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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
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:
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.
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?
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.
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.
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.
“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.
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
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?
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
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.
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
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.
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
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.
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)
moswavleebma ician algebruli gantoleba, cxbxay о , romliTac kvadratuli funqcia moicema da ician isic, rom am funqciis grafiki aris parabola. am aqtivobis mizania,
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?
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
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
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.
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.
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.
(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.
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:
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.
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.
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.
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
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.
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.
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.)
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.
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:
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)
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.
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.
sinaTlis wyaros mdebareobis nebismieri cvlileba Crdilis cvlilebasac iwvevs. am dros icvleba Crdilis forma, zoma da mdebareoba. am aqtivobaSi mze sinaTlis wyarod iqneba gamoyenebuli.
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.
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.
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.
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):
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);
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.
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
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
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
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
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.
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.
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.