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 info@intelekti.ge inteleqti@caucasus.net

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