matematika - sulakauri.edu.geƒ›ათემატიკა-1... · an 1) sagakvetilo saats...

maswavleblis wigni

maTematika1

grifminiWebulia saqarTvelos ganaTlebis, mecnierebis,

kulturisa da sportis saministros mier 2018 wels.

guram beriSvili

iaTamze kotetiSvili

bakur sulakauri

maTematika 1maswavleblis wigni pirvelklaselTaTvisTbilisi, 2018

avtorebi: guram beriSvili, iaTamze kotetiSvili, bakur sulakauri

redaqtori: Tamar gavaSeliSvilidizaineri: ia maxaTaZe teqnikuri dizaineri: nino kublaSvili

© sulakauris gamomcemloba, 2018

Sps `sulakauris gamomcemloba~aRmaSeneblis 150, Tbilisi 0112tel.: 910954, 911165elfosta: [email protected]

ISBN 978-9941-30-025-7

Mathematics 1

Teacher's Book

© Sulakauri Publishing, 2018

all rights reserved.

Tbilisi, Georgia

www.sulakauri.ge

sarCevi

maTematika 1-is komponentebi da maTi mokle mimoxilva . . . . . . . . . . . . . . . . 4

axali erovnuli saswavlo gegmiT gansazRvruli maTematikis programa . . . . . . . 8

pirvel klasSi wlis bolos misaRwevi Sedegebi da maTi indikatorebi . . . . . . . . . 8

standartis Sedegis miRwevisa da saxelmZRvanelos Sinaarsis urTierTkavSiris matrica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

ra unda icodes dawyebiTi klasebis maswavlebelma ricxvebis Sesaxeb . . . . . . . . . 13

TvalsaCinoebebis roli maTematikis swavlebisas . . . . . . . . . . . . . . . . . . . 19

maTematikuri TamaSebi da aqtivobebi . . . . . . . . . . . . . . . . . . . . . . . . . 23

zepiri angariSis strategiebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

teqstiani amocanebis swavleba . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

beWduri da eleqtronuli resursebi, romelTa gamoyeneba SesaZlebelia saswavlo procesSi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

saproeqto davalebebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

moswavleTa Sefaseba maTematikis swavlebisas . . . . . . . . . . . . . . . . . . . . . 36

gakveTilebis scenarebi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Tavi 1

ricxvebi 1-dan 5-mde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Tavi 2

vivarjiSoT 5-mde angariSSi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Tavi 3

ricxvebi 6-dan 10-mde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Tavi 4

vivarjiSoT 10-mde angariSSi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Tavi 5

ricxvebi 11-dan 15 mde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Tavi 6

vivarjiSoT 15-mde angariSSi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Tavi 7

ricxvebi 16-dan 20 mde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Tavi 8

vivarjiSoT 20-mde angariSSi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

danarTibavSvis asakobrivi Taviseburebebi (piaJes kognituri ganviTarebis Teoriis mokle mimoxilva) . . . . . . . . . . . . . 124

4

moswavlis wigni

moswavlis wigni 8 Tavisagan Sedgeba. raki pirvel klasSi Zir-

iTadi saswavlo masala ricxvebi da maTze moqmedebebia, xolo

raodenobebi Seiswavleba 20-is fargalSi, Tavebi am raodenobebis

Seswavlis mixedviTaa danawilebuli: kerZod, kenti Tavebi eTmo-

ba uSualod ricxvebis, maTi saxeldebis da numeraciis Seswavlas,

xolo luwi Tavebi – wina TavSi naswavl ricxvebze moqmedebebis

Sesrulebas.

Tavi 1: ricxvebi 1-dan 5-mde

Tavi 2: vivarjiSoT 5-mde angariSSi







maTematikis danarCeni mimarTulebebi danawilebulia da

integrirebulia am TavebSi. yoveli Tavis bolo nawili eTmoba:

geometriasa da sivrcis aRqmas; kanonzomierebebs; monacemebsa

da maT analizs.

wigni isea Sedgenili, rom masSi raimes Cawera praqtikulad

SeuZlebelia. moswavleebi amisaTvis iyeneben moswavlis savar-

jiSo rveuls da damatebiT, standartul ujrian rveuls (ix.

qvemoT).

TiToeul TavSi daaxloebiT 10 paragrafia. mTlianad wignSi,

rvave TavSi erTad ki 82 paragrafia. yovel maTgans aqvs calke

saTauri gverdis zeda nawilSi da eTmoba zustad erTi gverdi.

yoveli paragrafi sinamdvileSi udris 2 (zogierT SemTxvevaSi 3

an 1) sagakveTilo saaTs (pirvel klasSi maTematikis gakveTili 35

wuTiania). ratom aris ase? igulisxmeba, rom pirvel klasSi, mos-

wavleTa asakobrivi Taviseburebebidan gamomdinare, swavlebis

ZiriTadi datvirTva modis ara saxelmZRvaneloSi muSaobaze,

aramed maswavleblis wignSi mocemuli meTodikis mixedviT klas-

Si konkretul sagnebze manipulaciebze, maTze moqmedebebze,

radgan uamisod moswavleebi ver gaiazreben raodenobis, ricxvis

cnebas. Sesabamisad, wigni da rveuli damxmare resursebia da

maTze muSaobas SedarebiT mcire dro eTmoba. magaliTad, gan-

vixiloT romelime konkretuli ricxvis swavleba, vTqvaT 5. amas

ori dRe eTmoba: pirvel dRes saerTod ar viyenebT wignisa da

rveulis Sesabamis savarjiSoebs da muSaoba mxolod konkretu-

li sagnebis gamoyenebiT xdeba, xolo meore dRes SedarebiT

abstraqtul masalaze – wignsa da rveulze gadavdivarT.

maTematika 1-is komponentebi da maTi mokle mimoxilva

5

moswavlis wignis standartuli gverdis struqtura

paragrafis nomeri

paragrafis saTauri

davalebebis SekiTxvebi maswavlebelma unda waukiTxos moswavleebs.

sxvadasxva davaleba erTmaneTisgan xazebiTaa gamoyofili.

yovel gverdze miTiTebulia Tavis nomeri.

gverdis nomeri

6

moswavlis rveuli

savarjiSoebis rveuli zustad mihyveba moswavlis wignis

struqturas. mxolod erTi mciredi gansxvavebaa: vinaidan

rveulis mizani, garda uSualod maTematikuri davalebebisa,

motorikis unaris ganviTarebacaa, rveulis pirveli nawili

(ase vTqvaT Tavi 0, romelsac hqvia „movemzadoT werisaTvis“)

eTmoba iseT davalebebs, romlebic natifi motorikis ganvi-

Tarebas emsaxureba da amzadebs moswavles imisaTvis, rom man

uproblemod SeZlos momdevno Tavebis davalebaTa Sesruleba.

danarCeni Tavebi TiTqmis 100%-iT emTxveva wignis Sesabamis

gverdebs. dasaTaurebebic identuria. aqac, iseve rogorc

moswavlis wignSi, TiToeul paragrafs TiTo gverdi eTmoba

(gamonaklisia ramdenime gakveTili, romelsac eTmoba 2 gver-

di; aseve aris SemTxveva, rodesac moswavlis wignis or gverds

Seesabameba rveulis erTi gverdi). Sesabamisad, arc moswavles

da arc maswavlebels ar gauWirdeba rveulSi orientireba.

yovel ganSlaze miTiTebulia Sesabamisi Tavis nomeri.

paragrafebis saTaurebi

gverdis nomeri

sav

arj

iSo

s

no

me

ri

moswavlis rveulis gverdebis struqtura

7

maswavleblis wigni

winamdebare wigni warmoadgens maswavleblisTvis gankuT-

vnil saxelmZRvanelos, romlis bolo, yvelaze mozrdil naw-

ilSi, mocemulia gakveTilebis scenarebi. TiToeul gakveTils

aqvs saTauri, romelic moswavlis wignis Sesabamisi paragrafis

saTaurs emTxveva (gamonaklisia ramdenime gakveTili, romelic

mTlianad klasSi sagnebiT muSaobazea orientirebuli da wignis

paragrafi ar Seesabameba).

maswavleblis wignSi detaluradaa aRwerili 1-li Tavis yvela

gakveTili da danarCeni Tavebis yvela mniSvnelovani gakveTili.

is sakiTxebi, romlebic wina gakveTilebis msgavsi meTodikiT

unda aixsnas, detalurad aRaraa mocemuli.

maswavleblis wignis sagakveTilo scenarebis gverdis struqtura

gakveTilis rigiTi nomeri

gakveTilis mizani

resursebis CamonaTvali

moswavlis wignis Sesabamisi gverdi

moswavlis rveulis Sesabamisi gverdi

erovnuli saswavlo gegmis is indikatori, romelic am gakveTilis

mTavar Temas Seesabameba.

gakveTilis saTauri, romelic TiTqmis yovelTvis emTxveva paragrafis saTaurs.

8

mimarTuleba: ricxvebi da moqmedebebi

maT. I.1. moswavles SeuZlia erTmaneTs Seusabamos ricxvebi, ricxviTi saxelebi da raodenobebi.

Sedegi TvalsaCinoa, Tu moswavle:

y irCevs da qmnis mocemuli ricxvis Sesabamisi raodenobis saganTa erTobliobas da piriqiT –

mocemul saganTa erTobliobas Seusabamebs ricxvs;

y qmnis toli raodenobis saganTa mowesrigebul erTobliobas maTi dawyvilebiT;

y kiTxulobs da wers ricxvebs; gamosaxavs maT sxvadasxva modelis gamoyenebiT;

y gamoyofs miTiTebuli ricxvebis Sesabamisi raodenobebis jgufebs grovaSi (magaliTad,

gamoyofs sameuls, xuTeuls, aTeuls grovaSi).

maT. I.2. moswavles SeuZlia rigobiTi ricxviTi saxelebis gamoyeneba.


y iTvlis win/ukan nebismieri ricxvidan, ganmartavs 11-dan 20-mde ricxvebis saxeldebas;

asaxelebs mocemuli ricxvis wina da momdevno ricxvebs;

y saganTa mowesrigebul erTobliobaSi asaxelebs miTiTebuli sagnis rigs; mocemuli Tanmim-

devrobiT da miTiTebul poziciebze ganaTavsebs sagnebs;

y iyenebs rigobriv ricxviT saxelebs movlenaTa an qmedebaTa Tanmimdevrobis aRwerisas;

y adekvaturad iyenebs nuls da mis aRmniSvnel simbolos Sesabamis situaciebSi;

y ganasxvavebs da asaxelebs erovnuli fulis niSnebs (monetebs da banknotebs) 20-is farglebSi.

maT. I.3. moswavles SeuZlia erTmaneTTan daakavSiros Tvla, ricxvebs Soris damokidebulebebi

da Sekreba-gamoklebis moqmedebebi.


y sityvierad aRwers Sekrebis, gamoklebis, tolobisa da Sedegis cnebebs sxvadasxva konte-

qstSi (magaliTad, "davumatoT", "movakloT", mimateba – gazrda; gamokleba – Semcireba,

gancalkeveba, gansxvaveba);

y axdens Sekreba-gamoklebis TvalsaCinod demonstrirebas, gansazRvravs gansxvavebas (mag-

aliTad, `ramdeniT gaizarda/Semcirda?") da aRwers ricxvebs Soris damokidebulebebs;

y zepirad angariSisas iyenebs 1-is toli bijiT Tvlas an sxva xerxs da axdens Sekreba-gamoklebis

moqmedebaTa urTierTSebrunebulobis demonstrirebas modelis gamoyenebiT;

y mocemuli grovisaTvis asaxelebs am grovis miTiTebul raodenobamde Sesavsebad saWiro

damatebiT raodenobas; zepirad asrulebs 10-is gavliT Sekreba-gamoklebas da axdens gam-

oyenebuli xerxis demonstrirebas.

maT. I.4. moswavles SeuZlia raodenobebis Sefaseba da Sedareba.


y dauTvlelad asaxelebs zust raodenobas erTgvarovan, mcire zomis saganTa grovaSi (saganTa

raodenoba ar aRemateba 5-s) da amowmebs Tavis pasuxs;

y akavSirebs "-iT" metoba/naklebobas Sekreba/gamoklebis moqmedebebTan da axdens amis mod-

elze demonstrirebas;

axali erovnuli saswavlo gegmiT gansazRvruli maTematikis programa

pirvel klasSi wlis bolos misaRwevi Sedegebi da maTi indikatorebi

9

y saganTa dawyvilebiT adarebs raodenobebs grovebSi, iyenebs Sesabamis terminebsa da aRniS-

vnebs (<, >, =) da gansazRvravs gansxvavebas ("ramdeniT meti/naklebi?");

y irCevs ori grovidan erTs, romelSic sagnebis raodenoba daaxloebiT mocemuli ricxvis

tolia, amowmebs Tavis varauds.

mimarTuleba: kanonzomierebebi da algebra

maT. I.5. moswavles SeuZlia ganavrcos, warmoadginos da erTmaneTs Seadaros sagnebis period-

uli ganlagebebi (mimdevrobebi).


y mimdevrobis mocemuli fragmentis mixedviT avsebs am mimdevrobis ramdenime Tanmimdevrul

Ria pozicias;

y adarebs erTnairi sagnebiT warmodgenil or mocemul mimdevrobas (romlebSic saganTa

raodenoba tolia) da Sesabamis SemTxvevaSi miuTiTebs im mimdevrobebs, romlebic ganlagebis

erTsa da imave wess emorCileba;

y sityvierad mocemuli wesis mixedviT, mimdevrobiT ganalagebs mxolod erTi atributiT

gansxvavebul sagnebs (magaliTad, erTi zomis burTebis aseT mimdevrobas: wiTeli burTi,

lurji burTi, wiTeli burTi . . .).

mimarTuleba: geometria da sivrcis aRqma

maT. I.6. moswavles SeuZlia brtyeli geometriuli figuris amocnoba da aRwera.


y yofiTi daniSnulebis sagnebSi an maT ilustraciebSi uTiTebs dasaxelebul brtyel figurebs;

y SearCevs miTiTebuli figuris models Sereuli grovidan;

y aRwers miTiTebul geometriul figuras (magaliTad, asaxelebs mocemuli mravalkuTxedis

wveroebis raodenobas).

maT. I.7. moswavles SeuZlia brtyeli geometriuli figurebis gamosaxva da obieqtTa urTierT-

mdebareobis amocnoba.


y romelime xerxiT (magaliTad, aplikaciiT an naxatis saSualebiT) qmnis dasaxelebuli formis

brtyeli figuris models an gamosaxulebas;

y uTavsebs sxvadasxva brtyeli figuris modelebs erTmaneTs nimuSze mocemuli gamosaxulebis

(naxatis) misaRebad;

y sworad pasuxobs kiTxvebs obieqtTa urTierTmdebareobis (marjvniv/marcxniv, zemoT/qve-

moT, win/ukan) Sesaxeb;

y miTiTebuli wesiT aerTebs ramdenime wertils sibrtyeze da moniSnavs gzas miTiTebul

obieqtamde martiv sqemaze.

10

standartis Sedegis miRwevisa da saxelmZRvanelos Sinaarsis

urTierTkavSiris matrica

Tavi 1. ricxvebi 1-dan 5-mde

N paragrafis saTaurisaaT.

raod.standartis indikatori

1 marcxniv, marjvniv, SuaSi 2 sT. 1.7.3.

2 zeviT, qveviT, SuaSi 1 sT. I.7.3.

3 win, ukan 1 sT. I.7.3.

4 dawyvileba 1 sT. I.4.3.

5 SigniT da gareT 3 sT. 1.7.3.

6 striqoni da sveti 2 sT. 1.7.3.

7 mimdevroba 1 sT. 1.5.1, 1.5.2, 1.5.3

8 erTi 2 sT. 1.1.1, 1.1.2, 1.1.3, 1.4.1

9 ori 2 sT. 1.1.1, 1.1.2, 1.1.3, 1.4.1

10 sami 2 sT. 1.1.1, 1.1.2, 1.1.3, 1.4.1

11 oTxi 2 sT. 1.1.1, 1.1.2, 1.1.3, 1.4.1

12 xuTi 2 sT. 1.1.1, 1.1.2, 1.1.3, 1.4.1

13 met-naklebobis niSani 2 sT. 1.4.3.

14 tolobis niSani 2 sT. 1.1.2. ,1.4.3.

Tavi 2. vivarjiSoT 5-mde angariSSi



1 Sekreba 3 sT. 1.3.1. , 1.3.2.

2 meramdenea? 1 sT. 1.2.2. , 1.2.3.

3 sameulebi 1 sT. 1.1.4.

4 oTxeulebi 1 sT. 1.1.4.

5 xuTeulebi 1 sT. 1.1.4.

6 cxrili da cifrebi 1 sT. damatebiTi sakiTxi, romelic ar aris esg-Si

7 TeTrebi 1 sT. 1.2.5.

8 larebi 1 sT. 1.2.5.

9 ramdenime are 1 sT. 1.7.3., 1.7.4.

11




1 eqvsi 2 sT. 1.1.1, 1.1.2, 1.1.3

2 Svidi 2 sT. 1.1.1, 1.1.2, 1.1.3

3 rva 2 sT. 1.1.1, 1.1.2, 1.1.3

4 cxra 2 sT. 1.1.1, 1.1.2, 1.1.3

5 aTi 2 sT. 1.1.1, 1.1.2, 1.1.3

6 gamokleba 3 sT. 1.3.1., 1.3.2.

7 areebis sazRvari 1 sT. 1.7.4

8 ramdeniT metia? ramdeniT

naklebia?

2 sT. 1.4.2, 1.4.3

9 5-mde Sevseba 2 sT. 1.3.4.





1 ricxvebis dalageba

zrdadobiT

2 sT. 1.4.3

2 ricxvebis dalageba

klebadobiT

2 sT. 1.4.3

3 ricxvebis kibe 2 sT. 1.4.2, 1.4.3

4 nuli 2 sT. 1.2.4.

5 gamosaxuleba 2 sT. 1.1.4.

6 gamosaxulebis da ricxvebis

Sedareba

2 sT. 1.1.4. , 1.4.2.

7 gzajvaredinebi wirze 2 sT. 1.7.4

8 Sesakrebebi da jami 2 sT. 1.3.3.

9 saklebi, maklebi, sxvaoba 2 sT. 1.3.3.




1 aTeuli 2 sT. 1.1.4.

2 TerTmeti 2 sT. 1.2.1., 1.2.2.

3 Tormeti 2 sT. 1.2.1., 1.2.2.

4 cameti 2 sT. 1.2.1., 1.2.2.

5 ToTxmeti 2 sT. 1.2.1., 1.2.2.

6 TxuTmeti 2 sT. 1.2.1., 1.2.2.

7 gaxsnili wiri da monakveTi 2 sT. 1.6.2, 1.7.1

8 texili 2 sT. 1.6.3, 1.7.1

9 jamebis Sedareba 2 sT. 1.4.2

10 sxvaobebis Sedareba 2 sT. 1.4.2

11 10 TeTri da 10 lari 2 sT. 1.2.5.

12

Tavi 7. ricxvebi 16-dan 20 mde



1 Teqvsmeti 2 sT. 1.2.1., 1.2.2.

2 Cvidmeti 2 sT. 1.2.1., 1.2.2.

3 Tvrameti 2 sT. 1.2.1., 1.2.2.

4 cxrameti 2 sT. 1.2.1., 1.2.2.

5 oci 2 sT. 1.2.1., 1.2.2.

6 ricxvis daSla or

Sesakrebad

2 sT. 1.3.1

7 samkuTxedi, oTxkuTxedi,

xuTkuTxedi

2 sT. 1.6.1., 1.6.2., 1.6.3.

8 marTkuTxedi 2 sT. 1.6.1., 1.6.2., 1.6.3.

9 wre da wrewiri 2 sT. 1.6.1., 1.6.2., 1.6.3.




1 ramdenime Sesakrebi 2 sT. 1.3.1., 1.3.2.


3 15-mde Sekreba 2 sT. 1.3.4.

4 Sekrebisas aTeulis

warmoqmna

2 sT. 1.3.4.

5 Sekrebis cxrili 2 sT. 1.3.1, 1.3.2, 1.3.3

6 gamoklebis cxrili 2 sT. 1.3.1, 1.3.2, 1.3.3

7 gamosaxulebebis Sedareba

dawyvilebiT

2 sT. 1.4.3

8 samkuTxedi da oTxkuTxedi 2 sT. 1.6.1., 1.6.2., 1.6.3, 1.7.2

9 wre, mravalkuTxedi 2 sT. 1.6.1., 1.6.2., 1.6.3

10 romeli saaTia? 2 sT. damatebiTi sakiTxi, romelic ar aris esg-Si




1 ricxvebis RerZi 2 sT. 14.2

2 gaormageba 2 sT. damatebiTi sakiTxi, romelic ar aris esg-Si

3 ganaxevreba 2 sT. damatebiTi sakiTxi, romelic ar aris esg-Si

4 Sekreba aTeulis

warmoqmniT

2 sT. 1.3.4

5 gamokleba aTeulis daSliT 2 sT. 1.3.4

6 20-mde Sevseba 2 sT. 1.3.4

7 20 TeTri da 20 lari 2 sT. 1.2.5.

8 sworia Tu mcdari? 2 sT. damatebiTi sakiTxi, romelic ar aris esg-Si

9 monacemebis Setana cxrilSi 2 sT. damatebiTi sakiTxi, romelic ar aris esg-Si

13

raodenoba, ricxvi da cifrimaTematikis swavlebisas umniSvnelovanesia esg-s mimarTuleba `ricxvebi da moqmedebebi ricxve-

bze~. Sesabamisad, umniSvnelovanesia ricxvis cneba. rogorc zogjer amboben xolme, raodenobrivi

wigniereba ricxvis „SegrZnebis“ unaria. ra gansxvavebaa raodenobasa da ricxvs Soris? raodenoba

da ricxvi sinonimebia. orive sityva erTsa da imave Sinaarss gamoxatavs.

Tumca zogjer ricxvs ureven cifrSi, rac uxeSi Secdomaa. ricxvi da cifri sruliad gansx-

vavebuli cnebebia. es daaxloebiT imas hgavs, erTmaneTSi rom avurioT „sityva“ da „aso“. rogorc

asoebiT xdeba sityvebis dawera, xolo bgerebiT sityvebis warmoTqma, aseve, ricxvebis Cawera xdeba

cifrebiT, xolo warmoTqma – bgerebiT.

Sesabamisad, gamoTqma „jandacvaze daixarja 800 milioni lari. es cifri gviCvenebs, rom jan-

dacvis saxelmwifo politika....“ uxeSi Secdomaa. 800 milioni ar aris cifri, es aris ricxvi, raode-

noba, romlis Cawera SesaZlebelia rogorc cifrebiT, ise – asoebiTac.

ra aris raodenoba?calkeul sagnebs sxvadasxva Tviseba aqvs. magaliTad, vaSli SeiZleba iyos mwvane, momrgvalo,

gemrieli da a.S.

zustad ise, rogorc sagnebs aqvs Tvisebebi, saganTa erTobliobasac aqvs Tviseba, romelsac

raodenoba hqvia. raodenoba isevea saganTa simravlis Tviseba, rogorc feria Tviseba calkeuli

sagnisa. Cven SegviZlia vikiTxoT ama Tu im saganze „ra feria?“ da pasuxad miviRoT am sagnis es

konkretuli Tviseba – „mwvanea“. zustad aseve, saganTa erTobliobazec SegviZlia vikiTxoT „ram-

denia?“ „ra raodenobaa am erTobliobaSi/simravleSi?“ da pasuxad miviRoT raime konkretuli

raodenoba – „sami“, „Svidi“ da a.S.

raodenobebis aRmniSvneli sityvebi zustad iseve gamoiyeneba msazRvrelad, rogorc zedsar-

Tavi saxelebi:

„Svidi msxali“, „gemrieli msxali“

„oci gogona“, „lamazi gogona“

da a.S.

saintereso isaa, rom es Tviseba, raodenobrioba, aqvs ara mxolod saganTa ramdenimecalian

erTobliobas, aramed erT sagansac. rogorc SegviZlia erT vaSlze vikiTxoT, „ra feria“, aseve

SegviZlia vikiTxoT „ramdenia“.

saganTa simravleebs SeiZleba gansxvavebuli raodenoba hqondeT. Zalian xSirad es erTi Sexed-

viTac ki aSkaraa da amas patara bavSvebic ki amCneven. adreuli asakidanve, miuxedavad imisa, rom ar

ician raodenobebi, bavSvebi ganasxvaveben sxvadasxvaraodenobian erTobliobebs.

mTavari maxasiaTebeli raodenobebisa maTi met-nakleboba da tolobaa.

rogorc wesi, metoba/nakleboba xSirad TvaliTac ki ioli aRsaqmelia. aseT dros raodenobebs

zustad aravin adarebs erTmaneTs. magaliTad, erT mxares Tu uamravi Txili yria da meore mxares

Zalian cota, met-naklebobis Sesafaseblad, rogorc wesi, raime gansakuTrebuli procedura ar

gvesaWiroeba – yvelaferi Tvalis erTi SevlebiTac ki naTelia.

SedarebisTvis aucilebeli procedurebis saWiroeba mxolod maSin Cndeba xolme, rodesac

Tvalis erTi SevlebiT yvelaferi aSkara araa.

Tumca patara bavSvebSi, ZiriTadad skolamdeli asakis bavSvebSi, TvaliT Sefaseba Secdomis

daSvebis mizezi xdeba. patara bavSvs gafantuli 5 Txili ufro meti eCveneba, vidre erTad Tavmoy-

rili 7 Txili; 3 sazamTro meti hgonia, vidre 5 vaSli.

bavSvi ver xvdeba, rom raodenoba ucvleli rCeba, rodesac simravlis elementebs gavfantavT.

ra unda icodes dawyebiTi klasebis maswavlebelma ricxvebis Sesaxeb

14

rogorc fsiqologebi ityvian, ver wvdeba raodenobis invariantulobas (ucvlelobas).

es ucnauri movlena pirvelad eqsperimentulad Seiswavla da aRwera didma Sveicarielma

fsiqologma Jan piaJem (Piaget), rodesac ikvlevda inteleqtis ganviTarebis kanonzomierebebs.

imisaTvis, rom ufro ukeT gavigoT, ra problemebs SeiZleba waawydnen maswavleblebi raode-

nobebis swavlebisas, Zalian mokled unda SevexoT piaJes Teorias. (ix. danarTi)

raodenobebis SedarebaimisaTvis rom ori sxvadasxva simravle, maTi raodenobebi SevadaroT (anu gavarkvioT, rome-

lia meti), sulac araa saWiro maTi daTvla. raodenobebis Sedareba Zalian martivi proceduriT,

dawyvilebiT xdeba. TiToeuli simravlidan viRebT TiTo sagans da erTad vdebT, vawyvilebT. romel

simravleSic darCeba dauwyvilebeli sagnebi, isaa meti.

Zalian xSirad skolebSi ricxvebis met-naklebobis swavlebisas, maswavleblebi SecdomiT

aswavlian am mniSvnelovan sakiTxs. rodesac or simravles adarebineben, met-naklebobis dasasabuTe-

blad iyeneben gadaTvlas da, magaliTad, amboben: „es metia amaze, radgan aq 5 fanqaria, aqeT ki 4“.

sinamdvileSi daTvla argumenti ar aris. 5 imitomaa meti 4-ze, rom Tu Sesabamisi raodenobis sim-

ravleebs SevqmniT (magaliTad sagnebiT davawyobT) da davawyvilebT, im simravleSi, romelSic 5

sagania, darCeba dauwyvilebeli sagani.

Sedarebis erTaderTi procedura, erTaderTi argumenti, riTac vasabuTebT ama Tu im simravlis

met-naklebobas, dawyvilebaa.

am proceduriT dgindeba nebismieri ori simravlis ara mxolod gansxvaveba, aramed ufro zusti

mimarTebac – met-nakleboba.

amave proceduriT dgindeba simravleTa tolobac. rodesac ori simravlis elementebs

davawyvilebT da arc erTSi ar darCeba dauwyvilebeli, es simravleebi tolia, maT erTnairi

raodenobis elementebi aqvT.

dawyvilebis saSualebiT SesaZlebelia samyaroSi arsebuli nebismieri simravleebis Sedareba.

ra Tqma unda, Zalian bevri simravle iqneba, romelTac erTnairi raodenobis elementebi aqvT,

tolebi arian.

raodenoba anu ricxvi erTnairi (toli) simravleebis saerTo Tvisebaa.

magaliTad, 5 samyaroSi arsebuli yvela xuTelementiani simravlis saerTo Tvisebaa.

raki dawyvilebis proceduris safuZvelze dgindeba sxvadasxva raodenobis met-nakleboba,

Sesabamisad ricxvebis dalageba zrdadoba-klebadobiT da ricxvTa RerZis ageba dawyvilebis

safuZvelze xdeba.

raodenoba, raodenobis saxeli, raodenobis Canaweri

oci 20

nebismier raodenobas, ricxvs aqvs Sesabamisi qarTuli saxeli. es saSualebas iZleva zepiri

komunikaciisas Tanamosaubres gavagebinoT, ra raodenobazea saubari.

cxadia, raodenobis saxeli sxva romelime enaze sxvagvarad gamoiTqmis.

garda zepiri komunikaciisa, xSirad raodenobebis Caweraa saWiro. Tanamedrove adamianebi

raodenobebis Casawerad cifrebs iyeneben. sul aTi sxvadasxva cifri arsebobs: 0, 1, 2, 3, 4, 5, 6, 7,

8, 9 da maTi saSualebiT nebismieri raodenobis Caweraa SesaZlebeli, zustad iseve, rogorc 33

qarTuli asoTi SeiZleba nebismieri sityvis Cawera.

garda cifrebisa, raodenobebis Cawera, gamoxatva sxva saSualebebiTac SeiZleba. magaliTad,

Zalian didi xnis winaT, cifrebis gamogonebamde, raodenobebis fiqsirebas amgvari niSnebiT axer-

xeb dnen:

15

aseT niSnebs dResac ki iyeneben xolme. am suraTze gamosaxulia havais kunZulebze, hanakapi-

ais plaJTan moTavsebuli gamafrTxilebeli warwera, sadac talRebSi damxrCvali vizitorebis

raodenoba (82 kaci) ara cifrebiT, aramed msgavsi niSnebiTaa aRricxuli.

rodesac patara bavSvs ekiTxebian, ramdeni wlis xaro da is 3 TiTs gaiSvers, am xerxiT gamox-

atavs raodenobas.

raodenobis gamoxatva uamravi sxvadasxva xerxiTaa SesaZlebeli, Tumca yvelaze gavrcelebulia

raodenobis saxelis Tqma da cifrebiT Cawera. magram, rogorc zemoT moyvanili suraTi gviCve nebs,

zogjer saxelze da cifrebze ukeTesi sxva saSualeba SeiZleba iyos. patara bavSvis gaSverili

TiTebi amis saukeTeso magaliTia.

zogjer raodenobis Cawerisas cifrebis nacvlad pirdapir saxelebs iyeneben, zogjer ki kom-

binirebul variants – nawils cifrebiT weren, nawils – asoebiT. magaliTad:

800 milioni lari

cxra Zma xerxeuliZe

me-19 saukunemde, sanam saqarTveloSi cifrebi damkvidrdeboda, raodenobebis Casawerad qar-

Tuli anbanis asoebi gamoiyeneboda:

a 1

b 2

g 3

d 4

e 5

da a.S.

magaliTad, mowameTaSi Sesrulebul kedlis warweraze miTiTebulia TariRi Cymv anu 1846.

16

cxadia, SeuZlebelia imis Tqma, rom raodenoba aq SecdomiTaa Cawerili. raodenobis gamosaxva,

Cawera nebismieri saSualebiT daSvebulia, ubralod, dResdReobiT yvelaze miRebulia cifrebiT

Cawera.

ricxviTi saxeliraodenobebis saxelebi enaSi sityvaTa calke klass qmnis, romelsac ricxviTi saxeli ewodeba.

ricxviTi saxeli samgvaria – raodenobiTi ricxviTi saxeli (magaliTad, erTi, ori, sami, da a.S.),

rigobiTi (pirveli, meore, mesame, da a.S.) da wilobiTi (meoredi, mesamedi, meoTxedi da a.S.). amaTi

dasaxelebebi gviCvenebs, rom pirveli qvejgufi mTeli ricxvis saxelebia, meore qvejgufi raode-

nobas ki ar gviCvenebs, aramed rigobiTobas, xolo mesame qvejgufi wiladebis saxelebia.

bunebrivia, enaSi arsebobs sxva sityvebic, romlebsac mWidro kavSiri aqvT raodenobasTan,

odenobasTan, magram eseni ar arian ricxviTi saxelebi. magaliTad: yoveli, zogierTi, ramdenime,

nebismieri, meti da a.S. aseTi sityvebi mniSvnelovan rols TamaSobs maTematikis swavlebis procesSi

da maTi sworad gamoyeneba raodenobrivi wignierebis unaris formirebis erT-erTi safuZvelia.

gansakuTrebiT sainteresoa sityvaTa erTi jgufi, romelic ar arsebobs evropul enebSi da

Zalian karg efeqts iZleva maTematikis swavlebisas imis gaazrebaSi, ra gansxvavebaa raodenobas,

mis saxelsa da Canawers Soris. ganvixiloT ramdenime magaliTi:

sami sameuli samiani

pirveli maTgani raodenobis saxelia, meore samelementiani simravlisa, xolo mesame – Sesabamisi

cifrisa. „sameuli“ da „samiani“ ar aris ricxviTi saxelebi. gansakuTrebiT sainteresoa es „sameu-

lis“ SemTxvevaSi. es sityva konkretuli raodenobis simravleze miuTiTebs, TiTqos raodenobac

Cans masSi, magram aqcenti mainc mTlian simravlezea gakeTebuli da ara mis Tvisebaze.

is, rom cifris da Sesabamisi ricxvis saxelebi gansxvavebulia, SesaniSnav saSualebas aZlevs

maswavlebels, ganasxvavebinos bavSvebs ricxvi („sami“) da cifri („samiani“) erTmaneTisagan.

rogor gaCnda raodenobebis saxelebi da Tvlis sistemapirvelyofil adamianebs, romlebic monadireobiTa da nayofis SegrovebiT iyvnen dakavebuli,

raodenobebis codna ar esaWiroebodaT. Sesabamisad, im dros enaSi ricxviTi saxelebi ar arsebob-

da. es dasturdeba gadaSenebis piras myofi im Tanamedrove enebiT (ZiriTadad, amazonis auzSi;

magaliTad peruSi arabelas ena), sadac raodenobebis aRmniSvneli sityvebi, garda „erTi“-sa, ar

arsebobs. arsebobs enebis meore jgufi (magaliTad, avstraliis aborigenebi), sadac fiqsirdeba

mxolod sityvebi „erTi“ da „ori“. ufro didi raodenobebis aRmniSvneli sityvebi am enebSi araa.

pirvelyofili adamianebis saqmianobis tipis cvlilebam, kerZod, Sinauri cxovelebis moSenebam

da vaWrobam, ganapiroba raodenobebis dadgenis da maTi saxeldebis saWiroeba.

Tavdapirvelad adamianebs SedarebiT mcire raodenobebTan hqondaT saqme da yvelafers TiTebis

daxmarebiT iTvlidnen; Sesabamis raodenobebs ki calke saxelebi daarqves: erTi, ori, sami, oTxi,

xuTi, eqvsi, Svidi, rva, cxra, aTi.

raki raodenobebi, ricxvebi usasruloa, TiToeulisTvis calke saxelis darqmevas azri ara aqvs,

radgan amden gansxvavebul sityvas veravin daimaxsovrebs. saWiro xdeba saxelis darqmeva raime

principis, meTodis gamoyenebiT.

10-is zeviT raodenobebis saxelebi qarTul enaSi 10-Tan Sedarebis safuZvelzea SerCeuli:

TerTmeti anu (a)TerTmeti, aTze erTiT meti;

Tormeti anu (a)Tormeti aTze oriT metia da a.S.

anu SedarebiT didi raodenobis gamoxatva mcire raodenobebis saSualebiT xdeba. magaliTad,

Cvidmeti aris aTi da Svidi anu aTSvidmeti=Cvidmeti

20-s isev calke saxeli hqvia. 20-is zeviT raodenobebisaTvis 100-mde qarTulSi aseTi principi

moqmedebs: es ricxvebi oc-ocad daTvlis safuZvelzea saxeldebuli.

magaliTad, „ormocdaSvidi“. sityva gviCvenebs, rom es raodenoba aris ori oci da Svidi. „oTx-

mocdaTxuTmeti“ aris oTxi oci da TxuTmeti (es ukanaskneli Tavis mxriv aTi da xuTia).

100-s isev calke saxeli hqvia.

17

100-is zeviT raodenobebisaTvis as-asad daTvlis principi moqmedebs: orasi, samasi da a.S.

mokled rom SevajamoT, qarTuli Tvlis sistema aseTia:

arsebobs raodenobebis specialuri, gansxvavebuli saxelebi aTamde ricxvebisaTvis, agreTve

20-isa da 100-isaTvis da yvela sxva ricxvis saxeli am saxelebis kombinaciiTaa miRebuli.

anu imisaTvis, rom didi raodenoba gamovxatoT, igi unda movawesrigoT, anu davastruqturoT

patara raodenobebad (aTebad, ocebad, asebad). didi, ucnobi raodenobis gamosaxatavad, gamo-

saTqmelad unda gamoviyenoT mcire, nacnobi raodenobebi. amas Tvlis sistema hqvia.

qarTuli Tvlis sistema arsebiTad gansxvavdeba ZiriTadi evropuli enebis Tvlis sistemebisagan

(SedarebiT axlosaa mxolod franguli enis Tvlis sistemasTan). evropul enebSi Tvlis sistema

metwilad aTobiTia, xolo qarTulSi 100-mde ricxvebisTvis – ocobiTia.

es erTgvar „winaaRmdegobas“ qmnis ricxvebis swavlebisas. qarTvel bavSvs, rodesac esmis „oTx-

mocdaxuTi“, xSirad mosdis Secdoma da 45-s wers, raki sityvaSi, saxelSi pirvelad esmis „oTxi“.

Tavis droze, meoce saukunis 20-30-ian wlebSi qarTvel enaTmecnierebs Soris gaCnda idea,

SeecvalaT 100-mde ricxvebis qarTuli saxelebi da daemkvidrebinaT axali: „samaTi“, „oTxaTi“,

„xuTaTi“ da a.S. magram am ideam fexi ver moikida da ricxvebs isev is saxelebi hqvia qarTulad,

romlebic odiTganve erqva.

es erTgvari „winaaRmdegoba“ ricxvis qarTuli saxelwodebis ocobiTobasa da cifrebiT Canaw-

eris aTobiTobas Soris, romelic zogs swavlebisas sirTuled miaCnia, sinamdvileSi upiratesobaa,

Tuki swavleba dazepirebiT ki ar mimdinareobs, aramed raodenobebis kargad gaazrebiT. Canawersa

da saxels Soris arsebiTi sxvaoba swori swavlebiT bavSvs kargad gaaazrebinebs Tvlis sistemis

arss da ukeT gaagebinebs raodenobis cnebas.

raodenobis/ricxvis Caweris sistemebiadamianebs raodenobebis simboloebiT Cawera kacobriobis ganviTarebis adreul etapebze ar

dasWirvebiaT. Caweris saWiroeba SedarebiT gvian gaCnda, rodesac maT did raodenobebTan mouxdaT

Sexeba. pirveli civilizaciebis Seqmnisas, rodesac gadasaxadebis akrefis saWiroeba warmoiSva,

bunebrivad gaCnda raodenobebis fiqsirebis aucileblobac.

sainteresoa, aRiniSnos, rom TiTqmis yvela Zvel civilizacias raodenobebis, ricxvebis Caweris

sakuTari sistema hqonda. ar arsebobda raime saerTaSorisod aRiarebuli standarti.

ricxvebis babilonuri, egvipturi, Cinuri, induri, maias tomis Tu berZnuli Canawerebi arseb-

iTad gansxvavdeboda erTmaneTisagan.

yvela maTgani Taviseburad gamoxatavda raodenobas.

ai, magaliTad, rogor werdnen ricxvebs maias tomebi:

Cveni winaprebi ricxvebs anbanis asoebiT werdnen. yoveli aso romeliRac konkretul raodenobas

Seesabameboda. magaliTad C aRniSnavda 1000-s, xolo a – 1-s. aseTi Canawerebi Zalian mouxerxebelia

gamoTvlebisaTvis.

18

ricxvis Caweris poziciuri sistemaricxvebis Caweris is sistema, romliTac dRes mTeli kacobrioba sargeblobs, indoeTSi Seiqmna.

mogvianebiT indoelebisagan is arabebma gadaiRes da arabebisagan gavrcelda evropaSi. amitom am

simboloebs arabuli cifrebi uwodes.

sul arsebobs aTi sxvadasxva simbolo:

0 1 2 3 4 5 6 7 8 9

da nebismieri raodenobis Cawera SesaZlebelia maTi meSveobiT. zustad ise, rogorc anbanis

asoebiT nebismieri raodenobis sityvis Cawera SeiZleba.

mTavari principi, romelic safuZvlad udevs am sistemas, isaa, rom imis mixedviT, ra adgilas,

ra poziciaze weria simbolo, igi sxvadasxva raodenobas gamoxatavs.

magaliTad, SevadaroT ori Canaweri:

54 da 45

am orive CanawerSi zustad erTnairi simboloebia gamoyenebuli, magram marcxenaSi 5-iani aRniS-

navs xuT aTeuls anu ormocdaaTs, xolo marjvenaSi – xuTs.

anu erTi da igive simbolo, imis mixedviT, ra poziciaze dgas, sxvadasxva raodenobas gamoxatavs.

swored am mizeziT ewodeba numeraciis (es sityva ricxvis simboloebiT Caweras niSnavs) am

sistemas aTobiTi poziciuri sistema.

Canaweri 458 sul sam simbolos Seicavs, magram gamoxatavs raodenobas, sadac 4 aseuli, 5 aTeuli

da kidev 8 erTeulia. es raodenoba sityvebiT rom gamovTqvaT, ori grZeli sityva dagvWirdeba –

oTxas ormocdaTvrameti.

sinamdvileSi Canaweri 458 aris Semoklebuli Canaweri aseTi gamosaxulebisa:

100•4 + 10•5 + 8

garda imisa, rom aTobiTi poziciuri sistema saSualebas iZleva, ricxvebi Zalian mokled Cavw-

eroT, igi rTuli gamoTvlebis Casatarebladac Zalian mosaxerxebelia. amitom, bunebrivia, rom

mTel msoflioSi gavrcelda da amJamad yvelgan gamoiyeneba.

19

TvalsaCinoebebis roli maTematikis swavlebisas

rodesac bavSvebi skolaSi maTematikis da, kerZod, raodenobebis Seswavlas iwyeben, maTi intele-

qti sagrZnoblad gansxvavdeba ufrosis inteleqtisgan. am asakis moswavleebi inteleqtis ganvi-

Tarebis specifikur safexurze, piaJes mixedviT e.w. winaoperaciul an konkretuli operaciebis

stadiaze imyofebian (ix. danarTi). es niSnavs, rom bavSvebs SeuZliaT mxolod iseTi problemebis

gadaWra, rac konkretul sagnebs, obieqtebs ukavSirdeba da ver Zleven abstraqtul, hipoTetur

amocanebs.

swored amitom, am stadiaze (anu daaxloebiT dawyebiTi klasebis pirveli 3-4 wlis ganmavlobaSi)

umniSvnelovanesia TvalsaCinoebebis roli maTematikis swavlebisas.

Zalian xSirad amas ugulebelyofen rogorc mSoblebi, ise samwuxarod, maswavleblebic da

maTematikis swavlebisas ZiriTadi aqcenti gadaaqvT cifrebiT Cawerili raodenobebis damaxsovre-

ba-dazepirebaze. bavSvebi saaTobiT „xsnian“ cifrebiT Caweril magaliTebs da Sedegad maTTvis

raodenoba asocirebulia ara konkretul sagnebTan, obieqtebTan, aramed CanawerTan, cifrebTan.

amitom aRaraa gasakviri, rom meoTxeklaseli qarTveli bavSvebis umravlesoba saerTaSoriso saSu-

alo doneze gacilebiT dabal Sedegebs aCvenebs, rodesac saerTaSoriso kvlevebiT maTematikur

unarebs amowmeben.

imisaTvis, rom raodenoba, ricxvi gaigos, moswavles mudmivi Sexeba unda hqondes konkretul

sagnebTan. am sagnebis gadawyoba-gadmowyobiT igi nel-nela iazrebs raodenobis invariantul

bunebas anu imas, rom raodenoba ar icvleba gafantviT an grovad moquCebiT. raodenoba icvleba

mxolod masze sxva raodenobis damatebiT an misTvis raodenobis moklebiT.

sxvadasxva raodenobebis dastruqturebiT konkretuli sagnebis meSveobiT, bavSvi TandaTan

xvdeba raodenobis gamoxatvis princips, iazrebs ricxvs. misTvis raodenoba araa mxolod cifrebis

erToblioba, ricxvs konkretuli Sinaarsi aqvs da realobasTanaa kavSirSi.

rac ufro meti sxvadasxva sagniT gadaTvlis bavSvi sxvadasxva raodenobebs, miT ufro swrafad

da Rrmad igebs, rom ricxvi aris is saerTo, rac am sxvadasxva simravleebs aqvT. misTvis ricxvis

cifrebiT Canaweri araa ubralod abstraqtuli simbolo. am simbolos konkretuli Sinaarsi aqvs

da uSualo kavSirSia sinamdvilesTan.

swored aseTi elementaruli moqmedebebiT iwyeba maTematikis Seswavla sawyis klasebSi. amis-

aTvis ki skolaSi sxvadasxva tipis TvalsaCinoebebi (e.w. manipulativebi) aris saWiro.

ra manipulativebi esaWiroebaT moswavleebs da maswavlebels?

vinaidan manipulativebis roli gadamwyvetia maTematikis Seswavlisas (gansakuTrebiT dawyebi-

Ti klasebis pirveli sami wlis ganmavlobaSi), Sesabamis saklaso garemos ganuzomeli mniSvneloba

aqvs. amave dros misi mowyoba SesaZlebelia ise, rom TiTqmis aranair danaxarjebTan ar iyos daka-

vSirebuli.

rogorc ukve vTqviT, bavSvebs mudmivi Sexeba unda hqondeT konkretul sagnebTan da es sagnebi

xSirad unda icvlebodes. magaliTad, Tu zogjer raodenobebs daawyoben da gadaTvlian CxirebiT,

mere SesaZlebelia igive gaakeTon RilebiT, simindis marcvlebiT, boTlis TavsaxurebiT da a.S.

Sesabamisad, maswavlebels klasSi unda hqondes sxvadasxva tipis erTgvarovani sagnebis garkveu-

li raodenobebi rogorc dafasTan samuSaod, aseve moswavleebisaTvis individualurad.

20

idealuri saSualeba mTel klasTan muSaobisaTvis aris magnituri dafa da minimum ori sxvadasxva

feris magnituri rgolebi.

aseT dros maswavlebels SeuZlia dafasTan rigrigobiT gamoiyvanos moswavleebi da raode-

nobebTan dakavSirebuli davalebebi Seasrulebinos ise, rom mTeli klasi xedavdes. Tu skolas

magnituri dafa ara aqvs, maSin mis nacvlad SesaZlebelia Cveulebrivi liTonis Txeli furclis

gamoyeneba (minimaluri zoma 60X90 sm). mTavaria, garkveuli samuSaoebi da davalebebi yvelas Tval-

win sruldebodes konkretuli sagnebis gamoyenebiT.

garda magnituri rgolebisa (an nebismieri brtyeli sagnisa, romelsac patara magniti aqvs ukan,

raTa dafas miekras da ar Camovardes), maswavlebels aucileblad sWirdeba baraTebi, minimum 10

smX15 sm-ze zomis muyaos an qaRaldis furceli, romelzedac iqneba gamosaxuli maTematikuri

simboloebi (+, - , <, >, =) da ricxvebi (0-dan 20-mde).

1

2

3

5

7

4

=

+

-

<

>

damatebiTi TvalsaCinoebisaTvis kargia baraTebi, romlebzedac gamosaxulia konkretuli

raodenobebi (magaliTad, 5 rgoli, 4 wre, 3 varskvlavi da a.S.).

21

aseve sasargebloa e.w. „maTematikuri kamaTeli“ – kubi, romelsac waxnagebze aweria +1, +2, +3

(ix. maTematikuri TamaSebi da aqtivobebi).

garda amisa, umniSvnelovanesia, rom TiToeul moswavles

hqondes erTgvarovani sagnebis garkveuli raodenoba (es

raodenoba damokidebulia imaze, romel klasSi arian. pir-

velklaselebs 20-20 saganic eyofaT, meoreklaselebs 100-100

sWirdebaT, xolo mesameklaselebs 1000-1000. es SeiZleba iyos

nebismieri sagani: simindis an lobios marcvlebi, plastmasis

boTlebis Tavsaxurebi, legos naWrebi, Cxirebi, Rilebi da a.S.

rac ufro mravalferovania es sagnebi, miT ukeTesi Sedegi

eqneba maswavlebels maTematikis swavlebisas.

22

garda am sagnebisa, maswavlebels dasWirdeba kedlebze sxvadasxva tipis maTematikuri Sinaar-

sis xelnakeTi posterebis gakvra (es yvelaferi SesaZlebelia klasSive damzaddes) imis mixedviT,

romel klasSi arian moswavleebi: ricxvTa RerZi, geometriuli figurebi saxelebiT, isrebiani

saaTi sxvadasxva poziciaSi, didi kalendari, erovnuli fulis niSnebi (gadidebulad amobeWdili

printerze an daxatuli), Sekreba-gamoklebis cxrili (gamravlebis cxrili me-3 klasidan) da a.S.

cnobilia, rom maTematikuri SinaarsiT datvirTuli saklaso garemo arsebiTad aumjobesebs

moswavleTa Sedegebs.

23

maTematikuri TamaSebi da aqtivobebiam TamaSebisa da aqtivobebis gamoyeneba sasurvelia minimum yovel meore dRes.

1. damaluli ricxvebis gamocnoba

dagWirdebaT baraTebi (zoma minimum 10sm 10 sm-ze), romlebzedac aweria ricxvebi cifrebiT,

im farglebSi, ra farglebSic bavSvebma ician raodenobebi. Tavdapirvelad es iqneba 1-dan 10-mde,

mogvianebiT ki 1-dan 20-mde.

101

2

3

6

moaTavseT baraTebi dafaze ise, rom zogierTi ricxvi moCandes, xolo zogi baraTi Setriale-

buli iyos. miuTiTeT romelime Setrialebul baraTze da hkiTxeT klass, ra ricxvi SeiZleba iyos

baraTis ukan. Tu romelime daasaxelebs iseT ricxvs, rac ukve amotrialebulia, vuTiTebT am

ricxvze da veubnebiT, rom ukve Cans. Tu gansxvavebul ricxvs daasaxelebs, amoatrialebT baraTs

da Tu ricxvi daemTxva, SeaqebT moswavles sworad gamocnobisaTvis.

ase vagrZelebT manam, sanam yvela baraTi ar iqneba amocnobili.

2.maTematikuri domino (TamaSi mcire jgufebSi)

dayaviT klasi mcire jgufebad da TiToeul jgufi moaTavseT calke magidasTan.

maswavlebels winaswar momzadebuli unda hqondes dominos msgavsi baraTebi (zoma 15sm 20 sm-ze),

romlis orive nawilSi aris ricxvebi, oRond Cawerili sxvadasxvagvarad: Tu erT mxares cifrebiT

weria, meore mxares sityviT anda wertilebiT unda iyos gamosaxuli. amave dros marcxena da mar-

jvena mxares raodenobebi ar unda emTxveodes.

magaliTad ase:

1 ori oTxi 5TiToeul jgufs unda daurigdes erTi dasta da es dasta moaTavseT piriT magidisken. yovelma

moTamaSem unda aiRos erTi baraTi. jgufidan TamaSs iwyebs is, visac yvelaze didi ricxvi Sexvdeba

(sul erTia, baraTis romel mxaresaa es raodenoba). moTamaSe debs Tavis baraTs magidaze da iRebs

axals. axla Semdegi moTamaSis jeria (rigiToba ganisazRvreba magaliTad saaTis isris moZraobis

mimarTulebiT an piriqiT). es moTamaSe Tavis baraTs Sexedavs da Tu masze aris ricxvi, romelic

ukve moCans wina baraTze, miudebs gverdiT da aiRebs axal baraTs. Tu ricxvi ar daemTxva, axal

baraTs mainc aiRebs dastidan da Semdegi moTamaSe agrZelebs.

24

4

0 32

xu

Ti

TamaSi dasruldeba, rodesac dastaSi baraTebi amoiwureba. gamarjvebulia is moswavle, romel-

sac yvelaze naklebi raodenobis baraTi eqneba xelSi.

3.10-mde Sevseba

TamaSi mimdinareobs mcire jgufebSi.

TiToeul jgufs urigdeba baraTebis dasta (daaxloebiT banqos qaRaldis zomis baraTebi), zed

dawerili cifrebiT. garda am dastisa, maswavlebeli magidaze dadebs 12 baraTs, romlebzedac

moCans Semdegi ricxvebi:

1

2

4

5

6

8

3

2

9

1

7

8moTamaSeebi rigrigobiT iReben dastidan baraTebs. Tu baraTze iseTi ricxvia, rom romelime

baraTTan wyvilSi 10-s Seadgens, moTamaSe am wyvils TavisTan idebs. Tu ar daemTxva, Tavis baraT-

sac magidaze debs.

aseve agrZelebs momdevno moTamaSe.

rodesac dasta amoiwureba, moTamaSeebi magididan iReben iseT wyvils, romelic 10-s Seadgens.

gamarjvebulia moswavle, romelsac yvelaze meti baraTi eqneba mogrovebuli.

4. maTematikuri domino 10-mde SevsebiT

TamaSi mcire jgufebSi (3-4 bavSvi) mimdinareobs. gamoiyeneba iseTive baraTebi, rogoric me-2

aqtivobaSi.

TiToeul moTamaSes urigdeba 3-3 baraTi, erTi baraTi magidaze daideba, xolo danarCeni dasta

piriT magidisken moTavsdeba. TamaSs iwyebs erT-erTi da Tavisi romelime baraTidan irCevs iseTs,

romelic magidaze moTavsebul baraTs uwyvildeba (wyvili Sedgens 10-s). am baraTs magidaze miu-

debs meore baraTs. baraTebi ise unda moTavsdes, rom 10-is Semadgeneli wyvili gverdigverd iyos.

TamaSi mTavrdeba, rodesac arc erT moTamaSes aRar aqvs iseTi baraTi, romelic magidis baraTebs

uwyvildeba.

gamarjvebulia is moswavle, romelsac arc erTi baraTi ar eqneba, an is moswavle, romelsac

yvelaze cota baraTi darCeba.

25

5. maTematikuri kamaTeli

am aqtivobisaTvis saWiroa mcire zomis kubi, romelsac waxnagebze dawerili eqneba „+1“,

„+2“ da „+3“ (or-ori warwera)

dayaviT moswavleebi jgufebad da TiToeul jgufs mianiWeT romelime cxovelis saxeli (maga-

liTad: zRarbi, Tevzi, cxvari da a.S.) sasurvelia am cxovelis suraTi gqondeT da jgufs daudoT,

rom ar agerioT.

dafaze ganalageT baraTebi ricxvebiT 0-dan 10-mde. cxovelebis suraTebi an saxelebi moaTavseT

vertikalur svetSi:

0 1 2 3 4 5 6 7 8 9 10

26

TamaSs iwyebs erT-erTi gundi. maTi romelime wevri agorebs kubs. imis mixedviT, ra mouvaT (1,2

Tu 3) maTi gundis suraTi gadaiwevs amdenive danayofiT.

magaliTad, Tu pirvelad zRarbebma gaagores +2, maSin dafaze maTi saxeli ase gadaiwevs:

0 1 2 3 4 5 6 7 8 9 10

amis Semdeg kubs agorebs Semdegi gundi da maTi saxeli gadaiwevs Sesabamisi raodenobis ujriT.

Tu romelime gundis saxeli moxvdeba iseT svetSi, romelic ukve dakavebulia, axali gundi

ikavebs am adgils, Zvelebi ki ubrundebian sawyis pozicias.

Tu romelime gunds mouva iseTi ricxvi, rom gadawevisas 10-s unda gadaaWarbos (magaliTad,

iyvnen 9-ze da mouvidaT +2), maSin brundebian 0-ze.

gamarjvebulia is gundi, romelic pirveli miaRwevs 10-s.

SeniSvna: imisaTvis, rom TamaSi metismetad didxans ar gagrZeldes, maswavlebels SeuZlia

garkveuli dro gamohyos da am drois gasvlis Semdeg gamarjvebuli iyos is gundi, romelic yvelaze

win iqneba.

6. magidis TamaSi ori sxvadasxva kamaTliT

TamaSisaTvis saWiroa qaRaldis didi furceli (minimum a3 formatis), romelzedac daixateba

daaxloebiT aseTi suraTi:

3 6 1 2 8 5 2 4

8 7 10 9 3 2 6 9

9 7 3 5 1 2

dasawyisi

6 3 8 10 7 10

27

aseve saWiroa ori kubi, romelTagan erTs waxnagebze aweria 1, 2, 3, 4, 5, 6 meores ki 0, 1, 2, 3, 4, 4.

dayaviT moswavleebi iseTi zomis jgufebad, rom TiToeulma jgufma moaxerxos komfortulad

TamaSi magidasTan. TiToeul moTamaSes urigdeba erTi, danarCenebisgan gansxvavebuli momcro

sagani (es SeiZleba iyos Cipi, Rili, moneta da a.S.).

TamaSis dawyebisas yvela Cipi unda moTavsdes im adgilas, sadac aweria „dasawyisi“. TiToeuli

moswavle, rodesac misi rigi modis, agorebs kubebs erTdroulad. daiTvleba orive kubis ricx-

vebis jami da Tu es jami emTxveva romelime ricxvs momdevno kvadratSi, moswavlis Cipi gadadis im

ricxvze. Tu ar daemTxveva, Cipi adgilze rCeba. erT kvadratSi SeiZleba erTdroulad ramdenime

Cipi aRmoCndes da es dasaSvebia wesebiT.

amis Semdeg gagorebebi grZeldeba, sanam romelime moswavlis Cipi ar miaRwevs bolo kvadrats.

7.TamaSi Sekrebis/gamoklebis damaxsovrebaze

maswavlebels esaWiroeba baraTebi, romlebzedac erT mxares aweria Sekrebebi/gamoklebebi 5-is

farglebSi (yvela SesaZlo varianti), xolo ukana mxares pasuxebi.

wina mxare ukana mxare

4 + 1

5dayaviT moswavleebi or an sam nawilad, moaTavseT baraTebi dafaze.

gundebidan rigrigobiT gamodian moswavleebi da miuTiTeben romelime baraTze da amboben

pasuxs. baraTi amotrialdeba da Tu pasuxi daemTxva, gundma moipova erTi qula.

rodesac yvela baraTi amotrialdeba, SesaZlebelia isev Setrialeba da TamaSis manam gagrZeleba,

sanam maswavlebeli dasrulebas saWirod ar CaTvlis.

28

zepiri angariSis strategiebikidev erTi mniSvnelovani problema, romelic yovelTvis dgas maTematikis swavlebisas, gaxlavT

e.w. zepiri angariSi. winamdebare saxelmZRvaneloebiT pirvel sam klasSi zepir angariSs eTmoba

yoveldRiurad daaxloebiT 5 wuTi: 3 wuTi gakveTilis dawyebisas da 2 wuTi gakveTilis msvlelo-

bisas. zepir angariSSi varjiSi gansakuTrebiT sasargebloa xolme, rodesac maswavlebels klasis

erTbaSad mobilizeba sWirdeba. am dros frontaluri kiTxvebis dasmiT an rigebs Soris Sejibris

mowyobiT (am yvelafers metismetad didi dro ar unda daeTmos, maqsimum zedized – 5 wuTi) yvela

moswavlis erTdrouli, mobilizebuli CarTva xdeba da Zalian advilia momdevno Temaze gadasvla.

amitomac, nebismier momentSi SeiZleba misi gamo yeneba. mTavaria, maswavlebelma ar gadaamlaSos.

zepir angariSSi varjiSi aucileblad umartivesi SekiTxvebiT unda daiwyos. Tanac jer unda

vkiTxoT `Zlier~ moswavleebs (es imisTvisaa, rom dasawyisi warmatebuli gamovides da es warmateba

yvelas gadaedos). SekiTxvebi nel-nela unda garTuldes.

maswavleblis moqmedeba sami mimarTulebiT SeiZleba warimarTos:

a) kiTxva-pasuxi frontalurad

b) wyvilebSi muSaoba

g) rigebs Soris Sejibri

am sami mimarTulebidan TiTo jerze mxolod erTis gamoyenebaa mizanSewonili.

sul gamoiyeneba 5 tipis SekiTxva.

SekiTxvebis tipebi:

1. TvlasTan da numeraciasTan dakavSirebuli SekiTxvebi

magaliTad: `daTvale 7-dan 12-mde~, `daTvale 18-dan 28-mde TiTos gamotovebiT~, `gaagrZele

daTvla: 10, 13, 16, 19, .....~, `daTvale ukuRma 20-dan 9-mde~ da a.S.

2. SedarebebTan dakavSirebuli SekiTxvebi

magaliTad: `romelia meti: 17 Tu 27~, `romelia 9-ze 2-iT meti ricxvi~, `romeli ricxvia 20-is

win?~, `daasaxele 40-is wina da momdevno ricxvebi~.

3. ricxvebis SekrebasTan dakavSirebuli SekiTxvebi

magaliTad: `ramdenia 5-s davumatoT 7?~, `ramdenia/ras udris 6-is da 9-is jami~, `pirveli

Sesakrebia 20, meore 10, ramdenia jami?~

4. gamoklebasTan dakavSirebuli SekiTxvebi

magaliTad: `ramdenia 5-s gamovakloT 3?~, `ramdenia/ras udris 16-is da 9-is sxvaoba~, `saklebia

20, maklebi 10, ramdenia sxvaoba?~

5. gamravlebasTan dakavSirebuli SekiTxvebi

magaliTad: `ramdenia 5 gavamravloT 3-ze?~, `ramdenia/ras udris 2-is da 3-is namravli~, `sam-

ravlia 10, mamravli 2, ramdenia namravli?~ `ramdenia 2-jer 3?~

masala pirobiTad SeiZleba davyoT ramdenime doned. imis mixedviT, romel klasSi arian mos-

wavleebi (anda rogoria klasis saerTo mdgomareoba), maswavlebeli Sesabamisi donis masalidan

iRebs SekiTxvebs.

araviTar SemTxvevaSi ar SeiZleba SekiTxvebSi im masalis CarTva, romelsac im dros gadian mos-

wavleebi (magaliTad, Tu Seiswavleba 10-is farglebSi Sekreba-gamokleba, zepiri angariSis dros

ar unda gamoiyenoT SekiTxvebi am masalidan, aramed 5-is farglebidan).

I done 5-is fargali

daTvla X-dan X-mde; romelia meti? (3 Tu 5)1+2 da a.S.5-3 da a.S.5-mde Sevseba.

II done 10-is fargali

daTvla X-dan X-mderomelia meti? (8 Tu 9)1-is damateba1-is gamokleba2-is damateba2-is gamokleba da a.S.10-mde Sevseba

III done 20-is fargali

daTvla X-dan X-mdeX-dan X-mde ukuRma daTvlaTiTos gamotovebiT daTvlaromelia meti? (14 Tu 17)1-iT meti da 1-iT naklebi (16-ze 1-iT meti, 15-ze 1-iT naklebi)2-iT meti da 2-iT naklebi (16-ze 2-iT meti, 15-ze 2-iT naklebi)1-is damateba1-is gamokleba2-is damateba2-is gamokleba10-is damateba (5+ 10, 8+ 10)10-is gamokleba (12-10, 18-10)10-ze damateba (10+3, 10+6)mcire raodenobebis gamokleba (19-5)mcire raodenobebis damateba (12+4)Sekreba aTeulis warmoqmniT (7+5)mcire raodenobis gamokleba aTeulis daSliT (12-5)gamokleba (18-13)gamokleba aTeulis daSliT (13-8)

IV done 100-is fargali

DAdaTvla X-dan X-mdeaTeulebad daTvlaxuTeulebad daTvlaTiTos gamotovebiT daTvlaor-oris gamotovebiT daTvlaX-da X –mde ukuRma daTvlaromelia meti? (14 Tu 17, 56 Tu 65)aTeulebis Sekreba-gamokleba (20+30, 80-60)1-iT meti da 1-iT naklebi (26-ze 1-iT meti, 45-ze 1-iT naklebi)2-iT meti da 2-iT naklebi (26-ze 2-iT meti, 45-ze 2-iT naklebi)3-is damateba (25+3)3-is gamokleba (29-3)aTeulebze damateba (20+3, 40+7)aTeulebis damateba (15+20, 27+30)aTeulebis gamokleba (47-10, 89-40)aTeulebidan mcire raod. gamokleba (40-6, 70-8)Sekreba aTeulis warmoqmniT (25+7, 56+9)gamokleba aTeulis daSliT (42-4, 35-8)

iwyeba da mTavrde-ba pirveli klasis I

semestrSi

iwyeba pirveli kla-sis II semestridan da dasruldeba semes-

tris miwuruls

iwyeba 1-li klasis bolos da dasrul-deba me-2 klasis I semestris SuaSi

iwyeba me-2 klasis I semestrSi da das-

ruldeba me-3 klasis I semestrSi

30

V done1000-is farga-

li

daTvla X-dan X-mdeaTeulebad da aseulebad daTvlaxuTeulebad daTvlaTiTos gamotovebiT daTvlaor-oris gamotovebiT daTvlaX-da X –mde ukuRma daTvla

romelia meti? (142 Tu 171, 656 Tu 565)aseulebis Sekreba-gamokleba (200+300, 800-600)1-iT meti da 1-iT naklebi (216-ze 1-iT meti, 415-ze 1-iT naklebi)2-iT meti da 2-iT naklebi (216-ze 2-iT meti, 415-ze 2-iT naklebi)3-is damateba (215+3)3-is gamokleba (219-3)aseulebze damateba (200+12, 300+48)aTeulebis damateba (115+20, 247+30)aTeulebis gamokleba (447-10, 879-40)aseulebidan mcire raod. gamokleba (400-6, 700-8)Sekreba aseulis warmoqmniT (275+72, 566+91)gamokleba aseulis daSliT (420-44, 350-82)

gamravlebis cxrili (3X5, 7X9)aTeulebis gamravleba (20X3, 40X2)aseulebis gamravleba (100X3, 200X4)100-mde ricxvebis gamravleba (27X4, 45X6)1000-mde ricxvebis gamravleba (137X6, 236X3)

iwyeba me-3 klasis II semestrSi da das-ruldeba me-4 kla-

sis I semestrSi

31

teqstiani amocanebis swavlebateqstiani amocanebis, an rogorc mokled uwodeben xolme, amocanebis amoxsnas sakmaod did

dros uTmobs bevri maswavlebeli.

zogierT SemTxvevaSi maswavleblebi sTxoven moswavleebs, srulad gadaiweron amocanis teqsti

da mxolod amis Semdeg daiwyon misi amoxsna. ra Tqma unda, amocanis teqstis srulad gadaweras

araviTari mniSvneloba ara aqvs teqstis gasagebad. SeiZleba bavSvma gadaiweros teqsti, magram

mainc ver gaigos, ras ekiTxebian da piriqiT.

Cveni rekomendaciaa, ar daakargvinoT moswavleebs ZviradRirebuli dro amocanis teqstis

gadaweraze.

imisaTvis, rom amocana amoxsnas, moswavles unda SeeZlos erTmaneTisagan ganacalkevos amocanis

piroba da SekiTxva da SeeZlos, amocanis pirobaSi mocemuli monacemebis analizi da dakavSireba

SekiTxvasTan.

Tavdapirvelad unda aRiniSnos, rom amocanebis sistemuri Seswavla Cveni saxelmZRvaneloe-

bis mixedviT iwyeba me-4 klasidan. es ar niSnavs, rom amocanebi amogdebulia pirveli sami wlis

saxelmZRvaneloebidan. es niSnavs, rom Tavad moswavlis wignebSi teqstiani amocanebi naklebadaa,

samagierod danarTis saxiT SegiZliaT ixiloT me-2 da me-3 klasebis maswavleblis wignebSi.

amocanebis amoxsna Semodis etapobrivad:

pirvel klasSi maswavlebeli zepirad eubneba moswavleebs (an Tavad ukiTxavs) amocanebs. am

etapze araa saWiro imis axsna, Tu rogor, ra formiT unda Caiweros amocanis amoxsna. amocanebis

amoxsna xdeba vizualizaciis saSualebiT (ix. qvemoT).

meore klasSi ukve dgeba etapi, rodesac moswavles SeuZlia gamarTulad, damoukideblad kiTxva

da Sesabamisad, SegviZlia mivceT teqstiani amocanebi, raTa man Tavad waikiTxos da modelirebis

(ix. qvemoT) gamoyenebiT amoxsnas. sul arsebobs amocanis ramdenime modeli da Cveni mizania, mos-

wavle mivaCvioT modelis sworad misadagebas amocanasTan. man yuradRebiT unda waikiTxos piroba

da Seqmnas modelis naxazi.

meore klasis bolos (kerZod, me-7, boloswina Tavidan) iwyeba momdevno etapi amocanis amoxsnis

swavlebaSi, rodesac ukve simboloebis saSualebiT xdeba rogorc pirobis, ise amocanis amoxsnis

Cawera.

simboloebiT Caweraze gadasvla ar niSnavs modelirebaze uaris Tqmas. modelis daxatva ar unda

Sewydes momdevno klasebSic.

Tavdapirvelad saWiroa muSaoba imaze, rom moswavlem teqstidan gamoyos piroba da SekiTxva.

amis Semdeg vaswavliT, rogor unda amokribos monacemebi pirobidan da rogor gaakeTos Semok-

lebuli Canaweri; agreTve gansazRvros, rame monacemi xom ar aklia pirobas, an zedmeti xom araa.

mxolod am yvelafris Semdeg gadavdivarT simboloebiT Caweraze.

anu amocanis amoxsnis swavleba gulisxmobs sam etaps:

1-li etapi aris amocanis vizualizacia anu amocanis pirobebis gadmocema xiluli obieqtebis

(iqneba es qaRaldis zolebi, Cxirebi Tu raime sxva fizikuri obieqti) saSualebiT. (1-li klasi)

me-2 etapia amocanis modelis Seqmna naxazze. (me-2 klasidan)

me-3 etapia amocanis amoxsnis Cawera simboloebis (cifrebisa da moqmedebaTa niSnebis saSualebiT)

(me-2 klasis bolodan)

ra aris amocanis vizualizacia?

vTqvaT, pirveli klasis moswavleebs maswavlebeli eubneba amocanas:

„gegas 5 saTamaSo aqvs, xolo Tikos 4 saTamaSo. ramdeni saTamaSo aqvs orives erTad?“

imisaTvis, rom moswavleebma ukeT warmoidginon amocana, maswavlebeli dafaze alagebs Sesa-

bamis raodenobebs:

32

jer dadebs 5 rgols da ambobs:

– es gegas saTamaSoebia.

mere dadebs 4 sxva feris rgols da ambobs:

– es Tikos saTamaSoebia.

– ras gvekiTxebian? (ramdeni saTamaSo aqvs orives erTad)

– ra unda vqnaT, rogor gavigoT? (SevkriboT)

– sworia (maswavlebeli SeaerTebs grovebs)

– vin daTvlis, ramdeni saTamaSo hqonia orives erTad?

analogiurad gakeTdeba msgavsi amocanebi moswavleebis mier individualurad, merxebze. maswav-

lebeli ambobs amocanas da moswavleebi Sesabamisi raodenobis sagnebs alageben TavianT merxebze.

amocanis modelireba

amocanis gagebis da amoxsnis momdevno etapia amocanis modelireba. modelis daxatva Zalian

efeqturi strategiaa amocanis amosaxsnelad. garda amisa, modelebis gamoyeneba karg safuZvels

uyris samomavlod algebris Seswavlas.

sul arsebobs ramdenime sxvadasxva tipis modeli, romelTa daxmarebiTac moswavle amocanas

advilad amoxsnis.

modeli 1. SekrebasTan dakavSirebuli amocana

erT Taroze 30 wignia, meoreze – 25 wigni. ramdeni wignia orive Taroze erTad?

30 25>?

30 + 25 = 55

modeli 2. gamoklebasTan dakavSirebuli amocana

Tamars da nikas erTad 70 saTamaSo aqvT. ramdeni saTamaSo aqvs Tamars, Tu nikas aqvs 40 saTamaSo?

40 ?>70

70 – 40 = 30

modeli 3. SedarebasTan dakavSirebuli amocana

dawyebiT skolaSi swavlobs 90 gogona da 75 biWi. ramdeniT meti gogona swavlobs dawyebiT

skolaSi?

gogonebi 90

biWebi 75 > ?

90 – 75 = 15

33

modeli 4. Sedareba SekrebiT an gamoklebiT

saTamaSo manqana 25 lari Rirs, xolo molaparake Tojina 15 lariT meti. ra Rirs Tojina?

manqana 25

Tojina 15 > ?

25 + 15 = 40

modeli 5. gamravlebasTn dakavSirebuli amocanebi

leqsom iyida 6 vaSli, 3-jer meti msxali vidre vaSli da 2-jer meti gargari, vidre msxali. sul

ramdeni sxvadasxva xili uyidia leqsos?

vaSli 6

msxali 2 ?

gargari

6 • 10 = 60

modeli 6. gamravleba da Sedareba

pirvel klasSi 15 moswavlea, meore klasSi 5-iT meti moswavlea vidre pirvel klasSi, xolo

mesame klasSi 3-jer meti moswavlea, vidre pirvel klasSi. ramdeni moswavlea samive klasSi erTad?

1-li klasi 15

me-2 klasi 5 2 ?

me-3 klasi

5 • 15 + 5 = 80

arsebobs kidev ramdenime sxva modelic, magram es 6 modeli aris sabaziso da amocanebis umrav-

lesoba maTi an maTi variaciebis gamoyenebiT ixsneba.

34

beWduri da eleqtronuli resursebi, romelTa gamoyeneba SesaZlebelia

saswavlo procesSi

maTematikuri TamaSebi

1. http://kargiskola.ge/teacherintro/teacher-kompiuteruli-tamashebi.php

aq mocemulia ramdenime kompiuteruli saganmanaTleblo TamaSi, romelTa gamoyeneba SesaZle-

belia pirveli klasis maTematikis gakveTilebze. kerZod, maSin, rodesac Seiswavleba raodenobebis

Sedareba, moqmedebebi ricxvebze da grovebidan Tanabari jgufebis gamoyofa.

2. http://buki.ge/programs-list.html

kompiuteruli maTematikuri TamaSebi. maTi gamoyeneba SesaZlebelia ricxvebis da ricxvebze

moqmedebebis Seswavlisas.

3. https://learningapps.org/1774684

es aris saganmanaTleblo aplikacia da misi daxmarebiT Seiswavleba ricxvebi da ricxvebze

moqmedebebi 10-is farglebSi.

amave saitze aris kidev sxva resursebi, romelTa gamoyeneba SesaZlebelia pirvel klasSi.

beWduri resursebi

1. http://kargiskola.ge/SC/tempmath.php

aq mocemulia saqarTvelos erovnuli saswavlo gegmis Sedegebisa da indikatorebis Sesabamisad

Seqmnili testebi maTematikaSi dawyebiTi klasebisaTvis. SesaZlebelia eleqtronulad mocemuli

testebis amobeWdva da moswavleebisaTvis darigeba.

2. avtorTa jgufi. testebis rveuli maTematikaSi. 1-li klasi. Tbilisi, 2018

testebis es rveuli, romelic axlaxan gamoica, moicavs 7 tests erovnuli saswavlo gegmis 7

Sedegis Sesabamisad. TiToeuli testis nawilebi indikatorebis mixedviTaa dayofili da maswavleb-

els saSualebas aZlevs, Semajamebeli Sefaseba, romelic werilobiT iwereba, iolad Seasrulobs.

35

saproeqto davalebebi pirvel klasSi qvemoT mocemulia ori saproeqto davaleba, romlebic sruldeba pirvel da meore semestrebSi.

1. maTematika Cven garSemo (piradi bloknoti)

daavaleT moswavleebs, SeiZinon an TavianTi xeliT daamzadon Txeli bloknotebi, romlebsac

garekanze daakraven ferad furcels da daaweren:

maTematika Cven garSemo

Cveni mizania, pirvelklasels vaswavloT, „SeamCnios“ maTematika yoveldRiur cxovrebaSi

da Tavisi dakvirvebebi „aRnusxos“. iseTi maTematikuri sakiTxebi, rogorebicaa: formebi, dro,

ricxvebi da fuli, bavSvebs yovel fexis nabijze xvdebaT. moswavlem bloknotSi unda Caiweros/

Caixatos maTematikasTan dakavSirebuli Tavisi gamocdilebebi; magaliTad: erT gverdze SeuZlia,

daxatos, rogoria saaTi, romelic sadilis dros aCvenebs, meore gverdze - Tavis mier Segrovebuli

monetebi, mesame gverdze - Jurnal-gazeTebidan amoWrili Senobebis fotoebi, romlebic sxvadasxva

geometriul figuras mogvagonebs da a. S.

proeqti minimum erT Tves unda gagrZeldes. bavSvebi nel-nela avseben bloknotebs, bolos ki

ewyoba gamofena.

2. aplikaciebi geometriuli figurebiT

moswavleebs urigdebaT feradi furclebi, raTa gamoWran sxvadasxva zomis geometriuli fig-

urebi: samkuTxedebi, kvadratebi, wreebi, marTkuTxedebi, xuTkuTxedebi. sanam gamoWras daiwyeben,

jer furclebze fanqriT unda daxazon es figurebi. maswavlebelma yvela moswavles individual-

urad unda Seumowmos, rom yvelaferi sworadaa daxazuli da figurebi sxvadasxva zomisaa.

geometriuli figurebis daxazvisa da gamoWris Semdeg, TiToeul moswavles urigdeba didi

zomis furceli, romelzec moswavle iwyebs aplikaciis keTebas geometriuli figurebiT.

moswavleebi furcelzeve xazaven cxrils, romelSic monacemebia imis Sesaxeb, ramdeni samkuTxe-

di, oTxkuTxedi da a.S aris maT mier momzadebul aplikaciaze.

36

moswavleTa Sefaseba maTematikis swavlebisas

erovnuli saswavlo gegmis Tanaxmad moswavleTa Sefaseba SeiZleba iyos ori tipis: ganmsaz-

Rvreli da ganmaviTarebeli.

ganmsazRvreli Sefaseba adgens moswavlis miRwevis dones sagnobrivi saswavlo gegmis SedegebTan

mimarTebaSi, xolo ganmaviTarebeli Sefaseba adgens TiToeuli moswavlis ganviTarebis dinamikas

da mimarTulia swavlis xarisxis gaumjobesebaze.

dawyebiTi skolis pirveli oTxi klasis da mexuTe klasis pirveli semestris ganmavlobaSi

ganmsazRvreli Sefaseba ar gamoiyeneba. wlis bolos sagnis maswavlebelma unda daweros moswavlis

mokle werilobiTi Sefaseba, romelSic daaxasiaTebs moswavles, aRniSnavs mis warmatebebs da miu-

TiTebs, raSi sWirdeba moswavles daxmareba sakuTari SesaZleblobebis ukeT gamosavlenad. xolo

swavlis mimdinareobisas is iyenebs mxolod ganmaviTarebel Sefasebas (ix. qvemoT).

imisaTvis, rom maswavlebels gauadvildes wlis bolos dasaweri werilobiTi Sefasebis Seqmna,

qvemoT mokled CamovayalibebT e.w. rubrikebs SefasebisaTvis.

magaliTisaTvis aviRoT erovnuli saswavlo gegmiT gansazRvruli romelime Sedegi, vTqvaT,

maT. 1.1 moswavles SeuZlia, erTmaneTs Seusabamos ricxvebi, ricxviTi saxelebi da raodenobebi

imisaTvis, rom SevamowmoT, gavediT Tu ara am Sedegze, pirvel yovlisa, saWiroa iseTi davale-

bebis SerCeva, romlebic am Sedegis Sesabamis sxvadasxva indikators miemarTeba. am davalebebis

SerCeva SeiZleba rogorc moswavlis rveulidan (ix. standartis Sedegis miRwevisa da saxelmZR-

vanelos Sinaarsis urTierTkavSiris matrica), ise, vTqvaT, gv. 34-ze mocemuli beWduri resurse-

bidan. magaliTad:

5 12 3 13

2. დათვალე და მიუწერე, რამდენია.

xazebiT daakavSire ricxvi raodenobasTan

bunebrivia, bavSvebi sxvadasxvagvari warmatebiT arTmeven Tavs am davalebebis Sesrulebas.

zogierTi maTgani saerTod ver axerxebs erTmaneTs Seusabamos ricxvebi, ricxviTi saxelebi da

raodenobebi; zogi amas axerxebs nawilobriv; zogierTs srulad gamosdis, Tumca epareba meqani-

kuri Secdomebi; zogierTi bavSvi ki davalebas srulyofilad asrulebs.

rubrikebi Sesabamisad iqneba:

sami Tormeti xuTi cameti

37

uWirs, erTmaneTs

Seusabamos ricxvebi,

ricxviTi saxelebi da

raodenobebi

erTmaneTs usabamebs

ricxvebs, ricxviT

saxelebs da raode-

nobebs, Tumca amas

andomebs Zalian did

dros da xSirad uSvebs

Secdomebs

erTmaneTs usabamebs

ricxvebs, ricxviT

saxelebs da raode-

nobebs, Tumca xandaxan

uSvebs meqanikur Sec-

domas

erTmaneTs uSecdo-

mod da swrafad usa-

bamebs ricxvebs, ricxviT

saxelebs da raode-

nobebs

imis mixedviT, rogori namuSevari hqonda moswavles, maswavlebeli Sesabamis rubrikas SearCevs

da Tavis saboloo werilobiT SefasebaSi gamoiyenebs.

Semajamebeli Sefasebis davalebebi da Sefasebis rubrike-bi pirvel klasSi

qvemoT sanimuSod mocemulia ori sxvadasxva tipis Semajamebeli davaleba. orive davalebaSi

kombinirebulia esg-s ramdenime sxvadasxva Sedegi.

pirvel davalebaSi moswavlem naxatSi unda amoicnos geometriuli figurebi, gadaTvalos da

monacemebi amoiweros.

meore davaleba teqsturi saxisaa.

davaleba 1.

daTvale naxazze figurebi da miuwere, romeli ramdenia.

38

Sefasebis rubrika

uWirs geometriuli

figurebis amocnoba, ver

axerxebs maT gadaTvlas

da Caweras

axerxebs figurebis

umetesobis amocnobas,

Secdomebs uSvebs maTi

gadaTvlisas da Cawer-

isas

kargad axerxebs

figurebis amocnobas

naxazze, magram gadaT-

vlisas da Cawerisas

zog monacemSi epareba

Secdoma

srulyofilad amoic-

nobs figurebs naxazze

da uSecdomod iTvlis

da iwers maT raodenobas

davaleba 2.

ninos dabadebis dReze buStebi aCuqes: 6 wiTeli buSti da 4-iT meti mwvane buSti. daxate ninos

yvela buSti. sul ramdeni buSti aqvs ninos?

Sefasebis rubrikaaqtivoba

amocanis piro-

bis gageba-gaazreba

ver axerxebs

amocanis pirobis

amokiTxvas da gaaz-

rebas

axerxebs piro-

bis amokiTxvas,

magram ver iazrebs,

ra unda gaakeTos

gamarTulad

axerxebs pirobis

amokiTxvas da iaz-

rebs kidec, Tumca

Secdomas uSvebs

„-iT metis“-s gage-

bisas.

srulyofilad

igebs amocanis

pirobas

amocanis amoxs-

na da pasuxis miReba

ver axerxebs

amocanis amoxsnas

da pasuxis miRebas

maswavleblis

daxmarebiT axerx-

ebs naxatis Seqmnas

da pasuxis Caweras

damoukideblad

axerxebs amocanis

amoxsnas da naxatis

Seqmnas, magram ver

iRebs zust pasuxs

uSecdomod

akeTebs Sesabamis

Canawers.

39

ganmaviTarebeli Sefaseba

gamocdili maswavleblebi xSirad iyeneben ganmaviTarebel Sefasebas, Tumca zogjer ar arqmeven

am saxels da ar gamoyofen calke, rogorc swavlebisaTvis mniSvnelovan komponents.

ganmaviTarebeli Sefaseba aris procesi, romelic gulisxmobs sxvadasxva aqtivobiT, swavlebis

meTodiTa Tu sxva saSualebebiT informaciis mopovebas moswavleTa mier masalis gagebis/gaazrebis

Sesaxeb da am informaciis gamoyenebas maTi progresis xelSesawyobad.

ganmaviTarebeli Sefaseba maswavlebels saSualebas aZlevs, Seamowmos moswavleebis gagebis/

gaazrebis done da Sesabamisad dagegmos swavlebis procesi. maswavlebels SeuZlia, dafiqrdes

saswavlo praqtikaze da TiToeuli bavSvis miRwevebze; imaze, Tu ra daexmareba mas TiToeuli

moswavlis saWiroebebis dakmayofilebaSi.

nebismieri aqtivoba Tu strategia ganmaviTarebeli Sefasebis instrumenti xdeba mxolod maSin,

Tuki maswavlebeli da moswavle (garda imisa, rom gaarkveven, rogoria moswavlis progresi, ras

ver igebs is) ipovian gzebs, rogor unda gaiazros moswavlem esa Tu is sakiTxi. Sesabamisad, ganmavi-

Tarebeli Sefasebis verc erTi instrumentis gamoyeneba ver CaiTvleba efeqturad, Tuki saboloo

Sedegi ar iqneba sakiTxis/cnebis Rrmad gageba/gaazreba Tu unaris aTviseba.

qarTul enaze arsebobs ramdenime naSromi ganmaviTarebeli Sefasebis Sesaxeb.

am bmulze (http://mastsavlebeli.ge/?p=11953) SegiZliaT ixiloT s.gorgoZis statia „efeqturi

ganmaviTarebeli Sefaseba“, sadac ufro detaluradaa mocemuli qvemoT mocemuli strategiebi.

• Semajamebeli baraTebi

• kiTxvebis dasma

• auxseni Senze pataras

• TanatolTa Sefaseba

• teqnologiebi da ganmaviTarebeli Sefaseba

• komentari/ukukavSiri

• dakvirveba, rogorc ganmaviTarebeli Sefaseba

gakveTilebis scenarebi

yoveli gakveTili dayofilia ramdenime nawilad. gakveTilis

saTaurad miTiTebulia axali (ZiriTadi) masalis saxeli. TiToeuli

nawili dataluradaa aRwerili. sasurvelia, arc erT nawils ar daeT-

mos 10 wuTze meti. cxadia, SesaZlebelia am droiTi intervalidan

garkveuli gadaxvevebi. es praqtikosi maswavleblis gadasawyvetia

saklaso situaciidan gamomdinare.

yovel gverdze miTiTebulia gakveTilis rigiTi nomeri.

rCeva: ← am niSniT gamoyofilia praqtikuli rCevebi, romelTa

gaTvaliswinebac uzrunvelyofs sakiTxebis efeqtur swavlebas.

43

Tavi 1 ricxvebi 1-dan 5-mde

am Tavis mizania, moswavleebs SeeZloT:

y sivrceSi orientacia anu iseTi cnebebis sworad gamoyeneba praqtikul situaciebSi, rogore-

bicaa: zeviT, qveviT, marjvniv, marcxniv da SuaSi;

y raodenobebis Sedareba. iseTi raodenobebisac ki, romlebic jer ar uswavliaT. sxvadasxva

raodenobebis Sedarebisas dawyvilebis proceduris gamoyeneba da Semdeg daskvnis gakeTeba,

romelia meti da romeli – naklebi.

y met-naklebobisa da tolobis niSnebis sworad gamoyeneba rogorc saganTa grovebs Soris,

aseve raodenobebis simboloebs – cifrebs – Soris sworad CasmiT.

y erTidan xuTamde raodenobebis, maTi saxelebis da Sesabamisi simboloebis – cifrebis sworad

gamoyeneba, saxelis mixedviT cifris dawera; cifriT gamoxatuli raodenobis Sesabamisi

grovis Seqmna; konkretuli sagnebiT mocemuli raodenobis saxeldeba da cifrebiT Cawera.

y martivi geometriuli cnebebis sworad gamoyeneba: SigniT, gareT, wiri.

y cxrilebTan dakavSirebuli cnebebis sworad gamoyeneba: cxrilis striqoni, sveti, ujra.

I TavSi ar Seiswavleba moqmedebebi ricxvebze. es momdevno TavebSi xdeba.

gakveTilis N gakveTilis saTauri Sesabamisoba moswavlis wignTan Tavi I

gakv.1 marcxniv da marjvnivmoswavlis wigni: §1

gakv.2 marcxniv, marjvniv, SuaSi

gakv 3 zeviT, qveviT, SuaSi moswavlis wigni: §2

gakv 4 win, ukan moswavlis wigni: §3

gakv 5 met-naklebobis niSani moswavlis wignis gareSe

gakv 6 dawyvileba moswavlis wigni: §4

gakv 7 SigniT da gareT

moswavlis wigni: §5gakv 8 SigniT da gareT (rTuli wiri)

gakv 9 wiri. wertili wirze

gakv 10 striqoni da svetimoswavlis wigni: §6

gakv 11 cxrilis ujra

gakv 12 tolobis niSani moswavlis wignis gareSe

gakv 13 mimdevroba moswavlis wigni: §7

gakv 14 cifri 4 moswavlis wignis gareSe

gakv 15 cifri 1moswavlis wigni: §8

gakv 16 erTi

gakv 17 cifri 2 moswavlis wigni: §9

gakv 18 ori

gakv 19 cifri 3moswavlis wigni: §10

gakv 20 sami


gakv 22 oTxi


gakv 24 xuTi

gakv 25 met-naklebobis niSnis wera moswavlis wigni: §13

gakv 26 tolobis niSnis wera moswavlis wigni: §14

gakv 27 grovisa da cifris Sedareba moswavlis wignis gareSe

gakv 28 cifrebis Sedareba moswavlis wignis gareSe

gakv 29 Sedarebis Cawera simboloebiT moswavlis wignis gareSe

44

gakveTili 1: marcxniv da marjvniv

gakveTilis mizani moswavles SeeZlos cnebebis `marcxniv~ da `marjvniv~ sworad gamoyeneba

cxovrebiseul situaciebSi.

esg-s indikatori maT. I.7.3: sworad pasuxobs kiTxvebs obieqtTa urTierTmdebareobis (mar-

jvniv/marcxniv, zemoT/qvemoT, win/ukan) Sesaxeb.

pirveli gakveTiliT axali etapi iwyeba moswavlis cxovrebaSi. jerje-

robiT bavSvebi erTmaneTsac ki ar icnoben, ar ician klasSi moqcevis

wesebi (romelic maswavlebelma unda gaacnos). arc maswavlebeli

icnobs Tavis moswavleebs kargad.

amitom gakveTili unda daiwyos imis gamorkveviT, ra ician bavSvebma.

amisaTvis maswavlebeli SekiTxvebs svams da moswavleebis pasuxebis

mixedviT xvdeba, ramdenad kargad esmiT maT mcire raodenobebi.

pirvel gakveTilze arc saxelmZRvanelos vacnobT, radgan, rogorc

wesi, es dRe Zalian stresuli da emociuria bavSvebisaTvis da metis-

metad bevri axali informaciiT maTi gadatvirTva ar Rirs.

moswavleTa codnis donis garkvevamoswavleTa codnis donis gasarkvevad maswavlebeli ekiTxeba:

ramdeni Zma gyavs?

ramdeni da?

ramdeni xeli gaqvs?

ramdeni fexi?

ramdeni piri?

ramdeni TiTi xelze?

ramdeni kedelia klasSi?

ramdeni fanjaraa?

ramdeni rigia?

vin ufro maRalia, me Tu giorgi?

ra ufro maRalia, magida Tu merxi?

ra ufro grZelia, saxazavi Tu fanqari? da a.S.

rCeva: ar unda hkiTxoT raime, ris pasuxic xuTs aRemateba. am etapis

mizania moswavleTa gacnoba, imis dadgena, Tu raoden mtkiced ician maT

pirveli xuTi ricxvis dasaxeleba da mimdevroba.

sivrceSi orientacia. cnebebi „marcxniv“ da „marjvniv“am nawilis mizania imis gamorkveva, ramdenad kargad esmiT

moswavleebs iseTi cnebebis azri, rogoricaa „marjvniv“ da

„marcxniv“.

upirveles yovlisa, unda gamoarkvioT, ician Tu ara, romelia

marjvena xeli da romeli – marcxena.

– maCvene marjvena xeli! aba, axla Sen maCvene marjvena xeli!

y magnituri dafa

y magnituri rgolebi

resursebi

45

– aswie marcxena xeli! da a.S.

amis Semdeg gadavdivarT cnebebze „marjvniv“ da „marcxniv“.

maswavlebeli dafaze erTmaneTisagan moSorebiT ganalagebs

raime or gansxvavebul sagans (es SeiZleba iyos ori suraTi an

ori sxvadasxva feris magnituri rgoli) da ekiTxeba:

– romelia marjvniv?

– wiTeli rgoli marjvnivaa Tu marcxniv? da a.S.

imave SekiTxvebiT varkvevT, romeli fanjaraa marjvniv da

romeli – marcxniv.

marjvniv da marcxniv sakmaod rTuli cnebebia da maTi srul-

yo filad daufleba mTeli klasis mier erT gakveTilSi warmoud-

genelia. amitom am Temas momdevno gakveTilebzec drodadro

vubrundebiT.

met-naklebobis vizualurad dadgenadafaze maswavlebeli ganalagebs lurji da wiTeli magnitu-

ri rgolebis or grovas, ise, rom maTSi Zalian gansxvavebuli

raodenobebi iyos, magaliTad, lurji – 26 cali, wiTeli – 7

marjvniv ufro metia Tu marcxniv? romelia bevri, lurjebi

Tu wiTlebi? (lurjebi)

romelia cota? (wiTlebi)

romel grovaSia meti? (lurjebSi)

– romelSia naklebi? (wiTlebSi)

amis Semdeg sxva raodenobebs viRebT, magaliTad, 25 da 4 .

mTavaria, raodenobebi ise SevarCioT, rom maT Soris met-nak-

lebobis dadgena vizualurad umartivesi iyos.

meti raodenoba xan marcxniv unda iyos, xan – marjvniv.

araviTar SemTxvevaSi ar dauSvaT ricxvebis xseneba. gad-

awyvetilebis misaRebad sruliad sakmarisia mxolod Sexedva.

aq araviTari dasabuTeba saWiro ar aris. dafaze imitomaa es

raodenobebi, rom moswavlem mxolod SexedviT daaskvnas, Tu

romeli grovaa meti.

46

resursebi

y magnituri dafa

y magnituri rgolebi

gakveTili 2: marcxniv, marjvniv, SuaSi

gakveTilis mizani moswavles SeeZlos cnebebis `marcxniv~ da `marjvniv~ sworad gamoyeneba

cxovrebiseul situaciebSi.



sivrceSi orientacia. cnebebi „marcxniv“, „marjvniv“ da „SuaSi“isev viwyebT varjiSs sivrceSi orientaciaze da Semogvaqvs

axali cneba „SuaSi“. bunebrivia, bavSvebis umetesobam icis es

sityva, magram Cveni mizania ara am sityvis gacnoba, aramed imis

gamorkveva, ramdenad sworad SeuZliaT moswavleebs am sityvis

gamoyeneba praqtikul situaciaSi.

Tavdapirvelad yvelaferi keTdeba dafasTan, mTeli klasis

dasanaxad.

maswavlebeli dafaze moaTavsebs sam suraTs (magaliTad,

Tagvi, kata da ZaRli) da ekiTxeba:

– romelia marjvniv? romelia marcxniv? romelia SuaSi?

Semdeg sxva suraTebs ganalagebs an amave suraTebs adgilebs

Seucvlis da ekiTxeba:

– kata marjvnivaa, marcxniv Tu SuaSi? da a.S.

gamohyavs sami bavSvi da dafasTan daayenebs.

– romelia SuaSi? romelia Tqvengan marjvniv?

Zalian sasargebloa aseTi aqtivoba, saxelad „mouxvie mar-

jvniv/marcxniv“.

maswavlebels gamohyavs dafasTan erT-erTi moswavle. mos-

wavlem unda iaros da maswavleblis naTqvamze unda mouxvios an

marjvniv, an marcxniv.

am aqtivobis Sesruleba SesaZlebelia skolis ezoSic.

mas Semdeg, rac darwmundebiT, rom yvela moswavles met-nak-

lebad warmatebiT esmis am cnebebis azri, gadavdivarT saxelmZ-

Rvanelos gacnobaze.

pirveli Tavis pirvelive gakveTili eTmoba amave cnebebs.

amjerad moswavleebma unda ivarjiSon am cnebebis gamoyenebaze

wignis naxatebSi.

wignis Sesabamis gverdze ori naxatia Sesabamisi SekiTxvebiT.

resursebi

47

met-naklebobis vizualurad dadgenadafaze maswavlebeli ganalagebs lurji da wiTeli magnituri

rgolebis or grovas: wiTeli – 28 cali, lurji – 5, marcxniv –

lurjebi, marjvniv – wiTlebi.

romlebia bevri, lurjebi Tu wiTlebi? (wiTlebi)

romlebia cota? (lurjebi)

romel grovaSia meti? (wiTlebSi)

romelSia naklebi? (lurjebSi)

rCeva: igive keTdeba, rac pirvel gakveTilze. sruliad sakmarisia, Tu

moswavleebi mkafiod da naTlad gamoTqvamen TavianT mosazrebebs. amiT

bavSvi bevr rames swavlobs: maswavleblis mimarTvaze reagirebas, saku-

Tari azris gamoTqmas da yuradRebiT mosmenas.

Sedarebis Tema meordeba, magram lurj da wiTel rgolebs

adgilebs SevunacvlebT. cnobilia, rom bavSvs kargad aqvs gan-

viTarebuli adgilis mexsiereba, amitom meti xan marjvniv unda

iyos da xan – marcxniv, rom bavSvma kargad gaigos metoba adgilze

miwebebis gareSe. am asakis bavSvma kargad icis `bevri~ da `cota~,

magram `metia~ da `naklebia~ misTvis odnav win gadadgmuli nabi-

jia. met-nakleboba perceptul donezea mocemuli, TvalsaCinoa

da sxva damatebiT dasabuTebas ar saWiroebs.

muSaoba rveulSimoswavleebs vacnobT moswavlis savarjiSo rveuls. aq mniS-

vnelovani isaa, rom wignisagan gansxvavebiT, rveulSi SesaZle-

belia Cawera.

rveulis pirveli gverdebi motorikis savarjiSoebs eTmoba.

rveulis am nawils hqvia `movemzadoT werisaTvis~.

Tu bavSvebi moaswreben pirvelsave gverdze arsebuli wyveti-

li xazebisTvis kalmis gayolebas da dro darCeba, SesaZlebelia

momdevno gverdis damuSaveba.

48

y magnituri dafa

y markerebi

y magnituri rgolebi

gakveTili 3: zeviT, qveviT, SuaSi

gakveTilis mizani moswavles SeeZlos cnebebis `zeviT~ da `qveviT~ sworad gamoyeneba cxovre-

biseul situaciebSi.



sivrceSi orientacia. cnebebi „zeviT“, „qveviT“ da „SuaSi“isev viwyebT varjiSs sivrceSi orientaciaze da Semogvaqvs

axali cnebebi: „zeviT“ da „qveviT“. bavSvebis umetesobam icis es

sityvebi, magram Cveni mizania, moswavleebs SeeZloT am sityvebis



dasanaxad.

maswavlebeli dafaze moaTavsebs sam suraTs (magaliTad,

Tagvi, kata da ZaRli) erTmaneTis Tavze da ekiTxeba:

– romelia zeviT? romelia qveviT? romelia SuaSi?

Semdeg sxva suraTebs ganalagebs an amave suraTebs adgilebs

Seucvlis da ekiTxeba:

– kata zeviTaa, qveviT Tu SuaSi? da a.S.



Rvanelos Sesabamis gverdze – pirveli Tavis meore gakveTilze.


wignis naxatebSi.





romlebia bevri, lurjebi Tu wiTlebi? (wiTlebi)

romlebia cota? (lurjebi)

romel grovaSia meti? (wiTlebSi)

romelSia naklebi? (lurjebSi)

varjiSi xuTamde TvlaSiTanamedrove bavSvebis umetesoba skolaSi Sesvlamde ukve

icnobs raodenobebis saxelebs 5-mde. marTalia, es jer kidev

ar aris raodenobis gageba-gaazrebaze dafuZnebuli codna,

magram imisaTvis, rom raodenobis Rrmad gasaazreblad niadagi

movamzadoT, vavarjiSoT moswavleebi xuTamde TvlaSi.

am aqtivobaSi mTavaria, moswavleebma kargad icodnen sity-

resursebi

49

vaTa mimdevroba da raodenobebis saxelebs mkafiod, garkveviT

warmoTqvamdnen.

– modi, xmamaRla davTvaloT 5-mde, – ambobs maswavlebeli.

jer TviTon daiTvlis, mere mTel klass erTad daaTvlevinebs,

Semdeg romelime moswavles sTxovs daTvlas.

mcire raodenobebis dadgena gadaTvliTmaswavlebeli aZlevs moswavles sam mcire sagans da sTxovs,

daTvalos. moswavle TiTo-TiTod debs sagnebs magidaze da

warmoTqvams: erTi, ori, sami.

ramdeni sagania magidaze? (sami)

maswavlebeli magidaze debs oTx fanqars da sTxovs moswav-

les, daTvalos. moswavle TiTo-TiTod iRebs fanqrebs da war-

moTqvams: erTi, ori, sami, oTxi.

ramdeni fanqari gaqvs xelSi? (oTxi)

rac SeiZleba met moswavles gadaaTvlevineT sul sxvadasxva

sagani. moswavlem kargad unda Seiswavlos sityvebi: erTi, ori,

sami, oTxi, xuTi da maTi mimdevroba. es jer kidev ar niSnavs

maTi Sinaarsis gagebas, magram am sityvaTa gamarTulad war-

moTqma dagvexmareba momavalSi. nela da auCqareblad CaatareT

gakveTilis es nawili. moswavleebma, albaT, ician xuTamde Tvla,

magram Tqven aqcenti gadaitaneT imaze, Tu raoden gamarTulad

da mkafiod warmoTqvamen isini ricxvebis dasaxelebebs.

muSaoba rveulSiTu bavSvebi moaswreben me-8 gverdze savarjiSoebis Ses-

rulebas da dro darCeba, SesaZlebelia momdevno gverdis (gv.

9) damuSaveba.

50

y magnituri dafa

y markerebi

y magnituri rgolebi

resursebi

gakveTili 4: win, ukan

gakveTilis mizani moswavles SeeZlos cnebebis `zeviT~ da `qveviT~ sworad gamoyeneba cxovre-

biseul situaciebSi.



sivrceSi orientacia. cnebebi „win“, „ukan“isev viwyebT varjiSs sivrceSi orientaciaze da Semogva-

qvs axali cnebebi: „win“ da „ukan“. bavSvebis umetesobam icis es

sityvebi, magram Cveni mizania, moswavleebs SeeZloT am sityvebis



dasanaxad.



Rvanelos Sesabamis gverdze – pirveli Tavis mesame gakveTilze.


wignis naxatebSi.





romlebia bevri, lurjebi Tu wiTlebi? (lurjebi)

romlebia cota? (wiTlebi)

romel grovaSia meti? (lurjebSi)

romelSia naklebi? (wiTlebSi)

varjiSi xuTamde TvlaSi– modi, xmamaRla davTvaloT 5-mde, – ambobs maswavlebeli.

jer TviTon daiTvlis, mere mTel klass erTad daaTvlevinebs,

Semdeg romelime moswavles sTxovs daTvlas.

mcire raodenobebis dadgena gadaTvliTmaswavlebeli aZlevs moswavles xuT mcire sagans da sTxovs,








51

muSaoba rveulSiTu bavSvebi moaswreben me-10 gverdze savarjiSoebis Ses-

rulebas da dro darCeba, SesaZlebelia momdevno gverdis (gv.

11) damuSaveba.

52

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 5: met-naklebobis niSani

gakveTilis mizani moswavles SeeZlos, saganTa grovebs Soris sworad ganaTavsos met-nakle-

bobis niSani.

esg-s indikatori

maT. I.4.3: saganTa dawyvilebiT adarebs raodenobebs grovebSi, iyenebs Se-

sabamis terminebsa da aRniSvnebs da gansazRvravs gansxvavebas (“ramdeniT

meti/naklebi?~).

met-naklebobis niSanimaswavlebeli dafaze ganalagebs lurj da wiTel rgolebs,

marjvniv – lurjebs (24 cali), marcxniv – wiTlebs (7 cali).

lurjebi metia Tu wiTlebi? (lurjebi)

romeli grovaa naklebi? (wiTlebis) maswavlebeli debs

dafaze met-naklebobis niSans <.

>

– es met-naklebobis niSania, gaSlili mxare metisken unda

iyos Sebrunebuli.

maswavlebeli TiTiT mianiSnebs da ambobs:

wiTlebi naklebia lurjebze. lurjebi metia wiTlebze.

maswavlebeli aiRebs met-naklebobis niSans, Seucvlis adg-

ilebs lurj da wiTel grovebs da sTxovs moswavles, sworad

dados maT Soris met-naklebobis niSani.

ratom dade ase? (imitom, rom wiTlebi naklebia lurjebze)

rCeva: rodesac dafidan waikiTxavT miRweul Sedegs, aucileblad miu-

TiTeT im obieqtze, romelzec saubrobT. wiTlebi (uTiTebT wiTlebze)

metia (uTiTebT met-naklebobis niSanze) lurjebze (uTiTebT lurjeb-

ze). igive mosTxoveT moswavleebsac. moswavles nu avaCqarebT, davaca-

53

doT, jer daadasturos, romeli grovaa meti da romeli – naklebi da

mxolod amis Semdeg dados met-naklebobis niSani. moswavlem yovelTvis

unda ganmartos Sesrulebuli davaleba. SekiTxva `ratom?~ xSirad unda

gamoviyenoT. yovelTvis vekiTxebiT klass: `sworia?~. klasis daTanxmebaa

sisworis kriteriumi da ara Tqveni dasturi. Tqven Tavi unda Seikav-

oT yovelgvari Sefasebisagan. yoveli moswavlis mier gamoTqmuli eWvi

aucileblad unda gadamowmdes. ar dainanoT dro. am etapze konkretuli

codnis miRebaze ufro mniSvnelovania Cvevebis gamomuSaveba.

rac Seexeba met-naklebobis niSnis damaxsovrebas, imisaT-

vis, rom moswavleebs es gauadvildeT, maswavlebels SeuZlia

mcire ambavi gamoiyenos da Seadaros met-naklebobis niSani Citis

niskarts.

– SexedeT, rogor hgavs Citis niskarts. niskartis wveri yov-

elTvis patariskenaa mimarTuli, deda Citi jer yvelaze pataras

unda daexmaros.

rodesac or grovas Soris met-naklebobis niSnis moTavsebaa

saWiro, jer moswavleebs vekiTxebiT:

– romelSia ufro cota? maS, saiTken unda iyos am niSnis,

met-naklebobis niSnis wveri?

rCeva: aqamde bavSvs sagnebTan hqonda saqme (maTi gadaTvla, met-nakle-

bobis dadgena da sxva). axla igi axal etapze gadadis, simbolos unda

daeuflos, romelic met-naklebobas gamoxatavs. yoveli axali simbolos

Semotanas didi sifrTxile unda, rom simbolo ar mowydes Tavis Sinaarss

da damoukidebel obieqtad ar iqces. aseTi tendencia bavSvTan sakmaod

Zlieria. simbolo aRmniSvnelia, warmoadgens aRsaniSns, romelic Sei-

Zleba iyos saganic, movlenac da moqmedebac. met-naklebobis niSani ukve

dadasturebul, Seswavlil, misTvis kargad cnobil mimarTebas aRniSnavs.

Cveulebriv, es niSani Znelad dasauflebel niSanTa rigs miekuTvneba. mas

xmaroben sxva simboloebTan (cifrebTan) erTad, romlebic jerjerobiT

gaugebaria bavSvisTvis da simbolos xmarebis siZneles es gaugebroba

ganapirobebs. Tu bavSvs sagnebze kargad esmis danaxuli met-nakleboba,

maSin am niSnis sworad gamoyenebas win araferi eRobeba

gakveTilis momdevno nawilebi eTmoba wina dReebSi naswavli

masalis gameorebas. kerZod:

jer varjiSi cnebebze: marjvniv, marcxniv, zeviT, qveviT,

SuaSi, win, ukan.

Semdeg mcire, 5-mde raodenobebis gadaTvla.

muSaoba rveulSime-11 gverdi (an is gverdi, romelzedac gaCerdnen wina

gakveTilze)

54

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 6: dawyvileba

gakveTilis mizani moswavles SeeZlos, Seadaros saganTa ori grova dawyvilebis saSualebiT.

esg-s indikatori

maT. I.4.3: saganTa dawyvilebiT adarebs raodenobebs grovebSi, iyenebs Sesa-

bamis terminebsa da aRniSvnebs da gansazRvravs gansxvavebas (“ramdeniT

meti/naklebi?~).

dawyvilebaaqamde moswavleebi erTmaneTs adarebdnen TvalisaTvis

iolad aRsaqmel arsebiTad gansxvavebul raodenobebs.

amjerad maswavlebeli davalebas arTulebs da iseT raode-

nobebs awyobs dafaze, romelTa TvaliT, vizualurad Sedareba

gauWirdeba ufrossac ki. magaliTad, dafaze marjvena mxares

vaTavsebT 23 lurj magnits, marcxena mxares – 26 wiTel magnits.

– romelia meti, lurjebi Tu wiTlebi?

mosalodnelia sxvadasxva pasuxi.

Seiqmna problemuri situacia, rodesac arsebuli codna aRar

aris sakmarisi kiTxvaze pasuxis gasacemad.

– rogor gavarkvioT?

savaraudoa, rom zogierTi moswavle moisurvebs gadaTvlas,

magram maswavlebelma unda SeaCeros isini da Tavad SesTavazos

sakiTxis garkvevis procedura:

– modi, davawyviloT da gavarkvioT.

maswavlebeli TviTon iwyebs grovaTa dawyvilebas, debs erTi

meoris gverdiT erT lurjs da erT wiTels (sjobs zemodan qve-

moT Camoamwkrivos) da warmoTqvams: `erTi lurji, erTi wiTeli~.

rodesac igi amgvarad daawyvilebs ramdenime cals, sTxovs rome-

lime moswavles, ganagrZos. dawyvilebaSi ramdenime moswavle

iRebs monawileobas. dawyvilebas amTavrebs maswavlebeli.

– erTi lurji, erTi wiTeli. naxeT, dauwyvilebeli darCa

wiTlebi, e.i. romeli yofila meti? (wiTlebi)

55

– daimaxsovreT, rac miviReT! – maswavlebeli abrunebs

grovebs Tavis adgilze da miawodebs met-naklebobis niSans

romelime moswavles:

– moaTavse es niSani grovebs Soris!

<

rCeva: maswavlebeli mxolod moqmedebis damwyebi da biZgis mimcemia. Zal-

ze mniSvnelovania moswavleTa rac SeiZleba meti aqtivoba. dawyvilebuli

rgolebi dafaze CamoamwkriveT, raTa moswavleTaTvis sruliad naTeli

gaxdes met-naklebobis faqti.

rCeva: es metad mniSvnelovani situaciaa. TvaliT aRqma aRar aris

sakmarisi mimarTebis gasarkvevad. saWiro xdeba garkveuli proceduris,

dawyvilebis Semotana, romlis Sedegadac gairkveva, Tu romeli grovaa

meti da romeli – naklebi. dawyvileba, es moqmedebiT Sesrulebuli

dasabuTebaa, romelic gaTavisebis (interiorizaciis) Semdeg azrovnebis

operaciad iqceva. SemdgomSic, ricxvebis Sedarebis dros, sagnebis

dawyvilebaa is ZiriTadi da erTaderTi procedura, romelsac Sedareba

emyareba. dawyvilebis Semdeg grovebi ukan brundeba. bavSvma mexsiere-

baSi unda aRadginos dawyvilebis Sedegi, is, Tu romeli grova iyo meti

da amis Semdeg dados met-naklebobis niSani. es oTxsvliani moqmedebaa:

dawyvileba, grovebis ukan dabruneba, met-naklebobis niSnis dadeba da

TiTis dadebiT miRebuli gamosaxulebis wakiTxva. mniSvnelovania is, rom

met-nakleboba dadginda ara uSualo aRqmiT, aramed SemovliTi gziT

(dawyvilebiT) da met-naklebobis niSani ukve eyrdnoba mimarTebis warmod-

genas da ara TvaliT mocemulis aRqmas.




SuaSi;


56

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 7: SigniT da gareT

gakveTilis mizani moswavles SeeZlos, ganarCios erTmaneTisagan Sekruli wiris Sida da gare

areebi.



SigniT da gareTmaswavlebeli dafaze xatavs Sekrul wirs da aTavsebs wiTel

rgols wiris SigniT, xolo lurj rgols wiris gareT.

wiTeli rgoli SigniTaa Tu gareT? (SigniT)

lurji rgoli SigniTaa Tu gareT? (gareT) maswavlebeli

Seucvlis adgilebs rgolebs da ekiTxeba:

axla romeli rgolia gareT da romelia SigniT?

rCeva: am etapze ar aris saWiro sityva `wiris~ xmareba da arc imazea

yuradRebis gamaxvileba saWiro, ris SigniT an gareT gulisxmobT rgols.

ubralod ekiTxebiT: `wiTeli rgoli SigniTaa, Tu gareT?~ sxvas arafers

azustebT. bunebrivia, dafaze araferi unda iyos, wirisa da rgolebis

garda, wiri ki Zalian mkafiod unda Candes. im geometriuli warmodgene-

bi, romelsac Cven vuqmniT moswavleebs, eyrdnoba J.piaJes gamokvlevebs

(J.Piaget „La geometrie spontanee chez l’enfants“). Tavdapirvelad bavSvi buneb-

rivad eufleba topologiur mimarTebebs (Sida are, gare are, sazRvari

da a.S.), xolo proeqciulsa da evklidurs — ufro mogvianebiT. amitomac

daviwyeT umartivesiT.

gakveTilis momdevno nawilebi wina dReebSi naswavli masalis

gameorebas eTmoba. gansakuTrebiT mniSvnelovania met-nakle-

bobis niSnis sworad gamoyenebaze da dawyvilebis proceduraze

varjiSi.

standartuli savarjiSo aseTia:

dawyvilebadafaze vaTavsebT or sxvadasxva grovas, romelTa gadaTvla

TvaliT SeuZlebelia da moswavleebs vTxovT, gaarkvion, rome-

lia meti.

57

– rogor gavarkvioT, romelia meti?

– unda davawyviloT.

maswavlebels dafasTan rig-rigobiT gamohyavs moswavleebi

da awyvilebinebs sagnebs. imis mixedviT, sad darCa dauwyvile-

beli, moswavleebi amboben, romelia meti.

– maS rogor unda davdoT met-naklebobis niSani? saiT unda

hqondes wveri?

– patarisken.

– vin dadebs?

da a.S.




SuaSi;


58

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 8: SigniT da gareT (rTuli wiri)

gakveTilis mizani moswavles SeeZlos, rTuli Sekruli wiris SemTxvevaSi, sworad moaTavsos

wiris Sida an gare areSi wertili.



SigniT da gareT (rTuli wiri)amjerad daixazeba ufro rTuli formis wiri, sadac erTi

SexedviT ar Cans, rgoli SigniTaa Tu gareT.

gakveTilis momdevno nawilebi wina dReebSi naswavli masalis

gameorebas eTmoba. gansakuTrebiT mniSvnelovania met-nakle-

bobis niSnis sworad gamoyenebaze da dawyvilebis proceduraze

varjiSi.

59

dawyvilebadafaze vaTavsebT or sxvadasxva grovas, romelTa gadaTvla

TvaliT SeuZlebelia da moswavleebs vTxovT, gaarkvion, rome-

lia meti.

– rogor gavarkvioT, romelia meti?


maswavlebels dafasTan rigrigobiT gamohyavs moswavleebi da

awyvilebinebs sagnebs. imis mixedviT, sad darCa dauwyvilebeli,

moswavleebi amboben, romelia meti.

– maS, rogor unda davdoT met-naklebobis niSani? saiT unda

hqondes wveri?

– patarisken.

– vin dadebs?

da a.S.

mcire raodenobebis dadgena gadaTvliTmaswavlebeli aZlevs moswavles sam mcire sagans da sTxovs,








rac SeiZleba met moswavles gadaaTvlevineT sul sxvadasxva

sagani. moswavlem kargad unda iswavlos sityvebi: erTi, ori,

sami, oTxi, xuTi da maTi mimdevroba. es jer kidev ar niSnavs

maTi Sinaarsis gagebas, magram am sityvaTa gamarTulad war-

moTqma dagvexmareba momavalSi. nela da auCqareblad CaatareT

gakveTilis es nawili. moswavleebma, albaT, ician xuTamde Tvla,

magram Tqven aqcenti gadaitaneT imaze, Tu raoden gamarTulad

da mkafiod warmoTqvamen isini ricxvebis dasaxelebebs.

60

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 9: wiri. wertili wirze

gakveTilis mizani moswavles SeeZlos, Sida da gare areebis sazRvari gaarCios.



wiri. wertili wirzeamjerad daixazeba SedarebiT martivi formis wiri. maswavle-

beli jer SigniT dadebs rgols (an daxatavs wertils) da ekiTxeba

moswavleebs, mere gareT dadebs.

amis Semdeg dadebs wertils zustad wirze, xazze da ekiTxeba:

– SigniTaa Tu gareT?

atydeba kamaTi. zogierTi moswavle ityvis, rom SigniTaa, zogi

ityvis, rom gareTaa. aqac igive situaciaa, Zveli codna aRar

aris sakmarisi amocanis gadasaWrelad. maswavlebeli ambobs:

– arc SigniTaa da arc gareT. xazzea, wirzea.

amis Semdeg maswavlebeli piruku davalebas aZlevs romelime

moswavles:

– dade rgoli (an daxate wertili) wirze! axla dade SigniT.

axla gareT da a.S.

amis Semdeg gadavdivarT saxelmZRvanelos Sesabamis

gverdze – pirveli Tavis me-6 gakveTilze.

am gverdze ramdenime davalebaa. Tavdapirvelad aris didi

naxati. maswavlebeli ambobs:

– bavSvebma skolis ezoSi carciT daxates wiri.

naxatis qveS miwerilia SekiTxvebi, romlebsac maswavlebeli

bavSvebs usvams.

Semdeg gadadis momdevno savarjiSoze. aqac, iseve rogorc

wina SemTxvevaSi, SekiTxvebi wignSivea mocemuli. bunebrivia,

SesaZlebelia damatebiTi SekiTxvebis dasmac.

61

am gakveTilzeve iwyeba moswavlis rveulSi muSaoba.

Tavidan umartivesi davalebebia, radgan am etapze mniSvnelo-

vania motoruli Cvebis ganviTareba. amitom moswavleebi wyveti-

lad mocemul wirebs Semoxazaven da gaaferadeben Sida areebs.

ar gaumaxviloT yuradReba cnebaze „are“, romelic momdevno

TavSi Semodis!

Tu ver moaswreben dasrulebas, ara uSavs, daamTavron meore

dRes.

darCenili dro wina dReebSi naswavli masalis gameorebas

eTmoba. gansakuTrebiT mniSvnelovania met-naklebobis niSnis

sworad gamoyenebaze da dawyvilebis proceduraze varjiSi.

62

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 10: striqoni da sveti

gakveTilis mizani moswavles SeeZlos, cxrilis svetis da striqonis sworad miTiTeba.



cxrilis sveti, cxrilis striqonimaswavlebeli dafaze xazavs cxrils. zeda striqonSi aTavsebs

sagnebis baraTebs.

cxrilSi manqanis svets Camoayolebs xels da ambobs:

– es aris manqanis sveti.

– maCvene buStis sveti!

moswavle Camoayolebs xels svets da warmoTqvams:

– es aris buStis sveti.

maswavlebeli pirvel svetSi aTavsebs ferebis baraTebs,

gaayolebs xels wiTelis striqons da kiTxulobs:

– es ris striqonia? (es wiTlebis striqonia)

– maCvene lurjebis striqoni!

63

rCeva: pirvel yovlisa, saWiroa cxrilis struqturaze moswavleebs naTe-

li warmodgena SeeqmnaT. amitom ar aCqardeT, yvelaferi gaakeTeT nela

da mkafiod. sityvebi: `striqoni~, `sveti~ moswavleTaTvis axali sityve-

bia, magram ar aris saWiro maTze gansakuTrebuli yuradRebis miqceva,

Tavi ise unda daiWiroT, TiTqos darwmunebuli xarT, rom maT es sityvebi

kargad ician. am wlovanebis bavSvi mas swrafad aitacebs, Tu Tqven am

sityvebs moqmedebasTan erTad gamoiyenebT. striqonica da svetic Tavi-

dan bolomde unda aCvenoT da ara mxolod misi dasawyisi. moswavlesac

ase mos TxoveT, striqonis an svetis Cvenebisas Tavidan bolomde mkafiod

gaataros TiTi an joxi.


masalis gameorebas: mcire raodenobebis gadaTvlas; raode-

nobebis Sedarebas dawyvilebis gamoyenebiT da mere grovebs

Soris met-naklebobis niSnis sworad moTavsebas; varjiSs cne-

bebze marjvniv, marcxniv, zeviT, qveviT, SuaSi; sxvadasxva wirze

rgolebis moTavsebas SigniT, gareT da wirze.

64

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 11: cxrilis ujra

gakveTilis mizani moswavles SeeZlos, cxrilis ujris, rogorc striqonisa da svetis

TanakveTaze myofi adgilis sworad moZebna.



cxrilis ujramaswavlebeli dafaze xatavs cxrils. zeda striqonSi aTavsebs

sagnebis baraTebs, xolo pirvel svetSi – ferebis baraTebs.

maswavlebeli iRebs baraTs, romelzec lurji pepela xatia da

ambobs:

am cxrilSi yvela baraTs Tavisi adgili aqvs.

Semdeg sTxovs moswavles, moaTavsos baraTi saWiro ujraSi.

moswavlem ukve icis striqoni da sveti. axla ki saWiroa, baraTze

gamosaxuli sagnisa da misi feris mixedviT gansazRvros ujra.

davalebis Sesrulebis Semdeg maswavlebeli mimarTavs klass:

– sworadaa? ratom? (pepelas svetia da lurjis striqoni)

ase agrZelebs bolomde, sanam cxrili ar Seivseba.

65

amis Semdeg gadavdivarT saxelmZRvaneloSi muSaobaze. Sesa-

bamis gverdze ori sxvadasxva tipis davalebaa. pirveli davale-

ba dafaze Sesrulebulis msgavsia. SekiTxvebi cxrilis qveSaa

mocemuli. am SekiTxvebs maswavlebeli sxvadasxva moswavles

usvams. gansakuTrebiT mniSvnelovani bolo SekiTxvaa, radgan

misi pasuxi TvaliT ar Cans da bavSvebma unda imsjelon da daas-

abuTon TavianTi varaudi.

momdevno davaleba gansxvavdeba winasagan da, cxrilis garda,

ukavSirdeba pirvel gakveTilebze naswavl cnebebs: „marcxniv“,

„marjvniv“, „Sua“, „zeda“, „qveda“.

am davalebis mizania, moswavlem SeZlos ujrebis identifi-

cireba cxrilSi.




Soris met-naklebobis niSnis sworad moTavsebas; varjiSs cne-

bebze marjvniv, marcxniv, zeviT, qveviT, SuaSi; sxvadasxva wirze

rgolebis moTavsebas SigniT, gareT da wirze.

66

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 12: tolobis niSani

gakveTilis mizani moswavles SeeZlos, dawyvilebiT gaarkvios saganTa ori grovis toloba.

esg-s indikatori

maT. I.4.3: saganTa dawyvilebiT adarebs raodenobebs grovebSi, iyenebs Ses-

abamis terminebsa da aRniSvnebs (<, >, =) da gansazRvravs gansxvavebas (`ram-

deniT meti/naklebi?~).

tolobis niSanimaswavlebeli dafis marjvena mxares aTavsebs 26 lurj mag-

nits, marcxena mxares – 26 wiTel magnits da ekiTxeba klass:

– romelia meti, lurjebi Tu wiTlebi?

gamoiTqmeba sxvadasxva azri. maswavlebeli ambobs:

– rogor gavarkvioT?

– davawyviloT.

moswavle awyvilebs.

maswavlebeli ikiTxavs:

– darCa dauwyvilebeli?

– dauwyvilebeli ar darCa.

– rogor davdoT met-naklebobis niSani?

Seiqmneba problemuri situacia. moswavleebi Seecdebian,

met-naklebobis niSani aqeT-iqiT Seatrialon.

bolos, rodesac aRmoCndeba, rom met-naklebobis niSani ver

asaxavs situacias, maswavlebeli ambobs:

– aseT SemTxvevaSi sxva niSans xmaroben, mas tolobis niSani

hqvia. aCvenebs klass am niSans da moswavles grovebs Soris moaT-

avsebinebs.

=

aseve damuSavdeba kidev erTi magaliTi.

67

rCeva: moswavleebi, romlebic jer kidev ar icnoben tolobis niSans, Seec-

debian met-naklebobis niSani sxvadasxvanairi SemobrunebiT moaTavson

grovebs Soris. yoveli aseTi pasuxisas hkiTxeT klass: `sworia?~. hkiTxeT

agreTve: `aba, rogor waikiTxav, ra aris dafaze?~. Tu romelime moswav-

lem Tqva, rom grovebi tolia, daeTanxmeT da aCveneT tolobis niSani. am

gakveTilze Semodis toloba, rogorc met-naklebobis kerZo SemTxveva.

sagnebis dawyvilebiT tolobis dadasturebis Semdeg Semogvaqvs tolobis

niSani. aq iqmneba problemuri situacia, radgan Zveli saSualebebiT ver

xerxdeba problemis gadawyveta. tolobis dadasturebis Semdeg moswav-

les vaZlevT met-naklebobis niSans, vTxovT, dados igi grovebs Soris

da TiTis dadebiT waikiTxos. bavSvi maSinve grZnobs Seusabamobas, niSans

aiRebs, gadaatrialebs da isev debs. wakiTxvis Semdeg isev aiRebs da gaoce-

buli Sehyurebs maswavlebels. man unda dainaxos, rom axali mimarTebis

Zveli saSualebebiT aRniSvna SeuZlebelia. Cndeba axali simbolos

saWiroeba da es simbolo maswavlebels Semoaqvs. es ukve meore simboloa,

romelsac Tqven moswavleebs acnobT. miaqcieT yuradReba am simboloTa

swor da gamarTul gamoyenebas. faqtiurad, Tqven ukve SeaswavleT moswav-

leebs simbolizacia anu aRniSvnebis meTodika, kodireba. Tu Tqveni mos-

wavleebi simboloebs daeuflnen, CaTvaleT, rom maT ganaTlebaSi sakmaod

mniSvnelovani nabiji gadagidgamT.


masalis gameorebas:

mcire raodenobebis gadaTvla

raodenobebis Sedareba dawyvilebis gamoyenebiT da mere grovebs Soris met-naklebobis niSnis sworad moTavseba

varjiSi cnebebze: marjvniv, marcxniv, zeviT, qveviT, SuaSi

sxvadasxva wirze rgolebis moTavseba SigniT, gareT da wirze

68

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 13: mimdevroba

gakveTilis mizani moswavles SeeZlos mimdevrobis mocemuli fragmentis mixedviT mimdev-

robis gagrZeleba.

esg-s indikatori maT. 1.5.1. mimdevrobis mocemuli fragmentis mixedviT avsebs am mimdevrobis

ramdenime Tanmimdevrul Ria pozicias.

mimdevrobamaswavlebeli dafaze ganalagebs wiTel da lurj magnitur

rgolebs mimdevrobiT: jer wiTeli, mere lurji, mere wiTeli,

mere lurji da a.S. sul 6 rgols.

rodesac alagebs, Tan ambobs:

– modi jer wiTeli davdoT, axla lurji. axla isev wiTeli.

axla lurji.

rodesac daalagebs, klass ekiTxeba:

– rogor fiqrobT, ra feris rgoli unda davdoT axla? vin

dadebs?

aseve gaakeTebinebs ramdenime sxvadasxva moswavles.

amis Semdeg gadavdivarT saxelmZRvaneloze, sadac Sesabamis

gverdze 3 davalebaa. TiToeuls miwerili aqvs SekiTxvebi, rom-

lebic maswavlebelma unda dausvas klass. ra Tqma unda, SeiZleba

damatebiTi SekiTxvebis dasmac.

gakveTilis nawili eTmoba moswavlis rveulis saTanado

gverdze muSaobas, sadac 2 savarjiSo mimdevrobebis gaferadeb-

iT gagrZelebazea, xolo ori – ujrebSi CaxatviT gagrZelebaze.


masalis gameorebas:

69





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y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 14: cifri 4

am gakveTilamde moswavleebma Seiswavles ori simbolo (< da =),

romelTa saSualebiTac grovebad mocemul raodenobebs vadarebT

erTmaneTs.

axla kidev erTi axali simbolo Semodis, amjerad raodenobis aRm-

niSvneli simbolo.

SegaxsenebT, rom wina gakveTilebis ganmavlobaSi bavSvebi iTvlid-

nen mcire raodenobebs, anu erTmaneTs usabamebdnen raodenobas da

raodenobis saxels. amjerad viwyebT raodenobis anu ricxvis aRmniS-

vneli simboloebs TandaTanobiT Seswavlas.

Tavdapirvelad gavacnobT 4-s (SesaZlebelia 4-is nacvlad 5-ianis

gacnobac. amas arsebiTi mniSvneloba ara aqvs). ratom vacnobT 4-s?

saqme is gaxlavT, rom erT saganSi raodenoba kargad ara Cans. raode-

noba, ricxvi sagnebis simravlis Tvisebaa, maxasiaTebelia. saganTa

simravle SesaZlebelia erTelementianic iyos, magram erTi sagnis

(magaliTad vaSlis) romel Tvisebas vgulisxmobT rodesac mis raode-

nobaze vlaparakobT, Cans mxolod maSin, rodesac raodenobis cneba

met-naklebad gvesmis. amitom ricxvis simbolos gacnobis dawyeba

1-iT ar varga.

mxolod mas Semdeg, rac moswavle gaigebs, rom simboloTi, cifriT

SegviZlia raodenoba gamovxatoT, SegviZlia mimdevrobiTac gavac-

noT ricxvebi.

cifri 4maswavlebeli aZlevs moswavles oTx sagans da sTxovs, daT-

valos. moswavle rigrigobiT debs sagnebs magidaze da warmoTq-

vams: erTi, ori...

– ramdeni sagania magidaze? (oTxi)

Semdeg maswavlebeli amagrebs dafaze baraTs, romelzedac

cifri 4-ia gamosaxuli:

– es cifri oTxia, amdeni (miuTiTebs cifrze) sagania magidaze.

cifri 4-is Semosvlasac sagnobrivi safuZveli aqvs: jer

sagnebi, Semdeg simbolos gacnoba. es procesi ufro advilia

bavSvisTvis, vidre piruku procesi: jer cifris dadeba da Semdeg

misi Sinaarsis gaxsna anu realizacia sagnebiT.

gakveTilis mizani moswavle mixvdes, rom simbolo SeiZleba konkretul saganTa erTobliobas

aRniSnavdes, maTze miuTiTebdes.

esg-s indikatori

maT. 1.1.1: irCevs da qmnis mocemuli ricxvis Sesabamisi raodenobis saganTa

erTobliobas da piriqiT – mocemul saganTa erTobliobas Seusabamebs ricxv s;

maT. 1.1.2: qmnis toli raodenobis saganTa mowesrigebul erTobliobas maTi

dawyvilebiT; maT. 1.1.3: kiTxulobs da wers ricxvebs; gamosaxavs maT sxvadasxva

modelis gamoyenebiT.

71

rCeva: am etapze mniSvnelovania moswavles kargad gaagebinoT, rom cifri 4

aris ara ubralod oTxi, aramed oTxsagniani grovis aRmniSvneli simbolo.

amisTvis gamoiyeneT frazebi: `es gviCvenebs, Tu ramdeni rgolia dafaze~,

`es am raodenobas aRniSnavs~.

axali simboloebis Semotana da maTi Sinaarsis dafiqsire-

ba sakmaod rTuli momentia. xangrZlivi da mravalferovani

muSaobaa saWiro, rom cifri 4 (oTxiani) nebismieri oTxi sagnis

aRmniSvnelad iqces. es kavSiri pirvel etapze asociaciuria

(meqanikuri), mas ori mimarTuleba aqvs, grovidan cifrisaken da

piruku (cifri 4-is aRqmisas moswavlis cnobierebaSi gaCndeba

oTxi sagnis warmodgena). am ori momentis Serwymaze mTeli wlis

muSaobaa saWiro, radganac am asakis bavSvTan simbolo advilad

mowydeba Tavis Sinaarss da damoukidebel, TavisTavad obieqtad

iqceva.

analogiurad gaakeTebinebs ramdenime sxva moswavles sxva

sagnebis gamoyenebiT.

jerjerobiT ar vavarjiSebT 4-ianis daweraSi.


masalis gameorebas:





72

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

15Tavi 1

რამდენი ხელთათმანია?

რამდენი კარადაა ოთახში?

რამდენი საათი კიდია

კედელზე?

რამდენი ბურთია იატაკზე?

რამდენი საწოლია ოთახში?

იპოვე განსხვავებული.

რამდენი განსხვავებული

საგანია? რამდენი ბურთულაა

შიგნით?

1

1 1 1 ვივარჯიშოთ წერაში

e r T i

ერთი 8


am gakveTilidan iwyeba raodenobebis, ricxvebis sistemuri Seswavla.

yoveli ricxvis Seswavlas ori sagakveTilo saaTi eTmoba. Tavdapir-

velad konkretul sagnebs davawyobT, vaTvlevinebT moswavleebs

(anu vigebT, sworad icis Tu ara am ricxvis saxeli) da mere vacnobT

Sesabamis cifrs. momdevno dRes piriqiT, cifris mixedviT unda daa-

lagos sagnebi, vaswavliT cifris daweras da mis saxels.

cifri 1maswavlebeli dafaze ganalagebs ramdenime sxvadasxva feris

rgols (magaliTad, wiTeli, yviTeli da lurji).

– ramdeni lurji rgolia?

– erTi.

– ramdeni wiTeli rgolia?

– erTi.

maswavlebeli dafaze datovebs mxolod erT rgols da mis

gverdiT moaTavsebs baraTs, romelzedac weria cifri 1.

– es cifri (miuTiTebs) 1-ia. amdeni rgolia dafaze.

mere gadavdivarT saxelmZRvanelos Sesabamis gverdze. gver-

dis zeda nawilSi mocemulia TiTo sagnis suraTi, agreTve cifri

1 da sityva „erTi“. is, rom moswavleebma jer SeiZleba am sityvis

amokiTxva ar icodnen, araa problema, maT, ubralod, veubnebiT,

rom aq weria sityva „erTi“.

momdevno davalebebSi aris suraTebi da maTi Sesabamisi SekiT-

xvebi. yvela davaleba unda SevasruloT, garda bolo weriTi

davalebisa.

gakveTilis darCenili nawili eTmoba wina dReebSi naswavli



Soris met-naklebobis an tolobis niSnis sworad moTavsebas;

varjiSs cnebebze marjvniv, marcxniv, zeviT, qveviT, SuaSi; sxva-

dasxva wirze rgolebis moTavsebas SigniT, gareT da wirze.

gakveTilis mizani moswavles SeeZlos, saganTa erTelementian simravles sworad Seusabamos

saxeli „erTi“ da cifri 1.

esg-s indikatori


erTobliobas da piriqiT – mocemul saganTa erTobliobas Seusabamebs ricxvs;




73

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y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 16: erTi

erTimaswavlebeli dafaze moaTavsebs baraTs, romelzedac aweria

cifri 1 da ambobs:

– dade dafaze amdeni (miuTiTebs cifrze) lurji rgoli.

– dade dafaze amdeni (miuTiTebs cifrze) wiTeli rgoli.

– ra hqvia am cifrs?

mere auxsnis, rogor iwereba 1-iani da rveulis Sesabamis

gverdze amuSavebs 1-ianebis gamoweraSi.







gakveTilis mizani moswavles SeeZlos, cifr „1“-is danaxvisas daawyos Sesabamisi raodenobis

sagnebi.

esg-s indikatori






74

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y markerebi

y magnituri rgolebi

y baraTebi

resursebi


cifri 2maswavlebeli dafaze ganalagebs or-or sxvadasxva feris

rgols (magaliTad, 2 lurji da 2 wiTeli).


– ori.


– ori.

maswavlebeli dafaze datovebs mxolod lurj rgolebs da

maT gverdiT moaTavsebs baraTs, romelzedac weria cifri 2.


mere gadavdivarT saxelmZRvanelos Sesabamis gverdze.

gverdis zeda nawilSi mocemulia or-ori sagnis suraTi, agreTve

cifri 2 da sityva „ori“. is, rom moswavleebma jer SeiZleba am

sityvis amokiTxva ar icodnen, araa problema, maT, ubralod,

veubnebiT, rom aq weria sityva „ori“.

momdevno davalebebSi aris suraTebi da maTi Sesabamisi

SekiTxvebi. yvela davaleba unda SevasruloT, garda bolo weri-

Ti davalebisa.


masalis gameorebas: raodenobebis Sedarebas dawyvilebis gam-

oyenebiT da mere grovebs Soris met-naklebobis an tolobis

niSnis sworad moTavsebas; varjiSs cnebebze marjvniv, marcxniv,

zeviT, qveviT, SuaSi; sxvadasxva wirze rgolebis moTavsebas

SigniT, gareT da wirze.

gakveTilis mizani moswavles SeeZlos, saganTa orelementian simravles sworad Seusabamos

saxeli „ori“ da cifri 2.

esg-s indikatori






75

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y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 18: ori

orimaswavlebeli dafaze moaTavsebs baraTs, romelzedac aweria

cifri 2 da ambobs:













sagnebi.

esg-s indikatori






76

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

17Tavi 1

3

რამდენი ცხვარია ნახატზე?

დათვალე, რამდენი ხეა, რამდენი სახლია?

მეცხვარე რამდენია?

ცაში რამდენი ღრუბელი მოჩანს?

რამდენი ბურთულაა გარეთ?

რამდენი ბურთულაა შიგნით?

რამდენი წითელი მანქანაა?

3 3 3ვივარჯიშოთ წერაში

s a m i

სამი 10


cifri 3maswavlebeli dafaze ganalagebs sam-sam sxvadasxva feris



– sami.


– sami.





gverdis zeda nawilSi mocemulia sam-sami sagnis suraTi, agreTve

cifri 3 da sityva „sami“. is, rom moswavleebma jer SeiZleba am

sityvis amokiTxva ar icodnen, araa problema, maT, ubralod,

veubnebiT, rom aq weria sityva „sami“.



Ti davalebisa.


masalis gameorebas: raodenobebis Sedarebas dawyvilebis gam-

oyenebiT da mere grovebs Soris met-naklebobis an tolobis

niSnis sworad moTavsebas; varjiSs cnebebze marjvniv, marcxniv,

zeviT, qveviT, SuaSi; sxvadasxva wirze rgolebis moTavsebas

SigniT, gareT da wirze.

gakveTilis mizani moswavles SeeZlos, saganTa samelementian simravles sworad Seusabamos

saxeli „sami“ da cifri 3.

esg-s indikatori






77

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 20: sami

samimaswavlebeli dafaze moaTavsebs baraTs, romelzedac aweria

cifri 3 da ambobs:













sagnebi.

esg-s indikatori






78

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi


cifri 4maswavlebeli dafaze ganalagebs oTx-oTx sxvadasxva feris



– oTxi.


– oTxi.





gverdis zeda nawilSi mocemulia oTx-oTxi sagnis suraTi,

agreTve cifri 4 da sityva „oTxi“. is, rom moswavleebma jer

SeiZleba am sityvis amokiTxva ar icodnen, araa problema, maT,

ubralod, veubnebiT, rom aq weria sityva „oTxi“.



Ti davalebisa.

gakveTilis darCenili nawili eTmoba wina dReebSi naswav-

li masalis gameorebas: mcire raodenobebis gadaTvla; raode-

nobebis Sedareba dawyvilebis gamoyenebiT da mere grovebs

Soris met-naklebobis an tolobis niSnis sworad moTavseba;


dasxva wirze rgolebis moTavseba SigniT, gareT da wirze.

gakveTilis mizani moswavles SeeZlos, saganTa oTxelementian simravles sworad Seusabamos

saxeli „oTxi“ da cifri 4.

esg-s indikatori






79

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

1. daakavSire xazebiT.

2. gaaferade imdeni, ramdensac ricxvi giCvenebs.

ori

oTxi

erTi

sami

2

4

1

3

ori oTxi sami erTi

4 3 1 2

22

ricxvi 4

gakveTili 22: oTxi

oTximaswavlebeli dafaze moaTavsebs baraTs, romelzedac aweria

cifri 4 da ambobs:













sagnebi.

esg-s indikatori






80

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi


cifri 5maswavlebeli dafaze ganalagebs oTx-oTx sxvadasxva feris



– xuTi.


– xuTi.





gverdis zeda nawilSi mocemulia xuT-xuTi sagnis suraTi,

agreTve cifri 5 da sityva „xuTi“. is, rom moswavleebma jer

SeiZleba am sityvis amokiTxva ar icodnen, araa problema, maT,

ubralod, veubnebiT, rom aq weria sityva „xuTi“.



Ti davalebisa.

gakveTilis darCenili nawili eTmoba wina dReebSi naswav-

li masalis gameorebas: mcire raodenobebis gadaTvla; raode-

nobebis Sedareba dawyvilebis gamoyenebiT da mere grovebs

Soris met-naklebobis an tolobis niSnis sworad moTavseba;


dasxva wirze rgolebis moTavseba SigniT, gareT da wirze.

gakveTilis mizani moswavles SeeZlos, saganTa xuTelementian simravles sworad Seusabamos

saxeli „xuTi“ da cifri 5.

esg-s indikatori






81

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 24: xuTi

xuTimaswavlebeli dafaze moaTavsebs baraTs, romelzedac aweria

cifri 5 da ambobs:






mas Semdeg, rac 1-dan 5-mde ricxvebi Seiswavles, am Temaze

varjiSi Semdegnairad SeiZleba warimarTos xolme:

a) cifris mixedviT grovis Seqmna

maswavlebeli aCvenebs (an dafaze wers) romelime cifrs da

eubneba moswavles:

– dade dafaze amdeni (miuTiTebs cifrze) rgoli.

– ra hqvia am raodenobas?

b) raodenobis mixedviT cifris moZebna

maswavlebeli dafaze awyobs ramdenime rgols da eubneba

moswavles:

– daTvale ramdenia.

– romeli cifri gviCvenebs, rom amdenia?

moswavlem baraTebidan unda SearCios saTanado cifri.

g) sityvis mixedviT cifris moZebna da grovis Seqmna

maswavlebeli dafaze wers 1-dan 5-mde romelime ricxvis

saxels da ambobs:

– ra weria? vin moZebnis am raodenobis Sesabamis cifrs? vis

SeuZlia amdeni rgoli dados dafaze?

da a.S.








sagnebi.

esg-s indikatori






82

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

20 Tavi 1

5 44 1

2 33 1

5 11 2

თუ დავაწყვილებთ, დაგვრჩება 1 კნუტი.

რომელი ყოფილა მეტი?

ვივარჯიშოთ წერაში ვივარჯიშოთ წერაში

მეტ-ნაკლებობის ნიშანი რომ ჩავწეროთ, საით უნდა

იყოს წვერი, ქათმებისკენ თუ წიწილებისკენ?

გადაიწერე და შეადარე:

ეს მეტ-ნაკლებობის ნიშანია.

მისი წვერი ყოველთვის ნაკლებისკენაა

მიმართული.

მეტ-ნაკლებობის ნიშანი13

gakveTili 25: met-naklebobis niSnis wera

gakveTilis mizani moswavles SeeZlos met-naklebobis niSnis dawera.

esg-s indikatori




met-naklebobis niSnis werakidev erTxel vubrundebiT dawyvilebis proceduras da

met-naklebobis niSans. maswavlebeli kvlav iseTi raodenobis

sagnebs awyobs, romelTa gadaTvla TvaliT SeuZlebelia.

– rogor gavigoT, romelia meti?

– davawyviloT.

dawyvilebis Semdeg grovebi dabrundeba TavTavianT adgilas

da maT Soris Caismeba met-naklebobis niSani.

Semdeg gadavdivarT saxelmZRvaneloze muSaobaze.

amis Semdeg maswavlebeli axsnis, rogor iwereba es niSani da

avarjiSebs mis gamoweraSi orive poziciaSi: niSnis wveri marcx-

niv da niSnis wveri marjvniv.


masalis gameorebas:

mcire raodenobebis gadaTvlas da maTi Sesabamisi cifris

moZebnas;

cifris mixedviT saganTa grovis Seqmnas;

raodenobebis Sedarebas dawyvilebis gamoyenebiT da mere

grovebs Soris met-naklebobis an tolobis niSnis sworad

moTavsebas;

sxvadasxva wirze rgolebis moTavsebas SigniT, gareT da

wirze.

83

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

21Tavi 1

ბავშვები მეტია თუ ბუშტები?

თუ დავაწყვილებთ, არცერთი

ბავშვი არ დარჩება ბუშტის

გარეშე. არც ბავშვებია მეტი

და არც – ბუშტები.

დააკვირდი სურათებს და თქვი, რომელი ნიშანი

უნდა ჩაიწეროს, მეტ-ნაკლებობის თუ ტოლობის?

ვივარჯიშოთ წერაში

ეს ტოლობის ნიშანია.

როცა რაოდენობები ტოლია,

ამ ნიშანს ვიყენებთ.

ტოლობის ნიშანი 14

gakveTili 26: tolobis niSnis wera

gakveTilis mizani moswavles SeeZlos tolobis niSnis dawera.

esg-s indikatori




tolobis niSnis weraamjerad maswavlebeli tol raodenobebs adarebinebs mos-

wavleebs da dawyvilebis mere ekiTxeba:

– romeli yofila meti? ratom?

– arc erTi ar darCa dauwyvilebeli.

– maS ra niSani unda CavweroT?

– tolobis niSani.

Semdeg gadaaSlevinebs wigns saTanado gverdze da daamuSave-

binebs savarjiSoebs.

amis Semdeg axsnis, rogor iwereba es niSani da avarjiSebs

gamoweraSi


masalis gameorebas:


moZebnas;




moTavsebas;


wirze.

84

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 27: Sedareba, rodesac Sesadarebeli obieqtebidan erTi realuri sagnebiTaa mocemuli, meore ki ricxvis saxiT.

gakveTilis mizani moswavles SeeZlos, saganTa grovisa da simboloTi (cifriT) mocemuli

raodenobis Sedareba.

esg-s indikatori




grovisa da ricxvis SedarebaTuki aqamde moswavleebs vadarebinebdiT saganTa grovebs

da maT Soris unda moeTavsebinaT met-naklebobis an tolobis

niSnebi, amjerad situacias odnav varTulebT:

maswavlebeli dafaze ganalagebs saganTa mcire grovas

(vTqva T, 7 rgols) da misgan cota moSorebiT moaTavsebs cifr 5-s

5

– romelia meti, es (uTiTebs grovaze) Tu es (uTiTebs

cifrze)?

bunebrivia, zogierTi bavSvi pirdapir ityvis swor pasuxs,

rom grova metia, magram aseT dros maswavlebeli ekiTxeba:

– ratom? rogor daasabuTeb, rogor daamtkiceb?

gavixsenoT, rom met-naklebobis dasabuTebis erTaderTi gza

dawyvilebaa, magram rogor unda dawyvildes saganTa grova da

ricxvi? amisaTvis jer ricxvis Sesabamisi grova unda Seiqmnas

(sasurvelia sxva feris rgolebiT) da mere dawyvildes.

es procedura rom damTavrdeba grovac da ricxvic Tav-Tavis

adgilas dabrundeba da maT Soris moTavsdeba met-naklebobis

niSani. analogiurad gakeTdeba sxva grovebze da ricxvebze.

grovaSi SegiZliaT aiRoT nebismieri raodenobebi, radgan

Cveni mizani ar aris maTi gadaTvla da raodenobebis Sesadare-

blad viyenebT ara Tvlas, aramed dawyvilebas.


masalis gameorebas:


moZebnas;




moTavsebas;


wirze.

85

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 28: Sedareba, rodesac Sesadarebeli obieqtebidan orive simboloTia mocemuli.

gakveTilis mizani

moswavles SeeZlos, mxolod simboloebiT gamoxatuli raodenobebis

Sedareba, maTi Sesabamisi raodenobis grovebis SeqmniT da dawyvilebiT,

Semdeg ki cifrebs Soris met-naklebobis an tolobis niSnis Cawera.

esg-s indikatori


abamis terminebsa da aRniSvnebs da gansazRvravs gansxvavebas (“ramdeniT

meti/naklebi?~).

cifrebis Sedarebaam gakveTilze wina gakveTilis msgavsi davalebaa, oRond

sul odnav garTulebuli – Sesadarebeli obieqtebidan orive

simboloTia mocemuli

maswavlebeli dafaze moaTavsebs cifrebs:

54

– romelia meti?

– ratom? rogor davasabuToT?

cifrebis qveS unda dalagdes Sesabamisi raodenobis sagnebi

(sasurvelia ori sxvadasxva feriT) da dawyvildes.

– maS romeli yofila meti, 5 Tu 4?

– dawere amaT Soris saTanado niSani. saiT unda iyos wveri?

analogiurad Sesruldeba sxva ricxvebisTvisac.

Semdeg saxelmZRvanelos gverdze, sadac met-naklebobis

niSania, bolo savarjiSos vasrulebinebT:

bavSvebma unda gadaiweron ori cifri da Seadaron erTmaneTs.


masalis gameorebas:


moZebnas;




moTavsebas;


wirze.

86

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 29: Sedarebis Cawera simboloebiT

gakveTilis mizani moswavles SeeZlos, saganTa ori grovis Sedareba da Sedarebis Sedegebis

cifrebiTa da met-naklebobis niSniT Cawera.

esg-s indikatori




Sedarebis Cawera simboloebiTam gakveTilzec wina gakveTilis msgavsi davalebaa oRond

piruku: sagnebiT mocemuli Sedareba simboloebiT unda Caiw-

eros.

maswavlebeli dafaze

ganalagebs 4 wiTel da 5

lurj rgols da ekiTx-

eba:

– rogor unda gavig-

oT, romelia meti?

– davawyviloT.

– ramdenia marcxniv

(miuTiTebs)? ramdenia marjvniv (miuTiTebs)?

– dawere amis qveS (miuTiTebs wiTel rgolebze) ramdenia.

dawere amis qveS (miuTiTebs lurj rgolebze) ramdenia.

– saiT unda iyos met-naklebobis niSnis wveri?

4 5<

sabolood dafaze aseTi

suraTi iqneba


masalis gameorebas:


moZebnas;




moTavsebas;


wirze.

87

Tavi 2 vivarjiSoT 5-mde angariSSi


y 5-mde raodenobebis Sekreba sagnebze moqmedebis SesrulebiT; Sekrebis Cawera simboloebiT

(cifrebi, Sekrebis da tolobis niSnebi);

y fulis iseTi nominalebis cnoba, romlebzedac gamosaxulia ricxvebi 5-is farglebSi;

y saganTa grovebidan sameulebis, oTxeulebisa da xuTeulebis gamoyofa;

y 5-mde rigobiTi ricxviTi saxelebis sworad gamoyeneba;

y SedarebiT rTuli wirebiT Seqmnili areebis gamoyofa da maTi gadaTvla;

y cxrilis svetis, striqonis da ujris identificireba, rodesac cxrilis ujrebSi sagnebis

nacvlad cifrebi weria.

gakveTilis N gakveTilis saTauriSesabamisoba moswavlis wignTan

(II Tavi)

gakv.30 Sekreba

moswavlis wigni: §1gakv.31 Sekrebis niSani

gakv 32 Sekrebis Cawera cifrebiT

gakv 33 meramdenea? moswavlis wigni: §2

gakv 34sameulebi moswavlis wigni: §3

gakv 35

gakv 36oTxeulebi moswavlis wigni: §4

gakv 37

gakv 38xuTeulebi moswavlis wigni: §5

gakv 39

gakv 40 cxrili da cifrebi moswavlis wigni: §6

gakv 41 TeTrebi moswavlis wigni: §7

gakv 42 larebi moswavlis wigni: §8

gakv 43 ramdenime are moswavlis wigni: §9

88

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 30: Sekreba

SekrebaSekreba, rogorc grovebis SeerTeba

maswavlebeli dafis erT mxares awyobs wiTeli magnituri

rgolebis grovas da ambobs:

– eseni Cveni klasis gogonebi arian, ezoSi gamovidnen da

TamaSoben. eseni ki – biWebi (dafis meore mxares awyobs lurj

magnitebs). movida maswavlebeli da dauZaxa moswavleebs: aq

mogrovdiT yvelani, aq SeikribeT! (igi orive xeliT moswevs

magnitebs da moagrovebs dafis centrSi)

Semdeg magidis orive mxares maswavlebeli awyobs raime

sagnebis or grovas.

– vin gamova da Seagrovebs, Sekrebs amaT magidis SuaSi?

moswavle gamodis da orive xeliT moswevs sagnebs magidis

SuaSi. vidre moswavle am moqmedebas Seasrulebs, maswavlebeli

ekiTxeba:

– ra unda gaakeTo? (unda Sevkribo)

Tavdapirvelad saWiro ar aris SesakrebTa dasaxeleba da arc

miRebuli Sedegis raodenobrivi aRniSvna. am etapze mxolod

Sekrebis operacia sruldeba. yuradReba mimarTulia TviT moq-

medebaze.

rCeva: Sekrebis procesSi ricxvebs imitom ar vasaxelebT, rom moswavlem

kargad dainaxos TviTon moqmedeba – Sekreba, da kargad gaiazros. es mniS-

vnelovani momentia. saxelmZRvaneloTa umetesobaSi moswavles Sekrebas

ricxvebTan erTad acnoben, moswavle orientirebulia ricxvebze, misaReb

Sedegze da kargad ver acnobierebs, ra moqmedeba Seasrula. moqmedebis

iseTi gamonawevreba, rogorsac Cven gTavazobT, moswavles SemdgomSi

Zalian gauadvilebs ricxvebze Sekrebis operaciis Catarebas.


masalis gameorebas:


moZebnas;


raodenobebis Sedarebas dawyvilebis gamoyenebiT, mere


moTavsebas bolos Sedarebis Sedegis somboloebiT Caweras.


wirze.

gakveTilis mizani moswavles SeeZlos, Sekrebis moqmedebis Sesruleba saganTa or grovaze.

esg-s indikatori

maT. I.3.1: sityvierad aRwers Sekrebis, gamoklebis, tolobisa da Sedegis

cnebebs sxvadasxva konteqstSi; maT. I.3.2: axdens Sekreba-gamoklebis Tval-

saCinod demonstrirebas, gansazRvravs gansxvavebas da aRwers ricxvebs

Soris damokidebulebebs.

89

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 31: Sekrebis niSani

Sekrebis niSanimagnitur dafaze maswavlebeli ganalagebs magnitebis or

grovas da mouwodebs moswavles Sekribos isini. moqmedebis

Sesrulebis Semdeg maswavlebeli ganacalkevebs grovebs

(daabrunebs pirvandel mdgomareobas) da dadebs grovebs Soris

Sekrebis niSans (+).

– es Sekrebis niSania. es niSani gveubneba, rom saWiroa am ori

grovis, ori Sesakrebis Segroveba, SeerTeba. am niSans rom dain-

axavT, unda aiRoT es niSani da SeasruloT saWiro moqmedeba.

– ra unda gaakeToT, roca dainaxavT grovebs Soris am niSans?

(SevkriboT)

– SeasruleT moqmedeba!

moswavle aiRebs niSans da gaaerTianebs grovebs.

magidaze maswavlebeli awyobs or grovas, maT Soris debs

Sekrebis niSans (+) da sTxovs moswavles, Seasrulos moqmedeba.

moswavle aiRebs niSans, gadascems maswavlebels da agrovebs

ganlagebul sagnebs magidis SuaSi.

am gakveTilze Semodis axali simbolo — Sekrebis niSani (+).

is aqamde Seswavlili simboloebisgan arsebiTad gansxvavdeba.

met-naklebobis da tolobis niSnebi (<) sagnebiT ukve mocemuli

mimarTebis gamoxatvaa, misi simbolizacia, cifri 4 - oTxele-

mentiani grovis, anu obieqtis simboloa. Sekrebis niSani (+) ki

brZanebis, garkveuli moqmedebis Sesrulebisaken mowodebis sim-

boloa. es niSani unda `miebas~ Sekrebis moqmedebis Sesrulebas,

mis aRmniSvnelad unda iqces.


masalis gameorebas:


moZebnas;






wirze.

gakveTilis mizani moswavles SeeZlos, Sekrebis niSnis mixedviT moqmedebis sworad Sesruleba.

esg-s indikatori





90

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 32: Sekrebis Cawera cifrebiT

Sekrebis Cawera cifrebiTmaswavlebeli dafaze debs sam magnits, maTgan cota moSore-

biT or magnits da maT Soris niSans – +.

– ra moTxovnaa dafaze? (gvTxoven SevkriboT)

– ra da ra aris Sesakrebi? (ori grova)

– ramdeni rgolia Sekrebis niSnis marcxniv? (sami)

– ramdenia pirvel SesakrebSi? (sami)

– ramdenia meore SesakrebSi? (ori)

mas Semdeg, rac kargad dadgindeba, Tu ra aris Sesakrebi, ram-

denia TiToeul SesakrebSi, unda movTxovoT am moqmedebis Ses-

ruleba. moswavlem unda aiRos niSani da gaaerTianos Sesakrebe-

bi, SeaerTos isini. unda gameordes sityvierad:

– ra da ra iyo Sesakrebebi? (samisTvis unda migvematebina ori,

sami da ori iyo Sesakrebebi)

– ra moqmedeba SevasruleT? (SevkribeT)

– ra SevkribeT? (sami da ori)

– ramdeni miviReT? (xuTi)

– maSasadame, sams mivumatoT ori tolia xuTis.

rCeva: am etapze mniSvnelovania moswavleTa mier sityva `Sesakrebis~ gage-

ba. amis gasaadvileblad, Sesakrebis yoveli xsenebisas miuTiTeT Sesabamis

grovaze.


masalis gameorebas:


moZebnas;

cifris mixdviT saganTa grovis Seqmnas;





wirze.

gakveTilis mizani moswavles SeeZlos, Sekrebis moqmedebis Cawera simboloebis (cifrebi,

Sekrebis niSani da tolobis niSani) saSualebiT.

esg-s indikatori





91

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 34: sameulebi

ramdenime toli grovamaswavlebeli dafaze awyobs oTx grovas – sami, sami, oTxi da

sami rgoliT, Semoxazavs maT cal-calke.

Semdeg miuTiTebs samrgolian grovaze da ekiTxeba moswavles:

– ramdenia am grovaSi? (sami) amaSi? (sami) amaSi? (oTxi) amaSi?

(sami)

– sul ramdeni grovaa? aba davTvaloT, ramdeni grovaa.

Cveni mizania, moswavlem grova erT obieqtad aRiqvas.

amis Semdeg maswavlebeli mxolod sam cal samrgolian grovas

ganalagebs dafaze da ekiTxeba bavSvebs:

– ramdenia am grovaSi? (sami) amaSi? amaSi?

– amas hqvia sameuli. amasac sameuli.

– sul ramdeni sameulia dafaze?

aiRebs yvelafers dafidan da gamohyavs sxva moswavle:

– dade erTi sameuli. dade kidev erTi sameuli.

dafaze 15 rgols ganalagebs da eubneba:

– modi, sameulebi SemovxazoT.

mas Semdeg, rac yvela sameuli Semoixazeba, ikiTxavs:

– sul ramdeni sameuli yofila?

rCeva: am etapis umniSvnelovanesi amocanaa sityvis – „sameuli“ - kargad

gaazreba moswavleebis mier. amaSi moswavleebs SegiZliaT xelis moZ-

raobiT daexmaroT: Sesabamisi sityvis dasaxelebisas xeliT SemoxazeT

saTanado grova.

aq ZiriTadia is, rom grova bavSvma ganixilos, rogorc erTi

obieqti. sagnebis Semoxazva calkeul sagnebs erT grovad aer-

Tianebs da vizualurad TvalsaCinos xdis. grovaze, romelic

ramdenime elements Seicavs, bavSvma unda Tqvas `erTi~. iwyeba

didi erTeuliT Tvla, romlis kerZo SemTxveva iqneba aTobiT da

ocobiT Tvla. amave dros, bavSvisTvis naTeli xdeba saTvleli

erTeulis pirobiToba. rom is nebismierad SeiZleba iyos Ser-

Ceuli. bavSvi dainaxavs, rom erTi da igive raodenoba SeiZleba

sxvadasxva saxiT warmoCindes.

gakveTilis mizani moswavles SeeZlos, saganTa grovaSi sameulebis gamoyofa, agreTve gamoy-

ofili sameulebis raodenobis garkveva.

esg-s indikatori maT. I.1.4: gamoyofs miTiTebuli ricxvebis Sesabamisi raodenobebis jgufebs

grovaSi (magaliTad, gamoyofs sameuls, xuTeuls, aTeuls grovaSi).

92


masalis gameorebas:


moZebnas;






wirze.

analogiurad Seiswavleba oTxeulebi da xuTeulebi.

am Tavis kidev erTi mniSvnelovani Temaa „ramdenime are“.

maswavlebeli xazavs wirs, romelsac ori Sida are aqvs. es wiri

sinamdvileSi sam ares gamohyofs: ori Sida area da erTi gareTa

are. bavSvebi amas TvaliT mSvenivrad xedaven. Cveni mizania isini

vavarjiSoT areebSi sxvadasxva raodenobis rgolebis CadebaSi

da imis gadaTvlaSi, romel areSi ramdeni rgolia.

qarTuli fulis niSnebs moswavleebi sakmaod kargad icnoben,

amitom ZiriTadi aqcenti keTdeba ara gacnobaze, aramed gamoy-

enebaze, gadaTvlaze.

93

Tavi 3 ricxvebi 6-dan 10-mde


y 6-dan 10-mde raodenobebis, maTi saxelebis da Sesabamisi simboloebis - cifrebis sworad

gamoyeneba, saxelis mixedviT cifris dawera; cifriT gamoxatuli raodenobis Sesabamisi

grovis Seqmna; konkretuli sagnebiT mocemuli raodenobis saxeldeba da cifrebiT Cawera;

y gamoklebis moqmedebis Sesruleba da gamoklebis niSnis sworad gamoyeneba;

y raodenobebis ara mxolod Sedareba, aramed ukve imis dadgenac, ramdeniT metia Tu naklebia

esa Tu is raodenoba meoreze;

y SedarebiT rTuli wirebis areebis identificireba da am areebis sazRvrebis dadgena.

ricxvebis 6, 7, 8, 9, 10 Seswavla zustad imave mimdevrobiT da meTodikiT xdeba, rogorc es 1-dan

5-mde ricxvebisTvis gakeTda.

amitom aq aRvwerT mxolod im gakveTilebs, romlebic principulad axalia.

gamoklebis Seswavla ramdenime gakveTilzea gadanawilebuli.

gakveTilebi gakveTilis saTauriSesabamisoba moswavlis wignTan

Tavi III

gakv.44eqvsi moswavlis wigni: §1

gakv.45

gakv 46

Svidi moswavlis wigni: §2gakv 47

gakv 48rva moswavlis wigni: §3

gakv 49

gakv 50cxra moswavlis wigni: §4

gakv 51

gakv 52aTi moswavlis wigni: §5

gakv 53

gakv 54 gamoklebis moqmedebis gacnoba

moswavlis wigni: §6gakv 55 gamoklebis niSani

gakv 56 gamoklebis simboloebiT Cawera

gakv 57 areebis sazRvari moswavlis wigni: §7

gakv 58 ramdeniT metia?moswavlis wigni: §8

gakv 59 radeniT naklebia?

gakv 605-mde Sevseba moswavlis wigni: §9

gakv 61


gakv 63

94

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 54: gamoklebis moqmedebis gacnoba

gamoklebis moqmedebis gacnobapirvel dRes vacnobT mxolod moqmedebas, simbolos gareSe.

es ase xdeba:

maswavlebeli dafaze ganalagebs magnitur rgolebs (vTqvaT

10 rgols) da erT-erT moswavles eubneba:

– modi am grovidan (uTiTebs) aviRoT ramdenime cali. modi,

aiRe, moakeli 5 cali.

moswavle aiRebs 5 rgols da calke daawyobs.

– ra gaakeTe? (aviRe, movakeli 5 cali)

yvelaze mniSvnelovani gamoklebis swavlebisas isaa, rom

Tavdapirvelad ar vamaxvilebT yuradRebas, ramdenia saklebi,

magram imisaTvis, rom moqmedeba sagnebiT Sesruldes maklebi

cnobili unda iyos.

amitom zemoT aRweril proceduras SeasrulebT sxvadasxva

sagnebze, rodesac maklebi sxvadasxvaa (ajobebs, maklebi 1-dan

5-mde ricxvi iyos, rom bavSvebs moqmedebis Sesruleba gauad-

vildeT).


masalis gameorebas:

raodenobebis gadaTvlas da maTi Sesabamisi cifris moZebnas;






wirze.

gakveTilis mizani moswavles SeeZlos, gamoklebis moqmedebis Sesruleba.

esg-s indikatori





95

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 55: gamoklebis niSani

gamoklebis niSanimomdevno dRes maswavlebeli isev ganalagebs rgolebs dafaze

da am grovas gverdiT miudebs gamoklebis niSans da romelime

ricxvs 1-dan 5-mde

3-

Semdeg miuTiTebs gamoklebis niSanze da eubneba:

– es gamoklebis niSania. es niSani gveubneba, rom gamoklebis

moqmedeba unda Sesruldes. ramdeni unda gamovakloT? (miu-

TiTebs maklebze, romelic cifriTaa mocemuli)

aq unda aRiniSnos is faqti, rom maklebis gasagnobriveba ver

xerxdeba, maklebi yovelTvis igulisxmeba, igi saklebis nawilia.

gamodis moswavle, jer aiRebs gamoklebis niSans da cifrs (an

Tu es yvelaferi dafazea dawerili, waSlis) da Semdeg saklebs

moaSorebs maklebis Sesabamis raodenobas.

imaze, Tu ramdeni iyo saklebi an gamoklebis Sedegad ramde-

ni darCa, jer ar vamaxvilebT yuradRebas. es yvelaferi mesame

gakveTilze xdeba.


masalis gameorebas:

raodenobebis gadaTvlas da maTi Sesabamisi cifris moZebnas;






wirze.

gakveTilis mizani moswavles SeeZlos, gamoklebis niSnis mixedviT gamoklebis moqmedebis

Sesruleba.

esg-s indikatori





96

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 56: gamoklebis simboloebiT Cawera

gamoklebis simboloebiT CawerakeTdeba zustad igive, rac wina gakveTilze, oRond amjerad

jer davaTvlevinebT saklebs da moqmedebis Sesrulebis Semdeg –

darCenil raodenobas da vekiTxebiT moswavles:

– ramdeni iyo Tavdapirvelad?

– radeni gamovakeliT?

– ramdeni darCa?

– modi es yvelaferi CavweroT.

dafaze daiwereba:

25 – 3 =

momdevno gakveTilebis ganmavlobaSi, rodesac vavarjiSebT

gamoklebaSi, yovelTvis am TanmimdevrobiT vekiTxebiT:

ramdeni iyo? ramdeni gamovakeliT? ramdeni darCa?

an piriqiT, Tu mocemulia cifrebiT Cawerili gamokleba,

magaliTad 5-2, vekiTxebiT:

– ramdeni unda davdoT? (5) dade.

– ramdeni unda movakloT? (2)

– vin moaklebs?

– ramdeni darCa?

da bolos daiwereba:

35 – 2 =


masalis gameorebas.

gakveTilis mizani

moswavles SeeZlos, gamoklebis moqmedebis simboloebiT Cawera da piriqiT,

simboloebiT Cawerili gamoklebis mixedviT sagnebze konkretuli moq-

medebis Catareba.

esg-s indikatori





97

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

1. gaaferade Sida areebi yviTlad da wiTlad.

gareTa are gaaferade cisfrad.

daxate yviTeli

da wiTeli areebis

sazRvarze 5 wertili.

2. daakvirdi naxazs da Seasrule davaleba.

a. gareTa aris da lurji aris sazRvarze

burTulaa.

b. lurji da nacrisferi areebis sazRvarze

burTulaa.

g. gareTa aris da nacrisferi aris sazRvarze

burTulaa.

Tavi 3

43

areebis sazRvrebi

gakveTili 57: areebis sazRvari

gakveTilis mizani moswavles SeeZlos, wiris mier Seqmnili areebis sazRvrebis identificireba.

esg-s indikatori maT. I.7.4: miTiTebuli wesiT aerTebs ramdenime wertils sibrtyeze da moniS-

navs gzas miTiTebul obieqtamde martiv sqemaze.

areebis sazRvarimaswavlebeli dafaze xazavs wirs, romelsac ori Sida are aqvs.

– ramden ares gamohyofs es wiri? ar dagaviwydeT gareTa are.

– modi, gavaferadoT areebi.

areebis gaferadeba mniSvnelovania, raTa areebis sazRvris

identificireba iolad moxdes.

– aba, vin Cadebs rgols wiTel areSi? lurj areSi?

– Cade 3 rgoli gareTa areSi.

amis Semdeg moaTavsebs rgols wirze, wiTeli da lurji aree-

bis sazRvarze.

– romel areSia rgoli? (wirzea)

– marTalia, wirzea, wiTeli da lurji areebis sazRvarzea.

– aba vin dadebs gareTa aris da lurji aris sazRvarze am

rgols?

da a.S.


masalis gameorebas.

99



y 10-mde raodenobebis Sekreba da gamokleba sagnebze moqmedebis SesrulebiT; Sekrebis Cawera

da gamoklebis Cawera simboloebiT (cifrebi, Sekrebis da tolobis niSnebi);

y cnebebis „Sesakrebi“, „jami“, „saklebi“, „maklebi“, „sxvaoba“ sworad gamoyeneba;

y wiris gzajvaredinebis identificireba;

y grovis patara tol grovebad (sameulebad, oTxeulebad da a.S.) mowesrigeba da Cawera sim-

boloebiT gamosaxulebis saxiT;

y ramdenime ricxvis zrdadobis da klebadobis mixedviT dalageba.

am TavSi gansakuTrebuli mniSvneloba eniWeba gakveTilebs, sadac grovebad Tvlas vaswavliT.

grovebad Tvlas safuZveli Caeyara me-2 TavSi, rodesac moswavleebs gavacaniT „sameuli“, „oTx-

euli“ da „xuTeuli“.

axla gadavdivarT grovebad Tvlis sistemur Seswavlaze.


Tavi IV

gakv.64 ricxvebis dalageba zrdadobiT moswavlis wigni: §1

gakv.65 ricxvebis dalageba klebadobiT moswavlis wigni: §2

gakv 66 ricxvebis kibe moswavlis wigni: §3

gakv 67 nuli moswavlis wigni: §4

gakv 68 gamosaxuleba

moswavlis wigni: §5gakv 69 gamosaxulebis mixedviT grovebis Seqmna

gakv 70 SedarebiT rTuli gamosaxuleba

gakv 71 gamosaxulebis da ricxvis Sedareba moswavlis wigni: §6

gakv 72 gzajvaredinebi wirze moswavlis wigni: §7

gakv 73Sesakrebebi da jami moswavlis wigni: §8

gakv 74

gakv 75saklebi, maklebi, sxvaoba moswavlis wigni: §9

gakv 76

gakv 7710 TeTri da 10 lari moswavlis wigni: §10

gakv 78

100

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 68: gamosaxuleba

gakveTilis mizani moswavles SeeZlos, Tanabari raodenobis grovebis gadaTvla da Sedegis

simboloebiT Cawera.

esg-s indikatori maT. I.1.4: gamoyofs miTiTebuli ricxvebis Sesabamisi raodenobebis jgufebs


gamosaxulebamaswavlebeli dafaze ganalagebs 4 rgols erTad da gverdiT,

cota moSorebiT kidev 4 rgols.

TiToeul oTxeuls Semoxazavs.

– es ra aris? (oTxeuli) es? (oTxeuli)

– sul ramdeni oTxeuli yofila? (ori oTxeuli)

maswavlebeli dafaze dawers

4 • 2

gaayolebs TiTs nawers da ambobs:

– oTxeulebi (miuTiTebs 4-ze) aRebulia (miuTiTebs wertil-

ze) 2-jer (miuTiTebs 2-ze).

– maS ras gviCvenebs 4? es niSani ras niSnavs? (rom aRebulia)

2 ras gviCvenebs? (ramdeni oTxeulia)

es gamosaxuleba SegviZlia wavikiTxoT rogorc „4 aRebuli

2-jer“ an „ ori oTxeuli“ an „oTxeulebi aRebuli orjer“ da a.S.

moswavleebs unda SeeZloT imis gaazreba, rom am CanaweriT,

oTxeulebs viTvliT.

analogiuri savarjiSo Sesruldeba sameulebze, xuTeulebze,

eqvseulebze da a.S.


masalis gameorebas.

101

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebigamosaxulebis mixedviT grovebis Seqmnamaswavlebeli dafaze wers gamosaxulebas

5 • 3

– ras gviCvenebs 5? (xuTeulebi unda davawyoT) es wertili

ras niSnavs? (aviRoT) 3 ras gviCvenebs? (rom 3 xuTeulia)

– vin daalagebs amden (miuTiTebs gamosaxulebaze) rgols?

maS ramdeni xuTeuli unda davdoT?

analogiurad gakeTdeba sxvadasxva gamosaxulebebisaTvis.

magaliTad:

4 • 3

5 • 2

6 • 4

7 • 3da a.S.

am gakveTilis mizania, moswavles SeeZlos gamosaxulebis

mixedviT grovebis Seqmna.


masalis gameorebas.

gakveTili 69: gamosaxulebis mixedviT grovebis Seqmna

gakveTilis mizani moswavles SeeZlos, gamosaxulebis mixedviT Tanabari raodenobis grovebis

dawyoba.

esg-s indikatori

maT. I.1.4: gamoyofs miTiTebuli ricxvebis Sesabamisi raodenobebis jgufebs


maT. I.4.2: akavSirebs `-iT~ metoba/naklebobas Sekreba/gamoklebis moqmede-

bebTan da axdens amis modelze demonstrirebas.

102

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 70: SedarebiT rTuli gamosaxuleba

SedarebiT rTuli gamosaxulebamaswavlebeli dafaze ganalagebs 3 cal oTxeuls da gverdiT

miudebs kidev 2 cal rgols. oTxeulebs Semoxazavs.

– amas ra hqvia? (oTxeuli) amas? (oTxeuli)

– sul ramdeni oTxeulia? (sami)

– rogor iwereba sami oTxeuli?

moswavle dawers:

4 • 3

– mxolod oTxeulebi gvaqvs Tu, oTxeulebis garda, kidevaa

rame? (kidev ori calia)

maswavlebeli dafaze 4•3-s miuwers:

24 • 3 +

da xmamaRla kiTxulobs (Tan TiTs ayolebs gamosaxulebas)

– oTxeulebi aRebulia samjer da kidev ori cali. sami oTx-

euli da ori.

gakveTilis mizani

moswavles SeeZlos, sxvadasxva sirTulis gamosaxulebis Sesabamisi grove-

bis Seqmna da piriqiT, grovebad dawyobili sagnebis gamosaxulebis formiT

Cawera.

esg-s indikatori

maT. I.1.4: gamoyofs miTiTebuli ricxvebis Sesabamisi raodenobebis jgufebs


maT. I.4.2: akavSirebs `-iT~ metoba/naklebobas Sekreba/gamoklebis moqmede-


103

Cveni mizania gamoTqma „sami oTxeuli da ori“ (da analogiuri

gamoTqmebi sxva ricxvebze) raodenobis gamomxatvel sityvebad

iqces moswavleTaTvis. maTSi konkretul Sinaarss unda xeda-

vdnen.

rogorc cifri 9-is danaxvaze xedaven isini konkretul

raodenobas, romelic SeuZliaT, sagnebis gamoyenebiT daalagon

da es raodenoba daasaxelon sityvierad („cxra), zustad aseve

unda SeeZloT grovebad mowesrigebul-dastruqturebul did

grovaSi raodenobis danaxva.

aseTi varjiSi Zalian mniSvnelovania Tvlis sitemebis Sesa-

mzadeblad.

rodesac moswavles SeuZlia sxvadasxva saTvleli erTeuliT

Tvla (sameulebad, xuTeulebad, Svideulebad da a.S.), Semdeg

misTvis Zalian bunebrivia aTobiTi da ocobiTi sistemebiT Tvla.

misTvis sityva „ormocdaSvidi“ ukve analogiuri gamosaxule-

baa – ori oci (oceuli) da Svidi.

mas Semdeg, rac sxvadasxva raodenobebze analogiur mag-

aliTebs gaakeTeben (vTqvaT, 5•2+1, 7•4+5 da a.S.), SesaZlebelia

Sebrunebuli davalebis micema:

dafaze vwerT gamosaxulebas da moswavlem misi Sesabamisi

grovebi unda Seqmnas.

zustad iseve, rogorc cifrebis Seswavlisas, gamosaxule-

bebis Seswavlisasac mniSvnelovania, moswavleebs konkretuli

sagnebiT mocemuli raodenobis, am raodenobis Canawerisa da

saxelis erTmaneTTan dakavSireba SeeZloT.


masalis gameorebas.

am TavSi kidev erTi mniSvnelovani Temaa „wiris gzajvared-

inebi“.

zogadad, sibrtyeze mocemul wirebs ramdenime maxasiaTe-

beli aqvT. pirvel rigSi, es aris areebi, romlebic gamoiyofa;

sazRvrebi, romlebic am areebs erTmaneTTan aqvT da bolos,

gzajvaredinebi. gzajvaredinebi wiris iseTi wertilebia, sadac

ramdenime are esazRvreba erTmaneTs. bavSvebi, rogorc wesi, amas

iolad igeben da gzajvaredinebis identificireba ar uWirT.

105

Tavi 5 ricxvebi 11-dan 15 mde


y 10-dan 15-mde raodenobebis, maTi saxelebis da Sesabamisi simboloebis - cifrebis sworad

gamoyeneba, saxelis mixedviT cifrebis dawera; cifrebiT Cawerili raodenobis Sesabamisi

grovis Seqmna; konkretuli sagnebiT mocemuli raodenobis saxeldeba da cifrebiT Cawera;

y 10-dan 15-mde raodenobebis Sekreba da gamokleba sagnebze moqmedebis SesrulebiT; Sekrebis

da gamoklebis Cawera simboloebiT (cifrebi, Sekrebis da tolobis niSnebi);

y gaxsnili wirebis identificireba; cnebebis „monakveTi“ da „texili“ daufleba

10-dan 15-mde raodenobebis Seswavla zustad imgvarad xdeba, rogorc mcire raodenobebisa.

TiToeuli ricxvi Seiswavleba ramdenime gakveTilis ganmavlobaSi, Tumca sanam ricxvebis Ses-

wavlaze gadavalT, jer moswavleebs vuxsniT, ra aris aTeuli. raki grovebiT Tvla ukve naswavli

aqvT, aTeulobiT Tvla maTTvis grovebad Tvlis kerZo SemTxvevaa da advilad iTviseben.

kidev ori mniSvnelovani Tema am TavSi aris „gaxsnili wiri da monakveTi“ da „texili“.


Tavi V

gakv.79aTeuli moswavlis wigni: §1

gakv.80

gakv 81

TerTmeti moswavlis wigni: §2gakv 82

gakv 83Tormeti moswavlis wigni: §3

gakv 84

gakv 85cameti moswavlis wigni: §4

gakv 86

gakv 87ToTxmeti moswavlis wigni: §5

gakv 88

gakv 89TxuTmeti moswavlis wigni: §6

gakv 90

gakv 91 gaxsnili wiri da monakveTi moswavlis wigni: §7

gakv 92 texili moswavlis wigni: §8

gakv 93jamebis Sedareba moswavlis wigni: §9

gakv 94

gakv 95sxvaobebis Sedareba moswavlis wigni: §10

gakv 96

106

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 91: gaxsnili wiri da monakveTi

gakveTilis mizani moswavles SeeZlos, gaxsnili wirebisa da monakveTebis identificireba.

esg-s indikatori

maT. I.6.2: SearCevs miTiTebuli figuris models Sereuli grovidan;

maT. I.7.1: romelime xerxiT (magaliTad, aplikaciiT an naxatis saSualebiT)

qmnis dasaxelebuli formis brtyeli figuris models an gamosaxulebas.

gaxsnili wiri da monakveTimaswavlebeli dafaze xatavs aseT wirs da moaTavsebs rgols.

– SigniTaa Tu gareT?

bavSvebisTvis es axali situaciaa. gaimarTeba kamaTi. zogi

ityvis, rom SigniTaa, zogi – gareT.

maswavlebeli auxsnis, rom es sxvanairi wiri, mas Sida are da

gare are ara aqvs. aseT wirs hqvia gaxsnili wiri.

– gaxsnil wirs aqvs boloebi, - ambobs maswavlebeli da wiris

boloebSi wertilebs gaamuqebs.

mere dafaze sxvadasxvanair gaxsnil wirebs daxazavs da mos-

wavleebsac daaxazvinebs.

am wirebs Soris daxazavs monakveTsac da ambobs:

– zogierTi gaxsnili wiri swori xazia. aseT wirs hqvia mon-

akveTi. monakveTs aqvs boloebi.


masalis gameorebas.

107

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

1. ramdeni monakveTisgan Sedgeba es texili?

texilSi monakveTia.

texilSi monakveTia.

2. am wirebidan romelia texili? Semoxaze.

3. ramdeni Sekruli da ramdeni gaxsnili texilia?

gaxsnili texilia.

Sekruli texilia.

62

texili

რამდენი შეკრული ტეხილია? რამდენი გახსნილი

ტეხილია? შეკრული და გახსნილი ტეხილები

ერთად რამდენია?

რამდენი მონაკვეთია ამ ტეხილში?

რამდენი მონაკვეთია ამ ტეხილში?

ამ წირებიდან რომელია ტეხილი?

რამდენი მონაკვეთისგან შედგება?

ეს წირი მონაკვეთებისგან

შედგება. მას ტეხილი ჰქვია.

ეს შეკრული ტეხილია.

67Tavi 5

8ტეხილი

gakveTili 92: texili

gakveTilis mizani moswavles SeeZlos, texili wirebis identificireba.

esg-s indikatori

maT. I.6.3: aRwers miTiTebul geometriul figuras (magaliTad, asaxelebs

mocemuli mravalkuTxedis wveroebis raodenobas);

maT. I.7.1: romelime xerxiT (magaliTad, aplikaciiT an naxatis saSualebiT)

qmnis dasaxelebuli formis brtyeli figuris models an gamosaxulebas.

texilimaswavlebeli dafaze xazavs wirs, romelic erTmaneTze gad-

abmuli monakveTebisgan Sedgeba.

– es wiri monakveTebisgan Sedgeba. ramdeni monakveTia am wir-

Si?

– aseT wirs hqvia texili.

– es texili gaxsnilia Tu Sekruli?

– es Sekruli texilia. ramdeni monakveTisagan Sedgeba es

Sekruli texili?


masalis gameorebas.

109



y 15-mde raodenobebis Sekreba da gamokleba sagnebze moqmedebis SesrulebiT; Sekrebis da

gamoklebis Cawera simboloebiT (cifrebi, Sekrebis da tolobis niSnebi);

y iseTi ori raodenobis Sekreba, rodesac Sekrebisas aTeuli warmoiqmneba;

y Sekrebisa da gamoklebis cxrilebis sworad Sevseba;

y gamosaxulebebad Cawerili ori raodenobis Sedareba sagnebad dawyobiTa da dawyvilebiT;

y Sekruli texilebis da, kerZod, sxvadasxva mravalkuTxedebis (samkuTxedi, oTxkuTxedi)

identificireba;

y sruli saaTebis cnoba.

gansakuTrebiT mniSvnelovani Temebia „ramdenime Sesakrebi“ da „gamosaxulebebis Sedareba“


Tavi VI

gakv.97ramdenime Sesakrebi moswavlis wigni: §1

gakv.98

gakv 99

15-mde Sevseba moswavlis wigni: §2-3gakv 100

gakv 101 15-mde Sekreba moswavlis wigni: §3

gakv 102Sekrebisas aTeulis warmoqmna moswavlis wigni: §4

gakv 103

gakv 104Sekrebis cxrili moswavlis wigni: §5

gakv 105

gakv 106gamoklebis cxrili moswavlis wigni: §6

gakv 107

gakv 108gamosaxulebis Sedareba dawyvilebiT moswavlis wigni: §7

gakv 109

gakv 110samkuTxedi da oTxkuTxedi moswavlis wigni: §8

gakv 111

gakv 112wre. mravalkuTxedi moswavlis wigni: §9

gakv 113

gakv 114romeli saaTia? moswavlis wigni: §10

gakv 115

110

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 97: ramdenime Sesakrebi

gakveTilis mizani moswavles SeeZlos, ramdenime Sesakrebis gamoyenebiT moqmedebis Sesruleba

da simboloebiT fiqsireba.

esg-s indikatori

maT. I.3.1: sityvierad aRwers Sekrebis, gamoklebis, tolobisa da Sedegis cne-

bebs sxvadasxva konteqstSi (magaliTad, `davumatoT~, `movakloT~, mimateba

– gazrda; gamokleba – Semcireba, gancalkeveba, gansxvaveba);

maT. I.3.2: axdens Sekreba-gamoklebis TvalsaCinod demonstrirebas, gansaz-

Rvravs gansxvavebas (magaliTad, `ramdeniT gaizarda/Semcirda?~) da aRwers

ricxvebs Soris damokidebulebebs.

ramdenime Sesakrebimaswavlebeli dafaze ganalagebs 3 sxvadasxva grovas: 2 rgo-

li, 3 rgoli da 4 rgoli da maT Soris Casvams Sekrebis niSnebs

+ +

– ra moqmedebebi unda SevasruloT?

– ramdenia pirveli Sesakrebi? meore Sesakrebi“ mesame

Sesakrebi?

– vin Seasrulebs moqmedebebs?

gamodis moswavle, aiRebs moqmedebaTa niSnebs da SeaerTebs

grovebs.

– ramdenia jami?

moswavle gadaTvlis rgolebs da ambobs:

– cxra.

– CavweroT es yvelaferi.

da maswavlebeli dafaze wers:

4 92 + 3 + =

111

amis Semdeg Sesruldeba Sebrunebuli davaleba: dafaze dai-

wereba

25 + 1 +

– ramdenia pirveli Sesakrebi? (5) meore Sesakrebi? (1) mesame

Sesakrebi? (2)

daalageben Sesakrebebis Sesabamisi raodenobebis sagnebs,

SeaerTeben grovebs da moswavle gadaTvlis xelaxla. dafaze

Caiwereba Sedegi:

2 85 + 1 + =


masalis gameorebas.

112

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

7

7 2 + 5 6 3 + 4

78 Tavi 6

გადაიწერე გამოსახულებები. თითოეულს ქვეშ

მიუხატე შესაბამისი რაოდენობის რგოლები და

დააწყვილე.

5 2 + 3 4 3 + 2

რამდენი ხუთეულია მარცხენა მხარეს?

ხუთეულების გარდა კიდევ რამდენია?

მარჯვენა მხარეს რამდენი ოთხეულია?

ოთხეულების გარდა კიდევ რამდენია?

რომელ მხარეს დარჩა დაუწყვილებელი?

რომელი ყოფილა ნაკლები?

გამოსახულებების შედარება დაწყვილებით

gakveTili 108: gamosaxulebebis Sedareba

gakveTilis mizani moswavles SeeZlos, gamosaxulebebis Sedareba maTi Sesabamisi grovebis

SeqmniTa da dawyvilebiT.

esg-s indikatori




gamosaxulebebis Sedarebamaswavlebeli dafaze wers or gamosaxulebas erTmaneTisagan

sakmaod moSorebiT:

3

2

5

4

•

•

2

3

+

+– vin waikiTxavs, ra weria aq? (miuTiTebs pirvel gamosax-

ulebaze)

– xuTeulebi aviRoT orjer da sami.

– davalagoT ori xuTeuli da sami rgoli.

moswavle gamodis da gamosaxulebis qveS daalagebs Sesabamisi

raodenobis wiTel rgolebs.

analogiurad dalagdeba meore gamosaxulebis qveS Sesabamisi

raodenobis lurji rgolebi.

– rogor gavigoT, romelia meti?


– vin daawyvilebs?

dawyvilebis Semdeg aRmoCndeba, rom marjvena gamosaxulebaSi

1 cali darCa dauwyvilebeli.

– maSasadame, romeli yofila meti?

– CavweroT met-naklebobis niSani.

113

sabolood daiwereba:

3

2

5

4

<

•

•

2

3

+

+analogiurad Sedardeba sxvadasxva gamosaxulebebi.

Cveni mizania, moswavleebs SeeZloT gamosaxulebebis Sesa-

bamisi grovebis Seqmna da dawyvilebis saSualebiT am grovebis

Sedareba, bolos ki miRebuli Sedegebis Cawera.


masalis gameorebas.

115

Tavi 7 ricxvebi 16-dan 20 mde


y 16-dan 20-mde ricxvebis, maTi saxelebis da Sesabamisi simboloebis - cifrebis sworad gamoy-

eneba, saxelis mixedviT cifrebis dawera; cifrebiT Cawerili raodenobis Sesabamisi grovis

Seqmna; konkretuli sagnebiT mocemuli raodenobis saxeldeba da cifrebiT Cawera;

y ricxvis daSla-warmodgena or Sesakrebad;

y marTkuTxedis cnebis gaazreba da sxvadasxva figurebs Soris marTkuTxedebis identifi-

cireba; cnebebis „wre“ da „wrewiri“ daufleba.

ricxvebis (16, 17, 18, 19, 20) Seswavla imave meTodiT xdeba, rogorc wina TavebSi.

gansakuTrebiT mniSvnelovania Semdegi gakveTili:


Tavi VII

gakv.116Teqvsmeti moswavlis wigni: §1

gakv.117

gakv 118

Cvidmeti moswavlis wigni: §2gakv 119

gakv 120Tvrameti moswavlis wigni: §3

gakv 121

gakv 122cxrameti moswavlis wigni: §4

gakv 123

gakv 124oci moswavlis wigni: §5

gakv 125

gakv 126ricxvis daSla or Sesakrebad moswavlis wigni: §6

gakv 127

gakv 128samkuTxedi, oTxkuTxedi, xuTkuTxedi moswavlis wigni: §7

gakv 129

gakv 130marTkuTxedi moswavlis wigni: §8

gakv 131

gakv 132wre da wrewiri moswavlis wigni: §9

gakv 133

116

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

89Tavi 7

6

გადაიწერე რვეულში და ფერადი უჯრების

ადგილას დაწერე შესაბამისი რიცხვები.

ა. 7 = 4 +

ბ. 12 = 10 +

გ. 18 = 9 +

დ. 10 = 5 +

ე. 15 = 11 +

ვ. 17 = 8 +

9 = 4 + 5

სულ რამდენი ფანქარია?

რამდენია ცისფერი?

რამდენია მწვანე?

სულ რამდენი ბავშვია? რამდენი ბიჭია?

რამდენი გოგონაა? სურათის მიხედვით დაწერე

რიცხვი და დაშალე ორი შესაკრების ჯამად.

გადაიწერე რვეულში და დაშალე ორ შესაკრებად.

ა. 20 = + გ. 11 = +

ბ. 13 = + დ. 18 = +

9

4 5

რიცხვის დაშლა ორ შესაკრებად

ფაზლის რამდენი ნაჭერია სულ?

რამდენია ყვითელი? რამდენია მწვანე?

gakveTili 126: ricxvis daSla or Sesakrebad

gakveTilis mizani moswavles SeeZlos, ricxvis warmodgena ori Sesakrebis saxiT.

esg-s indikatori

maT. I.3.1: sityvierad aRwers Sekrebis, gamoklebis, tolobisa da Sedegis cne-

bebs sxvadasxva konteqstSi (magaliTad, `davumatoT~, `movakloT~, mimateba

– gazrda; gamokleba – Semcireba, gancalkeveba, gansxvaveba).

ricxvis daSla or Sesakrebadaqamde bavSvebs vaswavleT, rom ori sxvadasxva raodenobis

SeerTebiT axali, ufro didi raodenoba miiReba. amjerad saw-

inaaRmdego process vaswavliT, kerZod, imas, rom nebismieri

raodenoba, ricxvi SegviZlia davanawiloT da es nawilebic ricx-

vebia, oRond ufro patara ricxvebi.

maswavlebeli dafaze gaamwkrivebs 4 lurj da 5 wiTel rgols

– ramdeni rgolia dafaze? vin daTvlis?

gamodis moswavle da Tvlis:

– cxra rgolia.

maswavlebeli dafaze dawers: 9

– ramdenia amaTgan wiTeli? (5)

– ramdenia lurji? (4)


masalis gameorebas.

117

maswavlebeli erTmaneTs cotaTi daaSorebs wiTel da lurj

rgolebs da dawers:

9 = 4 + 5

– cxra or nawilad, or Sesakrebad davSaleT.

maswavlebeli calke dawers 9-s da Semoxazavs, mere mis qveS

dawers 4-s da 5-s da maTac Semoxazavs da 9-sTan xazebiT daakav-

Sirebs. gamova aseTi suraTi:

9

4 5

analogiurad gaakeTebs sxvadasxva ricxvebze.

am aqtivobebis mizania, bavSvma gaiazros, rom ricxvis nawi-

lebic ricxvebia.


masalis gameorebas.

118

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 130: marTkuTxedi

gakveTilis mizani moswavles SeeZlos, marTkuTxedebis identificireba da yofiT sagnebSi

marTkuTxedis formis sagnebis gamoyofa.

esg-s indikatori

maT. I.6.1: yofiTi daniSnulebis sagnebSi an maT ilustraciebSi uTiTebs

dasaxelebul brtyel figurebs;

maT. I.6.2: SearCevs miTiTebuli figuris models Sereuli grovidan;

maT. I.6.3: aRwers miTiTebul geometriul figuras (magaliTad, asaxelebs

mocemuli mravalkuTxedis wveroebis raodenobas).

marTkuTxediam gakveTiliT moswavleebi gaecnobian kidev erT figuras,

marTkuTxeds.

jer maswavlebeli ikiTxavs, romeli mravalkuTxedebi ician

moswavleebma da bavSvebi daasaxeleben samkuTxeds, oTxkuTxeds,

xuTkuTxeds.

amis Semdeg maswavlebeli dafaze daaxazvinebs sxvadasxva

oTxkuTxedebs, daaTvlevinebs, ramdeni monakveTisgan Sedgeba

TiToeuli da ramdeni wvero aqvs.

amis Semdeg daxazavs marTkuTxeds da eubneba:

– daakvirdiT am oTxkuTxeds. mas swori anu marTi kuTxeebi

aqvs da amitom marTkuTxedi hqvia. aba, vis SeuZlia moZebnos da

daasaxelos marTkuTxedis formis sagnebi?

Tu moswavleebi verafers moifiqreben, maswavlebeli ram-

denime variants SesTavazebs: wigni, furceli, oTaxi (Tu oTaxi

marTkuTxedis formisaa) da a.S.

amis Semdeg Tavad moswavleebsac gaaxsendebaT sxva sagnebi,

romlebic marTkuTxedis formisaa.


masalis gameorebas.

119



y 20-is farglebSi Sekreba-gamokleba, sagnebis gamoyenebiT; Sekreba-gamoklebis Cawera simbo-

loebiT, maT Soris, Sekreba-gamokleba aTeulis warmoqmniT da aTeulis daSliT;

y ricxvebis gaormageba-ganaxevreba 20-is fargalSi;

y ricxvTa RerZze saTanado ricxvis moZebna da Sekreba-gamoklebebis moqmedebebis Sesruleba;

y tolobebsa da utolobebze imis dadgena, sworia Tu mcdari;

y martivi monacemebis moZieba da cxrilSi Setana


Tavi VII

gakv.134 ricxvebis RerZi (I etapi)

moswavlis wigni: §1gakv.135 ricxvebis RerZi (II etapi)

gakv.136 moqmedebebi ricxvTa RerZze

gakv 137

gaormageba moswavlis wigni: §2gakv 138

gakv 139ganaxevreba moswavlis wigni: §3

gakv 140

gakv 141Sekreba aTeulis warmoqmniT moswavlis wigni: §4

gakv 142

gakv 143gamokleba aTeulis daSliT moswavlis wigni: §5

gakv 144


gakv 146

gakv 14720 TeTri da 20 lari moswavlis wigni: §7

gakv 148

gakv 149sworia Tu mcdari? moswavlis wigni: §8

gakv 150

gakv 151monacemebis Setana cxrilSi moswavlis wigni: §9

gakv 152

120

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

gakveTili 134: ricxvTa RerZi (1-li etapi: ricxvebis dalageba zrdadobiT)

ricxvTa RerZi (1-li etapi: ricxvebis dalageba zrdadobiT)maswavlebeli dafaze areulad ganalagebs ramdenime baraTs,

romlebzedac sxvadasxva ricxvebi weria (magaliTad, 4, 7, 11, 16,

20).

– aba, vin daalagebs am ricxvebs zrdadobis mixedviT? rome-

lia amaTgan yvelaze patara ricxvi?

moswavle gamodis da awesrigebs ricxvebs zrdadobis mixed-

viT.

amis Semdeg maswavlebeli cvlis ricxvebs (amave dros zrdis

maT raodenobas - ukve dasalageblad sTavazobs 7 sxvadasxva

ricxvs) da isev akeTebinebs imave savarjiSos.

bolos daalagebs baraTebs, romlebzedac 0-dan 20-mde yvela

ricxvia da moawesrigebinebs zrdadobis mixedviT.

imisaTvis, rom es aqtivoba ufro saxalisod warimarTos,

SesaZlebelia moswavleebis (imdenive moswavlis, ramdeni sxva-

dasxva baraTicaa) gamoyvana dafasTan da TiToeulisaTvis TiTo

baraTis micema; Semdeg moswavleebi unda dadgnen mimdevrobiT,

ricxvebis zrdadobis mixedviT.


masalis gameorebas.

gakveTilis mizani moswavles SeeZlos, ramdenime ricxvis zrdadobis mixedviT dalageba.

esg-s indikatori maT. I.4.2: akavSirebs `-iT~ metoba/naklebobas Sekreba/gamoklebis moqmede-


121

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

94 Tavi 8

1 რიცხვების ღერძი

5 7 8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

რა რიცხვია 10-ის წინ? 10-ის მომდევნო?

რომელია 20-ის წინა რიცხვი? 8-ის წინა?

გადაიხატე რვეულში რიცხვების ღერძის ნაწილი და

ჩაწერე გამოტოვებული რიცხვები.

0 1 2 3 4 5

+5

6 7 8 9 10

0 1 2 3 4 5

+1 +1 +1 +1 +1

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4 + 5 = 9

იმისათვის, რომ 4-ს დავუმატოთ 5, რიცხვთა ღერძზე

4-ის მარჯვნივ 5 დანაყოფი უნდა გადავთვალოთ.

ამის დახატვა ასეც შეიძლება:

ორი რიცხვიდან მეტია ის რიცხვი, რომელიც მარჯვნივაა.

gakveTili 135: ricxvTa RerZi (me-2 etapi)

gakveTilis mizani moswavles SeeZlos, 0-dan 20-mde ricxvebis RerZze orientireba da ama Tu

im ricxvis wina da momdevno ricxvebis dasaxeleba.



ricxvTa RerZi (me-2 etapi)maswavlebels momzadebuli aqvs 0-dan 20-mde ricxvebis

baraTebi, agreTve dafaze gavlebuli xazi, romelic dayofilia

Tanabar Sualedebad (sul 21 danayofia).

– es wertilebi (uTiTebs naxazze), ricxvebisTvisaa. – ambobs,

Tavad iRebs baraTs, romelzedac weria 0 da aTavsebs ganapira

marcxena wertilis qveS.

– aba, vin ityvis, ra ricxvi iqneba Semdegi? (1)

– marTalia. vin dadebs erTians am adgilas? (miuTiTebs)

analogiurad gaakeTebinebs yvela ricxvisaTvis. rodesac

yvela ricxvi Tavis adgilas aRmoCndeba, maswavlebeli ambobs:

– romelime ricxvi xom ar gamogvrCa? yvela Tavis adgilzea?

– amas (TiTs gaayolebs xazs) ricxvTa RerZi hqvia. yvela ricx-

vi zrdadobiT rom davalagoT, ricxvTa RerZi gamogviva.

amis Semdeg aCvenebs ricxvTa RerZs moswavlis wignebSi da

usvams imave SekiTxvebs, rac wignSia.

momdevno savarjiSo ricxvTa RerZis nawilze gamotovebuli

ricxvebis moZebnaa:

maswavlebeli dafaze xazavs ricxvTa RerZis erT nawils (zus-

tad iseTs, rogoric wignSia)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

– SexedeT, yvela ricxvi araa miwerili. aq ra ricxvi unda

eweros? ratom? aq? da a.S.


masalis gameorebas.

122

y magnituri dafa

y markerebi

y magnituri rgolebi

y baraTebi

resursebi

94 Tavi 8

1 რიცხვების ღერძი

5 7 8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

რა რიცხვია 10-ის წინ? 10-ის მომდევნო?

რომელია 20-ის წინა რიცხვი? 8-ის წინა?

გადაიხატე რვეულში რიცხვების ღერძის ნაწილი და

ჩაწერე გამოტოვებული რიცხვები.

0 1 2 3 4 5

+5

6 7 8 9 10

0 1 2 3 4 5

+1 +1 +1 +1 +1

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4 + 5 = 9

იმისათვის, რომ 4-ს დავუმატოთ 5, რიცხვთა ღერძზე

4-ის მარჯვნივ 5 დანაყოფი უნდა გადავთვალოთ.

ამის დახატვა ასეც შეიძლება:

ორი რიცხვიდან მეტია ის რიცხვი, რომელიც მარჯვნივაა.

gakveTili 136: moqmedebebi ricxvTa RerZze

gakveTilis mizani moswavles SeeZlos, Sekrebis da gamoklebis moqmedebebis Sesruleba ricx-

vTa RerZis gamoyenebiT.



moqmedebebi ricxvTa RerZzemaswavlebels dafaze winaswar momzadebuli aqvs ricxvTa

RerZi 0-dan 20-mde da dafaze dawers:

4 + 5

– SexedeT, ricxvTa RerZis daxmarebiT, SesaZlebelia Sekreba

da gamokleba. (miuTiTebs ricxvTa RerZis 4-ianze) 4-s unda davu-

matoT 5. amisaTvis, raki damatebas, Sekrebas gvTxoven, ricxvTa

RerZze imdeni nabiji unda gadavdgaT, ramdensac es ricxvi (miu-

TiTebs 5-ze) gviCvenebs.

maswavlebeli TiTiT an saCvenebeli joxiT nela aCvenebs

(gadadis momdevno ricxvebze):

– erTi, ori, sami, oTxi da xuTi. ra ricxvTan movediT (9-sTan).

maswavlebeli dafaze miuwers:

4 + 5 = 9

analogiurad gaakeTebinebs gamoklebis magaliTs da auxsnis,

rom gamoklebisas ricxvTa RerZze marcxniv gadavdivarT.


masalis gameorebas.

danarTi

124

bavSvis asakobrivi Taviseburebebi

(piaJes kognituri ganviTarebis Teoriis mokle mimoxilva)

imisaTvis, rom maTematika aswavlos, maswavlebeli kargad unda icnobdes Sesabamisi asakis mos-

wavlis asakobriv Taviseburebebs.

es Taviseburebebi mkvlevarTa mier intensiurad Seiswavleboda me-20 saukuneSi. gansakuTre-

biT unda gamoiyos didi Sveicarieli fsiqologis, Jan piaJes kvlevebi. piaJem faqtobrivad myari

mecnieruli safuZveli SesZina bavSvis inteleqtis ganviTarebis etapebis kvlevas.

zogjer piaJes Teorias stadiebis Teoriasac uwodeben, radgan piaJem inteleqtis ganviTarebis

oTxi stadia gamoyo: sensomotoruli (0-dan 2 wlamde), winaoperaciuli (2-dan 7 wlamde), konkret-

uli operaciebis (7-dan 11 wlamde) da formaluri operaciebis (11-dan 15 wlamde).

sensomotoruli periodi dabadebidan enis dauflebamde grZeldeba. am stadiaSi bavSvi TandaTa-

nobiT iyalibebs codnas garemomcvel samyaroze ara ubralod smena-mxedvelobis meSveobiT, aramed

obieqtebTan fizikuri kavSiris (Sexeba, alokva da a.S.) gziT. bavSvi swavlobs, rom is garemosagan

gamocalkevebulia. iZens codnas, rom garemo arsebobs maSinac ki, rodesac grZnobis organoebiT

uSualod ver aRiqvams. am stadiaze umniSvnelovanesi miRweva aris is, rom bavSvs uviTardeba obi-

eqtTa ucvlelobis/mudmivobis aRqma. igi xvdeba, rom sagnebi maSinac ki ganagrZoben arsebobas,

rodesac Tavad maT ver xedavs an smeniT ver grZnobs.

winaoperaciuli stadia iwyeba, rodesac bavSvi laparaks eufleba da grZeldeba daaxloebiT 7

wlis asakamde. am periodSi bavSvs ar SeuZlia konkretuli logikuri msjelobis gageba da gonebiT

operireba. uWirs Sexedos sagnebs sxvisi TvalTaxedviT.

es stadia or qvestadiad iyofa: simboluri funqciis qvestadia (2-4 wlebi) da intuiciuri

azrovnebis qvestadia (4-7 wlebi).

simboluri funqciis qvestadiaze bavSvs jer kidev ar SeuZlia informacia logikurad

gadaamuSaos. am dros simboluri TamaSi did rols asrulebs. bavSvs hyavs warmosaxviTi megobrebi

da TamaSobs rolur TamaSebs megobrebTan erTad (magaliTad, „saxlobanas“).

am etapze adgili aqvs bavSvis azrovnebaSi egocentrizms da winaremizezobriv azrovnebas. ego-

centrizmi Cans piaJes cnobil cdaSi, romelsac „sami mTis problema“ hqvia. eqsperimentis dros

bavSvs uCveneben mTis sami sxvadasxva rakursiT gadaRebul suraTs da ekiTxebian, ras dainaxavda

mogzauri Tojina sxvadasxva kuTxidan. bavSvi yovelTvis ambobs imas, rasac Tavad xedavs, mas ar

SeuZlia Sexedos suraTs sxvisi perspeqtividan.

4-dan 7 wlamde asakSi bavSvebi Zalian cnobismoyvareebi arian, uamrav SekiTxvas svamen da iwyeben

martiv msjelobas. uCndebaT interesi, gaarkvion, ratom arian sagnebi ise, rogorc arian. piaJe

amas intuiciur qvestadias imitom uwodebda, rom bavSvebi xvdebian, rom aqvT codnis mozrdili

maragi, magram ver icnobiereben, rogor SeiZines es codna. winaoperaciuli azrovnebis maxasiaT-

eblebia: centrireba (bavSvs SeuZlia yuradRebis mipyroba sagnis mxolod erT maxasiaTebelze

da danarCenebs ver xedavs) da konservacia (Semonaxva). es ori Tviseba kargad Cans piaJes cnobil

eqsperimentSi: bavSvs aZleven or identur Wiqas da avseben Tanabari raodenobis siTxiT. bavSvi

advilad xvdeba, rom WiqebSi Tanabari odenobis siTxea. Semdeg erT-erTi Wiqidan gadaasxamen siTxes

sxva WiqaSi, romelic ufro viwro da maRalia. 7 welze mcire asakis bavSvebi aseT dros amboben, rom

axla aRar aris Tanabari odenobis siTxe WiqebSi da viwro da maRal WiqaSia ufro meti, miuxedavad

imisa, rom siTxis gadasxmamde ambobdnen, rom Tanabari odenoba iyo. bavSvi ver xvdeba, rom formis

Secvla odenobis cvlilebas ar iwvevs. bavSvs ara aqvs SeqceviTobis unari. mas ar SeuZlia gonebaSi

Caataros SeqceviTi operacia: Tu maRali da viwro Wiqidan isev ukan gadavasxamT wyals, odenobebi

isev Tanabari gaxdeba. kidev erTi magaliTi (da sxva eqsperimenti) exeba cnebebs „meti“ da „nakle-

125

bi“. bavSvs win uwyoben kubebis or erTnair rigs, Semdeg erT-erT rigs moaSoreben da gafantaven.

bavSvs hgonia, rom gafantul rigSi meti kubia.

bavSvs aqvs problema gaigos nawilisa da mTelis mimarTeba. piaJe 4 wlis gogonas aCvenebda

suraTs, romelzedac gamoxatuli iyo rva ZaRli da sami kata. gogonam icoda, ra aris ZaRli da ra

aris kata da rom eseni cxovelebi arian. miuxedavad amisa, rodesac ekiTxebodnen „ZaRlebi metia

Tu cxovelebi?“ igi pasuxobda: „ZaRlebi“. es im mizeziT xdeba, rom bavSvs ar SeuZlia erTdrou-

lad aRiqvas didi simravle da misi ori nawili/qvesimravle. mas SeuZlia aRiqvas ZaRli an rogorc

ZaRli, an rogorc cxoveli, magram uWirs es gaakeTos erTdroulad.

winaoperaciul stadiaze bavSvs ara aqvs e.w. tranzituli mimarTebebis wvdomis unari. man Sei-

Zleba icodes, rom „A metia B B-ze“ da „BB metia C-ze“, magram aqedan ver gaakeTebs daskvnas, rom „A

metia C-ze“.

konkretuli operaciebis stadia (7-11 wlebi)

am stadiaze bavSvi ukve iyenebs logikas. nel-nela bavSvis azrovneba emsgavseba ufrosisas. jer

kidev araa ganviTarebuli abstraqtuli, hipoTeturi azrovneba da amitom bavSvs SeuZlia mxolod

iseTi problemebis gadaWra, romlebic konkretul obieqtebTanaa dakavSirebuli. am stadiaze

bavSvi iwyebs konservaciis (Semonaxvis) principis gagebas. uviTardeba induqciuri azrovneba anu

dakvirvebebidan axdens ganzogadebas. Tumca uWirs deduqciuri azrovneba, rac gulisxmobs imis

unars, rom SeeZlos zogadi principidan konkretuli Sedegis varaudi. kidev erTi mniSvnelovani

ram xdeba am stadiaze: bavSvs uqreba e.w. egocentrizmi anu ukve SeuZlia Sexedos movlenebs ara

mxolod sakuTari Tavidan gamomdinare, aramed sxvisi perspeqtiviTac. magaliTad, Tu bavSvs vaCven-

ebT suraTebs, romelzedac nino debs Tojinas yuTSi da gadis oTaxidan; Semdeg mariami gadadebs

Tojinas yuTidan karadaSi da mere nino brundeba oTaxSi. winaoperaciul stadiaze, bavSvis azriT,

ninos Tojina karadaSi hgonia. amas imitom ambobs, rom TviTon ukve icis, rom Tojina karadaSia da

ar SeuZlia sxvisi TvaliT Sexedos movlenebs. konkretuli operaciebis stadiaze, bavSvis azriT,

ninos egoneba, rom Tojina yuTSia.

Tumca am stadiaze bavSvebs SeuZliaT mxolod konkretul obieqtebTan dakavSirebuli amo-

canebis gadaWra da ver Zleven abstraqtul cnebebs an hipoTetur amocanebs.

azrovnebis ganviTarebis bolo stadiaa formaluri operaciebis stadia (11-dan daaxloebiT

15 wlamde). am dros viTardeba hipoTeturi da deduqciuri msjelobis unari. mozardebi iwyeben

abstraqtuli koncefciebis aRqma-gagebas. dawyebiTi skolis asakSi bavSvebi metwilad iyeneben

induqciur msjelobas, pirad gamocdilebaze da konkretul faqtebze dayrdnobiT akeTeben zogad

daskvnebs. es unari gansxvavdeba hipoTeturi azrovnebis unarisagan. Tumca aqve unda aRiniSnos,

rom sxvadasxva kulturebis warmomadgeneli yvela adamiani rodi aRwevs formaluri operaciebis

stadias da arc adamianebis umravlesoba iyenebs formalur operaciebs TavianTi cxovrebis yvela

aspeqtSi.

piaJem Caatara ramdenime eqsperimenti, raTa gaerkvia, rogor funqcionirebs azrovneba for-

maluri operaciebiT.

cnobilia, magaliTad, sawonebiani sasworiT Catarebuli eqsperimentebi. cdispirebs evalebodaT,

sxvadasxva sawonis gamoyenebiT gaewonasworebinaT saswori. imisaTvis, rom warmatebiT daeZliaT

amocana, bavSvebs unda gamoeyenebinaT formaluri operaciuli azrovneba da mimxvdariyvnen, rom

sasworze gavlenas axdenda rogorc sawonis simZime, aseve misi daSoreba centridan. ufro mZime

sawoni unda CamoekidaT centrTan ufro axlos, xolo ufro msubuqi sawoni – centridan moSorebiT,

raTa saswori gaewonasworebinaT. 3-5 wlis bavSvebi gawonasworebis arss saerTod ver xvdebodnen.

7 wlis bavSvebi awonasworebdnen saswors mxolod erTnairi sawonebiT, magram ver xvdebodnen

sawonis mdebareobis mniSvnelobas. 10 wlis bavSvebi xvdebodnen mdebareobis mniSvnelobas, magram

logikis nacvlad iyenebdnen cdis da Secdomis meTods. da bolos, 13-14 wlis mozardebi ukve

iazrebdnen wonasa da daSorebas Soris kavSirs da axerxebdnen warmatebiT ganexorcielebinaT

TavianTi hipoTeza.

126

swored piaJes Teorias eyrdnoba winamdebare saxelmZRvanelos meTodologia:

upirveles yovlisa imas, rom 6 wlis bavSvi imyofeba winaoperaciul stadiaze da male unda

gadavides konkretuli operaciebis stadiaze. Sesabamisad, iseTi abstraqtuli cnebis gaazreba,

rogorebicaa „ricxvi“, „raodenoba“, aucileblad konkretul sagnebze moqmedebebiT unda xdebodes.

aseve, frTxilad unda Semodiodes simboloebi, raTa moswavle mieCvios simboloSi konkretuli

Sinaarsis danaxvas. misTvis cifrebi da moqmedebaTa niSnebi SinaarsiT datvirTuli simboloebi

unda gaxdes. yovel CanawerSi unda xedavdes konkretul raodenobas da, piriqiT, SeeZlos konk-

retuli moqmedebebis simboloebiT Cawera.

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