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II nawili
gamomcemloba
inteleqti
inteleqti
guram gogiSvili, Teimuraz vefxvaZe,
ia mebonia, lamara qurCiSvili
maTematika
III klasis saxelmZRvanelo
II nawili
gamomcemloba inteleqti
Tbilisi 2011
redaqtori Teimuraz vefxvaZe
2
guram gogiSvili, Teimuraz vefxvaZe,
ia mebonia, lamara qurCiSvili
m a T e m a t i k a
II nawili
III klasis saxelmZRvanelo
gamomcemloba inteleqti
Tbilisi 2011
Guram Gogishvili, Teimuraz Vepkhvadze,
Ia Mebonia, Lamara Kurchishvili
MaTHS II I
Part II
InTeLeKTI Publishers
Tbilisi 2011
gamomcemloba inteleqtiTbilisi, ilia WavWavaZDis gamz. 17b. tel.: 25 05 22, 91 22 83.
www.intelekti.ge [email protected] [email protected]
intelekti Publishers17b ilia Chavchavadze Ave., Tbilisi, Georgia. Tel.: (995 22) 25 05 22, 91 22 83.
ISBN 978-9941-430-51-0 (`maTematika~, III klasi)ISBN 978-9941-430-43-5 (`maTematika~, III klasi, II nawili)
gamomcemloba `inteleqti~, 2011.
sarCevi
rCevebi wigniT sargeblobisTvis .............................................4
13 zepiri angariSis xerxebi ............................................................5
14 viyenebT zepiri angariSis xerxebs ..........................................9
15 SevadaroT ricxviTi gamosaxulebebis mniSvnelobebi .....12
16 Sesabamisoba ......................................................................................16
17 ricxvebis gamoyenebis magaliTebi ...........................................21
18 Sekrebisa da gamoklebis ucnobi wevrebis povna ...............25
19 gameoreba...........................................................................................30
IV. monacemTa analizi
1 monacemTa amokreba teqstidan .................................................36
2 monacemTa Segrovebis magaliTebi ...........................................40
3 monacemTa dajgufeba ...................................................................44
4 SevadginoT da aRvweroT cxrili ............................................48
5 piqtograma ........................................................................................54
V. ricxvebis gamravleba da gayofa
1 ricxvebis gamravleba ...................................................................62
2 viyenebT marTkuTxovan cxrils gamravlebisas. gamravlebis Tviseba......................................................................66
3 ricxvebis gayofa ...........................................................................70
4 amovxsnaT amocanebi (viyenebT 2-ze gamravlebas) .............75
5 amovxsnaT amocanebi (viyenebT 2-ze gayofas) ......................80
6 gavamravloT 5-ze ..........................................................................83
7 gavyoT 5-ze ......................................................................................87
8 gavamravloT 10-ze. gavyoT 10-ze ............................................90
9 gavamravloT 1-ze. gavamravloT 0-ze ....................................99
10 gavamravloT 3-ze, gavyoT 3-ze ................................................102
11 gavamravloT 4-ze, gavyoT 4-ze ................................................108
12 SevadginoT gamravlebis cxrili .............................................114
13 SevadginoT ricxviTi gamosaxuleba. vipovoT ricxviTi gamosaxulebis mniSvneloba ..................120
14 vipovoT gamravlebisa da gayofis ucnobi wevri ..............127 gameoreba...........................................................................................133 maTematikuri niSnebi da maTi gamoyenebis magaliTebi ...140 geometriuli figurebi ...............................................................140 maTematikuri terminebi ..............................................................140 pasuxebi..............................................................................................141
4
r C e v e b i w i g n i T s a r g e b l o b i s T v i s
waikiTxeT es rCevebi, gaecaniT specialuri niSnakebis dan-
iSnulebas.
es niSnaki klasSi Sesasrulebeli samuSaoe-
bis dawyeba ze migviTiTebs. am amocanebis
nom rebi wreebSia Casmuli, feradicaa, maga-
li Tad, 4 .
es niSnaki Sin muSaobisas gankuTvnil amoca-
nebs warmogvidgens. am amocanebis nomrebi
samkuTxedebSia Casmuli, magaliTad, 1 .
am suraTs mosdevs amocanebi, romelTa amo-
saxsnelad xSirad sakmao gamWriaxobis gamov-
lenac mogviwevs. am amocanebis nomrebi oTx-
kuTxedSia Casmuli, magaliTad, 4 .
am niSnakiT jgufuri muSaobisTvis gankuT-
vnili amocanebia gamoyofili.
am niSnakiT TamaSebia aRniSnuli. maTSi ga-
mar jveba SeuZlebelia maTematikuri cod-
nis ga reSe.
vin iqneba pirveli. am niSnakiT warmodge-
nili amocanebis amoxsnisas ecadeT, gam-
WriaxobasTan erTad sxa rti azrovnebac ga-
moavlinoT.
am niSnakiT gamoyofili yvela amocana unda
gadaita noT rveulSi da DSemdeg SeasruloT.
jgufuri
saSinao
moisazre
klasSi
gaufrTxildiT wigns!
masSi Tqvenma Canawerebma wigni SeiZleba sxvebisTvis gamousadegari gaxados!
5
20 + 50
30 + 40
80 50
200 + 500
400 + 500
800 500
2000 + 5000
3000 + 2000
3000 1000
zepiri angariSis xerxebi 13klasSi
1
4
7
836 + 30
746 + 20
946 40
936 + 50
856 30
836 20
12 13
14 15
16 17
765 4011
729 + 200
ramdeni aseuliT gaizrdeba aseulebi? ramdeni aseulia jamSi? ipoveT jami.
18
725 200
ramdeni aseuliT mcirdeba aseulebis raodenoba? SeasruleT gamokleba.
19
2
5
8
3
6
9
SevkriboT an gamovakloT aTeulebi, aseulebi, aTaseulebi:
vumatebT an vaklebT aTeulebs, aseulebs, aTaseulebs:
725 + 4010 aTeulis Tanrigis cifri ram-den aTeuls gviCvenebs?
ramdeni aTeuliT gaizrdeba aTe ulebi?
725 + 40 = ?
765 40 = ?
?
6
836 + 100
2 500 + 3 000
6 500 3 000
836 400
3 500 + 2 000
ramdeni aTaseuliT gaizrdeba aTaseulebi? ramdeni aTaseuli miiReba?
7 500 2 000
ramdeni aTaseuliT mcirdeba aTaseulebi? ramdeni aTaseuli miiReba?
725 + 232
vumatebT aseulebs: 725 + 200
vumatebT aTeulebs: 925 + 30
vumatebT erTeulebs: 955 + 2 = 957
qarTvel moragbeTa saqomagod pirvel TamaSze 6800 mayurebeli mivida. meore TamaSze ki _ 3000-iT meti. ramdeni mayurebeli daeswro meore TamaSs?
746 + 200
1 500 + 4 000
7 500 4 000
786 500
535 + 300
736 300
20
27
30
23
26
29
32
36
21
28
31
24
22
857 + 12233
25
734 + 13334
631 + 12535
3 500 + 2 000 = ?
7 500 2 000 = ?
Sekreba aseulis Tanrigidan daviwyoT:
SeasruleT moqmedebebi:
7
756 235es gamoklebac aseulis Tanrigidan daviwyoT.
vaklebT aseulebs: 756 200
vaklebT aTeulebs: 556 30
vaklebT erTeulebs: 526 5 = 521
ra SemTxvevebSi airCevdiT Sekrebisa da gamoklebis am gzas? iqneb moqmedebis dawyeba erTeulis Tanrigidan jobs?
37
SearCieT swori pasuxi
400+500=a) 700 b) 800 g) 900.
675 40 =a) 645 b) 635 g) 625.
876 200 =a) 476 b) 576 g) 676.
684 + 300 =a) 687 b) 984 g) 714.
4 000 + 3 000 =a) 6 000 b) 7 000 g) 8 000.
729 + 100 =a) 929 b) 829 g) 629.
1
3
5 6
2
4
saSinao
736
500 + 300
500 300
1
4
7
436
800 + 100
400 200
2
5
8
536
900 + 100
600 500
3
6
9
CawereT gaSlili saxiT (saTanrigo Sesakrebebis jamis saxiT).
SeasruleT moqmedebebi:
8
530 + 40
636 + 200
624 + 212
746 30
1200 + 2000
758 + 121
marikas xelfasi gaizarda 200 lariT. adre _ 375 lari iyo. ramdeni laria axla marikas xelfasi?
beqam 748 laridan 100 lariT qurTuki iyida, 20 lariT _ wigni. ramdeni lari darCa beqas?
2009 wels erT-erTi qalaqis 1748 mcxovrebs hyavda avtomobili. 2010 wels avtomflobelTa odenoba 123-iT gaizarda. ramdeni avtomflobeli iyo 2010 wels?
10
16
22
13
19
25
28
29
29
746 + 40
757 300
635 204
577 40
8000 2000
625 + 243
11
17
23
14
20
26
536 + 30
576 400
798 236
678 60
4000 2000
689 245
12
18
24
15
21
27
moqmedebis Sesruleba daiwyeT umaRlesi Tanrigidan:
9
738 + 198
ramdeniT meti mivumateT? ramdeni gamovakloT 938-s, rom vipovoT saZiebeli jami?
149 + 34
278 35
237 + 22
286 33
viyenebT zepiri angariSis xerxebs 14klasSi
1
12
12
13
13
gamoTvlebis gamartivebis mizniT gamoviyenoT aTeulebi, aseulebi
viyenebT aTeulebiT an aseulebiT `gadaxtomas~, viyenebT Tvlas:
198-is uaxloesi aseulia 200 738+200=938
465 199
587 198
638 29
465 + 297736 198
736 200 = 536 536 + 2 = ?
2 357 + 199
357 + 200 = 557 557 1 = ?
3
5
8
11
357 + 495
638 + 28
7
10
4
562 + 3986
748 + 199
478 20916 ra Sedegs miiRebT, Tu jer ukuTvlas gamoiyenebT, Semdeg ki aseulebiT gadaxtomas?
10
SevavsoT aTeulebamde, aseulebamde:
gamovakloT aTaseuls, aseuls:
797 + 28
SevavsoT aseulebamde: 797 + 3 = 800kidev ra ricxvi unda davumatoT?
500 345
ra xerxiT SeasrulebT gamo kle-bas?
axla ra ricxvi unda miumatoT 154-s?
5000 457
axla ra ricxvs miumatebT?
17
21
26
800 + ? = ?
500 1 = 499
5000 = 4999 + 1
499 345 = 154
4999 457 = ?
895 + 36
697 + 49
19 + 9
18
400 236
4000 756
22
27
19
700 447
3000 426
23
28
20
300 125
1000 525
24
29
600 14825
saSinao
749 + 197
745 99
1
4
658 199
647 + 19
2
5
838 + 199
765 19
3
6
viyenebT aTeulebis, aseulebis mimatebas an gamoklebas:
200 3
11
349 + 24
698 + 36
698 + 2 = 700700 + 34 = ?
600 346
378 + 109
199 + 27
7
15
19
10
17
5000 45821
345 + 23
799 + 45
700 136
349 24
49 + 19
300 137
8
16
20
11
18
22
443 2813 453 10414
449 + 329
446 2212
viyenebT aTeulebiT an aseulebiT `gadaxtomas~:
SevavsoT aseulebamde, aTeulebamde:
gamovakloT aseuls, aTaseuls:
maTematikuri TamaSi:
`SevarCioT Sekrebisa da gamoklebis xerxi~
moswavleTa jgufebs urigdebaT baraTebi, rom leb-zec gamosaxulia ricxvebis Sekreba an gamokleba. moswavleebma unda SearCion Sekrebis, gamoklebis romelime xerxi _ qveSmiweriT, zepiri angariSis romelime xerxi da imsjelon sakuTari arCevanis Sesaxeb. magaliTebi SeiZleba iyos aseTi:
2000 + 3000
765 + 199
6500 2000
763 135
800 368
465 + 40
769 199
765 + 121
765 + 24
400 278
567 40
765 + 139
765 121
765 24
2000 186
1 599