maTematika IV klasi moswavlis wigni

maTematika

IV klasi

nino gvilava

eka CiloCava

salome CxeiZe

moswavlis wigni

5

6

§ 1. marSruti ..............................................................................................................................................8

§ 2. samniSna ricxvebi ...............................................................................................................................16

Seamowme Seni codna ...........................................................................................................................20

§ 3. svetovani diagrama ............................................................................................................................22

§ 4. gamravleba-gayofa .............................................................................................................................28

§ 5. ariTmetikuli moqmedebebi ...............................................................................................................31

§ 6. gamosaxuleba......................................................................................................................................34

§ 7. moqmedebaTa Sesrulebis Tanmimdevroba gamosaxulebaSi .............................................................36

§ 8. wrfe, sxivi. ........................................................................................................................................38

§ 9. ricxvidan jamis gamokleba, jamidan ricxvis gamokleba ..............................................................40

§ 10. Tanafardoba sigrZis sazom erTeulebs Soris ............................................................................42

Seamowme Seni codna..........................................................................................................................46

§ 11. marSrutis arCeva da gamosaxva aRniSvnebiT .................................................................................48

§ 12. vin ufro swrafad? .........................................................................................................................50

§ 13. marSrutis arCeva da gamosaxva aRniSvnebiT .................................................................................52

§ 14. simetria ............................................................................................................................................54

§ 15. naxevari .............................................................................................................................................56

Seamowme Seni codna ........................................................................................................................58

testi ................................................................................................................................................60

§ 16. samniSna ricxvebis Sekreba ............................................................................................................62

§ 17. primetri ...........................................................................................................................................64

§ 18. samniSna ricxvebis Sekreba ..............................................................................................................66

§ 19. jamis gamravleba ricxvze ..............................................................................................................68

§ 20. samniSna ricxvebis gamokleba .........................................................................................................70


§ 21. kilogrami .........................................................................................................................................76


§ 22. 10-ze, 100-ze gamravleba-gayofa ....................................................................................................84

§ 23. erTniSna ricxvis srul aTeulze gamravleba ..............................................................................86

§ 24. vin ufro swrafad? .........................................................................................................................88

§ 25. erTniSna ricxvis srul aTeulze gamravleba-gayofa .................................................................90

§ 26. geometriuli figurebi ...................................................................................................................92


sarCevi

9

marSruti

ramdeni kilometria TiToeuli bavSvis mier gavlili gza?

matareblis bileTi Tbilisidan baTumamde 15 lari Rirs. mariamis ojaxi 4 wevri-

sagan Sedgeba. ra Tanxis gadaxda mouwevs mariamis ojaxs Tbilisidan baTumamde

matarebliT mgzavrobisaTvis, Tu yvela bileTi erTi da igive fasi Rirs?

mariami 100 m manZils fexiT 5 wuTSi faravs. ra dro dasWirdeba mas 200 m-is gasav-

lelad? 300 m-is gasavlelad? 400 m-is gasavlelad?

iraklis ojaxma quTaisamde matarebliT imgzavra. quTaisidan zugdidamde ki

_ avtobusiT. matareblis erTi bileTi quTaisamde Rirs 10 lari, avtobusis ki

quTaisidan zudgidamde _ 7 lari. iraklis ojaxi sami wevrisagan Sedgeba. ra Tanxa

daujdaT maT zugdidamde mgzavroba, Tu yvela bileTi erTi da igive Tanxa Rirs?

elene isvenebda xaSursa da suramSi, giorgi _ sagarejosa da gurjaanSi, nino _

quTaissa da qobuleTSi. gamosaxe TiToeuli bavSvis mier gavlili marSruti.

vin gaiara yvelaze meti manZili? yvelaze naklebi?

mariami

gaecani Seni mewyvilis namuSevars. sworad gamosaxa Tu ara man TiToeuli bavSvis mier gav-

lili marSruti?

saqarTvelos romel kuTxeSi imogzaurma TiToeulma bavSvma? daadgine maT mier ganvlili

manZili. (Seecade, saqarTvelos rukis mixedviT daadgino qalaqebs Soris manZili).

15 lari

5 wT + 5 wT = 10 wT

5 wT 5 wT

100 m 100 m

15 lari 15 lari 15 lari

irakli ana daviTi

2.

3.

4.

5.

6.

10 710 710 7

elene giorgi

nino

Tbilisi Tbilisi

Tbilisi

10

marSruti

Sekreba Secvale gamravlebiT da gamoiangariSe:


gaagrZele:

Seadare:


erTi cali asanTis kolofi 5 TeTri Rirs, ra eRireba 2 cali asanTis kolofi? 3

cali asanTis kolofi?

erTi cali `bambis nayini~ Rirs 50 TeTri, ra eRireba 2 cali `bambis nayini~? 3 cali?

iraklim SeiZina 2 wigni, TiTo 10 larad, mariamma ki _ 3 wigni TiTo 5 larad.

romels da ramdeniT meti Tanxa daexarja wignebis SesaZenad?

1 + 1

1 + 1 + 1

1 + 1 + 1 + 1

1 + 1 + 1 + 1 + 1

100 + 100

100 + 100 + 100

1; 2; 4; 7; 11; ...; ...; ...10; 20; 40; 70; 110; ...; ...; ...

10+10

10+10+10

10+10+10+10

10+10+10+10+10

2 + 2

2 + 2 + 2

2 + 2 + 2 + 2

2 + 2 + 2 + 2 + 2

200 + 200

200 + 200 + 200

20+20

20+20+20

20+20+20+20

20+20+20+20+20

3 + 3

3 + 3 + 3

3 + 3 + 3 + 3

3 + 3 + 3 + 3 + 3

300 + 300

300 + 300 + 300

40+40

40+40+40

40+40+40+40

40+40+40+40+40

7.

11.

13.

14.

9.

8.

10.

12.

da20+20 20.3

da5+5+5-5 5.4

da3+3+3+3+3+2 3.5

da10+10+10-5 10.2

da4+4+4–5 4.3

da6+6-7 6.3

11

gza dayofilia 10-kilometrian monakveTebad:

Seavse cxrilebi:

romelia ufro mokle marSruti:

amoarCie marSruti, romlis gavlasac naklebi dro sWirdeba:

10 km-is gavlas 6 wuTi sWirdeba, ramdeni wuTi dasWirdeba 20 km-is gavlas? ra

dro dasWirdeba TiToeuli marSrutis gavlas Tu siswrafe ar icvleba?

gamoiangariSe:

TiToeuli monakveTis gavlas avtobusi 6 wuTs andomebs, ramdeni wuTi

dasWirdeba avtobuss mTeli gzis gasavlelad?

15.

16.

17.

19.

18.

10 km

100 m

300 m

20 km

20 km

20 km

20 km20 km10 km

10 km10 km 10 km

10 km

100 m 200 m

200 m 200 m

skola

marketi

saxli

saxli

200 m

200 m100 m

100 m

100 m

100 m

10 km 10 km 10 km 10 km

5

6

7

50

60

70

80

90

100

200

300

400

.2 .2 .2 .2

7 . 2

2 . 7

5 . 4

4 . 5

8 . 3

3 . 8

4 . 6

6 . 4

7 . 3

3 . 7

9 . 4

4 . 9

marSruti

12

baTumSi mariami sastumroSi cxovrobda, irakli ki naTTesavTan stumrobda.

isini yoveldRiurad dilis 10 saaTze xvdebodnen erTmaneTs kafeteriaSi. aR-

were TiToeuli maTganis marSruti sacxovrebeli adgilidan kafeteriamde.

ra manZils gadioda TiToeuli maTgani? romels uxdeboda meti manZilis

dafarva?

mariams 100 m-is gasavlelad 6 wT. sWirdeba, iraklis _ 4 wT. ra dro dasWird-

eba TiToeul maTgans saxlidan kafeteriamde misasvlelad?

romeli maTgani miva kafeteriaSi daTqmul dros?

gamosaxe mocemuli marSutebi sqematurad. gaucvale namuSevari mewyviles da

Seamowme, rogor Seasrula man samuSao.

20.

mariami

diliT adgoma momzadeba gza kafeteriamde sul saWiro dro

9 sT 30 wT

irakli

diliT adgoma momzadeba gza kafeteriamde sul saWiro dro

10-is naxevari 20 wT

marSruti

500 m

500 m

200 m

200 m300 m

200 m

sastumro

kafe

13

mariams da iraklis mSoblebma misces 10-10 lari, rac maT 10 dRis ganmavloba-

Si unda eyoT kafeteriaSi sasauzmod.

gamosaxe Seni saxlidan skolamde marSruti. ramden xans emzadebi skolaSi

droulad misasvlelad? daadgine, romel saaTze unda adge, rom skolaSi

droulad mixvide?

21.

26.

mariami miirTmevs

wveni _ 20 TeTri

xaWapuri _ 50 TeTri

ra Tanxas xarjavs dReSi TiToeuli maTgani? eyofaT Tu ara maT 10 lari 10

dRis ganmavlobaSi? Tu eyofaT, darCebaT Tu ara xurda? ramdeni? ramdeni

TeTria 10 lari? ramden TeTrs xarjavs TiToeuli maTgani yoveldRiurad?

irakli miirTmevs

wveni _ 20 TeTri

nayini _ 40 TeTri

funTuSa _ 30 TeTri.

gamoiangariSe:22.350+300+50

400+250+50

450+200+50

2; 4; 8; 16; ...; ...; ...

500+150-50

500+200-100

500+250-150

500-300-100

500-200-200

500-100-300

gamoiangariSe:23.7 . 2

2 . 7

4 . 3

3 . 4

5 . 2

2 . 5

6 . 3

3 . 6

7 . 2 . 3

3 . 2 . 7

2 . 3 . 7

2 . 7 . 3

8 . 2 . 1

1 . 2 . 8

2 . 8 . 1

2 . 1 . 8

9 . 2 . 3

2 . 3 . 9

9 . 3 . 2

3 . 2 . 9

Seadare:

gaagrZele:

24.

25.

da da da

da da da

7 . 2 8 . 2 6 . 2 - 46 . 4 9 . 4 3 . 2 + 3

7 . 3 8 . 3 6 . 2 - 56 . 5 9 . 5 3 . 3 + 1

marSruti

14

2 . (10 + 5)

3 . (10 + 5)

4 . (10 + 5)

4 . 6

4 . 60

6 . 4

6 . 40

4+11+15+16+16

30+30+14+20

31+31+49

17+17+17+17-18

30+30+30-50

16+16+16+16-19

9 . 4

9 . 40

4 . 9

4 . 90

5 . 3

5 . 30

3 . 5

3 . 50

7 . 3

7 . 30

3 . 7

3 . 70

8 . 4

4 . 90

4 . 8

4 . 80

2

3

4

5

6

7

8

9

10

11

12

13

2 . (25 + 5)

3 . (25 + 5)

4 . (25 + 5)

2 . (35 + 5)

3 . (35 + 5)

4 . (35 + 5)

2 . (35 + 15)

3 . (35 + 15)

4 . (35 + 15)

gamoiangariSe:

TiToeul ricxvs miuwere masze 2-jer meti ricxvi:

gamoiangariSe:

Tu erTi wigni 5 lari Rirs, ramdeni wignis SeZenas SeZlebs mariami 30 larad?

sadac mosaxerxebelia, Secvale Sekreba gamravlebiT da gamoiangariSe:

Seavse cxrilebi:

gaagrZele:

27.

28.

29.

30.

31.

32.

33.

. 2 4 6

8

10

. 20 40 60

8

10

. 3 5 7

8

10

2; 4; 8; ...; ...; ...20; 40; 80; ...; ...; ...

marSruti

15

gamoiangariSe:

gamoiangariSe:

Seadare:

Tu 20 kanfets Tanabrad gaunawileb 5 bavSvs, ramdeni kanfeti Sexvdeba TiToeuls?

iraklis 40 lari aqvs, eyofa Tu ara es Tanxa 5 wignis SesaZenad, Tu erTi wigni

10 lari Rirs?

Semoxaze ricxvebi, romlebic iyofa 2-ze. ra hqvia aseT ricxvebs?

60 kilometris gavlas avtobusi 60 wT-s andomebs; ramden wuTSi moaxerxebs

avtobusi 1 km-is gavlas? 10 km-is gavlas?

34.

36.

37.

35.

38.

39.

40.

3 . 6

6 . 3

18 : 3

18 : 6

80 : 2

80 : 4

80 : 8

4 . 5

5 . 4

20 : 5

20 : 4

60 : 2

60 : 4

60 : 6

6 . 7

7 . 6

42 : 6

42 : 7

40 : 2

40 : 4

40 : 5

5 . 8

8 . 5

40 : 5

40 : 8

100 : 2

100 : 4

100 : 5

9 . 2

2 . 9

18 : 9

18 : 2

7 . 4

4 . 7

28 : 4

28 : 7

90 : 2

90 : 3

90 : 5

da da

da da

(9 + 9) : 2

9

10 10 10

60 km

10 10 10

1617

1413

27

11

15

1024

2337

51

(7 + 7 + 7) : 3

(10 + 10) : 2 (8 + 8 + 8) : 2

8 : 2 6

20 : 4 9

marSruti

16

warmoadgine TiToeuli ricxvi saTanrigo Sesakrebebis jamis saxiT:

aseuli aTeuli erTeuli

Cawere gamotovebuli ricxvebi ise, rom miiRo erTmaneTis momdevno ricxvebi.

Seavse aTasamde mocemuli ricxvebi:

romelia meti?

gamoiangariSe:

gaagrZele:

axeseni, rogor Seadare.

daasaxele, sul ramdeni erTeulia TiToeul ricxvSi? sul ramdeni aTeulia?

sul ramdeni aseulia?

romel TanrigSi dgas cifri 2 ricxv 512-is CanawerSi? daasaxele TiToeuli

ricxvis CanawerSi cifri 5-is mniSvneloba; cifri 0-is mniSvneloba.

385; 512; 700; 850; 905; 1000.

542 - sul 542 erTeuli

542 - sul 54 aTeuli

da 2 erTeuli

542 - sul 5 aseuli, 4 aTeuli

da 2 erTeuli

5 4 2

100, 110, 120, . . ., . . ., . . .,. . . , . . . , . . . ,. . . ,

500; 750; 950; 600; 300; 200.

...; 126; ... ...; ...; 457 ...; 381; ...

1.

2.

3.

4.

5.

6.

2. samniSna ricxvebi

Tu Tu Tu Tu

Tu Tu Tu Tu

500 250 540 722300 460 221 844

400 300 550 723200 470 231 845

100+150

280+20

150+200

350+100

450+50

500+100

97+10

47+28

64+27

36+47

59+25

16+18

17

dawere xuTi samniSna ricxvi, romlebSic 31 aTeulia; warmoadgine TiToeu-

li ricxvi saTanrigo Sesakrebebis jamis saxiT.

ramdenia umciresi samniSna ricxvisa da udidesi orniSna ricxvis sxvaoba?

ipove, ricxvi romelic 100-iT metia:

Seadare:

daasaxele sul ramdeni aTeulia mocemul ricxvebSi:

Cawere gamotovebuli ricxvebi:

anas giorgize 20 TeTriT meti aqvs. ramdeni TeTri aqvs TiToeul bavSvs, Tu

orives erTad 100 TeTri aqvs?

mocemuli ricxvebidan Semoxaze ricxvebi, romlebSic 52 aTeulze metia.

a) 100-ze; b) 300-ze; g) 900-ze; d) 50-ze.

7.

8.

9.

10.

11.

12.

13.

14.

da da da

da da da

261+100

436; 720; 380; 530; 495; 510; 600; 880; 1000; 521.

731

125

... - ... = 100

... - ... = 200

... - ... = 300

... - ... = 50

... - ... = 15

... - ... = 30

... - ... = 9

... - ... = 10

... - ... = 11

600

507

320

800

1000

430

198

283

205

909

150+50 600+200

153+100 200+300 750+100

360 100+100 600+300

253 300+200 700+150

samniSna ricxvebi

18

gaecani Sens qalaqs:

mariamma da misma megobrebma gadawyvites eqskursiis mowyoba Tbilisis erT-

erT ubanSi. SeirCa ori marSruti: 1. Sexvedris adgili � skola � xelovnebi

muzeumi � kafe. 2. Sexvedris adgili _ skola � suraTebis galerea � kafe.

moniSne orive marSruti.

eqskursia SeiZleba moewyos fexiT an avtobusiT. bavSvebma Caatares gamokiTxva:

eqskursiis mowyoba fexiT girCevnia Tu avtobusiT?•

romel marSruts airCev, pirvels Tu meores?•

gamokiTxvis Sedegebi ase warmoadgines:

ra hqvia aseT cxrilebs? kidev rogor SeiZleba mogrovebuli monacemebis

warmodgena? rogor ggonia, eqskursiaze bavSvebi fexiT gaemarTnen Tu av-

tobusiT? ratom fiqrob ase? romeli marSruti airCies pirveli Tu meore?

rogor ggonia, ratom? ra manZilis gavla mouwevT bavSvebs? ra dro dasWird-

ebaT am manZilis dasafarad, Tu isini 200 m-is gavlas 10 wT-s andomeben.

SegiZlia moawyo msgavsi eqskursia TanaklaselebTan erTad sacxovrebeli

adgilis mixedviT.

15.

fexiT

avtobusiT

1

2

samniSna ricxvebi

19

menius Sesadgenad Caatares gamokiTxva:

dausvi SekiTxvebi Sens Tanaklaselebs da daadgine, sportis romel saxeobas

aniWeben upiratesobas. gamokiTxvis Sedegebi warmoadgine cxrilis saxiT.:

daadgine ra Janris films aniWeben upiratesobas Seni ojaxis wevrebi? (ko-

medias Tu saTavgadasavalos)

xaWapuri girCevnia Tu pica? atmis wveni, Tu forToxlis?

monacemebi warmoadgines cxrilis saxiT:

erTi xaWapuri Rirs 50 TeTri, pica _ 60 TeTri, atmisa da forToxlis wveni ki _

40-40 TeTri. ra Tanxa dasWirdebaT bavSvebs TiToeuli produqtis SesaZenad?

sul ramdeni erTeulia 350? ramdeni laria erTi aseuli TeTri? gamosaxe

cxrilSi warmodgenili TiToeuli Tanxa larebiT da TeTrebiT. Tqven Segi-

ZliaT moawyoT msgavsi eqskursia sacxovrebeli adgilis mixedviT.

daasaxele ricxv 350-is CanawerSi TiToeuli cifris mniSvneloba. romel

TanrigSi dgas cifri 5? cifri 0?

xaWapuri 50 + 50 + 50 +. . . + 50 = 600 TeTri

pica.............. atmis wveni .............. forToxlis wveni ..............

16.

17.

18.

xaWapuri pica atmis wveni forToxlis wveni

7 13 9 11

Tanxa aseuli aTeuli erTeuli dasaxeleba

xaWapuri 350 3 5 samasormocdaaTi

pica

atmis wveni

forToxlis wveni

samniSna ricxvebi

20

gaanawile mocemuli ricxvebi raime niSnis mixedviT or jgufad:

elene, daviTi, ana da giorgi TeatrSi midian. erTi bileTis fasi 5 laria.

eyofaT Tu ara bavSvebs 17 lari bileTebis SesaZenad? Tu ar eyofaT, ra Tanxis

damateba dasWirdebaT? romeli kupiurebiT SeiZleba 17 laris warmodgena?

daasaxele ori varianti.

Seavse cxrilebi:

Cawere Sesabamisi ricxvebi:

romel gamosaxulebebs eqnebaT ernairi Sedegi? daakavSire xazebiT.

gamoiangariSe:

daasaxele niSani, romlis mixedviTac gaanawile ricxvebi.

Sea

mow

me S

eni

co

dna

S

eamo

wme

Sen

i c

od

na

Sea

mow

me S

eni

co

dna

S

eamo

wme

Sen

i c

od

naSeamowme Seni codna Seamowme Seni codna Seamowme Seni codna Sea

1.

3.

4.

5.

6.

2.

10; 9; 31; 100; 5; 250; 14.

480+20+44

481+19+42

482+18+32

54+16=50+ . . .

63+17=60+. . .

25+25=20+ . . .

31+39=30+ . . .

47+33=40+ . . .

82+18=80+ . . .

320+80+15

321+79+16

322+78+20

450+50+71

451+49+73

452+48+71

. 2 3

8 24

6

. 2 3

2

4 12

. 2 3

5

7 14

3 . 2

4 . 4 5 . 55 + 5 + 5 + 5 + 5

4 + 4 + 4 + 4

6 + 6 + 6

3 + 36 . 3

21

amowme Seni codna Seamowme Seni codna Seamowme Seni codna

Cawere gamotovebuli ricxvebi ise, rom miiRo erTmaneTis momdevno ricxvebi:

Seadare:

daasaxele mocemuli ricxvebis uaxloesi sruli aTeuli:

gaagrZele ricxvTa mimdevroba ise, rom ricxvebSi aTeulebis raodenoba iyos 41.

mocemuli variantebidan aarCie qveiTi an satransporto marSruti. axseni Seni

arCevani.

dausvi SekiTxvebi Sens mewyviles da gaarkvie, rogor dasvenebas aniWebs is upi-

ratesobas. (mag. wignis kiTxvas, Tu kompiuteris TamaSs)

Seamo

wme S

eni co

dna

Seamo

wme S

eni co

dna

Seamo

wme S

eni co

dna

Seamo

wme S

eni co

dna

7.

8.

9.

10.

11.

12.

211; 426; 517; 91; 637; 354.

414, ..., ..., ..., ..., ...,

...; 451 ...

213; ...; ...

...; 615 ...

898; ... ...

...; ...; 312

...; ...; 1000

da da da da

da da da da

da da da da

321 342 361 518143 171 183 883417 456 477 939

421 332 362 520243 161 184 880517 546 476 1000

10 wT

5 wT

15 wT

qveiTi marSruti

satransporto marSruti

saxli skola

7 wT

38

bavSvebi isvenebdnen banakSi. ramdeni gza midis banakidan soflamde? ramden wertilSi

ikveTeba gzebi? mari da gia banakidan tbisken gaemarTnen. romeli gzaa umoklesi?

gamosaxe naxatze mocemuli gzebi wirebis saSualebiT. rogor wirebs gamoiyeneb?

riT hgavs? riT gansxvavdeba?

monakveTi

sxivi

wrfewrfe

1

2 3

wrfe, sxivi8.

3.

1.

Semoxaze naxazze mrudi wiri lurjad, wrfe _ wiTlad, monakveTi _ mwvaned.

aiRe wertili da gaavle masze 3 wrfe.

2.

4.

39

ramdeni wrfe gadis 1 wertilze? gaavle am

wertilze kidev 2 wrfe. SeiZleba Tu ara kidev wr-

feebis gavleba?

or wertils akavSirebs 1 monakveTi. ramdeni monakveTi daakavSirebs 3 wer-

tils? 4 wertils? Seavse cxrili:

wertilebis raodenoba 2 3 4 5

monakveTebis raodenoba 1 3 6

5.

6.

ramdeni sxivia gavlebuli erTi wertilidan?

SeiZleba Tu ara kidev sxivebis gavleba?

daxaze Semdegi figurebi xelisauReblad:

wrfe, sxivi

8.

7.

Seasrule mocemuli naxati

geometriuli figurebis

gamoyenebiT. daasaxele

gamoyenebuli figurebi. ris

daxatvisas gamoiyeneb sxivs?

mrud wirs? swor wirs?

9.

52

ana da irakli zRvaze isveneben. maTi sofelic iqvea. bavSvebma gadawyvites, moin-

axulon bebia da babua da daexmaron maT bostnis gamargvlasa da xilis mokrefaSi.

200 m 1300 m

avtobusis sadgomi

30 km

30 km

1000 m

bebia-babuis saxlidan bostnamde 20 metria, saxlidan yvavilis baRamde 30 m, xolo

xexilis baRamde _ 100 m. iraklim manZilebi gamosaxa sqematurad. Senc igive gaa-

keTe; aRwere obieqtebis mdebareoba erTmaneTis mimarT.

romel marSruts airCeven bavSvebi soflamde misasvlelad? axseni, ratom?

gamosaxe arCeuli marSruti sqematurad aRniSvnebis gamoyenebiT.

saxlidan mdinaremde 30 km-ia, mdinaridan soflamdec _ imdenive. sul ramdeni

km-ia soflamde? bavSvebi da maTi mSoblebi avtobusiT gaemgzavrnen. avtobusi

1 sT-Si gadis 30 km-s. ramden saaTSi gaivlis avtobusi mTel manZils?

romel saaTze Cavlen bavSvebi sofelSi Tu adgilidan dilis 9 saaTze gavlen?

aRwere obieqtebis mdebareoba erTmaneTis mimarT.

gamosaxe manZilebi decimetrebiT. ra mdebareobs saxlidan yvelaze Sors?

13.1.

2.

Sesasvleli

marSrutis arCeva da gamosaxva aRniSvnebiT

53

bavSvis samgzavro bileTi Rirs: 2 lari, didis ki _ 3 lari. ra Tanxa dasWird-

eba ojaxs samgzavrod saxlidan soflamde da ukan?

iraklis da anas saxlidan skolamde ori gza midis: samanqano da fexiT sa-

siarulo. avtobusi gaCerebidan gaCerebamde manZils 3 wT-Si gadis. saxlidan

gaCerebamde misasvlelad saWiroa 7 wT; gaCerebidan skolamde _ 5 wT fexiT;

bavSvebi skolamde fexiT 35 wT-Si midian.

bavSvebma moagroves bostneuli da xili:

Seadare bavSvebis mier mogrovebuli

xilis da bostneulis raodenobebi

erTmaneTs. ras amCnev?

monacemTa warmodgenis romel saSu-

alebas airCevdi? axsni, ratom?

ana

svetovani diagramis mixedviT Seavse cxrili:

Seni azriT, romeli gziT sjobs skolaSi siaruli? axseni, ratom?

gamosaxe saxlidan skolamde avtobusis marSruti sqematurad.

irakli

pomidori pomidorikitri kitri

rao

de

no

ba

rao

de

no

ba

leRvi leRvivaSli vaSli

109

1813

20 20

25

40

ana irakli

pomidori

kitri

leRvi

vaSli

3.

4.

5.

marSrutis arCeva da gamosaxva aRniSvnebiT

76

gamgzavrebamde dedam bazarSi xili SeiZina. ramdeni kilogrami xili SeuZenia

dedas?

wonis sazomi erT-erTi erTeuli aris kilogrami _ kg. wona SeiZleba dadg-

indes sasworis saSualebiT.

irakli da mariami ojaxTan erTad TviTmfrinaviT mgzavrobisTvis emzadebian.

TviTmfrinavSi dasaSvebia mxolod garkveuli wonis xelis tvirTis atana,

amitom bavSvebma unda gaiTvaliswinon da daadginon im nivTebis wona, rasac

xelSi daiWeren.

rogor SeiZleba amis gakeTeba?

daakvirdi naxatebs da CamoTvale sagnebi, romlebic iwonis 1 kg-s; 1 kg-ze

mets; 1 kg-ze naklebs.

gamoiyene saswori da awone Seni CanTa, wigni da Cawere TiToeuli maTgani me-

tia Tu naklebi 1 kilogramze?

rogor fiqrob, 1 kg bamba ufro mZimea Tu 1 kg lursmani?

mzareulma skolis sasadilosaTvis SeiZina 30 kg kartofili, 50 kg fqvili, 25 kg

sosisi, 50 kg kombosto. sul ramdeni kilogrami produqti SeuZenia mzareuls?

2 kg + 1 kg + 3 kg= . . . .kg.

kilogrami21.

1.

1.

2.

3.

4.

5.

77

1 kilogramze naklebi wonis aRsaniSnavad gamoiyeneba grami.

1 cali kitri 120 g-s iwonis. ramden grams aiwonis 3 aseTi kitri?

1 cali pomidori 90 g-s iwonis. ramden grams aiwonis 4 aseTi pomidori?

1 cali vaSli iwonis 200 g-s. ramdens aiwonis 5 aseTi vaSli?

ramden kg-s iwonian nias ojaxis wevrebi erTad?

icodi Tu ara, rom yvelaze didi frinvelia siqarlema?. is daaxloebiT 70 kg-

dan 80 kg-mde iwonis, yvelaze patara frinveli ki _ daaxloebiT 2 g-s.

daadgine Seni ojaxis wevrebis wona da Seitane monacemebi cxrilSi. vin iwo-

nis yvelaze mets? naklebs? ramdenia gasxvaveba yvelaze met da yvelaze nakleb

wonas Soris? romeli monacemia SuaSi?

liftSi SemsvlelTa wona ar unda aRematebodes 140 kg-is. SearCie, ra wonis ramdeni

adamiani SeiZleba liftSi Sevides, imisaTvis rom man daubrkoleblad imoZraos?

1 kilogrami aris 1 000 grami. 1 kg= 1000 g. naxevari kilogrami aris _ 500 g.

a) vin iwonis yvelaze mets?

b) vin iwonis yvelaze naklebs?

g) ramdeni kg-iT mets iwonis nias deda niaze?

d) ramdeniT naklebs iwonis bibi zukaze?

waikiTxe TiToeuli sagnis wona:

1 kg.

7 kg.

30 kg.

50 kg.

22 kg.

70 kg.

500 g 259 g 100 g10 g

kilogrami

6.

7.

8.

9.

10.

wona

78

cxvari

dRe mSrali sakvebi Tiva

1 2 kg 1 kg

2

10

30

Rori

dRe mSrali sakvebi silosi

1 2 kg 1 kg

2

10

30

Txa

dRe mSrali sakvebi Tiva

1 1 kg 1 kg

2

10

30

kilogrami

11. sofelSi babuasTan stumrad Casulma nikam ezoSi dainaxa: Rorebi, cxvrebi da

cxeni. daakvirdi cxrils da Seavse:

nikas babuas hyavs 2 cxvari da 10 Txa.

ramdeni kilogrami sakvebi dasWird-

ebaT maT1 dRis ganmavlobaSi?

ramdeni kg sakvebi dasWirdeba 3

Rors erTi kviris ganmavlobaSi?

ramdeni kg sakvebi dasWirdeba 20

cxvars 10 dRis ganmavlobaSi?

nikas babuis mezobels hyavs 10 Rori.

da 2 Txa. ramden kilogram sakvebs

iReben isini yoveldRiurad?

gamoiangariSe:12.4 . 155 . 136 . 15

4 . 203 . 2020 . 5

18 . 418 . 518 . 7

19 . 419 . 519 . 6

17 . 517 . 417 . 6

16 . 416 . 516 . 6

vefxvs yoveldRiurad sWirdeba 15 kg axali xorci. ramdeni kg xorci das-

Wirdeba vefxvs erTi kviris ganmavlobaSi?

13.

79

vefxvi

lomi

zebra

kenguru

gorila

delfini

vefxvi

lomi

zebra

kenguru

gorila

delfini

kilogrami

250 kg

180 kg

270 kg

10w

200kg 300kg100kg

20w 30w

240 kg

160 kg

70 kg

40 kg

90 kg

271 + 728649 + 239348 + 429

898 - 276372 - 146723 - 461

555 - 366667 - 271888 - 499

475 - 284331 - 140674 - 281

daakvirdi cxrils da cxrilis meSveobiT aage svetovani diagrama:

ramdens iwonis TiToeuli cxoveli? Seavse cxrili da aage svetovani diagrama.

gamoiangariSe:

14.

15.

96

geometriuli figurebi27.1. elenem da misma Tanaklaselebma xelovnebis gakveTilze daaTvalieres naxatebi:

ra figurebiT aris gakeTebuli nivTebi? daasaxele waxnagebi, wiboebi, saerTo wibo.

bavSvebs Zalian moewonaT geometriuli figurebiT Seqmnili xelovnebis

nimuSebi da Seecadnen naxatebidan amoecnoT geometriuli figurebi. iqneb

Senc scado?

maT gadawyvites saaxalwlo zeimisaTvis Tavad daemzdebinaT lamazi nivTebi

geometriuli figurebis gamoyenebiT.

bavSvebi daiyvnen oTx jgufad da gainawiles samuSao:

I jgufi _ saWiro masalis momarageba;

II jgufi _ saTamaSoebis damzadeba;

III jgufi _ zeimisaTvis saWiro produqtebis momarageba;

IV jgufi _ saklaso oTaxis momzadeba da morTva.

97

geometriuli figurebi

I jgufis bavSvebma daTvales ramdeni feradi qaRaldi, webo, dasamagrebeli

dasWirdebodaT da monacemebi ase warmoadgines:

daexmare bavSvebs da daTvale, ra Tanxa dasWirdeba mocemuli nivTebis SeZe-

nas?

TiToeuli saxeobis ramdeni produqti sWirdebaT bavSvebs? risi dadgena ar

SeiZleba ase warmodgenili monacemebiT?

ra Tanxa dasWirdebaT bavS-

vebs produqtebis SesaZenad?

sul ramdeni lari dasWird-

ebaT bavSvebs zeimisaTvis?

III jgufis bavSvebma daTvales zeimisTvis saWiro produqtebi da monacemebi

warmoadgines svetovani diagramis saSualebiT:

dasaxeleba fasi fasi

feradi qaRaldi 200 cali 5 TeTri

webo 10 cali 50 TeTri

dasamagrebeli 30 cali 10 TeTri

meniu

namcxvari 30 TeTri

wveni 20 TeTri

xaWapuri 2 lari

lobiani 1 lari da 50 TeTri

buterbrodi 40 TeTri

namcxvari wveni xaWapuri lobiani buterbrodi

5

10

15

20

25

30

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maTematika IV klasi moswavlis wigni