000
– Agaciro k'ibinyajana (j) ari umubare wabyo × 100
– Agaciro k'ibinyacumi (c) ari umubare wabyo × 10
– Agaciro k'ibinyabumwe (b) ari umubare wabyo × 1
Reka nisuzume
Sesengura iyi mibare mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
Urugero:
a) 4 765 = 4 000 + 700 + 60 + 5
b) 3 567 = (3 × 1 000) + (5 × 100) + (6 × 10) + (7 × 1)
c) 2 893 = Ibinyagihumbi 2; Ibinyajana 8; Ibinyacumi 9; Ibinyabumwe 3
a) 4 652 =
b) 2 879 =
c) 3 574 =
d) 2 634 =
e) 4 971 =
f) 3 695 =
g) 3 916 =
h) 2 397 =
i) 4 645 =
Nsuzuma ngusuzume
Mutahure imibare yasesenguwe
a) (2 × 1 000) + (6 × 100) + (3 × 10) + (9 × 1) =
b) 4 000 + 300 + 70 + 9 =
c) Ibinyagihumbi 3; Ibinyajana 7; Ibinyacumi 4; Ibinyabumwe 2 =
1) Koresha imbonerahamwe y’ibara uvuge umwanya n’agaciro k’imibarwa iciyeho akarongo
a) 3 564
b) 4 759
c) 2 342
d) 4 925
e) 2 917
f) 3 759
2) Shaka umubare wasesenguwemo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) b 5 h 4 c 7 j 9 =
b) b 7 c 4 h 3 j 6 =
c) c 9 h 2 b 6 j 7 =
d) j 5 b 8 c 2 h 3 =
e) j 8 b 9 h 4 c 7 =
f) b 7 h 2 c 7 j 6 =
3) Sesengura imibare ikurikira mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) 4 657 =
b) 2 726 =
c) 3 965 =
d) 4 425 =
e) 2 645 =
f) 3 371 =
4) Shaka umubare wasesenguwe
a) (2 × 1 000) + (6 × 100) + (9 × 10) + (4 × 1) =
b) 4 000 + 500 + 40 + 9 =
c) Ibinyagihumbi 3 + Ibinyajana 4 + Ibinyacumi 7 + Ibinyabumwe 5 =
2.4 Kugereranya imibare 2 itarenze 5 000
Igikorwa
Mwitegereze ibiri gukorwa ku ishusho. Mukurikize urugero mwahawe maze mugereranye imibare ikurikira:
Urugero:
3 956 urutwa na 4 187 bikandikwa gutya: 3 956 < 4 187
Nsobanukiwe ko:
Iyo ugereranya imibare ibiri wita kuri ibi bikurikira:
1. Uhera ku binyagihumbi ugana ku binyabumwe ukagenda ugereranya buri mubarwa.
2. Iyo ibinyagihumbi bingana uhita ugereranya ibinyajana
3. Iyo ibinyajana bingana uhita ugereranya ibinyacumi
4. Iyo ibinyacumi bingana ugereranya ibinyabumwe
5. Ibyo byose iyo birangiye wamenye umubare umunini n’umuto cyangwa wabonye ko imibare ingana
ukoresha ibimenyetso by’igereranya ari byo:
< (Birutwa), > (Biruta) na = (Bihwanye)
Ikitonderwa:
Ibimenyetso by’igereranya bya < na > bigomba kuba bireba buri gihe ahari umubare munini.
Reka nisuzume
Koresha <, > na = ugereranye abantu batuye mu kagari ka
Kamukina
Gereranya umubare
a) w’abagore n’uw’abagabo
b) w’abagabo n’uw’urubyiruko
c) w’abana n’uw’abagabo
d) w’abagabo n’uw’abana
Nsuzuma ngusuzume
Mwitegereze ishusho mugereranye imibare y’abaturage batuye muri utu tugari.
Muri utu tugari ni akahe kagari gafite
1) Abagabo bake?
2) Abagore bake?
3) Abagabo benshi?
4) Abagore benshi?
5) Mukoresheje <, > na = mugereranye:
a) Umubare w’abagabo batuye mu kagari k’Umutuzo n’Akagari k’Amahoro
b) Umubare w’abagabo batuye mu kagari k’Ubumwe n’Akagari k’Umubano
c) Umubare w’abagabo batuye mu kagari k’Amahoro n’Akagari k’Umubano
d) Umubare w’abagabo batuye mu kagari k’Umutuzo n’Akagari k’Ubumwe
Mukoreshe <, > na = mugereranye imibare ikurikira
2.5 Gutondeka imibare kuva ku 2 000 kugera ku 5 000
A. Gutondeka imibare kuva ku muto ujya ku munini
Igikorwa cya 1
Tondeka iyi mibare uhereye ku mubare muto ujya ku munini ukurikije urugero wahawe:
Urugero: 4 725, 3 257, 4 752
1) 3 248, 2 348, 4 832 3) 4 334, 3 438, 4 833
2) 3 247, 4 237, 2 743 4) 2 437, 3 472, 4 327
Igikorwa cya 2
Mukurikize urugero rugaragara ku ishusho mutondeke imibare ikurikira muva ku muto mujya ku munini.
1) 2 345, 3 245, 4 245, 2 435, 3 425
2) 4 425, 2 534, 3 542, 4 524, 2 349
3) 4 329, 3 429, 2 934, 4 293, 3 942
4) 2 493, 4 939, 3 249, 4 328, 2 483
Nsobanukiwe ko:
Iyo utondeka imibare, ukoresha imbonerahamwe y’ibara ukagereranya:
– Ibinyagihumbi ureba uko birutanwa.
– Wasanga bingana ukagereranya ibinyajana.
– Na byo wasanga bingana ukagereranya ibinyacumi kugeza ubonye uko imibare irutana.
– Maze ukayikurikiranya uko wategetswe kuyitondeka.
Reka nisuzume
Tondeka iyi mibare iri ku makarita uva ku mubare muto ujya ku munini. Sobanura uko wabonye igisubizo.
B. Gutondeka imibare uva ku mubare munini ujya ku muto
Igikorwa cya 1
Mukoreshe amakarita mwigane ibiri gukorwa ku ishusho mutondeke imibare muhereye ku munini mujya ku muto:
a) 4 321 3 214 2 431
4 231 3 412 2 312
b) 2 341 4 123 3 124
2 143 3 345 4 533
Igikorwa cya 2
Tondeka iyi mibare uhereye ku mubare munini ujya ku muto ukurikije urugero wahawe
Urugero: 4 526, 4 735, 4 647
1) 2 543, 3 254, 4 352 3) 4 932, 2 439, 3 942
2) 4 235, 2 435, 3 453 4) 3 294, 4 293, 3 492
Nsuzuma ngusuzume
1) Tondeka uhereye ku mubare muto ujya ku munini
a) 2 938, 2 893, 3 892 b) 4 328, 3 428, 2 834
2) Tondeka uhereye ku mubare munini ujya ku muto
a) 4 369, 3 496, 4 693 b) 4 153, 4 315, 3 451
1) Tondeka uhereye ku mubare muto ujya ku munini
a) 4 739, 4 973, 4 397
b) 3 479, 4 749, 4 973
c) 4 128, 4 182, 4 018, 4 108
d) 4 107, 4 701, 4 170, 4 071
2) Tondeka uhereye ku mubare munini ujya ku muto
a) 2 643, 4 362, 3 263
b) 3 647, 4 763, 4 367
c) 2 974, 2 479, 2 947
d) 3 238, 3 823, 3 283, 3 832
2.6 Guteranya imibare igiteranyo cyayo kitarenze 5 000
A. Iteranya ritabitsa ry’imibare igiteranyo cyayo
kitarenze 5 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 1 213 + 2 675 =
Nsobanukiwe ko:
Iyo uteranya imibare ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara ukandikamo imibare
2. Ugahera ku binyabumwe uteranya ugaherukira ku binyagihumbi.
3. Wandukura igiteranyo ubonye.
Reka nisuzume
Teranya imibare ikurikira:
a) 4 235 + 763 = d) 2 990 + 2 009 =
b) 2 567 + 1 421 = e) 3 735 + 1 251 =
c) 3 909 + 1 090 = f) 4 056 + 823 =
Nsuzuma ngusuzume
Ifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso bya + na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo +
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
B. Iteranya ribitsa ry’imibare igiteranyo cyayo kitarenze 5 000
Igikorwa
Kurikiza urugero wahawe uteranye imibare ikurikira:
Urugero: 2 725 + 1 579 =
Nsobanukiwe ko:
Iyo uteranya imibare ubitsa ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara ukandikamo imibare
2. Uhera ku binyabumwe ugana ku binyagihumbi uteranya
3. Iyo igiteranyo k’ibinyabumwe kigizwe n’imibarwa 2 ni ukuvuga uhereye ku 10 kuzamura wandika ikinyabumwe k’icyo giteranyo ukabitsa ikinyacumi hejuru y’ibinyacumi by’imibare iteranywa ugakomeza utyo uteranya.
4. Wandukura igiteranyo ubonye.
Reka nisuzume
Teranya imibare ikurikira:
a) 2 943 + 1 979 =
b) 3 967 + 797 =
c) 1 239 + 3 678 =
d) 2 795 + 2 089 =
Nsuzuma ngusuzume
Ifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso
byo + na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo +
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
Teranya iyi mibare
2.7 Amahurizo yo guteranya imibare igiteranyo cyayo kitarenze 5 000
Urugero:
Inzu itubura ibitabo itubura ibitabo 2 567 ku manywa na 2 433 n’ijoro. Shaka umubare w’ibitabo bituburwa buri munsi.
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ryo guteranya imibare:
1. Ugaragaza ibyo baguhaye
2. Ugaragaza ibyo bakubaza
3. Wandika impagarike ibyo wahawe ukabiteranya.
Nsuzuma ngusuzume
1) Uruganda rukora amabati 2 345 mbere ya saa sita na 2 649 nyuma ya saa sita. Shaka umubare w’amabati urwo ruganda rukora buri munsi.
2) Akagari kacu kateye ibiti 1 897 umwaka ushize naho uyu mwaka kamaze gutera ibiti 3 098. Akagari kacu kamaze gutera ibiti bingahe muri iyi myaka ibiri?
3) Urwunge rw’amashuri rwo mu murenge wacu rwigamo abanyeshuri 3 785 mu mashuri abanza n’abandi 1 215 mu mashuri yisumbuye. Shaka umubare w’abanyeshuri biga muri iryo shuri.
4) Muri sitade y’umupira w’intoki hari abafana b’abagore 2 178 n’ab’abagabo 2 789. Shaka umubare w’abafana bose bari muri iyo sitade.
Reka nisuzume
1) Mu bitaro harimo abarwayi 2 679, abarwaza 1 829, abaforomo 245 n’abaganga 79. Shaka umubare w’abantu bari muri ibyo bitaro.
2) Muri gariyamoshi harimo abagabo 2 189, abagore 1 689 n’abana 789. Shaka umubare w’abantu bari muri iyo gariyamoshi.
3) Mu cyumba k’inama harimo abagabo 3 978 n’abagore 978. Muri icyo cyumba harimo abantu bangahe?
4) Umwaka ushize Butera yasaruye amashu 3 197 naho uyu mwaka yasaruye 1 789. Mu myaka yombi amaze gusarura amashu angahe?
1) Ishuri ryacu ryahumbitse ingemwe z’ibiti by’inturusu 1 765 n’iz’ibiti by’imbuto 2 103. Ubwo ryahumbitse
ingemwe zingahe zose hamwe?
2) Mu masengesho harimo abagabo 1 265, abagore 1 620 n’abana 210. Ubwo hari abantu bangahe bose hamwe?
3) Mu ishyamba ry’ishuri ryacu hateye inturusu 1 543 gereveriya 746 n’imisave 1 220. Ubwo ibyo biti byose
hamwe ni bingahe?
2.8 Gukuramo imibare itarenze 5 000
A. Ikuramo ridatira ry’imibare itarenze 5 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 4 568 – 3 226 =
Nsobanukiwe ko:
Iyo ukuramo imibare:
1. Wifashisha imbonerahamwe y’ibara
2. Wandika imibare mu mbonerahamwe y’ibara
3. Uhera ku binyabumwe ukuramo ugaheruka ibinyagihumbi.
4. Wandukura ikinyuranyo ubonye.
Reka nisuzume
Kuramo imibare ikurikira:
a) 4 795 – 2 563 =
b) 3 765 – 2 431 =
c) 2 897 – 1 794 =
d) 4 965 – 3 941 =
e) 2 765 – 1 312 =
f) 3 956 – 2 932 =
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo – na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo –
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
B. Ikuramo ritira ry’imibare itarenze 5 000 Igikorwa
Mukore ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 4 755 – 2 967 =
Nsobanukiwe ko:
Iyo ukuramo imibare utira ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara
2. Wandika umubare munini hejuru y’umuto
3. Uhera ku binyabumwe ugana ku binyagihumbi
4. Iyo ukuramo ibinyabumwe bidashoboka, utira ikinyacumi kikongera 10 ku binyabumwe ugakuramo.
5. Ukomeza utyo, kugeza ukuyemo ibinyagihumbi.
Reka nisuzume
Kuramo imibare ikurikira
a) 4 571 – 3 796 = d) 2 345 – 1 687 =
b) 3 423 – 2 975 = e) 4 567 – 2 789 =
c) 4 234 – 3 596 = f) 3 567 – 1 678 =
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi arihoibimenyetso byo – na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo –
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
Shaka ikinyuranyo
2.9 Amahurizo yo gukuramo imibare itarenze 5 000
Urugero
Mu kagari kacu hatuye abaturage 4 352 muri bo 3 974 bafite mituweri. Ubwo abaturage badafite mituweri ni bangahe?
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuramo imibare:
1. Ugaragaza ibyo baguhaye
2. Werekana ibyo bagusabye
3. Wandika umubare munini wahawe mu ihurizo
ubuhagaze maze ukawuvanamo umubare muto
wahawe mu ihurizo hanyuma ukandika ikinyuranyo.
Nsuzuma ngusuzume
1) Keza yabumbye amatafari 3 567 arayanika. Ayanure hamenekamo amatafari 987, ubwo yasigaranye amatafari angahe?
2) Umuyobozi w’ishuri ryacu yaguze ibitabo 4 123, abigejeje ku ishuri ahaho abanyeshuri n’abarezi ibitabo 1 456. Yasigaranye ibitabo bingahe?
3) Umurerwa yasaruye avoka 3 214 arazitara, azitaruye asanga 789 muri zo zaraboze. Yasigaranye avoka nzima zingahe?
4) Akagari ka Kamukina gafite abaturage 4 132. Muri bo 1 968 bari mu kiciro cya 2 cy’ubudehe. Shaka umubare w’abaturage bari mu bindi byiciro by’ubudehe.
Reka nisuzume
1) Mu kagari dutuyemo harimo inzu 4 356 muri zo 2 789 ni inzu z’ikitegererezo. Shaka umubare w’inzu ziciriritse ziri muri ako kagari?
2) Inkoko za Tunga zaturaze amagi 3 456, uwo munsi mu nzu yazo hinjiramo inturo. Zirasahinda zihunga hameneka amagi 987. Hasigaye amagi angahe?
3) Umurenge wacu wateye ibiti 4 321 ku munsi w’umuganda. 3 567 muri byo ni byo byameze. Shaka umubare w’ibiti bitameze.
Itegereze neza iyi mbonerahamwe maze ukore neza ibyo wabajijwe
1) Shaka igiteranyo k’imibare ikurikira
a) A 1 + C 1 =
b) A 1 + D 1 =
c) A 2 + C 2 =
d) A 2 + D 2 =
e) A 3 + C 4 =
f) A 3 + D 3 =
2) Shaka ikinyuranyo k’imibare ikurikira
a) A 1 – B 1 =
b) A 1 – C 1 =
c) A 1 – D 1 =
d) A 1 – D 3 =
e) A 2 – B 2 =
f) A 2 – C 2 =
2.10 Ikuba ry’umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo kitarenze 5 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe:
Urugero:
Nsobanukiwe ko:
Iyo ukuba umubare w’imibarwa 3 n’undi w’imibarwa 2:
1. Wandika imibare mu mbonerahamwe y’ibara
2. Ukubisha ikinyabumwe kugeza urangije imibarwa yose
3. Ukubisha ikinyacumi k’igikuba ukandika ikinyabumwe k’igikubo munsi y’ikinyacumi k’igikubo wabonye.
4. Uteranya ibikubo byose uhereye ku binyabumwe.
Nsuzuma ngusuzume
Ifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo × na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo ×
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
Soma imbonerahamwe ikurikira, ushake igikubo wabajijwe.
a) A 1 × B 1 =
b) A 1 × C 1 =
c) A 1 × B 2 =
d) A 1 × C 2 =
e) A 1 × B 3 =
f) A 1 × C 3 =
2.11 Amahurizo yo gukuba umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo kitarenze 5 000
Urugero:
Mu rusengero harimo intebe 297. Kuri buri ntebe hicara abantu 16. Urwo rusengero rwakwakira abantu bangahe?
Ndakubisha 6
• 6 × 7 = 42 Twandika 2 Tukabika 4
• 6 × 9 = 54 Twongeraho 4 tukandika 8 tukabika 5
• 6 × 2 = 12 Twongeraho 5 tukandika 17
Ndakubisha 1
• 1 × 7 = 7 • 1 × 9 = 9 • 1 × 2 = 2
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuba imibare,
1. Werekana ibyo baguhaye mu ihurizo
2. Werekana ibyo bakubaza mu ihurizo
3. Wandika imibare wahawe mu ihurizo mu buryo buhagaze maze ukayikuba hanyuma ukandika igikubo.
Nsuzuma ngusuzume
1) Gahire yateye inanasi ku mirongo 316. Shaka umubare
w’inanasi yateye niba kuri buri murongo yarahateye
inanasi 15.
2) Muhongerwa afite udutebo tw’amagi 159. Shaka umubare w’amagi afite niba muri buri gatebo harimo amagi 30.
Reka nisuzume
1) Mu cyumba k’inama harimo ibihande 28 birimo intebe 189 muri buri gihande. Shaka umubare w’intebe ziri muri icyo cyumba k’inama.
2) Ku munsi w’ingabo, abasirikari bakoze imirongo 245 kuri buri murongo hajyaho abasirikari 19. Shaka
umubare w’abasirikari bitabiriye uwo munsi mukuru.
2.12 Ikuba ry’imibare na 100 na 1 000 igikubo kitarenze 5 000
Igikorwa cya 1
Mukube iyi mibare mukurikije urugero mwahawe
Urugero:
a) 29 × 100 = 2 900
b) 45 × 100 = 4 500
a) 5 × 1 000 =
b) 4 × 1 000 =
Nsobanukiwe ko:
– Iyo ukuba umubare na 100 wandika uwo mubare ukandika amazeru abiri (00) inyuma y’uwo mubare.
– Iyo ukuba umubare na 1 000 wandika uwo mubare ukandika amazeru atatu (000) inyuma y’uwo mubare.
Reka nisuzume
Murushanwe gushaka byihuse igikubo k’iyi mibare:
a) 42 × 100 =
b) 37 × 100 =
c) 2 × 1 000 =
d) 36 × 100 =
e) 49 × 100 =
f) 1 × 1 000 =
Nsuzuma ngusuzume
– Muhagarare imbere y’utudobo tubiri: Kamwe karimo amakarita yanditseho imibare 10 itandukanye,
– Akandi karimo amakarita yanditseho ibikubo 10 bitandukanye.Buri wese age agenda akoremo ikarita
imwe mu kadobo ka mbere
– Mugenzi we ashake igikubo cyawo na 100 cyangwa 1 000 mu kadobo ka kabiri.
Uzurisha 10, 100 cyangwa 1 000
2.13 Igabanya ridasagura ry’umubare w’imibarwa 4 n’umubare w’umubarwa 1 imibare
itarenze 5 000
Igikorwa
Gabanya imibare ikurikira ukurikije urugero wahawe
a) 3 975 : 3 =
b) 4 648 : 4 =
c) 4 985 : 5 =
d) 2 706 : 6 =
e) 4 256 : 7 =
f) 3 872 : 8 =
Nsuzuma ngusuzume
Ifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso
byo : na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo :
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ugabanya imibare ukora ibi bikurikira:
1. Wandika imibare mu mahembe
2. Uhera ku binyagihumbi ugabanya; ugakurikizaho ibinyajana; hagakurikiraho ibinyacumi; ugaheruka
ibinyabumwe.
3. Iyo ibinyagihumbi ari bike ugereranyije n’ikigabanya ufatira hamwe ibinyagihumbi n’ibinyajana.
4. Iyo ibyasigaye ku binyagihumbi n’ibinyajana hiyongereyeho n’ibinyacumi ari bike ugereranyije
n’ikigabanya ushyiramo zeru (0) ugakuramo hanyuma ukamanura ibinyabumwe.
Reka nisuzume
Gabanya a) 4 985 : 5 = c) 2 736 : 9 =
b) 3 872 : 8 = d) 4 963 : 7 =
1) Itegereze imbonerahamwe ushake ikigabanyo k’imibare ikurikira:
a) A 1 na B 1
b) A 2 na B 2
c) A 3 na B 3
d) A 4 na B 4
e) A 5 na B 5
f) A 4 na B 2
2) Shaka imibare y’imibarwa 3 yagabanyijwe n’umubare w’umubarwa 1 kugira ngo haboneke ibigabanyo bikurikira:
a) _ : 5 = 153 b) _ : 4 = 124 c) _ : 6 = 496
2.14 Amahurizo yo kugabanya
Urugero:
Gabanya ku buryo bungana inzitiramibu 4 875, imidugudu
5. Buri mudugudu uzahabwa inzitiramibu zingahe?
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo kugabanya imibare:
1. Werekana ibyo baguhaye mu ihurizo
2. Werekana ibyo bakubaza mu ihurizo
3. Wandika imibare wahawe mu ihurizo mu mahembe maze ukayigabanya hanyuma ukandika ikigabanyo.
Nsuzuma ngusuzume
1) Ibigo by’amashuri 9 byasaranganyijwe ibitabo by’imibare 4 581 ku buryo bungana. Buri kigo cyahawe ibitabo bingahe?
2) Ibigo nderabuzima 7 byatewe inkunga y’ibitanda 4 991. Ibyo bitanda babigabanye ku buryo bungana. Buri kigo nderabuzima cyahawe ibitanda bingahe?
3) Gabanya ku buryo bungana ingemwe z’ikawa 4 986, imirenge 9. Buri murenge uzahabwa ingemwe zingahe?
4) Mbabazi asarura inanasi 3 795 mu bihembwe 5 by’ihinga. Shaka umubare w’inanasi asarura buri muri buri gihembwe k’ihinga niba asarura inanasi zingana buri gihembwe.
Reka nisuzume
1) Ibigo by’amashuri 8 byo mu karere kacu byahawe inkunga y’intebe 3 848. Shaka umubare w’intebe buri
kigo cyabonye niba barazigabanye ku buryo bungana?
2) Gabanya ku buryo bungana amabati 2 598, abubatsi 6. Buri mwubatsi azahabwa amabati angahe?
3) Umucuruzi agemura amashu 4 764 mu bigo bya gisirikari
4. Ubwo buri kigo gihabwa amashu angahe niba buri kigo kibona amashu angana n’ay’ikindi kigo?
4) Uwamahoro acuruza imifuka ya sima 4 365 mu mezi 3. Shaka umubare w’imifuka ya sima acuruza mu kwezi kumwe niba acuruza sima zingana buri kwezi.
2.15 Isuzuma risoza umutwe wa 2
1) Andika 4 978 mu magambo
2) Shaka umubare wasesenguwe
a) b 7 c 5 h 4 j 9 = b) b 9 h 3 c 6 j 7 =
3) Mutahure imibare yasesenguwe
a) (4 × 1 000) + (8 × 100) + (7 × 10) + (5 × 1) =
4) Andika umwanya w’imibarwa iciyeho akarongo
a) 3 586 b) 2 789 c) 4 362 d) 3 978
5) Gereranya ukoresheje <, > na =
a) 4 659
4 695 b) 4 871
4 8676) Tondeka uhereye ku mubare muto ujya ku munini
4 879, 4 897, 4 798, 4 789, 4 987, 4 978
7) Tondeka uhereye ku munini ujya ku muto
3 687, 3 678, 3 768, 3 786, 3 867, 3 876
8) Shaka igiteranyo k’imibare ikurikira:
a) 3 154 + 1 659 = b) 3 876 + 1 112 =
9) Shaka ikinyuranyo k’imibare ikurikira:
a) 4 587 – 3 267 = b) 3 967 – 2 563 =
10) Shaka igikubo k’imibare ikurikira
11) Shaka ikigabanyo k’imibare ikurikira
a) 4 959 : 9 = b) 3 785 : 5 = c) 2 988 : 6 =
12) Mu kagari ka Nyakabanda hatuye abagore 879, abagabo 839 n’abana 3 267. Shaka umubare w’abaturage bose.
13) Amahugurwa yitabiriwe n’abantu 4 789. Abagore bari 2 097. Shaka umubare w’abagabo.
14) Ku muganda buri rugo rwateye ibiti 18. Shaka umubare w’ibiti byatewe mu kagari kacu niba karimo ingo 276.
15) Gabanya ku buryo bungana imifuka y’isima 4 298 abacuruzi 7. Buri mucuruzi azahabwa imifuka ingahe?
Umutwe wa 2: Imibare kuva kuri 0 kugera ku 5 000 - Umutwe wa 3:Imibare kuva kuri 0 kugera ku 10 000Umutwe wa 3:Imibare kuva kuri 0 kugera ku 10 000Label: 1Umutwe wa 3:Imibare kuva kuri 0 kugera ku 10 000
3.1 Gusoma imibare kuva kuri 0 kugera ku 10 000
Igikorwa cya 1
Mwitegereze maze musome imibare iri ku ishusho
Nsuzuma ngusuzume
Mukore imirongo ine imbere y’agakarito karimo udupapuro twanditseho imibare. Buri wese age atombora agapapuro kamwe asome umubare wanditseho aranguruye ijwi.
Mukoreshe amakarita y’imibare mukore imibare iri hagati ya 5 000 na 10 000 muyisomere abandi.
Igikorwa cya 2
Musome imibare iri kuri uru ruziga muhereye ku muto mujya ku munini.
Reka nisuzume
Fata amakarita yanditseho imibare ikurikira:
Ukore imibare iri hagati ya
1) 5 000 na 5 100 4) 7 400 na 7 500
2) 5 500 na 5 600 5) 8 600 na 8 700
3) 6 200 na 6 300 6) 9 800 na 9 900
Ikitonderwa: Buri mubarwa ukora inshuro imwe mu mubare
3.2 Kwandika imibare kuva kuri 0 kugera ku 10 000
Igikorwa
Mukoreshe amakarita y’imibare mwahawe mukore imibare 3 mwihitiyemo iri hagati ya 5 000 na 10 000. Muyandike mu magambo hanyuma muyisomere bagenzi banyu.
Ikitonderwa: Buri mubarwa ukora inshuro imwe mu mubare
Nsuzuma ngusuzume
Mukoreshe amakarita y’imibare mwahawe, mukore imibare 5 mwihitiyemo iri hagati ya 5 000 na 10 000, muyandike mu magambo hanyuma muyisomere abandi.
Ikitonderwa: Buri mubarwa ukora inshuro imwe mu mubare
Mushake imibare ibura kuri uyu murongo w’ibara, muyisome munayandike mu magambo.
Reka nisuzume
Shaka imibare wabajijwe hanyuma uyandike mu mibare no mu magambo: Imibare yose iri hagati ya
1) 5 017 na 5 020
2) 6 031 na 6 033
3) 7 050 na 7 055
4) 8 097 na 8 00
5) 9 121 na 9 123
6) 9 266 na 9 269
1) Andika mu mibare cyangwa mu magambo
a) 9 249:
b) Ibihumbi bitandatu magana inani na cumi n’ikenda:
2) Koresha amakarita y’imibare akurikira ukore nibura imibare 6 iri hagati ya 5 000 na 10 000 uyisome kandi uyandike mu mibare no mu magambo.
3) Uzuza uyu murongo w’ibara
4) Soma imibare iri muri iyi mbonerahamwe
a) Iyanditse mu magambo uyandike mu mibare
b) Iyanditse mu mibare uyandike mu magambo
3.3 Gusesengura imibare kuva kuri 0 kugera ku 10 000
Igikorwa cya 1
1) Mwandike imibare ikurikira mu mbonerahamwe y’ibara mukurikiza urugero mwahawe.
Urugero:
a) 5 465
b) 6 392
c) 7 968
d) 8 974
e) 9 539
f) 6 749
2) Mukoreshe imbonerahamwe y’ibara mushyire umubare mu mwanya wawo.
a) 8 654 = h _ j _ c _ b _
b) 6 974 = c _ h _ b _ j _
c) 7 935 = j _ b _ h _ c _
d) 5 923 = b _ j _ c _ h _
e) 6 179 = c _ j _ h _ b _
f) 9 756 = j _ b _ h _ c _
3) Mwandike umubare wasesenguwemo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) h 6 c 7 b 5 j 3 =
b) b 9 j 6 h 7 c 1 =
c) j 7 b 4 c 6 h 5 =
d) c 5 j 8 h 8 b 9 =
e) b 7 c 9 h 9 j 9 =
f) c 9 h 7 b 4 j 4 =
Nsobanukiwe ko:
– Agaciro k’ibinyagihumbi (h) ari Umubare wabyo × 1 000
– Agaciro k’ibinyajana (j) ari Umubare wabyo × 100
– Agaciro k’ibinyacumi (c) ari Umubare wabyo × 10
– Agaciro k’ibinyabumwe (b) ari Umubare wabyo × 1
Igikorwa cya 2
Musesengure imibare mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b) mukurikije urugero mwahawe.
Urugero:
1) 8 745 = 8 000 + 700 + 40 + 5
2) 9 537 = (9 × 1 000) + (5 × 100) + (3 × 10) + (7 × 1)
3) 7 853 = Ibinyagihumbi 7 + Ibinyajana 8 + Ibinyacumi 5 + Ibinyabumwe 3
a) 6 248 =
b) 5 879 =
c) 7 574 =
d) 7 649 =
e) 6 719 =
f) 8 659 =
g) 9 761 =
h) 7 367 =
i) 8 625 =
Nsuzuma ngusuzume
Mutahure imibare yasesenguwe
a) (8 × 1 000 ) + (5 × 100 ) + ( 4 × 10 ) + (7 × 1 ) =
b) 9 000 + 800 + 70 + 6 =
c) Ibinyagihumbi 7 + Ibinyajana 2 + Ibinyacumi 5 =
1) Koresha imbonerahamwe y’ibara uvuge umwanya w’imibarwa iciyeho akarongo
a) 9 465
b) 8 957
c) 7 237
d) 6 958
e) 5 871
f) 6 597
2) Shaka umubare wasesenguwemo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) b 8 h 5 c 7 j 9 =
b) b 3 c 6 h 3 j 1 =
c) c 3 h 7b 6 j 7 =
d) j 5 b 8 c 7 h 2 =
e) j 8 b 2 h 9 c 7 =
f) b 3 h 8 c 7 j 6 =
3) Sesengura imibare mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b) mu mibare ikurikira.
a) 8 567 =
b) 7 526 =
c) 9 615 =
d) 6 452 =
e) 6 435 =
f) 7 361 =
3.4 Kugereranya imibare 2 itarenze 10 000
Igikorwa cya 1
Mukurikize ibyo mwitegereje ku gishushanyo n’urugero mwahawe mugereranye imibare ikurikira.
Urugero:
6 543 Urutwa na 9 876 bikandikwa gutya: 6 543 < 9 876
Nsobanukiwe ko:
Iyo ugereranya imibare ibiri wita kuri ibi bikurikira:
1. Uhera ku binyagihumbi ugana ku binyabumwe ukagenda ugereranya buri mubarwa.
2. Iyo ibinyagihumbi bingana uhita ugereranya ibinyajana
3. Iyo ibinyajana bingana uhita ugereranya ibinyacumi
4. Iyo ibinyacumi bingana ugereranya ibinyabumwe
5. Ibyo byose iyo birangiye wamenye umubare umunini n’umuto cyangwa wabonye ko imibare ingana ukoresha ibimenyetso by’igereranya ari byo: < (Birutwa), > (Biruta) na = (Bihwanye)
Igikorwa cya 2
Mutombore amakarita yanditseho imibare n’andi ariho ibimenyetso by’igereranya, mugereranye imibare mufite.
Igikorwa cya 3
Koresha <, > na = ugereranye
Nsuzuma ngusuzume
Mwitegereze iyi shusho maze mugereranye imibare y’abaturage bafite ubwisungane mu kwivuza batuye mu tugari tugize Umurenge wa Nyakabanda.
1) Ibibazo
a) Ni akahe kagari gafite abaturage bake bafite ubwisungane mu kwivuza?
b) Ni akahe kagari gafite abaturage benshi bafite ubwisungane mu kwivuza?
2) Mukoresheje <, > na = mugereranye
a) Umubare w’abaturage bafite mituweri mu kagari ka Nyakabanda I n’abo mu kagari ka Nyakabanda II
b) Umubare w’abaturage bafite mituweri mu kagari ka Nyakabanda I n’abo mu kagari ka Munanira I
c) Umubare w’abaturage bafite mituweri mu kagari ka Nyakabanda I n’abo mu kagari ka Munanira II
d) Umubare w’abaturage bafite mituweri mu kagari ka Nyakabanda II n’abo mu kagari ka Munanira I
e) Umubare w’abaturage bafite mituweri mu kagari ka Nyakabanda II n’abo mu kagari ka Munanira II.
f) Umubare w’abaturage bafite mituweri mu kagari ka Nyakabanda I n’abo mu kagari ka Nyakabanda II
g) Umubare w’abaturage bafite mituweri mu kagari ka Munanira I na Munanira II.
Reka nisuzume
Koresha <, > na = ugereranye abarwayi bivuriza mu bitaro byitiriwe umwami Fayisali buri cyumweru.
a) Umubare w’abagore n’uw’abagabo bahivuriza buri munsi
b) Umubare w’abagore n’uw’abana bahivuriza buri munsi
c) Umubare w’abagabo n’uw’abana bahivuriza buri munsi
Mukoreshe <, > na = mugereranye imibare ikurikira
3.5 Gutondeka imibare kuva ku 2 000 kugera ku 10 000
A. Gutondeka imibare kuva ku muto ujya ku munini
Igikorwa cya 1
Mukoreshe amakarita mwigane ibiri gukorwa kuri iyi shusho mutondeke imibare muhereye ku muto mujya ku munini.
1) 6 439, 9 825, 7 564, 8 943, 9 754
2) 5 482, 6 357, 7 845, 8 015, 6 497
3) 5 739, 9 384, 8 049, 7 193, 7 496
4) 9 437, 8 391, 6 427, 7 409, 8 274
Nsobanukiwe ko:
– Iyo utondeka imibare uva ku muto ujya ku munini ukoresha imbonerahamwe y’ibara.
– Ukabanza ukagereranya ibinyagihumbi byose, ugakurikizaho ibinyajana, ibinyacumi kugeza ubonye uko imibare yose ikurikirana ukayitondeka uhereye ku mubare muto ujya ku munini.
Igikorwa cya 2
Tondeka iyi mibare uhereye ku muto ujya ku munini ukurikije urugero wahawe.
Urugero: 6 572, 7 852, 5 792, 7 562
Igisubizo: 5 792, 6 572, 7 562, 7 852
1) 7 804, 6 218, 5 386 2) 7 358, 6 804, 5 748
B. Gutondeka imibare kuva ku munini ujya ku muto
Igikorwa cya 1
Mukoreshe amakarita mwigana ibiri gukorwa ku ishusho mutondeke imibare muhereye ku munini mujya ku muto.
1) 5 734, 9 354, 6 507
2) 6 709, 9 675, 5 084
3) 6 901, 8 654, 5 789
4) 6 057, 8 765, 5 293
Nsobanukiwe ko:
Iyo utondeka imibare uva ku munini ujya ku muto ukoresha imbonerahamwe y’ibara ukabanza ukagereranya ibinyagihumbi, ugakurikizaho ibinyajana, ibinyacumi kugeza ubonye uko imibare yose ikurikirana, ukayitondeka uva ku munini ujya ku muto.
Igikorwa cya 2
Tondeka iyi mibare uhereye ku mubare munini ujya ku muto ukurikije urugero wahawe.
Urugero: 9 126, 8 965, 5 869, 6 739, 7 629, 8 469
Igisubizo: 9 126 > 8 965 > 8 469 > 7 629 > 6 739 > 5 869
1) 7 483, 8 534, 5 192 3) 8 976, 7 456, 6 012
2) 7 345, 9 567, 6 978 4) 7 105, 9 271, 6 823
Reka nisuzume
Tondeka uhereye ku mubare munini ujya ku muto
a) 6 015, 7 247, 8 156, 9 375
b) 7 245, 7 254, 7 524, 7 542
1) Tondeka uhereye ku mubare muto ujya ku munini
a) 9 876, 7 869, 8 687
b) 5 678, 7 856, 7 658
c) 7 654, 5 746, 6 475
d) 7 896, 7 689, 7 869
2) Tondeka uhereye ku mubare munini ujya ku muto
a) 5 923, 9 325, 5 392
b) 6 541, 5 146, 6 154
c) 6 789, 7 698, 9 876
d) 8 279, 8 972, 8 729
3.6 Guteranya imibare igiteranyo cyayo kitarenze 10 000
A. Iteranya ritabitsa
Igikorwa
Kurikiza urugero wahawe uteranye imibare ikurikira:
Urugero: 5 432 + 4 567 = 9 999
Nsobanukiwe ko:
Iyo uteranya imibare ukora ibi bikurikira:
– Kwandika imibare mu mbonerahamwe y’ibara
– Gukoresha utubarisho ugahera ku binyabumwe uteranya ugaheruka ibinyagihumbi.
– Kwandukura igiteranyo.
Reka nisuzume
Muteranye imibare ikurikira:
a) 4 125 + 3 873 =
b) 3 756 + 132 =
c) 5 234 + 4 543 =
d) 3 256 + 732 =
e) 5 715 + 4 054 =
f) 4 650 + 4 239 =
Nsuzuma ngusuzume
Mwifashishe amakarita y’imibare n’ibimenyetso byo + na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo +
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
a) 5643 + 256 =
b) 7215 + 2784 =
c) 4572 + 4316 =
d) 4567 + 421 =
B. Iteranya ribitsa
Igikorwa
Kurikiza urugero wahawe uteranye imibare ikurikira:
Urugero: 7 698 + 1 479 = 9 177
Nsobanukiwe ko:
Iyo uteranya imibare isaba kubitsa ukora ibi bikurikira:
1. Guca imbonerahamwe y’ibara ukayandikamo imibare
2. Gukoresha utubarisho ugahera ku binyabumwe uteranya
3. Iyo igiteranyo k’ibinyabumwe kigizwe n’imibarwa 2 wandika ikinyabumwe k’icyo giteranyo maze ukabitsa
ikinyacumi ku binyacumi, ukabiteranya, ugakomeza utyo no ku yindi myanya, ukandukura igiteranyo
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo + na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo +
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Reka nisuzume
Teranya imibare ikurikira
a) 1 943 + 7 689 = d) 4 239 + 4 876 =
b) 2 976 + 6 387 = e) 5 795 + 3 498 =
c) 3 987 + 5 679 = f) 6 467 + 2 944 =
3.7 Amahurizo yo guteranya imibare igiteranyo cyayo kitarenze 10 000
Urugero:
Ishyirahamwe ryateye ingemwe z’amashu 4 567 ku wa mbere bukeye bwaho ku wa kabiri ritera izindi 3 978. Ubwo ryateye ingemwe zingahe muri iyo minsi uko ari ibiri?
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ryo guteranya imibare ukora ibi bikurikira:
1. Kuvana mu ihurizo ibyo baguhaye
2. Kuvana mu ihurizo ibyo bakubaza
3. Gutondeka ibyo wahawe impagarike ukabiteranya.
Nsuzuma ngusuzume
1) Uyu mwaka mu Karere ka Huye hakingiwe abana b’abahungu 5 321 n’ab’abakobwa 3 789. Ubwo hakingiwe abana bangahe?
2) Umwaka ushize ishyirahamwe rihinga ikawa ryateye ibiti 3 657 naho uyu mwaka rimaze gutera ibiti 5 794. Ubwo iri shyirahamwe rifite ibiti by’ikawa bingahe byose hamwe?
3) Mu Karere hatanzwe inka 3 576 muri gahunda ya Girinka Munyarwanda naho mu kandi Karere hatangwa 5 879. Utwo turere twombi twahawe inka zingahe?
4) Muri kaminuza higa abahungu 4653 n’abakobwa 4 978. Iryo shuri ryigamo abanyeshuri bangahe?
Reka nisuzume
1) Umupira w’amaguru wahuje Akarere ka Gasabo n’Akarere ka Kicukiro witabiriwe n’abafana b’abagabo
7 543 n’ab’abagore 1 978. Shaka igiteranyo cy’abafana bitabiriye uwo mukino.
2) Mu ibarura ryashize basanze Umurenge wa Kamurehe urimo ingo 4 987 naho uwa Kabuye urimo ingo 4 678. Iyo mirenge yombi irimo ingo zingahe?
3) Ikigo gitubura ibitabo cyahaye Akarere ka Karongi ibitabo by’imibare 5 423 naho Akarere ka Ngororero gahabwa 3 798. Utwo turere twombi twahawe ibitabo bingahe?
4) Uruganda rukora amasabune rwakoze amakarito 3 456 ukwezi gushize naho uku kwezi rwakoze amakarito 4 649. Shaka umubare w’amakarito rufite mu bubiko.
3.8 Gukuramo imibare itarenze 10 000
A. Ikuramo ridatira ry’imibare itarenze 10 000
Igikorwa
Mukuremo imibare ikurikira mukurikije urugero mwahawe:
Urugero: 6 789 – 5 676 = 1 113
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo – na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo –
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuramo imibare ukora ibi bikurikira:
1. Guca imbonerahamwe y’ibara ukandikamo imibare
2. Gukoresha utubarisho ugahera ku binyabumwe ukuramo ugaherukira ku binyagihumbi.
3. Kwandukura ikinyuranyo ubonye.
Reka nisuzume
Kuramo imibare ikurikira
a) 9 745 – 5 203 =
b) 7 256 – 4 032 =
c) 8 769 – 3 539 =
d) 6 789 – 5 456 =
e) 5 876 – 4 674 =
f) 9 863 – 4 730 =
B. Ikuramo ritira ry’imibare itarenze 10 000
Igikorwa
Mukore ibibazo bikurikira mukurikije urugero mwahawe;
Urugero: 9 531 – 6 789 = 2 742
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo – na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo –
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuramo imibare isaba gutira ukora ibi bikurikira:
1. Guca imbonerahamwe y’ibara ukandikamo imibare, umunini hejuru y’umuto.
2. Gukoresha utubarisho ugahera ku binyabumwe ukuramo.
3. Iyo ibinyabumwe byo gukurwamo birutwa n’ibinyabumwe bikurwamo utira 1 ringana n’ibinyabumwe 10 ku binyacumi by’umubare ukurwamo ukabyongera ku binyabumwe wari usanganwe maze ugakuramo ukandika ikinyuranyo.
4. Ukomeza utyo ku yindi myanya ikurikiye kugeza urangije.
Reka nisuzume
Kuramo imibare ikurikira
a) 9 013 – 7 457 = d) 6 543 – 4 675 =
b) 8 234 – 6 957 = e) 5 376 – 389 =
c) 7 432 – 5 678 = f) 5 021 – 2 658 =
a) 6 120 – 3 249 = c) 8 105 – 5 258 =
b) 7 432 – 4 567 = d) 9 043 – 6 398 =
3.9 Amahurizo yo gukuramo imibare itarenze 10 000
Urugero
Intara yacu yateguye amarushanwa yo kwandika imivugo hitabira abanyeshuri 9 768. Niba harasezerewe 8 989 mu majonjora, shaka umubare w’abashoboye gukomeza amarushanwa.
Nsuzuma ngusuzume
1) Mu nkambi y’impunzi irimo impunzi 9 732. Muri zo 7 986 zahawe imfashanyo n’abagiraneza. Shaka umubare w’impunzi zitabonye imfashanyo.
2) Mu ishuri rikuru ry’u Rwanda higa abanyeshuri 9 321. Muri bo 5 867 biga mu ishami rya siyansi. Shaka umubare w’abanyeshuri batiga siyansi.
3) Akagari gatuwe n’ingo 6 830. Muri zo 5 987 zabonye inzitiramibu. Shaka umubare w’ingo zitabonye inzitiramibu.
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuramo imibare ukora ibi bikurikira:
1. Kuvana mu ihurizo ibyo baguhaye
2. Kuvana mu ihurizo ibyo bakubaza
3. Kwandika umubare munini wahawe mu ihurizo ukawuvanamo umubare muto, ukandika ikinyuranyo.
Reka nisuzume
1) Gisa yasaruye amashu 7 120, agurisha 6 987 muri yo. Yasigaranye amashu angahe?
2) Umwaka ushize mu murenge wacu habarurirwaga abana 9 123. Muri bo 879 ntabwo bakingiwe inkingo zose. Shaka umubare w’abana bakingiwe inkingo zose.
3) Abantu 7 345 biyamamarije kuba abagenzuzi mu Karere, 789 muri bo baratorwa. Shaka umubare w’abataratowe.
4) Mu ngemwe z’ibiti 9 351 zatewe mu murenge wacu umwaka ushize hameze ingemwe 7 984 gusa. Shaka umubare w’ingemwe zitameze.
Soma neza imbonerahamwe ikurikira maze ukore neza ibyo wabajijwe:
1) Shaka igiteranyo k’imibare ikurikira:
a) A 1 + B 1 =
b) A 1 + C 1 =
c) A 2 + B 2 =
d) A 2 + C 2 =
e) A 3 + B 3 =
f) A 3 + C 3 =
2) Shaka ikinyuranyo k’imibare ikurikira
a) A 1 – B 1 =
b) A 1 – C 1 =
c) C 1 – B 1 =
d) A 2 – B 2 =
e) A 2 – C 2 =
f) B 2 – C 2 =
3.10 Ikuba ry’umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo kitarenze 10 000
Igikorwa
Mukore imyitozo ikurikira mukurikije urugero mwahawe.
Urugero: 325 × 29 = 9 425
Ndakubisha 9
• 9 × 5 = 45 nandika 5 nkabika 4
• 9 × 2 = 18 nongeraho 2 nabitse bikaba 22 nkandika 2 nkabika 2
• 9 × 3 = 27 nkongeraho 2 nabitse bikaba 29 nkandika 9 mu binyajana na 2 mu binyagihumbi.
Ndakubisha 2
• 2 × 5 = 10 nandike 0 mu binyacumi mbike 1
• 2 × 2 = 4 nkongeraho 1 nabitse bikaba 5
• 2 × 3 = 6 Ndateranya ibikubo byombi 2 925 + 650
= 9 425
Nsobanukiwe ko:
Iyo ukuba umubare w’imibarwa 3 n’undi w’imibarwa 2 ukora ibi bikurikira:
1. Kwandika imibare mu mbonerahamwe y’ibara
2. Gukubisha ikinyabumwe kugeza urangije imibarwa yose
3. Gukubisha ikinyacumi kugeza urangije imibarwa yose Ukandika igikubo uhereye mu mwanya w’ibinyacumi ugana ibumoso.
4. Guteranya ibikubo byose.
Nsuzuma ngusuzume
Ifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo × na =
– Ufate ikarita imwe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cyo ×
– Ukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Ukurikizeho ikarita yanditseho ikimenyetso cya =
– Uhitemo igisubizo mu makarita yo muri C
Reka nisuzume
Shaka igikubo k’iyi mibare
Soma imbonerahamwe ukore neza ibyo wabajijwe
Shaka igikubo k’imibare ikurikira
a) A 1 × B 1 =
b) A 1 × B 3 =
c) A 2 × B 2 =
d) A 2 × C 2 =
e) A 3 × B 3 =
f) B 2 × C 3 =
3.11 Amahurizo yo gukuba umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo kitarenze 10 000
Urugero
Umurima w’ikawa urimo imirongo 357 kandi kuri buri murongo hariho ibiti 28. Shaka umubare w’ibiti by’ikawa biteye muri uwo murima.
Nsuzuma ngusuzume
1) Leta y’u Rwanda yoroje inka abaturage bo mu mirenge 416. Ubwo Leta y’u Rwanda yatanze inka zingahe niba buri Murenge warahawe inka 23?
2) Mu cyumba k’inama k’Intara harimo intebe 798 kandi kuri buri ntebe hicara abantu 12. Muri icyo cyumba hajyamo abantu bangahe?
3) Shaka umubare w’abanyeshuri bashyizwe mu bigo 29 niba muri buri kigo harashyizwemo abanyeshuri 287.
4) Ishyirahamwe ryorora inkoko rifite inkoko 479 kandi buri nkoko ituraga imishwi 18 buri mwaka. Ryunguka imishwi ingahe buri mwaka?
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuba imibare ukora ibi bikurikira:
1. Kuvana ibyo nahawe mu ihurizo
2. Kuvana mu ihurizo ibyo mbazwa
3. Kwandika imibare wahawe mu ihurizo buhagazi ukayikuba hanyuma ukandika igikubo ari cyo gisubizo.
Reka nisuzume
1) Ishyirahamwe rifite inkoko 278. Iryo shyirahamwe ribona amagi angahe niba buri nkoko itera amagi 29 buri kwezi?
2) Shaka umubare w’amakarito y’amazi akorwa n’uruganda mu minsi 27 niba urwo ruganda rukora amakarito 367 buri munsi.
3) Uwamahoro yahinze amashu ku mirongo 549. Shaka umubare w’amashu yahinze niba kuri buri murongo yarahateye amashu 18.
4) Mu isoko rya Kimironko harimo ameza yo gucururizaho 589. Shaka umubare w’abacuruzi bacururiza muri iryo soko niba kuri buri meza hacururizaho abacuruzi 15.
3.12 Ikuba ry’imibare na 100 na 1 000 igikubo kitarenze 10 000
Igikorwa cya 1
Itegereze ingero usobanure ibyakozwe.
Urugero
1) 75 × 100 = 7 500 2) 5 × 1 000 = 5 000
Igikorwa cya 2
Mukube iyi mibare mukurikije ingero mwahawe
1) 8 × 1 000 =
2) 9 × 1 000 =
3) 67 × 100 =
4) 5 × 1 000 =
Igikorwa cya 3
– Muhagarare imbere y’utudobo tubiri: Kamwe karimo amakarita y’imibare itandukanye.
– Akandi karimo amakarita yanditseho ibikubo 10 bitandukanye.
– Buri wese age agenda akure umubare mu kadobo ka mbere maze mugenzi we ashake igikubo cyawo na 100 cyangwa na 1 000 mu kadobo ka kabiri.
Nsobanukiwe ko:
– Iyo ukuba umubare na 100 wandika uwo mubare ukongeraho amazeru abiri (00)
– Iyo ukuba umubare na 1 000 wandika uwo mubare ukongeraho amazeru atatu (000)
Reka nisuzume
Murushanwe gushaka byihuse igikubo k’iyi mibare:
a) 99 × 100 =
b) 7 × 1 000 =
c) 6 × 1 000 =
d) 78 × 100 =
e) 57 × 100 =
f) 9 × 1 000 =
Uzurisha 100 cyangwa 1 000
3.13 Igabanya ridasagura ry’umubare w’imibarwa 4 n’umubare w’umubarwa 1
Igikorwa
Gabanya imibare ikurikira ukurikije urugero wahawe:
1) 7 496 : 8 =
2) 6 327 : 9 =
3) 7 049 : 7 =
Nsobanukiwe ko:
Iyo ugabanya imibare ukora ibi bikurikira:
1. Kwandika ikigabanywa n’ikigabanya mu mahembe
2. Guhera ku binyagihumbi ugabanya, ugakurikizaho ibinyajana, ibinyacumi, ugaheruka ibinyabumwe.
3. Iyo ibinyagihumbi ari bike ku kigabanya ufatira hamwe ibinyagihumbi n’ibinyajana.
4. Iyo umubare ukurikiyeho ari muto ku kigabanya ushyira zeru (0) mu kigabanyo ugakuramo hanyuma
ukamanura ibinyabumwe.
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo : na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo :
– Mukurikizeho iyo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Reka nisuzume
Shaka ibigabanyo by’imibare ikurikira:
a) 9 549 : 9 =
b) 8 728 : 8 =
c) 7 952 : 7 =
d) 6 906 : 6 =
e) 6 585 : 5 =
f) 8 976 : 4 =
Soma neza imbonerahamwe ushake ibigabanyo wabajijwe
a) A 1 na B 1
b) A 2 na B 2
c) A 3 na B 3
d) A 4 na B 4
e) A 5 na B 5
f) A 6 na B 6
3.14 Amahurizo yo kugabanya
Urugero:
Gabanya ku buryo bungana ibitabo 9 872 ibigo by’amashuri 8. Buri kigo kizahabwa ibitabo bingahe?
Nsuzuma ngusuzume
1) Uturere 7 twagabiwe n’umuryango nterankunga inka 9 891. Buri karere kagabiwe inka zingahe niba twarazigabanye ku buryo bungana?
2) Komisiyo y’amatora yagabanyije ku buryo bungana impapuro z’itora 7 992 ibiro by’itora 8. Buri biro by’itora byahawe impapuro z’itora zingahe?
3) Shyira amakayi 5 490 mu bikarito 9 ku buryo ibikarito byose bijyamo umubare ungana w’ibitabo. Buri gikarito uzagishyiramo amakayi angahe?
4) Kaneza yabumbye amatafari 9 896 ashaka kubakisha inzu 4 zingana. Shaka umubare w’amatafari azajya kuri buri nzu.
Nsobanukiwe ko:
Iyo ukora ihurizo ririmo kugabanya imibare ukora ibi:
1. Kuvana mu ihurizo ibyo baguhaye
2. Kuvana mu ihurizo ibyo bakubaza
3. Kwandika imibare wahawe mu ihurizo mu mahembe maze ukayigabanya hanyuma ukandika ikigabanyo.
Reka nisuzume
1) Ihogoza yasaruye inanasi 5 496 bazipakira imodoka 8 ku buryo bungana. Buri modoka yatwaye inanasi zingahe?
2) Abanyeshuri 7 895 basoje ikiciro rusange bagize amanota meza boherejwe ku buryo bungana mu bigo by’amashuri
5. Buri kigo cyoherejwemo abanyeshuri bangahe?
3) Saranganya ku buryo bungana imifuka 8 793 y’ifumbire mvaruganda mu turere 9. Buri karere kazahabwa imifuka ingahe?
4) Gabanya ku buryo bungana mudasobwa 6 797, uturere 7. Shaka umubare wa mudasobwa buri karere kazahabwa.
1) Kagabo yacuruje amacupa 8 750 y’amavuta mu minsi 5. Buri munsi yacuruzaga amacupa angahe?
2) Saranganya ku buryo bungana ingemwe z’imbuto 9 400 mu midugudu 4. Buri mudugudu uzabona
ingemwe zingahe?
3.15 Isuzuma risoza umutwe wa 3
1) Andika 9 678 mu magambo
2) Shaka umubare wasesenguwe
a) b 8 c 9 h 7 j 6 = b) b 5 h 8 c 4 j 3 =
3) Tahura imibare yasesenguwe: 5 000 + 900 + 60 + 8 =
4) Vuga umwanya w’imibarwa iciyeho akarongo
a) 8 759 b) 7 645 c) 6 975 d) 9 542
5) Gereranya ukoresheje <, > na =
6) Tondeka iyi mibare uhereye ku muto ujya ku munini
7 365, 7 356, 5 746, 4 784, 8 497, 6 479
7) Tondeka uhereye ku munini ujya ku muto
5 708, 6 718, 4 738, 9 786, 6 827, 8 710
8) Shaka igiteranyo k’imibare ikurikira:
a) 6 574 + 2 695 = b) 7 865 + 1 879 =
9) Shaka ikinyuranyo k’imibare ikurikira:
a) 7 856 – 5 976 = b) 8 761 – 6 819 =
10) Shaka igikubo k’imibare ikurikira
11) Shaka ikigabanyo k’imibare ikurikira
a) 7 985 : 5 = b) 8 526 : 6 =
12) Kaneza yaranguye imifuka 8 759 agurishaho 5 784. Yasigaranye imifuka ingahe?
13) Mu isomero ry’ishuri ryacu harimo ibitabo 968 by’imibare. Niba abanyeshuri baratiriye ibitabo 378 ubwo mu isomero hasigayemo ibitabo bingahe?
14) Niba ikamyo imwe itwara imifuka ya sima 300, ubwo amakamyo 24 yatwara imifuka ingahe ya sima?
15) Gabanyiriza ku buryo bungana imyembe 981 mu bitebo 9. Buri gitebo kizajyamo imyembe ingahe?
- Umutwe wa 4:Imigabane ifite ikita kitarenze 10Umutwe wa 4:Imigabane ifite ikita kitarenze 10Labels: 2URL: 1Umutwe wa 4:Imigabane ifite ikita kitarenze 10
4.1 Gusoma no kwandika imigabane itarenze ikizima kandi ikita kitarenze 10
Igikorwa cya 1
Mwitegereze ibyakozwe ku ishusho mubiganireho mubyandike.
Nsobanukiwe ko:
– Umugabane ari igice k’ikizima kimwe.
– Buri mugabane uba ugizwe n’ibice bibiri: ikita n’ikibara.
– Iyo basoma imigabane bahera ku kibara bajya ku kita.
– Ikita kivuga umubare w’ibice bihari.
– Akarongo gatambitse hagati y’ikita n’ikibara ni umurongo w’umugabane, kakavuga ugabanije na
– Ikibara kikavuga umubare w’ibice byagabanyijwe mu kizima.
Urugero:
Igikorwa cya 2
1) Muhine urupapuro mo ibice bibiri bingana.
2) Muvuge kandi mwandike umugabane wa buri gice mu mibare no mu magambo.
3) Muhine urupapuro mo ibice bitatu bingana maze ibice bibiri mubisige ibara hanyuma muvuge kandi mwandike mu mibare no mu magambo umugabane w’igice gisize ibara n’uw’igice kidasize ibara.
4) Kuri buri mugabane mwanditse, mwerekane ikita n’ikibara.
Nsuzuma ngusuzume
Andika mu mibare no mu magambo imigabane isize amabara
1) Mwitegereze hanyuma mwandike umugabane uhagarariye amabara akurikira:
a) Umutuku c) Umukara
b) Ubururu d) Umuhondo
2) Mwitegereze ishusho musubize ibibazo
Ibibazo: Mwandike umugabane uhagarariye
1) Abakobwa
2) Abahungu
3) Abafite ubumuga
4) Abambaye amataratara
5) Abambaye amakabutura, imipira n’inkweto bya siporo
6) Abari kunywa umutobe
7) Abambaye amajipo n’inkweto z’umutuku
8) Abambaye amapantaro, inkweto z’umukara, amashati n’ingofero
9) Abari gukina umupira w’intoki
4.2 Gushushanya no gusiga amabara imigabane itarenze ikizima kandi ikita kitarenze 10
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Igikorwa cya 2
Itegereze usobanure ibice by’ibi bishushanyo bisize amabara n’ibidasize amabara.
Igikorwa cya 3
Mwandike imigabane yashushanyijwe mu mibare no mu magambo.
Nsobanukiwe ko:
– Iyo ushushanya umugabane ushyira ibara mu bice bingana n’ikibara.
– Iyo wandika umugabane washushanyijwe, umubare w’ibice birimo ibara uba ikibara.
– Umubare w’ibice byose ni ukuvuga ibirimo ibara n’ibitarimo ibara uba ari ikita.
1) Soma, wandike mu magambo, ushushanye maze usige
amabara iyi migabane:
5) Soma, wandike mu mibare, unashushanye iyi migabane:
a) Ikenda by’icumi:
b) Birindwi by’umunani:
c) Birindwi by’ikenda:
d) Bitatu by’icumi:
e) Birindwi by’icumi:
f) Bitanu by’umunani:
4.3 Kugereranya imigabane ihuje ikita kitarenze 10 kandi itarenze ikizima 1
Igikorwa
Ukurikije urugero wahawe, gereranya imigabane ikurikira.
Urugero: Koresha >, < na = ugereranye iyi migabane
Nsobanukiwe ko:
Iyo utondeka imigabane ihuje ikita uhereye ku muto ujya ku munini, umugabane muto ni wo uba ufite ikibara gito. Umugabane munini ni wo uba ufite ikibara kinini.
B. Gutondeka imigabane ihuje ikita kitarenze 10 kandi itarenga ikizima 1 uhereye ku munini ujya ku muto
Igikorwa
Tondeka iyi migabane uhereye ku munini ujya ku muto ukurikije urugero wahawe.
Nsobanukiwe ko:
Iyo utondeka imigabane ihuje ikita uhereye ku muto ujya ku munini, umugabane munini ni wo uba ufite ikibara kinini. Umugabane muto ni wo uba ufite ikibara gito.
Reka nisuzume
1) Tondeka uhereye ku mugabane muto ujya ku munini
2) Tondeka uhereye ku mugabane munini ujya ku muto
4.5 Iteranya ry’imigabane ihuje ikita kitarenze 10 kandi itarenze ikizima 1
Igikorwa
Mushake igiteranyo k’imigabane ikurikira mukurikije urugero mwahawe.
Urugero: Shaka igiteranyo k’imigabane ikurikira
Nsobanukiwe ko:
Iyo uteranya imigabane ihuje ikita uteranya ibibara maze ukandukura ikita utagihinduye.
Nsuzuma ngusuzume
Shaka igiteranyo k’imigabane ikurikira:
4.6 Amahurizo yo guteranya imigabane ihuje ikita kitarenga 10
Igikorwa
Kurikiza urugero wahawe ukore aya mahurizo
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo guteranya imigabane ihuje ikita, ukora ibi bikurikira:
– Werekana ibyo baguhaye
– Werekana ibyo bakubaza
– Wandika imigabane wahawe mu ihurizo maze ukandukura ikita ugateranya ibibara.
Reka nisuzume
4.7 Ikuramo ry’imigabane ihuje ikita kitarenze 10 kandi itarenze ikizima 1
Igikorwa cya 1
Shaka ikinyuranyo k’imigabane ukurikije urugero wahawe
Nsobanukiwe ko:
Iyo ukuramo imigabane ihuje ikita ukuramo ibibara maze ukandukura ikita utagihinduye.
Reka nisuzume
4.8 Amahurizo yo gukuramo imigabane ihuje ikita kitarenga 10
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ukora ihurizo ririmo gukuramo imigabane ukora ibi:
1. Ugaragaza ibyo baguhaye mu ihurizo
2. Ugaragaza ibyo bakubaza mu ihurizo
3. Kwandika imigabane wahawe mu ihurizo maze ukandukura ikita ugakuramo ibibara.
Reka nisuzume
4.9 Gushaka icyuzuzo cy’umugabane kugira ngo haboneke ikizima 1
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Igikorwa cya 2
Mushake icyuzuzo k’iyi migabane kugira ngo mubone ikizima kimwe
Nsobanukiwe ko:
Iyo ushaka icyuzuzo cy’umugabane ureba ikita cy’umugabane baguhaye, ukakifashisha ukora ikizima,
maze ugakuramo umugabane baguhaye.
Nsuzuma ngusuzume
Uzuza ukore umugabane ukwiye.
4.10 Umugabane w’umubare ushyitse
Igikorwa
Itegereze urugero wahawe, ushake imigabane ikurikira:
Nsobanukiwe ko:
Iyo ushaka agaciro k’umugabane w’umubare ushyitse ufata uwo mubare ukawukuba n’ikibara. Igikubo ubonye ukakigabanya n’ikita.
Reka nisuzume
Itegereze amashusho maze uvuge kandi wandike umubare w’ibintu wabajijwe.
Nsuzuma ngusuzume
Shaka agaciro k’umugabane w’imibare ishyitse ikurikira:
4.11 Amahurizo ku mugabane w’umubare ushyitse
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo kugabanya imibare:
1. Werekana ibyo baguhaye mu ihurizo.
2. Werekana ibyo bakubaza mu ihurizo.
3. Wandika umugabane n’umubare wahawe mu ihurizo maze ugakuba ikibara n’umubare ushyitse hanyuma igikubo ubonye ukakigabanya n’ikita.
Reka nisuzume
4.12 Akamaro k’imigabane
Igikorwa cya 1
Mwitegereze buri shusho musobanure ibiri gukorwa.
Nsobanukiwe ko:
– Iyo abantu bagabana ibintu bitandukanye bakoresha imigabane.
– Abantu bashobora kugabana ibintu ku buryo bungana.
– Abantu bashobora kugabana ibintu ku buryo butangana.
Igikorwa cya 2
Buri wese abwire abandi ibyo iwabo bagabana.
Igikorwa cya 3
Muganire ku kamaro k’imigabane mutanga ingero z’aho ikoreshwa.
4.13 Isuzuma risoza umutwe wa 4
1) Andika mu mibare no mu magambo imigabane isize ibara
2) Shushanya maze usige ibara imigabane ikurikira :
4.1 Gusoma no kwandika imigabane itarenze ikizima kandi ikita kitarenze 10
Igikorwa cya 1
Mwitegereze ibyakozwe ku ishusho mubiganireho mubyandike.
Nsobanukiwe ko:
– Umugabane ari igice k’ikizima kimwe.
– Buri mugabane uba ugizwe n’ibice bibiri: ikita n’ikibara.
– Iyo basoma imigabane bahera ku kibara bajya ku kita.
– Ikita kivuga umubare w’ibice bihari.
– Akarongo gatambitse hagati y’ikita n’ikibara ni umurongo w’umugabane, kakavuga ugabanije na
– Ikibara kikavuga umubare w’ibice byagabanyijwe mu kizima.
Urugero:
Igikorwa cya 2
1) Muhine urupapuro mo ibice bibiri bingana.
2) Muvuge kandi mwandike umugabane wa buri gice mu mibare no mu magambo.
3) Muhine urupapuro mo ibice bitatu bingana maze ibice bibiri mubisige ibara hanyuma muvuge kandi mwandike mu mibare no mu magambo umugabane w’igice gisize ibara n’uw’igice kidasize ibara.
4) Kuri buri mugabane mwanditse, mwerekane ikita n’ikibara.
Nsuzuma ngusuzume
Andika mu mibare no mu magambo imigabane isize amabara
1) Mwitegereze hanyuma mwandike umugabane uhagarariye amabara akurikira:
a) Umutuku c) Umukara
b) Ubururu d) Umuhondo
2) Mwitegereze ishusho musubize ibibazo
Ibibazo: Mwandike umugabane uhagarariye
1) Abakobwa
2) Abahungu
3) Abafite ubumuga
4) Abambaye amataratara
5) Abambaye amakabutura, imipira n’inkweto bya siporo
6) Abari kunywa umutobe
7) Abambaye amajipo n’inkweto z’umutuku
8) Abambaye amapantaro, inkweto z’umukara, amashati n’ingofero
9) Abari gukina umupira w’intoki
4.2 Gushushanya no gusiga amabara imigabane itarenze ikizima kandi ikita kitarenze 10
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Igikorwa cya 2
Itegereze usobanure ibice by’ibi bishushanyo bisize amabara n’ibidasize amabara.
Igikorwa cya 3
Mwandike imigabane yashushanyijwe mu mibare no mu magambo.
Nsobanukiwe ko:
– Iyo ushushanya umugabane ushyira ibara mu bice bingana n’ikibara.
– Iyo wandika umugabane washushanyijwe, umubare w’ibice birimo ibara uba ikibara.
– Umubare w’ibice byose ni ukuvuga ibirimo ibara n’ibitarimo ibara uba ari ikita.
1) Soma, wandike mu magambo, ushushanye maze usige
amabara iyi migabane:
5) Soma, wandike mu mibare, unashushanye iyi migabane:
a) Ikenda by’icumi:
b) Birindwi by’umunani:
c) Birindwi by’ikenda:
d) Bitatu by’icumi:
e) Birindwi by’icumi:
f) Bitanu by’umunani:
4.3 Kugereranya imigabane ihuje ikita kitarenze 10 kandi itarenze ikizima 1
Igikorwa
Ukurikije urugero wahawe, gereranya imigabane ikurikira.
Urugero: Koresha >, < na = ugereranye iyi migabane
Nsobanukiwe ko:
Iyo utondeka imigabane ihuje ikita uhereye ku muto ujya ku munini, umugabane muto ni wo uba ufite ikibara gito. Umugabane munini ni wo uba ufite ikibara kinini.
B. Gutondeka imigabane ihuje ikita kitarenze 10 kandi itarenga ikizima 1 uhereye ku munini ujya ku muto
Igikorwa
Tondeka iyi migabane uhereye ku munini ujya ku muto ukurikije urugero wahawe.
Nsobanukiwe ko:
Iyo utondeka imigabane ihuje ikita uhereye ku muto ujya ku munini, umugabane munini ni wo uba ufite ikibara kinini. Umugabane muto ni wo uba ufite ikibara gito.
Reka nisuzume
1) Tondeka uhereye ku mugabane muto ujya ku munini
2) Tondeka uhereye ku mugabane munini ujya ku muto
4.5 Iteranya ry’imigabane ihuje ikita kitarenze 10 kandi itarenze ikizima 1
Igikorwa
Mushake igiteranyo k’imigabane ikurikira mukurikije urugero mwahawe.
Urugero: Shaka igiteranyo k’imigabane ikurikira
Nsobanukiwe ko:
Iyo uteranya imigabane ihuje ikita uteranya ibibara maze ukandukura ikita utagihinduye.
Nsuzuma ngusuzume
Shaka igiteranyo k’imigabane ikurikira:
4.6 Amahurizo yo guteranya imigabane ihuje ikita kitarenga 10
Igikorwa
Kurikiza urugero wahawe ukore aya mahurizo
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo guteranya imigabane ihuje ikita, ukora ibi bikurikira:
– Werekana ibyo baguhaye
– Werekana ibyo bakubaza
– Wandika imigabane wahawe mu ihurizo maze ukandukura ikita ugateranya ibibara.
Reka nisuzume
4.7 Ikuramo ry’imigabane ihuje ikita kitarenze 10 kandi itarenze ikizima 1
Igikorwa cya 1
Shaka ikinyuranyo k’imigabane ukurikije urugero wahawe
Nsobanukiwe ko:
Iyo ukuramo imigabane ihuje ikita ukuramo ibibara maze ukandukura ikita utagihinduye.
Reka nisuzume
4.8 Amahurizo yo gukuramo imigabane ihuje ikita kitarenga 10
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ukora ihurizo ririmo gukuramo imigabane ukora ibi:
1. Ugaragaza ibyo baguhaye mu ihurizo
2. Ugaragaza ibyo bakubaza mu ihurizo
3. Kwandika imigabane wahawe mu ihurizo maze ukandukura ikita ugakuramo ibibara.
Reka nisuzume
4.9 Gushaka icyuzuzo cy’umugabane kugira ngo haboneke ikizima 1
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Igikorwa cya 2
Mushake icyuzuzo k’iyi migabane kugira ngo mubone ikizima kimwe
Nsobanukiwe ko:
Iyo ushaka icyuzuzo cy’umugabane ureba ikita cy’umugabane baguhaye, ukakifashisha ukora ikizima,
maze ugakuramo umugabane baguhaye.
Nsuzuma ngusuzume
Uzuza ukore umugabane ukwiye.
4.10 Umugabane w’umubare ushyitse
Igikorwa
Itegereze urugero wahawe, ushake imigabane ikurikira:
Nsobanukiwe ko:
Iyo ushaka agaciro k’umugabane w’umubare ushyitse ufata uwo mubare ukawukuba n’ikibara. Igikubo ubonye ukakigabanya n’ikita.
Reka nisuzume
Itegereze amashusho maze uvuge kandi wandike umubare w’ibintu wabajijwe.
Nsuzuma ngusuzume
Shaka agaciro k’umugabane w’imibare ishyitse ikurikira:
4.11 Amahurizo ku mugabane w’umubare ushyitse
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo kugabanya imibare:
1. Werekana ibyo baguhaye mu ihurizo.
2. Werekana ibyo bakubaza mu ihurizo.
3. Wandika umugabane n’umubare wahawe mu ihurizo maze ugakuba ikibara n’umubare ushyitse hanyuma igikubo ubonye ukakigabanya n’ikita.
Reka nisuzume
4.12 Akamaro k’imigabane
Igikorwa cya 1
Mwitegereze buri shusho musobanure ibiri gukorwa.
Nsobanukiwe ko:
– Iyo abantu bagabana ibintu bitandukanye bakoresha imigabane.
– Abantu bashobora kugabana ibintu ku buryo bungana.
– Abantu bashobora kugabana ibintu ku buryo butangana.
Igikorwa cya 2
Buri wese abwire abandi ibyo iwabo bagabana.
Igikorwa cya 3
Muganire ku kamaro k’imigabane mutanga ingero z’aho ikoreshwa.
4.13 Isuzuma risoza umutwe wa 4
1) Andika mu mibare no mu magambo imigabane isize ibara
2) Shushanya maze usige ibara imigabane ikurikira :
- Umutwe wa 5: Isano iri hagati y’ingero z’uburebureUmutwe wa 5: Isano iri hagati y’ingero z’uburebureLabel: 1Umutwe wa 5: Isano iri hagati y’ingero z’uburebure
5.1 Ingero z’uburebure
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho, mutange ingero z’ibikoresho byifashishwa mu gupima uburebure bw’ibintu, abantu n’ahantu.
Igikorwa cya 2
Mukoreshe imetero mupime ibi bikurikira:
a) Uburebure n’ubugari by’ikibaho cyo mu ishuri ryanyu.
b) Uburebure n’ubugari by’urugi rw’ishuri ryanyu.
c) Uburebure n’ubugari by’akabati k’ibitabo ka mwarimu.
Igikorwa cya 3
Mukoreshe agacamurongo mupime ibi bikurikira:
a) Uburebure n’ubugari bw’igitabo k’imibare
b) Uburebure n’ubugari by’ikayi nini
c) Uburebure bw’ikaramu
Igikorwa cya 4
Ni uruhe rugero rw’uburebure rukoreshwa iyo ushaka kumenya ibi bikurikira:
a) Intera iri hagati y’Igihugu n’ikindi
b) Uburebure bw’umuhanda uva i Kigali ukagera i Rubavu
c) Umuzenguruko w’ikibanza
d) Ubutumburuke bw’umusozi
e) Uburebure bw’akabati
f) Uburebure n’ubugari by’igitabo
g) Uburebure bw’umwenda
Igikorwa cya 5
Mwitegereze aya mashusho muvuge ibyo muyabonaho.
Nsobanukiwe ko:
Ingero z’uburebure ari:
1) Kilometero (km) 5) Desimetero (dm)
2) Hegitometero (hm) 6) Santimetero (cm)
3) Dekametero (dam) 7) Milimetero (mm)
4) Metero (m)
– Metero ni urugero fatizo mu ngero z’uburebure
– km, hm na dam ni zo ngero z’uburebure ziruta metero
– dm, cm na mm ni zo ngero z’uburebure zirutwa na metero (m)
– Iyo upima uburebure, ubugari, ubutambike, ubuhagarike cyangwa ubutumburuke bw’ahantu
ukoresha bimwe mu bikoresho bikurikira:
– Dekametero – Agacamurongo
– Metero buhine – Metero bushumi
– Imetero – Umugozi
Muvuge ubwoko bw’ibikoresho mwakoresha mupima uburebure bw’ibintu bikurikira
a) Inzu y’igorofa d) Umurima
b) Ikanzu e) Akabati
c) Ikibanza f) Imyambaro y’ishuri
Uzurisha ijambo rikwiye (metero, km, hm, dam icumi, dm, cm, mm, dekametero)
a)------- ni urugero fatizo mu ngero z’uburebure.
b) Ingero z’uburebure zirutanwa inshuro-------
c) -------,------- na ------ni zo ngero z’uburebure ziruta metero
d) Ingero z’uburebure zirutwa na metero ni------ ,------- na-------
e) Iyo ushaka gupima umuzenguruko w’inzu ukoresha---------
5.2 Isano iri hagati y’ingero z’uburebure
Igikorwa
Mwitegereze imbonerahamwe y’ingero z’uburebure, musobanure uko ingero z’uburebure zirutana hagati yazo.
Nsobanukiwe ko:
Ingero z’uburebure zirutana inshuro 10 uva ku rugero ruto ujya ku runini cyangwa uva ku rugero runini ujya ku ruto.
5.3 Guhindura ingero z’uburebure
A. Guhindura ingero z’uburebure uva ku rugero runini ujya ku rugero ruto
Igikorwa cya 1
Mwitegereze imbonerahamwe y’ingero z’uburebure, muyigane mukore imyitozo iyikurikira
km 1 = hm 10
hm 1 = dam 10
dam 1 = m 10
m 1 = dm 10
dm 1 = cm 10
cm 1 = mm 10
Nsuzuma ngusuzume
a) km 8 = hm-----
b) km 7 = dam-----
c) Hm 2 = dam-----
d) Hm 4 = m-----
B. Guhindura ingero z’uburebure uva ku rugero ruto ujya ku rugero runini
Igikorwa cya 2
Mwitegereze imbonerahamwe yo guhindura ingero z’uburebure muyigane mukore imyitozo
hm 10 = km 1
dam 10 = hm 1
m 10 = dam 1
dm 10 = m 1
cm 10 = dm 1
mm 10 = cm 1
Reka nisuzume
a) hm 90 = km------
b) dam 800 = km-----
c) dam 60 = hm----
d) m 500 = hm----
Nsobanukiwe ko:
– Uhindura ingero z’uburebure wifashisha imbonerahamwe y’ingero ukandikamo imibare wahawe.
– Uva ku rugero runini ujya ku ruto wongeraho zeru (0).
– Uva ku rugero ruto ujya ku rugero runini ukuraho zeru (0). Ibi bikorwa gusa ku mubare uherwa n’amazeru.
Hindura mu rugero wabajijwe
a) m 450 = dam---
b) hm 13 = m----
c) dam 56 = dm---
d) mm 3500 = dm---
e) dm 4300 = m---
f) dam 234 = m----
g) km 8 m 7 = m---
h) dm 4 mm 7 = mm---
i) m 6 dm 8 = dm----
j) dam 9 cm 4 = cm-----
5.4 Kugereranya ingero z’uburebure
Igikorwa
Mukoreshe >, < na = mugereranye ingero z’uburebure zikurikira mukurikije urugero mwahawe.
Nsobanukiwe ko:
Iyo ugereranya ingero z’uburebure, ubanza guhindura mu rugero ruto wahawe mu kibazo hanyuma
ukagereranya imibare ukoresheje <,> na =
5.5 Kugereranya ingero z’uburebure upima
uburebure bw’ibintu binyuranye
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho.
Nsobanukiwe ko:
– Iyo ugereranya uburebure bw’ibintu binyuranye, urabipima maze ukagereranya uburebure bwabyo
ugendeye ku mibare.
– Ukamenya ikigufi n’ikirekire ubigereranyije.
Igikorwa cya 2
a) Ikibuga dukiniramo umupira w’amaguru gifite umuzenguruko wa m 300. Ikibuga cy’umupira w’amaguru cya sitade
Amahoro gifite umuzenguruko wa m 400. Mugereranye ibi bibuga byombi muvuge ikinini n’igito.
b) Mupime uburebure n’ubutambike by’ishuri mwigamo. Mugereranye ibipimo mubonye.
5.6 Kugereranya uburebure bw’ahantu usanisha intera n’inshuro zirimo
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho.
Igikorwa cya 2
Mugereranye maze musubize ibi bikurikira:
a) Umuhanda wa km 20 urimo inshuro zingahe z’undi wa km 4?
b) Muhoza yagenze km 30 naho mukuru we Shema agenda km 5. Vuga uwagenze ahantu harehare. Urugendo rwa Muhoza rukubye inshuro zingahe urwa Shema?
Nsobanukiwe ko:
Kugira ngo umenye inshuro uburebure bw’ahantu buruta ubwo ahandi hantu ufata uburebure bw’ahantu harehare ukabugabanya n’uburebure bw’ahagufi.
Igikorwa cya 3
a) Mutere agapira n’amaboko maze muvuge uburebure buri hagati yanyu n’aho ako gapira kaguye. Nimurangiza muhapime murebe ko uburebure mwavuze mbere yo gupima bungana n’ubwo mubonye nyuma yo gupima.
b) Mwitegereze ikibuga mukiniraho umupira, mugenekereze umuzenguruko wacyo. Mugipime murebe ko umuzenguruko mwavuze ungana n’uwo mubonye nyuma yo gupima.
1) Koresha >, < na = ugereranye
a) km 3 m 5
hm 30 c) dm 575 
m 57b) hm 4 m 7
m 407 d) dam 49 
hm 92) Umuhanda ufite km 45 z’uburebure urimo inshuro zingahe undi ufite km 9 z’uburebure?
5.7 Gutondeka ingero z’uburebure
A. Itondeka ry’ingero z’uburebure uva ku rugero ruto ujya ku rugero runini
Igikorwa
Mutondeke izi ngero z’uburebure muhereye ku rugero ruto mujya ku runini mukurikije urugero mwahawe.
a) m 125, hm 2, dam 8
b) cm 34, mm 245, dm 5
c) 9 km, hm 75, m 8759
d) dm 765, m 98, dam 6
e) dam 54, km 8, m 256
f) cm 356, m 7, dm 49
Nsobanukiwe ko:
Iyo utondeka ingero z’uburebure ubanza guhindura ingero zose baguhaye mu rugero ruto rurimo warangiza ugatondeka uva ku rugero ruto ujya ku rugero runini uhereye ku mibare yazo.
B. Gutondeka ingero z’uburebure uva ku rugero runini ujya ku rugero ruto
Igikorwa
Mutondeke izi ngero z’uburebure muhereye ku rugero runini mujya ku ruto mukurikije urugero mwahawe.
a) m 785, hm 9, dam 54
b) m 247, dam 79, hm 76
c) 39 cm, mm 91, dm 49
d) dam 237, km 8, hm 56
e) dm 797, dam 8, m 92
f) dam 59, km 9, hm 48
Nsobanukiwe ko:
Iyo utondeka ingero z’uburebure ubanza guhindura ingero zose baguhaye mu rugero ruto rurimo warangiza ugatondeka uva ku rugero runini ujya ku rugero ruto uhereye ku mibare yazo.
1) Tondeka izi ngero z’uburebure uhereye ku rugero ruto ujya ku runini:
a) m 7, mm 985, cm 565 c) cm 324, mm 765, m 8
b) dm 897, m 79, dam 9 d) mm 98, dm 987, cm 87
2) Tondeka izi ngero z’uburebure uhereye ku rugero runini ujya ku ruto
a) km 6, m 9124, dam 698 c) dam 7, dm 987, cm 3 695
b) hm 74, km 9, dam 768 d) m 76, cm 4 897, dm 915
5.8 Guteranya ingero z’uburebure Igikorwa
Koresha imbonerahamwe y’ingero z’uburebure ukore imyitozo ukurikije urugero wahawe.
a) km 9 + m 789 = m
b) hm 56 + m 238 = m
c) dam 475 + m 250 = km
d) m 5 + cm 500 = dam
e) dm 375 + m 2 dm 5 = dam
f) cm 35 + m 9 = cm
Nsobanukiwe ko:
Iyo uteranya ingero z’uburebure ubanza guhindura ingero zose baguhaye mu rugero wabajijwe warangiza ukabona guteranya.
Nsuzuma ngusuzume
Mukoreshe imbonerahamwe y’ingero z’uburebure mwuzuze urugero rubura muri buri mwitozo.
a) dam 145 + m 2 855= ------3
b) hm 39 + dam 610 =----- 10
c) hm 74 + ------260 = km 10
d) dam 76 + m 240 =------- 1
e) dm 63 + cm 37 =------- 667
f) cm 27 + m 6= ------6 270
Reka nisuzume
a) hm 47 + dam 930 = km----
b) m 3 cm 8 + dm 25 = cm----
c) m 45 + cm 5 500 = hm------
5.9 Amahurizo yo guteranya ingero z’uburebure
Urugero:
Mu rwego rw’ubukerarugendo, Muhoza yagenze km 7 ku wa mbere, ku wa Kabiri agenda hm 80 naho ku wa gatatu agenda dam 400. Shaka km yagenze muri iyo minsi itatu.
Nsuzuma ngusuzume
1) Umuyobozi w’imodoka yanditse uburebure bw’ingendo yakoze mu minsi itatu asanga ari km 359 umunsi wa mbere, hm 4 360 ku munsi wa kabiri na km 405 ku munsi wa gatatu. Shaka umubare wa km amaze kugenda muri iyo minsi itatu.
2) Mutesi afite m 175 z’igitambaro naho musaza we Gasana afite dm 1 250. Ubwo bombi bafite igitambaro kireshya na metero zingahe?
3) Mukiza yaguze umugozi wa m 150, ageze mu rugo asanga ari mugufi. Asubira kugura undi wa dm 2 500. Ubwo iyo migozi yombi ireshya na m zingahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo guteranya ingero, ubanza kwerekana ibyo baguhaye. Ugakurikizaho ibyo bakubaza hanyuma ugateranya ibyo baguhaye kugira ngo ubone
igisubizo. Mbere yo guteranya ingero ubanza guhindura mu rugero bakubajije.
Reka nisuzume
1) Umunyonzi yagenze m 900 ava iwe ajya ku iseta. Agezeyo atwara umugenzi ku isoko riri kuri hm 11. Shaka hm yagenze kuva iwe kugera ku isoko.
2) Mu myitozo abasiganwa ku maguru birutse km 21 mu gitondo naho nimugoroba biruka dam 1 200. Shaka umubare wa hm birutse uwo munsi.
1) Umuhanda uva i Kigali ujya i Huye ureshya na km 125 naho uva i Huye ujya i Rusizi hm 1670. Ubwo uvuye i Kigali ukajya i Rusizi wagenda km zingahe?
2) Kaneza afite umurima ureshya na m 95 z’uburebure naho mushiki we akagira ureshya na m 105 uri haruguru y’uwa musaza we. Ubwo iyo mirima uyiteranyije yombi yareshya gute?
5.10 Gukuramo ingero z’uburebure n’umubare ushyitse
Igikorwa
Koresha imbonerahamwe y’ingero z’uburebure ukore imyitozo ukurikije urugero wahawe.
a) hm 5 – m 298 = m
b) km 9 – dam 832 = dam
c) dm 74 – cm 490 = dm
d) cm 75 – mm 579 = mm
e) dam 753 – hm 69 = m
f) dm 835 – dam 7 = dm
Nsobanukiwe ko:
Iyo ukuramo ingero z’uburebure ubanza guhindura ingero zose baguhaye mu rugero wabajijwe, warangiza
ukabona gukuramo.
Nsuzuma ngusuzume
Mukoreshe imbonerahamwe y’ingero z’uburebure mwuzuze urugero rubura muri buri mwitozo.
a) km 5 – hm 28 =------ 220
b) hm 9 – dam 73 = -------170
c)------ 724 – dm 62 = cm 104
d) dam 415 – -------3 = m 1 150
e) dam 64 – m 440 =-------- 2
f) m 36 – cm 973 =------ 2 627
5.11 Amahurizo yo gukuramo ingero z’uburebure
Urugero: Abakozi bakora umuhanda batangiye gusana umuhanda ufite km 56. Niba bamaze gusana
dam 4 600 ubwo basigaje gusana km zingahe?
Nsuzuma ngusuzume
1) Gisa yagiye mu marushanwa yo kwiruka km 42, amaze kwiruka dam 2900 arananirwa yikura mu irushanwa. Ubwo yari asigaje hm zingahe ngo arangize irushanwa?
2) Ishyirahamwe ry’abubatsi b’imihanda ryahawe akazi ko gushyira kaburimbo mu muhanda wa dam 987. Bamaze kuyishyira muri m 5870 bararihagarika. Barihagaritse risigaje km zingahe ngo rirangize akazi kose?
Nsobanukiwe ko:
Iyo ukora amahurizo yo gukuramo ingero z’uburebure ubanza kugaragaza ibyo baguhaye n’ibyo bakubaza
mu ihurizo ugahindura mu rugero ruto, ugakuramo, hanyuma ugahindura mu rugero bakubajije.
Reka nisuzume
1) Kariza yaguze m 175 z’ijyora agurishaho dam 9. Yasigaranye m zingahe?
2) Muhizi afite cm 186 z’uburebure. Kaneza afite cm 169. Ni nde muremure muri bo? Amurusha cm zingahe?
1) Gisa yari afite dam12 z’ijyora maze akuraho m 20 azidodeshamo imyenda y’abana. Yasigaranye m zingahe?
2) Ishimwe na Mugisha basimbutse umurambararo. Ishimwe asimbuka m 3. Mugisha asimbuka dm 25. Ni nde wasimbutse harehare? Yamurushije cm zingahe?
5.12 Gukuba ingero z’uburebure n’umubare ushyitse
Igikorwa cya 1
Koresha imbonerahamwe y’ingero z’uburebure ukore imyitozo ukurikije urugero wahawe.
a) m 2 cm 3 × 3 = cm __ c) hm 5 dam 4 × 2 = m __
b) dam 42 × 5 = hm __ d) m 81 × 5 = dm __
Nsobanukiwe ko:
Iyo ukuba ingero z’uburebure n’umubare ushyitse ubanza ugakuba nk’uko bisanzwe hanyuma igikubo ubonye ukagihindura mu rugero wabajijwe.
Mukoreshe imbonerahamwe y’ingero z’uburebure mwuzuze urugero rubura muri buri mwitozo.
a) m 375 × 2 = -----75
b) m 72 dm 3 × 3 =----- 2 169
c) hm 45 × 4 =----- 18
d) dam 4 m 8 × 5 =------- 24
e) m 4 cm 2 × 6 =------ 2 412
f) dm 215 × 8 =------- 172
5.13 Amahurizo yo gukuba ingero z’uburebure n’umubare ushyitse
Urugero: Abacuruzi 4 bagurishije m 25 z’ijyora buri wese. Shaka uburebure bw’amajyora yose bagurishije muri hm.
Nsuzuma ngusuzume
1) Shaka uburebure bw’amajyora 6 niba buri jyora rifite m 50.
2) Shema, Keza na Mucyo buri wese afite m 30 z’urutsinga rw’amashanyarazi. Bateranyije izo nsinga
zose bagira urutsinga rureshya rute?
3) Kazuba yaguze amajyora 56. Niba buri jyora rireshya na m 15, ubwo ayo majyora yose areshya ate?
Nsobanukiwe ko:
– Iyo ukora amahurizo yo gukuba ingero z’uburebure n’umubare ushyitse ubanza kwerekana ibyo baguhaye mu ihurizo, ugakurikizaho ibyo bakubaza, ugakuba
– Igisubizo ubonye ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Shaka uburebure bw’umuturirwa w’amagorofa 8 niba buri gorofa rifite m 4 z’uburebure.
2) Mahoro afite ibidongi 9 by’ubudodo ashaka gukoramo ikidongi kimwe. Shaka uburebure bw’ikidongi azagira niba buri kidongi gifite m 100 z’uburebure.
3) Ikompanyi ikora imihanda ikora km 7 buri munsi. Shaka uburebure bw’umuhanda iyo kompanyi ikora mu minsi 29.
1) Abacuruzi 6 bagabanye ijyora buri wese atwara irifite dam 9. Iryo jyora bagabanye ryari rifite m zingahe
z’uburebure?
2) Ngarambe yaguriye abana be 8 ibitambaro byo kudodeshamo imyambaro y’ishuri. Niba yaraguriye
buri mwana m 5, ubwo bose hamwe yabaguriye dam zingahe?
3) Umuturirwa munini ku isi ugizwe n’amagorofa 127. niba buri gorofa riresha na m 5, ubwo uwo muturirwa wose ureshya ute?
5.14 Kugabanya ingero z’uburebure n’umubare ushyitse
Igikorwa cya 1
Koresha imbonerahamwe yo guhindura ingero z’uburebure ukore imyitozo ukurikije urugero wahawe
a) dm 580 : 5 = cm------
b) dam 2 400 : 6 = km------
c) mm 5 400 : 9 = dm------
d) cm 480 : 8 = dm------
e) m 1 200 : 3 = hm-------
f) dm 2 000 : 4 = dam-----
Nsobanukiwe ko:
Iyo ugabanya ingero z’uburebure ubanza kugabanya mu mahembe hanyuma ikigabanyo ubonye ukagihindura mu rugero wabajijwe.
Igikorwa cya 2
Mukoreshe imbonerahamwe yo guhindura ingero z’uburebure mwuzuze urugero rubura kuri buri mwitozo.
a) hm 248 : 8 =------ 3 100
b) dam 485 : 5 =----- 970
c) m 2 800 : 7 =------ 4
d) cm 680 : 4 =------ 17
e) dm 650 : 5 =------- 13
f) cm 960 : 3 =------ 3 200
5.15 Amahurizo yo kugabanya ingero z’uburebure n’umubare ushyitse
Urugero: Abadozi 8 bagabanye ku buryo bungana igitambaro cy’umwenda cya m 96. Buri wese
yahawe igitambaro cy’umwenda kireshya gite?
Nsuzuma ngusuzume
1) Abacuruzi 6 b’insinga z’amashanyarazi bagabanye ku buryo bungana m 240 z’urutsinga. Buri wese yatwaye dam zingahe?
2) Abantu 9 bagabanye ku buryo bungana igisheke gifite dm 18 z’uburebure. Buri wese yatwaye igisheke gifite cm zingahe?
Nsobanukiwe ko:
– Iyo ukora amahurizo yo kugabanya ingero z’uburebure ubanza kuvana mu ihurizo ibyo baguhaye,
ugakurikizaho ibyo bakubaza, ukagabanya.
– Ukagabanya igisubizo ubonye ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Tunga arashaka kubaka umuturirwa ufite m 50 z’uburebure. Niba ashaka ko uwo muturirwa uzaba ugizwe n’amagorofa 10 angana ubwo buri gorofa rizaba rireshya rite?
2) Umurenge wacu wahaye abantu 8 akazi ko gukubura umuhanda ufite hm 8. Nibawugabana ku buryo bungana buri wese azakubura ahafite m zingahe?
Umucuruzi afite umwenda upima m 49 z’uburebure. Nacamo ibipande 7 bingana ubwo buri gipande kizaba gifite dm zingahe?
5.16 Isuzuma risoza umutwe wa 5
1) Hindura izi ngero mu rugero wabajijwe
a) km 2 m 6 = m --- c) m 7 mm 8 = mm---
b) dm 240 = m--- d) dm 2 400 = dam---
2) Koresha <, > na = ugereranye izi ngero z’uburebure
a) m 456
hm 8 c) mm 46 
cm 4b) km 8
dam 789 d) dam 7 
m 793) Tondeka uhereye ku rugero ruto ujya ku rugero runini
m 259, hm 2 m 9, dam 29 m 5
4) Tondeka uhereye ku rugero runini ujya ku rugero ruto
km 6 dam 8, hm 608, dam 68
5) Kora
a) dam 75 × 4 = km c) m 4 cm 8 × 5 = dm
b) m 590 : 5 = dm d) dm 6400 : 8 = dam
6) Itegereze iyi shusho usubize ibibazo
Ibibazo
a) Hagati y’amashuri n’ikibuga cy’umupira w’amaguru hari dm zingahe?
b) Hagati y’amashuri n’ubwiherero hari dam zingahe?
c) Uvuye ku mashuri ukajya mu biro by’ubuyobozi, waba ugenze m zingahe?
d) Uvuye ku mashuri ukajya mu gikoni, waba ugenze m zingahe?
e) Kamana yavuye ku mashuri yiruka aca ku gikoni, anyura ku biro, akomereza ku cyumba k’inama, aca
ku bwiherero maze akomereza ku kibuga cy’umupira asubira ku mashuri aho yaturutse. Ubwo yagenze
m zingahe zose hamwe?
7) Soma aka gakuru neza usubize ibibazo.
Jabo, Gatari, Kamanzi na Kagabo basiganwe kwiruka kugeza igihe uzajya yumva ananiwe azajya yivana mu isiganwa. Jabo yiruka km 8 arananirwa, Gatari yiruka dam 897 arananirwa, Kamanzi ananirwa amaze kwiruka hm 95 naho Kagabo we ananirirwa kuri m 9 759.
a) Muri bose ni nde wirutse m nyinshi? Ni zingahe?
b) Muri bose ni nde wirutse m nkeya? Ni zingahe?
c) Batondeke uhereye ku wirutse ahantu harehare ujya kuwirutse ahantu hagufi
d) Batondeke uhereye ku wirutse ahantu hagufi ujya ku wirutse ahantu harehare
8) Shimwa bamuhaye intego yo kwiruka km 50 adahagaze, amaze kwiruka dam 487 arananirwa yemera ko atsinzwe intego. Yananiwe asigaje kwiruka m zingahe?
9) Ku munsi w’ikiruhuko niruka m 500 inshuro 6. Ubwo niruka km zingahe?
10) Uwase yaboshye umugozi wo gusimbuka ufite m 36, awugabanyamo imigozi 9 ingana. Shaka uburebure bwa buri mugozi muri cm.
- Umutwe wa 6:Ingero z’uburemere kuva 6 kuri kg kugera kuri gUmutwe wa 6:Ingero z’uburemere kuva 6 kuri kg kugera kuri gLabel: 1Umutwe wa 6:Ingero z’uburemere kuva 6 kuri kg kugera kuri g
6.1 Ingero z’uburemere
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho
Igikorwa cya 2
Mwitegereze aya mashusho muvuge ibyo muyabonaho
Igikorwa cya 3
Musome maze mwandike amazina n’uburemere bw’ibintu biri ku mashusho
Igikorwa cya 4
Muganire ku kamaro ko gukoresha umunzani ndetse n’ahandi hantu ingero z’uburemere zikoreshwa hatagari mu mashusho.
Nsobanukiwe ko:
− Garama (g) ni rwo rugero fatizo mu ngero z’uburemere.
− Garama (g) ikoreshwa iyo ibyapimwe ari utuntu tworoshye nk’amavuta yo kwisiga, imiti, …
− Kilogarama (kg) ni rwo rugero mu ngero z’uburemere rukunze gukoreshwa cyane.
− Usibye kg na g hari n’izindi ngero z’uburemere nka hg (hegitogarama) na dag (dekagarama)
− Iminzani y’isaha, iya gakwege n’uw’amabuye ni yo idufasha kumenya uburemere bw’ibintu bitandukanye.
− Ingero z’uburemere zikoreshwa mu bucuruzi, mu nganda, mu rugo, kwa muganga, mu bwikorezi, mu myidagaduro.
6.2 Isano iri hagati y’ingero z’uburemere
Igikorwa
Mwitegereze imbonerahamwe y’ingero z’uburebure,musobanure uko ingero z’uburebure zirutana hagati yazo.
Nsobanukiwe ko:
Ingero z’uburemere zirutana inshuro 10 uva ku rugero ruto ujya ku runini cyangwa uva ku rugero runini ujya ku ruto.
6.3 Kwandika no gusoma ingero z’uburemere kuva kuri kg kugera kuri g
Igikorwa cya 1
Mwitegereze ishusho musobanure ibiri gukorwa
Igikorwa cya 2
Itegereze uce imbonerahamwe y’ingero z’uburemere imeze nk’iyi, maze wandike uko basoma buri rugero mu ikayi yawe.
1) Soma uhuze impine z’ingero z’uburemere n’uko zisomwa ukurikije urugero wahawe
2) Subiza yego cyangwa oya
a) Ni byiza kugura ibintu bidapimye.
b) Kg ni rwo rugero fatizo mu ngero z’uburemere.
c) Garama (g) ni rwo rugero rw’uburemere rukoreshwa
cyane kurusha izindi.
6.4 Guhindura ingero z’uburemere kuva kuri kg kugera kuri g
Igikorwa cya 1
Mwitegereze iyi shusho muvuge ibyo muyibonaho.
Igikorwa cya 2
Muce imbonerahamwe yo guhindura ingero z’uburemere mu makayi y’imyitozo. Mukore ibibazo mukurikiza ibyo mwabonye mu gikorwa cya 1.
Nsobanukiwe ko:
− Ingero z’uburemere zirutanwa inshuro icumi hagati yazo
− Iyo uhindura ingero z’uburemere wifashisha imbonerahamwe yo guhindura ukandikamo imibare wahawe
− Iyo uva ku rugero runini ujya ku rugero ruto wongeraho zeru (0)
− Iyo uva ku rugero ruto ujya ku rugero runini ukuraho zeru (0) ibi bikorwa gusa ku mibare iherwa n’amazeru.
6.5 Kugereranya ingero z’uburemere
A. Kugereranya ingero z’uburemere uterura
Igikorwa cya 2
Muterure amabuye, amatafari, ibikapu by’amakayi, udukarito tw’ingwa, udukarito tw’amakayi n’utw’amakaramu.
Uteruye ikintu age agereranya avuge uburemere bwacyo,mubiganireho.
Igikorwa cya 3
Muterure ibintu bitandukanye mugereranye uburemere bwabyo, mubishyire mu matsinda 2. Itsinda rya mbere rigemo ibihuje uburemere naho irya kabiri rigemo ibidahuje uburemere mubiganireho.
B. Kugereranya ingero z’uburemere upima
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho.
Igikorwa cya 2
Mukoreshe umunzani mupime uburemere bw’ibi bikurikira, mwandike uburemere bwabyo hanyuma mubugereranye.
1) Agakarito kuzuye ingwa n’akarimo ubusa
2) Ibitabo 5 by’imibare n’ibitabo 5 by’Ikinyarwanda
3) Agakarito karimo utubuye n’akarimo ingwa
Igikorwa cya 3
Mukoreshe umunzani upima uburemere bw’abantu buri wese yipime ibiro bye, yandike amazina ye n’ibiro yagize nimurangiza murebe ufite ibiro bike, ababinganya; n’ufite byinshi kubarusha.
C. Kugereranya ingero z’uburemere ukoresheje <, > na =
Igikorwa
Mwifashishije imbonerahamwe muhindure ingero z’uburemere
mwahawe mu rugero ruto ruri mu zo mwahawe hanyuma
mugereranye mukoresheje >, < na =
Nsobanukiwe ko:
− Iyo ugereranya ingero z’uburemere ubanza guhindura
ingero zigereranywa mu rugero ruto mu ngero baguhaye.
− Ugakurikizaho kugereranya imibare.
− Ukabona gushyiramo ikimenyetso kimwe muri ibi
bimenyetso by’igereranya (<, > cyangwa = )
Gereranya ingero z’uburemere wahawe.
6.6 Gutondeka ingero z’uburemere kuva kuri kg kugera kuri g
A. Gutondeka ingero z’uburemere uva ku rugero ruto ujya ku rugero runini
Igikorwa
Mutondeke izi ngero z’uburemere muhereye ku rugero ruto mujya ku rugero runini mukurikije urugero mwahawe.
a) dag 45, hg 79, g 530
b) hg 52, dag 549, kg 9
c) dag 79, g 310, hg 48
d) hg 76, kg 4, dag 576
e) dag 345, kg 8, hg 56
f) g 271, 54 dag, 9 kg
Nsobanukiwe ko:
Iyo utondeka ingero z’uburemere uva ku rugero ruto ujya ku runini ubanza guhindura ingero zose baguhaye mu rugero ruto ruri mu zo baguhaye. Warangiza ugatondeka uva ku rugero ruto ujya ku rugero runini wifashishije imibare yazo.
B. Gutondeka ingero z’uburemere uva ku rugero runini ujya ku rugero ruto
Igikorwa
Mutondeke izi ngero z’uburemere muhereye ku rugero runini mujya ku rugero ruto mukurikije urugero mwahawe.
a) g 791, kg 7, hg 65
b) dag 24, g 869, kg 4
c) dag 153, hg 68, kg 9
d) dag 64, kg 5, hg 245
Nsobanukiwe ko:
Iyo utondeka ingero z’uburemere uva ku rugero runini ujya ku ruto ubanza guhindura ingero zose baguhaye mu rugero ruto ruri muzo baguhaye. Warangiza ugatondeka uva ku rugero ruto ujya ku rugero runini wifashishije imibare yazo.
1) Tondeka izi ngero uhereye ku ruto ujya ku runini
a) dag 54, g 84, hg 6
b) hg 27, dag 45, kg 9
c) dag 87, g 58, hg 7
d) dag 96, g 97, kg 6
2) Tondeka izi ngero uhereye ku runini ujya ku ruto
a) g 897, hg 57, kg 5
b) dag 29, hg 18, g 47
c) g 538, dag 648, kg 7
d) hg 68, g 291, dag 164
6.7 Guteranya ingero z’uburemere kuva kuri kg kugera kuri g
Igikorwa
Koresha imbonerahamwe y’ingero z’uburemere usubize ibibazo ukurikije urugero wahawe.
Urugero: kg 4 g 7 + hg 25 g 3 = dag 651
Nsobanukiwe ko:
Iyo uteranya ingero z’uburemere ubanza guhindura ingero zose baguhaye mu rugero wabajijwe ukabona guteranya.
Mukoreshe imbonerahamwe y’ingero z’uburebure mwuzuze urugero rubura muri buri mwitozo.
6.8 Amahurizo yo guteranya ingero z’uburemere kuva kuri kg kugera kuri g
Urugero:
Baho, Gaju, Teta na Gisa bagiye ku munzani basanga Baho afite kg 36, Gaju afite kg 33, Teta afite kg 35 naho Gisa afite kg 34. Bose hamwe ubashyize ku munzani bapima kg zingahe?
Nsuzuma ngusuzume
1) Masabo yaranguye kg 56 z’ifu y’amasaka, kg 195 z’ifu y’ingano kg 189 z’ifu y’uburo na kg 205 z’ifu ya sosoma.Niba yaravanze ayo mafu yose agakora ifu y’igikoma ivanze yagize kg zingahe?
2) Butera yasaruye hg 987 za kawa umwaka ushize naho uyu mwaka yasaruye dag 9 130. Ubwo yasaruye
kg zingahe muri iyi myaka ibiri?
Nsobanukiwe ko:
Iyo ukora amahurizo yo guteranya ingero z’uburemere, ubanza kuvana mu ihurizo ibyo baguhaye n’ ibyo bakubaza. Hanyuma ugateranya, igisubizo ubonye ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Ejo Uwamahoro yacuruje dag 975 z’umuceri naho
uyu munsi yacuruje g 9 250. Shaka umubare wa kg yacuruje mu minsi ibiri.
2) Kamariza yajyanye na murumuna we Gatoni kurangura ubunyobwa, bagezeyo Kamariza arangura kg 375 naho murumuna we arangura hg 2 250. Bombi baranguye kg zingahe z’ubunyobwa?
1) Umucuruzi w’imyaka yaranguye hg 1 000 z’ibishyimbo, kg 50 z’isukari, kg 50 z’umuceri, kg 50 z’umunyu na dag 7 500 z’ubunyobwa. Shaka uburemere muri kg bw’ibintu byose yaranguye.
2) Nganji bamutumye guhaha agura g 500 z’umunyu, hg 10 z’inyama, dag 50 z’isukari, kg 2 z’inyanya, dag 300 z’ifu na hg 10 z’umuceri. Shaka uburemere bw’ibintu byose yahashye muri kg.
6.9 Gukuramo ingero z’uburemere kuva kuri kg kugera kuri g
Igikorwa
Koresha imbonerahamwe yo guhindura ingero z’uburemere usubize ibibazo ukurikije urugero wahawe.
Urugero: dag 425 – kg 3 = dag 125
a) g 321 – dag 27 = g
b) dag 756 – kg 5 hg 7 = dag
c) hg 98 – dag 95 = g
d) kg 7 dag 6 – g 2860= hg
e) dag 498 – hg 39 = g
f) g 976 – hg 8 g 6 = dag
Nsobanukiwe ko:
Iyo ukuramo ingero z’uburemere ubanza guhindura ingero zose baguhaye mu rugero wabajijwe warangiza ukabona gukuramo.
Mukoreshe imbonerahamwe yo guhindura ingero z’uburemere mwuzuze urugero rubura muri buri mwitozo.
6.10 Amahurizo yo gukuramo ingero z’uburemere kuva kuri kg kugera kuri g
Urugero:
Niga mu mwaka wa kabiri napimaga kg 32 g 800. Ubu nsigaye mpima hg 390.Ubwo maze kwiyongeraho hg zingahe?
Nsuzuma ngusuzume
1) Manzi yaranguye kg 65 z’isukari agurishaho hg 390.Ubwo yasigaranye kg zingahe?
2) Mu rugo twaguze umufuka w’umuceri wa kg 50 duhaho umuturanyi dag 1 200. Ubwo twasigaranye hg zingahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo gukuramo ingero z’uburemere ubanza kwerekana ibyo baguhaye n’ibyo bakubaza
mu ihurizo. Ugahindura mu rugero ruto ugakuramo,igisubizo ubonye ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Keza apima kg 39 akarusha murumuna we Mugeni kg 6.Ubwo Mugeni apima kg zingahe?
2) Umwaka ushize Mariza yapimaga kg 98. Aho atangiriye gufata indyo yihariye no gukora imyitozo ngororamubiri ubu asigaye apima kg 65. Ubwo yatakaje kg zingahe?
6.11 Gukuba ingero z’uburemere kuva kuri kg kugera kuri g n’umubare ushyitse
Igikorwa
Koresha imbonerahamwe yo guhindura ingero z’uburemere usubize ibibazo ukurikije urugero wahawe.
Urugero: kg 2 dag 5 × 4 = hg 82
Nsobanukiwe ko:
Iyo ukuba ingero z’uburemere n’umubare ushyitse ubanza guhindura ingero zose baguhaye mu rugero wabajijwe warangiza ukabona gukuba.
Nsuzuma ngusuzume
Mukoreshe imbonerahamwe yo guhindura ingero z’uburemere mwuzuze urugero rubura muri buri mwitozo.
6.12 Amahurizo yo gukuba ingero z’uburemere kuva kuri kg kugera kuri g
Urugero:
Nziza yaguze amakarito 8 y’isabune. Niba buri karito yari ifite kg 25 ubwo ayo makarito yose yari afite uburemere bungana iki?
Nsuzuma ngusuzume
1) Niba ipaki imwe y’umunyu ipima g 500. Ubwo amapaki 9 y’uwo munyu apima hg zingahe?
2) Mu rugo duteka g 500 z’umuceri buri munsi. Ubwo mu minsi 8 tuba tumaze guteka kg zingahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo gukuba ingero z’uburemere n’umubare ushyitse, ubanza kwerekana ibyo baguhaye.Ugakurikizaho ibyo bakubaza, ugakuba ibyo baguhaye hanyuma igikubo ubonye ukagihindura mu rugero bakubajije
Reka nisuzume
1) Mugabo yaguze amapaki 8 y’ifarini. Niba buri paki iba irimo kg 5, ubwo yaguze kg zingahe z’ifarini zose hamwe?
2) Icyuma gitunganya umuceri gitonora kg 1 875 buri munsi.Ubwo gitonora kg zingahe mu minsi 4?
1) Mu minsi 2 uruganda rw’isukari ruzaba rukoze kg zingahe niba buri munsi rukora kg 2 750?
2) Muhizi yasaruye imifuka 9 y’umuceri ipima kg 100 buri mufuka. Ubwo yasaruye kg zingahe z’umuceri zose hamwe?
6.13 Kugabanya ingero z’uburemere kuva kuri kg kugera kuri g n’umubare ushyitse
Igikorwa
Koresha imbonerahamwe y’ingero z’uburemere ukore imyitozo ukurikije urugero wahawe.
Nsobanukiwe ko:
Iyo ugabanya ingero z’uburemere n’umubare ushyitse ubanza kugabanya, warangiza ugahindura mu rugero wabajijwe.
Mukoreshe imbonerahamwe y’ingero z’uburemere mwuzuze urugero rubura muri buri mwitozo.
6.14 Amahurizo yo kugabanya ingero z’uburemere kuva kuri kg kugera kuri g n’umubare ushyitse
Urugero:
Umucuruzi yaranguye kg 100 z’umuceri azigabanyiriza mu dufuka 4 ku buryo bungana. Ubwo buri gafuka yagashyizemo kg zingahe?
Nsuzuma ngusuzume
1) Naranguye kg 75 z’isabune y’ifu nzigabanyiriza mu tudobo 5 ku buryo bungana. Muri buri kadobo nashyizemo kg zingahe?
2) Abantu 8 bishyize hamwe barangura kg 200 z’isukari bageze iwabo bayigabana ku buryo bungana. Ubwo buri muntu yatwaye kg zingahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo kugabanya ingero z’uburemere n’umubare ushyitse, ubanza kwerekana ibyo baguhaye.
Ugakurikizaho ibyo bakubaza, ukagabanya ibyo baguhaye.
Ikigabanyo ubonye ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Gabanya ku buryo bungana dag 9 600 z’imbuto y’ibirayi abahinzi 8. Buri wese uzamuha kg zingahe?
2) Ishyirahamwe ryahaye ku buryo bungana hg 720 z’ibishyimbo abanyamuryango baryo 9.Buri munyamuryango yahawe kg zingahe?
3) Shyira g 9 750 mu mapaki 5 angana. Buri paki uzashyiramo dag zingahe?
4) Gabanya ku buryo bungana hg 240 z’ubunyobwa abantu 8. Buri muntu uzamuha kg zingahe?
1) Shyira ku buryo bungana g 840 z’ifumbire mvaruganda ku ngemwe z’ibiti 7. Buri rugemwe uzarushyiraho ifumbire ingana ite?
2) Gabanya ku buryo bungana hg 4 000 z’imbuto y’ingano Imirenge 5. Buri Murenge uzawuha kg zingahe?
3) Shyira ku buryo bungana kg 8 mu dupaki dupima g 8 kamwekamwe. Uzashyira uwo muti mu dupaki tungahe?
4) Saranganya ku buryo bungana dag 1 200 z’umuceri abantu 6. Buri muntu uzamuha kg zingahe?
6.15 Isuzuma risoza umutwe wa 6
6) Kora aya mahurizo
a) Mugabe yaranguye hg 750 z’ibishyimbo ku wa mbere, ku wa kabiri arangura dag 6 500 naho ku wa gatatu arangura kg 60. Yaranguye kg zingahe muri iyo minsi itatu?
b) Ineza yaguze amapaki y’isukari 7. Niba buri paki yari irimo kg 5 ubwo yaguze hg zingahe z’isukari?
c) Mu mpera z’umwaka ishyirahamwe ryahembye ku buryo bungana hg 1 000 z’umuceri abanyamuryango baryo 4 bagize imyitwarire myiza. Buri wese yahawe kg zingahe?
d) Musinga yajyanye dag 857 z’ubunyobwa ku isoko, agezeyo agurishaho g 6 570 ibisigaye abisubiza mu rugo. Ubwo yagurishije kg zingahe z’ubunyobwa?
- Umutwe wa 7:Ingero z’ibitembabuzi kuva kuri L kugera kuri MLUmutwe wa 7:Ingero z’ibitembabuzi kuva kuri L kugera kuri MLLabel: 1Umutwe wa 7:Ingero z’ibitembabuzi kuva kuri L kugera kuri ML
7.1 Ingero z’ibitembabuzi kuva L kuri kugera kuri ML
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho
Igikorwa cya 2
Mukoreshe icupa rya ml 500 cyangwa rya l 1 mupime kandi mwandike ubunini bw’ibi bivomesho:
a) Indobo ijyamo amacupa 10
b) Ijerikani nini ijyamo amacupa 20
Igikorwa cya 3
Mukoreshe akajerekani k’amazi ka l 5 mupime kandi mwandike ubunini bw’ibi bivomesho:
a) Ijerekani nini ijyamo utujerekani 4
b) Ingunguru ijyamo utujerekani 20
Reka nisuzume
Ni uruhe rugero mu ngero z’ibitembabuzi rukoreshwa iyo ushaka kumenya ibi bikurikira:
a) Urugero rw’umuti w’amazi uha umwana
b) Ingano y’ijerekani y’amazi
Nsobanukiwe ko:
• Ingero z’ibitembabuzi zirimo
– Litiro (l) – Santilitiro (cl)
– Desilitiro (dl) – Militiro (ml)
• Litiro (l) ni rwo urugero fatizo mu ngero z’ibitembabuzi
• Desilitiro (dl), santilitilo (cl) na mililitiro (ml) ni zo ngero z’ibitembabuzi zirutwa na litiro.
7.2 Gusoma no kwandika ingero z’ibitembabuzi kuva kuri L kugeza kuri ML
Igikorwa cya 1
Mwitegereze ishusho musobanure ibiri gukorwa
Igikorwa cya 2
Mwitegereze imbonerahamwe y’ingero z’ibitembabuzi:
a) Muganire uko basoma buri rugero.
b) Mwandike uko basoma buri rugero mu makayi yanyu.
Nsobanukiwe ko:
Ingero z’ibitembabuzi zirutana inshuro 10 uva ku rugero ruto ujya ku runini cyangwa uva ku runini ujya ku ruto.
Uzuza izi nteruro n’ijambo rikwiye: (desilitiro, santilitiro, litiro icumi, mililitiro, icupa rya litiro, ingero z’ibitembabuzi)
7.4 Guhindura ingero z’ibitembabuzi kuva kuri L kugera kuri ML
A. Guhindura ingero z’ibitembabuzi uva ku rugero runini ujya ku rugero ruto
Igikorwa
Mwitegereze imbonerahamwe ikurikira y’ingero z’ibitembabuzi muyigane mukore imyitozo ikurikira yo muri “Reka nisuzume”.
Reka nisuzume
B. Guhindura ingero z’ibitembabuzi uva ku rugero ruto ujya ku rugero runini
Igikorwa
Mwitegereze imbonerahamwe yo guhindura ingero z’ibitembabuzi muyigane mukore imyitozo ikurikira yo muri “Nsuzuma ngusuzume”
Nsuzuma ngusuzume
Nsobanukiwe ko:
– Iyo uhindura ingero z’ibitembabuzi wifashisha imbonerahamwe y’ingero ukandikamo imibare wahawe
– Iyo uva ku rugero runini ujya ku rugero ruto wongeraho zeru (0)
– Iyo uva ku rugero ruto ujya ku runini ukuraho zeru (0). Ibi bikorwa ku mibare iherwa n’amazeru gusa.
Hindura mu rugero wabajijwe
a. Kugereranya ingero z’ibitembabuzi uterura
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho.
Igikorwa cya 2
Muterure ibivomesho bitandukanye. Uteruye ikintu age agereranya abwire bagenzi be litiro z’amazi ateruye mubyandike hanyuma mubiganireho.
Igikorwa cya 3
Mugereranye muvuge umubare w’ibirahuri byuzuye mwavana mu bintu bikurikira:
–ml 500 z’amazi
–L1 y’amata
–L 2 z’umutobe
b. Kugereranya ingero z’ibitembabuzi upima
Igikorwa cya 1
Mwitegereze aya mashusho muvuge ibyo muyabonaho
Igikorwa cya 2
Mukoreshe ijagi ya litiro (L) ndetse n’amazi ari mu ibase
mupime maze mwandike ingano y’ibi bikurikira mubigereranye.
– Umubare w’amajagi y’amazi ajya mu kadobo
– Umubare w’amajagi y’amazi ajya mu kajerekani
– Umubare w’amajagi y’amazi ajya mu kabase
a) Ni ikihe gikoresho gitwara amazi make?
b) NI ikihe gikoresho gitwara amazi menshi?
C) Sobanura igisubizo watanze
c. Kugereranya ingero z’ibitembabuzi ukoresheje <, > na =
Igikorwa
Muhindure ingero mwifashishije imbonerahamwe y’ingero z’ibitemababuzi mwahawe muhindure mu rugero ruto hanyuma mugereranye mukoresheje >, < na =
Nsobanukiwe ko:
– Iyo ugereranya ingero z’ibitembabuzi ubanza guhindura ingero zigereranywa mu rugero ruto mu zo wahawe.
– Ukagereranya imibare
– Ugashyiramo kimwe muri ibi bimenyetso by’igereranya (<, > cyangwa = )
Koresha >, < na = ugereranye
7.6 Gutondeka ingero z’ibitembabuzi kuva kuri L kugera kuri ML
a. Gutondeka ingero z’ibitembabuzi uva ku rugero ruto ujya ku rugero runini
Igikorwa
Mutondeke izi ngero z’ibitembabuzi muhereye ku ruto mujya ku runini mukurikije urugero mwahawe
Reka nisuzume
Tondeka ingero z’ibitembabuzi zikurikira uva ku ruto ujya ku runini:
Nsobanukiwe ko:
Iyo utondeka ingero z’ibitembabuzi ubanza guhindura ingero zose baguhaye mu rugero ruto. Hanyuma ugatondeka uva ku rugero ruto ujya ku runini wifashishije imibare yazo.
b. Gutondeka ingero z’ibitembabuzi uva ku rugero runini ujya ku rugero ruto
Igikorwa
Mutondeke izi ngero z’ibitembabuzi muhereye ku runini mujya ku ruto mukurikije urugero mwahawe
Reka nisuzume
Tondeka ingero z’ibitembabuzi zikurikira uva ku runini ujya ku ruto.
Nsobanukiwe ko:
Iyo utondeka ingero z’ibitembabuzi ubanza guhindura ingero zose baguhaye mu rugero ruto. Hanyuma ugatondeka uva ku rugero runini ujya ku ruto wifashishije imibare yazo.
1) Tondeka izi ngero z’ibitembabuzi uhereye ku rugero ruto ujya ku rugero runini
2) Tondeka izi ngero z’ibitembabuzi uhereye ku rugero runini ujya ku rugero ruto
7.7 Guteranya ingero z’ibitembabuzi kuva kuri L kugera kuri ML
Igikorwa
Koresha imbonerahamwe yo guhindura ingero z’ibitembabuzi usubize ibibazo ukurikije urugero wahawe.
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo uteranya ingero z’ibitembabuzi, ubanza guhindura ingero zose baguhaye mu rugero wabajijwe. Warangiza ukabona guteranya.
Reka nisuzume
Teranya ingero zikurikira maze wuzuze urugero rubura ahabugenewe.
Teranya ingero zikurikira maze wuzuze urugero rubura ahabugenewe.
7.8 Amahurizo yo guteranya ingero z’ibitembabuzi kuva kuri L kugera kuri ML
Urugero:
Muhizi yaguze L1 y’umutobe w’amatunda,cl 500 z’umutobe w’inanasi,dl 10 z’umutobe w’amacunga,na cl 100 z’amazi. Niba yaravanze iyo mitobe yose n’amazi ubwo yagize L zingahe z’umutobe uvanze?
Nsuzuma ngusuzume
1) Mu rugo dukama L42 z’amata mu gitondo na cl4 800 nimugoroba. Ubwo dukama L zingahe buri munsi?
2) Ku wa mbere Butera yacuruje dl 450 z’amavuta naho ku wa kabiri acuruza cl 5 500. Ubwo yacuruje L zingahe muri iyo minsi yombi?
Nsobanukiwe ko:
Iyo ukora amahurizo yo guteranya ingero z’ibitembabuzi,ubanza kwerekana ibyo baguhaye mu ihurizo.
Ugakurikizaho ibyo bakubaza, ugahindura mu rugero ruto ugateranya igisubizo ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Uwera akoresha L 75 z’amazi avomerera imboga ze mu gitondo naho nimugoroba agakoresha dl 550. Ubwo ku munsi akoresha amazi angana iki avomerera imboga ze?
2) Shaka ingano ya litiro z’amazi dukoresha mu rugo buri munsi niba dukora ibi bikurikira:
• Guteka:dl 200 • Koza ibyombo:L 60
• Gukoropa:cl 3 000 • Gukaraba:L 100
1) Ku munsi w ‘ikiruhuko Gatoni yameshe imyenda y’ishuri akoresha dl 200, mukuru we Mutoni akoresha dl 400 naho ababyeyi babo bakoresha L 100. Ubwo urwo rugo rwameshesheje amazi angana iki?
2) Ku wa gatanu sitasiyo ya lisansi yacuruje L 658 naho ku wa gatandatu icuruza dl2 320. Shaka umubare wa L yacuruje muri iyo minsi ibiri.
7.9 Gukuramo ingero z’ibitembabuzi kuva kuri L kugera kuri ml
Igikorwa
Koresha imbonerahamwe y’ingero z’ibitembabuzi usubize ibibazo ukurikije urugero wahawe
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ukuramo ingero z’ibitembabuzi ubanza guhindura ingero zose baguhaye mu rugero ruto ukabona gukuramo, igisubizo ukagihingura mu rugero wabajijwe.
Reka nisuzume
7.10 Amahurizo yo gukuramo ingero z’ibitembabuzi kuva kuri L kugera kuri ml
Urugero:
Ingabire yari afite cl100 z’umutobe, ahaho inshuti ye Bugingo dl30. Ubwo yasigaranye cl zingahe?
Nsuzuma ngusuzume
1) Mu ijerekani irimo L 20 z’amazi bavanyeho dl 169 barayatekesha. Ubwo muri iyo jerekani hasigayemo cl zingahe?
2) Ku munsi w’ibirori twateguye dl 3 000 z’umutobe wo kuzimanira abashyitsi. Nyuma y’ibirori twasanze twasigaranye L 40. Ubwo abo bashyitsi twabazimaniye L zingahe z’umutobe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo gukuramo ingero z’ibitembabuzi ubanza kwerekana mu ihurizo ibyo baguhaye.
Ugakurikizaho ibyo bakubaza, ugahindura mu rugero bakubajije, ugakuramo ibyo baguhaye.
Reka nisuzume
1) Navomye L 60 z’amazi mesheshaho dl 375. Ubwo nasigaranye cl zingahe?
2) Kugira ngo Mugabo abumbe amatafari azubakisha igikoni akeneye L 225 z’amazi. Niba yaratangiye kuyavoma yageza kuri dl 1 750 amazi akabura ubwo arabura amazi angana iki ngo abumbe ayo matafari?
1) Mu rugo dukoresha L 145 z’amazi buri munsi. Niba dufite dl 950 gusa, ubwo turabura L zingahe kugira ngo tugire amazi ahagije ku munsi ukurikira?
2) Hirwa yavomye dl 750 z’amazi azisuka mu ndobo ebyiri. Imwe yibagirwa kuyipfundikira ya mazi aratokorwa barayamena. Niba amazi bamennye yari L 38 ubwo yasigaranye L zingahe?
7.11 Gukuba ingero z’ibitembabuzi kuva kuri L kugera kuri ml n’umubare ushyitse
Igikorwa
Koresha imbonerahamwe yo guhindura ingero
z’ibitembabuzi usubize ibibazo ukurikije urugero wahawe
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ukuba ingero z’ibitembabuzi ubanza guhindura ingero zose baguhaye mu rugero wabajijwe warangiza ukabona gukuba.
Reka nisuzume
7.12 Amahurizo yo gukuba ingero z’ibitembabuzi n’umubare ushyitse
Urugero:
Gatesi anywa ml 2500 z’amazi buri munsi. Shaka umubare wa L z’amazi anywa mu minsi 2.
Nsuzuma ngusuzume
1) Ireme yavomye inshuro 4 avomesha ijerekani yaL 15. Ubwo yavomye amazi angana iki yose hamwe?
2) Inka ya Gashumba ikamwa L 32 buri munsi. Shaka ingano y’amata iyo nka ikamwa mu minsi 5
Nsobanukiwe ko:
Iyo ukora amahurizo yo gukuba ingero z’ibitembabuzi ubanza kwerekana ibyo baguhaye mu ihurizo. Ugakurikizaho ibyo bakubaza, ugakuba ibyo baguhaye. Hanyuma igikubo ubonye ukagihindura mu rugero bakubajije.
Reka nisuzume
1) Mu rugo turi abantu 8. Niba buri wese anywa cl 500 z’amata buri munsi, twese tunywa amata angana iki?
2) Shaka ingano ya lisansi Uwineza akoresha mu minsi 6 niba buri munsi akoresha cl 750.
1) Shaka z’amazi Uwingabire akoresha mu minsi 6 niba buri munsi akoresha dl 250.
2) Buri munyeshuri anywa uducupa 3 twa cl 50 tw’amazi. Abanyeshuri 9 mu minsi 2 banywa amazi angana iki?
7.13 Kugabanya ingero z’ibitembabuzi kuva kuri L kugera kuri ml
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Igikorwa cya 2
Koresha imbonerahamwe yo guhindura ingero z’ibitembabuzi usubize ibibazo ukurikije urugero wahawe mu gikorwa cya 1.
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ugabanya ingero z’ibitembabuzi ubanza guhindura ingero zose baguhaye mu rugero wabajijwe warangiza ukabona kugabanya.
Reka nisuzume
7.14 Amahurizo yo kugabanya ingero z’ibitembabuzi n’umubare ushyitse
Urugero:
Wakoresha utujerekani tungahe tujyamo L 3 z’amazi kugira ngo wuzuze ingunguru ijyamo L 225 z’amazi?
Nsuzuma ngusuzume
1) Mu ijerekani ya dl 500 z’amazi wakuramo utujerekani tungahe tujyamo L 5 kamwekamwe?
2) Gabanya ku buryo bungana cl 800 z’umutobe abana L 8. Buri wese uzamuha zingahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo kugabanya ingero z’ibitembabuzi ubanza kwerekana ibyo baguhaye mu ihurizo, ugakurikizaho ibyo bakubaza, ukagabanya ibyo baguhaye hanyuma ikigabanyo ubonye ukagihindura mu rugero bakubajijwe.
Reka nisuzume
1) Gabanya ku buryo bungana dl 450 z’amavuta ingo 9. Buri rugo uzaruha cl zingahe?
2) Muhoza ateka L 4 z’amavuta mu minsi 8. Shaka cl z’amavuta ateka buri munsi.
1) Gabanya ku buryo bungana cl 900 z’amazi abana 9. Buri mwana uzamuha L zingahe?
2) Kamariza arashaka kugabanya ku buryo bungana dl 56 z’amata abana be 7. Buri mwana azamuha cl zingahe?
7.15 Isuzuma risoza umutwe wa 7
- Umutwe wa 8:Amafaranga y’u Rwanda kuva ku F 1 kugera ku F 5 000Umutwe wa 8:Amafaranga y’u Rwanda kuva ku F 1 kugera ku F 5 000Label: 1Umutwe wa 8:Amafaranga y’u Rwanda kuva ku F 1 kugera ku F 5 000
8.1 Ibiranga amafaranga y’u Rwanda n’agaciro kayo kugera ku F 5 000
Igikorwa cya 1
Mwitegereze ibiceri bigize F y’u Rwanda muvuge agaciro kabyo ndetse n’ibibiranga
Nsobanukiwe ko:
Ibiceri by’amafaranga y’u Rwanda birangwa n’ibikurikira:
Igiceri cya F 1
Uruhande rumwe Urundi ruhande
– Ibara rya feza – Ibara rya feza
– Ikirangantego – Ihundo ry’ingano
– Umubare 1
Igiceri cya F 5
Uruhande rumwe Urundi ruhande
– Ibara ry’umuringa – Ibara ry’umuringa
– Ikirangantego – Ikawa
– Umubare 5
Igiceri cya F 10
Uruhande rumwe Urundi ruhande
– Ibara ry’umuringa – Ibara ry’umuringa
– Ikirangantego – Insina iriho igitoki
– Umubare 10
Igiceri cya F 20
Uruhande rumwe Urundi ruhande
– Ibara rya feza – Ibara rya feza
– Ikirangantego – Ishami ry’igiti k’icyayi.
– Umubare 20
Igiceri cya F 50
Uruhande rumwe Urundi ruhande
– Ibara rya feza – Ibara rya feza
– Ikirangantego – Ikigori
– Umubare 50
Igiceri cya F 100
Uruhande rumwe Urundi ruhande
– Ibara rya feza rizengurutse iry’umuringa – Ibara rya feza rizengurutse iry’umuringa
– Ikirangantego – Agaciro k’igiceri cy’amafaranga 100
– Umubare 100
Igikorwa cya 2
Mwitegereze ibiceri bigize amafaranga y’u Rwanda mutahure ikirango kiboneka ku biceri byose.
Igikorwa cya 3
Mwitegereze inoti zigize F y’u Rwanda muvuge agaciro kazo n’ibiziranga.
Nsobanukiwe ko:
– Inoti zigize amafaranga y’u Rwanda ari 4 zifite agaciro gakurikira F 500, F 1 000, F 2 000 na F 5 000.
– Inoti ifite agaciro gato ni iya F 500.
– Inoti ifite agaciro kanini ni iya F 5 000.
– Ibiranga inoti z’amafaranga y’u Rwanda ari ibi:
Inoti ya F 500
Uruhande rumwe Urundi ruhande
– Ikirangantego cya Leta y’u Rwanda – Ikirangantego cya Leta y’u Rwanda
– Ibara ry’ubururu bukeye – Ibara ry’ubururu bukeye
– Inka ebyiri – Abana bane bakoresha mudasobwa
Inoti ya F 1 000
Uruhande rumwe Urundi ruhande
– Ikirangantego cya Leta y’u Rwanda – Ikirangantego cya Leta y’u Rwanda
– Ibara ry’ubururu – Ibara ry’ubururu
– Inzu ndangamurage y’u Rwanda ihagazeho inuma – Inkende
Inoti ya F 2 000
Uruhande rumwe Urundi ruhande
– Ikirangantego cya Leta y’u Rwanda – Ikirangantego cya Leta y’u Rwanda
– Umunara wubatse ku kirunga cya Kalisimbi – Ikawa zumye zitonoye
– Ibara ry’umwura – Agatako ka nyamuraza
– Udutako dukoze muri mpandeshatu n’impande esheshatu
– Agaseke
Inoti ya F 5 000
Uruhande rumwe Urundi ruhande
– Ingagi iri mu migano – Inkangara n’agaseke
– Ibara ry’umutuku – Agatako k’inyegamo
– Ikirangantego cya Leta y’u Rwanda – Ibara ry’umutuku
– Ikirangantego cya Leta y’u Rwanda
Igikorwa cya 4
Mwitegereze inoti zigize amafaranga y’u Rwanda maze mutahure ikirango kiboneka ku noti zose.
Nsuzuma ngusuzume
Itegereze inoti n’ibiceri bigize amafaranga y’u Rwanda, utahure ikirango kiboneka hose haba ku noti ndetse no ku biceri.
1) Ibiceri byose bigize amafaranga y’u Rwanda biri mu mabara abiri. Yavuge.
2) Sobanura itandukaniro riri hagati y’ibiceri n’inoti
3) Vuga muri make iby’ingenzi biranga inoti zigize amafaranga y’u Rwanda.
8.2 Akamaro k’amafaranga
Igikorwa cya 1
Mwitegereze amashusho muvuge ibyo muyabonaho.
Igikorwa cya 2
Usibye ibyo mwabonye ku mashusho muvuge akandi kamaro muzi k’amafaranga.
Nsuzuma ngusuzume
Mukore urutonde rw’ibyo mwakora mufite amafaranga 1 000.
Nsobanukiwe ko:
– Amafaranga tuyagura ibyo dukeneye byose nk’ibiribwa, ibinyobwa n’imyambaro. Amafaranga tuyishyura serivisi zitandukanye nk’ubwishingizi bw’ubuzima, umutekano, isuku, ibyangombwa ndetse n’abadukoreye akazi.
– Amafaranga kandi tuyagura imitungo itandukanye nk’inzu, ubutaka, amatungo, imodoka n’ibikoresho bitandukanye.
Igikorwa cya 3
Muganire ku bibazo bikurikira buri wese atange igitekerezo hanyuma muze guhitamo ibitekerezo 5 byiza kurusha ibindi
a) Ufite F 2 000 wayagura iki?
b) Ufite F 5 000 wayagura iki?
1) Tanga ingero za serivisi zishyurwa amafaranga.
2) Sobanura akamaro k’amafaranga ku muryango wawe.
8.3 Uko amafaranga aboneka
Igikorwa cya 1
Mwitegereze amashusho muvuge ibyo muyabonaho
Nsuzuma ngusuzume
Vuga ubundi buryo butagaragaye ku mashusho umuntu yabonamo amafaranga.
Nsobanukiwe ko:
Abantu bavana amafaranga mu mirimo ikurikira:
– Ubuhinzi – Ubucuruzi
– Ubwikorezi – Ubukorikori
– Imirimo yo mu biro – Ubworozi
– Ubukerarugendo – Amarushanwa
Igikorwa cya 2
Musobanure uko imiryango yanyu ibona amafaranga
Reka nisuzume
Wakora iki kugira ngo ubone amafaranga wunganire umuryango wawe kugira ngo ubone ibyo ukeneye?
Igikorwa cya 3
Muganire ku buryo buboneye bwo gukoresha amafaranga
1) Tanga ingero z’imirimo iwanyu bakora ibazanira amafaranga.
2) Vuga zimwe mu ngeso mbi tugomba kwirinda zishobora gutuma uzikora abona amafaranga.
8.4 Kuvunja amafaranga y’u Rwanda
8.5 Amahurizo yo kuvunja amafaranga y’u Rwanda
Urugero:
Munezero bamuhembye inoti 3 za F 1 000 n’izindi 2 za F 500. Ubwo bamuhembye F angahe yose hamwe?
Nsuzuma ngusuzume
1) Rugira yatanze inoti 2 za F 2 000 n’izindi noti 2 za F500 bamuha umupira wo kwifubika. Ubwo uwo mupira wo kwifubika yawuguze F angahe?
2) Naguze ikayi nini n’ikaramu nishyura inoti 2 za F 1 000 n’indi imwe ya F 500. Ubwo nabiguze F angahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo kuvunja amafaranga ubanza kwerekana ibyo baguhaye mu ihurizo. Ugakurikizaho ibyo bakubaza, ugakuba umubare w’inoti cyangwa ibiceri n’agaciro kabyo. Hanyuma ugateranya ibikubo ubonye kugira ngo ubone igisubizo.
Reka nisuzume
1) Nagiye kwa masenge mu biruhuko ngiye kuvayo ampa inoti 3 za F 1 000 n’inoti 1 ya F 2 000. Ubwo masenge yampaye F angahe?
2) Mugabo yishyuye Uwera ibiceri 4 bya F 100 n’inoti 8 za F 500. Ubwo yari amurimo F angahe?
1) Mu rugo twaguze inkoko twishyura inoti 2 za F 2 000 n’inoti 3 za F 500. Ubwo twayiguze F angahe?
2) Iranzi yahembwe inoti 1 ya F 2 000, inoti 2 za F 500 n’inoti 2 za F 1 000. Shaka umubare wa F Iranzi yahembwe.
Nsuzuma ngusuzume
Vuga umubare w’inoti cyangwa ibiceri wakwishyura kugira ngo ugure ibintu bikurikira batakugaruriye:
a) Kg 1 y’isukari ku F 1 200
b) Imiti 2 y’isabune ku F 900
c) l 1 y’amavuta ku F 1 800
d) Igitabo ku F 4 500
e) Ishati ku F 2 500
f) Inkweto ku F 3 500
8.6 Amahurizo yo guteranya amafaranga y’u Rwanda
Urugero:
Tunga yaguze igitabo ku F 3500 n’ amakayi ku F 1 200. Byose yabiguze F angahe?
Nsuzuma ngusuzume
1) Rukundo yaguze ishati ku F 1 500 bamugarurira F 500. Ubwo yari yishyuye F angahe?
2) Ishimwe yaguze igikapu cyo gutwaramo ibitabo ku F 3 500 n’amakaramu ya F 900. Byose yabiguze F angahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo guteranya amafaranga ubanza kwerekana ibyo baguhaye mu ihurizo. Ugakurikizaho ibyo bakubaza. Hanyuma ugateranya ibyo baguhaye kugira ngo ubone igisubizo.
Reka nisuzume
1) Mutabazi yahaye abana be 4 ari bo Ingabire, Gato,Mucyo na Bwiza amafaranga yo kugura ibikoresho by’ishuri ku buryo bukurikira:
– Ingabire yamuhaye F 750
– Gato yamuhaye F 1 450
– Mucyo yamuhaye F 1 150
– Bwiza yamuhaye F 950
Bose hamwe yabahaye F angahe?
2) Ku munsi w’isabukuru y’amavuko yange banguriye ishati ya F 1 500, isengeri ya F 500, ipantaro ya
F 2 000 n’inkweto zo kogeramo za F 1 000. Byose hamwe babiguze F angahe?
1) Naguze irangi ku F 2 500 na l 1 ya peteroli yo kurivanga ku F 970. Byose hamwe nabiguze F angahe?
2) Uwamahoro yampembye ibisuguti bigura F 1 200, bombo za F 500 n’umutobe w’imbuto wa F 800. Shaka agaciro k’ibihembo byose nahembwe.
3) Abaturanyi ba Mbabazi bamutwerereye umwe F 3 400 naho undi F 1 300. Bombi bamutwerereye F angahe?
8.7 Amahurizo yo gukuramo amafaranga y’u Rwanda
Urugero:
Uwingabire yari afite F 5 000 aguraho kg 1 y’inyama ku F 2 500 na l 1 y’amavuta ku F 1 900. Yasigaranye F angahe?
Nsuzuma ngusuzume
1) Kangabe yari afite inoti ya F 1 000 aguraho kg 1 y’umunyu ku F 400 n’umuti umwe w’isabune ku F 450. Bamugaruriye F angahe?
2) Uwitonze afite F 4 500 kandi arashaka kugura ipantaro igura F 5 000. Ubwo arabura F angahe?
Nsobanukiwe ko:
Iyo ukora amahurizo yo gukuramo amafaranga ubanza kwerekana ibyo baguhaye mu ihurizo, ugakurikizaho ibyo bakubaza ugakuramo ibyo baguhaye.
Reka nisuzume
1) Kaneza bamutumye kugura indobo nini yo gushyiramo amazi bamuha F 5 000. Agezeyo yishyuye bamugarurira F 900. Ubwo iyo indobo yayiguze F angahe?
2) Nagiye guhaha mfite F 4 500. Ngeze mu isoko mpahisha F 3 900. Ubwo nasigaranye F angahe?
1) Mwarimu yagiye kugura ingwa za F 3 750 maze yishyura inoti ya F 5 000. Bamugaruriye F angahe?
2) Ku munsi w’amanota nabaye uwa mbere data ampemba F 5 000 ngo nzayagure icyo nshaka maze njyana na mama mu iguriro ry’ibitabo angurira igitabo k’imibare ku F 3 900. Ubwo nasigaranye F angahe?
8.8 Amahurizo yo gukuba amafaranga y’u Rwanda n’umubare ushyitse
Urugero:
Kabayiza yaguze amagi 56 ku F 80 rimwerimwe. Yose hamwe yayaguze F angahe?
Nsuzuma ngusuzume
1) Uwagutuma guhaha wakwishyura F angahe kuri buri bicuruzwa bikurikira:
a) kg 4 z’isukari ku F 1 200 buri kg 1
b) l 2 z’amavuta ku F 1 800 buri l 1
c) Imiti y’isabune 8 ku F 500 umuti umwe
d) Amaseri 2 y’ibitoki ku F 1 700 iseri rimwe
e) kg 4 z’umuceri ku F 1 250 kg imwe.
2) Niba igi rimwe rirangurwa F 85, ubwo amagi 27 arangurwa F angahe?
Reka nisuzume
1) Marume yaguze amagi 119 ku F 80 igi rimwe. Ubwo yose yayaguze F angahe?
2) Niba ikayi imwe igura F 250 ubwo amakayi 8 agura F angahe?
3) Ngiye kugura l 3 z’amavuta nsanga imwe bayigura F1400 maze nishyuye bangarurira F 800. Ubwo nagiye kuyagura mfite F angahe?
1) Niba m 1 y’ijyora igura F 1 600, ubwo m 6 z’iryo jyora zigura F angahe?
2) Gicanda yaguze fanta 12 ku F 350 icupa rimwe. Shaka umubare wa F yishyuye yose hamwe.
3) Umutoza w’ikipe afite abakinnyi 18. Yaguriye buri mukinnyi icupa ry’umutobe. Niba icupa rimwe ry’umutobe rigura F 250 ubwo yishyuye F angahe yose hamwe?
8.9 Amahurizo yo kugabanya amafaranga y’u Rwanda n’umubare ushyitse
Urugero:
Muhoza yari afite F 5 000 aguramo kg 8 z’ibishyimbo. Shaka ikiguzi cya kg imwe y’ibishyimbo.
Nsuzuma ngusuzume
1) Gabanya ku buryo bungana F 4 800 abakozi 4.Buri wese uzamuha F angahe?
2) Gahima yahembye abana be 5 ku buryo bungana.Buri wese yamuhembye F angahe niba yarakoresheje F 4 500?
Nsobanukiwe ko:
Iyo ukora amahurizo yo kugabanya amafaranga ubanza kwerekana ibyo baguhaye mu ihurizo. Ugakurikizaho ibyo bakubaza. Hanyuma ukagabanya ibyo baguhaye kugira ngo ubone igisubizo.
Reka nisuzume
1) Naguze amakaye 4 ku F 4 400. Ubwo buri kayenayiguze ku F angahe?
2) Abayede 3 bahembwe F 3 900 yo kugabana ku buryobungana. Ubwo buri muyede yahawe F angahe?
1) Umuganwa yaguze amacupa 9 y’umutobe w’ibitoki ku F 4 500. Buri cupa ry’umutobe w’ibitoki yariguze ku F angahe?
2) Karangwa yacuruje kg 7 z’umuceri ku F 4 900. Ubwo kg 1 y’umuceri yayigurishaga ku F angahe?
3) Niba l 5 z’amata zigura F 2 250 ubwo l 1 igura F angahe?
4) Amacupa 9 ya fanta agura F 2 250. Ubwo icupa rimwe rigura F angahe?
8.10 Kugura no kugurisha
Igikorwa
Mwitegereze ibicuruzwa biri muri iri duka maze mukore imyitozo
1) Shaka igiciro cy’amacupa 5 y’umutobe.
2) Bagutumye L 3 z’amavuta na L1 y’amata wakwishyura F angahe?
3) Shaka F Mahame yishyuye niba yaraguze kg 2 z’isukari n’imiti 4 y’isabune.
4) Nagiye kugura akadobo 1 ka omo n’ibiro 4 by’ibishyimbo bangarurira F 1 000. Ubwo nari nishyuye F angahe?
5) Twagiye gusura umuvandimwe tumushyira amacupa 3 y’umutobe, agakarito 1 k’amata na kg 1 y’isukari. Ubwo twishyuye F angahe?
8.11 Akamaro ko kuzigama
Igikorwa cya 1
Musome inkuru ikurikira nimurangiza musubize ibibazo. Ababyeyi ba Hirwa bamuhaye ibibazo by’imibare, maze bamusezeranya ko nabikora byose atibeshye bamuhemba F 2 000. Arabikora, bamukosoye basanga yabikoze byose kandi neza. Birabashimisha bamuha igihembo ke. Nyirarume na nyirasenge bari aho na bo birabashimisha buri wese amuhemba F 1 000. Ayabika mu gasanduku kari gafatanye n’igitanda ke. Hashize iminsi abwira ababyeyi be ko ashaka kugura inkoko 2 akazorora. Baramwemerera bamufasha kuzihitamo arazigura arazorora. Hashize umwaka amaze kugira inkokokazi 12 n’amasake 8. Ababyeyi be baje kurwara yose bari bafite bayivuzamo. Igihe cy’amashuri kigeze Hirwa abura ibikoresho by’ishuri. Asaba nyirarume ko yajyana amasake 6 ku isoko akayagurisha akamugurira ibikoresho by’ishuri maze amafaranga asigara akayaguramo ibyo kondora ababyeyi be bari barazahajwe n’indwara.
Ibibazo ku nkuru
1) Kugira ngo Hirwa agire inkokokazi 12 n’amasake 8 yahereye ku nkoko zingahe?
2) Amafaranga yatangije yayakuye he? Ni angahe?
3) Kugira ngo Hirwa agire inkokokazi 12 n’amasake 8 byamufashe igihe kingana iki?
4) Hirwa abuze ibikoresho by’ishuri yabigenje ate?
5) Ni iki Hirwa yafashije ababyeyi be mu gihe bari barwaye?
6) Ni irihe somo uvanye muri iyi nkuru?
7) Hari inkuru isa n’iyi waba warumvise? Yibwire bagenzi bawe.
8) Nyuma yo gusoma iyi nkuru ufashe uwuhe mugambi?
Igikorwa cya 2
Buri wese asobanurire abandi uko umuryango we wizigamira.
Nsobanukiwe ko:
Kuzigama ari umuco mwiza kuko ibyo uzigamye bikugoboka.
Kuzigama bituma umuntu agira ikerekezo gifite intego.
Uzigama uteganyiriza igihe kizaza ugamije kuziteza imbere.
Igikorwa cya 3
Garagaza ibyo wakora baguhaye amafaranga 5 000 kugira ngo uzigamire igihe kizaza.
8.12 Udushinga duciriritse twunguka
Igikorwa cya 1
Musome urutonde rw’udushinga duciriritse twunguka dukurikira maze muhitemo utwunguka kurusha utundi mubisobanure.
1) Guhumba ibishyimbo mu mirima iwacu bamaze gusaruramo ibyo mvanyemo nkabigurisha F 3 000 nkaguramo inkoko nkayorora.
2) Kubika amafaranga 2 000 bampaye nk’impano nkazayaguramo agakwavu nkakorora.
3) Kwiharika akarima k’imboga nka karoti n’amashu umusaruro mvanyemo nkawugurisha F 4 000.
4) Gukora ibikinisho nkajya mbigurisha n’abana babishaka. Igikinisho kimwe nkakigurisha F 100.
5) Gutera igiti k’imbuto cy’avoka cyazera nkazajya nsoroma avoka nkazigurisha. Amafaranga nkuyemo nkayagura ibikoresho by’ishuri
Igikorwa cya 2
Mufatanye gushaka utundi dushinga duciriritse twunguka mwakora ku rwego rwanyu tutabonetse mu rutonde rwo mu gikorwa cya 1.
Nsobanukiwe ko:
Buri wese afite ubushobozi bwo gukora agashinga gaciriritse kunguka kamufasha kubona ibyo akeneye byose no kwiteza imbere.
Nsuzuma ngusuzume
Tegura agashinga gaciriritse kunguka ugiye gukora.
Gararagaza uko uzagakora n’ibyo uteganya kunguka muri ako gashinga.
8.13 Isuzuma risoza umutwe wa 8
a) Uguze umugati, L 1 y’amata, na L1 y’ubuto wakwishyura F angahe?
b) Munezero afite F 5 000 kandi arashaka guhaha kg 6 z’ibishyimbo, L 1 y’ubuto na kg 2 z’isukari. Ubwo arabura F angahe?
c) Ireme yaguze kg 1 y’umuceri, kg 1 y’isukari na kg 2 z’ubunyobwa bamugarurira F 100. Ubwo yari yagiye guhaha afite F angahe?
d) Uguze igicuruzwa kimwekimwe kuri buri bicuruzwa by’ibitembabuzi kuri iyi ndangabiciro wakwishyura F angahe?
3) Gabanya ku buryo bungana F 4 800 akakozi 4. Buri wese uzamuha F angahe?
4) Muhoza bamuhaye F 3 500 ngo age kugura ikanzu agezeyo asanga igura F 5 000. Ubwo yaburaga F angahe ngo ayigure?
- Umutwe wa 9:Ingero z’igiheUmutwe wa 9:Ingero z’igiheLabel: 1Umutwe wa 9:Ingero z’igihe
9.1 Gusoma ukavuga igihe kerekanwa n’isaha
A. Isaha yuzuye
Igikorwa cya 1
Mwitegereze amasaha muvuge igihe yerekana:
Nsobanukiwe ko:
1. Isaha y’inshinge
Isaha iba yuzuye iyo urushinge rugufi rubara amasaha ruri ku mubare uwo ari wo wose uri mu isaha naho urushinge rurerure rubara iminota n’agashinge karekare cyane kabara amasegonda bihuriye ku mubare 12.
2. Isaha y’imibare
Umubare uhagarariye amasaha ukurikirwa n’utudomo tubiri hanyuma hakaza amazeru abiri.
Nsuzuma ngusuzume
Shushanya isaha y’inshinge n’iy’imibare ibara:
a) Saa saba b) Saa tanu
Itegereze amasaha uvuge igihe
B. Isaha irengaho iminota 30
Igikorwa
Mwitegereze amasaha muvuge igihe yerekana:
Nsobanukiwe ko:
1. Isaha y’inshinge Isaha iba irengaho iminota mirongo itatu iyo urushinge rubara amasaha ruri hagati y’imibare 2 iri mu isaha naho urushinge rurerure rubara iminota ruri ku mubare 6. Usoma umubare ubanziriza urushinge rubara amasaha ukongeraho iminota 30.
2. Isaha y’imibare Umubare uhagarariye amasaha ukurikirwa n’utudomo tubiri natwo tugakurikirwa n’umubare 30.
Reka nisuzume
1) Shushanya isaha y’inshinge yerekana:
a) Saa sita n’igice b) Saa tatu n’igice
2) Shushanya isaha y’imibare ibara
a) Saa kumi n’imwe n’igice b) Saa saba n’igice
C. Isaha iburaho iminota 30
Igikorwa
Mwitegereze amasaha muvuge igihe yerekana:
Nsobanukiwe ko:
1. Isaha y’inshinge
Bavuga ko isaha iburaho iminota mirongo itatu (30) iyo urushinge rugufi rubara amasaha ruri hagati y’imibare 2 iri mu isaha naho urushinge rurerure rubara iminota ruri ku mubare 6. Usoma umubare ukurikira urushinge rubara amasaha ukongeraho ko ibura iminota mirongo itatu (30).
2. Isaha y’imibare
Umubare uhagarariye amasaha ni umubare ukurikira uri mu isaha ukurikirwa n’utudomo tubiri natwo tugakurikirwa n’umubare 30.
Nsuzuma ngusuzume
Mwitegereze amasaha muvuge igihe yerekana
Shushanya isaha y’inshinge n’iy’imibare werekana:
a) Saa munani zibura iminota 30
b) Saa kumi n’ebyiri zibura iminota 30
D. Isaha irengaho iminota 15
Igikorwa
Mwitegereze amasaha muvuge igihe yerekana
Nsobanukiwe ko:
1. Isaha y’inshinge
Isaha iba irengaho iminota cumi n’itanu iyo urushinge rugufi rubara amasaha rurenze gatoya ku mubare uwo ari wo wose uri mu isaha naho urushinge rurerure rubara iminota ruri ku mubare 3.
2. Isaha y’imibare
Umubare uhagarariye amasaha uba ukurikiwe n’utudomo tubiri natwo tugakurikirwa n’umubare 15.
Nsuzuma ngusuzume
Mwitegereze amasaha muvuge igihe yerekana:
Reka nisuzume
1) Shushanya isaha y’inshinge yerekana:
a) Saa saba na cumi n’itanu
b) Saa yine n’igice
2) Shushanya isaha y’imibare ibara
a) Saa kumi n’imwe na cumi n’itanu
b) Saa saba na cumi n’itanu
Umwitozo
Shushanya isaha y’inshinge n’iy’imibare yerekana:
a) 8:00
b) 10:30
c) 11:15
d) 6:30
E Isaha iburaho iminota 15
Igikorwa
Mwitegereze amasaha muvuge igihe yerekana:
Nsobanukiwe ko:
1. Isaha y’inshinge
Bavuga ko isaha iburaho iminota cumi n’itanu (15) iyo urushinge rugufi rubara amasaha rurenze gatoya ku mubare uwo ari wo wose uri mu isaha naho urushinge rurerure rubara iminota ruri ku mubare 9. Icyo gihe usoma umubare ukurikira uriho urushinge rubara amasaha ukongeraho ko ibura iminota cumi n’itanu (15).
2. Isaha y’imibare
Umubare uhagarariye amasaha uba ukurikiwe n’utudomo tubiri natwo tugakurikirwa n’umubare 45.
Nsuzuma ngusuzume
Mwitegereze amasaha muvuge igihe yerekana:
1) Shushanya isaha y’inshinge yerekana:
a) Saa mbiri zibura iminota 15
b) Saa kumi n’imwe zibura iminota 15
2) Ni gihe ki?
a) 12:15
b) 7:15
9.2 Gusoma ukandika igihe kerekanwe ku isaha
Igikorwa cya 1
Musome mwandike igihe kerekanwe n’aya masaha y’imibare
Nsobanukiwe ko:
Iyo bandika isaha bandika umubare w’isaha ugakurikirwa n’utudomo tubiri hagakurikiraho umubare w’iminota.
Nsuzuma ngusuzume
Mwitegereze, musome hanyuma mwandike amasaha yerekanwe mu mibare no mu magambo.
1) Andika mu mibare no mu magambo igihe kerekanwe n’amasaha akurikira:
2) Shushanya amasaha y’inshinge yerekana:
a) 10:45 c) Saa saba na 15
b) Saa munani na 30 d) 6:00
9.3 Indangaminsi
Igikorwa cya 1
Mwitegereze indangaminsi y’umwaka wa 2018 musubize ibibazo.
3) Umwaka wa 2018 ufite ibyumweru bingahe?
4) Umwaka wa 2018 ufite iminsi ingahe?
5) Mwandike amatariki akurikira:
a) Amatariki y’amavuko yanyu
b) Amatariki mwafungiyeho igihembwe cya mbere
c) Amatariki mwafunguriyeho igihembwe cya 2
Igikorwa cya 2
Mwigane indangaminsi ya 2018 muyishushanye mugarukire ku mezi 4 abanza.
9.4 Umwaka usanzwe n’umwaka udasanzwe
Igikorwa cya 1
Mwifashishe indangaminsi, muganire ku myaka ikurikira maze muvuge iminsi igize ukwezi kwa Gashyantare.
a) Umwaka wa 2018
b) Umwaka wa 2017
c) Umwaka wa 2016
d) Umwaka wa 2015
Nsobanukiwe ko:
– Imyaka ya 2015, 2017, na 2018 ari imyaka isanzwe
– Umwaka usanzwe uba ufite ukwezi kwa Gashyantare gufite iminsi 28.
– Umwaka usanzwe ugira iminsi 365.
– Umwaka usanzwe ntabwo ugabanyika na 4
– Umwaka wa 2016 ni umwaka udasanzwe
– Umwaka udasanzwe uba ufite ukwezi kwa Gashyantare gufite iminsi 29.
– Umwaka udasanzwe ugira iminsi 366.
– Umwaka udasanzwe ugabanyika na 4. Ese muri iyi myaka ni uwuhe ugabanyika na 4?
Igikorwa cya 2
Itegereze urugero uvuge imyaka isanzwe iri mbere ya 2018.
Urugero:
Umwaka wa 2018 ni umwaka usanzwe, ufite iminsi 365
Umwaka wa 2016 wari umwaka udasanzwe ufite iminsi 366.
1) Hitamo imyaka isanzwe muri iyi ikurikira:
a) 1990 c) 1994 e) 1993
b) 1992 d) 1995 f) 1991
2) Vuga imyaka idasanzwe iri muri iyi ikurikira:
a) 1990 c) 1998 e) 1994
b) 1996 d) 1992 f) 1999
3) Shaka imyaka idasanzwe iri hagati ya 1998 na 2021
9.5 Guhindura imyaka mu mezi
Igikorwa
Mwitegereze ibyakozwe ku rugero maze musobanure.
Urugero: Imyaka 6 ingana n’amezi angahe?
Umwaka 1 ungana n’amezi 12
Imyaka 6 ingana n’amezi 12 × 6 = Amezi 72
Nsobanukiwe ko:
Iyo uhindura imyaka mu mezi ufata amezi 12 agize umwaka ukayakuba n’umubare w’imyaka baguhaye.
Nsuzuma ngusuzume
Reka nisuzume
9.6 Guhindura ibyumweru mu minsi
Igikorwa
Mwitegereze ibyakozwe ku rugero maze musobanure.
Urugero: Ibyumweru 3 = Iminsi ingahe?
Icyumweru 1 kingana n’iminsi 7
Ibyumweru 3 bingana n’iminsi 7 × 3 ni iminsi 21
Nsobanukiwe ko:
Iyo uhindura ibyumweru mu minsi ufata iminsi 7 igize icyumweru ukayikuba n’umubare w’ibyumweru baguhaye.
Nsuzuma ngusuzume
Reka nisuzume
9.7 Guhindura iminsi mu masaha
Igikorwa
Mwitegereze ibyakozwe ku rugero maze musobanure.
Urugero: Iminsi 2 ingana n’amasaha angahe?
Umunsi 1 ungana n’amasaha 24
Iminsi 2 ingana n’amasaha 24 × 2 ni amasaha 48
Nsobanukiwe ko:
Iyo uhindura iminsi mu masaha ufata amasaha agize umunsi ari yo 24 ukayakuba n’umubare w’iminsi baguhaye.
Nsuzuma ngusuzume
Reka nisuzume
9.8 Gahunda z’ibikorwa
A. Gahunda y’ibikorwa bya buri munsi
Igikorwa cya 1
Mwitegereze gahunda y’ibikorwa bya buri munsi bya Muhoza muyigereranye n’ibyo musanzwe mukora.
Igikorwa cya 2
Ukurikije gahunda y’ibikorwa bya Muhoza umaze kubona, kora gahunda y’ibikorwa byawe by’ejo.
B. Gahunda y’ibikorwa bya buri cyumweru
Igikorwa cya 1
Mwitegereze gahunda y’ibikorwa bya buri cyumweru bya Mugisha muyigereranye n’ibyo musanzwe mukora.
Igikorwa cya 2
Ukurikije gahunda y’ibikorwa bya Mugisha umaze kubona, kora gahunda y’ibikorwa byawe by’icyumweru gitaha.
C. Gahunda y’ibikorwa by’ukwezi
Igikorwa cya 1
Mwitegereze gahunda y’ibikorwa bya buri kwezi bya Kamariza muyigereranye n’ibyo musanzwe mukora.
Igikorwa cya 2
Ukurikije gahunda y’ibikorwa bya Kamariza umaze kubona, kora gahunda y’ibikorwa byawe by’ukwezi gutaha.
Nsobanukiwe ko:
Gukora gahunda y’ibyo ukora mbere yo kubikora bigufasha kubahiriza igihe neza. Gukoresha igihe neza bituma udatakaza umwanya.
Gukora gahunda y’ibikorwa bigufasha gukora neza ufite intego.
9.9 Isuzuma risoza umutwe wa 9
1) Soma wandike igihe kerekanwe kuri aya masaha
4) Hitamo imyaka isanzwe muri iyi ikurikira
a) 2000 c) 2002 e) 2005
b) 2004 d) 2007 f) 2008
5) Vuga imyaka idasanzwe iri muri iyi ikurikira
a) 2000 c) 2010 e) 2012
b) 2016 d) 2019 f) 2008
6) Shaka imyaka idasanzwe iri hagati ya 2010 na 2030
- Umutwe wa 10: Amoko y’imirongo n’imfuruka.Umutwe wa 10: Amoko y’imirongo n’imfuruka.Label: 1Umutwe wa 10: Amoko y’imirongo n’imfuruka.
10.1 Amoko y’imirongo
A. Imirongo igororotse
Igikorwa cya 1
Mwitegereze imirongo ikurikira muvuge ibiyiranga.
Igikorwa cya 2
a) Mwifashishije uducamurongo muce imirongo iteye nk’iyo mumaze kwitegereza mu gikorwa cya 1;
b) Muyice nta kintu mwifashishije kindi uretse ikaramu n’urupapuro;
c) Mugereranye munaganire kuri iyo mirongo yo muri a) n’iyo muri b).
Nsobanukiwe ko:
Imirongo igiye umujyo umwe ari imirongo igororotse.
B. Imirongo iteganye
Igikorwa cya 1
Mwitegereze imirongo ikurikira muvuge ibiyiranga
Reka nisuzume
Ifashishe agacamurongo uce imirongo ibiri igororotse uheze urupapuro urebe niba ihura.
Nsobanukiwe ko:
Imirongo igororotse iteganye idashobora guhura. Imirongo igororotse iteganye iba ifite intera ingana hagati yayo.
Nsuzuma ngusuzume
1. Mwifashishije agacamurongo muce imirongo itatu itatu iteganye.
2. Mwitegereze mu ishuri mwerekane ibintu biriho imirongo iteganye muvuge ibindi musanzwe muzi biriho iyo mirongo.
C. Imirongo inyuranamo igakora imfuruka zigororotse
Igikorwa cya 1
Mwitegereze imirongo ikurikira muvuge ibiyiranga
Reka nisuzume
Mwifashishije agacamurongo muce imirongo ibiri igororotse uhagaze n’utambitse, ihura igakora imfuruka igororotse.
Nsobanukiwe ko:
Imirongo inyuranamo iba igiye mu byerekezo bitandukanye.
Umurongo ugororotse utambitse n’umurongo ugororotse uhagaze iyo inyuranamo bikora imfuruka 4 zigororotse.
Nsuzuma ngusuzume
a) Mushushanye imirongo inyuranamo igakora imfuruka zigororotse.
b) Mukoreshe amarati, uduti, utubuye n’amakaramu mukore imirongo ibiri igororotse ihura igakora imfuruka igororotse.
D. Imirongo inyuranamo igakora imfuruka zagutse n’izifunganye
Igikorwa cya 1
Mwitegereze imirongo ikurikira muvuge ibiyiranga
Reka nisuzume
Ifashishe agacamurongo uce imirongo ibiri igororotse iberamye,inyuranamo igakora imfuruka zagutse n’izifunganye.
Nsobanukiwe ko:
Imirongo inyuranamo iba igiye mu byerekezo bitandukanye.
Umurongo ugororotse uberamiye iburyo n’uberamiye ibumoso iyo bihuye bikora imfuruka 4. Ebyiri zagutse n’ebyiri zifunganye.
Nsuzuma ngusuzume
a) Shushanya imirongo igororotse inyuranamo igakora imfuruka zagutse n’izifunganye.
b) Koresha amarati, uduti, utubuye amakaramu ukore imirongo 2 igororotse iberamye ihura igakora imfuruka.
Itegereze uvuge amazina y’imirongo wabajijwe
10.2 Amoko y’imfuruka
A. Imfuruka igororotse
Igikorwa cya 1
Mwitegereze iyi shusho muvuge ibyo mubonaho.
Reka nisuzume
Ifashishije ingeramfuruka ushushanye imfuruka igororotse.
Nsobanukiwe ko:
Imfuruka igororotse ikorwa n’imirongo 2 igororotse.
Uhagaze n’utambitse. Imfuruka igororotse ipima dogere 90.
Nsuzuma ngusuzume
a) Shushanya imfuruka 4 zigororotse.
b) Erekana ibintu biriho imfuruka igororotse biri mu ishuri cyangwa uvuge ibindi usanzwe uzi biriho iyo mfuruka.
B. Imfuruka ifunganye
Igikorwa cya 1
Mwitegereze iyi shusho muvuge ibyo mubonaho
Reka nisuzume
Ifashishe agacamurongo n’ingeramfuruka ushushanye imfuruka ifunganye.
Nsobanukiwe ko:
Imfuruka ifunganye ikozwe n’imirongo igororotse umwe uhagaze cyangwa utambitse n’undi uberamye inyuranamo ku buryo ihura isa n’ifungana. Ibipimo by’imfuruka zifunganye biba munsi ya dogere 90.
Igikorwa cya 3
a) Mushushanye imfuruka 4 zifunganye.
b) Mwerekane ibintu biriho imfuruka ifunganye biri mu ishuri cyangwa ibindi bintu muzi.
C. Imfuruka yagutse
Igikorwa cya 1
Mwitegereze iyi shusho muvuge ibyo mubonaho.
Reka nisuzume
Ifashishe ingeramfuruka ushushanye imfuruka yagutse.
Nsobanukiwe ko:
Imfuruka yagutse ikozwe n’imirongo igororotse umwe uhagaze cyangwa utambitse n’undi uberamye inyuranamo ku buryo ihura ikora inguni yagutse. Ibipimo by’imfuruka zagutse biba biri hagati dogere 90 na dogere 180.
Igikorwa cya 3
a) Shushanya imfuruka 4 zagutse.
b) Erekana ibintu biriho imfuruka zagutse biri mu ishuri cyangwa ibindi bintu usanzwe uzi.
10.3 Uko bakoresha ingeramfuruka bapima imfuruka
Igikorwa cya 1
Mwitegereze iyi shusho muvuge ibyo muyibonaho.
Nsobanukiwe ko:
– Ushyira ingeramfuruka ku nshonda (aho imirongo ikora imfuruka ihurira) y’imfuruka uteganyije na dogere 90.
– Ureba ko umurongo wa mbere w’imfuruka yawe unyura muri dogere zeru na dogere 180.
– Usoma dogere ziringaniye n’umurongo wa kabiri w’imfuruka yawe.
Reka nisuzume
Itegereze uvuge ingano y’imfuruka iri kuri buri ngeramfuruka:
Reka nisuzume
Itegereze uvuge ingano y’imfuruka iri kuri buri ngeramfuruka:
a) b)
c) d)
Nsuzuma ngusuzume
Koresha agacamurongo n’ingeramfuruka ushushanye
imfuruka zifite dogere:
a) 75 c) 125 e) 76
b) 90 d) 150 f) 35
1) Koresha ingeramfuruka upime ingano y’imfuruka ikozwe n’inshinge z’isaha (urubara amasaha n’urubara iminota).
2) Itegereze mbere yo gushushanya imfuruka wabajijwe hanyuma uvuge amazina yazo unazipime ukoresheje ingeramfuruka
A• •B C• •D
E• •F G• •H
I• •J K• •L
a) Huza B na A hamwe na B na E
b) Huza J na K hamwe na J na F
c) Huza G na B hamwe na G na H
d) Huza I na J hamwe na I na F
10.4 Kugereranya imfuruka bapima
A. Imfuruka igororotse n’ifunganye
Reka nisuzume
Shushanya imfuruka igororotse n’ifunganye, uzipime hanyuma ugereranye ibipimo byazo.
Nsobanukiwe ko:
Imfuruka igororotse iruta imfuruka ifunganye.
Nsuzuma ngusuzume
Shushanya imfuruka 2 zigororotse n’izindi 2 zifunganye, koresha ingeramfuruka uzipime hanyuma ugereranye ibipimo byazo.
B. Imfuruka igororotse n’iyagutse
Reka nisuzume
Shushanya imfuruka igororotse n’iyagutse, uzipime hanyuma ugereranye ibipimo byazo.
Nsobanukiwe ko:
Imfuruka igororotse irutwa n’imfuruka yagutse
Nsuzuma ngusuzume
Shushanya imfuruka 2 zigororotse n’izindi 2 zagutse, ukoreshe ingeramfuruka uzipime hanyuma ugereranye ibipimo byazo.
C. Imfuruka ifunganye n’iyagutse
Igikorwa cya 2
Shushanya imfuruka igororotse n’iyagutse, uzipime hanyuma ugereranye ibipimo byazo.
Nsobanukiwe ko:
Imfuruka ifunganye irutwa n’imfuruka yagutse
Nsuzuma ngusuzume
Shushanya imfuruka 2 zifunganye n’izindi 2 zagutse, ukoreshe ingeramfuruka uzipime hanyuma ugereranye ibipimo byazo.
Reka nisuzume
Shushanya amasaha y’inshinge akurikira upime imfuruka zikozwe n’inshinge zibara iminota n’amasaha.
a) Isaha ibara saa kenda na mirongo ine n’itanu
b) 8:30
c) Isaha ibara saa tanu na cumi n’itanu.
Pima izi mfuruka zikurikira ugereranye ingano yazo ukoresheje >, < na =
10.5 Isuzuma risoza umutwe wa 10
1) Koresha ingeramfuruka upime ingano y’izi mfuruka
2) Itegereze imirongo ikurikira uvuge amazina yazo
3) Vuga amazina y’imfuruka zikurikira
4) Koresha agacamurongo n’ingeramfuruka ushushanye imfuruka zifite:
a) 56° b) 98° c) 170° d) 135°
5) Shushanya
a) Imirongo inyuranamo igakora imfuruka zigororotse.
b) Imirongo ibiri iteganye.
c) Imirongo inyuranamo igakora imfuruka zagutse n’izifunganye.
6) Subiza yego cyangwa oya
a) Imfuruka igororotse iruta imfuruka yagutse.
b) Imirongo igororotse iteganye ntishobora guhura.
c) Imfuruka igororotse iruta imfuruka ifunganye.
d) Imfuruka yagutse iruta imfuruka ifunganye.
- Umutwe wa 11:Kare, urukiramende, mpandeshatu n’uruzigaUmutwe wa 11:Kare, urukiramende, mpandeshatu n’uruzigaLabel: 1Umutwe wa 11:Kare, urukiramende, mpandeshatu n’uruziga
11.1 Kare
A. Ibiranga Kare
Igikorwa cya 1
Mwitegereze ishusho mwigane ibirimo gukorwa
Igikorwa cya 2
Mwitegereze iyi kare muvuge amazina y’imirongo ihuza inyuguti ziyiriho.
Nsobanukiwe ko:
Kare ni ikinyampande, kandi irangwa n’ibi bikurikira:
– Kare igira impande 4 zingana ( A C = CE = EG = AG)
– Kare igira imfuruka 4 zigororotse
– Kare igira ingwagati 2 zingana (BF) na (HD)
– Kare igira impuzampembe 2 zingana (AE) na (CG)
– Ingwagati ni imirongo igororotse igabanyamo impande za kare ziteganye mo ibice bibiri bingana.
– Impuzampembe ni imirongo igorotse ihuza imfuruka 2 za kare ziteganye. Ingwagati n’impuzampembe bya Kare bihurira mu kadomo rwagati k’imbere muri kare.
Igikorwa cya 3
Shushanya kare ifite cm 8 uyishyiremo ibi bikurikira:
a) Ingwagati
b) Impuzampembe
Reka nisuzume
1) Mu mashusho akurikira garagazamo kare
2) Shushanya kare ifite cm 4 z’uruhande muyishyiremo
ingwagati n’impuzampembe.
Nsuzuma ngusuzume
1) Mushake kandi muvuge ibintu bifite ishusho ya kare mu ishuri ryanyu.
2) Mukore amashusho ya kare mu mpapuro cyangwa ibikarito, muyakate neza, muyamanike mu ishuri ryanyu.
1) Muvuge ibintu muzi bigira ishusho ya kare.
2) Itegereze usubize ibibazo
B. Umuzenguruko wa Kare
Igikorwa
– Mushushanye kare ifite cm 12 z’uruhande
– Muyizengurutseho akagozi. Mugakate
– Mupime buri ruhande muteranye uburebure bw’impande
zose uko ari 4
– Mupime n’uburebure bwa ka kagozi
– Musobanure ibyo mubonye
Nsobanukiwe ko:
– Umuzenguruko wa kare ungana n’igiteranyo cy’uburebure bw’impande 4 ziyigize.
– Umuzenguruko = Uruhande + uruhande + uruhande
+ uruhande.
– Umuzenguruko wa kare ungana n’uburebure bw’uruhande rumwe inshuro 4.
– Umuzenguruko = Uruhande × 4
– Uruhande rwa kare rungana n’umuzenguruko wa
kare ugabanyije 4.
– Uruhande = Umuzenguruko : 4
Urugero:
1) Shaka umuzenguruko wa kare ifite cm 75 z’uruhande.
2) Shaka uburebure bw’uruhande rumwe rwa kare ifite cm 900 z’umuzenguruko.
Reka nisuzume
Shaka umuzenguruko wa kare ifite
a) cm 125 z’uruhande
b) cm 407 z’uruhande
c) cm 602 z’uruhande
d) cm 765 z’uruhande
Nsuzuma ngusuzume
1) Shaka uburebure bw’uruhande rumwe rwa kare ifite:
a) cm 640 z’umuzenguruko
b) cm 196 z’umuzenguruko
c) cm 312 z’umuzenguruko
d) cm 676 z’umuzenguruko
2) Shaka umuzenguruko w’ikibanza cya kare gifite uruhande rupima m 80.
3) Shaka uburebure bw’uruhande rw’umurima wa kare ifite m 1 700 z’umuzenguruko.
1) Shaka umuzenguruko w’idirishya rya kare rifite uruhande rwa cm 145
2) Shaka uburebure bw’uruhande rumwe rw’ikibanza gifite ishusho ya kare ifite m 160 z’umuzenguruko.
3) Shaka umuzenguruko wa kare zikurikira
11.2 Urukiramende
A. Ibiranga urukiramende
Igikorwa cya 1
Mwitegereze ishusho mwigane ibyo barimo gukora
Igikorwa cya 2
Mushushanye urukiramende rufite cm 16 z’uburebure na cm 12 z’ubugari murwitegereze hanyuma muvuge ibiranga urukiramende. Mugendeye ku mpande zarwo n’imfuruka zarwo.
Igikorwa cya 3
Mwitegereze ishusho muvuge ibiranga urukiramende.
Nsobanukiwe ko:
– Urukiramende ari ishushongero rigira impande 4. Ebyiri ebyiri ziteganye zingana (Uruhande AC =
uruhande GE naho uruhande A G = uruhande C E).
– Impande ndende kurusha izindi z’urukiramende zitwa uburebure.
– Uruhande AC n’uruhande GE ni uburebure bw’urukiramende ACEG
– Impande ngufi kurusha izindi z’urukiramende zitwa ubugari.
– Uruhande AG n’uruhande CE ni ubugari bw’urukiramende ACEG
– Urukiramende rugira imfuruka 4 zigororotse.
– Urukiramende rugira ingwagati 2 zingana (BF) na (HD)
– Urukiramende rugira impuzampembe 2 na zo zingana (AE) na (CG) ( ebyiri zinganya uburebure,
n’izindi ebyiri zinganya ubugari)
Nsuzuma ngusuzume
Mwitegereze uru rukiramende muvuge amazina y’imirongo
Reka nisuzume
1) Mushushanye urukiramende rufite uburebure bwa cm 7 n’ubugari bwa cm 5 murushyiremo ingwagati
n’impuzampembe.
2) Mu mashusho akurikira mugaragazemo urukiramende.
1) Shaka ibintu bifite ishusho y’urukiramende mu ishuri
2) Kora amashusho y’urukiramende mu mpapuro cyangwa mu bikarito uyakate neza, uyamanike mu ishuri ryanyu
3) Vuga ibintu uzi bigira ishusho y’urukiramende.
B. Gushaka umuzenguruko w’urukiramende
Igikorwa
– Mushushanye urukiramende rwa cm 20 z’uburebure na cm 10 z’ubugari
– Muruzengurutseho akagozi maze mugakate
– Mupime buri ruhande muteranye uburebure bw’impande zose uko ari 4
– Mupime n’uburebure bwa ka kagozi
– Musobanure ibyo mubonye.
Nsobanukiwe ko:
– Umuzenguruko w’urukiramende ungana n’igiteranyo cy’uburebure bw’impande zose.
– Umuzenguruko = Uburebure (L) + Uburebure (L) + Ubugari (l) + Ubugari (l).
– Umuzenguruko = Uburebure (L) + Ubugari (l) × 2
Urugero:
Shaka umuzenguruko w’urukiramende rufite cm 56 z’ubugari na cm 74 z’uburebure.
Nsuzuma ngusuzume
Shaka umuzenguruko w’urukiramende rufite:
a) Uburebure bwa cm 350 n’ubugari bwa cm 100
b) Uburebure bwa cm 475 n’ubugari bwa cm 215
c) Uburebure bwa cm 564 n’ubugari bwa 245
d) Uburebure bwa cm 368 n’ubugari bwa cm 162
Reka nisuzume
1) Shaka umuzenguruko w’umurima ufite ishusho y’urukiramende rwa m 570 z’uburebure na m 450 z’ubugari.
2) Shaka umuzenguruko w’urugi rw’igipangu rupima cm 750 z’uburebure na cm 250 z’ubugari
1) Shaka umuzenguruko w’urukiramende rufite:
a) Uburebure bwa cm 124 n’ubugari bwa cm 98
b) Uburebure bwa cm 259 n’ubugari bwa cm 198
c) Uburebure bwa cm412 n’ubugari bwa cm 395
2) Shaka umuzenguruko w’ikibanza gifite ishusho y’urukiramende rwa m 63 z’uburebure na m 39 z’ubugari.
3) Shaka umuzenguruko w’ameza yo mu ruganiriro apima cm 250 z’uburebure na cm 150 z’ubugari
11.3 Mpandeshatu
A. Ibiranga mpandeshatu
Igikorwa cya 1
Mwitegereze ishusho muyiganireho muvuge ibiyiranga.
Nsobanukiwe ko:
Mpandeshatu ni ishushongero rigizwe n’impande 3 n’imfuruka 3.
Igikorwa cya 2
Mu mashusho akurikira mugaragazemo mpandeshatu
Igikorwa cya 3
a) Mushake ibintu bifite ishusho ya mpandeshatu mu ishuri ryanyu.
b) Mukore amashusho ya mpandeshatu mu mpapuro cyangwa mu bikarito, muyakate neza, muyamanike mu ishuri ryanyu.
c) Muvuge ibindi bintu muzi bigira ishusho ya mpandeshatu.
B. Amoko ya mpandeshatu
1. Mpandeshatu ndinganire
Igikorwa cya 1
Mwitegereze iyi mpandeshatu, mupime impande n’imfuruka
byayo maze muvuge ibiyiranga.
Nsobanukiwe ko:
Mpandeshatu nyampanga igira:
– Impande 2 zingana (Uruhande AB = Uruhande BC)
– Imfuruka 2 zingana (BAC = BCA).
– Igiteranyo k’imfuruka zose za mpandeshatu ni dogere 180.
Igikorwa cya 2
a) Mushake ibintu bifite ishusho ya mpandeshatu nyampanga biri mu ishuri ryanyu
b) Mukore amashusho ya mpandeshatu nyampanga mu mpapuro cyangwa mu bikarito, muyakate neza,
muyamanike mu ishuri ryanyu
c) Muvuge ibindi bintu muzi bigira ishusho ya mpandeshatu nyampanga.
3. Mpandeshatu nyanguni
Igikorwa cya 1
Mwitegereze iyi mpandeshatu, mupime impande n’imfuruka byayo maze muvuge ibiyiranga.
Nsobanukiwe ko:
Mpandeshatu nyanguni igira:
– Impande 3 zitangana
– Imfuruka 1 igororotse n’imfuruka 2 zifunganye
– Igiteranyo k’imfuruka zose za mpandeshatu ni dogere
Igikorwa cya 2
a) Mushake ibintu bifite ishusho ya mpandeshatu nyanguni biri mu ishuri ryanyu.
b) Mukore amashusho ya mpandeshatu nyanguni mu mpapuro cyangwa mu bikarito, muyakate neza,
muyamanike mu ishuri ryanyu.
c) Muvuge ibindi bintu muzi bigira ishusho ya mpandeshatu nyanguni.
4. Mpandeshatu ibonetse yose
Igikorwa cya 1
Mwitegereze iyi mpandeshatu, mupime impande n’imfuruka byayo maze muvuge ibiyiranga.
Nsobanukiwe ko:
Mpandeshatu ibonetse yose igira:
– Impande 3 zitangana
– Imfuruka 1 yagutse n’imfuruka 2 zifunganye
– Igiteranyo k’imfuruka zose za mpandeshatu ni dogere 180.
Igikorwa cya 2
a) Shaka ibintu bifite ishusho ya mpandeshatu ibonetse yose biri mu ishuri ryanyu.
b) Mukore amashusho ya mpandeshatu ibonetse yose mu mpapuro cyangwa mu bikarito, muyakate neza,
muyamanike mu ishuri ryanyu.
c) Vuga ibintu uzi bigira ishusho ya mpandeshatu ibonetse yose.
Nsuzuma ngusuzume
Vuga amazina y’izi mpandeshatu
Reka nisuzume
Uzuza izi nteruro
a) Igiteranyo k’imfuruka zose za mpandeshatu ni dogere
b) Mpandeshatu ndinganire igira impande zingana n’imfuruka zingana.
c) Imfuruka imwe yo muri mpandeshatu ndinganire ipima dogere
d) Mpandeshatu igira impande ebyiri zingana yitwa
e) Mpandeshatu igira imfuruka imwe igororotse.
f) Mpandeshatu nyampanga igira imfuruka zingana.
B. Umuzenguruko wa mpandeshatu
Igikorwa
Mushushanye mpandeshatu mushatse, mupime buri ruhande rwayo, mwandike igipimo cyarwo, mubiteranye musobanure ibyo mubonye.
Nsobanukiwe ko:
– Umuzenguruko wa mpandeshatu ungana n’igiteranyo cy’uburebure bw’impande 3 ziyigize.
– Umuzenguruko = Uruhande + Uruhande + Uruhande
– Umuzenguruko wa mpandeshatu ndinganire ungana n’uburebure bw’uruhande rumwe ukubye 3.
Umuzenguruko = Uruhande × 3
– Uburebure bw’uruhande rwa mpandeshatu ndinganire bungana n’umuzenguruko wayo ugabanyije 3.
Uruhande = umuzenguruko : 3
Urugero:
Shaka umuzenguruko wa mpandeshatu ifite impande zipima cm 145, cm 172 na cm 159
Nsuzuma ngusuzume
Mushake umuzenguruko wa mpandeshatu ifite impande zikurikira:
a) cm 230, cm 250 na cm 350
b) cm 150, cm 150 na cm 150
c) dm 270, dm 270 na dm 110
d) cm 75, cm 59 na cm 68
Reka nisuzume
1) Shaka umuzenguruko wa mpandeshatu ndinganire ifite cm 97 z’uruhande.
2) Shaka umuzenguruko w’umurima ufite ishusho ya
mpandeshatu ndinganire upima cm 195 z’uruhande.
Shaka umuzenguruko w’izi mpandeshatu
11.4 Uruziga
1. Ibiranga uruziga
Igikorwa cya 1
Mwitegereze amashusho akurikira muvuge ibyo muyabonaho. Buri shusho ifite impande zingahe? Imfuruka zingahe?
Igikorwa cya 2
Mwitegereze iyi shusho, muvuge izina ryayo n’ibiyiranga:
Nsobanukiwe ko:
– Uruziga ari itsinda ry’utudomo turi ku ntera ingana uvuye mu izingiro.
– Iryo tsinda ry’utudomo ni ryo rikora umuzenguruko w’uruziga.
– Izingiro ni akadomo rwagati ko mu ruziga.
Igikorwa cya 3
Mwitegereze mutahure ibigize uruziga munabisobanure.
Nsobanukiwe ko:
– Akarambararo ni akarongo kagororotse kava mu izingiro kakagera ku murongo w’uruziga.
– Umurambararo ni umurongo ugororotse wambukiranya uruziga unyuze mu izingiro
– Umurambararo ungana n’akarambararo inshuro 2.
– Akarambararo kangana n’umurambararo ugabanyije 2.
– Izingiro ni ryo baheraho mu gushushanya uruziga.
Umuzenguruko w’uruziga ni umurongo warwo ufunze.
Igikorwa cya 4
Mushushanye uruziga mukoresheje agacaruziga. Musobanure uko mwabikoze.
Reka nisuzume
1) Shaka ibintu bifite ishusho y’uruziga biri mu ishuri ryawe.
2) Vuga ibindi uzi bifite ishusho y’uruziga
3) Uzuza izi nteruro
a) Umurambararo ni inshuro 2 z’-------
b) Akarambararo ni kimwe cya kabiri cy’----
c) Inshuro 2 z’akarambararo ni--------
d) Akadomo ko hagati mu ruziga kitwa------
e) Umurongo unyura mu izingiro ugabanyamo uruziga ibice 2 bingana witwa-----
Nsobanukiwe ko:
Agacaruziga ari igikoresho gikoreshwa mu gushushanya uruziga. Iyo ushushanya uruziga ukora ibi bikurikira:
– Ugenzura ko aho agacaruziga gafungiye hafunze neza.
– Ushyiramo ikaramu y’igiti ureshyeshya neza n’urushinge rw’agacaruziga warangiza ugafunga neza
– Wandika akadomo kaza kuba izingiro ry’uzuziga rwawe
– Ukoresha agacamurongo ugaca akarambararo k’uruziga
– Ushinga urushinge rw’agacaruziga kawe mu izingiro ry’uruziga rwawe.
– Ufungura agacaruziga kawe maze ugashyira ikaramu y’igiti ku mpera y’akarambararo kawe.
– Uzengurutsa ya karamu y’igiti ushushanya uruziga ariko ugenzura ko urushinge rw’agacaruziga kawe
rutavuye mu izingiro kugeza ugarutse aho wahereye.
Nsuzuma ngusuzume
– Koresha agacaruziga ushushanye uruziga ugaragaze izingiro, akarambararo n’umurambararo warwo.
– Ca uruziga ruriho izingiro, akarambararo n’umurambararo ku mpapuro cyangwa ibikarito maze urumanike mu ishuri.
Itegereze uruziga usubize
Vuga amazina y’imirongo ikurikira:
a) OD ni ------- d) AC ni-----
b) OB ni ------ e) OE ni-----
c) BE ni ------ f) OA ni-----
11.5 Isuzuma risoza umutwe wa 11
2) Shushanya:
a) Mpandeshatu ndinganire ifite uruhande rwa cm 16
b) Kare ifite uruhande rwa cm 13
c) Urukiramende rufite cm 10 z’ubugari na cm 20 z’uburebure
d) Uruziga rufite cm 8 z’akarambararo
3) Shaka umuzenguruko wa :
a) Kare ifite cm 135 z’uruhande
b) Urukiramende rufite cm 364 z’uburebure na cm 132 z’ubugari
c) Mpandeshatu ifite impande zingana na cm 605,
cm 235, cm 385
4) Subiza yego cyangwa oya
a) Kare igira imfuruka zagutse
b) Urukiramende rugira imfuruka zigororotse
c) Akarambararo karuta umurambararo
d) Izingiro ni akadomo rwagati ko mu ruziga.
e) Mpandeshatu nyampanga igira impande 3 zingana.
5) Shaka umuzenguruko w’aya mashusho
- Umutwe wa 12:IkinyatuzuUmutwe wa 12:IkinyatuzuLabel: 1Umutwe wa 12:Ikinyatuzu
12.1 Ibiranga ikinyatuzu
Igikorwa cya 1
Mwitegereze ikinyatuzu gikurikira, mukigane, muvuge ubwoko bw’imirongo icyubatse n’umubare wayo.
Nsobanukiwe ko:
– Ikinyatuzu kigizwe n’imirongo ihagaze yitwa inkingi n’indi itambitse yitwa imbariro.
– Gushyira inomero ku nkingi uhera ibumoso ujya iburyo.
– Gushyira inomero ku mbariro uhera hasi ujya hejuru.
12.2 Kuranga akadomo mu kinyatuzu
gikorwa cya 1
Mwitegereze iki kinyatuzu murange utudomo A, B, C, D na E
Nsobanukiwe ko:
– Ibirango by’akadomo mu kinyatuzu biba bigizwe n’imibare 2.
– Umubare wa mbere werekana inkingi, uwa kabiri werekana urubariro.
Nsuzuma ngusuzume
Mwubake ikinyatuzu kigizwe n’inkingi 6 n’imbariro 6
Mushyiremo utudomo: A (2, 4) B (4, 3) C (3, 2)
Igikorwa cya 2
12.3 Gushushanya amashushongero mu kinyatuzu no kuranga impembe zayo
A. Gushushanya kare mu kinyatuzu
Igikorwa cya 1
Igikorwa cya 2
Shushanya ikinyatuzu kigizwe n’inkingi 10 n’imbariro 10 maze ushyiremo ibi bikurikira:
– Shyira akadomo A ku nkingi ya 3 no ku rubariro rwa 2
– Shyira akadomo B ku nkingi ya 8 no ku rubariro rwa 2
– Shyira akadomo C ku nkingi ya 3 no ku rubariro rwa 7
– Shyira akadomo D ku nkingi ya 8 no ku rubariro rwa 7
– Huza utudomo: A na C D na B C na D A na B
– Muvuge ubwoko bw’ishusho ABDC
Nsobanukiwe ko:
Iyo ushushanya kare mu kinyatuzu ukora ibi bikurikira:
– Banza ushyire utudomo mu mahuriro y’inkingi n’imbariro baguhaye.
– Huza utudomo ukoresheje agacamurongo kugira ngo ubone ishusho wasabwe gushushanya.
Reka nisuzume
Shushanya ikinyatuzu ushaka, ushyiremo ishusho ya kare, hanyuma urange utudomo tugize impembe zayo.
B. Gushushanya Urukiramende mu kinyatuzu
Igikorwa cya 1
Mwitegereze iki kinyatuzu musobanure uko cyubatswe, ibyo kerekana hanyuma mupime impande z’ishusho irimo, kandi muvuge ubwoko bwayo.
Igikorwa cya 2
Mushushanye ikinyatuzu kigizwe n’inkingi 9 n’imbariro 9 maze mushyiremo ibi bikurikira:
– Mushyire akadomo A ku nkingi ya 2 ku rubariro rwa 3
– Mushyire akadomo B ku nkingi ya 8 ku rubariro rwa 3
– Mushyire akadomo C ku nkingi ya 2 ku rubariro rwa 6
– Mushyire akadomo D ku nkingi ya 8 ku rubariro rwa 6
– Muhuze utudomo: A na C D na B
C na D A na B
– Musobanure ibyo mubonye maze mupime impande z’ikinyampande mwashyizemo.
– Muvuge izina ry’ikinyampande mubonye.
Nsobanukiwe ko:
Iyo ushushanya urukiramende mu kinyatuzu ukora ibi:
– Banza ushyire utudomo mu mahuriro y’inkingi n’imbariro baguhaye.
– Huza twatudomo wifashishije agacamurongo kugira ngo ubone ishusho wasabwe gushushanya.
Nsuzuma ngusuzume
Shushanya ikinyatuzu ushaka, ushyiremo ishusho y’urukiramende. Ranga utudomo tugize impembe zayo.
C. Gushushanya mpandeshatu mu kinyatuzu
Igikorwa cya 1
Mwitegereze iki kinyatuzu musobanure uko cyubatswe, ibyo kerekana hanyuma muvuge ubwoko bw’ishusho irimo.
Igikorwa cya 2
Mushushyanye ikinyatuzu kigizwe n’inkingi 8 n’imbariro 8 maze mushyiremo ibi bikurikira:
– Mushyire akadomo A ku nkingi ya 6 ku rubariro rwa 6
– Mushyire akadomo B ku nkingi ya 2 ku rubariro rwa 6
– Mushyire akadomo C ku nkingi ya 2 ku rubariro rwa 2
– Muhuze akadomo A n’akadomo B
– Muhuze akadomo A n’akadomo C
– Muhuze akadomo C n’akadomo B
– Musobanure ibyo mubonye maze muvuge ubwoko bw’ishushongero mwashyizemo.
Nsobanukiwe ko:
Iyo ushushanya mpandeshatu mu kinyatuzu ukora ibi:
– Banza ushyire utudomo mu mahuriro y’inkingi n’imbariro baguhaye.
– Huza twatudomo wifashishije agacamurongo kugira ngo ubone ishusho wasabwe gushyiramo.
Reka nisuzume
– Shushanya ikinyatuzu k’inkingi 7 n’imbariro 7
– Ushyire akadomo A aho urubariro rwa 6 ruhurira n’inkingi ya 6
– Uhere kuri ako kadomo, ubare utundi tuzu 4 umanuka , ushyireho akadomo B
– Uhere kuri ako kadomo ubare utuzu 5 ujya ibumoso, ushyireho akadomo C.
– Uhuze utudomo C na B; B na A; C na A
– Uvuge izina rya mpandeshatu ubonye
Nsuzuma ngusuzume
Mushushanye ikinyatuzu gifite imbariro 10 n’inkingi 10.
Mushushanye mpandeshatu ihuza utu tudomo:
A (4, 6); B ( 2, 2); C ( 6, 2)
Mushushanye ibinyatuzu mushaka, mushyiremo amashusho:
a) Urukiramende b) Kare c) Mpandeshatu
d) Murange utudomo tugize impembe za buri shusho.
Igikorwa cya 3
Muganire musobanura aho bakoresha ikinyatuzu mu buzima busanzwe
12.4 Isuzuma risoza umutwe wa 12
3) Shushanya ikinyatuzu k’inkingi 7 n’imbariro 7 ushyiremo utudomo dukurikira: A (4, 3); B (2, 6); na C (5, 7). Huza utwo tudomo uvuge ishusho ubonye.
- Unit 13: Umubare ubura mu iteranya, ikuramo, ikuba, n’igabanyaUnit 13: Umubare ubura mu iteranya, ikuramo, ikuba, n’igabanyaLabel: 1Unit 13: Umubare ubura mu iteranya, ikuramo, ikuba, n’igabanya
13.1 Gutahura umubare ubura mu iteranya
Igikorwa
Mutahure umubare ubura mukurikije urugero mwahawe
Urugero:
Nsobanukiwe ko:
– Ufata igiteranyo ukavanamo umubare baguhaye.
– Ikinyuranyo ubonye ni wo mubare uba ubura mu iteranya.
Nsuzuma ngusuzume
13.2 Gutahura umubare ubura mu ikuramo
Igikorwa
Mutahure umubare ubura mukurikije urugero mwahawe
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo ushaka umubare ubura mu ikuramo ukora ibi bikurikira:
– Iyo hari imibarwa ibura mu mubare ukurwamo, bafata
uwo mu kinyuranyo bakongeraho uwo mu mubare
ukurwamo.
– Iyo hari imibarwa ibura mu mubare ukurwamo bafata
umubare ukurwamo bagakuramo uwo mu kinyuranyo.
Reka nisuzume
13.3 Gutahura umubare ubura mu ikuba
Igikorwa
Mukurikize urugero mwahawe mutahure umubare ubura
Nsuzuma ngusuzume
13.4 Gutahura umubare ubura mu igabanya
Igikorwa
Mukurikize urugero mwahawe mutahure umubare ubura
Urugero:
Nsobanukiwe ko:
– Iyo umubare ubura ari ikigabanywa ufata ikigabanya
ukagikuba ikigabanyo.
– Iyo umubare ubura ari ikigabanya ufata ikigabanywa
ukagabanya ikigabanyo.
Nsuzuma ngusuzume
a) 648 : • = 8 b) 729 : • = 9 c) 847 : • =7
Reka nisuzume
a) • : 6 = 45 b) • : 5 = 89 c) • : 4 = 125
a) 8795 : • = 5 b) • : 9 = 818 c) 9534 : • = 6
13.5 Inshoza y’inganyagaciro n’ikimenyetso cya =
A. Inganyagaciro mu iteranya
Igikorwa cya 1
Mwitegereze urugero muganire ku byakozwe.
Urugero
Igikorwa cya 2
Mukurikize urugero mwahawe mu gikorwa cya 1mutahure
umubare ubura
a) 80 + 30 = 50 + •
b) 150 + • = 200 + 45
c) 265 + 35 = 250 + •
d) 479 + 51 = 350 + •
Nsuzuma ngusuzume
a) 913 + 97 = 803 + •
b) • +575 = 195 + 875
c) • +597 = 987 + 519
d) 825 + 795 = • + 658
Nsobanukiwe ko:
Iyo ushaka umubare ubura mu iteranya,
– Ufata imibare ibiri yatanzwe yegeranye ukayiteranya.
– Igiteranyo cyayo ukakivanamo umubare ukeneye
uwo biteranywa ngo bingane n’igiteranyo k’iyo ibiri.
– Ikinyuranyo ubona ni cyo wongera kuri wa mubare
maze ibiteranyo by’iyo mibare yombi bikaba bingana.
Reka nisuzume
a) 875 + • = 1 256 + 459
b) • + 1 575 = 2 145 + 875
c) 654 + 746 = • + 598
d) 1 208 + 726 = 576 + •
a) 1 758 + • = 1 526 + 954
b) • + 575 = 215 + 758
c) 1 546 + 647= • + 985
d) 2 801 + 1 267 = 2 567 + •
B. Inganyagaciro mu ikuramo
Igikorwa
Mukurikize urugero mwahawe mutahure umubare ubura.
Urugero:
a) 235 – 45 = 540 – •
b) 725 – • = 600 – 10
c) 430 – 180 = 320 – •
d) 978 – • = 763 –220
Nsuzuma ngusuzume
a) 685 – 175 = 1380 – •
b) 185 – • = 485 – 375
c) • – 459 = 897 – 319
d) • – 975 = 1 785 – 995
Nsobanukiwe ko:
Iyo ushaka umubare ubura mu ikuramo
– Ufata imibare ibiri yatanzwe yegeranye ukayikuramo.
– Ikinyuranyo cyayo ukacyongera ku mubare ukeneye
gukurwamo.
– Hari n’isaba ko ubanza gukuramo imibare 2 yegeranye
maze ikinyuranyo cyayo kikavanwa mu mubare uri
wonyine mu kibazo.
Reka nisuzume
a) 456 – • = 564 – 298
b) 975 – • = 721 – 432
c) • – 345 = 856 – 534
d) • – 548 = 729 – 509
a) 765 – 348 = • – 205
b) 1 234 – 978 = • – 725
c) 1 567 – 1 198 = 2 018 – •
d) 1 453 – 832 = 1 519 – •
C. Inganyagaciro mu ikuba
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Urugero:
Igikorwa cya 2
Mukurikize urugero mwahawe mutahure umubare ubura.
a) 9 × 18 = 6 ×…
b) 36 × 4 = 9 × …
c) • × 7 = 49 × 3
d) • × 5 = 75 × 8
Nsuzuma ngusuzume
a) 5 × • = 25 × 8
b) 9 × • = 72 × 3
c) 88 × 5 = • × 4
d) 98 × 6 = • × 3
Nsobanukiwe ko:
Iyo ushaka umubare ubura mu ikuba:
– Ufata imibare ibiri yatanzwe yegeranye ukayikuba.
– Igikubo cyayo ukakigabanya n’umubare ukeneye
uwo byikuba ngo bingane n’igikubo k’iyo ibiri.
Reka nisuzume
a) 25 × 8 = • × 2
b) 45 × 8 = 6 × •
c) 125 × 4 = • × 5
d) • × 9 = 27× 45
a) • × 7 = 35 × 84
b) 105 × 89 = 5 × •
c) 3 × • = 76 × 9
d) 5 × • = 138 × 65
D. Inganyagaciro mu igabanya
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Urugero:
Igikorwa cya 2
Mukurikize ingero mwahawe mutahure umubare ubura
a) 824 : 8 = • : 4
b) • : 9 = 2016 : 4
c) 945 : 9 = • : 3
d) • : 7 = 2 020 : 5
Nsuzuma ngusuzume
c) 636 : 6 = • : 2
b) 81 : • = 72 : 8
c) 90 : •= 100 :10
d) 546 : 6 = • : 5
Nsobanukiwe ko:
Iyo ushaka umubare ubura mu igabanya:
– Ufata imibare ibiri yatanzwe yegeranye ukayigabanya.
– Ikigabanyo cyayo ukagikuba n’umubare ukeneye uwo
byigabanya ngo bingane n’ikigabanyo k’iyo ibiri.
Reka nisuzume
a) 808 : 8 = • : 4
b) • : 7 = 175 : 5
c) 918 : 9= • : 3
d) • : 5 = 992 : 8
a) • : 9 =1950 : 6
b) • : 8 = 436 : 4
c) 2464 : 8= • : 9
d) 12 : 4 = 9 : •
13.6 Gushaka umubare ubura mu rukurikirane rw’imibare
A. Gushaka intera idahinduka yakoreshejwe mu
rukurikirane rw’imibare ruhera ku mubare muto
rujya ku mubare munini
Igikorwa
Mwitegereze uko bashaka intera idahinduka yakoreshejwe mu
rukurikirane rw’imibare hanyuma mukore imyitozo ikurikira.
Urugero:
Nsuzuma ngusuzume
a) 1 005, 1 075, 1 145 b) 239, 300, 361, 422
Nsobanukiwe ko:
Iyo ushaka intera idahinduka yakoreshejwe mu rukurikirane
rw’imibare ruhera ku mubare muto rujya ku munini, ufata
umubare wa kabiri ugakuramo umubare ubanza bityo bityo.
Reka nisuzume
Shaka intera idahinduka yakoreshejwe muri uru rukurikirane.
a) 295, 333, 371, 409 b) 178, 299, 420, 441
Shaka intera idahinduka yakoreshejwe muri uru rukurikirane.
a) 397, 630, 863, 1096 b) 524, 700, 876, 1052
B. Gushaka intera idahinduka yakoreshejwe mu
rukurikirane rw’imibare ruhera ku mubare munini
rujya ku mubare muto
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Urugero:
Igikorwa cya 2
Mukore imyitozo mukurikije urugero mwahawe.
a) 2 456, 2 306, 2 156 c) 4 032, 3 957, 3 882
b) 1 890, 1 751, 1 612 d) 2 476, 3 000, 3 524
Nsuzuma ngusuzume
a) 2 018, 1 653, 1 288, 923 b) 956, 878, 800, 722
Nsobanukiwe ko:
Iyo ushaka intera idahinduka yakoreshejwe mu rukurikirane
rw’imibare ruhereye ku mubare munini ujya ku muto ufata
umubare ubanza ugakuramo uwukurikiye bityo bityo.
Reka nisuzume
Shaka intera idahinduka yakoreshejwe muri uru rukurikirane
rw’imibare
a) 756, 641, 526, 411 b) 1 879, 1 811, 1 743
Shaka intera idahinduka yakoreshejwe muri uru rukurikirane
rw’imibare:
a) 1 519, 1 470, 1 421 c) 789, 691, 593, 495
b) 976, 937, 898, 859
C. Kuzuza imibare ibura mu rukurikirane rw’imibare
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe.
Urugero:
a) 150, 850, 1 550, 2 250, 2 950, 3 650
Intera idahinduka ni 850 – 150 = 700
b) 125, 250, 375, 500, 625, 750
Intera idahinduka ni 250 – 125 = 125
c) 475, 400, 325, 250, 175, 100
Intera idahinduka ni 475 – 400 = 75
d) 1249, 949, 649, 349, 49
Intera idahinduka ni 1249 – 949 = 300
Igikorwa cya 2
Mwitegere uko buzuza urukurikirane rw’imibare hanyuma
mukore imyitozo.
Nsuzuma ngusuzume
Nsobanukiwe ko:
Iyo wuzuza urukurikirane rw’imibare ubanza gushaka intera
idahinduka yakoreshejwe hanyuma ukagenda uyongeraho
cyangwa uyikuraho bitewe n’uko imibare itondetse.
Reka nisuzume
- Umutwe wa14 :Ibishushanyo byifashishwa mu kubaraUmutwe wa14 :Ibishushanyo byifashishwa mu kubaraLabel: 1Umutwe wa14 :Ibishushanyo byifashishwa mu kubara
14.1 Igishushanyo kifashishwa hagaragazwa
ingano y’ibintu
Igikorwa cya 1
Mwitegereze iyi shusho murebe ibintu biriho maze muvuge umubare wabyo kuri buri tsinda ry’ibintu.
Nsobanukiwe ko:
Mu kureba ingano y’ibintu ku gishushanyo ureba umubare uringaniye na byo.
Igikorwa cya 2
Mwitegereze ibintu biri kuri iki gishushanyo murebe imibare biringaniye muyivuge maze aho bigarukira mushyiremo ibara
14.2 Gukora amatsinda y’ibintu no kubyerekana ukoresheje igishushanyo
Igikorwa
Mwitegereze aya mashusho muvangure ibintu biriho mubigaragaze ku gishushanyo.
14.3 Gusesengura ibishushanyo binyuranye byifashishwa mu mibare hagaragazwa
ingano y’ibintu
Igikorwa
Mwitegereze ibishushanyo bikurikira muvuge ingano y’bintu biriho.
14.4 Gukora igishushanyo kifashishwa mu kubara uhereye ku byatanzwe
Igikorwa cya 1
Mukore igishushanyo kifashishwa mu kubara mugaragazeho ibintu bikurikira:
Igikorwa cya 2
Mukore igishushanyo kifashishwa mu kubara mugaragazeho ibintu bikurikira:
14.5 Isuzuma risoza umutwe wa 14
1) Mushushanye ibikoresho 5 byo mu rugo bitandukanye. Mubishyire ku gishushanyo kigaragaza
ingano y’ibyo mwahisemo, mukore amatsinda atandukanye y’ibikoresho bitanu buri tsinda.
2) Mushushanye ibikoresho 5 byo mu ishuri bitandukanye. Mubishyire ku gishushanyo kigaragaza
ingano y’ibyo mwahisemo, mushyiremo amabara abigaragaza neza. Mukore amatsinda atandukanye
y’ibikoresho.
3) Barura ibikoresho byo mu ishuri ufite maze werekane ingano yabyo wifashishije igishushanyo.
4) Mwitegereze ibishushanyo mubisesengure musobanure ibyo mwabonye:
15. Urugero rw’isuzuma risoza umwaka wa 3
A. Ibara n’amategeko yaryo
1) Andika mu mibare cyangwa mu magambo
a) Ibihumbi ikenda magana atatu na cumi n’umunani:
b) 7 546:
c) Ibihumbi bitanu magana arindwi na mirongo ine na gatatu:
d) 6 978:
2) Andika imibare ikurikira mu mbonerahamwe y’ibara
a) 5 478 b) 7 231 c) 9 768
3) Andika umubare wasesenguwe
a) h 7 j 6 c 5 b8 =
b) h 9 c 6 b 7 =
c) h 6 j9 c 3 b4 =
4) Gereranya ukoresheje <, > na =
a) 7 865
7 685b) 9 456
9 546c) 8 798
8 798d) 5 798
5 9875) Tondeka uhereye ku muto ujya ku munini
a) 5 768, 5 678, 5 786, 5 687
b) 8 769, 8 796, 8 976, 8 967
6) Tondeka uhereye ku munini ujya ku muto
a) 6 435, 6 354, 6 453, 6 345
b) 9 567, 9 675, 9 576, 9 657
7) Shaka igiteranyo
a) 5 785 + 2 957 =
b) 4 678 + 5 099 =
8) Shaka ikinyuranyo
a) 9 123 – 7 987 =
b) 8 005 – 5 678 =
c) 7 234 – 6 789 =
9) Shaka igikubo
a) 82 × 65 = b) 154 × 45 = c) 256 × 38 =
10) Andika mu mahembe ugabanye
a) 7 896 : 4 = b) 8 469 : 9 = c) 9 891 : 7 =
11) Uzuza n’imibare ibura
a) • + 5 678 = 9 876
b) 8 × • = 6 312
c) 8 567 – • = 2 789
d) 9 785 : • = 5
e) 4 567 + 3 578 = • + 5 986
f) 6 754 – • = 7 523 – 5 398
g) 504 × 8 = 9 × •
h) • : 5 = 7 000 : 8
12) Shaka intera idahinduka yakoreshejwe muri uru rukurikirane rw’imibare
a) 987, 1 092, 1 197, 1 302
b) 875, 780, 685, 590
13) Uzuza uru rukurikirane rw’imibare n’imibare ibura
a) 1 543, 1 474, 1 405, 1 336,------ ,----- ,------
b) 2 675, 2 500, 2 325, 2 150,------ ,----- ,------
14) Uzuza iyi mbonerahamwe
15) Amahurizo
a) Gabanya ku buryo bungana inzitiramubu 9 875 Imirenge 5. Umurenge uzahabwa inzitiramibu
zingahe?
b) Akagari ka Bibare gatuwe n’abagabo 1 368, abagore 1 579 n’abana 6 487. Ubwo ako kagari gatuwe
n’abantu bangahe?
c) Umurenge wacu wateye ingemwe z’inturusu
8 764. Shaka umubare w’ ingemwe zitameze niba
7 985 ari zo zameze gusa.
d) Muri sitade ntoya harimo intebe 1 009 zicarwaho n’abantu 9 imwimwe. Shaka umubare w’abantu
bakwirwa muri iyo sitade.
B) Ingero n’amafaranga y’u Rwanda
1) Ni uruhe rugero fatizo rw’ingero:
a) Z’uburebure c) Z’ibitembabuzi
b) Z’uburemere
2) Hindura mu rugero wabajijwe
a) kg 5 g 80 = dag----- c) m 5 cm 9 = mm----
4) Subiza
a) Inoti 9 za F 1 000 = F 2 000 + F -------+ F-----
b) Ufashe inoti y’u Rwanda nini, ukongeraho intoya, ukongeraho ibiceri bibiri binini wagira F angahe?
c) Bagutumye kg 1 y’isukari ya F 1 200, umugati wa F 900, umunyu wa F 400, isabune za F 950,
Kg 1 y’umuceri ya F 800 n’ifu y’igikoma ya F 1 500. Wagarura amafaranga angahe niba
baguhaye inoti 2 za F 5 000?
5) Ni gihe ki?
6) Hindura izi ngero z’igihe:
a) Imyaka 4 = Amezi-------
b) Ibyumweru 8 = Iminsi-----
c) Iminsi 30 = Amasaha------
d) Iminsi 35 = Ibyumweru-----
7) Sobanura itandukaniro riri hagati y’umwaka ugira
iminsi 365 n’ugira iminsi 366.
8) Kagabo yatunze kg 2 700 z’ibirayi ku ngorofani abivana
mu rugo abijyana ku isoko. Niba yarabitunze inshuro 9
ubwo buri nshuro yatwaraga kg zingahe?
9) Mahoro afite utujerikani 8 tujyamo 5L kamwekamwe. Ubwo yose hamwe afite amazi angana iki?
10) Imyaka ikurikira izaba ifite iminsi ingahe?
a) 2 018 b) 2 019 c) 2 020 d) 2 024
C. Amashushongero
1) Itegereze uvuge amazina y’imirongo iri ku ishusho:
2) Uzuza izi mbonerahamwe
A) Kare
5) Shaka umuzenguruko wa kare ifite cm 45 z’uruhande
6) Shaka umuzenguruko w’umurima ufite cm 89 z’ubugari na cm 121 z’uburebure.
7) Shaka umuzenguruko wa mpandeshatu ndinganire ifite cm 18 z’uruhande
8) Shaka umuzenguruko w’aya mashushongero
Vuga amazina y’imirongo ikurikira:
a) AC = c) AG = e) AE = g) GE =
b) CG = d) BF = f) HD = h) CE =
10) Shushanya ikinyatuzu k’imbariro 8 n’inkingi 8:
a) Shyiramo utudomo A (3, 6) B (6, 7) C (3, 3) D (7, 3)
b) Vuga izina ry’ishusho ubonye
c) Pima imfuruka zayo
11) Shushanya imfuruka ya dogere 60 n’iya dogere 135
12) Ifashishe ibishushanyo bikoreshwa mu mibare ugaragaze
a) Imipira 6 yo gukina d) Inkweto 9
b) Imodoka 7 e) Imipira yo kwambara 10
c) Amacunga
16. Inyunguramagambo yo muri iki gitabo k’Imibare
Agacamurongo: Irati ikoze mu giti, mu cyuma cyangwa muri pulasitiki yifashishwa mu guca imirongo no gushushanya amashushongero.
Agacaruziga: Igikoresho kifashishwa mu gushushanya uruziga
Akarambararo: Umurongo ugororotse uva mu izingiro ukagera ku muzenguruko w’uruziga.
Biruta: Ikimenyetso k’igereranya kiba kireba ahari umubare munini (>)
Birutwa: Ikimenyetso k’igereranya kiba kireba ahari umubare munini (<)
Dekametero: Urugero rw’uburebure / igikoresho kifashishwa mu gupima uburebure bw’umuhanda,
ikibanza, umurima, …
Gusesengura imibare: Kuvuga umwanya n’agaciro bya buri mubarwa ugize umubare
Gutondeka imibare: Gukurikiranya imibare uhereye ku muto ujya ku munini cyangwa uhereye ku munini ujya ku muto
Ibinyabumwe: Umwanya w’umubarwa utangira iburyo mu mibarwa igize umubare
Ibinyacumi: Umwanya w’umubarwa wa kabiri uhereye iburyo mu mibarwa igize umubare
Ibinyagihumbi: Umwanya w’umubarwa wa kane uhereye iburyo mu mibarwa igize umubare
Ibinyajana: Umwanya w’umubarwa wa gatatu uhereye iburyo mu mibarwa igize umubare
Ibitembabuzi: Ibintu byose bisukika nk’amazi.
Icyumweru: Igihe k’iminsi irindwi
Igabanya ridasagura: Uburyo bwo kugabanya bushyitse ntihagire igisigara
Igiciro: Amafaranga umucuruzi yifuza kugurisha igicuruzwa ke.
Igikuba: Umubare ukubishwa undi, mu ikuba ry’imibare
Igikubo: Igisubizo babona bakubye imibare
Igikubwa: Umubare ukubwa n’undi ngo haboneke igikubo
Igiteranyo: Igisubizo babona mu iteranya ry’imibare
Ikibara: Umubare uri hejuru y’umurongo w’umugabane
Ikigabanwa: Umubare ugabanywa
Ikigabanya: Umubare bagabanyisha
Ikigabanyo: Igisubizo babona mu igabanya ry’imibare
Ikinyatuzu: Igishushanyo kirimo utuzu dukozwe n’imirongo ihagaze bita inkingi n’indi itambitse bita
imbariro
Ikinyuranyo: Igisubizo babona mu ikuramo ry’imibare
Ikita: Umubare uri munsi y’umurongo w’umugabane
Ikizima: Umubare ushyitse cyangwa ikita kingana n’ikibara
Imbariro: Imirongo igororotse ihagaze yifashishwa mu kubaka ikinyatuzu
Imbonerahamwe y’ibara: Imbonerahamwe yifashishwa mu gusesengura imibare
Imfuruka: Inguni ikorwa n’imirongo ibiri inyuranamo Imfuruka ifunganye: Imfuruka iyo ari yo yose ipima
dogere ziri munsi ya 90
Imfuruka igororotse: Imfuruka iyo ari yo yose ipima dogere 90
Imfuruka yagutse: Imfuruka iyo ari yo yose ipima dogere ziri hagati ya 90 na dogere 180
Imibarwa: Imibare igize umubare
Imigabane: Imibare igaragaza ibice byagabanijwe mu kizima igira ikibara, ikita n’umurongo w’umugabane
utandukanya ikibara n’ikita
Imirongo: Urukurikirane rw’utudomo tugiye umujyo umwe Imirongo inyuranamo: Imirongo ifite ibyerekezo
binyuranye kandi ihurira mu kadomo kamwe igakorana imfuruka
Indangaminsi: Igikoresho kerekana iminsi, amatariki, ibyumweru, n’amezi bigize umwaka
Inganyagaciro: Imibare inganya agaciro bigaragajwe n’ikimenyetso cya bihwanye, kiri hagati yayo.
Ingeramfuruka: Igikoresho kifashishwa mu gupima imfuruka
Ingero z’igihe: Ingero zifashishwa mu kwerekana igihe
Ingero z’uburebure: Ingero zifashishwa mu gupima indeshyo y’ahantu, abantu cyangwa ibintu.
Ingero z’uburemere: Ingero zifashishwa mu gupima ingano y’ibintu
Inkingi: Imirongo igororotse ihagaze yifashishwa mu kubaka ikinyatuzu Intera idahinduka: Intera ikoreshwa mu rukurikirane rw’ibara rukozwe ku buryo budahinduka
Isaha: Igihe k’iminota mirongo itandatu. Iteranya ribitsa: Iteranya rigira ibiteranyo by’imibarwa
bigera cyangwa birenga 10 Iteranya ritabitsa: Iteranya rigira ibiteranyo by’imibarwa bitarenga 10
Izingiro: Akadomo ko mu ruziga hagati kifashishwa mu gushushanya uruziga
Kare: Ikinyampande gifite impande enye zingana n’imfuruka enye zigororotse.
Kugereranya imibare: Kureba umunini n’umuto
Kuvunja: Guhinduza amafaranga mu yandi bihwanyije agaciro
Kuzigama: Kwiteganyiriza
Metero buhine: Metero ikunjwa, ihinahinwa
Metero bushumi: Metero iteye nk’agashumi
Mpandeshatu: Ishushongero rifite impande eshatu
Mpandeshatu ibonetse yose: Ishushongero rifite impande eshatu zose zitangana n’imfuruka 3 zitangana
Mpandeshatu ndinganire: Ishushongero rifite impande eshatu zingana
Mpandeshatu nyampanga: Ishushongero rifite impande eshatu n’imfuruka eshatu ariko ebyiri muri zo zingana
Mpandeshatu nyanguni: Ishushongero rifite impande eshatu ariko ebyiri muri zo zikora imfuruka igororotse
Nsuzuma ngusuzume: Ubwoko bw’isuzuma rikorwa n’abanyeshuri babiribabiri
Reka nisuzume: Ubwoko bw’isuzuma rikorwa n’umunyeshuri ku giti ke
Ukwezi: Igihe kingana n’ibyumweru 4 bigizwe n’iminsi 30, cyangwa 31, 28 cyangwa 29
Umunota: Igihe kingana n’amasegonda 60 Umunzani: Igikoresho cyo gupima ibiro by’ikintu cyangwa
by’abantu
Umurambararo: Umurongo ugororotse uva ku muzenguruko w’uruziga ukanyura mu izingiro ry’uruziga
ukongera ukagera ku muzenguruko
Umurongo ugororotse: Umurongo ugiye umujyo umwe
Umurongo w’umugabane: Umurongo utandukanya ikibara n’ikita
Umuzenguruko: Uburebure bungana n’intera izengurutse ishusho runaka cyangwa ahantu runaka
Umwaka udasanzwe: Umwaka ugira iminsi 366
Umwaka usanzwe: Umwaka ugira iminsi 365
Urukiramende: Ikinyampande gifite impande 4, ebyirebyiri ziteganye zingana n’imfuruka 4 zigororotse.
Urukurikirane rw’imibare: Imibare itondetse uhereye ku muto, ujya ku munini cyangwa uhereye ku munini ujya ku muto ariko hagati yayo harimo intera idahinduka (umubare ugenda wiyongerwaho cyangwa ukurwamo)
Uruziga: Ishushongero rigizwe n’umurongo ufunze uri ku ntera ingana uturutse mu izingiro.
- INGERO Z’IBIBAZO BY’ISUZUMAINGERO Z’IBIBAZO BY’ISUZUMALabel: 1INGERO Z’IBIBAZO BY’ISUZUMA
UMWAKA WA GATATU W’AMASHURI ABANZA
ISOMO: Imibare
IMBUMBANYIGISHO: IBARA N’AMATEGEKO YARYO
UMUTWE WA 1: imibare kuva kuri 0 kugera ku
2000
Ingero z’ibibazo
Icyiciro cya1 : Ubumenyi /knowledge
1.Kora imibare 3 igizwe n’imibarwa ikurikira 1; 2; 3; 4.
Icyiciro cya 2: Gusobanukirwa /Understanding
Tondeka iyi mibare uhereye ku muto ujya ku munini
1251; 1452; 1254; 1245; 1542
Icyiciro 3: Gushyira mu bikorwa/Application
1. Kora iyi mibare
a) 1248 + 659 =
b) 637÷7 =
Icyiciro cya 4: Gusesengura/Analysis
Sesengura iyi mibare usobanure uko wabikoze
a) 1835 = c…j…h…b…
b) 1052+674 = b…c…h…j…
Icyiciro cya 5: Isuzuma /Evaluation (Nta mibare irimo?)
Icyiciro cya 6: Guhanga/Creation
Mu muganda w’ukwezi mu mudugudu bubakiye umukecuru. Abagore batwaye amatafari 562, abagabo nabo batwara 782.
a) Ubwo abagabo batwaye amatafari angahe kurusha abagore?
b) Ubwo bose hamwe batwaye amatafari angahe?
UMWAKA WA GATATU W’AMASHURI ABANZA
ISOMO: Imibare
IMBUMBANYIGISHO: Ingero n’amafaranga
UMUTWE WA 9 : Ingero z’igihe
Ingero z’ibibazo
Icyiciro cya1 : Ubumenyi
1. Vuga igihe kerekanwa n’iyi saha.
Icyiciro cya 2: Gusobanukirwa/understanding
Vuga amezi 4 y’umwaka afite iminsi 30.
Icyiciro cya 3:Gushyira mu bikorwa/Application
1. Shushanya amasaha maze ugaragaze igihe 10:30’
Icyiciro cya 4: Gusesesengura
Gereranya ukoresheje >,< na =
Iminsi y’ukwezi kwa Mutarama……… iminsi y’ukwezi kwa Gashyantare
Icyiciro cya 5: Isuzuma / Evaluation
1.Vuga igihe kigaragazwa n’iyi saha
2.Ukwezi kwa 12 bakwita irihe zina mu Kinyarwanda?
Icyiciro cya 6: Guhuza /Guhanga/Creation
a)Ni ukuhe kwezi k’umwaka gufite iminsi mike
b)Uko kwezi kugira iminsi ingahe?
c)Sobanura igihe kugira iminsi mike n’igihe kugira iminsi myinshi.
- IMYITOZO
