saerto sefasebis sqema saklaso davalebebisatvis - ncp.gencp.ge/files/sasargeblo...
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saerTo Sefasebis sqema saklaso davalebebisaTvis(weriTi da zepiri komunikaciisaTvis)***
Q
qulebi1-10
-ciisaTvis***
komentarebi
1-2 ver asrulebs weriT/zepir davalebebs; asrulebs, magram elementarul doneze ver akmayofilebs davalebis moTxovnaTa umetesobas;
3-4 asrulebs da elementarul doneze akmayofilebs davalebis moTxovnaTa erT nawils
5-6 damakmayofileblad pasuxobs davalebis moTxovnebis did nawils
7-8 Tavisuflad akmayofilebs davalebis iseT moTxovnebs, rogoricaa SemoqmedebiToba (saintereso Sinaarsi, enobrivi gabeduleba, originaluri azrebi da sxva), kritikuli azrovneba da sxva.saSualoze maRal doneze akmayofilebs davalebis moTxovnaTa umetesobas;
9-10 Tavisuflad akmayofilebs davalebis yvelamoTxovnas
Sefasebis sqemebis konkretuli nimuSebiweriTi da zepiri davalebisTvis
sasurvelia, Sefasebis kriteriumebi ganisazRvros Semdegi 4 parametris gaTvaliswinebiT:
pirobasTan Sesabamisoba anu ramdenad pasuxobs Sesrulebuli davaleba instruqciis moTxovnaskomunikaciuri unar-Cvevebienobrivi unar-Cvevebi (gramatika, leqsika, marTlwera)sasicocxlo unar-Cvevebi (es SeiZleba iyos SemoqmedebiTi azrovneba, TanamSromloba, kritikuli azrovneba da sxva).
ar aris aucilebeli, yovel jerze yvela parametri aisaxos Sefasebis sqemebSi; parametrebsa da kriteriumebs maswavlebeli SearCevs davalebis Sinaarsidan da prioritetuli miznebidan gamomdinare.
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nimuSi # 1. weriTi komunikaciisaTvis
davalebis piroba: mocemuli biografiuli cnobaris mixedviT, dawere am mwerlis
minimaluri raodenoba _ 130.
qulebi
0 - 1
(wers mocemul biografiul cnobarze dayrdnobiT; iyenebs miTiTebul konstruqcias)
komunikaciuri unar-Cvevebi
gasagebad da Tanamimdevrulad gadmoscems informaciebs 0 - 2
azustebs, rodis ra moxda 0 - 1
enobrivi unar-Cvevebi
iyenebs naswavl gramatikul konstruqciebs, formebs 0 - 2
iyenebs saTanado leqsikas 0 - 1
SemoqmedebiTi unar-Cvevebi
iCens gabedulebas enobrivi TvalsazrisiT 0 - 2
qulaTa maqsimaluri raodenoba 10
nimuSi # 2. zepiri komunikaciisaTvis
davalebis piroba: mocemul suraTze dayrdnobiT (nebismieri gamodgeba), Seadgine
da moyevi ambavi - ra xdeboda suraTis gadaRebidan ori-sami saaTiT adre
da ra moxda mis Semdeg. daazuste personaJTa vinaoba, daaxasiaTe isini,
gadmoeci ambebi, miuTiTe moqmedebaTa Tanimimdevroba, dro da adgili. saubris
minimaluri dro _ 2 wuTi
qulebi
icavs drois limits 0 - 1
0 - 1
komunikaciuri unar-Cvevebi
0 - 2
0 - 1
saubrobs garkveviT 0 - 1
enobrivi unar-Cvevebi
iyenebs naswavl gramatikul konstruqciebs, formebs 0 - 1
iyenebs saTanado leqsikas 0 - 1
SemoqmedebiTi unar-Cvevebi
avlens fantaziis unars, originalurobas 0 - 1
iCens gabedulebas enobrivi TvalsazrisiT 0 - 1
qulaTa maqsimaluri raodenoba 10
ucxouri e n eb i : i nglisuri , ger ma nuli , franguli , rusuli
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nimuSi # 3. zepiri komunikaciisaTvis
a) waikiTxe komentarebi da teqstebi. daazuste, gmiris ra Tvisebebi vlindeba TiToeulteqstSi. imuSaveT wyvilebSi.
b) imsjeleT klasSi _ warmoadgine da daasabuTe Seni mosazrebebi
qulebi
0 - 1
komunikaciuri unar-Cvevebi
gasagebad ayalibebs azrs 0 - 2
sakuTar mosazrebas asabuTebs 0 - 1
saubrobs garkveviT
sasicocxlo unar-Cvevebi, damokidebulebebi
originalur, saintereso mosazrebebs gamoTqvams
avlens kritikul azrovnebas 0 - 1
muSaobs mewyvilesTan erTad 0 - 1
usmens da acdis Tanaklaselebs mosazrebebis gamoTqmisas 0 - 1
kamaTisas koreqtulia
qulaTa maqsimaluri raodenoba 10
grafikulad ase gamoiyureba saerTo Sefasebis sqemebi da zepiri Tu weriTi davalebebis urTierTmimarTeba:
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igive, rac saklaso davalebaSia damokidebulebebis gamoklebiT.unar-Cvevebi fasdeba Semdegi aqtivobebiT
gramatikuli da leqsikuri xasiaTis testis Sesruleba; sakiTxavi da mosasmeni teqstebis gagebaze orientirebuli testebis Sesruleba, sakontrolo zepiri aqtivobis Sesruleba, sakontrolo weriTi aqtivobis Sesruleba.
1. damatebiTi komponenti
Sefasebis es nawili SeirCeva maswavleblis mier moswavleebTan SeTanxmebiT da mas SeiZleba mieniWos araumetes 10%
saerTo Sefasebis sqema Semajamebeli davalebebisTvis
qulebi1-10
Sefasebis doneebi Semajamebeli davalebebisTvis komentarebi
1-2 ver asrulebs Semajamebel davalebebs;auTvisebeli darCa ganvlili masalis umetesoba;dasaxuli miznebis nawili elementarul donezea miRweuli, nawili miuRwevelia
3-4 ganvlili masalis nawili aTvisebulia elementarul doneze, nawili _ dakmayofilebel doneze dasaxuli miznebis erTi nawili elementarul donezea miRweuli, nawili _ damakmayofilebel doneze
5-6 ganvlili masala aTvisebulia damakmayofilebel doneze; dasaxuli miznebi miRweulia damakmayofilebel doneze;ganvlili masalis nawili aTvisebulia elementarul doneze, nawili _ saSualo doneze;dasaxuli miznebis erTi nawili elementarul donezea miRweuli, nawili _ saSualo doneze
7-8 ganvlili masala aTvisebulia saSualo doneze; dasaxuli miznebi miRweulia saSualo doneze; ganvlili masalis nawili aTvisebulia damakmayofilebel doneze, nawili _ maRal doneze; dasaxuli miznebis erTi nawili damakmayofilebel donezea miRweuli, nawili _ maRal doneze
9-10 ganvlili masalis umetesoba aTvisebulia maRal doneze; dasaxuli miznebis umetesoba miRweulia maRal doneze;
ucxouri e n eb i : i nglisuri , ger ma nuli , franguli , rusuli
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grafikulad ase gamoiyureba saerTo Sefasebis sqemisa da Semajamebeli davalebebismimarTeba:
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I k l a s i
aqtivobis nimuSebi
aqtivoba 1
“koSkebi da matareblebi”
reziume
moswavleebi axarisxeben erTnair (tol) kuburebs feris mixedviT da maTi erTmaneTze mkvidrad dadgmiT (mWidrod midgmiT) awyoben erTi da imave feris kuburebis koSkebs (matareblebs). isini iyeneben agebul sivrcul figurebs (marTkuTxa paralelepipedebs) sxvadasxva feris kuburaTa raodenobebis Sesadareblad da pasuxoben SekiTxvebs figurebis saSualebiT warmodgenili monacemebis Sesaxeb. Semdeg isini rveulebSi xataven Sesabamis brtyel figurebs (marTkuTxedebs) imave monacemebis warmosadgenad.
aqtivobis mizani
moswavleebma ganiviTaron saganTa da maTi jgufebis Sedarebis unari raodenobrivi da Tvisebrivi maxasiaTeblebis (niSnebis) mixedviTmoswavleebi daeuflon geometriuli (maRali-dabali, grZeli-mokle) da raodenobrivi (meti-naklebi, imdenive) mimarTebebis dadgenasa da gamoyenebas problemebis gadasaWreladmoswavleebma aiTvison erTi problemis gadaWris gansxvavebuli strategiebi
aucilebeli wina codna
saganTa Tvla aTamdeaTis farglebSi ricxvebis Cawera/wakiTxvaferebis amocnobacnebebis “maRali-dabali”, “grZeli-mokle”, “meti-naklebi”, “imdenive” floba
saWiro masalebi
ormockuburiani kompleqtebi oTxi sxvadasxva feris kuburebiT (TiToeuli feris 10 kuburiT)oTxi yuTi TiToeuli feris kuburebisTvisoTxi Sesabamisi feris baraTebis kompleqtiflomasterebi an feradi fanqrebiujredebiani furclebi
aqtivobis aRwera
moswavleTa codnis aqtivacia
ganaTavseT ormoci feradi kubura (magaliTad, wiTeli, yviTeli mwvane da lurji) mouwesrigebel grovad maswavleblis magidaze (an iatakze) ise, rom yvela moswavle xedavdes maT (amisaTvis umjobesia dasxaT moswavleebi wriulad, Tuki es SesaZlebelia). aiReT oTxi sxvadasxva feris kubura da morigeobiT sTxoveT moswavleebs daasaxelon kuburaTa ferebi. Semdeg sTxoveT sxva moswavleTa wyvils daaxarisxon kuburebi ferebis mixedviT. sTxoveT sxva moswavleebs daTvalon calkeuli feris kuburebi da daasaxelon
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maTi raodenoba. dabolos, sTxoveT sxva moswavleebs ganaTavson erTi feris kuburebi Sesabamis yuTebSi.
kvleva-Zieba
sTxoveT moswavleTa oTxeuls, rom TiToeulma maTganma aiRos erTi feris kuburebi (ramdensac moereva an xelSi daiWers). yovelma maTganma daiTvalos Tavisi kuburebi da daasaxelos maTi ricxvi. aCveneT moswavleebs feradi baraTebi da ganaTavseT isini maswavleblis magidaze (an iatakze).
sTxoveT moswavleebs, rom TiToeulma maTganma aago kuburebisgan an koSkebi an matareblebi da ganaTavson isini Sesabamisi feris baraTebTan. dausviT kiTxvebi:
ramdeni wiTeli kuburaa?wiTeli kuburebi ufro metia Tu yviTeli? rogor daaskveni? (Tu moswavleebi iyeneben Tvlis strategias sxvadasxva feris kuburaTa met-naklebobis dasadgenad, SeekiTxeT “SegiZlia daTvlis gareSe miTxra?” ubiZgeT (ar ukarnaxoT) kuburebiT Sedgenili figurebis geometriuli maxasiaTeblebis (ufro maRali, ufro dabali, ufro grZeli, ufro mokle) gamoyenebis strategiisken.lurji kuburebi ufro naklebia Tu mwvane? rogor daaskveni? (Tuki lurji kuburebi imdenivea, ramdenic mwvane, hkiTxeT “ras ityvi lurji da mwvane kuburebis raodenobaTa Sesaxeb?” (tolia). “rogor daasabuTeb Sens pasuxs agebuli figurebis gamoyenebiT?” (toli simaRlisaa/sigrZisaa);aris Tu ara yvelaze maRal koSkSi yvelaze meti kubura (yvelaze mokle matarebelSi _ yvelaze cota kubura)?
sTxoveT klass, rom ujrian furcelze mijriT daxaton da Sesabamis ferad gaaferadon imdeni ujra, ramdeni kuburacaa TiToeul koSkSi/matarebelSi; iqve miuweron kuburaTa ricxvic da TvliT gadaamowmon, sworia Tu ara maTi naxati. CamoiareT rigebSi da dausviT moswavleebs SekiTxvebi naxatebTan dakavSirebiT. mizanSewonilia imave kiTxvebis dasma; SesaZlebelia daisvas kiTxvebic “ramdeniT meti”, “ramdeniT naklebi”.
Tu kuburaTa kompleqtebis raodenoba saSualebas iZleva, maSin aqtivoba mizanSewonilia Catardes ramdenime jgufSi erTdroulad ise, rom sxvadasxva jgufebs gansxvavebuli naxatebi gamouvideT. jgufebma SesaZloa gacvalon da Seamowmon erTmaneTis namuSevrebi. am SemTxvevaSi individis/jgufis warmateba fasdeba ara marto sakuTari namuSevris, aramed megobrebis namuSevarTa sworad Sefasebis safuZvelzec.
gafarToeba/gaRrmaveba (arasavaldebulo nawili)
kuburaTa erTi kompleqtis SemTxvevaSi gaimeoreT savarjiSo moswavleTa sxva oTxeulebTan ise, rom cvaloT koSkebi matareblebiT, matarebelTa horizotaluri da vertikaluri poziciebi, matarebelTa pozicia baraTebis mimarT (baraTidan marjvniv-marcxniv, zemoT-qvemoT). dausviT igive kiTxvebi da gaarkvieT, icvleba Tu ara pasuxebi kiTxvebze figuraTa orientaciis cvlilebis kvalobaze.
cvaleT kuburaTa raodenobaTa koSkebSi/matareblebSi. icvleba Tu ara pasuxebi imave kiTxvebze? maS raze yofila damokidebuli pasuxebi?
kuburaTa mravali kompleqtis SemTxvevaSi Catarebuli jgufuri aqtivoba saSualebas iZleva imave efeqts mivaRwioT sxvadasxva jgufebis mier Sesrulebuli gansxvavebuli namuSevrebis safuZvelze.
aqtivobis ganxilva/Sefaseba
naTelia, rom garda zemoaRniSnulisa, aqtivoba (SesaZloa mcire modifikaciiT) emsaxureba
maTem atika
248
sivrceSi orientacia; sazomi erTeulis saSualebiT geometriul sidideTa kvantifikacia da figuraTa zomebis Sedareba/dadgena; obieqtTa da maTi jgufebis Sesaxeb monacemTa Segroveba, mowesrigeba da warmodgena (magaliTad, svetovani diagramis saSualebiT).
aqtivoba 2
geometriuli dizainis (geometriuli figurebis modelebis gameorebadi ganlageba) Seqmna da gavrcoba.
reziume
moswavleebi amzadeben geometriul dizains, warmoadgenen namuSevars, msjeloben dizainSi figuraTa ganlagebis kanonzomierebaze.
aqtivobis mizani
moswavlem SeZlos figurebis amocnoba maTi mdebareobis miuxedavadgaiwafos brtyeli figuris gamosaxulebis (modelis) SeqmnaSi da maTze manipulaciebSiaRmoaCinos kanonzomiereba saganTa periodul ganlagebaSi; erTmaneTs Seadaros saganTa perioduli ganlagebebi
savaraudo dro 45 wuTi
aucilebeli codna
geometriuli figurebi (samkuTxedi, oTxkuTxedi, wre)
masala
feradi qaRaldebisagan damzadebuli geometriuli dizainis (geometriuli figurebis modelebis gameorebadi ganlageba) nimuSi (mcire zomis) _ imdeni, ramden jgufadac daiyofa klasifigurebis modelebis Casawebeblad gamzadebuli badiani furceli _ imdeni, ramden jgufadac daiyofa klasiferadi qaRaldebi, webo, makrateli.
aqtivobis aRwera
klasis momzadeba xdeba Semdegi ZiriTadi SekiTxvebis saSualebiT:romel geometriul figurebs vicnobT?SegviZlia Tu ara maTi aRmoCena Cven irgvliv?gvinaxavs Tu ara sadme erTad Tavmoyrili geometriuli figurebi? (magaliTad, xaliCaze ornamentebis saxiT an sabnis zedapirze)SevZlebT yvelani erTad figurebisagan "lamazi" aplikaciis Seqmnas?
maswavlebeli dayofs klass jgufebad (4 jgufi) da urigebs dasamzadebeli geometriuli dizainis nimuSebs.
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maswavlebeli sTxovs moswavleebs aRweron dizaini (daasaxelon figurebi, maTi raodenoba, modelebis feri da a.S.) da avalebs geometriuli dizainis aslis damzadebas (TiToeuli jgufi daamzadebs mxolod erT striqons). yovel jgufs gadaecema dizainis dasamzadeblad saWiro masala: figurebis modelebis Casawebeblad gamzadebuli badiani furceli, feradi furclebi, makrateli, webo da a.S.
TiToeul jgufSi moswavleebi amoicnoben nimuSze gamosaxul figurebs, iTvlian TiToeuli saxeobis raodenobas (mag. 2 samkuTxedi, 4 oTxkuTxedi, 2 wre), Wrian feradi qaRaldebisagan geometriuli dizainis nimuSze gamosaxuli figurebis modelebs da qaRaldze awebeben Sablonis mixedviT. (aqtivobis am etapze mniSvnelovania maswavlebelma gaamaxvilos yuradReba Semdeg aspeqtebze: rogor SeiZleba erTi gamoWriT ramdenime figuris miReba; Tu gamoWrili figura ar eteva misTvis gankuTvnil ujraSi, maSin rogor unda davapataravoT figuris modeli ise, rom figuris forma ar SevcvaloT da a.S.)TiToeuli jgufi warmoadgens Tavis naxelavs (asaxelebs gamoyenebul figurebs da maT raodenobas. maswavlebeli maT ganaTavsebs (gaakravs) kedelze an dafaze.Semdeg moswavleebi maswavleblis daxmarebiT cdiloben amoicnon figuraTa ganlagebis kanonzomiereba yoveli jgufis namuSevarSi. isini adareben erTmaneTs namuSevrebs da aRniSnaven, rom I da IV mimdevrobebi ganlagebis erTsa da imave wess emorCileba, xolo I da II _ ara.amis Semdeg moswavleebi maswavleblis daxmarebiT erTmaneTze awebeben dizainis oTxive nawils mTliani suraTis misaRebad.maswavlebeli avalebs moswavleebs saxlSi daxaton ujrian rveulSi geometriuli dizainis raime nimuSi.
aqtivoba 3
Tanxis Sefaseba da gamoTvla realur viTarebasTan dakavSirebuli problemis gadaWrisas
reziume
klasSi TiToeul moswavles vaZlevT 20 TeTrs saTamaSo fulis niSnebiT, romliTac isini yiduloben „xils“ (SeiZleba damzaddes feradi qaRaldis aplikaciebi) saklaso oTaxSi mowyobil virtualur “maRaziaSi”. moswavleebi msjeloben “vaWrobis” Sedegebze: SeZenili produqtis raodenobaze, daxarjul da darCenil Tanxaze.
aqtivobis mizani
ariTmetikuli operaciebis (Sekreba/gamokleba) da ricxvebis raodenobebis Sedarebis (“tolia”, “metia”, “naklebia, “-iT meti/naklebi”, . . .) praqtikaSi gamoyenebis unaris ganviTareba. ricxvis warmodgena sxvadasxva ricxvebis jamis saxiT da am proceduris dakavSireba realur viTarebasTan.
savaraudo xangrZlivoba: erTi gakveTili.
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maTem atika
250
aucilebeli codna
20-is farglebSi ricxvebis Sekreba, gamokleba da ricxvebis Sedareba.
saWiro resursebi
saTamaSo fulis monetebiT Sedgenili 20 TeTri. TiToeuli moswavlisaTvis 2 xuTTeTriani moneta, 3 orTeTriani moneta da 4 erTTeTriani moneta.sxvadasxva saxeobis xili (SeiZleba iyos ara namdvili, aramed saTamaSo) da qaRaldis furclebi TiToeuli moswavlisaTvis romlebzec Camowerilia maswavleblis mier Sedgenili xilis sia Sesabamisi fasebiT.1 paketi TiToeuli moswavlisaTvis, SeZenili xilis Casalageblad.Tanxis aRsaricxi saSualeba (SeiZleba iyos ubralod qaRaldis furceli).qaRaldis furceli da kalami TiToeuli moswavlisaTvis, SesaZeni xilis siis Casawerad.
aqtivobis mokle aRwera
TiToeul moswavles mivceT 20 TeTri saTamaSo monetebiT: 2 xuTTeTriani moneta, 3 orTeTrian moneta da 4 erTTeTrian moneta. maT unda SeiZinon xili saklaso oTaxSi mowyobil warmosaxviT maRaziaSi. moswavleebi winaswar adgenen sasurveli xilis sias da
cdiloben gansazRvron, Tu ra Tanxa darCebaT xilis SeZenis Semdeg.
aqtivoba
maswavleblis magidasTan movawyoT “xilis maRazia” da moswavleebs vuTxraT, rom dRes isini wavlen “maRaziaSi“ xilis sayidlad.TiToeul moswavles mivceT: saTamaSo monetebiT Sedgenili Tanxa, romelic 20 TeTrs utoldeba; furclebi, im xilis siiTa da Sesabamisi fasebiT, romlidanac maT unda airCion sasurveli saxeobebi; carieli furclebi saangariSod. SevTavazoT moswavleebs, gadaxedon xilis siasa da maT fasebs. avuxsnaT moswavleebs, rom maT SeuZliaT iyidon siaSi mocemuli xilidan zogierTi. es xili SeiZleba iyos sxvadasxva saxeobis an yvela erTi saxeobis, magram mTavaria, rom isini ver daxarjaven 20 TeTrze mets.SekiTxva klass: romelia TqvenTvis yvelaze sayvareli saxeoba am siidan? calke furcelze CaiwereT misi dasaxeleba.SekiTxva (mas Semdeg rac wina davaleba Sesrulebulia): Tqven mier SerCeuli xilis ra raodenobis SeZena SegiZliaT im TanxiT, romelic gaqvT? ra Tanxa dagrCebaT?saTiTaod mivideT yvela moswavlesTan da SevamowmoT misi Canaweri. zogma maTganma SeiZleba xilis ori an meti sayvareli saxeoba SearCia da, aqedan gamomdinare, mas Sedegis ori an meti varianti aqvs. SevecadoT, rom TviToeulma maTganma swori Sedegi miiRos.axla SevTavazoT moswavleebs, rom maT mxolod erTi saxeobis (maTi sayvareli) xili ki ar SeiZinon, aramed SearCion ramdenime: yvelaze sayvareli, naklebad sayvareli da a.S., daalagon SerCeuli saxeobebi prioritetis mixedviT da Camoweron furcelze Sesabamis fasebTan erTad.saTiTaod mivideT TiToeul moswavlesTan da SevamowmoT maTi namuSevari.SevTavazoT moswavleebs, rom TavianTi TanxiT SeiZinon sxvadasxva saxeobis xili: jer ramdenime sayvareli saxeoba, Semdeg Seamowmon darCenili Tanxa Tanxa da SeiZinon siaSi meore adgilze mdgomi ramdenime saxeoba da a.S.
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samuSaos dasrulebis Semdeg TiToeuli moswavle modis “maRaziaSi” da moaqvs mis mier Sedgenili sia sasurveli xilis saxeobebisa da saWiro Tanxa. viangariSoT is Tanxa, romelic saWiroa xilis sayidlad da SevadaroT moswavlis mier naangariSeb Tanxas. Tu Sedarebis Sedegad es ori sidide erTmaneTs daemTxva, paketSi CavulagoT xili.vidre moswavles gadavcemT mis mier SeZenil xils, vkiTxoT mas, darCa Tu ara Tanxa da Tu darCa, xom ar isurvebda, kidev ramdenime saxeobis damatebas?aqtivoba graZeldeba manamde, vidre TiToeuli moswavle ar miva maRaziaSi xilis SesaZenad.
aqtivobis mimoxilva
aqtivoba aviTarebs ara mxolod ricxvebis Sekrebis, gamoklebisa da maTi Sedarebis wminda operaciul unars, aramed moswavles uviTardeba ricxvebze moqmedebebis Sedegebis mixedviT garkveuli gadawyvetilebebis miRebis unari. savaraudoa, rom moswavle daiwyebs xilis im saxeobebis SerCevas, romlebic mas yvelaze metad uyvars, magram Semdeg igi aRmoaCens, rom maT SesaZenad sakmarisi Tanxa ar gaaCnia. igi koreqcias Seitans Tavis siaSi, da a.S. es garkveulwilad safuZvels uyris momavalSi optimizaciis amocanebis gadaWris zogadi unarebis ganviTarebasac. zogierTma moswavlem SeiZleba SeimuSaos am amocanis amoxsnis raRac “algoriTmis” msgavsic ki. aqtivobis dasrulebis Semdeg sasargeblo iqneba, Tu moswavleebs SevTavazebT Tavisi sityvebiT aRweron, rogor SearCies xilis saxeobebi da rogor gamoTvales Sesabamisi Tanxa. mivaqcioT yuradReba, isini am proceduras spontanurad asrulebdnen Tu zogma raime principi SeimuSava da am principis mixedviT Seasrula moqmedebebi.
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maTem atika
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I I k l a s i
aqtivoba: samkuTxedis modelis Sedgena nawilebisagan
misaRwevi miznebi erovnuli saswavlo gegmis miedxviT:
maT. II.8.
adarebs da ajgufebs brtyel figurebs geometriuli atributebis (mag. wveroebis/gverdebis raodenobis) mixedviT.uTiTebs saerTo sazRvris mqone figurebis saerTo gverdebsa da
wveroebs.
maT. II.9.
ganalagebs obieqtebs miTiTebuli wesis mixedviT.
maT. II.10.
urTierTSeTavsebiT adarebs figuraTa wrfiv zomebs da gamoxatavs Sedarebis Sedegs Sesabamisi terminebiT (mag. grZeli, mokle, toli).
reziume
moswavleebi ikvleven samkuTxedis ZiriTad Tvisebebs da damokidebulebebs zogierT geometriul figuras Soris.
saswavlo miznebi
geometriuli obieqtebis ganlageba miTiTebuli figuris misaRebad.geometriuli obieqtebis urTierTSeTavsebis Seswavla.saerTo sazRvris mqone geometriuli figurebis amocnoba.geometriuli figurebis dajgufeba.
saWiro resursebi
qaRaldis furceli figurebis dasawebeblad.qaRaldis samkuTxa naWrebi (sanimuSod).sxvadasxva zomis, formisa da feris qaRaldis naWrebi, romelTa daWra SesaZlebelia miTiTebuli sqemis mixedviT (ix. nax. 1).makrateli da webo.
nax. 1
aqtivobis aRwera
moswavleebs vaCvenebT qaRaldis samkuTxa naWrebs da vusvamT kiTxvebs: “ra figurebia?”, “ra iciT samkuTxedis Sesaxeb?”. am saubris Semdeg moswavleebma unda gaixsenon, rom samkuTxeds aqvs sami gverdi da sami wvero.klass vyofT 4 - 5 wevrian jgufebad da TiToeul jgufs vaZlevT naxatze gamosaxuli formis mqone qaRaldis figurebis kompleqts.
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TiToeul jgufs evaleba mocemuli figurebisagan rac SeiZleba meti gansxvavebuli (zomiT an/da ferebiT) samkuTxedis awyoba.moswavleebi iyeneben gamzadebul figurebs da samuSao furcelze awebeben ise rom miiRon samkuTxedebi.TiToeuli jgufi warmoadgens Tavis namuSevars: asaxelebs gamoyenebuli figurebis saxeobas, raodenobas da gamouyenebeli figurebis raodenobas.moswavleebs eZlevaT damatebiTi SekiTxvebi:
ramdeni gansxvavebuli samkuTxedis ageba SegviZlia ori, sami, oTxi figurisagan?ra moxdeba Tu SevecdebiT yvela figuris gamoyenebiT erTi “didi” samkuTxedis agebas? (erTi “patara” samkuTxedi dagvakldeba, radgan “didi” samkuTxedis daWrisas “patara” samkuTxedebad miRebuli samkuTxedebis SesaZlo raodenobebia: 1, 4, 9, 16, 25, . . .).rogor avagoT “udidesi” samkuTxedi am 12 naWrisagan?
nax. 2. (SesaZlo amonaxsnebi)
Sefaseba
maswavlebeli CainiSnavs Tu ramdenad srulyofilad gaarTva Tavi davalebas TiToeulma
romelma jgufma SeZlo yvelaze meti figuris gamoyeneba (konstruireba).rogor aRweren moswavleebi TavianT namuSevars da davalebis Sesrulebis process (komunikacia).
sworad asaxelebs figurebs.axasiaTebs figurebs da asaxelebs maT elementebs.sworad aRwers figurebis urTierTganlagebas.
rogor afaseben moswavleebi erTmaneTis namuSevars da eZeben amoxsnis sxva variantebs
esmiT Tu ara iseTi cnebebi, rogoricaa “gansxvavebuli”, “didi”, “patara”, “udidesi”, “umciresi (raodenoba, zoma)” cnebebis/terminebis floba da gamoyeneba.gansazRvraven figurebis saWiro raodenobebs sxvadasxva kompoziciisaTvis.gansazRvraven optimaluri amonaxsnisaTvis saWiro figurebis Semadgenel nawilebs da maT rodenobas (logikuri azrovneba).
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V I I k l a s i
aqtivobis nimuSebi
aqtivoba 1
jibis fuli
reziume
moswavleebi ageben wriul diagramebs, romlebic asaxavs maTi jibis fulis ganawilebas yoveldRiur saskolo danaxarjebze. naSromTa analizis da maswavleblis evristikuli kiTxvebis daxmarebiT moswavleebi ecnobian diagramis agebis gansxvavebul strategiebsa da dasaSveb gamartivebebs; agreTve faqtorebs, romelTa gauTvaliswineblobam SesaZloa gamoiwvios Secdoma diagramaSi.
aqtivobis mizani
moswavleebi daeuflon monacemTa warmodgenas wriuli diagramis saSualebiTmoswavleebma ganiviTaron Sefardebisa da proporciis gamoyenebis unar-Cvevebi amocanaTa amosaxsneladmoswavleebi gaiwafon geometriuli xelsawyoebis da gamoTvliTi saSualebebis gamoyenebaSi problemaTa gadasaWrelad
ї«Ѕ·ґ»ѕ»ґ· ©·Ії Ѕ±јІїkuTxis gradusuli zomawris nawilebi, centruli kuTxericxvis wiladuri nawili, procentiricxvis dayofa proporciul nawilebad
їЙ·®± іїїґ»ѕ·fargali, transportiri, saxazavisaweri furceli da fanqrebikalkulatori (ar aris aucilebeli)
aqtivobis aRwera
moswavleTa codnis aqtivacia
sTxoveT moswavleebs daasaxelon Tanxis raodenoba, romelic maT surT, rom hqondeT saxarjod. raze ramdens daxarjaven (SesaZloa Seadginon cxrili); gamoTvalon sruli Tanxis ra nawils Seadgens TiToeuli danaxarji.
hkiTxeT moswavleebs, ramden graduss moicavs wre, romelia centruli kuTxe, wris ra nawilia marTi kuTxe, gaSlili kuTxe; ramdeni gradusia wris mesamedi, ori mesamedi; rogor gamovTvaloT kuTxis gradusuli zoma, Tuki cnobilia wris ra nawils Seadgens igi.
diagramis agebasTxoveT moswavleebs gamoTvalon im centruli kuTxis gradusuli zoma, romelic
Seesabameba pirvel danaxajs, risTvisac maT unda gamoiyenon ukve cnobili Sefardeba; Semdeg ki transportiris saSualebiT aagon cetruli kuTxe da moniSnon Sesabamisi seqtori zed danaxarjis miTiTebiT (fuladi Tanxis, wiladuri nawilis an procentis saxiT). analogiurad aagebineT yoveli danaxarjis Sesabamisi seqtori da sTxoveT
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daarqvan saxeli diagramas. dasaSvebia kalkulatoris gamoyeneba gamoTvliTi samuSaoebis gasamartiveblad.
yoveli momdevno kuTxis agebisas dausviT kiTxva, Tu saidan unda aizomos kuTxe da ra SeiZleba moxdes araswori azomvis SemTxvevaSi; dasaSvebia Tua ara wiladuri nawilis an kuTxis zomebis maCvenebeli ricxvebis survilisamebr damrgvaleba; ra makontrolebeli meqanizmi (kanonzomiereba) arsebobs imis gasarkvevad, sworadaa agebuli diagrama Tu ara.
samuSaos dasrulebis Semdeg hkiTxeT moswavleebs: SesaZlebelia Tu ara konkretuli danaxarjis Sesabamisi centruli kuTxis gansazRvra sxva xerxiT; ubiZgeT (ar ukarnaxoT) proporciis an proporciul nawilebad ricxvis dayofis gamoyenebisken, sruli kuTxisa da ukve cnobili kuTxeebis jamis saSualebiT bolo kuTxis gradusuli zomis gamoTvlisken.
sTxoveT moswavleebs gaaanalizon xarjebis warmodgenili suraTi da upasuxon kiTxvebs: ZiriTadad raze gexarjebaT fuli? SesaZlebelia Tu ara gaswioT ekonomia zogierTi danaxarjis Tavis aridebiT? mainc romlis? rogor moixmardiT damatebiT an ekonomiiT dazogil Tanxas?
sakuTari naSromis prezentaciis msurvelebi gamoiyvaneT dafasTan da sTxoveT sxva moswavleebs moifiqron kargi kiTxva TanaklaselebisTvis. gaiTvaliswineT dasmuli kiTxvebisa da pasuxebis efeqtianoba moswavleTa Sefasebisas.
gafarToeba/gaRrmaveba (arasavaldebulo nawili)moiyvaneT arasworad agebuli wriuli diagramebis magaliTebi da sTxoveT moswavleebs
gansazRvron Secdomebi da maTi daSvebis savaraudo mizezebi.Semdeg sTxoveT moswavleebs daweron wriuli diagramis agebis Sesaxeb mokle
Txzuleba/esse da gacvalon erTmaneTSi; waaxaliseT maTi kritikuli da konstruqciuli azrovneba, raTa gaaanalizon da Seafason erTmaneTis naSromebis Sinaarsis sisrule da koreqtuloba.
aqtivobis ganxilva/SefasebanaTelia, rom mocemuli aqtivoba saSualebas iZleva moxdes mimarTulebaTa integracia
erTi aqtivobis farglebSi: wriuli diagramis asagebad gamoiyeneba codna mimarTulebebidan “ricxvebi da gamoTvlebi”, “geometria da sivrcis aRqma”, “kanonzomierebebi da algebra”, “monacemTa analizi, statistika da albaToba”. garda amisa, aqtivoba gamoirCeva aqcentiT codnis praqtikul gamoyenebaze da kavSirze moswavleTa yofa-cxovrebasTan.
aqtivoba 2
Semoklebuli gamravlebis formula da marTkuTxa miwis nakveTebis farTobebis Sedareba
aqtivobis mizania marTkuTxedis farTobisa da Semoklebuli gamravlebis formulis erTmaneTTan dakavSireba. igi moicavs kvleviT saqmianobas (rogorc individualur aseve wyvilebSi), maswavleblis mier warmarTul diskusias da diskusias mTeli klasis monawileobiT. moswavleebi Seiswavlian sidideebs Soris damokidebulebas marTkuTxedis farTobis magaliTze. moswavleebi akvirdebian, Tu ra gavlenas axdens marTkuTxedis erTi gverdis sigrZis gazrda da meore gverdis sigrZis Semcireba, ise rom marTkuTxedis perimetri ar Seicvalos, marTkuTxedis farTobze da iyeneben miRebul Sedegebs realur viTarebasTan dakavSirebuli amocanis amoxsnisas.
savaraudo xangrZlivoba: 1 gakveTili.
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aqtivobis mizani
cxadia, rom algebruli gamosaxulebebis igivuri tolobebis miReba SeiZleba wminda alegebruli gzebiT da am tipis saqmianoba dakavSirebulia wminda operaciuli unarebis ganviTarebasTan, magram gacilebiT mniSvnelovania Tu am igiveobebs geometriul Sinaarsac mivaniWebT. am dros moswavle ukeT acnobierebs kavSirebs sxvadasxva (algebrul da geometriul) obieqtebsa da operaciebs Soris.
garda amisa, am konkretul SemTxvevaSi (kvadratebis sxvaobis daSla mamravlebad), SesaZlebeli xdeba algebruli igiveobis gamoyeneba wminda geometriuli optimizaciis amocanis amoxsnisas, rac, Tavis mxriv, efeqtianad SeiZleba davukavSiroT praqtikul amocanas.
aqtivobis aRwera
demonstrireba: gakveTilis dasawyisSi dafaze davxazoT kvadrati, romlis gverdi
3 erTeulis tolia, xolo am kvadratis mezoblad davxazoT marTkuTxedi,
romlis sigrZe 2 erTeuliT metia kvadratis gverdis sigrZeze, xolo sigane
2 erTeuliT naklebia kvadratis gverdis sigrZeze, orive figuras mivaweroT
maTi zomebi. SekiTxva mTel klass: “vTqvaT, es kvadrati gamosaxavs Tqvens
miwis nakveTs da gTavazoben, rom igi gaucvaloT am marTkuTxa miwis nakveTSi.
daTanxmdebodiT Tu ara aseT SemoTavazebaze?”
cxadia, rom TvalzomiT rTulia imis SemCneva, rom am figurebs toli perimetri aqvT, aseve rTulia ramis Tqma maTi farTobebis Sesaxeb, amitom garkveul etapze saWiroa SevTavazoT moswavleebs, rom maT gamoTvalon am figurebis perimetrebi da farTobebi.
SekiTxva klass: risi tolia TiToeuli maTganis farTobi? risi tolia TiToeuli
maTganis garSemoweriloba?
kvadratuli formis miwis nakveTis farTobi 9 kvadratuli erTeulis tolia.marTkuTxa formis miwis nakveTis farTobi 5 kvadratuli erTeulis tolia.am ori miwis nakveTis garSemoweriloba erTmaneTis tolia da udris 12 erTeuls.
moswavleebi amCneven, rom am konkretul SemTxvevaSi kvadratis formis miwis nakveTis farTobi metia marTkuTxedis formis miwis nakveTis farTobze. SevTavazoT, ganazogadon es faqti, risTvisac saWiro iqneba garkveuli kvleviTi samuSaos Catareba.
wyvilebSi muSaoba: klasi davyoT wyvilebad da davurigoT winaswar gamzadebuli
cxrili.
kvadrati marTkuTxedi
DfarTobebis sxvaobagverdissigrZe
AfarTobi LsigrZe sigane AfarTobi
3 9 5 1 5 4
4
5
6
7
x
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“svetebi, romlebic gamosaxavs marTkuTxedis sigrZes da siganes, unda Seivsos ise, rom marTkuTxedis perimetri toli iyos Sesabamisi kvadratis perimetris, xolo marTkuTxedis sigrZisa da siganis sxvaoba mudmivi iyos. gamoTvaleT kvadratisa da marTkuTxedis farTobebi da SeavseT Sesabamisi svetebi“. gamartivebul SemTxvevaSi SeiZleba SevTavazoT iseTi cxrili, romelSic es ori sveti winaswaraa Sevsebuli ricxvebis erTiT mzardi mimdevrobiT.
rodesac yvela wyvili asrulebs davalebas, erTi an ramdenime moswavle avsebs kedelze gamokrul didi zomis cxrils.
SekiTxva: “ra kanonzomierebis SemCneva SeiZleba miRebuli cxrili saSualebiT?” garkveuli diskusiis Semdeg klasi Tanxmdeba imaze, rom ZiriTadi kanonzomiereba warmoCenilia bolo svetSi, sadac erTi da igive ricxvi weria. e.i. farTobebis sxvaoba mudmivia.
Semdeg ganixileba meore magaliTi, romelSic marTkuTxedis gverdebis sigrZeebs Soris sxvaoba sxva ricxvis tolia da vekiTxebiT: aris Tu ara kanonzomiereba imave tipis? ZiriTadi yuradReba mivaqcioT im faqtis SemCnevas rom kvadratisa da marTkuTxedis farTobebis sxvaoba orive SemTxvevaSi mudmivia, Tumca sxvadasxva ricxvis tolia.
amis Semdeg klass vTavazobT gamoiyenon algebruli teqnika miRebuli kanonzomierebis dasabuTebisa da ganzogadebisaTvis. msjelobis dasawyisi unda iyos daaxloebiT aseTi:
vTqvaT, kvadratis gverdis sigrZe X -is tolia. risi toli iqneba misi farTobi? ( оX )vTqvaT, marTkuTxedis sigrZe 2-iT metia kvadratis gverdis sigrZeze, risi toli unda iyos am marTkuTxedis sigane, Tu gvinda rom misi perimetri kvadratis perimetris toli iyos? (marTkuTxedis sigrZe iqneba оX xolo misi sigane
оX )risi toli iqneba am marTkuTxedis farTobi? ( чошчош XX )
moswavleebma unda gaigon, Tu cxrilis romeli svetebi Seesabameba algebrul
gamosaxulebebs X , оX , оX , оX da чошчош XX . SevTavazoT moswavleebs miRebuli gamosaxulebebis Semowmeba: ei mocemuli ricxvebi Casma da cxrilSi gamosaxul sidideebTan Sedareba.
zogierTma moswavlem SeiZleba damoukideblad miiRos мчошчош оXXX igiveoba marTkuTxedis farTobisaTvis da is, rom swored am igiveobiT aixsneba farTobebis sxvaobis mudmivoba.
cxadia, rom am igiveobis miReba SesaZlebelia wminda algebruli meTodebiT, magram SevTavazoT moswavleebs geometriuladac daasabuTon igi. amisaTvis gamoviyenoT aseTi naxazi
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aqtivobis mimoxilva da garTulebuli varianti
algebruli igiveobebis miRebis tradiciuli meTodi gulisxmobs algebruli operaciebis gamoyenebas, xolo am igiveobebis dakavSireba maTematikis sxva mimarTulebebTan, rogorc wesi, ar ganixileba. am aqtivobis mizania warmovaCinoT erT-erTi gavrcelebuli algebruli igiveobis geometriuli Sinaarsi da misi gamoyeneba. garda amisa, moswavleTa motivaciis gazrda SesaZlebelia am yovelives praqtikul amocanebSi gamoyenebis demonstrirebiT.
aqtivobis gagrZeleba SeiZleba optimizaciis martivi amocanis dasmiT: оочшчш aXaXaX igiveobis gamoyenebiT moswavleebma SeiZleba TviTon aRmoaCinon
is faqti, rom mocemuli perimetris mqone marTkuTxedebs Soris udidesi farTobi aqvs kvadrats (“mocemuli sigrZis Tokis saSualebiT rogor SemovsazRvroT udidesi farTobis mqone marTkuTxa are?”).
aqtivoba 3
samkuTxedis Tvisebis gamokvleva sxvadasxva xerxiT
reziume
moswavleebi aRmoaCenen samkuTxedis Tvisebas (samkuTxedis Siga kuTxeebis jamis Sesaxeb) modelebze manipulaciebis saSualebiT, asabuTeben debulebebs am Tvisebis Sesaxeb sxvadasxva xerxis gamoyenebiT, msjeloben dasabuTebis xerxebis sarwmunoobis Sesaxeb.
aqtivobis mizani
moswavle gaiwafos amocanis konteqstis Sesabamisad geometriul obieqtTa gamosaxvaSiCamouyalibdes kritikuli azrovnebis, msjelobisa da dasabuTebis unari.
ZiriTadi SekiTxvebi:
SeiZleba Tu ara figuris Tvisebis aRmoCena misi modelis gamoyenebiT?SesaZlebelia Tu ara sazomi xelsawyoebis gamoyenebiT figuris Tvisebis Sesaxeb varaudis gamoTqma?debulebis samarTlianobis dadgenis romeli xerxi migaCniaT ufro sarwmunod - zemoTCamoTvlili Tu dasabuTebis gziT miRebuli?
savaraudo dro: 1 gakveTili
masala: didi zomis qaRaldi (formati), feradi furclebi, saxazavi, transportiri,
fanqari, webo,..
aqtivobis aRwera:
1. maswavlebeli sTxovs moswavleebs` gaixsenon Seswavlili masala kuTxeebis Sesaxeb: gansazRvreba, klasifikacia, Tvisebebi, kuTxeTa jami da misi Tvisebebi da a.S.
2. Semdeg, klass dayofs oTx jgufad. ori jgufis davalebaa sxvadasxva saxeobis samkuTxedebis modelebis gamoyenebiT (mag. erTmaneTze midgmiT) gamoTqvas varaudi samkuTxedis Siga kuTxeebis jamis Sesaxeb da moaxdinos Tavisi varaudis samarTlianobis demonstrireba
1.2.
3.
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3. danarCen or jgufs eZleva davaleba gamoiyenos transportiri, gazomos da aRricxos sxvadasxva saxeobis samkuTxedebis kuTxeebi da amis safuZvelze gamoTqvas varaudi samkuTxedis Siga kuTxeebis jamis Taobaze (sxvadasxva jgufs gamosakvlevad SeiZleba mivceT sxvadasxva saxeobis samkuTxedi)
4. oTxive jgufi axdens Tavisi namuSevris prezentacias.5. amis Semdeg, maswavleblis daxmarebiT moswavleebi kuTxeebis Sesaxeb maTTvis
cnobil debulebebze dayrdnobiT amtkiceben debulebas6. Semdeg imarTeba diskusia, Tu romeli xerxia ioli da romeli _ sarwmuno.7. maswavlebeli saSinao davalebad aZlevs moswavleebs daadginon samkuTxedis
kuTxeebTan dakavSirebuli romelime debuleba (mag. gare kuTxis Tviseba)
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V I I I k l a s i
aqtivoba: monacemTa erTobliobis analizi
misaRwevi miznebi erovnuli saswavlo gegmis mixedviT:
maT. VIII.5. amoicnobs, aanalizebs da gamosaxavs sidideebs Soris wrfiv damokidebulebas.maT. VIII.6. agebs, gamosaxavs da ikvlevs Sesabamisobas or simravles Soris.maT. VIII.7. iyenebs gantolebaTa sistemebs da utolobebs problemis gadaWrisas.erTi grafikuli formiT warmodgenil monacemebs warmoadgens gansxvavebuli grafikuli formiT da warmoaCens TiToeuli formis xelsayrel da araxelsayrel mxareebs.maT. VII.16. akeTebs Tvisebriv da raodenobriv monacemTa interpretacias da analizїі±ЅїІ· µ±І¬»Ї¬· №їМЄїґ·©·І»ѕ·Мт
reziume
moswavle agebs monacemTa gabnevis diagramebs, amCnevs diagramaze monacemTa wrfiv tendencias, agebs misadagebis wrfes, msjelobs misadagebis wrfis cnebis garSemo, monacemebis (manqanis SekeTebaze daxarjuli Tanxebis, sportisa Tu medicinis sferos Sesaxeb monacemebi) analizis safuzvelze akeTebs daskvnas/prognozs im SesaZlo monacemebiTvis, romlebic mocemul monacemTa diapazonis gareT an SigniT mdebareoben.
saswavlo miznebi
monacemTa gabnevis diagramis ageba (monacemTa ori jgufisaTvis).diagramaze monacemTa Sesabamisi wertilebis ganlagebis interpretireba da tendenciis Sesaxeb varaudis gamoTqma.misadagebis wrfis ageba da misi gantolebis Sedgena.prognozis gakeTeba.
saWiro resursebi
manqanaSi wlis ganmavlobaSi zeTis Secvlis
jeradobisa da igive manqanis SekeTebaze wlis ganmavlobaSi daxarjuli Tanxis urTierTmimarTebis Sesaxeb.
savarjiSo #2
sportuli Sejibrebis dros gakeTebuli naxtomis simaRlis urTierTmimarTeba
savarjiSo #3 _ adamianis wonisa da samedicino preparatis dozebis mimarTeba.
savarjiSo #4 _ gogonaTa Soris Tavisufali stiliT curvaSi gamarjvebulTa
Sedegebi wlebis mixedviT.
aqtivobis aRwera
moswavleebs individualurad urigdebaT savarjiSo #1 da TandarTuli cxrili (cxrili #1).
261
savarjiSo #1
cxrilSi mocemulia monacemebi manqanaSi wlis ganmavlobaSi zeTis Secvlis jeradobisa da igive manqanis SekeTebaze wlis ganmavlobaSi daxarjuli Tanxis urTierTmimarTebis Sesaxeb.
ramdenjerSecvaleszeTi
3 5 2 3 1 4 6 4 3 2 0 10 7
ra Tanxa daxarjesSekeTebaze
300 300 500 400 700 400 100 250 450 650 600 0 150
moswavleebs evalebaT: aagon warmodgenili monacemebis misadagebis wrfe da
Seafason misi sizuste.
moswavleebi davalebas asruleben maswavlebelTan erTad.maswavlebeli etapobrivad aZlevs moswavleebs instruqcias:
warmodgenili monacemebis mixedviT aagon diagrama.imsjelon, aris Tu ara am monacemebis misadagebis wiri wrfe da Tu es asea - gaavlon es wrfe.ipovon misadagebis wrfis daxris koeficienti da ganmarton misi Sinaarsi (ras gamosaxavs). ipovon wrfis gantoleba.ipovon wrfis sakoordinato RerZebTan gadakveTis wertilebis koordinatebi da ganmarton maTi mniSvneloba amocanis konteqstidan gamomdinare.Seafason, ramdenad sworad aris gavlebuli misadagebis wrfe.maswavlebeli svams kiTxvas: ra SemTxvevaSi SeiZleba CaiTvalos misadagebis wrfe saukeTesod?
maswavlebeli klass yofs jgufebad (TiTeul jgufSi 2-3 moswavle) da TiToeul
moswavleebi asruleben davalebas da TiToeuli jgufi axdens sakuTari namuSevaris prezentacias.
Sefaseba
1.1. mocemul monacemebze dayrdnobiT gansazRvravs romeli cvladia damokidebuli da romeli - damoukidebeli.
1.2. poulobs sakoordinato sistemaSi im wertilebs, romelTa koordinatebi Seesabameba cxrilSi mocemul monacemebs.
2.1. msjelobs miRebul gafantulobis diagramaSi monacemTa tendenciaze.2.2. avlebs misadagebis wirs.3.1. irCevs or wertils SerCeul misadagebis wrfeze da poulobs maT
koordinatebs.3.2. poulobs wrfis daxris sakuTxo koeficients.3.3. msjelobs wrfis daxris sakuTxo koeficientis mniSvnelobaze amocanis
konteqstTan mimarTebaSi (cvlilebis siswrafe).3.4. adgens wrfis gantolebas.
1.2.
3.
4.
5.6.
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262
4.1. poulobs wrfis sakoordinato RerZebTan gadakveTis wertilebis koordinatebs.
4.2. ganmartavs maT mniSvnelobas amocanis konteqstSi.5.1. poulobs wrfivi funqciis mniSvnelobebs argumetis iseTi mniSvnelobebisTvis,
romelebic cxrilSi ar aris moyvanili (rogorc diapazonis gareT, agreTve mis SigniT).
5.2. poulobs damoukidebeli cvladis mniSvnelobebs damokidebuli cvladis sxvadasxva mniSvnelobisaTvis.
5.3. gansazRvravs monacemTa ra raodenobaa saWiro, rom saSualeba gvqondes SevafasoT misadagebis wrfe.
5.4. afasebs ramdenad sworad aris gavlebuli misadagebis wrfe.maswavlebeli akvirdeba ramodenime (winaswar SerCeul) moswavles da CainiSnavs,
micemuli davalebis realizaciis romeli etapi Seasrules srulyofilad da romeli xarvezebiT. mag. erT-erTi ver axerxebs 5.1 da 5.2 punqtebis Sesrulebas, meore asrulebs procedurebs, Tumca uWirs am proceduris Sedegis interpretireba. amasTanave, maswavlebels eqmneba warmodgena (saerTo suraTi) klasis mier aRniSnuli sakiTxis aTvisebis Sesaxeb, rac ZiriTadad gansazRvravs mis Semdgom samoqmedo strategias: ra tipis aqtivobebze unda gakeTdes gansakuTrebuli aqcenti.
moswav-lisgvari,saxeli
diagramis ageba, misadagebiswrfis gavleba
wrfis gantolebis Sedgena, sakuTxo koeficientis ga-moTvla, sxvadasxva argumentisaTvisfunqciis mniSvn-elobebis gamoT-vla
daxris kuTxis
amocanis konte-qstSi, misadagebis wrfis sizustis Sefasebis krite-riumebis dadgena
maswavlebliskomentari da miTiTeba.
abaSiZe aago, magram araakuratulad:ar aris gamoyo-fili erTeuli, yvela monace-mis Sesabamisi wertili ar
diagramaze
wrfis gantoleba ver Seadgina, Tumca mza gantolebis
funqciis mniSvn-eloba ramodenime argumentisaTvis da
ver SeZlo ganemarta, Tu ras niSnavs wrfis daxris kuTxe am amocanasTan mimarTebaSi.
muSaoba mona-cemTa grafi-kuli gamosaxvis dizainis Ser-Cevasa da real-izaciaze.
--
durebis Ses-
maTTematikuri-
263
beriZe aago diagrama, yvela monacemis Sesabamisi wer-
masze, gaavlo misadagebiswrfe
ver dawera wrfis gantoleba, Tumca mza gantolebis
funqciis mniSvn-eloba ramodenime argumentisaTvis,
--
ZebTan gadakveTis wertilebis koor-dinatebi, wrfis daxris kuTxe
-adagebis wrfis SefasebisaTvis
raodenoba, ma-gram ver SeZlo ganemarta, Tu ras niSnavs wrfis daxris kuTxe am amocanasTan mimarTebaSi.
damoukidebladver asrulebs zogierT alge-
-
maTematikuri
damoukideblad
gogo-laZe
aago diagrama, yvela monacemis Sesabamisi wer-
masze, gaavlo misadagebiswrfe. ganasxvava damokidebulida damoukide-beli cvladebi.
dawera misad-agebis wrfis gan-
funqciis mniSvn-eloba ramodenime argumentisaTvis,
--
ZebTan gadakveTis wertilebis koor-dinatebi, wrfis daxris kuTxe.
-adagebis wrfis SefasebisaTvis
raodenoba.imsjela misad-agebis wrfis Sesaxeb: Seafasa misi siswore,
saSualebiT gamo-tanili daskvnebis adekvaturoba.
10
maswavlebeli Sefasebis Sedegebze dayrdnobiT (ramdenad kargad iqna gagebuli da aTvisebuli masala) gegmavs Sedeg aqtivobas, aZlevs sxvadasxva sirTulis saSinao
davalebas (warmatebis SemTxvevaSi savarjiSo #3).
savarjiSo #2
cxrilSi mocemulia motociklis wonisa da igive motociklis miersportuli Sejibrebis dros gakeTebuli naxtomis simaRlis urTierTmimarTeba.
wona (kg) naxtomis
(sm)8.6 25.98.8 25.89.0 25.69.2 25.59.5 24.69.9 24.510.1 24.510.4 24.310.6 24.0
aageT diagrama da Tu monacemebi ~wrfivia~, aageT misadagebis wrfe.
aRwereT wonisa da simaRlis damokidebulebaipoveT misadagebis wrfis daxris kuTxe da ganmarteT misi mniSvneloba am amocanis konteqstSi.ipoveT naxtomis simaRlis savaraudo mniSvneloba im SemTxvevaSi, roca motociklis wona 9.6 kilogramia.
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savarjiSo #3
cxrilSi mocemulia adamianis wonisa da samedicino preparatis dozebis mimarTeba.
wona (kg) stan-dartdoza (mg)
maqsimdoza (mg)
40 40 66
45 45 75
50 50 83
54 55 91
59 60 100
64 65 108
69 70 116
74 75 125
79 80 133
84 85 141
aageT wonisa da standartuli dozis mimarTebis diagrama da gaavleT misadagebis wrfe.aageT wonisa da maqsimaluri dozis mimarTebis diagrama da gaavleT misadagebis wrfe.ipoveT orive wrfis daxris koeficientebi da SeadareT erTmaneTs. moaxdineT Sedarebis Sedegis interpretacia amocanis konteqstis gaTvaliswinebiT.dawereT orive wrfis gantoleba. paraleluria Tu ara es wrfeebi?
(pasuxi daasabuTeT)
ivaraudeT wamlis standartuli da maqsimaluri doza 105 kilogramiani pacientisaTvis.
savarjiSo #4
cxrilSi mocemulia gogonaTa Soris Tavisufali stiliT curvaSi gamarjvebulTa Sedegebi wlebis mixedviT.
weli dro (wT:wm)
1924 6:02.2
1936 5:26.4
1956 4:54.6
1968 4:31.3
1980 4:08.8
1992 4:07.1
mocemuli monacemebis mixedviT aageT diagrama.
gaavleT misadagebis wrfe.ipoveT daxris koeficienti da ganmarteT misi mniSvneloba amocanis konteqstidan gamomdinare.CawereT wrfis gantoleba da ivaraudeT, ra SeiZleboda yofiliyo
Sedegi, Tu olimpiada Catardeboda 1940 an 1944 wlebSi.dasaSvebad migaCniaT Tu ara (ramdenad azriania) misadagebis wrfis gamoyeneba Semdegi
olimpiadis Sedegebis sawinaswarmwtyvelod? dadebiTi pasuxis SemTxvevaSi gamoTqviT Tqveni varaudi.
265
X k l a s i
aqtivobis nimuSebi
aqtivoba 1
“saSualo xelfasi”
reziume
moswavleebi cxrilis saxiT warmodgenili monacemebis safuZvelze aanalizeben sawarmoSi TanamSromlebsa da direqtors Soris xelfasis momatebis Taobaze warmoqmnil winaaRmdegobas. amisaTvis isini iTvlian xelfasebis diapazons, saSualos, modas da medianas. Sesrulebuli gamoTvlebis safuZvelze isini ayalibeben sakuTari pozicias da asabuTeben mis marTebulobas SerCeuli (sakuTari poziciisTvis Sesaferisi) Semajamebeli ricxviTi maxasiaTeblis saSualebiT.
aqtivobis mizani
moswavleebi gaerkvnen tipuri monacemebis aRwerisas centraluri tendenciis sxvadasxva sazomebis SesaZleblobebSimoswavleebma SeZlon ststistikuri cnebebis gaTvaliswinebiT gadawyvetilebebis miRebamoswavleebma SeZlon statistikuri xasiaTis argumentebiT sakuTari poziciis dasabuTeba
aucilebeli wina codna
Semaj
cxrilis wakiTxva
saWiro masalebi
situaciuri amocanis teqstisaweri qaRaldi da kalamikalkulatorikompiuteri (ar aris savaldebulo)
aqtivobis aRwera
moswavleTa codnis aqtivacia
sTxoveT moswavleebs ganixilon SemTxvevebi, rodesac monacemTa diapazoni sakmaod mcirea/didia da sami-oTxi monacemis SemTxvevaSi daakvirdnen: 1) ramdenad “axlosaa” ermaneTTan monacemTa saSualo, moda da mediana; 2) centraluri tendenciis romelime sazomis ricxviTi mniSvneloba xom ar emTxveva romelime konkretul monacems; 3) saSualo kidura wevrebTan ufro “axlosaa” Tu medianasTan.
SeekiTxeT moswavleebs, maTi azriT, romeli sazomi ufro “grZnobieria” kidura wevrebis sididis mkveTri cvlilebebisadmi? ratom?
gamokvlevasTxoveT moswavleebs, yuradRebiT waikiTxon situaciuri amocanis teqsti da cxrilis
dasamuSaveblad erTmaneTs dausvan kiTxvebi; SesaZlebelia isini daiyon jgufebad da
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gaiTamaSon amocanaSi miTiTebul TanamSromelTa CamonaTvalis mixedviT rolebi sakuTari mosazrebebis mkafio formulirebiT da cxrilidan moxmobili monacemebis warmoCeniT.
TanamSromlebi cxrilSi moyvanil informaciasa da Semajamebel ricxviT maxasiaTebleblebs sakuTari interesebis warmosaCenad da dasacavad?
sTxoveT moswavleebs, gamoTqvan varaudi saSualos, modas da medianis mniSvnelobebis Sesaxeb im SemTxvevaSi, Tuki mcire xelfasis mqone 24 TanamSromlis xelfasi 15 000 lari gaxdeba.
Semdeg sTxoveT moswavleebs gamoTvalon kalkulatoris an kompiteris saSualebiT centraluri tendenciis sazomebi gazrdili xelfasebis SemTxvevaSi da Seadaron sakuTari varaudi gamoTvlebis Sedegebs.
dausviT moswavleebs Semdegi SekiTxvebi: 1) centraluri tendenciis romeli sazomis ricxviTi mniSvneloba ar Seicvala? 2) centraluri tendenciis romeli sazomis ricxviTi mniSvneloba Seicvala? 3) Tundac erTi xelfasi rom SegecvalaT, centraluri tendenciis romeli sazomis mniSvneloba Seicvleboda aucileblad? (saSualo) 4) mxolod erTi-ori xelfasi rom SegecvalaT, savaraudod, centraluri tendenciis romeli sazomis mniSvneloba ar Seicvleboda? (savaraudod, moda) 5) mxolod erTi-ori xelfasi rom SegecvalaT, ramdenad savaraudoa, rom medianis mniSvneloba Seicvleboda? (sazogadod, es damokidebulia medianis mdebareobaze - Tu mediana ganTavsebulia mravali toli xelfasis SuaSi, maSin igi ar Seicvleboda, xolo Tu igi erTmaneTisgan mkveTrad gansxvavebuli xelfasebis maxloblobaSia, maSin igi, albaT, Seicvleboda)
situaciuri amocanis bolo kiTxva sadiskusioa. roluri TamaSis SemTxvevaSi
xedvebi da poziciebi ise, rom bunebrivi moeCvenoT amocanebi, romelTac ramdenime amonaxsni/pasuxi aqvs da kvlevisas eZebon gansxvavebuli gzebi da dasabuTebebi.
gaRrmaveba-gafarToebasTxoveT moswavleebs iwinaswarmetyvelon, Tu direqtoris xelfasis rogori nazrdi
gamoiwvevda saSualos gazrdas 1000 lariT da Seamowmon sakuTari varaudi gamoTvlebiT kalkulatorze an kompiuterze.
SeekiTxeT moswavleebs, gaizrdeboda, Semcirdeboda Tu igive darCeboda saSualo xelfasi im SemTxvevaSi, Tuki direqtori daiqiravebda kidev erT inJenersa da ostats. sTxoveT moswavleebs daasabuTon varaudi. mxolod amis Semdeg CaatarebineT saWiro gamoTvlebi.
aqtivobis ganxilva/Sefaseba
codnis dauflebas da statistikuri alRos Camoyalibebas, aramed zogadi inteleqtualuri
unari, gadawyvetilebis miRebis unari, msjelobisa da dasabuTebis unari, saswavlo-kvleviTi unarebi. ramdenime am tipis sayofacxovrebo konteqstis mqone amocanis gadaWris Sedegad moswavleebs uviTardebaT imis garkvevis unaric, Tu rodis romeli sazomis gamoyeneba jobia monacemTa simravlis warmosadgenad da romeli sazomi ufro “mdgradia” cvlilebebis mimarT.
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situaciuri amocana
sawarmos TanamSromelTa profesiuli gaerTianebis Tavmjdomare molaparakebas awarmoebda sawarmos direqtorTan TanamSromelTa xelfasebis Taobaze. misi azriT, cxovreba gaZvirda, saqonelze fasebi gaizarda da sawarmos TanamSromlebi met fuls saWiroeben sayofacxovrebo danaxarjebisTvis, gaerTianebis wevrebidan ki arc erTi ar iRebs weliwadSi 18 000 larze mets.
sawarmos direqtori daeTanxma mas imaSi, rom marTlac yvelaferi gaZvirda, maT Soris, nedli masalis fasic; Sesabamisad, sawarmos mogeba Semcirda. garda amisa, sawarmoSi saSualo xelfasi xom weliwadSi 22 000 lars aRemateba. amitom mas verc warmoudgenia aseT viTarebaSi xelfasebis momateba.
im saRamosve gaerTianebis Tavmjdomarem Caatara gaerTianebis wevrTa kreba. gamyidvelma sityva iTxova. “Cven, gamyidvelebi mxolod 10 000 lars viRebT weliwadSi, gaerTianebis wevrTa umravlesoba ki 15 000 lars. Cven gvsurs, rom Cveni xelfasebi am donemde mainc gaizardos”.
gaerTianebis Tavmjdomarem gadawyvita, rom yuradRebiT Seeswavla sruli informacia sawarmos TanamSromelTa xelfasebis Sesaxeb. saxelfaso ganyofilebaSi mas misces Semdegi cxrili:
samuSaos dasax-eleba
TanamSromelTaraodenoba
xelfasi larebSi gaerTianebis wev-roba
direqtori 1 250 000 ara
moadgile 2 130 000 ara
inJineri 3 55 000 ara
ostati 12 18 000 diax
muSa 30 15 000 diax
3 13 500 diax
mdivani 6 12 000 diax
gamyidveli 10 10 000 diax
mcveli 5 8 000 diax
sul 72 1 593 500 _
TanamSromelTa gaerTianebis Tavmjdomarem gamoTvala sawarmos TanamSromelTa saSualo xelfasi da miiRo daaxloebiT 22 131, 94 lari. “direqtori marTalia, _ gaifiqra man, _ magram xelfasebis saSualo maRalia sawarmos xelmZRvanelTa maRali xelfasebis xarjze. xelfasebis saSualo ar iZleva swor warmodgenas TanamSromelTa tipuri xelfasis Sesaxeb”.
Semdeg man gaifiqra: “gamyidvelic marTalia. ocdaaTi muSidan TiToeuls 15 000 lari aqvs. esaa xelfasebis moda. miuxedavad amisa, gaerTianebis danarCeni 36 wevridan, vinc ar iRebs 15 000 lars, 24 iRebs amaze naklebs”.
bolos gaerTianebis Tavmjdomarem gadawyvita gaerkvia risi toli iyo WeSmaritad Sua xelfasi da sawarmos xelfasebi daalaga zrdadobis mixedviT. aRmoCnda, rom Sua anu medianuri xelfasi 36-e da 37-e xelfasebs Sorisaa da raki orive es xelfasi 15 000 laria, amitom medianac 15 000 laria.
kiTxva: rogor Seicvleboda xelfasebis mediana, moda da saSualo, Tuki yvelaze
mcirexelfasiani 24 TanamSromlis xelfasi 15 000 laramde gaizrdeboda?
Tqven ra pozicias dauWerdiT mxars xelfasebTan dakavSirebiT?
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aqtivoba 2
reziume
moswavleebi ecnobian cnebas „oqros kveTa“, swavloben monakveTis gayofas oqros kveTis proporciiT, ifarToeben Tvalsawiers, ecnobian maTematikis gamoyenebis nimuSebs xelovnebasa da bunebaSi.
aqtivobis mizani
moswavlis SemecnebiTi interesis xelSewyoba, misi Tvalsawieris gafarToebagaremomcveli samyaros silamazisa da harmoniis "kanonebis" gacnoba da maTze msjeloba.
gakveTilis gegma:
4. “oqros kveTa” maTematikaSi: amocanis dasma, misi algebruli da geometriuli amonaxsni
5. „oqros kveTa“ bunebasa da xelovnebaSi
savaraudo dro: 1 gakveTili
masala: didi zomis qaRaldi (formati), plakatebi adamianis, mcenarisa da
cxovelis gamosaxulebiT (gvaTxovebs biologiis maswavlebeli), saxazavi,
fanqari, fargali, Suasaukuneebis arqiteqturis an mxatvrobis nimuSebis
reproduqciebi.
aqtivobis aRwera:
8. maswavlebeli Sesaval sityvaSi saubrobs “mudmiv” problemaze: eqvemdebareba Tu ara silamaze da harmonia raime maTematikur kanonebs da SesaZlebelia Tu ara maTi “gazomva” raime algebruli xerxebiT (SesaZlebelia mokle istoriuli eqskursi Zvel saberZneTsa da aRorZinebis epoqaSi)
9. Semdeg maswavlebeli svams amocanas - rogor gavyoT AB monakveTi C wertiliT ise, rom
10. klasi iyofa or jgufad. pirveli jgufi eZebs dasmuli amocanis algebrul amonaxsns, xolo meore xsnis mas geometriulad (agebis amocanis sirTulis gamo, jobia, maswavlebelma warmoadginos agebis gza da moswavleebs mosTxovos misi samarTlianobis dasabuTeba).
11. orive jgufi warmoadgens TavianT namuSevars da maswavleblis mier xdeba gaweuli samuSaos Sejameba. maswavlebeli gaacnobs moswavleebs agreTve oqros samkuTxedisa da oqros marTkuTxedis cnebebs.
269
12. amis Semdeg, pirvel jgufs miecema plakati adamianis sxeulis gamosaxulebiT da eZleva davaleba, daadginos saxisa da xelis mtevnis ra nawilebia oqros proporciebSi (vfiqrobT, jgufSi gamoCndeba moxalise, romelic gariskavs daadginos TviTon ramdenad jdeba oqros kveTis proporciebSi).
13. meore jgufis davalebaa mcenarisa da cxovelis nawilebs Soris proporciebis dadgena
14. Seajamebs ra jgufebis muSaobis Sedegebs, maswavlebeli aCvenebs moswavleebs Sua saukuneebis romelime xuroTmoZRvruli Zeglis reproduqcias (mag. parizis RvTismSoblis taZari. am reproduqciis naxva SesaZlebelia Tundac qarTul sabWoTa enciklopediaSi) da uCvenebs moswavleebs romeli nawilebia oqros kveTis
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270
15. proporciebSi.
17. Semdeg imarTeba mcire diskusia garemomcveli samyaros silamazisa da harmoniis “kanonebisa” da Cveni maTdami damokidebulebis Sesaxeb. (igulisxmeba, rom maswavlebels aqvs saRi azri da iumoris grZnoba)
18. maswavlebeli moswavleebs aZlevs saSinao davalebas:a. moiZion masalebi oqros kveTis Sesaxeb (mag. qarTuli sabWoTa enciklopediis me-6
tomi, a. benduqiZis “maTematika-seriozuli da saxaliso” da a.S.).b. daadginos, eqvemdebareba Tu ara oqros kveTis princips romelime qarTuli
xuroTmoZRvruli Zegli misi reproduqciis mixedviT.
aqtivoba 3
parabolis geometriuli Tvisebebi da misi kavSiri realur obieqtebTan
moswavleebi muSaoben mcire jgufebSi, raTa SeimuSaon strategia parabolis gantolebis Sesadgenad. garda amisa isini akavSireben miRebul Sedegs iseT cnobili da gavrcelebuli realuri obieqtebis formasTan, romlebsac parabolis forma aqvT (mag. satelituri antena, zogierTi xidi, TaRebi) da agreTve kvadratuli gantolebiT mocemuli funqciis grafikTan. sasurvelia iseTi cnebebis Semotana, rogoricaa: parabolas wvero, fokusi, simetriis RerZi da direqtrisa.
savaraudo dro: 1 an 1.5 gakveTili.
aqtivobis aRwera
moswavleebma ician algebruli gantoleba, cxbxay о , romliTac kvadratuli funqcia moicema da ician isic, rom am funqciis grafiki aris parabola. am aqtivobis mizania,
271
gaigon parabolis geometriuli Sinaarsi da agreTve is, rom parabola, rogorc geometriuli obieqti, farTod gamoiyeneba realur viTarebaSi. aqtivoba iwyeba aseTi samotivacio amocaniT:zRvis napiridan 10 km manZilze dgas gemi, pirobiTad CavTvaloT, rom napiri aris wrfis monakveTis formis. vTqvaT, navi Tanabradaa daSorebuli gemidan da napiridan da es manZilebi 5 km-is tolia. navi cdilobs imoZraos ise, rom nebismier momentSi Tanabrad iyos daSorebuli rogorc gemidan, aseve napiridan. ra SesaZlo traeqtoriaze SeiZleba imoZraos navma?
maswavlebeli dafaze xazavs wrfis monakveTs, romelsac aRniSnavs X-iT da misgan 10 pirobiTi erTeuliT daSorebul A wertils. wrfis monakveTi pirobiTad gamosaxavs napirs, xolo A
davaleba: moZebneT iseTi wertilebi, romlebic Tanabradaa daSorebuli X RerZidan da A wertilidan.
davalebis Sesasruleblad moswavleebma unda gaixsenon, risi tolia manZili wertilidan wrfemde. aqedan gamomdinare, maT unda aagon X RerZis perpendikularuli wrfe. am dros ar aris aucilebeli maRali sizuste da amdenad am safexurze araa sasurveli maTgan agebis amocanis Sesruleba, Tumca am gadawyvetilebis miReba SeiZleba moswavleebsac mivandoT.
SekiTxva: X ReZis perpendikularuli L wrfe ukve avageT, rogor movZebnoT am wrfeze iseTi P wertili, romelic Tanabradaa daSorebuli A wertilisa da X RerZisagan?
aseTi wertilis moZebna TavisTavad aris damoukidebeli agebis amocana, romelic moswavleebma maswavleblis daxmarebiT unda amoxsnan. kerZod, gavaxsenebT maT tolferda samkuTxedis Tvisebas, risi mixedviTac moswavleebi SeZleben im proceduris aTvisebas, romlis gamoyenebiTac SesaZlebelia miTiTebuli wertilebis moZebna. moswavleebs SeuZliaT gaimeoron zemoaRniSnuli procedura ramdenjerme. mTavaria, agebuli wertilebis raodenoba iyos sakmarisi maTi SeerTebiT miRebuli geometriuli figuris formis Sesaxeb warmodgenis Sesaqmnelad. am etapze SesaZlebelia amocanis gadatana sakoordinato sibrtyeze. es gauadvilebT maT SemdegSi analizuli amoxsnis gzis gaazrebasac. sakoordinato RerZebad umjobesia gamoviyenoT X wrfe da A wertilze gamavali misi perpendikularuli Y RerZi.wertilebis agebis procesSi maT unda SeamCnion, rom figura, romlis agebasac isini cdiloben, aucileblad simetriuli iqneba Y RerZis mimarT. amitom, agebis procesis gasamartiveblad, maT SeuZliaT Y RerZis erT mxares agebuli wertilebis simetriulad gadatana mis meore mxares.
SekiTxva: SevaerToT miRebuli wertilebi da davakvirdeT miRebul figuras. aRwereT igi. ras gvagonebs es figura?
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aRweris procesSi dasaxeldeba figuris iseTi Tvisebebi, rogoricaa misi simetriuloba, is, rom mas gaaCnia wvero, rom igi zemoT iSleba ... . maswavleblis daxmarebiT moswavleebma SeiZleba aRmoaCinon, rom es figura hgavs maT mier naswavl kvadratuli funqciis grafiks. sasurvelia, rom moswavleebs am safexurze SevaxsenoT am figuris saxelwodeba.
SekiTxva:
romeli wertilia parabolis wvero? daasaxeleT misi koordinatebi?vTqvaT X ReZis paraleluri wrfeebi gavavleT 0, 1, 2, 3, ...., 20 wertilebSi. SeadgineT orsvetiani cxrili, miRebuli wertilebis koordinatebis mixedviT SeadgineT orsvetiani cxrili. ra kanonzomierebas amCnevT?aris Tu ara romelime wertili ganlagebuli X RerZze? Y RerZze?zemoaRniSnuli SekiTxvebis Semdeg SeiZleba gadavideT miRebuli geometriuli obieqtis algebrul aRweraze, kerZod misi gantolebis Sedgenaze. amisaTvis moswavleebma unda gaixsenon manZilis formula koordinatebSi da Seadginon gantoleba, romelic gamosaxavs wess: “wertili Tanabradaa daSorebuli X RerZidan
da A wertilidan” _ ооо чпшчрш yxy da gaamartivon igi _ рпоо yx . am
procedurebis Serulebis Semdeg moswavleebi advilad SeamCneven, rom miRebuli gantoleba aris kvadratuli funqciis gantoleba.
gantolebis Sedgenis Semdeg SeiZleba zemoaRniSnuli kiTxvebi gavimeoroT da SevTavazoT, rom moswavleebma maT upasuxon gantolebis gamoyenebiT. miRebuli Sedegebi SevadaroT adre miRebuls.
meore etapze SeiZleba davaleba Sesruldes X RerZis paraleluri romelime wrfisaTvis, xolo A wertili kvlav Y RerZze darCes. SemdgomSi ki A wertili iyos nebismieri wertili sibrtyeze. sasurvelia etapobrivad Semovides iseTi cnebebi, rogoricaa: “fokusi”, “direqtrisa”, “wvero”, “simetriis RerZi” da moswavleebma TviTon gamoikvlion mimarTeba am obieqtebs Soris. kerZod SeiZleba daisvas aseTi tipis SekiTxvebi:
ra moxdeba, Tu fokusi mdebareobs direqtrisaze?ratom mdebareobs parabolis wvero yovelTvis simetriis RerZze?SeiZleba Tu ara parabolis wvero mdebareobdes direqtrisaze?rogor icvleba parabolis forma, rodesac misi fokusi Sordeba direqtrisas?
yovelive amis Semdeg maswavlebeli unda Seecados miRebuli codna daukavSiros realur viTarebas da realur obieqtebs. kerZod, SesaZlebelia aseTi magaliTebis ganxilva
praqtikaSi Zalze gavrcelebulia paraboluri antenebis (e.w satelituri TefSebis) gamoyeneba. moswavleebs Zalze daainteresebT imis aRmoCena, rom paraboluri antenebis forma “marTlac” paraboluria. xolo is faqti, rom paraboluri antenis ZiriTadi maxasiaTeblebia misi diametri da misi fokusis daSoreba diametrisagan. moswavleebs SeiZleba mieceT davaleba, rom maT daadginon sakmarisia Tu ara es monacemebi antenis formis gansazRvrisaTvis, xolo Tu sakmarisia maSin maT TviTon gansazRvron antenis forma, kerZod Seadginon Sesabamisi parabolas gantoleba. agreTve gamoikvlion Tu rogor icvleba antenis forma rodesac fokusi uaxlovdeba diametrs.moswavleebs SeiZleba vuTxraT parabolis kidev erTi mniSvnelovani Tviseba: Tu parabolis mimarTulebiT, mis SigniT, gavuSvebT Y RerZis paralelur sxivTa konas, maSin es sxivebi parabolisagan arekvlis Semdeg fokusSi moiyrian Tavs. SevaxsenoT maT sinaTlis sxivis arekvlis is Tviseba, rom “dacemis kuTxe tolia arekvlis kuTxisa” da es amocana SeiZleba daviyvanoT wminda geometriul amocanaze. Tumca am yvelafris kargad gasagebad saWiroa parabolis (an saerTos
1.
2.
273
wiris) mxebis cnebis kargad gageba, Tumca aramkacri dasabuTebis Semdeg es Tema sainteresod daukavSirdeba wina magaliTs. kerZod, moswavleebi gaigeben, Tu ratom aris paraboluri antenis centrSi Camagrebuli liTonis “Rero,” rom swored es Reroa antena da danarCeni mxolod “TefSia”, romelic radiotalRebs ireklavs da fokusisaken mimarTavs. parabolis Tvisebebis ganxilva da kvleva SeiZleba am etapze dasruldes da danarCeni SemdgomisTvis gadaidos.
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X I k l a s i
aqtivoba: eqspertuli Sefasebebi da centraluri tendenciis sazomebi
misaRwevi miznebi erovnuli saswavlo gegmis mixedviT:
maT. XI.15 akeTebs monacemTa analizs da ayalibebs daskvnebs
iTvlis da iyenebs Semajamebel ricxviT maxasiaTeblebs daujgufebel monacemTa erTobliobebis dasaxasiaTeblad/Sesadareblad da mosazrebaTa/argumentebis Sesafaseblad.gansazRvravs modalur klass da afasebs saSualos, medianas da diapazons dajgufebul monacemTa simravlisTvis, iTvaliswinebs maT realur viTarebaSi gadawyvetilebis miRebisas.
maT. XI.13 warmoadgens monacemebs dasmuli amocanis amosaxsnelad xelsayreli
formiT da axdens maT interpretacias
irCevs monacemTa warmodgenis Sesaferis grafikul formebs, asabuTebs Tavis arCevans, agebs da ganmartavs cxrilebs/diagramebs (maT Soris intervalTa klasebad dajgufebuli monacemebisaTvis).
adgens sixSireTa ganawilebas, warmoadgens mas grafikuli formiT da aRwers mas simetriulobis, modebis raodenobis, gaSlilobis an sxva niSnebis saSualebiT.
reziume
moswavle poulobs centraluri tendenciis sazomebs (saSualos da medianas) sxvadasxva monacemebisaTvis da adarebs maT erTmaneTs. poulobs dispersias da msjelobs am sidideebs Soris kavSiris Sesaxeb.
saswavlo miznebi
Sesaferisi Semajamebel ricxviT maxasiaTeblebis SerCeva amocanis konteqstis gaTvaliswinebiT, Tavisi arCevanis dasabuTeba da maTi gamoyeneba monacemTa erTobliobis dasaxasiaTeblad.monacemebis gamoyeneba statistikuri Sinaarsis mosazrebis wamosayeneblad.
saWiro resursebi
cxrilebi:
#1
1 53
2 90
3 45
4 53
5 71
#2
1 53
2 100
3 45
4 53
5 71
(“amovardnili” monacemis Semcveli cxrili)
#3
1 20
2 100
3 45
4 10
5 71
gadaxris da saSualo kvadratuli gadaxris mqone monacemebis cxrili)
275
didi formatis furclebi da saxatavi saSualebebi, monacemTa warmosadgenad.
aqtivobis aRwera
maswavlebeli acnobs klass an urigebs situaciur amocanebs
situaciuri amocana
amocana: mesakuTres surs sawarmos gayidva. saWiroa sawarmos sawyisi fasis
dadgena. amisaTvis man moiwvia eqspertTa sabWo. mowveuli eqspertebidan
TiToeulma unda daasaxelos sawarmos Rirebuleba. gayidvebis menejeris
mizania, am monacemebis safuZvelze daasaxelos adekvaturi Rirebuleba.
ganixileT SemTxvevebi (warmodgenili Tanxis erTi erTeuli 1,000,000 laris
tolia).
moswavleebs evalebaT cxrilebis safuZvelze daasaxelon sawarmos optimaluri Rirebuleba.
klasi iyofa 5-6 moswavlian jgufebad.jgufebs eZlevaT gansxvavebuli saxis cxrilebi, romlebSic monacemTa gafantva sxvadasxvaa da garda amisa aris “amovardnili” monacemebis Semcveli cxrilebic.TiToeul jgufs eZleva davaleba gansazRvros Tu romeli Rirebuleba iqneba yvelaze adekvaturi mocemuli monacemTa erTobliobisaTvis. moswavleebma unda daadginon Tu ra SeiZleba iyos “adekvaturobis sazomi”. (kerZod, adekvaturobis sazomi SeiZleba iyos is Tu ramdenadaa “daSorebuli” esa Tu is Rirebuleba eqspertis mier dasaxelebuli Tanxisagan. unda SeirCes iseTi ricxvi, romlisTvisac eqspertebis mier dasaxelebuli ricxvebidan “daSorebebis” jami umciresia.)rekomendacia maswavleblisaTvis: SegiZliaT damatebiTi instruqciiT daexmaroT jgufebs. davaleba iyofa ramodenime safexurad:
airCion romelime konkretuli Rirebuleba (ricxvi) da imsjelon imis Sesaxeb Tu ramdenad Seesabameba es Rirebuleba, eqspertebis mier dasaxelebul Rirebulebebs.vurCevT gaixsenon saSualo kvadratuli gadaxra da standatuli gadaxra, ris Semdegac vTavazobT, rom am formulebSi saSualo ariTmetikulis magivrad gamoiyenon maT mier SerCeuli konkretuli ricxvi.Seadaron miRebuli Sedegebi saSualo ariTmetikulis SemTxvevaSi gamoTvlil Sedegs. ris Semdegac Seecadon damoukideblad gamoitanon daskvna.
Sedegi miRweulia, Tu zemoaRniSnuli etapebis gavlis Semdeg, moswavleebi aRmoaCenen
(SesaZlebelia maswavleblis daxmarebiT) or gansxvavebul models: erT
SemTxvevaSi, or monacems Soris manZili ganisazRvros rogorc maTi sxvaobis
absoluturi mniSvneloba, xolo dasaxelebuli Rirebulebis adekvaturoba
ganisazRvros rogorc am absoluturi mniSvnelobebis jami; xolo meore
SemTxvevaSi, ki manZili ganisazRvros rogorc monacemTa Soris sxvaobis
kvadrati, xolo adekvaturobis sazomi iyos am kvadratebis jami.
(ganzogadeba) davalebis pirveli etapis dasrulebis Semdeg moswavleebs eZlevaT davaleba, rom damoukideblad daamtkicon rom pirveli modelis SemTxvevaSi umciresi
1.
2.
3.
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276
saSualosaTvis.
rekomendacia maswavleblisaTvis: mieciT instruqcia moswavleebs, rom gamoiyenon
maTematikur induqcia da kvadratuli funqciis Tvisebebi (minimumis
formula).
(modelis kvleva) am etapze sasargebloa Semdegi saxis SekiTxvebis dasma:ra gavlenas axdens “amovardnili” monacemi (e.i. iseTi monacemi romelic mkveTrad gansxvavdeba sxva monacemebisagan) saSualo ariTmetikulze da medianaze?rodesac monacemTa gafantva maRalia (eqspertTa mosazrebebi mkveTrad gansxvavebulia), icvleba Tu ara saSualo ariTmetikulis da medianas mniSvneloba? ra SemTxvevaSi icvleba ufro metad?ra gavlenas axdens monacemTa raodenoba monacemTa raodenobriv maxasiaTeblebze? (mag. rogor Seicvleba es maxasiaTeblebi Tu arsebul monacemebs ar SevcvliT da eqspertebis raodenobas gavzrdiT?)
Sefaseba
maswavlebeli akvirdeba, Tu ramdenad akuratulad da sworad asruleben gamoTvlebs didi raodenobis monacemTa SemTxvevaSi.maswavlebeli akvirdeba, Tu ramdenad ganviTarebuli aqvT ganzogadebis unari: SeuZliaT Tu ara konkretuli monacemebis SemTxvevaSi miRebuli Sedegebis ganzogadeba.floben Tu ara moswavleebi msjelobisa da damtkicebis xerxebs: maT mier gamoTqmuli hipoTezis mkacrad damtkicebisas.SeuZliaT Tu ara Seafason maTematikuri modeli: Seafason misi gamoyenebis adekvaturoba ama Tu im SemTxvevaSi da erTmaneTs Seadaron ori modeli.
-cedurebisa da gamoTvlebis
Sesruleba didi raodenobis mona-
cemebisaTvis.
konkretulimonacemebisaT-
Sedegebis ganzo-gadebis unari.
-moTqmis unari.
modelis agebis unari. msjelo-
unari.modelis adek-vaturobis Se-fasebis unari.
maswavleblis komentari.
esmis ricxvebTan dakavSirebulimaTematikuri cne-bebi (mag. absolu-turi mniSvneloba). asrulebs gamoTv-lebs, magram mniS-vnelovani xarve-zebiT: uSvebs bevr Secdomas.
ver axdens Sdegebis ganzo-gadebas, Tumca maswavleblisdaxmarebiT,SeuZlia Camoay-alibos Tu ra safexurebis
gamoTqmuli-
mowmeblad.
ver agebs gamarTulmodels. ver axerxebs gamar-Tul msjelo-bas warmodge-nili modelis Sesaxeb.
Sesrulebaze, Tumca moti-
mieces iseTi davalebebi, romlebic Seicavs Semoqmede-biTobis elementebs. es xels
gamoTqma, amoxsnis origi-naluri xerxis mofiqreba).
-mos msjeloba-dasabuTebis xerxebze muSaobas.
•
•
•
277
esmis ricxvebTan dakavSirebuliZiriTadi maTema-tikuri cnebebi. uS-ecdomod asrulebs gamoTvlebs.
miTiTebebisSemdeg (mag., “gaixsene risi tolia saSualo absoluturigadaxra”, “saSua-lo kvadratuli gadaxra”) ga-
-Tezas.
gamoTqmul
gardaqmnisCamoyalibebulmaTematikurmodelad, ma-gram SeuZlia msjelobaSeTavazebulimodelis Ses-axeb.
-tikis ZiriTadi cnebebisa
--
lebebis micema, romlebSic aucilebelia am cnebebisa da
ufro sasargeblo iqneba Tu davalebebi realur viTa-rebebTan iqneba dakavSire-
gamaxvildes sayofacxovrebo sasaubro enaze Camoyalibe-buli debulebebis maTema-tikur enaze Camoyalibebis unaris ganviTarebaze.
esmis ZiriTadi maTematikuricnebebi, maT Soris statistikidan (mag. sixSire, sixSireTa gnawileba, gafantu-loba). uSecdomo-daa Sesrulebuli gamoTvlebi.
damoukidebladganazogadebs
-gebs. ayalibebs
saxavs misi Semowmebis gzebs.
gamoTqmuli
safuZvelzeagebs gamar-Tul maTema-tikur models (mag., absolu-tur saSualo gadaxris fun-qciaze da-fuZnebuls),Tanac ramoden-imes (mag., absoluturikvadratuligadaxris fun-qciaze da-fuZnebulsac).adarebs sx-vadasxva mod-els erTmaneTs da gamoTqvams mosazrebebsmaTi adekva-turobis Ses-axeb.
10
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V I I I k l a s i
proeqtis nimuSebi
Tema: saskolo avtobusis optimaluri marSutis dadgena
problemis dasma
skolis avtobusisaTvis, romelsac qalaqis sxvadasxva ubnebidan skolaSi miyavs moswavleebi da maswavleblebi, unda SeirCes avtobusis moZraobis optimaluri marSruti (am marSrutis dasafarad saWiro drois TvalsazrisiT).
misaRwevi miznebi: moswavleTaTvis maTematikis kursSi Sexvedrili
cnebebis gamoyenebis; rogorc jgufSi TanamSromlobis, agreTve damoukideblad muSaobis unaris ganviTareba da maTTvis keTebiT swavlis pirobebis Seqmna.
saswavlo gegmis SedegebTan da indikatorebTan Sesabamisoba:
maT. VIII.11. (monacemTa analizi, albaToba da statistika)
Sedegi: moipovebs monacemebs da warmoadgens maT dasmuli amocanis amosaxsnelad
xelsayreli formiT
maT. VIII.4. (ricxvebi da moqmedebebi)
(2) irCevs da iyenebs sididis cvlilebis Sesaferis erTeulebs; gamosaxavs mcire erTeuls didi erTeulis gamoyenebiT.
(3) iyenebs gamoricxvis an amowurvis meTods ricxvebze amocanebis amoxnisas da ganmartavs gamoyenebul xerxs.
maT. VIII.5. (kanonzomierebebi da algebra)
(1) misTvis nacnobi sidideebisaTvis asaxelebs sidideebs Soris wrfiv damokidebulebebs.
maT. VIII.10. (geometria da sivrcis aRqma)
(3) iyenebs dekartes koordinatebs geometriuli obieqtis Tvisebebis dasadgenad da dasabuTebisTvis.
realizaciis gegma
1. saWiro informaciis moZieba
proeqtze momuSeve moswavle an moswavleTa jgufi atarebs gamokiTxvas im mizniT, rom gaarkvion vin ra transportiT sargeblobs skolaSi misasvlelad (qmnis martiv kiTxvars, gasazRvravs respondentebs, atarebs gamokiTxvas da agrovebs monacemebs da warmoadgens maT grafikuli saxiT).
2. monacmeTa analizi
am monacemebis safuZvelze moswavle adgens im ubnebs, sadac cxovrobs moswavleebisa da maswavleblebis mniSvnelovani raodenoba.
279
3. vizulizacia, amocanis sqematurad gamosaxva
ruqaze aRniSnavs skolis avtobusis gaCerebis savaraudo punqtebs, am punqtebis erTmaneTTan damakavSirebel gzebs.
4. saWiro codnis gamoyeneba
ruqaze miTiTebuli masStabis gamoyenebiT adgens punqtebs Soris manZilebs, am manZilebis dasafarad saWiro dros, iTvlis yvela marSrutis savaraudo sigZes da warmoadgens mas cxrilis saxiT.
marSruti1 OA AB BC CD DE EO
marSruti2 OA CO OD DE EO
marSruti3
5. Sefaseba da sinTezi
adarebs da akavSirebs moZiebul informacias erTmaneTTan da irCevs saukeTeso marSruts. msjelobs arCeuli gzis optimalobis Sesaxeb Tematikuri da eTikuri TvalsazrisiT (mizanSewonlia Tu ara im punqtis gavliT mgzavroba, sadac erTi maswavlebeli, an moswavleTa/maswavlebleTa mcirericxovani jgufi cxovrobs). sTavazobs aseTi tipis balansis dacvis gzebs (mag. skolis gadasaxadis Semcireba, maswavleblis xelfasSi mgzavrobis xarjebis gaTvaliswineba).
6. proeqtis prezentacia
moswavle an moswavleTa jgufi axdens dasmuli problemis gadaWris gzebis prezentacias.
saWiro resursebi
ruqakalkulatoriformatis qaRaldi, saweri saSualebebi
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X I k l a s i
Tema: fexsacmlis sawamos mogebis maqsimizacia
optimizaciis (raime sididis udidesi/umciresi mniSvnelobis moZebnis) amocanebi xSirad gvxvdeba realur viTarebaSi. magaliTad, rodesac saWiroa SezRuduli resursebis efeqtianad gamoyeneba. SeviswavloT amocana, romelic SeiZleba wamoWriliyo fexsacmlis sawarmoSi.
problemis dasma
fexsacmlis sawarmos direqtors surs sawarmos mogebis maqsimizacia. sawarmo amzadebs ori saxis fexsacmels, sportuls da yoveldRiurs. sawarmos mogeba sportuli fexsacmlis erTi wyvilisaTvis Seadgens 10 lars, xolo yoveldRiuri fexsacmlis erTi wyvilisaTvis - 8.5 lars. fexsacmlis damzadebis erT-erT safexurze, saWiroa masalis daWra da miRebuli naWrebisagan fexsacmlis Sekerva.
I safexuri. problemis gaazreba.
I.1. cvladi sidideebis dadgena
moswavlem gamoyos is sidideebi, romelTa cvlilebis SesaZlebloba gaaCnia sawarmos. swored maTi cvlilebiT unda moxdes mogebis maqsimizacia, Tumca am sidideebis nebismierad cvlileba ar SeiZleba. maT adevT garkveuli SezRudvebi, romelTa gaTvaliswineba aucilebeli iqneba. es sidideebia:
S - erTi kviris ganmavlobaSi gamoSvebuli wyvili sportuli fexsacmlis raodenoba;D - erTi kviris ganmavlobaSi gamoSvebuli wyvili yoveldRiuri fexsacmlis
raodenoba.
I.2. modelis SemuSaveba
I.2.1. miznis funqciis gansazRvra
sawarmos direqtoris mizania, rac SeiZleba meti mogebis miReba (mogebis maqsimizacia). moswavlem gansazRvros sidide, romelic gamosaxavs mogebas da romelic damokidebulia zemoaRniSnul cvlad sidideebze.
am funqcias ewodeba miznis funqcia.
miznis funqciafunqcia, romelic gamosaxavs
-
warmoadgens amocanis amoxs-nis mizans.
I.2.2. SezRudvebis gansazRvra
moswavlem unda gaiazros, rom realur viTarebaSi, sidideebis cvlileba nebismierad ar SegviZlia. TanamSromelTa da mowyobilobebis raodenoba, sawarmos yoveldRiuri samuSao saaTebis raodenoba, iZleva SezRudvebs gamoSvebuli produqciis raodenobaze. davuSvaT, rom fexsacmlis sawarmos aqvs Semdegi SezRudvebi. sawarmos gaaCnia masalis dasaWreli 6 dazga, sawarmoSi muSaobs 850 muSa, romlebic muSaoben kviraSi 40 saaTs.
simwiriT (igulisxmeba, ro-gorc droiTi, aseve nedleu-li da sxva saxis resursebi).
gamoisaxeba utolobebis saxiT.
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II safexuri. modelis Sedgena
II.1. SezRudvebis gamosaxva algebrulad
saWreli dazgebis SesaZleblobebiT gansazRvruli SezRudvebimoswavle damoukideblad daadgens Semdegs: 6 dazgidan TiToeuli muSaobs kviraSi
мр кр омрр wuTis ganmavlobaSi. amitom mTliani samuSao dro wuTebSi iqneba
к омрр пммрр wuTi. yoveli wyvili sportuli fexsacmlis masalis daWras esaWiroeba 4 wuTi, xolo yoveldRiuri fexsacmlis masalis daWras esaWiroeba 3 wuTi. amitom saWreli dazgebis SesaZleblobebiT gansazRvruli SezRudvebi maTematikurad gamoisaxeba aseTi utolobiT: 14400
TanamSromelTa Sromis nayofierebiT gansazRvruli SezRudvebimoswavle damoukideblad daadgens Semdegs: risi tolia 850 TanamSromlis mTliani
samuSao dro erTi kviris ganmavlobaSi - илр мр нмррр ;TiToeul muSas esaWiroeba 7 saaTi erTi wyvili sportuli fexsacmlis asawyobad da
8 saaTi, erTi wyvili yoveldRiuri fexsacmlis asawyobad. amitom, TanamSromelTa Sromis nayofierebiT gansazRvruli SezRudvebi gamoisaxeba aseTi utolobiT: 7 34000
sxva SezRudvebi
fexsacmlis wyvilebis raodenoba ar SeiZleba iyos uaryofiTi, Tumca romelime maTgani SeiZleba iyos 0-is toli (ratom?). aqedan gamomdinare, fexsacmlis wyvilTa raodenobebze ganisazRvreba kidev ori damatebiTi SezRudva: S 0 da D 0.
II.2. Sejameba
Catarebuli samuSaos Sedegad Sedgeba mocemuli viTarebis maTematikuri modeli, romelSic SezRudvebi gamosaxulia utolobaTa sistemis saxiT:
14400 7 34000 S 0 D 0
xolo mizani (sidide, romlis maqsimizacia moiTxoveba), gamoisaxeba ori cvladis funqciiT:
III safexuri. modelis kvleva
III. 1. utolobaTa sistemiT gamosaxuli SezRudvebis gamosaxva grafikulad.
moswavle miRebuli sistemas gamosaxavs sakoordinato sibrtyeze grafikulad, sadac sakoordinato RerZebze gadaizomeba S - erTi kviris ganmavlobaSi gamoSvebuli sportuli fexsacmlis wyvilebis raodenoba da D - erTi kviris ganmavlobaSi gamoSvebuli yoveldRiuri fexsacmlis wyvilebis raodenoba.
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282
grafikuli TvalsaCinoebisaTvis umjobesia gamoiyenon didi formatis furceli, romelic prezentaciis dros dafaze gaikvreba. naxazs daaxloebiT aseTi saxe eqneba:
umjobesia, Tu TiToeul wrfes miewereba Sesabamisi gantoleba, xolo wrfeebis gadakveTis wertilebs miewereba Sesabamisi koordinatebi. amisaTvis, moswavles mouwevs gantolebaTa sistemis amoxsna. rac kidev erTi punqtia, romelic gaTvaliswinebuli iqneba Sefasebis dros.
III. 2. sidideebis cvlileba da cxrilis Sedgena
moswavle gamuqebul areSi irCevs ramodenime sxvadasxva wertils da am wertilebisaTvis gamoTvlis mogebis ( ) Sesabamis mniSvnelobas. adgens cxrils, romelsac aqvs sami sveti.
S D P - mogeba
500 500 9250
1000 1000 18500
1000 2000 27000
2000 1000 28500
III.3. monacemebze dakvirveba
cxrilze dakvirvebiT, moswavle aRmoaCens, rom mogebis mniSvneloba izrdeba sibrtyeze wertilis raRac garkveuli mimarTulebiT moZraobisas (romelic ufro “marjvniv” aris). amitom savaraudoa, rom mogebas udidesi
mniSvneloba unda qondes romelime ukidures wertilSi, e.i. sibrtyeze gamosaxuli gamuqebuli mravalkuTxedis romelime wveroSi. dgeba Sesabamisi cxrili.
S D P - mogeba
0 0 0
0 4250 36125
1200 3200 39200
3600 0 36000
283
miRebuli cxrilis, pirvelad Sedgenil cxrilTan Sedarebis Sedegad Cans, rom mogebis mniSvnelobebi am SemTxvevaSi aSkarad metia (Tu ar CavTvliT wertils). xolo am monacemebs Soris, udidesi mniSvneloba miiRweva wertilisaTvis.
IV safexuri. kanonzomierebis aRmoCena.
IV.1. problemis gadaWra da dasabuTeba.
am yovelives Semdeg SeiZleba gadavideT sakiTxis ufro mkacr maTematikur dasabuTebaze. kerZod moswavleebs SevTavazoT aagon
gantolebiT mocemuli wrfe P-s sxvadasxva mniSvnelobisaTvis.
maT unda SeamCnion, rom yvela am wrfes aqvs erTi da igive daxris koeficienti da SeiZleba iTqvas, rom wrfe “moZraobs” paralelurad. rodesac mogebis mniSvneloba izrdeba, wrfe moZraobs marjvniv, xolo misi is “ukiduresi marjvena” mdgomareoba, romlis drosac wrfe kveTs gamuqebul ares, aris maSin, rodesac igi gadis gamuqebuli aris wveroze, romlis koordinatebia (1200, 3200). swored amis gamoa, rom mogebis funqcias am wertilSi aqvs udidesi mniSvneloba.
prezentaciis dros mosaxerxebelia didi zomis saxazavis gamoyeneba, romelsac moswavle amoZravebs naxazze da yvela daakvirdeba Tu rogor icvleba “mogeba” da rodis aris igi udidesi. SeiZleba damzaddes Sesabamisi TvalsaCinoeba.
maTem atika
284
IV.2. ganzogadeba
am konkretuli amocanis SemTxvevaSi, utolobebis raodenoba sakmaod mcirea. realur viTarebebSi, analogiuri amocana xSirad ismeba, magram utolobebis (iseve rogorc parametrebis) raodenoba gacilebiT metia. amitom amocana SeiZleba ganzogaddes da problema daisvas zogadi saxiT. Tumca, unda SevizRudoT iseTi SemTxveviT, rodesac parametrebis (cvladebis) raodenoba 2-s ar aRemateba.
Sedegad Camoyalibdeba sibrtyeze wrfivi optimizaciis amocanis amoxsnis zogadi wesi: utolobaTa sistemiT mocemul SezRudvebs grafikulad gamovsaxavT sibrtyeze; Sedegad unda miviRoT mravalkuTxedi (es etapi aucilebelia, radgan SeiZleba utolobaTa sistemas amonaxsni ar gaaCndes); vpoulobT mravalkuTxedis wveroebis koordinatebs; TiToeuli wverosaTvis vpoulobT miznis funqciis mniSvnelobas, ris Semdegac, miRebul sidideebs Soris virCevT udidess; mravalkuTxedis Sesabamisi wveros koordinatebi iqneba parametrebis is mniSvnelobebi, romelTaTvisac miznis funqcia Rebulobs udides mniSvnelobas.
rogorc vxedavT, problemis gadaWra dayofilia IV safexurad. TiToul safexurze saWiroa maswavleblis Careva instruqciebis micemis gziT. instruqciebis detaluroba unda ganisazRvros wina safexurze miRebuli SedegiT. amave dros saWiroa moswavleebs mieceT azris damoukideblad gamoTqmis saSualeba imis Sesaxeb, Tu rogor unda gagrZeldes muSaoba, ra unda gakeTdes Semdeg safexurze, ra damatebiTi monacemebia saWiro.
285
rekomendebuli Sefaseba maTematikaSi
Sefasebis ori ZiriTadi tipi
skolaSi ZiriTadad misaRebia ori tipis Sefaseba: ganmsazRvreli da ganmaviTarebeli. rodesac maswavlebeli niSans uwers moswavles da mxolod amiT Semoifargleba, es niSani gansazRvravs moswavlis miRwevis dones dasaxul miznebTan mimarTebiT. maSin, rodesac maswavlebeli Sefasebis iseT formas iyenebs, romelic moswavles ara mxolod sakuTari
Sefasebaa. ganmaviTarebeli Sefasebis tipuri formaa komentarebi, romelic trimestris ganmavlobaSi an bolos, an romelime davalebis Sesrulebis Semdeg iwereba da romelic aRwers namuSevris Zlier da sust mxareebs da amavdroulad Seicavs rekomendaciebs miRwevebis gaumjobesebis Taobaze. ganmaviTarebeli Sefasebis erT-erTi gavrcelebuli xerxia Sefasebis cxrilebis (rubrikebis) gamoyeneba.
mniSvnelovania ganmsazRvreli da ganmaviTarebeli Sefasebis mudmivad gamoyeneba swav-lis procesSi. rekomendebulia, rom ganmaviTarebeli Sefasebis wili saswavlo procesisas ufro meti iyos, vidre ganmsazRvrelis.
ganmaviTarebeli
mimdinareSesruleba, gakveTilze Car-
iwereba.
Sesruleba, gakveTilze CarTu-
moswavles, rogor gaaumjo-besos Sedegebi.
Semajamebe-li
raime Temis, drois monakve--
buli niSani.
raime Temis, drois monakveTis,
sityvieri Sefaseba, komentari, rubrikiT Sefaseba da sxv.
trimestruli niSnis Semadgeneli nawilebi
moswavlis niSani unda gamomdinareobdes mis mier sagnis Seswavlis sxvadasxva komponentisgan. moswavle SesaZlebelia Sefasdes Semdegi komponentebis mixedviT:
a) gakveTilze CarTuloba;b) saSinao davalebebi;g) mimdinare saklaso davalebebi;d) Semajamebeli davalebebi (sakontrolo/gamocda/testireba da sxv.);e) proeqtebi;v) damatebiTi komponenti, romelic araumetes saerTo Sefasebis 10%-ia da romelic
moswavleebis mier dgindeba (mag. organizebuloba, SemoqmedebiToba, jgufSi efeqturi muSaoba da sxv.).
TiToeuli sagnis swavlebisas, skola kaTedrebis meSveobiT adgens minimum sam komponents pirveli xuTidan, romelsac aniWebs procentul wonebs 90%-is farglebSi. danarCeni 10 % - is ganawileba xdeba maswavleblis mier ukve moswavleebTan SeTanxmebiT. pirvelad maswavleblebi acnoben moswavleebs kaTedris mier SemuSavebul komponentebs da uxsnian, Tu ras moelian TiToeuli komponentis Sefasebisas. amis Semdeg moswavleebTan
maTem atika
286
erTad eZeben im kriteriums, romelic, maTi azriT, kargi iqneboda, rom damatebiT aTi procentis farglebSi yofiliyo gamoyenebuli. maswavlebeli SesaZlebelia exmarebodes moswavleebs am komponentis gaazrebaSi, magram mniSvnelovania, rom moswavleebma TviTon gadawyviton am komponentis raoba da Sefasebis doneebi.
TiToeuli komponentis mixedviT dgeba Sefasebis doneebi erTidan aTamde, romelic ganmartavs, Tu ra qulebi iwereba sxvadasxva donis mixedviT. rekomendebulia, trimestruli Sefaseba ganmaviTarebeli formiT iyos Sedgenili. rekomendebulia komentarebis dawera trimestris bolos yvelasTvis da trimestris SuaSi imaTTvis, vinc aucileblad unda gamoasworos sakuTari swavla, raTa trimestruli Sefaseba dadebiTi hqondes. trimestris SuaSi aseve SeiZleba daiweros komentari, Tu moswavlem wina trimestrTan SedarebiT mniSvnelovnad gaaumjobesa Tavisi moswreba. amis aRniSvna mniSvnelovan stimuls miscems
moswavles imisTvis, rom swavlis xarisxi trimestris bolomde SeinarCunos.
saSinao davaleba
unarebi
maTematikuri cnebebisa da debulebebis gamoyeneba.kavSirebisa da mimarTebebis dadgena.maTematikuri obieqtebis warmodgena da maTematikuri enis flobadamxmare teqnikuri saSualebebisa da sainformacio teqnologiebis gamoyeneba
unarebi fasdeba Semdegi aqtivobebiT:
moswavle
aRiqvams amocanis Sinaarss, gaiazrebs da gamijnavs amocanis monacemebsa da saZiebel sidideebs axdens monacemebis (maT Soris problemis gadasaWrelad saWiro monacemebis) organizebas da maT warmodgenas.gadmocemisas sworad da efeqtianad iyenebs maTematikur terminebsa da aRniSvnebs. adekvaturad irCevs simkacris dones da rodesac saWiroa, dasabuTebisas iyenebs mkacr maTematikur msjelobas (maT Soris induqciur da deduqciur msjelobas).poulobs, arCevs da iyenebs gzebsa da meTodebs (maT Soris teqnologiebs) figurebis da obieqtebis zomebis, agreTve maT Soris manZilebis, masis, temperaturis da drois gasazomad. arCevs da moipovebs procesis an realuri viTarebis modelirebisaTvis saWiro monacemebs.kopleqsur (rTul) problemas yofs safexurebad, martiv amocanebad da Wris etapobrivad (amoxsna), maT Soris standartuli midgomebisa da procedurebis gamoyenebiT.
Semajamebeli samuSao
unarebi
maTematikuri obieqtebis warmodgena da enis floba.maTematikuri cnebebisa da debulebebis gamoyeneba.kavSirebisa da mimarTebebi.amocanis amoxsnis gza da misi realizeba.gamoTvlebi.
1.2.3.4.
1.
2.
3.
4.
1.2.3.4.5.
287
unarebi fasdeba Semdegi aqtivobebiT:
moswavle
axdens monacemebis (maT Soris problemis gadasaWrelad saWiro monacemebis) organizebas da maT warmodgenas.gadmocemisas sworad da efeqtianad iyenebs maTematikur terminebsa da aRniSvnebs.amocanebis gadaWrisas (maT Soris yofiTi), iyenebs maTematikur obieqtebs, procesebs da maT Tvisebebs.irCevs efeqtian strategias da mokled aRwers problemis gadaWris safexurebs. miyveba arCeul strategias.irCevs gamoTvlebis adekvatur / optimalur xers da axdens mis realizebas.amyarebs kavSirebs (mag. sxva maTematikur struqturebTan, obieqtebTan an sxva disciplinebTan) da iyenebs am kavSirebs rogorc problemis gadaWrisas aseve miRebuli Sedegebis gaanalizebisas.
mimdinare saklaso davalebebi
unarebi
cnebebisa da debulebebis gamoyenebamaTematikuri obieqtebis warmodgenamaTematikuri enis floba
unarebi fasdeba Semdegi aqtivobebiT:
moswavle
moswavle arCevs dasabuTebis meTods (mag. sawinaaRmdegos daSvebis gamoyeneba damtkicebisas, evristikuli meTodis gamoyeneba dasabuTebisas).koreqtulad iyenebs terminologias, maTematikur aRniSvnebsa da simboloebs.informaciis gadacemisas warmoaCens sakiTxis arss (mag. obieqtis arsebiT Tvisebebs).auditoriisa da saprezentacio masalis mixedviT irCevs prezentaciis formas da damxmare saSualebebs (maT Soris sainformacio teqnologiebs).axdens problemis formulirebas auditoriisaTvis gasagebi formiT. asabuTebs problemis aqtualurobas da mniSvnelobas (igulisxmeba problemis praqtikuli an/da wminda mecnieruli aqtualuroba).msjelobisas, sxvadasxva safexurze, adekvaturad irCevs simkacris dones da rodesac saWiroa, dasabuTebisas iyenebs mkacr maTematikur msjelobas (maT Soris induqciur da deduqciur msjelobas).
proeqti
fasdeba Semdegi unarebi
cnebebisa da debulebebis gamoyenebakavSirebisa da mimarTebebis dadgenaamocanis Camoyalibeba da amoxsnamaTematikuri obieqtebis warmodgenamaTematikuri enis floba
1.
2.3.
4.
5.6.
1.2.3.4.
1.
2.3.
4.
5.
6.
1.2.3.4.5.
maTem atika
288
damxmare teqnikuri saSualebebisa da sainformacio teqnologiebis gamoyenebamodelireba
unarebi fasdeba Semdegi aqtivobebiT:
moswavle
poulobs, arCevs da iyenebs gzebsa da meTodebs (maT Soris teqnologiebs) figurebis da obieqtebis zomebis, agreTve maT Soris manZilebis, masis, temperaturis da drois gasazomad. arCevs da moipovebs procesis an realuri viTarebis modelirebisaTvis saWiro monacemebs.axdens monacemebis (maT Soris problemis gadasaWrelad saWiro monacemebis) organizebas da maT warmodgenas.Cveul garemoSi (maT Soris yoveldRiur cxovrebaSi) amCnevs maTematikur obieqtebsa da procesebs. iyenebs maT Tvisebebs praqtikuli (maT Soris yofiTi) amocanebis gadaWrisas.gansazRvravs da ayalibebs problemas, maT Soris arastandartul viTarebaSi (mag. rodesac problemis gadasaWrelad saWiro maTematikuri procedura calsaxad araa gansazRvruli).irCevs efeqtian strategias da mokled aRwers problemis gadaWris safexurebs. miyveba arCeul strategias. aanalizebs arCeul strategias da asabuTebs arCeuli strategiis efeqtianobas, mimoixilavs SesaZlo alternatiul strategiebs da msjelobs maT upiratesobebsa da naklze.amyarebs kavSirebs (sxva maTematikur struqturebTan, obieqtebTan an sxva disciplinebTan) da iyenebs am kavSirebs rogorc problemis gadaWrisas aseve miRebuli Sedegebis gaanalizebisas.axdens mocemuli modelis elementebis interpretirebas im realobis konteqstSi,
miRebuli monacemebis interpretirebas Sesabamisi modelis enaze. gansazRvravs modelis vargisianobas da afasebs misi gamoyenebis sazRvrebs.auditoriisa da saprezentacio masalis mixedviT irCevs prezentaciis formas da damxmare saSualebebs (maT Soris sainformacio teqnologiebs). efeqtianad iyenebs prezentaciisaTvis gankuTvnil dros.axdens problemis formulirebas auditoriisaTvis gasagebi formiT. asabuTebs problemis aqtualurobas da mniSvnelobas (igulisxmeba problemis praqtikuli an/da wminda mecnieruli aqtualuroba).zogadi Sedegebis sademonstraciod iyenebs magaliTebs, rogorc realuri viTarebidan aseve maTematikidan.axdens miRebuli Sedegebis ganzogadebas, amyarebs kavSirebs (mag. sxva maTematikur struqturebTan, obieqtebTan an sxva disciplinebTan) da iyenebs am kavSirebs rogorc problemis gadaWrisas aseve miRebuli Sedegebis gaanalizebisas.afasebs maTematikis adgilsa da mniSvnelobas sxvadasxva disciplinebSi, biznesSi, xelovnebaSi da adamianis moRvaweobis sxvadasxva sferoebSi.13. informaciuli teqnologiebis gamoyenebisas acnobierebs eTikur/socialuri xasiaTis problemebs da icavs eTikur normebs.
6.7.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
289
klasSi CarTuloba
fasdeba Semdegi unarebi
TanamSromlobaTviTorganizebaprincipulobasxvisi darwmunebis unaridaTmobis unari
unarebi fasdeba Semdegi aqtivobebiT:
moswavle
keTilsindisierad asrulebs davalebebs (vadebisa da raodenobis TvalsazrisiT).koreqtulia maswavlebelTan da megobrebTan mimarTebaSi. igebs da aanalizebs sxvis naazrevs.TanamSromlobs TanaklaselebTan jgufuri samuSaoebis Sesrulebisas.monawileobs diskusiaSi. mimdinare sakiTxis irgvliv adekvaturad ayalibebs SekiTxvebs. gaazrebulad pasuxobs maswavleblisa da megobrebis SekiTxvebs.
semestruli niSnis Semadgeneli komponentebis ganawilebis magaliTi
1.2.3.4.5.
1.2.
3.4.
maTem atika
290
(wera)
1 - 3 4 - 5 6 - 7 8 - 10
araadekvaturadiyenebs cnebebs,
--
rulyofiladwarmoadgensmonacemebs.
iyenebs amocanis amosaxsnelad
cnebas, termi-
Tumca araorgani-zebulad warmoad-gens monacemebs.
iyenebs amoca-nis amosaxsne-
cnebebis, deb-ulebebisa da
-dens monacemTa organizebas da warmoadgenas.
iyenebs amocanis amosaxsnelad
-bas, debulebas da
monacemTa organi-zebisa da warmod-
formas.
amosxnis rome-lime gzas.
romelime gzas, iwyebs magram ver asrulebs amoxs-nas.
-canis amoxsnis gzas, miyveba mas, Tumca xarvezebiT.
-alur) gzas, bo-lomde axdens mis realizebas.
amoicnobs or, odnav gansxvave-buli formiT warmodgenil,identur maTema-tikur obieqts (mag. gansxvavebu-
-vnebiT Caweril erTsa da imave algebrul gamo-saxulebas).
amoicnobs or, gansxvavebuliformiT warmod-genil, identur maTematikurobieqts (mag. sxvadasxva for-miT warmodgenil erTsa da imave asaxvas).
sxvadasxva stan-dartul maTema-tikur obieqtsa
Soris (mag. gan-tolebis amoxs-na da mocemuli asaxvisaTvismocemuli mniS-vnelobis wina-
kavSirs sxvadasxva maTematikur obi-
-durebs Soris (mag. iyenebs algebrul gardaqmnebs da
Tvisebebs geome-triul debulebaTa dasabuTebisas).
gamoTvlebi ar metyvelebs amo-canis gagebaze, Sedegi araadek-vaturia.
Seicavs gamoTv-lebis ZiriTad nawils, reali-zeba nawilobriv arasworia.
gamoTvlebiZiriTadadsworia, Tumca Seicavs teqni-kuri xasiaTis xarvezebs.
gamoTvlebisworia, arCeuli da gamoyenebuli aqvs gamoTvlebis
291
proeqti (VII _ XI klasebi)
1-3 4-5 6-7 8-10
damoukidebladver axerxebs
-tifikacias, ver
-wavleblis mier dasmul kiTx-vebs momijnave sakiTxebidan.
nawilobrivmijnavs amoca-nis monacemebs da saZiebel si-dideebs, monace-mebis organizebas da warmodgenas axerxebs xarveze-biT.
mijnavs erTmane-Tisgan amocanis monacemebs da saZiebel sididee-bs. SeuZlia mona-cemebis organize-ba da warmodgena srulyofilad
damoukideblad-
mijnavs amocanis mo-nacemebs da saZiebel sidideebs, axdens mo-nacemebis organize-bas da warmodgenas efeqturi xerxiT.
damoukidebladver axerxebs
maTematikurenaze formu-
-werili situa-ciis sqematurad gamosaxva.
maswavleblisdaxmarebiT aya-
maTematikur enaze, maswavleblisdaxmarebiT ad-
Tumca, SeuZlia gegmis safexurebs Soris kavSirebis axsna.
-lemas maTemati-kur enaze, sqemat-urad gamosaxavs amocanaSi ar-weril situacias, damoukidebladgamoyofs da
amoxsnis ZiriTad
safexurebad, gamo-
amoxsnis ZiriTad
sxva SesaZlo strat-egiebs da msjelobs maT efeqtianobaze.
maswavleblisdaxmarebiT
TemasTan da-kavSirebulCaketili ti-
amocanebs stan--
eraciebis gamoy-enebiT.
damoukideblad
romelime safex-urze Caketili
standarttuli
gamoyenebiT.
-eqtis TemasTan dakavSirebulimaTematikuriobieqtebis Tvise-
-
calkeul safex-urze irCevs
-durebs da koreq-tulad anxorcie-lebs maT.
-sas iyenebs adekva-tur damxmare te-qnikur saSualebebs da teqnologiebs. iyenebs gamoTvlebis da damtkicebis warmarTvis efeqtur xerxs. koreqturad
-
ver axerxebs faqtebis erT-maneTTan daka-
-gebis sisworis Sesaxeb raime argumentismoyvana.
-buli Sedegebis adekvaturobaze,Tumca ver asax-
-lemas, romelic analogiuradSeiZleba iqnas
sad SeiZleba -
gebis gamoyeneba)
Sedegebis inter--
uri viTarebis konteqstSi, Tumca
arCeuli mod-eli gamoyenebis CarCoebis gansaz-
-retirebas realuri viTarebis konteqst-Si. SeuZlia arCeuli modelis vargisiano-bisa da gamoyenebis
msjeloba.
maTem atika
292
maswavleblisdaxmarebiT
wardgenis xerxs,
ZiriTadi arsis warmoCena.
ZiriTadad swo-rad iyenebs maTematikurterminebs da
-suxobs SekiTxvaTa nawilze.
koreqtuladiyenebs maTema-tikur terminebs
-mis aqtualuro-baze msjeloba auditoriisaTvisgasagebad.
wardgenis efeqtur -
lemis formulireba auditoriisaTvisgasagebi eniT. zogadi Sedegebis sademon-straciod moyavs magaliTebi rogorc maTematikidan, ise sxva sferoebidan. informaciis gada-cemisas warmoaCens sakiTxis arss.
naklebad Tanam-Sromlobs sxva moswavleebTanan maswavle-belTan;enTuziazmiT ar ekideba saqmes;akeTebs mxolod minimums da ar cdeba mocemul farglebs
TanamSromlobsmaswavlebelTan,sxva moswavlee-bTan magram ver
-bebs. cdilobs enTuziazmiTimuSavos, magram xSirad drois cu-dad ganawilebis gamo, ver axerxebs
dacvas;-
eqtis mimdin-areobisas gacdes moTxovnebs,magram xSirad
resursebis an ideebis moZieba
aqtiurad Tanam-Sromlobs mas-wavlebelTan da moswavleebTan,organizebulia,moiZiebs damate-biT resursebs an ideebs, ZiriTa-dad flobs disku-siaSi monawile-obis kulturas.
aqtiurad TanamS-romlobs maswavle-belTan da moswav-leebTan. gamoirCeva TviTorganizebulo-
imavdroulad is-mens da afasebs sxvis argumentacias da Sexedulebebs, amis safuZvelze akeTebs sakuTari Sefasebis koreqcias, eTikuria diskusiaSi monaw-ileobisas. SeuZlia sakuTari Secdomis
ideis Sefaseba da
warmodgenili ma-salis sicxadesa da esTetiurobaze,
293
їѕ«І»ѕ·і»¬§Є»ґ± і»ЅІ·»®»ѕ»ѕ·
294
I k l a s i
aqtivobis nimuSebi
aqtivoba 1
bunebismetyveleba
mizani: saswavlo garemos gacnoba moswavleebSi gaucxoebis grZnobis daZleva aRwerisa
da Sedarebis unarebis ganviTareba
Tema: saswavlo garemo
saWiro masala: danarTi N#1 _ TiTo wyvilze erTi egzemplari
gakveTilis mimdinareoba:
maswavlebeli sTxovs moswavleebs xeli Cahkidon erTmaneTs. maswavlebeli miuZRvis moswavleebs da Semoatarebs saklaso oTaxs. man yuradReba unda miaqcevinos moswavleebs saklaso oTaxSi ganTavsebul mniSvnelovan obieqtebze: dafa, merxi da sxva. aucilebelia siwynaris dacva am `eqskursiis~ dros.
Semdeg moswavleebi sxdebian sakuTar adgilebze. maT urigdebaT samuSao furclebi (danarTi #1).
samuSao sruldeba wyvilebSi. wyvilebma unda ganixilon naxatebi da saklaso oTaxis amsaxvel naxatebze moZebnon is sagnebi, romlebic maT klasis daTvalierebis dros SexvdaT. amis Semdeg moswavleebi unda daakvirdnen sacxovrebeli oTaxis suraTs, ipovon da xazebiT SeaerTon saklaso oTaxisa da sacxovrebel oTaxis msgavsi aveji da nivTebi. samuSaos dasrulebis Semdeg maswavlebeli moswavleebs rigrigobiT CamoaTvlevinebs maT mier xazebiT dakavSirebul sagnebs da svams kiTxvebs, romlebic avlens skolisa da saxlis nivTebs Soris arsebiT msgavsebas. moswavleebma unda daaskvnan, rom skolac `saxlia~, skolis nivTebi maTia da iseve unda gaufrTxildnen, rogorc saxlisas.
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aqtivoba 2
bunebismetyveleba
mizani: SegrZnebis organoebis mniSvnelobis Cveneba. instruqciebis Tanmimdevruli
Sesrulebis Cvevis gamomuSaveba.
Tema: SegrZnebis organoebi _ Sexeba.
aqtivobebi: sagnebis amocnoba SexebiT.
saWiro masala:
jgufebis raodenobis Sesabamisi:gaumWirvale (Savi) parki.sxvadasxva nivTi: burTi, vaSli, liTonis Wiqa. xis joxi, qva (nivTebi SeiZleba ganmeordes)furclebi, fanqrebi.
damatebiTi rekomendacia: gaanawileT nivTebi parkebSi: TiTo nivTi _ TiTo parkSi.
yovel parks gaukeTeT raime niSani, raTa muSaobis dros ar agerioT.
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parkebis raodenoba unda Seesabamebodes jgufebis raodenobas. kargi iqneba,
Tu maswavlebels eqneba sarezervo egzemplarebi, radgan pirvelklaselebs
jer ara aqvT gamomuSavebuli instruqciebis zustad Sesrulebis Cveva. iseTi
sagnebi SearCieT, rom formac martivi hqondeT da faqturac mravalferovani
iyos _ magari, rbili, civi, priala, xorkliani da sxva. nivTis forma unda
iyos martivi, raTa pirvelklaselma moswavlem SeZlos misi daxatva.
gaanawileT klasi jgufebad. auxseniT davalebis arsi: TiToeul jgufs maswavlebeli miutans parks, romelSic jgufis yoveli wevri Cayofs xels da SexebiT gamoikvlevs sagans.
jgufis wevrebi ar uziareben erTmaneTs STabeWdilebebs manam, sanam am jgufis yvela wevri ar gamoikvlevs parkSi Cadebul nivTs. aucileblad miuTiTeT, rom Zalian mniSvnelovania parkebSi ar Caixedon. moswavleebs gamokvlevisTvis sakmarisi dro mieciT. nu aaCqarebT, magram yuradReba miaqcieT, rom zogierTma moswavlem Zalian didi dro ar moandomos am process.
mas Semdeg, rac jgufis TiToeuli wevri mosinjavs nivTs, parki ideba maswavleblis magidaze. maswavlebeli msgavs proceduras atarebs TiToeul jgufTan.
Semdeg jgufebs eZlevaT davaleba, gauziaron mosazrebebi erTmaneTs. moilaparakon, Tu ra nivTi devs parkSi, SeZlebisdagvarad daxaton. TiToeulma jgufma unda Seasrulos erTi saerTo naxati da ara _ ramdenime.
TiToeuli jgufi warmoadgens pasuxs. maswavlebeli ekiTxeba, Tu rogor mixvdnen ra sagani ido parkSi.
jgufis pasuxis mosmenis Semdeg maswavlebeli aCvenebs am jgufis parkidan amoRebul nivTs. moswavleebi TviTon afaseben, Tu ramdenad sworad amoicnes nivTi, an Tu ver gamoicnes, ra iyo amis mizezi. maswavleblis kiTxvebi unda daexmaros moswavleebs imis mixvedraSi, Tu sagnis ra Tvisebebi SeigrZnes SexebiT. adamianis ra SegrZneba daexmara maT sagnis amocnobaSi.
aqtivoba 3
bunebismetyveleba
mizani: cocxalis da aracocxalis erTmaneTisagan garCeva, obieqtebis daxasiaTeba da
dajgufeba.
Tema: cocxali da aracocxali
maswavlebeli ekiTxeba moswavleebs: gaakeTeT aqcenti maT mier dasaxelebul swor
pasuxze. SeecadeT gamoavleninoT gansxvaveba am ori jgufis obieqtebs Soris. SeecadeT gamoavleninoT msgavseba erT jgufSi gaerTianebul obieqtebs Soris. (pirvelklasel moswavleebTan am Temaze laparakis dros sasurvelia, isini uSualod xedavdnen saubris obieqtebs.)
rogorc parqtikidan Cans, pirvelkaselebi cocxalSi aerTianeben ZiriTadad imas, rac
mivakuTnoT is, rac axlaa cocxali an adre iyo cocxali (mag. mowyvetili yvavili), xolo aracocxals _ is, rac ar aris da arc arasodes iyo cocxali.
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moswavleebs urigdebaT samuSao furclebi (danarTi # 1). maT evalebaT cocxali obieqtebi Semoxazon mwvaned, xolo aracocxali _ lurjad.
maswavlebeli rigrigobiT ekiTxeba TiToeul moswavles, Tu ra feriT Semoxaza esa Tu is obieqti da ratom. Semdeg kiTxulobs, Tu vis aqvs msgavsi pasuxi, vis _ gansxvavebuli. msjeloben, romeli pasuxia swori.
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I I k l a s i
gakveTilis scenaris nimuSebi(Sefasebis rekomendaciebiT)
gakveTilis scenari
bunebismetyveleba
, ,Crdili icvlis adgils”
kavSiri standartTan
mimarTuleba: dedamiwa da garesamyaro
bun. II. 6. moswavle axasiaTebs mzes, dedamiwas da mTvares
aRwers dRis manZilze mzis mdebareobas misTvis nacnobi obieqtebis (mag., oTaxis fanjara) mimarT.mowmendil amindSi akvirdeba dRis manZilze Crdilis sigrZis cvalebadobas da akavSirebs mas garkveul drosTan (dila, SuadRe, saRamo);
mimarTuleba: sxeulebi da movlenebi
bun. II. 4. moswavle ganarCevs da aRwers sinaTlis da siTbos bunebriv da xelovnur
wyaroebs.
ilustraciebze da/an bunebaSi amoicnobs sinaTlis da siTbos bunebriv da xelovnur wyaroebs;
gakveTilis mizani:
dRis sxvadasxva monakveTSi Crdilis mdebareobis CaniSvna.mzis mdebareobis cvlilebaze dakvirveba.Crdilis mdebareobis cvlilebisa da mzis moZraobis erTmaneTTan dakavSireba.
Temis Seswavlas eTmoba ori gakveTili:
saWiro masala:
moswavleTa wyvilebisaTvis: carci
moswavleTa jgufebisaTvis: danarTiN#1
gakveTilis dagegmvasTan dakavSirebuli rekomendaciebi:
gakveTilebi unda Catardes mzian amindSi.SearCieT ezoSi iseTi adgili, sadac SesaZlebeli iqneba miwaze an asfaltze carciT
xatva.I gakveTili tardeba diliT, roca mze axal amosulia da sxivebi dedamiwis zedapirs
iribad ecema.II gakveTili tardeba SuadReze, roca mze zenitSi gadainacvlebs da sxivebi dedamiwisadmi
marTobulad iqneba mimarTuli.
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I gakveTili
1. gakveTilis dasawyisSi dausviT moswavleebs kiTxvebi:
moswavleebs saSualeba mieciT daaxasiaTon mze.
moswavleebma unda gamoTqvan varaudebi. am SekiTxvaze pasuxs moswavleebi aqtivobis dasasruls miiReben.2. kiTxvebze pasuxis Semdeg moswavleebi dayaviT
wyvilebad da gaiyvaneT ezoSi.
wyvilebs mieciT davaleba:,,Tqvengan erT-erTi moswavle dadges gaunZrevlad.
meore moswavlem ki carciT Semoxazos pirveli moswavlis terfebi da miwaze dacemuli Crdili. Semoxazul Crdilze im moswavlis saxeli daawereT, visi Crdilic Semoixaza. amis Semdeg gacvaleT rolebi. yuradReba miaqcieT, rom mze Tqvengan marcxena mxares iyos.“
mieciT TiToeul wyvils carci. daayeneT moswavleebi ise, rom mzis sxivebi maT marcxnidan ecemodes. amasTan, moswavleebs Soris manZili ganmklavze mcire ar unda iyos.
3. mas Semdeg, rac wyvilebi Seasruleben samuSaos, dasviT kiTxvebi:
Tqvengan romel mxares aris mze? Tqvengan romel mxares aris Crdili?zogierTma moswavlem SeiZleba daasaxelos marcxena/marjvena, zogma SeiZleba aswios
is xeli, romlis mimarTulebis Cvenebac undoda.
4. dabrundiT saklaso oTaxSi. sTxoveT moswavleebs Caawyon carci yuTSi.
mieciT davaleba: ,,daxateT, rogor gamoiyureboda Tqveni mewyvilis Crdili, ras miamsgavseT?“
samuSaos dasrulebis Semdeg TiToeuli moswavle adgilidanve aCvenebs namuSevars mTel klass da ambobs, Tu ras miamsgavsa Crdili.
II gakveTili
1. SuadReze moswavleebi gaiyvaneT ezoSi imave adgilas, sadac dilas iyvnen. wyvilebma
moZebnon sakuTari namuSevari. yoveli moswavle dadges sakuTari terfebis
Semoxazul adgilas zustad ise, rogorc diliT.
SekiTxva: Tqvengan romel mxares aris axla mze?
am periodisaTvis, savaraudod, mze zenitSi iqneba, TiTqmis moswavleebis Tavze.
2. wyvilebs igive davaleba mieciT:
,,Tqvengan erT-erTi moswavle dadges gaunZrevlad. meore moswavlem carciT Semoxazos pirveli moswavlis terfebi da miwaze dacemuli Crdili. Semoxazul Crdilze daawereT im moswavlis saxeli, visi Crdilic Semoixaza. amis Semdeg gacvaleT rolebi.“
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3. mas Semdeg, rac wyvilebi Seasruleben samuSaos,
dasviT kiTxvebi:
ra daemarTa Tqvens Crdils?savaraudod moswavleebi upasuxeben, rom Crdilebi
Seicvala.erTmaneTis msgavsia Tu ara es ori Crdili?riT gansxvavdeba isini erTmaneTisagan?savaraudod moswavleebi aRniSnaven: isini sxvadasxva
adgilasaa; gansxvavdebian formiT; erTi ufro grZelia meoreze.
savaraudod, Crdilebs aseTi forma eqnebaT
4. dabrundiT saklaso oTaxSi. sTxoveT moswavleebs Caawon carci yuTSi.
mieciT davaleba: ,,naxats daamateT, Tu rogor gamoiyureboda Tqveni mewyvilis Crdili SuadReze.”
5. dasviT kiTxvebi gakveTilis SejamebisaTvis:
Crdilebis garda kidev ra Seicvala I da II gasvlas Soris?moswavleebma unda upasuxon, rom Crdilebis garda Seicvala mzis mdebareoba.Tu moswavleebs gauWirdaT swori pasuxis gacema, dasviTdamatebiTi kiTxvebi:Tqvengan romel mxares iyo mze pirveli gasvlisas? meore gasvlisas?rogor fiqrobT ratom Seicvala forma Crdilma?moswavleebma unda SeZlon Crdilis formisa da mdebareobis cvlilebis mzis mdebareobis
cvlilebasTan dakavSireba.moswavleebi amowmeben, ramdenad gamarTlda maTi varaudi.
6. Semajamebeli etapi:
dayaviT klasi jgufebad. daurigeT jgufebs samuSao furclebi da sTxoveT moswavleebs, moniSnon is ori naxati, romelzec biWis Crdilebi erTnairi iqneba. (swori pasuxia pirveli da bolo suraTebi)
7. pasuxebis Ziebisas moswavleebs SeiZleba Crdilebis daxatva dasWirdeT.
mas Semdeg, rac moswavleebi daasruleben samuSaos, dausviT kiTxvebi imis gasarkvevad, Tu ra msjelobiT mividnen jgufebi gadawyvetilebamde.
I da II gakveTilis Sefaseba
am gakveTilis Catarebisas maswavlebeli SeiZleba mraval komponents daakvirdes. kerZod, ramdenad yuradRebiT usmenen moswavleebi instruqcias da SeuZliaT Tu ara am instruqciis realizeba; ramdenad organizebuli arian da ezoSi gasvlisas maTi yuradReba ifanteba Tu ara sxvadasxva obieqtze; ramdenad kolegialuria moswavle wyvilSi muSaobisas; ramdenad sworad iyenebs terminebs: ,,bunebrivi sinaTlis wyaro”, ,,mze”, ,,Crdili” da sxva. gakveTili Zalian kargia imis Sesamowmeblad, Tu ramdenad esmiT moswavleebs mimarTebebi da SeuZliaT Tu ara maTi gamoyeneba sxvadasxva obieqtebis mdebareobis gansazRvrisas.
Tu Cven davubrundebiT gakveTilis mizans, iq mkafiodaa Camoyalibebuli sami punqti. maswavlebelma unda Seafasos, Tu ramdenad gaiyvana moswavleebi im Sedegebze, rac dasaxuli hqonda.
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ezoSi gasvliTi aqtivobebis identurobis gamo aqtivobebis Sefaseba erTi da imave kriteriumebiT SeiZleba:
Crdilis mdebareobis CaniSvna;mzis mdebareobis cvlilebaze dakvirveba;mimarTebebis floba.
maswavlebelma CaniSvnebi SeiZleba Semdegi saxiT awarmoos:
Crdilis mdebareo-bis CaniSvna
mzis mdebareobis cvlilebaze dak-virveba
mimarTebebis-
qvemoT) floba
rekomendaciebi
-lis konturs da xazs zustad mihyveba
mzesTan akav-Sirebs sinaTles
gadanacvlebas
mimarTebebis
misaTiTebladiyenebs terminebs, maSin roca mar-
misaniSnebladxeliT miuTiTebs mimarTulebebsda iZaxis _ iqiT aqeT.
marcxniv mimarTebe-bze muSaoba
Crdilis konturs zustad mihyveba. Crdils sakuTari SexedulebiTumatebs Tvalebs,
-won sxva detalebs
- mimarTebiTterminebs saer-Tod ar iyenebs, magram sworad miuTiTebs mimar-Tulebebs xeliT.
-atebiTi svarjiSo, romelic aCvenebs anas sinaTlis wy-aros moZraobas. es SeiZleba gakeTdes naTuris modelze. mimarTebiTi ter-minebis dauflebaze aris samuSao
mihyveba Crdilis konturs. xSirad aqvs acdenebi xazi-dan, magram Tavad asworebs. uyurebs megobrebis namuSe-vars, rom darw-mundes sakuTar sisworeSi
ar gamoxatavs
sanam sxvebi ar ityvian versiebs
mimarTebiT ter-minebs sworad
mimarTulebismisaniSneblad
ninos aklia TviT-dajerebuloba,amisaTvis, klasis winaSe iseTi na-muSevris wardgena unda SevTavazoT, romelic namdvilad kargad gamosdis.
saerTod ver mi-hyveba Crdilis konturs. mis mier Semoxazuli obieqti ar hgavs Crdilis konturs, rac mew-yvilis garkveul wyenas iwvevs. amis gamo davexmare naxa-zis SesrulebaSi
mzes, rogorc sinaTlis wyaros
_ iZaxis ,,mzeze bnela da cxela“, samagierod zus-
mzis gadaadgile-bas. asabuTebs
da mohyavs mag-aliTebi
kargad erkveva mimarTebebSi.sworad gansaz-
-Tulebebs, iyenebs terminebs
motoruli unarebis gansaviTarebelisamuSaoebi unda da-vugegmo
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Semajamebeli etapis Sefaseba
es davaleba saSualebas iZleva vnaxoT, ramdenad SeZles moswavleebma Crdilis mdebareobis cvlilebisa da mzis moZraobis erTmaneTTan dakavSireba. savarjiSo moswavleebisagan naxatze warmodgenili situaciebis analizs moiTxovs.
Zalian mniSvnelovania yuradReba miaqcioT, Tu ra logikiT xelmZRvanelobdnen moswavleebi gadawyvetilebis miRebisas.
# 1 jgufis namuSevari
jgufis pasuxi: ,,pirveli da bolo suraTebi erTnairia”
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pasuxi sworia, magram moswavleebi ver asabuTeben mas imiT, rom mze orive suraTze erTsa da imave mdebareobaSia, ris gamoc biWis Crdilic erTnairi iqneba. dausviT kiTxvebi, romlebic moswavleebs logikur msvlelobas daanaxeben.
#2 jgufis namuSevari
jgufis pasuxi: ,,pirvel da meore suraTebze Crdili iqneba erTnairi, radganac mze
orive suraTze naxatis kuTxeSia da Crdili erTnairi formis iqneba”
pasuxi arasworia, magram moswavleebi cdiloben argumentis moyvanas. maTi pasuxis is nawili, rom ,,Crdili forma erTnairia“, sruliad marTebulia. am SemTxvevaSi gansxvavebuli iqneba Crdilis mdebareoba biWis mimarT. savaraudod, jgufma naxatebi bolomde ar ganixila da arCeul variantze SeCerda. am situaciaSi maswavlebelma unda sTxovos moswavleebs TviTSefasebas, Tu ras fiqroben, ratom mouvidaT maT es uzustoba da urCios SemdgomSi, vidre gadawyvetilebas, miiReben samuSaos yvela nawili bolomde ganixilon.
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damatebiTi informacia maswavleblisaTvis
sinaTlis wyaros mdebareobis nebismieri cvlileba Crdilis cvlilebasac iwvevs. am dros icvleba Crdilis forma, zoma da mdebareoba. am aqtivobaSi mze sinaTlis wyarod iqneba gamoyenebuli.
mze aris varskvlavi, romlis garSemoc orbitaze moZraobs dedamiwa. dedamiwis RerZisa da mzes Soris poziciis cvlileba iwvevs Crdilis cvlilebas.
am aqtivobis Catarebis dros moswavleebma SeiZleba Tqvan, rom mze dedamiwis garSemo moZraobs. am SemTxvevaSi, moswavleTa asakidan gamomdinare, Tqven SegiZliaT uTxraT maT, rom sinamdvileSi dedamiwa moZraobs mzis garSemo, magram ar girCevT am sakiTxis detalurad garCevas.
rogorc aRvniSneT, Crdili SeiZleba icvlebodes Semdegi parametrebis mixedviT: forma, zoma da mdebareoba. am aqtivobis mizania moswavleebma aRmoaCinon mxolod es faqtebi, xolo am cvlilebebis gamomwvev mizezebTan dakavSirebul sakiTxebs isini momdevno klasebSi gaecnobian.
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V I I k l a s i
aqtivobis nimuSebi
aqtivoba 1
biologia
mizani: dakvirveba da Sesabamisi monacemebis mogroveba.
Tema: organizmTa mravalferovneba (organizmebis aRwera)
am aqtivobis mizania, davanaxoT moswavleebs gansxvaveba aRwerilobiT teqstebs Soris da davexmaroT Camoayalibon mecnieruli aRwerilobiTi teqstebis Taviseburebebi.
maswavlebeli wyvilebs urigebs sxvadasxva stiliT dawerili cxovelebis aRwerilobiTi teqstis ramdenime nimuSs _ danarTi #1.
moswavleebma unda amoicnon, romel teqstSi romel organizmzea saubari.(pasuxebi: 1. vazis lokokina; 2. daTvi; 3. kalia)es aris sxvadasxva stilis teqstebi, magram samive maTgani cxovelebis aRweras
emsaxureba.vaCvenoT gansxvaveba am teqstebs Soris.
ra cxovelebzea saubari?ra msgavsebaa am teqstebs Soris?ra gansxvavebaa maT Soris?romeli teqstis mixedviT amoicaniT cxoveli ufro advilad?
ratom.?kidev rogor aRwerilobiT teqstebs gaixsenebT?
adamianebi saukuneebis manZilze aRweren cocxal bunebas, magram aRweris mecnieruli meTodi eyrdnoba faqtebs da garkveuli sistemiT aris mowesrigebuli.
Tqveni azriT, rogor unda iyos organizebuli mecnieruli aRwerilobiTi teqstebi.romeli monacemebia (dakvirvebis Sedegebi) mniSvnelovani organizmebis aRwerisas;rogor CaviniSnoT aRwerebi (mag., kidurebis raodenoba, sxeulis feri an sxva.)
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1. ,,muclis mxareze ganieri kunTovani fexi aqvs. Tavze ori wyvili saceci aqvs.
sacecebis ufro mokle wyvili ynosvisa da Sexebis organoa. sacecebis ufro
grZeli wyvili mxedvelobis organoa. upiratesad Ramis cxovelia: dRisiT
mzis Suqs erideba. gadaadgildeba xoxviT. mcenareebiT ikvebeba. araxelsayrel
pirobebSi sxeuls niJaraSi malavs, xolo xvrelze gadaikravs apks. zamTars
ZilSi atarebs.”
pasuxi: . . . . . . . . .
2. `saqarTveloSi misi ricxovnoba TandaTan klebulobs, risi mizezic ukontrolo
nadiroba da sabinadro garemos ganadgurebaa. igi saqarTveloSi mobinadre
yvelaze msxvili mtacebelia. Cvens pirobebSi am cxovelis wona 150-250
kilogramia. upiratesad mcenareuli sakvebiT ikvebeba, magram mis racionSi
cxoveluri warmoSobis produqtic Sedis.~
pasuxi: . . . . . . . . .
3. ,,es mavnebeli mweri didxans ar cocxlobs. oTxi kviris Semdeg poulobs
udabur adgils, miwaSi kvercxebs debs da kvdeba. daxocili . . . Cinebuli
sasuqia miwisaTvis. amas garda, bevr qveyanaSi moxrakuli . . . mcxovrebTa
sayvareli saWmelia. ise moswonT es kerZi, rom am dros yvela sxva sakvebi
iafdeba.”
pasuxi: . . . . . . . . .
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aqtivoba 2
biologia
mizani: aRwerilobiTi Cvevebis gamomuSaveba.
mimdinareoba: maswavlebeli TiToeul moswavles urigebs danarTs #1 da acnobs
davalebis pirobas:
dawereT am organizmebidan erT-erTis mokle aRwerilobiTi teqsti(miaxloebiT 50 sityviani) da aCveneT Tqvens mewyviles. sainteresoa, mixvdeba Tu ara
is, romel organizmzea saubari.
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aqtivoba 3
qimia
Tema: nivTierebaTa agregatuli mdgomareoba
mizani:gamoikvlion nivTierebaTa agregatuli mdgomareoba.
arsebul codnaze dayrdnobiT axsnan da ganmarton dakvirvebisa da gazomvis Sedegebi da gaakeTon daskvna.
2. dahyon nivTierebebi myar, Txevad da gazisebr nivTierebebad da daasabuTon TavianTi mosazreba.
saWiro masala 1: danarTi #1 - jgufebis Sesabamisi raodenobiT; formati cxriliT
#1, formati cxriliT #2, markerebi, dafa, carci
saWiro masala 2: danarTi #2, 3 Sprici, qviSa da wyali _ jgufebis Sesabamisi
raodenobiT
mosalodneli Sedegebi:yvela moswavlem unda SeZlos aRweros dakvirvebis Sedegebi da scados maTi axsna. agreTve, unda SeZlos nivTierebebis dayofa myar nivTierebebad, siTxeebad da gazebad.moswavleTa umravlesobam unda SeZlos axsnas, ris safuZvelze dahyo nivTierebebi amgvarad.moswavleTa nawilma siTxeebis, gazebisa da myari nivTierebebis Sesaxeb sakuTari warmodgenis safuZvelze unda SeZlos axsnas, ra iwvevs maT Soris gansxvavebas.
dasawyisi :
moswavleebs veubnebiT, rom Cveni mizania, maT SeZlon siTxeebs, airebsa da myar nivTierebebs Soris gansxvavebis aRwera.
aqtivoba I: nivTierebaTa agregatuli mdgomareobis gansazRvra
moswavleebi muSaoben jgufebSi, TiToeul jgufs urigdeba danarTi #1.
moswavleebs evalebaT, gaanawilon CamoTvlili 20 nivTiereba Sesabamis grafebSi (aRniSnon ujra) _ myari, Txevadi, airadi. maT unda miiRon saerTo gadawyvetileba da daasabuTon TavianTi mosazreba.
jgufebma unda warmoadginon TavianTi namuSevrebi. eTanxmebian Tu ara isini erTmaneTs? maT unda daasabuTon sakuTari mosazrebebi, Seajeron isini da erToblivi daskvna gamoitanon, rac aisaxeba dafaze an formatze cxriliT #1.
klasi msjelobs _ cdilobs, gansazRvros is ZiriTadi Tvisebebi, romlebic axasiaTebs TiToeul nivTierebas mocemul agregatul mdgomareobaSi. gonebrivi ieriSis safuZvelze vavsebT cxrils #2 formatze.
cxrili #2
myari Txevadi airadi
1.
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aqtivoba II _ dguSis gadaadgileba SpricSi
samuSao sruldeba jgufurad. TiToeul jgufs urigdeba sam-sami Sprici, qviSa, wyali da danarTi #2.
moswavleebi sami Spricidan erTs avseben haeriT, meores _ qviSiT, mesames _ wyliT. isini Spricis wvers mWidrod afareben TiTs da cdiloben dguSis gadaadgilebas yovel maTganSi. moswavleebi akvirdebian, romel SpricSi ufro iolia dguSis gadaadgileba anu ramdenad iolia TiToeuli nivTierebis SekumSva? moswavleebi iniSnaven da xsnian dakvirvebis Sedegebs.
yoveli jgufi warmoadgens Tavis mosazrebebs, Seajereben da akeTeben erTobliv daskvnas.
cxrili #1
masala myari Txevadi airadi safuZveli
haeri
alumini
orTqli
vaJini
wyali
marili
cementi
grafiti
koka-kola
wyalbadi
qviSa
qva
nayini
rZe
gamdnari nayini
s abu ne bi smetyv elo me c ni er eb e bi
310
dguSis gadaadgileba SpricSi
sami Spricidan erTi aavseT haeriT, meore _ qviSiT, mesame _ wyliT. scadeT dguSis gadaadgileba yovel maTganSi. romel SpricSi ufro advilad gadaadgildeba dguSi anu ramdenad iolia TiToeuli nivTierebis SekumSva? CainiSneT da axseniT dakvirvebis Sedegebi.
Sedegebis axsna
ramdenad iolad axsna
haeri
wyali
qviSa
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aqtivoba 4
fizika
mizani: dakvirvebis, monacemebis aRricxvis da maTi interpretaciis unar-Cvevebis
ganviTareba; xaxunis Zalis Semcirebisa an gazrdisaTvis konkretuli problemis
gadaWra.
Tema: xaxunis Zala da misi moqmedebis Sedegebi
gakveTilisaTvis saWiroa:
magida, xis Zelaki, dinamometri, qsovili (magidaze gadasafareblad), wyali (mag.
mimdinareoba :
Sesavali 5 wT
maswavlebeli ganmartavs gakveTilis mizans.moswavleebis winaSe dgeba amocana:
gamoikvlion, Tu rogoraa damokidebuli sxeulis srialisas aRZruli xaxunis Zala am sxeulisa da zedapiris masalis gvarobaze;dasaxon gzebi aRZruli xaxunis Zalis Sesamcireblad, an gasazrdelad;
eqsperimenti 30 wT
muSaoba jgufebSi: TiTo jgufSi 4-5 moswavle.
moswavleebi CamoTvlian im xelsawyoebsa da sagnebs, romlebsac gamoiyeneben eqsperimentis dros:
xis Zelakidinamometrimagida
moswavleebi akvirdebian xis Zelakis srials (xis Zelaks gamodeben dinamometrs da akvirdebian mis Cvenebas):
magidis priala zedapirze,rodesac magidaze qsovilia gadafarebuliZelakis srials sveli magidis zedapirze
aRweren process, adgenen cxrils da monacemebi SeaqvT cxrilSi (cxrils xazaven dafaze)
Zalis sidide
1
2 magidaze qsovilia gadafarebuli
3
I jg. IIjg.
IIIjg.
IVjg.
#jg.
saS.
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dafaze xataven Zelaks da maswavlebeli moswavleebTan erTad miuTiTebs xaxunis Zalis mimarTulebaze.
klasSi xdeba azrTa gacvla-gamocvla, cxrilis analizi da keTdeba Sesabamisi daskvnebi xaxunis Zalis Semcirebis an gazrdis mizezebis Sesaxeb.
ganzogadeba 5wTmaswavlebeli urigebs moswavleebs formula 1-is manqanis suraTebs (danarTi #1) da
ekiTxeba:romeli saburavi gamoiyeneba sisvelisa (rodesac wvims) da romeli simSralis (rodesac kargi amindia) dros?
saSinao davaleba:
axseniT werilobiT, formula 1-is romel saburavs aqvs meti moWiduloba? ratom?
313
V I I I k l a s i
gakveTilis scenaris da aqtivobis nimuSebi
aqtivoba
qimia
bun.VIII. 10. _ amzadebs mcenareul nayenebs da ikvlevs maT SesaZlo indikatorul
Tvisebebs. Sedegebs cxrilis saxiT warmoadgens.
gakveTilis mizani: Warxlis indikatoruli Tvisebebis eqsperimentuli gamokvleva.
mimdinareoba: ,,_ ra Tvisebas unda akmayofilebdes nivTiereba, rom SesaZlebeli iyos
misi indikatorad gamoyeneba? _kvlevis safuZvelze davadginoT, ramdenad
akmayofilebs am moTxovnas Warxali.”
aqtivoba:
Warxlis indikatoruli Tvisebebis eqsperimentuli kvleva mJavas, fuZisa da neitraluri xsnarebis gamoyenebiT.
aRWurviloba:
erTi Zirxveni Warxali;bostneulis saxexi;qvabi iseTi raodenobis wyliT, romelic gaxexili Warxlis dasafaradaa saWiro;sawuri bade;mJavas da fuZis xsnari. (mJavad egiZliaT gamoiyenoT Zmari, fuZed ki _ wyalSi gaxsnili romelime detergenti/sarecxi saSualeba);qimiuri Wiqa an jami;qura.
eqsperimentis Catarebis wesi
gaxexili Warxali moaTavseT wylian qvabSi;Warxali xarSeT 20-30 wuTis ganmavlobaSi, vidre xsnari muq wiTel Seferilobas ar miiRebs;sawuris saSualebiT siTxe, WiqaSi an jamze gadmowureT;moamzadeT, romelime mJava/fuZe xsnari. (mag. TeTri Zmari, gaziani wyali an spirti, limonis an forToxlis ganzavebuli wveni);fuZe xsnaris dasamzadeblad SegiZliaT wyalSi romelime sarecxi saSualeba/detergenti gaxsnaT, an wyals natriumis bikarbonati (sasmeli soda) daamatoT. saWiroa sakontrolo xsnari an (neitraluri) wyali. sasurvelia gamoxdili wylis gamoyeneba;CaasxiT WiqaSi indikatori da mcire ulufebiT daamateT sakvlevi xsnari. yoveli ulufis damatebis Semdeg mourieT da daakvirdiT, Seicvlis Tu ara indikatori fers. yoveli cdisTvis gamoiyeneT sufTa Wiqa/jami da kovzi.
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6.7.
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3.4.
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SeniSvna: instruqciis Sesabamisad SesaZlebelia romelime sxva xilis an bostneulis
wvenis indikatoruli Tvisebebis kvleva.
monacemebis aRricxva
yovel cdaze dakvirvebis Sedegebi SeitaneT cxrilSi.
nivTiereba
indikatori
mJava fuZe neitraluri(sakontrolo
xsnari)
Joloswveni
mayvlis wveni
gakveTilis scenari
fizika
msoflio mizidulobis Zala
kavSiri standartTan:
mimarTuleba: fizikuri movlenebi
bun.VIII. 6. moswavle aRwers sxeulTa moZraobas da urTierTqmedebebs
akvirdeba da axasiaTebs gravitaciuli Zalis moqmedebas. mohyavs msoflio mizidulobis Zalis gamovlenis magaliTebi;gamoTqvams varauds dedamiwis mizidulobis Zalis SemcirebiT gamowveuli cvlilebebis Sesaxeb da agrovebs informacias varaudis Sesamowmeblad.
gakveTilis miznebi:
kvleviTi unar-Cvevebis ganviTareba eqsperimentis magaliTze;gravitaciis Zalis Seswavla, haeris winaaRmdegobis gavlena sxeulTa vardnaze;informaciis moZiebis unar-Cvevis ganviTareba;diskusiis warmarTva msoflio mizidulobis kanonis ganzogadebis magaliTze.
Temis Seswavlas eTmoba ori gakveTili:
I gakveTili - eqsperimenti
II gakveTili - diskusia
1.2.3.4.
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saWiro masala:
enciklopediuri xasiaTis literatura, an internetSi CarTuli kompiuteri TiToeuli jgufisaTvis;saganTa wyvilebi, rogoricaa magaliTad sxvadasxva zomisa da wonis burTebi, an wigni da muyaos qaRaldi, romelTa zomebi (sigrZe, sigane da sisqe) erTnairia;sagnebi, rogoricaa bumbuli da qaRaldis furceli, romlisTvisac haeris winaaRmdegoba vardnisas didia, vidre sxva sagnebisaTvis.wammzomiani saaTi.
komentari:
wina dRes moswavleebs unda mieceT davaleba moiZion informacia:mzis sistemis planetebis, maTi zomebis Sesaxeb;msoflio mizidulobis kanonis aRmoCenis Sesaxeb. gaecnon galileo galileis, niutonisa da kavendiSis eqsperimentebs.
es saSinao davaleba ganixileba II gakveTilze, I gakveTilze ki moswavleebi gamoiyeneben moZiebul masalas eqsperimentis sworad dasagegmad da gansaxorcieleblad.
I gakveTili
eqsperimenti
procedura:
gakveTilis dasawyisSi sTxoveT moswavleebs gamoTqvan varaudi: iqneba Tu ara gansxvaveba mZime, didi sagnebisa da msubuqi, patara sagnebis vardnis xangrZlivobaSi, Tu maT raime simaRlidan xels gavuSvebT?dayaviT klasi jgufebad, da mieciT TiToeul jgufs sxvadasxva sagnebi eqsperimentisaTvis;mieciT jgufebs instruqcia, raTa dagegmon eqsperimenti mizidulobis Zalis Sesaswavlad. gaaxseneT, rom eqsperiments yuradReba da mobilizeba Wirdeba da masSi mxolod erTi cvladi unda daikvirvebodes. TiToeul jgufs unda hqondes furceli, sadac aRricxavs gazomvis Sedegebs (maswavlebels SeuZlia SesTavazos cxrilis Sedgena);jgufebi atareben eqsperiments sxvadasxva saganTa wyvilebiT, jgufis erT-erTi moswavle dgas skamze an raime simaRleze da xels uSvebs sagnebs. jgufis danarCeni moswavleebi akvirdebian, romeli sxeuli miaRwevs iataks pirveli, Tu orive sxeuli miaRwevs erTdroulad. moswavleebma zustad unda aRricxon TavianTi Sedegebi. amisaTvis isini CainiSnaven TiToeuli sagnisTvis vardnis dros (moswavleebma unda aRmoaCinon, rom sxvadasxva zomisa da masis burTebi erTi da igive siCqariT vardebian, da erTdroulad daecemian, aseve wigni da igive zomis muyao); rodesac moswavleebi uSveben xels erTi da imave simaRlidan bumbuls da qaRaldis furcels, unda aRmoaCinon, rom bumbuli da qaRaldi vardeba ufro nela, vidre sxva sagnebi. SesTavazeT, rom maT qaRaldis furclebisagan gaakeTon burTi da gauSvan xeli igive simaRlidan. isini aRmoaCenen, rom qaRaldis burTi miaRwevs iataks ufro swrafad, vidre qaRaldis furceli;moswavleebi jgufebSi ganixilaven miRebuli Sedegebis SesaZlo mizezebs da gamoaqvT daskvna. (maT unda daaskvnan, rom haeris winaaRmdegoba anelebs bumbulis da qaRaldis furclis vardnas);
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2.
3.
4.
5.
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hkiTxeT moswavleebs, ras fiqroben isini, ra moxdeba, Tu igive eqsperiments vakuumis milSi Caatareben (bumbuli igive siCqariT daeSveba Zirs, rogorc burTi).gakveTilis bolos moswavleebs eZlevaT saSinao davaleba:
TiToeulma moswavlem unda daweros angariSi da axsnas eqsperimentis Sedegebi, gamoitanos daskvnebi, Tu ra zemoqmedebas axdens gravitacia da haeris winaaRmdegoba vardnili sxeulis aCqarebaze. urCieT moswavleebs dakvirvebis Sedegebi warmoadginon grafikebiT an diagramebiT.
Sefaseba
am gakveTilis msvlelobisas maswavlebeli unda daakvirdes moswavleebs, Tu ramdenad sworad gegmaven isini eqsperiments, ramdenad zustad da organizebulad atareben gazomvebs, ra formiT CainiSnaven miRebul Sedegebs.
qvemoT mocemulia Sefasebis rubrika, romelic SesaZloa maswavlebelma gamosaxos qulebis saxiT (gradacia mocemulia 4 etapad), an gamoiyenos, rogorc sityvieri komentari.
eqsperiments gegmavs sworad, gamsazRvravs specifikur detalebs, detalurad CamoTvlis kvlevis etapebs, ayalibebs da asabuTebs varauds, gazomvebs awarmoebs zustad, gazomvebis Canaweri kargad organizebulia (8-10).eqsperiments gegmavs sworad, Tumca mciredi uzustobebiT, damakmayofileblad CamoTvlis kvlevis etapebs, ayalibebs da nawilobriv asabuTebs Tavis varauds, gazomvebs awarmoebs kargad, Sedegebi aRricxulia damakmayofileblad, Tumca Canawerebi nakleb organizebulia (6-7);eqsperiments gegmavs arazustad, garkveuli xarvezebiT, arasworad CamoTvlis kvlevis etapebs, ayalibebs, magram ver asabuTebs Tavis varauds, gazomvebs awarmoebs arazustad, aRricxavs monacemebs nawilobriv, Sedegebis gadmocema zedapirulia da arazusti, Canawerebi sustadaa organizebuli (4-5);eqsperiments gegmavs arasworad, arasworad CamoTvlis kvlevis etapebs, arasworad ayalibebs varauds, aRricxavs araswor monacemebs, Sedegebs gadmoscems arazustad, Canawerebi qaosuria da usistemo (1-3).
gTavazobT sityvieri komentaris magaliTs:nino, Sens mier dagegmili eqsperimenti zustia da Tanmimdevruli, sworad gaqvs
logikuria, sworad warmarTav msjelobas. gazomvebic zustad gaqvs Sesrulebuli, Canaweri organizebulia, naTlad ikiTxeba eqsperimentis Sedegi. yoCaR, Seni naweri umaRles Sefasebas imsaxurebs.Tamar, girCev yuradReba miaqcio eqsperimentis dagegmvas, ar ikiTxeba proceduris Tanmimdevroba, ramac gavlena iqonia mis Sedegze. Tumca SemdgomSi kvleva kargad warmarTe. varaudis dasabuTebisas meti argumentebis moyvana SegeZlo. Sedegebs kargad aRricxav, Tumca saboloo Canawerebis gaformebisas girCev ukeTesi forma SearCio, raTa advilad ikiTxebodes Seni naweri. imedi maqvs, SemdegSi ukeTes namuSevars waradgen;oTar, girCev momavalSi ufro zustad dagegmo eqsperimenti, raTa mosalodneli Sedegi miiRo. kvlevisas mniSvnelovani yuradReba unda miaqcio, Tu romeli sagnebis vardnis dros adareb erTmaneTs. aseve varaudis dasabuTebisas girCev saTanado argumentebi moiyvano. yuradReba miaqcie Canawerebis gaformebas. imedi maqvs, momavalSi gaiTvaliswineb yvela rekomendacias. amJamad Seni muSaoba damakmayofilebel Sefasebas imsaxurebs.
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lela, girCev meti yuradRebiT moekido eqsperimentis etapebis dagegmvas, raTa SesaZlebeli iyos Sesabamisi Sedegebis miReba. aseve varaudis dasabuTebisas mniSvnelovania argumentirebuli msjeloba, romelzec Sen muSaoba mogiwevs. mniSvnelovania monacemebi aRricxo zustad, girCev yuradReba gaamaxvilo aseve maTi Caweris formaze, da daskvna saboloo saxiT naTlad Camoayalibo. momavalSi girCev meti pasuxismgeblobiT moekido samuSaos.
II gakveTili
komentari
gakveTilis dasawyisSi maswavlebeli ibarebs eqsperimentis angariSs TiToeuli moswavlisagan Semdgomi komentarisa da SefasebisaTvis.
diskusia
sadiskusiod dasviT Semdegi SekiTxvebi. moswavleebma diskusia I gakveTilis saSinao davalebisa (informaciis moZieba) da eqsperimentis Sedegebis analizis safuZvelze unda warmarTon.
aRwereT, rogoraa Seguebuli adamiani dedamiwis mizidulobas. ra moxdeboda, gravitacia rom ar yofiliyo?SeadareT da ganasxvaveT gravitacia dedamiwasa da mzis sistemis erT-erT planetaze. romel planetas aqvs yvelaze Zlieri gravitaciuli veli? ras ganicdian astronavtebi, Tu isini aRmoCndebian am planetaze xangrZlivi drois ganmavlobaSi?aRwere dedamiwis zedapiris mdgomareoba, romelic gamowveulia gravitaciuli ZalebiT misi formirebis periodSi, an am Zalebis moqmedebiT axla. ra cvlilebebi daikvirveba, Tu gravitaciis Zala mniSvnelovnad Zlieri, an susti iqneba?imsjele niutonis kanonebis Sesaxeb. romeli kanoni, an kanonebi exeba gravitaciis Zalas? moiyvane TiToeuli kanonis magaliTi Seni yoveldRiuri cxovrebidan;aRwere eqsperimentebi, romlebic Caatares galileo galileim, niutonma da kavendiSma gravitaciis Sesaswavlad. ra msgavseba iyo am eqsperimentebs Soris? rogor eyrdnoboda TiToeuli mecnieri sxvaTa kvlevebsa da dakvirvebebs, raTa gaekeTebina Tavisi aRmoCenebi?
Sefaseba
am gakveTilze maswavlebeli afasebs weriT saSinao davalebas da diskusias.
saSinao davalebis _ eqperimentis angariSis Sefaseba:
akeTebs monacemTa zust analizs, Sedegebi warmodgenilia grafikebis, an diagramebis saxiT. daskvnebi Camoyalibebulia logikurad da kargad organizebulia Canaweris saxiT;akeTebs monacemTa analizs, Sedegebi adeqvaturadaa gadmocemuli, moicavs ilustraciebs an diagramebs, akeTebs ZiriTad daskvnebs, magram Canaweri daxvewas saWiroebs;akeTebs monacemTa nawilobriv analizs, warmodgenilia grafikebi an diagramebi, magram arazustad, akeTebs nawilobriv swor daskvnebs, magram ver asabuTebs maT, darRveulia logikuroba. Canawerebi usistemod aqvs warmodgenili;ver akeTebs monacemTa swor analizs, warmodgenili grafikebi arasworad asaxavs process, daskvnebi arazustia, Canawerebi qaosuradaa warmodgenili.
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diskusiis Sefaseba:
gamoiyena mravalferovani sainformacio saSualebebi, moiZia damatebiTi masala da efeqturad gadmoscems mas. mosazrebebs ayalibebs Tanmimdevrulad, logikurad akeTebs daskvnebs da asabuTebs Tavis mosazrebebs, yuradRebiT usmens Tanatolebs da afasebs sxvaTa mosazrebebs;gamoiyena mxolod ramdenime informaciis wyaro, cdilobs mosazrebebi Camoayalibos sainteresod, gamarTulad, akeTebs daskvnebs, Tumca nawilobriv asabuTebs Tavis mosazrebebs, afasebs sxvaTa mosazrebebs;gamoiyena mxolod saxelmZRvaneloSi mocemuli informacia, uWirs masalis gadmocema, daskvnebi aralogikuria, cdilobs daasabuTos sakuTari mosazrebebi, usmens Tanaklaselebs.gamoiyena mxolod sakuTari informacia, diskusiaSi TiTqmis ar monawileobs, uWirs sakuTari mosazrebebis gadmocema da daskvnebis gamotana.
zemoT mocemuli Sefasebis rubrikebi SesaZloa maswavlebelma gamosaxos qulebis saxiT (gradacia mocemulia 4 etapad), an gamoiyenos, rogorc sityvieri komentari, rogorc I gakveTilis nimuSSia mocemuli).
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X k l a s i
aqtivobis nimuSebi
gakveTilis scenari
fizika
mizani: dakvirvebis, aRweris, aRricxvis, komunikaciis, hipoTezirebis, monacemebis
interpretaciis unar-Cvevebis ganviTareba
Tema: yinulis dnobis kuTri siTbos gamoTvla eqsperimentulad
gakveTili gaTvlilia Sewyvilebuli saaTisaTvis (95-100wT)maswavlebeli klass yofs jgufebad: TiToeul jgufSi 4-5 moswavle.
maswavleblis daxmarebiT gansazRvravs cdis mizans da Sesaswavl maxasiaTeblebs.maswavlebeli ganmartavs gakveTilis mizans: yinulis dnobis procesis Seswavla da
dnobis siTbos daTvla.klasSi etapobrivad, SekiTxvebiTa da pasuxebiT xdeba cdis dagegmva da gasazomi
sidideebis gansazRvra:rogoria Tqveni mosazreba, rogor SeviswavloT yinulis dnobis procesi?rogori temperaturis wyalTan umjobesia yinulis Sereva cdis swrafi mimdinareobisaTvis?Tvisebrivad aRwereT procesi, rodesac cxeli wyali da yinuli ereva erTmaneTs.ra sidideebis gansazRvra gvWirdeba wylis mier gacemuli da yinulis mier miRebuli siTbos raodenobis dasaTvlelad?rogor ganvsazRvroT wylisa da yinulis masa?rogoria yinulis dnobis temperatura?rogor ganvsazRvroT miRebuli narevis temperatura?
iyenebs miTiTebul xelsawyoebs raodenobrivi da TvisebiTi monacemebis mosapoveblad.asrulebs instruqcias da mihyveba dasaxul gegmas cdis dros:cdis Catarebisas icavs usafrTxoebis wesebs da racionalurad iyenebs drosa da resursebs.
cdis dawyebamde xdeba usafrTxoebis wesebis SemuSaveba: maswavlebelTan erTad saubarSi moswavleebi Tanxmdebian Semdeg wesebze:
cxeli WurWlis, an yinulis aRebisas iyeneben siTbogaumtar specialur xelTaTmanebs;racionalurad iyeneben dros, raTa yinulis dnobam ar SeuSalos xeli swori monacemebis miRebas;SesaZlebelia agreTve yuradRebis gamaxvileba Semdeg momentze: yinulis temperaturis SenarCunebisaTvis misi masis gansazRvra xdeba yinulian jamSi.moswavleebi aduReben wyals maduRaris daxmarebiT, romlis masas winaswar gansazRvraven (WiqaSi asxamen wyals menzuris saSualebiT).sasworis saSualebiT gansazRvraven yinulis masas;
1.2.
3.4.
5.6.7.
1.
2.
s abu ne bi smetyv elo me c ni er eb e bi
320
Semdeg awonil yinuls aTavseben aduRebul wyalSi da misi srulad gadnobis Semdeg Termometris saSualebiT zomaven narevis temperturas.
aRricxul raodenobriv monacemebs gamosaxavs maswavleblis miTiTebul erTeulebSi:
yinulisa da wylis masas gansazRvraven kilogramebSi, temperaturas gradusebSi
cdis monacemebi Seaqvs gamzadebul cxrilSi
maswavlebeli agrZelebs gamokiTxvas (erT-erTi moswavle gamodis dafasTan):dawereT siTbos raodenobis formula da gamoTvaleT wylis mier gacemuli da yinulis mier miRebuli siTbos raodenoba;dawereT siTburi balansis gantoleba aRniSnuli procesisaTvismaswavlebeli ganmartavs yinulis dnobisTvis saWiro siTbos raodenobas, Semdeg ki dnobis kuTr siTbos, gamohyavs misi erTeuli.
mis mier Catarebuli cdis monacemebs adarebs Tanaklaselebisas da poulobs msgavseba-gansxvavebas
(dafaze iwereba jgufebis monacemebi da xdeba Sedareba)
saSinao davaleba:
cdis msvlelobas aRwers saTanado terminologiiTmaswavlebeli aZlevs saSinao davalebas: aRweron Catarebuli cdis msvleloba
Tanmimdevrulad werilobiT da gamoiyenon Sesabamisi terminologia:(kuTri siTbotevadoba, dnobis temperatura, narevis sawyisi da saboloo temperatura,
dnobis kuTri siTbo)
wylismasa(kg)m1
wylissawyi-si tem-
-tura(grad)t1
yinu-lismasa(kg)m
2
wylissab-oloo
-atura(grad)t2
1
kj2
kj3
kjdnobiskuTrisiTbo
dnobiskuTrisiTbossaS.mniSv
SeniS-vna
3.
1.
2.3.
321
aduRebuli wylis mier gacemuli siTbos raodenoba -- 1 1 1
- t2
yinulis dnobis Sedegad miRebuli wylis t2 gradusamde gasaTbobad saWiro siTbos raodenoba -- 2 2 2
siTburi balansis gantoleba 1 2 3
sadac3yinulis dnobisaTvis saWiro
siTbos raodenobaaQ
aqtivoba
biologia _ dakvirveba daobebaze
standarTan kavSiri:
bun.X 6.
uSualo dakvirvebiT da/an eqsperimentulad swavlobs mikroorganizmebis (mag. virusi, baqteria, safuari soko) cxovelqmedebis gamovlinebebs (mag. produqtis damJaveba, daduReba, comis afueba,zogierTi virusuli daavadeba), ajgufebs maT adamianisTvis sasargeblo an saziano moqmedebis mixedviT da warmoadgens dakvirvebis Sedegebs.
saWiro masala: TiToeuli jgufisaTvis: puri (an mWadi an moxarSuli brinji), wyali,
oTxi celofnis parki.
rekomendacia: warmodgenil aqtivobas win unda uswrebdes mikroorganizmebis, kerZod
obis sokos gacnoba.
mimdinareoba: samuSao sruldeba jgufebSi. TiToeul jgufs urigdeba danarTi #1,
eZlevaT davaleba, gamoTqvan varaudi, ra pirobebSi, (temperatura: siTbo/
sicive, tenianoba: nesti/simSrale) obdeba puri ufro swrafad. mosazrebebi
fiqsirdeba samuSao gverdze (danarTi #1).
varaudis Sesamowmeblad, CavataroT cda.
procedura:
1. puris Tanabari naWrebi gadaanawileT oTx parkSi2. danomreT parkebi 1, 2, 3, 43. parkSi #1 daumateT cota wyali da datoveT bnel adgilas oTaxis temperaturaze
(sinotive+siTbo)4. parki #2 daumateT cota wyali da CadeT macivarSi (sinotive+sicive)5. parki #3 Tavsdeba sibneleSi oTaxis temperaturaze (simSrale+siTbo)6. parki #4 Tavsdeba macivarSi (simSrale+sicive)amgvarad gvaqvs daobebis pirobebis oTxi kombinacia:
1 2 3 4
sinotive+siTbo sinotive+sicive simSrale+siTbo simSrale+sicive
7. yvela parks Tavi kargad unda qondes mokruli.8. yovel dRe SeamowmeT parkebi 7-10 dRis ganmavlobaSi da CaiwereT Sedegi mocemuli
cxrilis mixedviT
s abu ne bi smetyv elo me c ni er eb e bi
322
1 2 3 4
sinotive+siTbo sinotive+sicive simSrale+siTbo simSrale+sicive
1
2
3
. . .
. . .
Sefasebis kriteriumi: obi kargad SeimCneva puris naWris zedapiris mesamedze, naxevarze, or mesamedze, mTel zedapirze.
mas Semdeg rac jgufebi waradgenen dakvirvebis Sedegebs maswavlebeli dafaze xazavs cxrils. sadac fiqsirdeba yvela jgufis pasuxi (romel kombinaciis SemTxvevaSi moxda yvelaze intensiuri daobeba). maswavlebels monacemebi saerTo cxrilSi Seaqvs.
savaraudod cxrils Semdegi saxe eqneba Sedegebs.
1 2 3 4
sinotive+siTbo sinotive+sicive simSrale+siTbo simSrale+sicive
* * * * * * *
miRebuli Sedegebis mixedviT keTdeba daskvna.Semdeg TiToeuli jgufi pasuxs adarebs Tavis varauds.SesaZlo daskvna: daobeba xdeba gansakuTrebiT swrafad notio, bnel garemoSi.
jgufis # . . . . . . . . . . . . . . . . . .
ra pirobebSi, (temperatura: siTbo/sicive, tenianoba: nesti/simSrale) daobdeba puri ufro swrafad?
dawereT Tqveni varaudi: ______________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
323
1 2 3 4
sinotive+siTbo sinotive+sicive simSrale+siTbo simSrale+sicive
1
2
3
4
5
6
7
8
cdis SedegigamarTlda Tu ara Tqveni varaudi?
____________________________________________________________________________
____________________________________________________________________________
rekomendaciebi erTi da igive sakiTxis sxvadasxva doneze swavlebisaTvis.
fizika
Tema: nivTierebis agregatuli mdgomareoba
Sedegi
bun. X. 3. moswavle obieqtis an movlenis Sesaswavlad moipovebs monacemebs cdis
saSualebiT
bun. X. 10. moswavle aRwers nivTierebis agregatul mdgomareobebs da gadasvlebs
erTi mdgomareobidan meoreSi
atarebs cdebs nivTierebis agregatuli mdgomareobis cvlilebis procesis Sesaswavlad da aRwers am procesebs Tvisebrivad da raodenobrivad;
aseTi tipis gakveTilisaTvis rekomendebulia Sewyvilebuli saaTi ---- 95-100wT.
I trimestri 10wT
s abu ne bi smetyv elo me c ni er eb e bi
324
maswavleblis daxmarebiT gansazRvravs cdis mizans da Sesaswavl maxasiaTeblebs: yinulis dnobis procesis Seswavla da dnobis siTbos daTvla.
klasSi etapobrivad, SekiTxvebiTa da pasuxebiT igegmeba cda da ganisazRvreba gasazomi sidideebi:
saWiroa gansazRvruli raodenobisa da gansazRvruli temperaturis wyali; (e.i. winaswar unda ganisazRvros wylis masa da gaizomos temperatura)gansazRvruli raodenobis yinuli (e.i. saWiroa yinulis masis gansazRvra)yinulisa da wylis Serevis Semdeg, rodesac yinuli srulad gadneba, narevis temperaturis gansazRvra.
iyenebs miTiTebul xelsawyoebs: maduRaras, Termometrs, menzuras, saswors yinulis dnobis procesis raodenobrivi da TvisebiTi monacemebis mosapoveblad.
asrulebs instruqcias da miyveba dasaxul gegmas cdis dros:
da iTvlis masas;sasworis saSualebiT gansazRvravs yinulis masas;yinulisa da wylis Serevis Semdeg, rodesac yinuli srulad gadneba, Termometris saSualebiT gansazRvravs wylis temperaturas.
aRricxul raodenobriv monacemebs gamosaxavs maswavleblis miTiTebul erTeulebSi: yinulisa da wylis masas gansazRvravs kilogramebSi, temperaturas _ gradusebSi
cdis monacemebi Seaqvs gamzadebul cxrilSi
akeTebs damatebiT gamoTvlebs maswavleblis daxmarebiT (iTvlis siTbos raodenobebs), wers siTburi balansis gantolebas da akeTebs analizs. msjelobs yinulis dnobisaTvis saWiro siTbos raodenobis Sesaxeb, Semdeg ki dnobis kuTri siTbos Sesaxeb, gamohyavs misi erTeuli.
mis mier Catarebuli cdis monacemebs adarebs Tanaklaselebisas da poulobs msgavseba-gansxvavebas.
cdis msvlelobas aRwers saTanado terminologiiT (kuTri siTbotevadoba, dnobis temperatura, narevis sawyisi da saboloo temperatura, dnobis kuTri siTbo)
cdis Catarebisas icavs usafrTxoebis wesebs da racionalurad iyenebs drosa da resursebs.
cxeli WurWlis, an yinulis aRebisas xmarobs siTbogaumtar specialur xelTaTmanebs, racionalurad iyenebs dros, raTa yinulis dnobam ar SeuSalos xeli swori monacemebis miRebas.
1.
2.3.
1.
2.3.
325
II trimestri
jgufTan erTad gansazRvravs cdis mizans da Sesaswavl maxasiaTeblebs -- yinulis dnobis procesis Seswavla da dnobis siTbos daTvla.
etapobrivad, jgufebSi, msjelobiT igegmeba cda da ganisazRvreba gasazomi sidideebi:
saWiroa gansazRvruli raodenobis gansazRvruli temperaturis wyali; (e.i. winaswar unda ganisazRvros wylis masa da gaizomos temperatura)gansazRvruli raodenobis yinuli (e.i. saWiroa yinulis masis gansazRvra)yinulisa da wylis Serevis Semdeg, rodesac yinuli srulad gadneba, narevis temperaturisa da masis gansazRvra.maswavleblis daxmarebiT irCevs da iyenebs Sesabamis xelsawyoebs: maduRaras, Termometrs, menzuras, saswors yinulis dnobis procesis raodenobrivi da TvisebiTi monacemebis mosapovebladjgufTan erTad gegmavs da warmarTavs kvlevas:
da iTvlis masas;sasworis saSualebiT gansazRvravs yinulis masas;yinulisa da wylis Serevis Semdeg, rodesac yinuli srulad gadneba, Termometris saSualebiT gansazRvravs wylis temperaturas.aRricxul raodenobriv monacemebs miusadagebs Sesabamis erTeulebs: yinulisa da wylis masas gansazRvravs kilogramebSi, temperaturas _ gradusebSiirCevs monacemebis Caweris formas: adgens cxrils, Cawers monacemebs Tanmimdevrulad da zustad, akeTebs cdis Canaxats.akeTebs damatebiT gamoTvlebs (iTvlis siTbos raodenobebs), wers siTburi balansis gantolebas da akeTebs analizs. msjelobs yinulis dnobisaTvis saWiro siTbos raodenobis Sesaxeb, Semdeg ki dnobis kuTri siTbos Sesaxeb, gamohyavs misi erTeuli. atarebs sakontrolo cdebs, cvlis cdis pirobebs (mag. wylis temperaturas, wylis an yinulis masas) da iTvlis siTbos raodenobebs axali monacemebisaTvis.atarebs ganmeorebiT cdebs, adarebs miRebul monacemebs da iTvlis saSualo maCvenebels yinulis dnobis kuTri siTbosaTvis.
kuTri siTbos gansazRvra yinulis magaliTze.maswavlebelTan da/an jgufTan erTad SeimuSavebs konkretuli kvlevisaTvis usafrTxoebis zomebs, droisa da resursebis efeqturad gamoyenebis gzebs. cxeli WurWlis, an yinulis aRebisas xmarobs siTbogaumtar specialur xelTaTmanebs, racionalurad iyenebs dros, raTa yinulis dnobam ar SeuSalos xeli swori monacemebis miRebas. yinulis zedmetad dnobis Tavidan acilebis mizniT saWiroa ganisazRvros misi masa yinulian jamSi (asawoni yinuli unda moTavsdes SuSis WurWelSi, romelic damatebiT moTavsebulia yinulSi, raTa ar moxdes zedmeti siTbocvla garemosTan).
1.
2.3.
1.
2.3.
s abu ne bi smetyv elo me c ni er eb e bi
326
III trimestri
gansazRvravs da aRwers kvlevis mimdinareobas: yinulis dnobis procesis Sesaswavlad da maxasiaTebeli sidideebis misaRebad moiazrebs cdis mimdinareobas: yinuli unda Seerios aduRebul wyals, gaizomos narevis temperatura da daiweros siTburi balansis gantoleba. am miznis misaRwevad saWiroa:gansazRvruli raodenobisa da gansazRvruli temperaturis wyali; (e.i. winaswar unda ganisazRvros wylis masa da gaizomos temperatura)gansazRvruli raodenobis yinuli (e.i. saWiroa yinulis masis gansazRvra)yinulisa da wylis Serevis Semdeg, rodesac yinuli srulad gadneba, narevis temperaturisa da masis gansazRvra.damoukideblad irCevs da iyenebs xelsawyoebs: maduRaras, Termometrs, menzuras, saswors yinulis dnobis procesis raodenobrivi da TvisebiTi monacemebis mosapoveblad da adarebs Tavis arCevans Tanaklaselebisas.jgufTan erTad gegmavs da ikvlevs Sesaswavl maxasiaTeblebs, miRebul monacemebs adarebs sxva jgufebis monacemebs da afasebs maT:
da iTvlis masas;sasworis saSualebiT gansazRvravs yinulis masas;yinulisa da wylis Serevis Semdeg, rodesac yinuli srulad gadneba, Termometris saSualebiT gansazRvravs wylis temperaturas.aRricxul raodenobriv monacemebs miusadagebs Sesabamis erTeulebs: yinulisa da wylis masas gansazRvravs kilogramebSi, temperaturas _ gradusebSiamzadebs cdis oqms. aRwers monacemebs dawvrilebiT, Tanmimdevrulad da warmoadgens cxrilis saxiTakeTebs damatebiT gamoTvlebs (iTvlis siTbos raodenobebs), wers siTburi balansis gantolebas da akeTebs analizs. msjelobs yinulis dnobisaTvis saWiro siTbos raodenobis Sesaxeb, Semdeg ki dnobis kuTri siTbos Sesaxeb, gamohyavs misi erTeuli. atarebs sakontrolo cdebs, cvlis cdis pirobebs (mag. wylis temperaturas, wylis an yinulis masas) da iTvlis siTbos raodenobebs axali monacemebisaTvis.atarebs ganmeorebiT cdebs, adarebs miRebul monacemebs da iTvlis saSualo maCvenebels yinulis dnobis kuTri siTbosaTvis.cdis Catarebisas irCevs Sesabamisi meTodebidan erT-erTs -- nivTierebis dnobis kuTri siTbos gansazRvra yinulis magaliTze. asabuTebs arCevanis upiratesobas. magaliTad, dnobis kuTri siTbos gansazRvris sirTule tyviisaTvis an vercxlisaTvis.jgufTan erTad SeimuSavebs droisa da resursebis efeqturad gamoyenebis gzebs. cxeli WurWlis an yinulis aRebisas xmarobs siTbogaumtar specialur xelTaTmanebs, racionalurad iyenebs dros, raTa yinulis dnobam ar SeuSalos xeli swori monacemebis miRebas. yinulis zedmetad dnobis Tavidan acilebis mizniT saWiroa ganisazRvros misi masa yinulian jamSi (asawoni yinuli unda moTavsdes SuSis WurWelSi, romelic damatebiT moTavsebulia yinulSi, raTa ar moxdes zedmeti siTbocvla garemosTan). SemuSavebul usafrTxoebis zomebs adarebs arsebuls.
1.
2.3.
1.
2.3.
327
X I / X I I k l a s i
aqtivobebis da proeqtis nimuSebi
aqtivoba
fizika
fiz. XI/XII. 6. adgens kiTxvars da awarmoebs mosaxleobis gamokiTxvas birTvuli
iaraRis mimarT damokidebulebis gamosavlenad. Sedegebs warmoadgens diagramis
saxiT.
aqtivobis mizani:
gamokiTxvis gziT informaciis Segroveba;Temis Sesabamisi kiTxvaris Sedgena.
aqtivobebi :
1. maswavlebeli svavs Semdeg kiTxvebs:
rogor SeiZleba gamovarkvioT mosaxleobis damokidebuleba birTvuli iaraRis mimarT?ra saxiT SeiZleba SevagrovoT informacia?ra unda ganvsazRvroT kiTxvaris Sedgenamde?
2. klasi gansazRvravs respondentTa jgufebs (moswavleebi, pensionerebi, mSoblebi,
maswavleblebi da sxva ) da arCevs misTvis saintereso jgufs.
3. gansazRvreT kiTxvaris struqtura da Sinaarsi. CamoayalibeT 7-20-punqtiani
kiTxvari.
kiTxvaris Sedgena:
moswavle
asaTaurebs kiTxvars;ayalibebs respondentisadmi mimarTvis formas;adgens kiTxvebs (SesaZloa, kiTxvebis qveS eweros damatebiTi instruqcia. mag.: ramdeni Tviseba unda CamoTvalos respondentma);adgens miTiTebebs gulaxdili pasuxebis misaRebad;arCevs respondentisaTvis madlobis formas.
1.2.3.
4.5.
s abu ne bi smetyv elo me c ni er eb e bi
328
SesaZlebelia ramdenime tipis kiTxvaris Sedgena. magaliTad:a) mxolod damokidebulebis gamosavlenad;b) respondentTa informirebulobisa da damokidebulebis gamosavlenad.gTavazobT SesaZlo variantebs:
a) kiTxvari damokidebulebis gamosavlenad:
xarT Tu ara momxre birTvuli iaraRis warmoebis?xarT Tu ara momxre birTvuli iaraRis gamocdis?rogor fiqrobT, aris Tu ara birTvuli iaraRi qveynisaTvis erTaderTi Tavdacvis saSualeba?gamoricxavT Tu ara SesaZleblobas, rom birTvuli iaraRi teroristebs CauvardeT xelSi?gamoricxavT Tu ara SesaZleblobas, rom kvlevebi birTvuli iaraRis warmoebaSi mosaxleobis sasikeTod warimarTos?amarTlebT Tu ara amerikis SeerTebuli Statebis mier 1945 wels iaponiis mSvidobiani mosaxleobis winaaRmdeg birTvuli iaraRis gamoyenebis faqts?xarT Tu ara momxre saqarTvelos teritoriaze birTvuli iaraRis warmoebis?xarT Tu ara momxre saqarTvelos teritoriaze birTvuli iaraRis gamocdis?migaCniaT Tu ara marTebulad, rom birTvuli iaraRis gamoyenebisas mosaxleoba informirebuli unda iyos mosalodneli Sedegebis Sesaxeb?
aseTi kiTxvaris analizi, saSualebas iZleva davadginoT, ras fiqroben respondentebi da rogori damokidebuleba aqvT maT birTvuli iaraRis mimarT.
b) kiTxvari respondentTa informirebulobisa da damokidebulebis gamosavlenad
1. ra Sedegebi SeiZleba mohyves birTvuli iaraRis gamoyenebas?a) radiaciuli fonis momateba;b) garemos JangbadiT gamdidreba;g) araviTari cvlileba.
2. ra ekologiuri cvlilebebi SeiZleba gamoiwvios birTvuli iaraRis gamoyenebam?a) ekologiuri katastrofa;b) cocxali samyaros ayvaveba;g) araviTari cvlileba.
3. rodis iqna gamoyenebuli birTvuli iaraRi mSvidobianimosaxleobis sawinaaRmdegod?
a) 1939;b) 1945;g) 1972;
4. romel qveyanaSi iqna gamoyenebuli birTvuli iaraRi?a) ruseTi;b) iaponia;g) aSS.
5. ramdeni saxelmwifoa birTvuli iaraRis mwarmoebeli?a) 5-ze naklebi;
g) 10-ze meti.6. xarT Tu ara momxre birTvuli iaraRis warmoebis?
1.2.3.
4.
5.
6.
7.8.9.
329
7. xarT Tu ara momxre birTvuli iaraRis gamocdis?8. rogor fiqrobT, aris Tu ara qveynisaTvis birTvuli iaraRi erTaderTi Tavdacvis
saSualeba?9. gamoricxavT Tu ara SesaZleblobas, rom birTvuli iaraRi teroristebs CauvardeT
xelSi?10. gamoricxavT Tu ara SesaZleblobas, rom kvlevebi birTvuli iaraRis warmoebaSi
mosaxleobis sasikeTod warimarTos?11. xarT Tu ara momxre, saqarTvelos teritoriaze moxdes birTvuli iaraRis
warmoeba?12. xarT Tu ara momxre, saqarTvelos teritoriaze moxdes birTvuli iaraRis
gamocda?13. migaCniaT Tu ara, rom birTvuli iaraRis gamoyenebisas, mosaxleoba informirebuli
unda iyos mosalodneli Sedegebis Sesaxeb?
am tipis kiTxvaris analizi gamoavlens respondentis informirebulobas da sakiTxisadmi mis damokidebulebas.
magaliTad, moswavle iTvlis respondentebis ra nawilia sworad informirebuli birTvuli iaraRis gamoyenebisas mosalodneli Sedegebis Sesaxeb da am nawlidan ramdenia momxre misi gamoyenebis, an ar gamoyenebis da a.S.
4. moswavleebs unawildebaT kiTxvarebi. isini midian respondentebTan da avsebineben
kiTxvars.
5. Sedegebis dajameba da analizi:
moswavle
1. iTvlis gamokiTxvaSi monawile adamianTa raodenobas;2. gamoyofs misTvis saintereso mniSvnelovan sakiTxebs;3. ajgufebs da iTvlis erTnair pasuxebs;4. agebs diagramas;5. akeTebs diagramis analizs;6. warmoadgens gamokiTxvis Sedegebs.
aqtivoba
qimia
Tema: elementTa perioduli sistema. gardamavali metalebi
kavSiri standartTan
bun X1 - XII 5. moswavle axasiaTebs qimiuri elementebisa da maTi naerTebis Tvisebebs,
msjelobs maTi mniSvnelobis Sesaxeb
damatebiTi informacia
Tanauri jgufis (gardamavali) metalebi erTdroulad silamaziT da gamZleobiT xasiaTdebian. qromi gamoiyeneba koroziis sawinaaRmdegod, spilenZi Sedis monetebisa da xelovnebis uZvelesi nimuSebis SedgenilobaSi, vercxlis Tvisebebma ganapirobes
s abu ne bi smetyv elo me c ni er eb e bi
330
fotografiisa da kinos arseboba da ganviTareba. sxvadasxva metalis mniSvnelobis, faseulobis gansazRvrisa da Sesabamisad gamoyenebisTvis saWiroa maTi Tvisebebis codna. moswavleebi msjeloben gardamavali metalebisa da maTi Tvisebebis Sesaxeb. Semdeg atareben cdas, romlis drosac spilenZi Zmrisa da marilis xsnarSi moTavsebuli monetidan gadadis rkinis lursmanze.
maT SeiZleba imsjelon gardamavali metalebis gamoyenebis Sesaxeb fulis monetebis dasamzadeblad, agreTve, imaze, Tu rogor iJangeba moneta JangbadTan Sexebisas.
gakveTilis mizani:
gardamavali metalebis Seswavlametalebis da maTi Senadnobebis gamoyenebadakvirvebis unar-Cvevis ganviTareba eqsperimentis safuZvelze
saWiro masala
elementTa perioduli sistema: Tanauri jgufis metalebidanarTi #1 (instruqciebi)danarTi #2 (cxrili 1)
yoveli jgufisTvis:
instruqciis furceliqimiuri Wiqa1/4 Wiqa Rvinis Zmari1 mwikvi mariliminis sufTa qila10 cali 50-TeTriani moneta an spilenZis Semcveli saganifiltris qaRaldiori cali axali, dauJangavi lursmanipatara jami wyliT
procedurebi
1. CamoaTvlevineT moswavleebs gardamavali metalebis saxelebi (rkina,
nikeli, titani, spilenZi, vercxli, oqro, qromi, TuTia). CamowereT dafaze
dasaxelebuli gardamavali metalebi. sTxoveT moswavleebs, CamoTvalon
gardamavali metalebis umetesobis damaxasiaTebeli Tvisebebi (simagre,
simyare, bzinvareba, maRali lRobisa da duRilis temperaturebi, siTbosa da
eleqtrobis kargi gamtaroba, Wedadoba da plastikuroba).
rekomendacia maswavleblisaTvis:
50-TeTriani monetis SedgenilobaSi Sedis spilenZi da nikeli. moneta SeiZleba Seicvalos nebismieri SenadnobiT, romelic spilenZs Seicavs.
2. dayaviT moswavleebi jgufebad, mieciT davaleba:
daadgineT monetis an Senadnobis SedgenilobaSi gardamavali metalis, spilenZis, Semcveloba.
moswavleebs daurigeT saWiro masala da danarTi #1 (instruqciebi)
3. eqsperimentis damTavrebis Semdeg TiToeuli jgufi warmoadgens Sedegebs.
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rogor fiqrobT, Senadnobi, moneta kidev ra metalebs SeiZleba Seicavdes?pasuxebi fiqsirdeba dafaze.
4. mieciT moswavleebs saSinao davaleba: daakvirdiT cxrils, SeadareT cxrilis
monacemebi, CamowereT monetebis SedgenilobaSi Semavali yvela gardamavali
metali da upasuxeT kiTxvebs:
romel sam monetas aqvs erTnairi Sedgeniloba?romeli monetis Sedgenilobaa mkveTrad gansxvavebuli?ratom gamoiyeneba mocemuli metalebi monetebis dasamzadeblad?
cxrili#1
1-cen-tiani
5-centiani 10-centiani 25-centiani 50-centiani dolari oqrosdolari
rekomendacia maswavlebels:
gardamavali metalebi idealuri masalaamonetebis dasamzadeblad (axasiaTebT Wedadoba, SeiZleba maTTvis nebismieri formis
micema, maTze anabeWdebis gakeTeba, xolo sxva masala wnexis qveS gatydeba an daimsxvreva. amave dros, isini didi gamZleobiT gamoirCevian).
isaubreT imis Sesaxeb, Tu ra iwvevs metalis dafarvasnadebiT (qimiuri reaqcia mimdinareobs spilenZsa da Jangbads Soris. spilenZis
atomebi da Jangbadis atomebi warmoqmnian spilenZis oqsidis molekulebs. spilenZis oqsidi monetaze nadebs warmoqmnis.) oqsidebis sxva magaliTia Jangi rkinis WiSkarze an nadebi vercxlis finjanze. es oqsidebi, spilenZis oqsidis msgavsad, warmoiqmneba rkinis/ vercxlis JangbadTan urTierTqmedebiT.
monetebis ori kompleqtidan erTi, iqneba priala dambzinavi, danarCenebze iqneba momwvano cisferi nadebi. momwvano cisferi nadebi
aris naerTi, romelsac malaqiti hqvia da miiReba spilenZis, marilisa da Jangbadis urTierTqmedebiT. Zmris xsnari xels uwyobs am reaqciis msvlelobas. ( SeniSvna: zogjer malaqitis warmoqmnas meti dro sWirdeba da Cndeba mxolod gakveTilis bolosken. gansakuTrebiT kargad Cans Semdeg dReebSi. amitom Tu SesaZlebelia, SeinaxeT monetebi da kvlav daaTvaliereT ramdenime dRis Semdeg).
rekomendacia SefasebisaTvis doneebis mixedviT (ganawilebulia oTx doneze)
moswavleebi asaxeleben mraval gardamaval metals. srulyofilad axasiaTeben maT;asaxeleben ramdenime gardamaval metals da srulad axasiaTeben maT;moswavleebi asaxeleben gardamavali metalebis Zalian mcire nawils da axasiaTeben maT;moswavleebi asaxeleben gardamavali metalebis Zalian mcire nawils da ver axasiaTeben maT.
s abu ne bi smetyv elo me c ni er eb e bi
332
rekomendacia saSinao davalebis SefasebisaTvis doneebis mixedviT (ganawilebulia
oTx doneze)
CamoTvlian monetebis SedgenilobaSi Semaval gardamaval metalebs, adgenen msgavsebasa da gansxvavebas monetebs Soris, xsnian, ram ganapiroba am metalebis gamoyeneba;CamoTvlian monetebis SedgenilobaSi Semaval gardamaval metalebs, adgenen msgavsebasa da gansxvavebas monetebs Soris, magram ver asabuTeben metalebis gamoyenebas monetebis dasamzadeblad;CamoTvlian monetebis SedgenilobaSi Semaval gardamaval metalebs, nawilobriv adgenen msgavsebasa da gansxvavebas monetebs Soris, magram ver asabuTeben metalebis gamoyenebas monetebis dasamzadeblad;CamoTvlian monetebis SedgenilobaSi Semaval gardamaval metalebs, ver adgenen msgavsebasa da gansxvavebas monetebs Soris, ver asabuTeben metalebis gamoyenebas monetebis dasamzadeblad.
rekomendacia eqsperimentis SefasebisaTvis doneebis mixedviT (ganawilebulia oTx
doneze)
dakvirvebis safuZvelze srulad aRweren cdis Sedegebs, iZlevian metalebze oqsidebis, kerZod, Jangisa da nadebis warmoqmnis mkafio da swor werilobiT axsnas.dakvirvebis safuZvelze srulad aRweren cdis Sedegebs, iZlevian metalebze oqsidebis, kerZod, Jangisa da nadebis warmoqmnis nawilobriv werilobiT axsnas.dakvirvebis safuZvelze srulad ver aRweren cdis Sedegebs, iZlevian metalebze oqsidebis, kerZod, Jangisa da nadebis warmoqmnis nawilobriv werilobiT axsnas.dakvirvebis safuZvelze srulad ver aRweren cdis Sedegebs, ver xsnian metalebze oqsidebis, kerZod, Jangisa da nadebis warmoqmnas.
333
saWiro masala:
danayofebiani Wiqa1/4 Wiqa Rvinis Zmari1 mwikvi mariliminis sufTa qila10 cali 50-TeTriani moneta an spilenZis Semcveli saganifiltris qaRaldiori cali axali, dauJangavi lursmanipatara jami wyliT
instruqcia:
erTi mwikvi sufris marili CayareT Zmrian WiqaSi. Wiqa SeanjRrieT, rom marili gaixsnas. CayareT miRebul xsnarSi monetebi da erTi cali lursmani, meore lursmani ki iqve, QqaRaldze moaTavseT. dawereT jgufurad Tqveni varaudi, ra moxdeba.10 wuTis Semdeg amoiReT Wiqidan 5 cali moneta, gaamSraleT da filtris qaRaldze dadeT.darCenili 5 cali monetac amoiReT Wiqidan, gaavleT wyalSi, SeaSreT filtris qaRaldze da calke dadeT qaRaldze.lursmani CatoveT Zmrian WiqaSi kidev 10 wuTiT an cota meti xniT, Semdeg amoiReT Wiqidan da SeadareT meore lursmans. CainiSneT, Tu SeamCnevT gansxvavebas.SeadareT erTmaneTs monetebis 2 kompleqti: 5 cali, romelic wyalSi ar gagivliaT da 5 cali, romlebic wyalSi gaavleT. dakvirvebis Sedegebi CainiSneT.CaiwereT Tqvens mier Catarebuli cdis Sedegebi. gakveTilis bolos dawereT cdis Sedegebis Tqveneuli axsna.
cxrili #1
1-cen-tiani
5-centiani 10-centiani 25-centiani 50-centiani dolari oqrosdolari
1.
2.
3.
4.
5.
6.
s abu ne bi smetyv elo me c ni er eb e bi
334
proeqti
biologia / qimia
Tema: mumia
proeqtis mizani: kvlevis unar-Cvevebis ganviTareba; samodelo eqsperimentis monacemebis
ganzogadeba; TanamSromlobis unaris ganviTareba.
proeqtis xangrZlivoba: 7-10 dRe.
miznobrivi jgufi: XI-XII klasis moswavleebi.
amocanebi:
saproeqto Temis _ sakvlevi obieqtis gansazRvra;mumiebTan da mumificirebis procesTan dakavSirebuli informaciis mogroveba;mumificirebis procesSi marilis rolis dasadgeni eqsperimentis gegmis SemuSaveba;eqsperimentis Catareba da monacemebis aRricxva;monacemebis grafikebis da diagramebis saxiT warmodgena;daskvnebis gakeTeba;mokle werilobiTi angariSis (oqmis) momzadeba;prezentaciis momzadeba.
1. saproeqto Temis _ sakvlevi obieqtis gansazRvra
_ ra asociacias iwvevs TqvenSi sityva ,,mumia”?rodesac adamianebs esmiT sityva ,,mumia” _ isini, Cveulebriv, fiqroben egvipteze.
Tumca, mumiebi aRmoCenilia mTel msoflioSi: CineTis, evropis, perus da meqsikis CaTvliT. mumiebis didi nawili, bunebrivad, adamianis Carevis gareSe warmoiqmneba.
ra pirobebia saWiro mumificirebisaTvis?rogor amzadebdnen Zveli egviptelebi mumiebs?rogor SegviZlia Tavad gavakeToT mumia?
2. mumiebTan da mumificirebis procesTan dakavSirebuli informaciis
mogroveba
mumifikaciis dros unda moxdes organizmis sruli gauwyloeba. mumiebis umetesoba, mSrali klimatis pirobebSia aRmoCenili. Tumca, isini torfis WaobebSic gvxvdeba, sadac wylis mJavianoba maRalia, xolo Jangbadis koncentracia _ dabali. mumificirebuli organizmebi gvxvdeba tundraSic, sadac isini gayinuli saxiT aris Semonaxuli. yvela qvemoT CamoTvlil garemoSi baqteriebs ar SeuZliaT arseboba da amitom ar xdeba organuli qsovilebis gaxrwnisa da daSlis procesi.
Zveli egviptelebis mumiebi TariRdeba Cvens welTaRricxvamde 3200 wliT. samarxebis kedlebze arsebuli warwerebis analizis safuZvelze mecnierebma daadgines, rom mumiebis damzadebis procedurebi droTa ganmavlobaSi ixveweboda. yvelaze adrindel mumiebs mxolod bunebrivi mariliT (amJamad, sasmeli sodis saxeliT cnobili) amuSavebdnen. Semdeg, amSralebdnen da axvevdnen dolbandis saxvevebSi. daaxloebiT, Cvens welTaRricxvamde 1500 wels, mumificirebis xelovnebam piks miaRwia. Tavdapirvelad, gvams aclidnen tvins da Sinagan organoebs. Semdeg, muclis Rrus amuSavebdnen sodiT, qviSiT, naxerxiT
1.2.3.
4.5.6.7.8.
335
da aTavsebdnen sodaSi daaxloebiT 40 dRis ganmavlobaSi. Semdeg, sxeuls recxavdnen, amuSavebdnen nelsacxeblebiT, sodiT da axvevdnen saxvevebSi. mTel proceduras daaxloebiT 70 dRe sWirdeboda.
3. mumificirebis procesSi marilis rolis dasadgeni eqsperimentis gegmis
SemuSaveba.
_ davadginoT, marilis saxeobis damokidebuleba vaSlis mumificiebis procesze.
masala: ori vaSli; erTi mozrdili kolofi (1 kg) sufris marili; erTi mozrdili
kolofi (1 kg) inglisuri marili; erTi mozrdili kolofi (1 kg) sasmeli
soda; dana; rva 200 ml-iani erTjeradi Wiqa; menzura; didi Tasi; markeri;
webovani qaRaldi; mgrZnobiare saswori; ujrebiani qaRaldis furceli;
fanqari; danarTi #1.
4. eqsperimentebis Catareba da monacemebis aRricxva:
TiToeuli vaSli daWeriT oTx nawilad ise, rom miiRoT rva Tanabari zomis naWeri.daawebeT TiToeul Wiqas webovani qaRaldi. awoneT vaSlis naWeri, moaTavseT WiqaSi, qaRaldze miuTiTeT wona da QWiqis nomeri. gaimeoreT es procedura vaSlis yoveli naWrisaTvis.Wiqas #1 daamateT daaxloebiT 1/2 Wiqa sasmeli soda. darwmundiT, rom vaSlis naWeri daifara. qaRaldze miawereT ,,mxolod sasmeli soda”.Wiqas # 2 daamateT ½1/2 Wiqa inglisuri marili, qaRaldze miawereT ,,mxolod inglisuri marili”Wiqas #3 daamateT 1/2½ Wiqa sufris marili, qaRaldze miawereT ,,mxolod sufris marili”.Wiqa #4-Si CayareT ¼1/4 Wiqa sufris marilisa da ¼1/4 Wiqa inglisuri marilis narevi.Wiqa # 5-Si moaTavseT 1/4 sufris marilisa da 1/4 sasmeli sodis narevi,Wiqa # 6-Si sasmeli 1/4 sodisa da 1/4 inglisuri marilis narevi.Wiqa # 7-Si CayareT 1/6 Wiqa sasmeli soda, 1/6 Wiqa inglisuri marili da 1/6 Wiqa sufris marilis narevi.Wiqa # 8-Si kontrolisaTvis mxolod vaSlis naWeri CadeT.moaTavseT Wiqebi Taroze erTnair pirobebSi, mzisgan moSorebiT da datoveT 7 dRis ganmavlobaSi.erTi kviris Semdeg amoiReT vaSlis yoveli naWeri. ramdenadac SesaZlebelia, gawmindeT marilisagan (naWrebis garecxva ar SeiZleba) da kvlav awoneT. SeadareT vaSlis naWrebis sawyisi da saboloo wonebi, gamoTvaleT TiToeul sinjSi wonis cvlileba procentebSi da monacemebi SeitaneT cxrilSi. (danarTi #1)
1.
2.
3.
4.
5.
6.
7.8.9.
10.11.
12.
s abu ne bi smetyv elo me c ni er eb e bi
336
6. monacemebis grafikebis da diagramebis saxiT warmodgena
gansazRvreT, rogori diagramis agebaa ufro mosaxerxebeli monacemebis warmosaCenad:(am konkretul SemTxvevaSi, uprianad migvaCnia svetovani diagramis gamoyeneba da
savaraudod diagramas msgavsi saxe eqneba)mag.
1 2 3 4 5 da a.S.marilebis saxeoba da Tanafardobis variantebi
6. daskvnebi
romel WiqaSi iyo mumificirebisaTvis saukeTeso pirobebi? ram ganapiroba es?ra procesi moxda?gamoikvlieT, miaRwevdiT Tu ara imave Sedegs, mTliani vaSlis mumificirebisas?ra mizniT datoveT marilebis gareSe vaSlis erTi naWeri?sad wavida vaSlis naWrebidan siTxe? rogor daadasturebT Tqvens mosazrebas?mumificirebis sxvadasxva xerxi dResac gamoiyeneba. rogor fiqrobT sad gamoiyeneba?
1.2.3.4.5.6.
337
monacemebis aRricxva
nomeriMmarilis raodenoba, saxe-oba da Tanafardoba sawyisi wona
vaSlis-
oloo wona
wonis cvli-leba %
1.
2.
3.
4.+ ¼
5.+
6.+
7.+
+
8. _
marilebis saxeoba da Tanafardobis variantebi
s abu ne bi smetyv elo me c ni er eb e bi
338
proeqti sabunebismetyvelo sagnebSizogadi rekomendaciebi
proeqti
mizani: saskolo samecniero proeqtis saSualebiT kvleviTi unar-Cvevebis
ganviTareba.
amocanebi:
proeqtis Temis gansazRvra;sakiTxTan dakavSirebuli informaciis mogroveba;kvlevis gegmis SemuSaveba;eqsperimentebis Catareba da monacemebis aRricxva;grafikebi da diagramebi;daskvnebi;mokle werilobiTi angariSis (oqmis) momzadeba;prezentaciis momzadeba.
1. proeqtis Temis gansazRvra
gaiTvaliswineT, rom samecniero proeqti gulisxmobs kvlevis safuZvelze kiTxvaze pasuxis povnas, dasmuli problemis gadaWras da ara imis Cvenebas, Tu ra icin moswavleebma am sakiTxis Sesaxeb. pirvel rigSi, amorCeuli sakiTxi unda iyos moswavleebisaTvis saintereso da aqtualuri. gamoarkvieT, ra ainteresebT maT. magaliTad, sporti. es mSvenieri Temaa, romelic adamianis anatomiisa da fiziologiis Seswavlis saSualebas gvaZlevs. am TemasTan dakavSirebiT SeiZleba Semdegi proeqtebis ganxorcieleba, mag:
_ rogor gavlenas axdens varjiSi gulis SekumSvis siCqareze da sisxlis wnevaze._ rogor unda davzogoT da optimalurad gadavanawiloT energia sportuli TamaSebis
dros.zogierTi moswavlisaTvis saintereso Temaa musika, SeiZleba davukavSiroT bgeris
gavrcelebas, yuris agebulebas da sxva saswavlo Temebs.mniSvnelovania, rom sakvlevi sakiTxi iyos mkafiod Camoyalibebuli. gaurkvevlad
an Zalian zogadad Camoyalibebuli sakiTxebi arTulebs proeqtis ganxorcielebas. warmogidgenT karg da cud magaliTebs:
kargi magaliTi:_ rogor icvleba kanis elastiuroba asakis matebasTan erTad?_ rogor icvleba haerSi Wvartlis raodenoba wvimis an Tovis dros?cudi magaliTebi:_ romeli musika ufro moswons xalxs, repi Tu klasika? _ (sakiTxi Zalian farToa.
ar Cans romeli ,,xalxi” igulisxmeba. SeuZlebelia, gamovkiTxoT dedamiwaze yvela adamiani. aseTi situaciisaTvis misaRebi variantia magaliTad: romeli musika moswonT ufro 59-e skolis moswavleebs, repi Tu klasika?)
2. sakiTxTan dakavSirebuli informaciis mogroveba
daavaleT moswavleebs, Seagrovon iseTi saxis informacia, romelic daexmareba maT sakiTxis ukeT danaxvaSi.
1.2.3.4.5.6.7.8.
339
SeagrovebineT informacia maT mier SerCeul Temaze wignebidan, Jurnalebidan, internetidan, gamokiTxviT. ar dagaviwydeT miuTiToT, rom CainiSnon moZiebuli informaciis wyaro.
3. kvlevis gegmis SemuSaveba
am etapze, winaswar unda ganisazRvros kvlevis etapebi, dazustdes yvela detali. maswavlebels winaswar unda hqondes gaTvlili, Tu ra dros saWiroebs eqsperimentuli nawili. sasurvelia, eqsperimentuli nawili Tavad maswavlebels winaswar hqondes gakeTebuli, raTa gaiTvaliswinos yvela teqnikuri detali (mag, romeli jiSis vaSlze ufro TvalnaTliv Cans sasurveli Sedegi, an romeli xilis wvenis gamoyenebaa ufro mosaxerxebeli vitaminis aRmosaCenad da sxva):
_ gansazRvreT, ris garkveva, aRmoCena gsurT;_ gansazRvreT cvladebi, romlebsac unda daakvirdeT SekiTxvaze pasuxis misaRebad;_ CamoayalibeT hipoTeza, anu gansazRvreT mosalodneli Sedegi;_ gansazRvreT saWiro masala da aRWurviloba;_ gansazRvreT cdis mimdinareobis etapebi;_ gansazRvreT, rogor aRwerT Ddakvirvebis Sedegebs.
4. eqsperimentebis Catareba da monacemebis aRricxva
gansazRvruli gegmis mixedviT eqsperimentis Catareba.
5. grafikebi da diagramebi
SekiTxvaze pasuxis gacemis Semdeg gamosaxeT monacemebi grafikulad da diagramebiT.
6. daskvnebi
miRebuli monacemebis analizi, imis gansazRvra, Tu ramdenad gamarTlda gamoTqmuli hipoTeza.
aq mniSvnelovania, maswavlebelma dasvas swori SekiTxvebi, romlebic daexmareba moswavleebs arsebiTi aqcentebis gakeTebaSi.
7. mokle werilobiTi angariSis momzadeba
proeqtis aRwerisas konkretulad CamoayalibeT ra gaakeTeT da rogor. miuTiTeT gamoyenebuli wyaroebi.
1. satitulo gverdi:proeqtis saTauri, Semsruleblis saxeli, gvari, skola, klasi, TariRi.2. Sinaarsi (sarCevi)warmodgenili nawilebis nusxa, Sesabamisi gverdebis miTiTebiT (es gverdi iwereba
yvelaze bolos, mas Semdeg, rac daiwereba mTeli samuSao).3. Sesavaliproeqtis mokle aRwera 1 an 2 winadadebiT.4. mimoxilvasakiTxis Sesaxeb mopovebuli informaciis analizi an hipoTeza.5. kvlevis proceduris aRwera
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340
saWiro resursebis da ganxorcielebuli procedurebis detaluri aRwera.6. Sedegebidakvirvebis Sedegebis aRricxva, monacemebis warmodgena.7. daskvnebiSedegebis analizi. imis dadgena, Tu ramdenad gamarTlda Tqveni molodini.8. gamoyenebuli informaciis wyaroebis nusxaliteraturis (wignebi, Jurnalebi, statiebi), respondentebis CamonaTvali, gamoyenebuli
saitebi.
8. prezentaciis momzadeba
prezentacia msmenelTaTvis gasagebad da sainteresod unda warimarTos.
341
rekomendebuli Sefaseba sabunebismetyvelo sagnebSi
Sefasebis ori ZiriTadi tipi
skolaSi ZiriTadad misaRebia ori tipis Sefaseba: ganmsazRvreli da ganmaviTarebeli. rodesac maswavlebeli niSans uwers moswavles da mxolod amiT Semoifargleba, es niSani gansazRvravs moswavlis miRwevis dones dasaxul miznebTan mimarTebiT. maSin, rodesac maswavlebeli Sefasebis iseT formas iyenebs, romelic moswavles ara mxolod sakuTari
Sefasebaa. ganmaviTarebeli Sefasebis tipuri formaa komentarebi, romelic trimestris ganmavlobaSi an bolos, an romelime davalebis Sesrulebis Semdeg iwereba da romelic aRwers namuSevris Zlier da sust mxareebs da amavdroulad Seicavs rekomendaciebs miRwevebis gaumjobesebis Taobaze. ganmaviTarebeli Sefasebis erT-erTi gavrcelebuli xerxia Sefasebis cxrilebis (rubrikebis) gamoyeneba.
mniSvnelovania ganmsazRvreli da ganmaviTarebeli Sefasebis mudmivad gamoyeneba swav-lis procesSi. rekomendebulia, rom ganmaviTarebeli Sefasebis wili saswavlo procesisas ufro meti iyos, vidre ganmsazRvrelis.
ganmaviTarebeli
mimdinareSesruleba, gakveTilze
romelSic niSani iwereba.
-ruleba, gakveTilze CarTuloba,
romelSic vuxsniT moswavles, ro-gor gaaumjobesos Sedegebi.
Semajamebeli raime Temis, drois mon- raime Temis, drois monakveTis, -
ieri Sefaseba, komentari, ru-brikiT Sefaseba da sxv.
trimestruli niSnis Semadgeneli nawilebi
moswavlis niSani unda gamomdinareobdes mis mier sagnis Seswavlis sxvadasxva komponentisgan. moswavle SesaZlebelia Sefasdes Semdegi komponentebis mixedviT:
a) gakveTilze CarTuloba;b) saSinao davalebebi;g) mimdinare saklaso davalebebi;d) Semajamebeli davalebebi (sakontrolo/gamocda/testireba da sxv.);e) proeqtebi;v) damatebiTi komponenti, romelic araumetes saerTo Sefasebis 10%-ia da romelic
moswavleebis mier dgindeba (mag. organizebuloba, SemoqmedebiToba, jgufSi efeqturi muSaoba da sxv.).
TiToeuli sagnis swavlebisas, skola kaTedrebis meSveobiT adgens minimum sam komponents pirveli xuTidan, romelsac aniWebs procentul wonebs 90%-is farglebSi. danarCeni 10 % - is ganawileba xdeba maswavleblis mier ukve moswavleebTan SeTanxmebiT. pirvelad maswavleblebi acnoben moswavleebs kaTedris mier SemuSavebul komponentebs da uxsnian, Tu ras moelian TiToeuli komponentis Sefasebisas. amis Semdeg moswavleebTan
s abu ne bi smetyv elo me c ni er eb e bi
342
erTad eZeben im kriteriums, romelic, maTi azriT, kargi iqneboda, rom damatebiT aTi procentis farglebSi yofiliyo gamoyenebuli. maswavlebeli SesaZlebelia exmarebodes moswavleebs am komponentis gaazrebaSi, magram mniSvnelovania, rom moswavleebma TviTon gadawyviton am komponentis raoba da Sefasebis doneebi.
TiToeuli komponentis mixedviT dgeba Sefasebis doneebi erTidan aTamde, romelic ganmartavs, Tu ra qulebi iwereba sxvadasxva donis mixedviT. rekomendebulia, trimestruli Sefaseba ganmaviTarebeli formiT iyos Sedgenili. rekomendebulia komentarebis dawera trimestris bolos yvelasTvis da trimestris SuaSi imaTTvis, vinc aucileblad unda gamoasworos sakuTari swavla, raTa trimestruli Sefaseba dadebiTi hqondes. trimestris SuaSi aseve SeiZleba daiweros komentari, Tu moswavlem wina trimestrTan SedarebiT mniSvnelovnad gaaumjobesa Tavisi moswreba. amis aRniSvna mniSvnelovan stimuls miscems moswavles imisTvis, rom swavlis xarisxi trimestris bolomde SeinarCunos.
ras iTvaliswinebs TiToeuli komponeneti sabunebismetyvelo sagnebSi
a) gakveTilze CarTuloba
fasdeba Semdegi unarebi:1. socialuri unar-Cvevebi2. komunikaciis unar-Cvevebi
b) saSinao davalebebi
davalebis tipebi: savarjiSoebis Sesruleba, saSinao eqsperimenti, dakvirveba
obieqtebsa da procesebze, informaciis moZieba, konceptualuri rukis
Sedgena, modelireba, referatis momzadeba da sxva.
fasdeba Semdegi unarebi:saazrovno unar-Cvevebikvlevis unar-Cvevebiproblemis gadaWris unar-CvevebiTviT-marTvis unar-Cvevebi
Sefasebis sqemis (rubrikis) magaliTi erT-erTi aqtivobisaTvis:
informaciis moZieba
1-3 4-5 6-7 8-10
informaciismoZiebiswyaroebi
iyenebs mxolod sakuTar cod-nas da ra aqvs moZiebuliinformacia
iyenebs mxolod -
vanelos infor-macias
iyenebs mxolod ramdenimesainformacio
-alebebs
iyenebs mraval-ferovan sain-formacio
-alebebs
moZiebuliinformaciisSesabamisoba
masala ar aris sakiTxis Ses-abamisi
masala nawilo-briv Seesabameba sakiTxs
masala ZiriTa-dad Seesabameba sakiTxs
masala srulad SeesabamebasakiTxs
informaciisorganizeba
masala ar aris sworad orga-nizebuli
masala nawilo-briv organize-bulia
masala organi-zebulia, magram
-saqmeli
masala kargad da mosaxerxe-bladaa organi-zebuli
1.2.3.4.
343
g) mimdinare saklaso davalebebi
davalebis tipebi: Tematuri sakiTxis ganxilva, diskusia, eqsperimentis Catareba,
testebze muSaoba, amocanebis amoxsna, monacemebis aRricxva/damuSaveba,
modelireba, savele/gasvliTi samuSaoebi da sxva.
fasdeba Semdegi unarebi:1. saazrovno unar-Cvevebi2. kvlevis unar-Cvevebi3. problemis gadaWris unar-Cvevebi4. socialuri unar-Cvevebi5. komunikaciis unar-Cvevebi6. TviT-marTvis unar-Cvevebirubrikis magaliTi erT-erTi aqtivobisaTvis:
eqsperimenti
1-3 4-5 6-7 8-10
kvlevis miz-nis gansaz-
arasworad
mizans
nawilobrivsworad gansaz- mizans, magram
formulirebaarazustia
sworad gansaz-
formulirebazustia
inventaris(masalis da
-bis) gansaz-
CamoTvlis ram-denime
CamoTvlis
nawils
CamoTvlis
masalas
CamoTvlis--
vilobas
kvlevisSedegisvaraudi
kvlevis Sedegis varaudi miznis Seusabamoa
kvlevis Sedegis varaudi mizans nawilobriv See-sabameba
kvlevis Sedegis varaudi miz-nis Sesabamisia, formulirebaarazustia
kvlevis Sedegis varaudi miz-nis Sesabamisia, formulirebasrulyofilia.
kvlevis mim-dinareobis
arasworadCamoTvlis kv-
CamoTvlis kvle- CamoTvlis kvle- detaluradCamoTvlis
-
monacemebis -ricxavs monace-mebs
nawilobrivsworad, magram
-ricxavs monace-mebs
srulad, magram -
ricxavs monace-mebs,
-cemebs srulad da sistemurad
monacemTaanalizi
arasworadaanalizebs mo-nacemebs
monacemebis ana-lizi arasrulia
monacemTa anal-izi ZiriTadad srulia
monacemTa anal-izi srulyofil-ia.
daskvna daskvnebi aras-woria
akeTebs nawilo-briv swor daskvnebs
akeTebs ZiriTad daskvnebs
akeTebs srulfa-sovan daskvnebs
s abu ne bi smetyv elo me c ni er eb e bi
344
d) Semajamebeli davalebebi
davalebis tipebi: sakontrolo, gamocda, testireba, savele/gasvliTi samuSaoebi,
prezentacia da sxva.
SeniSvna: arCeviTpasuxiani testuri tipis davalebebi ar saWiroebs rubrikebis
saSualebiT Sefasebas. qulebi iTvleba testis swori da araswori pasuxebis
raodenobis mixedviT.
fasdeba Semdegi unarebi:1. saazrovno unar-Cvevebi2. kvlevis unar-Cvevebi3. problemis gadaWris unar-Cvevebi4. TviT-marTvis unar-Cvevebi
e) proeqtebi
davalebis tipebi: kvleviTi, modelirebis tipis, aqcia, gamofena, warmodgena da
sxva.
fasdeba Semdegi unarebi:1. saazrovno unar-Cvevebi2. kvlevis unar-Cvevebi3. problemis gadaWris unar-Cvevebi4. socialuri unar-Cvevebi5. komunikaciis unar-Cvevebi6. TviT-marTvis unar-Cvevebirubrikis magaliTi erT-erTi aqtivobisaTvis:
kvleviTi tipis proeqti
1-3 4-5 6-7 8-10
ar Seesabameba-
os
nawilobrivSeesabameba
-os magram bun-dovania
nawilobrivSeesabameba
-os magram araz-ustia
Seesabam-
sferos naTlad aris gansaz-
mizani bundovania (Ses-aZlebelia ar ukavSirdebodes
bundovania, ma-gram ukavSird- dakavSirebulia,
Tumca formuli-reba arazustia
mizani srulad Seesabameba
sakiTxTandakavSire-buli in-formaciismogroveba
iyenebs mxolod sakuTar cod-nas da ra aqvs moZiebuli in-formacia
iyenebs mxolod -
vanelos infor-macias
iyenebs mxolod ramdenime sain-formacio wy-
-bebs
iyenebs mraval-ferovan sain-formacio
-alebebs
345
kvlevisgegmis Se-muSaveba
kvlevis gegmadroSi ar aris gawerili da SesasrulebelisamuSaobi ara-sakmarisia
kvlevis gegma droSi araTan-mimdevruladaris gawerilia da moicavs Ziri-Tad samuSaoebs
kvlevis gegma droSi gawer-ilia da moicavs ZiriTadi samuS-aoebs
gegma Tanmim-devruliadmoicavs yvela samuSaoebs
kvelevisCatareba da monacemebis
arasworad kiTx-ulobs gegmas, ar miyveba gegmis
-mebs arasworad
ZiriTadadgegmis mixedviT atarebs,monacemebs aras-
-avs
gegmis mixedviT atarebs, monace-mebs ZiriTadad
-avs
gegmis mixedviT atarebs, mona-cemebs srulfa-
-avs
grafikebida diagr-amebi
arasworad agebs diagramebsada grafikebs, ver gansaz-
-rad cvladebis damokidebule-bas
agebs grafikebs, cvladebsnawilobrivsworad gansaz-
agebs diagrameb-sa da grafikebs, sworad
cvladebisdamokidebule-bebs, aqvs xarve-zebi monacemebis Setanisas
agebs dia-gramebsa da grafikebs,sworad gansaz-
-ladebs. swo-rad Seaqvs monacemebi,asabuTebs ama Tu im grafikis gamoyenebis
samuSaosSefaseba da daskvnebisgakeTeba
daskvnebi war-modgenilia,magram ar ga-momdinareobsmonacemebidan
daskvnebi uka-vSirdeba mona-cemebs, magram arasworadaa
-buli
daskvnebi mona-cemebidan ga-momdinareobs,magram mxolod nawilobrivsworia
daskvnebi mo-nacemebidan ga-momdinareobsda sworadaa
-buli
moklewerilobiTiangariSis(oqmis)momzadeba
oqmSi ar asax-
detalebi
oqmSi detalebi qaosuradaa war-modgenili
oqmSi asaxulia mxolod ZiriTa-
oqmSi srulfa-sovnad asaxu-
ar akmayofi--
taciisaTvismniSvnelovani
-cerT moTxovnas
akmayofilebs-
isaTvis mniS-vnelovani
mxolod mcire nawils
akmayofilebs-
isaTvis mniS-vnelovani
mxolod nawils
akmayofilebs-
vis mniSvnelo--
trebs
s abu ne bi smetyv elo me c ni er eb e bi
346
mosazrebebi safexurebis mixedviT komponentebis prioritetulobis Sesaxeb
(im SemTxvevisaTvis, Tu maswavlebeli airCevs yvela SemoTavazebul variants)
I dawyebiTi safexuri
1-li klasi me-6 klasi
1. gakveTilze CarTuloba 25 % 15 %
2. mimdinare saklaso davalebebi 55 % 40 %
3. Semajamebeli davalebebi 5 % 15 %
4. saSinao davalebebi 5 % 15 %
_ 5 %
10 % 10%
II їѕї¦± їє»Ё«®·
me-7 klasi me-9 klasi
1. gakveTilze CarTuloba 15 % 10 %
2. mimdinare saklaso davalebebi 40 % 30 %
3. Semajamebeli davalebebi 15 % 20 %
4. saSinao davalebebi 15 % 15 %
5 % 15 %
10% 10 %
347
III saSualo safexuri
me-10 klasi me-12 klasi
1. gakveTilze CarTuloba 10 % 5 %
2. mimdinare saklaso davalebebi 30 % 20 %
3. Semajamebeli davalebebi 20 % 25 %
4. saSinao davalebebi 15 % 20 %
15 % 20 %
10 % 10 %
s abu ne bi smetyv elo me c ni er eb e bi
349
proeqti
proeqti dawyebiTi klasebisaTvis
mizani: moswavleebSi damoukidebeli muSaobis, TanamSromlobis, komunikaciis, weris,
xatvis, simReris unar-Cvevebis ganviTareba.
1.mosamzadebeli samuSao
proeqti iTvaliswinebs saganTaA integracias. proeqtze muSaobisas saxvadasxva sagnis maswavleblebi erTad arCeven Tematikas da gansazRvraven amocanebs.
amocanebi:
moswavleTa motivacia anu werilis gacnoba;jgufebSi Sesasrulebeli samuSaoebis SerCeva; samuSaoebis Sesrulebis vadebis dadgena;prezentacia mSoblebisaTvis; Sefaseba.
miznobrivi jgufi: meore klasis moswavleebi
proeqtis ganxorcieleba
1. moswavleTa motivacia. werilis gacnoba
maswavlebeli acnobs moswavleebs werils.
werili
Cven okeanis erT patara kunZulze vcxovrobT, romelic Zalian lamazia. vswavlobT meore klasSi. CvenTan sul cxela da mze anaTebs.
gakveTilebis Semdeg, erTad vTamaSobT da kargad verTobiT. samwuxaroa, rom CvenTan sul zafxulia da araferi icvleba. TqvenTan ki gacilebiT ukeTesia, radgan zamTari modis da SegiZliaT TovlSi TamaSi. sainteresoa, ramdeni dRe SegiZliaT iTamaSoT TovlSi? Cven Tovli arasdros gvinaxavs, arc simRera viciT zamTarze, Tovlze. Cvens kunZulze erTi saTamaSo saxli gaixsna, sadac xelovnuri Tovli moitanes da ar viciT, rogor viTamaSoT da gaverToT. iqneb dagvexmaroT.
2. jgufebSi Sesasrulebeli samuSaoebis SerCeva.
maswavlebeli moswavleebTan erTad gegmavs: ra SeiZleba gaugzavnon okeanis kunZulel bavSvebs dasaxmareblad.
3. savaraudo CamonaTvali:
upasuxon werilze (sad cxovroben, romeli skolis da klasis moswavleebi arian);daxaton zamTari;daxaton, rogor TamaSoben zamTarSi da gaukeTon warwerebi;Caweron simRera zamTarze da gaugzavnon;gamoiangariSon zamTris dReebis raodenoba.
1.2.3.4.5.
dawyeb iTi klas eb i
350
4. samuSaoebis Sesrulebis vadebis dadgena
maswavlebeli Tanxmdeba moswavleebTan, rom erTi kviris ganmavlobaSi qarTulis, maTematikis, xelovnebis da musikis gakveTilebze imuSaveben am proeqtze.
moswavleebi iyofian jgufebad da TiToeuli jgufi iwyebs CamoTvlil sakiTxebze muSaobas.
5. prezentacia mSoblebisaTvis.
proeqtis dasrulebis Semdeg, dapatiJeben mSoblebs da TiToeuli jgufi gaacnobs im masalebs, romelic moamzades gasagzavnad.
6. Sefaseba
mSoblebi afaseben moswavleTa namuSevrebs da yvelas ukeTeben pozitiur komentarebs.