aTwiladebiT. msjeloba SeiZleba gagrZeldes manam, vidre moswavleebi ar mivlenim daskvnamde, rom sasurvelia arCeuli iqnes iseTi ricxvi, romelic sayovelTaostandarti iqneba amgvari saxis raodenobrivi informaciis gamoqveynebisas. amisSemdeg, bunebrivad SeiZleba procentis cnebis Semotana (ix. paragrafi me–5. procenti).vTxovoT moswavleebs, gaixsenon sad SexvedriaT es simbolo, vaCvenoT raime, razedacaRniSnulia Semadgenel nawilebs Soris TanafardobT procentuli saxiT (mag. wamlisyuTi an Sokoladis fila) da vTxovoT procentTan dakavSirebuli warwerebisganmarteba.mokled gavacnoT moswavleebs procentis da misi gamomsaxveli simbolos warmoSobisistoria, ganvumartoT sityva „procentis“ etimologia (5 wT).vavarjiSoT moswavleebi wiladebisa da aTwiladebis procentis saxiT gamosaxvaSi dapiriqiT (sav. 2, sav. 3, sav. 7, sav. 11, sav. 12); ricxvis procentis povnaSi (sav. 4, sav. 8, sav.9, gv. 16) (15 wT).sasurvelia savarjiSoebis miTiTebul nomrebSi mocemuli magaliTebidan nawiligairCes gakveTilze, nawili ki mieces saSinao davalebad.„procenti“ me–15 saukunis bolos vaWrobasTan dakavSirebulma saqmianobam warmoSva.magaliTad, mogebam, wagebam, gadasaxadebma, Tumca es idea gacilebiT adre gaCnda, maSin,roca romis keisarma avgustusma gadasaxadebi gaadida yvela im produqtze, romelicgayidvaSi iyo. vaWrobidan amoRebuli gadasaxadi 1/100–s Seadgenda. gadasaxadi yovelgaTavisuflebul monaze 1/20–s, xolo yovel gayidul monaze — 1/25–s.me–15 saukunis italiuri „manuskriatebi“ Seicavs 20 procentis aseT Canawers:„20??????100“.me–16–17 saukuneebSi komerciul saqmianobaSi ukve aqtiurad gamoiyeneboda procenti– mogebisa Tu wagebis saCveneblad.italieli vaWrebi mogebas yovel 100 dukatze ase angariSobdnen: „20 per cento?“ (e.i.yoveli 100–dan 20). mokled ki werdnen `20 pc“ Cqari werisas pc waagavda „%“–s da aseTandaTanobiT „%“ simbolo gaxda aRmniSvneli „measedisa“.500–is 20% niSnavs – 20 500–is yoveli 100–dan, e.i. 500–is 20%=20·500100 =100.20masc_cigni_VII_kl_cor.indd 20 03.07.2012 15:46:25
saprezentacio gakveTili „damoukidebeli kvlevisTvis“ micemuli amocanisaTvissaswavlo miznebimoswavleebmaganaviTarondakvirvebisunaridaeuflonmonacemebiswarmodgenasdiagramissaSualebiTmieCvion cxrilSimocemulimonacemebismixedviT sworidaskvnebisgakeTebasTemisprezentaciagaiwafongamoTvlebisCatarebaSi,geometriulixelsawyoebisgamoyenebaSiSeZlon droisukeT ganawilebamecadineobisa dadasvenebisaTvisaucilebeliwina codnacxrilisSedgenamonacemTasaSualosgamoTvlawris nawilebicentralurikuTxeerTi anramdenimemoswavlericxviswiladinawili,procentiricxvisdayofaproporciulnawilebadaqtivobebimoswavleTacodnisaqtivizaciawinaswarmomzadebulcxrilzemuSaobamoswavleTaorganizebadroisganawilebaresursebiSefasebisformamTeli klasi 5 wT fargali dakvirvebaindividualuri15 wT saxazavitransportiriCanawerisgacnobadiskusia mTeli klasi 10 wT dakvirveba kuTxisgradusulizoma10 wT furceli dasaweri kalamiCanawerisSemowmebasaprezentacio gakveTili „damoukidebeli kvlevisTvis“micemuli amocanisaTvis (III Tavi. § 4)gakveTili sasurvelia Catardes me–3 TavSi gadmocemuli masalis Seswavlis Semdeg.savaraudo xangrZlivoba: 45 wT.me–4 paragrafis 12 savarjiSo moswavleebs gagrkveuli drois ganmavlobaSidakvirvebis Sedegad unda gadaewyvitaT. maT ukve Sedgenili aqvT cxrili, aqvTgamoTvlili saSualod ra dros andomeben yoveldRiurad gakveTilebis momzadebasda ra dro rCebaT daskvnebisa da garTobisaTvis, TiToeul sagnis momzadebazesaSualod daxarjuli dro.gakveTilze ki moswavleebma unda aagon wriuli diagrama, romelic gamosaxavssaSualod dRis ganmavlobaSi daxarjul dros: Zilze, mecadineobaze, garTobaze dasxva danarCenze.moswavleTa codnis aqtivizacia.Sesrulebuli davalebis irgvliv sasurvelia daisvas SekiTxvebi: daaxloebiT ra drosxarjaven moswavleebi mecadineobaze. sxvadasxva sagnebis momzadebaze, maTematikissaSinao davalebis Sesrulebaze. ra dro rCebaT garTobisaTvis?SevaxsenoT is aucilebeli wina codna, rac saWiro iqneba mocemuli davalebisSesasruleblad davsvaT SekiTxvebi: ras ewodeba wre, seqtori ramden graduss moicavswrewiri, wris ra nawilia 90°–ian, 60°–iani, 120°–iani seqtori?21masc_cigni_VII_kl_cor.indd 21 03.07.2012 15:46:26
- Page 2 and 3: nana jafariZemaia wilosaninani wula
- Page 4 and 5: IV Tavi .. . . . . . . . . . . . .
- Page 6 and 7: erovnuli saswavlo gegmaწლის
- Page 11 and 12: მიმართულება:
- Page 13 and 14: III Tavimonacemebi.cxrilebi.wriuli
- Page 18 and 19: gTavazobT ramdenime gakveTilis sani
- Page 22 and 23: diagramis ageba:sTxoveT moswavleebs
- Page 25 and 26: aqtivobis aRwerademonstrireba: gakv
- Page 27 and 28: eziume:I Tavi1. gameorebamoswavlem
- Page 29 and 30: 13. a) ((2(x+1)+10):5+8)·3-6=30((2
- Page 31: 27. P=2(2x+12)=4(x+6)sigrZe x+12sig
- Page 34 and 35: 12. ipoveT, ra cifriT bolovdeba ric
- Page 36 and 37: 4. naSTi movZeboT rogorc cifrTa jam
- Page 38 and 39: 4. amocana gamodgeba jgufuri muSaob
- Page 40 and 41: 21. x+2x+3x=222.x=3722. I - x II -
- Page 42 and 43: 4. 144-isa da 162-is umciresi saerT
- Page 44 and 45: g) d)4. a) 1 wertili b) 3 wertili5.
- Page 47 and 48: 15. a) yvela meSvideklaseli wiTuria
- Page 50 and 51: Seamowme Seni codna1. wrfeze agebul
- Page 53 and 54: 6. (180°-130°)·2=100°.7. a=6m+2
- Page 56: 14. ar SeiZleba _ Tu A, B da C wert
- Page 61 and 62: 5. procenties gakveTili sasurvelia
- Page 63 and 64: amoxsnebi, miTiTebebi:2 # 1003. kla
- Page 65 and 66: amoxsnebi, miTiTebebi:AC1. g) BC=3.
- Page 67 and 68: 4. rioni — 300 km; enguri — 300
- Page 69 and 70: 2505. a) = 0, 2 =40020%; b) . 0,29
- Page 71 and 72:
gaecnobiTIV TaviuaryofiT ricxvebs.
- Page 73 and 74:
eziume:3. ricxvis modulimoswavlem u
- Page 75 and 76:
amoxsnebi, miTiTebebi:6. WeSmaritia
- Page 77 and 78:
eziume:7. gamravlebis ganrigebadobi
- Page 79 and 80:
17. AC=2x da BC=5x; 7x=14, e.i. x=2
- Page 81 and 82:
25.iyorom yofiliyosiCqare x x+10man
- Page 83 and 84:
24. drois erTeulad CavTvaloT is dro
- Page 85 and 86:
amoxsnebi, miTiTebebi:1. a) 7; 10;
- Page 87 and 88:
eziume:3. grafikimoswavlem unda SeZ
- Page 90 and 91:
eziume:8. samkuTxedis kuTxeebis jam
- Page 92 and 93:
7. A(-2;-1) B 1(2;1).8.9.1 $ 10% +
- Page 94 and 95:
12. monakveTis SuamarTobireziume:mo
- Page 96 and 97:
amoxsnebi, miTiTebebi:2. ABC samkuT
- Page 98 and 99:
4. wertilidan wrfemde manZilis da s
- Page 100 and 101:
AP6. ∠BPN=∠NPB=45°.BNC8. a= b
- Page 102 and 103:
19. rombi, rombis farTobiamocanebi:
- Page 104 and 105:
11. a) simetriis centria diagonaleb
- Page 106 and 107:
24. samkuTxedis erT wverosTan mdeba
- Page 108 and 109:
sakontrolo wera №51. Tu A 1wertil
- Page 111 and 112:
8. b) 8x-3-(5-2x)=4,38x-3-5+2x=4,31
- Page 113:
OR12. B ∆OAB-Si AB
- Page 116 and 117:
9. kubebis jami da kubebis sxvaoba1