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89Im Ibare y'abakuze IKIGWA CYA 30: GUSOMA NO KWANDIKA IMIBARE Y'IMIBARWA 3 INTEGO Y'ISOMO: Nyuma y'ikigwa umwigishwa araba ashobora gusoma no kwandika imibare 3 ( kuva ku 100 kugeza ku 999) IMFASHANYIGISHO: Amakaye, Ikibaho, ingwa UKO IKIGWA GITANGWA 1. INTANGIRIRO: Umwigisha aratanga imyitozo y'intangiriro kugira ngo abigishwa biyibutse ibyo bize mu masomo aherutse. Urugero: Kwandika no gusoma imibare ishyitse kuva kuri zeru (0) kugera ku ijana (100) herekanwa ibinyabumwe n'ibinyacumi. 2. IKIGWA GISHYA Gusoma no kwandika imibare y'imibarwa 3 2. 1. Gutahura Umwigisha yandika imwe mu mibare y'imibarwa 3 ku kibaho 2. 2. Gusesesengura Umwigisha aha urugero abigishwa rwo gusoma imibare y'mibarwa 3, atanga ingero zikurikira; Ijana : 100 Ijana na cumi : 110Ijana na makumyabiri : 120Ijana na mirongo itatu: 130Ijana na mirongo ine : 140Ijana na mirongo itanu : 150 Ijana na mirongo itandatu: 160 Ijana na mirongo irindwi: 170 Ijana na mirongo inani : 180Ijana na mirongo ikenda : 190Magana abiri : 200 Magana atatu : 300 Magana ane : 400 Magana atanu : 500Magana atandatu : 600 Magana arin dwi : 700 | REB_igitabo_abakuze_imibare.pdf |
90Ig Itabo cy'umw Ig Isha Magana inani : 800 Magana ikenda : 900 Umwigisha asaba abigishwa gusoma imibare yanditse Umwigisha avuga imibare y'imibarwa 3,agasaba abigishwa kuyandika ku kibaho. Umwigisha buri gihe agenzura ko barimo babikora neza. 2. 3. Ikomatanya Umwigisha aratanga incamake y'ikigwa ariyo gusoma no kwandika imibare y'imibarwa 3 Umwigisha yandika ku kibaho imibare y'imibarwa 3 Abigishwa bayandika mu makayi yabo. 2. 4. Imyitozo ntsindagirabumenyi Kora imyitozo ikurikira a. Andika mu magambo iyi mibare ikurikira : 432: Magana ane na mirongo itatu na kabiri207:............................................................. 318:............................................................. 206:............................................................. 999:............................................................. 1. Andika mu mibare a. Magana arindwi n'umunani= b. Ijana na mirongo inani na rimwe = c. Magana inani mirongo inani na gatanu = d. Ijana na mirongo itandatu na karindwi = e. Magana abiri na makumyabiri na kabiri = 4. ISUZUMA Umwigisha atanga imyitozo yo gusuzuma niba intego y'ikigwa yagezweho 38:................................................................... 307 :................................................................... 508:................................................................... 701:................................................................... 999:................................................................... 2. Andika mu mibare a. Magana kenda na mirongo kenda n'ikenda | REB_igitabo_abakuze_imibare.pdf |
91Im Ibare y'abakuze b. magana inani mirongo inani na karindwi = c. Magana atatu mirongo itandatu n'ikenda=d. Magana atanu mirongo kenda n'umunanie. Magana ane na kane 4. UMUKORO 1. Andika mu magambo 777; 869; 731; 199; 872; 983; 457; 638; 586 2. Andika mu mibare a. Magana abiri na mirongo ine n'umunani; b. Ijana na makumyabiri na kabiri; c. Magana atanu na cumi na rimwe;d. Magana arindwi na karindwi; e. Magana inani na makumyabiri n'ikenda. | REB_igitabo_abakuze_imibare.pdf |
92Ig Itabo cy'umw Ig Isha IKIGWA CYA 31 : GUSESENGURA IMIBARE ISHYITSE Y'IMIBARWA 3 MO IBINYABUMWE, IBINYACUMI N'IBINYEJANA INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gusesengura imibare y'imibarwa 3 mo ibinyabumwe, ibinyacumi n'ibinyejana. IMFASHANYIGISHO: Ibintu byo kubara, amakaye, ikibaho, ingwa,imbonerahamwe y'ibara,... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha afasha abigishwa gusubiramo isesengura ry'imibare y'imibarwa ibiri mo ibinyabumwe n'ibinyacumi. 1) 57 ; umubare 57 ugizwe n'ibinyacumi 5 n'ibinyabumwe 7 2) 74; umubare 74 ugizwe n'ibinyacumi 7 n'ibinyabumwe 4 3) 19; umubare 19 ugizwe n'ikinyacumi 1 n'ibinyabumwe 9 4) 96; umubare 96 ugizwe n'ibinyacumi 9 n'ibinyabumwe 6 Ibinyacumi (C) Ibinyabumwe (b) 5 7 7 4 1 9 9 6 57 = c5 b7 74 = c7b4 19 = c1b9 96=c9b6 2. IKIGWA GISHYA 2. 1. Gutahura Kwitegereza Umwigisha yifashisha urugero rw'amafaranga kuko ariyo abigishwa bamenyereye. Agenda abaza umubare w'ibiceri by'amafaranga 100 n'ibiceri by'amafaranga 10 bigize amafaranga 220, 350,430, 510,......, 970 Ingero: 1) Amafaranga 220 agizwe n'ibiceri 2 by'amafaranga 100 n'ibiceri 2 by'amafaranga 10. 2) Amafaranga 350 agizwe n'ibiceri 3 by'amafaranga 100 n'ibiceri 5 by'amafaranga 10. | REB_igitabo_abakuze_imibare.pdf |
93Im Ibare y'abakuze 3) Amafaranga 430 agizwe n'ibiceri 4 by'amafaranga 100 n'ibiceri 3 by'amafaranga 10. 4) Amafaranga 970 agizwe n'ibiceri 9 by'amafaranga 100 n'ibiceri 7 by'amafaranga 10. 2. 2. Gusesengura Umwigisha yifashishije igishushanyo gikurikira asobanurira abigishwa ko ikiziga kinini kigizwe n'ibinyacumi 10 ari ikinyajana 1. Umwigisha asaba abigishwa kugaragaza umubare w'amajana,w'amacumi agize umubare runaka no kugaragaza umubare usigara uri munsi ya 10. Ingero: 1) Umubare 112 ugizwe nijana 1n'icumi 1 hagasigara 2. 2) Umubare 231 ugizwe n'amajana 2, amacumi 3 hagasigara 1. 3) Umubare 725 ugizwe n'amajana 7, amacumi 2hagasigara 5. Umwigisha ahereye kungero zatanzwe haruguru, asobanura ko ibinyajana ari umubare w'amajana agize umubare runaka, ibinyacumi ari umubare w'amacumi agize umubare runaka naho ibinyabumwe ni umubare usigara utagera ku 10 kandi akerekana uko byandikwa ku kibaho. 1) Umubare 112 ugizwe n'ikinyajana1, ikinyacumi1 n'ibinyabumwe 2 2) Umubare 231 ugizwe n'ibinyajana 2, ibinyacumi 3 n'ikinyabumwe 1 3) Umubare 725 ugizwe n'ibinyajana 7, ibinyacumi 2 n'ibinyabumwe 5 2. 3. Ikomatanya Umwigisha yereka abigishwa uko bandika ibinyabumwe, ibinyacumi n'ibinyajana bifashishije imbonerahamwe y'ibara kandi asobanura ko ibinyajana byandikwa hakoreshejwe inyuguti ya j, ibinyacumi byandikwa hakoreshejwe inyuguti ya c naho ibinyabumwe bikandikwa hakoreshejwe inyuguti ya b. Imbonerahamwe y'ibara: Urugero Umubare Ibinyajana (j)Ibinyacumi (c)Ibinyabumwe (b) 112 1 1 2 231 2 3 1 725 7 2 5 | REB_igitabo_abakuze_imibare.pdf |
94Ig Itabo cy'umw Ig Isha Cyangwa Umubare Jc b 112 11 2 231 23 1 725 72 5 1) 112 = j1c1 b2 2) 231=j2c3 b1 3) 725=j7c2b5 Abigishwa bamaze kumenya gukoresha imbonerahamwe, umwigisha atanga imyitozo inyuranye ku isesengura ry'imibare yerekana isano iri hagati y'isesengura ry'imibare n'iteranya. Urugero : Uburyo bwa mbere: 795 = j7c9b5 Uburyo bwa kabiri: 795 = 700 + 90 + 5 2. 4. Imyitozo ntsindagirabumenyi Umwigisha atanga imyitozo itandukanye yo kugaragaza ibinyajana, ibinyacumi n'ibinyabumwe bigize umubare 1) 384 2) 905 3) 198 4) 870 3. ISUZUMA Sesengura imibare mo ibinyacumi, ibinyabumwe, n'ibinyejana 723, 459,817,433,691 Hindura mu mibare j2c8b2=.... j7c0b3=..... j4c6b9=..... j9c8b0=..... j6c5b7=... 4. IMYITOZO Y'UMUKORO Sesengura imibare ikurikira mo ibinyajana, ibinyacumi n'ibinyabumwe 834 211 918 700 987 Hindura mu mibare j4c5b0= j7c0b6= j9c4b2= j3c4b3= j1c9b6= j5c7c9= | REB_igitabo_abakuze_imibare.pdf |
95Im Ibare y'abakuze IKIGWA CYA 32 : GUTERANYA IMIBARE Y'IMIBARWA 3 : ITERANYA RITABITSA, IGITERANYO KITARENGA 999. INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora guteranya imibare y'imibarwa 3 igiteranyo kitarenga 999. IMFASHANYIGISHO Igitabo cy'umwigisha, ingwa, ikibaho,.... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo gusesengura imibare mo ibinyabumwe, ibinyacumi, ibinyajana Urugero: Sesengura mo ibinyabumwe, ibinyacumi n'ibinyajana 123= j... c... b 989 = j....c..b 752= j....c..b 2. Ikigwa gishya 2. 1. Gutahura Umwigisha asaba abigishwa kwitegereza ingero yatanze 2. 2 Gusesengura Umwigisha asobanurira abigishwa uko bateranya batabitsa imibare y'imibarwa itatu ahereye ku ngero Umwigisha arakora urugero rumwe, asaba abigishwa gukora izindi buri gihe basobanura uko bikorwa. Ingero 142+236= j c b 1 4 2 +2 3 6 3 7 8 325+253= | REB_igitabo_abakuze_imibare.pdf |
96Ig Itabo cy'umw Ig Isha J c b 3 2 5 +2 5 3 5 7 8 Umwigisha asobanura ko 0 gutaranya n'umubare bingana n'uwo mubare Urugero: J c b 3 0 0 +2 7 8 5 7 8 Umwigisha atanga izindi ngero nyinshi zo guteranya imibare 2 cyangwa itatu y'imibarwa 3 iri hagati ya 100 na 999 2. 3. Ikomatanya Hamwe n'abigishwa, umwigishwa atanga incamake y'ikigwa kizwe Iyo bateranya imibare y'imibarwa itatu babanza gutondeka neza imibarwa ya buri mubare mu mbonerahamwe y'ibara ( ibinyajana bijya munsi y'ibinyajana, ibinyacumi bijya munsi y'ibinyacumi, n'ibinyabumwe bikajya munsi y'ibinyabumwe) hanyuma bakagenda bateranya iyo mibarwa. 2. 4. Imyitozo nsindagirabumenyi Teranya iyi mibare ukoresheje imbonerahamwe y'isesengura 314+ 155=, 871+ 128=, 511+ 457=, 732+246=, 600+ 389= 3. ISUZUMA Shaka igisubizo 123+214= 486+313= 527+402= 632+267= 345+534= 4. UMUKORO Kora iyi myitozo ikurikira:400+399=, 802+187=, 814+162=, 355+223=, 431+569= | REB_igitabo_abakuze_imibare.pdf |
97Im Ibare y'abakuze IKIGWA CYA 33: GUTERANYA IMIBARE Y'IMIBARWA 3 : ITERANYA RIBITSA, IGITERANYO KITARENGA 999 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora guteranya ubitsa imibare y'imibarwa 3 igiteranyo kitarenga 999 IMFASHANYIGISHO igitabo cy'umwigisha, ingwa, ikibaho,.... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo guteranya batabitsa 343+236= j c b 3 4 3 + 2 3 6 142+627= j c b 1 4 2 +6 2 7 2. IKIGWA GISHYA Iteranya ribitsa imibare y'imibarwa 3 2. 1. Gutahura Umwigisha asaba abigishwa kwitegereza ingero yatanze 1) 134 + 218 = 2) 271 + 149 = 2. 2 Gusesengura Umwigisha asobanurira abigishwa uko bateranya babitsa imibare y'imibarwa itatu ahereye ku ngero Umwigisha arakora urugero rumwe, asaba abigishwa gukora izindi buri gihe basobanura uko bikorwa | REB_igitabo_abakuze_imibare.pdf |
98Ig Itabo cy'umw Ig Isha Urugero: 134+218=352 J 1 c b 1 3 4 +2 1 8 3 5 2 b4+b8= c1 b2 bateranya buri gihe bahereye ku binyabumwe wandika ibinyabumwe (b2) bakabitsa ibinyacumi (c1) c1 kijyanwa mu mwanya w'ibinyacumi bityo bikiyongera babona c1 + c3+c1=c5 bikandikwa mu mwanya wabyo bateranya ibinyajana hagati yabyo( j1+j2=j3) 1j 1c b 2 7 1 +1 4 9 4 2 0 Umwigisha atanga izindi ngero zo guteranya imibare 2 cyangwa itatu y'imibarwa 3 iri hagati ya 100 na 999 babitsa. Ingero 345+285= 631 1j 1c b 3 4 5 +2 8 6 6 3 1 291+619=910 1j 1c b 2 9 1 6 1 9 9 1 0 2. 3. Ikomatanya Umwigisha asobanura iyo bateranya imibare y'imibarwa itatu babitsa bashobora kubitsa inshuro imwe cyangwa ebyiri Buri gihe asobanura ko iyo bateranyije ibinyabumwe bikarenga icumi bandika ibinyabumwe bakabitsa ibinyacumi bikandikwa mu mwanya wabyo bityo bikongera umubare w'ibinyacumi. Iyo bateranyije ibinyacumi bikarenga icumi bandika ibinyacumi bakabitsa ibinyajana (j) bikandikwa mu mwanya wabyo bityo bikongera umubare (j) Umwigisha atanga imyitozo yo gusuzuma niba intego y'ikigwa yagezweho2. 4. Imyitozo ntsindagirabumenyi | REB_igitabo_abakuze_imibare.pdf |
99Im Ibare y'abakuze Teranya iyi mibare ikurikira: 314+ 198=, 881+129=, 771+ 157=, 632+246=, 660+ 249= 3. ISUZUMA Teranya iyi mibare ikurikira: 328+159=463+278= 718+133= 672+239= 745+178= 4. UMUKORO Kora iyi myitozo 490+399=, 672+187=, 814+19= | REB_igitabo_abakuze_imibare.pdf |
100Ig Itabo cy'umw Ig Isha IKIGWA CYA 34 : GUKURAMO BADATIRA IMIBARE Y'IMIBARWA 3 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gukora nta kwibeshya imyitozo y'ikuramo ridatira ry'imibarwa 3. IMFASHANYIGISHO Igitabo cy'umwigisha, ikibaho, ingwa, imbonerahamwe y'ibara. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yibutsa ikuramo ridatira ry'imibarwa 2. 97-73= Ibinyabumwe 7 ukuyemo ibinyabumwe 3 hasigara ibinyabumwe 4. Ibinyacumi 9 ukuyemo ibinyacumi 7 hasigara ibinyacumi 2. 97-73=c2b4 97-73=24 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha yereka abigishwa ko iyo bakuramo badatira imibare y'imibarwa 3 bakoresha uburyo babonye igihe bakoraga imyitozo y'ikuramo badatira ry'imibare y'imibarwa 2 2. 2. Gusesengura Umwigisha atanga urugero mbonwa 786-432= Ibinyabumwe 6 ukuyemo ibinyabumwe 2 hasigara ibinyabumwe 4 b6-b2=b4 Ibinyacumi 8 ukuyemo ibinyacumi 3 hasigara ibinyacumi 5 c8-c3=c5 Ibinyajana 7 ukuyemo ibinyajana 4 hasigara ibinyajana 3 786-432=354 | REB_igitabo_abakuze_imibare.pdf |
101Im Ibare y'abakuze 2. 3. Ikomatanya Batondeka imibare nk'uko bikorwa mu ikuramo ry'imibare y'imibarwa 2 Umubare munini ni wo wandikwa hejuru ugakurwamo umuto. Bakuramo bahagaritse bahereye iburyo bagana ibumoso: Ibinyabu akuramo ibinyajana Urugero: J C b 7 8 6-4 3 2 3 5 4 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo ikurikira: 1) 358-217=2) 760-650=3) 879-745=4) 407-304=5) 874-523=6) 554-544= 3. ISUZUMA Kora ikuramo uhagaritse. 1) 707-206= 2) 615-414= 3) 780-650= 4) 747-543= 5) 679-172=6) 547-543= 4. UMUKORO Kora iyi myitozo ikurikira:1) 407-307=2) 587-285=3) 679-568=4) 863-760= 5) 997-197= | REB_igitabo_abakuze_imibare.pdf |
102Ig Itabo cy'umw Ig Isha IKIGWA CYA 35 : GUKURAMO BATIRA IMIBARE Y'IMIBARWA 3 INTEGO Y'IKIGWA : Nyuma y'ikigwa, umwigishwa araba ashobora gukora nta kwibeshya imyitozo inyuranye yo gukuramo batira imibare y'imibarwa 3 IMFASHANYIGISHO: Ikibaho, ingwa, igitabo cy'umwigisha, imbonerahamwe y'ibara,... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha yibutsa ikuramo ritira ry'imibare y'imibarwa 2 akoresheje urugero92-47= Ibinyabumwe 2 ukuyemo ibinyabumwe 7 ntibishoboka, ndatira ikinyacumi 1gisimburwa n'ibinyabumwe 10, ubwo dufite ibinyabumwe 12; ibinyabumwe12 gukuramo ibinyabumwe 7 hasigara ibinyabumwe 5 Ku binyacumi 9 hasigaye ibinyacumi 8 kuko havuyemo cya kinyacumi 1. Ibyo binyacumi 8 gukuramo ibinyacumi 4 hasigara ibinyacumi4 92-47=c4b5 92-47= 45 Bakuramo bahagaritse bahereye iburyo bagana ibumoso ibinyabumwe munsi y'ibinyabumwe, ibinyacumi munsi y'ibinyacumi 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha yereka abigishwa ko iyo bakuramo batira imibare y'imibarwa 3 bakoresha uburyo babonye igihe bakoraga imyitozo y'ikuramo ritira ry'imibare y'imibarwa 2. 2. 2. Gusesengura Umwigisha atanga urugero maze agasaba abigishwa kugerageza kwibonera igisubizo 723-454= Bandika umubare muto munsi y'umubare munini 723-454 | REB_igitabo_abakuze_imibare.pdf |
103Im Ibare y'abakuze Ibinyabumwe 3 ukuyemo ibinyabumwe 4 ntibishoboka; ndatira ikinyacumi 1 gisimburwe n'ibinyabumwe 10, ubwo dufite ibinyabumwe 13 dukuyemo ibinyabumwe 4 hasigara ibinyabumwe 9 Ku binyacumi 2 hasigaye ikinyacumi 1, ikinyacumi 1 dukuyemo ibinyacumi 5 ntibishoboka; Twatira ikinyajana 1 gisimburwe n'ibinyacumi 10; ubwo tugire ibinyacumi 11; ibinyacumi 11 dukuyemo ibinyacumi5 hasigara ibinyacumi 6 ku binyajana 7 hasigaye ibinyajana 6; ibinyajana 6 dukuyemo ibinyajana 4 harasigara ibinyajana 2. J C b 6 710+1=111 210+3=13 3-4 5 4 2 6 9 723-454=j2c6b9 723-454=269 2. 3. Ikomatanya J C b 6 789155-6 9 6 0 9 9 b5-b6 ntibishoboka ku binyacumi c9 haratirwaho c1 hasigare c8, c1 irashyirwa mu mwanya w'ibinyabumwe bibe b10 + b5= b15, bityo b15-b6=b9 c8-c9 ntibishoboka haratirwa ikinyajana 1J1 mu mwanya j7-j1=j6, ibinyacumi biraba c10 +c8=c18 kuko j1=c10 bityo c18-c9 birashoboka hasigara c9 Ibinyajana 6-ibinyajana 6 hasigara ubusa(j6-j6=0) | REB_igitabo_abakuze_imibare.pdf |
104Ig Itabo cy'umw Ig Isha 2. 3. Ikomatanya Batondeka imibare nk'uko bikorwa mu ikuramo ry'imibare y'imibarwa 3 Umubare munini ni wo wandikwa hejuru ugakurwamo umuto. Bakuramo bahagaritse bahereye iburyo bagana ibumoso: Ibinyabumwe bakuramo ibinyabumwe Ibinyacumi bakuramo ibinyacumi Ibinyajana bakuramo ibinyajana Iyo ibinyabumwe by'umubare munini ari bike ku binyabumwe by'umubare muto batira ikinyacumi C1 mu mwanya w'ibinyacumi Icyo kinyacumi gishyirwa ku binyabumwe bikaba b10+ b Ibinyabumwe bibonetse aribyo b10+b biruta umubare w'ibinyabumwe by'umubare muto bityo ikuramo rigakorwa mu buryo bworoshye. Iyo ibinyacumi byasigaye by'umubare munini bakuyeho cya kinyacumi 1 biruta ibinyacumi by'umubare muto ikuramo rirashoboka Iyo ibinyacumi byasigaye ari bicye hakorwa itira, batira ikinyajana kimwe(j1) mu mwanya w'ibinyajana, maze kigashyirwa mu mwanya w'ibinyacumi Ibinyacumi biriyongera (j1=c100 bikaba c10+c Kuko ibinyacumi by'umubare munini biruta iby'umubare muto ikuramo rirashoboka Mu gukuramo ibinyajana, hakoreshwa ibinyajana by'umubare munini byasigaye hakuwemo cya kinyajana 1,bagakuramo ibinyajana by'umubare muto. 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo, ukuramo uhagaritse 1) 795-696= 2) 487-389= 3) 123-59= 4) 687-578= 5) 594-494= 3. ISUZUMA Uhagaritse kora iyi myitozo 1) 922-877= 2) 466-358= 3) 877-788= 4) 172-167= 5) 735-226= 4. UMUKORO Kora iyi myitozo uhagaritse 1) 222-133= 2) 733-655= 3) 678-469=4) 947-749=5) 821-128= | REB_igitabo_abakuze_imibare.pdf |
105Im Ibare y'abakuze IKIGWA CYA 36 : GUSESENGURA IMIBARE ISHYITSE Y'IMIBARWA 4 MO IBINYABUMWE, IBINYACUMI, IBINYEJANA N'IBINYAGIHUMBI INTEGO IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gusesengura imibare y'imibarwa 4 mo ibinyacumi, ibinyejana n'ibinyagihumbi. IMFASHANYIGISHO Ibintu byo kubara, amakaye, ikibaho, ingwa,imbonerahamwe y'ibara,... UKO IKIGWA GITANGWA 1. INTANGIRIRO Isesengura ry'imibare y'imibarwa 3 herekanwa: ibinyajana, ibinyacumi n'ibinyabumwe hakoreshwa imbonerahamwe nk'uko byizwe mu masomo abanza. 1) 834 2) 211 3) 918 4) 700 Umubare Ibinyajana (j) Ibinyacumi (c) Ibinyabumwe (b) 834 8 3 4 211 2 1 1 918 9 1 8 700 7 0 0 834 = j8c3b4, 2)211 = j2c1b1, 3) 918 = j9c1b8, 4)700 = j7c0b0 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha agomba kuba yateguye imbonerahamwe y'ibara n'imyitozo (imibare ishyitse) yo gusoma no kwandika. Asaba abigishwa, umwe umwe kwandika imibare ya teguwe mumbonerahamwe. Umubare Ibinyagihumbi Ibinyajana (j) Ibinyacumi (c) Ibinyabumwe (b) 3810 3 8 1 0 1000 1 0 0 0 2638 2 6 3 8 2. 2. Gusesengura Umwigisha afasha abigishwa gusesengura umubare umwe yateguye mo ibinyabumwe, ibinyacumi, ibinyajana n'ibinyagihumbi. Urugero : gusesengura umubare 2 638 mo ibinyabumwe, ibinyacumi, ibinyajana, | REB_igitabo_abakuze_imibare.pdf |
106Ig Itabo cy'umw Ig Isha n'ibinyagihumbi ukoresheje imbonerahamwe y'ibara. Imbonerahamwe y'ibara Ibinyagihumbi (h)Ibinyajana (j)Ibinyacumi (c)Ibinyabumwe (b) 2 6 3 8 Mu mubare 2638 harimo Ibinyabumwe bingahe? ( Ibinyabumwe 8 ) Mu mubare 2638 harimo Ibinyacumi bingahe? ( Ibinyacumi 3) Mu mubare 2638 harimo Ibinyajana bingahe? ( Ibinyajana 6) Mu mubare 2638 harimo Ibinyagihumbi bingahe? (Ibinyagihumbi 2) Umwigisha asobanurira abigishwa atsindagira ku kazu gashya k'ibinyagihumbi, ahereye ku bibazo bikurikira: Ibinyajana n'ibinyagihumbi ibyinshi ni ibihe? Ni ibinyagihumbi Umwigisha yifashisha imbonerahamwe y'ibara, akereka abigishwa uko bandika umubare 2638 mu buryo bw'imibare yifashishije inyuguti h, j, c na b Uko byandikwa mu buryo bw'imibare: h 2j6c3b8 = 2638 cyangwa 2638 = h2j6c3b8 2. 3. Ikomatanya Abigishwa bamaze kumenya gukoresha imbonerahamwe, umwigisha atanga imyitozo inyuranye ku isesengura ry'imibare yerekana isano iri hagati y'isesengura ry'imibare n'iteranya. Urugero :Uburyo bwa mbere:3695 = h3j6c9b5Uburyo bwa kabiri:3695 = 3000 + 600 + 90 + 5 2. 4. Imyitozo ntsindagirabumenyi Uzuza iyi mibare mu mbonerahamwe 1) 3 425 2) 2 379 3) 6 824 3. ISUZUMA Sesengura mo ibinyagihumbi, ibinyejana, ibinyacumi, ibinyabumwe7 384 9 905 1 198 3 870 4. UMUKORO Uzuza iyi mibare mu mbonerahamwe y'ibara kandi ugaragaze n'umubare w'ibinyagihumbi, ibinyajana, ibinyacumi n' ibinyabumwe 4 235 2 703 8 246 | REB_igitabo_abakuze_imibare.pdf |
107Im Ibare y'abakuze IKIGWA CYA 37: GUTERANYA BATABITSA IMIBARE IRI HAGATI YA 1000 NA 10 000 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gukora imyitozo yo guteranya atabitsa imibare iri hagati ya 1000 na 10 000 IMFASHANYIGISHO Igitabo cy'umwigisha, ingwa, ikibaho UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo guteranya batabitsa imibare y'imibarwa 3 Urugero Shaka igiteranyo 354+632= 267+312= 453+546= 712+277= 2. IKIGWA GISHYA Guteranya batabitsa imibare iri hagati y'igihumbi (1000) ni bihumbi cumi (10000) 2. 1. Gutahura Umwigisha asaba abigishwa kwitegereza urugero ruri ku kibaho 2. 2 Gusesengura Umwigisha asobanurira abigishwa uko bateranya batabitsa imibare y'imibarwa ine ahereye ku rugero Umwigisha arakora urugero rumwe, asabe abigishwa gukora izindi buri gihe basobanura uko bikorwa. Ingero 1) 2342+1213 +2123= 2)1820 + 2006 = 3) 2345 + 7002 = | REB_igitabo_abakuze_imibare.pdf |
108Ig Itabo cy'umw Ig Isha h j c b +2 1 23 2141 22 33.... h jcb 1 820 +2 006 3 826 h j c b 2 3 4 5 +7 0 0 2 9 3 4 7 Umwigisha atanga izindi ngero zo guteranya imibare 2 cyangwa itatu y'imibarwa 4 Ingero: Teranya iyi mibare 4150+ 3 4 28=, 2) 8183+ 18 16=Teranya uhagaritse. 2. 3. Ikomatanya Hamwe n'abigishwa, umwigisha atanga inshamake y'ikigwa kizwe Iyo bateranya imibare y'imibarwa ine babanza gutondeka neza imibarwa ya buri mubare mu mbonerahamwe y'ibara ( ibinyagihumbi bijya munsi y' ibinyagihumbi (h), ibinyajana (j) bijya munsi y'ibinyajana, ibinyacumi (c)bijya munsi y'ibinyacumi, n'ibinyabumwe bikajya munsi y'ibinyabumwe) hanyuma bakagenda bateranya iyo mibarwa. 2. 4. Imyitozo yo gutsindagira ubumenyi. Teranya iyi mibare 1) 2905 + 8054 = 2) 4628 +3341 = 3) 7142+1627= 4) 2436+1232= 3. ISUZUMA Teranya iyi mibare 2738+7101= 1257+8632= 4680+5319= 8532+1367=6073+3926= 4. UMUKORO Kora iyi myitozo1) 3821+6163= 2) 3224+4355= 3) 5423+3245= 4) 3625+5264= 5) 7620+2379= | REB_igitabo_abakuze_imibare.pdf |
109Im Ibare y'abakuze IKIGWA CYA 38 : GUTERANYA BABITSA IMIBARE IRI HAGATI YA 1000 NA 10 000 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora guteranya imibare iri hagati ya 1000 na 10 000 babitsa IMFASHANYIGISHO Igitabo cy'umwigisha, ingwa, ikibaho. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo guteranya batabitsa 1) 3625+5264= 2) 5423+3245= 2. IKIGWA GISHYA Iteranya ribitsa imibare iri hagati ya 1 000 na 9 999 2. 1. Gutahura Umwigisha asaba abigishwa kwitegereza urugero yatanze maze akabasaba gushaka igisubizo. 1)2349+1686= 2. 2 Gusesengura Umwigisha asobanurira abigishwa uko bateranya babitsa imibare y'imibarwa itatu ahereye ku ngero Umwigisha arakora urugero rumwe, asabe abigishwa gukora izindi buri gihe asobanura uko bikorwa 15 wandika ibinyabumwe 5 ukabitsa ikinyacumi 1 ugakomeza utyo. 13 wandika 3, ukabitsa 1 10 wandika 0 ukabitsa 1, mu binyagihumbi ukandika 4. | REB_igitabo_abakuze_imibare.pdf |
110Ig Itabo cy'umw Ig Isha 1 h 1j 1c b 2 4 5 9 1 7 6 1 4 2 2 0 Umwigisha atanga izindi ngero nyinshi zo guteranya imibare 2 cyangwa itatu y'imibarwa 3 iri hagati ya 1000 na 9999 babitsa 2. 3. Ikomatanya Umwigisha asobanura uko bateranya babitsa Umwigisha,yifashishije ingero zinyuranye, asobanura ko iyo bateranya imibare y'imibarwa ine babitsa bashobora kubitsa inshuro imwe, ebyiri cyangwa eshatu ; Asobanura ko iyo bateranyije ibinyabumwe bikarenga icumi bandika ibinyabumwe bakabitsa ibinyacumi bikandikwa mu mwanya wabyo bityo bikongera umubare w'ibinyacumi; Iyo bateranyije ibinyacumi bikarenga icumi bandika ibinyacumi bakabitsa ibinyajana (j ) bikandikwa mu mwanya wabyo bityo bikongera umubare w'ibinyajana j; Iyo bateranyije ibinyajana bikarenga ijana, bandika ibinyajana (j) bakabitsa ibinyagihumbi (h) bikandikwa, mu mwanya wabyo bityo bikwongera umubare w'ibinyagihumbi (h) 2. 4. Imyitozo ntsindagirabumenyi Teranya iyi mibare: 1) 4361+1289= 2) 3821+6163= 3) 2246+4355= 4) 15423+3245= 5) 3625+2649= 3. ISUZUMA Teranya iyi mibare 4657 + 3458 =3657 + 2896 =7895 + 1997 =5978 + 3485 = 4. UMUKORO Kora iyi myitozo 4 499+3995= 2672+1879= 7814+1194= 6891+2329= 5483+1659= | REB_igitabo_abakuze_imibare.pdf |
111Im Ibare y'abakuze IKIGWA CYA 39 : GUKURAMO, BADATIRA, IMIBARE IRI HAGATI YA 100 NA 10 000 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gukuramo badatira imibare iri hagati ya 100 na 10 000IMFASHANYIGISHO Igitabo cy'umwigisha, imbonerahamwe y'ibara UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha aributsa uko bakora ikuramo ritira n'iridatira ku mibare igizwe n'imibarwa 3 Urugero 233-121= 932-389= 2. IKIGWA GISHYA ikuramo ridatira, imibare iri hagati ya 100 na 10 000 2. 1 Gutahura Umwigisha yandika urugero ku kibaho asaba abigishwa kurwitegereza Urugero Shaka igisubizo 3468-1342 = 2. 2. Gusesengura: Umwigisha asobanurira abigishwa uko bakora ikuramo ry'imibare iri hagati ya 100 na 10 000 badatira ahereye ku rugero Ikuramo ridatira dukoresha imbonerahamwe Urugero : 3468-1342 = 2126 h j c b 3 14 36482 2 1 2 6 3468-1342 = 2126 Abigishwa bazakora izindi ngero zikurikiyeho bahawe n'umwigisha- | REB_igitabo_abakuze_imibare.pdf |
112Ig Itabo cy'umw Ig Isha Shaka igisubizo 1698-356 = 5435-2324 = 2. 3. Ikomatanya Mu ikuramo ridatira ry'imibare 2 iri hagati ya 100 na 10 000, bandika iyo mibare bahagaritse ku buryo ibinyabumwe bijya munsi y'ibinyabumwe, ibinyajana bijya munsi y'ibinyajana, ibinyacumi bijya munsi y'ibinyacumi, ibinyagihumbi munsi y'ibinyagihumbi bityo bagakuramo ibinyabumwe ukwabyo, ibinyacumi ukwabyo, ibinyajana ukwabyo, n'ibinyagihumbi ubwabyo. 2. 4. Imyitozo ntsindagirabumenyi Kuramo imibare 1) 4826-3414 = 2) 8953-5632 = 3) 6577-4323 = 4) 9678-3243 = 5) 4898-797 = 3. ISUZUMA 5984-5970= 8434-7234= 6076-5074= 5997-977= 5703-4702= 4. UMUKORO Kuramo iyi mibare uhagaritse | REB_igitabo_abakuze_imibare.pdf |
113Im Ibare y'abakuze IKIGWA CYA 40 : GUKURAMO,BATIRA, IMIBARE IRI HAGATI YA 100 NA 10 000 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gukuramo,batira, imibare iri hagati ya 100 na 10 000 IMFASHANYIGISHO Imbonerahamwe y'ibara, igitabo cy'umwigisha, ingwa, ikibaho UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha aributsa uko bakora ikuramo ritira ku mibare igizwe n'imibarwa 3Urugero: Kora iyi myitozo 454-269=674-188= 2. IKIGWA GISHYA Ikuramo ritira 2. 1. Gutahura Umwigisha atanga urugero rwo gukuramo imibare iri hagati ya 100 na 10 000 agasaba abigishwa gushaka igisubizo 1) 9324-2697 = 2) 6528-4749 = 2. 2. Gusesengura Umwigisha asobanurira abigishwa uko bakora ikuramo ry'imibare iri hagati ya 100 na 10 000 batira ahereye ku ngero Ikuramo ritira dukoresha imbonerahamwe Urugero rwa 1) 6528-4749 = h j c b 5 6 414 5 7112 41 88 9 1 7 7 9 Dutira 10 mu mubare ubanza 2) 6528-4749 = 1779 Mu buryo busanzwe twandika duhagaritse | REB_igitabo_abakuze_imibare.pdf |
114Ig Itabo cy'umw Ig Isha Urugero rwa 2) 758 230-72 850 = Ibinyagihumbi Ibinyabumwe bisanzwe j c b j c b 15 7 11 13 7 5 8 2 3 0-7 2 8 5 0 6 8 5 3 8 0 2. 3. Ikomatanya Umwigisha atanga incamake y'ikigwa kizwe Iyo bakuramo imibare batira babanza gutondeka neza imibarwa ya buri mubare mu mbonerahamwe y'ibara. Iyo ibinyabumwe by'umubare munini birutwa n'ibinyabumwe by'umubare muto, batira ku binyacumi by'umubare munini ikinyacumi kimwe (bakandika ibinyacumi bisigaye), kikandikwa mu mwanya w'ibinyabumwe bityo ibinyabumwe bikiyongeraho 10 kuko c1=b10, icyo gihe ikuramo rirashoboka. Iyo ibinyacumi bisigaye by'umubare munini birutwa n'ibinyacumi by'umubare muto, batira ku binyajana by'umubare munini ikinyajana kimwe(bakandika ibinyajana bisigaye),kikandikwa mu mwanya w'ibinyacumi bityo ibinyacumi bikiyongeraho 10 kuko j1=c10, icyo gihe ikuramo rirashoboka. Babigenza gutyo no ku binyajana iyo ibinyajana by'umubare munini birutwa n'ibinyajana by'umubare muto. 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo wifashishije imbonerahamwe 1) 5624-3738 = 2) 1860-974 = 3) 2706-1842 = 4) 8342-7457 = 5) 7103-4436 = 3. ISUZUMA Shaka igisubizo 4. UMUKORO Kora iyi myitozo 1) 6223-3568 = 2) 7354-3928 = 3) 7072-4569 = 4) 3023-1875 = 5) 2103-1324= 6) 8207-5579= | REB_igitabo_abakuze_imibare.pdf |
115Im Ibare y'abakuze IKIGWA CYA 41 : GUKUBA UMUBARE W'IMIBARWA 3 N'UMUBARE W'IMIBARWA 2 INTEGO Y'IKIGWA : Nyuma y'ikigwa, umwigishwa araba ashobora gukuba umubare w'imibarwa 3 n'umubare w'imibarwa 2. IMFASHANYIGISHO: Igitabo cy'umwigisha, ikibaho, ingwa, imbonerahamwe y'ibara. UKO IKIGWA GITANGWA : 1. INTANGIRIRO: Umwigisha atanga imyitozo inyuranye ku ikuba ry'imibare y'imibarwa 2 n'umubare w'umubarwa 1 30x4= 47x8=95x6=88x9= 2. IKIGWA GISHYA Ikuba ry'umubare w'imibarwa 3 n'umubare w'imibarwa 2 2. 1. Gutahura Umwigisha akora imyitozo-ngero 2 (umwe wo ku ikuba ritabitsa undi ari uwo ku ikuba ribitsa ) y'ikuba ry'imibare 2 umwe(igikubwa) ugizwe n'imibarwa 3 undi(igikuba) ugizwe n'imibarwa 2 Urugero: 412x 24= 246 x 23 = 2. 2. Gusesengura Umwigisha asobanurira abigishwa uko ikuba rikorwa ahereye ku ngero yatanze Urugero: 412x24 h j c b 4 1 2 X 2 4 1 6 4 8 + 8 2 4 9 8 8 8 412x24=9888 | REB_igitabo_abakuze_imibare.pdf |
116Ig Itabo cy'umw Ig Isha 2) 246 x 23 = 246 x 23 = 5658 Umwigisha asaba abigishwa gukora imyitozo yo gukuba umubare w'imibarwa itatu n'umubare w'imibarwa 2, kandi akabafasha iyo bibaye ngombwa. Kora iyi myitozo 2. 3. Ikomatanya Umwigisha atanga incamake y' ibimaze kwigishwa byose mu kigwa Iyo bakuba umubare w'imibarwa 3 n'umubare w'imibarwa2, babanza kwandika iyo mibare bahagaritse, igikuba kikajya munsi y'igikubwa kuburyo ibinyabumwe byandikwa munsi y'ibinyabumwe, ibinyacumi bikandikwa munsi y'ibinyacumi nk'uko bikorwa mu mbonerahamwe y'iteranya. Buri gihe bahera iburyo bagana ibumoso; buri mubarwa w'igikubwa bawukubisha ibinyabumwe by'igikuba,ibyo babonye byandikwa munsi y'igikuba bahereye iburyo bajya ibumoso;babitsa iyo bibaye ngombwa. Buri mubarwa w'igikubwa bawukubisha ibinyacumi by'igikuba, ibyo babonye byandikwa munsi y'ibyo babonye bahereye mu mwanya w'ibinyacumi bagana ibumoso. Igikubo kiboneka bateranyije ibyo babonye bahereye iburyo bagana ibumoso. 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo 1)236x27=2) 672x15 = | REB_igitabo_abakuze_imibare.pdf |
117Im Ibare y'abakuze 3) 162 x 19 = 3. ISUZUMA Kora ikuba rikurikira 1) 117 x 29 =2) 312 x 17 =3) 236 x 34 =4) 195 x 18 = 4. UMUKORO: Kora imyitozo ikurikira: 345x75= 172x92= 524x22= Uduhurizo : Mukamusoni afite udutebo 12 turimo amagi 161 kamwe kamwe. Shaka umubare w' amagi yose afite. Muhinza afite inzuri 23 zororerwamo inka. Niba buri rwuri rurimo inka 237, ubwo Muhinza afite inka zingahe? | REB_igitabo_abakuze_imibare.pdf |
118Ig Itabo cy'umw Ig Isha IKIGWA CYA 42: GUKUBA UMUBARE W'IMIBARWA 4 N'UMUBARE W'IMIBARWA 3 IGIKUBO KITARENGA 1 000 000 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gukuba umubare w'imibarwa 4 n'umubare w'imibarwa 3 IMFASHANYIGISHO Igitabo cy'umwigisha, ikibaho n'ingwa UKO IKIGWA GITANGWA : 1. INTANGIRIRO: Umwigisha atanga imyitozo yo gukuba batabitsa cyangwa babitsa, umubare w'imibarwa 3 n'umubare w'imibarwa2 bibukiranya uko bikorwa 246 x23 = 2. IKIGWA GISHYA Ikuba ry'umubare w'imibarwa 4 n'umubare w'imibarwa 3 2. 1. Kwitegereza Umwigisha aratanga urugero rw'ikuba ry'imibare 2, umwe ari uw'imibarwa 4 undi ari uw'imibarwa 3. 1234 x 111 = 2. 2. Gusesengura Umwigisha arasobanurira abigishwa uko ikuba ry'umubare w'imibarwa 4 n'umubare w'umibarwa 3 rikorwa ahereye ku ngero zinyuranye Urugero 1234 x 111 = 1 2 3 4 X 1 1 1 1 2 3 4 1 2 3 4 + 1 2 3 4 1 3 6 9 7 4 Umwigisha atanga izindi ngero ariko zigakorwa n'abigishwa we akabafasha kurushaho kubyumva iyo bibaye ngombwa Kora iyi myitozo uhagaritse kandi wandike igisubizo 1) 1172 x 121= 2) 4312 x 217= | REB_igitabo_abakuze_imibare.pdf |
119Im Ibare y'abakuze 2. 3. Ikomatanya Umwigisha atanga incamake y' ibimaze kwigishwa byose mu kigwa Iyo bakuba umubare w'imibarwa 4 n'umubare w'imibarwa3, babanza kwandika iyo mibare bahagaritse, igikuba kikajya munsi y'igikubwa ku buryo ibinyabumwe byandikwa munsi y'ibinyabumwe, ibinyacumi bikandikwa munsi y'ibinyacumi,ibinyajana bikandikwa munsi y'ibinyajana, nk'uko bikorwa mu mbonerahamwe y'iteranya. Buri gihe bahera iburyo bagana ibumoso; buri mubarwa w'igikubwa bawukubisha ibinyabumwe by'igikuba,ibyo babonye byandikwa munsi y'igikuba bahereye iburyo bajya ibumoso;babitsa iyo bibaye ngombwa. Buri mubarwa w'igikubwa bawukubisha ibinyacumi by'igikuba, ibyo babonye byandikwa munsi y'ibyo babonye bahereye mu mwanya w'ibinyacumi bagana ibumoso. Buri mubarwa w'igikubwa bawukubisha ibinyajana by'igikuba, igisubizo bakacyandika munsi y'ibinyajana by'ibyo babonye bahereye mu mwanya w'ibinyajana bagana ibumoso. Igikubo kiboneka bateranyije ibyo babonye bahereye iburyo bagana ibumoso. 2. 4. Imyitozo ntsindagirabumenyi 1233 x 341= 5134 x 123= 3796 x 272= 3. ISUZUMA Kora imyitozo ikurikira 1) 2345x213= 2) 3021x132= 3) 4032x231= 4) 5274x103=5) 6701x112= 4. UMUKORO Kora imyitozo ikurikira 1) 3054 x 307= 2) 3207 x 212= 3) 4592 x 107= 4) 5717 x 116= 5) 2978 x 351= | REB_igitabo_abakuze_imibare.pdf |
120Ig Itabo cy'umw Ig Isha IKIGWA CYA 43: KUGABANYA UMUBARE W'IMIBARWA 4 N'UMUBARE W'IMIBARWA 3 INTEGO Y'IKIGWA Nyuma y'ikigwa, umwigishwa araba ashobora gukora igabanya ridasagura n'irisagura ry'umubare w'imibarwa 4 n'umubare w'imibarwa 3. IMFASHANYIGISHO Igitabo cy'umwigisha, ikibaho, ingwa,... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo ku igabanya ry'umubare w'imibarwa2 n'umubare w'umubarwa umwe bakorera mu mahembe. Urugero: Gabanya imibare ikurikira mu buryo bwihuse 22:2=36:340:8=72:9=Umwigisha atanga imyitozo 2 yo kugabanya ; uwo ku igabanya ridasagura n'uwo ku igabanya risagura( kuko bikorwa kimwe) umubare w'imibarwa 3 n'umubare w'imibarwa 2. Yibutsa uko bikorwa iyo bibaye ngombwa Igabanya ridasagura 945 : 27 = 945:27 =35 Igabanya risagura 914 : 17 = | REB_igitabo_abakuze_imibare.pdf |
121Im Ibare y'abakuze 914 : 17 =53 hagasigara 13 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha asobanurira abigishwa ko iri gabanya rikorwa nk'iryo babonye mu gihe bagabanya umubare w'imibarwa 3 n'umubare w'imibarwa 2. 2. 2. Gusesengura Umwigisha atanga urugero mbonwa ku igabanya ridasagura n'igabanya risagura ry'umubare w'imibarwa 4 n'umubare w'imibarwa 3. Igabanya ridasagura 3672:136=27 Igabanya risagura 4573:136= 4573:136=33 hasigara 85 | REB_igitabo_abakuze_imibare.pdf |
122Ig Itabo cy'umw Ig Isha 2. 3. Ikomatanya Umwigisha atanga incamake y'ikigwa. Iyo bagabanyije hagasigara zeru babyita igabanya ridasagura. Naho iyo bagabanije ntibishire hagasigara umubare unyuranye na zeru bavuga ko iryo gabanya ari igabanya risagura. Iri gabanya rikorwa kimwe n'igabanya ry'umubare w'imibarwa 3 n'umubare w'imibarwa 2. 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo 1656:138= 2496:192= 2250:150 = 2952: 160 = 3. ISUZUMA Umwigisha atanga imyitozo y'isuzuma ngo amenye niba intego yagezweho Kora igabanya ry'imyitozo ikurikira1) 9911:187=2) 8390:112=3) 4784:104=4) 5450:147=5) 6912:256= 6) 7960:117= 4. UMUKORO: Ihurizo Umworozi w'inkoko afite imishwi 3440 arashaka kuyubakira ibibaro bihagije. Niba yarabaze agasanga buri kiraro kizajyamo imishwi 215 ubwo hakenewe ibiraro bingahe? Kora imyitozo y'igabanya ikurikira 1) 7790 :116=2) 7366:127= 3) 9800:213= 4) 8211:483= 5) 9591:417= | REB_igitabo_abakuze_imibare.pdf |
123Im Ibare y'abakuze IKIGWA CYA 44 : ISUZUMA CYA KABIRI RY' IMIBARE 1. Andika mu magambo 489 907 99 999 1 000 000 2. Andika mu mibare Ibihumbi magana inani na mirongo itandatu n'umunani Ibihumbi icumi na magana abiri na makumyabiri na kabiri 3. Shaka igisubizo 345+143= 123425+64515= 625+178= 439 830+57 832= 3468-1342= 6528-4749= 2461x23= 1172x121= 1320:110= 4. Amahurizo Umukozi wo mu rugo yagiye guhaha ku isoko yitwaje amafaranga 13000, agura litiro 5 z'amavuta yo guteka ku mafaranga 6500, agura ikiro kimwe cy'umunyu ku mafaranga 200, agura ibiro bitatu by'inyama ku mafaranga 4500, amafaranga asigaye ayaguramo ibiro bitatu by'inyanya. Ubwo ikiro kimwe k'inyanya kigura amafaranga angahe ? Niba ikiro kimwe k'inyama kigura amafaranga 1500, nibamutuma ibiro 6 by'inyama azitwaza amafaranga angahe? Gabanya litiro z'amata 2496 imiryango 192 ku buryo butabatera ishyari. Umucuruzi wa Butike GAKIRE yaranguye utujerekani 4 tw'amavuta yo guteka twa litilo 3 ku mafaranga 12 000. Akajerikani kamwe yakaranguye amafaranga angahe ? Niba akajerikani kamwe akagurisha amafaranga 3 500, GAKIRE azunguka amafaranga angahe kuri ayo mavuta yo guteka ? | REB_igitabo_abakuze_imibare.pdf |
124Ig Itabo cy'umw Ig Isha IKIGWA CYA 45 : GUKOSORA ISUZUMA 1. Andika mu magambo 489 : Magana ane na mirongo inani n'ikenda 907 : Magana akenda na karindwi 99 999 : ibihumbi mirongo ikenda n'ikenda na magana akenda na mirongo kenda n'ikenda 1 000 000 : Miliyoni imwe 2. Andika mu mibare Ibihumbi magana inani na mirongo itandatu n'umunani 868 000 Ibihumbi icumi na magana abiri na makumyabiri na kabiri 10 222 3. Shaka igisubizo 345+143 = 488 123425+64515 = 187 940 625+178 = 803 439 830+57 832 = 497662 3468-1342 = 1126 6528-4749 = 1779 2461x23 = 56 603 1172x121 = 141 812 1320:110 = 12 2. Gabanya litiro z'amata 2496 imiryango 192 ku buryo butabatera ishyari. 2496 : 192= 13 4. Ibisubizo by'amahurizo Ihurizo rya 1: Ibyo batanze Amafaranga umukozi yajyanye ku isoko : 13 000 Haguzwe litiro 5 z'amavuta ku mafaranga 6500 Haguzwe ikiro 1 cy'umunyu ku mafaranga 200 Haguzwe ibiro 3 by'inyama ku mafaranga 4500 Amafaranga asigaye yaguzwe ibiro 5 by'inyanya. Ibyo basaba Amafaranga umukozi yaguze ibiro 5 by'inyanya / amafaranga yasigaye Ikiguzi k'ikiro 1 k'inyanya | REB_igitabo_abakuze_imibare.pdf |
125Im Ibare y'abakuze Igisubizo Amafaranga yose hamwe yakoreshejwe ataragura inyanya : 6 500 + 200 + 4500 = 11 200 Amafaranga yaguzwe ibiro 5 by'inyanya : 13 000-11 200 = 1 800 Amafaranga yaguzwe ikiro 1 k'inyanya : 1 800 : 5 = 360 Ibiro 6 by'inyama bizagura: 1500 x 6 = 9000 Ihurizo rya 2: Litiro z'amata 2496 uzigabanyije imiryango 192 ku buryo bungana, buri muryango watwara litiro 13 z'amata: l 2496 : 192= l 13 Ihurizo rya 3: Ibyo batanze Gakire yaranguye utujerikani 4 twa litiro 3 kamwe, ku mafaranga 12 000 Akajerikani kamwe akagurisha 3500 Ibyo basaba Amafaranga yaranguje akajerikani 1 Amafaranga Gakire azunguka ku mavuta yose Igisubizo Amafaranga yaranguye utujerikani 4 tw'amavuta : 12 000 Amafaranga azagurisha utujerikani 4 tw'amavuta : 3500 x 4 = 14 000 Amafaranga Gakire azunguka ku mavuta yose : 14 000-12 000 = 2 000 | REB_igitabo_abakuze_imibare.pdf |
126Ig Itabo cy'umw Ig Isha IGICE CYA GATATU: IMIGABANE UMWITOZO W' IVUMBURAMATSIKO Gatarayiha mu gihe yabonagako ageze mu zabukuru yatekereje guha abana be umunani kugirango bizabafashe gutangira kwishakira ubuzima mu gihe azaba atakiriho. Buri mwana mu bana be 6 yamuhaye 1__ 8 k'isambu ye. Yahaye abana be umugabane ungana ute? We yasigaranye isambu ingana n' uwuhe mugabane ? Uyu musaza kandi yari afite inka 18 nazo 2__ 3 byazo yazigabiye abana be ku buryo bungana. Ubwo buri mwana yatwaye inka zingahe ? we yasigaranye inka zingahe ? IGISUBIZO Umugabane w' isambu Gatarayiha yahaye abana be :1__ 8 x 6 =6__ 8 Isambu Gatarayiha yasigaranye = 8__ 8 =6__ 8 =2__ 8 Umubare w' inka yahaye abana be = inka 18 x 2__ 3 = inka 12 Umubare w' inka buri mwana yatwaye = inka 12: 6 = inka 2 IKIGWA CYA 46 : GUSOMA NO KWANDIKA IMIGABANE ITARENGEJE IKIZIMA KIMWE, IKITA KITARENGA 10. INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gusoma no kwandika imigabane itarengeje ikizima ikita kitarenga 10. IMFASHANYIGISHO Uduti, imigozi, Amacunga, imineke, ibintu bifatika bivunika biboneka aho abigishwa baherereye cyangwa aragabanyamo uduce twinshi tungana UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo kugabanya badasagura/ basagura 140 : 2= 70 513: 4=128 Hasigara 1 | REB_igitabo_abakuze_imibare.pdf |
127Im Ibare y'abakuze 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha ahera ku kintu gifatika yazanye akagicamo uduce tungana abigishwa bitegereza. Urugero icunga, agakoni/ agati,... Umwigisha yerekana icunga ryose atararisatura, agakoni kadaciye,... akababwira ko ari ikizima kimwe. 1__ 4 1__ 4 basoma kimwe cya kane Iri cunga rigabanyijemo uduce 4 tungana buri gace ni kamwe muri bine bigize icunga ryose 2. 2. Gusesengura Umwigisha arerekana kandi asobanure buri gace kagaragara ku kizima 1 Aka gakoni kagabanijemo ibice 2 bingana Buri gace ni kimwe cya 2 ( kamwe muri tubiri) Ibi bice 2 birangana. 1__ 2Ubwo igice 1 n'icya 2 cy'agakoni. a. Kwandika imigabane Umwigisha yerekana uko bandika umugabane n'ibice biwugize Umugabane ugizwe n'ikibara n'ikita bitangukanwa n'akarongo gatambitse Ikibara kiri hejuru y'umurongo naho ikita kikaba munsi y'umurongo. Urugero 1__ 2Ikibara, Ikita. Umwigisha atanga izindi ngero zo gusoma no kwandika imigabane zigakorwa n'abigishwa nawe akagenzura ko babikora neza. b. Gusoma imigabane 1__ 2,1__ 4 umwigisha asobanurira abigishwa uko basoma imigabane ahereye kuyo banditse | REB_igitabo_abakuze_imibare.pdf |
128Ig Itabo cy'umw Ig Isha : basoma Kimwe cya kabiri. : basoma Kimwe cya kane. Umwigisha atanga izindi ngero zo gusoma no kwandika imigabane zigakorwa n'abigishwa nawe akagenzura ko babikora neza Urugero: Mu bishushanyo bikurikira andika umugabane werekanwa n'ahasize ibara, uvuge uko bawusoma. 1__ 2 basoma kimwe cya kabiri 1__ 3 basoma kimwe cya gatatu 1__ 4 basoma kimwe cya kane 2__ 6 basoma bibiri bya gatandatu 6__ 9 basoma bitandatu by'ikenda 2. 3. Ikomatanya Umwigisha atanga incamake y'ibyo bize ku migabane. Umugabane ugizwe n'ikibara n'ikita Ikibara cyerekanwa n'umubare w'uduce dusize cyangwa twakoreshejwe mu tundi biri hamwe. Ikita kerekanwa n'umubare w'uduce twose tugize ikintu. Urugero : Utuzu twose ni 9 ubwo ikita ni 9; Utuzu dusize ibara ni 3, ubwo ikibara ni 3 Umugabane ugaragazwa n'igishushanyo ni 3__ 9 Basoma bitatu by'ikenda. | REB_igitabo_abakuze_imibare.pdf |
129Im Ibare y'abakuze 2. 4. Imyitozo ntsindagirabumenyi Andika imigabane yerekanwe n'ibi bishushanyo 1. 2. 3. 3. ISUZUMA Soma iyi migabane 1__ 2, 1__ 5, 3__ 5, 1__ 8, 4__ 8, 1__ 3, 1__ 10, 1__ 9, 2__ 7 4. UMUKORO Andika mu migabane Bibiri bya karindwi Bine bya gatanu Birindwi by'ikenda Bitanu bya munani Bitandatu bya karindwi Kimwe cya kane Birindwi bya kenda Bibiri bya gatanu Bitanu bya munani Bitatu bya karindwi Ikenda by'icumi Andika iyi migabane mu magambo Urugero: 2__ 3: bibiri bya gatatu (Ibice bibiri kuri bitatu bitanga) 4__ 5: 2__ 7: 7__ 8: | REB_igitabo_abakuze_imibare.pdf |
130Ig Itabo cy'umw Ig Isha IKIGWA CYA 47 : GUSOMA NO KWANDIKA IMIGABANE ITARENGEJE IKIZIMA KIMWE, IKITA KIGABANYIKA NA 10 KANDI KITARENGA 100. INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gusoma no kwandika imigabane itarengeje ikizima, ikita kigabanyika na 10 kandi kitarenga 100. IMFASHANYIGISHO Uduti, Imigozi, Amacunga, imineke, ibintu bifatika kandi byacibwa mo uduce biboneka aho abigishwa baherereye. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo gusoma no kwandika imigabane itarengeje ikizima 1, ikita kigabanyika na 10, kandi kitarengeje 100 Urugero Andika mu mibare Bine by'icumi 4__ 10 Bibiri bya karindwi 2__ 7 Andika mu magambo 6__ 9bitandatu by'ikenda 3__ 7bitatu bya karindwi 2. IKIGWA GISHYA Gusoma, kwandika imigabane itarenze ikizima kimwe, ikita kigabanyika na 10 kandi kitarengeje 100 2. 1. Gutahura Umwigisha ahera ku kintu gifatika yazanye akagicamo uduce tungana abigishwa bitegereza Urugero icunga, agakoni/ agati,... Umwigisha afatanyije n'abigishwa baraca ikintu bazanye mo uduce 10, cyangwa 20,......... 100 ni ukuvuga ko umubare w'uduce afata uba ugabanyika na 10 ugashira kandi nturenge ijana Urugero Bafate indimu bakatemo uduce 10 tungana | REB_igitabo_abakuze_imibare.pdf |
131Im Ibare y'abakuze Bavuge kandi bandike umugabane babonye uko bafashe buri gace mu 10 Babona 1__ 10, 2__ 10, 3__ 10,...., 9__ 10 2. 2. Gusesengura Umwigisha ashushanya imigabane ku kibaho akagenda abazaho abigishwa ibibazo Urugero rwa 1 Itegereze iki gishushanyo Igishushanyo kigizwe n'utuzu tungahe? twose hamwe ni 10 Utuzu dusize irangi ni tungahe? ni tune Ahasize irangi herekanwa n'uwuhe mugabane? ni bine bya cumi Wandikwa 4__ 10 Urugero rwa 2 Iki gishushanyo kigizwe n'utuzu tungahe twose hamwe? ni 30 Udusize irangi ni tungahe ? ni 20 Ahasize irangi herekanwa n'uwuhe mugabane? ni makumyabiri bya mirongo itatu Wandikwa 20__ 30 a. Kwandika imigabane Umwigisha yerekana uko bandika imigabane itarengeje ikizima 1, ifite ikita kigabanyika na 10 kandi kitarengeje 100 Bahereye ku ngero abigishwa bandika imigabane babonye Urugero Bafate agakoni bakatemo uduce mirongo itatu tungana Umwe afatemo uduce 14, ubwo utwo twerekana uwuhe mugabane mu duce twose duhari ? Uwo mugabane ni cumi na kane bya mirongo itatu Wandikwa 14__ 30 Umugabane ugizwe n'ikibara n'ikita bitandukanwa n'akarongo gatambika | REB_igitabo_abakuze_imibare.pdf |
132Ig Itabo cy'umw Ig Isha Ikibara kiri hejuru y'umurongo naho ikita kikaba munsi y'umurongo. Umwigisha atanga izindi ngero zo gusoma no kwandika imigabane zigakorwa n'abigishwa nawe akagenzura ko babikora neza. b. Gusoma imigabane umwigisha asobanurira abigishwa uko basoma imigabane ahereye kuyo banditse 14___ 100 basoma mirongo irindwi na gatanu by' ijana 54___ 90 basoma mirongo itanu na kane bya mirongo ikenda Umwigisha atanga izindi ngero zo gusoma no kwandika imigabane zigakorwa n'abigishwa nawe akagenzura ko babikora neza Urugero: Andika umugabane werekanwa n'ibishushanyo uvuge uko bawusoma Ahasize irangi ni cumi n'umunani bya mirongo itatu Bandika 18___ 30 Ahadasize ni cumi na kabiri bya mirongo itatu 12___ 30 Ahasize irangi ni makumyabiri na kane bya mirongo ine Bandika 24___ 40 Ahadasize irangi ni cumi na gatandatu bya mirongo ine 16___ 40 | REB_igitabo_abakuze_imibare.pdf |
133Im Ibare y'abakuze 2. 3. Ikomatanya Umwigisha atanga incamake y'ibyo bize ku migabane. Umugabane ugizwe n'ikibara n'ikita. Ikibara kerekanwa n'umubare w'uduce dusize cyangwa twakoreshejwe mu tundi biri hamwe. Ikita kerekanwa n'umubare w'uduce twose tugize ikintu 2. 4. Imyitozo ntsindagirabumenyi 1. Bara wandike imigabane yerekanwa n'ibi bishushanyo (umugabane werekana ahasize ibara n'umugabane werekana ahadasize ibara) 2. Bara wandike imigabane yerekanwa n'ibi bishushanyo (umugabane werekana ahasize ibara n'umugabane werekana ahadasize ibara) 4. Soma iyi migabane 23 40 65 80 36 100 | REB_igitabo_abakuze_imibare.pdf |
134Ig Itabo cy'umw Ig Isha 3. ISUZUMA Andika mu migabane Cumi na bitatu bya mirongo ine Makumyabiri na birindwi bya mirongo irindwi Mirongo itatu n'ikenda bya mirongo itanu Mirongo ine na bitatu bya mirongo inani Mirongo itanu na birindwi bya mirongo itandatu 4. UMUKORO Andika iyi migabane mu magambo 35 50 64 80 56 90 98 100 | REB_igitabo_abakuze_imibare.pdf |
135Im Ibare y'abakuze IKIGWA CYA 48 : IMYITOZO YO GUSOMA NO KWANDIKA IMIGABANE Umwigisha atanga imyitozo yo gusoma no kwandika imigabane y'amasomo ya 45 na 46. 1. Andika kandi usome imigabane yerekanwa n'ibi bishushanyo, ahasize irangi n'ahadasize irangi 2. Andika mu magambo 4 5 ; 12 20 ; 24 40 ; 68 80 3. Andika mu mibare Bitanu by'ikenda Umunani by'icumi Mirongo itatu na kane bya mirongo itanu Mirongo itanu na bitatu bya mirongo inani Mirongo irindwi bya mirongo ikenda | REB_igitabo_abakuze_imibare.pdf |
136Ig Itabo cy'umw Ig Isha IKIGWA CYA 49 : GUTERANYA IMIGABANE IHUJE IKITA ITARENGEJE IKIZIMA KIMWE, IKITA KITARENGA 10 INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora guteranya imigabane ihuje ikita,igisubizo kitarenze 1, kandi ikita kitarenze 10 IMFASHANYIGISHO Igitabo cy'umwigisha, ingwa, ikibaho. UKO IKIGWA GITANGWA 1. INTANGIRIRO Soma iyi migabane: 1) 5__ 8,2__ 10,1__ 6,7__ 9 2) Andika umugabane mu mibare a) ikibara =1,ikita=7 b) ikibara=3, ikita =8 c) ikibara =1,ikita =10 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha ahereye kuri iki gishushanyo asaba abigishwa uko bateranya imigabane ihuje ikita yifashishije ibishushanyo. Urugero: 2__ 10+4__ 10= 6__ 10 2. 2. Gusesengura Umwigisha asobanura uko bateranya imigabane ihuje ikita ahereye ku rugero rwatanzwe Nimwitegereze igishushanyo | REB_igitabo_abakuze_imibare.pdf |
137Im Ibare y'abakuze Umubare w'utuzu twose udusize n'utudasize ni tungahe? Ni 10 Ahasize ibara ry'icyatsi herekana uwuhe mugabane? ni 2 10 Ahasize ibara ry'ubururu harerekanwa n'uwuhe mugabane? ni 4 10 Iyo ubaze ahasize icyatsi hamwe n'ahasize ubururu herekanwa n'uwuhe mu gabane? 6 10 Umwigisha asobanura ko kubarira hamwe byegeranye ari nko guteranya ibyo bice byasaga nk'aho bitatanye akabereka n'uko byandikwa. 2__ 10+4__ 10= 6__ 10 Umwigisha asobanura uko iteranya ry'imigabane ihuje ikita rikorwa Umwigisha atanga izindi ngero zikorwa n'abigishwa we akagenzura ko babikora neza. =+61 63 4 6 =+81 84 5 8 3__ 4+1__ 4= 3+1____ 4 =4__ 4= 1 2. 3. Ikomatanya Umwigisha atanga incamake y'ibyizwe. Iyo bateranya imigabane ihuje ikita bateranya ibibara byayo, maze umubare ubonetse ukaba ikibara cy'umugabane w'igisubizo bakandukura ikita rusange. 2. 4. Imyitozo ntsindagirabumenyi 1) 23 77+= 2) 64 10 10+= 3) 13 55+= | REB_igitabo_abakuze_imibare.pdf |
138Ig Itabo cy'umw Ig Isha 3. ISUZUMA Mariya yaguze umwenda wo kudodesha, bwa mbere yaguzeho 2 6 byawo, awuhaye umudozi arapima asanga ntabwo wamukwira amutegeka kongera kuguraho 1 6 cyawo. Ubwo yaguze umwenda ungana n'uwuhe mugabane wose hamwe. 4. UMUKORO Teranya iyi migabane 1) 5__ 8+2__ 8= 2) 1__ 4+2__ 4= 3) __ 5+__ 5= 7__ 5 4) 5__ 10+4__ 10= 5) 1__ 9+5__ 9= 6) __ 6+2__ 6= | REB_igitabo_abakuze_imibare.pdf |
139Im Ibare y'abakuze IKIGWA CYA 50 : GUKURAMO IMIGABANE IHUJE IKITA ITARENGEJE IKIZIMA KIMWE, IKITA KITARENGA 10 INTEGO Y'IKIGWA Nyuma y'iki kigwa umwigishwa araba ashobora g ukuramo imigabane ihuje ikita igisubizo kitarenze 1, kandi ikita kitarenze 10 IMFASHANYIGISHO Ibintu bishobora kubarwa,ibishushanyo. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo guteranya imigabane ihuje ikita ku kibaho,abigishwa bayikore. Urugero: =+71 74 =+52 53 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha ahereye ku gishushanyo abaza abigishwa uko bakuramo imigabane. Umwigisha asaba abigishwa kugaragaza umugabane usigara,igihe ibice bine bingana byaba bikuwe mu kizima kimwe. Umwigisha asaba abigishwa kubyandika mu mibare 2. 2. Gusesengura Umwigisha abaza abigishwa ibibazo bijyanye n'iki gishushanyo Urugero: Umubare w'utuzu dusize ibara ni tungahe ? ni 4 Ni uwuhe mugabane ? ni 4 6 Utuzu dusigaye tudasize ibara twerekanwa n'uwuhe mugabane? ni 2 6 | REB_igitabo_abakuze_imibare.pdf |
140Ig Itabo cy'umw Ig Isha Utuzu dusize, dukuye ibara mu kazu kamwe hazigara utuzu tungahe dusize? Ni 3 Twerekamwa n'uwuhe mugabane? 3/6 Umwigisha asobanura uko bakuramo imigabane ihuje ikita ahereye ku rugero yatanze kandi akerekana uko byandikwa. 41 3 666-= 2. 3. Ikomatanya Umwigisha atanga incamake y'ibyizwe Iyo dukuramo imigabane ihuje ikita dukuramo ibibara hagati yabyo, tukandukura ikita rusange. Urugero: 41 3 666-= 2. 4. Imyitozo ntsindagirabumenyi 99-98 = 63-63 = 3. ISUZUMA 31 66-= 32 44-= 30 22 45 45-= 4. UMUKORO Kora iyi myitozo 3__ 9-3__ 9= 5__ 10-4__ 10= 6__ 6-2__ 6= | REB_igitabo_abakuze_imibare.pdf |
141Im Ibare y'abakuze IKIGWA CYA 51: GUKUBA UMUGABANE N'UMUGABANE, IGIKUBO KITARENGA IKIZIMA KIMWE. INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora g ukuba umugabane n'umugabane igikubo kitarenga ikizima 1 IMFASHANYIGISHO Igitabo cy'umwigisha, ingwa,ikibaho. UKO IKIGWA GITAGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo guterenya no gukuramo imigabane ihuje ikita Shaka igisubizo 31 55+= 84 99-= 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha asaba abigishwa gufata urupapuro maze bakarugabanyamo ibice 2 bingana. Igice babonye bakakigabanyamo ibindi bice bibiri bingana. Umwigisha abasaba kuvuga umugabane w'agace gato babonye. Umwigisha yifashisha igishushanyo agasaba abigishwa kwitegereza bagatahura ko umubare w'utuzu dusize amaba atandukanye ari utuzu 2. | REB_igitabo_abakuze_imibare.pdf |
142Ig Itabo cy'umw Ig Isha Abigishwa babara utuzu twose maze bakavumbura ko umubare watwo ari 12. Abigishwa bandika umugabane w'utuzu dusize amabara atandukanye bakabona ko ari 2_ 12 Umwigisha aratanga urugero rw'ikitegererezo rw'uko bakuba imigabane 2 itarengeje ikizima. urugero: 2__ 4x1__ 3= 2__ 12 2. 2. Gusesengura Umwigisha atanga urundi rugero, rwo gukuba imigabane, rukorwa n'abigishwa akabayobora aho bibaye ngombwa. Urugero: 3__ 5x2__ 5= 6__ 25 2. 3. Ikomatanya Umwigisha atanga incamake y'uko bakuba imigabane Iyo bakuba imigabane bakuba ibibara by'iyo migabane, igikubo kikaba ikibara cy'umugabane w'igisubizo hanyuma bagakuba n'ibyita by'iyo migabane igikubo kibonetse kikaba ikita cy'umugabane w'igisubizo. | REB_igitabo_abakuze_imibare.pdf |
143Im Ibare y'abakuze 2. 4. Imyitozo ntsindagirabumenyi Shaka igisubizo 3__ 4x1__ 2= 7__ 8x3__ 4= 6__ 8x2__ 3= 9__ 10x3__ 4= 7__ 9x6__ 10= 3. ISUZUMA Kora imyitozo y'ikuba 3__ 10x5__ 7= 2__ 20x3__ 4= 1__ 10x7__ 9= 24__ 30x1__ 2= 4__ 7x8__ 9= 4__ 7x2__ 3= 4. UMUKORO Shaka igikubo 2__ 5x3__ 4= 3__ 4x1__ 2= 2__ 8x1__ 3= | REB_igitabo_abakuze_imibare.pdf |
144Ig Itabo cy'umw Ig Isha IKIGWA CYA 52 : GUKUBA UMUGABANE UFITE IKITA 100 N'UMUBARE USHYITSE UGABANYIKA N'IJANA. INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gukuba umugabane ufite ikita 100 n'umubare ushyitse ugabanyika na 100 IMFASHANYIGISHO Igitabo cy'umwigisha, ingwa,ikibaho. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigishwa atanga imyitozo yo gukuba imigabane igisubizo kitarenga ikizima 1 Urugero: 2__ 8x1__ 3= 2__ 24 2__ 20x3__ 4= 6__ 80 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha yandika ingero ku kibaho agasaba abigishwa kurwitegereza Urugero rwa 1: 2___ 100 x 100 = 2 Urugero rwa 2: 3___ 100 x 200 = 6 2. 2. Gusesengura Umwigisha abaza ibibazo ku ngero bamaze kubona : Urugero rwa 1 Vuga ikita cy'uyu mugabane? Vuga ikibara cyawo? Vuga umubare bakubye n'umugabane ? Igisubizo cyabonetse ni umugabane cyangwa ni umubare ushyitse? Urugero rwa 2 Erekana ikita cy'uyu mugabane: 100 Erekana ikibara cyawo: 3 Bawukubye n'uwuhe mubare: 200 Igisubizo cyabonetse ni kangahe: 6 | REB_igitabo_abakuze_imibare.pdf |
145Im Ibare y'abakuze 2. 3. Ikomatanya Umwigisha atanga incamake y'uko bakuba umugabane n'umubare ugabanyika na 100 Iyo bakuba umugabane n'umubare ugabanyika na 100 bakuba ikibara n'uwo mubare, igikubo kikaba ikibara cy'umugabane w'igisubizo naho ikita cy'uwo mu-gabane ( umugabane w'igisubizo ) ukaba 100. Kuko ikibara cy'uwo mugabane w'igisubizo kigabanyika na 100 bakora igabanya, ridasagura bakandika igisubizo. 2. 4. Imyitozo ntsindagirabumenyi 37___ 100 x 200 = 57___ 100 x 300 = 48___ 100 x 500 = 68___ 100 x 700 = 72___ 100 x 900 = 3. ISUZUMA Kora imyitozo 47___ 100 x 300 = 63___ 100 x 700 = 39___ 100 x 600 = 25___ 100 x 500 = 69___ 100 x 2700 = 4. UMUKORO 4___ 100 x 1000 = 50___ 100 x 400 = 36___ 100 x 200 = Amahurizo 1. Mfite amafaranga ibihumbi 150 000, niba narishyuyeho umuhinzi 20___ 100 byayo mu minsi itatu twakoranye, ubwo namuhaye amafaranga angahe ? 2. Nafashe inguzanyo muri banki ingana n'amafaranga 100 000. Maze kwishyuraho 20___ 100 byayo. Ubwo maze kwishyura amafaranga angahe? | REB_igitabo_abakuze_imibare.pdf |
146Ig Itabo cy'umw Ig Isha IKIGWA CYA 53 : IMYITOZO YO GUKUBA IMIGABANE Umwigisha atanga imyitozo yo gukuba imigabane y'amasomo ya 53 na 54. Shaka igisubizo 5__ 6x2__ 7= 3__ 7x1__ 3= 3__ 10x5__ 7= 22__ 30x1__ 7= 17__ 20x2__ 3= 15__ 30x1__ 2= 7__ 9x9__ 10= Shaka igisubizo 3___ 100 x 300 = 12___ 100 x 500 = 25___ 100 x 400 = 45___ 100 x 8600 = 21___ 100 x 7200 = IKIGWA CYA 54 : ISUZUMA RYA GATATU RY' IMIBARE Imyitozo y'Isuzuma I. Shaka igisubizo 15___ 100 x 700 = 14___ 100 x 800 = 25___ 100 x 7200 = 37___ 100 x 1700 = 6__ 9+1__ 9= 2__ 7+1__ 7= 6__ 7-2__ 7= 3__ 5+2__ 5= II. Andika umugabane ahasize ibara, ahadasize ibara 1. Utuzu twose turangana, andika umugabane w' ahadasize ibara 2. Utuzu twose turangana, andika umugabane w' ahasize ibara | REB_igitabo_abakuze_imibare.pdf |
147Im Ibare y'abakuze III. Andika mu migabane 1. mirongo ine na kane bya mirongo inani2. mirongo ikenda by'ijana IV. Andika mu magambo: 6 10, 2 3 V. Amahurizo ku migabane 1. Mfite umugozi upima m 25 maze guko reshaho 1 5 cyawo nubaka agatara k'amasahani n'ibindi bikoresho byo mu gikoni. Ubw o nakoresheje umugozi ureshya ute? Nsigaranye umugozi ureshya ute? 2. Uwera afite amacunga 36, yahaye inshuti ye bitatu bya kenda byayo a) Uwera yatanze amacunga angahe? b) Uwera asigaranye amacunga angahe? 3. Kabano afite ihene 90, yagurishijemo 2 6 byazo. a) Vuga umubare w'ihene yagurishije. b) Asigaranye ihene zingahe? 4. Nafashe umwenda muri banki ungana na 2 000 000. Niba nzatanga inyungu ingana na byayo buri kwezi, ubwo inyungu ya buri kwezi ingana n'amafaranga angahe? 5) Petero ni umuhinzi mworozi. Petero yahinze umurima w' amacunga asarura amacunga 5000. 2__ 5 byay' ayo macunga yabigemuye ku ruganda rukora imitobe. Kuri urwo ruganda yagemuyeyo amacunga angana iki ? Petero bamwishyuye amafaranga angahe niba buri cunga yararigurishije amafaranga 50? Amacunga asigaye Petero yayajyanye ku isoko buri cunga arigurisha ku mafaranga 30. Umugabane w' amacunga yajyanye ku isoko ni uwuhe? Yakuyemo amafaranga angahe ? Amacunga yose yayakuyemo amafaranga angahe ? Petero kandi yoroye inka 12, ariko 1__ 4 cy' inka ze nizo zikamwa. Buri inka ikamwa l 20 z' amata ku munsi akagemurwa ku ruganda. Inka zikamwaga ni zingahe ? zikamwaga l zingahe z' amata ku munsi? 6) Karekezi yateye ishyamba ry' ibiti 344 by' ubwoko bunyuranye. 3__ 8 byabyo ni inturusu, 4__ 8 ni pinusi naho 4__ 8 ni gereveriya. Shaka umubare w' ibiti bya buri bwoko ? Shaka amafaranga yakuye mu ishyamba rye niba igiti cy' inturusu yarakigurishije ku mafaranga 5000, icya pinusi ku mafaranga 4000, icya gereveriya ku mafaranga 3500 | REB_igitabo_abakuze_imibare.pdf |
148Ig Itabo cy'umw Ig Isha IKIGWA CYA 55 : GUKOSORA ISUZUMA Ibisubizo 15___ 100 x 700 = 105 25___ 100 x 800 = 112 25___ 100 x 7200 = 1800 37___ 100 x 1700 = 629 6__ 9+1__ 9= 7__ 9 2__ 7+1__ 7= 3__ 7 6__ 7-2__ 7= 4__ 7 3__ 5+2__ 5= 7__ 9 II. Erekanisha umugabane ahasize ibara 1. Umugabane w' ahadasize ibara ni 4__ 9 2. Umugabane w'ahasize ni 5__ 9 III. Andika mu migabane 1) Mirongo ine na kane bya mirongo inani: 44__ 80 2) Mirongo ikenda by'ijana: 99___ 100 IV. Andika mu magambo 6 10 : bitandatu by'icumi 2 3 : bibiri bya gatatu V. Amahurizo ku migabane 1) Mfite umugozi upima metero 25 maze gukor eshaho 1 5 cyawo nubaka agatara k'amasahani n'ibindi bikoresho byo mu gikoni. Ubwo nakoreshe je umugozi ureshya ute? Nsigaranye umugozi ureshya ute? Nakoresheje umugozi ureshya na metero 5 =metero 25 x 1 5 | REB_igitabo_abakuze_imibare.pdf |
149Im Ibare y'abakuze 2) Uwera afite amacunga 36, yahaye inshuti ye bitatu bya kenda byayo a. Uwera yatanze amacunga angahe? Ni amacunga 12 = 36 x3__ 9 b. Uwera asigaranye amacunga angahe? Ni amacunga 36-amacunga 12 = 24 3) Kabano afite ihene 90, yagurishijemo 2 6 byazo. a) Vuga umubare w'ihene yagurishije. Yagurishije ihene 30 = 90 x2 6 b) Asigaranye ihene zingahe? Ihene 90-ihene 30= ihene 60 4) Nafashe umwenda muri banki ungana na 2 000 000. Niba nzatanga inyungu ingana na 22___ 100 byayo mu mwaka. Ubwo inyungu mu mwaka ni amafaranga angahe? Inyungu mu mwaka ni 2 000 000 x 22___ 100 = 44 000 5) Umubare w'amacunga yagemuwe ku ruganda= 5000 x 2__ 5= amacunga 2000 Amafaranga bamuhaye ku macunga yagemuye ku ruganda= frw 50 x 2000= frw 100. 000 Umubare w' amacunga Petero yajyanye ku isoko = amacunga 5000-amacunga 2000= amacunga 3000 Amafaranga bamuhaye ku macunga yagemuye ku isoko= frw30 x 3000= frw 90000 Amafaranga yose yakuye mu macunga = 100000+90000= frw190000 Umubare w' inka zikamw a= inka 12x1__ 4= inka 3 Ingano y' amata akamwa buri munsi = l 20 x 3 = l 60000 6) Umubare w' ibiti by' inturusu = 344x3__ 8 = 129 Umubare w' ibiti bya Pinusi= 344x 4__ 8 = 172 Umubare w' ibiti bya gereveriya = 344x1__ 8 = 43 Umubare w' amafaranga yagurishijwe inturusu = frw 129 x 5000= 645000 Umubare w' amafaranga yagurishijwe pinusi = 174 x frw 4000 = 696000 Umubare w' amafaranga yaguris hijwe gereveriya = frw 3500 x 43= 150500 Amafaranga yakuye mu ishyamba = frw 645000 + 696000 +150500= 1491500 | REB_igitabo_abakuze_imibare.pdf |
150Ig Itabo cy'umw Ig Isha IGICE CYA KANE: INGERO UMWITOZO W'IVUMBURAMATSIKO (IGICE CYA 1: INGERO) Mu kiruhuko cya Noheri umuryan go wa Semana ugizwe n' umugabo n' umugore n' abana 3 utuye i Kigali wagiye kuruhukira mu giturage mu muryango avukamo utuye i Muhanga. Urugendo bagombaga gukora rwari km 50 kandi bakarukora mu gihe k' isaha imwe. Bageze ku Kamonyi bari bamaze gukora 1__ 2 cy' urugendo rwabo bagize inyota n' inzara maze kugirango bice isari buri wese yanyoye icupa ry' umutobe rya cl 100 arya n' umugati wa g 200. Kugera ku Kamonyi bagenze iminota ingahe ? bahageze ryari niba barahagurutse saa sita z' amanywa? Bari bamaze gukora urugendo rungana iki niba bari bageze mu cya kabiri cy' urugendo bagombaga gukora? Ese bose hamwe banyweye umutobe ungana na l zingahe n' imigati ipima ibiro bingahe mu gihe bicaga isari ? IBISUBIZO KU IVUMBURAMATSIKO Urugendo bari bamaze gukora kugera ku Kamonyi = km 50 : 2 = km 25 Igihe bakoresheje kuva i kigali kugera ku Kamonyi= iminota 60 : 2 = iminota 30 Igihe yagereye ku Kamonyi = 12h00+ iminota 30= 12h30 Ingano y' umutobe banyoye = cl 100x5 = cl 500=l 5Ingano y' imigati bariye = g 200 x 5 = g 1000= kg1 IKIGWA CYA 56: GUPIMA, GUSOMA NO KWANDIKA INGERO Z'UBUREBURE INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gupima,gusoma no kwandika ingero z'uburebure IMFASHANYIGISHO Igitabo cy'umwigisha, udukoni, metero bushumi, metero buhine, dekametero. UKO IKIGWA GITANGWA 1. INTANGIRIRO Gusaba abigishwa kuvuga uburyo bakoresha kugira ngo bamenye indeshyo y'umuntu,uburebure bw'umurima,bw'ishuri....... 2. IKIGWA GISHYA Ipima ry'ingero z'uburebure | REB_igitabo_abakuze_imibare.pdf |
151Im Ibare y'abakuze 2. 1. Gutahura Umwigisha yereka abigishwa ibikoresho byo gupima uburebure, abaza ho ibibazo 2. 2. Gusesengura: Umwigisha akoresha imyitozo yo gupima uburebure bw'ibintu binyuranye bifashishije metero cyangwa uduti tureshya na metero cyangwa dekametero Bimwe mu bikoresho byifashishwa mu gupima uburebure Abigishwa bavuga igisubizo babonye k'ikandikwa 2. 3. Ikomatanya Umwigisha akusanya ibyo bamaze kwiga byose bikandikwa ku kibaho abigish-wa bakabyandika mu makayi yabo Mu gupima uburebure bw'ibintu, bw'ahantu n'ubw'abantu twifashisha : i metero, imetero bushumi na metero buhine. | REB_igitabo_abakuze_imibare.pdf |
152Ig Itabo cy'umw Ig Isha 2. 4. Imyitozo ntsindagirabumenyi Umwigisha aratanga imyitozo yo gupima ingero z'uburebure bakoresheje imetero cyangwa ibindi bikoresho byabugenewe mu gupima uburebure bavuga kandi bandika umubare babonye Pima uburebure n'ubugari bw'icyumba k'ishuri Pima uburebure n'ubugari bw'ikibuga cy'umupira, Pima uburebure bwa mugenzi wawe Pima uburebure n'ubugari bw'ubusitani bw'ishuri Pima uburebure n'ubugari bw'ikibaho Pima uburebure n'ubugari bw'urugi 3. ISUZUMA Vuga kandi wandike umuzenguruko w'ubusitani bwapimwe. Vuga kandi wandike umuzenguruko w'icyumba k'ishuri cyapimwe Vuga kandi wandike umuzenguruko w'ikibaho cyapimwe Gereranya wandika uburebure bwa bagenzi bawe babiri bapimwe 4. UMUKORO pima uburebure bw'urukuta rw'inzu yawe pima uburebure bwa mugenzi wawe vuga ibikoresho uzi bikoreshwa mu gupima uburebure bw'ibintu bitandukanye n' akamaro kabyo | REB_igitabo_abakuze_imibare.pdf |
153Im Ibare y'abakuze IKIGWA CYA 57 : GUHINDURA INGERO Z'UBUREBURE INTEGO Y'IKIGWA Nyuma y'iki kigwa umwigishwa araba ashobora guhindura ingero z'uburebure IMFASHANYIGISHO Metero buhine, metero bushumi, dekametero, umugozi, uduti,... UKO ISOMO RITANGWA 1. INTANGIRIRO Umwigisha aratanga imyitozo yo gupima uburebure bw'ibintu bifashishije ibikoresho byabugenewe. Urugero: uburebure n'ubuhagari bw'ishuri, uburebure n'ubugari bw'ikibuga,.... 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha yandika ku kibaho ingero nto z'uburebure ahereye ku rugero fatizo arirwo metero, agasaba abigishwa kuzitegereza. Umwigisha asaba abigishwa kuvuga muri kilometero uburebure buri hagati y'ahantu habiri hazwi mu karere baherereyemo; Umwigisha asobanurira abigishwa ko uretse metero na kilometero hari izindi ngero z'uburebure zikoreshwa mu buzima busanzwe arizo: hegitometero, dekametero, desimetero, santimetero na mirimetero. 2. 2 Gusesengura Umwigisha agenda asobanura isano riri hagati y'ingero z'uburebure nto kuri metero yerekana n'uko zirutana amaze kwerekana uko zandikwa mu buryo buhinnye: km;hm; dam; m; dm; cm; cm. Umwigisha asobanura uko izo nge ro zigenda zirutanwa yifashisha imbonerahamwe: km 1 = hm 10 hm 1= dam 10 dam 1 = m 10m 1 = dm 10dm 1 = cm 10 cm 1 = mm 10 | REB_igitabo_abakuze_imibare.pdf |
154Ig Itabo cy'umw Ig Isha 2. 3. Ikomatanya Umwigisha atanga incamake y'ikigwa gishya yigishije: Urugero-fatizo mu ngero z'uburebure ni metero: m; Izindi ngero ni km;hm;dam;dm;cm na mm. Ingero z'uburebure zigenda zirutanwa inshuro 10 nk'uko bigaragara mu mbonerahamwe Km hm dam m dm Cm mm 1 0 1 01 01 01 0 1 0 2. 4. Imyitozo ntsindagirabumenyi Uzurisha umubare ahari utudomo 1) km2= hm.... 2) hm3 = dam... 3) dam5 = m... 4) m8 = dm... 5) dm 7 = cm... 6) cm11 = mm... 3. ISUZUMA Uzurisha umubare ahari utudomo 1) km5 = dam..... 2) dam13 = dm.... 3) dm 21= mm... 4) dam 100 = km... 5) m3000 = hm... 4. UMUKORO Kora iyi myitozo wifashishije imbonerahamwe y'ingero z'uburebure dm 1 = cm.... m 3 = dm... m 1 = mm.... dm 1 = mm... dm 8 = mm... cm 15 = mm... m 6 = mm... mm 900 = m... mm 540 = cm... | REB_igitabo_abakuze_imibare.pdf |
155Im Ibare y'abakuze IKIGWA CYA 58 : GUTERANYA NO GUKURAMO INGERO Z'UBUREBURE INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora guteranya no gukuramo ingero z'uburebure yifashishije imbonerahamwe y'izo ngero. IMFASHANYIGISHO Metero buhine, metero bushumi. Dekametero. Umugozi, uduti,... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo guhindura ingero z'uburebure Urugero : m6 = mm... km15 = cm.. 2. IKIGWA GISHYA 2. 1. Gutahura: Umwigishwa yandika ingero z'imyitozo yo guteranya no gukuramo ingero z'uburebure kandi akayikosora. 1) km1+ hm2 = m.... Igisubizo: km1+ hm2 = m 1000 + m 200 = m1200 2) km 5-dam 200 = m... Igisubizo: km 5-dam 200 = m 5000-m 2000 = m 3000 3) m25 + dm 15 = cm... Igisubizo: m25 + dm 15 = cm 2500 + cm150 = cm 2650 2. 2. Gusesengura Umwigisha abwira abigishwa gukora indi myitozo we akagenzura uko babikora, akabayobora aho bibaye ngombwa. km 1=dam 100hm2=dam 20 km hm dam m dm Cm mm 1 0 0 2 0 m9-m8=dm..... cm434-dm13= cm... | REB_igitabo_abakuze_imibare.pdf |
156Ig Itabo cy'umw Ig Isha km23-dam135= dam.. hm30+m2500= dm... 2. 3. Ikomatanya Umwigisha atanga incamake y'uko bakora iteranya n'ikuramo ry'ingero z'uburebure Iyo bateranya cyangwa bakuramo ingero z'uburebure, buri gihe babanza guhindura ingero zakoreshejwe mu rugero rumwe rutangwa mo igisubizo bifashishije imbonera-hamwe maze bagateranya /bagakuramo ibyo babonye. 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo 1) (dm 48 + m 5)-dm 25 = mm... 2) (mm 7036-dm 14)-dm 5 = mm... 3) (dm 27 + cm 146)-( cm 110 + dm 3) = mm... 4) km 5-hm 20= dam... 5) dam 150-m 150= m.... 3. ISUZUMA Shaka igisubizo 1) hm34-m40 +30dm =dm... 2) ( mm 669-mm 346)-( cm 12-mm 70) = mm... 3) mm 4850-( m 3 + dm 17) = mm... Amahurizo 1) Ku gahanda ko mu rusisiro rwacu kareshya na km6, tumaze guteraho ibiti birwanya isuri ahareshya na hm25. Ubwo dusigaje gutera ahantu hareshya na dam zingahe? 2) Batondetse imishumi ibiri y'impapuro. Umwe upima cm 35, undi upima dm 5. Shaka uburebure bw'iyo mishumi yombi hamwe muri cm. 4. UMUKORO Kora iyi myitozo 1) km 5 +dam1000-dm 700 = dm... 2) m 7+ dm 4 = dm... = cm.... 3) dam 15-m 45=m... = dm... 4)m 2 + cm 120 = dm... = 5) cm 580-dm 3 = cm... m400+ hm20= dam.. 6) dam 70-m..=m520 7) (km3+km4)-m..=km8 8) hm2+dam14=dam9) m40+m30=m... =hm... na dam... 10) m150+hm1=m... 11) hm2+dam7=dam... | REB_igitabo_abakuze_imibare.pdf |
157Im Ibare y'abakuze IKIGWA CYA 59 : IKUBA, IGABANYA RY'INGERO Z'UBUREBURE N'UMUBARE USHYITSE. INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gukuba no kugabanya ingero z'uburebure IMFASHANYIGISHO Ibikoresho byo gupima uburebure UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha akoresha imyitozo yo gupima uburebure bw'ibintu bifatika Urugero uburebure bw'ishuri, bw'ikibuga,.... 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha atanga ingero zo gupima, abigishwa bakurikiye, bitegereza neza ibyo arimo akora yifashisha ingero z'uburebure zizwe ( m, dm, cm, mm ) Urugero Pima m 3 inshuro 2 2. 2. Isesengura Abigishwa bahereye ku rugero bahawe n'umwigisha bakora imyitozo yo gukuba no kugabanya ingero z'uburebure | REB_igitabo_abakuze_imibare.pdf |
158Ig Itabo cy'umw Ig Isha 2. 3. Ikomatanya Iyo bakora imyitozo yo gukuba ingero z'uburebure n'umubare ushyitse, bafata umubare w'urugero bakawukuba n'umubare ushyitse maze bakandika urugero imbere y'igisubizo. Iyo bakora imyitozo yo kugabanya ingero z'uburebure n'umubare ushyitse, bafa-ta umubare w'urugero bakawugabanya n'umubare ushyitse maze bakandika uru-gero imbere y'igisubizo. 2. 4. Imyitozo ntsindagirabumenyi Kora iyi myitozo 1) dm64x 4 = mm.... 2) m240: 32 = dm... 3) cm24 x 3= mm... 4) km360 : 4= dam... 3. ISUZUMA shaka igisubizo 1) dm 15x5=dm.. 2) dm 32x4=cm.. 3)m 47x8= cm... 4)m 25x12= mm. 5)dm 15x4= mm 4. UMUKORO Shaka igisubizo 1)hm 40x5= m... 2)m 12x9=cm.... 3)km124x12=dam... 4)dm 321x10=mm.... 5)m75x14= dm... Amahurizo ku ngero z'uburebure1. Umuhanda wa KIGALI-MUSANZE ufite uburebure bwa km 116. Imodoka imaze kugenda ahareshya na km 72. Iyo modoka isigaje kugenda km zingahe ? 2. Kugira ngo hapimwe ubujyakuzimu bw'umwobo, hoherezwamo umugozi wa dam. Shaka ubujyakuzimu bw'uwo mwobo niba umugozi urengaho m 3 3. Batondetse imishumi ibiri. Umwe upima cm 35, undi upima dm 5. Shaka uburebure bw'iyo mishumi yombi hamwe. | REB_igitabo_abakuze_imibare.pdf |
159Im Ibare y'abakuze IKIGWA CYA 60 : GUPIMA, GUSOMA, KWANDIKA NO GUHINDURA INGERO Z'IBITEMBABUZI INTEGO Y'IKIGWA Nyuma y'iki kigwa umwigishwa araba ashobora gupima, gusoma, kwandika no guhindura ingero z'ibitembabuzi IMFASHANYIGISHO Ibigikombe, ibirahuri, ibesani, indobo, amacupa,utujerekani, amazi, ifu y'imyumbati....... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo gupima ibintu bisukika yifashishije ibikoresho bisanzwe byabugenewe 2. IKIGWA GISHYA Gupima, gusoma, kwandika no guhindura ingero z'ibisukika 2. 1. Gutahura Umwigisha abaza abigishwa gusobanura uburyo basanzwe bakoresha mu gupima ibisukika bitembabuzi n'ibikoresho bifashisha. Urugero: Mu buzima busanzwe mu gupima amazi, n'ibindi bisukika bitembabuzi hifashishwa ibikoresho bitandukanye 2. 2. Isesengura Umwigisha hamwe n'abigishwa bibukiranya uburyo buboneye bukoreshwa mu gupima ibitembabuzi n'ibindi bisukika. Hamwe n'abigishwa barebera hamwe akamaro ko kumenya ingero zikoreshwa mu gupima ibitembabuzi mu buzima busanzwe kuribo ubwabo ndetse n'ahandi hose Umwigisha ababwira ko urugero fatizo mu gupima ibisukika ari litiro. Bandika l | REB_igitabo_abakuze_imibare.pdf |
160Ig Itabo cy'umw Ig Isha Urugero : Abigishwa bapima amazi angana na litiro 3 bakoresheje icupa rya litiro kandi bakayasuka mu kajerikani ka litiro 3 Ingero ziri munsi ya litiro: hifashishijwe imbonerahamwe y'ingero z'ibitembabuzi, umwigisha ahera ku rugero fatizo “litiro” n'ibikoresho bipima litiro 1 agasobanurira abigishwa izindi ngero nto kuri litiro, isano zifitanye n'aho zikunze gukoreshwa. Icupa rya litiro (l) rikunze gukoreshwa bapima cyangwa batwara ibintu bitandukanye : gupima amata, inzoga, amavuta,.... Desilitiro (dl) ni urugero ruto kuri litiro dukunze gukoreshwa mu buzima bwa buri munsi mu gupima ibisukika bitemba buzi : dl 10 = l 1 cyangwa l 1 = dl 10 Santilitiro (cl) na miliritiro (ml), ni ingero nto kuri litiro na desilitiro kandi n' ingero zifashishwa cyane mu gupima ibintu bitembabuzi bike cyane. Bakunze kuzikoresha mu nganda zikora imiti no kwa muganga l1=dl10 dl1=cl10l1=cl100 dl1=ml100l1=ml1000 Izi ngero zirutana inshuro 10 nk'uko imbonerahamwe y'ingero ibyerekana Ingero zisumba litiro: hifashishijwe imbonerahamwe y'ingero z'ibitembabuzi, umwigisha ahera kurugero fatizo “litiro” n'ibikoresho bipima litiro 1 agasobanurira abigishwa izindi ngero nini kuri litiro, isano zifitanye n'aho zikunze gukoreshwa. Dekalitiro (dal) na Hegitolitiro(hl)ni ingero nini Kuri litiro (l) kandi zikunze gukorerwa n'inganda hakorwa ibikoresho bibika amazi menshi, cyangwa ibindi bikoresho bitwara | REB_igitabo_abakuze_imibare.pdf |
161Im Ibare y'abakuze ibitembabuzi nk'ibigega by'amazi, ibidomoro, ingunguru,.... Izi ngero zirutana inshuro 10 nk'uko imbonerahamwe y'ingero ibyerekana hl dal l 1 0 1 0 0 1 0 2. 3. Ikomatanya Umwigisha asobanura ko hari ingero nto kuri litiro ko hari n'izindi ngero ziruta litiro, kandi ko izikunda gukoreshwa ari l nk'urugero fatizo, cl na ml nk'ingero nto kuri l,dal na hl nk'ingero nini kuri l kandi agasobanurira ko ingero z'ibitembabuzi zirutana inshuro 10 Menye ko: Litiro ni urugero rw'ingenzi (rw'ifatizo) mu ngero z'ibitembabuzi hl dal l dl cl ml 1 0 0 1 0 0 0 2. 4. Imyitozo ntsindagirabumenyi 1) Hindura izi ngero hl 3 dal 4 = l... dl 5600 = hl... dal... hl 30 = dal... hl 14 = dal... l... 3. ISUZUMA 1)Tondeka izi ngero uhereye ku rugero ruto: dal 6, hl 5, l 585, dl 7 2)Tondeka izi ngero uhereye ku rugero runini: cl 2347, dl 3427, l 247, hl 1 3)Hindura ingero dal 38 = l... dal 23 = dl... dal 2357 = dal... l... dl... cl... 4. UMUKORO Hindura izi ngero wandike igisubizo dal 10 = cl... dal 2 = dl... dal 27 = l... Tondeka izi ngero z'ibitembabuzi uhereye ku rugero ruto dl 360, l 2, ml 4500, dal 1, l 240Tondeka ingero z'ibitembabuzi zikurikira uhereye ku rugero runini l 6, dl 75, dal 12, cl 39 | REB_igitabo_abakuze_imibare.pdf |
162Ig Itabo cy'umw Ig Isha IKIGWA CYA 61 : ITERANYA, IKURAMO, IKUBA N'IGABANYA RY'INGERO Z'IBITEMBABUZI INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gukoresha amategeko ane y'ibara mu ngero z'ibitembabuzi IMFASHANYIGISHO Ikibaho, amakaye, ingwa, amakaramu UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha aratanga imyitozo yo guhindura ingero z'ibitambabuzi Uzuza ahari utudomo igisubizo gikwiye a) cl 100 = dl... b) hl 2 = l... c) dl 3845 = hl... dal... l... dl... d) ml 1263 = l... dl... cl... ml... 2. IKIGWA GISHYA Gukoresha amategeko ane y'ibara mu ngero z'ibitembabuzi 2. 1. Gutahura Umwigisha atanga ingero zo guteranya, gukuramo, gukuba no kugabanya ingero z'ibitembabuzi zisumba litiro. 2. 2 Gusesengura Umwigisha atanga ingero zo guteranya, gukuramo, gukuba no kugabanya ingero z'ibitembabuzi Abigishwa bakora indi myitozi bakurikije urugero bahawe n' umwigisha 1. Hindura ingero kandi uteranye, wifashishije imbonerahamwe Urugero: l 6 + dl 25 = dl 85 cl 850 dl 60 + dl 25 = dl 85 cl 850 | REB_igitabo_abakuze_imibare.pdf |
163Im Ibare y'abakuze 1) hl 1 + l 134 = l... 2) dal 32 + l 80 = l... 3) cl 186 + ml 16 = ml... 4) dl 878 + l 12 = dl... 5) hl 5 + dal 12 = dal... 2. Hindura ingero kandi ukuremo, wifashishije imbonerahamwe Urugero: hl 2-dal 5 = dal 15 1) dal 78-dl 250 = hl... dal... l... dl... 2) l 15-l... = dal 1 3) l 250-l... = hl 2 4) ml 3427-dl 32 = ml... 5) dl 405-cl... = cl 1409 6) dal 9-dal 5 = l... 7) dal 28-l 16 = l... 3. Hindura ingero kandi ukube wifashishije imbonerahamwe Urugero: dl 18 x 2 = cl 360 cl 180 x 2 = cl 360 1) l 4 x 4 = dl... 2) dal 6 x 2 = dal... l... 3) cl 102 x 5 = ml... 4) l 6 x 7 = l... 5) hl 5 x 3 = dal... 6) ml 2 x 4 = ml... 7) dl 9 x 9 = dl... 8) dal 1 x 2 = l... 9) dal 5 x 4 = dal... | REB_igitabo_abakuze_imibare.pdf |
164Ig Itabo cy'umw Ig Isha 4. Hindura ingero kandi ugabanye wifashishije imbonerahamwe Urugero: dal 24 : 3 = l 80 l 240 : 3 = l 80 1) dl 30 : 2 = cl... 2) hl 15 : 5 = hl... dal... 3) (l 2 + dl 30) : 2 = dl... 4) (dal 10 x 2) : 4 = dal... 5) (cl 370-ml 700) : 2 = ml... 6) l 280 : 7 = l... dl... 7) dl 320 : 4 = cl... 8) ml 480 : 6 = ml... cl... 9) hl 360 : 4 = dal... 2. 3. Ikomatanya Mu iteranya,ikuramo,ikuba cyangwa igabanya ry'ingero z'ibitembabuzi, babanza guhindura ingero zose mu rugero rumwe rushakirwamo igisubizo hanyuma bagateranya, bagakuramo, bagakuba cyangwa bakagabanya hakurikije igisabwa Mu guhindura bifashisha buri gihe imbonerahamwe y'ingero 2. 4. Imyitozo ntsindagirabumenyi 1) hl 3 + dal 2 = l... 2) dal 12 = dl... 3) dl 463-cl 36 = cl 4)hl 1 = dal... l... 3. ISUZUMA 1) hl 1 x 2 = dal... 2) l 8 + dl 17= dl... 1) dal 65-l 62 = l... 2) dl 2 + l 5 = dl... | REB_igitabo_abakuze_imibare.pdf |
165Im Ibare y'abakuze 4. UMUKORO 1) dal 4 + hl 1 = dal... 2) hl 1-dl 100 = dl... 3) cl 100-dl 1 = cl... 4) hl 10 : 5 = l... 5) l 124 x 2 = dl... 6) hl 1+ dal 6-l 1 = l... Amahurizo ku ngero z'ibitembabuzi 1. Ikidomoro cyuzuzwa n'amasafuriya 12 ya l 3 imwe imwe n'indobo ya l 15. Vuga ingano y'itwara ry'icyo kidomoro. 2. Igunguru yuzuzwa n'amabesani 5 y'amazi ya l 20 imwe. Shaka itwara ry'iyo ngunguru muri dl 3. Mu ngunguru irimo ubusa basutsemo l 138 za lisansi, bukeye barongera basukamo l 26. Ubwo basutsemo l zingahe za lisansi? Habuzeho l zingahe ngo zuzure l 200? 4. Mu ruganda rwenga imitobe y'inanasi bari bafite umutobe wa hl 4. Bagurishije hl 1 na dal 5. Bashigaje kugurisha l zingahe z'umutobe? 5. Mu rwego rwo kurwanya imirire mibi, umukangurambaga mu by'ubuzima afite l 20 z'amata ashaka kugabanya ku buryo bungana imiryango 4 ifite abana bagaragaraho imirire mibi. Buri muryango uzatwara l zingahe z'amata? | REB_igitabo_abakuze_imibare.pdf |
166Ig Itabo cy'umw Ig Isha IKIGWA CYA 62 : GUPIMA, GUSOMA, KWANDIKA NO GUHINDURA INGERO Z'UBUREMERE INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora gupima, gusoma, kwandika no guhindura ingero z'uburebure IMFASHANYIGISHO Iminzani inyuranye,Ibirayi, ibishyimbo, isukari n'ibindi.. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha atanga imyitozo yo gupima uburemere bw' ibintu binyuranye 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha abaza abigishwa gusobanura uburyo basanzwe bakoresha bapima uburemere bw'ibintu 2. 2. Isesengura Umwigisha hamwe n'abigishwa bibukiranya uburyo buboneye bukoreshwa mu gupima uburemere bw'ibintu Hamwe n'abigishwa barebera hamwe akamaro ko kumenya ingero zikoreshwa mu gupima uburemere bw'ibintu bitandukanye mu buzima busanzwe n'ibikoresho bikoreshwa mu gupima uburemere. Mu gupima uburemere bw'ibintu hifashishwa iminzani inyuranye n'amabuye y'umuzani. Ingero ziri munsi ya kirogarama: hifashishijwe imbonerahamwe y'ingero z'uburemere, | REB_igitabo_abakuze_imibare.pdf |
167Im Ibare y'abakuze umwigisha ahera kuri “kirograma” n'umunzani bapimisha kirogarama1 agasobanurira abigishwa izindi ngero nto kuri kirogarama, isano zifitanye n'aho zikunze gukoreshwa. Kirogarama (kg) ikunze gukoreshwa bapima ibintu bitandukanye mu mabutike, ku isoko :umunyu, isukari, ibirayi, ibishyimbo,.... Hegitogarama (hg) ni urugero ruto kuri kirogarama ku buryo zirutanwa inshuro 10: kg 1 = hg 10 Dekagarama (dag) ni urugero ruto kuri kirogarama na hegitogarama kg1=hg10 hg1=dag10 kg1=dag100 Garama (g) ni urugero ruto Kuri kirogarama kandi rukunze gukoreshwa cyane mu gupima uburemere. Garama ni rwo rugero fatizo mu ngero z'uburemere. Kg 1= g 1000 Desigarama (dg), santigarama (cg) na miligarama (mg) ni ingero nto Kuri garama (g) kandi zigenda zirutana inshuro 10. Ingero zose z'uburemere zirutana inshuro 10 nk'uko imbonerahamwe y'ingero ibyerekana Ingero zisumba kirogarama: hifashishijwe imbonerahamwe y'ingero z'uburemere, umwigisha ahera kuri “kg” n'iminzani itandukanye agasobanurira abigishwa izindi ngero nini kuri kirogarama, isano zifitanye n'aho zikunze gukoreshwa. Toni (T) ni urugero runini kuri kirogarama kandi rukunze gukoreshwa mu buzima bwa buri munsi, ku buremere bw'ibintu byinshi cyane. Toni 1 ingana na kirogarama 1000 (T1=kg 1000) Umwigisha afatanya n'abigishwa gukora imyitozo itandukanye yo guhindura ingero z'uburemere bifashisha imbonerahamwe kandi bagakora imyitozo ikurikira: 1) hg 3 = dag... g... 2) hg 15 = g... 3) hg 4 dag 2 g 5 = g... 4) hg 7 g 6 = g... 5) hg 1 dag 6 = g... | REB_igitabo_abakuze_imibare.pdf |
168Ig Itabo cy'umw Ig Isha 2. 3. Ikomatanya Umwigisha atanga incamake y'ibimaze kwigwa ku ngero z'uburemere : Garama (g) ni urugero fatizo mu ngero z'uburemere, desigarama (dg) santigarama (cg) na miligarama (mg) n'ingero nto kuri garama (g) kandi zose zigenda zirutana inshuro 10. Toni (T), kilogarama (kg), hegitogarama (hg) na dekagarama (dag) ni ingero nini kuri garama(g) kandi zose zigenda zirutana inshuro 10 T1=kg 1000; kg 1 = g 1000; kg 1 = hg 10 ; kg 1 = dag 100g 1= dg 10= cg100= mg1000 2. 4. Imyitozo ntsindagirabumenyi 1) kg 41 = dag... 2) hg 49 = dag... g... 3) g 1435 = kg... hg... g... Subiza vuba Muri kg 2 harimo garama zingahe?Muri kg 3 harimo garama zingahe? Muri kg 7 harimo garama zingahe? 3. ISUZUMA Uzuza iyi mbonerahamwe Kg 1 Kg 8 Kg 57.... Kg 41...... Kg 86 hg 10........... hg 850...... hg 910 ...... 4. UMUKOROUzuza ukoresheje igisubizo gikwiye. 1) kg 4 = hg... 2) kg 4 hg 5 = dag... 3) kg 1 = g... dag 2 = g... 4) hg 5 = dag... | REB_igitabo_abakuze_imibare.pdf |
169Im Ibare y'abakuze IKIGWA CYA 63 : GUKORESHA AMATEGEKO ANE Y'IBARA MU NGERO Z'UBUREMERE INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora guteranya, gukuramo, gukuba, kugabanya mu ngero z'uburemere. IMFASHANYIGISHO igitabo cy'umwigisha, ikibaho, ingwa. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha asaba abigishwa kwibukiranya ingero z'uburemere n'uko zigenda zirutana. kg1 =10hg=100dag=1000g 1g=10dg=100cg=1000mg Umwigisha yibutsa amategeko ane y'ibara asaba gukora iyi myitozo 305+2205=2510 3005-178=2829 375x12=4500 12339:457=27 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha yifashisha ingero zitandukanye zo mu buzima bw'abigishwa, akabafasha gutahura uko bateranya, bakuramo bagabanya cyangwa bagakuba ingero z'uburemere Guteranyiriza kg 3 na kg 17 z'ibishyimbo mu mufuka umwe Guteranya kg 4 na kg 24 z'amasaka zaguzwe ku bahinzi babiri batandukanye Gukura kg 17 z'ibigori by'imbuto muri kg 25, Naguze kg 5 z'umuceri inshuro eshatu; ubwo naguze umuceri ungana iki? Nagabanije kg 6 z'ubunyobwa bukaranze abana 20. Ubwo buri wese azabona g zingahe z' ubunyobwa ? 2. 2. Gusesengura Umwigisha atanga amahurizo yoroheje abonekamo ikoreshwa ry'amategeko ane y'ibara hanyuma akerekana uko akorwa. | REB_igitabo_abakuze_imibare.pdf |
170Ig Itabo cy'umw Ig Isha Urugero: 1. Naguze ibiro 3 by'ibirayi ( kg 3) hanyuma ngura indi nusu y'ibirayi. Ubwo mfite g zingahe z'ibirayi? Igisubizo: Kg3= g 3000; Inusu y'ikilo = g 500. Byose hamwe = g 3000+g 500=3500g 2. Mfite dag 200 z'umuceri. Mpayeho mubyara wanjye g 500. Ubwo nsigaranye umuceri ungana iki muri g Igisubizo : dag 200= g 2000; Muri g 2000 nkuyemo g 500 hasigara g 1500. Ubwo nasigaranye g1500 2. 3. Ikomatanya Iyo bateranya cyangwa bakuramo ingero z'uburemere, babanza guhindura mu rugero rwabajijwemo igisubizo hanyuma bagakuramo cyangwa bagateranya. Mu ikuba babanza guhindura ingero mu rugero rwasabwemo igisubizo hanyuma bagakuba n'umubare watanzwe. Urugero1 :kg 1 + dag 24 = dag 100 + dag 24= dag 124 Urugero 2 : g 18-dag 6 = g 180-g 60 = g 120 Urugero 3: hg 4 x 2 = dag 40 x 2= dag 80 Urugero 4: dag 64 : 8 = g 640 : 8= g 80 2. 4. Imyitozo ntsindagirabumenyi Umwigisha atanga imyitozo yo kugira ngo afasha abigishwa gucengerwa n'isomo biga. Kora iyi myitozo ku ngero z'uburemere. 1) Kg 410 z'umuceri uzishyize mu dufuka twa kg 4 kamwe kamwe. Hasigara kg zingahe? 2) kg 2-dag 125 = dag 3) dag 3 x 3 = g... 4) dag 36 : 6 = g... 3. ISUZUMA Umwigisha atanga imyitozo yo kugenzura ko abigishwa bamenye neza ikigwa bize. Kora iyi myitozo 1. Umucuruzi yari afite kg 2300 z'ibishyimbo. Yagurishije imifuka 5 ya kg 80 umwe umwe. Yasigaranye kg zingahe? 1. hg 16 + dag 4 = dag... 2. hg 1 dag 15-g 164 = g... 3. kg 8-hg 8 = hg... | REB_igitabo_abakuze_imibare.pdf |
171Im Ibare y'abakuze 4. g 268 : 2 = g... 5. kg 10 : 5 = dag... 6. hg 5 x 4 = dag... 7. kg 6 x 5 = dag... 4. UMUKORO Umwigisha atanga imyitozo y'umukoro abigishwa bakorera mu rugo Kora imyitozo 1. kg 6 hg 4 + dag 10 g 8 = g... 2. Mama acuruza ibiribwa. Mu gitondo yaranguye kg 35 z'ibirayi, saa sita arangura kg 76 z'ibirayi. Yaranguye kg zingahe z'ibirayi ku munsi? 3. Ishyirahamwe ry'abahinzi ba soya bejeje kg 64 za soya, barashaka kuyigabanya abanyamuryango 8 b' abakene. Buri munyamuryango azatwara kg zingahe? 4. kg 2 hg 2 + kg 1 hg 6 = kg..hg.. g... 5. Agakarito karimo ubusa gapima g 120. Kaba kuzuye ibigori kagapima hg 3 na g 25. Shaka ub uremere by'ibyo bigori. | REB_igitabo_abakuze_imibare.pdf |
172Ig Itabo cy'umw Ig Isha IKIGWA CYA 64 : GUSOMA NO KWANDIKA IGIHE CYEREKANWA N'ISAHA INTEGO Z'IKIGWA Nyuma y'iki kigwa umwigishwa araba ashobora : -Gusoma, kwandika no kuvuga igihe cyerekanwa n'isaha-Gukora amahurizo arimo ingero z'igihe IMFASHANYIGISHO Igitabo cy'umwigisha, isaha y'imibare, isaha y'urushinge, isaha itagira inshinge. UKO IKIGWA GITANGWA 1. INTANGIRIRO Gusaba abigishwa kuvuga uburyo bakoresha ngo bamenye igihe runaka cy'umunsi, uburyo bakoresha ngo bamenye umunsi w'icyumweru cyangwa w'ukwezi,... Gusaba abigishwa kuvuga ubwoko bw'amasaha bazi cyangwa bakoresha 2. IKIGWA GISHYA Igihe kerekanwa n'isaha Kwitegereza Kwifashisha amasaha y'imibare, abigishwa bakavuga igihe yerekana Kwifashisha amasaha y'urushinge abigishwa bakavuga igihe yerekana: umwigisha afasha abigishwa gusobanukirwa n'amoko 3 y'inshinge (urushinge rugufi rw'amasaha, urushinge rurerure rw'iminota n'urushinge rw'amasegonda kandi agasobanura ko amasaha amwe atagira urushinge rw'amasegonda) a. 12: 30b. 10:45 | REB_igitabo_abakuze_imibare.pdf |
173Im Ibare y'abakuze 2. 2. Gusesengura Umwigisha afasha abigishwa kwandika no gusoma isaha y'urushinge yerekana ko urushinge rugufi rw'amasaha rwerekana amasaha mu mibare iri hagati ya 1 na 12 naho urushinge rurerure rw'iminota rwerekana iminota kuva kuri 0 kugera kuri 60. Urugero: Saa tanu, urushinge rugufi rw'amasaha ruba ruri muri 11 naho urushinge rurerure rw'iminota ruba ruri muri 12 Saa mbiri n'iminota mirongo itatu, urushinge rugufi rw'amasaha ruba ruri mu 8 naho urushinge rurerure rw'iminota ruba ruri muri 6 Saa kumi n'iminota itanu, urushinge rugufi rw'amasaha ruba ruri muri 4 naho urushinge rurerure rw'iminota ruba ruri muri 1,....... 2. 3. Ikomatanya- Mu isaha imwe harimo iminota 60, mu munota umwe harimo amasegonda 60 kandi urushinge rw'iminota ruzenguruka ubutitsa.-Urushinge rw'amasaha ruva ku mubare umwe rujya ku wundi ukurikiyeho hashize iminota 60. -Inshinge z'isaha zizenguruka ziva iburyo zijya ibumoso uhereye ku mubare 12 kandi hagati y'umubare n'uwundi harimo iminota 5: urugero, iyo urushinge rw'iminota ruri ku mubare 3, tubara iminota 15, iyo urushinge rw'iminota ruri ku mubare 6 tubara iminota 30 -Amasaha ya mugitondo ari hagati ya saa sita z'ijoro ( 12:00) kugeza saa sita z' amanywa ( 12:00). Amasaha ya nyuma ya saa sita ari hagati ya saa sita z'amanywa (12:00) kugera saa sa sita z'ijoro (12:00 ). 2. 4. Imyitozo ntsindagirabumenyi Umwigisha atanga imyitozo yo gufasha abigishwa kubara isaha y'urushinge no kwerekana igihe 1. Erekana igihe cyatanzwe hakoreshwa urushinge rugufi rw'amasaha n'urushinge rurerure rw'iminota. Ibisubizo | REB_igitabo_abakuze_imibare.pdf |
174Ig Itabo cy'umw Ig Isha 3. ISUZUMA Erekanisha urushinge igihe 5:48 2:31 9:57 1:28 4. UMUKORO 1. Niba utangira akazi saa mbiri za mugitondo ( 8:00 ), kandi ukaba ukoresha iminota makumyabiri (20) kugira ngo ugere ku kazi. Ubwo uzava imuhira ryari ? 2. Kore y'imbaho ifata iminota 45 kugira ngo yume. Niba ikoreshejwe ku mbaho 10:15 z'amanywa, ubwo izuma gihe ki? | REB_igitabo_abakuze_imibare.pdf |
175Im Ibare y'abakuze IKIGWA CYA 65: KWEREKANA IGIHE KU NDANGAMINSI INTEGO Nyuma y'ikigwa umwigishwa araba ashobora kuvuga no kwerekana igihe yifashishije indangaminsi IMFASHANYIGISHO Indangaminsi (karendari) n'igitabo cy'umwigisha UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha n'abigishwa bibukiranya ko ibihe by'umwaka bibarirwa mu minsi (amatariki, ibyumweru n'amezi 2. IKIGWA GISHYA Kwerekana umunsi, itariki n'ukwezi by'umwaka 2. 1. Gutahura: Gushobora kwerekana ibice bigize indangaminsi,ukwezi, iminsi na matariki Urugero: Indangaminsi y'umwaka barimo 2. 2. Gusesengura - Icyumweru kigizwe n'iminsi irindwi-Ukwezi turimo kugizwe n'iminsi ingahe?-Ukwezi gushije kwari kugizwe n'iminsi ingahe?-Ukwezi gutaha kuzaba kugizwe n'iminsi ingahe?-Umwaka ugizwe n'ibyumweru bingahe? 2. 3. Ikomatanya Umwigisha asobanurira abigishwa ko indangaminsi igaragaza : iminsi, amataliki, ibyumweru, n'amezi by'umwaka turimo- Icyumweru kigizwe n'iminsi 7; - ukwezi kugizwe n'iminsi 30 cyangwa 31 (ukwezi kwa Gashyantare kugizwe n'iminsi 28 cyangwa 29) - umwaka ugizwe n'amezi 12 ;umwaka ugizwe n'iminsi 365 cyangwa 366 2. 4. Imyitozo ntsindagira-bumenyi 1. Ku wa kane ni tariki ya 17 z'ukwezi kwa karindwi. Ukwezi gutaha kwa munani | REB_igitabo_abakuze_imibare.pdf |
176Ig Itabo cy'umw Ig Isha kuzatangira ari ku wa kangahe? 2. Mu cyumweru gishize ku wa kabiri hari tariki ya 12. Mu cyumweru gitaha ku wa kane hazaba ari tariki ya kangahe? 3. ISUZUMA 1. Umwaka wa 2012 wari ufite iminsi 366. Ukwezi kwa kabiri kwari gufite iminsi ingahe? 2. Tariki ya gatanu z'ukwezi kwa kenda hari ku wa mbere. Uko kwezi kuzarangira ari ku wa kangahe? 4. UMUKORO Ku wa gatandatu w'icyumweru gitaha hazaba ari tariki ya kenda z'ukwezi kwa gatatu. Tanga imbonerahamwe yerekana uko iminsi y'ukwezi kwa kane izaba iteye. | REB_igitabo_abakuze_imibare.pdf |
177Im Ibare y'abakuze IKIGWA CYA 66 : GUHINDURA INGERO Z'IGIHE INTEGO Nyuma y'iki kigwa umwigishwa araba ashobora guhindura ingero z'ibihe amasaha mu minsi, iminsi mu byumweru, amasaha mu minota cyangwa mu masegonda IMFASHANYIGISHO igitabo cy'umwigisha, ikibaho, ingwa, isaha nini, indangaminsi. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha akoresha imyitozo yo gusoma isaha no gukoresha indangaminsi. 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha asaba abigishwa kwerekana no kuvuga umubare w'amasegonda yujuje umunota, iminota yujuje isaha, n'amasegonda yujuje isaha. 2. 2. Gusesengura Umwigisha yerekana ko isaha imwe irimo iminota 60, umunota umwe urimo amasegonda 60, bityo isaha imwe irimo amasegonda 3600. Amasegonda 3600= iminota 60 x amasegonda 60 Umunsi ugizwe n'amasaha 24; amasaha 12 y'amanywa n'amasaha 12 y'ijoro. Icyumweru kigizwe n'iminsi 7 Ukwezi kugizwe n'iminsi 30cyangwa 31, ariko ukwezi kwa kabiri kugira iminsi 28 cyangwa 29(biterwa n'uko umwaka uteye) Ilisiti y'amezi agira iminsi 30 n'agira iminsi 31. 2. 3. Ikomatanya Umwigishwa yifashisha imyitozo inyuranye yerekana ko mu guhindura ingero z'ibihe bakoresha cyane cyane ikuba n'igabanya, babanza guhindura ingero mu rugero igisubizo gitanzwemo? 2. 4. Imyitozo ntsindagirabumenyi 1. Ibyumweru 3= iminsi...... 2. Iminsi 12=Amasaha...... 3. Amasaha 7=iminota...... 4. Iminota 23= amasegonda... | REB_igitabo_abakuze_imibare.pdf |
178Ig Itabo cy'umw Ig Isha 5. Ukwezi kwa 7 n'ukwezi kwa 8 = iminsi..... 3. ISUZUMA Iminsi 2 n'amasaha 4 bingana n' iminota.... Amasaha 3 n'iminota 30 bingana n' iminota.... Iminota 37 n'amasegonda27 bingana n' amasegonda...... ibyumweru 4 bingana n' iminsi....... 4. UMUKORO 1) amasaha 67angana n' iminsi..... n'amasaha..... bingana n' iminota....... 2) iminota 762ingana n' amasaha......n'iminota......bingana n' amasegonda....... | REB_igitabo_abakuze_imibare.pdf |
179Im Ibare y'abakuze IKIGWA CYA 67 : ISUZUMA RYA KANE RY'IMIBARE Iri suzuma rikwiye gukorwa mu byiciro 3 kandi buri kiciro kikaba kirimo imyitozo ku mibare ishyitse, ku migabane no ku ngero. I. Kora iyi myitozo ku mibare ishyitse 1) 25007+35006=2) 125 708+67 004= 3) 26 722-21 999=4) 368b412-359 888=5) 4784x15=6) 578x679=7) 26180:44=8) 70 125:17= II. Kora iyi myitozo ku migabane 4__ 7+1__ 7= 8__ 9-2__ 9= 2__ 7x4__ 9= 7__ 9+1__ 9= 7__ 9-__ 9= 5__ 9 2__ 9x5__ 8= III. Imyitozo ku ngero 1) dam17+m27=2) km12+dam8=3) km17-m217=m. 4) l27+dl217=5) l28-dl18=cl..... 6) l35-cl30=dl....7) km20+hm20=m..... 8) dam17-m17=m....9) kg 20-g200=dag.... IV) Ikigega cy' amazi cyuzuzwa n' amajerikani 100 ya l 20 imwe imwe, bakivomeyemo | REB_igitabo_abakuze_imibare.pdf |
180Ig Itabo cy'umw Ig Isha amazi ag era muri 1__ 2 cyacyo. Icyo kigega cyuzuzwa na l zingahe z' amazi ? Iyo amazi ageze muri 1__ 2 aba angana na dal zingahe ? Ese iki kigega cyakuzura mu gihe kingana iki niba 1__ 2 cyacyo cyuzura mu gihe cy' iminota 20. v) Mariya yahagurutse saa kumi n' ebyiri n' iminota 30 yerekeza kwa Sekuru. Yakoze urugendo rw' amasaha 2 n'iminota 30 kugirango agereyo. Yagezeyo ryari kandi yari agenze km zingahe niba mu minota 30 yaragendaga km2. IKIGWA CYA 68 : GUKOSORA ISUZUMA I. Imyitozo ku mibare ishyitse 1) 25007+35006= 60013 2) 125 708+67 004= 192 712 3) 26 722-21 999= 4723 4) 368b412-359 888= 8524 5) 4784x15= 71 760 6) 578x679= 392 462 7) 26180:44= 595 8) 70 125:17 =4125 II. Imyitozo ku migabane 4__ 7+1__ 7= 5__ 7 8__ 9-2__ 9= 6__ 9 2__ 7x4__ 9= 6__ 63 7__ 9+1__ 9= 8__ 9 7__ 9-2__ 9= 5__ 9 2__ 9x5__ 8= 10__ 72 | REB_igitabo_abakuze_imibare.pdf |
181Im Ibare y'abakuze III. Imyitozo ku ngero 1) dam17+m27= m170+m27= m197 2) km12+dam8=m12000+m80= m12080 3) km17-m217=m 17000-m217= m16 783 4) l27+dl217= dl 270+dl17=dl287= cl2870 5) l28-dl18= dl280-dl18=d262= cl2620 6) l35-cl30= dl 347 7) km20+hm20= m 22 000 8) dam17-m17= m153 9) kg 20-g200= dag1980 IV) Ingano y' amazi yuzuza ikigega= l 20 x 100= l 2000 Ingano y' amazi agera muri 1__ 2= l 2000: 2= L 1000= dal 100 Igihe bifata kugirango ikigega cyuzure = iminota 20 x 2 = iminota 40 V) Igihe Mariya yagereye kwa sekuru = 6h30 +2h30 = 9h00. 2h30 = ( iminota 60 x2 ) + iminota 30 = iminota 150Ingano y' urugendo yari akoze mu gihe cya 2h30 = iminota 150= km2 x150: 30 = km 10 km UMWITOZO W'IVUMBURAMATSIKO ( IGICE CYA 2: INGERO, ITEGEKO RY'ITATU, IJANISHA) Umunyamuryango w'ikigo k'imari yatse inguzanyo y'ubuhinzi maze bamusaba ingwate. Yatanze 1__ 2 k' isambu ye ho ingwate ariko kugaragaza ibipimo byawo (uburebure, ubugari n'ubuso) bimubera imbogamizi. Yakoresheje intambwe maze ibipimo abonye bitandukan a n'ibyo ibyangombwa by'ubutaka bigaragaza. Amafaranga bamuhaye bamusabye kuyishyura mu gihe cy'umwaka kandi akabungukira 10% ariko byaramugoye kumenya inyungu azungukira ikigo k'imari. Ibibazo Niba umurima ufite ishusho y'urukiramende (igishushanyo), uburebure bwa m100 n'ubugari bwa m 20. Fasha umunyamuryango w'ikigo k'imari kugaragaza ingano y'umurima we, Ese ingano y'umurima ipimwa mu zihe ngero ? shaka ubuso bwawo ? Niba ikigo k'imari gitanze inguzanyo y'ubuhinzi ingana na F150 000 umuntu azishyura yunguka amafaranga 10% mu gihe cy'umwaka, shaka amafaranga umuntu azungukira ikigo k'imari?. Ese gukorana n'ikigo k'imari bifite akamaro? Niba warigeze ukorana n'ikigo k'imari garagaza ibyiza wabonye n'imbogamizi waba waragize. | REB_igitabo_abakuze_imibare.pdf |
182Ig Itabo cy'umw Ig Isha Ibisubizo: Ingano y'umurima: m100xm20 = m2 2000 Ingano y'umurima ipimwa muri m2 cyangwa ingero z'ubuso Amafaranga azungukira banki 150000 x 10 __________________ = 15000 100 Buri mwigishwa avuga uko abona bimugendekeye mu gukorana n'ikigo k'imari (Buri gisubizo kiremerwa) IKIGWA CYA 69 : IMYITOZO N'AMAHURIZO KU NGERO Z'IGIHE INTEGO Y'IKIGWA Nyuma y'iki kigwa umwigishwa araba ashobora g ukora imyitozo irimo ingero z'igihe. IMFASHANYIGISHO Igitabo cy'umwigishwa, isaha nini,indangaminsi... UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha akoresha imyitozo yo gusoma isaha; Umwigisha atanga imyitozo yo gushyira inshinge z'isaha mu mwanya uboneye kugira ngo isaha yerekane igihe cya tanzwe: Ingero: -Saa saba n'iminota itanu-Saa kumi n'ebyiri n'iminota icumi 2. IKIGWA GISHYA Gukora amahurizo kungero z'igihe 2. 1. Gutahura 1. Amahurizo atangwa agomba kuba ajyanye n'ibikorwa byo mu buzima bwa buri munsi bw'abigishwa ( igihe gikoreshwa mu ngendo za buri munsi,..... ) 2. Mu kwigisha ikigwa cy'amahurizo, umwitozo w'intangarugero ukorwa kubufatanye n'umwigisha n'abigishwa, indi isigaye igakorwa n'abigishwa mu matsinda kandi bagakosorera hamwe n'umwigisha; 3. Mu gukora imyitozo, abigishwa bifashisha ibishushanyo. | REB_igitabo_abakuze_imibare.pdf |
183Im Ibare y'abakuze 2. 3. Gusesengura Ihurizo ry'intangarugero Imodoka itwara abagenzi yahagurutse i Huye saa mbiri n'iminota 20 igera i Nyanza saa tatu. Urugendo Huye-Nyanza rwamaze igihe kingana iki? Iyo modoka yakomeje urugendo, ihaguruka i Nyanza saa tatu n'iminota 15 igera i Muhanga saa yine n'iminota 25. Urugendo Nyanza- Muhanga rwamaze igihe kingana iki? Iyo modoka kandi yahagurutse i Muhanga saa yine n'iminota 40 igana i Kigali, ikoresha isaha imwe n'iminota 5 kugira ngo igere yo. Iyo modoka yageze i Kigali ryari? Garagaza igihe abagenzi bavuye i Huye bamaze mu nzira kugirango bagere i Kigali. Igisubizo: -Imidoka yahagurutse i Huye saa 8:20, igera i Nyanza saa 9:00, ikoresheje iminota 30-Imodoka yahagurutse i Nyanza saa 9:15, igera i Muhanga saa 10:25, ikoresheje isaha 1 n'iminota 10-Imodoka yahagurutse i Muhanga saa 10:40, igera i Kigali saa 11:45-Kuva saa 8:20, abagenzi bahagurutse i Huye kugera saa 11:45 abagenzi bageze i Kigali harimo amasaha 3 n'iminota 25. Ihurizo ryo kwimenyereza Umunyeshuri yaturutse i muhira saa moya n'iminota itanu agera ku ishuri akoresheje iminota 45. Uwo munyeshuri yageze ku ishuri gihe ki? Niba amasomo atangira saa mbiri, uyu munyeshuri azaruhuka igihe kingana iki? Igisubizo: -Umunyeshuri yaturutse i muhira saa 7:5, agera ku ishuri akoresheje iminota 45, ubwo yageze ku ishuri saa 7:50-Niba amasomo atangira saa 8:00, umunyeshuri azaruhuka iminota 10 2. 4. Imyitozo ntsindagirabumenyi 1. Umuntu yaturutse i muhira ajya ku Karere agerayo saa mbiri n'iminota 20. Yakoresheje igihe kingana n'isaha imwe n'iminota 45. Ubwo yari yavuye mu rugo ryari? Igisubizo: -Umuntu yavuye imuhira ajya ku Karere agerayo saa 8:20, akoresheje isaha 1 n'iminota 45-Yaha gurutse mu rugo 8:20 dukuyemo isaha 1 n'iminota 45, ni ukuvuga ko yahagurutse 6:35 | REB_igitabo_abakuze_imibare.pdf |
184Ig Itabo cy'umw Ig Isha 3. ISUZUMA Mu mwaka wa kane, kuva saa mbiri kugera saa mbiri n'iminota 50, abigishwa babona isomo ry'imibare, kuva saa mbiri n'iminota 50 kugera saa tatu n'iminota 20, babona isomo ry'icyongereza, kuva saa tatu n'iminota 20 kugera saa ine babona nanone isomo ry'imibare maze bakabona kujya gukina. Isomo rya mbere ry'imibare rimara igihe kingana iki? Isomo ry'icyongereza rimara igihe kingana iki? Isomo rya kabiri ry'imibare rimara igihe kingana iki? Amasomo yose ya mbere yo gukina amara igihe kingana iki(iminota ingahe, amasaha angahe)? 4. UMUKORO Kabirigi yavuye mu rugo saa mbiri n'iminota 5, akoresha iminota 45 kugirango agere ku isoko. Mu guhaha yakoresheje isaha imwe maze atashye agera imuhira saa ine n'iminota 45. Ubwo yakoresheje igihe kingana iki kuva ku isoko kugera i muhira. | REB_igitabo_abakuze_imibare.pdf |
185Im Ibare y'abakuze IKIGWA CYA 70 : INGERO Z'UBUSO INTEGO Z'IKIGWA Nyuma y'Iki kigwa umwigishwa araba ashobora: Gusoma no kwandika ingero z'ubuso Guhindura ingero z'ubuso Gukora amahurizo arimo ingero z'ubuso IMFASHANYIGISHO Igitabo cy'umwigisha, imetero, umugozi wa m 10, dekametero. UKO IKIGWA GITANGWA 1. INTANGIRIRO Umwigisha ajyana abigishwa hanze y'ishuri, akabaremamo amatsinda, kandi abasaba gupima kare ifite uburebure bwa metero 1 y'uruhande bifashisha ibikoresho bafite. Reba urugero ku gishushanyo gikurikira: Umwigisha abaza abigishwa uko igice kizengurutswe n'umugozi kitwa ? (ubuso) Umwigisha yerekana ubuso bwa kare ya metero imwe y'uruhande Mu matsinda hanze y'ishuri, abigishwa bashobora no gupima mu matsinda ubuso bwa kare ya dekametero 1 (metero 10 ) z'uruhande. | REB_igitabo_abakuze_imibare.pdf |
186Ig Itabo cy'umw Ig Isha 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha asaba abigishwa gushaka ubuso bw'ishuri bigiramo Mu ishuri, umwigisha yifashisha igishushanyo cya kare ya metero 1 y'uruhande, umwigisha agasobanurira abigishwa uko m 2 1 (m1xm1=m21) iboneka n'uko yandikwa kandi akababwira ko m2 ari urugero rw'ifatizo mu ngero z'ubuso. m1 x m1 = m21, kandi m2 ni urugero rw'ifatizo mu ngero z'ubuso. 2. 2. Gusesengura Umwigisha afasha abigishwa kwandika ingero z'ubuso yibanda cyane kuzimenyerewe atanga n'ingero z'aho zikoreshwa. Urugero: Akarima k'imboga gafite m 2 kuri m 3 gafite ubuso bungana na m 21 x 2 x 3 = m2 6. Ni ukuvuga ko ubuso bw'ako karima ari incuro 6 ubuso bw'agapande gafite m 1 kuri m 1 Metero 3Metero 2 Ubuso = m 2 1x2x3 = m2 6. Umwigisha asobanura ko ubuso butageze kuri m2 babipima bakoresheje ingero nto kuri m2 arizo dm2, cm2 na mm2. Umwigisha asobanura ko ubuso burenze m2 babupima bakoresheje ingero ziruta m2 arizo dam2, hm2 na km2. | REB_igitabo_abakuze_imibare.pdf |
187Im Ibare y'abakuze 2. 3. Ikomatanya Imyandikire y'ingero z'ubuso mu magambo arambuye n' ahinnye n'uko zirutana incuro 100.-Kilometerokare : km 2 km2 1 = hm2 100-Hegitometerokare : hm2 hm2 1 = dam2100-Dekameterokare : dam2 dam21 = m2 100-Meterokare : m2 m2 1 = dm2100-Desimeterokare : dm2 dm2 1 = cm2100-Santimeterokare : cm2 cm2 1 = mm2100-milimeterokare : mm2 Imbonerahamwe y'ingero z'ubuso km2hm2dam2m2dm2cm2mm2 1 0 0 1 0 0 0 0 1 0 0 dam21=m2100 m21=cm210 000 cm21=mm2100 2. 4. Imyitozo ntsindagirabumenyi Hindura mu rugero bagusaba: a. dam2 4= m2......... b. hm2 83= dam2......... 3. ISUZUMA Kora imyitozo ikurikira: 1. cm2 90 000 = m2......... 2. mm25 000 = cm2......... Kagabo afite umurima wa dam2 105 (dekameterokare 105), 1 3 cyawo gihinze ho karoti naho igice gisigaye gihinzeho ibinyomoro . Shaka ubuso buhinzeho karoti muri meterokare( m2)? Shaka ubuso buhinzeho ibin yomoro muri meterokare( m2)? 4. UMUKORO Gereranya ingero zikurikira ukoresha ibimenyetso bya >,<,= dm2 1000........... m2 10 dam21..........dm2 100 mm2 1000 = 10.......... m2 10 000 = hm2........... | REB_igitabo_abakuze_imibare.pdf |
188Ig Itabo cy'umw Ig Isha IKIGWA CYA 71 : INGERO ZIKORESHWA MU BUHINZI. INTEGO Z'IKIGWA Nyuma y'iki kigwa umwigishwa araba ashobora: Gusoma no kwandika ingero zikoreshwa mu buhinzi Guhindura ingero z'ubuso mu ngero zikoreshwa mu buhinzi Gukora imyitozo irimo ingero zikoreshwa mu buhinzi IMFASHANYIGISHO: Igitabo cy'umwigisha, imetero, umugozi wa m 10, dekametero. UKO IKIGWA GITANGWA 1. INTANGIRIRO: Umwigisha n'abigishwa bakosora imyitozo yo mu ikigwa ry'ubushize. 2. IKIGWA GISHYA 2. 1. Gutahura Umwigisha abaza abigishwa ingero zikunze gukoreshwa iyo bapima imirima n'uko zirutanwa. Umwigisha atanga amazina y'ingero z'ikoreshwa mu buhinzi, akerekana uko zigenda z'irutanwa n'isano zifitanye n'ingero z'ubuso. Kwereka ingero zikoreshwa mu buhinzi n'uko zisomwa. Imbonerahamwe y'ingero zikoreshwa mu buhinzi ha (hegitare) a (ari) ca (santiyari) 1 0 0 1 0 0 0 0 a 1 = ca 100 ha 1 = a 100 = ca 10 000 2. 2. Gusesengura ha, a, ca ni ingero z'imirima/ ingero zikoreshwa mu buhinzi. Umwigisha afasha abigishwa kugaragaza isano iri hagati y'ingero z'ubuso n'ingero z'imirima yifashishije imbonerahamwe y'ingero. 2. 3. Ikomatanya Umwigishwa agomba kumenya ko; ingero zikoreshwa mu buhinzi mu magambo arambuye n'uko zirutanwa inshuro 100. ha 1= a 100 a 1= ca 100 ha 1 =hm 2 1 a 1= dam2 1 ca 1=m2 1 Hegitari Ari sentiyari | REB_igitabo_abakuze_imibare.pdf |
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