maTematika - diogene.ge · maswavlebeli amowmebs, SeuZliaT Tu ara moswavleebs sibrtyeze orientireba...

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eka CiloCava

salome CxeiZe

maTematika IV klasi

maswavleblis wigni

1

maTematikis IV klasis saxelmZRvanelo

maswavleblis wigni

Sesavali

IV klasis saxelmZRvanelo I, II da III klasebis saxelmZRvaneloebis logikuri

gagrZelebaa da erovnuli saswavlo gegmis moTxovnebs iTvaliswinebs.

saxelmZRvanelo imgvaradaa agebuli, rom gaTvaliswinebulia am asakis

bavSvis rogorc saWiroebebi da interesebi, ise misi fsiqo-fizikuri

SesaZleblobebi. saxelmZRvanelo orientirebulia Sedegze, rac imas

gulisxmobs, rom yuradReba maxvildeba ara mxolod konkretuli informaciis

miwodebaze, aramed miRebuli codnis praqtikulad gamoyenebis unar-Cvevebis

gamomuSavebazec.

saxelmZRvaneloSi warmodgenili masala Temebad ganawilebulia sam TavSi.

TiToeuli Tema Sedgeba erTi an ramdenime gakveTilisagan. gakveTilebi

imgvaradaa dagegmili, rom naTlad Cans maTematikis kavSiri rogorc

cxovrebasTan, aseve sxva sagnebTan (mag.: bunebasTan, xelovnebasTan,

geografiasTan da a.S.). gakveTilis pirvel etapze moswavleebi ecnobian masalas

interaqtiuli swavlebis meTodikis sxvadasxva xerxisa da meTodis gamoyenebiT

(rac emsaxureba moswavlisaTvis Sesaswavli masalis saWiroebis Cvenebas, mis

dainteresebas). Semdeg xdeba gacnobili masalis Seswavla da bolos Sejameba-

Sefaseba (rac xorcieldeba saxelmZRvaneloSi mocemuli savarjiSoebis

saSualebiT). savarjiSoebis Sesrulebis meTodebi mocemulia gakveTilis

scenarSi. axali masalis axsna Seswavlil masalas eyrdnoba. axali masalis

Sesaswavli TiToeuli savarjiSo Seswavlili masalis gameorebas emsaxureba. es

savarjiSoebi sruldeba SeZenili codnis gamoyenebiT (konstruqtivizmi).

gakveTilis sqema SeiZleba Semdegnairad gamovsaxoT:

provocireba.

siRrmiseuli wvdoma

refleqsia, anu gaazreba

I etapi (provocireba) — gakveTili iwyeba provocirebiT, romlis drosac

maswavlebeli cdilobs, moswavleebs misces konkretuli sakiTxis codnis

gamovlenis saSualeba. igi SekiTxvebisa da savarjiSoebis gamoyenebiT klass

amzadebs konkretul sakiTxze samuSaod.

II etapi (siRrmiseuli wvdoma) — gulisxmobs masalis Seswavlas.

III etapi (refqlesia, anu gaazreba) — aris Semajamebeli etapi. xorcieldeba

saxelmZRvaneloSi mocemuli konkretuli savarjiSos saSualebiT (miTiTebulia

gakveTilis scenarSi).

gakveTilis msvlelobisas saswavlo masalis wardgenis etapebi

uzrunvelyofs saazrovno unarebis ganviTarebas blumis taqsonomiis mixedviT

(codna-gageba-gamoyeneba).

yovel gakveTils axlavs savarjiSo, romlis Sesruleba saSualebas aZlevs

maswavlebels Seamowmos, miRweulia Tu ara gakveTilis mizani, aseve exmareba

maswavlebels mimdinare SefasebaSi. mimdinare Sefaseba saSualebas aZlevs

2

maswavlebels, daakvirdes swavlis process, TiToeuli moswavlis mier miRweul

Sedegebs da Sesabamisi unarebis ganviTarebas.

amisaTvis SeuZlia gamoiyenos Semdegi cxrili:

gaigo Sesasrule-

beli davalebis

arsi

moZebna savar-

jiSos Sesru-

lebis gza

praqtikulad

Seasrula

samuSao

axsna, rogor

Seasrula

davaleba

maswavlebeli TiToeul ujraSi akeTebs aRniSvnebs `+~-s an `_~-s. cxrili

ivseba TiToeuli moswavlisaTvis.

erTi `+~ _ pirobiTad CaeTvla,

ori `+~ _ CaeTvala,

sami `+~ _ CaeTvala,

oTxi `+~ _ CaeTvala warCinebiT.

cxrili saSualebas iZleva TvalnaTliv warmovidginoT moswavlis codnisa

da unarebis ganviTarebis done (SeuZlia codnis gamoyeneba _ praqtikulad

ganaxorciela; saazrovno unari _ moZebna savarjiSos Sesrulebis gza;

sakomunikacio unari _ axsna, rogor Seasrula davaleba).

sasurvelia, mocemuli savarjiSo maswavlebelma moswavleebs Seasrulebinos

Semdegnairad: mas Semdeg, rac ukve garkveulia klasis moswavleTa SesaZleb-

lobebi, maswavlebeli moswavleebs svams wyvilebad (susti-Zlieri: momdevno

gakveTilze cvlis wyvilebis Semadgenlobas da a.S.). moswavleebs jer aZlevs

saSualebas, damoukideblad Seasrulon Semajamebeli savarjiSo. Tu wyvilis

orive moswavle gaarTmevs Tavs samuSaos, maSin isini gacvlian namuSevrebs da

erTmaneTs Seafaseben (swori pasuxis gaswvriv weren, `+~, araswori pasuxis

gaswvriv_ `-~ da asabuTeben, ratom Tvlian ase). amgvarad xdeba TviTSefaseba da

urTierTSefaseba. Semdeg maT namuSevrebs amowmebs maswavlebeli.

Tu wyvilidan erT-erTi moswavle ver Seasrulebs davalebas, mas daexmareba

meore moswavle, romelic Seecdeba auxsnas, Tu rogor unda Sesruldes

samuSao. saWiroebis SemTxvevaSi maT daexmareba maswavlebeli.

samuSaos wyvilebad Sesruleba xels uwyobs TanamSromlobis unar-Cvevis

gamomuSavebas, urTierTswavlebas, aCvevs moswavleebs erTmaneTisTvis azris

gaziarebas, mosmenas da saerTo gadawyvetilebis miRebas. organizebis am formis

gamoyeneba maswavlebels daexmareba saswavlo procesSi sxvadasxva

SesaZleblobebis mqone moswavleebis ufro aqtiurad CarTvaSi.

Semajamebeli savarjiSoebis nomrebi saxelmZRvaneloSi aRniSnulia

stafilosferiT.

gakveTilis scenarSi miTiTebulia, romeli savarjiSo gamoiyeneba gakveTilis

konkretul etapze, aseve miTiTebulia, romeli savarjiSoebia gankuTvnili

saSinao davalebebisaTvis. saSinao davalebis Semowmeba xdeba momdevno

gakveTilze. Semowmebisas, pirvel yovlisa, yuradReba mieqceva imas, iyo Tu ara

davaleba yvelasaTvis gasagebi. sasurveli iqneba, gaugebari savarjiSoebis axsna

moswavleebs daevaloT. es xels Seuwyobs maTSi, pasuxismgeblobis, saTqmelis

naTlad da gasagebad gadmocemis, sakuTari mosazrebis dasabuTebis unarebis

ganviTarebas.

saSinao davalebisaTvis gankuTvnili savarjiSoebis nomrebi

saxelmZRvaneloSi aRniSnulia mwvane feriT.

yovel 5-6 gakveTils mosdevs gakveTili `Seamowme Seni codna~, romelic

exmareba maswavlebels daadginos, miiRweva Tu ara nabij-nabij erovnuli

saswavlo gegmiT gaTvaliswinebuli Sedegebi (perioduli Sefaseba). gakveTilis

Catarebis erTi scenari mocemulia maswavleblis wignSi, yvela msgavsi

gakveTili tardeba analogiurad.

3

ra SemTxvevaSi SeiZleba maswavlebelma Sesrulebeli samuSao

damakmayofileblad CaTvalos?

samuSao SeiZleba damakmayofileblad CaiTvalos, Tu moswavle sworad

gaigebs savarjiSos pirobas da moZebnis misi Sesrulebis gzas. yoveli

savarjiSos Sesrulebis Semdeg moswavleebs moeTxovebaT sakiTxis Sesaxeb

msjeloba. amiT maswavlebels SeuZlia daadginos, esmiT Tu ara moswavleebs

davalebis arsi, rac, Cveni azriT, yvelaze mniSvnelovania.

yovelive amis Sesafaseblad maswavlebels SeuZlia gamoiyenos Semdegi

cxrili:

savarjiSo 1 2 3 4 5 6 7 8 9 10

gaigo Sesasrulebeli davalebis

arsi

moZebna savarjiSos Sesrulebis

gza

praqtikulad Seasrula samuSao

axsna, rogor Seasrula davaleba

maswavlebeli wers `+~-s an `_~-s. cxrili ivseba TiToeuli moswavlisaTvis.

erTi `+~ _ pirobiTad CaeTvla,

ori `+~ _ CaeTvala,

sami `+~ _ CaeTvala,

oTxi `+~ _ CaeTvala warCinebiT.

Sevsebuli cxrili saSualebas miscems maswavlebels, Seafasos TiToeuli

moswavle.

maswavlebels SeuZlia, mTeli klasisTvisac gaakeTos aseTi cxrili:

samuSaos nomeri 1 2 3 4 5

abulaZe

. . .

cxrili keTdeba did formatze da gamoikvreba saklaso oTaxSi.

vertikalurad Camowerilia klasis moswavleTa sia, horizontalurad _

samuSaos nomrebi (`Seamowme Seni codna~). trimestris ganmavlobaSi cxrili

Semdegnairad ivseba: Tu sworad aris Sesrulebuli savarjiSoebis naxevarze

naklebi _ aRniSvna keTdeba wiTeli feriT, naxevari _ yviTeli feriT, naxevarze

meti _ mwvane feriT.

cxrili saSualebas miscems moswavleebs, Tavad Seafason sakuTari Tavi tri-

mestris ganmavlobaSi. moswavleebi agroveben monacemebs da trimestris bolos

akeTeben Sesabamis daskvnebs. rodesac moswavleebi gaecnobian `mesameds~ da

`meoTxeds~, SeiZleba ufro meti feris gamoyeneba, mag.: erTi meoTxedi _ muqi

wiTeli; sami meoTxedi _ muqi mwvane da a. S. (garegani motivacia).

yoveli Tavis bolos aris Semajamebeli testi (Semajamebeli Sefaseba),

romelic imave mizans emsaxureba. es gakveTilebi xels uwyobs SeZenili codnis

gamoyenebisa da samuSaos damoukideblad Sesrulebis unar-Cvevebis

gamomuSavebas.

saxelmZRvaneloSi aris gakveTilebi saTauriT `vin ufro swrafad~. am

gakveTilebis mizania, saxalisod Catardes ganvlili masalis Sejameba-Sefaseba,

romelic xels uwyobs jansaRi konkurenciis ganviTarebas, moswavleTa

waxalisebas. gamoiyeneba igive teqnologia, rogoric Semajamebeli savarjiSos

Sesrulebisas.

msgavsi gakveTilebi maswavlebels SeuZlia Caataros ufro xSirad (or

kviraSi erTxel. savarjiSoebis SerCeva SeiZleba saxelmZRvanelodan, ganvlili

masalis mixedviT).

4

codnis praqtikuli gamoyenebis unar-Cvevis gamomuSavebisaTvis gamoiyeneba

swavlebis interaqtiuli meTodika, misi meTodebi da saSualebebi.

saxelmZRvaneloSi mocemuli gakveTilebis struqtura aseTia:

globaluri mizani _ globaluri mizani uSualod dakavSirebulia erovnuli an

saskolo gegmiT gansazRvrul mizanTan.

lokaluri mizani _ lokaluri mizani aris is, ris miRwevasac emsaxureba

konkretuli gakveTili. igi erT-erTi safexuria globaluri miznis misaRwevad.

winaswari codna da unarebi _ am nawilSi aRwerilia is masala, romelic

gamoiyeneba gakveTilis ganmavlobaSi.

gakveTilis msvleloba _ am nawilSi detalurad aRwerilia gakveTilis

mimdinareoba.

yoveli gakveTilisaTvis aucilebeli resursia saxelmZRvanelo, rveuli, kalami,

fanqari, saxazavi. amitom es resursebi gakveTilis scenarSi miTiTebuli ar

aris, miTiTebulia mxolod damatebiTi resursebi.

wyvilebi da jgufebi

wyvilebad da jgufebad muSaoba xels uwyobs TanamSromlobis Cvevis gamomu-

Savebas. am savarjiSoebis Sesrulebisas bavSvebi swavloben erTmaneTis mosmenas,

sxvisi azris gaziarebas, kritikul azrovnebasa da Sefasebas, sakuTari azris

gamoTqmas da dasabuTebas. isini eCvevian funqciebis danawilebas, drois

racionalurad gamoyenebas.

wyvilebad muSaobis wesebi:

1. maswavlebeli klass yofs wyvilebad;

2. wyvilebs eZlevaT saerTo an gansxvavebuli davaleba;

3. moswavleebi samuSaos asruleben wyvilebad;

4. samuSaos Sesrulebis dro gansazRvrulia.

wyvilebad muSaobis dros bavSvebs moeTxovebaT yuradRebis koncentrireba.

isini pasuxismgeblobas grZnoben Tavisi mewyvilis mimarT.

wyvilebSi gamomuSavebuli TanamSromlobis Cveva kidev ufro ganmtkicdeba

jgufuri samuSaos Sesrulebisas.

jgufuri muSaobis wesebi:

1. klasi iyofa 4-5-moswavlian jgufebad;

2. jgufebs eZlevaT saerTo an gansxvavebuli davaleba;

3. davaleba sruldeba jgufebSi;

4. jgufebi unda muSaobdnen SeTanxmebulad, ar unda moxdes konfliqti;

5. saqmianobaSi unda CaerTos jgufis yoveli moswavle;

6. samuSao sruldeba erT furcelze;

7. davaleba sruldeba maswavleblis mier winaswar gansazRvrul droSi;

8. jgufi muSaobs erTi magidis garSemo.

samuSaos damTavrebis Semdeg jgufebi warmoadgenen sakuTar namuSevrebs.

maswavlebels winaswar unda hqondes gansazRvruli namuSevrebis Sefasebis

forma.

sasurvelia, moswavleebma Tavad Seafason sxva jgufis namuSevrebi.

TiToeuli bavSvi asaxelebs, misi azriT, saukeTeso jgufur namuSevars da

asabuTebs, ra kriteriumiT isargebla Sefasebisas. yoveli gamomsvlelis azrs

maswavlebeli dafaze aRniSnavs — wers `+~-s. qulebis raodenoba gamoavlens

gamarjvebuls, Tumca maswavlebelma aucileblad unda Seaqos yvela jgufi da

aRniSnos, rom yvelam sainteresod imuSava. maswavlebels vTavazobT jgufebisa

da wyvilebis mier Sesrulebul davalebaTa Sefasebis cxrls:

TanamSromloba CarTuloba msjeloba-dasabuTeba

namuSevris warmodgena

5

I Tavi

I Tavi moicavs 15 paragrafs. am TavSi warmodgenili masaliT moswavle imeorebs

mesame klasSi Sesawavlil masalas da swavlobs axals. iwyeba muSaoba Sedegebze:

IV.1 _ mowmdeba indikatorebiT - 1,2, 3, 4.


IV.3 _ mowmdeba indikatorebiT - 1,2.


IV.5 _ mowmdeba indikatorebiT - 1, 4.

IV.6 _ mowmdeba indikatorebiT - 1, 2, 3.

IV.7 _ mowmdeba indikatorebiT -1, 2, 4.

IV.8 _ mowmdeba indikatorebiT - 2

IV.9 _ mowmdeba indikatorebiT - 2


IV.11 _ mowmdeba indikatorebiT - 3.


IV.14 _ mowmdeba indikatorebiT 1, 2, 3.

# Temis dasaxeleba sT.

§ 1

§ 2

§ 3

§ 4

§ 5

§ 6

§ 7

§ 8

§ 9

§ 10

§ 11

§ 12

§ 13

§ 14

§ 15

marSruti

samniSna ricxvebi

Seamowme Seni codna

svetovani diagrama

gamravleba-gayofa

Seamowme Seni codna

ariTmetikuli moqmedebebi

gamosaxuleba

moqmedebaTa Sesrulebis Tanmimdevroba gamosaxulebaSi

wrfe, sxivi

ricxvidan jamis gamokleba, jamidan ricxvis gamokleba

Tanafardoba sigrZis sazom erTeulebs Soris

Seamowme Seni codna

marSrutis arCeva da gamosaxva aRniSvnebiT

vin ufro swrafad?

marSrutis arCeva da gamosaxva aRniSvnebiT

simetria

naxevari

Seamowme Seni codna

testi

4

2

1

3

1

1

1

1

1

1

2

2

1

1

2

1

1

1

1

1

§ 1 marSruti

6

globaluri mizani: sqemaze orientirebisa da marSrutis aRmweri martivi sqemis

Seqmnis, aseve, martivi maTematikuri amocanis amoxsnisas algebruli

gamosaxulebis Sedgenis unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon aRweris mixedviT marSrutis dadgenisa

da misi sqematurad gamosaxvis xerxebs. erTeulis Rirebulebis mixedviT SeZlon

ramdenime erTeulis Rirebulebis gamoTvla.

winaswari codna da unarebi: obieqtis mdebareobis aRwera meore obieqtis

mimarT; obieqtebs Soris manZilis dadgena; toli Sesakrebebis jamis povna;

amocanis pirobis mixedviT, cnobili da ucnobi sidideebis organizeba.

saWiro resursebi: saqarTvelos ruka an qaRaldis formati.

I saaTi

saWiro dro:

gacnoba _ 15 wT. _ savarjiSo #1

Seswavla _ 15 wT. _ savarjiSoebi #2, #3, #4

Sejameba-Sefaseba _ 10 wT. _ savarjiSo #6.

gakveTilis msvleloba:

zafxulis ardadegebis Semdeg skolaSi dabrunebul moswavleebs

daainteresebT iseTi davaleba, romelic zafxulis TemasTan iqneba

dakavSirebuli da mieZRvneba axali masalis gacnobas.

savarjiSo # 1-is saSualebiT maswavlebeli acnobs moswavleebs, ra aris

marSruti (gza, romelsac gaivli mocemuli adgilidan daniSnul adgilamde).

aRwerilobis mixedviT, moswavlebma unda amoicnon TiToeuli bavSvis marSruti.

maswavlebeli amowmebs, SeuZliaT Tu ara moswavleebs sibrtyeze orientireba

(qalaqebis erTmaneTis mimarT mdebareobis aRwera).

gakveTili ufro sainteresod warimarTeba, Tu maswavlebeli winaswar

moamzadebs saqarTvelos rukas (SeiZleba igi sqematurad gamoisaxos formatze),

romelzec aRniSnavs qalaqebs, xolo TiToeuli moswavle moniSnavs im adgils,

sadac zafxulSi daisvena.

Semdeg moswavleebi gaecnobian marSrutis sqematur gamosaxvas: maswavlebeli

asaxelebs qalaqs an sofels, sadac man gaatara zafxuli da Tavis marSruts

sqematurad gamosaxavs dafaze.

saSinao davaleba: moswavleebma analogiurad unda gamosaxon TavianTi

zafxulis marSruti.

Semdeg moswavleebi ecnobian savarjiSo #3-is amocanis pirobas.

maswavlebeli azustebinebs moswavleebs pirobis mixedviT cnobil sidideebs

(erTi bileTis Rirebuleba da ojaxis wevrebis raodenobis Sesabamisi bileTebis

raodenoba) da aZlevs saSualebas, TviTon moZebnon ucnobi sidide

(TvalsaCinoebis daxmarebiT). Tu moswavleebs gauWirdebaT amocanis amoxsna,

maswavlebeli daexmareba maT, mag.:

maswavlebeli:

_ ramdeni bileTis SeZena dasWirdeba mariamis ojaxs? (4)

_ ra Rirs TiToeuli bileTi? (10 lari).

_ ra Rirs 2 bileTi? (10+10=20). ra Rirs sami bileTi? (10+10+10=30). ra Rirs

4 bileTi? (10+10+10+10=40).

_ ra moqmedeba sruldeba saerTo raodenobis mosaZebnad?

savarjiSos saSualebiT moswavleebi igeben, rogor SeiZleba erTeulis

Rirebulebis mixedviT, ramdenime erTeulis fasis povna.

7

analogiurad ganixileba savarjiSo #4 da savarjiSo#5-Si mocemuli

amocanebi. maswavlebeli jer aZlevs moswavleebs saSualebas, TviTon moZebnon

amocanis pasuxi da Semdeg, saWiroebisamebr, exmareba maT.

Sejameba-Sefaseba: savarjiSo #6

maswavlebeli amowmebs, SeZleben Tu ara moswavleebi aRwerilobis mixedviT

marSrutis gamosaxvas.

bolos maswavlebeli aZlevs moswavleeebs saSinao davalebas da uTiTebs, sad

SeiZleba moipovon informacia.

gakveTilze dawyebuli savarjiSo moswavleebma unda daasrulon saxlSi:

daadginon qalaqebs Soris manZili da aseve, saqarTvelos romel kuTxeSi

mdebareobs TiToeuli qalaqi (an am informacias maswavlebeli TviTon awvdis

maT).

II saaTi

momdevno savarjiSoebi (#7-dan #12-is CaTvliT) imave mizans emsaxureba.

moswavleebi, aseve, ixseneben wina wels Seswavlil masalas, kerZod, ra aris

moqmedeba gamravleba (mravaljeradi Sekreba).

savarjiSoebi #7-dan #16-is CaTvliT sruldeba gakveTilze.

savarjiSo #17 da #18 gaTvaliswinebulia saSinao davalebisaTvis.


III saaTi


savarjiSoebi #24 da #25 gaTvaliswinebulia saSinao davalebisaTvis.

Sejameba-Sefaseba: savarjiSo #26.

IV saaTi


savarjiSoebi #36 da #37 gaTvaliswinebulia saSinao davalebisaTvis.

Sejameba-Sefaseba: savarjiSoebi #39 da #40.

§ 2 samniSna ricxvebi

I saaTi

globaluri mizani: poziciuri sistemis gamoyenebiT ricxvebis gamosaxvis,

dalagebisa da Sedarebis unarebis ganviTareba.

lokaluri mizani: moswavleebma SeZlon ricxvis CanawerSi Sesabamis TanrigebSi

mdgomi cifrebis mniSvnelobis dasaxeleba da ricxvis warmodgena saTanrigo

Sesakrebebis jamis saxiT.

saWiro dro:


8

Seswavla _ 20 wT. _ savarjiSoebi #2-dan #11-is CaTvliT

Sejameba-Sefaseba _ 10 wT. _ savarjiSo #14


saxelmZRvaneloSi mocemuli TvalsaCinoebis saSualebiT maswavlebeli

acnobs moswavleebs samniSna ricxvis CanawerSi Tanrigebis dasaxelebas da

mniSvnelobas.

_ 542. ras aRniSnavs CanawerSi TiToeuli cifri? maswavlebeli azustebinebs

moswavleebs TiToeuli ricxvis mniSvnelobas.

_ 2 aris erTeulis TanrigSi mdgomi cifri, 2 erTeuli rCeba mas Semdeg, rac

542-dan moxdeba 5 aseulisa da 4 aTeulis gamoyofa. 542-Si sul aris 542

erTeuli.

_ 4 aris aTeulis TanrigSi mdgomi cifri, 4 aTeuli rCeba mas Semdeg, rac 542-

dan moxdeba 5 aseulis gamoyofa. 542-Si sul aris 54 aTeuli.

_ 5 aris aseulebis TanrigSi mdgomi cifri. 542-Si aris 5 aseuli.

ricxvebis Sedarebisas moswavleebma unda gamoiyenon Sesabamis TanrigebSi

mdgomi cifrebis mniSvneloba. mag.: 500 metia 400-ze, imitom, rom 500-Si aseulis

TanrigSi mdgomi cifris mniSvneloba metia 400-Si aseulis TanrigSi mdgom

cifrze (5>4).

ricxvebis Sekrebisas maT unda SeZlon Tanrigebis dajgufeba, mag.:

450+50=400+(50+50)=400+100=500.

saSinao davaleba: savarjiSoebi #12 da #13

II saaTi

globaluri mizani: sqemaze orientirebisa da Tvisebriv da rodenobriv

monacemTa mogrovebis unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon cxrilidan monacemebis amokrefa.

gaecnon, rogor SeiZleba arCevanis Semcveli SekiTxvebis dasma.

saWiro dro:


Seswavla _ 20 wT. _ savarjiSo #16



moswavleebi ecnobian saxelmZRvaneloSi mocemul savarjiSo #1-s.

aRwerilobis mixedviT maT unda gaarCion I da II marSruti; cxrilSi ukve gvaqvs

gamokiTxvis Sedegebi. maT unda gaixsenon, ra hqvia aseT cxrils (piqtograma) da

mocemuli monacemebis safuZvelze daadginon, romeli (I Tu II) da rogori

marSruti (fexiT Tu avtobusiT) airCies bavSvebma.

kargi iqneba, bavSvebma gamoTqvan varaudi, Tu ratom SeirCa I marSruti (is

ufro moklea; naklebi dro daixarjeba; muzeumis naxva ufro sainteresoa da

a.S.) aseve sasurvelia, xelovnebis maswavlebelTan konsultacia da moswavlee-

bisaTvis informaciis miwodeba imis Taobaze, Tu ris naxvas SeZleben isini

xelovnebis muzeumSi.

bavSvebma menius SesarCevad Caatares gamokiTxva da miRebuli monacemebi

warmoadgines cxrilis saxiT. saWiro Tanxis dasadgenad moswavleebma unda

SeZlon wina gakveTilze miRebuli codnis gamoyeneba (erTeulis Rirebulebis

mixedviT ramdenime erTeulis fasis dagena).

SesaZlebelia, aseTi eqskursia marTlac moewyos axlomdebare

RirsSesaniSnaobebis dasaTvaliereblad. maswavlebelma unda daavalos

9

moswavleebs (wyvilebs, jgufebs), Seadginon patara marSruti da Semdeg erTad

dagegmon da moawyon eqskursia.

savarjiSo #17 sruldeba Semdegnairad: bavSvebi gamokiTxvis Sedegebs weren

formatze da Semdeg adgenen, sportis romel saxeobas aniWebs upiratesobas

umravlesoba.

saSinao davaleba: savarjiSo #18

Seamowme Seni codna

gakveTilis mizania: daexmaros maswavlebels daadginos, SeuZliaT Tu ara

moswavleebs SeZenili codnis praqtikulad gamoyeneba.

I saaTi

savarjiSoebi sruldeba damoukideblad.

II saaTi

moswavleebis namuSevrebis Semowmebis Semdeg maswavlebeli ganixilavs im

savarjiSoebs, romelTa Sesrulebac moswavleebma ver SeZles (Tundac erTma).

Semdeg maswavlebeli romelime moswavles sTxovs axsnas, Tu rogor Seasrula

davaleba _ savarjiSo #1, danarCenebs ki _ daazuston Tu aqvT rame

dasamatebeli da a. S. ganixilavs yvela savarjiSos.

§ 3 svetovani diagrama

globaluri mizani: Tvisebrivi da raodenobrivi minacemebis interpretaciis

unaris ganviTareba.

I saaTi

lokaluri mizani: moswavleebi gaecnon svetovan diagramas, SeZlon svetovani

diagramis saxiT warmodgenili monacemebis daxasiaTeba.

winaswari codna da unarebi: monacemTa interpretacia.

saWiro dro:

gacnoba _ 20 wT. _ savarjiSoebi #1 da#2

Seswavla _ 10 wT. _ savarjiSoebi #3 da #5

Sejameba-Sefaseba _ 10 wT. _ savarjiSoebi #4 da #5

saWiro resursebi: qaRaldis formati, sxvadasxva feris flomasterebi.


moswavleebi asruleben saxelmZRvaneloSi mocemul savarjiSo #1-s, Semdeg

savarjiSo #2-s da akvirdebian mocemul naxazs. naxazze warmodgenili monaceme-

bis gamosaxvis saSualeba moswavleTaTvis ucnobia. maswavlebeli acnobs moswav-

leebs, rogor SeiZleba svetovani diagramis saSualebiT monacemebis gamosaxva.

yuradRebas amaxvilebs TiToeuli svetis simaRleze (TvalnaTliv Cans mona-

cemebs Soris gansxvaveba). Semdeg moswavleebi maswavleblis daxmarebiT asrule-

10

ben savarjiSo #3-s. maswavlebeli aswavlis moswavleebs, rogor isargeblon sve-

tovani diagramiT mag.: ramdeni moswavlea mariamisa da giorgis klasSi? radgan

Catarebulia gamokiTxva Temaze `kalaTburTis TamaSi girCevnia Tu fexburTis?~

unda dadgindes, moswavleTa ra raodenoba Sesabameba svets_`kalaTburTi~ (12)

da svets `fexburTi~ (14), Semdeg ki unda Seikribos fexburTisa da kalaTburTis

moyvarulTa raodenoba (12+14=26). igive SeiZleba gakeTdes meore diagramis

mixedviT. diagramaze wignis kiTxvis moyvarulTa raodenoba metia kompiuteris

moyvarulTa raodenobaze, rac gamarTlebulia pedagogiuri TvalsazrisiT da

es magaliTi maswavlebels SeuZlia wignis kiTxvisadmi interesis aRsaZvrelad

gamoiyenos. maswavlebeli yuradRebas amaxvilebs im SekiTxvebze, romlebsac

diagramis saSualebiT pasuxi ver gaeca.

SesaZlebelia, formatze sxvadasxva feris flomasteriT gamoisaxos klasis

moswavleTa raodenoba (mwvane sveti _ biWebi, wiTeli _ gogonebi). aseTi samuSao

saxaliso Sesasrulebelia da xels uwyobs praqtikuli unar-Cvevebis

gamomuSavebas.

II saaTi

lokaluri mizani: moswavleebma SeZlon svetovani diagramis saxiT warmodgenili

monacemebis aRwera.

saWiro dro:

gacnoba _ 30 wT. _ savarjiSoebi #6 da #7

Seswavla _ 10 wT. _ savarjiSo #10


savarjiSo #6-s Sesrulebisas maswavlebeli saSualebas aZlevs moswavleebs

TviTon moifiqron gansxvavebuli SekiTxvebi da Semdeg exmareba maT (mag.:

sayvareli tkbileuli, filmebi, TamaSi da a. S.).


III saaTi

lokaluri mizani: moswavleebma SeZlon svetovani diagramis saxiT warmodgenili

monacemebis aRwera; ricxviT sxivze wertilis Sesabamisi ricxvis moZebna;

gaecnon erTi da imave Sesabamisobis sxvadasxva xerxiT gamosaxvas.

saWiro dro:

gacnoba _ 10 wT. _ savarjiSoebi #11da #12

Seswavla _ 15 wT. _ savarjiSoebi #13, #14 da #15



§ 4 gamravleba-gayofa

globaluri mizani: gamravleba-gayofis moqmedebaTa Sesrulebis, Sekreba-

gamoklebis moqmedebebTan maTi dakavSirebis unaris ganviTareba.

lokaluri mizani: Seswavlili masalis gameoreba.

11

winaswari codna da unarebi: Sekreba-gamoklebis moqmedebaTa Sesruleba;

gamravlebis Secvla mravaljeradi SekrebiT gamravleba-gayofis moqmedebaTa

erTmaneTTan dakavSireba; amocanis amosaxsnelad Sesabamisi ariTmetikuli

moqmedebis SerCeva.

saWiro dro:

saxelmZRvaneloze muSaoba _ 40 wT.


maswavlebeli moswavleebs avalebs, Seasrulon saxelmZRvaneloSi mocemuli

savarjiSoebi:

savarjiSo #1 amocanis amoxsnaSi moswavleebs daexmareba naxati; saerTo

raodenoba unda daiyos xuTeulebad.

savarjiSo #2 savarjiSos Sesasruleblad ar aris aucilebeli gamoangariSeba.

moswavleebma unda axsnan, rom 7·2 es aris 7+7, xolo 7·3 aris 7+7+7, e. i. 7·2<7·3, 10:2>10:5, radgan raodenoba erT SemTxvevaSi or tol nawilad iyofa, meore

SemTxvevaSi _ xuT tol nawilad da a. S.

savarjiSo #4 sasurvelia, moswavleebma axsnan, rom radgan tolobis marcxena

mxares weria 4·4, es igivea, rac 4+4+4+4, e. i. unda Caiweros niSani `+~ da a. S.

savarjiSoebi #5, #6, #7, #8 sruldeba damoukideblad. samuSaos damTavrebis

Semdeg wyvilebi amowmeben erTmaneTis namuSevrebs da uxsnian erTmaneTs, rogor

Seasrules samuSao. Semdeg namuSevrebs amowmebs maswavlebeli.

savarjiSoebi #9 da #10 maswavlebels SeuZlia misces saSinao davalebad.

savarjiSo #11 moswavleebma unda axsnan, rom, radgan 4+4+4+4+4=4·5, xolo

tolobis marjvena mxares weria 5·5, cariel adgilas unda Caiweros 5 da a. S.

savarjiSo #12 moswavleebma unda axsnan, rom mimdevrobis yoveli momdevno

wevri miiReba wina wevris gaormagebiT.

Seamowme Seni codna

§ 5 ariTmetikuli moqmedebebi

globaluri mizani: Sesabamisi ariTmetikuli moqmedebebis Sesrulebis unaris

ganviTareba.

lokaluri mizani: moswavleebi gaecnon, rogor moqmedebebs hqvia ariTmetikuli.

winaswari codna da unarebi: Sesabamisi ariTmetikuli moqmedebebis Sesruleba.

saWiro dro:

gacnoba _ 10 wT.

12

Seswavla _ 20 wT.

Sejameba-Sefaseba _ 10 wT.


savarjiSoebis #1 da #2 saSualebiT moswavleebi ecnobian, rogor moqmedebas

hqvia ariTmetikuli.

maswavlebels SeuZlia gamoiyenos, aseve, azrobrivi ruka: igi wers dafaze

sityvas `moqmedeba~ da mimarTavs bavSvebs:

moqmedeba

_ Tqveni azriT, ras aRniSnavs dafaze dawerili sityva? (raimes gakeTebas da a.

S.), xolo Semdeg savarjiSoebis daxmarebiT akavSirebs moqmedebas da

ariTmetikul moqmedebas erTmaneTTan.

savarjiSoebis #3 da #4 saSualebiT xdeba gacnobili masalis Seswavla.

moswavleebi azusteben, rom kiTxvebze pasuxis gasacemad saWiroa ariTmetikuli

moqmedebebis Sesruleba.

Sejameba-Sefaseba: savarjiSoebi #6 da #7 sruldeba damoukideblad.

savarjiSo #6-is Sesrulebis Semdeg moswavleebma unda axsnan, rom Tu

raodenoba mcirdeba, es xdeba gamoklebis Sesrulebisas da am SemTxvevaSi

iwereba niSani `-“, xolo Tu raodenoba izrdeba, es xdeba moqmedeba Sekrebis

Sesrulebisas da unda daiweros niSani `+~.

savarjiSo #7-is Sesrulebis Semdeg moswavleebma unda axsnan: a) rom es aris

banakSi damsvenebelTa raodenoba ivnissa da ivlisSi; b) ramdeniT meti bavSvi

isvenebda banakSi ivlisSi; g) sul ramdeni bavSvi isvenebda banakSi.


§ 6 gamosaxuleba

globaluri mizani: problemis gadasaWrelad ricxviTi gamosaxulebebis Sedgenis

unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon amocanis amosaxsnelad ricxviTi

gamosaxulebis Sedgena; ganasxvaon, rodis aris Canaweri ricxviTi gamosaxuleba

da rodis _ ara.

winaswari codna da unarebi: svetovani diagramis ganmarteba; amocanis

amosaxsnelad Sesabamisi ariTmetikuli moqmedebebis Sesruleba; ricxvis

CanawerSi TanrigebSi mdgomi cifrebis Sesabamisi mniSvnelobebis dasaxeleba;

ricxvis warmodgena saTanrigo Sesakrebebis jamis saxiT.

saWiro dro:

gacnoba _ 10 wT.

Seswavla _ 20 wT.

13



maswavlebeli mimarTavs moswavleebs:

_ramdeni gogonaa Cvens klasSi? (11) _ wers dafaze.

_ ramdeni biWia? (10) _ wers dafaze.

_ rogor daadgenT, sul ramdeni moswavlea Cvens klasSi? (gogonebis

raodenobas davumatoT biWebis raodenoba).

_ e. i. es ori raodenoba unda SevkriboT. maswavlebeli dafaze daweril or

ricxvs Soris wers `+~ niSans.

_ klasSi moswavleebis saerTo raodenobis dasadgenad Cven SevadgineT ricxviTi

gamosaxuleba.

am martivi magaliTis saSualebiT moswavleebi ecnobian ricxviT gamosaxulebas.

maswavlebeli:

_ SeasruleT saxelmZRvaneloSi mocemuli savarjiSo #1 wyvilebad.

samuSaos damTavrebis Semdeg maswavlebeli amowmebs namuSevrebs (jer wyvilebi

asaxeleben SekiTxvebis pasuxebs, Semdeg romelime moswavle wers dafaze

Sedgenil gamosaxulebas, danarCenebi ki amowmeben).

savarjiSos mizania, moswavleebma SeZlon svetovani diagramiT warmodgenili

monacemebis wakiTxva da problemis gadasaWrelad ricxviTi gamosaxulebis

Sedgena.

savarjiSoebis #2, #3, #4 Sesrulebis Sedegad xdeba gacnobili masalis

Seswavla.

savarjiSoebi #7, #8 maswavlebels SeuZlia misces saSinao davalebad.

Sejameba-Sefaseba: savarjiSo #9 sruldeba damoukideblad.

§ 7 moqmedebaTa Sesrulebis Tanmimdevroba gamosaxulebaSi

globaluri mizani: ariTmetikul moqmedebaTa Tvisebebis gamoyenebis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon gansazRvra, ra mniSvneloba aqvs

moqmedebaTa Sesrulebis Tanmimdevrobis dacvas gamosaxulebaSi.

winaswari codna da unarebi: ricxviTi gamosaxulebis Sedgena; ariTmetikuli

moqmedebebis Sesruleba.

saWiro dro:

gacnoba _10 wT.

Seswavla _ 20 wT.



maswavlebeli:

- SeasruleT saxelmZRvaneloSi mocemuli savarjiSo #1. samuSaos dasrulebis

Semdeg maswavlebeli amowmebs namuSevrebs:

- ras aRniSnavs gamosaxuleba 300-170-130 ? (wignebis mTlian raodenobas jer

akldeba maTematikis saxelmZRvaneloebis raodenoba, Semdeg ki _ inglisuri enis

14

saxelmZRvaneloebis raodenoba. gamosaxulebis mniSvnelobis moZebniT vadgenT

danarCeni wignebis raodenobas).

_ ras aRniSnavs gamosaxuleba 300-(170+130)? (jer vadgenT maTematikisa da

inglisuri enis saxelmZRvaneloebis saerTo raodenobas da Semdeg is akldeba

wignebis mTlian raodenobas. gamosaxulebis mniSvnelobis moZebniT vadgenT

danarCeni wignebis raodenobas).

maswavlebeli yuradRebas amaxvilebs imaze, rom orive gamosaxulebis

mniSvneloba erTnairia. gamosaxulebebSi moqmedebebis Sesrulebis

Tanmimdevroba icvleba (jer sruldeba moqmedeba frCxilebSi).

savarjiSos saSualebiT moswavleebi ecnobian ricxviT gamosaxulebaSi

moqmedebaTa Sesrulebis Tanmimdevrobas, Semdeg asruleben savarjiSo #2-s.

savarjiSoebis #3, #4, #5, #6 Sesrulebis Sedegad xdeba gacnobili masalis

Seswavla.

savarjiSoebi #7da #8 maswavlebels SeuZlia misces saSinao davalebad.

Sejameba-Sefaseba: savarjiSoebi #9 da #10 sruldeba damoukideblad.

§ 8 wrfe. sxivi

globaluri mizani: geometriuli figuris aRweris, saganTa da obieqtTa Soris

manZilebis povnis unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon wertilis, wrfisa da sxivis amocnoba,

aseve obieqtebs Soris ori gzidan umoklesi manZilis arCeva.

winaswari codna da unarebi: geometriuli figuris amocnoba; obieqtebs Soris

manZilebis Sedareba.

saWiro dro:

gacnoba _ 10 wT.

Seswavla _ 20 wT.



maswavlebeli saklaso oTaxis erT kuTxeSi or moswavles ayenebs da avalebs

maT neli nabijiT mopirdapire kuTxisaken gaemarTon, oRond erTma swor xazze

(diagonalze) unda imoZraos, meorem ki_kedlis gaswvriv. Semdeg mimarTavs

klass:

_ romeli moswavle ufro male miva kuTxemde? (is, vinc swor xazze midis).

ratom? (es gza ufro moklea).

maswavlebeli xazavs dafaze:

A

15

B

_ orive moswavle A wveroSi imyofeboda, saboloo mizania B wvero. erTi

miemarTeboda ase (aCvenebs naxazze), meore ki _ ase (isev aCvenebs naxazze).

romelia umoklesi gza A wertilidan B wertilamde, swori wiri Tu texili?

(swori wiri).

savarjiSos saSualebiT moswavleebi TvalnaTliv dainaxaven umokles gzas or

wertils Soris.

_ SeasruleT saxelmZRvaneloSi mocemuli savarjiSo #1.

moswavleebma unda daasaxelon msgavseba da gansxvaveba mocemul figurebs

Soris. mag.: sxivs erTi bolo aqvs, monakveTs_ori, wrfes_arc erTi. sasurvelia,

moswavleebi TvalsaCinoebis saSualebiT gaecnon iseT figurebs, rogoricaa

sxivi da wrfe da TviTon aRweron isini (raTa Tavidan aviciloT araswori

warmodgenebis Camoyalibeba).

savarjiSoebis #3, #4, #5, #6 SesrulebiT xdeba gacnobili masalis Seswavla.

maswavlebeli yuradRebas amaxvilebs gadamkveT wrfeebze (aCvenebs moswavleebs).

Sejameba-Sefaseba: savarjiSoebi #9 sruldeba damoukideblad. maswvlebeli jer

amowmebs, SeZleben Tu ara moswavleebi gadamkveTi da aragadamkveTi wrfeebis

amocnobas, Semdeg ki, saWiroebisamebr, uxsnis, rodis gadaikveTeba

isini(gagrZelebisas) da rodis _ ara.


§ 9 jamidan ricxvis gamokleba. ricxvidan jamis gamokleba

globaluri mizani: ariTmetikul moqmedebaTa Tvisebebis gamoyenebis unaris

ganviTareba.

lokaluri mizani: Seswavlili masalis gameoreba; moswavleebma SeZlon jamidan

ricxvis gamoklebisa da ricxvidan jamis gamoklebis Tvisebebis gamoyeneba.

winaswari codna da unarebi: ricxviTi gamosaxulebis Sedgena; gamosaxulebaSi

moqmedebaTa Sesrulebis Tanmimdevrobis dacva; Sedareba; Sefaseba.

saWiro dro:

gameoreba _ 30 wT.



radgan gakveTilis mizania Seswavlili masalis gameoreba, maswavlebeli

wyvilebs Sesasruleblad aZlevs saxelmZRvaneloSi mocemul savarjiSoebs.

samuSaos dasrulebis Semdeg moswavleebma Tavad unda axsnan, rogor Seasrules

savarjiSoebi (maswavlebeli TiToeul savarjiSos sxvadasxva wyvils axsnevinebs).

16

savarjiSo #1 moswavleebma unda axsnan, ras aRniSnavs TiToeuli Sedgenili

gamosaxuleba (mag., 122-51-49 gamosaxulebaSi mTlian manZils akldeba jer

pirvel dRes gavlili manZili, Semdeg ki _ meore dRes gavlili manZili.

gamosaxulebis mniSvneloba aris darCenili manZili; 122-(51+49) gamosaxulebaSi

jer dgindeba pirvel da meore dRes gavlili manZili da akldeba mTlian

manZils. gamosaxulebis mniSvneloba aris darCenili manZili; maT aseve unda

ganmarton, romels aniWeben upiratesobas).

savarjiSo #2 moswavleebma unda axsnan, rom (26+17)-7 ... (17-7)+26

gamosaxulebebis Sedarebisas gamoyenebulia jamidan ricxvis gamokleba da

orive gamosaxulebis mniSvneloba erTnairia. (14+15)-15 ... (15-15)+13 _ am

SemTxvevaSic gamoyenebulia jamidan ricxvis gamokleba da radgan 14 metia 13-

ze, pirveli gamosaxulebis mniSvneloba metia meore gamosaxulebis

mniSvnelobaze.

savarjiSo #7 moswavleebma unda axsnan, rom gamosaxulebebis mniSvnelobebi

erTnairia, gansxvavebulia maTi Canaweri da mniSvnelobis gamosaTvlelad

xelsayrelia ricxvidan jamis gamoklebis wesis gamoyeneba (mag.: 78-(18+4) da

78-18-4. ufro martivia, rom 78-s jer gamoakldes 18 da Semdeg 4, vidre jamis

(18+4)-is mniSvnelobis moZebna da Semdeg 78-22 sxvaobis mniSvnelobis povna).

savarjiSo #8 moswavleebma unda SeZlon 1 laris warmodgena 100 TeTris

saxiT da Semdeg am ricxvidan jamis gamoklebis wesis gamoyeneba.

savarjiSo #9 moswavleebma unda gamoiyenon ricxvidan jamis gamoklebis

wesi.

savarjiSo #10 moswavleebma unda axsnan, rom mocemuli amocanis amoxsnisas

ufro xelsayrelia jer jamis (13+15+12) povna da Semdeg darCenili Tanxis

moZebna 40-40.

Sejameba-Sefaseba: savarjiSoebi #6 da #11 maswavlebels SeuZlia misces

saSinao davalebad.

§ 10 Tanafardoba sigrZis sazom erTeulebs Soris

globaluri mizani: saganTa da figuraTa zomebis povnis, obieqtTa Soris

manZilis dadgenis, sqemaze orientirebisa da marSrutis aRmweri martivi sqemis

Sedgenis, zomis sxvadasxva erTeulebis erTmaneTTan dakavSirebis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon saganTa zomebis dadgena, aseve

obieqtTa Soris manZilebis dadgena; gaecnon, ra aris marSruti, SeZlon

marSrutis aRmweri martivi sqemis amocnoba, aseve, sigrZis sazomi didi

erTeulis mcire erTeuliT gamosaxva.

saWiro dro:

Temas eTmoba 2 sT, saWiroebis SemTxvevaSi _ 3 sT.

gacnoba _ 15 wT.

Seswavla _15 wT.


17

I saaTi


maswavlebeli axsenebs moswavleebs, ra SemTxvevaSia xelsayreli wrfivi zomis

dadgena standartuli sazomi erTeuliT (rodesac saWiroa zusti zomis

dadgena, umjobesia gamoviyenoT standartuli sazomi erTeuli) da sTxovs

moswavleebs, CamoTvalon maTTvis cnobili standartuli (sm, m da a. S.) da

arastandartuli (nabiji, cida da a. S.) erTeulebi.

Semdeg moswavleTa wyvilebi asruleben savarjiSo #1-s, alageben manZilebs

zrdis mixedviT (700 m, 850 m, 1km), ecnobian, rom 1km=1000 m (zrdis mixedviT

dalagebisas iyeneben poziciur sistemas).

savarjiSoebis #2, #3 Sesrulebisas (wyvilebad) moswavleebi kidev erTxel

azusteben, ra aris marSruti (erTi obieqtidan meoremde misasvleli gza).

savarjiSoebis #4, #5, #6 saSualebiT xdeba gacnobili masalis Seswavla.

Sejameba-Sefaseba: savarjiSo #7 sruldeba damoukideblad.


II saaTi

Seswavla _ 30 wT._ savarjiSoebi #11-dan #18-is CaTvliT



Seamowme Seni codna

§ 11 marSrutis arCeva da gamosaxva aRniSvnebiT

globaluri mizani: figuraTa zomebisa da obieqtTa Soris manZilebis povnis,

sqemaze orientirebisa da marSrutis aRmweri martivi sqemis Sedgenis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon realuri viTarebis Sesabamisi sqematuri

gamosaxulebis mixedviT or obieqts Soris umoklesi manZilis povna, asoiTi

aRniSvnebis gamoyeneba sqemaze, realuri viTarebis Sesabamisi marSrutis

gamosaxva sqematurad.

winaswari codna da unarebi: umoklesi manZilis arCeva; sigrZis didi erTeulis

mcire erTeuliT gamosaxva; mTelis nawilis amocnoba da dasaxeleba; svetovani

diagramis saxiT warmodgenili monacemebis ganmarteba.

saWiro dro:

18

2 sT. (SeiZleba Temas daeTmos 3 sT.)

gacnoba _ 15 wT. _ savarjiSoebi #1 da #2



saWiro resursi: Tabaxis furclebi.


maswavlebeli mimarTavs klass:

- wyvilebma SeasruleT saxelmZRvaneloSi mocemuli savarjiSoebi #1, #2

maswavlebeli akvirdeba muSaobis process da gzadagza exmareba maT, mag.:

- 1km da kidev 1km erTad ramdenia? wers dafaze 1+1=2.

- mTeli gza aris 2 km, ramdenia 2-is naxevari? (1).

- ra manZilia (ramdeni km-ia) saxlidan gzamde? (1km), e. i.saxlidan gzamde

manZili mTeli gzis naxevri, meoredi nawilia.

moswavleebma unda SeZlon aseve wirebis klasificireba (mrudi, swori) da

axsnan, rom swori gziT ufro male mivlen daniSnul adgilas.

savarjiSos saSualebiT moswavleebi swavloben realuri viTarebis Sesabamisi

marSrutis gamosaxvas sqematurad.

savarjiSoebs #3, #4, #6 moswavleebi asruleben maswavleblis daxmarebiT.

maswavlebeli moswavleebs mofiqrebis saSualebas aZlevs, Semdeg,

saWiroebisamebr, exmareba maT, mag., savarjiSo #3: 2 km aris 1km+1km; Tu 1km-s

bavSvebi 1 sT-Si gadian, 2 km-s gaivlian 2 sT-Si. 1+1=2.

_ Tu saxlidan bavSvebi 8 sT-ze gavidnen da gzaSi 2 sT dayves, romel saaTze

mivlen isini daniSnul adgilas? 8+2=10, e. i. mdinris napiras 10 saaTze iqnebian.

savarjiSo #4

_ 3 mm _ Wiamaia; 30 mm _ pepela; 2 m _ naZvi; 100 sm _ buCqi; 1 dm _ yvavili.


§ 12 vin ufro swrafad?

savarjiSoebi maswavlebels SeuZlia gamoiyenos rigebs Soris Sejibris

Casatareblad.

§ 13 marSrutis arCeva da gamosaxva aRniSvnebiT

globaluri mizani: figuraTa zomebisa da obieqtTa Soris manZilebis povnis,

sqemaze orientirebisa da marSrutis aRmweri martivi sqemis Sedgenis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon realuri viTarebis Sesabamisi sqematuri

gamosaxulebis mixedviT or obieqts Soris umoklesi manZilis povna, asoiTi

aRniSvnebis gamoyeneba sqemaze, realuri viTarebis Sesabamisi marSrutis

gamosaxva sqematurad.

19

winaswari codna da unarebi: umoklesi manZilis arCeva; sigrZis didi erTeulis

mcire erTeuliT gamosaxva; mTelis nawilis amocnoba da dasaxeleba; svetovani

diagramis saxiT warmodgenili monacemebis ganmarteba. meordeba da ratom?

saWiro dro:




savarjiSoebs #1, #2 moswavleebi asruleben wyvilebad (10-15 wT.) samuSaos

dasrulebis Semdeg wyvilebi waradgenen namuSevrebs da ganixilaven

Sesrulebul savarjiSos.


§ 14 simetria

globaluri mizani: geometriuli figurebis aRweris unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon (TvalsaCinoebiT), ra aris simetria.

saWiro dro:

gacnoba _ 10 wT._ savarjiSoebi #1 da #2

Seswavla _ 15 wT._ savarjiSoebi #3 da #6

Sejameba-Sefaseba _ 10 wT._ savarjiSo #7

saWiro resursebi: Tabaxis furclebi, makrateli, fanqrebi, saxazavi.


§ 15 naxevari

globaluri mizani: mTelis nawilebis dasaxelebis, gansxvavebisa da Sedarebis

unarebis ganviTareba.

lokaluri mizani: moswavleebma SeZlon dadgena, rom meoredi da meoTxedi aris

rogorc mTelis, aseve garkveuli raodenobis or tol (4 tol) nawilad dayofis

Sedegi.

winaswari codna da unarebi: raodenobis ganaxevreba; svetovani diagramis saxiT

warmodgenili monacemebis ganmarteba; raodenobebis Sedareba; brtyeli

geometriuli figuris amocnoba; mimdevrobis agebis wesis gansazRvra da

gagrZeleba.

saWiro dro:

gacnoba _ 10 wT._ savarjiSoebi #1da #2


20

Sejameba-Sefaseba _ 10 wT._ savarjiSoebi #7 da #8

maswavlebeli TvalsaCinoebis saSualebiT acnobs moswavleebs mTels, naxevars,

meoTxeds.



_ wyvilebma SeasruleT saxelmZRvaneloSi mocemuli savarjiSo #1.

samuSaos dasrulebis Semdeg moswavleebi asaxeleben raodenobas, romelic

Sexvda TiToeul bavSvs (naxevari vaSli, naxevari atami, erTi msxali, ori banani).

maswavlebeli moswavleebTan erTad azustebs, rom xilis TiToeuli saxeobis

Tanabrad gasanawileblad saWiroa misi or tol nawilad gayofa (ganaxevreba),

TiToeuli nawili aris mTliani raodenobis meoredi (mTelis SemTxvevaSi _ misi

naxevari da a. S.). dafaze moswavleebTan erTad xatavs sxvadasxva raodenobas da

Semdeg maT anaxevrebs. TiToeul SemTxvevaSi yuradRebas amaxvilebs raodenobis

or tol nawilad gayofaze. mag.:

maswavlebeli:

_ ToTxmeti gaiyo or tol nawilad.

_ ramdenia TiToeuli nawili? (Svidi). Svidi aris ToTxmetis naxevari, misi

meoredi nawili da a. S.

savarjiSos saSualebiT moswavleebi TvalnaTliv xedaven, rom naxevari aris

mTelis an raodenobis or tol nawilad gayofis Sedegi da TiToeuli nawili

warmoadgens mTelis an raodenobis meoreds.

Semdeg moswavleebi asruleben savarjiSo #2.

savarjiSoebs #3, #4 da #5 moswavleebi asruleben maswavleblis daxmarebiT.

Sejameba-Sefaseba: savarjiSo #8 moswavleebma unda daadginon, rom momdevno

figura aris mTeli wre. maswavlebeli, saWiroebisamebr, SekiTxvebiT exmareba

maT:

- daakvirdiT figurebs, rogor icvleba yoveli momdevno figura? (emateba

nawili) da a. S.


Seamowme Seni codna

testi

II Tavi

am TavSi grZeldeba muSaoba Sedegebze:






21








IV.14 _ mowmdeba indikatorebiT 1, 2, 3.

da iwyeba muSaoba Sedegebze:



IV.7 _ mowmdeba indikatorebiT -3.


IV.9 _ mowmdeba indikatorebiT - 1, 3



§ 16

§ 17

§ 18

§ 19

§ 20

§ 21

§ 22

§ 23

§ 24

§ 25

§ 26

§ 27

§ 28

§ 29

§ 30

§ 31

§ 32

§ 33

§ 34

§ 35

§ 36

§ 37

§ 38

§ 39

samniSna ricxvebis Sekreba

perimetri

samniSna ricxvebis Sekreba

jamis gamravleba ricxvze

samniSna ricxvebis gamokleba

Seamowme Seni codna

kilogrami

Seamowme Seni codna

10-ze, 100-ze gamravleba-gayofa

erTniSna ricxvis srul aTeulze gamravleba

vin ufro swrafad?

erTniSna ricxvis srul aTeulze gamravleba

geometriuli figurebi

Seamowme Seni codna

geometriuli figurebi

erTniSna ricxvebis gamravleba orniSna ricxvebze

ucnobi Tanamamravli

Seamowme Seni codna

ucnobi Tanamamravli

jamis gayofa ricxvze

naSTiani gayofa

litri

samniSna ricxvis gayofa erTniSna ricxvze

Seamowme Seni codna

ramdeni nawilia?

saaTi

ucnobi gasayofi

ucnobi gamyofi

gamravlebis Tviseba

Seamowme Seni codna

testi

4

1

1

1

2

1

3

1

1

2

1

1

1

1

1

2

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

22

§ 16 samniSna ricxvebis Sekreba

globaluri mizani: naturalur ricxvebze Sekreba-gamoklebis moqmedebebis

sxvadasxva xerxiT Sesrulebis unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon Sekrebis Sesrulebis erT-erT xerxs da

SeZlon misi gamoyeneba.

winaswari codna da unarebi: ricxvis warmodgena saTanrigo Sesakrebebis jamis

saxiT; calkeuli Tanrigebis Sekreba.

saWiro dro:

gacnoba-Seswavla _ 30 wT._ savarjiSoebi #1da #2


saWiro resursebi: saqarTvelos ruka.


sasurvelia, maswavlebelma gamoiyenos saqarTvelos ruka da gamoavlinos,

rogor orientireben moswavleebi sibrtyeze (mag.: daasaxelon xaSuris marjvniv,

marcxniv, zeviT, qveviT mdebare qalaqebi). aseve saintereso iqneba saqarTvelos

im kuTxis dasaxeleba, sadac mdebareobs TiToeuli qalaqi da saqarTvelos

kuTxeebis erTmaneTis mimarT mdebareobis aRwera, Semdeg ki ukve qalaqebs

Soris manZilebis dadgena.

maswavlebelma yuradReba unda gaamaxvilos imaze, rom xdeba ricxvis warmod-

gena saTanrigo Sesakrebebis jamis saxiT, jgufdeba erTnairi Tanrigebi da

xdeba maTi Sekreba.

savarjiSoebi sruldeba klasSi.

Sejameba-Sefaseba: savarjiSoebi # 4 da #5


§ 17 perimetri

globaluri mizani: brtyeli figuris grafikuli gamosaxulebis Seqmnis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon figuris perimetris dadgena.

winaswari codna da unarebi: figuris wrfivi zomis dadgena; amocanis

amosaxsnelad Sesabamisi ariTmetikuli moqmedebis Sesruleba.

saWiro dro:

gacnoba _ 15 wT._ savarjiSo #1




23

konkretuli amocanis gadasaWrelad moswavleebs sWirdebaT figuris

garSemowerilobis (perimetris) dadgena. isini ecnobian, Tu ra aris perimetri.

sasurvelia, maswavlebelma savarjiSos Sesruleba jer moswavleTa wyvilebs

daavalos, Semdeg ki daexmaros da daazustos maT mier Sesrulebuli samuSaos

Sedegi (sxvadasxva figuris saSualebiT TvalsaCinod aCvenos, ra aris

perimetri).

skolis Senobis perimetris gasazomad maswavlebels moswavleebi gahyavs

ezoSi da iq asruleben gamoTvlebs. iqve SeiZleba SeirCes nakveTi yvavilebis an

xeebis dasargavad da saxelmZRvaneloSi mocemuli savarjiSo bavSvebma

realurad Seasrulon.

savarjiSo # 3 moswavleebi TviTon adgenen figuris perimetrs.

savarjiSo # 4 sasurvelia, moswavleebma gamoTqvan varaudi, Tu ratom

fiqroben, rom romelime figura grZelia an mokle. radgan meore da mesame

figurebi TiTqmis erTsa da imave adgilas iwyeba da mTavrdeba da mesame

figuris sigrZe ar aris swori xazi, aramed texili, savaraudod misi sigrZe

meti unda iyos, rasac Semdeg daadastureben gazomviT.

savarjiSo # 5-is Sesrulebis Semdeg moswavleebi aRmoaCenen, rom sxvadasxva

formis or figuras SesaZlebelia hqondes erTnairi perimetri.


§ 18 samniSna ricxvebis Sekreba



lokaluri mizani: moswavleebi gaecnon Sekrebis Sesrulebis erT-erT xerxs da

SeZlon misi gamoyeneba.


saxiT; calkeuli Tanrigebis Sekreba.

saWiro dro:




§ 19 jamis ricxvze gamravleba

globaluri mizani: martivi maTematikuri amocanis amoxsnisas algebruli

gamosaxulebis Sedgenis unaris ganviTareba.

24

lokaluri mizani: moswavleebma SeZlon amocanis amosaxsnelad gamosaxulebis

Sedgena; gamosaxulebis mniSvnelobis dasadgenad Sekrebis mimarT gamravlebis

distribuciulobis gamoyeneba.

winaswari codna da unarebi: Sekrebis da gamravlebis moqmedebaTa Sesruleba.

saWiro dro:





savarjiSoebis #1 da #2 Sesrulebisas moswavleebi TvalnaTliv xedaven Tu

rogor SeiZleba gamravlebis ufro advilad Sesruleba, mag.: 15 warmoadgines

ori iseTi Sesakrebis jamis saxiT, romelTa 4-ze gamravleba ufro advilia. rac

mTavaria, moswavleebi xedaven, rom mniSvneloba ara aqvs, jams gaamravleben

ricxvze, Tu TiToeul Sesakrebs da Semdeg Sekreben miRebul Sedegebs; amiT

gamosaxulebis mniSvneloba ar Seicvleba.

15 · 4 = 60 da (10+5) · 4=10·4+5·4=40+20=60

sasurvelia, maswavlebelma dafaze Camoweros savarjiSoebi, mag.:

27·3= (20+7) ·3=

24·4= (20+4) ·4= da a.S.

maswavlebelma unda sTxovos moswavleebs, daadginon gamosaxulebis

mniSvnelobebi, Semdeg ki daakvirdnen gamosaxulebebs da Tqvan, ratom aqvT 27·3

(20+7) ·3 gamosaxulebebs erTnairi mniSvnelobebi.

savarjiSo #3 gacnobili masalis safuZvelze, moswavleebma unda moZebnon

erTnairi mniSvnelobis mqone gamosaxulebebi.

savarjiSo #4 moswavleebma unda gamoiyenon gamravlebis distribuciuloba

Sekrebis mimarT.

savarjiSo #5 moswavleebma TviTon unda warmoadginon ricxvi xelsayreli jamis

saxiT, raTa ufro iolad Seasrulon gamravleba.


§ 20 samniSna ricxvebis gamokleba



lokaluri mizani: moswavleebi gaecnon gamoklebis Sesrulebis konkretul

(qveSmiweriT) xerxs da SeZlon misi gamoyeneba.


saxiT; Tanrigebis dajgufeba Sesabamisi ariTmetikuli moqmedebis

Sesasruleblad; or sidides Soris gansxvavebis gamoklebiT dadgena; svetovani

diagramis saSualebiT warmodgenili monacemebis aRwera.

25

I saaTi

saWiro dro:


Seswavla _ 15 wT. _ savarjiSoebi #3, #4, #5, #6 da #7



savarjiSoebis #1 -is Sesrulebisas moswavleebs sWirdebaT moqmedeba

gamoklebis Sesruleba. svetovani diagrama am SemTxvevaSi gamoiyeneba, rogorc

TvalsaCinoeba, radganac masze naTlad Cans, rom svetebis simaRleebs Soris

gansxvavebis moZebna SeiZleba gamoklebis saSualebiT.

sasurvelia, maswavlebelma Seaxsenos moswavleebs ricxvis warmodgena

saTanrigo Sesakrebebis jamis saxiT da dafaze dawvrilebiT aCvenos, rogor

xdeba qveSmiweriT gamokleba, mag.:

(300+70+5)-(200+40+2)=133

300-200=100

70-40=30

5-2=3

savarjiSo #4-is Sesrulebisas ki maswavlebeli kidev erTxel azustebs, rogor

xdeba gamoklebis Sesruleba.

mniSvnelovania, rom moswavleebma gaigon gamoklebis qveSmiweriT Sesrulebis

arsi da moqmedeba meqanikurad ar daimaxsovron.



II saaTi

saWiro dro:

Seswavla _ 25 wT. _ savarjiSoebi #11-dan 19-is CaTvliT



Seamowme Seni codna

§ 21 kilogrami

globaluri mizani: zomis sxvadasxva erTeulis erTmaneTTan dakavSirebis

unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon wonis erTeulebs _ kilograms da grams.

I saaTi

saWiro dro:




26


mas Semdeg, rac maswavlebeli moswavleebs savarjiSoebis saSualebiT

gaacnobs wonis sazom erTeulebs _ kilograms da grams, igi yuradRebas

amaxvilebs maT Soris Tanafardobaze (1 kg=1000 g.), aseve erTeulis wonis

mixedviT ramdenime erTeulis wonis dadgenaze, mag.: 1 cali vaSli iwonis

120 g-s, 2 cali 120 g+120 g=120 g· 2=240 g., sami cali iwonis 120 g+120 g+120

g=120 g·3=360 g da a. S.


II saaTi

saWiro dro:

Seswavla _ 25 wT. _ savarjiSoebi #11-dan 13-is CaTvliT



sasurvelia, moswavleebma savarjiSoebi #11-dan #13-is CaTvliT Seasrulon

wyvilebad.

III saaTi

saWiro dro:

Seswavla _ 25 wT. _ savarjiSoebi #19-dan # 22-is CaTvliT



sasurvelia, moswavleebma savarjiSoebi #19-dan #22-is CaTvliT Seasrulon

wyvilebad.

Seamowme Seni codna

§ 22 gamravleba-gayofa 10-ze, 100-ze

globaluri mizani: gamravleba-gayofis moqmedebebis Sesrulebis romelime

xerxis gamoyenebis unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon 10-ze da 100-ze gamravleba-gayofis

moqmedebebis Sesrulebis wess.

winaswari codna da unarebi: gamravleba-gayofis moqmedebebis Sesruleba

(mravaljeradi Sekreba, tol raodenobad dayofa), gamravlebis komutaciurobis

gamoyeneba.

saWiro dro:


Seswavla _ 20 wT. _ savarjiSoebi #3, #4, #5 da #6

Sejameba-Sefaseba _ 10 wT._ savarjiSoebi #9, #10

27


savarjiSoebis #1-is gacnobisas da Sesrulebisas moswavleebi unda

daakvirdnen konkretul tolobebs da ramdenime kerZo magaliTis safuZvelze

gakeTon zogadi daskvna. es xels Seuwyobs moswavleebSi induqciuri msjelobis

unaris ganviTarebas. aseve unda dazustdes, rom 2·10=10·2; 10+10 ori aTeuli

aris 20 da a.S. gamravlebis Sedegad miiReba imdeni aTeuli, ramden Sesakrebadac

aris 10 aRebuli, amitom 10-ze gamravlebisas SeiZleba am ricxvs pirdapir

mivuweroT erTi nuli. analogiurad 100-ze gamravlebisas miRebuli Sedegi

imdeni aseulia, ramden Sesakrebadac aris aRebuli 100, amitom ricxvis 100-ze

gamravlebisas SeiZleba am ricxvs pirdapir mivuweroT ori nuli.

momdevno savarjiSoebis Sesrulebisas maswavlebeli azustebinebs

moswavleebs moqmedebis Sesrulebas.


§ 23 erTniSna ricxvis srul aTeulze gamravleba



lokaluri mizani: moswavleebi gaecnon nuliT daboloebul ricxvebze

gamravlebis Sesrulebis wess.

winaswari codna da unarebi: erTniSna ricxvebis gamravleba; erTniSna ricxvis

orniSna ricxvze gamravleba; tolobis ucnobi wevris povna.

saWiro dro:


Seswavla _ 20 wT. _ savarjiSoebi #2, #3, #4, #5, #6, #7 da #10



iseve, rogorc 10-ze da 100-ze gamravlebis gacnobisas ,moswavleebi kerZo

magaliTebis safuZvelze akeTeben zogad daskvnas; aucilebelia dazusteba, rom

mag.: 4·70=280. 280-aris 28 aTeuli, e.i. miRebul SedegSi aris imdeni aTeuli,

ramdenic aris 4-sa da 7-is namravli, amitom nuliT daboloebuli ricxvebis

gamravlebisas SeiZleba martivi xerxis gamoyeneba: ricxvis CanawerSi 0-s

yuradReba ar eqceva, erTmaneTze mravldeba ricxvebi da miRebuli Sedegs

ewereba imdeni nuli, ramdeni nulic aris mocemul ricxvebSi.

savarjiSo #5-is Sesrulebisas moswavleebi tolobis ucnobi wevris

mniSvnelobas unda mixvdnen Sedegis mixedviT, radgan 7-s daemateba erTi nuli

e.i. gamravlda 10-ze da a. S.


28

§ 24 vin ufro swrafad

§ 25 erTniSna ricxvis srul aTeulze gamravleba-gayofa



lokaluri mizani: moswavleebi gaecnon nuliT daboloebul ricxvebze gayofis

Sesrulebis wess.

winaswari codna da unarebi: erTniSna ricxvebis gayofa; orniSna ricxvis

erTniSna ricxvze gayofa; tolobis ucnobi wevris povna.

saWiro dro:


Seswavla _ 20 wT. _ savarjiSoebi #26, #27, #28, #29, #30 da #33



§ 26 geometriuli figurebi

globaluri mizani: geometriuli figurebis aRweris da maTi klasifikaciis

unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon konkretuli sivrculi geometriuli

figuris aRwera.

winaswari codna da unarebi: brtyeli geometriuli figuris amocnoba da aRwera.

orientacia sivrceSi.

saWiro dro:

gacnoba _ 20 wT._ savarjiSoebi #1, #2 da #3



saWiro resursebi: Tabaxis furclebi, makrateli, webo, saxazavi, fanqari,

sivrculi figurebis (prizma, piramida) modelebi.

gakveTilis mokle aRwera:

sasurvelia, maswavlebelma sivrculi figuris waxnagisa da wibos gasacnobad

gamoiyenos TvalsaCinoeba. kubis models moswavleebi daamzadeben gakveTilze

maswavleblis daxmarebiT.


29

Seamowme Seni codna

§ 27 geometriuli figurebi

globaluri mizani: geometriuli figurebis aRwerisa da maTi klasifikaciis,

brtyeli da sivrculi figurebis grafikuli gamosaxulebebisa da modelebis

Seqmnis unarebis ganviTareba.

lokaluri mizani: moswavleebma SeZlon grafikuli gamosaxulebis mixedviT

geometriuli figuris Seqmna; garkveuli samuSaos dagegmva da Sesruleba.

winaswari codna da unarebi: geometriuli figuris amocnoba da aRwera;

monacemebis warmodgena cxrilis da svetovani diagramis saSualebiT;

warmodgenili monacemebis ganmarteba; saWiro monacemebis mosagroveblad

Sesaferisi xerxis gamoyeneba; erTeulis Rirebulebis mixedviT ramdenime

erTeulis fasis dadgena.

saWiro resursebi: feradi furclebi, makrateli, webo, saxazavi, fanqari,

samagri.


sasurvelia, saxelmZRvaneloSi warmodgenili mxatvris (kazimir maleviCi)

namuSevrebis Sesaxeb informacia moswavleebs gasagebi da saintereso formiT

miawodos xelovnebis maswavlebelma. aseTi gakveTili, SesaZlebelia, gaxdes

motivaciis safuZveli da moswavleebs aRuZras interesi ara marto maTematikis,

aramed xelovnebis sakiTxebis ufro Rrmad wvdomisadmi.

am gakveTilze moswavleebi aseve ecnobian rogor SeiZleba garkveuli

samuSaos dagegmva. aq maT unda gamoiyenon SeZenili codna. moswavleTa mier

gamomJRvavnebuli codnis Sefaseba saSualebas miscems maswavlebels, Seajamos

(gansxvavebuli xerxiT) ganvlili masala. moswavleebs saSualeba eZlevaT,

Tavadac dagegmon samuSao (es SeiZleba iyos ara marto saaxalwlo zeimi, aramed

patara eqskursia muzeumSi, an sxva RirsSesaniSnaobis daTvaliereba, romelime

moswavlis dabadebis dRe da a.S.). samuSaoSi CarTuli iqneba uklebliv yvela

moswavle, TiToeul maTgans miecema saSualeba, srulad gamoamJRavnos Tavisi

SesaZleblobebi. xels Seuwyobs maT TanamSromlobas da urTierTSefasebas.

§ 28 erTniSna ricxvebis gamravleba orniSna ricxvze



lokaluri mizani: moswavleebi gaecnon, rom orniSna ricxvis erTniSna ricxvze

gamravlebisas SesaZlebelia orniSna ricxvis warmodgena xelsayreli jamis

saxiT.

winaswari codna da unarebi: erTniSna ricxvebis gamravleba; ricxvis gamravleba

10-ze, 100-ze; ricxvis gamravleba nuliT daboloebul ricxvze; erTeulis

Rirebulebis mixedviT ramdenime erTeulis fasis dadgena; martivi amocanis

30

amoxsnisas algebruli gamosaxulebis Sedgena; Sekrebis mimarT gamravlebis

distribuciulobis gamoyeneba.

saWiro dro:





mniSvnelovania, moswavleebma gaigon, rom gamoTvlebis gasamartiveblad

orniSna ricxvis erTniSna ricxvze gamravlebisas SeiZleba orniSna ricxvis

warmodgena jamis saxiT (SesaZlebelia, es jami iyos saTanrigo Sesakrebebis

jami, radgan nuliT daboloebul ricxvze gamravleba advilia).

aseve, moswavleebma SeZlon amocanis amosaxsnelad asoiTi gamosaxulebis

Sedgena. (maswavlebeli yuradRebas amaxvilebs imaze, Tu risi aRniSvna xdeba

asoTi mag.: erTeulis Rirebulebis).

§ 29 ucnobi Tanamamravli

globaluri mizani: algebruli gamosaxulebis Sedgenis unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon tolobis ucnobi wevris (Tanamamravlis)

povna.

winaswari codna da unarebi: gamravlebis da gayofis urTierTSebrunebulobis

gamoyeneba; amocanis amosaxsnelad algebruli gamosaxulebis Sedgena.

saWiro dro:





savarjiSo #1-is Sesrulebis siswrafe damokidebulia imaze, SeZleben Tu ara

moswavleebi gamravleba-gayofis urTierTSebrunebulobis gamoyenebas.

sasurvelia, samuSaos Sesrulebis Semdeg wyvilebma erTmaneTs gauziaron

TavianTi mosazreba (rogor Seasrules miTiTebuli moqmedebebi). Semdeg ukve

maswavlebeli azustebs, rom Tu moswavleebi kargad daakvirdebian TiToeul

svetSi mocemul savarjiSoebs, Zalian swrafad Seasruleben gamoTvlebs

gamravleba-gayofis urTierTSebrunebulobis gamoyenebiT. es samuSao

moamzadebs klass axal masalaze gadasasvlelad.

savarjiSo #2 mocemuli amocana SeiZleba amoixsnas X-is nacvlad sxvadasxva

mniSvnelobis Casmis xerxiT, imis dasadgenad, Tu ra Tanxa unda Caagdos elenem

yovelTviurad yulabaSi, Sedgenil gantolebaSi saTiTaod unda Caisvas 5, 10, 7

da a.S. swori tolobis miRebis SemTxvevaSi SeirCes saWiro mniSvneloba.

Semdeg moswavleebi ecnobian, rom Tu gamoiyeneben gamravleba-gayofis

urTierTSebrunebulobas, 50-is 5-ze gayofiT miiReben saWiro Tanxis

mniSvnelobas.

31

savarjiSo #3-is Serulebis Semdeg ukve SesaZlebelia, gakeTdes ganzogadeba:

Tu tolobaSi ucnobia erT-erTi Tanamamravli, misi moZebna SeiZleba namravlis

cnobil Tanamamravlze gayofiT.

saSinao davaleba: savarjiSo #7 da #10

§ 30 ucnobi Tanamamravli

globaluri mizani: algebruli gamosaxulebis Sedgenis unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon tolobis ucnobi wevris (Tanamamravlis)

povna.

winaswari codna da unarebi: gamravlebis da gayofis urTierTSebrunebulobis

gamoyeneba; amocanis amosaxsnelad algebruli gamosaxulebis Sedgena.

saWiro dro:




§ 31 jamis gayofa ricxvze


xerxis gamoyeneba.

lokaluri mizani: moswavleebi gaecnon, rogor SeiZleba gamoTvlebis

gasamartiveblad ricxvis warmodgena raime jamis saxiT da Semdeg gayofis

Sesruleba cal-calke TiToeuli Sesakrebis gayofiT.

winaswari codna da unarebi: gayofis moqmedebis Sesruleba; tolobis ucnobi

wevris moZebna.

saWiro dro:





konkretuli magaliTebis safuZvelze moswavleebi ecnobian, rom erTi da

igive ricxvi SeiZleba warmoadginon sxvadasxa jamis saxiT da maT SeuZliaT

gamoiyenon daSlis iseTi varianti, romelic ufro xelsayrelia gamoTvlebis

Sesasruleblad.

Semdeg xdeba masalis Seswavla da bolos Sejameba.

momdevno gakveTilebis Casatareblad maswavlebels SeuZlia gamoiyenos ukve

nacnobi xerxebi. amitom scenarebi aRar iqneba dawvrilebiT aRwerili.

miTiTebuli iqneba mxolod miznebi da gakveTilis TiToeuli fazisaTvis

gankuTvnili savarjiSoebi.

32


§ 32 naSTiani gayofa


xerxis gamoyeneba.

lokaluri mizani: moswavleebma gamoTvlebze amocanebis amoxsnisas, naSTiT

gayofis SemTxvevaSi, SeZlon naSTis interpretacia.

saWiro dro:





§ 33 litri

globaluri mizani: zomis erTeulebis gacnoba.

lokaluri mizani: moswavleebi gaecnon, rogor SeiZleba imis dadgena, ramdeni

litri siTxe Caeteva WurWelSi.

saWiro dro:





§ 34 samniSna ricxvis gayofa erTniSna ricxvze


xerxis gamoyeneba.

lokaluri mizani: moswavleebi gaecnon, rogor SeiZleba gamoTvlebis

gasamartiveblad samniSna ricxvis warmodgena jamis saxiT da gamoTvlebis

Sesruleba.

saWiro dro:


33




Seamowme Seni codna

§ 35 ramdeni nawilia?

globaluri mizani: mTelis nawilebis gansxvavebis da Sedarebis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon mTelis nawilebis amocnoba.

saWiro dro:





§ 36 saaTi

globaluri mizani: zomis sxvadasxva erTeulis gamoyenebisa da erTmaneTTan

dakavSirebis unaris ganviTareba.

lokaluri mizani: moswavleebma SeZlon drois sxvadasxva erTeuls Soris

Tanafardobis dadgena, ariTmetikuli moqmedebebis gamoyenebiT drois

intervalis povna.

saWiro dro:





§ 37 ucnobi gasayofi

globaluri mizani: algebruli gamosaxulebis Sedgenis unaris ganviTreba.

lokaluri mizani: moswavleebma SeZlon ucnobi gasayofis povna gamyofisa da

ganayofis saSualebiT.

34

saWiro dro:


Seswavla _ 20 wT. _ savarjiSoebi #2, #3, #4, #5 da #6



§ 38 ucnobi gamyofi

globaluri mizani: algebruli gamosaxulebis Sedgenis unaris ganviTreba.

lokaluri mizani: moswavleebma SeZlon ucnobi gamyofis povna gasayofisa da

ganayofis saSualebiT.

saWiro dro:


Seswavla _ 20 wT. _ savarjiSoebi #2, #3, #4, #5, #6, #7 da #8



§ 39 gamravlebis Tviseba

globaluri mizani: ricxviTi gamosaxulebis mniSvnelobis moZebnis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon ricxviTi gamosaxulebis mniSvnelobis

mosaZebnad gamravlebis Tvisebis gamoyeneba.

saWiro dro:





Seamowme Seni codna

testi

III Tavi

35

am TavSi grZeldeba muSaoba Sedegebze:

IV.1 _ mowmdeba indikatorebiT - 1, 2, 3, 4.

IV.2 _ mowmdeba indikatorebiT - 1, 2, 3, 4.










§ 40

§ 41

§ 42

§ 43

§ 44

§ 45

§ 46

§ 47

§ 48

mravalniSna ricxvebi

vin ufro swrafad?

mravalniSna ricxvebi

tona

gamravleba erTniSna ricxvebze (qveSmiweriT)

gamravleba-gayofa 10-ze, 100-ze, 1000-ze

farTobi

nulebiT daboloebuli ricxvebis gamravleba da gayofa

Seamowme Seni codna

erTniSna ricxvebis gayofa

Seamowme Seni codna

3

1

4

1

2

1

1

1

1

1

3

§ 40 mravalniSna ricxvebi


dalagebisa da Sedarebis unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon raodenobebs 10 000-mde. SeZlon

ricxvebis gamosaxva da Sedareba.

I saaTi

saWiro dro:





II saaTi

saWiro dro:

Seswavla _ 30 wT. _ savarjiSoebi #11, #12, #13, #14, #15, #16, #17, #18 da #19



36

III saaTi

saWiro dro:

Seswavla _ 30 wT. _ savarjiSoebi #23, #24, #25, #26, #27, #28, #29, #30da #31



§ 41 vin ufro swrafad?

§ 42 mravalniSna ricxvebi


dalagebisa da Sedarebis unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon raodenobebs milionamde. SeZlon

ricxvebis gamosaxva da Sedareba.

I saaTi

saWiro dro:




saSinao davaleba: savarjiSo #5da #6

II saaTi

saWiro dro:

Seswavla _ 30 wT. _ savarjiSoebi #9, #10, #11, #12, #13, #14, #15da #16



III saaTi

saWiro dro:




IV saaTi

saWiro dro:




37

§ 43 tona

globaluri mizani: zomis sxvadasxva erTeulis erTmaneTTan dakavSirebis

unaris ganviTareba.

lokaluri mizani: moswavleebi gaecnon wonis sazom erTeuls _ tonas, SeZlon

misi gamosaxva kilogramebis saSualebiT.

saWiro dro:




saSinao davaleba: savarjiSo #5da #6

§ 44 gamravleba erTniSna ricxvze


xerxis gamoyeneba.

lokaluri mizani: moswavleebma SeZlon mravalniSna ricxvis erTniSna ricxvze

weriTi gamravlebis Sesruleba.

I saaTi

saWiro dro:





II saaTi

saWiro dro:




§ 45 gamravleba-gayofa 10-ze, 100-ze, 1000-ze



lokaluri mizani: moswavleebma SeZlon 10-ze, 100-ze da 1000-ze gamravleba-

gayofis Semoklebuli wesebis axsna da gamoyeneba.

saWiro dro:

38

gacnoba _ 10 wT._ TvalsaCinoeba




§ 46 farTobi

globaluri mizani: brtyeli figuris grafikuli gamosaxulebis Seqmnis unaris

ganviTareba.

lokaluri mizani: moswavleebma SeZlon figuris farTobi dadgena.

winaswari codna da unarebi: figuris wrfivi zomis dadgena; amocanis

amosaxsnelad Sesabamisi ariTmetikuli moqmedebis Sesruleba.

saWiro dro:





§ 47 nulebiT daboloebuli ricxvebis gamravleba-gayofa



lokaluri mizani: moswavleebi gaecnon nuliT daboloebul ricxvebze

gamravleba-gayofis Sesrulebis wess.

saWiro dro:

gacnoba _ 10 wT._ savarjiSoebi #1, #2, #6




Seamowme Seni codna

§ 48 erTniSna ricxvze gayofa


xerxis gamoyeneba.

39

lokaluri mizani: moswavleebma SeZlon mravalniSna ricxvis erTniSna ricxvze

weriTi gayofis Sesruleba.

I saaTi

saWiro dro:

gacnoba _ 15 wT._ savarjiSoebi #1, #2, #3




II saaTi

saWiro dro:

gacnoba _ 10 wT._ savarjiSo # 10


Sejameba-Sefaseba _ 15 wT. _ savarjiSoebi #19, #20 da # 21


III saaTi

saWiro dro:


Sejameba-Sefaseba _ 15 wT. _ savarjiSoebi #30 da # 31


Seamowme Seni codna

* * *

zogadi mizani: maTematikisa da fizkulturis integrirebuli swavleba,

saganTaSoris kavSirebis dadgena-ganmtkiceba.

lokaluri mizani: moswavleebma SeZlon maTematikis gakveTilze miRebuli

codnis praqtikuli gamoyeneba fizkulturis gakveTilze.

winaswari codna da unarebi: mocemuli wesis mixedviT mimdevrobis warmodgena;

monacemebis amokreba cxrilidan; siis daxasiaTeba; wrfivi zomis dadgena

arastandartuli zomis erTeulis gamoyenebiT; orniSna ricxvis CanawerSi

TanrigebSi mdgomi cifrebis mniSvnelobis ganmarteba.

saWiro resursebi: qaRaldis 2 formati, 6 cali joxi, baraTebi ricxvebiT _

(klasSi moswavleTa raodenobis mixedviT), 8 qudi.

saWiro dro:

1. savarjiSo 20 wT.

2. savarjiSo 20 wT.

3. savarjiSo 30 wT.

40

gakveTilis msvleloba: (2 sT)

gakveTili tardeba darbazSi an ezoSi.


_ dRes gansakuTrebuli gakveTili gveqneba. movawyobT sam Sejibrs, romelTa

warmarTvaSi maTematikis gakveTilze miRebuli codna dagvexmareba.

maswavlebeli moswavleebs yofs or jgufad; urigebs moswavleebs winaswar

damzadebul baraTebs (baraTebis raodenoba Seesabameba klasSi moswavleTa

radenobas). baraTebis erT naxevars aweria ricxvebi Semdegi TanmimdevrobiT: 5,

10, 15, 20, 25 da a.S. meore naxevars ki_40, 60, 80, 100 da a.S.

gamohyavs is moswavleebi, romelTac SexvdaT baraTebi nomrebiT 5 da 40 da

ambobs, rom isini iqnebian jgufis pirveli nomrebi. Semdeg mimarTavs danarCen

moswavleebs, rom daikavon TavianTi adgilebi jgufis pirveli nomrebis ukan

Semdegi wesiT: 5-is ukan yoveli momdevno ricxvi winaze 5-iT meti unda iyos, 40-

is ukan yoveli momdevno winaze 20-iT meti unda iyos.jgufebis dakompleqtebis

Semdeg maswavlebeli avalebs maT, CaarWon joxebi toli manZilis daSorebiT.

maswavlebeli:

_ rogor gavzomoT am joxebs Soris manZili?

moswavleebi maswavlebels sTavazoben sxvadasxva saSualebebs. maswavlebeli

usmens maT da Semdeg ambobs:

_ modiT, gavzomoT joxebs Soris manZili nabijebiT da imave daSorebiT

CavarWoT momdevno joxebi.

savarjiSos saSualebiT maswavlebels SeuZlia gaacnos moswavleebs, rogor

SeiZleba wrfivi zomis dasadgenad arastandartuli sazomi erTeulis (mag.

nabijis) gamoyeneba. Semdeg ewyoba Sejibri jgufebs Soris. jgufis TiToeulma

wevrma unda Semourbinos joxs da dabrundes ukan (estafeta). maswavlebeli

iniSnavs dros, gamarjvebulia is jgufi, romelic ufro swrafad daasrulebs

Sejibrs.

II Sejibri

meore Sejibris Casatareblad maswavlebeli isev urigebs moswavleebs baraTebs

ricxvebiT da mimarTavs:

_ Cems marjvniv damwkrivdiT moswavleebi luwi ricxvebiT, marcxniv ki _kenti

ricxvebiT.

Sejibris mimdinareoba:

TiToeuli jgufi iyofa or nawilad da dgeba bolo joxebTan. erTi bolodan

pirveli moswavle unda gamoiqces, TanmimdevrobiT yvela joxs unda Camoacvas

qudi da miirbinos meore bolos mdgar jgufTan, amis Semdeg am jgufidan

garbis moswavle da Camosxnis qudebs da a.S.

gamarjvebulia jgufi, romelic pirveli daamTavrebs Sejibrs.

maswavlebeli wamzomiT iniSnavs TiToeuli moswavlis mier daxarjul dros.

III Sejibri

mesame Sejibris dros ukve jgufebad dayofili moswavleebi erTmaneTs

ejibrebian burTis kalaTSi CagdebaSi, ise, rom TiToeuli jgufis TiToeulma

moswavlem burTi samjer styorcnos. TiTo Cagdeba fasdeba sami quliT.

maswavlebeli Seajamebs Sedegebs.

Semdeg samuSao grZeldeba klasSi. maswavlebeli mimarTavs moswavleebs:

_ me maqvs Sejibris Sedegebi. axla TvalsaCinod warmovadginoT, rogor

SeiZleba amis gakeTeba? (dafaze davweroT, formatze davweroT).

maswavlebeli hkidebs dafaze qaRaldis formats da xazavs cxrilebs:

I jgufi II jgufi

41

gvari, saxeli qula gvari, saxeli qula

maswavlebeli miuTiTebs moswavleebs Camoweril gvarebze da ekiTxeba:

_ ra hqvia aseT CamonaTvals? (sia).

_ mowesrigebulia Tu ara Cveni sia? (ki an ara).

_ ra niSnis mixedviT aris mowesrigebuli?

_ ra hqvia mogrovebuli monacemebis warmodgenis aseT saSualebas? (cxrili)

_ romelma jgufma moagrova qulebis meti raodenoba?

_ ramdenma moswavlem Caagdo I jgufidan burTi kalaTSi?

_ ramdenma Caagdo 2-jer? 3-jer II jgufidan?

_ ratom moigo Sejibri I jgufma? (II jgufma)?

savarjiSos saSualebiT moswavleebi amokreben cxrilidan monacemebs, aRniSnaven

Sejibris saboloo Sedegebs.

momdevno Sejibris Sedegebis gasaanalizeblad maswavlebeli kidev Camowers

moswavleTa sias da gvarebis gaswvriv miuTiTebs dros:

I jgufi II jgufi

1. abaSiZe - 51 wm 1. asaTiani _ 55 wm

. . . . . . . da a. S.

_ rogor ggoniaT, ratom moigo Sejibri II jgufma (an I jgufma?) (ufro meti

moswavle darbis swrafad).

_ ramden bavSvs aqvs Sedegi 51 wm?, 50 wm? da a.S.

_ TiToeul jgufSi romelia meti/naklebi 50 Tu 51?

_ gamoiangariSe, sul ra dro moandoma I jgufma Sejibrs? II jgufma?

_ ramdeni wuTiT meti/ naklebi moandoma I jgufma? da a. S.

amgvarad Catarebuli fizkulturis gakveTili moswavleTaTvis iqneba ufro

saintereso da sasargeblo, radgan miecemaT codnis praqtikulad gamoyenebis

saSualeba.

42

maTematika - diogene.ge · maswavlebeli amowmebs, SeuZliaT Tu ara moswavleebs sibrtyeze orientireba...

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Transcript of maTematika - diogene.ge · maswavlebeli amowmebs, SeuZliaT Tu ara moswavleebs sibrtyeze orientireba...