222moswavlis wigni

03

8

1

64

9

2

75

10 11 12

A B

pirveli nawili

9 789941 166693

SBN 9789941166693

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...

saqarTvelos macnesaqarTvelos macne

moswavliswigni

moswavlisrveuli

maswavlebliswigni

I da II nawili

saqarTvelos macne

saqarTvelos macne

saqarTvelos macne

I - II nawili

2

maTematikameore klasis moswavlis wigni

pirveli nawili

saqarTvelos macne

grifminiWebulia saqarTvelos ganaTlebisa da

mecnierebis saministros mier 2018 wels

izolda xuciSvili

maTematikameore klasis moswavlis wigni pirveli nawili

© gamomcemloba `saqarTvelos macne~, 2018

© i. xuciSvili, 2018

gamocemis weli da rigiToba 2008, 2018 weli

ISBN 978-9941-16-669-3

gamomcemloba `saqarTvelos macne~ mis: q. Tbilisi, e. maRalaSvilis q. #5tel: 568105467; 574 400 857el.fosta: saqmatsne@mail.ru, sakmacne@gmail.comwww.saqmatsne.ge

avtori izolda xuciSviliredaqtori maia yajriSvilidizainer- damkabadonebeli maia feiqriSvili

Cemo patara megobaro!

Sen gaizarde _ ukve meoreklaseli xar da mjera, meti mondo-

mebiTa da ZalisxmeviT ganagrZob maTematikis Seswavlas. amaSi

me dagexmarebi _ Seni saxelmZRvanelo.

modi, ufro axlos gagecnobi, raTa ukeT gamomiyeno.

Cems furclebze mTeli saswavlo masala gakveTilebadaa

dayofili. gakveTilebis umetesobaSi axal sakiTxebs gaecnobi.

garda amisa, gaimeoreb adre Seswavlils, gaiRrmaveb da gaifar-

Toeb codnas.

gakveTilis dasawyisSi axali masalaa mocemuli, Semdeg _

adre Seswavlili, bolos ki _ iseTi amocana, romlis amosaxs-

nelad codnis garda mixvedrilobisa da sazrianobis moSveli-

ebac dagWirdeba. aseTi amocanebis amoxsna dagexmareba ufro

dakvirvebuli da yuradRebiani gaxde, Seiyvaro maTematika da

dainteresde misi SeswavliT, iswavlo azrovneba da msjeloba,

SeiZino iseTi unar-Cvevebi, romlebic sxva sagnebis Seswavlasa

da yoveldRiur saqmianobas gagiadvilebs. Tu amocanas pirve-

live cdiT ver amoxsni, kidev scade. Tu mas mainc ver amoxsni,

klasSi yuradRebiT moismine, rogor Seasrules davaleba Senma

amxanagebma. araferi Caiwero da ramdenime dRis Semdeg Seecade

damoukideblad amoxsna igi.

axal masalas zogjer ver gagacnob, ufro xSirad ki dasmul

kiTxvebze pasuxis gacemiT amxanagebTan erTad Sen TviTon miag-

neb siaxles _ aRmoaCen axal faqts, gaecnobi axal maTematikur

obieqts, gamoiyvan moqmedebis Sesrulebis wess.amaSi Sen Tana-

tolebi ano, vano da gigoc dagexmarebian. me da Seni maswav-

lebelic Tqven gverdiT viqnebiT, Cems miTiTebebs gakveTilis

teqstSi an dasawyisSi mocemul suraTze ipovi. Tu es ar iqneba

sakmarisi, maswavlebeli dagexmareba.

ifiqre, iazrovne, iswavle SenTvis dasaZlevi problemebis

gadaWra. Sen amas SeZleb.

albaT gainteresebs anos, vanos da gigos vinaoba. isini Seni

Tanatolebi arian _ meoreklaselebi. maTac me vaswavli maTema-

tikas. ano da vano warCinebuli moswavleebi arian, gigo ki is

zarmaci gigoa, Txam rom Searcxvina saqveynod. mas Semdeg gigo

gamosworda, bejiTad swavlobs da axla anos da vanos ar Camou-

vardeba codniT, magram Tavisi eSmakoba da siance mainc Semor-

Ca, sul cdilobs iseT xerxs miagnos, rom saqme gaiadvilos.

Senc bevr rames iswavli misgan, magram gaxsovdes, mis kiTxvebsa

da pasuxebSi xSirad maxea dagebuli, unda, rom SecdomaSi Segi-

yvanos. amitom frTxilad iyavi, kargad daukvirdi mis yovel

sityvas.

Cems yvela amocanaSi miTiTebulia, ra unda gaakeTo. zogjer

es miTiTeba pirobiTi niSniTaa mocemuli. am niSnebs qvemoT

gagacnob.

masala, romelic yuradRebiT unda waikiTxo da icode, wiTe-

li xaziTaa moniSnuli. misi sityvasityviT damaxsovreba saWiro

araa. zustad dasamaxsovrebeli masala CarCoSia Casmuli da

aweria ̀ daimaxsovre!~ unda gaxsovdes terminebic, romlebic wi-

Teli feriTaa gamoyofili.

wignSi nurafers Cawer. davalebebi rveulSi unda Seasrulo!

yovel gakveTilze CemTan erTad unda gamoiyeno samuSao

rveulic. iq mocemuli savarjiSoebi da miTiTebebi mizanmimar-

Tulad avsebs Cems furclebze gadmocemul masalas da saWiro

unar-CvevaTa SeZenaSi dagexmareba.

swrafi angariSis dasaufleblad saaTi unda gamoiyeno. aseTi

savarjiSo miTiTebul droSi unda Seasrulo. Tu iyoCaReb da

ufro nakleb droSi Caetevi, es Seni rekordi iqneba. Seejibre

amxanagebs da ecade, gaimarjvo.

ai, Sen ukve micnob. danarCens maswavlebeli getyvis.

warmatebas gisurveb

gaxsovdes, qveyanas warCinebuli Svilebi sWirdeba.

es qveyana ki anosi, vanosi, gigosi da Senia, Cemo megobaro. mas

Tqveni imedi aqvs.

Seni saxelmZRvanelo

S i n a a r s i

I Tavi. ricxvebi 0-dan 20-is CaTvliT. . . . . . . . . . . . . . . .8 1. saganTa erTobliobebi. . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. ricxvebis wakiTxva da Cawera . . . . . . . . . . . . . . . . . . . . . 10 3. ricxvebi 10-dan 20-is CaTvliT . . . . . . . . . . . . . . . . . . . . 12 4. naturaluri ricxvTa mwkrivi. . . . . . . . . . . . . . . . . . . . . 14 5. ricxvebis Sedareba . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6. ori ricxvis jami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 7. ori ricxvis sxvaoba . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 8. ricxvis gazrda an Semcireba ramdenime erTeuliT . . . . . . 18 9. ramdeniT metia? ramdeniT naklebia? . . . . . . . . . . . . . . . . 20 10. Sekreba-gamokleba 10-is farglebSi . . . . . . . . . . . . . . . . . 22 savarjiSoebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 11. wertilis aRniSvna asoebiT . . . . . . . . . . . . . . . . . . . . . . 26

II Tavi. Sekreba da gamokleba 20-is farglebSi . . . . . . . . 27 1. Sekreba da gamokleba 20-is farglebSi aTeulze gadausvlelad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2. ricxvis Sevseba aTamde . . . . . . . . . . . . . . . . . . . . . . . . . 30 3. Sekreba 20-is farglebSi aTeulze gadasvliT . . . . . . . . . . 32 savarjiSoebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4. gamosaxuleba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5. moqmedebaTa Tanmimdevroba gamosaxulebaSi . . . . . . . . . . 38 6. SesakrebTa dajgufeba . . . . . . . . . . . . . . . . . . . . . . . . . . 40 7. roca Sesakrebia 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 8. roca Sesakrebia 8 an 7 . . . . . . . . . . . . . . . . . . . . . . . . . . 43 9. gamokleba 20-is farglebSi aTeulis daSliT . . . . . . . . . . 44 savarjiSoebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

III Tavi. texili. mravalkuTxedebi. simetria. . . . . . . . . . 48 1. texili . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2. gaxsnili da Sekruli texilebi. mravalkuTxedi . . . . . . . . 50 3. simetria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4. simetriis RerZis mqone figurebi . . . . . . . . . . . . . . . . . . 54 5. gaormageba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6. Suaze gayofa (ganaxevreba) . . . . . . . . . . . . . . . . . . . . . . . 58

IV Tavi. ricxvebi 0-dan 100-mde . . . . . . . . . . . . . . . . . . . 60 1. raodenobis daTvla sxvadasxva saTvleli erTeuliT. . . . . 60 2. 20-ze meti ricxvebis Cawera . . . . . . . . . . . . . . . . . . . . . . 62 3. ricxvebi 20-dan 39-is CaTvliT . . . . . . . . . . . . . . . . . . . . 64 savarjiSoebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4. ricxvebi 40-dan 59-is CaTvliT . . . . . . . . . . . . . . . . . . . . 68 5. ricxvebi 60-dan 79-is CaTvliT . . . . . . . . . . . . . . . . . . . . 70 6. ricxvebi 80-dan 99-is CaTvliT . . . . . . . . . . . . . . . . . . . . 72 7. asi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 8. mrgvali ricxvebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 9. Tanrigebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 10. saTanrigo SesakrebTa jami. . . . . . . . . . . . . . . . . . . . . . . 78 savarjiSoebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 11. ricxvTa cxrili . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 12. sityvierad mocemuli ocze meti ricxvebis Sedareba . . . . 82 13. cifrebiT Cawerili ricxvebis Sedareba . . . . . . . . . . . . . . 84 14. texilis sigrZe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 15. metri. Tanafardoba sigrZis erTeulebs Soris . . . . . . . . . 87

_ Cawere iseTi ricxvi, rom swori toloba miiRo.

_ imuSave rveulSi.

_ Secvale iseTi cifriT, rom swori toloba miiRo.

_ mravalwertili Secvale miTiTebuli moqmedebebidan

erT-erTiT ise, rom swori toloba miiRo.

_ mravalwertili Secvale erT-erTi niSniT ise, rom

swori toloba an utoloba miiRo.

_ unda moifiqro iseTi niSani, romelic mocemuli

sagnebidan yvelas aqvs erTis _ `zedmetis~ garda.

sxva dasxva niSnebis mixedviT sxvadasxva sagani SeiZleba

aRmo Cndes zedmeti. ganixile SesaZlo SemTxvevebi.

_ Cawere ramdeniT metia an naklebia erTi ricxvi meo-

reze.

moisazre!

_ amocana, romelic

mosazrebulobas moiTxovs

pirobiTi niSnebi

+, _

∗

erTi

`zedmetia~

>, <, =

>, <? ?

ano vano gigo

_ imuSave rveulSi.1.

I Tavi. ricxvebi 0-dan 20-is CaTvliT

gaixsene naswavli.

gaiRrmave da gaifarTove codna

a) daasaxele suraTze mocemuli erTobliobis sagnebi.

b) ra saerTo saxeli SeiZleba vuwodoT maT?

g) daasaxele kidev ramdenime sagani, romlebic

xil-bostneuls miekuTvneba.

d) kombosto, pomidori, badrijani, kitri, stafilo, wiwaka.

mocemuli erTobliobis am nawils bostneuli hqvia.

e) anom da vanom erTobliobis sxva nawilebic gamoyves.

anom gamoyo vaSli, pomidori, marwyvi, bali.

vanom gamoyo kitri, kombosto, yurZeni da wiwaka.

ra niSnis mixedviT gamouyviaT anos da vanos erTobliobis

nawilebi. ra saerTo saxels daarqmevdiT maT?

v) gamoyavi kidev ramdenime nawili da uwode saxeli.

anom unda iyidos

amaTgan risi yidva SeuZlia anos xil-bostneulis maRaziaSi?

1

1.

2.

saganTa erTobliobebi

ra ewodeba (a) suraTze mocemul erTobliobas?

(b) suraTze mocemul saganTa erTobliobas?

1) ras uwodeben bevri cxvris erTobliobas?

mglebis erTobliobas? irmebis erTobliobas?

cxenebis erTobliobas? mocekvaveTa erTobliobas?

momReralTa erTobliobas?

2) gaixsene, kidev romeli erTobliobebis saxelebi ici?

daasaxele ramdenime sagani mwerebis erTobliobidan;

frinvelebis erTobliobidan; saswavlo nivTebis

erTobliobidan; fexsacmelebis erTobliobidan;

risi erTobliobaa anbani?

a) ra saerTo saxel hqvia sagnebs, romelTac suraTze xedav?

b) gamoiyene sityvebi: win, Semdeg, Soris, marcxniv, marjvniv

da aRwere suraTi;

g) gamoyavi erTobliobis nawilebi raime niSniT.

ras daarqmevdi erTobliobas:

a) ? ! . , ;, , , , ?

b) nino, ana, Tea, gvanca?

3.

4.

5.

6.7.

8.

erTi `zedmetia~

ra SeiZleba uwodo danarCeni sagnebis jgufs?

8 9

I Tavi. ricxvebi 0-dan 20-is CaTvliT

gaixsene naswavli.

gaiRrmave da gaifarTove codna

a) daasaxele suraTze mocemuli erTobliobis sagnebi.

b) ra saerTo saxeli SeiZleba vuwodoT maT?

g) daasaxele kidev ramdenime sagani, romlebic

xil-bostneuls miekuTvneba.

d) kombosto, pomidori, badrijani, kitri, stafilo, wiwaka.

mocemuli erTobliobis am nawils bostneuli hqvia.

e) anom da vanom erTobliobis sxva nawilebic gamoyves.

anom gamoyo vaSli, pomidori, marwyvi, bali.

vanom gamoyo kitri, kombosto, yurZeni da wiwaka.

ra niSnis mixedviT gamouyviaT anos da vanos erTobliobis

nawilebi. ra saerTo saxels daarqmevdiT maT?

v) gamoyavi kidev ramdenime nawili da uwode saxeli.

anom unda iyidos

amaTgan risi yidva SeuZlia anos xil-bostneulis maRaziaSi?

1

1.

2.

saganTa erTobliobebi

ra ewodeba (a) suraTze mocemul erTobliobas?

(b) suraTze mocemul saganTa erTobliobas?

1) ras uwodeben bevri cxvris erTobliobas?

mglebis erTobliobas? irmebis erTobliobas?

cxenebis erTobliobas? mocekvaveTa erTobliobas?

momReralTa erTobliobas?

2) gaixsene, kidev romeli erTobliobebis saxelebi ici?

daasaxele ramdenime sagani mwerebis erTobliobidan;

frinvelebis erTobliobidan; saswavlo nivTebis

erTobliobidan; fexsacmelebis erTobliobidan;

risi erTobliobaa anbani?

a) ra saerTo saxel hqvia sagnebs, romelTac suraTze xedav?

b) gamoiyene sityvebi: win, Semdeg, Soris, marcxniv, marjvniv

da aRwere suraTi;

g) gamoyavi erTobliobis nawilebi raime niSniT.

ras daarqmevdi erTobliobas:

a) ? ! . , ;, , , , ?

b) nino, ana, Tea, gvanca?

3.

4.

5.

6.7.

8.

erTi `zedmetia~

ra SeiZleba uwodo danarCeni sagnebis jgufs?

8 9

a) ras xedavT suraTze?

b) risTvis gamoiyeneba asoebi?

g) ramdeni cifri gamoiyeneba ricxvebis Casawerad?

gadaitane rveulSi da Seavse cxrili nimuSis mixedviT:

a) ramdeni cifriT aris Cawerili TiToeuli ricxvi?

5, 7, 1, 9, 0, 4, 8.

erTi cifriT Caweril ricxvebs erTniSna ricxvebi hqvia.

b) kidev romeli erTniSna ricxvebi ici? dawere.

g) ramdenniSna ricxvi iqneba 16? ratom fiqrobT ase?

d) romelia yvelaze mcire da yvelaze didi erTniSna

ricxvebi?

e) romelia yvelaze mcire orniSna ricxvi?

2 ricxvis wakiTxva da Cawera

1.

2.

3.

i

d

z

k

a

o

e

nv

g

bm

T

l1 7 2

0

9

84635

0 nuli

1 erTi

2

3

4

5 xuTi

6

7

8

9

1) rogor unda miviRoT mocemuli ricxvis wina ricxvi?

momdevno ricxvi?

2) daasaxele

4, 7, 9, 3, 1, 5, 8, 2, 6

ricxvebis wina da momdevno ricxvebi.

+, _

Seavse toloba

4.

5.

6.

5 - = 4

+ = 1

5...1 = 6

7...1 = 6

+ 1 = 5

1 - = 0

9...1 = 8

3...1 = 4

10 - = 9

+ 1 = 8

6...1 = 7

5...1 = 4

0 + = 1

-1 = 2

8...1 = 7

9...1 = 10

cota ram warsulidan

adamianma ricxvebi uxsovari droidan SemoiRo.

maTi Cawera ki didxans ar SeeZlo. igi ricxvebs

aRniSnavda naWdevebiT xeze an qvaze, kvanZebiT Tokze da sxva.

Semdeg uZvelesma xalxebma _ babilonelebma, egviptelebma,

berZnebma, romaelebma, slavebma, arabebma ricxvebis Casawerad

sxvadasxva niSnebi SemoiRes. ai, am niSnebiT Cawerili ricxvebi:

Cveni winaprebi ricxvebis Casawerad qarTuli anbanis asoebs

iyenebdnen: a, b, g, d, e, v, z, T, i. a, b, g, d, e, v, z, T, i.

dRes msoflioSi arabul cifrebs iyeneben, zog SemTxvevaSi

romaulsac, magaliTad, zogierTi saaTis ciferblatze.

romauli cifrebiT daweril swor tolobebSi gigom asanTis TiTo Reri gadaanacvla da aras-wori tolobebi miiRo. daabrune Rerebi Tavis adgilze.

10 11

a) ras xedavT suraTze?

b) risTvis gamoiyeneba asoebi?

g) ramdeni cifri gamoiyeneba ricxvebis Casawerad?

gadaitane rveulSi da Seavse cxrili nimuSis mixedviT:

a) ramdeni cifriT aris Cawerili TiToeuli ricxvi?

5, 7, 1, 9, 0, 4, 8.

erTi cifriT Caweril ricxvebs erTniSna ricxvebi hqvia.

b) kidev romeli erTniSna ricxvebi ici? dawere.

g) ramdenniSna ricxvi iqneba 16? ratom fiqrobT ase?

d) romelia yvelaze mcire da yvelaze didi erTniSna

ricxvebi?

e) romelia yvelaze mcire orniSna ricxvi?

2 ricxvis wakiTxva da Cawera

1.

2.

3.

i

d

z

k

a

o

e

nv

g

bm

T

l1 7 2

0

9

84635

0 nuli

1 erTi

2

3

4

5 xuTi

6

7

8

9

1) rogor unda miviRoT mocemuli ricxvis wina ricxvi?

momdevno ricxvi?

2) daasaxele

4, 7, 9, 3, 1, 5, 8, 2, 6

ricxvebis wina da momdevno ricxvebi.

+, _

Seavse toloba

4.

5.

6.

5 - = 4

+ = 1

5...1 = 6

7...1 = 6

+ 1 = 5

1 - = 0

9...1 = 8

3...1 = 4

10 - = 9

+ 1 = 8

6...1 = 7

5...1 = 4

0 + = 1

-1 = 2

8...1 = 7

9...1 = 10

cota ram warsulidan

adamianma ricxvebi uxsovari droidan SemoiRo.

maTi Cawera ki didxans ar SeeZlo. igi ricxvebs

aRniSnavda naWdevebiT xeze an qvaze, kvanZebiT Tokze da sxva.

Semdeg uZvelesma xalxebma _ babilonelebma, egviptelebma,

berZnebma, romaelebma, slavebma, arabebma ricxvebis Casawerad

sxvadasxva niSnebi SemoiRes. ai, am niSnebiT Cawerili ricxvebi:

Cveni winaprebi ricxvebis Casawerad qarTuli anbanis asoebs

iyenebdnen: a, b, g, d, e, v, z, T, i. a, b, g, d, e, v, z, T, i.

dRes msoflioSi arabul cifrebs iyeneben, zog SemTxvevaSi

romaulsac, magaliTad, zogierTi saaTis ciferblatze.

romauli cifrebiT daweril swor tolobebSi gigom asanTis TiTo Reri gadaanacvla da aras-wori tolobebi miiRo. daabrune Rerebi Tavis adgilze.

10 11

waikiTxe ramdenia (suraTze mocemuli nimuSis mixedviT).

Cawere cifrebi mokled

daasaxele ricxvebi mimdevrobiT 10-dan 20-me da

20-dan 10-mde.

naturalur ricxvTa mwkrivis monakveTSi Cawere

gamotovebuli ricxvebi

1,2,3, ,5, , , ,9,10,11, , , , ,16.

miuwere Sesabamisi ricxvi sxivze wiTlad moniSnul

wertilebs

moniSne ricxviT sxivze 7-is, 10-is, 12-is, 17-is Sesabamisi

wertilebi

3 ricxvebi 10-dan 20-is CaTvliT

1.

2.

3.

4.

5.

1+1+1+1+1+1+1+1+1+1=10 erT. = 1 aT.

1 aT. 3 erT.

cameti

13

=

0

0

1

1

miuwere Sesabamisi ricxvi wertilebs, romlebic

ricxviT sxivze

a) 15-is marjvniv mdebareobs

b) 8-sa da 16-s Soris mdebareobs

dawere cifrebiT mokled:

6.

7.

8.

9.

10.

11.

0

0

1

1

1aT. 5erT.=

1aT. 9erT.=

1aT. 6erT.=

1aT. 1erT.=

18= aT. erT.

10= aT. erT.

2aT.=

1aT. 2erT.=

1aT. 4erT.=

1aT. 7erT.=

20= aT. erT.

16= aT. erT.

1aT.=

1aT. 3erT.=

1aT. 8erT.=

9erT.=

14= aT. erT.

17= aT. erT.

Seavse toloba:

gadawere rveulSi ricxvebi, romlebic

Cawere rveulSi mocemuli ricxvis wina da momdevno ricxvebi:

momdevno ricxvTa sameulSi Cawere gamotovebuli ricxvebi:

9-ze metia 0 9 12 19 3 10 20 16

17-ze naklebia 1 13 20 5 18 16 17 10

8-ze metia da 19-ze naklebia 8 10 6 18 17 20 9 11

,10,

,13,

, , 20

16, ,

, ,10

, 12,

19, ,

, , 15

,18,

, 5,

, 9,

,11,

,19,

,16,

es anos oTaxia. man oTaxSi

3 skami ise unda dadgas, rom

oTxive kedelTan TiTo skami

idges.

moisazre!

12 13

waikiTxe ramdenia (suraTze mocemuli nimuSis mixedviT).

Cawere cifrebi mokled

daasaxele ricxvebi mimdevrobiT 10-dan 20-me da

20-dan 10-mde.

naturalur ricxvTa mwkrivis monakveTSi Cawere

gamotovebuli ricxvebi

1,2,3, ,5, , , ,9,10,11, , , , ,16.

miuwere Sesabamisi ricxvi sxivze wiTlad moniSnul

wertilebs

moniSne ricxviT sxivze 7-is, 10-is, 12-is, 17-is Sesabamisi

wertilebi

3 ricxvebi 10-dan 20-is CaTvliT

1.

2.

3.

4.

5.

1+1+1+1+1+1+1+1+1+1=10 erT. = 1 aT.

1 aT. 3 erT.

cameti

13

=

0

0

1

1

miuwere Sesabamisi ricxvi wertilebs, romlebic

ricxviT sxivze

a) 15-is marjvniv mdebareobs

b) 8-sa da 16-s Soris mdebareobs

dawere cifrebiT mokled:

6.

7.

8.

9.

10.

11.

0

0

1

1

1aT. 5erT.=

1aT. 9erT.=

1aT. 6erT.=

1aT. 1erT.=

18= aT. erT.

10= aT. erT.

2aT.=

1aT. 2erT.=

1aT. 4erT.=

1aT. 7erT.=

20= aT. erT.

16= aT. erT.

1aT.=

1aT. 3erT.=

1aT. 8erT.=

9erT.=

14= aT. erT.

17= aT. erT.

Seavse toloba:

gadawere rveulSi ricxvebi, romlebic

Cawere rveulSi mocemuli ricxvis wina da momdevno ricxvebi:

momdevno ricxvTa sameulSi Cawere gamotovebuli ricxvebi:

9-ze metia 0 9 12 19 3 10 20 16

17-ze naklebia 1 13 20 5 18 16 17 10

8-ze metia da 19-ze naklebia 8 10 6 18 17 20 9 11

,10,

,13,

, , 20

16, ,

, ,10

, 12,

19, ,

, , 15

,18,

, 5,

, 9,

,11,

,19,

,16,

es anos oTaxia. man oTaxSi

3 skami ise unda dadgas, rom

oTxive kedelTan TiTo skami

idges.

moisazre!

12 13

naturalur ricxvTa mwkrivi

1.

2.

3.

4.

5.

6.

1) ras xedav suraTze?

2) ras uwodeben ricxvTa aseT mwkrivs?

3) romeli ricxviT iwyeba naturalur ricxvTa mwkrivi?

4) ramdeniT metia naturalur ricxvTa mwkrivis yoveli

Semdegi ricxvi winaze?

dawere sami ricxvi, romlebsac Tvlis dros vasaxelebT:

a) 15-mde; b) 8-is Semdeg; g) 10-is Semdeg17-mde.

dawere sami ricxvi, romlebic marcxnidan marjvniv

mimarTul rocxviT sxivze mdebareobs

a) 12-is marjvniv; b) 14-is marcxniv; g) 8-sa da 16-s Soris.

romelia naturalur ricxvTa mwkrivi? pasuxi axseni.

dawere mocemuli ricxvis wina da momdevno ricxvebi:

Seavse momdevno ricxvTa sameulebi:

0 1 2 3 4 5 6 7 8 9 10 11 12

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...0

3

8

1

64

9

2

75

1011

12

a) 0, 1, 2, 3, 4, 5, 6, ...

b) 1, 2, 3, 4, 5, 6, 7, ...

g) 2, 3, 4, 5, 6, 7, ...

d) 1, 2, 3, 5, 6, 7, ...

e) 1, 2, 3, 4, 5

v) 1, 2, 3, 5, 4, 6, ...

, 9,

, 15,

, , 6

, , 10

, 10,

, 1,

, , 20

8, ,

, 19,

, 18,

, , 2

18, ,

erTi zedmetia!

ricxvebis Sedareba

1.

2.

3.

4.

5.

0 1 2 3 4 5 6 7 8 9 10

6<8 8>6

6<8 8>6

16<18 18>16

6<8 8>6

6<8 8>6

0 1 2 3 4 5 6 7 8 9 10 ...

romelia naklebi 5 Tu 9? rogor Seadareb am ricxvebs?

anom Tvla daiwyo da daaskvna, rom 5 naklebia 9-ze.

rogor imsjela man?

vanom ricxvTa naturaluri mwkrivi moimarjva da igive

Sedegi miiRo. rogor?

gaixsene ori ricxvis Sedarebis sxva xerxi da axseni ratomaa

5 naklebi 9-ze.

1) daxede zemoT mocemul suraTs da axseni, rogor miiRe

TiToeuli utoloba;

2) 8 ramdeniT metia 6-ze? 6 ramdeniT naklebia 8-ze?

3) kvadratebisa da wreebis dawyvilebis romeli xerxi ufro

TvalsaCinoa?

Seadare ricxvebi da pasuxi axseni.

7 da 4; 9 da 3; 18 da 15; 16 da 10; 17 da 7.

gadaiwere rveulSi da daalage ricxvebi zrdis mixedviT:

5, 1, 14, 7, 11, 18, 15, 5, 13, 4, 10.

gadaiwere rveulSi da daalage ricxvebi klebis mixedviT:

8, 6, 13, 12, 19, 7, 3, 10, 5, 15, 2.

moisazre, romeli Taiguli visiaanos da vanos TaigulebSi oTx-oTxi titaa,

anos da gigos TaigulebSi ki _ sam-sami vardi. anos da gigos TaigulebSi ki _ sam-sami vardi.

14 15

naturalur ricxvTa mwkrivi

1.

2.

3.

4.

5.

6.

1) ras xedav suraTze?

2) ras uwodeben ricxvTa aseT mwkrivs?

3) romeli ricxviT iwyeba naturalur ricxvTa mwkrivi?

4) ramdeniT metia naturalur ricxvTa mwkrivis yoveli

Semdegi ricxvi winaze?

dawere sami ricxvi, romlebsac Tvlis dros vasaxelebT:

a) 15-mde; b) 8-is Semdeg; g) 10-is Semdeg17-mde.

dawere sami ricxvi, romlebic marcxnidan marjvniv

mimarTul rocxviT sxivze mdebareobs

a) 12-is marjvniv; b) 14-is marcxniv; g) 8-sa da 16-s Soris.

romelia naturalur ricxvTa mwkrivi? pasuxi axseni.

dawere mocemuli ricxvis wina da momdevno ricxvebi:

Seavse momdevno ricxvTa sameulebi:

0 1 2 3 4 5 6 7 8 9 10 11 12

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...0

3

8

1

64

9

2

75

1011

12

a) 0, 1, 2, 3, 4, 5, 6, ...

b) 1, 2, 3, 4, 5, 6, 7, ...

g) 2, 3, 4, 5, 6, 7, ...

d) 1, 2, 3, 5, 6, 7, ...

e) 1, 2, 3, 4, 5

v) 1, 2, 3, 5, 4, 6, ...

, 9,

, 15,

, , 6

, , 10

, 10,

, 1,

, , 20

8, ,

, 19,

, 18,

, , 2

18, ,

erTi zedmetia!

ricxvebis Sedareba

1.

2.

3.

4.

5.

0 1 2 3 4 5 6 7 8 9 10

6<8 8>6

6<8 8>6

16<18 18>16

6<8 8>6

6<8 8>6

0 1 2 3 4 5 6 7 8 9 10 ...

romelia naklebi 5 Tu 9? rogor Seadareb am ricxvebs?

anom Tvla daiwyo da daaskvna, rom 5 naklebia 9-ze.

rogor imsjela man?

vanom ricxvTa naturaluri mwkrivi moimarjva da igive

Sedegi miiRo. rogor?

gaixsene ori ricxvis Sedarebis sxva xerxi da axseni ratomaa

5 naklebi 9-ze.

1) daxede zemoT mocemul suraTs da axseni, rogor miiRe

TiToeuli utoloba;

2) 8 ramdeniT metia 6-ze? 6 ramdeniT naklebia 8-ze?

3) kvadratebisa da wreebis dawyvilebis romeli xerxi ufro

TvalsaCinoa?

Seadare ricxvebi da pasuxi axseni.

7 da 4; 9 da 3; 18 da 15; 16 da 10; 17 da 7.

gadaiwere rveulSi da daalage ricxvebi zrdis mixedviT:

5, 1, 14, 7, 11, 18, 15, 5, 13, 4, 10.

gadaiwere rveulSi da daalage ricxvebi klebis mixedviT:

8, 6, 13, 12, 19, 7, 3, 10, 5, 15, 2.

moisazre, romeli Taiguli visiaanos da vanos TaigulebSi oTx-oTxi titaa,

anos da gigos TaigulebSi ki _ sam-sami vardi. anos da gigos TaigulebSi ki _ sam-sami vardi.

14 15

erTi zedmetia!

1) gamoiyene sityva `jami~ da waikiTxe Canaweri

3 + 6 7 + 2 5 + 4 8 + 0 1 + 5

2) daasaxele Sesakrebebi;

3) Sekribe ricxvebi zepirad da daasaxele jamis mniSvneloba.

1) dawere jami

1) gadaiwere rveulSi da romeli jamis mniSvnelobac gaxsovs, miuwere;

2) danarCeni gamoiangariSe da Seecade daimaxsovro:

ori ricxvis jami

Sesakrebi

jamis

mniSvnelobajami

+ =

Sesakrebi

1.

2.

3.

4.

5-isa da 3-is

2-isa da 8-is

3-isa da 1-is

6-isa da 6-is

0-isa da 7-is

4-isa da 0-is

4+4 4+3 0+4 1+4 5+3

pirveli

Sesakrebi5 2 3 4 1 9

meore

Sesakrebi4 7 6 4 8 0

jami

jamis

mniSvneloba

2) ipove maTi mniSvnelobebi.

gadaitane rveulSi da Seavse cxrili:

3+0=

6+4=

5+5=

8+2=

5+3=

7+2=

6+2=

7+3=

3+2=

6+3=

4+3=

4+2=

1) gamoiyene sityva `sxvaoba~ da waikiTxe Canaweri:

9_4 10_3 7_2 8_0 6_1

2) daasaxele saklebi da maklebi;

3) gamoakeli zepirad da daasaxele sxvaobis mniSvneloba.

1) dawere sxvaoba

8-isa da 3-is

7-isa da 4-is

9-isa da 9-is

6-isa da 2-is

8-isa da 5-is

9-isa da 4-is

2) danarCeni gamoiangariSe da Seecade daimaxsovro:

ori ricxvis sxvaoba

saklebi

sxvaobis

mniSvnelobasxvaoba

_ =

maklebi

1.

2.

3.

4.

erTi zedmetia!

6_3 3_0 5_2 2+1 7_2

saklebi 8 4 9 5 8 7

maklebi 4 0 5 2 6 7

sxvaoba

sxvaobis

mniSvneloba

3+3=

6+4=

5+0=

7+1=

2+2=

5+2=

3+4=

7+0=

4+5=

2+6=

4+6=

3+5=

2) ipove maTi mniSvnelobebi.

gadaitane rveulSi da Seavse cxrili:

1) gadaiwere rveulSi da romeli jamis mniSvnelobac gaxsovs, miuwere;

16 17

erTi zedmetia!

1) gamoiyene sityva `jami~ da waikiTxe Canaweri

3 + 6 7 + 2 5 + 4 8 + 0 1 + 5

2) daasaxele Sesakrebebi;

3) Sekribe ricxvebi zepirad da daasaxele jamis mniSvneloba.

1) dawere jami

1) gadaiwere rveulSi da romeli jamis mniSvnelobac gaxsovs, miuwere;

2) danarCeni gamoiangariSe da Seecade daimaxsovro:

ori ricxvis jami

Sesakrebi

jamis

mniSvnelobajami

+ =

Sesakrebi

1.

2.

3.

4.

5-isa da 3-is

2-isa da 8-is

3-isa da 1-is

6-isa da 6-is

0-isa da 7-is

4-isa da 0-is

4+4 4+3 0+4 1+4 5+3

pirveli

Sesakrebi5 2 3 4 1 9

meore

Sesakrebi4 7 6 4 8 0

jami

jamis

mniSvneloba

2) ipove maTi mniSvnelobebi.

gadaitane rveulSi da Seavse cxrili:

3+0=

6+4=

5+5=

8+2=

5+3=

7+2=

6+2=

7+3=

3+2=

6+3=

4+3=

4+2=

1) gamoiyene sityva `sxvaoba~ da waikiTxe Canaweri:

9_4 10_3 7_2 8_0 6_1

2) daasaxele saklebi da maklebi;

3) gamoakeli zepirad da daasaxele sxvaobis mniSvneloba.

1) dawere sxvaoba

8-isa da 3-is

7-isa da 4-is

9-isa da 9-is

6-isa da 2-is

8-isa da 5-is

9-isa da 4-is

2) danarCeni gamoiangariSe da Seecade daimaxsovro:

ori ricxvis sxvaoba

saklebi

sxvaobis

mniSvnelobasxvaoba

_ =

maklebi

1.

2.

3.

4.

erTi zedmetia!

6_3 3_0 5_2 2+1 7_2

saklebi 8 4 9 5 8 7

maklebi 4 0 5 2 6 7

sxvaoba

sxvaobis

mniSvneloba

3+3=

6+4=

5+0=

7+1=

2+2=

5+2=

3+4=

7+0=

4+5=

2+6=

4+6=

3+5=

2) ipove maTi mniSvnelobebi.

gadaitane rveulSi da Seavse cxrili:

1) gadaiwere rveulSi da romeli jamis mniSvnelobac gaxsovs, miuwere;

16 17

ricxvis gazrda an Semcireba ramdenime erTeuliT

+ = =

5 + 3 = 8

5 gaizarda 3-iT

6 _ 2 = 4

6 Semcirda 2-iT

kargad gaiazre suraTze mocemuli tolobebi da upasuxe

kiTxvebs:

a) rogor Seicvleba ricxvi ramdenime erTeulis mimatebiT?

b) rogor Seicvleba ricxvi ramdenime erTeulis gamokle-

biT?

g) rogor gavzardoT ricxvi 3-iT? 5-iT? 2-iT? 1-iT?

d) rogor SevamciroT ricxvi 2-iT? 4-iT? 1-iT? 8-iT?

e) SeiZleba Tu ara, raime ricxvis mimatebiT mocemuli

ricxvi ar Seicvalos? moiyvane magaliTi.

v) SeiZleba Tu ara raime ricxvis gamoklebiT mocemuli

ricxvi ar Seicvalos? moiyvane magaliTi.

1.

2.

3.

4.

a) mivumatebT 7-s?

b) gamovaklebT 9-s?

g) mivumatebT 0-s?

d) gamovaklebT 0-s?

e) mivumatebT 8-s?

v) gamovaklebT 6-s?

gadaitane rveulSi da Seavse cxrili:

rogor Seicvleba ricxvi, Tu mas

>, <, = Sedarebis niSani Cawere gamouangareSeblad

msjelobiT da Semdeg Seamowme gamoangariSebiT.

ricxvi 3 5 0 6

4-iT meti

ricxvi

ricxvi 9 6 3 8

3-iT naklebi

ricxvi

7 ... 7 + 2

3 + 4 ... 2

6 + 0 ... 6 _ 0

9 + 1 ... 9 _ 1

9 ... 9 _ 3

8 _ 5 ... 8

3 _ 0 ... 3

7 _ 1 ... 7 + 1

4 ... 4 + 0

6 _ 6 ... 6

5 + 2 ... 2

8 _ 1 ... 8 + 1

rogor Seicvleba jamis mniSvneloba, Tu

a) erT Sesakrebs gavzrdiT 5-iT, meores ucvlelad

davtovebT?

b) TiToeul Sesakrebs gavzrdiT 1-iT?

g) erT Sesakrebs SevamcirebT 6-iT, meores ucvlelad

davtovebT?

d) erT Sesakrebs gavzrdiT 2-iT, meores gavzrdiT 3-iT?

amoxseni amocana:

a) ano 6 wlisaa, Zma masze 4 wliT ufrosia. ramdeni wlis

yofila anos Zma?

b) vano 7 wlisaa, misi da 5 wliT umcrosia. ramdeni wlis

yofila vanos da?

moifiqre, ra moqmedeba unda Seasrulo da Seavse cxrili:

rogor Seicvleba sxvaobis mniSvneloba, Tu

a) saklebs gavzrdiT 2-iT, maklebs ucvlelad davtovebT?

b) maklebs gavzrdiT 2-iT, sxvaobas ucvlelad davtovebT?

g) saklebs SevamcirebT 3-iT, maklebs ucvlelad davtovebT?

d) maklebs SevamcirebT 3-iT, saklebs ucvlelad davtovebT?

? 4 0 1 5 3

4

3 4

5 8

? 2 6 0 7 5

9

7 0

8 2

5.

6.

7.

8.

9.a) 5 gazarde 4-iT

7 Seamcire 6-iT

b) 6 Seamcire 0-iT

3 Seamcire 3-iT

g) 9 Seamcire 0-iT

0 gazarde 0-iT

dawere gamosaxulebis saxiT da ipove misi mniSvneloba:

a) saklebi gazardes 5-iT. rogor

unda Secvalo maklebi, rom sxvaobis

mniSvneloba ucvleli darCes?

b) erTi Sesakrebi Seamcires 5-iT. ro-

gor unda Secvalo meore Sesakrebi, rom

jamis mniSvneloba ucvleli darCes?

rogor

moisazre!

18 19

ricxvis gazrda an Semcireba ramdenime erTeuliT

+ = =

5 + 3 = 8

5 gaizarda 3-iT

6 _ 2 = 4

6 Semcirda 2-iT

kargad gaiazre suraTze mocemuli tolobebi da upasuxe

kiTxvebs:

a) rogor Seicvleba ricxvi ramdenime erTeulis mimatebiT?

b) rogor Seicvleba ricxvi ramdenime erTeulis gamokle-

biT?

g) rogor gavzardoT ricxvi 3-iT? 5-iT? 2-iT? 1-iT?

d) rogor SevamciroT ricxvi 2-iT? 4-iT? 1-iT? 8-iT?

e) SeiZleba Tu ara, raime ricxvis mimatebiT mocemuli

ricxvi ar Seicvalos? moiyvane magaliTi.

v) SeiZleba Tu ara raime ricxvis gamoklebiT mocemuli

ricxvi ar Seicvalos? moiyvane magaliTi.

1.

2.

3.

4.

a) mivumatebT 7-s?

b) gamovaklebT 9-s?

g) mivumatebT 0-s?

d) gamovaklebT 0-s?

e) mivumatebT 8-s?

v) gamovaklebT 6-s?

gadaitane rveulSi da Seavse cxrili:

rogor Seicvleba ricxvi, Tu mas

>, <, = Sedarebis niSani Cawere gamouangareSeblad

msjelobiT da Semdeg Seamowme gamoangariSebiT.

ricxvi 3 5 0 6

4-iT meti

ricxvi

ricxvi 9 6 3 8

3-iT naklebi

ricxvi

7 ... 7 + 2

3 + 4 ... 2

6 + 0 ... 6 _ 0

9 + 1 ... 9 _ 1

9 ... 9 _ 3

8 _ 5 ... 8

3 _ 0 ... 3

7 _ 1 ... 7 + 1

4 ... 4 + 0

6 _ 6 ... 6

5 + 2 ... 2

8 _ 1 ... 8 + 1

rogor Seicvleba jamis mniSvneloba, Tu

a) erT Sesakrebs gavzrdiT 5-iT, meores ucvlelad

davtovebT?

b) TiToeul Sesakrebs gavzrdiT 1-iT?

g) erT Sesakrebs SevamcirebT 6-iT, meores ucvlelad

davtovebT?

d) erT Sesakrebs gavzrdiT 2-iT, meores gavzrdiT 3-iT?

amoxseni amocana:

a) ano 6 wlisaa, Zma masze 4 wliT ufrosia. ramdeni wlis

yofila anos Zma?

b) vano 7 wlisaa, misi da 5 wliT umcrosia. ramdeni wlis

yofila vanos da?

moifiqre, ra moqmedeba unda Seasrulo da Seavse cxrili:

rogor Seicvleba sxvaobis mniSvneloba, Tu

a) saklebs gavzrdiT 2-iT, maklebs ucvlelad davtovebT?

b) maklebs gavzrdiT 2-iT, sxvaobas ucvlelad davtovebT?

g) saklebs SevamcirebT 3-iT, maklebs ucvlelad davtovebT?

d) maklebs SevamcirebT 3-iT, saklebs ucvlelad davtovebT?

? 4 0 1 5 3

4

3 4

5 8

? 2 6 0 7 5

9

7 0

8 2

5.

6.

7.

8.

9.a) 5 gazarde 4-iT

7 Seamcire 6-iT

b) 6 Seamcire 0-iT

3 Seamcire 3-iT

g) 9 Seamcire 0-iT

0 gazarde 0-iT

dawere gamosaxulebis saxiT da ipove misi mniSvneloba:

a) saklebi gazardes 5-iT. rogor

unda Secvalo maklebi, rom sxvaobis

mniSvneloba ucvleli darCes?

b) erTi Sesakrebi Seamcires 5-iT. ro-

gor unda Secvalo meore Sesakrebi, rom

jamis mniSvneloba ucvleli darCes?

rogor

moisazre!

18 19

ramdeniT metia?ramdeniT naklebia?

kargad gaiazre suraTze mocemuli Canawerebi da

daimaxsovre!

rom gavigoT erTi ricxvi ramdeniT metia an naklebi

meoreze, met ricxvs unda gamovakloT naklebi ricxvi.

ramdeniTac metia erTi ricxvi meoreze, imdeniTve nak-

lebia meore ricxvi pirvelze.

gamoTvale

5 metia 3-ze 2-iT

3 naklebia 5-ze 2-iT

5 metia 2-ze 3-iT

2 naklebia 5-ze 3-iT

5 _ 3 = 2

5 _ 2 = 3

3

5

2

1.

2.

3.

4.

10 ramdeniT metia 8-ze;

6 ramdeniT naklebia 9-ze;

7 ramdeniT metia 3-ze;

2 ramdeniT naklebia 5-ze;

6-ze metia 4-iT;

5-ze metia 3-iT;

7-ze metia 2-iT;

4-ze metia 5-iT.

8 ramdeniT metia 2-ze;

3 ramdeniT naklebia 8-ze;

9 ramdeniT metia 3-ze;

3 ramdeniT naklebia 9-ze.

1) rogor vipovoT 6-ze 3-iT meti ricxvi?

2) ipove ricxvi, romelic

gadaitane rveulSi da Seavse cxrili:

saklebi 9 6

maklebi 5 5

sxvaoba 8_4 9_6

sxvaobismniSvneloba

2 1

1) rogor vipovoT 6-ze 3-iT naklebi ricxvi?

2) ipove ricxvi, romelic

yovel tolobaSi Semoxazuli ricxvi mTelia, xazgasmuli ki

misi nawili. Cawere moqmedebis niSani da gamotovebuli ricxvi.

gadaitane rveulSi da Seavse cxrili:

daxaze rveulSi 9 sm sigrZis monakveTi da masze 3 sm-iT

mokle meore monakveTi. ra sigrZis iqneba meore monakveTi?

amoxseni amocana:

a) ezoSi 5 fiWvis da 3-iT meti naZvis xea. ramdeni naZvis xe

yofila ezoSi?

b) ano 6 wlisaa, misi da ki 10-is. ramdeni wliT umcrosi

yofila ano daze?

g) vanom 10 qarTuli da 7 ucxouri marka iyida. ramdeniT

meti qarTuli marka uyidia vanos?

9-ze naklebia 4-iT;

8-ze naklebia 3-iT;

10-ze naklebia 7-iT;

6-ze naklebia 6-iT.

Sesakrebi 5 3

Sesakrebi 4 3

jami 6+4 3+5

jamismniSvneloba

7 9

5.

6.

7.

9.

8.

7 ... 3 =

7 ... 3 =

5 ... 2 =

5 ... 2 =

6 ... 3 =

6 ... 3 =

8 ... 5 =

3 ... 4 =

7 ... 3 =

6 ... 4 =

4 ... 3 =

8 ... 4 =

kalaTSi 3 wiTeli da 5 mwvane vaS-

li Zevs. ramdeni vaSli unda amoiRo Sig

Cauxedavad, rom maT Soris aucileblad

iyos: a) erTi mwvane vaSli mainc. b) erTi

wiTeli vaSli mainc.

moisazre!

20 21

ramdeniT metia?ramdeniT naklebia?

kargad gaiazre suraTze mocemuli Canawerebi da

daimaxsovre!

rom gavigoT erTi ricxvi ramdeniT metia an naklebi

meoreze, met ricxvs unda gamovakloT naklebi ricxvi.

ramdeniTac metia erTi ricxvi meoreze, imdeniTve nak-

lebia meore ricxvi pirvelze.

gamoTvale

5 metia 3-ze 2-iT

3 naklebia 5-ze 2-iT

5 metia 2-ze 3-iT

2 naklebia 5-ze 3-iT

5 _ 3 = 2

5 _ 2 = 3

3

5

2

1.

2.

3.

4.

10 ramdeniT metia 8-ze;

6 ramdeniT naklebia 9-ze;

7 ramdeniT metia 3-ze;

2 ramdeniT naklebia 5-ze;

6-ze metia 4-iT;

5-ze metia 3-iT;

7-ze metia 2-iT;

4-ze metia 5-iT.

8 ramdeniT metia 2-ze;

3 ramdeniT naklebia 8-ze;

9 ramdeniT metia 3-ze;

3 ramdeniT naklebia 9-ze.

1) rogor vipovoT 6-ze 3-iT meti ricxvi?

2) ipove ricxvi, romelic

gadaitane rveulSi da Seavse cxrili:

saklebi 9 6

maklebi 5 5

sxvaoba 8_4 9_6

sxvaobismniSvneloba

2 1

1) rogor vipovoT 6-ze 3-iT naklebi ricxvi?

2) ipove ricxvi, romelic

yovel tolobaSi Semoxazuli ricxvi mTelia, xazgasmuli ki

misi nawili. Cawere moqmedebis niSani da gamotovebuli ricxvi.

gadaitane rveulSi da Seavse cxrili:

daxaze rveulSi 9 sm sigrZis monakveTi da masze 3 sm-iT

mokle meore monakveTi. ra sigrZis iqneba meore monakveTi?

amoxseni amocana:

a) ezoSi 5 fiWvis da 3-iT meti naZvis xea. ramdeni naZvis xe

yofila ezoSi?

b) ano 6 wlisaa, misi da ki 10-is. ramdeni wliT umcrosi

yofila ano daze?

g) vanom 10 qarTuli da 7 ucxouri marka iyida. ramdeniT

meti qarTuli marka uyidia vanos?

9-ze naklebia 4-iT;

8-ze naklebia 3-iT;

10-ze naklebia 7-iT;

6-ze naklebia 6-iT.

Sesakrebi 5 3

Sesakrebi 4 3

jami 6+4 3+5

jamismniSvneloba

7 9

5.

6.

7.

9.

8.

7 ... 3 =

7 ... 3 =

5 ... 2 =

5 ... 2 =

6 ... 3 =

6 ... 3 =

8 ... 5 =

3 ... 4 =

7 ... 3 =

6 ... 4 =

4 ... 3 =

8 ... 4 =

kalaTSi 3 wiTeli da 5 mwvane vaS-

li Zevs. ramdeni vaSli unda amoiRo Sig

Cauxedavad, rom maT Soris aucileblad

iyos: a) erTi mwvane vaSli mainc. b) erTi

wiTeli vaSli mainc.

moisazre!

20 21

10Sekreba-gamokleba

10-is farglebSiipove Secdomebi da gaaswore nimuSis mixedviT:

Seavse cxrili:

Seavse toloba:

amoxseni amocana:

a) anom 6 calxaziani da 4 ujredebiani rveuli iyida.

sul ramdeni rveuli uyidia anos?

b) vanos 10 rveuli hqonda, 3 gigos aCuqa. ramdeni rveuli

darCa vanos?

+, _

1.

3.

4.

5.

2.

2+2 4

2+2 5 4

7_2 5

6+3 8

4

7

5

6

4

3

6

5

7

8

3

4

9_4 4

5+3 8

8+0 8

6_4 4

8_5 4

3+6 8

7_3 4

4+5 8

8 . . . 3 = 5

6 . . . 2 = 8

7 . . . 4 = 3

6 . . . 4 = 10

10 _ = 7

7 + = 10

9 _ = 2

6 + = 9

_2 _3_4+3 +2+4

5 . . . 3 = 6 + 2

9 . . . 3 = 6 - 2

8 . . . 2 = 5 + 5

8 . . . 5 = 7 - 4

+ 5 = 4

8 _ = 5

+ 4 = 8

6 _ = 3

6 . . . 2 = 8 . . . 4

7 . . . 2 = 6 . . . 3

5 . . . 1 = 7 . . . 1

8 . . . 0 = 9 . . . 1

4 + = 8

_ 3 = 2

3 + = 3

_ 6 = 0

gamouangariSeblad daawyvile gamosaxulebebi, romelTa

mniSvnelobebi tolia (pasuxi axseni).

Cawere gamosaxulebis saxiT da gamoiangariSe ra eRireba:

feradi fanqrebi da rveuli; rveuli, saRebavebi da funji;

feradi fanqrebi, saRebavebi da funji; funji da ori rveuli.

gaeci pasuxebi 1 wuTSi zepirad:

ricxvebis Sekreba-gamoklebas aTis farglebSi swrafad unda

asrulebde. es SemdegSi Zalian gamogadgeba.

+, _

7.

8.

9.

6.5 . . . 2 < 6

4 . . . 2 < 3

7 . . . 3 < 5

5 + 3

6 + 0

7_3 =

7+3 =

8_5 =

4+4 =

3_1 =

6_6 =

7 + 2

7 - 0

5+2 =

4+3 =

8_4 =

3+6 =

10_1 =

9_7 =

3 + 5

2 + 3

4_2 =

10_7 =

3+5 =

4+5 =

6_4 =

9_5 =

2 + 7

6 - 0

8_8 =

5_3 =

2+7 =

6+4 =

7_5 =

6+2 =

3 + 2

7 + 0

8 . . . 5 < 7

8 . . . 2 < 6

2 . . . 4 < 5

9 . . . 4 < 6

6 . . . 3 < 7

6 . . . 2 < 4

asanTis erTi Reris gadaadgilebiT

gaaswore toloba

gaeci pasuxebi 1 wuTSi zepirad:

feradifanqrebi

saxatavi rveuli

4 l. 5 l. 2 l.

1 l.

22 23

10Sekreba-gamokleba

10-is farglebSiipove Secdomebi da gaaswore nimuSis mixedviT:

Seavse cxrili:

Seavse toloba:

amoxseni amocana:

a) anom 6 calxaziani da 4 ujredebiani rveuli iyida.

sul ramdeni rveuli uyidia anos?

b) vanos 10 rveuli hqonda, 3 gigos aCuqa. ramdeni rveuli

darCa vanos?

+, _

1.

3.

4.

5.

2.

2+2 4

2+2 5 4

7_2 5

6+3 8

4

7

5

6

4

3

6

5

7

8

3

4

9_4 4

5+3 8

8+0 8

6_4 4

8_5 4

3+6 8

7_3 4

4+5 8

8 . . . 3 = 5

6 . . . 2 = 8

7 . . . 4 = 3

6 . . . 4 = 10

10 _ = 7

7 + = 10

9 _ = 2

6 + = 9

_2 _3_4+3 +2+4

5 . . . 3 = 6 + 2

9 . . . 3 = 6 - 2

8 . . . 2 = 5 + 5

8 . . . 5 = 7 - 4

+ 5 = 4

8 _ = 5

+ 4 = 8

6 _ = 3

6 . . . 2 = 8 . . . 4

7 . . . 2 = 6 . . . 3

5 . . . 1 = 7 . . . 1

8 . . . 0 = 9 . . . 1

4 + = 8

_ 3 = 2

3 + = 3

_ 6 = 0

gamouangariSeblad daawyvile gamosaxulebebi, romelTa

mniSvnelobebi tolia (pasuxi axseni).

Cawere gamosaxulebis saxiT da gamoiangariSe ra eRireba:

feradi fanqrebi da rveuli; rveuli, saRebavebi da funji;

feradi fanqrebi, saRebavebi da funji; funji da ori rveuli.

gaeci pasuxebi 1 wuTSi zepirad:

ricxvebis Sekreba-gamoklebas aTis farglebSi swrafad unda

asrulebde. es SemdegSi Zalian gamogadgeba.

+, _

7.

8.

9.

6.5 . . . 2 < 6

4 . . . 2 < 3

7 . . . 3 < 5

5 + 3

6 + 0

7_3 =

7+3 =

8_5 =

4+4 =

3_1 =

6_6 =

7 + 2

7 - 0

5+2 =

4+3 =

8_4 =

3+6 =

10_1 =

9_7 =

3 + 5

2 + 3

4_2 =

10_7 =

3+5 =

4+5 =

6_4 =

9_5 =

2 + 7

6 - 0

8_8 =

5_3 =

2+7 =

6+4 =

7_5 =

6+2 =

3 + 2

7 + 0

8 . . . 5 < 7

8 . . . 2 < 6

2 . . . 4 < 5

9 . . . 4 < 6

6 . . . 3 < 7

6 . . . 2 < 4

asanTis erTi Reris gadaadgilebiT

gaaswore toloba

gaeci pasuxebi 1 wuTSi zepirad:

feradifanqrebi

saxatavi rveuli

4 l. 5 l. 2 l.

1 l.

22 23

savarjiSoebi

Seadgine oTxi swori toloba romeli sami ricxviTac

SesaZlebelia.

gamosaxe santimetrebiT:

gadaixate rveulSi, Siga are gaaferade wiTlad, gare areSi

daxate sami wre.

gadaiwere rveulSi da Seavse toloba:

dawere ricxvi, romelic

a) 1 aTeulisa da 5 erTeulisgan Sedgeba;

b) 18-ze 1-iT metia;

g) 14-ze 1-iT naklebia;

d) 16-is wina ricxvze 5-iT naklebia;

e) udides erTniSna ricxvze 7-iT metia;

v) umciresi orniSna ricxvis momdevnoa;

z) umciresi orniSna da udidesi erTniSna ricxvebis

sxvaobis mniSvnelobis tolia.

1.

2.

2.

3.

5.

4.

2, 3, 6 2, 9, 7 4, 5, 10

1dm 7sm = sm

1dm 9sm = sm

14sm = dm sm

12sm = dm sm

1dm 1sm = sm

1dm 6sm = sm

15sm = dm sm

18sm = dm sm

1dm = sm

2dm = sm

13sm = dm sm

19sm = dm sm

+, _

9 ... 1 ... 3 = 7

6 ... 2 ... 3 = 5

6 ... 2 ... 3 = 1

6 ... 2 ... 3 = 7

4 ... 3 ... 1 = 6

4 ... 3 ... 1 = 2

4 ... 3 ... 1 = 0

4 ... 3 ... 1 = 8

10 ... 4 = 6

5 ... 3 = 8

8 ... 4 = 4

6 ... 4 = 10

gadawere rveulSi, ipove Secdomebi da gaaswore:

dasvi iseTi kiTxva, rom miRebuli amocana amoixsnas

SekrebiT.

a) Svidi wlis ano Zmaze 3 wliT umcrosia.

b) anom xis qveS 5 kakali ipova, vanom _ 3-iT meti.

g) vanos 4 feradi fanqari aqvs, gigosac amdenive.

d) vanom 3 rveuli iyida, gigom _ 4. anom ki imdeni,

ramdenic vanom da gigom erTad.

7.

8.

9.

10.

2+2 4

2+2 5 4

10_7+6 9

9_8+7 6

4+6_7 3

10_4+2 8

4+5_8 2

9_6+4 7

7+1_4 3

9_6+0 7

2+8_5 5

6+0_0 8

dominos qvebiT Sedgenil kvadratSi

gadaalage qvebi ise, rom kvadratis yve-

la gverdze

wertilebis erTi

da igive raodenoba

miiRo.

daxate 2 figura, romlebic erTmaneTisgan gansxvavdeba

formiT, zomiTa da feriT.

dasvi iseTi kiTxva, rom miRebuli amocana amoixsnas

gamoklebiT.

a) vanos 10 rveuli hqonda, 3 rveuli man gigos aCuqa.

b) gigos 7 axali marka aqvs, vanos _ 5.

g) anom 5 amocana amoxsna, gigom _ 2-iT naklebi.

24 25

savarjiSoebi

Seadgine oTxi swori toloba romeli sami ricxviTac

SesaZlebelia.

gamosaxe santimetrebiT:

gadaixate rveulSi, Siga are gaaferade wiTlad, gare areSi

daxate sami wre.

gadaiwere rveulSi da Seavse toloba:

dawere ricxvi, romelic

a) 1 aTeulisa da 5 erTeulisgan Sedgeba;

b) 18-ze 1-iT metia;

g) 14-ze 1-iT naklebia;

d) 16-is wina ricxvze 5-iT naklebia;

e) udides erTniSna ricxvze 7-iT metia;

v) umciresi orniSna ricxvis momdevnoa;

z) umciresi orniSna da udidesi erTniSna ricxvebis

sxvaobis mniSvnelobis tolia.

1.

2.

2.

3.

5.

4.

2, 3, 6 2, 9, 7 4, 5, 10

1dm 7sm = sm

1dm 9sm = sm

14sm = dm sm

12sm = dm sm

1dm 1sm = sm

1dm 6sm = sm

15sm = dm sm

18sm = dm sm

1dm = sm

2dm = sm

13sm = dm sm

19sm = dm sm

+, _

9 ... 1 ... 3 = 7

6 ... 2 ... 3 = 5

6 ... 2 ... 3 = 1

6 ... 2 ... 3 = 7

4 ... 3 ... 1 = 6

4 ... 3 ... 1 = 2

4 ... 3 ... 1 = 0

4 ... 3 ... 1 = 8

10 ... 4 = 6

5 ... 3 = 8

8 ... 4 = 4

6 ... 4 = 10

gadawere rveulSi, ipove Secdomebi da gaaswore:

dasvi iseTi kiTxva, rom miRebuli amocana amoixsnas

SekrebiT.

a) Svidi wlis ano Zmaze 3 wliT umcrosia.

b) anom xis qveS 5 kakali ipova, vanom _ 3-iT meti.

g) vanos 4 feradi fanqari aqvs, gigosac amdenive.

d) vanom 3 rveuli iyida, gigom _ 4. anom ki imdeni,

ramdenic vanom da gigom erTad.

7.

8.

9.

10.

2+2 4

2+2 5 4

10_7+6 9

9_8+7 6

4+6_7 3

10_4+2 8

4+5_8 2

9_6+4 7

7+1_4 3

9_6+0 7

2+8_5 5

6+0_0 8

dominos qvebiT Sedgenil kvadratSi

gadaalage qvebi ise, rom kvadratis yve-

la gverdze

wertilebis erTi

da igive raodenoba

miiRo.

daxate 2 figura, romlebic erTmaneTisgan gansxvavdeba

formiT, zomiTa da feriT.

dasvi iseTi kiTxva, rom miRebuli amocana amoixsnas

gamoklebiT.

a) vanos 10 rveuli hqonda, 3 rveuli man gigos aCuqa.

b) gigos 7 axali marka aqvs, vanos _ 5.

g) anom 5 amocana amoxsna, gigom _ 2-iT naklebi.

24 25