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Автор: Горецкий В.Г.
Теги: педагогика пособие для учителей издательство просвещение школьное образование советская школа
Год: 1971
Текст
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OKOHQaTe.nbHoe cym,neHHe 06 OBJIa,lteHHH H8BbIKOM tlTeHMH Toro HJIH HHoro TpeTbeKJIaCCHHKa MO>KHO BbIItoCHTb TOJlbKO Ha OCHO- BaHR" CBO){HbIX )J.aHHbIX, T. e. 8HHbIX, nOJIYtIeHHbIX npH 38Me- pax no J<a>K){OMY H3 KOMnOHeHTOB, COCTaBJIHlOlUHX HaBbIK tlTeHHH. B MeTO){HtIeCKOH pa3paooTKe ypOKOB TeHHH YQH- nnaHHposaHHe CMCTe- TeJIeM MO>KHO Hal\1eTHTb TPH Ba:n{Hble cTyneHH: Mbi YPO08 no OT- 1. 03HaKOMJleHHe C co.nep}KaHHeM nporpaMMbl no AenHHo:H "!eo,::8M- qTeHHIO Ii ;'SlcHeHHe Tex TpeooBaHHH, KOTopbIe OHa npe,lt'bHMHeT KO BceMY KYpCY qTeHHH BIll KJlaCce. 2. 06JtYMbJBaHHe CO){ep>KaHHH H IJ.eJIeBOrO Ha3Ha1JeHHSI KOHKpeT- U u HOH nporp8MMHoH TeMbI; BbIRBJIeHHe JIOrHKH B paCnOJIO)KeHHH MaTepHa" u JIOB, pe,nHa3HaqeHHbIX ,nJIH pacKpbITHH ,naHHOH TeMbI B KHHfe M5I KJIaCCHOro qTeHHH; pacnpe){eJIeHHe 3THX MaTepHaJlOB no .qaCTHM B co- . u OTBeTCTBHH C CHCTe&IOH ypOKOB no 'feMe. 3. npoeKTHpoBaHHe B paMKax YCTaHOBJleHHOH CIfCTeMbI ypOKOB no TeMe Ka>KJ{oro OT,l{eJlbHOrO ypOKa H npo.nYMbInaHHe cnoc060B ero Half- JIYllwero npOBe){eHHH. Ka)K.D.aH H3 9THX cTyneHeH Ba>KHa caM no ceoe H onpe.D.eJ1ReT Ka- qeCTBO nOAfOTOBKH H npOBe,neHHH ypOKon tITeHHH. O.D.HaKO Ha BTOpOH CTyneHH - nJlaHHpOBaHHe CHCTeMbl ypOKOB no OT){eJIbHOH nporpa{- MHOH TeMe - HY>KHO OCTaHOBHTbCH no,npo6Hee. By.neT He' COBceM BepHO, eCJIH BCIO paOOTY Ha 3TOH cTyrreHH CBe- CTH JIHWb K- 03HaKOMJIeHHIO C pacnpe){eJleHHeM ypOKOB no TervIe, KOTO- poe, HanpHMep, npeJ{JIaraeTCH B MeTOJl.HqeCKHX YKa3aHHHX K KHHre ,ltJlSl qTeHHH. nO,Z{OOHbIe peKOMeH){aI.{HH MO>KHO, KOHetIHO, B3RTh 3a OC- HOBY, OTJlO}l{HB BbI60p OKOHqaTeJIbHOrO BapHaHTa Ha TO BpCl\fH, KOf)J.a) Bo-nepBbIX, Oy,nYT TLUaTeJlhHO rrpOCIOTpeHbI MaTepHaJIbI B KHHre .nTJH tITeHHH H COOTHeceHbl C CHCTervlOH ypOKOB, pa3pa60TaHHOH B «MeTO,l{HtI- Ke», Ii, BO-BTOPbIX, Kor,Z{a 6y.neT npo,nYM8H8 B03MO>KHOCTb BHeseHHH B 3TY CHCTeMY H3eCTHblx H3MeHeHHH t HymHbIx ,l{JlH Toro, qTOOhl OKOH- qa'fMbHblH BapHaHT C HaH60JIbllIeH nOJIHOTOH OTBetI8J1 ocooeHHOCTSlM ){aHHOrO KJIaCCa H n03BORHJI TBOpqeCKH HCrrOJlb30BaTb pa3JIHqHMe Me- TO){HqeCKHe npHeMbl )J.JISI ycnewHoro perneHHH 06pa3pBaTeJIbHO-BOCHH- T8TeJIbHblX 38){8tI, CTOSlInHX nepe,l{ CHCTeMOH ypOKOB no Tef\1e If nepe;:l Ka>K,nbIM OTJ{eJlbHbIM YPOKOM. TaK, HanpHMep, nepBaH nporpaMMHaH TeMa «nHOHepbI - IOHbIe JleHHHlJ,bl» no CBoeMY u.e.neBOMY Ha3HaqeH'HIO, .nOJI}KHa, KaK" 06 3TOM CKa3aHO B «MeTO){HQeCKHX YKa3aHHHx K KHHre ,n.nH qTeHHH «Hallia PO)J.H- Ha», «BbI3bIBaTb y ,neTeH "HTepeC K }KH3I1H " ,lteHTeJIbHOCTH TIHOHepCKoH opraHH3alJ,HH, BocnHTbIBaTb yna}KeHHe k CTapmel\iY nOKOJIeHHIO KO- MYHHCTOB, 38BoeBaBllIeMY ){JIH HHX CqaCTJIHBOe ,neTCTBO, B030Y>KJ(aTb }KeJIaHHe CTaTb nHoHepaMH»l. TOT <paKT, liTO 9TOH TeMoH Ha1JHHal0TCH YPOKH" qTeHHH B I I I KJIaCce, BbI.ltBHraeT nepe.lt HeM H ,nonOJIHHTeJIbHble IJ.eJIeBbIe YCTaHOBKH: Bo-nep" / 1 c'4TeHHe BIll KJIaCce. MeTOJJ.HQeCKHe YKa3aHHB K KHHre J{JIH qTeHIUl «Hawa PO,luiH(1». M., CnpocBexneHHe», 1971, CTp. 7. 12
BIJIX, «nO)ll1ep>KaTb XOpOlnee, paJl-OCTHOe HaCTpOeHHe YQallU1XCH npH BCTpetle co WKOJIOH, YllHTeJ1eM, TOBapHmaMH; o606rnHTb BneQ8TJIeHHH, JlOJJYtJeHHbIe eTbfH BO BpeMH JIeTHerO OT,nbIXa»l; BO-BTOpbIX, cpa3Y >He BI<JlIOtJHTb eTeH B YQe6HYIO paOOTY, KOTopaH He TOJIbKO BOOpY>KHT HX :UIClIHiHMH, no O){HOBpeMeHHO oy,neT cnOCOOCTBOBaTb (jJOpMHpOBaHHIO II coneprneHCTBOB8HHIO psr,na HaBbII<OB H ocooeHHO HaBbIK8 QTeHH'H. B KHHre )tI1H tITeHHH «HaIIJa Po,nHHa» .nnH peaJIH3aUHH Bcex 9THX ur.nc" B pa3eJIe «nHOHep rOTOB K 6qpboe 38 JIeHHHCKoe ,lleJIO» nOMe- IHPHO 14 TeKCTOB, 9 H3 KOTOpblX CTHXOTBopHbIe, 8 OCT8JIbHbIe OTHO- (TCH K 6eJIJIeTpHCTHtJeCKHM npOH3BeeHH51M H ,lleJIOBbIf\i CTaTbHf: Ha H3YQeHHe BceH TeMbI nporpaMfOH OTBO,nHTCH 6 tJ8COB 2 . npH 9TOM JIOrHKa pacnpe,neHH51 MaTepHaJIOB no ypOK8M OJlH3Ka K JIOrHKe pncnOJIO}KeHHH TeKCTOB B KHHre )J.JIH lITeHHH. B IIMOM BCH CHCTeI\fa ypOI<OB CnJIaHHpOnalla TaK: N, y po;", h\aT(pIta.nLJ A-SI 1JTeHIiH )l(aHp 2 J1. 0 ill a H H H. OT1JH3Ua CTHXII 1\'\. 11 J1 b H H. Hallla LI.eJIOBa CTaTb POJlHU3 " H. K. K p y n C K a H. ,D.CJl013aH CTaTbfi BY.Il-b rOTOS! C. llI. H n 3 11 e B. nHO' CTHXH HepCKHA raJICTYK 10., a H T H H. nepBO- CTHX", OT11I B81eJ1 H , I. 1(. p n e H K o. BeJJJleTpHCTHlJe- . TopacecTBeHfloe oC5ew.8HHe CKoe npOH3Be,l{e- Hue E. T P Y THe B 8. TpH CTHXH I<OHu.a H. M 9 B e K 0 n a. nep- 88 Sf BblCOTa 8 4 5 BeJ1JIerpHCTHlle- CKoe npOH3Be,l{e- Hue CTHXH 6 3. A JI e K C 8 H .II- po B a. BOT MbI KaK8H CHna! 10. 51 K 0 B J1 e B. noxo)J.- HbIA p33roBop B. JI e 6 e ,lJ. e B. I< Y M a q. BYAb rOToBI \ A. )1\ 8 P 0 B. B3BeATecb KocTpaMH! eMs nHCbM8 10. rsrapHH8 C9BeTCKHM fiHOHepaMt r. P y 6.11 e B. nHonep- CK8H npa3,lJ.HH1IH8H .lle.nOBag CTaTbH CTHXH CTHXH CTHXH CTHXH 7 Cnoco6 npOBe,lJ.eHHs) nepnOHa- qanbHono qTeHUSI TeKCTa Y lJ" T{,.JI b Yqaw.HecH, npo Ce6fl YlJ3111HeCH, nCJ1Yx Y lJHTenb Y llalllHeCH, npo ce6S1 YtlHTenb Y tJHTenb Yqaw.ReCH. npo ce6H Y t.(HTenh ¥IIHTenb YtJHTeJlb Y tUfTeJlb YIJaw.HeCH, BcnyX BJlH npo ce6H ¥IIHTeJlb 1 «lJTeHHe B III Knacce. MeTO,lJ.HtleCKHe YKa3aHHSI K KIIHre .Il-JISI 'freHHB cHama POJU.fU8». M., «TIpocseweHHe», 1971, CTp. 8. 2 ABTOpbl KHRJ'H ,lJ.JlSI q:reHHSl H MeTO,lJ.H1IeCKHX paapaOOTOK K HeB YBeJlHqBSSIO'l 'JHCJIO ypOKOB }J.O 7. 13
MO}i{HO. KOHetIHO, OCTaHOBHTb CBOH, Bb160p Ha ,naHHOH CHCreMe ypOKOB. O)J.HaKO B03MO>KeH H RHOA BapHa'HT. npH ero pa3paOOTKe YtlH- TbIBalOTCSI He TonbKO rnaBHbIe n03HaBaTeJIbHbIe 3aJ(a1JH, cToHw.He nepe,n; BeH TeMOH, HO H ononHHTenbHe oopa30BaTenbHO-BocnHTaTenbHwe UeJlH, 0 KOTOpbIX Y>Ke llIJla petIb BbllIIe. TaK, ecnH Ha ypoke llJIalIH- pyeTcH 3yqeHHe .l1BYX npoH3Be,neHHH, MeTOAHqeCKH UeJIeC006pa3Ho nepBbll\f II3yqaTb np03aHQeCKHH TeKCT, oco6eHHo KorJ].a OH ,ne.nOBoro co,nep>KaHHH. Ee K. ,a. YlllHHCKHH OT&letIaJI, liTO npH TaKOR noc-neJ].o- naTeJIbHOCTH H3YtIeHHH MaTepHanOB nepBblH TeKCT CBOHM COAepiKaHHeM II CJlOBapeM H8HJiYtlllIHM 06p830M no,nrOTOBHT BocnpHHTHe Broporo, no- rHQeCKaH MbIcnb OTbIeT ce6e n03THtleCKOe BbIpaiKeHHe, a OHO 3aKpe- nHT caIY MbICJIb l . KpOMe TOro, cneyeT B3BecHTb, Bcerj\a nH J1OJ1!KeH YQHTeJIb npH nepBOf 3HaKOMCTBe Y1JarnHXCH C npOH3Be,lleHHel\1 6paTb ero tlTeHHe H8 ce6fl. TaKHf 06pa30:VI, CHCTeMa ypOKOB no nepnOH TeMe MO}KT 6bITb CnJIaHHpOBalla TaK: , N2 ypoKa MaTepHa.'bJ A-'SI 'ITeHIUI 2 M. H JI b H H. Hawa POHHa 11. 0 w a H H H. l-Iarna POHHa H. K. K p y n C K a H. BY.IJ.b rOToal C. III. H n a t[ e B. nHO- HepcKHH raJ1CTYK r. K a p n e H K O. Top- >KeCTBeHHoe ooem.aHHe 3 4 H a .n 0 M: caMOCTon- TeJ1hHOe 4TeHne CTUXOB E. TpYTHeBoH «Tpli KOHua» H. H 3 Be K 0 B a. nep- BaSI BbICOTa 5 6 3. A JI e K C a H P 0- B a. BOT MbI KaI<aH cHJ1al 10. 51 K 0 B JI e B. noxo)).. Hbli pa3rOBOp «113 nHCbMa 10. rara- pHlIa COBeTCKH1 nHOHepa1» f. P y 0 JI e B. nHOIIep- CK8H npa3.ltHHtlHan B. 11 e 6 e .D. e B- K Y M a q. BYb rOToB! A. )K a p 0 B. B3Beu- · TeCb KocTpaMH! 0606ueHHe no TeMe 7 ')KaHp , ,l:LeJIOBaH craTbSI CTHXH ,lLenoaaH craTbH CTHXH 5eJIJleTpHcTHtte. CKoe npoH3BeAe- HHe CTHXH 5eJ[neTpHcTH lle- CKoe npoH3Bee-_ HHe CTHXH CTH.XH ,l:LenooaH CTaTbH CTHXH CTHXH CTHXH BHA nCpnOHaqilJI bHOro tlTem.m TeKCTa Yqaw.Hecn, nCJIYx YtlHTMb ¥tlalll-HecSI, BCJlYX ¥ tl8Ll(HeCH, npo ceoSl H BCJI Y X Yqaw.HecSI, BCJ1YX YqaIl.{HeCSI, npo ceoH H BCJlYX YttaIl.{HeCH, BCJJYX H npo ceo H , ¥ tlHTeJlb ¥tIHTCJ1b ¥tlall.{HeCSl, Bcnyx ¥llaulHecH; npo Ce6S1 H BCJlYX YtlHTeJlb Y qHTeJlb 1 CM.: 1<. ,a. Y W H H C K H H. Coop. COq., T. 5. M., 113.;1.-80 AnH PC<1>CP, 1949, CTp. 32. 14
CTHXOTBopeHHe 10. 9HTHHa «nepBOOTKpbIBaTeJlH» MOmHO npeMo" )KHTb ,llJ11 C8tOCT05ITeJIblIOrO Jl.OnO"TJHHTeJIbHOrO tfreHHH. npO,Z(YlaIllIOe H CBOeBpeMeHHOe nJIaHHpOBaHHe CHCTeMbI ypOKOB no 'feMe - Ha,ne>KHbIH MeTOJl.HQeCKI1H HHCTpYMeHT, n03BOJI5IIOInHH ytfHTe- '1I0 nO,Z(H5ITbC.H Ha,1J. Te{OH - H npe,Z(Ha3HatIeHHblMH ,nJl.H ee npOXO}I<}J.eHHSI MaTCpHaJIaMH H OTbICKaTb HanOOJIee npaBHJlbHblC nOJJ.XObI K HX Hay- lJeHHIO. C nOMOIIJ.blO 9Toro HHCTpYMeHTa l'YfO}l{HO Jl.06HTbCH P83YMHoro pa3Hoo6pa3H.H MeTOJl.HlIeCKHX npHeMOB H8 Kam,Z(OM ypOKe, llOJIHee 3arpy- 3HTb ytIarnHXCH HHTepeCHblMH 3aJl.aHHHMH, 3aMeTHO aKTHBH3HpOBaTb pa60TY no COBeprneHCTBOBaHHlOlHaBbIKa tITCHH5I H ,OT,lJ.eJlbHbIX ero CTOpOH. OC06eI-lIIO na)KlIO BceCTopOHHe npOJJ.YMbIB8Tb H 3a6'1arOBpeMeHHO IlJIaHnpOBaTb Te TeMbI, KOTopble 3aJ{JIlOtIalOT B ceoe TaK Ha3blBaeMbIii OOU1.eCTBeHHO-liCTopHtJeCI{liH MaTepUaJl, T. e. npOH3BeJl.eHH5I, PHCYIO- IIlIIC HCTOpntIeCKHe KapTHHbl npOUlJIOrO, 8 TaKJKe nOJl.HHMalOIII.He OT- )ll\flbHbIe BonpOCbI nOJIHTHtIeCKOH, 9KOHOlHtIeCKOH II rOCYJJ.apCTBeHHOH il(I13I1H B npOlll,,'10M H H8CT05ICl\f. lleJIo B TO1, lITO B KHHr8X Jl.J15I IITeIlH5I r\'laTepHaJI8IH, npe,ll,Ha3Ha- 'lellllbJrvlH .rI5I cpOpMHpOBaHHH Y TpeTbeKJIaCCHHKOB 06eCTBeHHO-HCTO- pll1JCCKlIX npc,nCTaBJ]eHHfI, tIame BcerO 5IBJI.HlOTC5I xYJJ.O}KeCTBeHHble II pOH3BeAeHHH. OHH, KaK 06 9TOM rOBOpH"TIOCb BbIIlle t tiMeIOT CBOIO CITe. IllICIJl-I KY Ii Tpe6YloT oc06oro nO'z(XOJl.a, o6eCnetIHBaIOero YtI8ll1.HMC "JCTCTUlleCKH nO'1HOIl.eHHOe BOCnpH5ITHe xY,Z(O}KeCTBeHHbIx o6pa30B H lIapHCOBaHHoM nHCaTeTIeM KapTHHbl B I.J:eJIorvl. npHpo,Qa )Ke o6ecTBeHHo-HcTopHtJecKHx 3IIaHHH Ii npeJJ.cTaBJIeHlIH 'l'HI<ona, lITO OHli B 3HatIHTeJIbHOH Mepe HMeIOT 0606m81OHii xapaKTep II 8 HX CTPYKType rJl8BHOe lvleCTO npHHa,l(JIeJKHT JIOrHIIeCKOl\1Y HatJa- J1Y, n09TOMY np" H3Y\leHHH npOH3Be,Z(eHHH, paCCHTaHHbIX Ha BO- 0pY>KeIiHe TpeTbeKJl8CCHHKOB onpe,lJ.eJ,1eHHbIMH OOIII.eCTBCHHO-HCTopHtJe- ('I(IJMH 3113IIJ1HMH, ypOKH HY>KHO MeTO,lJ.HtJeCKH CTpOHTb TaK, 1JTOObl oOeCnClJHlJaJIOCb HaHJIY1JWee B3aHMOJJ.eiicTBHe H B38HMoo6orameHlle XYJ1 0 >I<CCTBeHHo-o6pa3Horo H JIOrHlIeCKoro HaqaJI8. (),1.UIHM Ji3 cnoco60B ,ll,OCTH}I{eHlIH 9Toro 5IBJIHeTC.H TaKoe n,,'1aHHpO- IU111HC CHCTeMbl ypOKOB no TeMe, Kor,na Cnel(HaJIbHO_npeJJ.YCl\18TpHBaeTCSI npCMSI. Heo6xo,D.HMOe,lJ.JISI C}I{aTOrO, HO BMeCTe C TeM I.IeTKoro H cOAepLKa- Tt-JlbflOrO paCCI<838 YIJHTeJlR oc> 06m.eCTBeHHO-HCTopHlIeCKOll o6CTaHOB- IU, nonYQHBWeA OTpa>KeHHe B tJHTaeMblX TeKcT8X, H CJIOB8pHO-JIeKCH- 'ICCKoA pa(SOTbJ. BenH nporp8MMHoA TeoA OXBaTbIBaTCH HecKOJIbKO HCTOpHtleCKHX IIOPHOAOI (HlnpHMep. c)l(H3H& xpeCT&'HH H pa60tJHX ,ll,o BeJIHKOH OK- TJrGPlICXot .COI&HMHCTHoA peBOJlIOu.HH, HX 60pb6a npoTHB yrHeTa- TeneA»), to CJlOIO YlfHTMII ,ZtOJl>KHO npe,nBap.HTb tITeHHe OTJl.eJIbHbIX TCKCTOD, OTHOCII1QHXCJI K TOMY HJlH HHOMY H<?TopHtIeCKOMY oTpeaky npc.MeIiH. B ,D.8HHOM MeTo,lJ.HQecKOM noco6HH B CneUHaJIbHOM pa3eJIe nOMe- IIlellbl cnpaBOtJHble MaTepHanbl 06IUeCTBeHHO-HCTopHlleCKoro xapaKTe- Jill, I<OTopble nOMorYT YtJHTeJIIO B-nO,Z(fOTOBKe BBo,nHoro CJIOBa, a TaK)he JICI(CHlICCKoro H TepMHHOJIOfHtJeCKoro KOMMeHTapHH. 15
nJIaHHpOBaHHe CHCTeMbl ypOKOB no TeMe OtIeHb Ba>KHO .AJISI 9cpcpeK" THBHoro npOBeeHMH rrOBTOpHTeJIbHo-o606ll\alOIQ.HX ypOKOB. 11M" HY1K- 80 3aBepmaTb npOXO)K)leHHe Ka>K,ltOH nporpaMMHOH TefbI. CeHqaC 9TH ypOKH Hepe,ltKO CTpOHTCH no npHHUHny nepeqHCJIeHHH na3B3HHH npo. QHTaHHblX npOH3Be,lteHHH, OTBeTOB Ha BonpOCbl no HX co,nep>K3HHI0 H BblOOpOqHOrO lITeHHH OT)J.eJIbHbIX KYCKOB TeKCTa. nJIaHHpOBaHHe no- 3BonSieT npeJ{OTBpaTHTb nO)J.OOHbIH KOJIHtlecTBeHHbIH nO,l1xoJ{ K nocTpoe- HHIO nOBTOpHTeJ1bHO-o606InaIOIIJJIX 3aHSITHH; OHO nOMoraeT sapaHee .. u npe,ltYCMOTpeTb, qTO .lI.OJl}KeH np HBHeCTH Ka>K)lbIH OT)leJIbHbIH ypOK B i10BTOpHTeJlbHO-o6oornaIOInYIO paOOTY no TeMe H KaK HY>KHO C)J.eJI3Tb, qroObI YlIaUUieCH nO-HOBOMY B3rJIHHYJIH H3 Y>Ke npOHeHHbIH MaTe- pliaJ1, 3 3TO, Oe3ycnoBHo, npHBe,neT K H30eCTHblM KaqeC]BeHHbI:\f CJ{BH'" raM B OCMbICJ1eHHH IllKOJ1bHHKaMH Be,nYlllJIX BonpOCOB TeMbI. M OT Toro, KaK MeTo,nHqecKH OCHeH ypOK, Ha- 8To.qHllecKH8 YKa- 3aHN. K opraHM3aqHH CKOJIbKO ne.neCOOupa3Ha ero CTpYKTypa, 3.aBHCHT " np08e.qeHHIO oe. ero pesYJIbTaTHBHOCTb - K3qeCTBO npHoopeTaeMbIX HoaHIIIX .Tano. ypOKS yq3ll1.HHCH 3HaHHH, CHJ1a B03,lteHCTBHH yqeOHOrO 111eHH. M3TepHana H3 IlIKOJ1bHHKOB, XO,lt <pOpMHpOBaHHH pa3..TIHlIHbIX YMeHHH H HaBbIKOB, oc06eHHO H3BbIKa tITeHHR. CTPYKTypa ypOKa qreHHH MO)KeT CtIHTaTbCH ue.necoo6pa3HOH, eCJIH OHa, COOTBeTCTBYH cnenH<pHKe H3yqaeMOrO TeKCTa, oY)J.eT peaJIbHO oOecnellHBaTb MaKCHMaJJbHYIO sarpY3KY ypOqHOrO BpeMeHH qTeHHeM caMHX Y1JarnHXC5I. npH .9rof tITeHHe ,l10JI}KHO ObITb He TOJlbKO C03Ha- Te.1IbHbIM, npaBHJlbHbIM, 6erJIbIM H Bblpa3HTeJIbHbIM, HO H BbI3bIBalO- u u InHM y eTeH >KHBOH HHTepec. K CO>KaJIeHHIO, ,lt0 CHX nop Henocpe,nCTBeHHO Ha ypOKax qTeHHH \. caMH YlIeHHKH 1JHTalOT MaJlO. -npOHCXO,ltHT .9TO nOTOMY, tITO CJIHIllKOM MHoro qHTaeT YIIHTeJIb H CJlHlIJKOM BeJlHK YJ{eJlbHbIH BeC BCRKOi'O po,na 6ece,n H pa3rOBopOB B CH3H C qHTaeMbIM. nopoH Ha Bce 9TO YXO,nHT OT 30 ,no 45 MHHYT ypOIlHoro BpeMeHH (10-15 MHHYT - BBOHbIe 3a- HSITHH, 5-10 MHHYT - OTBerbl Ha Bonpocbl,- 10-15 MHHYT - COCT3B- neHHe ITJIaHa H nepecKa3bl, OKOJIO 5 MHHYT - OOOOrnalOll\a51 6ecea), npH1JeM Hepe)J.Ko oece,na CTpOHTCH Ha OCHOBe Toro BnetIaTJIeHHH 0 cOJ{ep- )l(aHMH TeKCTa, KOTopoe CJIO>KHJ10Cb y ,neTeH B XOJI.e ero nepBOHaQ3.Hb- Horo lJTeHHH. BH,lIJIMO, 3aMeTHoe YMeHblIIeHHe t:lTeHHH yqHTeJ1H Ha ypoKe, cOKpa- meHHe BpeMeHH H3 pa3HbIe 6eCe,ltbI H pasroBopbl npe,ltCTaBJUleT 060H TOT peaJIbHbIH pe3epB BpeMeHH, KoropblH HY>KHO licnO.n-b30BaTb ,nJ1H 3a- rpY3KH qTeHHeM yqaI.I.I-HXCH. B caMOM ,neJIe, eCJIH ,nonYCTHTb, liTO Bce 40 MHHYT ypollnoro Bp" MeHH (5 MHHYT COpOCHM Ha BCHKHe «oprMoMeHTbI») TpeTbeKJIaCCHHKH - u CTaHYT qHTaTb co cpe,nHeH ,ltJlH HHX CKOpOCTblO, TO npH IITeHHH BCJIYX OHH cnocoOHbI npOlJHTaTb 10 - 12 cTpaHHl, a npH tITeHHH npo ce6H - 14-15 CTp3HHn. PasYMeeTCH, liTO TaKoe YCJIOSHO J{orrym. eH - Hoe CllJlOlliHOe tJTeHHe (3a pe)J.lIaHLllHM HCKJII01JeHHeM) HepeaJIbHO H 1 B olIoii CTpaHHI1-C np03anqeCKOrO TeKCTa CO,Aep>KHTCH OT 300 o 330 cnOB. 16
He9cjJcpeKTHBHO. OJ{HaKO ono nOKa3blBaeT, KaK BenHKH B03MO>KHOCTM 3arpY3KH TpeTbeKJI3CCHHKOB 1JTeHHeM HenocpeJ{CTBeHHO Ha caMHX ypOK3X. HTaK, nOCMOTpHM, KaK MorYT tSblTb opraHH30naHbI OCHOBIIbIe 9TarrbI ypOKOB B nJI3He HaH60JIbWeH 3arpY3KH TpeTbeKJI3CCHHKOB llTeHHeM. B B 0 ,n H bI e 3 a H 51 T H 51, K3K H3BeCTHO, ,nOJI}KHbI nOJ{rOTOBHTb )J.eTeH K npe,nCTOHIneM]' CJlY1ll3HHlO HJJH qTeHHIO OToopaHHoro ,lJJIH ypo- K3 npOH3Be.neHHH. 06blqHO OHM CKJ1a)J.bIBaIOTCH H3 OO'b5lCHeHHH CJIOB; oece,nbI no Kpyry BonpOCOB, OJIH31{HX Tel\f, KOTopbIe nOJIYllHJIH oro- Op31KeHHe B npOH3Be.lleHHH; CJIOBa yqHTeJIH, opraHH3YlOIII.erO BHH- ,- M3HHe Y1JeHHKOB H BbI3bIBalOInero HHTepec K npeACTOSlIll.eMY 1JTeHHlO, H T. n. )l(enaTeJlbHO BBO){Hble 3aHHTHH CBO.llHTb K MMHHl\1YMY, KpOMe Tex CJIYllaeB, Kor.n.a OHM )J.OJILKHbI nO)lrOTOBHTb YllaInHxcsr K tlTeHHIO H pa3" ooPY TeKCTOB, paCCqHTaHHbIX Ha BoopY}KeHHe TpeTbeKJIaCCHHKOB OOIne- CTBeHHO-HCTOpHlIeCKHlYfH npe,nCTaBJIeHHHMH. ECJlH HMeeTCH B03MO>K- HOCTb B xo.ne BBOHbIX 3aHHTHH opraHH30B3Tb IITeHHe yqalI.{HXCR, TO 3THM HymHo BOCnOJIb30B3TbCH. HanpHMep, OO'bHCHeHHe CJ10B npo- BeCTH nYTeM tlTeMHSI 33paHee 3arOTOBJIeHHbIX KaprolIeK, nJlaKaTOB HJIH 3anHceH H3 )J.OCKe; npe){J10}KHTb )J.eTHM npOIlHTaTb THTPbi K AHa(j>HJIbMY, npOCMOTp KOToporo nO.nrOTaBJIHBaer K qTeHHIO TeKCTa, H T.,n. of n e p B a II a 11 a JI b Hoe q T e H H e TeKCT3 06eCneqHB3eT «He- nocpe)J.CTBeHHoe BocnpHHTHe JIHTepaTypHoro npOH3Be)J.eHHH»1 yqaI.II-H- MHCR. npH 1.JTeIlHH xY,AO>KeCTBeHHblX TeKCTOB B3>KH3 UeJIOCTHOCTb STOro HenocpeJtCTDeHHoro BocnpHHTHH, npH qTeHHH HaY1JHO-rronYJ1HpHOrO TeKCTI - npSBHJlbliOCTb olltero npeACT8BJleHHH 00 onHCblBae1vfOM npe,lJ.Mere, npou-ecce HnH HBJleHHH. B WKOJlbHOA npaKTHKe qame Bcero nepBoe tlTeHHe X Y)J.O>KeCTBeH- lIoro npOH3BeJ{eHHH YQHTeJIb oepeT H3 ceoH. He CTOJIb YLK peAI{O nO,Ao6Hb1M o6pa30M OH nocTyrraeT H C HaYIlHo..nonYJIRpHbUvIH TeK- CTaMH, OHaKo B YCJlOBHfIX p300Tbl no HOBbIM nporpaMMaM, Kor)J.3, nOBTO- pHeM, (50JlbW8H qaCTb ypotiHoro BpeMeHH )I.OJI>KHa 6bITb OT){an3 tJTe.. IIHIO yqaHxcsr, tJTeHHe ytlHTeJIeM HOBblX TeKCTOB CJ1e.llyeT CBeCTH .no pasYMHoro MHHHM}'Ma. 3Aech AeJlO He TOJlbKO B Tpe60BaHHRX nporpaM- Mbl. V1lHTeJlbCKOe tlTeHHe - STO OqeHb CHJlhHOe cpe)J.CTBO B03)J.eMCT- IHI al )'q8HXCSl - epReT CBOIO CHJlY, eCJIH, Bo-nepBbIX, HM nOJlUO.I".CI CJlHWKOM qaCTO H. BO.BTOpblX npOBO)J.HTb Oe3 TmaTeJIb- lIoA npUllpHTMhHOA norOTOBKH (a tl3CTOe 06pameHHe !{ HeMY cy- UecTBeHHO OCJIO>KHJleT BOSMO>KHOCTb TaKOH nOArOTOBKH). ITO.9TO!'ifY CBO- JIM tlTeHHeM B I{Jl8CCe YIlHTeJllO He CTOHT YBJIeKaTbCH H npH6eraTb I( lIeMY H3.ll0 TOJIbKO Tor.ll8, KOr,Aa 6ea 9Toro OOOHTHCb TPY){HO, H3npH" 1 O. H. H H K H CP'O P 0 8 a. BocnpHHTHe xYJlOmeCTBeHHOH JIHTepaTypbl WKOJIb- IIHKaMH. M., YQne.n.rH3. 1959, CTp. 12. 17
Mep, npH H3yqeHHH MHOfUX CTHXOTBOpelU1H H 6aCeH. nYCTb YtlHTeJlb- CKoe 1ITeHHe B KJIaCCe nepeCTaHeT 6blTb 6Y)J.HHtlHO nOBce,D.HeBubIM H flBHTCSI 06pa3UOM nO)I.JIHIIIIO BbIpa3HTeJIbHOrO tlTeHHH. npn paOOTe Ha xy,nO)KeCTBeHHbIMM. npOH3BeJl.eHHJIMH npOtlHX >KaH- , u pOB - paCCKa3aMH, CKa3KaMH, onHcaHHHMH neH3ama H np. - HY}K- HO IlIHpe npaKTHKOBaTb nepBoe qTeHHe, npOBo,nHl\fOe CHJlaMH ca- MHX TpeTbeKJIaCCHMKOB HJIH B l{ 0 M 6 H H a U H M C q T e H HeM y 11 M- T e JI n. nepBoe lITeHHe xYJl.O)KeCTBelIIloro npOH3Be,neHHH, opraHH30BaH- \ Hoe OO,nOOHbIM oopa30M, ,nOJI>KHO 6blTb 06H3aTeJ1bHO 3apaHee no,n- rOTOBJIeHO. A B llHCJIe yqaInHXCH, KOTOpblM OHO 6YJl.eT nopYlleHO, Ha- p 5],ny C XOpOIliO 1IHTalOInHMH AOJI)KHbI OKa3aTbCH tIHTalQIUHe cpe,nne H cJIa60. nonYTHO 3afeTHM, 1.11'0 YCTaHOBKa TO..rlbKO Ha CH..'IbIlbIX YlleHH- ){OB (a 1'IM-TO qaw.e Beero yqHTeJIb ,nOBcpHeT nepnOllal.faJIbHOe '-'lITe- HHe) ,naneKO He BCef){a onpaB.LlblBaCT ce05I MeTO)1.H4eCKH II nc,narorH- qeCKH. I1TaK, B O,nHH H3 ,nHeH, npeJl.llleCTBYIOInHX ypOKY, Ha KOTOpOM 33- nlaHHpOBaHO tITeHHe paCCKa3a CarvlHl\IH yqallI.HMHCH, MO,mHO, onYCTHIvI, Ha nepeMeHe HJIH nOCJIe ypOKOB nO,ll03BaTb 3-4 YtleHHKOB, HafeqeHHbIX 3apanee no tlHCJIY qaCTeH, BbI.LleJ1eHHbIX B paCCI{a3e, Ii npe.LlJlo.mHTb 11M xoporneHbKO norOTOBHTb ,nOf\.fa tlTeHHe YKa3aHHOH 1IaCTH. npH aTOM B KHHrax ,nJIH tJTeHHH Y CJIa6bIX yqeHHKOB "ymHo c,neJIBTb KapaH,nalliOM n01\1eTbI: BepTHKaJIbHbI1\1H tlepTaMH OTMeTHTb naY3bl (OJl.lIa tlepTa- KopOTKaH naY3a, ABe - OOJIee nIJOOJI}KHTeJ1bHaSi H T. n.); nOCTaBHTb yapeHHH B CJIOBaX, KOTopbIe MorYT ObITb npOtlHTaHbl OIlIH60tlJlO; no,ntIepKHYTb CJIOBa, KOTopble HeCYT B npe,nJIO>KeHHHX OCHOBHYIO CMbIC- JIOBYIO HarpY3KY, H T. n. . Kora Ha ypOKe eTH OAHH 3a pyrHM, Qen01lKOW, npOtlTYT BeCb paCCKa3, HM lvIO)KHO 6y.n-eT BbICTaBHTb OneHKH 3a lITeHHe. B03MO)KHbl CJIytJaH, KorJ(a nepBOHa1laJIbHOe IITeHHe KaKOrO-JIHOO npOH3Be.n-eHHH npOBoAHTCH TpeTbeKJIaCCHHKaMH caMOCTOHTeJIbHO ,nOMa. npH 3TOM .n-eTH BblnOJIHHIOT HeCJIO)KHble 3a,naHHH: OTMellalOT Heno- H.HTHble CJIOBa M Bblpa}KeHHH, pa30HBaIDT TeKCT Ha \ qaCTH, npH)l.Y- MblBalOT K Ka)KJl.OH H3 HHX 1-2 Bonpoca. Tor,na Ha ypoKe nOCJIe npo- BepKH BbIIIOJIHeHHH 3a.n-aHHH 6Y.D-eT opraHH30BaHa AaJIbHeHlllaH paoo.. Ta Ha TeKCTOM - lITeHHe. H pa360p no qaCTHM, OCTaBJIeHHe nJlaHa H T. . .... B03fO)KHbI H 1\1HOrHe APyrHe cpOpMbI npoBe)leHHSI nepBOHallaJIbHOrO tITeHHH TeKCTOB, HO na)KHO, lITOObl yqeHHtrecKoe tlTeHHe 3aMeTHO nOTeCHHJIO yqHTeJIbCI{Oe, BTIJlOTb o tlTeHHH OTJ,leJIbHbIX CTHXOT)JO- P€HHI1. 4reHHe (nepBOHallaJIbHoe) HaY1lHo-nonYJIRpHbIX npoH3Be,neHHH ue- JIeC006pa3Ho, KaK npaBHJIO, npoBoHTb CMJIaMH TpeTbeKJIaCCHHKoB 6e3. npeJl.BapHTeJIbHOH no,nrOTOBKH. II T e H II e H p a 3 6 ° P nOli aCT 51 M n e p B 0 H a tl a JI b- H 0 n p 0 q M T a II H 0 rOT e K C T a. nepBOHatlJIbHIM qTeHHeM TCKCTa ,D.OCTIIraeTCH, KaK Y>Ke OTMeqaJIOCb, CHenocpe)J.CTBeHIloe BOC. 1"8
npHHTHe JIHTepaTypHOrO npOH3Be,nenMH». YT06bl )I.OOHTbCH yrJIYOJleH- Horo npOHHKHOBeHHH B CMblCJI xy ,nO>KeCTBeHHoro npOH3DeeHH H, Bce- CTopOIIHe (XOTH H B npeJ{eJIax ,nocTynHoro JlH MJla,QIlIHX IlIKO.lIbHHKOB) oueHHTb npOqHTaHHOe, HYLKHO MeTo,nHqeCKH npaBHJlbIIO opraHli30naTb o 6 J( Y M bI B a 10 m e e B 0 C n p H 51 T Ii e. TaK nCHXOJIOrH HMe- HYIOT nTopyIO H oOJlee CJlO>KHYIO CTa,nHIO BocnpHSITHH xy,nO)l{eCTSeHHoro TeKCTa. CTaJ{HH 06,nYMbIBalOIlI.erO BocnpHHTHH lIpe3BblqaHHO Ba>Ka H lleOoxo,nHlvla ,lVI5I cpOpMHpOBaHHH cepbe3Horo, B3bICKaTeJ1bHOrO II 9CTe- THQecKH pa3BHToro 'HTaTenH. Ha 3TOH CTaJ(HH y ,neTeH HYLKHO BbI3BaTb eHTeJlbHYIO H HanpH>KeH- HYIO pa60TY l\ibICJlH H Boo6pa>KeHHH, TBOptIeCKHH no,nxo,n K 06pa3HOl\-IY co,nepJKaHHIO TeKcra. ,QOCTHraeTC5I 3TO pa3YMHbIM COqeTaHHe1 pa3.;1MQ- IIblX BH,nOB 1JTeHHH (OT BbI6opOllHOrO ,no Bblpa3HTeJlbHOrO qTeHH5I Bcero TCKCTa) C pa3Hoo6pa3HbIMH 3a,naHiiHl'tfH (HalJHllaH OT nOCTaHOB!<H Yt.IH- TeJIeM H caMHMH YlJeHHKaUf BonpOCOB, COCTaBJIeHHH n.naHa Ii KOllllaH IIpHBJIeqellHeM TaK Ha3bIBaeMbTX TDoplfeCKHX npHeMOB). I1MeHHo Ha 3TOM CTaJ{HH 06J{YMbIBalOIII.erO BocnpHHTHH J(eTH oO.TIee Bcero TpeHHpYIOTCH B qTeHHH. I1MeHHO 3eCb yqHTCJIIO npe,nCTaBJIHIOTCH peaJIbHbIe B03MO>KHOCTH no,nKOHTpOJlbHQ... oTpa6aTbiBaTb H COBeplIIeH- CTBOBaTb KOMnoHe"i-ITbl, H3 KOTOpblX C1JaraeTCH lIaBbIK qTellHH - C03Ha- TeJ1bIlOCTb Ii Bblpa3HTeJIbHOCTb, npaBHJIblIOCTb H 6er.nOCTb. ,QJIH Toro qTo6bl 3Ta pa60Ta He BbIna,naJla H3 0611(ei'l TCMaTHlJeCKOH: Ii II-eJIeBOH HanpaBJIeHIIOCTH ypOKa, "ymHo npHJ(aTb eM np06JIeMHblH xapaKTep. t1Halle rOBopH, OtIeHb Ba>KHO nepeJ( lITeHHeM H pa36opot TeKCTa_ no qaCTHM BblBHHYTb nepe,n KJIaCCO1 onpe,neJIeHHYIO npo6J1e- MY, KoropaH He TOJlbKO 6y,neT CTHMYJIHpOBaTb pa360p ,neTbMH xy,nO)Ke- CToellllblX CPSI<TOB, HO Ii cOOomHT aH&nH3Y nepcneKTHBY, 06Ha>KHT era IlcJlesylO HanpaBJIeHHOCTb. np06.neMHOCTb nOJlO>KHTeJlb)fo CK8>KeTCH 'TaKme H'a CTPYKTYPHOH: IlCJlOCTHOCTH ypOKa H CeJIaeT nOHStTHOfI ,nJIH Y1l3IlI.HXCH JlOfH}<Y nepe- XO)J.Cl OT o,nnoro 3Tana ypOKa K J(pyrOMY. CCHtiac OqeHb qaCTO MO}J{HO HaOJIIO,naTb ypOKlI, KOTopbIe npOXO)J.HT 'rEliC YlfUTeJIb coo6aeT ,neTHM Ha3BaHHe npoH3Be,a.elII1H, KOTOpoe I1pC)J.CTOHT npOtlHT8Tb H pa300paTb Ha ypoKe. 3aTel'vI, C]<a3aB: «ilpHro- TODbTeCb CJIYW8Tbf» - HaqHHaeT caM qHTaTb TeKCT. OKOHqHB qTeHHe, I'OUOpHT: «A Tenepb 6y,neM qHT8Tb H pa36HpaTb no qaCTSlM». Kor,na IIpon.enSH8 9Ta pa6oTa, CJIeAyeT 3aJ{aHHe: «A Tenepb COCTaBHM nn014J, ,aanee: «A Tenepb nepeCK8>KeM np0'lHT8HHoe». nOTOM: «A Te- nel'lI nppHT8eM 8 JJHuaX, H OnJlTh: «A renepb.. .». TIKHM "paloM, AnR AlTeR OCTseTCH a6COJIIOTHO neHcHbIM, nOqeMY II MR qero M npeAJIarSJIH CHSqaJIa .lleJIaTb OJ].HO, a nOTOM ,npyroe. IloJ06J18J1 KSpTHH8, nOBTOpHIOInaHCH 1-13 ypOKa B ypOK, npHYtJaer Itc'reA OTHOCHTbCR K paOOTe paBHo,nYllIIIO. B pe3YJIbTaTe Bce, 'ITO npeJ{.naraeT YQHTeJIb, BblnOJIHHeTC5I ,neT'b{H He JJ...1St ce6H, a Jt)IH 11('('0. llIaH KapTHHa, KOr}!a ypOl<Y C00611.1aeTCH npo6.lIe;"IHbIH xapaK- Tep. 19
H8npHMep nocJle Toro KaK TpeTbeKJl8CCHHKH npOtlTYT B nepBblH pa3 nereH,ny A. raitnapa «rOpHtlHH K8MeHb» H 061\feH5JIOTCH Henocpe)t- CTBeHHblMH BneqaTJleHHHMH OT npOqHTaHHOro, 8M MO}l{HO npe,n.nO>KHTb npOtIHT8Tb TeKCl' no 1IaCTHM, C Ter.1 qTOObI HaRTH OTBeTbl H8 BonpOCbI: «lIbe iRe C1IaCTbe caMoe HacTOHlnee - I1B3IlIKIf, CT3pHKa HJIH paCCK33- I1HIra?», «KaKOH qe.nOBeK CMor ObI pa30MTb K3Menb?», «CTaJI 6bI OH OT 3Toro CqaCTJlMBbIM?» YqaInHMCH CTaHOBMTCH Tenepb nOHHTHblM CMblCJI npeCTOHIlI.eH pa60TbI. Ka>K,nbJH a03an 6YJ{eT nepetlHTbIBaTbCR no He- CKOJIbKY p33, H Bcer,n;8 3TO 6y J(eT HHTepeCHO Jl.JIH ,n;eTeH, HOO n03BOJlHT H3XOJ{HTb Bce HOBbIe cJ>aKTbl, OKa3aTeJIbCTB8, KOTOpbJe y6eJK,A3IOT, 1ITO cqaCTbe - 9TO, KorJ{a }KH3Hb y qeJIOBeKa H,neT «HCHO H qecTHO», Kor,na OH BMeCTe co BceMH CTapaeTCH, qTo6bl «ero pOHaSI.CTpaH8 CTaJI3 f..{OryqeH H BeJIHKOH». J:laJIee ,neTH1 ,MOLKHO npe,QJIO>KHTb nOJ{rOTOBHTb nepeCI<33 «[OpR- tIero KaMHH», C TeM qTo6bI OHH CMOrJIH paCCKa3aTb ero CBOHM )lOM31II- HHM UJIH TOBapHIII.al. A lITOObl paCCK83 nonyqHJlCH CTpOHHblM H nOJl- HbIM, HY*HO CHaqaJIa COCT3BMTb nJlaH nepeCKa3a. !leTH caMH pewalOT, KaKH1\f J{OJI}KeH 6bITb nJIaH, eCJIH nepeCKa3blBaTb co,nep>K3HMe npOqHTaH- Horo OHn 6y,nYT nopo6HO, Ii K3KHf - eCJIH KpaTKO. ITaK ,n;J1R ,neTeH, CTaHOBHTCH nOHHTHOH paooTa Ha Bcex nOCJIe- .llYIOInHX 9Tanax ypoKa. 06yqeHHe MJIa,nIIlHX llIKOJIbHHKOB 1ITeHHIO Hepa3- Pa60T8 no p83BHTHIO pbIBHO CBH38HO C p36oTOH no pa3BHTHIO peQH. 3TO ;::ax y:::c. B I npOHCXOMT nOTOMY, qTO caM npou ecc qTeIlMH Kneece OTHOCHTCH K SlBJleHHHM peqeBOrO nOpHJl.Ka. He CJIyqaHHO )leTH, qHTalOrnHe MHoro, BJla,nelOT oora- ThIM aKTHBHbll\1 CJIOB8peM, OHH He HcnbITbIBalOT OC06blX 3aTpy,nHeHHH B H3bIKOBOM <>qJopMJIeHHH CBOHX MbICJlen, OT..l1HtlaJOTCR CI{t1'13,nHOCTblO peQH. 1.IHTaH, yqeHHK BocnpOH3Bo,nHf no 6YKBeHHbIM (rpacpHqeCKHM) 3H3KaM 3YKOBbIe $OpMbI CJI0B, OC03HaeT HX 3H811eHHH H CBH3H MeX{,ny u u CJJOBarvIH, YHCHHeT CMblCJI npe,nJlO)KeHHH, OTj{e.nbHbIX 1IaCTeH H Bcero TeKCTa B [(eJ10ft T. e. THBHO onepHpyeT OCHOBHbIMH peQeBbIl'\1IH eJ(HHH- U.8MH - CJIOB8MH, npe,l(JlO>KeHHHl\fH, KOHTeKCTOM. BHYTpeHHHe Mex8HH3Mbl CBH3H H B03,l(eHCTBHH' npouecca 1ITeHHH lIa peqeBOe pa3BHTHe ,neTeH rJIYOOKO CKpblTbI 11 Qpe3Bh]QaHHO CJlO>KHbI. TaKoro pOj{8 B03,neHCTBHe OCYIneCTBJIHeTCH He npHl\iO Ii He cpa3Y, 8 HeaafeTHO M nocreneHHO. O,QHaKO OHO HBHO B03paCT8eT, eCJIH B xo,ne o6yqeHHH qTeHHIO 9qxpCKTHBHO HCnOJlb30BaTb TaKHe BH,nI H npHeMbJ paOOTbl, KOTopbIe P8CCQHTaHbI Ha opraHIi3..aUHIO aKTHBHOM peqeBOH npaKTHKH Y1lalll.HXCH Ha OCHOBe npOllHTaHllblX H YCBoeHHblX HH TeK-; -crOB. CIO,na OTHOCHTCH p83J1Ht.JHbIe cpOpMbJ CJlOB8pHO-J1eKCHqeCKHX ynpa>KHeHHif 1 t npOBeJ{ellHe npOCTeHUlHX CTHJlHCTH1IeCKHX H3"OJIIOj{e- IHiH, aHaJlH3 HCnOJlb30BaHHH nHC8TeJIeM H306pa3HTeJlbHO-BbJpa3UTeJJb- HbIX cpe,nCTB Sl3bIKa, HaKOHeu, pa3J1H1IHhIe nepeCK83bl. 1 CM. 06 9TOM B noco6HH «06Y'leHHe 80 BTOpOM Kn3cce. KUHra .D.JIH Y'IHTenH». !\\., «n pocaew.eHHe», 1970. 20
11oCJIe,ltIlHe KaK cpOpMbI aKTHBHOH pa60TbI no pa3BHTHEO peqn YtJa- IlHXCH H8 ypOKax IlreHH.H HaXO,ltHT lJ1HpOKOe npHMeHeHHe B I Ii I I J{Jlaccax l . B I I I KJlaCCe HX pOJIb ee OOJlblIJe B03pacTaeT, npaBa, neHT- paJIbHOe MeCTO OTBO,nHTCH KpaTKoMY, TBOplleCKoMY Ii BbI6opOqHOIY lJepecKa3aM. Oepec"a3 nooY>KJtaeT YllarnHxcfI K MHoroKpaTHoMY npollTeHHIO OA- lIoro H Toro }l{e TeKCTa, 38CTaBJlHeT HX BYMbIBaTbCH B co,nep}KaHHe IJpOIJHTaHHOro, pa3MbIIllJlHTb Ha,n HHM, ,neJIaTb BC.HKOrO po,na conOCTaB- JICHHH H cpaBHeHHH. nO,ltrOTOBKa K nepeCI<a3Y H caM nepeCKa3 npOIJHTaHHOro co,neHCTBYlOT nY4111eIY 3anOIHHaHHIO lllKOJIbHHKaIH cO,ltep>KaHHSJ npOH3BeJ{eHHH, ero oGpa30B, CIQ)l{eTa H KOMn03HllHH, T. e. cnoco6CTBYIOT YCBoeHHIO :slIaHuii. nepeCKa3bl aKTHBH3HPYlOT He TOJIbKO JIOrHtIecKoe, HO H xy,nO>Ke- ('TneHHoe, oopa3Hoe MbIllIJIeHHe. OHH CTaB.HT YlleHHI<:a B cHTyaQHIO, I<or,na eMY HY}l{HO HpKO H >KHBO npeJ{CTaBHTb ceoe KaLK,lI.bIH xy,nO}KeCT- nCIIHbIH o5pa3 B OT,lteJIbHOCTIi Ii BCID HapHcoBaHHYID nHCaTeJIeM Kap- 'I'll BY B IJ.eJIOf. 4TeHHe C YCTaHOBKoA Ha nepeCKa3 Tpe6yeT OT YllaInHXCH BHHMa.. T('JIbHOrO OTHOmeHH.H K .H3bIKY npOH3Be,neHH.H, K ero H306pa3HTeJIbHO- nhfpa3HTeJlbHbIM cpeJ{CTBaM, K JleKCHKe H <ppa3eoJIOrHH. Bce 9TO n03BO" JISICT. UlKOJIbHHKY oc-'03HaHHO oTo6paTb H3 eKCTa H BBecTH B CBOH ne- peCKa3 TaKHe CJIOBeCHble cpeJ{CTBa, KOTopbre C HaHOOJIIlleH no.nHOTOH II TOtJHOCTblO nepefaJtYT co,nep)KaHHe npOH3Be,neHHH H OJ{HOBpeMeHHO 1I0MorYT BbIpa3HTb K Hel\fY CBoe OTHomeHHe. nepeCKa3bl 1Jpe3BbI t IaHHO 1l(llIibl ,nJlH o60rarneHHH H3blKa MJIaJ{IIIHX WKOJIbHHKOB, JIg BbIpaOOT- I(H DbJpaSHTeJlbHOCTH pettI-{ H HaBblKOB CBH3HOH pellH, npHQeM He Tonb" 1(0 YCTHoA t 110 H nHCbMeHHoA. nepeCI<:a3bl Y l l8T WKonbHHK8 paCCKa3b1BaHHIO, cpOpMHPYIDT B HeM I(U'ICC1'J1t) HHTepeCHoro co6eceAHHKa, YMeJlOrO paCCK8311HKa, 1JeJIOBe- IUI, clloco6uoI'O 6bICTpO H npaBHJIbHO C<f>oPMYJIHpOBaTb Ii BbICKa3aTb ('nOlO Mblcnb g nyGJI HIlHOM BbIcTynJIeHHH. ¥tlHTeJIb c nOMOblO nepeCKa3a MO}l{eT KOHTpOJlHpOBaTb IlTeHlie Ii pn(jOTY YllCIIH !(OD HaA TeKCTOM, MO>KeT C ,nOCTaroIlHoH OO'beKTHBHOCTblO CYJUfTb 0 TOM. K8K ,AeTH nOHRJIH H YCBOHnH cOJ{ep}KaHHe npOIJHTaHHOro IlpOI13DeeHHSI. KaqeCTBO nepeCK8sa 6anee Bcero saBHCHT OT Mepw nOHHMaHHH H C,JC0311allllOCTH yttaw.HMHCs1 cO;tep>l(8HH1I npOIlHTaHHoro. n03TOMY ne- pOCK.. 'IIUL\e Dcero H8XOAHT 'Mecto B, nponecce aHaJIH3a TeKCTa "JlIi nOCJl. pI.eoPI .cera npOH8BueHHJI. O"IIHO n.pecKI' CJIYeT s pa60ToA HaJ{ nJIaHOM; ecnH AaHHbIH 111-14 patSoTbi npeYCM,ITpHB8eTcSI B 06w.eM pa300pe TeKCTa, liO MO>KeT "pVJUUCCTB008Tb nna..y ,Hnk npoBoAHTbCH oJ{HoBpeMeHHo C ero COCTaB- JIIIIICM. B Tex CJIyqaSlx, KOr,Aa nnaB K np01JHTaHHOMY He COCTaBJIHeTCH, 1 CM. 06 9TOM B noco()HH «06YQeHHe BO BTOpOM KJJaCce. KHHra ,lJ.JISI YlfRTe..fJHt. J\'.. .npOCOeill-eHHe», 1970. 21
nepeCKB3 Bee paBHO no,nrOTaBJlHSaeTCH 3Ha.nH30M COJt:ep>K311HH npOH3- BeeHHH, HO TOJIbl{O 9TO MomeT npe.llOTBpaTHTb MeX31lHQeCKOe nepe- CK33bIBaH He TCKCTa. rOBOpSI 0 nepeCKa3e Ii nJIaHe1.. HY>KHO OTJlHlJaTb nJi aI-l , BblcTynalOI.IJ.HH B pOJlH ollHoro H3 BH.llOD paOOTbJ Hall. npOH3Bell.elIlfeM, OT nJJaHa, cne- UHaJ1bHO COCTaBJIHCMOrO llJ1S1 nepeCI{a3a. OJ1aH Kal{ BH.ll pa60Tbl Ha,n npOH3Be,LleHHeM COCTaBJIHeTCH I{O BceMY TCI<CTY H, pa3YMceTCH, MO>KeT 6bITb HCn0J1b30BalI ,LlJlH nepeCKa3a npo- H.3Be)teHHH B u.eJIO1: OH HaMeTHT 06UlYIO KaHDY, a KaJK,ZlbIM nYUI{TOM - onop Hble CMbICJI OBbIe BeXI1. O.llHaKO MOlKeT CTaTbC5I, qTO nepeCK33 neJIoro TeKCTa HYil{HO 6y,neT OJ u nOCTpOHTb B HHOH C[O)l{eTHO-KOIn03HII.HOIlHOH rrOCJIe,nOBaTeJIbHOCTH, HemCJIH olla npe,ACTaBJleHa B npOH3BeeHHH. B noo6IILIX CJIyqaHX 6 · v Heo XOHMbIM o}{a)l{eTC5I nJIaH, CneII.HaJIbHO paCCqHTaHHbIH llJI5I nepc- CKa3a. Ero npHlleTCH COCTaBJI5ITb HHaqe, qeM TOT, KOTOpbIH ObIJI pa3- paOOTaH DO BpeMH aHanH3a Bcero npOH3Be,LleHH5I. OJlaH, cneu.HaJIbHO npe,llH33HalleHHhIfl ,nJI.H nepeCKa3a, lleJIeco06- pa3HO TaK>Ke COCTaBJIHTb npH nepeCKa3e OTeJIbHbIX .9nH30)J.OB, onMca- IIHH H ,npyrHx qaCTeH npOH3ne.lleHHH. CI<a3aHHoe BbIllle HHKaK He HCKJlIOqaeT nepeCKa30B, npOBO,LlHMbIX Bo06rne 6e3 nJIaa. OHH nepCJ{KH Ha caMOH nepnOR cTyneHH HaqaJIb" Horo ooyqeHHH, npaKTHKY.lOTCH H BIll KJIaCce. O,nHaKo OTCYTcTBHe nJIaHa He 03HaqaeT OTKa3a OT JIOrHKM B H3JIO}KeHHH: OHa 6Y.lleT nO)J.CKa- sana yqeUHKY CIO)KeTHbIMM HJlM KOln03HaHOHHbI{H oco6ellHOCTHMH nepeCKa3hIBaeMoro TeKCTa. BOl1pot 0 npHB.HelJeHHH nepecK33a K paooTe Ha cO)J.ep}l{aHHeM npoH3BeeHHH, oT60p Toro H.nH HHoro BHa nepeCKa3a H npHeMOB, KOTopble n03BOJIHIOT ero ocymecTBHTb, 3aDHCHT OT }KallpOBoH cneII.l-!- q,HKH npOtlHTaHHOro TeKCTa. raK, )].JI5I neH3a:>KHhIX npo3aHlIeCI{HX onHcaIIHi-i (JI. TOJ1CTOH. «Bec- Ha» Ii ,l\p.) nOJIe3HbI rroJlpooHble nepecKa3bI H ne)'1fecTHbI KpaTKHe. CIO}KeTIIbIe rrp03aHQeCKHe TeKCTbI, a TaK>Ke oacHH ,nonycKalOT rrepe- CKa3bI Bcex BH,nOB, OHaKO IIpeycMaTpHBalOT Yf\1eHHe ,neTcH npaBHJIbllO I' BBOHTb B CBOn: nepeCKa3bI npHMYIO peqh H nepeBOHTh ee B KOCDeHHYIO. JIHPO-3I1HQeCI{He npoH3,eJleHHH (H. HeKpacoB. «,[LeJJ.YlllKa Ma3aH H 3aHII.bl» Ii .n-p.) Tpe6YIOT OCTOpOi'l{HOrO noxo,Zla B HCnOJlb30BaHHH no,n': P06UhIX nepeCK330B, TaK KaK KalleCTBO HX BO fHOr0l\11 3aBHCHT OT yrvlellliH YQeUHKOB OpraHHlJeCKH BKJIlOQaTb B nepecKa3 lI.HTaTbI, rrpeJ{- BapHTeJIbHO oToopaHHble B npOqHTaHHOM TeKCTe. Opn nepeCKa3e CKa- 30K HYi!{IlO coxpaHHTb HX Tpa,LlHIl.HOHHbIH 3a4HH (<<)KHJ1H-6bIJIH.. .»), x3paKTepHble nOBTopbl Ii KOHll.OBI{Y. JIHpHlleCI{He CTHXOTBopeHHH BO- Oome He JlOnYCKalOT nepecK330B, H60 9TO, KaI{ npaBHJIO, npHBO,ZlHT K pa3pyweHHlO 06pa3Horo cOJJ.ep)l{aHHSI CTHXOTBOpeHH5I, npHTynJl51er 3CTeTHqeCKOe qYBCTBO ,l\eTeH. no cTenellH ,neTaJIH3allHI1 COep}l{aHHH nepeCKa3bI JleJl5ITCSI Ha nOJIHble (nO,Llp06HbIe) H KpaTI{He (cmaTble). n 0 ,l( p 0 6 H bI e npe.n-- nOJlaralOT D03MO>KHO nOJlHYIO nepe)\aqy co,nep:>KaHH5I npOQHT3HHOro 22
TCKCTa IIYTe1 MaKCHMa"lbIlOH era n.eTaJlH33UHH. lJ.e.neBaSl YCTaHOBI{3 IIPH C}K 3 TOM nepecK33e/HH3H: BCKpbITb Ii nepeaTb, OIIYCKaH e- TanH, caMoe cyrn.eCTBeHHoe H rJI3BHOe B cOJ!ep>KaHHH IIpOQHTaHHOro TCI{CTa. ECJlH IIpe.ll.MeTOM nepeCK33a CT3nOBHTCSI He Bce npOH3BeeHH MJIM l\aKaH-TO qaCTb ero, 3 HeCKOJIbKO MeCT (3nH30,aOB, onHcaHHii, l1Ha1l0. rOB H T. n.). CB5I3aHHbIX Mem.1I.Y co6oii, TOr,lla lIepeCKa3 Ha3bIBaIOT B bI- e> 0 p 0 q H bl t. Or6op 3THX lvlaTepnaJlOB MOII<eT ObITb C,lleJIaH B BH,l\e ocnemellHH «HCroPHH» HJIH «iKH3HH» KaKOrO-JIH6o nepCOHaiKa (<<l1cropuH CTapHJ<a CTOpO>Ka» - A. raH.l{ap. «rOpHqUH KaMeHb»); cpaKTbl MorYT rpYlIIInpOBaTbCSI Ha TelaTMqCCKOI1 HJIH CIO/KerllOll OCHOBe nyreM cono- CTaBJIeHHH no CXO)(CTBY IiJlH KOHTaCTY. I-I a I\OHeil., nepeCKa3bl MorYT OCJIO}KHHTbC5I TaK Ha3bIBaeMblMH TBOp- IICCl{nnI 3a/{aHH5IMH, KorJI-a yqeHHKH ,l\OJI}KHbI onpe,neJIeHHbIM oopa- 'OM IIcpCpa60TaTb CO,llcpiKaHHC npOqHTaHHOro TeKCTa HJIM ero cpOpl\fY (lianpHIep, nepeCKa33Tb OT nepnoro JIHaa HJlH OT HMeHH aBTopa. BO- oopail<aeMoro OqeBHJI-u,a, yqaCTHHKa OIIHCbIBaeNfhIX C06hITHH Ii T. n.). IIcpccKa3bI nO,l(05Horo BH,l(a yc.nOBHO HMeHYIOTCH T BOp 11 e C K H M H. KaK BLI60pOqHbIe, TaK If TBoplIeCKHe lIepeCKa3bl 6bIBaIOT nOJlHblMH H CiKaTbIMH. _ 0 C TOtIKII 3peHHH CJlOBeCHOro ocpopMJIeHHSI Ka1K,llbIH H3 BH,l(OB lIepe- CKCl3a MO;'KeT C pa31I0H: creneIIblO np110JIHJI<aTbCSI K H3bIKY IIpOqHTaH- 1101"0 TeI<CTa. CTpeMJleHHe YlleHHKa BocnpOH3BeCTH npOqHTaHHOe C HaH- GOJIblllHM UCIIOJIb30BaHHeM JIeKCHKo-cppa3COJlOrliQeCKHX cpe.llCTB H CllllraKCHlJeCKHX KOllCTPY Kil.HM rrpOH3Be.ll.eHHH llopOIK/{aeT nepeCKa3, () JI H 3 K H H K T e K C T y. BJlH3KHH K TeKCTY rrepeCKa3 YlleHHK ocymeCTBJlHeT, nOHHTHo, He OJIbKO C nOMOI..nblO CJIOB H KOHCTpYKU.HH, 1I011epn1lYTbIX B npOH3Be.l1eHHH, HO TaKme rrpH H3BeCTHOM yqaCTHH CBO- HX CJlOB l . ECJlH IIOCJIe,nHHe npeOOJla,l(aIOT, Mbl HMeeM JI-eJIO c nOJl-poo- HblM RepeCKa30M- C B 0 H Mile .IT 0 B a M' H. Ha nepBhlX nopax Ha- tlaJlbHOrO 06YlIeHUH MJIa,nLlII1C lllKOJIbHHKH THrorelOT K .llOCJIOBHOMY ne- pCCKa3Y, npH6JIH)KalOw.eMYCH K tITeHHIO HaH3YCTb. 11M TPYHO aeTCH UKJllOlIeHHe B lIepecKa3 CBOHX CJI0B. 3TOIY I1pHXO,llHTCH CHCTeMaTIlq-ec- I{H 06yqaTb. I(poMe Taro, nepeCKa3bI Mory'f" pa3J1HqaTbCH O MeCTY H cnoco6y II x nO,AI"OTOBKH Ha K JI ace H bI e H 0 l'il a III H H e, K 0 11 JI e K- T H B H bl e H C a M 0 C T 0 H T e .n b H bI e. llCTO npHxo,nHTCH HaMlO,AaTb, KaK WKOJlbHHK, YMelOInHH no.npooHO H IIcnpHIIY>KAeHHo nepeCKa3b1B8Tb cOAep>KaHHe npOqHTaHHblX KHHr HJtH npOCMOTpel-lHblX KHHotl>HJlbMOB CBOHM cBepcTHHKaM, epo pac- UUCIIHS810UJ.HA cleft cCBo6o,AHbdb> nepeCKa3 HIITouau,UHMH pa3Hblx u Urrelll(OD, nays8MH. DblpS>KeHHeM rJla3, MHMHKOH H }KeCTaMH, B lllKOJ1b.. lIoii, TOll Hee, KJIaCCHOH o(5cTaHoBKe B,l(pyr KaK-TO HHKHeT. CTaHOBHTCH I nO.ll «CBOHMH CJIOBaMH» pa3YMelOTCSI Te CJIOB3pHo-cppa3eOJIOrlltIeCI{HeH CHHTaK- ClfClccHe pecypcbI pO.D.Horo H3L1K3, I<:OTOpbIMH lUKOJIbllHK J10BCe,l{lIeBIIO nOJJb3yeTcn II petleuoM OOlll-eHHH AJUI nepeAaqH CBOHX MblCJJeH, uoaMIO.D.eHHH H np. 23
Heo6b]QHO cKyn Ha CJIOBa " Ha Bce 9TH ,nonOJIHHTeJlbHble, HO CTOJIb neH- HbIe Cpe.llCTBa peqeBOH OKpacKH. )KHBOM, HHTepeCHblH paCCKa3t1HK npeBparnaeTCSI B CKyqHO OTBeqalOrnerO ypOK YtIeHHKa. I1cnXOJIOrHIIecKHe HCCJIe,nOBaHHH ,nalOT o6'bSlcHelllIe 9TOMY ct>aKTY Ii nOMoralOT YCTaHOBHTb, KaKHe YCJlOBH5I 6JI8rOnpHHTCTBYIOT no,npo6- HOMY H llpyrHM I3H,n8M nepeCKa30B. Bo-rrepBbIX, pa3'bHCHHIOT nCHXOJlO- flit, B KJIaCCe leII5IeTC5I 06'beKT nepeCKa3a - HymHo nepeCKa38Tb He TO, lITO XOIleTCH B .naHHbIH MOMeHT yqeHHKY, 8 HerrpeMeHHO ytle6Hblii ,...laTepHaJI, KOTOphIH onpe,neJleH Y4HTeJIeft H, He3aBHCHMO OT roro, YBJIeKaTeJIeH OH HJ1H HeT, ero HymHo 3HaTb H Yl\1eTb BocnpoH3BecTH. BO-BTOpbIX, HHbIMH CT8HOBHTCH MOTHBbI rrcpeCKa38 2 . BMeCTO BHYTpeH- HHX no6ym,AeHUiI, pO}KalOII(HXCH y paCCKa3t1HI<a, - npocb6a, Bb130B, Tpe60BaHHe co CTOpOHbI YIlHTeJIH. B pe3YJlbTaTe OCTaeTCH O,lJ.Ha norJlo. malOrnaH YQeHHK8 3860Ta - C Han60JIblIIeH TOtlHOCTblO BocnpOH3BeCTH npOlJHTaHHbIH TeKCT. B.TpeTbHX, nepe,n paCCI<a3I1HK01\1 pa3Hble 8y,nHTO" pHH H MaJIO B qeM Cxo,nHbIe eJIeBhIe YCT3HOBKH nepeCK83a. B O.llHOM CJIyqae - He60JlblliaH rpynna 6JIH3KHX J{pY3eM, K KOTOpbIt\.1 np5lMO OOpallJ.eH paCCKa3, ornyrneHue nenOcpe,lJ.CTBeHHOfO KOHTaKTa co CJ1Yllla- TeJIHMH, CTpeMJIeHHe CJ{eJI8Tb nOHHTlIhHvl H ,nOXO,lJ.qHBhIM co,nep}KaUHe paccK83bIaeMoro, )KeJl8HHe CKJIOHHTb HX K CBoeMY B033peHHIO Ha TOt o qel\f paCCKa3bIBaeTCH, a npH HeCOrJIaCHH - rOTOBHOCTb nocnopHTb, OTCTOHTb CBOH B3fJI5I,lI.. B ,npyroM CJIyqae - «O<jJHHaJIbHaH OOCTanOB- . u Ka», KJ1aCCHa51 8y,nHTOpHH, OTHorneHHe I{OTOPOH K nepCKa3Y OTHlO,lI.b lIe HMeeT pernalOllI.erO 3HatleHHH B oeHKe nepeCKa38, TaI{ KaK rvlelK,lly HelO H paCCKa3QHKOM CTOHT YIIHTeJJb: ero CY}K.l{eHHH H oeHKa nOIlTH eAHHOJ1HQHbI. HaKOHen, B-qeTBepTbIX, «BOJIbHbIH» p8CCKa3 t lHK onepH- pyeT no npeHMyrnecTBY CBOIiMH CJlOBaMH, H, XOTH HX 3an8C He CTOJIb BeJIHK, 3a Ka}KbIM CTOHT KOHKpeTHoe npe,nCTaBJIeHHe. Cna6ble CTOpOHhI «cBo6o,nHoro» nepeCKa3a TaKOBbI: 1) CnoBa Ii Bbl- pa}KCHHH H3 npOQHT8HIIOro TeKCTa, .n.a}Ke H3 qIiCJI8 HaH60JIee BbIpa3u- TeJlbHblX 11 lleHHblX B xy,nO>KeCTBeHHoM OTIIOI.lleHHIi, pe,lJ.KO BBO.llHTCH B nepecKa3, ,na H Booom.e B p.eqeBofl o6nxo,A paCCKa311HI{8. TaK KaK no- CJle,nHHH ,He Bcer.n.a 6bIB8eT B CHJ1ax ca10CTOHTeJIbHO pa300paTbCH B IiX lI.OCTOHHCTnax. 2) «CBo6o.llHbII)} nepecKa3aM npHcya HeoohIKHoBeH- HaH necTpoT8 Ii CJIyqaHHOCTb TeMaTliKH. OHH YCTynaloT KJIaCCHblM 8 KOtn03HlI.HOHHOH CTpoflll0CTn: «BOJIbHbIII» paCCKa3I1HK OOb]4HO CKJIO- Hell nepeCKaKHBaTb B CBoeM nOBeCTDOBallHII C O,AHOrO MeCTa H8 Jl.pyroe, OH JIerKO napyrnaeT JIOrHKY CIQ}I{eTa H Korvlno3HlU11O TeKCTa, TaK KaK He 3aJI.yrv1bIBaeTCH Ha,n HX CMbICJIOBOH U e JIecooopa3HOCTbIO. TaKHM 06pa30M, npH OOY4eHHH OCHOBHbIM BH.lla1 nepeCKa30B B03- HHKarOT UeJICrKl:le MeTo,nHtleCKlIe 3a)lallH: ,nOOUTbCH, qTo6bl 3a Ka>K,nbl]'.i CJ10B01\f TeKCTa CTOHJ10 KOHKpeTHoe 1I nOHHTHoe MSI IlIKOJlblllll{OB npe,ll- 1 CM.: A. H. JI n n K 11 II a. Pa3BHTHe MLIllJJleHHR yqalHXCSl Ha ypOKax 06'bHC- HHTeJ1bHOrO QTCHHR. M., 113D.-BO AnH PC<t>CP, 1961, crp. 14-17. 2 CM.: .T!. C. B bI rOT C K H it MbIUJ..'JeHHe H peQb. 1136paHHble DCHXOJ!orH'IeC- KHe HCCJIe.u.OBaHIHI. 1\t, 113A-BO AnH PCC1)CP, 1956, CTp. 264. 24
CraBJIeHHe HJlH nOHHTHe 0 npoM,eCce, HBJleHHH H.nli rrpe,lI.Mere; OCJ180HTb «TOpM03Hr.u.ee» ,l(eHCTDHe KJlaCCHOH OOCTaHOBKH na YlIeHHKa, 11 To6bI OH u B CBOH nepeCKa3 CMor npHBHeCTH MHoroe H3 Toro, liTO npHcyme ero «BJleay,nHTopHbIM» nepecKa3aM; ,ll06HTbCH, llTOObI yqeHHK CBOH paCCKa3 OopalllaJI I1pe>K,l(e Bcero K cJlymaTeJI5IM - CBOHM TOB8pHll\aM; npHJIO" il(HTb YCHJIHH K TOMY, tIT06bI yqeHHK C03HaTeJlbHO rrpH,l{aBaJI CBoeMY paCCKa3Y JIOrHQeCKYlO II KOMrr03HlI.HOHHYlO CTpOHHOCTb, o60rall\aJl era il{IiBbIMH H ecTecTBeHHbIMH HHTOHal.\HHMH, CJIOBafH H BbIpa>KeHHSlrvuf, xYO)KeCTBeHHaSl CH.na KoropbIx paCKpbIJlaCb nepe,Q HHM H 6blJla npo- 'IYBCTBOBaHa BO BpeMH pa360pa TeKCTa. 3TH 3a.lla4H B 3HallHTeJlblIOJJ f\1epe pa3pernalOTCH npn CJleJ{YIOIlJJIX ( )()CTOHTeJ1bCTBax: 1. Ma KCHMaJIbHO Mo6nJIH3YlOTC5I )KH3HeHHbIe BrrellaTJIeHHH Ii npeJJ. fT;JB.TIeHIIH ,lI.eTeH, CBH3aHHbIe C co,nep:tKallMeM lIHTaeMoro TeKcT8, OHH y rOlIHHIOTCH H 060rall\a1OTCH TaK}Ke 3a ClIeT rrpHBJIelleHHSI H8rJIH)1- II OCTH . 2. npH pa360pe npOllHTaHHOro TeKCTa 06pamaeTc5I BHHMaHHe Ba IIJo6pa3HTeJIbHO-BbIpa3HTeJIbHbIe Cpe,llcTBa Sl3bIKa. nepecKa3Y npeJl.Ba- pHIOTC5I pa3Hoo6pa3Hbie YCTHbIe Ii nHCbMeHHwe CTHJlHCTHlleCKHe ynpajl{- IlrHHH, HarrpHMep rrpe)J.JIaraeTCH H8HTH B TeKCTe c.nona, 0603HaqalOlIJJle )lpiicTBHe, Ha3BaHHe HJlH npH3HaKH KaKOrO-JIH60 rrpeJ{MeTa H T. n., H HocnpoH3BecTH HX (cKameM, li3 paccKa3a JI. TOJICTOrO «ilpbDKOK» - Ata./2b t lUK nOcpo3uA, KPUKHYA) CKUHYA KypmKY U 6POCU/lCfl, 8306paJlCR 1l0AE3 6bltUe, He onlcma8aA} a06paACfl) cmynuA Ha nepeIUlMUHY. ..). 3. YqeHHKH opHeHTHpYIOTCH Ha TO, lIT06bI B HX nepeCK83ax 6blJIH BCCMepHO HCrrOJIb30BaHbI npHoopeTeHHbIe HMM HaBbIKH BbIpa3HTeJlhHO" 1'0 llTeIlHH (,lI.eJIaJlHCb JIOrnqeCKHe y,napeHIi5I, npaDHJIbHO rro,n6HpaJIHCb IIY}!{HbJe HHTOHaJ;1HH, Hcno.nb30BaJlHC6 naY3bl pa3HblX THrrOB H T. A.). 4. !teTe" HY>KHO 3aHHTepeCOBaTb npe,lI.CTOHIII.HM nepeCKa30M Ii c,lte.naTb ero l.{eJIeHanpaBJIeHHbIM. D.JlH .9TOrO, HanpHMep. nepe,l\ yqe.. III1KOM CTaBHTCH KOHKpeTHaH 3a,nalla: «nepeCKa3bIBaH TaK, KaK 6Y.ZJ.TO 'fbl paCCKa3bIBaellib M8Me (HJlH rrarre, 6a6YlIlKe HJIH ,ne.lI.YII1Ke, cecrpe IfJlH opaTY, .llpyry HJIH rrO,l\pyre): ee HY)l{HO 3aHHTepeCOEaTb paCCKa- 30M, OHa ,l(OJI>I{Ha nOH5ITb Bce, 0 lIeM Tbl paCCKa3bIBaeWb». TaKYIO YCTa. 1I0BKY MO>KHO ,AaB8Tb C KpaTKHM HHCTpYKTa)l{eM. BOT npHMepHo KaK rOBopHT YIlIl1'eJIb: «nOlleMY re6e nOHpa}HJlCSI 3TOT paCCKa3? KaK Tbi JtYMaeWb, HHTepeCHO Jlli ObIJIO ObI YCJ1blWaTb ero TBoeH MaMe (UJIli lIane..,)? C lIero Obi Tbl H811aJI? 0 lIeM ObI CKa3aJ1 nOTOM? KaK 6bI pac- CK8S8JJ 0 C8MOM HHTepeCHOM? 4eM 6b1 OKOHIIHJI?» C ITeR )ICe UMblO BblSS8HHOMY JVlH nepeCKa3a yqeHliKY, 8 TaK}Ke lU'CM OCT8J1bHbIM npeAJlaraeTCB HapHCOBaTb B CBOel\i Bo06pa>KeHHH Ka.. I<Ylo-nH60 KOHKpeTHYIO cHTyaUHlo H npeCTaBHTb ce651 ee yqaCTHHKOM. 'renpb YlIeHHKY npe,nCTOHT, CqHTaHCb C ocooeHHOCTSIUi .llaHHOH cu- ...yal.\HH. BeCTH paCCKa3 TaK, KaK 0YJlTO 3TO 6bIJlO nepe>KHTO HM CaMJlM IIJIM: TOJIbl<O eMY H3BecTHO BO Bcex no-np06HOCTHX. YllHTeJIb, Hanpu.. MCP, rOBopHT: «Boo6p83H, lITO TbI ObIJ1 eJJ.HHCTBeHHbIM 01leBH,nnet (HJIK Y'laCTHHKOM) TOro, liTO onHCbIBaeTC5I B 3TOM 9n1i30,lle (HJIH np01f3BeJle- 25
IIHH). nepe.ll.aH Hai\ 3TO TaK, lIT06bl MbJ Bce >KHBO H nOJl 1I0 IIpe)\CTaBH- J1H npOI1CWeUlee». I1J1U: «Teo51 IIpl1fJIaCHJII1 na TeJIe-, paJ{HO CTYHf() H nOnpOCHJIH no.apOOHO rrepeCI<a3aTb COep}KaHHe 3TOfO 9nH3o,aa. Ho paCCKa3bJBaTb Ha,lJ.O T3K, QTo6bl BceM peOSlTaM, KOTopble CMOTpHT Te- JIeBH30p (C:JIYlllaIOT pa){HO), 3aXOTeJIOCb npOllHTaTb BeCb paCCKa3». I1J1H: «flepeCI{a>KH COJ{ep>KaHHe 9Toro Tel{CTa TaK, lIT06bl Y\1:bI nOqYB" CTBOBaJIH H nOTOM CMOfJIH CKa3aTb, KTO H3 J(eHCTBYlOIII.MX JII1lJ. Te6e OOJIbille Bcex nOHpaBHJICSI, a KOfO TbI ocym,naellIb» Ii T. II. ECJIH BbI3BaII.. HbIH yqCHHK He MO}l{eT cnpaBHTbCSI C TaKOfO pOAa TBOptIeCKHIH 3a,na- llaMH, eMY Ha nOMoh AOJI:>KHbI npHHTH ;:J;pyrHe yqeHHKH HJIII YlJI1TCJ1b. 5. ECJ1H BO Bpe!\HI nepecKa3a IlIKOJIbHHK HeBepHo rrpoH3HoCHT OT" l{eJIbHble CJIOBa, TO Y1JHTeJIb, He npepbIBaSl efO, JI.eJIaeT nonYTHhle IiCrrpaDJleHH5J; eCJIH ynoTpeOJIeIlbI HeY3qHble OOOpOTbl petIH, olIn HC- npaBJIHIOTCSI IIPH oocymeHHH nepeCKa3a Cal\IHMI1 YlIaIlJJIMI1C5I. B npo.. necce nepecKa30B, ocooeHHO KpaTKHX H BbIOOPOqHbIX, yqeHHKH ,lJ.eJIa.. lOT HepeKO npO,l(OJImHTeJIbIlble naY3bl. OTHOllIeHHe I{ HHM .lI-0.IT>KHO 6bITb pa3Hoe: OAHH H3 HHX 3anOJIHeHbl paOOTOH MbICJIH, TOr,l(a IIYLKHO DbDKJ{aTb H He rrO){rOH5ITb yqeHHKa; .npyrHe CBH,lJ.eTeJIbCTBYIOT 0 He3na.. HHH H TpeOYIOT COOTBerCTBYIOlllJIX HanpaBJISlIOHX BonpocOB yqHTeJIH. 6. YCHJIHST Ka}K,lJ.oro lllKO..TIbHHKa, ero y,lJ.atIH II npOMaXH B nepCCKa- 3e nOJIyqalOT OUeHKY npeJKe Bcero co CTOPOHbI caMHX :tKe yqaUl.HXCH, If TOJlbKO nOToM BbICKa3blBaeTCSI ytlHTeJIb. Dpn 3TOf era OueHOtlHble CY>K,neHI15J 3aTparl1BaIOT T3KHe MOMeHTbI: He 6blJIO JIH nponYCKa BaiK- HbJX B CMbICJIOBO:\t1 OTIIOIIIeHHI1 MeCT, nOCJIe,lJ.OBaTeJIeH JIB nepeCKa3, K3KHe ,lJ.onyrneHbI oTcTynuTIeHHH OT nJI3IIa, npaBHJIbHO JIM CTpOI1JII1Cb npe.l{O)KeHHH, Y,lJ.aQHO JIM 6bIJIH BBe,neHbI CBOH CJ10Ba H BbIpail<eUHH, BCTpeqaJIHCb JIH rrOBTopeHHSI H HeHYX{IIbIe, JIHlllHHe CJIOlla, BbJpa3HTe- neH JIM nepecKa3, nepeJ{aHbI JIH B HeM qYBCTDa H OTHOlllellHe paCCK33- qHK8 K TOMY, ° qeM OH paCCKa3b1BaJ1. Pa60Ta Ha,n CiK3TLIMH H nOJIHbIMI1 nepeCKa3aMI1 C03.1laeT YCJlOBHH, 6naronpHRTCTBYlOuU-Je napa,.TIJIeJIbHOMY OOYl!ellHIO ,neTeH T BOp q e c.. K H M n e p e C K a 3 a f\1. nOCJIe,nHHe COnpH)KeIlbl C nepepa60TI{oH COepil{aHHH H.lIH (pOpnJI TCKCTa H npHl\feHSlIOTCH npeHMYCCTBeHHO [J OTHOllleHl1H 3nUlJeCKHX H JIl1pO-9nHQeCKHX LKaHpOB, f,lJ.e 1l0BeCTDOBaHHe oOblqHO opraHH3yeTcH B T3Kl1X cpopMax: 1) OT nepBoro JIHna, KOf.l(a 3:1 «H» KpoeTCH aBTop-nOBeCTBOBaTeJIb (J1. naHTeJIeeB. «4eCTHoe cno.. BO»); 2) OT HMeHH KaKOrO-JIH6o ,lJ.eHcTBYlOlllero JII1l{a (H. I-IocoD. «BHTH MaJIeeB B IIJI{OJIe H ,l(ofa»); 3) B TpeTbe1\.f JIHl{e (lI. TOJICTOit «IlpbIiKOK»); 4) B cLVlcwaHHoif <popfe, I{Ora, HanpHl\1:ep, nOBecTBoBal(nc B TpeTbeM JlHu.e neperr.neTaeTcH C IIOBeCTBOBaHHeM OT HMeHH nepCOHaJKa (A. tIe.. XOB. «BaI-IbKa»). nepccr<a3 B TpeTbC1\f JII1u.e aeTCH JICrKO, OT nepBoro JIIiI(a- 'TpY,lUlee. YqHTeJlb Ha nepBbIX nopax JI.OJI}KeH nOl'rfOraTb )(eTHl\f, HCnOJlb- SYH J{JISI 3Toro pa3Hble IIpueMbI: naqaTb nepeCKa3 caMOMY, a 3aTeM npeA1l0mHTb npO,lJ.OJI>KHTb ero eTHM; yqeHHI{ lIaleqaeT «CMbICJ10.. Bhle BeXH» paCCKa3a, a nOTOM. npH.l1eplKHBa5lCb HX, nepeCKa3bIBaCT It T. II. 26
nplfHUlinJfaJlbHOe 3HaqellHe .l(..'ISJ TBOpqeCJ{MX nepeCKa30B HMeeT IICTI{a1 nOCTallOllKa H cpopMYJIHpOBKa «TBOpqeCKOH 3a,nalI!1» nepeCKa- a: B. KaKOH <fJopMe nY*HO nepeCKa3bJBaTb, Ha KaKHe 9nU30,nbI HJ1 If )].pyrHe MeCTa TeKCTa CJIeJlyeT OpMCHTHpOBaTbCH, K8KHe CJIOBa H3 Tel{- era HY}I{HO BBeCTH B nepeCK33, qTO MO}KHO nepe,lI.aTb CBOOMH CJIOBaMH. Jl YIIrne, Kor):la 9Ta 3aaqa 6bIBaeT Bblpa>KeHa B BH,lJ.e onpe,neJIeHHOH u u . iKH3HeHHO-pe3JIbHOH cHTyaUHM, HCXO)J.H H3 I<OTOpOH yqeHHK ,lJ.OJI}I(eH BCCTH CBOH paCCl\a3. I-IanpHl\lep, nplf nepe,lI.atle COJ{ep>KaHHH paCCI<a- 3a «nOCJIe)l.HHH ,lJ.eHb MaTBe5I KY3bMHHa» 6. nOJIeBOrO MOIKHO c<l><>--P- MYJJHpOSaTb 3a){a 1 JY TaK: «[JpeAcTaBb, qTO rr8pTHsaIlcKoe KOMaHOBa- IIIIe rropY1.JHJIO Teo-e CJIe.llHTb sa Tel\1, qTO ,neJIalOT cpaIlIHcTbI B ceJIe. Tbl BH,D,eJI, l<aK MaTBeR I<Y3bMHH BblllieJI OT KOMaH,nHpa rHT.n, epOBII.eB a nOTOM, ]{or,lI.a cTervIHeJIO, rrOBeJI 3a coaoH OTpH,l( BparoB B JIec. TbI npn- IlHMaemb perneuHe HJ{TH CJIeJ{OM 3a OTpH,nO1, YKpbIBaflcb 3a J{epeBbH" Mil. TBOH: nJIaH YJ{aJICH. 1l0cJIe pa3rpOl\fa cpaIIIHcTcKoro OTpH,lI.a H fH- 6lH cOBeTcKoro naTpHoTa MaTBe51 Te6H npocHT nO,lI.pOOHO p8ccKa- 3aTb, lITO ThI BHJJ.e.n». I1JIU: «Ope){CT8Bb, tITO ThI KOMallJI,Hp rrapTlf38H, J{ Tcoe npH6eraeT Bac5I, DHyqOHOI< MaTBe51 KY3b!dHHa. LITO II KaK OIl TeGe J{OJIOJKHJI?» npH nOCTaHOBKe 3a,lI.aQH )(JIH TBoplleCKoro rrepeCl{a3a neOOXO,l{H- u oS 10 yqeCTb, K KaKOH HCTOpHlIeCKOH 3IIoxe OTHOCSITCH onHCbIBaeMbIe COObITH5I H oopaSbI IIepCOHa}l{eiL PaOOTa HaJJ. TaKHMH nepcCI<a3aMH Tpe6yeT 60JIbllIOH npeABapl1Te..1bHOH nOJJ.rOTOBKH: yqeIIHKH' ,lI.OJI>KHbl nepeHeCTHCb B npOIlIJIOe If Y5lCHHTb ero xapaKTepHbIe COI.J.HaJIbHble oco- 6eHHOCTH, ,neTaJIH 6bITOBoro nopfl,AKa, B H3BeCTHOl\i CMbICJIe «B}I{HTbCU) B 06pa3bl J1IOAeH, 0 KOTOpbIX OHH 6YJJ.YT paCCKa3blBaTb. npH.3TOM no OTHOIIIeHHIO K nepCOHa)KaM npOH3Be)J.eHHH, BocnpOH3BOJJ.HllI,HX ,nope- BOJIIOI.J.HOHHOe npOlIlJIOe, yqeHHKaM JIYIIIIIe npe,nJIaraTb nepeCKa3bI (J TpeTbe1 J1Hue. lla>Ke B Tex CJIYtIaHX, Kora 3TH nepCOHaJKH B B03- paCTHOf If nCHXOJIOrlfqeCKOl\'I nJIaHax; MH3KM )J.eTHM, nepeCKa3 or nepBoro JU-Ina (paCCI<a3 A. LIexoBa «BaHbKa») CTaBHT cOBpeMeHHor:o LllKO..TIbl-IHKa. B HeBepoHTHo Tpy.nHble YCJIOBHSI. 3,necb 60JIec YMecTllbi 3a,QaHH5I TaKoro Tuna: «npe)J;CTaBb, qTO MaIlIHHa BpeMeHH Te6H rrepeHeCJIa B ,nOl\i K CanO}KHHKY AJIHXHHY. Tar..f TbI npOBeJI ABa ,lUIH K BHHMaTeJlbHO Ha6JIIOJ{a.1 3a Bce1 npOHCXOSIHM H oo6eHHO 3a 1aJIeHbKHf BaneH )l<YKOBbIM. PaCCKa)KH 0 ero LKH3HH TaK, KaK TbI ee YBHJ{eJI». TBOpt.IeCKHe nepeCKa3bI abIBalOT KpaTKHe H nOAPo6HbIe, OHM tO" rYT npOBOHTbCH 6e3 nJIaHa, no CMbICJIOBbIM BexaM H no nJiaHY, cne- UHaJIbHO .lJ)IH 3TOH l.(eJIIf COCTaBeHHOMY. aH60JIee CJtO>KHbIMM H TPYHbIMH HBJISllOTCSI B bI 6 0 P 0 q H hi e II e Ii e C K a 3 bI. OHH npOBOAHTC.H npeHMYIIT.eCTBeHHO nplf qTeHUH np03aHIIeCKHX TeKCTOB C OTlIeT.J1HBO Bblpa>KeHHhIM ClO}KeTOh-I. BbI60pOQ- lIb]" nepeCKa3 - 9TO He npOCTO nepe)J.aqa cOJ],ep>I{aHHH KaKOH-JIHOO qaCTH HJIH 9nH30,lJ.a npOH3Be,neHH5I. npH Bbl60pOtlHOM nepeCK33e (era Ha3blBalOT HHOr,lI.a nepeCKa30M-H3BJIetIeHHeM) YIIIfTbIBaeTCH co,ltep)K8.. lIMe Bcero npOH3BeeHH.H, HO B pafKax nOCJleJ],uero oT6HpalOTCB Te .1
II 3Re3AOqKB» tPO.A.lOe cn()B n:)}I<OI< [1HC aTeJ1 b A. n Y ill K H H «EJlb paCTeT «YTPO) nepe BOp- UOM. ..) JI. T 0 JI C T 0 H «\ypaBefi 11 «Oreu H CblHO. rO.ny6Ka» BhS1» «fP038 0 JIecy» «HJlHnnOK» «K TO CTp aWHee?» «YTPO» «Y}f( He60 oceHbfO AbI- UlaJlO.. .» «3MMHce YTPO) «CKa3Ka 0 pbl6aKe M pbIOKe» «KaKa51 6bIBaeT poca H 3 Tpa Be» «J1e6eH» A. r a Ii J1 a p «KaK ROJIKH CBOHX eTeH yqaT» «n 0 x 0 JI.» «EJIK8 B Tallre» «B Jlarcpe» <fJaKTbI, «oTOpble OTIIOCHTCH K OJ{HOH li3 ClO>KeTHbIX JIHHI-lii HJIH, qTO 6blBaeT lJame, K OHOMY 113 06pa30B-nepCOHa>KeM. MeTOHKa pa60TbI HaA 9THM BI1,nOM nepeCK33a TaKOBa: CHaqaJIa TeKCT AOJI>KeH OblTb rrO,nBeprHYT aHaJIli3Y H 113 Hero Bbl,neJIeHbI qaCTH, OTIIOCHLI.J.HeCH K OCHOBaIlHIO t no I{OTOPOMY npOBo,nHTCH H3BJIeQeUI1e (O- nYCTHM, K onpeJ{eJ1eHHOH CIO>KeTHOM JlHHHH). 3aTeM 9TH tIaCTH HymIlo o6'beAHHHTb, nepeKI1HYB le}l<AY HHUf CMbICJIOBble «rvIOCTHKH». HaKOHeII-, TO, QTO OblJIO OO'beJUflleHO, Ha,AO a6CTparI1pOBaTb OT OCTaBwerOCH Ma.. TepHaJIa II H3JIO}l{HTb B cpopte CBH3Horo nepeCKa3a. · I( BbIOOpOlIHOMY nepeCKa3Y Be.llYT TaKHe 3TanbI pa60TbI: npe.nJIa- raeTCH TeMa nepeCKa3a H OC03HaeTCH OCHonaHHe, no KOTopor\'IY HY>KHO H3I3J1elJb Tpe6yeMble MaTepHaJIbl; oT6upal:OTCH cpaKTbl C nOMOI..I.J.bIO BbI- 60pOllIIOrO tITeHHH; COCTaB'1HeTC5I nJIaH, 06..TIer l laIOInHH 06'be,a.HHeHHe oTo6paHHblX i'YlaTepHaJIOB; npOBo,nHTCH nepeCKa3. npH BbI60pOQHblX nepeCI<a3ax yqallI.Hl\fCSJ, oco6eHHO na nepBhTX nopax, 6bIBaeT Tpy,nHO OTBJIelIbCH OT lvlarepHaJIOB, KOTopble He OTHO" CHTCH I{ npe,lJ.JIO}KeHHorvIY OCHoaaHHlO. npeo,nOJIeTb 9TH Tpy,nHOCTH nOI'tfOraeT nJIaH, I{OTOPbIH XOpOillO cono.. CTaBHTb C 3anHcaHHbIM Ha .naCKe no,npo6I1bI1 nJIaHOM. OBJla,l{eHHe BbIOOpOIIl-IbIM nepeCKa30M CYll\eCTBeHHO 06TJerqaeT TaK" me YCTaHOBJIeHHe CMWCJIOBWX Bex, npHBJIeqeHHe HarJIHAHOCTH, Hn- '" nIOCTpaI{HH, OTHOCHInHXCH K co.nepLKaHH-lO npOqHTaHHOro TeKCTa. tIaHOOJIbIIlHH Ylle6HO-BOCnHTaTeJIbHbIH 9cp£jJeKT OT npHMeHeHHH nepeCKa30B npOqHTaHHOro ,nOCTHraeTCH ToraJ KOl1{a Ha ypOKax qTe- 28 .
- III IV .I'onlloo ('.nOMOI cHama POAHIIS» cPO,D.Hoe cnOBO» fnpo rpSMMa» «KOllb:O «BCTaeT 3apH BO MrJle «rOIlHMbI Belli- Xo.nOl\HOH...» HHMH JlyqaMH...» «BOT ceBep TYtlH HaroHSlSI...) «Y HblJlaH no- , pa. . .» «3HMI1HH Beqep» «3HMHHH ,Aopora» CCKB3KB 0 uape CaJlTaHe...» «Y nYKOMopbH...» cCKa3Ka 0 MepT- Bon apeBlle...» "(8KaH 6b1B3eT )()\I lia Tp3Be) ill PbUKOK» «KaBKaSCKHH nJleHHHK» «CnoeCTb» «JIaJIbHHe cpaHb1» «CKa3Ka 0 BoeH- «rOpHqHH KaMeUh) lIoii T aAHe...) «CKa3Ka 0 BOeJllIOH «BaCHJlHA KpJO- TaAue...» Kon» , , «tHMYP Hero KOMaH,Aa» '/ IIHH HCnOJIb3YIOTC5I nepeCKa3bI Bcex OCHOBHbIX BH){OB H KorJJ.a paOOTa no rrO){rOTOBKe K nepeCKa3Y CTpOHTCSI Ha OCHOBe npo,nYKTHBHoro MHO- rOlJreHH5I nepeCKa3bIBaeMoro TeKCTa. l{JISI OOJlbWeH CHCTeM3THsanHH, nOBTopeHHSI H nO.TOp",enltHO- S8KperrneHHst npH06peTeHHblX yq8II\HMHCSI' SH3HHH o606lqalOlqN8 38H'- ' TN_ . III Kn8cce 8 TalOKe ,l(JISI nepcneKTHBHoA no,nrOTOBKH K o6Y1Je- HMIO B IV KJIacce neneco06pa3Ho perynBpHo npo- BO,nHTb nOBTOpHTeJIbHO-OOoomalOmHe 38HSlTHSI. OHM MorYT CTpOHThCSI Ha OCHOBe >KaHpOBOro HJIH Te.M8THtJeCKoro CXO,l(CTB8 orrpeJJ-eJIeHHbI npOH3BeJJ.eHHH (HarrpHMep, no CKaSK8M, n0CJ10BH1I.aM, 6aCHSIM H T. n.), JiX l\fO}KHO rrpOBo,nHTb «no nHCaTeJl5IM», a MO>KHO SaBepWaTb HMH npo- v u . xom,neHHe K8OH npOrpa1\tMHOH TeMbJ, OTBOJJ.SI )tJlSl 9Toro nOCJle)tHHH no TeMe ypOK HJIH tJaCTb ero. ,/ OC06HHO Ba>KHO CBoeBpeMeHHO npeJtYCMOTpeTb, KaKHe M-aTepHaJlbl nymHbI 6y,nYT )lJISI nOBTOpHTeJIbHO-o606w.aIOIIlHX saHHTHH. B 9TOM OTHoweHHH nOMOb MomeT OKa38Tb TaK8S1 TaMHna (CM. BbIUJe). ' KOHKpeTH8S1 MeTO,l(HK3 npOBeAeHHSI nOBTOpHTeJIbF!o-o606w.alOHX 3aH5ITHA xopomo H .nOJJ.po6HO OCBerueH8 B pa"OOTax E. A. AJJ.aMOBHq. n03TOMY B A8HHOM nocot5HH MbI He OCTaHaBJIHB8eMCSI Ha MeTO){H- Ke nOBTOpeHHB H oOO6eHHSI H 8)1.pecyeM QHTaTeJlSI K TeM MeTO- ,lUiIIeCKHM peKOMeHltaUHSlM, Koropble CO)lep>K8TCSI B KHHre E. A. A)l.a- MOBHT.I H B. H. .sIKoanenoH «qreHHe B Hat.laJIbHblX KJI3CCaX». M., «npo- CBeIUeHHe», 1967, rJI8Ba «B38HMOCBSl3b p83JIHqHb]X S3HSlTHH H8 0600- InDlOInHX ypOKaX», 8 TaK>Ke B CT8Tbe E. A. AAaMOBHtI «3HaqeHHe 0606- 29
I..IJ.8IOWJIX ypOKOB qTeHIiH H OCIIOBHbIe Tpe60BaHHH K HHM», cG. «Bon- pOCbl MeTOHKH qTeHHH». M., «npOcBeeHHe», 1964. B 3aK.ITlotJeJ:lHe OTMeTHI, qTO nOBTOpHTeJIbHO-Ooo6IlI.alOlIJJ-te 3aHH- THH HrpalOT cyecTBeHHYIO pOJIb B nO)lrOTOBKe MJIa,AIlIHX WKOJIbHHl\OB K npOXO)l{jtelIHlO Kypca JIHTepaTypbI B IV KJI3Cce. OpH 3TOM cpeH pa3- JIHqHblX CPOpM opraHH3aUHH 3THX 3aHHTHH HaHoonblIIee 3Ha1.IeHHe HMelOT I10BTOpeIIHe H ooo6eHHe «no nHCaTeJIHI» M, KOHeqHO, B nepBYlO Oile- pe,l(b TeM H3 HHX, KOTopbIe cpHrYPHpYIOT B npOrpal\fle IV Knacca. C npaBOLfHblH MaTepHan 06IQ.eCTBeHHO- HCTOpHqeCKOrO XapaKTepa OnbIT npenoasaHHH .nOKa3hIBaeT, qTO Ha ypOKax qTeHH5I B HaqaJJb- HblX Knaccax YQHTen51 HcnbITbIBalOT TPYJUIOCTH, CBH3aHHbIC C Heo6xo- .lI-HMOCTblO pa3'bHCHHTb KOHKpeTHble <paKTbI HCTopHtJeCKoro II HCTOPH- KO-<t>HJIOJIOrHtJeCKoro X3paKTepa, Henocpe)I.CTseHHO OTHoCHHeC5I J{ H3YQaCMbIM TeKCTaT\f. npe,Harael\lbIe HH/Ke l\'laTepnanbI npH3BallbI no- MOIIb yqHTeJ110 npeO)l.O,,'1eTb 3TH TPYHOCTH. 1\1aTepHaJibI He cO)1.ep}KaT MeroHqeCKHX p eKOMeH,l(al(H H., nOCKO.ITbKY OHH )J.alOTCH B cooTBeTcTBYIO- Il.lHX pa3){eJ1aX aHHoH KHHrH, a TaK}Ke B CneHaJIbHbIX MeTOHlleCKHX YKa3auHHx K KHMraM «Hawa Po,nHHa» H «Po,nHoe cnOBO». c:I>aKTHqeCKHe CBe,neHHH, KOTopble MbI npe)J.JIaraeM, )1.aHbl B XpOHO- nOfHtleCI<OH noc..TIeOBaTeJIbHOCTH, He3aBHCHMO OT TeMaTHlIeCKOrO pac- nonomeHHH TeKCTOB B KHHrax nH qTeHHH, npH 3TOM TOQHO YK33- BaeTCH, K KaKOH TeMe 3TH CBC,AeHHH OTHOC5ITC5I. <l>aKTHQeCKHH MaTepHaJI aeTCH no OpeBOJIlOHOHHOMY nepHO- AY HCTOpHH HallleH CTpaHbl, TaK KaK HCTOpHqeCKHe CBeeHHH, OTHO- CSlI1(HecH K coseTCKOH 9noxe, 3HatlHTeJlbHO JIytlllIe H3BeCTHbI YllH- Te1ISlM. nOCKOJIbKY MaTepHaJI apecyeTcH YQHTeJIlO, eCTeCTBeHHO, qTO Ha ypOKe OH Hcnonb3yeTcH JIHUIb B TOM OO"beMe, KOTOpblH Heo6xoHM JIlIH OOhHCHeHHH YQaHMCH. KP A TKHE CBEAEHHSI 0 HA "lAnE MOCKBbl H. I(OH1I8JIOBCKaH. «I-Iawa JtpeBHsul CTOJIHlla» (OTpb1BOK) - «Hawa POJtHna» , CTp. 55, «POJJ.Hoe CJIOBO», corp. 58; M. l(oBaneblcKHH. «HaqaJlo MOCKBbl» - «PO.!l.HOe CJIOBO», CTp. 60. Ha TOM MecTe, re B03HHK ropo,n MOCKBa, JIlO){H >KHJIH H3aBHa. Ho BnepBbIe MocKBa ynoMHHaeTCH B nCTonHCH no 1147 f. B XII B. MocKBa 6bIJIa lorO-3ana){HOH oKpaHHoH POCTOBo-CY3){anbCKOro KHH- JKecTBa, KOTopoe n03}1{e CTaJIO Ha3bIB3TbCH BeJIHKHM BJIaHMHpcKHM KIUI>KecTBOM. KHH3b IOpHH BnaHMHpOBHQ .aOJIroPYKHH (CbIH BJIaH- MHpa MOHqMaxa) npHKa3aJ1 nOCTpOHTb HeOOJIbllIYIO .a.epeBHHHYIO I<pe- noCTb npH Bna)1.eHHH p. HerJIHHHOH B MocKBy-peKY. 9Ta KpenocTb au
UU3hIB3J1aCb «MOCKBa-rp:a,n», (T. e. 20pOO MockIJa. FopoiJ, no CTapHH- lIoii PYCCKOH TepMHHO.'10rHH, - nOCeJIeHHe, 06HeceHHoe KpenOCTHOH l'TCIiOll, orpaAOH). . B Te BpeMeHa MOCKBY OKpY}KaJlH ,npeMyqHe Jleca H OOJIOTa, nOKpbl- TI,rc MXOM, Me}KY XOJIMah1ij TeKJIH PYlILH H peqKH. BocnoMHHaHHH 06 ') H)M cOXpaHHJlHCb B cTapblx Ha3B3HHSlX: BOpoBHUKHe BopoTa - KpeMJISI (or CJIOBa 60p - rycToH xaoHHblH Jlec) , MoxoBaH ynHa, BOJIOTH3H IIJIOaAb, YJI. HerJIHHHaH, KaneJIblIbIH nep. (p. KanJISI)", npecHH (p. npecHH), CHau.ea BpaiKeK (p. CHBKa) HAp. Cal\fOCTOHTeJlbHbIM (y.neJIbHbIM) KHH}KeCTBOM MOCKB3 CTaJIa B KOH- ne X I I I B. npH MJIaJl-IIIeM CblHe AJIeKCaHApa HeBcKoro - l1aHMHJle !\JleKcaH,npoBH1Je. BCKope MOCKoBcKoe KHH}I{eCTBO CTaJIO OAHHM H3 l'HMbIX cHnbHbIx B CeBepo-BoCTOtlHOH PYCH. 3ro 6bIJIO npH CblHe JJ.a- IUIHJla A.neKCaH){pOBlflIa - I1BaHe JJ.aHHnO_BHqe KaJIHTe. npH l1aa- uc KaJIHTe OblJI nOCTpoeH AfOCKOBCKHH KpeIJIb. CTeHbl- ero 6blJlH l'JIOlKeHbI H3 BeKOBbIX Ay6oB. TorAa me nOHBHJIHCb B MocRBe H lIepBbIe KaMeHHbIe cOOpY)KeJIHH - epKBH, nocTpoeHHbIe H3 6eJ1oro I(UMHH. 3a KpenKHMM Ay60BbIl\tIH CTeHaMH KpeMJIH H B KaMeHHbIX IlCPI{BHX YKpbIBaJIOCb Hace.neHHe MOCKBbI OT CTpe.n H KaMHeH BparOB, J<OTopbIe aCTO HanaAaJIH na ropo,n. npHlIHHbl B03BbIweHHH MOCKBbI SaKJIlOqaJIHCb a TOM, qro ,ona sa- IIHMaJIa OtleHb y,n06Hoe nOJIO}KeHHe cpeAH ApyrHx ceBepO-BOCTOtlHblX PYCCKHX KHSI>KeCTB. ropOJ{ ne)KaJI Ha nepeCeqeHHH Ba}KHbIX ToprOBblX u u u nYTeH: H3 KpynHeHwero ueHTpa Me>KAYHapO){HOH TOprOaJIH Toro Bpe- MCHH - HOBropo,na - MO}KHO 6bIJIO Ha cYJl-ax npOHTH B MocKBy-peKY, n OTTYAa Ha OKY.M BOJI; C OKM Ha ,L:lOH H JlaJIee - B, A30BCKoe H lIepHoo MOpH. TaM, r){e KH 6JIM3KO nOAxoAHnH .npyr K ,npyry, cY.lla I1cpeTacKHBanH BOJIOKOM.'BocnoMHHaHHH 06 3TOM cOXpaHHJIHCb B HaSBa- IIHHX ropo,nOB BbIlIIHHH BOnOqeK, BOJIOKOJIaMCK HAp. MOCKBa OblJIa XOp0Il10 3alll.Hlll.ena OT Harra,neHHH Bparoa: OHa ObIJIa B u.eHTpe pyc- CKJlX 3el\tleJIb, p3CrrOJlO}KeHa Ha BbICOKOM, 06pbIBHCTOM oeper:y MOCKBbI- pe}{H, oKpymeHa rycTblMH JIeCaMH. Bce STO rrpHBJIeKaJIO B _ MOCKBY Mlloro Hapo,ny. ilpH BHYKe l1aaHa KaJ1HTbI ,QMHTpHH HaaHOBMqe J].OHCKOM l\10cKBa ("tile oonee YCHJIHJIaCb. BbIJI nOCTpoeH 6eJIoKaMeHHbIH KpeMJlb. Oco- ()eHHo B03pOCJIO 3HaqeHe MOCKBbI nOCJIe noqeJ{bl Halt nOJlqHlUaMli MaMaSi B 3HaMeHHTOH KynHKoBcKOH oHTBe (1380). : CnycTH 100 JIeT (npH npaBHYKe ,l{MH'fpHSI ,aOHCKot'O I1BaHe III) UblJIO OKOHqaTeJ'IbHO cBeprHYTO MOHrOJIO-TaTapcKoe Hro H MocKBa OO'beAHHHn'a 'PyccKHe SeMJlH. Tor,lJ.a me Ha1JanOCb cTpOHTeJIbCTBO 'HO- Boro KpeMJIB, KOrophIA ij no cea ,lJ.eHb YKpawaeT HaillY cTOJIHny. B CepeAHHe .XVI B. npH. HB3He IV (rp03HOM) MOCKBa CTaJIa ueH:r- pOM orpQMHOA ,nep>KaBhI - PYCCKoro (HH. POCCHHCKoro) l.lapCTa.. B HaqaJIe XVIII B. CTOJIH.ua POCCHH oblJIa nepeHeceHa B TO,JJKO 'ITO . C03,naHHblH HOBblM ropo,lt - nerepoypr. Ho MOCKBa He YTpaTHa II TorAa CBoero -3HaqeHH.SI. Ee no np3BY CQHT3JIH BTOpOH C1;OJIHueU I)OCCHH. He CJlY1J:aHHO HanOJleOH B 1812 r. ,nBHHYJI CBOH rrOJIqHa: H 31
na neTepoypr, a Ha MOCKBY. OH YTBepJK,llaJl. tITO, B3HB neTepoypr, nopa3HT POCCHIO B rOJIOBY, HO, OBJI8,neB MOCKBOH HaHeceT Y.llap B ca- t.toe cep,nue. B 1apTe 1918 r. HatIaJIaCb HosaSi MCTOpHSI CJIaBHOrO ropoa. (11 BeTCKoe npaBHTeJIbCTBO rrepeexaJIo H3 neTporpMa B MocKBY. MocKBa - .llpeBHeHIllIiH H 3aMeqaTeJIbHeHllIHH ropo){ HarneH POHHbI - CTaJl u CTOJIHueH nepBoro B MHpe COUHaJIHCTMtIeCOro rocy,napcTBa. KOMMeHTapt04 MocKoa. rrpOHCXOil{eHHe CJ10Ba MOC1C8a OKOHtlaTeJIbHO He BbIHCHeHO. He BbI3blBaeT COMHeHHH, tlro CBoe Ha3BaHHe ropo,a nOJIYA'lHJl (t" ua3Bat{HH peKH. CYlI.\eCTByeT HecKOJlbKO BepcHH, OODSICHHlOII.(HX npOHC- X01K,neHHe 3Toro CJlOBa. OHH CtlHT3IOT. tlTO CJIOBO MOCK8a yrpo-<pHHcKoro npOHCXOJK,aCHHH H 03HaQaeT «rHHJlaH» HJIH «l!epHaH BOa». ,apyrne- qro MocK8a - CJIOBO capMaTCKoro npOHCXO:>K){eHHH M 03HatlaeT «H3BH.. n HCTa H p eKa». CTOJlHa - npOHCXO,l{HT OT CJIOBa cmoA. (11pecmo/2), T. e. BeJIHKO" I{HH>KeCKHH (UapCI{HH) TpOH, MeCTO, Ha KOTOpOM CH,llHT npaBHTeJIb (l.lapb). OTclOa H Ha3BaHHe rJIaBHOrO ropoa - cmOA.ul{a, T. e. ropo,lt, B KOTOpO:vl CTOHT npeCTOJI npaBHTeJIH (UapH). J Ha3BaHH5I cmo.ll (npe" cmoA), cmObHblU (npeCmO/lbflblu) 20pOO, cmOAutfa BOIliJIH B 06HXO,l{ co BpeMeH KHeBcKoH PYCH. B «nOBecTH BpeM:eHHbIX JIeT» (uatlaJIbHOH PYCCKOH JIeTOnHcH) no,n 1015 r. rOBopHTCSI 0 TOM, KaK PY>KHHa yro- BapHBaJIa KHSl3H EopHca 3aHHTb KHeBCKHH npeCTOJI nOCJIe Cl\lepTH ero OTua BJIaHMHpa: «Ce ,nPY>KHHa Y reOH OTHH H BOH, nOH){H CHb B KHe- Be Ha CTOJI OTHHH», T. e. «Y Te6H OTl.{OBCKa51 ,npymHHa H BOHHbI, nOHH H saHMH OTOBCKHH npeCTOJI B KHeBe». KpeMJlb - TaK B ,llpeBHeH PYCH Ha3bIBaJIH KperrOCTHYlO CTeHY KOTO.. pOH OKpYIKaJIH ropo,n JIH 3aInHTbI OT Bpa>KeCKOrO Hana,neHHH. n03>Ke l<pel\fJIeM CTaJIH Ha3bIBaTb KpenOCTb BHYTPH ropoa. CJIOBO KpeAUlb npo- H30IllJlO, nO-BH){ID.iOMY, OT ,l{peBHepYCCKoro KpeM.b - KpenKHH CTpoeBOH nec. KpeMJIeBOe J{epeBo - 3TO AepeBo, BblpoclIIee Ha npocTope, Ha KP8IO JIeca. B ropo,nax ,npeBHeii PYCH KpeMJIb, KaK npaBHJlO, 6bIJI ,ne- peBHHHbIW, py6TIeHHbIH H3 KpeMJIeBOrO epeBa (){y6a). B03MOLKHO, tlTO c.nOBO KpeM.Ab npOH3011IJIO OT l('pOMa - Kpaii, rpaHHa, OFopomeHHoe MecTO. noca,lJ. - ToprOBo.peMeCJIeHHbIH. paHOH B ApeBHepYCCKHX ropo- ,nax, p aCnOJIOlKeHHblH 3a npe,l{e.TIaMH KpefJIeBCKOH CTeHbI. Bo Bpel\tSl Hana,neHHH BparOB HJlH oca,l{bl ropo,na >KHTeJIH nOC3,l{a 06bIlIHO YKpbIBa- JlHCb B KpeMJIe. 0POHCXO}l{):teHHe CJIOBa nOHHTHO: KopeHb -cao (ca- :JItamb J CaaUlnb " np.). B peBHepyccKOl'vf H3bIKe CJIOBO cecmb HMerJO C?vlbICJI ocecmb - npOqHO, Ha,nOJIrO YCTPOHTbCH >KHTb B ,naHHOM Mec- Te. OcpHIJ.HaJIbHO rrOHHTHe «nocaJicKoe Hace.neHHe» (TOp rOBIJ.bI H peMec.. neHHHKH) B npOTHBOnOJIOJKHOCTb KpeCTbHHBM, BopHHaM, OOSIpaM, Ay.. XOBeHCTBY cyecTBOBaJIO lJ.O rreTpOBCKHX npeo6pa30BaHHH (Haqa..TIO- XVIII B.). 32
Cpy6 - OCHOna J\epeBHHHOrO ota. OT CJlOB3 py6UJllb. 11 cefiqac n CeJlbCKHX MeCTHOCTHX CTaBHT Cpy6bI - ,nepeBHHHWe ,l\01\la. B peB-. .. \lit PYCH BCe >KHJIbie ,ltOMa (3a peJl-lIaHIIIHl\f HCK.TIlOlIeHHeM) 6blnH Aepe- 13S1HllbIMH. Hx «PYOHJIH», T. e. CTaBHJlH OpeBeHlIaTbIH cpyO. BblJIO BeCb- M3 paCnpOCTpaHeHHbIl\f Bblpa}KeHHe cpy6umb aO.lU, cpy6umb 20poiJ (T. c. nOCTpOHTb Ol\f, ropo,n). Coxa - CTapHHHoe 3eMne,l\eJIbt.leQKoe opy,nHe. ,QepeBHHHag coxa tSbins OJUUIM 113 caMblX Ba}KHbIX OPY)J.HH B X03HflCTBe -D-peBHHX CJIaBHH. nepaOHSqaJIbHO OHa rrpe,nCTaBn5IJl3 COOOR KpenKHH CTI!oJl ,nepeBa c OCTpblM CYKOM, KOTOpblM B3pblXJlHnH 3eM..'1IO. nOTOM coxy CTanH cne- I . ., .. '!UMbHO lteJIaTb H3 .nepeBa, Ha)l.eBa51 Ha Hee me.JIe3HbIH lIaKOHetJHHK '(COlllHHK). B coxy BnpHranH nOma-D-b H TaR rraXaJIH. Coxa, .J{3K O,nHO u u H3 rJ1aBHbiX opy,nHH CeJlbCKOrO X03HHCTBa, COXpaHMJIaCb BO nIorHX ,nepeBHHX POCCMH BflJIOTb ,no QKTSlOpbCKOH peBOJIK)[!HI1. nOWJlHHa - naJIor, ,neHe>KHbIH c60p c rrpO,lJ.aBaeMblX TOBapOB. - B ApenHeH PYCH nOlliJlHHa na3bIBa.'1aCb Mblm. OTCI9a Ha3BaHHe no.. MOCKOBHoro ropO,l\a MbunUU} T. e. Metro, r,lte 6paJ1H MbIT, rrOU1JIHHY 3a BB03IiMble: B MOCKBY TOBapbl. -- JIeTpnHcb- 3anHCb COOblTHH no rOJ{aM (Aemo - 3,lJ.eCb: rOA). nepBaH PyccKaSI JIeTOnHCb Ha3bIBaeTCH «nOBecTb BeMeHHbIX Jle». ABTOpCTBO ee npHilHcbIBaeTcH MonaxY-JIeTOnHcuy KHeBO-neqepCKOro MOHaCTbIpSl Hec- TOpy. J1eTonHcH Haqaw'lH c03aBaTbcH Ha 'PYCH He paHee KOHua XI B. 6oHpe. ,QPYiKMHa KHeBCKHX, a saTeM H pyrHx PYCCKHX KHg3eA )1eJ1HJlaCb Ha «cTapwylO» (6oHpe, HJIH cTapnbI) H «OJlOJI-W.yIO» (J\eTH 60gpCkHe, rpH)l.HH, OTpOKH). <l>aKTHqeCKH Ha BOHHY-- illJIa MJla,l(WaSi .u.pY>KHHa, a 60Slpe 6bIJIH JIH60 BOeaatlaJIhHHKaMH, JIHOO COCTOSlJlH npH ,l\BOpe BeJ1HKOrO KHg3H(B COBere H np. HeCKOJIbKO n03}Ke 60Slpe 9TO npe1KAe Bcero KpynHbre 3eMJIeBJlaAeJlbUbl-BOTIIHHHHKH. OHH 6bIJIH nOJIHblMH coocTBeHHHKal\1H 60JlbIIIOrO aelvIeJIbHOrO BJIaAeHHSI (BOTtlH- lIbI), ,HaCeJ1eHHOrO KpeCTb5IHaMH. ilPOHCXO}l{,neHHe CJlOBa, BepoHTHo, or «60JIHPHH» - 60JlblllOH t Ba>KHbIH (raK >Ke KaK CJIOBO Ma2Ham OT narHHckoro «1arHYC»- 60JlbIIIOH, Kp.ynHhIA)....... . AJleKcaHAP HeBcKHA (1220-1263). HOBropo.ncKIiH, a. 3aTeM I-{ BHKHH KHSl3b Bna.lJ.HMHpcKHH -o3HaMeHHThIH nOJIKOBO;l\en peB" HeH PYCH, paarpoMH:BUlHH WBe,l\OB B 1240 r. °Ha p. HeBe (OTclO,na Hera n0 1 1eTHoe npo3BHw.e). H' HaHeClliHH cOKpymHTeJIbHOe nOpa)KeI-lMe He. Meu.KHM .pbn.(apSiM Ha'.JlbAY 4y,ncKoro_ o3epa 5 anpeJISI 1242 r. (JIeJtoBoe noooHme). Y>Ke - coapeMeHHHKH nOHHMaJIH HKJUOqHTeJIbHble 3aCJIyrH A.neKcaHpa HeBCI<Oro. ne'peJt POJ(HHOH. «MHoro Tpy,ltHJICH OIl 3a HOB. ropoJJ.. H 3a IlcKOB, H sa BCID 3eMJlIO PYCCKYIO, >KH3Hb 3a Hee nOJlo. >KH..1», - rOBopHT J1eTOnHCel(. . CeMbCOT JIeT cnYCT nOCJIe .neJ\OBoro q060HW.a, B 1942 r., BO ...Bpe.. l.fSl BeJlHKOH OTeqeCTBHHOA BOHHbi 6b1Jl Yllpe>KJ1eH ooeBOH op,nelt AneKcaH,lJ.pa HeBCKoro. 11M Harpa>K,naJIHCb KOMaH)l.HpbI COBeTCKOH ApMHH 3a J1Ht{oe MYiKeCTBO H BoeIlHoe HCKYCCTBO. 2 3aKaJ 694 33
"Ban KaJlHTa (t 325 -134 t). HBaHa ,UaHHJIOBHt)a np03BaJlH KaJIHTOM 3a ero 60raTcTBo. HaKOnJIeHHble J{eHbfH OH OqeHb paCQeT,,1HBo TpaTHJI Ha npHoopeTeHHe HOBbIX BJla,AeHHH. Ha YCIfJleHHe CBoero BJlH5IHH.H H BJla- CTH. KO,.tuma - cotScTBeHHo, KOWeJIb HJIM c)'MKa C Jl.eHbraMH (CJ10BO u TarapCKoro npOHCX01K,neHHH, «KaJlTa» - KapMaH, KO:>KaHbIH MelliOK, KOllieJIel{). ,- KPEnOCTHOE i"IPABO B. H. «B 60SJpCKOH yca,ltb6e», «B H36e y MHKHl'KH»-=-«HaW3 POAHHa», cTp.56 f 58; «KpenocTlloo npaBo», C. A.neKceeB. «npOJtaJIH», «M3 Hapo,l\HoH neCHU», OTpblBOK H3 n09MbI H. A. HeKpacoBa «KOMY Ha PYCH >KHTb XOPOWO», \. Ca.nTbJKOB-I..l\e,u.p.HH. «B rOCTRX Y TeTeHbKU» - «POAHoe CJIOBO», CTp. 61, 62, 66. HHTeHcHBHoe 3aKpenoIneHHe KpecTbSiH HaqaJlOCb B XV B., Kor,lla oopa30BanOCb PYCCKoe ueHTpaJlH30BaHHoe rocy.n-apCTBO. npH BMH- KOM KH5I3e HB8He III B '1497 r. 6bIJl H3;J.aH «CYAe(5HHK» - KpaTKHA CBO;:\ saKOHOB. 110 9Toro BpeMeHH KpecTbRHHH Mor nOKHHYTb cBoero BJIa,neJIblla H nepeHTH K ,llpyroMY. «Cy e6HHK» J1BaHa I I I YCTanOBHJI )l.JISi KpeCTbllH npaBO nepexo.na TOJlbKO O,IIJIH pa3 B ro.ny, B lOpbeB JleHb (26 1I090P$J). KpecTbHHHH Mor yffTH OT 3ef\1JleBJI8AeJ1bQa JIHlllb 3a ne,ne... JHO AO IOpbeBa }.tHH H He,neJUO cnYCTH nOCJIe Hero. KpecTbHHHH ,nOJI>KeH ObIJI nOJIHOCTblO paCC1JUTaTbCH C 6apHHOM, 3anJIaTHTb 38 «rrO){{HJlOe». n03;:\HeH oceHblO HeMHorHe KpecTbSlHe pMCKOBaJlH YXOJ{HTb C HaCH1KeH- HbIX Y\ieCT. B KOHue napCTBOB8HHSI J.tB8Ha rp03Horo, B 1581 f.t 6bL'1 H3AaH YKa3 0 TaK Ha3h1B3eMblX «3anOBe)J.HbIX J1eT8X». Bnpe.lJ.b .no ocoooro paCnOpH>KeHHH IOpbeB ,nellb OTMeHHJlCH. 1-1 KpecThHHaM Boo6rne 3anpe.. In3J10Cb nOKH,naTb CBoero 3eMJIeBJla,lteJIbua. Tor,na-To 0 nOHBHII'IaCb no- rOBopKa «BoT TetSe, oa6YlIIKa, H IOpheo ,neHb». HHKaKoro - YKa3a 0 BO- 306HOBtTIeHHH IOpbeBa ,nHH TaK H He nOCJle;:\OBaJIO. Hao6opOT, aaKpeno- ll1.eHHe KpeCTbSlH Bee YCHJIHBaJIOCb. KpeCTb5lHe Oe}K8JIH OT CBOliX rocno,n. Tor,na ObIJI H3,naH YKa3 (npM l1ape <l>e;:\ope HBaHOBH1Je B 1597 r.), KOTOpblH paSpellIaJI nOMeI.JJ.HKa1 B TelleHHe nHTH JIeT PCJ.3bIcKHBaTb H B03BpamaTb 6erJIbJX KpecTbHH. "Ka3 1607 r. npoJ{JIHJf' CpOK p03bIcKa ,ZlO n5lTHauaTH TIeT. B 1649 r. npH uape AJleKCee MHXaWJIOBHQe 6blJIO npHHHTO «Co- t5opHoe YJlO>KeHHe» - nepBbIH nO;J.po6HblH CBOA 3aKOHOB POCcHHcKoro rOCY,AapCTBa. «CooopHoe YJIOmeHHe» OTMeH.HJlO Boo6e BCSlKMA CpOK p03bIcKa KpecTbSiH. KpecTbHHe nOJIHOCTblO 3aKpenOaJlHcb. nOcTeneHHo nOMeIUHKH YOeJIMqHBaJIO 6apWJIHY H 06pOK. npH EKa- TepHHe II (1762-1796) KpeCTb5lHe npeBpaTHJlHCb B nOJIHYIO cotS- CTBeJlHOCTb CBOHX rocnoJ{. KpenOCTJlbIX MOrJIH npo.naBaTb He TOJlbKO ceMbSlfHJ HO H B O,lJ.HHOllKY, pa3.TJY'I8S1 po,nHTe.neH C ,lleTbMH. JIIOJleH Bbn..teHHBa.TJH Ha ,noporHe BeIll,H, nopo.nHCTblX cooaK, ox npOHrpblBaJIH B KapTbI, AapHJlH. 3a MaJleHWYIO npOBHHHOCTb KpeCTbHH >KecTOKO H8K83bIB8J1H, HHOrJla 3anapblBaSi JlO CMepTH. )l(aJI0BaTbCH KpeCTbHH8M H3 nOMeHKOB 6blJlO CTporo 3anpem.eHO SaKOH01\1, H3,naHHbIM EK3Te- pHHOH II. 34
Oopaw.eHHe c KpenOCTHbIIU OT./IHQaJlOCb 3BepCKOA }KeCTOKOCTblO. B yca.nb6ax nOMelllHKoB HMeJlHCb UMble apCeHaJibI BceB03MO;>KHLIX OPY,lJ.HH .fIbITKH: nlIeTH, KHYTbI, na..'1KH, KOJlOJ{KM, uenH. TaK, Y O,ZlHorO nOMelll.HKa Ha JI-BOpe CTOSlJI8 OOIlTIblllaH JJ-cpeBHHHaH KOJIo,.Y].a, K HeA npH- KOBblB3JIH u.eFIblO rrpOBHHHBlIlMXCH KpeCTbHH 33 melo. n01\fer.nHII.bI He YCTyn8J1H B }l{eCTOKOCTH CBOHM !\.tY>KbHf. HanpHMep, OJI-Ha nOMelllHu.a uaxo.nHJIa y.nOBOJIbCTBHe B CeqeHHH J1.eTef( H cala nOpOJl3 HX no 111060- MY nOBOllY. .no Tex nop, nOKa peoeHOK He Tep SlJI C03H3HHH. Bce 3TO npo. XOHJlO COBepl1leHHO 6e3H.aKa3aHHo ,llJlH nOMelllHKOB l . nOJIO>KeHHe KpenOCTHblX KpeCTbSlH B XVI I I - nepBoA nOJlOBHHe X I X B. «Ha npaKTHKe OtleHb cJlaGo -6TJlHtJa.rrOCb OT nOJIO:>KeHHH pa60B B pa60BJIa.neJlbllecKoM rOCYllapCTBe»2, - rOBOpHJI B. 11. JIeHHH. KOMMeHTap"" nOMeID-HK (ABOpSlHHH), 6apHH. ,QBopHHe (noMeIUHKH) B XV- XVI I BB. - O,llHa H3 rpyrrn rocno,llcTBYIOInerO KJlaCCa <!>eO){aJIOB-3eMJIe- BJla,neJ1bueB. 91'0 JllO,llH, KOTopble CJIY>KHJlH npH ,l{BOpe BeJlHKOrO KHH3R (ltapSl) HJIH B ero BOHcKe. OrclOlla H Ha3BaHHe 080pRHe. 3a CBOIO CJIY>K6y BpSlHe rro.nYllaJIH SeMeJ1bHble yro.nbH C KpecTbSlHaMH - no- MecmbR (napb nOMeInaJI, «HcnOlelllan», KaK Torlla rOBOpHJIH, BOpHH Ha 3eMJIlO). OTCIO.n3 H Ha3BaHHe nOMeUU1(. B reqetIHe XVI-XVII BB. BHYTPH KJIaCCa 4>eOaJIOB (MeLKJty BO- pHH8MH-rrOl\eIIIJiK3MH H 6oSlpaMH-BoTIIHHHHKaMH) IlIJia 60pb6a sa 3eM- JIIO H KpenOCTHbIX. Oc05eHHo O>KecTOqeHHOH 9Ta 60pb6a 6bIJla BO Tp- pOR nOJlOBHHe XVI B. npH nape I1BaHe IV.. B pe3YJIbTaTe 9TOH 6Opb6bI K HaqaJlY XVIII B. (npH neTpe I) oGe rpynnbl <j)eoJJ-aJIOB CJIHJlHCb B O,ltHY: Bee 4>eOJ{aJIbl-3eMJIeBJlaeJIbI1b1 CT8J1H Ha3b1BaTbCH a80pH.HaMU, a HX 3eMeJlbHble BJla,lJ.eHHJI - nOMeCmbJlMU. CJlOBO 6apUH npOHCXO,llHT OT 601lpUH.\ KorAa HCQe3J10 pa3J1HQHe Me>KJ{Y 60HpaMH (.{ J(BopHHaMH, CBOHX rocno,ll KpeCTbRHe CTaJiH Ha.. 3bIBaTb 6apaMu. YcaJ\b6a - 6apCKHH AOM H Bce npHMblKaDiliHe K HeMY CTpoeHHH, CJlY>K6bl, yrO,ltbSl (OOSlpCKaH ycaJ(b6a, nOMeIUHQbH yca,llb6a). npOHC- xO>K)teHHe CJlOBa OT Toro >Ke KOpHR cao. EapHH KaK Obi npOllHO OCM (nOCeJlHJICH) B aHHOM MeCTe. TblH - 3a6op, qaCTOKOJl, BepOSlTHO, OT rJIarona InblKlllnb, 8mblKamb. B03MOiKHO H Pyroe rrpOHcxo»<,neHHe CJlOBa, OT mUH, 3a- tnUHbe - neperopO,D.Ka, CTeHa. ThlHOM OrOpa>KHBaJIHCb YC, a;llb6bI noceneHHSI, B npOTHBOnOJI01KHOCTb ropOllCKHM CTeHaM, PYOJleHHbIM H3 6peBeH. 1 HaKa3aHHe, KOTOPOMY nOJ1Beprana CaJJTbIqHXa (JJ.apbH C3JITblKOBa), HC npaBHJJO, a H CKJIEOtteH He. QHa 33MyttHJJ3 .no cMepTH 139 CBOHX KpenOCTHhJX J Cpe,lJ.H KOTOpblX 6bT'IH H .neTH. 3a 3TO ee JJHWHJlH )tOOpSlHCTB8 H noca)tHJJH 8 MOHa- CTblPCKYIO KeJIbJO 113 nenb. CaJIThJ'IHXa 6bJJIa H3Ka33Ha. BHAHMO. nOTOMY. 'ITO Y>K CJlHlllKOM lllHpOKYIO or",1aCKY npHIIHJ10 .neJJo. I B. 11. J1 e H H H. nonH. c06p. COq., T. 39, CTp. 76. 2* 35
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3aKpenornCHHe KpeCl'bHH, 6ecQHHCTBa 60Hp H ,nBOpSlH BbI3bIBaJIH B03- MymeHHe HapO,na, BCITLlXHBaJlH KpeCTbflHCI{He BOCCTaHHSI, KOTOpbJe IIHOfJla nepepaCTaJIH B HaCTOSlWJle KpecTbHHCKHe BOHHhI. nepBaSl TaK(;!H BOHHa B PyCCKOl\f rOCY3pCTBe OhIna B 1606-1607 rr. Bo rJIaBe KpeCTb- HHCKHX OTpSl.l10B BCTaJI MBaH l1caeBHQ EOJIOTHHKOB. BoccTaHHe 'EOJIOTHHKOBa npo,ltO.1l}KaJlOCh 60JIbllIe roa. He pa3 (,peCTb5JHe pa30HBaJIH I.(3pCKHX BoeBO.n. Ho B KOHne KOHUOB OTpH)tbI Eo.. J10THHICOBa-. 6b1J1H pa3rpoelIbi. a OH caM B3HT B nJIeH. IJ.apb H nOMetnHKH ()OH.1IHCb ,lta1Ke nJleHlIOrO KpeCTbSlHCKoro BO}K)J.SI. n03TOMY ero OTnpa- BHJlH D ,naJIeKMfI ceBepHbIH ropo,n, TaM BbIKO.TJOJlH fJla3a H TaHHO YTonHJIH. npOWJIO HeCKOJlbKO .lleCHTH.1IeTHM, H BCDbIXHYJIa HOBaSl, erne 60JIee (OHafl KpecTbHHcKaH BOMHa. BoccTaBlIlHx B03rJlaBHJI .llOHCKOH Ka3aK CrenaH THMo<t>eeBHlI Pa31IH. BoccTaHne BcnbIXHYJlO B HatlaJIe 1670 r. H npo,nOJI}KaJIOCb.nO KOHua 1671 r. BoccTaHue OXBaTHJIO pafloHbI lloHa, Yep H03eMHoro aeHTpa, I-IH.iKHero II Cpe.nHero nOBOJI}KbH. ' OCHOBHYIO CH..'1Y BOCCTaHHSI COCT3B..1HII1H KperrocTHbIe KpeCTb5lHe H Ka3al.{KaSi 6e,L(HOTa. npe.lI.BO.llHTeJ1b BOCCTaHHSI Pa3HH 6b1JI H3BecTeH cBoeH CMe.1l0CTblO, y,naJIblO, BoeHHblMH cnoc06HocTHMH. BhICOKHH pOCT, rpOMKHH fOJIOC, OOJIblliaSl <l>H31111ecKaSi CHJIa, MY>KeCTBO, YM Ii cnpaseA- JIHBOCTb npHBJIeKanH K HeMY JUO.lleH. Pa3HH Obl.1l BbI6paH Ka3aUKOH OeJt- HOTOH CBORM aT3MaHOI\'1 eu{e 3a TPH rO.l1a )to KpeCTbHHCKOH BOHHbI. Pa3HH- Ubi COBeplliHJIIi noxo.l1 B nepCHIO (l1paH) H BepHYJlHCb C ooraTOH .llOObl- 4eH. C.lIYX 00 Y.lI.aJIOl\f aTaMaHe, KOTOpblA 3aIIlHIII.aeT 6e,ltHHKOB, 6bICTpO l}aCnpOCTpaHHJICH no ropo,naM H CeJIaM. K Pa3HHY ULlIIi KpenOCTHbIe KpeCTbHHe, fopOD.CKaSl 6eD.HOTa, yrHeTeHHbIe HapObI nOBOJI>KbH. Cre- naH THlvt<Xf>eeBHq paCCbIJIaJI CBOH nOCJlaHHSI - rpaMOTbI - no pa3HblM MeCTaM. B HHX OR npH3b1BaJI HCTpeOMTb 60Hp H ,ltBOpHH, ,ZJ.aTb Hapo,ny cBo60.ny, lIT06b1 «BCHK BCSlKO1Y paBeH WJI». MHorlie ropo)ta C.l13BaJIHCb 0e3 60R, nOTOMY qro ropo,ncKaSl 6e.ll.HOTa OTKpbIBaJIa BopoTa pa3HHCKI1'1 oTpSlaM. TaK ObIJIa B3HTa ACTpaxaHb. fjejJ.HblH ropo,nCKOH JlIO,lt BCTpeqan Pa3HHa K8K CBoero H36aBHTen H H 3aHTHKa. EOHpe Ii nOMeI.UHKH'6bI.J1H cTpalliHo HanyraHbI BOCCTaHHeM. I Lapb AJleKCeH l\-\HxaHJlOBHq aIIpaBHJI npoTHB Pa3HHa 60JlbWOe ,ltao- pHHCKoe BOHCKO C KOHHHu.eH H apTHJIJIepHeH. B ynopHoM 6010 no,lt CWM- OllpCKOM (YJIbHHOBCKOM) OTpH,ltbl Pa3Hlla 6blJIH pa36HTbI, a caM CTenaH "rHMocpeeBMQ, TSI>KeJlO paHeHHblH, C HeOO.1lbWI1M OTPH;{OM YWeJI 3a .aOH. ()u Ha.neSl.nCH coopaTb TaM HOBbIe CHJlbI H npO.ll.OJI}KaTb BOBHY, 1-10 oora- Tille Ka3aKH HeHaBHe,,rIH CMeJ10rO aTaMaHa. OHH OOMaHOM CXB3TH.1IH l)a3"H3 H BbI,AaJlH uaplO. nOCJIe 3BepCKliX fibITOK Pa3HH ObIJI qeTBepTQ. Ban Ha JI06uO1 MeCTe B MocKBe. Ho Ka3Hb Pa3MH8 He HcnyraJIa Hapo,n. IIMH ero OC'FaJIOCb rp03HbIM Ii CTpallIHbl"t JlJIH yrHeTaTeJIeH, JII06HMbIM JlJ1 H Bcex yrHeTeuHbIX 11 o6e3,!J.O.1leHHblx. 06 yaJIOM Ka3allKOM aTaMaHe, UO)K,lte BOCCTaBllIHX KpecThS1l1, CKJla,nbIBaJIH neCHH H .JIereH,llbl. npOUIJIO 100 JleT nOCJIe BOCCTaHHSI KpecTbSlH no.D- npe,nBo,ZJ.uTeJlbCTBOM <:TenaHa Pa3HHa, H B POCCHH BCnblxHyna HOBaR KpecTbSlHcKaH BOHHa, raMaH 3Ha1JIiT'bHaH no cBoeMY pa3Maxy H CH.."Ie. Bo rJIaBe BOCCTaHHJI nfTaJI AOHCKOH Ka3aK EMeJIbHH I1BaHoBHQ nyraqca. nyraqeB Ha3BaJI 31.
ceOH u.apeM neTpoM I I I. L{en:o B TOM, liTO Y TeT\iHbIX, 3a6HTbIX, yrlleTeH- HWX nOMemHKaMH KpeCTbHH BeKaMH COXpaHHnaCb R Kpenna Bepa B «CnpaBe,lJ.JIHBOrO», «o6poro» u.apSl. Ha pOCCI-IiiCKOM npeCTOJIe B TO Bpe- MH 6blcH3 uapl1IJ.a EI{aTepHHa I I, npH KOTOPO", Kal{ yme rOBOpHJIOCb, nOJIO)l(eHHe !{penOCTHbIX CTano cOBepmeHHO HeBhIHOCHMhIM. 1\YJK EKa- TepHHbI I I DeTp I I I npaBHn OqeHb HeOJIrO (MeHbUle rOJ{a), 6br.1I cBepr- nYT c npeCTOJIa cBoeM )KeHOH H BCI{Ope y6HT. CaM no ce6e 11cTp I I I ObI.,l "lHqllOCTblO )KaJ1KOii H HlI1.ITO/I{HOil, HO HapoJ( 0 HeM HHqerO lIe 3HM, l{pO1e Toro 1JTO OH CBeprnYT H y6HT )KeHI.JJ.HHO:H, npH KOTOpOH )KHTb CTa,7!O eme xY)J{e. B HapO){e pacnpOCTpaHHnC5I CJlYX, tJTO CBeprHYTbIH aapb XOTeJI OCB06oj{HTb KpeCTbHH H 3a 9TO JtBOpJIHe, crOBopHBlinicb C EKaTepHHOM, nblTanHCb ero y6HTb. Ho OR He Yl\iep, a CYlvleJl 6e}I{3Tb Ii r,lle-To CI<pblBaeTCH. CKOpO 011 «06'bHBHTCID) H nOHHMeT BeCb HapO)t npOTliB j{BOpHH. PacnpOCTpaHeHlilO 3THX CJIYXOB CI10C06CTBOBaHH TaHHCT- BeHHbIe 06CTOTeJ]bCTBa ClvlepTH neTpa I I I, Bce YCHJ1HBaIOIII.aHCH B Ha- poJte }Ka*.lI.a OCBOOO)Kj{eHHH II pacTyaH HeHaBHCTb K yrHeTaTeJISllvl- ABOp5lHaM. I1MH Derpa I I I CT3JIO TaKHM 06pa30M KaK 6bI 3Ha{eHeM BOCCT3HHH, a «nOHBJIeHHe 1JYAecHo cnaCllIerOCH uap5I» - CnrH3JIOM K HeMY. nyralleB C3M 6bIJI H3 Hapoj{a, n06hIBaJl BO MHorHX MeCTax, BHeJI, KaK CTpa,nalOT JIIO){H, caM HcnblTan rOHeIlH5I M npecneoBaHHH. OH no- HHMaJI, I.ITO HMH neTpa I I I npUBnelleT I{ HeMY I\-faCCbl JIlo)l.eH. Tal{ H npo- H30111JIO. KOHetJno, Hapo nOllleJI 3a nyraHeBbl1\f He CTOJIbKO rrOTOlfY, QTO OH Ha3BaJl ceOff Hf\ieHeM nOKOHHoro l.(apH, CKOJIbKO nOTOMY, 'ITO OH npH3blBaJI K YHHqTOJKeHHlO }).BOpHH, OTMeH5JJI Bce JJOBMHHOCTM, OO'bHB- JI}lll KpecTbHII CBo66.lU-IbIMM. nyraqeB paCCbIJlan CBOH YKa3bT, T8I{ Ha- 3bIBaeJbIe f\.laHHcpeCTbI, B l{OTOPbIX, 06pa3SlCb )( caMbIM: yrHeTeHHbIM H 3 a,lI,aBJI eH HbIfi-1 HenOMepHOH HY)K)I.OH JIlO){SJM, 06elll.a.a 11M «BOJIbIIOCTb Ii CBo60,llY», «Bnaj{eHlIe 3eMnflMH, JIeCHbIMH II ceHOKOCHbIMH yrO)J..bHMH, pbI6HblfU JIOBJIHMH 11 COJIHlIblf\.IH 03epaMH oe3 nOKynKH Ii 6e3 06pOKY», oCBo6om)I.aJI HapO)I. OT «no,naTeii H OTHrorneUHH», «nOBeJIeBaJI 3JIo,neen- ,nBOpHH ..TIOBHTb, Ka3HHTb Ii BernaTb», qTo6bJ nOCJIe 9Toro 6bIJla «(TI1IllMlIa H cnoKoiinaH }Kli3I1b». DJIaMSI BOCCTalIli5I OXBaTHno orpOMHLIH palioll YpaJIa H OOBOJI}I{b51. I<pecTbSlHCKaSl BOMHa npO)l.OJI}!{aJIaCb OKOJIO JI.BYX JleT (1773-1775). CocTaB BOHcKa nyralleBa nOCTOHHHO nOIlOJIHSlJICH l{penOCTHIflI I<pe- CTbHal\11i, ypaJ1bCKHMI1 (51HUI{HMH) Ka3aKaMH, MaccaMH Tpy,noBoro Ha- ceneHHH yrHereuHbIx lI,apH3l'vl0M Hapo.l{oB YpaLl1a H nOnOJlLKb5I (6aIlIKlI- patfJI, TaTapan1, Ka.nfbIKaMM, Ka3axaMH, QYBaulaMH', 1'vlap(.u1II.aMH). EOJIbllIYIO nonb3Y nyralleBY OKa3bIBaJIH KpenocTHbIe pa601lue ypaTIh" . CKHX 33BO,n9B: OHIi cHa6*aJIH era nYlllKaMH, PY>KbHl\U1, H)l.paIH. Hecl\'loTpH Ha orpoMHblH pa3Max, BOCCTaHue 3TO 6bIJIO no):{aBJIellO TaK :>Ke, KaK If Bce ,llpyrHe KpecTbSJHcKHe BOCCTaHM5I. rJlaBHble CMJIbl nyralleBa 6bIJIIi pa36HTbI apMHeii EKaTepH{bI I I. nyratleB C Hc6oJIblllHl\{ OTpHAOf\i yrneJI Ha lOr Ii nepenpaBHJIC5I llepe3 BOcJ'1ry. OH paCC1JHTbIBaJl rrO,QHSlTb HOBbIe CHJlbT, HO 60raThle Ka3aKH BbJ)taJIH KpeCTbHHCKoro BomJ{H. B )K71e3Hoj% K"TIeTKe npHBe3.TIH OyratJeBa B MOCKBY H Ka3HHJlH Ha BOJIOT- 38
lIoii IlJIOll1.a,lUf B 5IHBape 1775 r. ITpaBHTeJlbCTBO co 3BepcKoH }KCCTOKOCTblO p:lclipaBH.nocb C BOCCT3HHeM. BHH3 no BOJIr'e nJIbIJIH nJIOTbI, Ha KOTOpbIX (,I'OSIJlH BHCeJlHIJ.bI C Ka3HeHHblMH KpeCTbHHal\'IH. Tal{ SaKOHtIHJIaCb ca- MUH MOLu,HaH KpecTbHHcKaH BOHHa B POCCHH. HMH nyratleBa, KaK If HMH P13I1Ha, Bcer.ll.3 nOf\fHHJI Hapo. 3TH HMeHa BAOXHOBJIHJlH OOpU.OB 33 t'uo(jO){Y. KOMMeHTap"H PaTh - TaR B ,lJ,peBHeH PYCH na3btBa.TIOCb BOHCKO. PamHUK, (pam- ""Ili Lle/lOOeK) - BOHH. OT rJI3rOJIa parn08amb - OHTbCH, Cpa}K3TbCH :,:t tITO-HI16YJlb, KorO-HH6Yb UJiH npOTHB Koro-HH6y,nb. ,apyroe 3Ha- 11'lIl1e CJIOBa pamb - BOHHa, oHTBa, Cpa>Kelll1e. «,Qpyr n03HaeTCSI Ha paTH Jla npH 6e,ne» (nOCJIOBHU.3). «Tbl CTOHWb;iIoHHK H He paTyellib C Ani- MO.1IeTHOI0 TYQeH-6ypelO» (A. K 0 JI b U 0 B). Toro me npOHCXOJKJ{eHHH \/10110 pamo6opel{ - BOHH, yq,aCTHHK Cpa>KeHHSI. BOeBo,Aa - B ,npeBHeH PYCH BOeHatlaJIbHHK, nOJIKOBO,lI.elI.. npouc- XO>I\AeflHe cnOBa OqeBH,lI.HO: eoeeoaa - TOT, I{TO BO,nHT (B nOXO,lI.) BoeB (IJOHHOB). Boeao,o.8MH 1183blsanH BoeHaqaJlbHHKOB B PYCCKOlvl rocy- JlnpCTBe AO Haqana XVIII B. (pe<J>0PM neTpa I). XOJlon.. (xOJlOnCKHe BoAcKa). XOJIOnaMH B)I.peBHeH PYCH Ha3bIBaJIH II()JHeBonbHbIX CJlyr. ,ao OKOHtIaTeJ1bHOrO 3aKpenom.eHHH KpeCTbHH B I ()49 I". pa3"JIHtl8JlHCb OT,lI.eJlbHble BHAbI XOJIOnCTBa (OT nOJIHOrO pa6CTBa JlO BpeMeHijorO ycnY)KeHHSI 3a nHInY H OAe>K,ny). BbIJIO TaK>n:e OT-!IHlIHe u nOJIO>KeIlHH KpeCTbHH H xononOB. B cepe,lI.HHe XVIII B. 3TO pa3JIHQHe flJ3KTHtiecKH HCtlea.n0 t 8 K HatJaJIY XVIII B. OHO HCtle3J10 H IOpHHqeCKH. XononlMH.. CT8Jla Ha3b1aTb scex nO,llHeBOJIbHblX KpeI!0cTHbIX JIIOefr. )BOpJlHe npHABanH 9TOMY CJlOBY npespHTenbHblH oTeHoK. Ha3BaTb 'ICJlOBeK8 XOJIOnOM SH8t1HJlO YHHSHTb, OCKOpOHTb ero. 31-0 OTpa3HJIOCb, IIIHlpHMep, B noroBopKe: «CTapblA XOJIon - cTaphIH nec: co ,ZtBopa ,l{O'IOH, JIH()O no,Zt JIaBKY»t a TalOKe B onpe,neJIeHHOM CMbICJle rJlaro.na XOAon- flfl008amb - paOOJIenCTBOBaTb, yrO>K,naTb, nO,ZtJlHtIaTb. B AaHHOM TeKCTe (<<Hawa POAHHa», cTp.64) XOAoncKue 80t1CKa- BOCCTaBWHe, 836YHToBaBwHecH XOJlOIIbl, JlIO,nH, rOTOBble cpaKaTbcH Ii IIOI'HOHYTb sa cBo60y. KasaKH (KasaKHe BoAcKa). CJIOBO TlOpKcKoro npOHCXO}K)(eHI1H. I )YI{BaJlbHO 03HaQaeT - BOJlbHbIH QeJIOBeK, Y,lI.aJIen. I(peCTbSIUe Oe}KaJlH err l<penocTHoH. HeBOJIH "Ha OI{paHHbI PycKoro rocy,ZtapCTBa. OcooeHHo Mlloro HX nOCeJIHJIOCb Ha lI.OHY. OHM cTanH Ha3bIBaTb ce6H Ka3aKaMH, T. e. CDOOO)(HbIMH, He KpenOCTHbIMH. 113 ,nOHCKHX Ka3al<OB 6blJIO 06pa- 'ODaHO BOHCKO, "KOTOPbIM KOMaH,1J.OBaJIH Bbl6paHI1ble aTaM3Hbl. I-Ia YK.. ptuiHe 6bIJIH Ka3aKH sanOpO>KCKHe. nOTOM nOSlBHJIHCb Ka3aI{H YP3JIb- l'I{l1 (HI1UKHe, no CTapOMY na3BaHHIO p. Yp3JI), TepCKHe (Ha p. TepeK), l<yuaHcKHe, YCCypHHCKHe, aMypCKHe H ,Ztp. Be,nHoe Ka3atleCTBO Bcer,na COCTaBJI5IJIO H,npO apMHH BOCCTaBlllHX I(PCCTbHH, Aa H caMH rrpe,nBO,lJ.HTeJIH BOCCTaHHH 6bIJIH, KaK npaBHJIO, 113 HlJ33J<on (Pa3HH, BYJIaBHH, I1yraQeB). 3TO nOHSlTHO, nOTOty qTO Ka- 39
saKH H{e.7JH OpraHU3au.JUO, BOCHHblH OnbJT, 0pYJK-He. Y Kp.enOCTHbIX K.pCTbS1H K Ha1.JaJIY BOCCTaHH5J HHtJerO 3TOfO He 6hJJIO. ,. BoMHa c npyccueH. B X VI I I B. He 6b1J10 €,llHlloro rcp.Maf:ICKOrO ro- cy,napCTBa. BCH repMaHHfI 6bIJIa paJl.po6J1ena Ha MllomeCTBO MeJlKHX H KpynHblx rocyp-apcTB, caMblMH BJIHHTeJ1bHbJMH H MorYU\eCTBeHHbIMH 113 KOTOpbIX 6bIJIJ1 npYCCH5I Ii ABCTpH5I. np.YCCH5I - O,llHO H3 Catblx CHJlbllbJX H arpeCCHBHbIX rocy,napCTD repMaHHH H. BceH EBpOnbI. Oco6eHHO arpeCCHBHOH 6bIJla npYCCM5I npH Kopo.ne <I>pH.llpHXe I I , KOTOpblll HCnOJIb30Ba.n Bce cpe]lCTBa ,nJl 51 3aXBaTa CoceJlHHX cTpaH H nOJ(OpeHHSI ,llpyrHx HapO,lJ.OB. POCCHH BOeBaLila C DpyccHei1 BO BpeM5I CeHIJleTlIeH BoiiBbl (] 756-1763) H HarOJIOny pa3rpOMHJ13 npyccKYIO apMHIO, CqWTaBlllYlOcSI Heno- 6e,llHtOM. B 1760 r. pyccKHe BOHC1<a 3aH5ITIH BepJ1HH. nyratleB yqaCT- BOBaJ1 B CeMH.neTHeH Boih-Ie COBceM eme MOJlO)\bHvl. (rO,ll pO/K,lleHHH_ E. H. llyraqeBa TOqHO Ha YCTaIJOBJlell, npe.llnOJIO)KMTe.nblIO 1142. 3HaIlHT, BO BpeM5I CeMHJ1eTHeH BOHHbl eMY 6blJ10 17-18 JleT.) reHepaJlbCKaH JleHTa '1epe3 nJle'lo. B POCCHH co BpefcH neTpa I 6bIJ1H Yllpe)f{,lleHbl 0pJl.ena )J.J1H ocouo OTJIlItIHBIlIHXCSI. (nepobIH B nCTO- pHH POCCHH op,lI.eH AHJlpeH nepB03BaHlloro 6blJ1 yqpeiK,lJ,elI B 1698 r., nOCJIe B03BpaeHH5I llcTpa I H3 3arpaHHQHOH noe3,llI{H.) Harpa»<,neHHhle op,neHoM, KpoMe caMoro Op,lleHCKOro 3ual<a (l<peCT, 3Be3,lla), HOCH.TJH IllH- POKYIO IDeJIKOBYJO JIeHTY qepe3 nJle1JO (OObllIHO rOJIyGoro IJ.neTa). POC- CHHCKHe BMnepaTopbI, pa3YMeeTCH, HMeJlH BbICllJHe 0pJleHa. nyratJeB HOCHJI opJJ.eHCKYIO JleHTY qepe3 nJleqo, tJT06bI npJI.IJepKHYTb CBO «HMne- paTopCKoe» nOJIOJKeHHe. H3 rEPOMLIECKOrO BOEHHOrO npownoro PYCCHOrO HAPOAA B. fpall)J.ona. «CnaBa PYCCKoro COJJ}J.aTa», C. A.neKceeB. «Paccla3bl 0 BHI{O"1 nOJ]I{OBOJ1.l1.e A. B. CYBopOBe H IJYJJ.0-60raTblpSiX - pOCCI-JHCKHX COJJaTax», M. Bpa- fHH. «Pa3rpOM H8 pflte Bepe3Hlle» - ({Hawa POJlHua» , CTp. 259, 263; c. AneKceeB. «nO-CYBOPOBCKH», «113MSHJJ», «H.neT KYTY30B 6HTb (j>paHu.Y30B», M. JIepMoHToB. d30pO.nHHO», +:Ope." H81lJ KYTY30B» - «POJlH8H pelJb», CTp. 295, 296, 297, 299, 300. A. B. CYBOpoa " PYCCHGe BoeHHoe HCKYCCTBO KOHL\8 XVIII B. " AneKCaHJl.p BaCUJIbeBHll \. CYBOPOD (1730-1800) npOR<Mll .nOJ1 rylO 66eBYlO :>KH3Hb. OH H3tJaJI BoeHHYIO CJlY}I<6y ] 7-JIeTHMM JO.JiOllJeH, npo. CTbIl\i CO.TI,llaTOM, a 3aKOHtlHJI ee 70-JleTHHM CTapHKOM: ,B 3B8HH.H reHepa- JlHCcHMyca - BblcweM BOHHCKOM 3BaHHH. CYBOPOB 6blJl O,nHHM,H3 Ca1\fbTX BeJlHKHX nOJIKOBo,nu.eB Bcex BpeMeH H napoJ:loB. Ou BblCOKO no,nHHJI CJIa- BY pYCCKoro OPYJKHSI, ApMHH, KOropbJMJI KOMaHAbB CYBOPOB, 6blJlH ueno6e.llHMbIMH. CYBOPOB He nOTepneJI HH O,lJ.HOro nOpa)l{eHHSI, BCer)l..a BbJHrpbIBa,,"I 611TBbI, B KOTOpblX Y'IaCTBOBaJI. 40
nO)l{aJlyif, CaMblMH OTJlHIIHTeJlbHbIMH qepraMH X3paKTepa BMOKO- fO nOJlKOBO;J.na 6bIJlH HCKnlOqHTeJlbllaSl neJIeYCrpeMJIeHHOCTb H CHna BWlH. CBOIO BOJIIOCYBOPOB Haqan BOCnHThIB8Tb C,l\eTCTB3, S8KaJIHH ceo, npeoAOJIeBaH $H3HtJecKYIO CJla60cTb M 60JleaHeHHTb. BcIO )J{H3Hb 11(J rJly6oKoH CTapOCTH, B J100blX YCJlOBHSlX CYBOPOB CTpeMHJlCSI C06JIIO,n8Tb YCTaHOBJIeHHblH 11M Caf\tH1 pe)KHM. OH cna.1J Ha nOKpbITOH npOCTbIHeH oxanKe ceHa, BCTaBaJI B 4 qaca YTp8, nR.."1 'laH, OKMO nonYtJaca ynpa)l{- H.HJlCH B oere Ii rHMHaCTHKe, a 3aTeM npHHHMaJlCSI 3a eJla. 06eJt3J1 AJIeKCaHp BacHJIbeBHq OObl1JHO B 8-9 1l3COB YTpa. CYBOPOB 6b1J1 otJeHb YMepeH B nl-IIne, He 3JIoynoTpe6LTIRJI HanHTKa"H, lIe KypHJI. OH rOBOpHJI, liTO H3HeJKeHHOCTb. pa3'heaeT BO.7HO 11 3opOBbe, nO)l.OOHO p}l{aBllHHe. Bc.,lI1KHM nOJlKOBO)l.en 3H&TI ueHY BpeMeHH. npOBe,llSl BCIO >KH3Hb B noxo,nax, OH OtfeHb MHoroe ycneJI. OH 3Ha..'I 8 .SI3bIKOB, HCTOpIUO, MaTe- MaTHKY, He rOBOpSl' y}Ke .0 BoeHHOM )l.eJIe. ,QJISI CYBopOBa fJI3BHblM B BOeHHOI'v1 ,ne.,'Ie C)blJl8 >RHOaSi CliJIa apMHH Ii YMeHHe elO ynpaBJI.SITb. B Te BpeMeHa, KorAa J\fHOfHe BOeHaqa.,'IbHHKH CIIHTaJIH, 'ITO fJIBHoe - 3TO OCa)l.8 KpenOCTeH, 38HflTHe reppHTopHH npOTHBlIHKa, CynopoB YTBep)K)la,,'1, tJTO nooe)).a - 3TO npeJK,ne Bcero pa3rpO:V1 HenpHHTeJ1bCKOH apMKH. OTCIO)l.a TaKoe BHHMaTeJIbHOe OT- HOllieHne no..TJKOBO)IJla K COJl,naTaM, 3aOOTa 0 BOHHax, 3alll.HTHHKax Po- ):lHHbI. B KpenOCTHlilleCKOH POCCHH, r,ne B aptHH uapHJIa naJI01JHaH HC- II.HnJlHHa, rAe COJ1,naTa CIIHTaJlH J1HIUb «MeXaHH3J\IOM, YCTaaOM npeJlYCMOT- peHHbIM» (CJIOBa HMnepaTopa naB..TJa I), CYBOPOB u.eHHJI Ii YBa>K.a.TJ pyc- CKoro BOHHa. OH Ha3bIBaJI CBOliX COLTI.21aT qYAo-6oraTb)pJlIH, OpJ1aMH, CnaCHTeJ1S1MIf H 33III.HTHHKaMH OTellecTB8. COJI;J.8Tbl BepHJIH CBoeMY nOJ1- u KOBony, nOTOMY liTO OR caM BIiAeJJ B HIIX J1IO)\eH, CYMeJI BHYUIHTb 11M IIYBCTBO AOCTOHHCTBa, ropOCTH 38 nopyqeHHoe ):leno, YBepCHHOCTb B no6eJte. CaM nOJlKOBO,lten 6bIJI B BblcweA CTeneHH ..aa)\eJIeH 3THM tIYB- CTBOM, He CreCHHJICH If He 60SlJICSI rOBopHTb npaB,ny B rJl833 MorYl1I.ecT- BeHHbIM BeJ1bMO)KaM, a HHOr){a Ii caMHf rocy,n.apSl.M. 3a 3TO ero He JIIO- 6HJlH EKarepHHa II H naBeJI I. CYBOPOB Tpe60BaJI, IIT06b1 ero BOHHbI nOCTO.SIHHO yqHJlHCb, COBep- llJeHCTBOBaJIH BoeHHoe MacrepcTBo. «BOlO" He tIlICJlOM, a YMeHbeM)}, «KajKJ1bIH BOHH ,lJ.OJl}KeH nOHHMaTb CBOH M811eBp», 9TH Ii MHorHe ,npyrHe np8BHJl8 BoeHHoro HCKYCCTBa CYBOPOB 38nHCaJi B YCT8se, KOropblH ,Ha- '3BaJI «HaYKa n06e>K,l1aTb». 113JIIOMeHHbIH M8HeBp CYSOpOBa SaKJlIOtI8JICSl B 6bICTpOTe nepe)].BH)KeHHSI, BHe3anHOM y,nape. TaKHM,oopa30M eMY He O)l.H3>KJ{bI yttaB8J10Cb pa3fpOMMTb H YHHtITO}KHTb 60JIee LMHOrOqHCJleH- HorO.H CHJIbHOrO Bpar8 (HanpHMep, B 3HaMeHHTOH 6HTBe npH p. PblMHHK, sa KOTOpylO CYBOPOB nOJ1YQRJI THTYJl rpacp8 PbIMHHKCKOro). . rJIaBHble no6e.zJpy CYBOPOB3 CB.SI3aHbI C TaK Ha3b1BaeMOH STOpOH PYC- fKo-rypeUKoH BOHHOA (1787-1791) Ii J1ereHAapHbIM AJlbnHHCKHM nOX0)10M (1799). nepB8S1_ PYCCKG-TypenKaSI BOHHa (1768-1774) KOH- tlHJlaCb BblrO,ZJ.HbJM ;J.nH POCCHH MHpOM, HO 3Ha'lHreJlbHaSi 1I3CTb no- 6epebB lJepHoro MOpg OCTaBaJl8Cb B pYKax TypnHH. POCCHH He06- .nHMO OblJIO OTBoeBaTb KpbIM II Bee ceBepRoe npHqepHOMopbe. 'BoHHa B0300HOBHJlacb. PyccKaH 8PiHg no.n KOM3HAOBaHHeM CysopoBa Haro- 41
"TIOBY pa3rpOMHiIa TypenKHe BOHCKa npH <I>oKlIIaHaX H PbIMHHKe (1789), IllTypMOf\1 OBJla):{eJI3 CHJIbHeHIIleH TYPC[(KOH KpenOCTblO I13MaHJI (17!JO). B 9TO me BpeMH TOJIbKO ttTO c03,llaHHbIH PYCCKHH BoelIHblH 1JepHOMOp- CKHH <pJIOT no)! KOMaH)lOBaHHeM aMHpaJIa cI>. <1>. YIllaKona OAep}l{aJI pH):{ no6e,n naA Typell.KII1 qmOTOM. TYPll.HH npH3HaJIa ce6H no6em)1.eH- HOM Ii B 1791 r. BbIHY}I{):{eHa 6blJIa npocHTb MHpa. no 9TOMY {HPHOrvlY oroBopy Bce ceBepHoe nOOepe}Kbe I.JepHoro f\fOpSI Il.O YCTbH p. LLHecTp, a TaK}Ke KpbII\.f BOlIlJIH B COCTaB POCCHH. BeJlHKHH nOJlKOBo):{eI.{ HMeJI MHoro 3BaHI1i%, THTYJlOB, narpa,n, op- }J.eHOB - PYCCKHX 11 HHOCTpaHHbIX, HO OB CtJHTaJI, ttTO ero HMSI CTOHT 60JIbllle Dcex THTYLTIOB H 3BaHHH. Ha ero 1'.fOrHJIe (B AJIeKCaH)lpO- HeB- CKOH ..TIaBpe B JIeHHHrpa):{e) JIeJKHT npocTaH KaleHHaR nJIHTa. Ha HeM HatIepTaHbI TOJIbKO TPH CJIOBa: «3,neCb JlemHT CYBOpOB». TaK nO}KeJIaJI nepe.n cM:epTblo Caf\f no.,"1 KOBoeu. B ro,nbI BeJIHKOH OTeqeCTBeHHoH BOHHbl COBeTcKoe npaBHTe.,1bCTBO yqpe):{HJIO 0pll.eH CYBopOBa. 11M HarpaiK):{alOTCH reHepaJIbl COBeTcKoM ApMHH 3a BbICOKoe BoeHHoe HCKYCCTBO - Ii JIHtJ:Hoe MYJKeCTBO. OTe'leCTB8HH8S1 BOHH8 1Stl r. M. H. KYTY30B OreqecTBeHHag BOHHa 1812 r. ObIJia nocJIe.nHeii 3aBOeBaTeJIbHOH BofI.. liaR Hano..TIeOHa. OHa >Ke CTaJIa HaqaLJIOM KOHua erO.BJla)lbltJ:eCTBa. B 1799 r. TpH.n[(aTHJIeTHHH reHepaJI <1>paHU.Y3CKOH pecny6J1HKH HanOJIeOH BOBanapT cOBepIIlH.n rocy,napcTDeHHbIfl nepenopoT 11 3 a.. XBaTRJI e):{lIHOJIMtJ:HYIO 'BJIaCTb. LJepea neCKOJIbI<O JleT OH 05nHBHJI ceOH HMneparopOM cI>paHUHH HanOJIeOHOM I. K 1812 r. HanOJleOI-IOBCKan <l>paHIUi51 no.ntJ:I1HHJIa ceoe nOqTH BCIO 3anaJ\HYlO H eHTpaJlbHYIO EBpony. TOJIbKO AHfJIHH He no.nqHHHJIaCb eii, Aa B HcnaHHli pa3rOpaJIOCb rr..rIaMH napTH3aHCKOH BOHHbI. [pa- HIiQbl HanOJIeOHOBCKHX BJIa,l(eHI1H nO)lXO):{H,,1H K POCCIiH. POCCH.H ObI- JIa caMbHvl Cpbe3llbIM npenHTCTBReM na nYTH OCYIl(eCTBJIeIIHH Hano- J1eOHOBCKoro nJIaHa MIipOBoro rocrrOJ{CTBa. BecHoH 1811 r. (3a rOA }\O OTeqeCTBeHHoH BOHHbI) HarrOJleOH rOBOpHJI: «4epe3 TPH rO)la 51 6Y)lY rOCrrO,lJ.HHOM cero CBeTa. OCTaeTcH POCCliSI, HO H pa3,lJ.aBJlfo ee». POBHO Qepe3 TPH rO,L\a «Be..TIHKaH HMnepHH» I-IanoneoHa 6bIJIa cOKpYIIIeHa H pa3BeHHa B npax. PYCCKHH COJl):{aT Ii PYCCKHH KpecTbHHHH HaHeCJlH CMepTeJlbHYIO p aHY rvforyrnecTBeHHoMY saBOeB-aTeJIIO, I\leQTaBIllervty 0 BRaCTH HaA BceM MHpOM. B HOqb Ha 12 (24) IUOHH 1812 r. BOHCKa HanoJIeona BTOprJII1Cb B POCCHIO. aTO 6bIJIa HeBH,l(aHHaH no TeM BpeMeHaM CH.na. «BeJIHI<aH ap- MAR» (KaK H33bIBa.,1J ee caM HanoneOH) HaCqMTblBaJla OKOJIO 600 TbIC. qe.nOBeK, npHqeM JIHllIb OKOJIO nOJlOBHHbI ee COCTaBJlHJIH cppaUU.Y3bI, OCraJIbHble CO.TI,lJ.aTbl Bep60BaJIHcb H3 nOKopei-IHbIX eBponeHCKHX cTpaH. He 3PH BTOp}i{eIIHe HanOJIeOHa cOBpeleHHHKH Ha3bIBaJIH «HallIeCTBHeM .lI.BYH3,necHTIi 513bIKOB» (T. e. BeHa,nuaTH HapOll.OB). BeJIH 9TY apMHIO npOCJIaBlleHHbIe reHepaJIbI Ii MaplllaJIbl. 42
B HatJaJIe BOMHbI PYCCKSH apMH5I HaClIHTbIBaJIa 240 ThIC. tieJIOBeK, OIJIJla pa3J1MeHa HS TPH qaCTH H paCcpe)I-OTOlIeHa Ha cppoHTe B 600 KAI. I-IanoJIeoH cTpeMMJicSI pa3rpoMHTb PyccKHe apMHH nOO)l.HHOqKe. Ho 9TO eMY He Y)J.aJIOCb. cI>paHII.Y3CKHe BOHCKa npOBHraJIHCb B rJIy6b CTpaHbI, PYCCKHe OTXO.l\HJIH C 60SlMH. B aBrycTe 1812 r. .nBe PyccKHe apr\'1HH co.. (')UIHHJIHCb y CMOJIeHCKa, r)I-e npOH301I1JlS O}KeCTOlleHHa5I 6HTBa. Hano,,1e- 011 MeqTaJI 0 reHepaJIbHOM Cpa)KeHHH, B KOTOpOM Oll paCCqHTbIBaJI pa3- rpOMHTb PYCCKYlO apMHIO. Ho PYCCKue, CHJIbI KOTOpbIX 6bIJIM 3Ha I IHTeJlb- 110 t\feHbIlIe, lie npHHHJlH reHepa..TJbHOH 6HTBbI H oTcTynUJIH J1.aJIbllIe na HOCTOK. C caMoro Haqana BOHHa 1812 r. CTaJIa BOHHOH OTelIeCTBeIIHoH, Ha. PO)HOH. BCH POCCHH nO)I-HHJIaCb npoTHB 3aBOeBaTeJIeH. iloCJIe coe)I-HHe.. IIH5I PYCCKHX apMMH Y CfOJIeHCKa rJlaBHOKOlaHJI.YIOllI.H1 6b!JI Ha3Haqell J\\nxaHJ1 I1nJIapHOHOBMtI KYTY30B (1745-1813). KYTY30Ba XOpOlIIO 3HanH M JI100MJlH B apT\1HH. 011 6blJI Bepllblrvf Ylle.. IIHKO1 CYBopoBa, Y1JaCTBOBaJI B lllTypMe H3MaHJIa. CYBOPOD 01leHb BbI- COI<O ou.eHH.TJ ,neHcTBHH KYTY30Ba B .9TOM Cpa}KeHHH: «OH KOMaH)l.OB3.11 MOH1 JIeBbIM cjmaHrOl'vf, HO ObIJI Moeu npsBoH PYKOH». B 1805 1". KYTY30B I<OMaHJI.OBaJI PYCCKOH apMHeH BO BpeMSI BOHHbI C cI>paHUHei1.. Hoe CJIY" '-JarlfIO B iOMeHT rpo3HoH onaCHOCTH, HaBHclIIeM Ha PoccMeH, Bbl6up 113J1 Ha KYTY30Ba. KYTY30B npeKpacHo nOHHMaJI, qTO ,naTb reHepaJIb- Hoe cpIDKeHHe HeOOXOJJJIMO. HanOJIeOH ObICTpO npHOJ1H:>I{aJICH K MocKBe. PYCCKHH rJIaBHOKOMaH,nYIOll(HH BbI6paJI JIH reHepaJlbHOH 6HTBbl 06111HP- noe BOpO,ltHHCKoe nOJIe, nOJIyqHBlllee CBoe na3BaHHe or ,AepeBHH Bo.. pOAHHO. KYTyaoB paCnOJIO:>KHJI CBOM BOHCI<a TaK, lITO OllM 3aropOAHJ1H nenpHJlTeJllO nYTb K MOCJ(Be. ct»paHUYSCKHe BoAcKa pacnOJIaraJIHCb npOTHB PYCCKHX. nJIalI Ha- IJOJIeOH8 SaKJIIOqanCB B TOM, IJTOt)bl CHJIbHblM y.napotvl pa3rpOMHTb JIeBbYH (l>JIaHr PYCCKMX, npopnaTb <l>POHT Ii BbIHTH B TblJI PYCCKOH apJtvfHII, a 3aTeM C Tblna Y,l{apHTb no UeHTPY Ii YUHqTO}KHTb BCIO PYCCKY(O apMHIO. DOpO)I.HHCKa5I OHTBa HaqaJIaCb Ha paccBeTe 26 sBrycTa (7 ceHTSI6p5I) II npooJ1}KaJ1aCb AO Beqepa. HeC!{OJIbl{O pa3 no,n;pH)I- cppaHUY3bI O:>KeCTO" 'ICUHO aTaKOBaJIH JIeBblJi cpJISHf t HO TaK M He MOrJIH npOpI3aTb ero. Tor,na l-IarroJIeOH npHKS3a.n nepeHeCTH rJIaBHblH Y)I-ap Ha UeHTp PYCCKHX no- HII.I.Hi.ft HO H 9TO 0 He npHBe"TIO K ycnexy. PYCCKHe cpa}K-aJIHCb C OTtISHH- 110H xpaopOCTbIO, a)Ke paHeHble He nOKH)J.aJIH nOJISI 0051. Ooe CTOpOHbl lIeCJIH OrpO!\IHble nOTepH. nOCTeneHIIO Cl\fOJIKJIM 0pYHH. BHTBa KOnqHJ1aCb. OrpoIHoe Eo.. pOJ1.H HCI{Oe nOJle OblJIO 3aBaJIeHO YOHTbIMH co.naTaMH, HCKoBepKaHHbIl\.JI1 II pa36HTbIi\H Opy,nHSIl\fH. PyccKaH pMHH nOTpHna OKOJIO 45 TbIC. 11C'J10BeK, $paHY3bI - OKOJIO 60 TbIC. 47 cppaHI.I.Y3cKHX reHegaJIOB Bbl- OhlJIII H3 CTpOH. nO,l{ BOpOHHOM «CPpaHUY3cl<aH aptHfI pS36H1acb 0 PYCCKYIO», - tvleTKO CKa3aJJ OHH H3 repoeB OTeqeCTBeHHoH BOHHhl . IHI2 r. reHepaJI A. n. EpMOJIOB. Caf HanOJIeOH BnOCJIe,l{CTBHH rOBOpHTJ, 'ITO 50pOHHCKoe Cpa/l{eHHe ObIJlO Ca1\fbIr-.-1 Y}J(aCHbItvI 113 Bcex ero cpa- )J{CIIHI1. 43
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>KHe (B 9TOM 3HaqeHHII oynaT J{aeTCSI B CTHXOTBOpeHHH J1epMOElTOBa). CnOBO nepCH,ltCKOrO npOHCXO.iK.1I-eHHH. Bawe CHHTeJlbCTBO - OcpHUHa..'IbHOe nOqTHTeJlbHOe oOpameHHe K rpa<l>Y. (Baule 8eJ1Uf.leCm80 - OOpa1ll.eHHe - K u.aplO (KOpOIl'IIO). 8au1.e OlC()t{£Cm80- K Be.lIHKHt KHH3bHf\{ (p0J1CTBeHHHI(a1 U.apH), BaUla csem- /lOCmb - K KHH3bH1 Ii rcpuora1 Ii T. ,n.) CYBOPOB liMeJI THTYJI rpacpa PbIMHHKCI{OrO (3a_ no6e.ay npH PblfijHKe) H KHSI3H I1TaJIHHcKoro (3a A.lIbnHHCKHH noxo.n). KyrY30B TOiKe I1leJI THTYJI KHH3H CMOJIeHCKOrO (3a 130pOJ{HHCKYIO OUTBY). ,n06pblH COJ1,AaT - B ClbICII'Ie «XOPOlIIIfU» (Xpa6pblH, {Y}KeCTBeHHbIH, .lIOBKHH H np.). B ,CrapHHY B PYCCKOM H3blKe C.l0BO a06pblU HMe.,10 rJ1aB- ([bIM 06pa30M 3TO 3HaqeHUe (UanpH1\lep,. a06pblU MOAOae B rrpOH3I!e.ne.. HHHX PYCCKOrO napO,AHOrO TBOpqeCTBa - nOCTOHHHLIH 3nHTeT). , I )l(M3Hb P.t&O"lHX M KPECTbSlH "PM HAnNTA.nH3ME A. Cepa<tJHfOB"tr. cLlae 60>KbnX MaTepH, A. 4exoB. «BaHbKa» - «Halla Po- .zUfHa», CTp. 67. 68; «HapoJl; OCBOOO/KlleH, HO CqaCT.,lH8 JlIi napo.n.?», H. HeKpacon. «He... C>KaT8S1 nOJloca, «B nOll1nOM pa3rapc cTpaJ{a ,lJ.epeBeHcKast», A. 4exoB. «BaubKa», JI. )l(.apHKoB. «lla 3aBO,!J.e - «Poltlloe CJJOBO», CTp. 73, 74, 92, 96. naAeHNe KpenOCTHOrO np.88; Aepe8HSI noene PecI'OPMW 1861 F. B cepeNiHe XIX B. CTa..'10 COBeprneHffO OtleBH){HO, tlTO coxp-aHRTb ,nOJlbrne KpenOCTHoe npaBO HeB03MOJKHO. POCCHSI, Bee 60.'1bllIe OTCTaBaJIa or nepeJ{oBblx KanHTaJlHCTH'I.eCKHX cTpaH, nOToMY tlTO KpenOCTH1tQeCT- ao MelIIaJIO pa3BHTHIO cTpaHbI. MeJlJIeHHO pa3BHBaJlaCb npOl\fblllJJIeH- HOCTb: MaJIO CTpOHJIOCb cJ>a6pHK, 3aBoAoB, }l{eJIe3HbIX .ltopor. He XBaTaJ'IO CBOOOJtllblX pat50tlHX, TaK KaK OOJlblIIHHCTBO Hace.1eHHH POCCHH COCTaB- JlHJIH KpenOCTHble KpeCTbHHe. KperrOCTHoe npaBO MernaJ10 pa3BUBaTbCR H Ce.'IbCKOMY X03RHCTBY: 3eMJlS1 oopa6aTbIB3J13Cb nnoxo, ypO>KaH ,C Ka*,nbIM rOAOM CTaHOBHJIHCb xY>Ke. OOpa/KeHHe POCCHH B KpbIICKOi' BOHHe (1853-1856), HeCl\lOTpH Ha repoHtlecKY1O OOOPOHY PYCCKHMH COJI,naTaMH CeBaCTOnOJIH, co BCe" OlleBHAHOCTblO rrOKa3aJ10, 1ITO tr.a>Ke B BoeHHOM OTHomeHHH POCCUH UaqHHaeT OTCTaBaTb. a 3TO He r-,fOrJIO He 6ecnOKOHTb uapSi H ITOMemHKOB. Ho, KOHetlH(>, OO.TIbl1Ie Bcero OOHJlOCb npaBHTeJlbCTBO H ABOpHHCTBO He BoeHHoro rrOpa>KeHIfH B 6opb6e c BHeUIHHMH Bparanl, a Bce06Inero KpecTbHHcKoro BOCCTaHHH. A TaKoe B9CCTaHHe BOT-BOT Morno BcnbIXHYTb. KpeCTbHHe ue KorenH 60JlbWe ne peHOCHTb KperrOCTHHqeCKHA rHeT H BCIO.ny 'no,nHIfMaJIHCb H3 60pb6y c nOMeIII.HKaMH. BOT nOtfcl'1IY Uapb AJIeKCa H,ltp I I BCKope nOCJIe BCTY n.lIe- HHH Ha npeCTOJI 3aHBHJI B MOCKOBCKOM Maropo.nHOM ,aBOpHHCKOM .COO'" paHIrIU: «J1Y'Iw"e OT'eHHTb KpenocTHoe npaBO caepxy, He>KeJlH .lI.0?KH'" .n.aTbCH TOro BpeleHH, KaK OHO caMO C060H HaqHeT OTMeHHTbCH CHfi3Y». 48
BOT nOqCMY npaBliJIbHeii rOBopUTb.O na,lleHllH l<penOCTlIoro npaBa. a He ero OTMene.. . nO.arOTOBKa KpecThSlHCKOH pecpOpMbI lllJIa HeCKO.,1bKO neT.. COTHH napCKHX qHHOBHHKOB H Bw60PHNX npeACTaBHTleH BOpHHCTBa TPY. .n;HJIHCb Ha,a COCT3BJIeHHeM npoeKTa pecpOpMbl. HaKoHeu,' 19 eBpaJI H 1861 r. AJIeKcaH,np I I no.n;rrHcan «MauM<jJecT» 06 «OcBoOo)K)].eHHH» KpeCTb- RH. O;UloBpeMeuHo C «MaHH<PecTOM» ObL1IH H3,naHbl «nqnO)KeUHH 0 KpeCTbH Hax t BblllIelUllHX H3 KpenocTHoH 3aBIfCHfOCTH}}. B 9TH X «nOJIOLKe.. HHHX» nopo6HO rOBOpHJlOCb 0 HOBbIX B3aHMOOTHowellHRX KpecTbHH H nOMeIllJIKoB. o CYTH «OCBOOO}KeHHH» cOBepllleHHo onpe.D.eJIeHHO H oTKpoBeHHo CKa3aJI cal\1 AJIeKCall.D.p I I, TOJlbKO He HapO.ltY, a rocy apcTBeHHOMY '" cOBeTY, T. e. BblCUII1M qHHOBHHKa[ H KpynHbIM ABopHHaM: «Bee, qTO tO>KHO 6b1J1o C.lllaTb lI,J1H orpa}K,lJ.eHHH Bblro.n nOMeIII.HKOB, cJ1-e- JIaHO» . npaBHTeJIbCTBO nOOOSlJlOCb cpa3Y fJyo.nHKoBaTb «MaHHcfJecT» If «no.. JIOH<eHHH», nOHUMaSl. qTO 06'bHBJIeHHaSl B ijHX «BOJIS!» BbI30BeT He pa,llOCTb, a rHeB HapOJ{a. Bo Bce KOlllbI cTpaHbI 6bIJIH pa30CJIaHbI BOHHCKHe Ko- taHJ{hl BO fJIaBe c rCHepaJlaMH - JIHqHbIl\IH npe,lI,cTaBHTeJISIMH uapS!. TOJIbKO rrocJle TaKoH no,nrOTOBKH (Y}I{e B MapTe) «MaHH<jJecT» H «noJlo- meHHH» 6bIJIH oO'bHBJleUbI Hapo.ny. fIpaBHTeJIbcTBO He OllIHOJlOCh. KpeCTbHue C HeroLloBaHHe1 BCTpeTHJlH UapCKYIO «BOJIIO», nOHHMaH, tlTO I1X 06faHYJ1H n orpaOH.nn. no BeeR cTpaHe npOKaTHJIaCb BOJiHa KpecTb- HHCKHX BoccTaHHH, KOTopble UblJIU cBHpeno nOa&'1ellbI. KpecTbHHcKaH pecpopla 1861 f. «obIJia KpenOCTHH1JecKoH pe<jJOpMOH 11 He forna OblTb HHOII, 1160 ee npOBo.ll.HJlH KpenoCTHHKH»l,- nHcan B. H. JleHHH. «npeCJIOBYToe «ocBo60)K)teHHe» (jbIJIO 6eccoBecTHeHwHM rpaOe}l{OM KpecTbHH, 6bl.'10 pSlJlOM HaCHJlHH H cnnOWHbIM Ha,llpyraTeJlb- CTBOM Ha,Lt HHMH»2. B qeM }Ke 3aKJIIOQaJlCH 3TOT rpa6HTeJlbCKHH xapaKTep pe<j>OPMbI? KpecTLHHe nO.'1YQH111 JlHqHYIO cBo6oJ1Y. nOMeHK -He Mor npoJ{aTb HJlH KynHTb KpeCTbHHHH8, He HMen' npaBa B:-VfeWHBaTbCH -B ero JlHqHYIO >-KH3Hb If T. . 1-10 cpaKTPlecKH KpeCTbHHI1H He CT8JI COBepweHHO CBOOO,A. IfblM OT nOMeIIUiKa. B TeqeUHC Heonpe,neJIeHHOrO cpol<a 'Bce ObIBWHe ( 1l0Mew.HtIbH KpecTbHHe CtIHTaJIHCb «BpeMeHHoo6H3aHHbHvIH», T. e. ,lJ.OJI>KHbI ObIJIH no-npe}I(HeMY nJIaTHTb o6P9K H HeCTH 6aplI1.HHY. Taxoe nOJIO>Ke- IIHe COXpaHHJIOCb ,ao 1881 r., T. e. erne 20 JleT nocJle pe<J>oPMbI. KpecTb. Hlle nOJIYQHJIH MH3epHoe KOJIHlIeCTBO 3eMJIH. nOJleBOH Ha,lJ.en KpecTbSlH- CKoro ,lI.BOpa 6bl,,'1" B cpe,nHer\'f no cTpaHe 3HaQHTeJIbHO MeHbIIle Toro, Ka- I<HM KpecTbSlHHH nOJI'630BaJlCH LlO pecpoPMbI. nOMeHKH «OTpe3JIH» o CBOlO nOv'lb3Y;OCoOeHHo B QepH03eMHhlx paHoHax cTpaHbl, AO 40% (ShIB.. uleA KpecTbHHcKOH 3eMJIH. Heo6xo,nHfO TaK>Ke OTMeTHTb, qro KpecTb- SlHe nOJ1YtlHJII:I Ha.ne.nbI. rJ{e 3eMJIH 6b1J1a xY>Ke, a nOfeI1l-HKaM OTOWJIa I B. H. n e H H u. nO,,'IEI. coop. COli., T. 20. CTp. 113. :a TaM H( e. 49
nytlmaH, HaHOOJlee n.nOltOpO,nH8$1 3eMJlH. B COOCTBeHHOCTb nOMemHKOB u nepelIIJIH JleCa, 3HaQHTe.,'1bHaSl tlaCTh JlyroB Ii ,lJ.pyrHx yrO)]:HH. ndcJle pe<j>oPMbI nOMeInHtlbe 3eMJIeBJlalte-HHe B POCCH" He YMeHb- WHJlOCb, a YBeJlHqHJIOCb. 10,5 MJIH. KpecTbS1HcKHX .l1J3OpOB (OKOJlO 50 l\IJIH. Hace.n:eHuH) BJIa)J.eJlH TaKHM me KOJlHqeCTBOM 3efJ]l1. 1{3K H 30 ThIC. nOMelI{lillbHX ceMeHCTB (He t50Jlee 150 TbIC. Hace.neHHn). Yt BbIxo,nHno B Cpe.l(HeM, qTO o)tHa nOMeIIIJllIbH ceMbH HMeJIa CTO.7IbKO }l{e 3eMJIH, CKOJIbKO 350 KpeCTbS1HCKHX X03HHCTB. Ho H 9TH CBOH l\fe.nKHe lIa.2\eJIbI l{pecTbHHe .n.O.n}J{HbI 6bIJIH Bb1KynaTb B TetleHHe pH,na JIeT y rOCY,AapCTBa, nOTOMY qro 0110 cpa3Y 3anJIaTHJIO nOMeInHKaM 900 MJlH. PyoJleii 30JIo- TOM. Ha caO1 ,neJJe BCSI KpeCThHHCKaH 3eMJIH CTOHJla no u.eHaM TOro apeMCHH He 60TIee 600 M.nH. py6J1eH, a 300 MJIH. py6.nefi pa3ltHnbi rocy- .napcTBo nOJ!apHJIO nOMeIll.HKaM B KallecTBe BhIKyna JlHtIHOCTH KpeCTbSl- HHHa. Ho 3a 9TOT no,napoK )to.n>KHhl OhlJIH paCnJla1lHBaTbCSl KpeCTbHlIe. rOCYAapcTBo 6paJIo C KpeCTbHH HeYKOCHHreJIhHO He TOJIbKO CYMMY Bbl- .. v Kyna, HO 11 OtIeHb BbICOKHH rO,llOBOH npOneHT. npH Bcex ee OTpHlI.aTeJJbH'bIX CTopOHax, KpeCTbSlHCKaS1. pecpopMa OblJIa 60JlbWJfllllarOM BnepeA. POCCHH KpenOCTHH1JeCKBSI npeBpaIII.aJIaCb B POCCHIO KanHTJIHCTH1JecKYIO. B OTJIHlJHe OT KpenOCTHHtJecKOH CHC- TeMM, re X03HHCTBO OCHOBaHO Ha nOHeBonbHoM Tpye KpenOCTHX u v KpeCTbRH, OCHOBOH Kannra..TJHCTHqeCKOrO X03HHCTBa HBJISleTCH lIaCTHaH cOOcTBeHHOCTb Ha cpe,lJ.CTBa npOH3BO)J.CTBa H 9KcnnyaTau.HH. HaeMHoro TpYJJ.a. Pa3BHTHe KanHTaJlHCTH1JeCKOrO X03HHCTBa HeB03MO>KHO 6ea KpynHbJX KanHTaJlOB, CBo6o,nHbIX paOOIlHX PYK Ii WHpOKoro pbIHKa C6bI- Ta. 3m B03MO>KHOCTH nOSlBHJIHCb B pe3YJIbTaTe naAeHHSI KpenocTHoro npaBa. O,l(HaKo B POCCHH H nocJle Pe<POPMbI COXpaHHJIHCb nepe)KHTKH KpenoCTHHttecTBa. Cl>aKTHtIeCKH co MHorHT\'IH H3 HHX nOKOn1JHJJa TOJlbKO BeJIHKaH OKTH6pbcKaH COIJ.nanHCTHqeCKaH peBOv11OIJ.Hn. EOJIbWHHCTBO KpeCTbHH nOCJIe pe<j>oPMbl CTa..TJH erqe oe,lJ.nee, lleM paHbIpe. JIHIllb Ue60JIbillaSl ,1JaCTb KpeCTbSlH, caMble aa)KHTOtlHbIe, cy- MeJlH 6bICTpO S8llJl8THTb BbIKYIJ H npHKyrrJfTb 3el\IJ1H y nOMeIIlHKOB. TaK nOSlBHJlHCb CeJJbCKHe 60ratlH - KYJIaKH. KYJIaKH HaHHMaJlH 3a nJIaTY cBonx me pa30pHBWHXCH O,nHOCeJIbtlaH. B pe3YJIbTaTC KpeCTb5IJ1e OKa- · 3aJiHCb no,Zl. rneTOM He TOJIb}{O nOMeIII.HKOB, HO H KYJIaKOB - CeJIbCKOH 6YP)f{ya3HH. ,QOJlfH nOMeIllJiKY, KYJlaKY, HaJIOrH rocy'apCTBY pa30plIJIH MHorne KpeCTbHHCKHe X03S1HCTBa. Pa30pHBWHecSI KpeCTbHHe OpOCaJIH .nepeBHIO n YXO,lJ.HJIH Ha 3apa6oTKU B ropo,ll. OHM _CTaHOBHTJMCb pa60- 1IH1\'IH - npo..1JeTapHSl1\fH. . KanHTanMCTlt1 M pa60'lNe . nOCJle na)teHHH KpenOCTHoro ,npaea 3Ha1lHTCJlbHO 6b1CTpee CTaJIO pa3BMBarbcH X03HHCTBO 'CTpaHbl, H OCOOeHHO npOMbJWJIeHHOCTb. nOH- Bli.TJOCb 1vfHOfO HOBblX cj)a6pHK, 3aBo,noB, waxT, >KeJIe3Hb1X JJ.opor, KO- TOpbJe rrpHHa,llJle)KaJJH 60rallaM-KanHTaJIHCTaM. Pa30peHHbIe KpeCTbH- He OT):taBa.nM 33 JJ.OJIfH nJlH npO)1.aBaJlH 3a 6ecneHOK KYJIaRaM CBOH He6oJlb- 50
rune yqaCTKH 3eMJIH If YXO){HJIH B ropo Ha 3apa6oTKH. OHM HaHHMaJIHCb Ha patJory K KanHTaJIHCTaM H CTaHODHJIHCb «HaeMHblMH patJOqHMH», T. e. >KHJlH TOJlbKO 3a CqeT CBoero TpYJJ.a, Ha CBOIO HHrneHCKYIO aapatJOT- HYIO nJIary - >KaJIOB8Hbe. B POCCRH nOSIBHJlOCb l\-fHOrO JlIOAeH, rOTO- BblX D3HTbCH 3a JIIOOYIO pa60ry Ha JlI06bIX YCJIOBHS1X. KpOMe pa30pHO- IllHXCfl KpeCTbHH, HaeIHbI{H paoOtJHMH CTaHOBH.'1HCb R pa30pHBWHeCH peMeCJIeHHHKH - OblBllIHe BJlaJ{eJIbUbI MaJleHbKHX MaCTepCKHX, rJ{e OHH caMH pa60TaJlH C IIOMOlIblO OAHoro-)tBYX nOAMaCTepbeB. TaKHM oopa30M, nocJle naeHHH KpeI10CTHOro npaBa rocno,nCTBYIOInHM B POC" CRH CTaJI KanHTaJIHCTHlIeCKHH CTpoA. Ha CMeHY KpenOCTH"HqeCKOH (<j)eo- aJIbHofi) 3KCIIJIynTau.HH npHUIJIa 9KCIIJIyaTaUHSI KanHTaJIHCTH1IecK3H, u CYIUHOCTb KOropOR 3aK..TIIOllaeTCSI B TOM, qTO Cpe,lJ.CTBa npOH3Bo.nCTBa (cpa6pHKH, waXTbI, >K1e3HbIe ,lJ.oporH, PYAHHKH, 6aHKH H np.) HaXO!tHT- CH B qaCTHOH co6CTDeHHOCTH KanHT3JIHCTOB, a patJOtJHe, JIHIlJeHHbIe coo. CTBeHHOCTH, BbIH;Y}I{J{ellbI npoaBaTb CBOH TPY,Zl. KanHTaJIHCTbI onJla.. llHBaJIH JIHllIb lIaCTh Tpy.na paOOQHX; 3Ha1JHTeJlbHYIO tIaCTb BpeMeHH paCO'-IHe Tpy.nH..rIHCb 6eCnJlaTHO, C03AaBaH npHObIJlb KanUTa. JIHCTaM. Ha 3aBO){aX lIOqTH nOJIHOCThlO OTCYTCTBOBaJIa oxpaHa Tpy,na. KanHTa.. tTIHCT, no cyrnecTBY, He Hec tIHKaKOH OTBeTCTBeHHOCTH 38 3,ZlOpOBbe H iKH3Hb pa601lHX. BOT onHcaHHe pa60TbI B JIHTeHHOH MacrepCKOH Oay- XOBCKoro 3aBoJ{a (B neTep6ypre): «OTKpblTbIe ropHbI H3BepraJIH naJlSl- ll\HH >Rap H .AbIl. Or CJIYIIaHHO npOJlHTOH CTaJIH KJIytJ8fH nO,ZlHHl.faJICH rOpHqIIH, y,nYIlIJIHBbIH nap. OT MaJIeHlIlerO TOJItIKa CTaJIb BbII1J1eCKH- BaJlaCh H, rrona,naSl Ha PYKY HJlH Hory, K8JIeqHJI8 lIeJ10BeKa». TaKHe YCJIOBH5I TpYJta npHBo,nHJIH K TSI}KeJlbIM YBetIbS1M. a HHorJta H K rI1t1eJ1H pa6oQero. qTo6 YI3eJIHtJHTb npH6bIJIb, Ha HeKOTophIe paOOTbl KafiHTaJIHCTbl npe.AnOQHTaJIH HaHHMaTb }KeHIII.HH H AeTeH, KOropblM nnaTHTb MO>KHO 6bIJ1o 3HallHTeJIhHO MeHbIne, 1.Ie1 patJolleMY MY>K'tJHHe. OcooeHHo T5I>Kf\.J1 6bIJI TPY.n .nereH. no BocnOMHHaHHHM nepBhIX pa60tIHX-peBOJIlOnHO" HepOB, KOTopbIe C ,lleTCTBa HaqaJlH pa60TaTb Ha cpa6pHKe (8. repacH- Moaa, n. AJIeKCeeBa, H. BaoYlllKHHa)t no,ltpOCTKOB 9KCIIJIyaTHpOBaJlH Hew.a,ltHO. TpYOBOH J{eHb J{JIH 12-14.JIeTHHx pe6HT HaqHHaJlCH B 4 qaca YTpa H 3aKaHlIIIB3J1CH B 8 Beqepa. l{eTeM tSHJIH nJIeTKOH 3a He- 3HaqHTeJIbHble npoBHHHOCTH. BbIBaJIH C.TIyqaH, Kor,na OHH )'MHpanH or hoooeB. HapS1.ny C KpynHbIMH npe,ZlnpHHTHH1\fH B POCCHH cyecTBOBaJIO MIIO)KeCTBO KycTapHbIx, He60JlblIlHX peMecJleHHbIX MacTepcKHx, KY.lJ.3 paJOpHBlIIHecSI KpecTbHue H pa60tIHe BbIHY1K,lJ.eHbl ObIJIH OTJlaBaTb CUOHX JleTeH B yqeHHKH. )l(H3Hb TaKoro yqeHHKa H nOKa3aHa B paccKa- :4e A. n. l.!exona «BaHbKa». BeJlHKOnenHbIe no xy,nO>KeCTBeHHoH CHJIe H npaB):{HBocTH KapTHHbI )KH3HH nOApocTKa t OT,lJ.aHHOrO «B yqeHbe», ,naCT M. rOpbKHH (<<B JIIOJlHX»). Ito 80-90-x rOOB XIX B. B POCCHH BootSe He cyrnecTBOBaJIO HIi- "., KaKoro paooero 3aKOHOaTeJIbCTBa, n09TOMY Ha rrpeAnpHHTHS1X na- p liJl nOJIHbIH npOH3BOJI cpa6pHKaHTa H ero nopytIHbIX. PaOOtlHX no- / 51
CTonHHO WTpa<pOBaJlH,. BbIBaJlO, 'ITO lllTpacpLJ Ii BbJqeTbI nOKpLIBaJlH .I1otJrn BeCh Sapa60TOK pa60tJero, a HHorj\a H npeBbllllaJ1H rero, TaK \lTO pa60"tJHH 6hIJI B nOCTOHHIIOM ,llOJIry y X03HHHa. )l(I1J1H pat>O\IMe B KC:t- 3ap!\lax-o(jw.eHTH.SJX, KOTophle npHHa;J.,,'1e>l<8J1H KanHTaJIl1cry. Ka)K- ,naSJ celbR CHntaJla He KOMHaTY, a yrOJI 38 3aHaBeCKOH. npO,llY.KTbI paootlue nOKynaJlH B <pa6pHtlHOH JIaBKe. Hx IO)J«IO 6b1JIO 6paTb B )J:OJIr, B CtleT 6y,nymeH nOJlYtlKIi. TaK pa6one nOn3,llaJlli B nOJIHYlO Ka6aJlY. Ka33J10Cb, TaKHe YCJ10BHR }KH3HH: H Tpy.na ,nOJI>KHbJ 6bITJH npHTY. nHTb C03H8HHe pa60QHX, napaJlH30BaTb HX CJlbl. Ho 9Toro He npo- H30rnJlO. KaTIHT3J1HCTHtlecKHe npe.anpH5ITHH 06'be,nHH5IJIH MaCCbI pa6o- 1.JHX, CnJ1aQHBaJIH HX. Pa601lHe HallHHa.lIH OC03HaBaTb oow.nOCTb CBOHX HHTepeCOB, nOHHMaTb, qTO e,ltHIICTBenHbIH BbIXO.ll H3 HeBblHOCHMoro nOJIO.>KeHHSI - COBMeCTHaH 6opb6a. K KOHUY X I X B. nOJlOBHHa Bcex npOMblWJleHHblX pa60tlHX POCCMM 6blJIa cocpe,n,OTOlleHa Ha KpynHblx npe)I.npHHTI1HX. 3TO npH,naBaJIO pa60tJeMY KJIaccy POCCHH oco6ylO cu- JlY, CnJIOqeHIlOCTb, CTOHKOCTh B Gopb6e. KOMMeHTapH" KanHTaJlHCT, 4»a6pHKaHT, 6YPJKYH. l(antlflla...1ucmbL - B,,1alleJIb- Ubl cpeCTn npOH3BO)lCTBa, DJI3)1.e..TIbUbJ KanHTa.na. K3nHT3JIHCTOB 'B POCCHH tJaCTO Ha3h1BaJIH cpa6pUKaHfnaJttu, 3a8od- t{,UKa"UJ T. e. B.l1a.lleJJbU8MH cpaGpHKt 3aBO,l{OB. 11Haqe KanHTaJIHCTOB Ha3BaIOT 6YPJlcyasueu. CJlOBO 3To CPpaHU.Y3- CKoro npOHCXOiKJl.eHH5I. nOcppaHu.Y3CKH, 6ypJIC - ropo)).. B 9noxy <f,>eOJl.£L,1H3Ma 3aIKHT01IHblX ropomaH Ha3bIBa.'1H 6YP'JICya. 113 HHX n03}Ke H pa3BHJlCH KJlacc 6YP.>Kya3HH. Pa60"lHH (npoJlerapHA). Pa60QHMH B KanHTaJlMCTHtJeCKOM o51Ie- CTBe Ha3bJBalOT JIIO)J.eA, JJHmeHHbJX co6CTBeHRbIX cpe,nCTB It Opy,nHH npOM3BO.llCTBa Ii BbJHYiK,neHHbIX npo.n.aBaTb CBOIO pa6oQYtO CHJlY. npli KanHTaJ1H3fe \ pa60QMe JIBJIHIOTCSI OCHOBHhlMH npOH3BO}.l.HTeJISllvlH MaTe.. pH8J1hHbJX LleJIHocTeH. Pa60llHH Kllacc - O)l.M" H3 OCHOBlIbIX KJl8CCOB 6YP>l{ya3Horo 06mecTBa. YrHereHHhJH H 9KCnJIyaTHpyeMblH KanHTaJlH- CTaMH pa60QHH KTJaCC SlBJlReTCSI caMhlM CnJIOqeHHbIM, opr8HH30BaH- HbIM H peBOTJIOUHOHHbIM KJIaCCOM. OH SlBJJSJerCH MOrHJIblll.MKOM KanHTa- nH3M8, oCB06o,D.HTeJIeM Bcex Tpy.nSlInHXCSI Macc OT KanHTaJIHCTHQeC- Koro rHeTa, rJ1BBHOH CMJlOH B C03,naHHH COUMaJIHCTHtJeCKoro 06II{eCTB3. I1HatJe pa60qHH KJ1aCC H83b1BaIOT npO/lemapuainoAf, a pa60tJHX- npo,,'1emapURMU. CnOBO npOAemapuu J1aTHHC){OrO npOHCXO}K,lleHRH. TaK B .llpeBHeM PHMe H33bIBa.'1H oe)I.HeHWee H8ce.neHHe (or CJIOB3 npo- Aec-nOTOMCTBO. npOJIeTapHSIIH H33blBaJlH B PHf\fe Tex JIIO)I.ei% KOTO- pbIe HHtJefO He liMeJlM, KpOMe J(ereA, nOTOMCTsa). KJIaCCHtleCKHH aHa,lJH3 B3aHt.-tOOTHOllleHHH (jyp>Kya3HIi II npo.neTa- pH8Ta ,naH B «\aHI.I(J>eCTe KOMMYHHCTH1IeCKOH napTHH» K. MapKca Ii 4>. 3HfeJ1bCa (CM. fJl. 1 «.5yp»cya H npOJIeTapHH»). 52
3aBOA, cI1aopHKa. 3asoo -KpynHoe npOMbllIIJIeHHoe npe.ll.npUHTHe C MallIHHHOH TeXHHKOH. OT rnarOJIa sasoiJumb - YCTpaHBaTb. 110 3no- XH KanHTa.,TIH3Ma B POCCHH 3aBo.nal\-fH H33blB3nH BOOOw.e Bce KpynHhle npOMbllIIJleHHble npeJ{npHHTHH (6e3 f\falllHHHOH TeXHHKH, C HCnOJIb30- -BaHHef PYIIHhIX Opyt{HH Tpya Ii 3KCnJIyaTaUHeH KpenOCTHblX paOOtIHX. HanpHMept 3aBOJI.bl npH neTpe I). C/Ja6puKa - no CMblCJ1Y nQHHTHe OtleHh OJlH3KOe K 3aBot{Y. 310 Tome npOfhIIlJJIeHHOe, KaK npaBHJIO, KpynHoe npe,l(npHHTHe, oopaa.. TbIBaee Cblpbe MalliHHHb[M CT10COOO1\.I. WOBO .naTHHCKoro npOHCXO>Kt{e- HHH, 6YKBaJIbHO -:- coopY/KeHHe:- Pa3J1UQ"e Me}K.lI.Y <t>a6pHKoA M 3'lBO- ,l1.0M, IlOMa.nYH, B TOM, lITO 3aBO B 60JIbWHHCTBe cJlyqaeB H3fOTOB-. .TJ steT npOJI.YKI{HIO Tfl)l{eJIOH npOlbIlIIJleHHOCTH (napoB03OCTpOHTeJIb- Hble, cTaHKoCTpOHTCJIbHble, tlyrYHOJIHTeHHble H J{p.), Tor.n3 KaK 4>a6- ..,,, u pHKa 8 OCHOBHOM CBfl3aHa C npOH3BO.ACTBO1 H3){CJIHH JIerKOH H nHIneBOH npOMhIlIIJIeHHOCTH (TKallKaSl, KOHHTepCKaH Ii np.). BnpOtIeM, 3TO .ne. neHHe BeCb!vla YCJlOBHO (eCTb }{(e JIeconHJIbHble, caxapHbIe, MbIJlOBa- peHHble 3aBO.l(bI H, HanpoTHB, rn03,l(HJIbHble, HanpHMep, cjJa6pHKH). B. llanb 06'bHCHHeT OTJ1lftIHe cfJa6pHKH OT 3aBo,na TaKHM 06pa30M: «<I>a6- pHKaMH 30BYT T3KHe 3aBO,l(bI, re orOHh (HaKaJIKa, nJlaBKa, -BapKa) He 3aHHMaCT nepBoro MeCTa» (TOJ1KOBhIH CJIOBapb >KHB6ro BeJlHKOpYCCKO- ro H3bIKa, T. IV, CTp. 531). 06'bHCHeHHe BeCbfa JII060nbITHOe, XOTSI H, pa3YMeercH, apXaHqHoe. B POCCHH <l>a6pHK3MH Ha3b1B8JIH TOJlbKO npe)(rrplfSlTHn C l\iaIlIHHHOH TeXHHKOH. .ao X I X ,B. t CJle,nOBaTeJIbHO, B POCCHH cpa6pHK He ObI1I10. Jl,BOpHA - TaK npH Kp.enOCTHOM npaBe Ha3bIBaJIH KpenOCTHbIX. cnyr B J5apCKOM ,llOMe (.,1aKeH t rOpHHtlHble, nOBapa. npatIKH t KOHIOXH H np.). HuatIe - JtBopOBble J1IOJtJi. OTClO.lI.a H Ha3BaHHe Il,ooCKaJl. KYXHfl, KOTopan ynofHHaeTCH B paCCKa3e «BaHbKa», T. e. KYXHH, _r.ne rOTOBH.I1H J1H JU30POBblX .nIO.lI.eH, CJIyr t B npOTHBOnOJIO>KHOCTb 6apc- KOU KYXH.e, re rOTOBHJ1H J{JI5I rocno,l(. KOHetlHO, B 6apCKoA KYXHe fO- TOBHJlH COBceM JtPyrHe' 6JlIOJ(3', He}l{eJlH B JIIO.lI.CKOH. XOTH paCCKa3 llexoBa OTHOCHTCH KO BpeleHH, Kor,l(a KpenOCTHoro npaBa B POCCHH Y>Ke He 6b1J10 (80-90-e rObI X I X B.), TeM He MeHee YKJI8P- nOMeInHtlb- pro .lI.OMa co BpeMeH KpenOCTHHlIecTBa H3MeHHJICH MaJlO. TOJlbKO Bo- pOBblMH ,,11O,l(bMH OblJlH Tenepb H KpenOCTHbIC, a naeMHbIe cnyrH. CHeJlbU.bI or r,,TlarOJla cudemb - TaK H33bIB3nH B CTapHHY npH- Ka3 l IHKOB, Koropble :roprOBa,,1'I" cafOCTOSlTeJIbHO B naBKe no J{oaepeH- IIOCTH Kyna. 5blnH CHeJlbl.(bl «Ha >KalIOBaHbH», OHM no.,'1YtlaJIH npOCTO 3apaOOTHYlO nJIaTY or KynII-a, H CHJ,J.eJIbl.(bI «Ha OTtIeTe», 9TH IIOJ1yqaJ1H tIaCTb npHObI.,1H. Bo BpeMeHa lJexosa nOHHTHe CUae/le14 II 'YI<33aHHOM 3HalleHHH Y>Ke BbIXO,AHJlO li3 ynoTpeoneHHSI. . HOlfb non po>K)J.ecTBO. POJICaecm80 Xpucm080 - O)\HH H3 xpHCTHanc- KH x np33.l1.HHKOB. B npaB0CJI3BHOH n.epKBH OH' OTMeqaJlCH e>KerOJ{HO 25 J\lKa6pSl no cTapoMY CTHJlIO (7 RHBapSl - no HOBortIY). np33JtHHK P0>K.. ACCTBa COBna.l(an no_ BpeMeHH C HOBOrOHHl\-IH npa3)J.HHK3MH. BblJI OObI- 53
liar! B HOqb no.n PO/l{.1J.eCTBO XOJ{MTb co 3Be3J{OH H CJIaBHTb X pHCT3. JIyqrne Bcero 3TOT npa3AHHK onHC3H y fOrOJlH (<<HOqb nepc)). PO}l{,nec- TBOIvI») . neTb Ha KJJHpoce. KAUPOC (rpe4eCKoe CJIOBO) - MeCTO .llJIH neB- qnx B u.epKBH. Cneu.HaJIbHOe "B03BbJIlIeHUe cnp3a H CJIeB3 OT ueUT- pa.TIbHOH qaCTH U.ePKijH (TaK H33bIBael\1bIX «U.apCKHX BpaT»). ¥IHorlla Ha KJlHpOCe BO BReMH 60rOCJIY)KeHMH neJI Xop MaJIb\IHKOB (n Tex Uepl{- BHX, fJ{e He ObIJIO rrpcxpeccHOllaJIbHbIX neBtIHX - 06blllno n .n.epeBH5IX HJIH He60JlbIllHX ropO)J.Kax). 3aYTpeHH - paHHSIH U.epKOBHaH cJlym6a B npaBOCJIaBHOH Uepl{BH. B HOqb no,lJ. pOiK,neCTBO 3aYTpeHH npOBO,l\HJ1aCb ocooeHHO Tp)KeCTBeHHO. TeMHblH o6pa3 - HKOHa. Y CanO)KHHKa AJISIXHH3 (X03HHH3 B3HbKH) HKOHa 6Mna TeMHOH, nOTOMY qTO KpaCKH, KOTOpMMH OHa 6bIJIa HanHcaHa, nOTeMHeJIM OT BpeMeHH, KpOMe Toro, MKOHa BUCeJ1a B M3CTepCKOH H nOI{pbIII1J3Cb nbIJIblO M I{OnOTblO. OTe "oaHU - CB5u.u.eHHHK. CB5IrneHHHKOB BCpYlOllJJle Ha3bIB3,,11}.i omet{ (omtle). 3To nOTOM CTaJIO HX KaK ObI CXPHIl.H3JIbHbIM Ha3BaHHeM. CB5ImeHHHKH ,lJ.JIH OOJlhllIefl TOpJKeCTBeHHOCTH l1MeHa eaOH npOH3110CH- JIM no-uepKOBHOMY (CTapHHHOMY) - He I1BaH, 3 1103HH, He CeMeH, a CH1\leOH H T. n. nepBaJl MupOBaB BOHHa npo,l10J1}KaJl3Cb 60JlbWe qeTblpex neT (c aBrycT3 1914 no HOH6pb 1918 r.). LLapcl<3$l Pocclla npHHHt3J1a Ytla- CTHe B .9rOM Hecnp3BeA.;1HB0V1, rpaOHTeJIbCKOH BOHHe. fJIaBHhle B01O- IOlI.\He rocY,lJ.apcTBa - CTpaHbI AHTaHTbl (AHrJIHH, paHUI5I, POCCHSI) npoTHD repMaHHH, ABcTpo-BenrpHH, TYPU.HH H J{pyrHx ICTp3H. aTO ObIJ1a BOMBa 3a nepeJJ.eJI 1\IUpa, orpa6J1eHHe IJY)J{HX CTpaH II Hap0)10B. nOCTeneHHO B BOHHY BTHHYJIHCb eCHTKH CTpaH, B TOM qHCJlC 5InoHM5J, I1T3JIHH, CIIIA. 3ra SOMHa ObIJIa CTpallIHbll\f 6e,l(cTDHef\i )1JIH Hapo,l10B, oco6eHHo POCCHH, noroMY qTO U3pcKoe npaBliTeJIbCTBO KpODLIO COTeH TbIC5IQ CBOHX COJI,lI.3T paCnJIatlHBaJIOCb 3a OTCTaJlOCTb cTpaHbI, HeXBaT" l{Y 0PY/KH5I, 33 np0,ll.a>J<IIOCTb IJHHOBHHI{OB. BO.;FJbllleBHKH BO r..TI3Be c B. vI, JIeHHHblM C caMora Haqa,na pC3KO BbIcTynHJlH npOTliB 9TOH He.. cnpaBeJIHBOH BOHHbI. He CJIyqaHHO nepBbI1\'1 ,l.(eKpeTOM, npHIHITbIM Co- BerCKoii B.TlaCTbIO Ha CLTIeAYlOlI.\HH )l{e ,lJ.eUb nOCJIe nooe,nbI OKT5IOpbCKO- fO BoopY)KelIHOro BOCCTalIHH B neTporpaJ{e, OblJI ,L\eKpeT 0 MMpe. Co- BerCI<35I POCCHH BblllIJIa 113 BOHHbI B <PeBpa.7Je - rvlapTe 1918 f.' .-- HA1JAJ10 PEBOJJIOl1.J.tOHHOA 60Pb6bl PA60lJHX npOTHB KAnHTAJJHCTOB M. KOPlllYHOB. «<I>JIar 3a6acToBI\H» - «I lama POAHHa», CTp. 72. PaOOqHH KJIaCC JIBJlHeTCSI caMblM OpraHH30BaHHbll\f, caMbI1 C03Ha TeJJbHbIM H peBOJI1OUHOHHIM KJIaCCOf\{ Cpe,nH Bcex TPYJ{HIUHXCH Macc. Pa60QHe, B OTJIHqHe OT KpeCTh£H) He HMeJIH HH ceto X03HHCTB3, Hli 54
l<aI{OH-JIHOO COOCTBeHHOCTH H8 Cpe,nCTBa npOH3BOACTBa. 11M, KaK CI<a3aHO B «KOMMYHHCTHtJeCKOM MaHH<PeCTe», «HellerO repSITb, KpOMe CBOHX u.erreii». B OTJlHQHe OT KpeCTbSIH, TPY,AHBlllHXCH B OHH01.JKY Ha CBOe{ KJIOlIKe 3eMJIH, paOOlIHe COool[{a paOOTaJIH H8 3aBo,nax H cpa6pH- I<ax. KOJIHtJeCTBO pa60QHX Bce BpeMSI p0CJ10 33 ctJeT pa30peHHbIX ({peCTb5lH Ii peMeCJIeHHHKOB. PaOOtlHH KJIaCC TO.'1bKO eIll.e <pOpMHpOBaJlCSI, a pa601.JHe Y>Ke BCTY- llHJIH B 60pb6y npOTHB KanHTaJIHCTOB. Ha1.JaJlH ee C8Mbie CMeJIbIe, co- 3HaTeJ1bHble, My*eCTBeHHbIe. I1MH ObIJIH nepBble pa601lHe-peBOJIlOnHO- llepbI: neTp ATJeKCeeBHtJ AJIeKCeeB (1849-1891), BaCHJIHH: repacHMo- BHQ repacHM:oB (1852-1892), BHKTOp naBJIOBHtJ 06HOpCKHH (1852- 1919), CrenaH HHKOJIaeBHtI XaJITYPHH (1856-1882), neTp AHHCHl\,to- UHtI MOHceeHKo (1852-1923) Ii ){p.1 31'0 6bIJIH 3afetlaTe.TIb Hble LTJIO- IUI, BbI6HBillHecSI H3 caMhIX H1f30B, CTaBWHC HaCT05llUHl\IH PYKoBoJ{HTe- TIHl\Uf paOOIlHX B liX 6opb6.e C KarrHTaJlH3MOM Ii 3pH3MOM. 80 MHororvT OHH cO):leflcTBOBaJIH peBOJIIOu.HOHHOMY BocnHTaHHIO pa60tlHx. OHH ClOSlJIH Y caMbIX HcrOKOB pa6otlero ,lJ.BHn<eHHSI B POCCHH. B. 11. lIe.. HHII bICOKO ou.eHHBaJI liX ){eHTeJ}bHOCTb, HX repOHtIecKYIO C8MOOT- BepLKeHHYIO 60pb6y. B SlHBape 1885 r. B POCCHH npOH:30WJIa He6bIBaJIaSl eIl(e lJ.O Tex nop CTaqKa pa60tlHX Ha TKalJ,KOH cpa6pHKe KarrHTaJIHCTa MOp030B8 B Opexo- Bo..3yeBe (no,nMoCI{BOH), KOTopaH BOIliJIa B HCTOpHIO noon H83BaHueM Mo- p030BCKOH CTatlKH. CTaQKH paootJHx ObIJIH H paubllle. OHH npoxo,nHJIH B 70-80-e rObI X I X B. B pa3Hblx MeCTax oTpaHbl. Ho MOpo30BcKaH CT3tIKa OTJlHqaJIaCb 60JILlliHM pa3MaXOM Ii opraHH30naHHocTblO. B Heft npHHHMaJIH YtJ8CTHe TbICgllH paOOqHX. Cy,n Ha.n p)'KOBOlJ.HTeJlHt.1H: CTaq.. KH npHBJ1eK BHHMaHHe BceK POCCHH. OO)t )J.aBJleHHe£\i1 paootJero ,nBH>Ke- HHH napCKoe npaBHTMbCTBO. BbIHYiK,neHO 6blJlO nOHTH Ha YCTynKH pa- 601IHM: ObIJIH OrpaHHQeHbl WTpacpbl, HeCKOJIbKO ynopHOqeH TPY >KeH- HH Ii )teTeH. Ho rJI8BHOe 3HaqeHHe MOp030BCKOH CTatIKH B TOt, lITO caMH pa601IHe nOqYBCTBOBaJIH CBOIO CHJIY. «3Taft'pOMa,nuaH CT811K8,-nH" caJI B. H. JIeHHH, - rrpOH3Be.na OqeHb CHJIbHOe BnetlaTJleHMe Ha np8BH- TeJ1bCTBO, Koropoe YBHaJIO, lITO paOOIIwe, KOf.l(a OHH t\eHCTBYIOT BMe- cre, npe){CTaB..'1HIOT on8CHYlO CHJIY, ocooeHHO, Kor,lJ.8 MaCC8 COBMeCTHO AeHCTBYlOHX pa60tIHX BbICTaBJISleT rrpHMO CBOH Tpe6oBaIlHH»2 nOCJIe MOp030BCKOH CTalIKH 386aCTOBOlIHOe ,lJ.BI'1}KCHHe pa60 t IHX, HX 60pboa 33 CBOH npaBa nO){HHJIaCb Ha HOByl6 cTyneHb. BaCTOaaJIH. pa601.JHe BO MHornx ropo,nax H paHOHax CTpaHbl. 3Ta Qopb6a nepepOCJIa B peBOJIlOnHOHHble BblcrynJIeHHH rrpOTHB C8l'ttO,Aep>K8BHOrO, nOMernHtlbe-KanHTaJ1HCTHQeCKOrO CTpOH POCCliH H npHBeJIa B peaYJIbTaTe K nooe,ne BeJIHKOH OKTSl6pbCKOH COl.(HaJIHCTHqeC- KOH peBOJIIOI.(HH, K nooee COIJ.HaJlH3r\'fa B HaweH crpaHe. 1 nO,ltp06HbIC CBe,neIlH5I 0 >KH3JUf H ,neHTeJlbHOCTH nepBblX paootlI1X-peBOJIIOl{{{()" lIepOB MOHO HaRTH B Jell.: n. 0 C T P 0 B e p. EypesecTIlIfKH. l\.J npo<tni3.n aT . 1948. a B. 1:1. JI e H H n. nOJIH. coop. COq., T. 2, CTp. 23. 55
KOMMeHTapMH . CraliKa (3a6aCrOBKa) - KO.i1JIeKTI1BHOe npeKpallI.eHHe pa60TbI C l1eJJhlO npHHY J\HTb KanHTaJIHCTOB BblnOJlHHTb TpeUOBaHM'H pa60'lHX (3KOHOMHtleCI<aH CTaQKa) HJIH 3aCTaBHTb npaBHTeJIbCTBO BblnOJ1HHTb nOJlHTHqeCKHe Tpe6oBaHHH. C.'10DO Cmal{,1(a npOMCXO,lJ.HT OT fJlarOJIa cmaKHymbcfl, T. e. .lI.Or0130pHTbCH 0 COBMeCTHbIX (KOJIJleKTHBHblX) ,neit- CTBliHX. HHatle CTatlKa Ha3b1I3aeTCH aa6acm08/Wu. 3TH CJlOBa paSHO- 3HaqHbI no Cl\ibICJlY. 3a6aCTOBKa npOHCXOJJ.HT or CJIOBa 6acma - ,no. BOJlbHO, xBaTHT, ,ltOcTaTOqHO, T. e. pa60 t lHe He )KeJl3JOT 60JIbllJe TPY- l(HTbCH Ha npeiKHHx YCJlOBHHX. PaHbille B PYCCKOM Sl3bIKe CJI0BO CmaLl1\Ll HfeJIO UeCKOJIbKO .npyroii CMbIC.1J - TaHHbIH B3aHMHblH croBop MH ,lI.ocTH}KenHH KaKoH-HH6y,nb oOLUeii l.{eJlH (BoHTH B CTatlKY). C pa3BIiTHe1\f pa601lero ,nBH>KeHHSI cno- BO cmattKa npll06peJIo e,zU1HcTBeHHblH ClbICJl, paBH03HatlHbJH CJIOBY sa6acm081ta. HHor,na riYTalOr CTatlKY C BOCCTaHHeM. 3TO pa3J1HQHbIe nOIUITHSI. Boccnzaflue - MaccoBoe BoopY>KeuHoe BblcTynJleHHe npoTHB npaBH- 'jeJIbCTBa BoccTaHHe - 60JIee BblCOKIiH yponeHb 60pb6b1, He)KeJIH CTatlKa. Bce06llI.aH CTatlKa MO)l{eT nepepacTH B BoopY}KeHuoe Boccra. HHe. TaK 6b1JIO, HanpIiMep, oceHbIO-3HMOH 1905 f., TaK 6blJIO B <PeB- paJIe 1917 f. CJIOBO 8OCCmaH.Ue npOHCo.llHT OT rJIarOJIa 8cmaeamb - nOAHIifaTbCH, paCnpSlMJlHTbCSI. CnOBO ecmaoamb B onpe,neJleHHOM SHatleHHH 01leUb 6J1H3KO CJlOBY Boccmasamb, HanpHMep «BoccTaHbTe, na.llllJHe pa6bI» (A. n Y ill K H H). CTalleQHbdi KOMHTeT - BbI60pHaSi KOJIJIeKTHBHaSi opraHH3anHSI H3 paOOtlHX AnD PYKOBOAcTBa CTaKOH. 06WtlHO pa60tlHe B6HpanH B CratletlHblH KOMHTeT caMblX pelllHTeJIbHblX, CMeJIbIX, YBa>KaeMblX paOO1JHX, npeJJ.aHHbIX 06w.eMY JJ.eJlY. PeBOJ1IOHH (COl\HaJIbHaH) - KopeHHOM nepeBopOT, JIOMalOlUHH CTapblH, OT>KHBWHH OOw.ecTneHHbIH CTpOH H YTBep>K,ZJ.aIOIII.HH HOBblM, nporpeccHBHblH CTpOH. PeBOJII01J.HSI - BbIcwaSi <lJopMa I(JlaCCOBOfl oopb6bl, BeJlHKHH YCKopHTeJIb OOInecTBeHHoro nporpecca. npOJleTapCKaH COUHaJlHCTHtlecKaSi peBOJIIOl1.HH OTJI'HtlaeTCH OT Bcex .apy- fHX TeM, 'ITO OHa YHHqTO>KaeT He TOJIbKO OT)KH Bum ii, CTapbIH nOpSI,l10J<, HO JIIiKBHAHpyeT BCSIKYIO 3KcnJlyaTaIJ,HIO QeJlOBeK.3 qeJ]OBeKOM H npHBo,nHT K C03,naHHIO COIJ.HaJlllCTHqeCKOrO (B KOHeqHOl\t HTore - KOMMYUHCTHtJeCKD- ro) oOlUeCTBeHHoro CTp05I, OCHOBaHHOrO Ha COTpY.l1HHQecTBe CB060,lJ.HblX OT 3KCnJlyarauHH JlIOJleH. BceMHpHO-HCTOpHtlecKoe 3HaqeHHe BeJlHKOH OKTSJ6pbCKOH C01J.HaJlHCTHlleCKOH peBOJIIOIJ.HH 3aKJIlOtlaeTCH B TOM, '1TO OHa JIBMJIaCb he p B 0 H co U H a JI H C T H 11 e C K 0 H peBOJUOIUieH, OTKpblBllIeii Aopory 1IeJloBetlecTBY K n06e,ll.e KO"iMYHH3ia so BCel.fHpHOM MacillTa6. CnOBo pe8o/lIotl,UJl cJ>paH1J.Y3cKoe, 6YKBaJIbHO - nepeBopoT (or Jla- THHCKoro peeo/lIol{uo - ot5paw.aTb, npeBpaw.aTb). Ha3BaHHe HaweR napTHH. KaK H3BeCTHO, H3wa napTIiSl 6b1JI3 C03,lJ.aHa H8 I I C'be3,ne pCJlPn JIeTOM 1903 r. (Ha nepBoM C'be3)1e, KO- TOp WHo ObJJI B MHHcKe B 1898 r., napTHIO c03AaTb He YA8J10Cb. K, 56
H36paHH,hlH ua 3TOM C'be3)1.e, GLln BCKOpe apecTOBaH.) napmSJ HS3h1Ba- Jl8Cb TOr)l.3 - POCCHDCI<8SJ C01I.H8J1-,neMOKpaTH'lCCKall p.a60tJaS{ RapmH (PCJ{PI1). -Hass3HMe COlfuaA-OeMOKpalnWUJCKaJil ptl6owm. fIOJJ.QepKHBa- JIO 'ITO D.eJlbIO napTHH JmJIHeTCg c03;taHMe tou.uaJlHCT-I-JA.lecKOt"O CTpOSl, 'ITO ORa SlBJIHeTCH "IlepeJlOBbIM OTpSlJ{OM. pa6Q1IeJ'O KJl4ICCa ", BbIp:aJKaeT J.-IHTepeCbl HapO;J.HbIX Mace (iJeMoKpamUJl - rpeqecKoe CJI0BO, 6YK- BaJlbHO - BJlaCTb HapOJ{a; fje,,f,OC - Hapo,n, Kpamoc - BJ13CTb). Y>Ke Ha I I C'be3.n.e, KaK H3BecTHO, npOH30eJ1 paCKOJI napTHH H.a Be rpyn- nbl - peBOJllOl.lHOHHYIO (60JlbUleBHKH"JleHHHl\bI) Ii OImOpTYHHCTH1Ie- CKYIQ, corJIarnareJIbcKYIO (1\.feHblIIeBHKH). Ha3BaHHe .60A.btue8UKU H MeHbU/£8UKU B03HHKJIO nOTOl\1IY, tJTO H8 C'be3)J.e npH rOJJ.OCOBaHHH no Borrpocy 0 Bbloope u.eHTpaJIbllblX opraHoB napTHH 60JlbllIMHCTBO npo. rOJlOCOBaJIO 3a npe;liIO>KeHHe JIeHHHa. Ha3B8HHe 60./lbUl£8UKU YTBep- ,nHJlOCb 3a JIeHHHCKOH napTHen. 11 XOTH ,no 1912 r. 60JIbWeBHKH H l\ifeHbllIeBHKH (j>opMaJIbHO BXO,lUIJIH" B O,Z{HY rrapTHIO, cp8KTH1JeCKH 6oJIb- llIeBHKH npe,ncTaBJIHJIH CroOM caMocToSlTebHYIO peBOJIIOlI.HOHHYIO npo- JleTapcKYlO napTHIO. «Eo.TJbllIeBH3M, - "MCaJi B. 11:' JIeHHH, - cy- l.l.leCTByer, K8K TeqeHMe nOJIHTH'IeCKOA MblCJIH Ii KaK nOJlHTHqeCKaJl napTHH, C 1903 ro,na)l. '- B 1912 r. Ha VI (npa}KCKoH) KoH<f>epeUII.HH pCJ1pn 60JIbllIeBHKH OKOHQaTeJIbHO OT,AeJIMJlHCb OT MeHbmeBHKOB. B ,llaJIbHeiirneM Hallia napTHSI CTa.na Ha3bIBaTbC5I POCCHMCKOH COIJ.HaJI-.n.eMoKpaTHtleCKoi% pa- 00llCH napTHeH 60JIbllleBHKOB - PCJ1pn(6). . B rO)lbl nepBoH MMpOBOH BOHHbI COUMaJlHCTllqeCKMe rrapTHH sa- l1a,nlloeBponeHKHx . '1-1 pSI,Aa .n.pyrMx CTpaH H3eHHJIH lJ.eJlY npOJleTap- CKoro HHrepHalI.HOHaJIH3Ma, rrpeBpaTHJlHCb B 3allJ.HTHHKOB 6YP}Kya3- Horo CTpOJf. Ha3BaHHe «CollHaJI-.n.eMOKp8THlJeCK8H napTHSI» t5b1JIO ,nHC- KpeAHTHpoS8HO. CpS3Y me no. B03Bp8eHHH Ha PO,nHHY B npeJIe 1917 f. B. H. J]eHHH npeAJIOJKHJI H3MeHHTb Ha3BHHe napTHH. «BMe- rTO «COllH8J1-,lteMOKpaTH"», OCPHU'H8J1bHb1e BO>KAH KOTOpoA BO BceM tv1l1 pc npe)J.aJIH COl\MaJIH3f\f, nepeH,ltfI K 6ypmya3MH... HanO H8SB8TbCH KOMM!JH.UC"lutteCK,OU napmueu»2. aTO npe.zvyO)KeHHe JIeHHHa 6b1JIo IIpHIITO H3 VII C'bea,ne napTHH B MapTe 1918 r. I-J81ua napTHH CTaJla It83hlB8TbCR PoccH",KaH KOfMYHHCTHqeCKaJl napTHH OOJlbWeBHKOB- I>KI"I(O). «HaQHHBH COUH8JIHCTHlIeCKHe npco6pa30B8HHH, - rOBOpRJI IJ. H. JlcHHH B ,ltOKJla,lte H3 VII C'bC3,lJ.e napTHH, - Mbl )tOJI>KHbI JlCHO 1I0l'T(1UIITb nepe,A C060H II.eJIb, K KOTOpOH 3TH npeo6pa30BaHHH, B KOH- Hl" KOllilOB, lIanpaB.neHbT, HMeHHO II.eJlb C03J{8HHR' KOMMYHHCTHlIecKoro OnIU('rTBB.. .»8 (<<COI030!vl KOtMYHHCTOB» Ha3bIBaJla(:b nep13aH B NHpe Mt'H<AY tlMPO)\1I8S1 peBOJIlOllHOHHaH npO.,'1eTapCKaSl opraHM3aUHSI, cm- Jt""lIaH MapKCOM H 3HrlbCOM eUI,e B Cepe.lJ.HHe XIX B.). I J()cn O()'beAHHeHHSI COBeTCKHX pecny6nHK H C03,ll8HHR CCCP (Jl('I<nt)ph 1922 r.) BCTaJi Bonpoc 0 HOBOM H3MeHeHHH HB3B8HH}1 nap. I B. II. JI e H H H. nOJJH. co6p. CO'I., T. 41, CTp. 6. U A, 1. Jl e H II H. nOJIII. co6p. COq., T. 3,1 t CTp. 116. ft U. 11. J1 e If H H. nOJlH. co6p. COq., T. 36, CTp. 44. 57.
THH. PeuleHHe 06 9TOM 6bIJ1o npllHHTO B 1925 r. Ha XIV C'be3,ne nap- THH. Harna rrapTHSI CTaJIa Ha3bIBTbCH BcecoI03HaH KOMM.yuHCTHtIec.. KaSl napTIIH OOJIbIlleBHKoB - B-KO(6). 3TO Ha3B3l1He cOXpaHSIJIOCb O 1952 r. B 1952 r. Ha XIX C'be3)te napTHH 6bIJIO perneHo 1i3Me-HHTb Ha3BaHHe napTHH. OHa CTaJIa Ha3hIBaTbCH KOMMYHHCTHttecKaH napTHfJ COBeTCKoro COID3a (KI1CC). 10-.... COL\HaJlH3M, KOMMYHH3M. He paCKpbIBaSi rJIy6oKoro CMblCJIa 9THX aaLKHeHIllHx nOHHTHH, CJIe,1J.yeT ,naTb JlHUlb caMoe KpaTKoe 06'bHC- HeHHe H YKa3aTb Ha npOHCXO}K,lleHHe caMHX CJIOB. COl.{UaAU3.M - npo.. HCXO,nHT OT J13TIiHCKoro CJlOBa COlUaJlUC - 06III.eeTBeHIIbIH, TOBapl1" IllaeCKHH. C0l1HaJIH3M - o6eCTBeHHJH If rocYJlapCTBeHHbJH CTpOH- nepBa51 c.pa3a KorvrMYHH3Ma, OCHOBaHHbIH n3 npHHIJ.Hne: «OT KaLK)(OrO- no cnoco6HOCTHM, KaLK,l(OMY - no TPY,ZI,Y». IlpH COlI.HaJIH3Me BJIaCTb npHHaJle)KHT TpYSllaHMCSI, YHHIlTomeHa llaCTHa51 co6CTBeH- HOCTb Ha cpeCTBa rrpOH3Bo,nCTBa H 9KcnJlyaTaUHH lIeJIOBeKa lleJIO- BeKOf. KOMMYflU31f1, - OT JIaTlfHCKOfO CJI0Ba KOM.A!YflUC - 06Il1.HH, DceooraHH. I(01\iMYHH3M - BblCIllaH <PoPMa tteJIOBeqeCKOfO 06rn.eCTBa. npH KO[IYHll3l\ie He oy,neT HHKaKHX KJIaCCOBbIX pa3,.'1HtIHH, YCTa- HOBHTCH nOJIHOe COlI.HaJlbHOe paBeHCTBO t t3y,neT OCYI1I-eCTBJIeH npHH" D-Hn: «OT l{a}K)J.oro -- no cnOCOOHOCTHM, Ka>K,ZI,OMY - no nOTpe6HOC" THM». no PYKOBOCTBOM KOMMYHHCTHqeCKOH napTHH COBeTCKoro COlO3a Halll napo,ll CTpOHT KONtMYHH3M. «HHTepHau.HOHaJ1». TaK Ha3bIBaeTCH Me}K,1J.YHapO.LlHbIH npOJIeTap- CKHH rH1H. ABTOp TeKCTa cppaHUY3CKHH n03T 3JKeH D9Tbe (1816- 1887), aKTHBHhIH YlIaCTHHK DapH}I{CKOH KOMMYHbl 1871 r. OOThe Ha.. nHCaJI «HHTepHaUHOHaJI}> B HlOHe 1871 r., lJepe3 l\1eCHIJ. nocJle KpOBaBO- fO no,ltaBJIeHHH l(oMMYHbI. ABTOp f\1Y3bIKH «vh-ITepIl3lJ,HOHaJla» - <ppaH" II.Y3CKHfi KOMno3HTop. pa60ttHH nbCp ,UereHTep (1848-1932). B nep- Bbre «I1HTepHaLlHOHaJI» 6bIJI HCnOJIHeH BO <1>paHHH B 1888 r. PYCCKHH TeKCT «v!EITepHaIJ.HOHaJIa» (aBTop A. 51. Ko) ony6JIMKOBaH BnepBble B 1902 r. C 1917 no 1944 r. «HHT-epHaUHOUaJI}> ObIJI rocy,napcTBeHHWl\1 rHM.. Hot COBeTcKoH CTpaHbl. nOCJIe BBe)J.eHHH HOBoro rOCY,1J.apCTBeHHoro rHMHa COBeTcKoro C0103a (1944) «J1HTepHaIJ.HOH3lI» BJIHeTC.H fHMHOl\i Knec. UIOBO uHmepHal1uOHaA JIaTHIICKoro npOHCXO)K,l(eHHH, 6YKBaJlbHO Me}l{,nYHapoAHbIH (uHmep - Me>K,1J.Y, Hal{UO - Hapo,n). MOHapxHH (caMO,1J.ep)KaBHaH l'ttOHapxHH) - rocYAapcTBeHHblH CTpOH. npH KOTOp9M BepxoBHaH BJIaCTb npHHa)J.JIe>KHT O,nHOMY lle.HO- BeKY (uapIO. KOpOJllO, HMnepaTopy) H nepe,1J.aeTC5I no Il3CJ1e,ZI,CTBY. Monapxufl, - rpetteCKoe CJIOBO t 6YKBanbHo BJIaCTb O,1J.Horo (MOH,OC- O.l{HH, apX3 - AepJKaBHaH BJIaCTb). CaMOep/l{aBHaH f\iOHapXH5I (B POCCHH OHa CYIII.eCTBOBaJIa AO cpeBpaJIbCKOH peBOJllOUHH 1917 f.Y 03Ha.. qaeT, tITO BJIaCTb uapH (KOpOJIH t H.MnepaTopa) HeOrpalIHlIeHa, B npcr THBOnOJIO>KHOCTb napJIaMeHTCKoH MOHapxHH, f)J.e BJl3CTb MOHapxa orpaHHtteHa BbIClllHM BbI60pHbIM (npeAcTaBHTeilbHbll\i) Y t lpeiK)leHl1eM. (HanpuMep, B AUfJlHH). -58
Pecny6JulI{a - <pop{a rOCY,IJ.apCTDeIIHOrO YCTpoicTBa, npI1 KO- TOpOH BepXODHa51 BJIaCTb npHHa,Z(JIemHT BbI6paHHbIM na OnpeeJ1eHHbIH CpOK OpraHaM BJIaCTH. npOH30111JIO OT JIaTI1HCKHX CJlOB pee ny6AuKa - ()6IleCTBeHHoe .zr.eJIO (pee - .AeJIO, ny6AuKa - oomeCTBeHHoe). He06xo,QH1\10 OTMeTHTb, tITO MOHapXHH H pecny6JIHKa JIMlllb «POp}\'1bl rocy,Z(apCTBeIlHOH BJIaCTH. OHM MorYT 6blTb npH pa3JIMQHOM o6rnecT- BrllIlOf CTpoe. DblJIH B HCTOpHH pa60BJIa.neJlbQeCKHe MOHapXHH (PHtf- C](35I HMrrepHll) M pa60BJIa,l{eJIbIIeCKHe pecny6J1MKH (B ,npeBHeH rpe- HIIH, .npeBHel\i PMMe), q>eO,ZlaJIbHbIe MOH8pXHH (AHrJIH51, <l>paHlI.H5I, POC- rlIH) H cpeOJ.\aJIbHbIe pecny6lIHKH (BeHeUHH, ,npeBHMH HOBropo). B HaCT05lee npeMSI cymeCTBYIOT 6yp>Kya3HbIe J\fOHapXMH (AUrJIHll, I USeu.HH) Ii 6YPfKya3Hble pecny6JIHKH (CIlIA, <1>paHII.H51). BbIcrn8H (I)Opfa pecrry6JIHKH - COI.1HaJIHCTHQecKaH, rAe BJIaCTb npHHa,ll.J1emllT Tpy,aOBOMY HapOAY (CCCP H .npyrHe COUliaJIMCTHtIeCKHe cTpaHbl). BHeKnaCCHoe qTeHHe BHeI{JlaCCHOe qTeHMe BIll KJIaCCe - 9TO 3aBeplll31OIUee 3BeHO B CHCTeMe HaqaLJIbHOH nO,ZlrOTOBKH ytJamHXCSI K caMOCT05.ITe.'1bIlOMY lITe- IIHIO. no cJ3oeI'iIY xapaKTepy OHO HBJlHeTCH ecreCTBeHHbIM npo.noJl}Ke.. IIHef 3aHHTHH BHeKJlaCCHbIM qTeHHef.f BO I I KJlaCce. Bce BHbl paooTbI no BHeKJIaCCHOMY lITeHMIO no-npe}J{HeMY HanpaB- JIeHbl H8 TO, tJroC)bl paclllHpMTb QHTaTeJ1bCKMA Kpyro30p ,neTeH, pa3BHT IIX HHTepecbl, a TaK}Ke 38J10)KHTb OCHOBbI HaBbIKOB, n03B0J1 HlOllI.HX lI.eTSlM caMOCTOHTeJlbHO opHeHTHpoBaTbcH B MHpe KHHr c n01\.fOInblO JJ.o- eTynHblx HX B03pacTY oH(5JIMOTe1JHO-oH(5J1HorpacpHQeCKHX noco()HH. 3a }J.Ba HCTCKIIIHX ro,na oOYtJeHH5I Y1.JaHecH Y>Ke OBJIa,neJIH: n.eJ1bIM p HJJ,Ol\i cnerU18J1bHbIX 3HaHHH, YMeHHH H HaBhIKOB no BHeKJI aCCHOMY 'lTelIliIo 1 . LJHTaTeJ1bCI{UH Kpyro30p Kam,AOrO pe(5eHI<a H31ep51eTcR Tcneph B Cpe,lI.HeM 3HaHHeM KHHr 20-24 nHC3TeJIeii, cpe,AH KOTOpbIX 113 nepBOM 1\.eCTe A. C. DYlllKHII, C. MapwaK, A. raH)J.ap, B. BHaIlKH, E. 4aPYllIHH, fit II<HTKOB, A. BapTO, A. KOHOHOB, 3. BocKpeCeHCJ<aH, JI.. POJLpH, 3.CeToH- TOMncoH H ,np. B 31IaqHTTfbHOrf CTeneHM H3MeHHJIaCb H KatJeCrBeUHaH HanpaBJleH- 1l0CTb 3HaHHH; yqar.u.HXCH. ECJ1H D.pBOkJlaCCHHKH Ha Bonpoc, KaKue 1\ IIHflf Hl\{ 3aI)OMHH"TIHCb, nepeqHCJIHIOT, KaK npaBHJIO, 3BTOpOB, c IIpOM3BeeHHHMH KOTOpbIX OHH n03HaKOMHJIHCb H8 ypOK8X BHeKJlac.. CHoro llTelIHfl, TO BTOpOKJlaCCHHKH, OTBeIIaSl Ha 9TOT me Bonpoc, yme B Haqa,ne BToporo nOJIyro,nHH HenpCMellHO BbI,neJl5JT H3 Kpyra cBoero 'rreHHSI HHTepeCHble TeMbl H CI35J)KYT HX C TBOp1JeCTBOM 'OT- ;eJ]bHbIX nHCaTeJIeH. Hanpllep, MapHHa M. JIJ06HT 1JMTaTb 0 1 HU)I{e npHBO,LlJITCH )J.aHHb1e cnelHaJlbIlhlX KOHTpO..1blIbIX pa60T no Bl1eKJI3C- ('UOMY 1.JTenHIO, Koropb1e CHCTeMBTH'IeCKJf npOBOJI.HTCn B KJIaCCaX t f)J.e oe>Y'IeHUe CTp011T- fi B nO,,'lHOY COOTBeTCTBHH C TpeooB31HIHMH HOBblX nporpaMM. 59
>KHBOTHbIX H rrOTOMY B qHCJIe KHHr, I<OTOpble OHa XOpOlliO nO/IHHT, 'rrpe>K,ne Bcero Ha3blBaeT paCCKa3bI E. 4apYllIHHa, KHHry «I<TO B JIecy >KHBeT H qro B .rrecy paCTeT» 10. LlMHTpHeBa, «nMTOMUbI 300napKa» B. LIanJIHHOH, «JIecHYIO ra3eTY» B. BHaHKH, «PaCCKa3bI 0 iKHBOTHbIX» 9. CerOHa- Tor\'HlcoHa, «PaCCKa3hI 0 X(HBOTHbIX» B. )KHTKoBa, «Pe6H- Ta Ii 3BepHTa» o. f1epoBcKoii; a yme nOTO1-nOHpaBHBUlHeCH en KHHfH pyro:H: TervlaTHKH. IlpaB,na, qTaTCJIbCKHe npHB5I3alllIOCTH ,nereH He HBJIHfOTCH na BTOpOM ro,ny 06YtleHHH ycrOWtJHBbll'ilH: OHH MeHHIOTCH HJIH l.(HcfxPepeHI.I.HPYfOTCH B TeqeHHe rO,Aa HeCKOJlbKO pa3, "PH 9TOM q Ii T 3 T e. JI b C K H H K P Y r 0 3 0 P Y q a I.U. -11 X C 51 pac III H" P Sf e T C 51 if 3 a n a C 3 H a H H H 0 II P 0 tJ H T a H II hI.X K II H- r a x COX P a H 51 e T C 51. BTopOK"laCCHHKH 3HalOT OCHOBIIbIe 9..1eMeHTbI KHHrH H ycnelliHo cnp3B.THUOTCH C 3a,aaHHeM B TetteHHC 3-5 MHHYT onpe,aeJIHTb npHMep- Hoe CO){ep*aHHe He3HaKol\tofl KHHf.'H, onllpa51Cb He TO.nbKO lIa Ha3B3- lIne If H.,TI,.'IfOCTpau.HH, HO H lIa J1.annble THTY"lbIIoro JIHCTa, OrJIaBJIeHHe, BBe,neHHC (aHHOTau.J-IIO) H T. n. TaK, paCCfOTpeB KHHry E. I1011bHHofI «IllY1 II lllYl\10K»t, nepBOKJI8CCHBKH OOblttHO '10rYT Cl<a3aTb JIHllIb, lITO 3Ta KIlHra 0 ,neTHX, a BTOpOKTJaCCHHKIi [lenpeteHtIO Yl<a3bIBaIOT, lITO B KHHre HHTepeCHbJe H CfeIlIf-lbIe CKa3KH 0 lllKOoJ1C H lliKOJIbHHKax. npaBH..TJbHOCTb CBoero npe,nnO,,10>KeHH5I yttarnHCC51 I I K..'IaCCa MOTHBH- PYIOT CCbUIKOH Ha nO.l(3arOJIOBOI{, KOTOpbIH Hl\feeTCH ua THTYJIbHOM JIH- CTe, 113 or"1an,,leHMe, r.l(e IIepetJHCJIeHO 5 GKa30I{ C HeOOblqHbIMH Ha- 3BaHHHJ\.tH 2 , Ha 3aoaBHbIe HJlJIIOCTpaI1.HH XYAO)KHHKa D. 4ynpblrHHa H, KOHetIHO, H3 o6paeHRe K qHT3TeJIHM, KOTopoe OHM 3a 3-5 MMHYT, OTBe,lJ.eHHble Ha npOCMOTp HOBOH KHHrH, ycneBaloT npOqeCTb. YqaUI.HecH I I K..rJacca OBJIa.l(1H YMeHHeM 3arrHcaTb KHHry no 00'" menpHHHTbIl\f npaBHJIaM 3 H, n0J1b3YHCb TaKOH 3aHCblO, ObICTpO OTbIC- l<aTb HY}KHYIO KHHry CpC,lJ.H ,npyrHx KHHr. HaKoHeu, y yqamHXCH K KOHUY BToporo roa ooytleHHH ..Bce llac u B03HHKaeT H3CTOHtlHBOe }I{eJI3-HMe caMOCTOSITe"lbHO C rrOMOblO KHHrH \ pa3pernaTb BorrpOCbI caMoro pa3.rIHQHOrO xapaKTepa, IIaI1pMMep: «KTO rrepBbui rronaH Ha CCBepHbIfl nOtl1Ioc?», «tlTO TaKoe opOHTa?», __}<KaKHe 6bIBalOT TpaKTopa?», «0 ,[(peBHux )KHBOTHbIX», «KaK }KHBYT )LeTH .npyrHx cTpaH?», «CI{OJIbKO 3,Be3,[( Ha He6e?», <PacCT05lHHe OT 3eM- J1H o Co.J1Hl{a H JIYHbI», «0 3MeHX» H T. n. D..l!51 OTBeTa lIa caOH BorrpocbI Y1.l3IUHecH HCnOJIb3YlOT ,AocTynHbIe HM 'cnpaBOqHHKH (<<.qTO TaKoc? KTO Tal\oi1:? CnYTHHK JII0603HaTeJIbllbIx>>, T. 1 H 2, pe>Ke L(eTCKYlO 3H- 1 CM.: E. 11 JI b H H a. llIY1 H WYMOI{. CKa3KH. \., «,[leTcKast JlHTepaTypa», 1968>. CM.: «naJ10ttKa-noroHH.101lKa». «l{HK-tIHK HOiKHHuaMH», «CKa3Ka npo Bttepalll- HR" ,AeHb» H Ap. .__ a u.r. CT. «BHeKJIaCcHoe qreHHe» B KHHre J:{JIn YtlHTeJIH: cOt5ytteHHe BO BTOpOf KJ1aCCC». M., «ITpOCBeLUeHHe», 1970, .CTp. 27. .. npHMepbl B3nTbI H3 aHKeT yqaw.HxcH I I A KJlaCCa WKOJIhI N 444 MOCK-8bI (YQH1'eJIbHHLla r. <1>. BOJIKOBa). LLeTH OTBe t laol1" Ha BonpoCbI, K KaKOH KHHre H no KaKOMY nOBOAY a6paaJlI1Cb OHI-I no co6CTBeHHoH HIIHUHaTHBe, 4.TOObi nOJlY([HTb HH- TepecYIOHe HX cae,n,eHKH. 60
ll..HKJlOne,nHIO) II I{HHfH HaY'l1HO-n03.1-13BaTeJlbHOrO XapaKTepa (Harrp,H- Mep, «1\\Hp 1JHCeJI», 11. LlenMaHa, «J1eCHYIO ra3ery» B. En3HKH, KHHry H. Hane)lJlHHOfl «K3)K)1.0H ObIJIHHKe 6p3T» M T. n.). CnOBOM, B pe3YJl'bTaTe eHCTeM3THQeCKOrO rxeJIellan,paBJIeHHOrO qTe- BMR H paCC1vlaTpHBaHHH KHHr y yqa1ll.HXCSI K HaQaJ1Y TpeTbro rOJ\a o6YQeUHH HaKan..l1HBaeTCH 60JIblllOe KOJ1MtJeCTBO CBe.nCHHH H Ha6JIlO,ne- HHH, KOTopble OHM ,nOJIJKHbl OCMbIC..rIHTb H OOOOInHTb. OpH 9TOM YCHJIH5I YQHTe.1IH no-npe-)I<HeIY H3np3BJIeHbl Ha 3HaKOMCTBO JJ.eTeH CO BCel\-IH BHJI.aMH ,nocTynHoM JIHTepaTypbI H HOBbIMH nMCaTeJ1HMH, HB BocnHTa- HHe Y HHX yrvreHHSi Ii npHBb]ql{H paccr.faTpHBaTb, BblonpaTb H qHTBTb KHHrn, PYKOBO,nCTBYHCb TeMH Tpe6oBaHHHIH, KOTopble npe,n'bHBu1HIOTCH K KYJIbType qTeHHH. B K a K 0 M H a n p a B JI e H H If H 3 a C q e Tile r 0 p a C- m H p JI e T C H H a q H T 3 H HOC T b T peT b e K JI a C C H .H- K 0 B? B I I I KJIacce YllallUleCH npo,nO.,'J)KalOT caMOCTOHTeJIbHO 1JHTaTb npe)K,ne Bcero JIHTepaTYPY XYJlO)I<eeTBeHHYIO: CKa3KM, 3araJlKH, n CJ10BHUbI, noroEopKH, paccKa3bI If nOBeCTH, 51 PI{O oTpa}J{aloIIJ.li }KH3Hb Harnero napo,na Ii HapoJI.oB JI.pyrHx cTpaH npe)l{,nc H Tenepb. B npo- l{eCce qTeHHH YQ3IUMeCH I I I KJIaCC3 H3pHJI.Y c JI.eTCKO KJIaCCMKOH (K. 4YKOBCKHH, A. EapTo, B. BHaHKH M )J.p.) nOCTeneHHO npHoorna- IOTCH K PYCCKOI'i II 3apy6e>KHOH KJIaCCHI{e (\. rOpbKHH, A. KynpHH, n. H. Mal\lIHH-CHOHpHK, A. C. OYllIKHH, M. J1epMoHTOB, .lJ,. JIOH,lI.OH, f. CeHKeBMQ, B. flOro, i\apK TBell H Jlp.). B Kpyr IITeHHH TpE:TbeKJIaCCHHKoB BKJII01JaIOTCH HOBbIe JIHTepa'fypIlble }KaHpbI.: npH- KJI1QQeHlleCKHe KHHrH (HanpHMep, «LlbThf B JIecy», «CYJlb6a oapaoaH-_ III.HK3» A. faH.Ilapa; «nOJIeCCKHe P06HH30HbI», «TBT» 51 HI{H MaBpa; «,POOHH30H KpY30» ,a. ,Lle<po «npHKJIlOlIeHHH TOMa COHepa», «npHHlt H HHw.uih> MapKa TBeHa; «):leTn KanHTaHa fpaHTa» )1(. BepHa; «npH- KJII01JeHHH ,nOHcTOpMlJeCKOrO MaJIbqHKa» LI.' 9pBHJIbH 3. H T. II.), KHHrH 0 nHCaTeJIHX HanpMMep, «PaCCKa3bl 0 nYIllKHHe», «BcTpellH c raM.napoM» K. naycToBcItoro, «PaCCK33bl 0 raHJJ-ape» ErvleJ1b5IHOBa H )J.p.). 'lIHTaH npOH3Be,neHHH H. K. KpyncKoH (<<MoH >KH3I1b», «Moe H Ham€», «HaYt.IHMCSI 'pa6OTaTb nO-HaCTOHI.U.eMY, nO....JICHHrHCKH!», «BYAb- , rr-e OOtnecT-BeHHH"K3MH», «OHoHep, B OHOJ1HOTeKY!», «3HaHHJI HY)!{Hbl B }KH3HH, KaK BHHTOBKa B 0010» M T. n.) HJIH A. raH.napa .(<<OObIKHoBeH- HaH 6Hor.paQ>HH B HeOObIKHOBeHHoe BpeMH» 'H T. n.), TpeTbeKJfaCClIHKH , 'BnepBble n03naKOMfiTCH C ,nneBHHKaMH, nHCbMaMH, aBToOHOra(lnJHnf, nanHCaHHblMH a8I\1e'4aTe..1IbHbIMH lIIO)J.bMH H aApecoBaHHwMH IIHTaTeJISIM- .lleTHM. He feHbllJMH HHTepec BbI3bIBaeT Y I1HX H JloKYMeHTa.7JbH3R rrpo33 (HanpHwJep, B. KaMoB. «napTH3aHcKoH TponoM faaJ!apa», 51. .Q.'1yro- ..T1eIICKHH H f. neTpoB. «IlOHCKH .n.JIHHOIO B ro,n» M T. n.). B TeqeHHe TpeTbero ro;:ta o6YQeHHH o6061ll.alOTc, paclIIHpHIOTCH npe,ncT3BJIeHHH ,neTeM 0 CnpaBOqHOH JIMTepaType. TaK, TpeTbeKJ{ac- CIIHKa!et1 BfiOJJHe .nocTynHbl l\IlaJleHbKHe TeiaTH1ieCKHe 3HUHKJlOne.l1HIf, BbJnycI{ KOTOphJX H3,naTeJIbCTBO «l{eTCK3S1 J1MTepaypa» OCYInecTBJISIeT 61
c 1965 r. l t H .ltBYXTOMHHK «4TO TaKoe? KTO TaKoft? CnYTHHK nJ0603Ha- TMbHbIX»2. HaKoHeU t ytlalllHecSl I I I KJIaCCa CHCTeMaTHqecKH qHTalOT nepHo,nH- KY, KpoMe jl{ypHa..'J3 «MYP3HJlK3», OHH MorYT H ,l10JI>KHbl n03HaKOMHTb- CR, HanpHMep, C >KypHaJIaMH «KocTep», «IOHblH HaTypaJIHCT», npH- yqHTbCSI lIHTaTb nHOHepCKHe ra3eTbi (<<nHoHepcKYIO npaB,ny», «JleHHH- CKHe HCKpbI>}3 " T. n.). TaKHM o5pa30M, Kpyr qTeHHH TpeTbeKJIaCCHHKa, TaK >Ke KaK H DTOpOKJIaCCHHK3 t COCTaBHer xYAoiKeCTBeHHaH, HayqHO-rr03HaB8renb- HaH JIHTepaTypa H ,l\eTCKaH nepHO,l1HKa, HO Ka}KJ{blH H3 9THX BH,nOB JIHTepaTypbT npe,l\CTaBJlCH 3HaqKTeJIbHO nOJIHee H WHpe, qeM BO I I KJIacce 4 , 3 H3 CnpaBOtIHYIO JIHTepaTYPY otSpaw.eflO oc06oe BHHMaHHe. Ha TpeTbeM rOAY Ot)yqeHHH 3aKperr..'UUOTCSI, YTOtJHHlO!CH H 0600- Iu.aIOTCH HaBb!KH KYJIbTypbI QTeHHSI, KOTopble CrJO>KHJIHCb B pe3YJIbTa- Te l(Byx.tIeTHero lIHT3TeJlbCKOrO OnblTa Ytl3III.HXCSI. npHqeM" Ha 9TOM 9Tane fJIaBH3H 3a,llaqa YllHTeJlH 3aKJUotJaeTCSI He TOJIbKO B TOM, lIT06bl HaYlIHTb eTeH npHeMaM pa60TW C KHuroA, nOKa3aTb HM, KaK nOJIb- v 30BaTbCS1 peKoMeH,ll3TeJJbHbIMH cnHcKaMH, KpTOTeKoH, CnpaBOtlHblMH H3,naHHHMH, HO H B TOM, tlToObl nOCTOHHHO no6Y}KaTb ,neTeH HCnOJIb- 30BaTb npHOOpeTeHHbIe HaBbIKlf B Cal\IOCTOflTlbIlOH lIHTaTeJIbCKOH npaKTHKe. Cor.naCHO TpeOoBaHHHM nporpaMfbl, BIll KJIaCCe yqaInHeCH OBJIa- )IesalOT HaBblKOM onpe,neJleHHH npHMepHoro co,ltep>KaHHH He3HaKoMoA KHHrH no ee 3.,'IeMeHTaM H BHeUlHHM npHMeTaM. Cpe,l\R HHX B flepnylO Oqepe):l-b yqaHeCSI o6paw.alOT BHHMaHHe Ha H a 3 B a H H e K H H r H, T H T Y .n b H bl it H C T - 9TY, no onpe,neJIeHHIO B. <I>aBopcKoro, .D.Bepb, «aBIlIYIO B03MO>KHOCTb 3arJISlHYTb B HYTPO KHH- rR», n p e .lI- Ii C J) 0 B H e H n 0 C JI e C JI 0 B He, 0 r JI 8 B JI e - H H e "JIH C 0 ,ll e p )I{ a H H e, M JI JI 10 C T P 3 U H H. LlJlH TpeTbe- KJIaCCHHKOB 3THX npHMeT (H TepMHHOB) BnOcl1He ,nOCT8TOQIlO. Yl\1eHHe nOJJb30BaTbCH HMH n03BOJIHeT peoeHKY c,ne.1JaTb BbI60p KHHrR Jt,'Ui 1J:Te- HHH MOTHDHpOB8HHbIM H IJ.eJJeH3npaBJIeHHbIM. HanpHMep, nepe,A Y1l31..U1il\fHCH KHHra ,nJUI qTeHHH 3. BocKpeceHcKoH CKOCTPbl». no na3BaHHIO KHHrH TpeTbeKJIaCCHHKaM Tpy,ltHO OnpeJleJIHTb cOllep>KaHHe. OUH MorYT BcnOIHHTb, lITO 30 HBaHOBHa BOCKpeceH- CKaH IIHWeT KHHrH 0 }KH3HH peOHT, HanpHMep «JIeHHBoe COJIH1\e». 1\\0- >KeT, M KHHr3 «KOCTPbl» 0 pe6HTax?.. Ho Ha nepenJleTe H306pa>KeH B. H. JIeHHH; OTCIO)\a npe,nnOJIO>KeHHe: ,llOJDKHO 6mb, 9Ta KHHra 0 B. 11. JIeHHHe. C,lteJIaHHOe npe,nfiOJIO>KeHHe nOJlKpenJIHeTCH H CCbIJI- KOH Ha 3HaKOMYlO .neTS1M no I-II KJIaccy KHHry 3. BocKpeceHcKoH . 1 I1MeloTcH B BHAY KHHrH-cnpaBo'tHRKH THna «Cnymy CoBeTCKOMY CoI03Y» HJlH «11po Terpa.ltb 11 KapTY, KapaH,lJ.aw H napTY» r. IOPMHH8, cOpo re6B CaMOrO) A. ,Qo. POXOB8, cB Bo,ae H Y BO.l1bI» H. OCHnoBa, «Mope JJ.bSlBOJlD B. MaJlbT H no,aOOHble. 8 M., «npoCBeIneHHe), 1967 II CJleJ{. . - :8 HHTepeCHbIA onbIT pa60TbI c "ra3eToH «nHOHepCK8B npaB.n.a» onaC8H YQHTeJ1b- HHu.eft 10. <P. JI.auH9JUIH. CM.: «Ha'lanbHaSi WKOJIa», 1970, lfg 5. . 4 CM. CT. H. M. ,l1PY>KHHHHOH. «HaqaJlbHaS WKOJIa., 1971, .N'! 1. 62
«CeKpeT», re paCCK83bIBaeTCH 0 CeMbe Y..TIbHHOBbIX, . CJIe.l(OBaTeJIbHO, 30R HBaHOBHa BOCKpCCeHCK8H nHWeT KHHrH He TOJIbKO a )l.eTHX; y Hee ecTb npOH3Be,Z(eHHH, nOCBSlIlI.eHHbIe BO.>K,lllO peBOJHOII.HH B.. H. JIe- HHHY. THTYJIbHbIH ..'1HCT H HJlJIIOCTpaUHH nOJtTBep}K8IOT nepBOHaQ8JIb- HYIO ,Z(oraKY: Ha THTYJIe eCTb nO;\38rOJIOBOK «PaccKa3bI 0 BJla)l.HMHp l1J1bHtle JIeHHHe»; lIa PHCYHK8X B0J10JtH Y JIbHHOB - WKOJIbHHK (rH\'l- H83HCT), nOTOf.,1 IOHOllia. A B KOHne KHHrH - BJlaHl'iIHp HJlbH'I T3- KOft, KaKHM MLI ero npHBbIKJlH BH,neTb Ha KapTHHax, <f>oTorpa<f>HHX.. OTCIO,Z(a C&l1e,lJ.yer BbIBO: HaBepHoe, 'a KHHre paCCKa3bIBaeTCfI 0 pa3Hbl x nep"oax }KH3HH BO>KD;I. 9TOT BbIBO HaXOHT nO,Z(TBepm)J.eHHe B ripc- HCJlOBHH K KHHre. 113 Hero )'llaInHeCH Y3H81OT TalOKe H 0 TOM, qTO KHHf, nOCBHllleHHblX BJIa,lI.HMHPY H.nbHIIY, ero ceMbe, B TBopllecTDe 3. 11. BocKpeceHcKoH Hel\18J10: 9TO H paCCK83bI, o6-beJtHIIeHHbIe 06- lll.Hf Ha3B8HHeM «CKB03b .ne,ll.HHYIO MrJlY», H nOBeCTH «BcTpetla», «Cepue M8TepH». B C6opHHKe, KOTOpblH aHaJIH3HpyIOT yqaInHecH, ,10 paccK330B 0 B. H. JIeHHHe (KOJlHqecTBO paccKasoB JIerKO onpe,neJ1HTb no orr}aBJIe- HHIO B KOHue KHHrH). H83B8HHe C60PHHKY ,naHo' 110 O,lJ.HOMY H3 BKJ11O- qeHHbIX B Hero p8CCKa30B (BepOHTHO, aTO 01JeHb B8)KHb1H paCCKa31 KCT8TH, OH H caMbIA 60JIbllIOH, qTO MomHO TO}Ke onpe,ne..TJHTb no or- JIaBJIeHHID). . PHCYHKH CeJl3HbI XYJtO}KHHKOM 11. [pHHWTeUHOM, II, 'CY,Z(H no HHM, B KHHre HeMo 3axBaTwBaroHx 3nH30oB. Jl.eTH HenpeMellHo 06parnslOT BHHMaHHe H na TO, )I.u'UI Koro npeJ{- Ha3HaqeHa KHHra; 06'bSlCHH1OT, K8K OHH 3TO OI:IpeJteJIH&'''IH. TaKOR ho/i.- XO K aHaJIH3Y HenpOIlHTaHHOH KHHrH COBepmeHIIO Heo6xo.llHM HJ TpeTbeM roy °OOY1JeHHSI. Beb B 3TO BpeMSI, K8K Y>Ke rOBOpHJlOCL, yqaInHeCH nOCTcneHHO npHooraalOTCH K qTeHHIO OTetleCTBeHHOH H 33- pyoe1KHOH JIJ-ITepaTypbI, H. )J.o.'Ir YQHTeJ1H - HaY1JHTb TpeTbeKlIaCCHH- 1<08 tIHTaTb TOJIbKO OCTynHble HX B03.p8C1'Y npOH3BeeHHH (B H3,Z1,aHH- HX ,nJIH JJ.eTeH HJIH B COOTBerCTBHH C peKOMeH..naTe.'1bHbIMH CfiHCK8MH). , ¥Qa1l{HecH K TpeTbeMY rOJlY o6YQeHHfI HaKOfiHJIli AOCT3TOtJHO Ha6JI1OeHHH, tlTOObl Y HHX MOJKHO 6bIJIO CcpOp:\IHpOBaTb rrepBHtlHoe nOHflTHe 0 cepHHX KHHr. Ha nepcn.TJeTaX, THTY.TJbHbIX 7IliCTaX, 06- JIO>KKaX KHHf, peKOieH,nOBaHHbIX ,lJ..'1H tlTeHHH.. yqaIltHecH nOCTO.H HHO BCTpeqa.HHCb C HaJ\nHCfliH: «30T)OTaH 6H6JIHOTeKa», «j\10H nepBble }{HHjKKH», «Bu6J1HOTeQK8 )l.eTCKOrO C3a», «CKa3KII ,nPY>KllOH ceMbH», «t..IHTaeM CafH», «KHHra 3a KHHfOH», «3HaH H YMeH», «B03bMH C co60il B .TJarepb» H T. n. Tenepb npliWJ10 Bpel\tfJ1 Y3HaTb, 'ITO 3TO - H83BaHBH pa3J}HqHbIX cepHH KHHr, BbInYCKael\fblX HallIHMH H3A3TeJIbCTB8MIf. C e p II 51 - 3TO noc.neOBaTeJIbHbIH pHA Qero-Hu6YJ\b (B HaLUeM CJIYQae p H Jt K H H r), 1JTO oOJI8,naeT 061UHM npH3HaKOM, 0 6 'b e A H- H e H 0 0 6 m. If 1.1 H 8 3 B a H Ii e M, COCTaBJlHeT OHY rpynny (eM. CJIOBapb pYCCKoro H3blKa C. 11. OJKerOBa). CymecTByeT llel-tfaJIO cepaii KHl1r. Ka8H CCpHfI paCC1JHTaHa H8 onpe.neJ1eHHblfI B03paCT, nOAfO- TOBJleHHOCTb H HHTepeCbl QlJTareJIfl. 0 TOM, Kaoe E,,'lHHHUe Ila CHcrc. 63..
. MaTH3aUHIO, tlTeHHH MO>KeT OKa3aTb BHHMaHHe K KHHfaM onpe,neJIen- HoA CepHH, nOK83hLBaer aHa."H3 cepHU «4HTaf CaMH». 3Ta cepltH H3qaJla H3;l1aBaTbCH B 1965 r. OTKpbIBa.TJa ee KHHra paCCKa30B B. )l(HTKoBa «nOMOIUb H.lI-eT» (M., «lleTcKaH JIHTepaTypa», 1965, 31 CTp. C HJlJIlOCTpanHHMH, THpa>K 600 000 9K3., u.ella 6 Kon.). 3a HCTeKWHe 5, neT B 910ft' cepitH BbIlllJIO 60JIee 40 KHIi}KeK. ALlpecoBa- Hbl OHM HaqHHalOIneMY qliTaTeJIIO. B KHHrax cepHH «4HTaeM CaMH» npe,ACTaBJIeHbI xy JtO>KecTBellllbIe npOH3Be,AeHHH caMblX pa3HblX BH,AOB H >KaHpOB, Ha carvlbIe pa3Hble TeMbl, II HanHcaHbI 9TH npOH3Be,11.eHHH OqeHb XOpOIlIHMH nHCaTeJIHMH. TOT, KTO npOqTeT Bce KHHiKKH 3TOH ce- pHH, n03HaKOMHTCH co CTlixaMH A. BJ10Ka, H. 6YHHHa, C. l1po}K}KU- Ha, C. EceHHHa, JI. l\\efl, C. MapmaKa, A. K. TO.TJCTOrO, A. nYIlI.KH- Ha, A. OJI eIneeB a , A. cI>eTa, E. BJIafHHHHoi1:, H. CaKoHcKoH, npH06.. llurrcH K np03e C. AKcaKoBa, B. BepecaeBa, H. -FOrO.1IH, .a. MaMHHa- CH6npHKa, JI. TOJICTOrO, M. npHWBliHa, B. )l(HTKoBa, A. raH.llapa, A. KOHoHoBa H JI.p. 3ra <;epHH 3HaKOMIIT HaqHHalOIII.HX QHTaTe.ileu c MHpOM KHHr Boo6IIJ.e. 06 HcropHH pOJtHOH CTpaHbI TpeTbeK,HaCCHHKH Y3HalOT H3 CepHH CMaJIeHbKaH HCTOpHtlecKaH 6HonHOTeKa»; 0 repOHX paccKIDKYT HM KHH- rH cepHH «repOHtlecKHe 6Horpa<l>HH», 0 nOBHrax cOJI.AaT3aw.HTHHKOB POJXHHbl peoHTa Y3Ham 83 cepHH «CJl8Ba COJIAaTCKaH» "u T. n. Cne,!tOBaTeJIbHO, I1pHHaJIe>KHOCTb KHHrH K" onpe,u.eJ1eHHOH ce- pHH - 9TO H JtonOJIHHTeJIbHhlH npH3Hax, nOK33bIBaIOInHH, KOMY KHH- fa apeCOBaHa, KaKOBO ee Ha3H.aQeHHe, H H3secTH&S rapaHTHS CHCTe- MbI B Cal'ttOCTOHTeJlbHOM IITeHHH no HHTepecyeMY IOHoro tlHTaTeJIR BOnpocy. KaK nOKa3blBaeT OfiblT, 3a,naQa coopaTb B KJIaCCe KHHrH XOTH 6y JtHOH KaKOH-TO cepHH QtleHb YBJ1eKaT pe6HT H npHHOCHT HeMao nOJIb3bI. nOJJ-6HpaH KHHfH )lJIH llTeHHH Ha HY>KHYIO TeMY, ytlaInHecH I I f' \ KJlacca )llKe He MOf'YT paBHOYllltlO OTKJIMblBaTb B CTOPOHY Te KHHrH, , u u KOTOpble X01'R. H He Ha TeMY, HO no CBoeH n03HaBaTe.,1bHOH Ii 3MOnHO- u HaJJbHO-9CTeTHtleCKOH HanpaBJIeHHOCTH COOTBeTCTBYIOT JH-IIIHblM BKY- e3M caMoro pe6eHKa H.TJH KorO-oI'H60 H'3 ero TOBa.pUllI.eii. Yq1UHeCH OOSl3aTeJIbHO 3aIIHCblBaKYr Ha3BaHHH 9THX KHHI' Ha KapTOqKY H HHcJ>Op- NH,pyIbT 0 HHX BeCb KJlaCC, a H3 KapTOqeK COCTaB.11HlOT KJIaCCHYIO Kap- roreKY (no TeM3M). B npou.ecce pa60Thl YleHHe qHTaTb KaTaJlO}KHYIO KapTOqI<Y Ii npaBHJIbHO 3anHcaTb KHH-ry, KOTopoe CctJOptHpOBa.HOCb 80 I I KJI3CCe, Ha TpeTbeM ro..ny 06yqeHHH nepeXOJI.liT 8 HaBbIK. 06p.a3eI.1 sanHCH KHlif-H H3 KapTOqKY B I I I KJIaCCe OCTaeTCH nOQTH npe>K H U1'iI: KynpHH A. 11. 4YIlecHblH AOKTOp. PaCCK33b1. !tJ1i1 MJIa)t- mero WKOJIbHOrO B03pacTa. PUC. B,. llIaxo- B8. hi., «Ller. JIHT.», 1969, C. 30 (cepHH «KHHfa 3a KHHrOH»). 64
KaK BH,ZtHO H3 npHBe,l1eHHOrO npHMepa, B 3anHCH ,A06aBJlHIOTCH Ii HHUHaJIbI nHCaTeJIH (HerrpeMeHHO nOCJIe <pat.tHJIHH!), YKa3aHHe, )J.JIH KOrO H3,l1aHa KHHra, H CepHH, ecJIH KHHra BXQAHT B KaKYIO-TO ce.. pHIO, a TaIOKe o6oeM npOQHTaHHOH KHHrH (KOJIHlIecTBO CTpaHHn). KaK H BO I I KJIaCCe, KapTOllKa M01KeT 6h1Tb HJIJIIOCTpHpoBaHa l . K KOH- uy rOJla Ka>KAbIH TpeTbeKJIaCCHHK ,AOJI>KeH CYMeTb cocraBHTb H 3a- nHcaTb KpaTKHH OT3bIB 0 KHHre, KOTOpylO OH ClIHTaeT Ba>KHOH H HH- TepecHoH. nHCbMeHHblH OT3blB - 9TO Tome JIHWb 0606w.eHHe tex SHaHHM H YMeHHH, KOTopbIe HaKOnHJIH YlIarnHecH 3a ,nBa ro,na pa6arbl C KHHrOH. BeAb, onpe,lI-eJIHH cO,Ztep>KaHHe He3HaKOMblX KHHrt YllamHeCH nOCTOHH- HO OTBeqaJlH Ha Bonpoc: «0 lIeM 3Ta KHHra?» B I KJlaCCe Jl.eTH COOTHO- CHJlH KHHry C onpe,ZtMeHHoH TeMo1% IITeHHH, BO II-npHyqaJIHcb ,ZtaBaTb pa3BepHYTblH YCTHblH OTBeT B 1-2 npJIO>KeHHH. npH 9TOl\f YlIHTeJ1b BHHMaTeJIbHO CJIeJl.H.1J 3a TeM, tlTOObI B OTBeTax .lI.eTH lIe OrpaHHIIHBaJIHCb nOBTopeHHeM Ha3BaHHH, a CTapaJIHCb KpaTKo nepe,ZtaTb cO,Aep>KaHne KHHrH. TaK, YiKe BTOpOKJIaCCHHKH 3HalOT, 'lTO CKa3aTb (HJIH HanHcaTb): «KHHra AH,AepceHa «l!IOHl\IOBOqKa» 0 LlIOHMOBOtlKe», 3Ha1lHT HHtlerO He CKa3aTb. Ha,no, tIT06b1 H3 OTBeTa 6bIJIO HCHO, 0 lIeM 9Ta KHHra H HHTe- peCHaH J1H OHa. HanpHMep: «AH,ZtepceH. «):bOHMOBOtlKa». 3To KHHra o npHKJII01JeHHHX Ma.'1eHbKOH CKa30tlHOH ,AeBOIlKH. npHKJIlOlIeHHSl B CKa3Ke pa3HbIe: H rpYCTHble, H BeceJlble». I1J1H: «8 KHHre paccKa3bI- BaeTCH 0 MaJleHbKOH ,A06pOH ,AeBOqKe, 0 oe,ZtHoH JlaCTOllKe, 0 cepoH MbIllIH H 0 npoTHBHOM KpoTe» H T. n. OnHpaHcb Ha YCTIIYIO norOToBKY H 3HaHHH yqal..UHXCH D 06JIaCTH PyccKoro Sl3bIKa, YllHTeJlb 06YtlaeT TpeTbeKJIaCCHHKoB TO¥Y, KaK Ha,AO nHcaTb KpaTKHH OT3bIB 0 KHHre. Or3bIB .lI.OJliKeH OTBellaTb CJle,AYlOrnHM Tpe6oBaHHHM: 1) 6bITb npeJl.eJIbHO KpaTKHM (2- 3 npeMO>KeHHH); 2) cO.llep*aTb TOJ1bKO cal'lloe BaiKHoe, panH tlero HanHcaHa KHHra (lIe.TJb35J .ll.onycKaTb nopot5Horo nepecKa3a cO.ll.ep>KaHHH KHHrH H paccKa3a 0 TOl\I, qeM oila KOH1.J:ae'fCH); 3) BKJIlOqaTb BbIBO,lt 0 TOl\f, 1Je1 rioHpaBIIJIaCb KHHra (9TO Tpe60BaHHe lie 06H3aTeJIbHo, HO meJ1aTeJlbHo). HanpHMep, COCTaBJIHeTCH OT3bIB Ha KHHry JI. )l(apHKoBa «no- CJle.ll.HHH HOtlb». Ope>K)le Bcero CTaBHTCH Bonpoc, a tleM 9Ta KHHra, H YllaIUHeCH npo- C>YIOT KpaTKO OTBeTHTb Ha Hero CHaqaJIa KOJlJIeKTHBHO B YCTHOH 4>opMe: «:7ra KHHra 0 rpa>KjlaHCKOH BOHHe, 0 KpacHbIX Ii 6eJIblX, 0 MaJlbtlH- Kax, KOTopbIe nOMOraJIH KpacHbIM 60pOTbCH 3a COBeTCKYIO BJlaCTb, Y t IHJ1HCb B 9Ton OOpbOe MYiKecTBY H craHOBHJIHCb repoSlMH HJlH npOCTo BblpaCTaJIH XOpOlllHMH ...'1IO,l{bMH». (OT3bIB 3anHCblBaeTCH YIIHTeJleM Ha JtOCKe.) 1 ....IJIJI(OCTpall,HS1 pa3MeaeTCH no;t aanHCblO, H pa3Mep KapTOQKH COOTseTCTBeHHO yneJ1l1 t IHSaeTCH. ' . 3 3aKaa 694 65
3aTe1 CY)K,lleHHe 0 KHHre yqanUieCSI COnOCTaBJIHIOT C npe,ZUiCJ.tQ- BHeM K HeM, 11 T06bl cOKpaTHTb H.TJH YTOtlHMTb 3anHCb. «nOCJIeJlHf.UI HOtlb»_- 3T0 paccKa3 0 C06b1THHX rpa>KJlaHCKOH BO- HhI B ,noH6acce. B HeM nHCaTeJ1b JIeoHH,ll MHXaHJIOBHtI )l(apHKoB pac'" CKa3blBaeT 0 nO,llBHre ,llBYX MaJIbtJHKOB, 06 HX Kpa6pocTH, 6ecnpe.neJIb- HOM npe.llaHHoCTH H JHo6BH K CBoeR POJlHHe, KpacHoH APMHH, 06 HX nOMOInH KpacHoapMeHuaM B oopb6e C 6enorBapAeAuaMH (CM. npeH- CJIOBHe K KHHre - M., LlerrH3, 1957). HCnOJIb30BaB npeJlHCJIOBHe, YtlarnHecSi MorYT BHeeTH B 3anHCb C B 0 e 0 THO III e H H e K n pOll H T a H H 0 MY, H3feHeHHH Ii COKpameHHH: . «91'0 zpycmHblu H eepOUfteCKUU paCCKa3 0 C06bITHSIX rpaiKaHC.KoH BORHbY, 0 nOMOInH ,nBYX MaJIbQHKOB KpaCHoapMeHU8M B 6opboe C 6e.no- rBapAeiiuaMH, 0 nOO8U2e oOH02O. U3 HUX». (3Ty paOOTY K8>K,llbIH yqeHHK BbInOJIHHeT HH)J.HBHAyaJIbHO.) HaKOHeu, IIHTaTeJIb MO}KeT BKJIlOtlHTb B OT3bIB K8KOH-TO He6oJIb- woA, nopa3HBWHH ero OTpbIBOK H3 KHHrH, a saTeM Bblpa3HTb CBoe OT- HoweHHe K C06bITHSlM: «TbI HHtlerO He OOHCH. B Te6H crpeJIHIOT, a TbI H,ltH! Te6e 60JlbHO, a TbI He nJIallb!..» , TaKHM 6b1JI -BaCbK8, repoA 3TOM KHHrH. 3TOMY OH ytlliJl CBoero J1pyra. 3TOMY nOCTapalOCb HaYllHTbCB H JI» (AH.ztpeif J1.). A BOT 0 TOM, 'ITO BaCbKa nOfH6, B OT3bIBe nHcaTb He CJIe,llYeT. Or3blB Ha KHHry )VIB KJIaCCHOH KapTOTeKH nHweTCSI H8 060pOTe KapT01JKH. nQ,lt HHM YKa3bIBaeTCH, KeM H3 ytleHHKoB OH COCTaBJJeH. Ho npe... qeM O<jJOpIJUITb KapTOtlKY, ytleHHK 3aOHCblBaeT CBoe CY>K- AeHHe 0 KHHre Ha OT)leJIbUbIH JIHCT ()YMarH, nOK83blB8eT ero" TOBapH- InaM, ,naeT Ha npOBepKY ytlHTeJIlO HJIH BO>KaTOMY H, TOJIbKO BHecSi Heo6- XO,llHMwe HCnpaBJIeHHB, nepenHCbISaeT Ha KapTOllKY. ToponHTbCSI, r HaT b C SI 3 a K 0 JI H tJ e C T B 0 M OT3b1BOB, ,nonYCKaTb Heopem- HOCTb B cxJ>opfJIeHHH (OCOOeHHO opcporpacJ>HlIeCKHe oWH6KH!) Hli - B KoeM CJIYtlae HeJlb3H. ToqHO Tal<: me, HCnOJIb3YH 3an8C Y)Ke HMelOInHXCB Y AeTeH CBe.ne- HHH H npeCTaBJIeHHH, YQHTeRb nOBOJlHT TpeTbeKJIaCCHHKoB K nep- BUtlHblM o606m.eHHHM, KaC8101Il.HPvtCH CnpaBOtlHOH JIHTepaTypbl. CorJIac- HO Tpe6oB8HH,SfM nporpaMMbl, ytlaIl(HecH III KJIaCCa K KOHny rO,lla ,nOJI>KHbl 3HaTb B8>KHeHWHe OTJIHlIHTeJlhHbIe npH3HaKH CnpaBOtlHOfi JIHTepaTypbl H YMeTb nOJIb30BaTbCB ,nocTynHbIMH cnpaBotJHblMIi KHH- raMH. Ytl8111HeCH J10JI}KHbI ycnoHTb, 1.JTO CnpaBOQUaH JlHTepaTypa- 9TO KHHrH, npeAH83HatleHHble ,It JI Sf 6 Et C T P 0 r 0 nOJIYtleHHSI - Ka- KHX-JIH60 cBelteHHH. CnpaBollHYIO RHTepaTYPY (CJIOB8pH, SHUHKRone- JlHH) He tlHTalOT OT KOpKH AO KOpKH (XOTH H B 9TOM HeT HHlIerO npe.llo'" CY,llHTeJlbHoror), a OTKpbIBalOT 1Ia HY}KHOH crpaHHue H no.nyqalOT Heo6xo,ltHMYIO HaYtJHYIO HJIH npHKJlaJlHYIO HH<I>oPManHIO. lJTOObi H8 nOHCKH HY>KHhIX cBeAeHHA 3aTpallHBaJICSI MHHHMYf Bpe- MeHH, CnpaB01JH8B JIHTep8Typa HMeeT OTJJHlIHYIO OT Bcex npOqHX KHHr CTPYKTYPY: B cnpaBOtJHOH ,KHHre 06R3aTeJIblJO eCTb Y K a saT e JI b, 66
KOTOpbIH nOMOraeT OTbicKaTb HY>KHoe CJlOBO; TeKCT KHHrH COCTOHT H3 He60JIbWHX no 06'beMY CTaTeH Ka>K,lJ.aH 83 KOTOpblX nOCBHIlleHa KaKOMY-JIH60 HUY, HBJIeHHIO, COObITHIO, npe.AMeTY1. A TaK KaK Bce HBneHHH, JIHna H npMeTbl Ha3bIBalOTCH CJIOBaMH, TO ,nJlH 6h1CTpOTbI nonb30BaHHH CnpaBOQHOA KHHrOH enOBa B HeA pacnonaraIDTCH no an- cpaBHTY. B YKa3aTeJIe CJlOBa TaK>Ke pacnOJIaraIOTCH no an<paBHTY t KpOMe Toro, TaM ,nalOTCH CCblJIKH Ha CTpaHHUY (HnH CTpaHHUY H TOM, ecJIH CnpaBOtiHaH KHHra B HeCKOJIbKHX TOMax) , r,ne HanetlaTaHO HY>K- Hoe CJIOBO. CTOHT TOJlbKO nonpaKTHKOBaTbCH, H HaxoJ1HTb TO HJIH HHoe CJIOBO B YKa3aTeJle a 38TeM COOTBeTCTBYIOII1YIO CTaTblO B HHre 6y,ne-r OqeHb HHTepecHo H JIerKO. KOHeIlHO, JIIOOaH KHHr8 .llaeT 3H3HHH. OcotSeHHO neHHoii B 9TOM OT- HomeHHH HBJJHeTCH HaYQHO-n03HaBaTeJlbHaH JIHTepaTypa. ECJIH YMeJIO nOJIh30BaTbCH OrJIaBJIeHHeM H JJ.pyrHMH cnpaBQtlHbIMH 9neMeHT8MH Ha- YQHO-n03HanaTeJlbHOH KHHTH, TO K Hen YtlaIUHeCH MorYT 06parnaThcH 3a OTBeTaMH na HHTepecYlOmHe HX BonpOCbl. O,nHaKO ,nOCTaTOtiHO cpaB- HHTb, HaCKOJIbKO y,nOOHee HCKaTb OTBeT, CKa>KeM 0 }l{H3HH 3aH- qaT, B MaJleHbKo:A: 9HUHKJlOne,nHH.JO. ,nMHTpHeBa «KTO B Jlecy >KHBeT H 'QTO B JICCY paCTeT», qeM B KHHre Toro >Ke aBTopa «PaCCK33bI MoeH nOJIH HI\H»2, tlT06bI He06XOHl\fOCTb BblJ1eJ1eHHH H3 Kpyra .lleTCKHX KHHr cneUHa.'lbllOH CnpaBOtiHOH JlHTep3Typbl CTaJ1a OtleBH.llHOH. C 3To:li UeJIblO B KJIaCCe Ha,no opraHH30BaTb nOCTOSIHHYIO BblCTaBKY CnpaBOqHOH JlHTepaTypbI, 1JTOObl yqaI.I(HecH npHYtlaJIHCb nOJIb30BaTb" CH CIO no Mcpe Ho6HOCTH. ITo >KeJlaHHIO yqHTeJlH BblCT3BKa MO>KeT OblTb OnOJIHeHa CJI0B8- pSlMM, H3npHMep BeCbMa yMecreH H3 9TOH BblCT3BKe Optporpa<pHtieCKHH CJ10Bapb Lt. H. YmaKOBa H C. E. KpIOIIKOBa, reorpa<}>HtJecKHH CJIOBapb C. B. AranOBa, C. H. CoKOJIOBa H .a. H. THXOMHpOBa, CnoBapb PYC- CKoro H3blKa C. H. O>KerOB3 H T. n. 13 KaqecTBe ocoooro pa3,neJIa Ha BbICT3BKe MorYT 6bITb npe,nCTaBJIC- IIbl HaYQHO-rr03HaBaTeJIbHbIe KHHrH, He HBJ1S1IOIlI.HeCH cnpanOtlHbIMH no CTpYKType, HO COCTOHIIJ.He 1-13 He60JIhllIHX paCCKa30B, B KOTOpbIX MO>KHO, nOJIb3YHCb OrJlaBJIeHHeM, 6blCTpO HaHTH OTBe Ha HHTepecylO- InHA Bonpoc. K TaKHl\1 KHHfaM OTHOCHTCH: B apT a H b H H 3. 113 >KH3HH CJIOBa. M., «eTCKaR JIHTepaTY- pa»,- 1960. A K H M Y III K H H H. I1nJtpHK - 3Bepb, pHC. r. HHKOJIbCKoro. M. , «13J1 bUll», 1968. 1 )leTcKan cnpanOIJHaR nHTepaTypa OTJlHqaeTCSI OT cnpaBOtlHblX H3,!laHHH .l1JUI 83pOCJIblX B OCHOBHOM xapaKTepOM CTaTeA-cnpaBOK: 3TO, KaK npaBHdo, x y .n 0 >K e- C T B e H H 0- n 0 3 H 8 BaT e n b H hi e paCCK83bI, HO KpaTKHe H ue.neHanpaBJIeH- Hye. 2 CM. TaK>Ke KHHfH 0 CoBeTCKoA ApMHH: C. B a p y 3 JJ. H H. llIeJl no ynHu.e COM8T; r. 10 p M H H. Cnymy Coae-rCKOMY CoIOSY. KOHeQHO. o6e KHHrH MO>KHO qH- T8Tb OT Ha1faJIa )10 KOHu.a, HO MSI nOJlyqenHR cee.l1ellHA no OT,D.eJIbHLlM BOnpOC8N 60- JIee yo6Ha BTopaH KHHra. 3* 67
,Ll M H T P H e B 10. ,llecllble 3araAKH, pRC. A. KCJIeHHHKOBa. M., «J].erCK8H "JIHTepaTyp8», 1967. . P >K e B C K H H B. OWH6K8 KOpOJUI aoonapKOB, pHC. r. HH- KOJIbCKoro. M., «MaJIbIw», 1966. H T. n. Pa60Ta co CnpaBOQHOB HTepaTYPoH 06lltero H qaCTHOfO xapaKTe- pa ,lI,M8er He06xo,lJ.HMbIM H cBoeBpeMeHHblM 3HaKOMCTBO TpeTbeKJIaC- CHHKOB C netJaTHblMH peKOMeH,lI,aTeJIbHbIMH YK83aTeJISlMH NUl MJIa,lJ.WHX WKOJIbHHKOB - C KHHraMH 0 KHHfax. TaKHx }:Ka3aTeJIeH cymecTByeT HeM8JIO, H8npHMep: «KHHfH 0 TBOHX APY3hHX-pOBecHHK8X», COCT. JI. Mei1epOB8. JI., .llerfH3, 1961.. . - «no pO,lJ.HOH CTp8He», COCT. H. BOHneXOBCK8H, J1. JlonaTHHa. JI., ,LleTrH3, 1959. «KHHfH 0, npHpO)(e», COCT. O. XY3e H .lI. MeiiepoBa'. JI., .LlerfH3, 1957. «0 HBmeA POAHHe, 0 .Hac. PaCCK83bI 0 KHHfax», COCT. K. lUHeH- Aep. .11., «.!leTcKaH JIHTepaTypa», 1966. «lITO" 'lHT8Tb», COCT. B. fpeBCKaB, r. naTbIHCKaH. M. , «JleTcKaSl JIHTep8Typa», 1969. H T. n. l . B KIDKAOH H3 3THX 6powIOp nocJle He6oJJhWOrO npe)(HCJIOBHH npH- BO)UlTCH cnHCOK KHHr no oAnoB HJIH HecKOJIbKHM TeMaM. llpH 9TOM co- Aep>KaHHe Ka>KAOH KHHrH (HJIH pHAa KHHr) pacKpblBaercff KpaTKo, HO YBJIeKaTMhHo. np01JHTaB onHcaHHe peKoMeH)toB8HHbIX KHHr, lIHT8- TeJIb OCMbICJ1eHHO BbioepeT Te KHHfH, KoropbIe era aaHHTepe.. cYIOT. KpOMe TOfO, yqaInHecH nOCTOSlHHO BCTpeqalOTCH C pa3JIH'lHOfO pOAa peKOMeH,lJ.aTeJJbHblMH cnHCKaMH B KHHfax (Ha 06JIo}KKax, Ha cne- I1.H8JIhHbIX.. CTpaHHIJKaX, 3aBepW81OHX KHHfY H npe,nWecTBYIOIIUIX nepenJIeTY), B >KypHaJIaX -«nHOHep», «Kocrep», «IOUblH HaTypaJIHCT»t B r83ere «nHOHepCKB npaB,na». Ooparn8Tb BHHM3HHe AeTeH Ha 3TH CnHCKH, 8n8JIH3HpOBaTb HK HanO npH Ka>K.nOM YA06HOM cJlyqae. BRH.; MaHHe K peKOleH,ltaTeJ]hHOH 6H6JIHOrpa<pHH - 38JIOf TOfO, tITO HaIlH- H810JnHH tJHTaTeJIb BCefn8 6y.ner B Kypce KHH>KHhIX HOBHHOK, 1IT0 Y Hero Ha npHMeTe nOCTOHHHO 6YYT KHHfH, KOTope HHTepecHO npo- tJHTaTb, 8 3HaQHT, HHKOf,lI,a He oyj(eT nepepbIBa B tJTeHHH H3-3a TOfO, qTO «Bce npOtJHTaJl» (HBJIeHHe, K OO>KaJIeHHIO, elI.{e OQeHb 1I8CToe B Ha- qaJlbHOH WKOJIe). PerYJIBpHO 'lHTaH ,lJ.eTCKYIO. nepHOJ{HKY, ytlaInHecSi OObItJHO cnpa- lliHBalOT Y1JHTeJIB, K8K npaBHJlbHO 3anHC8Th nOHpaBHBWHHCH 8 }KYP- H8J1e paCCKa3 HJIH fa3erHYlO CTaTblO, H oe3 oco6oro Tpy,na OBJIaneBalOT CJ v HaBbIKaMH rrpOCTeHweH 38nHCH: .. 1 B tJlyqae, ecJIH. nOAo6Hhle YKa3arenH B uiKOJJbHOB: 6HMHOTeKe OTCYTCTBYIOT, MOEHO BOCnOJIb30BaTbCSI ny6nBKaIUlSlMH >KypRaJla «Hatl8JIbHag WKOJIa»: «KHHrH 0 B. M. JIeHHHe Hero copaTHHKan (1969, Hi 8), cOKTJl6pb waraeT no CTpaH8 (1969, N2 11), «)I(HTb - PO.ARRe CJIY>KHTb» (1970, Nv 5), npeBpaTHB HX B KHH>KKH-caMO- Jl,e.. 'J KH. 68
PaeBCKHH B. Cal\10e CTpalllHOe. PaCCKa3. PHC. B. BecKa- paBaiiHoro (>KYPHaJI «Kocrep», 1968, N!? 8, c. 24-30}. 11J1 H : 4YPHJlHH B. KaK OhlJl BhlBe;teH Ha OPOHTY £0103-9» (ra- 3eT3 «nHoHepcKaR np3BJla», 1970, 5 HIOHH, C. 2). OpraHH3aUHOHHO-MeTOAHQeCKaH CHCTeMa P Y K 0 B 0 C T 8 a C a M 0 C T 0 H T e JI h H bI M JJ. e T c oK H MilT e- H HeM B I I I K JI a C C e B OCHOBHOM coxpaHHeTcH B TOM >Ke BHtl-e, liTO H Ha npeJlweCTBYIOll\HX 9Tanax 06yqeHHH I . B TelleHHe YQe6Horo rOJla CHCTeMaTHQecKH npOBOJJ.HTC ypOKH BHeK.'1aCCHOro tITeHHR. Ha ypOK3X no,nBOHTCH HTorH paOOTbl C KHHfOJ; 3a npowe,nIllHH nepHO,n, <P<>pMHPYIOTCH HOBbIe 3HaHHH H YMeHHH H ,naeTCH 3a,naHHe Ha CJIe,nYIOll\He ;tBe He,neJIH. B npOMe>KYTKe fe}K,ny ypOKal\.IH BHeK..'IaCCHOro tITeHHH Yllaw.HecSi caMOCTOTCJIbHO -BbI6HpalOT H tIHTalOT KHHrH, ra3eTbI, >KypHaJIbi Ha onpe,lle.neHHYIO TeMY; YQaCTSYIOT B KHH>KHbIX BbICT3BKax, YTpeHHHKax, 9KCKypCHRX, TeMaTHQecKH CBR3aHHbIX C qHTaeMblMH KHHraMH. 3HaHHH H YMeHHH, npHoopereHHbte )J.eThMH Ha ypOKax BHeKJIaC- CHoro \ITeHHH H nYTet car.IOCTOHTeJIbHOrO tJTeHHH, npHBJIeK3IOTCS1 yqHTHMH Ha ypOKax no JJ.pyrHM npeAMeTaM (no QTeHH, npHpOJlO- Be.n.eHHlo, TPY.llY H T. n.). HeocJla6HO BeJJ.eTCH nporraraH,na KHHr B ceMbHX yqaInHXCH. Ho 8 OTJIHqHe or nepBoro H BToporo roa o6yqeHHR B opraHH3a- UHH caMOCTOS1TeJIbHOrO tIreHHH TperbeKnaccHHKoB B03HHKaeT HeKOTO- poe 3aTpy;tHeHHe, BbI3BaHHoe TeM, tfrO 8 I I I KJuicce ypOKH BHeKJlaC- CHOfO IITeHHH npoBoHTCH He K3>K;tylO HeJleJIlO, K3K BO II KJIaCCe, a lIepe3 He;teJIIO (T. e. O.llHH qac B Jl-Be He.n.eJIH, UJIB 18 qaCOB B ro,lt). 3ro 3aTpYJ1HeHHe MO>KIIO npeo.noJleTb TOJlbKO npH YCJIOBHH HMHBH;tyaJlb- Horo PYKoBo.ACTBa ,AeTCKHM 1ffeHHeM H Tll\3TeJIhHO npO;tYM8HHOH CHCTe- MOH JlotawHHX 3a,lt8HHH no BHeKJI8CCHOMY 'ITeHHIO. OqeHb B8>KHO, tlT06bI 9TH 3a;taHHH COOTBeTCTBOBaJIH n03HaBaTeJIhHblM HHTepecaM TpeTbeKJIaCCHHKOB: Be,nb «K8K H BCHKaS1 nOTpe6HOCTb, n03HaBaTeJlb- IIwii HHTepcc HMeeT orpOMHYIO nOOYJJ.HTeJlbHYIO CHJlY: OH 3acr3BJlH" 1 <:M.: c06Y'leHHe BO II KJiacce. KHHra AJUI Y1lH1-eJUI». M., CnpOCBem.eHHe) 1970, pa3A. «BHeKJIaCCHoe ,QTeHHe». 69
eT tIeJIOBeK8 aKTHBHO CTpeMMTbCH K n03HaHHlO, aKTHDIIO HCKaTb cno- COOLI H cpe)J.CTBa Y,llOB.'1eTBOpeHHJI B03HHKweH y Hero «>Ka)K)U:1 3Ha- HliS!» 1 . He Menee Ba>KHO, llTOObl B KJlaCCe 6bIJ1 C03,naH nOCTOHHHO ,lleHcT- BYlOrnHH «YronoK qreHHH». ,llnH Hero OTBO,llHTCH onpe,neneltHoe MeCTO ()J.OCKa H CTOJI "JIM nOJlKa), r,ne Ha OTJleJIbHOM nHCTe OYMarH BbIBeWH- BaeTCH nporpaMMa pa(5oTbi Ha TeKYInHe )tBe He,AeJIH, a TaK1Ke e1Ke,l1- HeBHO BbiCTaBJISUOTCH Bce MarepHaJIbI,. OTpa}KalOm.He pesYJlbTaTbI Bbl- nOJlHeHHH 9TOA nporpaMMbI: KHHrH, KOTopbIe tJHTalOT yqaInHecH no 33)J.aHHoA reMe, HJIJIIOCTpaU-HH, no,neJIKH B CB5I3H C qTeHHeM, HJlJlIOCTpH- pOBaHHbIe KapTOtIKH H OT3blBbI Ha npOtJMTaHHble KHHrH H T. fi. YtImnHe- <;H C 60JIbWOH OXOTOH ytlaCTBYIOT B T3KHX cBoe06pa3HbIX e>KeJ{HeBHbIX BbICT3BKax. npH 9TO OHH .o(5MeHHB3IOTCH tlHTaTeJIbCKOH HH<I>0pMal{H- eM, KHHraMH, KOTopble Y}Ke npOtlnH, H oroHpalOT C3fble HHTepecHble M3TepH8JlbI H8 OqepeJlHoH ypOK. B CTpYKType ypoKa HeKJIaCClIOro IITeHHH B I I I KJlaCCe, KaK npa- BHJlO, npeJI.ycMaTpHB31OTCH 3 OCHOBHbIX 3J1eMellTa: 1) OTLJeT ytiarnHxcH 0 pe3YJlbTaTaX caMOCTOHTMbHoro qTeHHH (B pa3J1HLJHblX <J>oPM3X: oece,na, Hrpa-copeBHoB3HHe, aHKTa, KJlaCcH<pH- Kall.HH npolIHTaHHoro no pa3HbIM npH3HaKaM, peweHHe KaKHX-TO no- 3HaBaTenbHblX 3a,Aaq H np.). npH OTBeT3X yqalll.HecR HenpeMeHHo HC- nOJIb3YlOT teKcTbl np01.lHT3HHblX npoH3Be,lleHHH. 2) 4TeHHe BcnyX HJlH paccKa3'YQHTeJIH, B nponecce KOToporo OH coo6ll1.3eT Y'lalll.HMCSI HOBbIe 3Ha'HHH, 3H3KOMHT ,l1eTeH C HOBbIMH npoHa- BeAeH!fBMH, nHCaTeJI5IH, TeMaMH llTeHHJI, cJx>PMHpyeT HX qHTaTeJlb- CKHe HHrepecbl. . 3) npaKTHqeCKHe ynp3>KHeHHJI, 3aKpenJlSllOlllHe Y TpeTbeI<JlaCCHH- KOB H3SbIKH H YMeHHH n 0 JI b 3 0 BaT b C SI K H H r 3 M H HOp H- e H T H P 0 BaT h C H B HHX. B KaqeCTBe npHMepa npHBeJleM ypOK Ha TeMY «raHAap - 60en H rpa>K,ltaHHH». IJ.eJlb ypOKa: npeJlCTaBHTh ytJaIUHMCH raA,napa - tIe- JlOBeKa H I OMMYHHCTa «OObIKHOBeHHOM OHorpa<p HeH B Heo6bIKHOBeH- Hoe BpeMH»; n03HaKOMHTb C KHHraMH 0 nHcaTeJie, C ero aBToGHorpa- 4>HeA, ,nHeBHHKOM, nHCbMaMH; 3aHHTepeCOBaTb tlTe.HHeM npOH3Be,Ae.. HHH r3H,Aapa H 0 raHJlape. B npeAWecTBYIOInee ypOKY BpeMH TpeTbeKJIaCCHHKH tlHTalOT pe- KOMeHJlOBaHHble HM KHHrH 0 raHJlape H npOHSBe,AeHHH nHCaTeJ1H (no COOCTBeHHOMY BbIOOPY). KHHrH, ra3eTbI, >KypHanbI H HJlJlIOCTpaTHB- HblM M3TepHaJI no TeMe «raHAap - ooen H rpa>KAaHHH», K8K -o6bltlHO, e}Ke,l!HeBHO BhlcTaBJlHIOTCB B «¥ronKe qTeHHH», QTo6bl Bce Y1.Ialll.HeCSI CMornH C HHMH-- nOSHaKOMHTbCH. KpOMe Toro, Ha HaH6o.'1ee MHTepeCHble KHHrH, CTaTbH ytlmnHecH (no >Ke.naHHIO) orpOpMJIHlOT KapTOtlKH, ,KOTO- pbie TO>Ke )teMOHCTpHPYIOTCH no XOAY nO)J.rOTOBH!JJIbHoti pa60TbI 8 «YrOJlKe qreHHH». 1 cn03H8B8TeJlbHhle HHTepeCbI H yc.nOBHR HX <jJOpMHpOB8HHH B l1eTcKoM Bospac- Tel. «MsBecTHJI AnH PCc1>CPt. shin. 73. M.. 1955, CYp. 12. 70
3a AeHh-ABa AO ypOKa BHeKJlaCCHOrO tlTeHHH yqHTeJlh 06'bHBJlReT yqaWJIMCSI nporpaMMYt T. e. OCHOBHbIe BonpoCbI npe,ltCTOHllI.eA 6ece- Abl t BhlCTaBJISleT B «¥rOJIKe tITeHHSI» qeTblpe TOMa c06paHHH COqHHeHHH A. n. raiiAapa 1 H nopY1JaeT OHMHOTeKapJlM 3Be3A0tleK (HnH 3BeHbeB) npHrOTOBHTb K ypOKY HeCKOJlbKO TaKHX me KOMnJleKTOB. YpOK HaqHHaeTCH c OeceAbl npHMepHO TaKoro cOJlep>KaHHJI: - CKonhKO neT npO>KHJI 3TOT y,ltHBHTeJlhHblA qeJIOBeK, OCTaBHB- WH" nOCJIe COOH TaK MHoro ,ltooporo, xopomero? - 4TO BbI YSHaJiH 0 ero AeTCTBe? OTKYAa? - CKOJIhKO JleT OH BoeBaJl 3a COBeTCKYIO BJIaCTb? 4 TO oc06eHHO neHHJI B JlIOJlJlX? 4TO JlI06HJI oonhwe Bcero Ha CBeTe? - A qero OqeHh He JIIOOHn? lJero He npow.an? - I(aK H nOqeMY CTaJI nHcaren:eM? - JIerKo J1H OblTh nHCaTeJIeM? qTO Oll .nYMan H rOBOpHJI 06 3TOM? - KHHrH KaKHX DHCaTeJIeH OH OC06eHHO ueHHJI? - A MHoro JIH caM HanHCaJI KHHr? - KaKHe KHHrH A. n. raH,ltapa BbI qHTaJlH? OTBeTHTb Ha 3TH BOrrpOc.b1 yqarnHMCH nOMor8er BCSI npOqHT8HHaH . K ypOKY JlHTepaTypa. 6ece){a 0 A. n. raHJ{8pe OJlmHa cOnpOBO>KaTbCSI Bblpa3HTeJIh- HblM QTeHHeM, ,lteKJI, al\fau.HeH nepeCKa30M, MH3KHM K TeKCTY, OTpbIB- KOB H3 nocnOMHHaHHH COBpeMeHHHOB, paCCMaTpHBaHHeM HJlJlWCTpa- 1.I.H8, Q>oTorpacpHH. '- Ka>K,ltoe BbICKa3bIB3Hue, K8>K,nbIH BblBO,lt ,ltOJI1KHbI CBH3blsaTbCH yqall(HMHCH C COOTBeTCTBYIOW.HMH xy.nOiKeCTBeHHblMH onHCaHHJlMH, KapTHHaMH, 06pa3aMH. LlH<Pp H AaT ,llOJl>KHO OblTh He- IHOro. . ECJlH 6ece,lta 6y.neT nOCTpoeHa T3KHM 06p.a30M, TO TpeTbeKJIaCCHH- KH HaBcer,na 3anOMHHT HeOObIKHoBeHHoe BpeMH (peBMIOIJ.HIO, 60pbGy 3a COBeTCKYIO BJIaCTb) H nOJIIOOHT 06blKHOBeHHoro COBeTCKoro QeJIOBe- Ka C neoobIKHOBenllOH ouorpacpHeH nHCaTeJlH-6opl(a ApKa,ltHSI neTpo- BHqa raAapa. . TpH Bonpoca, KOTOpbIMH 38KaHIIHBaeTCJI.. 6ecea, ooecnetJHBalOT v CCTeCTBeHHbIH nepexott K npaKTHlIeCKOMY 3HaKOMCTBY TpeTbeKJI8CCHH- KOB c coopaHHeM COlIHHeHHH A. n. raH,ltapa. KHHfH H3 c06paHHH COtlHHeHHH Ha)J.O paCCMOTpeTh Ha ypOKe no BceM npaBHJIaM: BHH18TeJlbHO npOaH3J1H3HpOBaTb Ka>K,nblH HX 3JIeMeHT (.Aa*e THCHeHHe Ha nepenJleTax.; Be,ltb 01.leHb HHTepecHo H COBceM He- npOCTO OnpeeJIHTb, CIO)KeTbl KaKHX npOH3BeJleHHH raH,ltapa TaM OTpa.. >KeHbl) . Oco60 CJle,nyeT BbI,lteJIHTb KOl\iMeHTapHH K npoH3Be.n-eHHSlM rattu.apa (T. e. cnpaBKH, H3 KOTOpblX MO}KHO Y3HaTh, KorAa, Ha KaKOM MarepHa- ne HanHcaHO npOH3Be,l{eHHe, QTO .n-YMaJI 0 HeM caM aBTOp, KOf)ta OliO BnepBbIe ony6JJHKoBaHO H T. A.), npe,ltHCJlOBHe K T. I JI. A. Kac- 1 HanpHMep: A. r a A .l1 a p. Co6p. COq., B 4-x T. M" «..QeTCK3H nHrepaTypa., 1964-1965 (HJlH JIlOOOe pyroe H3JtaHHe). 71
CHJ1B, aBT06HOrpa<t>IIH raflJlapa (T. I H IV), ero nJ.ICbMa H paccKa3bl BoeHHbIX J1eT (T. IV). YqHTeJlb nOKa3b1BaeT eTSlM, KaK HHrepecno IJHT3Tb Bee 9TH lvt3- repHaJlbJ, KaK OHH nOMoralOT rJlY0)J{e nOHHTb TBop4eCTBO nHCaTeJISI H nOJI106uTb ero. - J1. 0 twl a III II e e 3 a ,l( a H H eKe JI e ,l( Y 10 Ill. e M Y Y P 0 K Y: npO.llo..'1>KHTb lJreHHe KIIHr 06 A. n. raH.llape, ero aBTo6HorpacpHH, nHceM (BCJlYX, no 3 Be3)J.OQKaM), npOH3Be){eHHH raHJJ.apa (no COOCTBeH" HOMY BbI60py); nOCTap3TbCH OTBeTHTb Ha BonpOCbl H BblnOJlHHTb 3a'Jla.. IIHSI BHKTOpHllbl, nOCBHIneHHOH A. n. raH,l(apy (nonpOCbJ H 3a,l(aHHH BHKTOpHHbI cpa3Y )l{e DblBeIllHBalOTCH B «YrO.,'1Ke 1ITellHH»); Opl\11HTb nepBble CTpaHHI.I.bI KJlaCCIIOro aJIb60Ma 06 A. n. raH,!(ape. J!olallIHee 3aj\aHHe, HanHcaHHoe YlIHTeJ1el\f OT .PYKH Ha OT,lleJlbIlOM JlHCTe 6YMarH, BblBCIllHBaeTCSI cpa3Y >Ke nOCJIC ypoKa B «YrO.ITKe qTe- HHH». TaM me nOMernalOTcH BonpocbI BHKTOpHllbI, nocBHlUeHHofi A. n. faHJlapy. HanpHMep: nOJJ.Y1\faHI Y3Haii! OrBeTbl 1. 4ro 3a 3H3K HapHcoB3H B BepxHef yrJlY JIHCTa? 2. Kor,na H KaK y ApKaJJ.H}I rO'lHKOBa nOSIBHJ1CSI nceB,nOHHM raH,l(ap? liTO 3l1a- lIHT «nceB,l(OHHf»? . 3. KaKHC"3 CBOHX npOH3Be,LteHHH Ap.. Ka,l(HH nerpOBHtI C'IHTaJl JIYllIllHMH? 4. KaKHe BblCKa3bIBaHHSI cOBpeMeHHlI" KOB 0 raH,l(ape HJ1H CJlOBa Cal\t10rO raHJJ.a. pa TbI CIJHTaellib caMbIMH Ba)KHbIMH, neH- HbIMH? 3anHllIH HX H3 KapTolJ)<Y .ZJ.JIfl KJ1 aCCHoro aJIb60Ma. npOHJlJIIOCTp.Hpyii KapTOtlKY. A cr]ej\YIOll(HH ypOK MomeT 6bfTb llOCBSlJ..qeH cnpaBotIHOH JIHTepaTY. pe, B tlaCTHOCTH 3HaKOMCTBY yqaJ..qHxcH co CTaTbeH «raH;tap» B KHHre «4TO TaRoe? KTO TaKOH?». -' , .: TaKoB, B 06meM, x3paKTep pa60TbI no BHeKJIaCCHoMY qTeHHIO D rn KJI3Cce. . TeMaTHKa ypOKOB BHeKnaCCHoro qTeHHSI BIll KJ1aCCe, KaK H npe.>Ke, onpe,ne.nSleTcH YlIHTeJICrvl caMOCTOHTeJlbllO H cpa3Y He MeHee lIeM Ha 'IeTBepTh, a JlY1.Jme Ha nOJIyro,nHe. tIpH nJla- HHpOBaHHH ,nOJl1KHbl YIlHTblBaTbCSI Tpe60BaHHSI nporpaMMhI no BHeKJlac.. CHOMY tlTeHHIO B I I I KJIaCce, YCTaHoBKa Ha CBB3b C KnaCCHbIM qreHHel\{ H nnaHOM yqeOHo"BocllHTaTenbHoH paGoTw AaHHoro Knacca B nenOM. KpoMe Toro, YIlHTblBaeTcSI <t>aKTH.tleCKHA cpOH,l( JlHTepaTypbl )VISI liTe.. HHSI, KOTOpbIM pacnOJlaraeT AaHHbIH KJlaCC, ,lt3HHaH IlIKOJl3, IHTaTeIlTIb" Cl<He 1I1ITepeCbI YtlaHXCH H Y1JHTeJIH. 72
II. rPAMMATHKA, nPABODMCAHME M PA8BMTME PElf" TpeTHH KJIaCC JlBJlReTCH 3aBeplllalOIJJ.J.lM B CHCTeMe Hatl8JJbHOrO 06YQeHHSI. 3THM onpe)teJIHIOTCH oeo- 6eHHOCTH nocTpoeHHJI HOBOH nporpSMMbI )tnH 9To- ro KJlaCCa H MeTOJ1HKa pa60TbI no HeA. nporpaMMa no PYCCKOMY Sl3b1KY' nOCTpoeHa TaKHM 06pa30M, tlTO OHa npe)tYCMaTpHBaeT .naJIbHeHWee pa3BHTHe u u nOJIYlIeHHblX )teTbMH B npeJ1b1)1YHX KJlaCCaX 3HaHHH, YMeHHH H HaBblKOB, a TaK>Ke nOJ1b1TO>KHBaeT H CHCTefaTH3HpyeT CBe)teHHH, MMe- IOLnHeCH Y HHX no HatlanbHOH III Ko.lle. npH nepBOl\.1 3HaKOMCTBe C HOBOH nporpaMMOH MO}KHO nOJl.YMaTb, 1.110 B Heft ;J;aIOTCSI CBe,neHHH B TOM »<e 06'beMe, B KaKOM OHH ,naBaJlHCb B npeIKHHX npOrpa1\'IMaX )J)ISI I I I H IV KJlaCCOB. OHaKO 310 He TaK. npH DHIDY1aTeJIbHOM paCC:MOTpeHHH CO)1ep>KaHHH Kypca rpaMM3THKH H npaBOITHCaHHH, KaK OHO HaMetieHO HOBOH nporpaMMOH )tJlH III KJ]ac- ca, oOHapY>KHBaeTCSI, liTO H CTeneHb nOrOTOBJIeHHOCTH HOBOro Kypca npe,nbl.l1YInHM 06yifeHHeM, H KOHKpeTHble oonpocbl, Bxoj:t5lIUHe B Teta- THKY Kypca, H xapKTep pa60Tbl 1Ia;t 9TOH Te?\.faTHKoif, HecMo1pH Ha CX, O,ACTBO 3HaQHTeJIbHO OTJIH1.IaIOTCSI. Mnor"e CBeeHHSI 0 qaCTHX pellH )teTH Y/Ke nOJlYIlHJlH BO II KJI3Cce. OH" 3HalOT TaKHe TepMHHbl, KaK «HMB CYll1.eCTBHTeJIbHoe», «npHJIaraTeJIbHoe», «rnarOJl», «npe,nJlor», HMelOT npeCTaBJleHHe 0 TOM, tleM xapaKTepH3YIOTCH 9TH tlaCTH petiH KaK co CTOpOHbl Co){ep}Ka. HHH, TaK B H3BeCTHoA creDeHH H co CTOpOHbl $<>pMbl (HanpliMep, HMH cymec1BHTeJlbHoe 0003HatiaeT npe,AMeT, OTBetiaeT ua BonpOCbI K T o? 11 T o?, Bcer)1a "feeT onpeJ1eJIeHHbIH pOA, H3MeHeTCH no qHCnaM, B 3aBHCHMOCTH OT ,npyrHx CJlOB npeMO>KeHHSI H3MeHHeT CBOH OKOHtlaHHH), HO BO II KJIaCCe yqall{HecSI He nOJIytlaIOT 3HaHHH 0 na,ne>Kax, 06 H3Me- HeHHHX HMeH CyruecTBHTeJIbHblX no na,ne}Ka1\.f, 0 THnax CKnOHeHHH, 0 npaBonHcaHHH na;teiKHhlX OKOHtlaHHH. To me cne.n.yeT CKa3aTh 06 HMeHH npHJlaraTeJlbHoM: BO I I Knac- ce .neTH Y3HaJlH 0 3HaqHHH HMeHH npHJIaraTbHoro, 06 H3MeHeHHH ero no po.naM H tlHCJlaM B 3aBHCHMOCTH OT pOJl.a H 'lHCJla HeHH cy- rueCTBH1eJIbHOrO, OHH YMeloT nHcaTb pO;toBbIe OKOHtlaHHH HMeH npHJla- raTeJlbHblX, HO 0 CKJlOHeHHH npHJlaraTeJJbHbIx HM eme HH1.JerO He H3- BeCTHO. n03uaKOMHBWHCb co 3HatleHHHMH rJlarOJlOB H HeKOTopbIMH Bonpo- 'cal'tIH K HHM, a TaK>Ke Y3HaB 06 H3MeHeHHH rJlarOJla n9 BpeMeHaM, )teTH BO II KJlaCCe He nonyqalOT HHKaKHX 3HaHHH 0 CnpH/KeHHH rJlarOJlOB, 0 " npaBonHcaHHH JlHQHWX OKOHtlaHHH rnarOJlOB. He CJlYtlaHHo npeAMeTOM saHSlTHA no Mop<J>onorHH BIll KJIaCce KaK pa3 H SlBJIReTCH CKJlOHeHHe Cym.ecTBHTeJIhHblX H npHJlaraTeJlbHbIX, CnpB>KeHHe rJlarOJlOB. 1(0HetlHO, Y1.JHTeJlb ,D.OJl}f(eH nOBTOpHTh C yqaLnH- MHCH TOT M3repHaJl, KOTOpbIH OHH H3YQaJlH BO II KJIaCCe, H, ecJIH 3Ha- OCOeeHHOC1H npo- rpaMMW no PYCCKOMY .3I11KY .qn. III HnaCCI H MeTOANK8 pl&OTIII no Hel 73
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nHTb B npouecce BblnOJlHeHHJI pa3HOOOpa3HblX )W1pa>KHeHHH. HanpH. Mep: 1. OCHoBHble CBe.l1eHHH 0 npe.lJ.J10}KeHHH ytlaInHecH MorYT BcnOM- HHTb, COCTaBJIHH KOJIJIeKTHBHO no,lt PYKOBO,ltC'tBOM ytlHTeJIH HeOOJIb- mon paccKa3 no KapTHHe HJIH no BneqaTJIeHHflM Ha TeMY JIeTHHX Ka- HHKYJI (<<Ha peKe», «B JIecy» , «3a rpH6aMH», «B noxo,lte» H T. ,It.). . B TaKOM paCCKa3 HenpeMeHHO C>y,ltYT npe,nJIO>KeHHB H nOBecTBoBaTeJIb- HbIe, H BonpOCHTeJlbHbIe, H BOCKJlHIJ.aTe..'1bHbIe. OAHO H3 npe,nJIO}KeHHH pa30HpaeTCH no qJIeHaM npe,ltJIO>KeHHH, liTO )taCT B03MO>KHOCTb BcnOI- HHTb npOHAeHHoe 0 rJIaBHbIX H BTopoCTeneHHbIX QJIeHaX npe)J.JIO>KeHHH, o CBB3H CJIOB B npe.ll)IO>KeHHH. ,aJlH 3TOH >Ke eJIH MO>KHO HCnOJIb30- BaTb H3JIO>KeHHe. npHtleM H3BeCTHbie ,lteTHM CBe)J.eHHH 0 npe.ll.JIO>KeHHH IJ.eJIeCooc>pa3HO nOBTopHTb B nponecce aHaJIH3a TeKCTa, Bblc>paHHoro JV11! H3JIO>KeHHH. .. nOBTopeHHe rpaMMaTH1JeCKHX cBeAeHHA no TeMe «COCTaB C.TJO- Ba» MomHO rrpoBecTH c.TJe,.aYfOInHM OOpa301\f: a) npe,llJIO>KHTb yqalUHMCH nepeHeCTH"'K ceoe B TCTpa,.ab ro.nOBKY TaOJIHLl.bI no COCTaBY C.rIOBa: 4aCTII C,,1038 CJrOBO . u 3aTeM CllpOCHTb HX, Ha CKOJIbKO qaCTeH OHH no)tJlT npaBYIO KOu10H- KY, H, nOJIytlHB OTBeT, BbIHCHHTb, nO'leMY Ha qeTbIpe lIaCTH (nOTOMY liTO H3YQaJlH 1JeTblpe '1aCTH CJIOBa: KopeHb, npHCTaBKY, CY<PCPHKC, OKOHqa- HHe);' / 6) B oopa30BaBlllHxcH KJleTKaX npaB.9H KOJ10HKH npe)tJIaraeTCJI 3a- nHcaTb ,1.IaCTH ciloBa B TOM nopR,nKe, B KaKOM OHH CJleAYlOT B CJIOBaX (pa60Ta BbInOJIHReTCH caMOCToHTe.TJbHO): 4aCTH CJlona CJtOBO I I I npHCTaSK3 KOpeHb CY<PHKC OK OH"a II J.fe B) YIIHTeJ1b )taeT pH.ll CJIOB .llJIH pa360pa no COCTaBY t yqaIIHecH 3a- u nHCbIBalOT HX B JIeBOH KOJIOHKe, 3aTe caMOCTOHTeJIbHO aHaJIH3HpYlOT Ii 3anOJIHHIOT npaBYIO KO..TJOHKY; , r) B pe3YJIbTaTe npOBepKH yqHTe.TJb OTMeqaer ,lJJIH ceOH, KTO H3 yqall{HXCH '3aTpYJ{HHJICH H KTO HenpaBHJIbHO pa300paJI CJIOBa no CO- CTaBY; ... A) OqeHb nOJIe3HO 3a)taHHe: caMOCTOJlTeJIbHO 3anHcaTb onpeAe.ne- HHH '1aCTeH c..'1oaa (Ha OAHOM ypoKe - OKOHQaHHH H KOpHH, Ha ,ltPY- rOM - cY<M>HKca H npHCTaBKH). B npoaecce 3anHCH YIlHTeJIb BbIJIB. 80
JlHeT, KTO' H3 JleTeH He 3HaeT onpe,neneHHH. H B .naJlbHeHflJeM .lJ.06H" B8eTCH OT ytlaII(HXCH YCBoeHHH 3THX nOHHTHH; e) nOCJIe sanHCH onpe.!l.eJleHHH y"aU(HMCH npeJtJIar8erCH npOBepHT& HX no yqeOHHKY. 3. npH BblnOJlHeHHH ynpa>KHeHHH H8 npaaonHcaHHe, oOYCJIOB- eHHoe COCTaBOM cnOB8 (npaBonHcaHHe 6e3YAapHwx rJIaCHX, 3BOH- KHX H rJlyxHx COrJlaCHbIX, HenpoHSHOCHIb1X H y,ltBoeHHblX COrJlaCHblx)t nOBTopHIOTCH He TonbKO npaBHJIa npaBonHcaHHH, HO H BaiKHeHWHe CBe.ll.eHUH H3 06J1CTH (jx>HeTHKH: y,napeHHe", yJtapHble H oe3y,ltapHbIe rJl8CHble, 3BOHKHe H rJIYXHe COrJIaCHbIe, TBep.lJ.ble H MHrKHe COrJIaCHbIe. 4. B npouecce BbInOJlHeHHH ynpa>KHeHHH Ha pa3.HHlIeHHe" cyw.ecT- BHTe.TIbHbIX, npHJIaraTeJIbHblX, r.'1arOJlOB y"aHecSI nOBTopHIOT H onpe,neJIeHHH nepeqHCJleHHbIx lIacTeH pellH. npH 3TOM B nepBYIO Oqe- u . pe,nb OHH BcnOMHuaIOT, tlTO npH onpe.lleJIeHHH Ka>KJtOH H3 9THX qacreH petlH y!<a3bIBaeTCH ,nB8 cyrneCTBeHHbIX npH3HaKa: 3HatleHHe (npeMeT, npH3HaK npe.llMeTa, eHCTBHe npe.llMeTa) H BonpOCbI (K T o? q T o? K a K 0 H? 11 T 0 .It e JI a e T?). YMecTHO HMeHHO CeHlIaC oopaTHTbCSI K nOBTopeHHIO npaBHJla npaBonHcaHHSI He c rJIarOJlaMH, TaK KaK YMe- u HHe OT.,1HtlaTb r JIarOJl OT ,ltpyrHx tlaCTeH peqH HBJlHeTCH .llJIH TPeTbe.. KJ1aCCHHKa ,nOCTaTOlIHblM OCHOBaHHeM ,nJIH npHMeHeHHH 9Toro oP4><>rpa- q>HlIecKoro npaBH.lla Ha npaKTHKe. .. nOBTopeHHe op<porpa4JHtleCKHX npaBHJI, CBSl3aHHblX C rpaMtaTH" lIeCKHMU npH3HaKarvlH qaCTeH petlIl (6 nOCJIe WHnHllI.HX Y cyme- CTBHTeJlbHbIX >KeHCKOro po,na Ii OTCYTCTBHe ero Y cyrnecxBHTeJIbHblX MY>KCKOrO po.n.a; npaBonHcaHHe pO,nOBbIX OKOHlIaHHH npH.J1araTeJlbHW;( B H. n.), HaO:CTapaTbCSI COlleTaTb C BblnOJIHeHHeM pa3JIH1IHbIX JIeKCH4e- CKHX ynpa>KHeHHH H TBOptlecKHX pa6oT, HanpHMep TaKHX, KaK: a) 3aMeHa JtaHHoro CJIOBa HJIH COqeraHHH cnOB 6JIH3KHM HJIH TeM >Ke no 3Ha1leHHIO CJJOB.oM, HO OKaHtlHBalOlltHMCH Ha WHnHHH COrJl3C- HbIH (aOKJ1l0p - 8pa'l.., PoOHUK 1CAl00, mUUlUHa - mUUlb, dfJtl,lC(], - iJO'l..b, Henpasaa - AOJICb, pe6eHOK - MaAbltU; KOMaHda IWpa6AJI, (caMO- /lema, maHKa) - S1\unaJIC, 2AYXoe Mecmo - 2AYUlb, cmpoumeAbHW MamepuaA - KupnUtt H T. .n.); 0) nO)J.bICKHBaHHe HaHOOJree nOJtXO.ll.Hero )J.JlSI )J.aHHoro KOHTeKCTa npH.l1araTeJIbHOrO (npH nOBTopeHHH npaBonHcaHHH pO,nOBbIX OKOH- lIaHH" npHJlaraTe.,'1bHbIX). HanpHlep: HacmynuAa oceHb. lloiJY/l ee.. I1lep. Bee "lae npRtl.emCR sa mytlu CO/1He; B) COCTaBJIeHHe OT.lleJIbHbIX npe.llnO}KeHHH HnH paCCKa3a no onop- HbIM CJIOBa (1!-Ollb, OOttb, 8pa'l.., noMOb); r) BbUiBJIeHHe npH3HaKOB KOHKeTHbIX npe,ltMeTOB (ap6ya, MOp- KOOb, R6J20KO) H 3anHCb COtlCTaHHH npHJlar8TeJIbHbIX c cyrnecrBHTeJIb- ({bIMH (ap6ya - cneAbliJ., CAaaKUa, KpY2Abla, 60AbUl0t1) H .llp. nOBTopeHHe e>Ke.llHeBHoe, «oecnpecTaHHoe», KaK reKyaqee nO.TopeHlfe Ha3b1BaJI ero K. L1. YWHHCKHH, HMeer UeJIblO, Bo-nepBbIX, 3aKpenHTb, yrJIy6HTb H paCWHpHTb 3H3HHH no TOMY MaTepHaJIY t Ha KOTOpblA CJIe,llyer onHpaTbCH npH co06eHHH HOBbIX 3HaHHH; BO-BTOPblX, TpeHHpOBaTb, pa3BHBaTb H 81
3aKpenJIHTb YMeHHH II HaBblKH rpaMOTHOH YCTHOH H nHCbMeHHOH pe- '1M, B qaCTIIOCTH YMeHHH H HaBbJKH npaBOnHCaHHH. CoAep:m:aHHeM TeKyw.erO nOBTOpeHHSI HB.,'IHeTCH Ifpee BCerO u u u npOH}J.eHHbIH MaTepHaJI no H3YQaeMOH TeMe, a TaKiKe MaTepHaJl no Te- Mal, B KaKOM-TO OTHOllleHHH CXO.llHbIM C H3ytJaeMOH. TaKon MaTepHaJl JlaeT B03MO}KHOCTb COnOCTaBJIHTb HOBbIe 3uaHHH C HB.lIeHHSlMH H3BeCT- HbIMH, YCTaHaB.'1HBaTb Mem,ny HHMH CXO}J.CTBO H pa3JIHQHe, BbIHBJIHTb CDH3H Me)K.n.y SlBJIeHHSlMH rpaMMaTHKH HJIH op<PorpacpHH, GTO cO,lteHCT- Byer 60Jlee rJIy60KoMY nOHHMaHHIO H .neHCTBeHHoMY YCBoeHHIO 3THX u H BJIeHH. CpaBHeHHe H co'nOCTaBJIeHHe pa3J1H1.JHbIX rpaMMaTHlJeCKHX HJlH op<j>orpa<t>HqeCKHX SlBJIeHH" OqeHb nJIO.llOTBOpHO CKa3bIoaeTCH Ha npoq- HOCTH YCBoeHHH 3HaHHH, YMeHHH H HaBbIKOB npH H3YQeHHH KaJK.noH TeMbJ; Ba>KHO npH 9TOM TO, llTO cpaBHeHHe H conOCT8B.neHHe HeB03MO)K- HO 6e3 npH&neqeHHH H nOBTopeHHH paHee npOH.AeIlHoro MaTepHa.na. BOCnOJJb3yeMcH XOTH Obi TaKHMH npHMepaMH. 1. npH H3Y'leHHH rpaMMaTHQeCKHX npH3HaKOB H npaBonHcaHHH naJle)KHbIX OKOHtlaHHH npH.naraTeJIhHbIX HeJJb3SJ 060HTHcb oe3 cpaBHC- HHS1 HX C rpaMMaTHtlecKHMH npH3HaKaMH H npaBonHcaHHeM naJte.>KHbIX OKOHQaHHH cymecTBHTeJIbHbIX. - Cne,noBaTeJlbHO, B )1.aHHOM CJIYllae CKJIOHeHHe cymecTDHTe..TJbHblX H na,ne>KHbIe OKOHllalIHH HX - Ma- TepHa.n nOBTopeHHH. npHIJeM nOBTopeHHe JlOJDKIIO OCYW.CCTB1JHTbCH. B npouecce Ha6.nIO,neHHSI H cpaBHeHHH npH.lIaraTe.T1bHbJX C cymecTBH- 1'e.nbHbMH, PPH BbUIBJIeHHH CXO,llCTBa H pa3J1HqHSI Me)K.ny HHP,fH. OpH- BeeM HeCKORbKO npHMepOB: . a) npHcTynaSi K H3YlIeHHIO CKJIOHeHHH npHJIaraTeJIbHbIX MY)K- CKoro H Cpe){HerO pOJla, B pe3YJlbTaTe Ha6JIIO,neHHH Ha,n H3MeHeHHeM 9TH X npHRaraTeJ1bHblX no n8)J.e>KaM H cpaBHeHHH) HX. c cym.ecTBHTeJIb- HblMlf t yqaIIJ.HecH npHxo,nHT K BbIBO,ny, 'ITO npHJlaraTeJIbHble cpeJlHero pO)l.a BO Bcex naAe)Kax, KpoMe HMeHHTeJIbHOrO, HMelOT Te )Ke OKOHlIa- HHSJ, QTO H npHJIaraTeJ1bHble MY/KCKOrO pOJta, n09ToMY npHJJaraTeJlb- l-Ible M)'*cKoro H cpe,AHero po,na CKJIOHSIIOTCH O){HHaKOBO. To LKe caMoe Hawno,naeTcH H npH CKJIOHeHHH cymecTBHTe.fJbHblX (KpOl\fe Tex He- MHorHX, KOTopble OKaHlIHBalOTCH Ha -a, -R: a!l.a!l., oe8YUlKa): CYInecT- BHTeJlbHbIe MY>KCKOrO H cpe.,AHero po.na Tome OTHOCHTCH K O,nHOMY THny CKJIOHeHHH - KO 2-MY. 6) PaccMaTpHBaH naJle>KHble OKOH1I8HHSI np,HJI8raTe..,1bHbIX, yqa- IlU1eCH cpaDHHBalOT HX C na.n.e>KHbIMH OKOHlIaHHHMH cym.ecTBHTeJIbHblx. TaKoe cpaBHeHHe l1eJIeCOOOpa3Ho MH Tex naJte}KeH, KOTopbIe yqaInHecSJ nYTaIOT, He YMelOT pa3.nHtlaTb. KaK np8BHJIO, .AeTH J10BO,,'1bHO ,nOJIro He YMelOT pa3J1HQaTb TBOPH- u u Te,,1bHb1H H npe.ztJIO)l{HblH na,ne>KH npHJIaraTbHblX MY>KCKOrO H cpe)l.- n. n. r. n. Hero pO.lla (Ha CUHeM He6e, 3Q. OUHUM MOpeM) H BHHHTeJ1bHbIH H T. II., TBOpHTeJ1bHbIH na,ne>KH npHJlaraTeJIbHbIX }KeHCKOro pOA8 (sa Oa./lbHeIO 6. n. OICOAueal 6 allAbHIOIO OOP02Y). 82
ConOCTaBJIeHHe OKOHtlaHHH npHJIaraTeJlbHbIX C OKOHqaHHHMH cy- neCTBHTenbHblX nOMOraeT q>opMHpOBaHHIO H8BblK8 HanHCaHHH na,ne>K- HbiX OKOHqaHHH. T. n. " n. n. MY>KCKOrO H cpe,ztHero pO,ll.a: K a K H M? q e M? T. C 20Ay6blM, CUHUM tuapOM. o K 8 K 0 M? 0 q e M? TI. 0 20/ly60M, CUHeM Ulape. npHJIaraTeJIbHble MY>KCKOrO CYllleCTBHTeJlbHble MY}KCKOrO H CpeHerO poa H CpeHerO pO,lJ.a T. -bIM, -UAI n. -OM, -eM -OM, -eM -8 ConOCTaWHIS1 OKOHQaHHH, ytlal.I(HecR eJI81OT BbIBO,lt, tffO B npe,lJ.JIO}K- HOM na,ne>Ke OKOHQaHHIO CyecTBHTeJIbHbIX -e COOTBeTCTBYIOT f.nac- Hble e, 0 B OKOH1.IaHHH npHJIaraTeJIbHbIX. TaKOrO COOTBeTCTBHSI. B TBO- pHTeJlbHOM na.ne*e HeT. nO,n06HOe Ha6.nIO){eHHe npOBO,ltHTCH H HaJJ: OKOHQaHHSlMH npHJIara- TeJIbllbIX H cymecTBHTeJIbHblX >KeHCKOro pO.lla. BblBO.llbI, KOTopbIe eJIaIOTC" npH conOCTaBJIeHHH OKOHQaHHH: npH- JIaraTeJIbHbIX H cymecTBHTeJIbHblX, KOHeQHO, lIe CJIeJ1.yeT 3ayqHBaTb HaH3YCTb, HO Ha,ltO HayqHTb yqaIII.HXCH nOJIyqaTb HX, HCnOJIb3YR CJIO- B3 C YJ{apHb1MH OKOHqaHHHMH (Ha 60/lbUlOM CfrlOAe, 8ll 60/lbWU.M cmo- /lOM) H 06pmnaTbcH K 9TH1 BblBO){aM npH BCTpeqe C 6e3YJ1apHbIMH OKOHqaHHSlMH. YKa3aHHble eHCTBHH Ha.n CJIOBaMH He TOJIbKO nOMora- lOT B YCBoeHHH op<p<>rpacpHH. na){e1KHbIX OKOHqaHHH, HO H npHyqalOT .lle- Tefl BHI1MaTeJIbHO OTHOCHTbCH K CJIOBY J aHaJIH3HpOBa:rb ero c pa3HblX CTOpOH. 2. a) npH H3Y1.IeIIHH npaBonHcaHHH OKOHqaHHH r JIarOJIOB 2-ro JIHua e,nHHCTBellHoro lIHCJIa (HacToHee H 6yyrnee BpeMH) ecTb npH- :MOH CMblCJI o6paTHTbcH K cpaBHeuHIO 9TH X nanHcaHHH C HanHcaHHeM CYI.IJ.eCTBHTeJIbHbIX, OKaHlIHBalOI.IJ.HXCH Ha IlIHnHInHe (MblUlb, KaMblW). Ha OCHOBe cpaBHeHHH ,l.leJIaeTCH 0600111eHHe (B npe.lleJIax H3BecTlloro yqalllJIMcH I I I KJIaCca): b nHweTCH nOCJIe IllHnHInHX 8 rJIarOJIax Bee I' J\ a, a B KOHue cymecTBHTeJlbHbIX TO.nbKO B TOM CJIYtlae, ecnH 9TO cym.eCTBHTeJIbHble JK e, H C K 0 r 0 p 0 J1 a. 6) 113YQaH npaBonHcaHHe fJIarOJIOB npome,Zunero BpeMenH, YMecT- HO npHBJIeqb rrpaBonHcaHHe pOOBbIX OKOHqaHHH cYW.ecrBTeJlbnblx B HMeHHTCJlb HOJ\f na,zte>Ke: COAHl{.e 830UlAO. BO/lomo BblCOXAO. PeKJJ o6.MeIle/la. 3eM-AII nompeClW/ltICb. llpyiJ aapoc. 83
I COJlepm8HHeM TeKyrn ero nOBTOpeHHSI ,llOJlmeH 6blTb H M8TepH8n AaBHO npojteHHbIHJ HO YCSoeHHblA TBepAo .n8J1eKO He BceMH yqa- lUHMHCSI HJlH nOBTopSieMblH MH Taro, qTOObl ,neTH He sa6wH paHee H3YlIeHHoe. TaK, BIll K.'1aCCe lie OTBOHTCSI cneUH8.nbHoro BpeMeHH H8 yrJly6- JleHHe H paCillHpeHHe 3HaHHM no cpoUeTHKC. O)l.HaKO ynpa>KHeIlHH, C13H3aHHble C MaTepHaJlOM no' OHeTHKe, )J.O.,'UKHbl npoBoJ{HTbCH B03- Mom no qaxne. HanpHMep, H8 O)lHOM ypOKe npe.D.J1araeTCH B CBH3H C BbtnOJIHeHHeM ynpa>KHeHHH no TeKyrneH TeMe Ha3BaTb Bce rJIaCHble 6YKBbl H YKa3arb B CJIOBe Y8PHYlO H 6eaYAapHble rJIaCHble; Ha .npyroM - 3BOHKHe H t JIYXHe cor JlaCHble; Ha TpeTbeM - IllHnHlll.He H T. ,n. BYKB8J1bHO H8 KamJ(oM ypoKe Ha.no YlIHTb ,neTeH pa36HpaTbcSI B cTpoeHHH CJ10B, npeJ1J18raTb ynpa>KHeHHH Ha cJIoBo06pa30BaHHe, SHaKoniTb C MHoro06pa3HblMH B03l\fOHOCTHMH 06pa30BaHHH CJlOB C nOMoblO .CY<M>HKCOB H npHcTaBoK. Ynpa}KHeHHH, CBH3aHHbIe C ceMaHTHKO-l\fopcpo..'10rH'IeCKHf.,{ aHaJlH- 30M CJlOB, CJIY>KaT ue..rIHM pa3BHTHH pellH H YCBoeHHSI opcl>orpacpHH. YnpamHeHHS1 no COCT8BY C.'10Ba H B CBH3U C 3THM no BblHBJIeHHIO CMhlCJIOBOH B3aHMocBH3H Me}KJ{y O,lJ.HOKopeHHhlMH CJlOBaMH J{OJl>KHbl Opr8HHlIecKH BnJleTaTbCH B KaHBY Ka}K)J.oro ypOKa. npHae.neM Hec- KOJlbKO npHMepOB: _ a) C UeJIblO COnOCTaBJ1eHOH naJlHblX OKOHqaHHH cymecTBHTeJ1b- HblX 3-ro CKJlOHeHHH C na,ne1KHbIMH OKOHQaHHS1MH cyrnecTBHTeJlbHblX . I-ro CKJlOHeHHSI npeJ{JlO>KHTb yqaHfCH OT CYW.ecTBHTeJ1bHblX 3-ra CKJIOHeHHH (nAOll{aab, /lOtuaiJb, HO'lb, neLlb, MblUlb, eAb) 06pa30BaTb C nOMOInblO cyqxpHKca -,,- OAHOKopeHHbIe CYlll.ecTBHTeJlbHble, onpe,ne- J1HTb THn CKJlOHeHHS1, nOIl86J1IOaTb, l<aK H3leHHTCH ox OKOHqallHH B cpaDueHHH C OKOHlIaHHHMH JJ.aHHblX CYlllecTBHTeJlbHbIX: 3-e CKJI. nllOb y nAOwp,aa " nAOU Ha nAOaaU l-e CKJI. . nJtO y nAOU4aaKU 1C nAOW,aaKe I Ha n/lowpOKe .P , 6) Or aHHbIX CYlll.ecTBHTeJlbHblX 06pa30BaTb npHJlaraTeJlbHble H raron, npHnaraTenbHe pa306paTb no COCTaBY: SU.Ma - SUMHUtl - 8UMOBamb - nepeaUM.Oeamb ... MOp03 - M.Op03Hbltl - MOpoaumb - SQMOpOSUmb ... . ClfteX - CMeUlHOU - CMetuUmb - pacCMeUlUmb ... 3/Cap - apKUa - "capeHblU - ",apumb - 8ll3ICapumb ... HO'lb - . . . eeceAbe - . . . 3eAeHb - . . . 84
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AHTCH H3 uero, KaK npaBH.no, 1-2 qaca). n03TOMY BaJKHO B npou.ec- ce 0600IneHHH 3HaHHH no Tele H36paTb II TaKYIO cpopMY H8rJIHJ(HocTH, KOTOp8H .naJI8 ObI B03MO>KHOCTb ytIalUHMCH npeJ{CTaBHTb nOJtyqeluible no TeMe CBe.neHHH B onpe,lJ.eJIeHHOH CHCTel\.te, B HX B3aHMocBH3H 4 . 3TOH U.e.'1H, KaK H3BeCTHO, OTBetIalOT cxeMbI H Ta6JIHI.I.bl. npHBeAe1 npHMep. CHcTeMaTH3HPYJOTCH CBe.l1eHHSI no TeMe «HMH npHJlaraTe.TJbHoe». TpeTbeKJIaCCHHKH .nO.TJJKHbI 3HaTb c.ne.l1YlOmee: 1. npHJIar8TeJIbHOe 38BHCHT OT cyecTBHTe.nbHoro, 3aBHCHMOCTb 9T8 npOHBJIHeTCjI npeJKJJ.e Bcero B TOM, liTO npHJIar8Te.TIbHOe ynOTpe6- JIHeTCH B npe,n...TJO)KeHHH TOJIbKO B COtIeT8HHH C cyrnecTBHTe..'1bHbIM; npHJIar8TeJlbHOe H3MeHHeTCH B 38BHCHMOCTH OT cyecTBHTe.nblloro, C KOTOpblM CBH33HO, T. e. CTOHT B TOM )Ke PO.l1e, lIHCJIe H naJI.e>Ke, lITO H cyrnecTBHTeJlbHoe. 2. Be3YJlapHble OKOnqaHHH npHJIaraTeJIbHbIX nHlliYTcSI TaK >Ke, KaK OKOHtIaHHH, H8 Koropble na)l8eT y,n8peHHe. Ee3Y.l1apHbIe OKOHQaHHSI M01KHO npoBepHTb BonpocaMH, )J)1H Toro Ha,ZlO YMeTb npaBHJIbHO CTa- BHTb BonpocbI OT cYlUecTBHTeJIbHOrO K np H.'1 a raTeJIb HOMY . Har JIH.l1HO Bce 9TH CBe.l1eHHS1 MorYT ObITb npeJI.CTaB.TJeHbI B BH}le T8- KoA Tao.') HUbl: HMH OpHJJaraTeJlbHOe (H3MeJUleMaS qaCTb peQH; H3MeHJlIOTCJI npHJlaraTeJ]bHe B saBHCHMOCTH OT cyw.eCTBHbHhlX, C KOTOpblMH CBJl3aHbI) npaBOOHcaHHe OKOHQaHMH EAHHcTBeHHoe HcnO MHO>KeCTocHHoe HCJlO POol' - J1a,u.e)K >KeHCKHA NY>KCKOD H CpeAHHft Bonpoc OKOH-qaHHe Bonpoc f OKoUQSHHe Bonpoc , OKOH1IaliHe , K8KOH? -oil, -61.4, H. K8KaH? -all, -RR K a K 0 e} -u/i. KaKHe? -ble, -ue -oe,-ee - P. K3KOA? -ad, -efi KaKoro? -QZQ,-elO KaKHx? -blX, -ux - ,a. KaKoii? -oft, -e4 K8KOMY? -OMY, KaKHM? -blM, -UM -eM, - B. KaKYIO? -Y'O, -1010 KaK H. KaK H. KaK H. KaK H. MinH P. HJJH P. "J1I-1 P. HJJH P. -oft, -ell -WMU, T. KaKoJi(-olO)? (-010), K3KHM? -blM, -11M KaKHMH? (-elO) -lUlU - n. 0 K 3 K 0 if? -ad, -ed 0 KaKoM? -OM,- eM o KaKHX? -btX, -ux 86
PaaYMeeTCSI, TaMHl1a He J{OJI>KHa )).aBaTbCfI B rOTOBOM BHAe, ee coc- T8MHIOT caMH yqalI\HecSi no)). PYKOBOJtcrBOM YllHTeJlR B npouecce 0606- eHHH 38HHTHH no TeMe. nOBTOpeHHe B KOHue YQe6HOrO rO.l(a npHHHTO Ha3b1- MroroB08 n08'0- BaTh HTorOBbIM. nO>KaJlyA, 3TO OHH H3 HaH60Jlee peNMe TPY,ltHblX BH,AOB nOBTopeHHH: Bo-rrepBblX, 38 KOPOT- Koe BpeMH Heo6XO,AHMO BOCCTaHOBHTb B n8MHTH 01leHb 6oJlbWOH H pa:J- Hoo6pa3HbIH MaTepHaJI; BO-BTOPbIX, nOBTopeHHe HaAo opraHH30BaTID TaK, qTOObl MHoroo6pa3Hble CBe.neHHH, nonyqeHHbIe yqalI.{HMHCH B re- qeHHe yqeOHOrO rO,l{8, npHBeCTH B C Ii C T e MY, TO ecTb Ha 06Il1Hp" HOM H pa3HOCTopOHHeM MarepnaJle nOK33aTb yqalllHMCH, tITO Bee flBJle- HHH rpaMMaTHKH H op<porpac}>HH B3aHMOCB-H3aHbI; B-TpeTbHX, 9TO nOBTO- peHHe HeCHHMaeT 3a..nallH 3aKperrJIeHHH 3HaHHH H TpeHHpOBKH YIeHHii H H8BbIKOB. HTorOBoe nOBTopeHlie IJ.e.necoo6pa3HO HaqaTb 06001UeHHeM 3Ha- HHH 0 npeJ{JlO>KeHHH no CJIe.l(YIOHM C006pa>KeHHHM. TeMa «npe)J.J10>Ke- HHe» HBJlHeTCH 3aKJIIOtlHTeJlbHOH B Kypce rpaMMaTHKH III KJI8CCa, no- 9TOMY nOBTopflTb ee nOCJIe nOBTOpeHHH ,ltpyrHx rpaMM8THlIecKHx TeM HeT CMblcna t TaK KaK TeM8 «np.e,ltnO>KeHHe» H 6e3 Toro H3YllaeTCH B KOB- 1.l e rO,Aa. TaK"4 o6pa301, nOBTopeHHe 9TOH TeMbI ,ltOJl}KHO CTaTb 3aKJlIO- qHTeJIbHbIM 9TanOM pa60TbI Ha,A HeA (T. e. TeMaTHtJeCKHM nOBTopeHHeM) 11 HallaJIOM HTorOBoro nOBTOpeHHH ( T. e. nOBTopeHHH MaTepHaJla, H3Y- qeHHOrO B TeqeHHe rO,Aa). . ECTecTBeHHblM .npo.llOJl}KeHHeM TeMbI «npe.n.nO}KeHHe» HBHTCH corro- cTaBneHH,e .llBYX nOHSlTHH: «tjJIeHbI npeJVIO}KeHH» H «tlaCTH petIH>? B pe3YJIbTaTe nOBTopeHHH (B nopHJ{Ke cOnOCTaBJIeHHH) HanO BbIHBHTb C x 0 JI. C T B 0 (H lIJIeHbI npe)J.JIO>KeHHSl t H tlaCTH petlH - CJIOBa) H p a 3 JI H tI "e (qJleH npe,nJIOJKeHHH - 9TO CJlOBO t KOTOpoe BCerAa H3XOAHTCH 8 npe,lJ)lO)KeHHH, CJ1eAOBaTeJlbHO, cBH3aHO C llpyrHMH cno- BaltlH, OTBettaer Ha KaKOH-JlH60 Bonpoc; CJIOBa, He OTBeqalOInHe HH H8 KaKOU Borrpoc, lIJIenaMH npe,ZVIOJKeHHSI 6blTb HC MorYT (C0103b1, npe,lt- norH, qaCTHUbI); qaCTb pellH - Jllo6oe CJlOBO, He3aBHCHMO OT Toro, HXO.l!.HTCH OHO B npe,n.,10mellHH HJlH HeT, OTBeqaeT na Bonpoc HnH neT, HanpHMep: c - npe.l(JIor t U - C0103, CHeZ - cymecTBHTenbHoe H T. .). CneJJ.YIOlll.aH cTyneHb HTorOBoro nOBTopeHHH - 06oo1UeHHe sHaHBu .0 lIaCTHX peqH. B 33KJIlO1.feHl1e nOBTopeHHSI TeMbI «l.{acTH peqH» nOJle3HO 06paTHTb BHHMaHHe 'yqaHXCH Ha TO, qTO qaCTH petlH ,lI.eJIHTCH Ha .D.oe rpynnbl: 1) cyecTBHTeJIbHoe npHJIaraTeJIbHOe rJlarOJI MeCTOHMeHHe HapellHe 2) npe,ltJlOrH COlO3bl QaCTHl.lbl 87
Pa3JIHtUe Me}KJ1Y 3THMH J].BYMSI rpynnaMH tJaCTeH petJH S8KJl101I8- eTCH B TOM, liTO CJlOBa nepBOH rpynnbJ OTBeqalOT Ha BonpOCbI II B u npe)l)10>KeHHH JlBJIHIOTCSI IIJleHaMH npe,nJ10>KeHHSI, CJ10Ba BTOpOH rpynnbl 1-IH Ha KaKHe BonpOCbI He OTBellalOT H qJIeHaMH npe,nJlOmeHHSI He SIB- JlBIOTCH; Ka>KAoe CJI0BO nepBOH rpynnbl MO)KeT 6b1Tb paso6paHO no COCTaBY. 3ro nOCJIe,nHee OOCTOHTeJlbCTBO MO>KeT CJIY>KHTb HCXO,nHOH TOIl- KOH ,lJ.JISI nepexo,na K nOBTopeHHlO TeMbl «COCTaB cnoBa». nOCJ1e)tHeM re- MOM HTorOBoro nOBTopeHHSI SlBHTCSI TeMa «3BYKH H 6YKBbI». HayqeHHe paSRena .aCTH peQHt MM. cyaqecT8"'- T eMa «H3felIeHHe Hl\1eH cymecTBHTeJ1bHbIX» - 0,lJ.- TenbHoe Ha H3 l1eHTpaJlbHbIX TeM B Kypce pYCCKoro Jl3blKa III KJlacca. B npouecce H3ytJeHHSI 9TOH TeMbI TpeTbe- KJIaCCHHKlI YtJaTCH H3MeHSlTb HMeHa cyecTBHTeJIbHbIe no na,lJ.e>KaM If CJ tlHCJlaM; pa3JIHlIaTb na,ne)KH H onpe,nenSlTb THnbI CKJIOHeHHH HMeH CY- meCTBHTeJ1bHbIX; Y ,neTe" cpopMHPYIOTCH YleHHSI H H3BbIKH npaBHJlbHo- ro lIanucaHHSJ rra){e}KHbIX OKOHlIaHHH liMeH cyecTBHTeJlbHblX B eHH- CTBeHHOM H MHO)KeCTBeHHOM tJHCJIe. TeMa «HMSI cymecTBHTeJlbHoe» OTKpbIBaeT nepe)t YIlHTeJIeJ\f 60nbwHe B03MO}KHOCTH MSI npOBe,neHHSI rpaMl\iaTHtJecKoro pa36opa, pa3BHTHH HaBbIKOB npaBHJlbHOrO ynOTpe6- JleHHSI HMeR CYIneCTBHTeJIbHblX B pellH. 113YtJeHHe HMeHH CY1ll.ecTBHTeJIb- Horo nOMoraeT yqallI.HMCH OC03H3Tb cHHTaKCHqecKYIO pOJIb 9TOH tJaCTH pelln. - OCHoBHoe BO BceH .3TOfl pa60Te - OCMblCJIeHHOe H np01.lHOe YCBoeHHe H3YllaeJ\foro MarepHana. YqaLUHecSl I I I KJIaCCa npaKTHlIeCKH n03HaKOMHJlHCb C HMeHeM ey- meCTBHTeJ1bHbIM B npe.u.bIAYHX KJIaccax. TaK, BO I I KJIaCCe WKOJIbHH- KH Y3HanH, qTO CJIOBa, o603HatJalOIII.He npe)tMeTbI H Bew.H (1CHU2a, cmoA), nlO,neH H >KHBOTHbIX (dHBJl J metnJl, SOAK, AUCUija), c06bITHH (c6op, ympeHHUICJ iJeMoHCmpaUJl,), HBneHHSI npHpOJlbI (eemep, iJoiJb, MO,1- HUll,. 2p03a, 6ypOJi), COCTOSlHHe (COH, neHue, iJ8UHue), npH3HaK (cu- lleoa, ttepHoma), B rpaMMaTHKe - npeAMeTbI, OHH OTBeqalOT Ha BO- npOCbI K T o? II T o? K 0 M y? II e M y? K e M? q e M? H T. JJ.. SlBJlHIOT- CH HteHaMH CyzneCTBHTeJIbHbIMH. Bo I I KJIacce AeTH Y3HaJIH, tJTO HMH cyecTBHTeJIbHoe HMeeT onpe- lleJIeHHblH po,lt (MY)KCKOH, >KeHCKHU, epe,nHHH), H3MeHHeTCSI no qHCJlaM (e,ltHI-ICTBeHHoe H MHO)KeCTBeHHoe), H3MeHSleT ceOH OKOHlIaHHSI npH CBH3H c .u.pyrHMH CJIOBaMH (Ha npHMepe y,napHbIx na,ne>KHbIX OKOHqa- IHIH). nporpaMMa III KJIaCCa OTBO)tHT 45 qaCOB H8 H3YQeHUe HMeHH cy- aneCTBHTeJIbHoro. no 'KpaHHeH Mepe nepBbIe 3 qaC8 >KeJ1aTeJIbHO YJJ.e- JlHTb nOBTopeHHIO H3YQeHHOrO BO II KJlacce: ynpamHeHHHM Ha onpe,ne- .'leHHe poa HMeH cyrnecTBHTeJIbHbIX, Ha H3MeHeHHe cym.ecTBHTeJ1bHblX no qHCnaM. Ulenecoo6pa3Ho TaKme npH nOBTopeHHH nopa6oTaTb Ha 88
YCT3HOBJIeHHeM CBH3H MeJK.Zty... CJIOBa{H, BhInHCbJBaB napbl CBSl38HHYX Me)K.ny COCOH CJlOB (9TO OlleHb npHro;J.HTcH npH H3YQeHHH na,ne1KeA H na,ne>KHbIX OKOHlJaIlHH). HY:>KHO eI.IJ.C pa3 - oopaTHTb BfIHM3HHe TpeTbeKJI3CCHHKOB H3 TOt liTO onpeMHTb po,tt HteH cYll.I.ecTBHTeJIbHbIX MomHO JlHWb B TOM CJlY- 1I3e, eCJIH OHM CTO.HT B e,nHHCTBeHHOf \IHCJIe. BnpOqeM, yme Ha nepBbIX ypOKax yqall(HeCH nOBTopSlIOT H CHCre- MaTH3HpYIOT CBOH 3HaHHSI 0 po,ne H!\-leH CYI.IJ.eCTBHTeJlbHbIX, no.nb3YJlCb He TOJlbKO nOJl-CTaHOBKOH leCToHMelIHH Oil, OHa., OHO J Moll j MOll, Moe. HO coeHHHSJ CYIIJ.eCTBHTeJ1bHbIe C npHJIaraTeJIbHbIMH, rJIarOJIaMH. Yqa- ll\HeCH YCTaHaBJIHB31OT' CBH3b MeJK)(Y CJIOBaMH B T3KHX, HanpHMep, COtteTaHHHX H npe;vIO}KeHHHX: CmpOUHbl.U monOAb pacl¥1eAj, KynUJ1U Hi)- 80e nO/lomeHl{e, II eM 8KYCHoe JWAOKO, CUHee Mope, pyccKOe nOlle, ape- HblU Kapmrxpe/lb, 8KljCHaJ1, KapaMeJlb J nO,1e n06eAeAo, Kapmot/JeAb coapUA- CJl, 20CnUmaAb omKpblACJI, H T. ,no B pe3YJIbT3Te 3TMX aaHHTHH ,neTH ,nOJI)KHbI CYMeTb npaBHJIbHO OT- HecTH cymecTBHTeJIblIOe K O)(HOMY H3 Tpex PO)\OB, a B caoeM pelleBOa npal{THKe COrJIaCOBblBaTb C ,naHHbIM CYIneCTBHTMbHbIM rrpHJlaraTeJlb- Hoe, MeCTOHMeBHe " fJlarO"T}. OCHODHbIM )I{e cO)l.ep*aHHeM 3aHHTHH B I I I KJlaCCe CKnOHeHHe NMeH cy- npH M3ytteHllH HMeHH CYll\ecTBHTeJIbHOrO SlBJ1HeTCH 11.I eCTBIfTenbHblX .W pa60Ta Ha CKTIOHeHlieM. Pa3JIUlJeHHe na,neiKeu, TMnOB CKJIOneHHH, YCBoeHHe npaBonHCaHH5I na,ne)KHbIX OKOH1JaHHA- .. u u caMblH Ba>KllbIH J.{ B TO >Ke BpeMSJ CJIO}I<HbIH pa3,lteJI npH H3ytteHHli Hl\leHH CYlAeCTBHTeJ1bHoro. 113 BeCTHo, 'ITO n a ,n e >K HMeH" CYInecTBHTeJlbH....oro - 3TO (OpMa CJIOBOH3MeHeHHH, npHtleM He TOJIbKO Mop(jx>JIOrHtteCKaSl, HO H CHHT81{- CHtteCKaH, nOKa3hIBalOrnaSl OTHomeHHSI CYll(ecTBHTeJIbHOrO c ,npyrHMH CJIOB3MH B npe)(JIO>Kel-1HH II CJIOBOCOqeTaHHH. CpaBHHTe: nUCb.M.O 6pama t nUCbMO 6pamy H nUCb.MO om 6pama. B 3aBMCH1\{OCTH OT H3MeHe- HHH CJlOBa 6parn MCHHeTCH CMblCJI Bcero BbICKa3blBaHHH. ,neTJlM H3)l.0 nOKa3aTb, liTO ,nJIH CBH3H 'C ,npyrHMH CJI0BaMH, T. e. )l.Jl5I BbIpame- HHH pa3JIHIIHblX OTHOllleHHH, HMSI CYll(eCTBHTeJ1bHOe CKLTIOHHeTCH, 113- MeHHeTCH no na,neJKaf; tITOObI onpe)leJIHTb naJI.e>K, He06xoll.HMO nOCTa- BMTb Bonpoc K ,naHHOMY CJIOBY OT ,npyroro CJIOBa, C KOTOpblM OHO CBSI- 3aHO no CMbICJIY H rpaMfaTHlIeCKH: uU{Y (1J TO?) OO/t1,; 3a60ttycb (0 K 0 M?) o cecmpe; nuUlY (q eM?) pyttKOU; ZOp:HCyCb (K eM?) apY20M; 8emKa (tt e r Of) Jl6AOHU; Hopa (K 0 r Of) IlUCbl H T. )\. 3HaKoMHTb yqam.HXCH C pa3Rooopa3HbIMH OTHOllleHHHMH Me>K,Zty CJIO- . '.. BaMH MO)KHO npH nOMOInH pa3JIHttHbIX ynpaLKHeHHH, HanpHMep: PUCV10 (11 TO?) KapmUHY, PUCYIO (\I eM?) I(pacKaMU; MOIO (\I TO?) nocyiJy, MOIO (1J eM?) 8000{/,; 8Uy (K 0 r o?) opyza J CMomplO (H a K 0 r Of) Ha apyza. npH pa360pe no,nooHblX CJIOBOCO'leTaHHH H npe)1JlO>KeHHH ,neTH y6e>K)J.aIOTCSI, ttTO na,neLK HeOQXo,nHM ,lJ)ISI Bhlpa1KeHHH. onpeAeJIeH- HbIX 3HaQeHHH, liTO ;tJlH rOBOpSItnHX A8J1eKO He 6espa3J1H'IHO, npaBHJ1b- HO HJlM HenpaBHJlbHO ynoTpe6JIeH na.Ae>K. HanpHMep, mo6uml? poiJUHY, HO oopO:J/Cumb poiJUHOU J a He «AOpO}KHTb pOj:lHHY». .ll.nB nOHHMaHHH OT- 89
.. HoweHHH Me>KJ1Y CJIOB3MH MO>KHO nOK333Tb, qTO CJIOBO B O,llHOM H TOM >Ke nane}Ke t HanpHMep B TBOpHTeJlbHOM, MO>KeT 0603HaQaTb MeCTO (r .A e?): exaJI, AeCOM, nOAeM- H 0pYAHe TpYlla (q e M?): KOnllll Aonamo(i,. nOCTpOeHHe yqeOHHKa, X3paKTep H paCnOJlOJKeHHe ynpa}KHeHHH B HeM OnpeAeJlHIOT CHCTeMY H MeTOJ(bl p360Tbi no H3YQeHHIO HMeHH cy- m.eCTBHTeJlbHoro. ,[{JIH 3U3KOMCTB3 C na-ne>KaMH (H33B3HHe na,ne>KeH, naAe)f{HbIe BonpOCbl, nOCTaHOBKa Bonpoca K A3HHblM CJlOBaM) B YQe6.. HHKe HMeeTCSI OOnbllIoe KOJIHtJeCTBO ynpa>KHeHHit TaK, BHallaJIe Y1JH- .w TeJlb n03HaKOMHT Yll3InHXCH C Ha3BaHHeM na,ne)KeH H naJ(e}KHbIMH BOllpocaMH, BHe 33BHCHMOCTH OT THn3 CKJIOHeHHH H naAe)KHblX OKOH" qaHHA; OJ(HOBpeMeHHO H3Yll3IOTCH npe,nJIOrH, ynoTpeMHIOInHeCH C ,naHHbIMH naAe>K3MH, 3 TaK)Ke Hena,ne>KHble, TaK na3bIBaeMbIe CMblC" nOBble BonpOCbI (r,n e? K Y J( a? 0 T K Y A a?). B npouecce Bblno.nHeHHSI ynpa}KHeHHH Ytle6HHKa AeTH J(OJI}KHbI no- USlTb, 'ITO HMeHa cYIUecTBHTeJlbHble H3MeHHlOTCS1 no naJ(e}KaM (CKJlO" HSlIOTCH); tlTO CYIneCTBHTeJlbHbIe. OTBellalOmHe Ha O,nHH H TOT me DO" npoc, OTHOCS1TC5I K O,AHOMY .ft'3)].e}KY, XOTSI HMelOT pa3Hble OKOnQaHIiH: (11 e t?) pyttKoii, o8epblO, l1£po.M, (n 0 II e MY)? no aOp02i!, no no- /l1O, no crnenu. B AaHHblH nepMoA 6o.nbwoe l\'lecTO ,nOJI}KHbI 3aHHMaTb ynpa}KHeHHH B pacn03HaBaHHH na,z\e>KeH nYTeM YCTaHOBJIeHMH CB5I3H Me>KJl.Y CJIOBa. MH H nOCT3HOBKH BonpOCOB: aamb (K 0 r o?) cecmpy, (II TO?) noeoo; AUCmbR. (11 e r o?) 6epe3bl K/leHa J monOAR; 20P3ICYCb (II eM?) empaHo{J,J ceAOM. ,. B CBSl3H C 9TMM >KeJIaTeJIbHO neCKOJIbKO paClllHpHTb 3aaHHH YQe6.. HHKa 3a ClleT Bbl){eJIeHMH nap CBH33HHbiX fe)K,ny C060H CJIOB (CJIOBOCO. IJeTaHHH) H3 TeKCTa ynpa)f{HeHHH H YCTaHOBJIeHHH CBH3H Me)K,AY CJIO" 8aM" no BonpocaM. BOJIblIIHe TPYJJ.HOCTH ,8 9TO BpeMH npe.nCTaBJIHeT MH MHorHX yqa- llUIXCH pa3J1liqeHHe na,rte}f{eH. DHH CMeIUHBalOT HMeHMTeJtbHblH H BM- HHTeJ1bHblH; pOAHTeJIbHblH H BHHHTeJIbHbIH; po,nHTeJIbHbIH, ,naTeJIbHbIH, npeAJIO}KHbIH nae)J{H. 4TOObi Hs6eiKaTb 9Toro, Heo6xo,nHMO npHBJ1e- KaTb BHIilaHHe ,AeTeR K npaBHJIaM, ,AaHHbIM B yqe6HHKe nOA PYOPHKOH «3aMeTbTe!», «3anOMHHTer». .l{eTH J].OJl>KHbI YQHTbCSI pa3JIUQaTb na,ne>K no OCHOBHbJM npeMoraM, HanpHMep: Udmu "aOMY, "ce/lY (K tI e M y? K Y ,n a?); uamu no noAJO, no AeeYJ no cmenu (n 0 II e M y? r,n e?). ,LleTH 3anOMHHalOT npeAJIOrH, C KOTOpbIMH ynoTpe6JIHeTC5I ,naHHbIR naJ{e>K, YQaTCH CT3BHTb CMblCJIOBble BonpOCbI K CJIOBaM H pa3JIHtlaTb naJ].e>KH Ha OCHOBe 9THX BonpOCOB. Cne.u-OBaTeJIbHO, ynpa}KHeHHH THna: 6bl/l 8 eopoOe (r)]. e?), lIO noexQ./l, 820pOO (K Y J( a?); noOHUMaJOCb Ha 20PY (K Y ,z\ a?), HoemolO Ha 20pe (r .n e?) - 6YJJ.YT npe,z\ynpe}K)\aTb B03M01KHbIe OlliHOKH B CMeIlle- v HHIi na,ne>KeH. JI;IH Bblpa60TK.H YMeHHH npaBHJlbHO Onpe,AeJIHTb na,nem HMeH CY- mecTBHTe-&l'IbHbIX, nOMHMO ynpa)KHeHHA YQe6HHKa, MO)KHO peKOMeU,l\O- BaTb CJle,nYIOHI.He: 90
, CnoBa t ,naIlllbIe B CKOOKaX, nOCT3BbTe B HY}KHOI na.n.eJKe, npaBHJIb" I HO ynoTpe6HTe rrpe,nJIorlf. B }l{apKYIO JIeTHIOID HOllb .TIollla,neii BblrOH5HOT ... (nO/2e). M3JIb1lHK DbIBeJl napTH3all ... (pettKa). OTpR,l1 Me,l1JIeHHO ,nBHraJICH . . . (mpOnUHKa). 5o.,1blllOe 3HaqellHe MMeeT no,n6op 3aBHCHMbIX CJIOB: a) K rJIarOJIaM-CHHOHHMaf: 8Uaelnb (q TO?) Mope, a CMompemb (H a 11 TO?) Ha ..«ope; CKll3amb (K 0 MY?) cecmpe (0 q eM?) 0 KHU2e, a U3- BecmunZb (K 0 r o?) cecmpy (0 II eM?) 0 nUCbMe; U.Memb (II TO?) 8e.M/1/0;, a (J/zaaem b (11 e M?) 3eMAeU; 6) K MHor03HaIIHblM CJlOBaM: u2pamb (q T o? 11 e M? C K e M? B 0 q TO?), HaDAlOaamb (11 T o? 3 a q e M? 3 a K e M? H a,n q eM?), HanOMHumb (K 0 M y? 0 q eM?), 6pocumb (11 T o? q" e M? B K 0 r o?); B) K O)lIlOKOpeHHbIM CJIOBaM: CAYU.lamb (q TO?) n ecH. 10, HO npUC/lY- LUU8wnbCfl (K q e l\tl y?) " necHe; nOAb30BambCJl (11 eM?) KapmuHot1} HO ucnoAb308amb (q TO?) KapmUHY. OC06eHHO 3aTpy,nHSIeT ,neTeH pa3JIHtJeHHe OMOHHMHqllblX <pOpM MMeHHTeJIbHOrO H BHHHTeJlbHOrO na,ne>KeH B npe,llJlO}KeHHHX THna: ropum Kocmep H mKOAbHUKU pa30/lU Kocmep; Ha Ma'lme 638UJlCJl cpAa2 H Mill nOOHJL/l.U l/JAa2. , . B TaKOM CJIyttae Ha nOfOb AOJI)KeH npMHTH CHHTaKCH'IecKHH pas. 60p, rrOK33 CBH3eH 3Toro CYW.eCTBHTeJIbHOrO C JlpyrHMH CJlOB3MH B npe,lJ;IO}l{eHHH. BOT neCKOJlbKO npe)J)IO}KeHHH Ha pa3JIHQeHHe HMeHHTeJlbHOrO H BHHHT1bHoro naeeH: Born. U cOAHqe Bcmaem. BecHou 8CR cmenb nepeMeHullacb. Kocmep npKO zopum. fI BU3ICY CO/lHqe. OceHblO AroOU nOICudarom cmenb. Pe6Jlma pa30:J/CMU "ocmep. AHaJlH3 npe'O}KeHHH JIeBoH KOJIOHKH nOMOJKeT Y1laHMcH c,lte. naTb BbIBO){, IITO cYIIJ.ecTBHTeJIbHhIe COAHl.{e, cmenb, Kocmep CTOHT B HMeHMTeJlbHOM nane}Ke. OHH HB.TJHIOTCSI B npe)J)lO)KeHHH nOJlJIeiKaH- MH. npH pa300pe no 1IJleH3M npe)lJIO}KeHHR npaBoH KOJlOHKH, Y1laInHe. CH onpe,neJIHIOT, QTO cYIneCTBHTeJIbHble cOAHl.{e, cmenb, Kocmep HBJISIlOT- CH B npeJ10>KeHHH BTopocreneHHbIMH 'lJIeHaMH, OTBeqalOT H8 Bonpoc q T o? H CTORT B DHHHTeJIbHOM naAe>Ke. .ll.JIR pa3J1H1IeHHH HMeHHTeJlb- Horo II BMHHTeJlbHOrO rra,lle>KeH JJ.eJIeCOOOpa3Ho T3K>Ke rrOJIb30BaTb,CH npHeMOl'll nO;J.CTaHOBKH: cYIll.ecTBHTeJIbHOe MY>KCKOrO HJIH cpe;J.Hero po- Jl-3 MO)KHO 3aMeHHTb cYllI.eCTBHTeJlbHbJM >KCHCKOro pOJla. HanpHMep, eCJIH B npe)lJIO}l{eHHH f/ nOMHIO Mope CJIOBO Mope 33MeHHTb CYInecTBHTeJIb" HblM JKeHCKOro po.n.a oopoea: f/ nOMHIO aOp02Y, TO OKOHQ3HMe -y HCIIO YKa}KeT Ha BHHHTeJIbHblH na,ne}l{. B npoII-ecce pa60Tbi no pa3JIMQeHHJO HMeHHTeJlbHOrO - BHHHTeJlbHOrO na)le1KeH JJ.eJIeC006pa3l1o HHOf,na HC- I1OJ1b30BaTb 06a na)te>KllbIX Bonpoca: HMeHHTeJ1bHblii K T o? II T o? M BHHHTeJlbHbJH K 0 r o? II T o? 9l_-
3arpy)tHHer yqarnHXCH pa3JIHQeHHe BHHHTeJlbHOrO H pOHTeJlbHOrO naemeH O,ll.yrneB.TleHHblX CYllleCTBHTeJlbHblX MY>KCKOrO pOAa: He 6bLAO (K 0 r o?) 6OAICll, eJICa (p. n.), HO (JuneAu (K 0 r o?) 60/IKQ, e3ICa (B. n.) HJlH C/leiJ (K 0 r o?) MeoseoR (p. n.), HO 6blC/ledUAU (K 0 r o?) MeOeeaR (B. n.). B nO,ltoOHbIX CJIYllaHX ,lI.JlSI pacn03HaBaHHH na)tema Ta K>Ke MO}KHO pe- KOMeH,ltOBaTb npHeM 3aMeHW cymecTBHTenbRoro MymcKoro poa cy- LUeCTBHTe.'1bHbIf meHCKoro po;ta: He 6bl.ll0 (K 0 r o?) 60AKa, /lUCU4bl, HO nOUAfUJ1U (K a r o?) 80AKa, AUCU14Y; CAea (K 0 r o?) MeafJeafl, 6e/lKu, HO 6blC/leaUAU (K 0 r o?) .Mea8ea.R, 6eAY. npH BblnOJlHeHHH ynpa>KHCHItM no pa3J1qeHHIO na.l).e>i<eH Hea6xo,ZlHMO nOCTOHHHO Tpe6oBaTb, IIT06hl yqaWJteCH ,lI.OKa3aJIH, nOqeMY OHM )tYfaIOT, qTO BbI)teJIeHHOe cymecTBH- TeJlbHOe CTOHT B BHHHTeJIbHOM HJIM pOJ(HTenbHOM na.ne>Ke. B npouecce H3YQeHH SI IiMeH CYW.eCTBHTeJIbHbIX ftfO>KHO peKOMeH.no- naTb CJle,lI,YIOI.lI.He .nonOJlHHTeJIbHble ynpa>KlleHHH: 1) Y nOTpe6.neuHe O){HarO npe,lVIora C pa311bIMH na.u.e)KaMH (noexaJl Ha YKpauHY, 6blA Ha YKpaUHe; 6epHg/lCR C YKpauHbl, 6blA C m06a- puU{e,,t; noexa;1 8 AcmpaxaHb, OmablXaA 8 AcmpaxaHu); 2) ynoTpe6..'1eHHe npeJ(norOB-aHTOllHfOB 8, Ha - U3, C: (JICUA 8 KPbl- MY, HO Ita J1p1e; npuexa;1 U3 Kpbl.Jfa, 11,0 C YpaAa); 3) no,n60p cYLLlecTBHTe.,lbHbIX, ynoTpeMRIOLLlHxCR B pa3HbIx na- ,ne}l{ax, HO IJ!\-1elOll.U1X OHHaKOBoe UKOHQaHHe (6 mempaBu!. U3 mempa- au, no mempaau; 8 aepe8He, no iJepe8He). ,QeTH !lOJI)KHbI 3HaTb npe,ll.JIOrH, ynoTpe6JISleMbIe C TCl\{ HJIH HHbIM na.n}KOM: C J(aTeJlbHblM - 1(, no,' C pO.nHTe.TIbHbIM - y, om) ao, c, us,- 01\.0/1.0; C BHHHTenbHblM - 8, Ha; C npeMomHblM - 0, 8, Ha H T. .l).. C.ne,ltonaTe.'1bHO, B npou.ecce ynpa>KHeHHH no pacn03HaBaHHIO na- Jte>KeH }KeJIaTeJIblIO HaYIIMTb yqamnXCH nO.nb30BaTbCH He OJJ;HHM, a pa3HbIMH npHel'ttaMH. 113BecTHo, HanpHMep, liTO llJKOJIbHHKH qaCTO CMe.. llJHBalOT BHHHTeJlbHbIH H npeJI.J10>KHbIH na,lle>K: 80lU£A 6 aOM, [JICUA 8 00- .Me; 8306pa./1aCb Ha ellb, cuoe/la Ha eAU. B caMOM eJle, C)'rneCTBHTeJIb- Hble B npl1Be,ll.eHHbIX npHMepax, 0603Ha1laH MeCTO, MfeIOT OJ(HHaKOBbIe npe.nJIOrH 8, Ha. ECJlH YlleHHK 6Y!leT nOJlb30BaTbCH TOJIbKO OJJ;HHM npHeMOM pa3JIHlleHHH na,lle>KeH - pacn03HaBaHHeM MX no npe!lJIOraM, TO OH JIerKO MO>KeT 01lIH6HTbCR. B aHHOM CJIYlIae HY>KHO 06paTHTb BHH- MaHHe J\eTeH He TOJIbKO Ha 06Il\HH npe,l{JIor, HO H Ha na.n.emHoe OKOHlIa- HHe, naJl-e>KHbIH Bonpoc, HCXO,ll.HID.HH OT rJIaBHOrO CJIOBa. TaKHM 06pa30f, ecJIH YQeHHK YMeeT Onpe,lteJIHTb naJ(em no na.ne>K- HOMY Bonpocy Ha OCHOBe YCTaHOBJIeHHH CBH3H Me>KAY CJIOBaMH, no CHH- TaKcHyecKoH ponM Jl-aHHOrO CJIOBa B npe,llO>KeHHHt a KpOMe Toro, no npe,ltJIory H CMblcnOBOMY Bonpocy, TO pa3JIHlleHHe naJl-e>KeH ,l{JlH Hero He COCTaBHT TpYJJ;a. Q,lI.HaKO B npaKTHKe pa60Tbi llIKO.,TIbl Jl-O CHX nap, K CO>KaneHHIO, H3ytleHHe CK.il0HeHHH HMeH CYW.€CTBHTeJIbHbIX HOCHT OJl-HOCTOpOHHHH xapaKTep: .l).eTH MeXaHHqeCKH Ha3bIBalOT na,neHble BonpOCbI, CTOJIb me MeXaHHQecKH H3MeHHIOT CJIOBO no na.l).e>Ka1. B pe3YJIbTaTe TaKoro -H3YlleHHH na.lle>KeA .neJIaeTCH BbIBO,ll., tlTO naAe/K MO>KHO onpe'HTb TOJIbKO no na.l).e/KHOMY Bonpocy. 92
notne TOfO KaK ytJaIII.MeCH YCBOHT ,lIa3B3HUH na.ne1KeH, Hayt.13TCH pa3J1H1I3Tb HX no BonpOC3M H npeMoraM, no CHHT3KCHtJeCKOH pOJIIi u CJI0Ba B npeJ],JlO>KeHHH, MOiKHO nepeHTH K H3Y1IeHHIO T H n 0 B C K JI 0- H e H "H HMeH CYInecTBHTeJIbHbIX. OT Toro, _ HaCKOJIbKO 6bICTpO H npaBHJI110 yqaw.HeCH, H3yqaTCH pa3JIH'IaTb TMnbl CKJ10HeHHH, 3aBHCHT YMeHHe 6e30mHOO1lHO nHcaTb naJle>KHble OKOH1I3HHH. CpaBHHBaH OKOH- 1I3HHH HMeH CYIIleCTBHTeJIbHblX B p33HblX na,lle>K3X e,nHHCTBeHHoro IIMC- u Jla H YCT3HaBJIHBaH po,n 3THX cymectBHTeJlbHblX, Y1l3mHecH nOHMYT, qTO CYIll.eCTBHTeJIbHbIe B 3aBHCHMOCTH OT pO,ll3 onpe,neJ1eHHbIM OOp330M pacnpe,neJIlOTCH no THnaM CKJlOneHHSI. 3ry 3aBHCHMOCTb HarJlH){HO MO>KIIO npe.nCTaBHTb H3 TaKOH Ta(i,1Hue: POA liMeu cyw.e- tTBIiTe.n bHblX I-e CI<JI. 2-c CKJI. 3-e CR.,. >1<. p. M. p. aeMJI JI, BOJI H a BaHH, nana CHpeHb, KpOBaTb c. p. nO.I1, )J.eHb, I1BaH. capa" OKHO, none JIJlH 33KpenneHHH YMeHHH onpeeJUlrb THn CKJIOHeHHH Hl\tleH CY- w.ecTBHTeJIbHbIX II.eneco06pa3Ho npeMO}KHTb Y1l3IllHMC5I ,llJIH 3HaJlH3a TaKHe CJlOBa, K3K /lOWaOb - /lowaOKO" nellb - n£flKa J MOpK08b - MOp- 1WBKll, Kp08amb - Kp08amICa, e.llb- eAKa, n/lOUlradb-nAow,aOKa, 8etn8b- semK,a. Bce npHBe,neHHble cyw.ecTBHTeJ1bHbIe >KeHCKOro pO,LI.a, lIO O,nHH H3 HHX OTHOCHTCH K I-MY CKJIOHeHHIO, a ,npyrHe - K 3-MY. npH 9TOM" Ba>KHO YTOllHHTb, nOqeMY 9TH CYIIleCTBHTeJIbHbIe OTIIOCSITCH K pa3HblM CKJIOHeHHHlvl, H y6e,nHTbCH, qro HMeHa cyw.eCTBHTeJIbHble }l{eHCKOfO pO- .na MorYT OTHOCHTbCSI HJlH TOJl,bKO K I-MY, HJIM TOJIbKO K 3-l\I1Y CKJlOHe- HHIO. HaMIO,lleHHH 3a cYIll.ecTBHTeJlbRbIMH THna BaH.Jl- H8QH, A Aetua - A/leKCeU, 50pH. - Eopuc TaK>Ke n03BOJlHT Y1IeHHK3M c,neJl3Tb Bbl, BO,n 1ITO .l13HHble cym.ecTBHTeJIbHble MY>KCKOfQ po,na MOfYT OTHOCHTbcn, B 38BHCHMOCTH OT OI{OH1.IaHHSI, HJlH K I-MY, HJlH KO 2-IY CKJlOneHHIO. B npouecce J(onOJlHHTeJIbHbIX ynpa>KHeHHH yqaw.HeCH npHxOJtHT K BbIBO)lY, 1.ITO cyru.eCTBMTeJlbHbIe THna aeHb, meHb, neHb, AeHb, cupeHb, iropmol/JeAb, anpe/lb, Kflpyce/lb, KapaMeAb My*cKoro H >KeHCKOro po,na B HMeHHTeJIbHOM n3,ne>Ke He HMelOT OKOH'IaHHH, OHH OK31f1IHB3lOTCH Ha MHfKHe COrJI3CHble, _n09TOMY, 1IT06bI onpe,neJIHTb, K K8KOMY CKnOHC- HRIO OTHOCHTCH .n3HHble HMeHa cymecTBHTeJIbHbIe, H3,l10 3H3Tb HX po. <I>opMHpoBaHHe Yl\feHHH np8BHJIbHO nHcaTb na,l1eJKHble OKOH1J3HHH- u 0 neHTp3J1bHblH Bonpoc paCCM3TpHBaeMOH H3MH TeMbI. Ynpa>KHeHHH Y1Ie6HHKa .nO,lt06paHbI T3KHM 06pa30 1ITO ,llalOT B03- MO>KHOCTb H3YQHTb n3J{e>KHble OKOHqaHH CHaqana CYInecTBHTenbHblX l-ro CKJlOHeHHH, saTeM 2-ro H, H3KoHeu., 3-ro. TaKoe p3cnpe.neJleHHe MaTe- pHaJIa HaHJIyqwHM oopaSOM cnoco6cTBYeT YCBoeHHlO OKOHlIaHHH K8>K- ,lloro n3AeIK3, a 3aTe1 cpaBHeHHIO 3THX na,l\e1KHbIX OKOHtJaHHH. , 93
COnOCTaBJIeHHe nane)KHblX OKOHQaHHH peKOMeH;tyeTcH npOBO)tHTb CH8t1aJIa BHYTPH OAHoro CKJIOHeHHH, saTeM cpaBH'HB3H ABa THn3 CKJlO- HeHnA, saTeM Bce TPH CKJlOHeHHH cpa3Y H, HaKOHeI.t paCCMaTpHBaSl na- J,te>KHble OKOHlIaHHSI cym.eCTBHTeJIbHbIX eJ{HHCTBeHHoro H MHO>KecTBeH- Horo IIHCJla. TaK, npH H3yqeHHH naJle>KHbIX OKoHllaHHH I-ro CKJlO- HeHHSI COnOCTaBJISlIOTCSI OKOHQaHHSI pOJl-HTeJ1bHOrO If AaTeJlbHOrO nSAe- meA (/lodICU, I( //'oiJK/J), ,l1aTenbHOrO" npeJI.JIO>KHOrO (" .Ilodlre, 6 /loa- tee) H, HaKOHen, pOJl-HTeJ1bHOrO (-.Q, -bl), .llaTeJlbHOrO (-e) H npe,D.JIo)l{.. Horo (-e) ( "HU2U, 1CHU2e, 8 1CH,Uze). . nOCJIe TOro KaK 6YJl-eT H3ytteHO 2-e CKJIOHeHHe, HY>KHO conOCTaSHTb na,ne}KHbIe OKOHqaHHH CYInecTBHTeJIbHbIX I-ro H 2-ro CKJIOHeHHSI (e B npeJVIO)KHOM naJle>Ke - 8 KOMHame, 6 aOMe, 8 nOlle). na.ne>KHble OKOHttaHHH MO>KHO cpaBHHBaTb no CXOCTBY, no pa3" JlHqHlO H O)tHOBpeMeHHO no CXO,lJ.CTSY H pa3nHlIHIO. HanpHMep, conOCT3B.. neHHe no pa3nHIIHIO: OKOHttaHHH TBopHTenbHoro na)tea Bcex Tpex CKJJOHeHHH (iJopo2ofi, nOAeM, cmenblO) , cOnOCTaBJIeHHe no CXOACTBY H pa3J1HttHlO: OKOHqaHHH B JlaTeJIbHOM H npe,lJ.JlO>KHOM na,lJ.e}l{ax I-ro H 2-ro CKJlOHeHHR H OKOHqaHHH B 9THX >Ke naJle>Kax cyu.\eCTBHTeJlbHbIX 3-ro CKJIOHeHHH (me/l no oopoze, 110 no cmenu; 6blA 8 iJoP02e, 8 nOlle, HO 6 cmenu). TaKoro po,aa paOOTa cnocoocTByeT (j>ppMHpOBaHHIO YMeHHH npaSHJtb- lIoro HanHcaHHH na,ne>KHblX OKOHqaHHii. npOTHBOnOCTaBJIHH, HanpH- Mep, -8, -U B OKOHQaHHSlX HMeH cyw.eCTSHTeJlbHbIX eAHHCTBeHHoro IIHCJI8, Y1JaIIlHecH npHXO)lHT K BbIBOy, !lTO CYInecTBHTeJIbHbIe I-ro CKJlO- HeHHH B pOHTeJIbHOM naAe>Ke HHKor,l1.a He HMelOT OKOHqaUHH -e, 3 TOJIbKO -IJ (-bl) (32MAU, mempaOu); ttTO cytnecTBHTeJIbHbIe 3-ro CKJIO- HeHHjJ B pO;tHTeJIbHOM, aTeJlbHOM H npe.l(JtOJKHOM naj(e1Kax HMelOT TOJIb- I{O OKOHQaHHe -u (y npucmaHU" K npucmaHU, Ha. npucmaHU); liTO OKOHQaHHe -e B ){aTeJIbHOM na.ne>Ke 6blBaeT TOJIbKO Y cytnecTBHTeJIb- HblX I-ro' CKJlOHeHHH (Ie seMAe, I( BeCHe), Tor.ll.a KaK OKOHttaHHe -e B npe,lJ.JI01KHOM naAe>Ke xapaKTepHO )J.JlH I-ro H 2.:ro CKJlOHeHHH (8 K8ap- mupe, 6 nOM, Ha cnlOAe). . !lJIH HarJlHJlHocTH yqalll.HMcH MO}KeT 6blTb npeJ{JlO)J{eHa TaKa51 Ta6JIHua: I-e C.(JJ. 2-e CKJI. 3e CM. BOJIHa, KHHra TeHb, .'IODlab (OHb. none, GeJtbe" capaA n. n. -e -u .4. n., n. fl. p. n. p., 11., n. B npoll.ecce H3YQeHHH CKJIOHeHHfI HMeH cywecTBHTeJ1blIbIX yqalUHe- CH YCTaHBBJlHBalOT naJ{eR<Hble OKOHlIaHHH Ha OCHoBaHHH onpe-ne.neHHR THna cK.iloHeHHH, na..Ae>Ka cymecTBHTeJlbHOrO (CJleAOBa'FeJIbHO, TalOKe' npeJlJIOra, CMblCJIOBOrO Bonpoca). 9i I j 1
K8K YlKe OblJlO CKa38I10, AJISI onpe,lJ.e,,1eHHH na,ne)KHOrO OKOH1JaHU" yqaIIJ.lfeCH He AO.TJ>KHbl nO.'1b30BaTbCH TOJIbKO O,lJ.HMl\f npHeMOt, Hanpn- l\iep nOCT8HOBKOH CMbICJIOBOrO Bonpoca, TaK KaK 3TO MO)Ker npHBeCTH K oWH6Ke B HanHC8HHH OKOH1JaHHH cyraecTBHTeJIbHOrO, HanpHMep: XoiJU.ll no aopoze, 8cmo'//'.yaop02U, cnlOfl/l Ha aopoze. Bce npHBC)(eHlIbIC CJIOBOCO- lIeTaHHH OTBe1.lalOT Ha Bonpoc r Jl e? , HO HMCIOT pa3HbIe OKOHlIaIUH1, nOCKo..TIbKY OTHOCHTCH K pa3Hb]f\f na,lJ.e)J{aM. B npouecce pa60TbI Y1.lHTe.J11O HymHo MMeTb B BHJlY, lITO 3HallHTenL- Hoe KOJIHqeCTBO OWH6K B npaBonMcaHHH naAe)KHblX OKOHtJaHHH Bo..q- HHKaCT B TOM CJ1Y1Jae, eCJIH Me}J{,ny npe)J.JIOrOf H CYIll.eCTBHTeJ1bHbIM.Cro- liT -npyroe CJIOBO, npHJ1araTeJIbHOe HJlM CYllleCTBHTeJIbHOe (UAU Ha OKpaUHe aepeOHU, OICUJlU B Clnapou. aepeBHe), a TaK)J{e eCJIH ,llBa paenOJlo- >KeHHbIX p,AOM CYW.eCTBMTeJIbHbIX OTHOCTCH K pa3HbIM CJlOBaM. Ha- npHMep, B npe,llJIO)KCHHIf nUOH£pbl ocmaH08U/IUCb Ha 6epe2Y pe'lKU C.n080 petiKU CBH3aHO no CMblCJIY O CJIOBOM Ha 6epezy (Ha 6epe2Y pe'lKU), a CJIOBO Ha 6epezy C r.1JarOJIOl\f ocmaH08u/2ucb (ocmaH08U/lUCb Ha 6epe2Y). ECJBf yqeHHK He CYMeeT BbIJ{eJIHTb npaBHJlbHO napbI CJIOB, TO OH YO- meT HanHC8Tb «Ha OKpaHHe ,nepeBHe», «H8 oepery peQKe», TaK KaK npe,n- Jlor Ha OH COOTHOCHT C OKOllqaHHeM -e. .8 npouecce H3ytJeHHH MHO)J{ e C T B e H H 0 r 0 11 H C JI a HMe... CyecTBHTe.nbHbIX Ba)KHO, qro6w yqaw.uecH nOIlHJ1H, QTO CKJ10HeHe HMeH cymecTBHTe.'1bllbiX MHO)l{eCTBeHHoro QHCJIa He aaBHCHT OT THnOB CKJlOHeHHH HMeH cyw.eCTBHTeJ1bHbIX e.D.HHCTBeHHoro 1JHCJla. npH H3YQeHHIi na,lJ.e}l{HblX OKOH1JaHM" HMeH cym.eCTBHTeJ1bHblX BO MHO)KeCTBeHIlOM 1JHCJlC YQaHeCH 3anOMHHalOT OKOHtJaHHH -bl, -U, -a', -R (20pbl, U/,Ot!JePbl, cmenu, yttutne/l!l.)' B HMeHHTeJIbHO1 naAe)Ke, -Olty- -es, -eii (cmOA08, Aec08, nOlleu, cmenefi) B pO,nMTeJIbHOM na.ne}Ke, KpOMe TorO t OHM 06paalOT BHHMaHHe Ha TO, 1ITO pSl,D. cymecTBHTeJIb- HblX B pOAI1TeJIbHOM na,ne)Ke Boo6we He HMeeT OKOHqaHH" (cmpaH., eop, cell, 6epes). B npou.ecce BblnOJIHeJlHH yn!'a}l{HeHHH YtJe6HHKa YQalllHeCH 6Y-D.YT 38nOMHHaTb OKOH1JaHHH cyrnecTBHTeJIbHbJX B AaTeJIbHOM (cea.M, ae- pe8HRM, 2opooaM, cmenRM), TBopHTe.TlbHOl'v1 (ceAQ.MU,. aepe8HRMII, eopooaMu, CmenR.Mu) H npe)l.JIO)l{HOM na,ne}J{ax (8 ceAa,,x, 8 depeBHRX, 20pooax, cmenJl.x). ¥ITaK, B pe3YJlbT8Te H3YlleHHSI TeMbl «H3MeHeHHe HMeH CYllleCTBHTeJlb" IIbIX» YQaIII.UeCH ,D.OJI)KHbI Yl\feTb npaBHJlbHO onpe,lJ.eJITb pO,D. H tIHCJIO CYllleCTBHTeJIbHbJX, THn CKJIOHeHHH, pa3.,1JHlIaTb naAe>KH cym. e - CTBHTCJIbHbIX H, Onlipa.HCb Ha 3TH 3HaHHH If YMeHH npaBHJlbHO fJHCaTb I naAeIlbIe OKOHqaHlfH; KpOMe Toro,""' CTaBH BonpOCbI YllalIJ,HeCH ,nOJl)K- lib! YJ\feTb onpe,lJ.eJlSlTb CHHTaKCH:tIeCKYIO pOJ1b cymecTBHTeJIbHoro. TeMa «H3MeHeHHe HfeH CYllleCTBHTeJIbHblX» P.SOT. no pa31HTMIO npe,D.CTaBJ1S1eT 60JIhWHe B03MO)KHOCTH ,llJIH pa60- peliM TbI no pa3BHTHIO peIJH. C 9TOA l..lblO B Y1JeOHHKe npe,D.YCMOTpeHbl ynpa>KHeHHSI CJle,nylO- w.ero xapaKTepa: 1) ynp8}KHeHlfH MH pa60TbI C MHOr03HallHblMH eJIO- BaMH; 2) ynpaJKHeHHB, HanpaBJIeHHbIe Ha npaBHJ1bHoe. ynoTpe6JIeHHe 95
"- npe.D.JIoros\ B petiH (npe.ztnOJKHOe ynpaBJleHHe); 3) ynpa>KHeHHH Ha COCTaBneHHe npe,lJ)IO>KeHHH C aHHblM" CJIOBaMH H CJlOBOCOlleTaHHHMH; 4) ynpa>KHeHHH no HcnpaBneHHK> }.te$opMHpoBaHlIoro TeKCTa; 5) yn... pa>KHeHHR 8 no,lt60pe OTBeTOB Ha Bonpocbl; 6) ynpa>KHeHHH )VISI pa.. 60Tbi Ha.zt 'H3nO>KeHHSlMH; 7) ynpa>KHeHHH ,AJ1 pa60Tbl Het,a COqHHe- HHHMH. ,aononHHTeJ1bHO K 3THM MorYT 6bITb peKoMeH.D.oJJaHbI H ynpa>KHeHHH B CJIoBoo6pa30BaHHH, HanpHMep: npH nOMOInH CyctxPHKCOB -meAb, "II." o6pa3YHTe HMeHa cymecTBHTeJIbHble OT CJle,AYlOmlix CJlOB: /le- mamb, 800umb, Yf.lUmb, apysumb, nYIleMem; HanHWHTe 5 CYlUecTDHTeJIb- HbiX C CyctxPHKCOf -It; onpe.zteJIHTe, KaKHe 3HaqeHHH BHOCHT 3TOT cY<P- cjJHKC. npH BblnOJlHeHHH 3Toro ynpa>KHeHHSI yqamHeCH YBH,ASlT, liTO CY<IxI>HKC -,,- npH,ttaeT 3HatIeHHe >KeHCKOro pOJ{a (nuoHep - nuoHepKa), a TaK>Ke 3HaqeHHe YfeHbIllHTeJ1bHOCTH (Kpo8anlb - Kp08amKll H T. }.t.). Pa36epHTe IIO COCTaBY CJlOBa: tlaUHUK, nucameAb j t(,umameJ1b, nUAb-. W,UK; Ha30BHTe CJlOBa, OT KOTOpbIX ,lJ.aHHbIe CYI.UeCTBHTeJ1bHble 06pa30- BaHbI. Kpo:Yle Toro, H3yqeHHe na,lte>KlIbIX OKOHqaHHH MO>KeT 6bITb CBH3a- 110 C onpe,lteJ1eHHeM na,lte>KHbIX OKOHQaHHH CJIOB-CHHOHHMOB: MemeAb, 8b1Oza, 6ypaH; poauHa, OfrltlU3Ha; C.nOB-aHTOHHMOB: ::lUMa - Aemo} Bee- Ha - oceHb. npe>K)te qeM CKJIOHHTb ,lI.aHHbIe cnOBa, CJleJ{yeT' 05paTHTb BIIHMaHHe yqaIlI.HXCH Ha TO, qTO OHH MH3KH no 3HaQel1HIO HJIH, Ha06o- pOT, npOTHBononOiKHbI no 3HaqeHHIO H T. .zt. Cne)lOBaTeJ1bHO, TeMa «113MeHeHHe HMeH CYI.UeCTBHTeJlbHbIX» npe,lJ.o- . CTaBJISleT yqHTeJIlO 60JIbllIHe B03MO>KUOCTH He TonbKO JVISI npOBeJ{eHHH paOOTbl no rpaMMaTHKe H opcl>orpa<t>HH, HO H no pa3BHTHEO peQH, no HaonEO,lteHHlO Ha,A COCTaBOM cnoBa, ero 3HaQeHHeM. B I KJIaCCe ;{eTH yqHJIHCb pa3JIHlIaTb CJIOBa, OTBe- MM. npHnaraTenbHoe qalOllI.He na BonpOCbI K a K 0 H? K a K 0 e? K a- K a SI? K a K H e? Bo I I KJIacce OHH Y3HaJIH, QTO CJlOBa, OTBeqalOInHe Ha 9TH BonpoCbl,.... 0603HaqalOT npH3HaKH npe,lJ.Me- TOB. Y3HaJIH )teTH H TepMHH «HMH npHnaraTeJIbpe» l! HeKOTopbIe cjJOpMaJlbHble npH3HaKH 9TOH qaCTH petIH, B qaCTHOCTH, qTO npHJIara- TeJlbHble Bcer,lJ.a OTHOCHTC5I B npeMO>KeHHH K cymecTBHTeJIbHblM H H3leHHIOTCH no po.aa1 H qHCJIaM B 3aBHCHf\.IOCTH OT CYW.eCTBHTeJIbHblX. B I I I Knacce B u.eHTpe BHHMaHHH yqaHXCH nae>KHble OKOHtlaHHH npHJ1araTeJlbHbIX MY>KCKOrO, >KeHCKOro H cpeHero poJt a TaK>Ke H3" MeneHHe npHJ1araTeJlbHblX BO MHO}KeCTBeHHOM IIHCJIe./ nporpaMMa 3Toro KJlaCCa OTBO,lJ.HT Ha H3yqeHHe npHJIaraTeJIbHblX 30 qaCOB. npH nOBTopeHHH Y>Ke H3BeCTHbIX yqamHMCH npH3HaKoB npHJlara- TeJlbHbIX UeJIeC006pa3Ho cpaBHHBaTb 9TY qaCTb peqH C HMeHaMH CYW.ecT- BHTeJIbHbIMH. L{eTH )J.OJl>KHbl nOHHTb, B qeM CXOACTBO H B qeM pa3nHtlHe 9THX tlacTea peqH. YqamHeCH HatlaJIbHblX KJIaCCOB OtleHb qaCTO CqH- TaIOT, liTO HMeHa cyw.eCTBHTeJlbHble H3MeHRIOTCH no pO,ttaM. CpaBHeHHe npHnarareJIbHblX C cyrneCTBHTeJIbHblMH nOMO>KeT YCT8:HOBHTb, tlTO npH- naraTeJIbHble B eAHHCTBeHHOM qnCJle H3ft,feHSIIOTCH no pO)J.aM, a cyecTBH- 96
TeJIbHble no poJtaM He U3MeHSlIOTCH: Ka}l{JlOe cyrnecTBHTeJlbHoe HMeeT onpeJteJIeHHblH pO)l (MY}I{CKOH, cpeJtHHH HnH >KeHCKHH). POJ( H tlHCJIO npHJIaraTeJ1bHOfO 3aBHCHT OT poa H tlHCJIa cyecTBHTeJlbHOrO, C KOTO- pblM npHnaraTeJlbHoe CBH3aHO B npeAJIO>KeHHH HnH cnOBOCOqeTaUMH (KpacHaJl nAow,ai)b, KpacHoe 3Ha.MJl, KpacHblU 2mYK, KpaCHble 30pU). TOIlHO TaK *e naJl.e./K HMeHH npHJIaraTeJIbHOfO BcerJla COOTBeTcTByeT na,lte}KY CYllleCTBHTenblloro, c KOTOpbIM CBH3aHO npHJlaraTeJ1bHoe B petfil (H acmynuAo Mat1cKOe ympo. 11.0A20 3ICOaJlU pe6nma Ma!lcKozo ympa. XOpOUlO 8 6epea080M Aecy paHHUM MaUCKUM ympoM H T. n.). Heo6xo,nHMO HaYQHTb yqarnHXCH npHBo,nHTb HpHMepbI liMen npHJ1a- raTeJlbHblX, 0003HatlaIOIUHX p a 3 JI H q H bl e npH3HaKH npeJlMeTOB. 3roro ytlHTeJlb CMO}KeT JlOCTHfHYTb, ec.nH nOCTOHHHO 6YJl.eT CJle){HTb 38 reM, 1JTOObI npHJIaraTeJIbHble, KOTopble npHBOJ{HT yqaIIJ.HeCH, onpe- AeJlHJlH npeMeTbl C pa3HbIX CTOpOH: no UBeTY (IOOPUi/,He8b1il, 6eAblU, CU- HUt1), no BKYCY (20pbKUU, CAaOKUU, COAeHblU, K,UCAblU); no pa3Mepy (60AbLUOU, MQ,J1£HbK,UU j 02pOMHblU); no MaTepHaJIY (KaMeHHblU, iJepe- 8RHHblU, CmeK,.llJlHHblil); no BpeMeHH (8"lepautHUU , 8eceHHUU, 3U.M.HUU): no 3anaxy (AUMOHHblU, MUHOaAbHblU); no BocnpHHTHIO Ha ornynb (MJl2Kutl, e/ltWKuu, urePWaBblU),. no cJ>oPMe fICPY2/lblU, nAocKuu); no MecTY (eopoocKOu, ooeUlHuu),. C TOqKH 3peHHH pa3J1HtlHbIX KaqecTB (0m3bl81lU8blU,. m08apuU{eC1(Uu, caMoOmeep[)ICeHHblu) H T.:.n. npll nOBTOpeHHH TeMbI «}13MeHeHHe HMeH npHJlaraTeJlbHbIX no po- .naM H tlHCnaM» (2 qaca) BIll KJIaCCe yqarnHecH JlOn>KHhl BbInonHHTb Ta- KHe ynpa}KHeHHH, KOTopbIe 6YJJ.YT cnoco6cTBoBaTb BblpaOOTKe y HHX HaBblKOB cOe,lJ.HHHTb HMeHa npHnaraTeJIbHble C HMeHaMH cyrnecTBHTeJIb- HhIMH p CTaBSI npH 3TOM Bonpocbl OT cYIIJ.ecTBHTeJIbHbIX K npHnaraTeJIb- HbIM. 3aAaqa YIlHTeJlH COCTOHT 8 TOM, llTOObI HaytlHTh JteTe" npaBHJIbHO CTaBHTb 3TH BonpOCbI. Ha6JnOJ{eHHH nOKa3b1BalOT, qTO B npaKTHKe WKOJlbHOrO ooyqeHHH OiliHOOK B OKOHtlaHHSlX npHnaraTeJIbHbIX BCTpe- qerCH 6oJlbllIe, qeM B OKOHqaHHHX cyrnecTBHTeJlbHblX. 06'bHCHHeTCH 9TO fJlaBHbIM oopa30M TeM, tlTO J{eTH He YfeIOT npaBHnbHO BbIJleJ1HTb H3 npe)l.JIO}KeHHH napbl cnOB - npHJIaraTeJIbHOe H cYIUeCTBHTeJIb- Hoe - Ii CTaBHTb BonpOCbI OT cytnecTBHTeJlbHOrO K npHJIaraTeJ1bHOMY, YCTanaBnHBaH reM caMblM OKOHqaHMSI npHJIaraTeJlbHblX. HanpHfep: 80UleA 8 aemcKutl nap/(; 8 napK (K a K 0 ii?) aemcuu; yexaJl, U3 eopHo2o caHamOpU!l; U3 caHamOpUR, (K a K 0 r o?) 20pH020,. nepeeXaA 8 H08glO 1C8apmupy; K8apmupy (K a K y IO?) H08Y'0 H T. n. npaBHnbHO nOCTaBneHHbIH Bonpoc nOMoraeT YCTaHOBHTb OKOHqa- BHe npHJlaraTeJIbHor.o H npeJtynpeaeT OlliH6KH npH nHCbMe. EOJlblliaH tlaCTb YtleOHOrO BpeMeHH, OTBeJteHHoro CKnoHeHMe MMeN Ha H3yqeHHe TeMbI «113MeHeHH HMeH npHnara- npMnaraTenbNwx TeJIbHbIX no nae>KaM», nOCBHrnaeTCSI paOOTe Ha,Zt OTAeJIbHbIMH na.n;e}l{HblMH q>opMaMH (CKJlOHeHHe HMeH npHJIaraTeJlb- HblX Mym:CKoro H cpe.n;Hero pOJla -8 tlaCOB; CKJlOHeHHe HMeH npHJIa- raTeJIbHbIX }KeHCKOro poa - 6 qaCoB). Heo6xoJ{HMO TaK BeCTH 06YQeHHe, qT06bI J{eTH nOHHnH, liTO YAap- Hble nane>KHble OKOHQaHHH npHJIaraTeJlbHbIX (TaK me KaK H cyecTBH- 4 3aK83 694 97
TeJlbHbIX) He HY>KAaIOTCSI B npOBepKe; npOBepHTb HeooxoAHMO TOJIbKO oe3Y.llapHble naAeLKHble OKOHqaHHH. l{enecooopa3HO BQOpY>KHTb yqarnHXCH pa3J1HQHbIMH cnocooaMH on- peAeJIeHHH npaBonHCaHHJI 6e3YJ{apHbIX OKOHQaHHH npHJIaraTeJlbHblx: 1) nocpeJtcTBoM BonpocoB OT CYInecTBHTeJIhHbIX K npHJIaraTeJIbHblM (coAHl{a (K a K 0 r o?) ICpacHOZO; acmpa (K a K a H?) KpacHQR; Hottb (K a K Y IO?) meMHYIO; 38eaMU (K a K H M H?) .npKUMU H T. JJ..); 2) nYTeM conOCTaaneHHH 6e3YJJ.apHwx OKOHqaHHH npHJIaraTeJIbHMX C YJtapHblMH OKOHqaHHSIMH (noiJ cllHUM He60M - nod 2oAy6bLM. He60M,. 8 C8emAYlO KlJMHamy - 8 60/1bwjlO KOAtHamy). Hano HMeTb B BH,ny, lITO He Bce 6e3y,napHble OKOHQaHHSI npHJIaraTeJIbHbIX nO)Ul8IOTCH no,noo- HaMY COI1OCTaBJIeHHIO. OKOHQaHHH Hl\ieHHTeJIbHOrO- BHHHTeJIbHOrO na- J\e>Ka MY>KCKOrO pOJ{a eJtHHCTBeHHoro 1.JHCJIa (-bIU, -uii) H MHoiKeCTBeH- Horo qHCJIa (-ble, -ue), pOJtHTeJ1bHOrO na,lle*a e,lll1HCTBeHHoro qHCJla MY*CKoro H cpe,nHero po,na (-OlO, -elO) He nOMalOTCH npOBepKe nYTeM conOCTaBJIeHHH, TaK KaK -btU, -uii, -ble, -ue Bcer,na. ObIBalOT 6e3Y- .napHbIe, a -OlO, -ezo npOH3HOCHTCH KaK «-OBa», «-eBa». !lJIH Toro qTOObl Y1.Ja{UHeCH YCBOHJIH YKa3aHHble na)le}KHbIe OKOHqa- HHH, UY}KHbl MHorOKp8THbie ynpa}l{HeHHH, B KOTOpbIX TpeoyeTcSI He TOJIh- KO HanHC8Tb HMeHa npHJIaraTeJlbHbIC, HO H pa306paTb HX. na"neJKH npHJIaraTeJIbHbIX H3Y1.JaIOTCSI npeHMYIlleCTBeHHO B cono- CTaBJIeHHH: HMeHHTeJlbHblH H BHHHTeJIbHblM ITa)te>KH MY>KCKOrO H cpe)J.- Hero pO)l.a, pO,nHTeJIbHblH H BHHHTeJIhHblH na,ne>KH MYJKCKOrO pO)la (Hem iJo6pozo 'leAOBeICa - 8U3ICY iJ06po2o tleAOBeKa) H T. ,n. ConOCTaBJIHH HMe- G U HHTeJIbHbIH H BHHHTeJIbHbIH na)le>KH, yqalllHeCH IIHT810T ,naHHble YtJH- TeneM HJII1 B yqeOHHKe npeo*eHHH napaMH, HaXOHT B HHX nOA- JIe>Kamee, onpe,neJIS1IOT HMeHUTeJIbHbIH H DHHHTeJIbllbIH na,nemH cy- mecTBHTeJIbHblX H no cYIllecTBI1TeJIbHbIM - na.lle}KH npHJlaraTe.ITbHbJX. HanpHMep: Ha KpalO Ileca cmOR/l MaMHb"uit OOM (H. n.). Meme..1.b 3a.MeAa Ma/WHb"uii dOM (B. n.). flUOHepbl pa30ICZAU 60Jl,blUOfi, I(,ocmep (B. n.). 60AbUlOli "ocmep (11. n.) nbl/laJl Ha nOIlRHe. npH 3TOM 06palllaeTCH BHHMaHHe He CTOJIbKO H8 OKOHlIaHHH npHJIaraTe"TJb- UbIX t CKOJIbKO Ha na)lem cymecTBliTCJIbHbIX: KaKOB na,lle}K CYIIlCCTBH- TeJIbHOrO, TaKOB na,ne>K H I1pHJIaraTeJIbHoro. npH H3yqeHHH OKOHQaHHH npHJIraTeJIbHbIX Tome ueJIeC006p83HO HCnOJIb30BaTb COnOCT8BJIeHHH. ConOCTaBJlHIOTCS1 OKOHqaHHSI HMeH npH- JIaraTeJIbHbIX -blii, -uii (B MY>KCKOM pOAe) H -ou, -eii (B meHCKOM pO.lle). npaKTHKa lliKOJIbHOH paooTbl nOCKa3b1BaeTt 'ITO ,neTH qaCTO nYTaIOT 3TH OKOHliaHIJSI. YqaIUHMCSI HeOOXO,llHMO 001>HCHHTb, qTO B MY>KCKOM poe Ha Bonpoc K a K 0 Ii? OKOHQ8HHH -blii, -au Bcer,l).a 6eaYJ{apHble (lCpticHblii, ctJ,Huii, HOObtU, 6 eA bIU), a OKOHqaHHe -ou y.nap Hoe (60Ab- wou, eO/ly6oii, MOAoiJOU),o B *eHCKOM pOAe Ha Bonpoc K a K 0 Ii? OKOHqaHHH npHJIaraTeJlbHblX BcerJta -OU, -eii, K8K YAapHbIe (60Jlb- wou, 20Ily60ii), TaK H oe3YAapHbIe (KpacHOU, cUHeii). B AaHHOM CJIyqae nOMoraeT H APyroH npHeM - nOHHMaHHe Y lla xn H - MHC pa3HHD.bI B na)J.e}K8X: MymcKoH pOA - K a K 0 i%? (ICpacHbltl, cu- HUU) - HMeHHTeJJbHbIH HJlH BHHHTeJlbHbJA na,n.e)K; :meHcKHH pO,lJ.- 98
K a K 0 H? - pO.AHTeJlbHbIA, ,naTeJ1bHblH, TBOpHTeJlbHhdi, npe,lVlO>KHblH nae}KH. 3,necb 'UeJIecoo6pa3HbI ynpa}l{HeHHH B COCTaBJIeHHH CJlOBO- COqeTallHH HJIH HeOOJlbWHX npe,l(JlO}KeHHH c YKa3aHHblMH npHJIaraTeJIb- HblfltlH, OTBeqalOIl\HMH Ha Bonpoc K a K 0 if? HanpHMep: 8bLCOKUU aOM, IWmaAUCb C 6blCOK,oii eopbl; B'tepa 6blA CHe3ICHb/,ii 6ypaH, Jl He BU- ae/l maKOU CHe3ICHOU 6ypu H T. n. Uenecoo6pa3Ho H conOCTaBJleHHe BH- HHTeJ1bHOrO (K a K Y IO?) H TBOpHTeJ1bHOrO (K a 0 it?) nae}KeH npHJIaraTeJlbHbJX B >KeHCKOM pOAe. YqarnHeCSI qaCTO CMellIHBalOT YKa3aH- lIbIe OKOHtlaHHH. H3BeCTHoe BcnOMOraTeJIbHOe 3HatleHHe HMeeT B Jl-aH- HOM CJIYtlae onopa Ha BonpOCbI: B. K a K Y IO? - KpacH»IO, CUHIOIO (AeHmy),. T. K a K 0 4-(0 fO)? - KpacHO(i, (-010), cUHeii (-elO) lleHmou. YKa3aHHbIe npHeMbI MorYT 6blTb HCnOJlb30BaHbl H npH M3YIJeHHH npaBonHcaHHSI CMellIHBaeMbIX OKOHtlaHHH TBOpHTeJlbHOrO (-61.."" -U.AI) H npe,ll.JIO}KHOrO (-OM, -eM) na,ll.e*eH B MY*CKOM H cpeJl-HeM: pOAe: 1) COnOCTaBJIeHHe OKOHtlaHHH B Bonpocax 11 OKOHIJaUHH npHJlaraTeJlbHbIX: K a K H M? - KpacHblM, CUHUM (nllamKoM, nilambeM), 0 K a K 0 M?- o Kpacu'OM, CUHeM (n/lambe, n/lamKe); 2) conOCTaBJIeHHe nae)Ke" H na,Ae>KHbIX BonpocoB: T. K a K H M ? - 2ycmblM, BbLCOKU.M (ay60M), n. 0 a K 0 M? - 0 2ycmoM, 06blCOKOM (ay6e). KpoMe pa360pa C ytIHTeJIel'.1 rOTOBblX npe,ZVIO}l{eHHH H tlTeHHSI npa- BHJI no yqeOHHKY, II.eJIeC006pa3Ho, lIT06b1 yqarnHeCSI caMH COCTaBJlSlJIH npe){JlO}l{eHHH HJlH CJIOBOCOtIeTaHH5I C HMeHaMH npHJlaraTeJlbHblMH B HY»<HbIX na,nemax t a TaK>KC caMOCTOSlTeJIbHO CKJlOHHnH npHJlaraTeJIb- Hble BMeCTe c cYIIecTBHTeJlbHbIMH. npH 3TOM nepe,n npHJlaraTeJlbHblMH (OT liMeH cyrnecTBHTeJIbHblX) B Ka>KltOM naJl-e*e OHH ,lI.OJl}l{Hbi nOCTaBHTb Bonpoc. HanpHMep: MC (K a K 0 it? ) 60JlbUlOU; Mca (K a K 0 r o? ) 60/lbLUOZO; nO.Aecy (K 8 K 0 M Y? ) 60AbUJ,OMY H T. n. OKOHtIaHHH Bon- pOCHTeJl6HOrO MeCTOHMeHIIH H npHJlaraTeJlbHOrO AeTH nOJl-tlepKHBaIOT; 3TO nOMoraeT YCTaHOBHTb COOTBeTCTBHe Me>KJlY BonpOCOM H OKOHtIaHH- eM npHJlaraTeJlbHOrO (K a K 0 H? - 60AbUloii, K a K a H? -60/lbtuaR). LlJI5I 60Jlee C03HaTeJIbHOrO YCBoeHH5I na,ll.e}l{HblX OKOHtlaHliH npH- n8raTeJlbHbIX Ba)KHO t tlTOObI ytlalllHecSI 3HaJl" 3TH OKOHtlaHH5I. Hanpn- Mep, B pOJtHTeJ1bllOM na,ne>Ke MY>KCKOrO H cpe,ll.Hero p0,ll.a OKOHtlaHJUI -OZO,- ezo, B TBOpHTeJIbIIOM na,l(C}Ke Tex >Ke npHJIaraTeJlbHbIX OKOH- qaHIIH -bIM, -UM, a B npe){JlO>KHOM - -OM, -eM H T. ,n. TaKHM 06pa30l\f, onpe){eJlHB nae)K npHJlaraTeJlbHOrO no na,ll.e}KY HMeHH cymecTBHTeJ1b- Horo, ytIeHHK He OUlH6eTCSI B HanHcaHHH OKOHtlaHHH. HepeKO YtlaIll.HecH no,l( BJlHSlHlleM na)le>KHOrO OKOHtlaHHH cyuecTBH- TeJIbHOrO HenpaBUJlbHO nHWYT OKOHtlaHHe B npHJlaraTeJIbHOM, HanpH- Iep: «no)!. CTapOM ,l(y60M» BMeCTO noiJ cmapblM ay60M. KaK YiKe 6bIJIO CKa3allO BbIIlle, B 9TOM cJlYtiae nOl\iOInb OKa>KeT cOnOCT8BJ1eHMe OKOHtIa- HHH BonpOCHTCJIbHblX CJlOB H OKOHQaHHH npHJlaraTeJlbHb[X: nod K 8 K H M? - cmapblM (Oy60M). B npou.ecce paGoTbI Ha)t HMeHaMH npHJIar8TeJ1bHhIMH YtlalllHecR I I I KJIaCCa HatlHH810T nOHHMaTb, tlro npHJIaraTeJIbHble MY>KCKOrO H cpe;J.Hero po,na BO scex KOCBeHHblX naJt}I{ax HMelOT o,nHHaKOBble OKOH- qaHHSI, a npHJIaraTeJIbHble >KeHCKOro poa CKJIOHRIOTCH HHatie. 4* 99
KpOMe ynpa}KHeHHH, KOT9pble ,lJ.eTH BbInOJIHSlIOT no ye6HHKY, 3a.. nOMHHaHHIO H C03HaTeJIbHOMY YCBoeHHIO natte>KHblX bKOHqaHHH nOMO- raeT COCTaBJleHHe Ta6JIHn CKJlOHeHH.H npHJlaraTeJlbHblX. TaOJlHUbl YllH- TeJlb COCTaBJlSleT H 3anHChlBaeT e yqaHMHCSI B npou.ecce ypOKa, o,lJ.ua- KO HeKOTopble Ta6JIHltbl yqamHeCH III KJlacea MorYT COCTaBJlJlTb caMO" CTOHTeJ1bHO. I..(e.necoo6pa3Ho pa60TaTb Ha,lJ. TaKHMH, HanpHMep, Ta{)- JlHltaMH: 1) TaMHl(a pO)J.OBbIX OKOHlIaHHH HMeH npHJlaraTeJIbHhlX; 2) Ta{)JIHl(a na,lJ.e:H<HhlX OKOHQaHHH MY>KCKOrO H cpeJI-Hero po,lta; 3) Ta6- JIHu.a na,lJ.e}l{HblX OKOHtlaHHH >KeHCKOro pOAa; 4) TaMHl(a na,ne>KHbIX OKOH- qaHHH npHJlaraTeJIbHhlX MHO>KecTBeHHoro qHCJla;. 5) 0606rnalOaH 'Tao- JlHlta «I1MSI npRJlaraTeJ1bHoe» H JI-p. BOT, HanpHMep, KaKoH BH,lJ. fO>KeT HMeTb Ta6J1Hu,a no.ll. Ha3BaHHeM «Pa3J1HIJaH OKOHqaHHSI npHJlaraTeJlbHblX -b'.M, -aM H -OM, -eM». T. K a K H M? - KpacHblM , CUHU.M (nJlaTKOM, nJlaTbeM). n. 0 K a K 0 M?' - KpaCHOM, CUHeM (nJlaTKe, nJlaTbe). COCTaBJleHHYIO KOJlJleKTHBHO TaOJlHUY YtiarnHeCH 3anHCbIBalOT B TeTpaJI-H. 3aTeM OHIl npHJI-YMblBalOT caMOCTOHTeJIbHO npeWIOIKeHHSI C HMeHaMH npHJIaraTeJIbHblMI:i (H cyrnecTBHTeJ1bHbIMH) B TBOpHTeJIbHOM H npe,lJ)lO>KHOl\f naJl-e)I{ax. OTAeJIbHbie npeMO>KeHHH pa36HpalOTCSI Ha ypOKe. npH 3TOM YIJHTeJ1b Tpe6yeT, tlT06bl Ytlm..nHecSI aprYMeHTHpOBa- JIH CBOH OTBeTbi. HanpHMep, pa36HpaeTCSI npeAJlO}KeHHe 3eM.Ilfl nOKpbl- . Jlacb 6e/lOCHeHbtM KOIJpOM. ¥IJaIUHHCSI BeJI-eT pa36op: nOKpblllacb (tl eM?) K08pOM - TBOpHTeJIbHbIH naJI-eIK, 3HatlHT, H ITpHJIaraTeJlbHOe 6e/lOCHe,;cHblM CroUT B TBOpUTeJIbllOM na,ae}Ke; MO}KHO npOBcpHTb OKOH- qaHUe npHJIaraTeJIbHOrO BonpOCOM: K08pOM (K a K H M?) 6e/lOCH..e3ICHbtM , B Bonpoce OKOHtlaHHe -UM, 3HatlHT, H y npHJlaraTeJIbHOrO -blAt. ,UpyroH npHMep. Ha ypOKe, nOCBHrneHHOM npaBonHcaHHIO npHJIa- raTeJtbHblX IKeHCKoro pO)la, YIJaIUHeCSI pa60TalOT Ha,A TaMHl(eH, no- MoralOIUeH pa3JIUtJaTb OKOHQaHHSI 9THX npHJJaraTeJIbHbIX B p,a3HhIX naAe>Kax. HanpHMep: /leHmy (K a K y IO?) KpacHYIO} CUHIOIO - BHHHTeJlbHbIH naAe>K; JleHmOU (K a K 0 H (0 10 )?) KpacHoa (-010), CUHeU (-elo) - TBOPH- TeJlbHblH na,ne>K. . YtJalll.HeCH COnOCTaBJISllOT OKOHtlaHHH B Bonpocax -YIO, -OU (-010) H OKOHtlaHHSI npHJlaraTeJlbHblX -YIO, -1010; -OU (-010), -eii (-elO). Ha ypOKax, nOCBSlw.eHHbIX H3YQeHHIO npaBonHcaHHSI 6e3yapHbIx OKOHlIallHH HMeH npHJlaraTeJlbHblX, YtlalllHecSl npe>K)l.e Bcero nOJI- PYKO- BOJI-CTBOM yqHTeJISI COCTaBJlSllOT TaMHbl CKJlOHeHHSI npHJlaraT'bHblX C 6e3yJtapHbIMH OI{OHIJaHIf5lMH (-b'", -aR, -oe; -aii, -JIll, -ee). HanpH- .. Mep: . «5e3YJtapHble OKOHqaHHSI npHJlaraTeJ1bHbIX»: H. q T o? - CHe:JICHbIU Y30P, CHe[}fCH,Oe nOlle}' cHi"'HaR 20pKa. P. q e r o? - CHeHOZO y30pa, - nO/lJl; c,.,eHofi, 20pICU. n. tI e M y? - CHe3ICHOMY ysopy, no./llO; CHf3ICHOU. 20pKe. B. IJ T o? - CHe3ICHbIU Y30P, nOlle; CHe3ICH'1O 20P1CY. T. q e M? - CHeHblM Y30POM, nO/leM; CHe3ICHoii 20pKOii. n. 0 tI e M? - 0 CHe:JICHOM ysope, nolle; 0 CHe3ICHO(J, 20pKe. 100
no 9TOMY oopa3UY yqarnneCH CMorYT caMOCTOSlTeJlbHO npOCKJIOIIHTb npHJIaraTeJIbHbIe BMeCTe C cyrnecTBHTeJ1bHbIMH (CJlOBOCOtleTaHHH); Han- pHMep: paH.HUt1 paccoem, paHHee ympo, paHHJIJl aapR.. UeJIeCOO6pa3HO conOCTaBHTb npaBonHcaHlle Oe3y.napHbIX OKOHqallHH npHnaraTeJIb- HbIX C TBep,lJ.OH H MHrKOH OCHOBOH (YlJaInHMCH TCpfHli He coooruaeTCH): CHeH,blU yaop' - paHHQ,U paCC8em; CHe3fCHOe nOlle - paftHee ytnpo; CHe:NCHaR 20pa - paHHJlR 3apfl. . YtU1TeJlb o6parnaeT BHHMaHHe yqalll.HXCH Ha TBep,llocTb H MSlfKOCTb COr.,1acHblx, KOTopble CTOHT nepe,lJ. OKOHQaHHHMH; JtJ1H 3Toro 011 npeJJ.JIa- raer .neTH1v1 HaqaJIa nOJJ-YMaTb, KaK npoH3HecTH OT){eJIbHO OT CJIOBa YKa3aHHbie COrJIaCHbIe, 3aTeM npoH3HecTH HX H nocTapaTbcSI 061>Hc- HHTb. HanpHMep: CHe'ICHblU [HIt paHHUU [u l '], cHealCHoe [H], paHHee [H b ), CHe"'HaJl [H], paHHRfl [H b ]. YqarnHeCSI 06'bHCHHIOT pa3HHUY B npOH3HoIlleHHH COfJlaCHblX (ecJlH OHH 3aTpYJlHHIOTCH, TO OO'bHCHeHHe MO>KeT HJJ-TH C nOMOIl(bIO YIU'ITCJISI): B CJlOBe CHi!JlCHblU H nepeJl bl, B cnoae paHHUU H nepeJl U H T. n. npH H3YtlCHHH MHO}KeCTBeHHoro tlHCJIa HMeH npHJlaraTeJIbHblX yqa- rnHecH YCTaHaBJlHBalOT t qTO: I) BO MHO>KeCTBeHHOM tlHCJle npHJlaram1b- Hble He H3MeHHOTCH no pO){af; 2) na.ne>K npHJIaraTeJIbHblX BO l\.fHOJKeCT- BeHHOM qUCJIC MOIKHO onpeJleJlHTb no na,lle>KY Hl\leHH cyrnecTBHTCJIbHOrOt C KOTOpbIM npHJIaraTe.nblloe CBH3aHO B npeMO}KeHHH HnH CJIOBOCOtle- TaHHH: 6e/lb/£ l{8embl, nAambR, JleHmbl (HMeHHTeJIbHbIH HJIH BHHHTenb- HblH na)le*); 6e/lbLt l6efn08, n./lambe8, JleHnl (p0,llHTeJIbHbIH naJle}K) H T. ,n. l..IT06bI. YCTaHoBHTb, B HMeHHTbHOM HJlII BHHHTeJlbHOM na,lle}l{'e CTOHT npHJIaraTeJlbHbIe MHO}l{ecTBeHHoro lIHcna, ytlaruHecH JlOJl>KHbI paao6paTb npe,llnO}KeHHe no lIJIeHaM npeAJIO>KeHHSI. HanpHl\lep: JIema- 10m KpacHble Ulapbl; Ulapbl - nO,llJle>Karnee, HMeHHTeJlbHbIH na){eiK, 3HaqHT, npHJIaraTeJlbHOe KpacHble B HMeHHTeJIbHOM na)te>Ke. Ba- CR. KynU/1 KpaCHbte Ulapbl; ulapbl- BTopocTeneHHblH tlneH npe,nJIO>KeHHSI, BHHHTeJIbHbIH na.ae)l{, 3HatlHT, H npHJIaraTeJlbHOe KpacHble B TOM JKC na)lCllie H T. n. . KaK nOKa3blBaeT npaKTHKa, Y1JarnHecSl lIaCTO .aonYCKaIOT OWH6KH B HanHcaHHH 6e3y.aapHblX OKOHtlaHHH npHJlaraTeJ1bHblX B .naTenbHOM, TBOpHTeJIbHOM H npeMO>KHOM na,lJ.eiKaX MHO}KCCTBeUHoro tlHCJ1a. 3TO npORCXOHT OTToro, qro YKa3allHbIe OKOHqaHHSI B npOH3HOllleHHH nOtlTH COBnaaIOT C OKOHtJaHHHMH cyrneCTBHTeJIbHblX. HanpHMep, KpaCHblMU tfBemaMU YtJall\HeCH npOH3HOCHT H 3atJaCTYlO nl1111YT «KpaCHaMH UBeTafH». B Ytle6HHKe AaHa TaMHua «PO,lJ.HTeJ1bHbIH, ,naTeJIbHbIH, TBOpHTenb- IIbIH, npeAJIO>KHblH na,ne}KH HMeH npHnaraTenbHblX BO MHO}KecTBeHHOl\l qHCJle». AnaJIH3 3TOH Ta6nHUbI nOMOJKeT ytJamHl'ffCH nOHSlTb cnoc06bl npOBepKH CMeIlIHBaeMblX OKOHtlaHHH npHJIaraTeJIbHbIX H 3anOl\fHHTb OKOHtlaHliH npHnaraTeJlbHbIX BO MHOJKecTBeHHoM tJHCJle: -bIJC,-tlX (p.n.), -hIM, -UM (.a. n.), -bIMU, -UM'" (T. n.), -bIX, -ax (n. n.). B npouecce H3tJeHHH liMen npHJIaraTeJIbHblX B I I I KJlaCCe YllauU1e- CH He TonbKO nOBTopHIOT Y>Ke H3BecTHoe Hf 06 3TOH qaCTH petlH (qro 060. 101
t. 3UaQaeT Ut.HI npIIJlaraTe..TJbHOe. e KaKOH tIaCTbIO petIH OHO BcerJ{a CBSI3aHO B npe,lJ.JIOLKeHHH), HO H Y3HalOT HOBoe. HOBbie 3HaHHH nOMoralOT H"f AaTb 06ocHoBaHHbIH OTBeT Ha TaKHe BonpOCbI: 1) KaK H3MeHHeTCSI MMH nplfJIarareJIbHoe? 2) KaK MO>KHO Y3HaTb pOA, tlHCJIO H na,Ite>K HMeHH npHJIaraTeJ1bHoro? 3) B KaKOM qHCJIe HMH npHJlaraTeJlbHOe He H3Me- HHeTCH no poaM? 4) KaK MOHO npoBepHTb 6e3yapHoe OKOHQaHHe MleHM npHJIaraTeJIbHoro? 5) KaKHe OKOHtlaHHSI HMeH npHJIaraTeJIbHbIX HeJIb3S1 npoBepHTb? H T. ,It. nOBTOpHSI H ooo6maSl Bee H3YQeHHOe 06 HMeHM npHJIaraTeJIbHOM, yqHTeJIb Ha ypOKe pa60TaeT Ha otSotSrnalOIneH TaOJIHueii «HMH np"HJIa- raTeJ1bHoe». Ta6JIHua MO>KeT HMeTb, HanpHMep, TaKOH BH. H.iMCUSIJOTCJI no nplf3HaK npeAMeT8 CSSl3h C APyrH- BonpocLJ MH c.nOB8MH B npe.o.nO}KeUHH JX>A8M 1JHCJJaM naJ].e>KnM , KpacIIblH, CHRHH C HMeHeM CY- 8KYCHbU1 xumpblii H. (jOJIbwoii lltecTBHTCJJ b- xne6 3Bepb nee HblM: P. OOnbworo neea BKYCHbJH, CJI a- K8KOH? H aCTynHJla 6ICYCHOJI xumpblf A. OOJlbWO' KHH K8K8S1? .xo./tooHal1 n HU{8 3BepH MY necy K 3MeIlHblA, Aepe- KaKoe? SUM a BSlHHhlH KaKHe? - 60J1bWOH, Ma- 3eMJ1S1 no- 61tgcHoe B. OOnbllJOH JleUbKHA K pblJIBCb 6e- OJlIO.110 nee AblM "08- T. 60J1bWHM pOM JleCOM XHTPWH, YMHblH n. 0 60n b- Bece_1 bI H , xpa6- WOM nece pblH - KaK C03.J{aeTCSI no,n06HaH TaOJIHna na ypoKe? YtlHTeJ1b nHllleT na ,nOCKe llICCTb BepxHHx KOJIOHOK 6y,ItYInefi 'Ta6JIHl.lbI. 3aTeM cnpallIHBaeT y .nereH, liTO 0603HatlalOT HMeHa npHJIaraTeJIbHbIe. YqaI.I.{HeCSI OTBeqalOT, QTO npliJlaraTeJIbHble otSo3HaqalOT npH3HaK npe,ll.MeTa. YtlHTe.TIb npo- CHT yqaInHXCH npHBeCTH npHMepbI npH3uaKOB npeJ{MeTOS: no UBeTY, BKYCY, MaTepHaJIY t pa3Mepy H T. ,It. LleTH npHHOJ{SlT npHMepbl, a yqn- TeJ1b 3anHCblBaeT HX B nepBOH KOJlOHKe. 3aTeM ytlaIII.HecH Ha3bIsalOT BonpOCbl, Ha KO'fOpble OTBeqalOT HMeHa npHJIaraTeJIbHbIe, Y1JHTeJlb 3anHCblB8eT HX BO BTOpOH KOJIOHKe Ta6JIHUbi H T. ,It. Yqall\.HeCSI, CCTecTBeHHo, npHBO,ItHT pa3Ho06pa3Hble npHMepbl' HMeH npHJlaraTeJlbHbJX, HO ytlMTeJIb OT6HpaeT AJISI 3anHCH B Ta6JIHue JIHllIb He... KOTOpb1e H3 HHX (S03MO>KHO, 9T0 6YYT Te npHMepbI, KOTopbIe ou caM npHfOTOBHJI 38paHee). KorA8 Ta6JIHua 3anOJlHeHa, yqHTeJIb npeJJ.JIaraer yqamHMCSI npo- CKJIOHSlTb HMeHa npHJlaraTeJIbHe MymcKoro t >KeHCKOro H cpe,l1H.ero - ]02
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BHTe.'1bHbIe. tuaPUK.. KpacHbltl, cyxoa, ICpacHafl, pbl3lCue, 3/CUOI«lJl. 4. CnllcaTb npe,l{JIC?>KeHHSI. OT cyecTBHTeJIbHbIX, CTOSlInHX B CKOO- Kax, 06pa30BaTb npHJIaraTeJIbHble p H3MeHHTb CJIOBa no CMbICJIY. . 1) ( Moc.K8a) MeTpO - nO)J.3eMHaSl (sAeKmpUtteClnoo) ,nopora. 2) (ruzaHm) JIecTHHUbl cnycKaIOT Ha CTaHUHH nOTOKH JIIOJleH. 3) Cao- ,l{bI 3aJIOB 06JIH110BaHbl (MpaMop) nJIaCTHHKaMH. 4) (l{ yao) 3aJIbI OCBe- meHbI H p KHM CBeTOl\{. TaKHM oopa30M, H3YQeHHe lIMeHH npHJIaraTeJIbHOrO OTKpbIBaCT 60JIbWHe B03MO}KHOCTH ,nJISI pa3HocTopoHHero rro,nxoa K SlBJIeHHHM Sl3bIKa p )J.JISI pa3BHTHSI petlH YllarnHXCH B npouecce H3ytleHHH rpaM- MaTHKH H rrpaBonHcaHHH. BIll KJIaCCe, npe>K.ne qeM nepeHTH K H3ytleHHIO r JIarOJIa, ytlaw.HecH JlOJI}KHbl n03HaKOMHTbCH ellI.e C O,nHOH lIaCTblO peqH - MecroHMeHHeM. OporpaMMa Tpe6yer TOJIbKO 3HaHHSI JIHtlHblX MecToHMeHHH, npaBHJIbHOrO ynoTpeOJIeHHSI MeCTOHMC- HHH B pa3JIHQHbIX rrane}Kax " YMeHHSI nHcaTb npeJlJIOfH C MeCTOHMeIIHH- MH. Ha 3TO OTBO,lJ.HTCH 7 qaCOB. npH H3ytleHHH rJlafOJIa yqamHecH Bep- HYTCH K MeCTOHMeHHIO, 3aKperrSlT nOJIYlleHHble 3H8HHH 0 J1HqHbIX MecTO- HMeHHSI x. nOHHTHe 0 MeCTOHMeHHH MO>KHO AaTb Ha MaTepHaJIe AHa10ra, KaK 9TO peKoMeHJtoBaJIH H. n. KaHoHblKHH H H. A. ep6aKOBa1. BOT npH- Mep TaKoro ,nHaJIOra-mYTKH: - Tbl lITO JleJIaewb? - f/ HHtIerO He )J.eJIalO. - A OH liTO ,lJ.eJlaeT? - On MHe nOMoraeT. YllalUHecSl tIHTalOT HanHcaHHbIH Ha AOCKe ,nHaJlOr-WYTKY, nOTOM ttHTaIDT nOBTopHO nepBoe, 3aTeM BTopoe npe,l{JIO:>KeHHe H YCTaHaBJlHBaIOT, liTO Tpy,nHO onpe.zteJIHTb, 0 KOM B HHX rOBopHTCH. no,n CJIOBaMR R, mbl MO>KHO nO)J.pa3YMeBaTb Koro yroAHO. nOTOM yqalII.HecH IIHTalOT ,nBa noc- ne,l1HHX npe,nJIO>KeHHSI, YCTaHaBJIHBaIOT, tlTO CJlOBO OH MO:>KHO 3aMeHHTb CJI0BaMH MuUllJ, MaAb'lUIC, ytleHUIC. CnoBa MUtUa, .Ma/1,btlUK, ytteHUIC HBJlHIOTCH HMeHaMH cYlllecTBHTeJlbHblMH. 3HatIHT, CJlOBa R, mbl, OH ynOTpeOJISlIOTCSI BMecTO HleH cYlI{ecTBHTeJlbHblX. ,QaJIee YQHTeJlb cootS- lII.aeT, liTO 3TH CJIOBa Ha3blBalOTcSl MeCTOHMHHHMH, nOTOIY tlTO OHH ynoTpe6JIHIOTCH B{ecTO HMeH (B ,l{aHHOM CJIYllae BMecTO HMeH CyecT- BHTeJ1bHbIX). YqalII.HeCSI COCTaBJIHIOT CBOH rrpHMepbl C MeCTOHMeHHSlMH, HaXOJlHT MecToHMeHHH B TeKCTe ynpa>KHeHHA. nOCJIe 9Toro YtIalUHMCH coo6aeTcSI p liTO MecroHMeHHSI il, tnbl, OH, OHa, OHO, Mbl, 8bl, onu Ha3b1BaIOTCH JlHqHbIMH MecToHMeHHHMH t nOTOMY ttTO OHH TOJIbKO YKa3b1BaIOT H8 JIHUO, HO He H83bIB81OT ero. MecTOHM HHe R ynOTpOOJISleTCH, Kor;ta rOBOpSllII.HH YKa3b1Baer Ha cet5S1; MecTOH- 3anHC8Tb CJIOBOCOQeraHHH: CUHUa - CUHeHbKUU MeCTOMMeHHe 1 CM.: H. n. K a H 0 H'bI K H H H H. A.lUe p 6 a K 0 B a. MeToAHKa PyccKoro S3b1Ka B HaqaJlbHOH WKOJIe. M., YQneJ1rH3, 1947, CTp. 303-304. 106
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H3fepeHHe nJlow.aJ].?fl llaQHII3eTCH C ynpa)f{HeHHH B DbIQHCJ1eHHH I1JIOwa,l1H npHMoyroJlbHoH ct>HrYPbI B KBa,!lpaTHbIX caHTHMeTpax, a Qepe3 J1el<OTopbIH npOMe)f{YTOK BpeMeHH YlIeHHKH 3HaKOMHTCH C BbILJliCJIeHHeM I1JIOU1,a.nH B KBaJl.paTHbIX ,neUHMeTpax Ii KBa.llp3THLIX MCTpax. B npouecce H3YIJeHHSl 3Toro pa3)leJ13 nporpaMIb1 npOBo,nHTCSl na6JlIOJ].eHHH no Ta6JIHnaM 33 TeM, KaK H3MeHHeTC5I nJlOll1.a,Zl.b B 3aBHCHMOCTH OT H3MeHeHHH O,nHOH H3 CTOpOH npSlMoyro.nbHI1I<a. J!eTH yqaTCH BbIp3>KaTb nJIOma)1b npSlMoyroJlbHHKa Qepe3 ero CTOpO- HbI, a TaK}Ke pern3Tb npSlMble H 06paTHble 3a"aqH H3 BblqHCJIellHe nJl Om3]lJi . B I I I KJlaCCe yt.leHHKH 3HaKOMHTCH C JIHHeHHblMM H cToJI6lJaTblMH !lHarpaMMal\fli, ynpa>KHHIOTCSI B I1X IITeHHH H nocTpocHUH. B 9TOM KJ1aCCe paclllHpHIOTCH 3H3HHH yqallI.HXCH H cOBepweHcTDY- IOTCH HX HaBblKH B 06JIaCTIi H3MepeHHSI Ii qepqeHHH. OHH yqaTCSl Bbl- - qepqHSaTb npHMble yrJIbI, npHMoyroJlbHHKH (KBa,lJ.paTbl) Ha HeJlHHo- BaHHOH 6YMare, nOJIb3YHCb JlHHeHKOH H qepTemHbIM TpeyrOJIbHHKOM; BblllepIJMBaTb OKPY}Kt{OCTH. rnecTHyroJlbHuKH H TpeyrOJlbHHKH, n<ATIb- 3Y HCb IJ.HPKYJlCM. BMeCTe C H3yqeHHeM HOBoro l\1aTepH3JIa npoBo,lJ.HTCH H 3aKpenJIe- Hue Toro, liTO H3YQaJlOCb B MJIaIIJHX KJIaCcax. npeYCIOTpeHHbIH nporpaMMOH 06'beM reoMeTpHlIecKHx npe]lCT3B- JIeHHH H nOHHTHH ,nocTaTOqeH ,l1JIH Toro, lITOObl c.nY}l{HTb OCHOBOH yc- nCWHoro H3yqelIHH reOMeTpHtJecKoro M3Tepl1aJIa B IV H V KJlaccax. B npou.ecce pa60TbI Bce paccMorpeHHblc OC,HoBIILle pa3,neJIbI npo- rpaMMbI TecHeHllIHM o6pa30M CB5I3bIBaIOTCH IvleJK.n.y C060H; OHIf BbICTY- nalOT BO B3aHMo,l1eHcTBHH KaK qaCTH e)lH Horo 'ueJIoro. 3JIel\ieHTbl aJl- re6pbI HBJlSlIOTCH t.IOmHbIM Cpe){CTBOM a6crparHpoBaHHH Ii 0006I.U.eIlH5I apH<pMeTHlIeCKHX 3HaHRH; reOMeTpHeCKHH MaTepH3J1, Hl\ieH B H3BeCT- U .. HOU CBoeH qaCTH caMOCTOHTenbHoe 3HaQeHHe, Hepe,l1KO HCnOJIb3yeTCH ,llJIH HJIJUOCTpaUHH apHcpMeTHqeCKHX 3aKoHOMepHoCTeH. TaKoB B OCHOBHbIX tIepTaX 06'heM 3HaHHH, YMeHHH Ii HaBbIKoB, IOTOpbIM 33BepwaeTCH TpeXJIeTHee na1Ia,TIbHOe 06yqeHHe. npn ,nocTa- TOtIHO BblCOKOM ypoBHe npenO)laBaHH5I OHO ){OJI}J{HO ooeCneqUTb xopo- 1l1YlO no,nroToBKY YtlamnxcSI K H3YQCHHlO MaTCMaTHKH na CJleJ1.YIOrn. e J'i cryrreHH 06YIJeHHH. HYM_paqMA MHOr03a'lHbll 'IHCeli 3aJl.aQa H3YQeHH5I Jl.aHHOH TeMbI COCTOHT B TOM, lIT06bl paClllHpHTb y AeTeH 3HaHHH eC5lTHQHO[1 CHCTeMbI CqHColTI(HHH, CTPYKTypbI MHoro- 3HaqHOrO tlHcna, HaTypabHOH' rrOCJleOBaTenbHOCTH lIMcen H Ha 3TOU OCHone CcpopMHponaTb y .n-eTefI Yl\feHHe npaBHnbliO lIHTaTb H 3anHCbIB3Tb rvHIOr03HatlHbIe qHCJIa B npeAeJIax KJlaCCa MHJIJlHOHOB. OCHOBHbIM cOJ{ep>KaHlieM 9TOH TeMbl HBJIHIOTCH cJleYIOllI.He Bonpocbl: 1. 03HaKOMJIeHHe YIJaIUHXCH C HOBbIMH ,D.JI H IlHX CQeTHbl'-fH (pa3- p H)l.lIbIMU) e,nHHHuaMH H BBeeHHe nOIIHTHH "/lace; YCBoeHHe pasp HJ1- 235
Horo H KJIaCCHOro COCTana qHCJIa nyreM ynpaJKHeHRH B 06pa30BaHMH QRCe.n H3 pa3pH)lHblX JI KJIaCCHbiX e)tHHHU H pa3J10>KeHHH QHCeJI Ha pa3- p H,llHble CJIaraeMbIe!.JJ CJlO)KeHHH H BbIqHTaHHR B CJIYtIaHX, OCHQBaHHblX ua 3HaHHH ,lleCHTHtIHOrO COCTaBa qHCJIa. 2. 03HaKOMJIeHHe C KJIaCCHblMH CqeTaMH KaK CqeTHbl1 npR6opoM; (j3opMHpoBaHHe YMeHH OTKJI3,lJ#BaTb qHCJla Ha ClleTax H qHTaTb qHC- JIB, OTJIO)KeHHble Ha HHX. 3". H3YlJeHHe HaTypaJIbHOH nOCJIe,nOBaTMbHOCTR qHCeJI 3a npeJ,te- JIaMU TbICS11.1H, OC06eHHO B MeCTax rtepexoJ,ta M3 o)J.lloro pa3pJl.lla HJIM H3 , u OJ,tHoro KJIaCCa B JlpyroH. 4. 4reHHe H 3anHCb fHor03HatlHbIx QHCeJI. 5. YCBoeHHe TepMHHOJIOrHH, CBH3aHHOH C <PoPMRpyeMblMH nOHJI- THHMH. 113 nepe1.IHH OCHOBHbIX BonpOCOB, COCTaBJIHIOInHX cO)J.ep}KaHHe .Jl.aH- HOH TeMbI, BHJ,tHO, liTO H3yqeHHe ee CBH3aHO C YCBoeHHeM pH,na OTBJle- lIeHHblX nOH5ITHH, HY}l{.lI-alOmHXCH B KOHKpeTH3al.l.HH. - TaK, JlPJI>KHbI OblTb KOHKpeTH3HpOBaHbI .lI-ecHTHqHaH OCHOBa Harne" CHCTeMbl CtIHCJIe- HHH, nOMeCTHoe 3HaQeUHe l.(Hpbl, MeCTa pa3pH,l10B H KJIaCCOB H ,llp. 3TOH eJlH c..1Y}I{aT CJIeJ,tYIOIII.He HarJIH)J.Hble noco6H5I: a) K JI ace H bI e C q e T bl JtBYX B}IOB - C ropH30HTaJlbHbIMH H BepTHKaJIbHbIMII npOBOJIOKaMH. K.1accHble CtlCTbl HaxoJ,tSlT npHMeneHHe Ha npOTH}KeHHH Bcero ne- pHoAa H3YQeHHH HYMepaUHH; 6) H Y I e- p a U H 0 H H a H T a 6 n H 11 a, HJlH TaooHua pa3pH- .nOB H KJIaCCOB, C «KapMaHaMH» )tJIH BCTaBKH IJ.HCPP, KOTOp8S1 o6nerqaeT YlleHHKY ero nepBbIe marn B OBJIa)teHIIH YMeHHM qHTaTb H 3anHCbIBaTb MHOr03Ha1.IHble qnc.TIa; B) a 6 a K oco6elllIO nOJIe3eH Ha nepBbIX ypOKax, npH H3yqeHHH BonpOCOB YCTIIOH HYMepau.HH NISI nOKa3a oopa30BaHHH qHCn3 Hero pa3JIO>KeHHH Ha pa3pHJ,tHbIe qHCJIa.' YIIeHHKU .lI-0JI}I{HbI HleTh y e6H yqeHHllecKHe CqeTbl H aoaKH TaKO- .u ro me Tuna, qTO H )J.eMOHCTpanHOHHblH, TOJIbKO MeHblIIero pa3Mepa. 113yqeHHe. .n.aHHOH TeMbI ,nOJle3HO CBH3aTb C >KH3HblO, C KOHKpeT- llbiM MaTepH8JIOM - qHCJlOBblMH ,naHHbIMH, xapaKrepH3YIOIII.HMH pa3- BHTHe npot.f.m..TJeHHOCTHt CMbCKoro X03S1MCTBa H KYJIbTypLI B CBoeM Kpae, ropo,ne. 1. K H3YQeHHIO ,l{aHHoH TeMbr ytteHHKH npHcTynalOT C XOPOWMM 311allHeM HYMepal1HH Tpex3HallHbIx 'IHCM, T. e. qHCeJI nepBoro KJJacca. 3TO 3HaHne H HY>KIIO nOJlO>KHTb B OCHOBY H3YQeHHH HYlepaIlHH qHCeJI K.nacca TbICSlq. OOJIb3]' SICb OTKJIMblBallHeM qUCM 1Ia KJIaCCHblX ClJeTaX t YQeHHKH nOJlyqalOT TPH HOBble ,llJISI HHX CtteTHhle (pa3pHAHble) eJ{HHHUbI - ThlCR- QH, AeCHTKH TblC}1I1, COTHH TblCHq. H 3,ltecb >Ke YIIHTeJ1b COO6III.aeT, qro paHee H3BecTHbIe TPH pa3pH,A8 (eAHHHUbI, .necHTKH H COTIIH) co- CTaBJISIIOT 1C/lacc edUIlUij, a BHOBb nOJlYlleHHble TP" pa3pHa (e,l{H- H"U.bI TbICHq, AeCHTKH TblCHq H COTHU TblCHq) COCTaBJIHIOT ICAacc mbtCRtt. 236 -'
D.aJIee 1I0.l\POt)HO DhIHCHHeTCH, QTO o6mero Ii tITO pa3J1HqHOrO :JTHX KJIaCCaX. · o 6 In e e: B Ka>KJ{OM KJIace no TPH pa3pH)!a; H33BaHHe pa3pH- )tOB (eJJ.HHHII.bl, )].ecSlTKH, COTHH B KJIacce .e,lUiHHn; e,lI.HHHUbI TblCBtI, )lecHTKH TblCSltI, COTHH TbICSlq B KJIaCCe TbiCHtJ). .OTHoweHHe coceAHHX pa3pHHblX e)!HHHIJ. (10); B Ka>K,lJ.OM KJlaCCe 10 e,nHHHI.{ HH3111ero pa3- PH)13 06pa3YIOT O,nHY eHHHUY CJIeJJ.YlOmero, Bblcwero pa3pHa. liTO pa3JIHtlHOrO B 3THX KJlaCcax: B KJlaCCe e,nHHHU CtIeT Be.neTCSI eJl.HlIHUaMH, B KJIaCCe TbICHq - TblCSllIaMH. CtJeTHaH e;tHHHua nepBoro I<Jlacca - npocTaH eAHH}na; CtleTHaB e)].HHHua BToporo KJIacca- TbICHqa. E,lUiHHu.aMH CqHTalOT OT 1 )].0 999, TbICHqaMH - OT 1 TblCHtlH ,llO 999 TbICSlq. 3Tn CBe)1eHHH 'nplioopeTalOT 60Jlee KOIIKpeTHblH xapaKTep, Kor)J.a OHM 33nHcaHLI B IlYiepaIlHOHHofi Ta6w'lHu.e: RJlacc TblC Slq I KJlacc eJ],HJJIUl COTHH I ,AeCHTKH e.AH H HU.bJ TblCHIJ TblCSlll ThICS t ( COTHH ,!J.eCHTKH e.ZJ,HHHUbI I IJI pa3pHA II pa3pB,lJ, I pa3pSIA 'III pa 3pSlA II pa3pSlA I pa 3 pnA ., I ,lI.aHH3S1 Ta6JIHua IlOtlepKHBaeT e)1I1HOOOpa3ue B nOCTpoeHHII KJIaCCOB; BMecTe C TeM B HCM BH,lJ.HO H TO, qTO pa3J1HtlaeT 3TH KJIacbl. 4T06b1 Y ,lI.eTeH CJlO)KHJ1OCb npaBHJIbHOe npe,llCTaaneHHe 0 uaTY- . ., paJlbHOH nOCJIeAOBaTeJlbHOCTH tlHCeJ1 3a npe,lleJIaMH TblCSItlH, HY>KHO lIa nepBOM HJIH Ha BTOpOM ypOKe npOBeCTH ynpa}l{HeHHe B ClIeTe - B npHCqHTblBallHH H OTCqliTblBalIHH no eAHHHu.e H rpynnaMH eJ{HHHU - no 5 10, 50, 100 H T. ,n. noc.TIe 3Toro cLTIeJJ.yeT OCTaHOBHTbCR Ha HYMepaII.HH qHCM KJIaCCa TbJCHq, T. e. KpyrJIbIX TbICHl.I, HaJlpldMep: 268 TbICHq, 306 TblCHQ, 500 TbJCHq, 420 TblCBtJ, H npoBecTH ynpaiKHeHHH: . a) B o6pa30BaHHIi TaKHX qHCM H3 .lJ.allHblX pa3pHHblX qHCeJI; 6) B tITeHHH qHCeJI KJIaCCa TbICHq, CHatlaJIa 3nHcaHHblx B uYMepa- lI.HOHUOH Ta6JIHIJ.e, a nOTOM - 6e3 TaM HUbI; n) B 3anMCH lIHCeJI, COCTOSlInHX H3 KpyrJIblX 1'bICSltI (noJi. .nHKTOBKY ytlHTeJl H); r) B BhIllOJlHeHHJI ,lI.eHCTBHH H3.ll tlHCJIaMH BToporo KJIaCCa, npH\IeM 3TH qHCJla AalOTCSI cnaqaJla B TaKOM BHAe: 320 TbIC. + 200 TbiC.; 600 TblC. - 400 TbIC., 18 TbIC..4, a nOTOM B 06WQHOfi HX 3anHCH: 7 000 -1- 9 000 40 000 - 25 000 . 4000 · 8 36 000 : 9 .. nocne 9Toro 1i3yqaeTCB ..HYMep,auHSI AI06blX tleTb1peX-, nBTH-, me- CTH3II31JHbIX 1JHCCJI, B KOTOpbJ Bce- HJlH TOJIbKO HeKoTopble paSpHJlbl 237 ... "
OUOHX KJ1aCCOB (B TOM tIHCJIe H KJlaCCa e,nHHHU) 3anUJIHeHbi pa3p51.llHLr- nl tJHCJIaMH, HanpHl\fep 516 824; 40 068 If ,np. nepexo.n K T3KHM IfHCJlaM MO}KeT 6bITb c,neJIaH nYTef\{ nOCTeneu- 1I0ro «3anOJIHeHHH» pa3pSI.nHb1MH tIHCnaMH !Ulacca e.ll.MHHU, npe;tcTaB- JIeHHoro. HYJIRMH. - CKonbKo nonyqHTC, - cnpaIlIHBaeT yqHTeJIb, - eCJlH K 325 TLICHQaM (325 000) npH6aBHTb 8 e,nHHHu? 48 e.nHHHl\? 648 e;tHHHI..{? OTBeTbI YQa1I1-HXCH 3anHCbIBa1OTCH H8' )lOCKe, H n pe3YJIbTaTe nOJIY- qaeTC rneCTH3HaQHOe QHCJlO, D KOTOpOM 06a Knacca npe,l1CTaBJlellbI_ 3HaqaIl.1aIH UHcppaMu: 325 TbIC. - 325 000 325 TbIC. 8 e){. - 325 008 325 TLIC. 48 e){. - 325 048 325 ThIC. 648 e,l.l. - 325 648 nOJIyqel1HOe 1JHCJIO (325 648) fJo,nBepraeTCH nO,l1poOHOMY aHaJ1I13Y: B HeM ,l1Ba KJlaCCa; n Ka}K)J.OM KJIaCCe no TPH pa3pH,l(a; B KJ1aCCe TblCH4 325 eJU1 II HlI., 3HatlHT, B lIHC4I1C 325 TbIC5I1J; B KJIacce eJl-HHHU 648. Bee qH10 tlUTaeTCH TaK: 325 TbIC5IQ 648. BCJIe.n 3a .3THM H,l.lYT ynpalKHcHHH B q T e H H Ii H 3 a n H C H aHaJ10rHqHX 1JHCen. LlaJIbIleHllla pa60Ta Ha.n tJHCJlaMH B npe,neJ1ax Knacca TbICHtI pa3- BepTblBaeTC npuMepHO B TOl\.l }Ke nJlaHe, B KaKONf OHa npoxo,nHJla C lfHcnaMH BToporo .KJ1aCca, T. e. C KpyrJIbIMH TbICQaIH. 3.necb TaK>Ke rrpoBo,nHTCH ynpa>KHeUHH B COCTaB..TJeHHH H pa3JIO>KeHHH tll1cna, npM1Jervl B KaqeCTBe .naHHbIX cpHrypHPYJOT He TOJlbKO pa3pH,l.lHbIe, 110 H KJlaCCHble e)J.HHHltbI: «COCTaBbTe, HanpHMep, tlHCnO, KOTopoe COCTOHT: a) H3 32 e)lHHIiI1 II KJIaCCa H 517 e)l.HHHII. I KJlaCCa; 6) 113 600 e.nHHHU II KJIaCCa H 75 eHnHl\ I KJlaCca. Ha CKOJIbKO 5 eJtHHHU I I KJIacca 60JlbllIe 5 CJI.HHHII. I KJlaCca?» Y HClIeHHIO CTPYKTypbl MHOr03HaQHOrO tlH('JIa, ero pa3p5l.llHOrO H nOKJlaCCHOro COCTaBa BO MHO rOM cnoco6CTBYfOT: - - a) npHMepbI Ha CJlOJKeHHe H BbIQHTaHHe, pewaeMble Ha OCHOBe 3HaHHH .lI.eCHTHtlHOrO COCTaBa qHCJIa. HanpHMep: 25 000 + 4 000 18 420 - 420 5 460 - 400 30 000 + 500 76 200 - 6 000 16 903 - 16 000 I 6) pa3J10}l{eHHe .naHHoro qHCJIa Ha ero pa3p5l,l.lHble CJlaraeMble H 06paTHaH onepal\uSI - 3anHCb Bblpa}l{eHH (CYMMbI) B BH,Ae o.nnoro tlHCJla. HanpHMep: 65 040 = 60 000 1- 5 000 + 40 4 000 -1- 700 + 30 + 8 = 4 738 Ha 9TOM 9Tane H3YQeHHH HYMepallHH npo;toJl>Kae-rcSI paooTa I-J no _ 33KpenJleHHIO 3HaHH5I HarypanbHOH nOCJIe.llOBaTeJIbHOCTH qHCM. C 9TOH l\eJIblO npoBo.l(51TCJ ynpalliHeHH5I B BblnOJlHeHHH pa3J1HQHblX 33- aHHH, HanpHMep: 238
a) npHCIIHTb]BaHTeno I H 3anHCbIDaHTe lIHCJIa: OT 9 997 Jl.0 10 004; OT 99 998 ,no 100 005. 6) OrCtIl1TblBaHTe no 1 " 3anHCbIBaHTe tIHCJla: OT 1 003 Jl.O 998; OT 10 002 Jl.O 9 996; OT 10 000 ,no 99 996. B) 3anHIIIHTe 1.JHCJlO, MeHbwee 100 000, H3 5; 60JlbllIee 19 998 H3 3. r) 3anHlllHTe «coCeJl-eH» I{HCeJI: 20 000; 90 000; 100 000. Jl.) CpaBHHTe 1.JHClla: 600 " 6 000; 7 009 H 7 090; 36 214 H 36 241. e} BCT3BhTe BMecTO T01.JCK Heo6xo,QHMbIe lIHCJIa: r 72&-< 17 ... t 10'0 060 > 100 0... 3HaHHe HaTYPaJIbHOH rrOCJIe,QOBaTeJIbHOCTH 1.JHCeJI HaXOJ].HT CBoe npHMeHeHHe H np" pemeHHH npHlepOB THna: 99 999 + I 10 000 - 1 ]99999+ 1 100000-1 70 000 + 30 000 90 000 -1- 1 000 Pema1l nepBhIH npHMep, Y1IeHHK paccYJK.naeT TaK: «ECJIH npH6a- DHTb K IIliCJ1Y e,nHHHUY, TO nOJlYlIHTCH 1.JHCJIO, cJle,nYlOmee 3a Jl.3HHbIM. A 1IHCJlO, KOTopoe CJIe,nyeT 3a 1JHCJ101 99 999, eCTb 100 TbICH'I. nO.9TOMY nHlllY: 99 999 + 1 = 100 000». ECJIH YlleHHK 3aTpy)tHHeTcH lIa3BaTb 9TO IIHCJ10, liTO BnOJlHe ec- TeCTBeHHO, TorJ(a 1IHCJ10 99 999 HYJKHO npe)I.cT3BHTb B BH,ne CYMMbl: 99 TbIC. -1- 999t n npHoaBHTb eHHuIlY I{ 999. 999 )I.a 1, 6Y)I.eT 1 000, 99 ThIC. ,na 1 TbIC. " 6y.n.eT 100 000. PemaH npHMep 10 000 - 1, yqeHHK paccY)I{Jl.aeT: «EclI" BbI1IeCTh H3 1IHCJ1a e,nHHHu.y, TO nOJIY1IHTCH 1IHCJ10, npellleCTBYIOIIJ.ee .lI.aIlHOMY. LIHCJlY 10 TblCHq rrpe,nlllecTByeT lIHCJIO 9 999. 3HaqHT t 10 000 - 1 = 9 999. ECJIH >Ke YlleHHK He CYMeeT H83BaTb 9TO npe)I.IlleCTBYIOlll.ee 1JHCJIO, TO o6DHC1feHHe MO>KeT ()blTb ,naHO B T3KOM BH)I.e: npe)I.CTaBHf IIHCJIO 10 TblC. B BH,ne CYMMbI )I.BYX CJI8raeMbiX 9 TblC. + 1 TbIC. Tenepb BbltlTeM I H3 1 TbICH1JH, nOJlytUIM 999, a Bcero OCT3HeTCH 9 999». K nOJ{ooHhlM ynpa)KHeHHHM TeCHO npHMbIKalOT yn"p3JKHeHHH B pa3- "TIUtleHHH Hau60JIbIllerO 11 HaHMeHblllero 1JHCJIa cpe)I.H 1.JeTbIpex-, nSlTH- Ii UleCTH3HaQHhIX 1IllCeJI. YqaHeCH 3HaIOT H3H00J1blllee H HaHMeHb- wee 1.JHCJl3 CpCAH O)I.H03H, allHbIX .lI.BY3Ha1lHbIx H TpeX3Ua1lHbIX QHCeJI. OH11 nO)I.MeTHJ1H, liTO HaHMeHbllIHe lIHCJla 3anHCblBalOTCH C nOMOll\bIO UJicpp 1 H Ot a H3H6oJIbIllHe - C nOMOlll.blO IJ.H<PPb[ 9. Tenepb HYiKHO np0)I.OJI}KHTb 9TY pa60TY H YCTaHoBHTb, \Iro Han- ...teHbll.lHMH H HaH6o.1JbllIHMH tIHCJl8MH HBJlHIOTCH: cpeJ{H tIeTblpeX3HaqHbIX 'IlICeJI: 'I 000 H 9 999; cpeJ{H rrHTH3Ha1JHbIX lfHCeJI: 10 000 H 99 999; cpeJlH IlleCT"3Ha1JHblX 1IHCM: 100 000 H. 999 999. OqeHb BaJKHO, J{eJIaH TaKYIO 3anHCb, 06'bHCHHTb, rr01leMY 1 000 HaHMeHblllee, 3 9 999 HaHOOJIbllIee B p5J,Il.Y tJeTbIpeX3Ha1lHbIX qUCM. OTBeT Ha 3TOT Bonpoc .naeT 3HaHHe HarypaJIbHOH nOCJIe)I.OB3TeJlbHOCTlf QHCeJI: 1 000 H3HMeHbllIee lIHCJIO B pH,ay QeTbJpeX3HaIlHbIX, nOToMY 'ITO tlUCJIO, MeHbIlJee ero H8 eJ{HHHUY (999), HBJIHeTCH Y>Ke Tpex3HallHb1M LJUCJIOM t a 9 999 - B PH)I.Y 1IeTbIpeX3Ha1lHblX QHCeJ1 HaH()OJlblll€C, 239
nOTOMY qro 1JHCJIO, 6o.nblllee ero Ha e.lUiHHI.lY (10 000), HBJIHerCH Y)Ke ATHTH3HaqllblM lIHCJIOM. nOCJIe OO'bflCHeHHSI 9Toro CJIytlaH C nOMOU{blO ytJHTeJISI YlleHHRH Yil\e cMorYT caIOCTOHTeJIbHO .naTb 06'bHCHeHHe, I10tIeMY B PHJI.Y nHTH- llleCTH3Ha 1 lHbIX tlHCeJJ 10 000 H 100 000 HBJIHIOTCS1 lIaHMeHblllHMH, a 99 999 n 999 999 - HaHt)OJIbWHMH. 2. CyecTBeHHoH oco6eHHocTblO CHCTeMbI H3ytteHHH HYMepall.HH, npHHHToH B HODOM YlleOHHKe, HBJIHeTCH 11"TO, liTO B HeH HYholepa[\HH OTBJlelleHHbIX IIHCeJI H3yqaeTCH B TeCHOH CBH3H C HYMepai.I.HeH HMeHD- uaHHblX IIHCeJI; pa3pHJlHble ej\lIHUll.bl cpaBHHBalOTCH C eJ{HHHLlaMH H3- MepeHHSI; 06pa30BaHHe OTOJIeqeHIIblX tlHCeJI COI1OCTaBJIHeTCH C oopa- 30saHHeM HMeHonaHHbIX tlHCeJI. OOCJ1e Toro KaK YlIeIIHKH I103HaKOMHCH c npaBHnorvl IITeHHH rne- CTH3HaqllbIX llnce.H H HayqaTCH Y3H3BaTb, CKO.HbKO Bcero e,nHHHLt I I I{JIacca coep}J{HTcH B ,ltaHHOM qHCJIe, IH\'I .n.aeTCH 3a.n.aHHe BbIpa3HTb n MeTpax: 803 000 MAt; 430 000 .MM; 920 000 MM. BblnOJIHHH 3TH 3a;:laHHH, ytteHHK paccym.D.aeT: TblCH4a MHJI.TIHMeT- pOD COCTaD.rlHeT I At, a 803 TbIC. .MM COCTaBJ1HIOT 803 M. lla.nee c.neAYloT ynpa>KUeHHH 06paTlloro xapaKTepa: «BbIpa3HTc 13 MIIJ1.nH{eTpax: 1 M; 80 CM; 3 J1( 20 CM; 4 M 05 CM». YllelIHK paccYJK,ltacT TaK: B 1 M TbICHQa MM.n.J1HMeTpOB, a B 2 At- 2 TblCHQU MM.TJcl1HleTpo_Il_ (2 000 MM). 13 1 'CM -- 10 MAt, a B 80 CM - 80 )J.ecHTKOB MM, HJIH 800 MM. B 3 At - 3 000 MAt JI.a ee B 20 CM - 200 MM, a Bcero 83M 20 C..t 3200 MM. nocne paCCMOTpeHHH pa3,.'IHIIHbIX CJlYlJaeB npe06pa30BaHuJl OTBJIe- lJeHHbIX llHCeJI, T. e. Bblpa)l{c.UHH HX B 6o,nee MeJIKHX HJIH B GOJIee KpynHbIx pa3pHj\HbIX e,AHHHI.I.aX, napa.TJJ1eJJbHO paCCMaTpHBalOTCH Ta- KHe BonpocbI: 1) CKOJIbKO Bcero COTeH B 1JHCJIe 3200? 2) CKO.TJbKO MeTpOB B 3 200 CM? CKOwTJbKO MeTpOB H caHTHMeTpOB B qHCJIe 5 846 CM? Bblpa3HTe B oO.TIee MeJIKHX e)lHHHu.ax; 8 COT. 9 ,nec. - B ,lleCHTKax, 8 M 9 aM - B )J.eUHMeTpax. B pe3Y.TIbTaTe COBl'tleCTHOro paCCMOTpeHHH OTBJIeqeHHblX H HMCHo- oaHHblX lJHCe&l1 Y4eHHK llaqHH3eT nOHHaTb, qTO qHCJIeHHaH - xapaKTc- pHCTHKa l\.IHO)I\eCTDa 3aBHCHT OT Bbloopa e,lJ.HHHl1b1 Ctler8, nOHHMaTb paseHCTBO qHCM, xapaKTepH3YIOw.HX OHO H TO >Ke 3HaqeHHe BeJIHqHllbI. 3. 4Toob) 3aKpenHTb Y,lJ.eTeH 3HaHHe nOMecTHoro 3HaqeHHH UHtj>Pbl t B co.a.ep>KaHHe pa60Th' no H3yqe,HHlO HYMepaUHH BKJlIOqeH Bonpoc: «YBeJIHlIeHHe HMeHbIlleHHe tlHCJIa B 10, 100, 1000 pa3». YMeHHe yne- J[HIIHTb H YMeHbIllHTb. IIHCJIO nYTeM npHnHcblBaHHR H OTopacblB3HHH uYJIeH cnpaBa n03BOJlHeT pew3Tb npHMepbl H 3a.ll.atlH, 8 KOTOpbDC Tpe6YeTCH YMHOIKHTb HJlH JI.eJ1HTb qHCJlO, OKaHQHBalOll{eecH HYJIHMH. 31'0 YMeHHe Tpe6yercH TaK>Ke npH npe06pa30BaHHH lI.aHHb(X tlHCeJI (npH Bblpa>KeHHH HX B oonee MeJlKHX H Kpynllblx CAHHHu.ax). 240
B OClIOBe MeTO].(HKH 3TOrO BOnpOCa JIeiKaT lIa6..rJlO;J.CHHC H CpaBHeHUe: YlJaInHec}1 Ha6.nlOalOT 3a TeM. KaK H3MeHHIOTCH QHC.13, KOr,na K HHM npnnHCblBalOT HJlH OTOpaCblBaIOT HYJlH, CpaBHHBalOr HCXO,nHble H 110- o ..TIyqeHHble qHCJIa 8 BbIBO,lJ.HT COOTBeTCTBYIOIllee npaBH.rIO. nOCJ1e 9Toro DBOJ).HTCH 3HaKH YMHO}KeHHH Ii l{eJIeHHSI, pernalOTCH npHMepbl II 3an.a. [IIi: 54 000 : 1 000; 3 800 · 100 H T. n. 4. B cOAepmaHHe «HYMepaUHH», KaK Y>Ke CKa3aHO Bblwe, BXOJUIT Bonpoc 0 npe06pa308aHUU IIHCJla, KOTopoe CBO,l{HTCH K ,nBY1 onepa- Ll.HHM - K pa3p00J1elnUO eJI.HHHIJ. KaKOrO-JlH60 pa3pSl].(a B e].(HHH[{bI HH3rnero pa3pH].(a H K BbIjleJ1eBHlO H3 .nanlIoro IIHCJla BCex e.nHHHlI. KaKoro-JIH60 pa3pH.lla.-, . B MeTO.lI.H 4ecKOM OTIIoweHHH 3TO CJIOJKHblH Bonpoc, H pernaeTCS1 OH no-pa3HoMY. npHBe.lleM 3eCb O.lI.HII 83 crroco60B OO'bHCllenHH. Ha KOHKpeTHbiX npHMepax BbIHCHfieTCH, liTO B tlHCJle, COCTOHrn.eM H3 Kpyrnblx .n.eCHTKOB, eJI.HHHU B 10 pa3 6o..1Jbrne, qeM JJ;eC5ITKOB; B tlHc.ne, COCTOSJU.I.eM 1f3 KpyrJ1bIX COTell, eJI.HIIHIl. B 100 pa3 OOJIbllIe, iteM COTCH t Ii T. ,n. n03TOMY, CCJ1H Tpe6ye-rCH, HanpHMep, 36 .n.eCHTKOB Bblpa3HTb B ej\HHHuax, }l.OCTaTOtIHO 36 YBC.1HlIHTb B 10 pa3; 9TO 10J{{HO ,c,nelIaTb nyreM npHnl1CbIBaHHH K lIHc.ny O}l.Horo Hy.HH cnpaBa. A ecJIH Tpe6yeTcH Y3HaTb, CKOJIbKO C,lI.HHHU B 36 COTHHX, AOCTaTOlIIIO 36 YBeJIHqUTb B 100 pa3, qTO IOJKHO c.n.e.TlaTb, npHnHcaB K tIliCJlY cnpaBa .lI-Ba UYJIH, H T. . OrclO,na npaBH.Tfo: tlTo6hl Y3HaTb, CKO..abKO e.n.HHHlJ. B qHCJle, COCTOH- ll(eM H3 .neCHTKOB, Hao npHnncaTb K qHCJIY cnpaB8 OHH HYJ1b; ttTo6bl Y3HaTb, CKOJIbKO eHHHlI. B j\aHHO1 ,qHCJle COTeH, HanO npHnHcaTb l{ 4HCJ1Y cnpaBa ABa HYJlH, H T. . . TOqHO TaK ,me Ha OT.lleJIbHblX npHMepax MOJKHO nOKa3aTb yqarn. HM - CSI, qro, ecJIH Tpe(5YeTCSI, HanpHMep, Y3HaTb, CKOJIbKO .n.eCHTKOB B tlHCJle 480, AOCT8TOqHO oT6pOCHTb B HeM HYJlb. nOJlYtlHM: 480=48 ].(CC. A ecJIH "ymHo Y3HaTb, CKOJIbKO COTeH B QHCJIe 1 200, p-OCTaTOqIlO OTOpOCHTb B HeM .n.Ba ilYlIH. J:lO..TJYQH!vI: 1 200 = 12 COT. CKOJlbKO ecHTKOB B 4HCJle 4 735? PaccYJK.!1-ael: ,necHTKOB He 6YJ!CT TOJlbKO B pa3pH,lI.e C,lI.HHHH, n03TOfY OT6paCblBaeM eHHHlI.bI; OCTaBIllHeeH UH<PPbI 0003HallaIOT IIHClIO, KOTopoe nOKaIKeT, CKOJIbKO ncero ,AecSlTKOB B .naHHOM lIHCJIe (4 73 ecHrKa). l{eHcTBHTeJIbHO, B 4 TbiCHtlaX 40 COTeH, a B 40 CHHX 400 .n.ecHTKOB. B 7 COTHHX 70 eCHT- KOB, a Bcero 6y.n.eT: 400 ,lI.ec. -t- 70 ,nec. + 3 ec. = 473 ,nee. TOQHO TaK 1Ke OODHcHHeTcH, CKOJIbKO COTeH, HanpHMep, BO BceM qaCJle 34 815. COTeH HeT TOJlbKO B pa3pH,nax .aeCHTKOB H e.D.HHliU; oropacblBaeM HX. OCT8BIIIeeCH IIHCJIO (348) _ nOKCllKeT, CKO.1bl{0 Bcero COTeH B IIHCJle (348 COT.). OrclO.n.a BbITeKaeT npaBHcllo: QTo6bl Y3H8Tb, CKMbKO Bcero coreH B .naHHOl\-1 tlHC.1Je, HaAo OTOpOCHTb B HeM AecSlTKH H e,nHHRl(bI H npOtlHTaTb OCTaBweeCH lIHCJlO KaK qHCJIO COTeH. 5. nOCJIe H3Y1leHHH HYMepal.I.HH meCTH3HatlHb£X QHCeJI BBOHTCH KJ1aCC MHJIJlHOHOB H .aeBHTH3HaQHle tIRC.Ha. nOpHJl-OK pa60TbI npHMep- HO TOT >Ke, qTO H Ha KJ1aCCOM TbICHlI H mecTH3HallHbIMH tlHCJIaMH: 06- pa30BaHHe Tpex HOBblX pa3pfJJ{lIblX e.n.HIIHll - l\lHJlJ1HOHa, .necHTKa 241
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M - 2''1-'-- n · · · · · · · · I 1 . t I' _ I : . ...20'l2flJ 224 2JI./ (}I./ III 2l/ JL/ 44/ .5L/ bq 711... -- - PIIC. 1. ne;eM npHMep perneHHH 3a-natIH: «nOe3 \OCKBa-JIeHHHrpa.1t BblllleJl 113 J\t\OCKBbl B 22 't H npH6bIJI B JIeHHHrpa.n. H3 CJ1eJlYlo1.l.lHe CYTKH 8 7 fl. CKOJIbKO qaCOB nOe3J). 6bI.'1 B nYTH?» BhIqCpqHBae1 npH1\fYIO H Ha HeH 0603HaQaCM TOllKaMH qaCbI OT- npaB..'1eHHH H npH6bITHH nOe3,tJ.a, tlaCbI npc6bIBaHHSI ro B nYTH, OT.ne- JH1Si >KHpllOrl TOtlKOH O}J.HH CYTKH OT pyrHx (CM. pHC. 1). BbJQnCJIHeM: c 22 It J\O 24 ti, T. e. ,no KOHl{3 nepBbIx CYTOK, B KOTopble Bblrn1 nDe3)l, npOlllJIO 2 'l (24-22 = 2); Ha CJIe;tYIOlJ.{He CYTKH npHXOAHTCH 7 'l, a Bcero noe.3 6bIJI B nYTH 2 "t n.nIOC' 7 tt, lITO Cocr3BJISIeT 9 "t. ECJ1H peweHHe TaKeR 3aJ\atIH 3anHC3Tb, TO, YCT3HOBHB, 1ITO BpeMH u HaXO>K.lleHHH nOe3;ta B nYTH COCTOHT 1-13 J\BYX 1IaCTeH - O)\Ha tIaCTb JJpHXO,AHTCSI H3 nepBble CYTKH, 3 .llpyraH - H3 BTopble CYTKH, Heo6xo- J\HMO HCnOJIb30B3Tb J1,Ba .lleHcTBH: · 1) 24 - 22 == 2 ({i) 2) 2 + 7 = 9 (tl) o T BeT. noe3,tJ. 6bI0I1 B nVTH Bccro 9 'i. Ha TaKOM )Ke 1IepTe)Ke YJ\06HO nOK33arb pewellHe o6paTHoH 3a.lla- llH: «nOe3,l1 MocKBa-JIeHHHrpaJl., BbIH.lUI H3 MOCKBbl BeqepOM, npH6blJI 8 JleHHHrpa.ll B '1 at. KorJ\a BbHlle..'I noe3.ll H3 MOCKBbl, ec"YJH OH 6bIJI B nYTH Bcero 9 ?» BHHMaTenbHO npOqHTaB ycnoBHe 3aJl.aQH, HeTpYJl.HO YCT.HOBHTb, qTO BpeMR ABH>KeHHR D0e3Aa (9 ) pacnpeJ\eJISIeTCSI. H3 ABOe CYTOK: 7 at npHxo.llHTCH Ha OAHH CYTKH, 3 OCT3JIbHOe BpeMR npH- XO,lJ.HTCH H3 .llpyrHe - npbI;{YInHe CYTKH. CKOJ1bKO >Ke q3COB npHXO- J\HTCH H3 npe,lJ.bI,lI.YI.l\He CYTKH? 3TOT Bonpoc pe1ll3eTCH BbIlIHT3HHeM 9--7 = 2 ('l). nOKIDKeM 9TO 1I3 lIepTeLKe. LIepTHM npHMYIO, H3 HeH KpynHoH T01lkoM OTJI.f.J1HeM O.llHH CYTKH OT ApyrHX: KOHeu nepBbIX cy- TOK (24' 'l) OT HatJa.,TJ3 BTOpblX (0 tt). BnpaBo OT Halla.n3 BTOpWX CYTOK 0603Ha1laeM ceMbIO T01lK3MH 7 it; BJIeBO OT Ha l laJI3. BTOpbIX CYTOK (24 'I) )lBYMH TOllKaMH 0003HaQaeM 2 It, KOTopble COBna.llaIOT C 22 't. I1raK, no- C3)1. BLlwe..TI H'J l\\OCKBbI B 22 "t. 3anncb peIJleHHH 9TOil 3aaqH 6YJ\eT BhIr40TI5I,!J.eTb T3K: 1) 9 - 7 = 2 (tl) 2) 24 - 2 = 22 (fl) . DO.llo6HO 9TO!\.fY ){aCTCH 06'bSICHeHHe TpeTbeii (oopaTHoli) 3a.llaQH: «nOe3.ll MocKBa-JIeHHHrpaJ\ oTnpaBH.'1CSI H3 l\\OCKBbI B 22 tt H, npH6b1J1 B JleHHHrpaA Ha CJJeAYIOlll.He CYTKH, npo6blB B nYTH 9 tt. Bo/ CKOJIbKO lJaCOB noe3 npH6bIJI B JleHHHrpa.ll?», npH p3360pe 33;I.311H YCT3HaBJIHBaeTCSI, QTO H3 9 tl 1I3CTb SpeMeHH npHxo.llHTCH Ita OJI.IlH CYTKH, .llpyraSl lIaCTb - lla JJ.PY fHe CYTKH. CKOJJb- 249 ........
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, u CTHraeTCH OOpa30BaHHe HaBbIKa, C O,l\HOH CTOpOllbl, XOpOlllO OC03HaH- u u v IJOrO B CBOeH OCHOBe, a C JlpyroH - B lIeKOTopOH 1\fepe aBTOMaTH3H- (lOB3HHoro. . B CBH3H C cpOpMHpOBaHHe!\f BblqHCJIHTeJIbHblX HaBbIKOB H3YQaeTCSI Bonpoc 06 H3MeHeHHH npOH3BeeHHSI B 3aBHCHMOCTH OT H3,.feHeHHH OJI.HOrO H3 COMHO)KHTeJ1eH. 3ecb npoHcxoHT o606rneHHe TCX <paKTOB, J{OTOpbIe Ha6JIl0J11HCb YtIaIllHIHcH HaQHHaSi co I I KJIacca. B CBfl3H t: H3YQeHHeM 3Toro Bonpoca npoBoJ(HTCSI ynpa}KHeHHSI, B KOTOpbJX :--JTO 3HaHHe HaXOJ(HT CBoe npHMeHeHHe. K TaKHM ynpamHeHHSlM OTHO- c ijTCSI CJIeYlOrnHe: I) HaHHTe TpeMSI cnocooafH 3HatleHHe BbIpa>Ke- IHISI; HanpHMep, npoH3BeJ).eHHe qHCen 50 H 4 YBCJIUIIHTb B 2 pa3a; 2) BbJ1JHCJIHTe caMbIM YJ).06HbIM cnoc06oM BbIpameHHe (75 · 5) · 2 HAp. npH 06'bHCHeHH!I H YCBoeHHH. BbIlIHCJIHTeJIbHOrO npHela YMHO}KC- I1HH Ha oH03HaIlHOe IIHCJIO YIlHTeJIb, a BCJ1e.n 3a HHI H ytIeHHKH ,llalOT I10,l1pOOHOe 06'bHCHelJHe, lIa3blBaH pa3pgbI MHO}KHMOrO H npoH3Be,lleuHB. 110 B npou.ecce ynpa}l{HeHHH H TpeHHpoBKH YQI1Tlb nOl{a3blBaeT .ne- THM cOKpameHHbIe iJpHCMbI nOSlcHeHHH, KorJ).a pa3pH,1I.bI MHO}KHMOrO H npOIl3Be,lleHHH He lIa3bIBalOTCH, 3 Ta6..TIHueH YM"HOmeHHSI nO.JIb3YIOTCH 8 l\paTKOM (CPOPMYJlHpOBKe. B 3TOH me TeMe ,1I.eTII 3HaKOMHTCSI co cnoc06oM YMHoiKeHHSI COCTaB- HbIX HleHODaHHbJX IIHCeJI. npH 9TOM COCT3BHoe H1\leHOBaHHoe 1JHCJlO 3a\tlelUIeTCH npocThlf H YMHO>KeHHe HMeHOBaHHblX tIHCeJI BblnOJIHHeTCSI }\(}I{ Y{HO)l{eHHe 01BJIeqeHHbIX tlHCeJL I1CKJIIOqeUHe u. eJIe coo6pa3Ho C,Qe.JIaTb TOollbKO .lI-JIH He60JIbIllHX COCTaBHblX I1MeHOBaHHbIX tlHCeJI, D!.,]pameHHLIX" B PYUJISIX H KoneHKax. B TaKHX CJIyqaHX J PYOJlH H KO- liel! KII YMHolKaIOTC5I OT)\eJIbHO oe3 pa3po6JIeHHSI 1.IHCJIa B KoneHKH. nYCTb, HanpHJ\.lep, Tpe6yeTcSI peWHTb 3a.ll-a1.JY: «Ha KOCTlOM KynHJlH 3..w MaTepHH no 6 py6. 25 Kon. 3a MeTp H 2 M nOAKJIa,l\KH no 1 pyo. 30 Kon. CKOJIbKO CTOHJla BCH .TloKynKa?» 3ecb YIHOJKeHHe BbI- nOJIHHeTCSI TaK: 6 py6. 25 KOII. · 3 -== 6 py6. · 3 + 25 Kon. · 3 18 pyo. 75 KOH. I py6. 30 I{on. · 2 = 2 pya. 60 Kon. 18 py6. 75 Kon. -t- 2 py6, 60 Korr. 21 py6. 35 KOTI. B )KH3UeHHOH npaKTHKe TaRHe cJlYQal1 BCTpeqaIOTC5I HepeJ).Ko, H IU'O:Ia .n.O..1i1{1I3 1103Hal<OMIfTb eTeH C palll101-13"TJbHbI:\Hf npnCMaMII Bbl- 1I1ICJ1eHHH B no,no6HbIX c.,'1yqaSlx. 113BecTHO t \lTO aJIrOpHTM".3TOrO ,lleHcTBH5I OTJlHlIaeT- AeneHHe Ha OAHO- cn Hau60JIbllleH CJIO/KHOCTblO a n03ToMY H HeKOTO- 3Ha'tHoe 'iMCnO u # , pOH TPYHOCTbJO ero BoCnpHHTPISI H YCBoeHHH. B MeTOHqeCKOH lIaYKe 3TOT anropHTf TaTeJIbHO pa3pa60T3H. Ho H IJlKOJlbHOH npaKTHKe OH He paCKphlBaJiCH nepe.n .neTbMH KaK CHCTeMa 4CTKO Ctjx>pl\fYJlHpOBaHHbJX npaBf1.,1, KOTopble OJI)I{HbI HanpaBJI.SITb KalKJ{bIll lllar C03HaTe.1JbHOH .lI-eSlTeJIbHOCTH yqeHHKa. B HOBOM YQe61IHKe YLKe np" 06'bSlCHeHHI1 nepnoro CJIYllaH IIHCb- f\.ICHHQR) e.,leHH5I aJI rOp.HTM 3Toro ,l1.eHCTBl1 H paCKphlBaCTCH qeTKO, 'fUqUO, SlCHO, nOC.TIC.lI-OBaTeJIbHO B BHe npHMepHo 10 npaBHJI, H3110- )1\eHl1bIX KpaTKo. BOT 3TH npaBH..qa: 255
npOQHTaHTe H 3anHllIHTe npHMep. BblJteJIJlTe nepBOe lIenOJlHOe .lI.eJIHIOe. YCTaHOBHTe BblCUIHH pa3p5l,n H lIHCJIO l.UUPP B lIaCTHOM. HaH,lUfTe UJICPPY BblClllerO pa3pH;ta qaCTHOrO. Y3HaitTe t CKOJIbKO elUffIHu. 3TOrO pa3pH,zta pa3.l1.eJIRJlH. Y3HaHTe, CKOJlbKO eAHHHU 9TOrO pa3pH,l{a OCraJIOCb pa3)leJIHTb. npOnepbTe, npaBHnbHO JIH nOJ.{OOpaHa I.1H<ppa lIaCTHOrO. ECJlH nO.TJyqHJICSI OCTaTOK, pa3,apOOHTe era B e,zU1HHlI.bl CJ1e;1YIOllI.e.. fO 33 HHM IIH31llerO pa3pH3 H npH6aBbTe K BUM e.ll.HHHUbI TaKoro me pa3pSla ,l{enHMoro. . npO,aO.HmaHTe ,zteJleHHe TaK /Ke, nOKa He. peIllHTe npHMep AO KOHll.a. npoBepbTe BblllHCJIeHHe. 3,aecb npeAycMoTpeH Ka>KblH IlIar yqeHHKa, KaJK,ztaH OT,lleJIbHaH BhlqHCJlHTeJIbHaSl onepaUHSI, BXO,aHmaH B npouecc ):{eJIeHHSI, H Ka>K,l{aH H3 HHX no.nYQHJIa HC1IepnhlB31Ornee OO'bHCHeHHe, o6eCnetIHBaJOlliee co.. 3HaTe.,TJbHOe BocnpliSlTHe II YCBoeHHe cnocooa J{fJIeHHH. B 1l0BOM Ylle6HHKe IIHcbMellH;blH npHeM ,aeJleHH pacKpblBaeTcSI Ha TaKHX npHMepax, Ha I<OTOpbIX npeHMYllI.eCTBa ero nepc.l1 YCTHblM npH- eMOM OtIeBH}\Hbl, T. e. Ila npHMcpax, B KOTOpblX pa3pHHbI c.naraeMble ,ne.nHMoro (Bce HnH HeI\OTOpLle) He .l1eJlHTCSI Ha eJIHTeJIb HaUeJlO, HanpHMep 376: 4. ECJJH )f{C B ){eJIHtOlwl Ka>KAoe pa3pH,nHoe tlncJlo JleJIHTCH Ha J{eJlHTeJJb, nanpHMcp 84248 :- 2, TO TaKHe npHMepbl pe- walOTCSI C HCnOJIb30BaHHif YCTHbIX npHe1fIOB BbIQHCJleHHSl 11 C sanHCblO B CTPOllKY (84248: 2 = 42124). TeOpeTHQeCI(OH OCHOBOH BbIqnCnHTeJlhHoro npHeM8 .ne.JIeIlHH lIa O.llH0311allHoe QHCJlO c.nY/KHT pacnpe.lleJ1HTeJlbHOe CBOHCTBO ,neJIeHliH (AeJleHHe CYMMbI' na IIHCJIO). OHO OCo6eHHO HpKO npOHBJlHeTCH 8 YCT- HbIX npHe:\13X BbltIHCJ1eHHH; HanpHl\iep: 963 : 3 = (900 + 60 + 3) : 3 UJIH 786: 6 = (600 + 180 + 6) : 6 = 100 + 30 -r- 1 = 131. . Do.HbwHHcTBo 3 a..na II , nOMemeHHblX B 3TOH Tel\-Ie, HanpaBJleHO H3 DbIpa60TKY Y J.{eTefI YleHHH npHMeHSlTb YMHO>KeHHe II JI.eJleHHe B pa3- J1HlIHbIX cJlyqaHX: npH uaXOiK,neHHH CYMMbI O,nIlH3KOBbIX CJIaraeMblX, npH YBew1HlIeHHH tlHCJIa B HeCKOJ1bKO pa3, npn YMHO}KeHHH, 3'a,n3H- HOM B KOCBeHHOM Bblpa>KeHHH. B HeKOTopblX 3aal{aX Tpe6yeTCH Y?rte.. v HHe Hcno..11b30BaTb pacrrpe;teJlHTCJlbHOe CBOHCTBO YMHomeIlHH. <1>opMHpoBaHHe HaBbIKOB YCTHoro H nHCbMeHHOfO l{eJIeHHSI TaKme Bce BpeMH cOnpOBO)K,Z(aercSI pellIeHHef 3a,ztaQ, B KoropbIX rrpHMeHHIOTCSI pa3JIH-QHble CJIYQaH e..TIeHHH: ,l{eJIeHHe ..Ha paBHbIe qaCTM H no COAep>Ka- HHlO, ;te.neHHe npH YMeHbllleHHH tIHC..TIa B HeCKOJIbKO pa3 H npH HaXO>K.ll.e.. IIKH qaCTIi tIHc.Ha, npH KpaTHOM cpaBneHHH tlHCeJI H B HeKOTopblX .npy'" rHX CJIY4aSlX. B perneHnH HeKOTopbIX 3a,l{aq Haxo,aHT npHMeHeHHe 3HaHHe, K3K H3MeUHCTCSI npOH3Be,zteHlie 8 3anHCHMOCTH OT H3MeneHHH COMHO}Klf.. u TeJIeu 11 QaCTHOe B 3aBHCHMoCTH OT H3MeHeHHH lleJIHMOro H !tenH- TeJI Sf . B 91'OH TeMe npOAOJI}f(aeTCSI npaKTHKa peweHHH 3a.natJ. Ha JlDH>Ke HHe - 80 BCTpeqHOl\t H 8 npOTHBOnOJlO)KHbIX lIanpaBJIeUuSlX. 256
4aCTb TaKHX 3a,lI.aq peUIaeTCST C COCTaBJIeIlHet QHCJlOnOH cpopMynbl, u IICKOTOpWe - no OT,neJIbHbI1 BonpocaM H ,neHCTBHHM. R MaTepHaJle 9TOH TeMbl HMelOTCH 3a,naHHH no COCTaBJIeHHIO 3BJtaq yqaHMHCSI no Bblpa}l{eHHS1M 6YKBellllbIl\i H lIHCJIOBblM: a. b; (120 : 6) . 4; a: b; 27: (12 : 4). Heo6xo.llHfO .no6HBaTbcH, QTo6bl no BbIpa}l{eHHIO a. b ,neTH co- CTaBHJlH Bce BHJJ.bl npocTblX 3a,l.ta4, pelliaeMblx YMHO>KeHHel\f, a ITO Dblpa}l\:eHH:lO a : b - Bce BHJJ.bl npocTblX 3a,nall, pelliaeMblx ,neJIeHHel\1. 3TOT cJIyqaii yme paccMaTpHBaJICH npn H3YQeHHH YMHOJHeHHe H ene. IIYMepaUHH {HOr03HaqHbIX qHCen. Ero HY>KHO "Me H8 10, 100, 1 000 TOJIbKO nOBTopHTb; BCnOl\'JHlITb npaBHJIa YMHO>Ke- HH:H H ){TIeHHS1 Ha pa3p5l,nHble e,lI.HHUll.bl. DOJIb3Y- HCb 9THMH IIp3BHJlaIH, yqCHH!<H AO.TI>KHbl BbInO..1IHHTb pH,A ynpa>KHe- HHH, qTo6bl J]:06HTbCH npaBlfJlbHOCTH, HeKOTopOH 6WCTpOTbi If ynepeH- HOCTII B BbIQHC..TJeHH5IX. Ocoooro BHHMaHHH 3aCJIY>KHBaeT ,ne.neIlHe C OCmamKOM. OpHClvl .l(CJIeHH5I B 3TOM CJIYlIae CBO,l].HTCH K TO{Y, qTO H3 ):{aHHoro qnCJIa Bbl.l(eJIHeTCH HaH6oC/TfbllIee qHCJIO, KOropoe ,nCJlHTCH Ha 10 (100, 1000) 6e3 OCT3TKa. TaKHl\1 qHCJlOM 6YJlYT KpyrJlble .l(CCHTKM npH ,ne.neHHH Ha 10, KpyrJlbIe COTHH npH ,neJIeHHH Ha 100, KpyrJlble ThlCHqH npH Jl-eJleHHH Ha 1000. OcraBllleecH MeHblllee QHCJIO COCTaBHT OCTarOK. nOCJl-e 3anlfCH pellIeHHH HecKOJlbKHX npHMepoB 368 : 10 == 36 (OCT. 8) 4 715 : 100 == 47 (OCT. I 5) 86 534 : I 000 86 (OCT. 534) .. ,nOCTaT04HO B Ka>KAOM Jl.e"TfHMOt no,ntIepKHYTb O,nHOH qeproii Te lI.McpPbl, KOropbIMH 3anHcaHO tIaCTHOe, H BYfH qepTaMH Te UHcppbl, KOTOpbIMH sanHcaH OCTaTOK 368, 4715, 86534, H 3aTeM conOCTaOHTb - -- tlHCJlO UH<J>p B OCTaTKe C tIHCJI OM Hyne1i B ,neJIH TeJIe, qT06bI ytIalI.(HecSl no,nMeTHJlH CJIe,lI.YIOIlI.YIO 3aI(OHOMepUOCTb: B eJlHTeJIe 10 O,nHH HYJlb H B OCTaTKC o,nHa llHcJ:>pa, B ,neJIHTeJIe 100 ,nBa HYJlH H B OCTaTKe Jl-Be llHCPPb[, B .l(eJIHTeJIe 1000 TPH llYJIH H B OCTaTKe TPH UHCPPbl. nOJIb3YHCb BbIHBJIeHHOH 3aKOHoMepHocTblO, ytJaInHecH pem810T p5I){ npHMepoB; B pe3YJIbTaTe o6pa3yeTcH HaBblK np3BHJlbHOrO H JJ.O- CTarOlIHO 6blcTporo Jl.eJIeHHH C OCTaTKOM. 3aMeTHM, liTO HaBbIK ]leJIeHHH C OCTaTKOf B aJIbHeHllieM 6y,neT HrpaTb 60JIbllIYIO pOJIb, n03TOMY 011 ,nOJl>KeH 6bITb oTpa6oTaH TInaTeJlbHO. TeOpeTHqeCKoit OCHOBOH BblllHCJlHTenbHOrO npH- YMHoHCeHHe 'fNCna Ha eM3 HcnoJlb3yeMoro n p H YMHO>KeHHH H8 K py rJIble npOM38eAeHMe M Ha ' . Kp,rnwe "Mcna tIHCJl3, SlBJIBeTCH np8BHJlO YMHomeHHH QHCJl8 H3 npOH3Be,neHHe. BCSlKoe KpyrJIoe qHCJlO MO>KHO npe,ncT8BHTb B BH,lI.e npOH3Be;teHHH KaKorO-TO IIHCJI8 JlHOO Ha 10, nHoo H3 100, JIHOO Ha 1000 H T. JI-. HanpHMep: 90 = 9 · 10 600 = 6 · 100 80008.1000 9 3aK8J 694 251
\ . n03TO:-dY eCJIH yqeHHK YMeeT YMHO)KaTb na O,AH03HalfHoe tlHCJIO " Ha pa3pH,llHble e;UiHMllbI, TO eMY OCTaeTCH TOJIbKO Y3H3Tb npaBHTJO YMHO>KeHHH tlHCJIa Ha npOH3BeeHHe, H Toro 6Y.lleT .nOCT3TOllHO llJISI <jJOpMHpOB3HHfI HaBblKa YMHOiI<eHHH Ha KpyrJ10e 1.IHCJlO. 4T06bI BblBeCTH npaBHJ10 YlHO)KCHHH llUCJIa Ha npOH3Be,neIlHe, yqeHHKaM npeJIaraeTCH paCCMOTpeTb Bblpa}KeHH5I, cpaBHMTb cnoco6bl HX BbItJHCJIeHHH H pe3YJIbTaTbI. H3npllep: 18 · (2 · 5) = 18 · 10 = 180 PaCCtOTpeB eme O.AHo-,nBa TaKHX BbIpaiKenHH, yqaHeCH c,ne.naIOT BbIBO,n: «4T06bl ynlofKHTb llUCJIO Ha npoH3Be.lI.eHHe, MO>KHO BbltJHCJIHTb npoH3Be,neHMe H Yf\1HOiKHTb qHCJIO Ha nOJIYtJeHHbU{ pe3YJIbTaT». ,UaJIee paccf3TpHBalOTcfl JlpyrHe cnoco6bI BbIQHCJIeHHH TaKHX BbIpa- >KeHHH: 18 . (2 · 5) = (18 · 2) · 5 = 36 · 5 = 180 18 · (2 · 5) = (1'8 · 5) · 2 = 90 · 2 = 180 OrCIo.n:a J{e"laeTC5I DbIBO){: «4 ro6bI YMHOiKHTb IIHCJIO Ha n poH3Be.ne- HHe, OCTaTOqHO yMlIOiKHTb tIHCJIO Ha O.lI.HH H3 cOnI9}KHTeJIeii H nOJIY- lJeHHbIH pe3y.J1bTaT YMHO>KHTb Ha J1pyroM COrvIHOiKHTMb». Ha OCHOBe 3Toro npaBHJla yqeHHKH peruaIOT npHfvlepbl TpeMJI cno- cooaMH. HanpHMep: 8. (5 · 3) I cnoeo6: 5 · 3 = 15; 8 · 15 = 8 · (10 + 5) = 80 + 40 = 120 II cnocoo: 8 · 5 = 40; 40 · 3 = 120 III cnoco6: 8 · 3 = 24; 24 · 5 = 120 CpeJ(H 9THX cnoco6oB eCTb 60JIee Y,Ao(h-lble II MeHee y,l106HbIe; BTOpoii cnoco6 npHBO,llHT K caMoMY JIerKoMY BbIqHCJIeHHlO. nO.3TOMY YlleHHKa HY>KHO rOTOBHTb K BbIOOPY HaH60JIee y,noC)Horo cnoc06a. JI.nH 3TOH UeJIH npe,l{JIaraeTCH ynpaIKHeHHe c 3a,naHHeM: «HaU,llHTe pe3YJIbT3T caMbIM y.n06HbIf cnocoooM». BbltlHCJlHH, HanpHMep, BbIpa>KeHHe 25 · (9 · 4), yqeHMK 3a4eqaeT, qTO pe3YJIbTaT nOJlytlaeTCH nerKO H 6bICTpO, ecJIH YMHO)KeHHe BbInOJIHHTb B TaKOM nopHAKe: (25 · 4) · 9. ,QaJIee YtIHTeJlb cOo6rnaeT, qTO npaBHJIO YMHO)KeHHH tlHCJIa Ha npo- H3Be,neHue I1CnOJIb3yeTcH B BbItlHCJIeHHHX B Tex CJIYllaHX, Kor,na OAHH 83 COiHO>KHTe.TIeiI MO}KHO npeCTaBHTb B BHe npOH3Be,neHHH. HanpH- Mep: 12. 30 = 12 · (3 · 10) = 12 · 3 · 10 = 36 · 10 = 360. no 3TOMY 06pa311Y Ytlall1.HeCH peW310T pHA npHMepOB THna: 54 · 20; 25 · 12 - H TaKHM 06pa301'vf YCB3HsalOT BbIlIHCJ1HTeJlbHbIH npH- eM, KOTOpbIH aJIbIIIe 6y):{eT HCnOJIb30BaH npH YMH01KeHHH lIa KpyrJIbIe (1I1CJI3. Tenepb, KOfJ{a YlleHHKaM H3DeCTeH npHeM YHOiKeHHH qHCJla H3 npOH3Be.lleHHe H npHet YMOiKeHHSI qHCJla Ha CYMMY, B03HHKaeT HeoG- XOAHlvlOCTb cpaBHHTb H conOCTaBHTb 9TH npHeMbl, c reM qTOObJ ,llHtP- 258
<PepeHUJlpOBaTb HX H npeAynpe,nHTb CMeUlHBaHHe. SToff ueJlH CJIY" >KaT: a) 38,ltallHe 3aKOH4HTb H cpaBHHTb cnoc06bI perneHHSI npHMepOB THna: 15 · 40 = 15 · (4 . 10) == 15. 14 = 15 · (10 +4) = 6) YCTHble ynpa>KHeUHH DHJta: 15 YMHOJKHJlH Ha 4 Ii nOJlY1.IellHbIH pe3YJlbT8T YMHOiKHJlII Ha 2. Ha KaKoe tIHCJlO B pe3YJlbTaTe YMHO- >KMJIH 15? 15 YMHOmHJIH CHaqa1a Ha 4, nOTO1 15 YMHO>KHJIH Ha 2 H nOJIyqeH.. HbJe npoH3Be,neHHH CJlO>KH..rIH. Ha KaKoe 4HCJlO D pe3YJlbTaTe YfHO>Ke- no 15? BJl8ro,napSl TaKoro po,lta ynpaLKHeHHSI1 yqalIIJ1ecH OKOll1.IaTeJlbHO YCBaHBaJOT BblQHCJ1HTeJ1bllbIH npHeM YMHO>KeHH5I 1.IHCJIa Ha npoH3Be,ne- "He, I10CJle 4ero MO/KHO nepeHTH K <PoPfHpoBaHHIO Ha8blKa YMHO)KeHHH MHOr03HaQHOrO tlHCJIa Ha Kpyr..'1ble qHCJla (H3 70, 400, 6000 H .ap.). Pa60Ta HaQHHaeTCH C ynpa>KHeHHH B pa3J10}J{CHHU. KpyrJlblx 1.IH- CM Ha rrpOH3BelI.CHIIe !I.RYX COtHO)l{HTeJleH, 113 KOTOpbIX nepBblH- OJ{Ho3HaqHOe qnCJIO, BTOpOH - pa3pH,nHbIe eJ{HHHbI (10, 100, 1000). HanpHMep: 500 5 . 100; 9000 :=-: 9 · 1000 H T. . nOCJIe 3TOro YllaWHrvlcH npe.n.J1araeTCH J1aTb o6DHcHeHHe perneHlf5I ,l\BYX npHMepoB: 24 · 300 -== 24 . (3 · 100) = 24 · 3 · 100 = 7200 38 . 20 == 38 . (2 . 10) == 38 · 2 · 1 0 760 npe)J.bI,ltyaH pa60Ta nO.ll.rOTOBHJla )(eTeH K TO!'vIY, qTO OHM MorYT CaMocmoR.meAbftO 06'bHCHHTb perneHHC 9TliX npHf"tepOB. LlaJlee YQH1'eJ1b nOKa3bIBaCT It 06'bHCHHeT yqaHMCH cnoco6 nHCb.. MeHHoro YMHO}KeHHH na KpyrJloe qHCJJO, Kor,na MHO>KHTeJIb nOnI1Cbl" BaeTCSI no)t MHO}KHMbIM H IIYJIb npHnHCbIBaeTCH K npOH3Be,l\eHHIO. OpH 3TOM HY>KHO ;:(00I13aTbCH, qTOObl Kam,l\hIH yqeHHK nOllHf\1aJI npH- nHChIBaHHe HYJlH KaK YMIIO}KeHUe qHCJIa H8 ,neCSlTb. BCJIe)t 3a 9THM H.n.YT ynpalI{HeHHH B 06pa30BaHHH HaBbIKa: pewa- IOTCH npHMepbI, pelllalOTCH 3a,na4H, B KOTOpbIX HcnoJlb3yeTcSI 9TOT HaBbIK. Tenepb B03HHKaeT He06xo.ll.HfOCTb conOCTaBHTb YMHO>KeHMe Ha KpyrJlOe qHC.TIO C YMHomCHHeM KpyrJIOro 1.IHCJIa Ha OJlH03HatlHOe qHCJIO: X 3700 X 468 6 600 B OOoHX npHlepax eCTb CXO)J.Hoe H eCTb p8SJIHQnoe. CXo,l\Hoe: YMHO>KeHHe BblnOJIHHeTCH, He o6pamaSl BHHMaHHH H8 HYJIH; HYJIH B 060HX npHMepax npHnHcblBalOTcSI K pe3YJIbTaTY. Pa3J1H1.JHoe: npHnH" CblBaHHe ,l\BYX HYJIeH B nepBoM npHMepe 03H8qaeT pa3,l\pOOJleHHe co- TeH B e,ltHHHUbI, BO BTOpOM npHMepe - YMHO>KeHHe Ha 100. nOCJle,ltHHH 3Tan pa60TbI Ha,n HaBbIKaMH YMHO>KeHHSI Ha KpyrJIble qHCJla - paccMorpeHHe cJIYllaSl YMHO>KeHHSI, Kor,na 06a COMHO>KH1H OKaHQHBalOTCH HYJlHMH (800 · 60). 2
npH 06'bHCHeIIHH 9TOrO CJIyqaSl Ha npHMepe 800 · 60 l.\eJIeCoo()pa3- HO K3iK,lI-b1H H3 COMHO>KHTeJIeH npe,l{CTaBHTb B BIi,lte npOH3Be)J.eHH5J: nepBbIH COMIlO/KHTCJIb - 8 . 100; BTOpOH COMHO)KHTeJ1b-6 · 10. Tor- )la nOJlyqHTCH CJIejJ.YlOaSl 3anHCb, pacKpblBalOlUaSl npouecc YMHO- )KeHH5I: BOO · 60 = 8 · 1 00 · 6 · 10 = 8 · 6. 1 00 · 10 = 48 · 1 000 = 48 000 nOCJIe 3Toro yqall\HecH MorYT caMOCTOHTeJlbHO 06'bHCHHTb pellleHMe npHMepOB X 8400 / 70 588000 X 1370 / 500 685000 X 8200 700 5740000 H nO)J.MeTHTb 33KOHOl\fep HOTb: B KOHue KalK.noro npoH3BejJ.eHHH no- JIyqaeTCSI CTOJIbKO HYJleft, CKOJIbKO HX B 060HX COMHO>KHTeJISIX BMec- Te. Ha 9THX npllMepax YCBaHBaeTCH BblqliCJlHTeJ1bHbIH npHeM, nocJle lJero n.nYT ynpa/KUeHHH B perneHHH alla.norHqHblX npHMepoB ,lJ.JIH 06- pa30B3HHH 3BTOMaTH3HpoBaHHoro HaBblKa. 06blllHO TaKlie npHMepbI pew3(OTcH nHCbMeHHO (c nOJlHO" 3anHCblO Db1\IHC.rleHHS1 CTOJI6HKOM). O.ll.HaKO MHOfHe H3 HHX BnOJlHe .llOCTynHbI u u jJ.JIH YCTHblX BblllHCJIeHHH C nOCJIe.nYIOIneH 13anHCblO TOJIbKO pe3YJIb- TaTOB. HanpHMep, npot.HITaB Bblpa/KeHHe 300 · 50, yqeHHK HaXO)J.HT npo- H3Be.neHHe qHCeJI 3 H 5 (15)t nO)J.CqHTbIBaeT HYJlH B COMHO)KHTeJlSlX (Tpn HYJIH) H 3anHCblBaeT pe3YJlbTaT: 15 000. YCTHoe pellleHHe TaKHX npHMepOB 3aKpenJlHeT 3HaHHe BblllUCJlH- Te..TIbHOrO npHeMa. 3aKpenJleHHIO H3BblKa YfHO}KeHHH Ha Kpyrnble tJHCJ1a H ,lU-IQxI>e- peHu.HponaHHlo HaBbIKOB YMHolKeHHSI Ha npoH3Be,l\eHHe H YMHO)KeHHH H3 CYMMY cnoco6cTByeT ynpIDKHeHHe B cpaBHeHHH Bblpa}l{eHHH c no- cTaHoBKoH Me/KJty HUMH 3HaKOB >, < HJIH - . HanpHMep, cpaBHHTb: 246 · 3. 100 H 246 . 300 568 . 70 II 568. 10 1- 568 . 7 B 3aK.TJlOtleHHe nOJIe3HO B u.eJI5IX OOo6lll.eHHH 3anHcaTb npaBHJIO YMHO)KeHHH t.IHCJla lIa npoH3Be.neHHe 6YKBa)fH: a · (b · c) = a. b. c, II npopern3Tb 3a;!a4H, B KOTOpbIX C<pOp!',fHpOBHHbIH lIaBbIK HaXOJ1HT CBoe npaKTHtJecKoe npHMeHeHHe. , TeOpeTHqeCKOH OCHOBOH BbItlHCJlHTeJIbHOrO npH- Aell8HMe IINcna H8 efa HCnOJIb3yeMoro npH .neJ1eHHH na Kpyrnble tIMC- npOM3BelteHMe "Ha ' Hpyrnwe IIMcna JIa, SlBJIHeTCH npaBHJlO AeJleHHH qHCJla Ha npoH3- Be)teHHe. n09TOMY «P<>pMHpoBaHHIO HaBblKa .lleJIe- HHH na KpyrJIble qHCJIa npeNlleCTByeT 03HaKOMJIeHHe yqamHXCH C npaBHnoM eneHHH qHCJIa Ha npoH3BeJ1eHHe. MeToJ1HKa H3YQeHHH 9Toro npaBHJIa aHaJlOrHIJHa pacKpbIToH BbJWe MeTO)JJIKC H3YQeHHSI npaBHna YMHO}KeHHSI tJHCJ1a Ha npoH3BeeHHe. 260
3)].ecb TaK>Ke yqall(HeCH CIIatfaJIa paCCMarpHBalOT H cpaBHHBaOT pa3JIHQHbIe cnoco6bI BbIqHCJIeHHH 3H34eHHH Bblpa/KeHMH, B KOTOpblX 1IHCJlO AeJIHTCSI H3 npOH3Be)J.eHHe pa3HblMH cnoco6aMlI, HO npH /9TOM nOJIyqalOrCH O,llHHaKOBble peaYJIbTaTbI. OTCIO,na BbIBO.L(MTCH nfraHJIO: Qro6b1 pa3)1.e.JIHTb tlHCJIO na flpOH3Be.L(eHHe, MO}KHO BbllIHCJlHTb I1pOH3- BC,L{eHHe H pa3,lle.JIHTb tlHCJIO Ha nOJlyqeHHblH pe3YJlbTaT. Ho rYfO}KHO IlOCTYI1HTb HHaqe: pa3.l1eJIHTb 1IHC.110 H3 O,!\HH H3 COMHO}KHTeJleH H no- JIyqeHHblH pe3YJIbTaT p33.l1.eJIHTb Ha ,lJ.pyroH COMHOiKHTeJIb. npaBHJlO 3anHCbIB3CTCH C nOfOllbId 6YKB: a : (b · c) = a : b : c -== = a : c ; b. BbInO.TJHHeTCH ynpa}KHeHHe D lleJIeHHH lIHC.na Ha npOH3Be,lI.ellHe HaH60JIcc Y,!\06HblM cnoco6orvl. YqHTeJIb nOK33blBaCT HCnOJIh30BaHHe 9Toro npaBHJIa B BblqHC.rICHH- HX, Kor,lla JJ;eJIHT1b f..fOiKHO npC,!\CTaBHTb B BH)1.e npOH3BC,lJ.eHHH. HanpHrvlep: 70 : 30 == 570 : (3. 10) = 570 : 10 : 3 = 57 : 3 = 19 420 : 14 = 420 : (7 · 2) = 420 : 7 : 2 = 60 : 2 = 30 Ha 9TOH OCHOBe yqeHHKH pClliaK>T rpynny npHMepoB H YCBaHBaIOT BblqHCJUITeJlbHbIH npHeM JJ;eJIeHHH tlHCJla Ha npoH3Be,!\eHHe. BCJIe,ll 3a 3THM <PoPMHPYeTCH HaBblK J{eJIeHHH IJHCJIa Ha KpyrJIble \lHCJIa. CHoBa paccMaTpHBalOTcH npHfepbI ,!\eJleHHB Ha Kpyr.T'fble ,!\eCHT04 KH, Ha KpyrJIbIe COTIIH. YqeHHa1 npe.ll.JIaraeTCH o6'bHCHHTb, KaK pe- IllCHbi npHMepbI: 360 : 40 ==- 360 : (4 · 10) = 360 : 10 : 4 = 36 : 4 = 9 7 200 : 900 = 7 200 : (9 · 100) = 7 200 : 100 : 9 = 72 : 9 = 8 LlaJIee ,llJIH oopa30BaHHH HaBblKa BbInOJIHHIOTCH ynpa/KUeHHH B pe- rnellHH npHMepoB BHJJ;a: 4800 : 600; 27000: 3000. 06'bHCHHH pellleHHe nepBoro npHMepa, YtleHHKH pacCY>K,AaIOT TaK: npeJJ;CTaBHM ,lleJIHTeJlb 600 B BHJ{e npoH3Be.neHHH QHCeJI 6 H 100. l{e.nHM 4 800 lIa lOOt nOJIYtl3cM 48; J{eJIHM 48 Ha 6, nOJIyqaeM 8. 4T06b1 3aKpe- nHTb 9TOT HaBbIK, nOvTJe3HO (KaK H npH YIHO}KeHuH) rpynny npHMepoB peIIlHTb ITO yqe6HHKY C 3anHCblO TOJIhKO OTBeTOB. HanpHMep, npOqH- TaB no YQe6HHKY BbIpa}KeHHe 45 000 : 9 000, YtleHHK YCTHO )(eJlHT 45 Ha 9 H 3anHCbIBaeT pesYJIbTaT: 5. 3aTeM CJJ eJty lOT y.npa>KHeHHH, Tpe6YIOInHe oc06oro BHHMaHUH: ,neJIeHHC H3 KpyrJlbIe tlHCJla C OCTaTKOM. 06hBcHeHHe )1aerCH CHaQaJI3 H3 He60vTJblliHX QHCJlaX C 3anHCblO peweHHH CT0JI6HKOM. HanpHMep: 152 30 150 - _ 5 2 o () 'b H C H e H H e. .lI.eJlHTeJIb - npoH3BeAeHHe tlHCeJI 3 HID. ,neJIHM 152 Ha 10, nOJIyqaeM 15 H 2 B OCTaTKe. l{e.nHM 15 H8 3, nOJlyqa- eM 5. YMHO>KaeM 5 Ha 30, qTo6bI Y3HaTb, KaKoe QHCJlO pa3)].eJIHJIH (150). Bbl\lHTaeM o IIHCJIO H3 AeJIHMOrO H nOJIY\laeM ocraToK 2. 261
llaJlee pelliaeTCfI pH.ll npHlepOB Ha ,ZI.eJIeHHe C OCTaTKOM npH O)t- H03HaqHOM ttaCTlIOM. BCH npeJlblJ1yruaH pa60Ta nO,l\fOTOBHJIa yqarnHXCH K C03HaTeJlbHOMY BOCnpHHTHIO aJIrOpHTMa nHCbMeHHOrO ,l\e.neHHH fHOr03HattHOrO 1JHCJ1a .Ha KpyrJIble qHCJla npH MHOr03HaQHOM qaCTHOM. CHaqaJIa paCCM8TpMBa- eTCH C nOJlPoGHblM OO'bHCHeHHeM (06pa3e o6DHcHeHHSI JlaH B yqe6HHKe) npHMep )1eJIeHHH Ha Kpyr JIbIe ,neCHTKH (27 680 : 80). nOT OM , noco/'1e peWCHHH rpynnbI npHl\fepOB J1e.neHHH H8 KpyrJIbIe ,l\eCHTKH, yqeHHKaf\f npe)1JIaraerCH paCCMOTperb H 06'bHCHHTb pellleHHe npHMepOB ,AeJIeHllH Ha KpyrJIbIe COTHH, Ha KpyrJIbIe TbICHqH. .ne.neHHe, K8K npaBHJIO, HymHo 38K8H1IHBaTb npOBepKOH. 3JleCb me HaJlO nOKa3aTb cnoco6 npOBepKH B CJIYlIae Jle.neHHH C OCTaT- KOM: YMHO>KHB qaCTHOe Ha ,AeJIHTeJIb, K nOJIYlJeHHOMY npOH3BeJ(eHHlO HY*HO npH08BHTb OCTaTOK; ecJIH npH 9TOM nOJIYIIHTCH ,neJIHMOe, TO )l.e.neHHe BbInOJlHeHO BepHO. TeOpeTHlJeCKOH OCHOBOH BblqHCJIHTe.1JbHbIX npHeMOB, YMHoHCeHMe Ha ABY- Hcno,,'1b3yeMblx npH <pOpMHpOBaHHH 9THX HaBbiKOB 3HaQHOe " TpeI3Ha- u' Hoe ,,"cno HBJIHeTCH pacnpeJ{eJlHTeJIbHOe CBOHCTBO YMHO}KeHHH, T. e. YMHO)KeHHe lJHCJJ8 Ha CYM1\IY. 31'0 CBOHCTBO SHaKOMO YtIaI.l\HMCH CO II KJI8CCa, H ero npHxoHTCH TOJIbKO nOBTopHTb B qHCJlOBOM H 6YKBeHHoM BbIpa>KeHHH nepeJl OO'bSlCHeHHeM npHeMa YM- HO>KCHHH H8 JlBY3H8 l IHoe H TpeX3HalJUOe !lHCJIO. BCH npe,!\bI,nYInaH pa- 6ma Ha)t YMHO)KeHHeM - YMHomeHHe H8 0)tH03H84Hoe 1.J:HCJIO, Ha P83- pHt{Hble e,nHHHbl (10, 100, 1000), Ha" pa3pHJlHble qHCJIa (30, 400, 6 (00)- BnonHe no,nrOTOBHJla yqarnHXCSI K C03HaTeJIbHoMY BocnpHHTHIO aJlrOpHT- Ma nHCbfeHHoro YMHomeHHH Ha l\-IHOr03HalJHOe qHCJIO, H B YCBoeHHH ero YllaInHeCH He HcnbIThIBalOT KaKHx-nH60 TpYAHocTei%. OOpa3l1-bI OO'bHCHeHHH BbI4HCJIHTeJ1bHbIX npHeMOB YMHO}KeHHH npJ{ BeJleHbI B YlIeOHHKe. OHH nOMor81OT yqeHHKaM XOpOlliO nOHSlTb, a 3a- TeM H YCBOHTb COOTBeTCTBYIOI.l\HH npHeM. YMHO>KeHHe H8 TpeX3HaQHOe qHCJIO He OJlep)KHT HHQerO npHHUH- nH8JIbHO HOBoro no cpaBHeHHIO C YMHO}KeUHeM Ha .ltBY3H8t1HOe qHCJ10: 3J:{ecb JlOoaBJIHeTCSI TOJlbKO TpeTbe HenOJIHOe npOH3BeJ1eHHe, a 3HaIlHT, TpeTbe CJIaraeMOe H BCJIe,nCTBHe 9Toro HecKOJIbKO YCJIO>KHHeTCH npouecc CJIO>KeHH. OnblT nOK33bIBaeT, lITO Tpe6YeTCSI 3HaqlireJ1bHOe KOJlHqecT- BO ynpa>KHeHHH H XOpOlll8H TpeHHpOBKa, IIT06b1.Z1.06HTbCH B JJ.8HHOM cny- qae 6e3011IHOOtIHbIX BbIqHCJIeHHrl. nOMHMO scero npoqero, ycnex ,AeJIa peIlI8er 6e3ynpeQHOe 3HaHHe T80JlH.UbI YIHO>KeIIHH H naBbIK npaBHJIbHO H 6blCTpO CKJI3JJ-bIBaTb YCTHO TPH-qeTblpe tlHCJIa B npeAeJlax ABYX-Tpex JlecHTKOB. HOBblM "PH YMH01KeHHH H8 TpeX3HaqHOe ttHCJIO S1BJIHeTCSI CJlytlaii, Kor,na B cepeJlH He MHO>KHTeJIH BCTpeqalOTCH HY JIH (308, 4 006 H T. ]J..). STar cJJYlJafi UOTpe6YeT oc06oro o6'bHcHeHHSI. BblqHCJlHTeJlbHblH npHeM D .naHHOM CJIYtIae HMeeT TY me OCHOBY - npaBHJIO YMHO>Ke- HHH tlHCJ1a H8 CYMMY, TOJlbKO B cYMMe 3)lecb 6YJ1YT OTCYTCTBOB3Tb e,llH- HHnbl KaKOro-JlH60 pa3pSlAa: JIH60 pa3pHA8 COTeH, JlH60 pa3pHJ1a Tb1CHQ. 262
HanpHMep: 746 · 303 = 746 · (300 1- 8) = 746 . 300 + 746 . 8 3.necb OTCYTCTBYIOT .neCHTKH, H n03ToMY npHXO,ltHTCH nepeXO)lHTb O'l' YMHO)KeHHH Ha CAHHHllbl cpa3Y K Yl\-IHO}KeHHIO Ha COTHH. aro HecKO.tIbKO yc.nO>KHHeT npouecc nO.llnKCblBaHHSI BToporo HenOJI- Horo npoH3Be,neHHH: ero HatlHHalOT no,nnHCblBaTb no,n COTHHMH. npH npaBHJlbHOH teTo,nHKe 9TO lie ,nOJI>KHO BeCTH K CHH>KeHHIO BbIqHCJlHTeJIb- HOR TeXHHKH. Or YllcHHKa Tpe6yeTcH TOJIbKO rJIy60Koe BHHM8HHe If Cocpe,l1OTOlleHHoCTb. 113BecTHo, tlTO YMHomeHHe Ha IIHCJIa, BblXO.llHInHe 3a npe.lleJIbI Tpex- 3HaQHblX (Ha lIeTbIpeX3HallHble,. Ha nHTH3HaqHbIe qHc.na H T. ,n.), no cy- lltecTBY He OTJIHlIaCTCSI OT YMHO}KeHHH H8 TpeX3Ha1lHOe QHCJIO. n09TOMY, OBJIa.lleB lIaBblKOM ,ne.neHHH Ha TpeX3Ha1lHOe IIHCJIO, Y1le- HHK III KJIaCCa J\OJl>KeH 6bITb y6e>K.n e H B TOM, liTO Tenepb OH YMeeT YM- HO>KHTb Ha A1060e tlUCAO. 4T06bl C03,naTb TaKoe y6e>K,neHHe, nOJIe3HO AaTb HeCKOJIbKO npHMepOB YMHomeHHH Ha QeTWpeX3HaQHoe qHCJIO H CTaBHTb Bonpoc, CKOJIbKO nOJIyqHTCH Heno.nHbIX npOH3Be,neHHH npH YMHO>KeHHI:I, HanpHMep, Ha nHTH3HaQHOe 1.IHCJIO. OCo6eHHO nOJIe311bl qeTbIpeX3HaQHbIe MHO>KHTeJIH C HYJIHMH B ce- pe,nHHe (7 003). TIpH YMHO}KeHHH Ha TaKHe IIHCJla nO.llqepKHBaerCH 3a- KOHoMepHocTb B nO.llnHCaHHH HenOJIHbIX npoH3B e .lleHHH: lIeM BbIwe pa3pH,n MHOiKHTeJIH, TeM J\3JIbIIJe npHXOJ\HTCH OTcTyn3Tb BJIeBO npH no.ll- nHCbIBaHHH nepnoH UHCPPbl Oqepe.llHoro HenOJIHOrO npOH3Be.neHHH. A..rrropHTM nHCbMeHHoro ,lle.neHHH, paccMOTpeHlIbIH AeneHM8 Ha AS'- DbillIC, KOr){a JleJIHTeeM 6bIJlH o,nH03Ha1lHoe QHCJlO, 3HI'IHOe .. 'pel3Hali. pa3pHJlHbIe eJlHHHUbI, pa3pHJJ.HbIe IIHCJIa, B OCHOB- Hoe lI..cno HOM COXpaHHeTCH H npH ,ne.neHHH Ha .nBY3HaQHoe H TpeX3Ha1lHoe 1.IHCJlO. Ho B nOCJIe.llHHX CJIY1I3HX cno- COO nHCbMeHHOrO ,lleJIeHHH HMeeT JlBe cymeCTBeHHbIe oco6eHHOCTH. nepBaSI R3 HHX 3aKJH01laeTCH B TOM, \ITO npH eJIeHHH Ha .llBY3HaIlHoe H TpeX3Ha1lHOe IIHCJIO, IIT06bI HaHTH UHcJ>py lIaCTHOro, Mbl ,naHHbIH .lleJIH- TeJIb H3MeHHeM, 3aMeHHH ero 6JJH>KaHllIHM (06bIQHO MeHbWHM) KpyrJlblM HCJIOM, H TaKHf 06pa30M CBO,nHM .lleJIeHHe H3 .llBY3HatlHblH J(eJIHTeJIb (HanpHMep, Ha 54. 82) K .n-eJIeHHIO Ha KpyrJIbIe ,necHTKH (Ha 50, Ha 80), ,neneHHe Ha TpeX3HatIHbIH ,neJIHTeJIb (HanpHMep, Ha 456, Ha 728) K ){eJIe- HHIO Ha KpyrJlble COTHH (Ha 400, Ha 700). TaKaR BpeMeHHaH 3aMeHa .naHHoro J(eJIHTeJIH KpyrJIblM QHCJIOf .llJIH Hac Bblro,nHa: OHa o6JIer1laer nponecc HaXO:>K,lleHHH D-H4>pbI tlaCTHOro, TaK K3K J(eJIeHHe Ha Kpyr- JIble qHCJla, KaK MbI BH){eJIH, COBepmaeTCH no onpeJleJICHHOMY npaBHJIY. Ho H3MeHeHHe ,lleJIHTeJIH (3aMeHa ero ,nPyrHM qHCJIOM, 6JIH>KaHWHM Kpyr JlbIM qHCJIOM) Be,lteT K TOMY, qTO nOJlYlIeHHaH npH ,lJ.eJIeHHH Ha Kpyr- J10e qHCJlO D-H<ppa QaCTHOro He 6y,neT OKOHtlaTeJlbHOA; H3MeHeHHe .lI.eJlH- TeJUI MO>KeT' H3MeHHTb H qaCTHOe; 9Ta D-H<j>pa HY>KnaercSI B npOBepKe, B HcnblT8HHH. 3a HeR B IeToJJ..HKe 3aKpenH.nocb n33BaHHe np06Hoii. D-H<j>pbl. B 3TO 3aKJIIOQaeTCH BTopaH cyecTBeHHaH oc06eHHocTb Jl.e- ... 263
'nCHHH Ha BY3HaHOe H TpeX3HaHOe qHCnO. Bo BCeX p8Hee paCCMOT- peHHbIX CJJY1J8HX ,lI.eJleHHH MbI eJlHTeJIb He H3MeHSlJIH, a n03TOMY cpa3Y nOJIytlaJIaCb Bep Hafl lI.H<ppa aCTHoro. npH JleJIeHHH Ha BY3HatlH H TpeX3HatlHOe 1JHCJIO Mbl H3MeHHeM -neJIHTeJ1b, 3aMeHHH ero Kpyr.'1bIM HCJIOM, H BCJIe,lI.CTBHe 9Toro nOJJyqaCM np06HYIO l\HCPPY qaCTHOro, H}'>K.A8 I0 11.1YlOCSI B npOBepKe. 3TH oc06eH- UOCTH aHHoro cJIyqaSl ,l{eJIeHHH OJI>KHhI 6bITb Jloae.neHbI ,LtO C03HaHHR Y1JeHHKa, H 9TO ,lteJIaercSi B npol.lecce oO'bSlCHeHHH nepBoro npHMepa; T8KHM. npHMepoM MO>KeT 6bITb ,lI.eJIenHe 488 Ha 61. npH 060HCHCHHH 9To- fO npHMepa CHaaJIa BMHCHHeTCH, KaK o6pa30BaTb nepB HenOJIHOe ,lleJIHMoe. 3,ltecb Bce tlHCtI'IO (488) npHxO,l{HTCH JleJIHTh Ha 61. .l1aJIee yqH- TeJJb Coo6UlaeT: «4T06bl nO.ll.06paTb lI.HCPPY tlaCTHOro, 3aMeHHM JteJIH- TeJlb 6JIH>KaHIIIHM Kpyr JIblM tlHCJlOM (60) H 6YJle}..f ,AeJIHTb TaK >Ke, KaK JteJIHJlH Ha KpyrJIbIeCflTKH: pa3){e.,TJHM 488 Ha 10, nOJIY1JHM 48; Te- nepb p83,lteJIHM 48 Ha 6, nOJIYtlHM 8». VI TYT )Ke npH6aB.'1HeT: «H<ppa 8 He OKoHttaTeJIbHaSl, a rrp06HaH, nOTOl\iY '1TO Tpe60BaJlocb pa3,LteJJHTb QHCJ10 Ha 61, a He Ha 60. 9Ty UH<PPY HanO npOBepHTb: y,.fHOiKHTb 61 Ita 8, nOJlYtlHTCH 488. 3HatlHT, IJ.H<ppa 8 Beplla». B 3TOM npHMepe 3aMeHa Jl-eJIHTeJIH KpyrJlblM ttHCJIO1 AJIH ,neTcfr y6e,l1.HTe.fJbHa (60 OqelIb 6J1H3KO K 61); npo6HblH /Ke xapaKTcp II.H<PPLI He OtleHb y6eJl-HTeJIeH, TaK KaK nepnaH >Ke II.H<ppa OKa38J1aCb BepHOH. Ho YLKe tlepe3 Ba-TpH ypOKa yttaHeCH BCTpeTflTCH C TaKHMH CJlYtlaH- MH ,Ae.neHHH, KOr,lI.a npo6HYlO l\H<Ppy tlaCTHOro npH){eTCH npOBepHTb t H He O,AHH pa3. Dpo6HaH l.lH<fJpa npOBCpHeTCH YCTHO - B 3TOM OCHOBH8H Tpy,ltHOCTb Ae.neHHH. Ytl8UlHMCH HY/KHO nOKa3aTb, '1TO npH JleJIeHHH Ha JlBY3HaQ- Hoe ttHC..TJO HeT Hao6HOCTH YMHO>KaTb JlBY3HatlHoe 1JHCJIO Ha ,neJIHTeJIb, a npH ,lteJIeHHH Ha TpeX3HattHOe qHCJIO - YMHO}l{aTb Ha ,LteJlHTeJIb TpeX- 3l1a1JIIOe HC.'10. L{ocTaTOtlHO YMHO>K3Tb KpyrJIbIe ,lteCflTKH H KpyrJIble COTHH. Ha,lI.o 3TO 06DHCHHTb, a nOCJIe 06DHCHeHHH JlaTh OCTaT01JHOe }{OJJHtleCTBO ynpa}KHeHHlf, ttT06bI C<pOpMHpOBaTb H8BbiK TaKOH npo- Bep KH . KaK H B npe.>KHHX TeMax, cpOpMHpOBaHHe DbltlHlITeJ1bHhJX H3BbT- KOB conpOBO>KA8eTCfl 06YQeHHeM ,n.eTeH peweHHIO 3a,ltaQ, B KOTOpbIX 3TH HaBblKH HaxO,ltHT CBoe npaKTHtlecKoe npHMeHeHHe. nO-npe1KHeMY y,lteJlfleTCH BHHMaHHe BbIpa60TKe Y ,lI.eTeH YMeHHSI npaBHJlbHO HCnOJ1b- 30BaTb YMHO.>KeHHe H ,lteJIe'HHe B pa3J1HQHblX CJlY1JaHX - B 3a,nallaX c pa3JIHtlHbIM faTeM8THqeCKHM co,nepiKaHHeM. B 9TOT nepHO,lt npoo.rl- 1KaeTCH paOOTa no H3yqeHHIO nponOpnHOHaJlbHOH saBHCHMOCTH Me.>KY BeJJHqHHaMH: HMeHHO B 9TO BpeMH npOCJIe>KHBaeTCSI 3aBHCHMOCTb Me>K- AY CKOpOCTblO t BpeMeHeM ,LtBH>KeHHH H paCCTOHHHeM, npOCJIe1KHBaeTCSI H3MeHeHHe o,nnOH BeJIHtIHHbI B 38BHCHMOCTH or ,npyroH H pewalOTCfl .OOTBeTCTBYIOHe 3aAaqH.
. H3MeHeHH8 peSYBbT8TOB AelcTIHA 8 S8BHCHMOCTH OT HSMeHeHHA OAHoro.. M3 KOMnOHeHTOB ..B H3YQelIHH H3felIellHH peay.nbTaToB apH£lJMeTHlIeCKHX .AeHcTBHH B 3aBHCHMOCTH OT H3MeHeHHH o,nHoro H3 KOMnOHeHTOB npe,nycMaTpHBaIOT- CH ,nBa 3Tana. Ha nepBoM H3 HHX (I H I I 1accbI) B pe3YJIbTaTe BblnO.I1HeHHSI cne- I1HaJIbllblX ynpa>KHeHH" Yllau.{HecH OJIiKHhl YCBOHTb xapaxmep H3MC.. neHHH pe3Y.TIbTaTO ,neHCTBHH B 3aBHCHMOCTH OT H3MeHeHHH o,nHoro H3 KOMnOHeHTon 3THX ,neHcTBHH (HanpHMep, eCJ1H O,nHO H3 C.,1araeMbiX YBeJIHqHTb, a pyroe OCTaBHTb 6e3 H3MeHeHHH, TO CYMfa YBC.fJHIIHTCH'. Ha BTOpOM 3Tane (III K.,'1acc) ,l{eTH YCBaHBalOT KO/lU'leCfrl8eHftble 83- v u MeHeHHH pe3YJIbTaTa ,neHCTBHH B 3aBHCHMQCTH OT H3MelleHHH o,nHorO"3 KOMnOHeHTOB, T. e., BbInOJIHHH HatJJlIO.zteIlHH, OHH YCTaHaBJIHBaIOT, "3 CKOJlbKO e,ll.HHHlt HJIH BO CKO.,'bKO pa3 YBe..TJHIIHBaeTCH HJ1H YMeHbUlaeTCH pe3YJIbTaT B 3aBHCHMOCTH OT YBeJIHlIeHHH H.TIH YMeHbllIellHH COOTBeTCT- BYIDHM 06pa30M O,llHoro H3 KOMnOHeHTOB. B MeTO,ll.HKe pa60TbI HaA YCBoeHHeM YllaInHMHCH Ko.rIHqeCTBeHHblX H3MeHeHHH pe3YJlbTaTa AJISI Ka}K){Oro H3 3pH£lJMeTH 1 1ecKHX eHCTBH H BbJ.zteJIHIOTCH ,nBe CTyneliH. Ha nepBOH cTyneHH YQ3Il(JieCH Ha6/1lOaalom qaCTHble <l>aKTbI H3MeHeHHH pe3YJlbTaTOB eHCTBHH B 3aBHCHMOCTH OT H3MeHeHlIH O.l1Horo H3 KOMnOHeHTOB, npHXO.l1HT K COOTBeTCTBYIOInHM 0606eHHHl\.1 H cpOPMY.TlliPYlOT BbIBO,nbI. Ha BTOpOH cTyneHH npOHCXO,l1HT 08/laOeHue 3H3HHHMH 06 H3MeHeHHH pe3YJlbTaTa Toro HJIH HlIoro apH<I>- J..feTH1.IeCKOrO ,neHcTBHH B 3aBHCHIOCTH OT H3MeHeHHH OJ{Horo fl3 ero KOM- nOHeHTOB B npou.ecce npUMeHeHUJl 3THX 3H3HHH. PaccMOTpHM no..npo6Hee MeTOJI.HKY H3Y1leHHH 3TO:H: TeMbI B I I I KJI3Cce. nepeXO,lJ.H K paCKpbITHIO KOJIHtleCTBeHHhIX H3MeHeHHH pe3YJlbTaTOB apHMeTHecKHx ,neHcTBHH B 3aBHCHMOCTH OT H3MeHeHlIH OHoro H3 KOMnOlIeHTOB, CJ1e.nYeT nOBTOpHl'b BbIBO,nbI 0 xapaKTepe H3teHeHHH pe- ... 3YJIbTaTOB apH<pMcTHlIecKHx ..neHcTBHH. C 3TOli ueJIblO npe,n.naraIDTcH TaKHe }l{e ynpalKHeHHH, KaK H BO I I K.JIaCce. 1) He BblllHC.7JHH, nOCTaBbTe BMeCTO 3De3)1.0QKH gHaK > H,,TIll <; 760 -t- 80 * 750 - 80 2) 3aKOHQHTe 3anHCb: 140 + 290 > 140 1- 3) nO,ntSepHTe lIcTbIpe 3Ha l leHHSI OYKBbI C TaK, tlTOObl CYMMa 32 + c YBeJlHQHBaJlacb. H me ynpaLKHeHHH CJIeJlyeT Hcno.nb30BaTb B KalleCTBe 1.IaCTHblX aKToB ,lJ.JUI npOCJIe>KHBaHHH KOJIHtlecTBeHHblX H3MeHeHHH pe3YJIbTaTOB apHcpMeTH'IeCKHX AeHcTBHH B 3aBHCHMOCTH OT HSMeHeHHH OAHoro H3 KOMnOHeHTOB. 265
HanpHMep. yqalll.HeCH CpaBHHJlH Bblpa>KeHHSI H nOCTaBHJlH COOTBe'f- CTBYIOInHH 3HaK: 760 + 80 > 750 + 80 - nOtleIY nOCTaBHtI'IH 3H3K «60JlbUle»? (3eCb BTOpble C,,1araeMbIe O,lUIHaKOBble, a nepBoe CJIaraeMOe B nepBOM BbIpa}KHHH 60.Hbllle, lIeM BO BTOpOM, 3HaQHT, H CYMMa 6y.neT 6oJIbUJe.) - Y 3HaHTe. Ha CKO..'IbKO eJ).HHHIl nepBaH CYMMa 60lIbllJe, qeM BTO- paSl. (Ha 10.) - Ha CKOJIbKO eJ{HHHlJ. nepBoe CJIaraeMOe nepBoH CYMl\lbI 60JIbllle nepBoro CJIaraetoro BTOpOH CYMMbl? (Ha 10.) - !la, nepBoe CJlaraeMOe nepBoH CYMMbI Ha 10 OOJl, bIlle qeM nep- Boe CJIaraeMOe BTOpOH CYMMbI, 1'1 caMa cYMMa Ha 10 eJlHHIfD- 60Jlbllle. nocne pH.Aa nO,llo6HbIX Ha6J1IO.lI.eHHH cJIeJ{YeT nO,llBCCTH .!teTeH I{ oooome- HHIO 3HaHH" 06 H3MeHeHHH pe3YJlbTaToB apH<pMeTHtleCKHX ,lteHcTBHH B 3aBHCHMOCTH OT H3MeHeHHH OJ{Horo 1'13 KOMnOHeHTOB. C 3TOH IJ.eJibIO oprallH3YeTCSI Ha6J11O){eH1-Ie erne pSI):{a qaCTHbIX <t>aKTOB, B pe3Y JIbTaTe qero J(eTH cpOPMYJlHPYIOT BbIBObl. HanpHMep, Y1Ialll.HMCH npeJ{JlaraeTCH HaHTH 3HalleHHH Bblpa>KeIlHH. Ha J{OKe II B TeTpa,lIJIX nOJIyqaeTCH 3anHCb: 56 + 20 = 76 30 + 27 = 57 148 + 10 = 58 40 + 23 = 63 60 + 20 = 80 30 + 37 = 67 42 + 10 = 52 40 --r 18 58 68 + 20 = 88 30 + 42 = 72 34 + 10 = 44 40 + 11 = 51 - CpaBHHTe npH{epbl nepBoro cToJI6HKa 1'1 CKa>KHTe, KaK H3MC- ,. HHJlH nepBoe C,,'1araeMoe. (YBeJIH1JRD8JIH.) - LITO MO/KHO CKa3aTb 0 BTOpOM c.naraeMOM? (OHO He M3MeHHeTCH.) - KaK H3MeHHeTCSI CYMMa? (YBeJIHtlHBaeTCSI.) - CpaBHHTe, Ha CKOJIbI<O eJ{HHHII. 60.nbllIe nepnoe CJIaraeMOe BTOpOH CYMMbl, qeM nepBOH. (Ha 4 e,llHHHlJ.bI.) - CpaBHHTe BTOpylO CYMMY C nepBoH. (OHa 6o.nbllIeTO)Ke Ha 4 e,zUI- HHUbl.) .. - CpaBHHTe TaK >Ke TpeTHH npHMep co BTOpbIM. (IlepBoe CJIarae- "Ioe YBeJIHtlHJlH Ha 8 e,ltHHHIJ., BTopoe - He H3MeHHJIH, CYMMa YBeJIHllH- naCb Ha 8 e,llHHHlI..) I TSK me cpaBHHBaeTC5I TpeTHH npHMep c nepBbIM. - KaKoH BbIBOJ{ MO>KHO c,lleJIaTb? (ECJIH nepBoe CJIaraeMOe YBeJIH- qHTb Ha HeCKOJlbKO e):(HIIHIJ., a BTopoe OCTaBHTh t>e3 H3f\ieHeHHH, TO CYMM8 y.aeJIHQHTCSI Ha CTOJlbKO >K e,ltHHHU). AHaJIOrHtIHbIM oopa30M BeeTCSI Ha6JIIO,lteHHe 3a H3MeHeHHeM CY1- MbI B a8BHCHMOCTH OT YB'HQeHHSI BToporo CJlaraeMOro (BTOpOH CTOJI 6HK npHMepOB). nOCJIe 3Toro cl>OPMYJlHpyeTcSI OOOOlI\eHHbIH BbIBOJ{: eCAU oiJHO U3 CAa2lleMblX yseAU"lUmb Ha HeCKOAbKlJ eaUHUt{, a apyzoe ocmasumb 6e3 U3MeHeHUJl, mo cgA-tMa Y6e/lU'lUlnCfl Ha CtnO/lb1(,() OICe eaUHUl{. HaonlO.naH 3a H3MeHeHHeM CYMMbI B TpeTbeM It tleTBepTOM CTOJIOH- K8X npHMepOB, ,l{eTH YCTaHaBJIHB81OT, lITO ecJIH OHO H3 CJIaraeMbIX YMeHbWHTb H8 HeCKOJIbKO eJ{HHHlJ., a Apyroe OCTaBHTb 6e3 H3MeHeHHH, TO CYMMa YMeHbWHTCH Ha CTOJIbKO me e,lI.HHHI.{. · 266
Ha)I.o HMeTb B BH.llY, liTO He Bce AeTH O,l{HOBpeMeHHO npUXO)l.HT K 0600IUeHH,IO. n09TOMY OlleHb Ba}KHO TaK opraHli30BaTb 06YQeHHe, 1IT06b1 Te yqeHHKH, KOTopbIe OOOOIUHJ1H c1JopMHpyeMble 3HaHHSI, CMOrJIH npHl\ieHHTb UK, a Te ,neTH, KOTopbIe He npHWJIH K 0606meHHIO, HMeJlH 6hI B03MO>KHOCTb rrpoHa6JIIO)l.aTb ee pfI)I. qaCTHbIX cpaKTOB H rrOCTeneH- HO rro.noHTH K o606rneHHIO. C 3TOH. UeJIblO CJIe..nyeT npe,Zl,JIaraTb TaKHe 3a.llaHHH, KOTopbIe MorYT 6bITb BbInOJIHeHbI BceMH JJ.eTbMH, HO Ha OCllo- Be pa3HbIX 3HaHHH: Te H3 ,neTeH, KOTopbIe Y:>Ke 0606H.TJH 3HaHHH 06 H3leHeHHH pe3YJIbTaTOB ,neHcTBHH B 3aBHCHMOCTH OT H3MeHeHHH OJ{HD- fO H3 KOMnOHeHTOB, 6y..nYT rrOJIb30BaTbCH 9THfH 3HaHHHIH, OCTaJIbHble me ,neTH BOrrOJlb3YlOTCH .npyrHMH 3HaHHHnl. TIpH 9TOf O)[.HH yqeHHKn, BbInOJIHH 06'bHCHeHHe BCJIYX, 6Y)l.YT nOMoraTb ,npyrHM obIcTpee npHH- TH K oOoOIII.eHHHl\.f. n9Kame:\-1 9TO H'a npHMepe. YqHTeJib npe.n..naraeT cpaBHHTb DbIpa}KeHHSI H Y3HaTb, Ha CKOJIbKO enHHu. rrepBaH cYMMa 60JIbIlle HJIH MeHbllIe, qeM BTopaH: 450 + 87 " 430 + 87. O,l(HII yqellHKH, erne He YCBOHBlliHe, KaK H3l\feHfIeTCH CYMMa B 3aBHCHMOCTH OT H3MeHeHHSI O.llHoro H3 enaraeMbIX, BbllIHCJUIT pe3YJIb- TaTbI H cpaBHHT HX: 537 - 517 = 20. Te H3 ,neTeii, KOTopble YCBOUJIH cooTBeTcTBYlOrnee npaBHJIO, BbInOJIHHT 3a,l{aHHe, nOJIb3YHCb HM: BTopbIe C.HaraeMble 3THX CYMM o,nHHaKOBbIe, a npBoe CJIaraeMoe nepBoH CYMMbI Ha 20 e.nHHHII. 60JIbllIC t qeM nepBoe CJlaraeMOe BTOpoii CYMl\fbI, 3HaqHT, ncpBaH cYMl\fa Ha 20 e.llHHHU 00",1 b llie, lIel\f BTopaH. npH TaKOH cHTyallHH yqeHHKH, KOTopbIe erne He 0606w.HJIH 3HaHHH 06 H3!'.ICHeHHH pe3YJIbTaTOB, HMelOT B0310JKHOCTb npOHaOJHOJ1aTb tJaCT- Hble <l>aKTbl (B AaHHOM c.nyqae - CJIaraeMOe 60JIbitIc Ha 20 eJJ.HHHU II CYMMa OO.'1bI1Ie Ha 20 eJJ.HHUIt npH o.nHHaKOBO?d JJ.pyroM CJIaraeMOf\i), a paccY>K.neHHe, BbInOJIHHeMOe BCJIYX ;teTbMH, YCBOHBllIHMH «popMHpye- Moe 3HaHHe, n01\OlKeT BceM yqeHHKaM npunTH K o606rneHulO. Ha 3TOH npOMe>KYToIIHOH cryneuH MO}l{HO npe){JlaraTb H APyrHe ynpa>KHeHHSI : 1) pewHTe rrpHMepbI CaMbIl'rf Y,lI.06HbIM cnoco601: 456 + 298 500 + 197 456 + 300 496 + 197 2) CocTaBbTe 'IeTbIpe npHMepa Ha CJIO}KeHHe TaK, tIT06bI cYMMa B03pacraJIa Ha 25. 3) rIoJJ.6epHTe 3HaqeHHH 6YKB a H b TaK, 1ffOObl cYMfvla YBeJIHQHBa- JIaCb Ha 8. a b a+ b 267
XapaKTepH3H OCo6cHHOCTb ynpa>KHeHHH, npe,l{JlaraeMblX B 3TOT nepHO))., COCTOHT B TOM, tlTO npH HX BbInOJIHeUHH yqaWHCCH MOryT HCnOnb30BaTb 3HaHHH 06 H3MeHeHHH pe3ynbT8ToB eHCTBHH B 3aBHCH- MOCTH OT H3MeHeUHSI O)).HOrO H3 KOMnOHeHTOB H.nH MOrYT BblnOJlHHTb UX, OCHOBWBaSlCb Ha BqHCeHHHX. llanee, Ha CJIe)).YIOIIleH cTyneHH, KaK TOJIbKO BCe YtiaInHeCSI npH.AYT K 0606IIleHHIO, npe,lJ.JlaralOTCH ynpaLKHeHHH, BbInOJlHeHHe KOTOpblX Tpe- 6yeT npHMeHeHHH 3HaHHH 06 H3MeHeHHH pe3ynbTarOB neHcTBHH. PacCMOTpHl\f HaH60Jlee THnHtlHbJe H3 HHX. 1. KaK H3MeHHTCH cYMMa,-eCJIH nepBoe' CJlaraeMOe OCTaBHTb OC3 H3MeHeHHH, a BTopoe YMeHbIIIHTb Ha 29 e.ltHHHU? . YqarnHeCH CCblJIalOTCH Ha H3BeCTHoe HM npaBHJlo: cYMMa YMeHbIIIHT- CH Ha 29 e)J.HHHl.{, nOToMY qTO eCJIH O)).HO CJIaraeMOe YMeHbllIHTb Ha HeCKO.nbKO e.llHHHl.{, 3 JlPyroe OCT8BHTb 6e3 H3MeHCHI1H, TO CYl\IM8 YMeHblllHTCH Ha CTOJIbKO me eAHHHU. 2. CYMMa YBeJIHQH.nacb na 45 eAHHHI.{, TaK KaK H3MeHHJIH O)).HO H3 CJIaraeMbIX. KaK ero H3MeHHnH? OO'bHCHeilHe aHa.TfOrHqHO npe)).bI){Yll(eMY. 3. PelllHTe 3a)).aQH naHOO.7lee y.lt06Hbll\t cnocooo1. a) B O,llHOM lllKacpy CTOHJIO 225 KIIHr, B JtpyroM 275 KHHr. CKOJlhKO KHHr 6bl.TJO B .ltBYx lllKacpax? 6) B nepBblH IIIKacp .lto6aBHJIH 18 KHHr. CKOJlbKO KHHr CTaTJO B ABYX wKa<l>ax? - PelllHTe nepBYIO 3a.ltaQY. (225 + 275 = 500.) - KaKoe BblpameHHe BbI nOJlyqHnH? (CYMMa qHCe.n 225 R 275.) - npOqHTaHTe BTOpylO. 3a.llalJY H no,nYMaHTe, KaK 1t10iKHO peIIIHTb ee, nOJIb3YSlCb perneHHeM nepBoH 3a.ltaqH. (MomHo K 500 npH6aBHTb 18, no.rryqHTCSI 518, nOTOiY qTO 3)).eCb nepBoe CJlaraeMOe YBe.I1HqHJIH Ha 18, 3HaQHT, CYLVIMa YBe,,TIHqHTCSI Tome Ha 18.) 4. CYIMa ABYX QHCeJI paBHa 870. tIeMY 6Y.AeT panHa HOBaH cYMMa, ecH nepBoe C.7IaraMOe YBeJIHtlHTb Ha 30 e)).HIUII1, 8 BTopoe OCTaBHTb 6e3 H3MeneHHH? . . o 6 'b SI C H e H H e. 0603 HatlHl\f cnaraeMbIe 6YK8a'IH, HanpHMep 6YKBaMH a H b. TorA8 MO>KHO 3anHcaTb: a + b = 870 (a + 30) + b = nepBoe CJIaraeMOe YBeJIRqH.7IH Ha 30 e,llHHHlI., 3HatlHT t H CYMfa YBeJIHqHTCH Ha 30 eHHHI.{: (a + 30) + b = 870 + 30 = 900. 5. J1cnoJlb3YH B Ka>K.ltoH nape paBeHcTBo, BblqHCJIHTe 3HaIJeHHe sanHcaHHoro no)). HHM Bblp81KeHHSI: 576 + 89 = 665 (576 + 20) + 89 c + d = 100 c + (d - 8) YqarnHeCH .ltOJl>KHbl cpaBHHTb Bblpa>KeHHSI H 3aMeTHTb, qTO B nep- BOM cnytlae O,l1HO cnaraeMoe YBeJIHqHJIH Ha 20, a BTopoe OCTaBHH oe3 H3MeHeHHH, 3HaQHT. cYMMa YBeJlHtlHTCH Ha 20. lIT06b1 BbltlHCnHTb CYM- 268
MY, Ha,nO K 665 npuoaBHTb 20. Bo BTOpOM cJlyqae nepBoe CJIaraeMoe OCT8BH.tlH ()e3 H3MeHeHHSI, a BTopoe YMeHbIIIHJIIi Ha 8, 3HatlHT, CYMMa YMeHbIIIHTcSI Ha 8. 1.ITOObI ee HaHTu, Ha,no H3 700 BbIqecTb 8. 6. CYMMY lIUCM 340 H 80 YBeJIHlIHTb Ha 60. PemeUHe MO)KHO BbInOJ1HHTb TpeMSI cnoc06aMH: a) (340 + 80) + 60 = 420 + 60 = 480. CYMMY YBeJIH'lHJIH Ha 60. 6) (340 + 80) + 60 = (340 + 60) + 80 -== 400 + 80 480. YBeJlHlIHJIH Ha 60 nepBoe CJ1araeMoe. B) (340 80) + 60 = 340 + (80 + 60) = 340 + 140 == 480. YBeJ1HlIHJ1H Ha 60 BTOpoe CJIaraeMoe. OqeHb Ba)KHO YCTaHoBHTb, qTO 9TH TPH cnoco()a Y>Ke H3BeCTHbl Jl.e- TflM, T. e. qTO 3TO H eCTb npaBHJla npHOaBJIeHHH qHC.na K CYMle. AHa.,1JOrHlIlIO paCCMaTpHBaeTCSI YMeHbUJeHHe CYl'tIMbl Ha lIHCJ10. 7. 3aKOHQHTe 3anHCb: 130 + 27 == 130 + 50 ... o 6 D Sf C H e H H e. CYMla B npaBoH llaCTli paBeHcTBa Ha 23 6o.nb- me, qeM B JIeBoii, nOTOMY liTO nepBbIe CJIaraeMbIe O,l{HHaKOBbIe, 3 BTopoe CJlaraeMOe BTOpOH CYMMbI Ha 23 OOJIbllIe. l.IT06bI cnpaBa no.nYlIHJ1OCb CTOJJbKO me, CKO.'1bKO CJ1eBa, HaAo crrpaBa DbIqecTb lIHc..'10 23. nOJIYQHM: 130 + 27 = 130 + 50 - 23. 8. nO)loepHTe H 33nUllIHTe B TaOJIHue 4 3HaqeHHSI 6YKBbi k TaK, tITo- ()bI cYMMa 35 -r k YBC.rJH t IHBaol1aCb Ha 15. I k 35 + k CHaqaJIa na,LlG YCTanoBHTb, KaJ(Ue 3HaqeHHH MO>KeT npHHHM3Tb 6YKB3 (k = 0 HJIll k > 0). B .naHHOf c.TJytlae nepBbI fO}KHO B3HTb JIlo60C qHC.nO, HanpHfcp 40, a Kam)lOe coI1e.nYIOw.ee opaTb Ha 15 e,LlHHHL{ (jOT}bWe (55, 70, 85). . nO,ltOouble ynpaJKHeHHH IOJKHO 3a.naBaTb H oe3 Ta6JIllI.I.bI: «TIO.lt- oepHTe 3 3HaqeHHH 6YKBbI C TaK, tJTOObl cyn\"a c -- 28 yrvleHblllaJIaCb Ha 9». 9. 31IaHHe H3MenellHSI pe3y..TIbTaTOB .neHcTBHH B 3aBHCHMOCTH OT H3- MeHeHHH O,LlHoro H3 KOfnOHeHTOB HCnOJIb3yeTcSI JV1H oOOCHOBaHHSI HO- BbIX BbIqHCJIHTe.J1bHbIX rrpHel\10B. TaK, onHpaSlCb Ha 3TH 3HaHHSI, 880- .llHTCH npHeM oKpyrJIeHHSI npH c.'10LKeHHH H Bbl 1 1HTaHHH H npHeM YMHomc- HHSI Ha 5, 25, 50 H Kpyr..'1ble qHCJIa. HanpHMep, Ha)lO BhIqHCJIHTb CYM- MY qHCM 85 H 68. KaK H3BeCTHO, JlefKO npH()aBJ1HTb KpyrJIble tlHCJIa, n09TOfY 3aMeHHM tJHCJIO 68 KpyrJlbIM tJHCJIOM - 70, T. e. YBeJIHqHM QUCJIO 68 lIa 2 e.llHHHI.I.bl H npH6aBHM 70 K qHCJIY 85, rrO.,'1YtJHTCSI 155. TaK KaK CJIaraeMoe YBeJlHqHJlH Ha 2 e.llHHHUbJ,TO' H cY1.IMa YBeJIHqHJ18Cb H3 2 e,llHHHUbI. 4T06bI nOJIyqHTb CYMMY qucen 85 H 68, H3AOH3 155 Bbl- qeCTb 2 eAHHHUhI, nOJ1ytJHTCH 153. .9
B TaKOM }Ke n.naHe BeeTCSl pacct>K,neHHe H npH oKpyrJIeHHH nep- Boro CJlaraeMOro, YMeHbWae1.fOrO HJIH BbltlHTaeMoro. lLnH paCKpbITHSJ npHeMOB YMHO}KeHHH H JleJIeHHH Ha 5, 25, 50 H Ha KpyrJIWe tlHCa Hcnonb3YKITCH 3HaHHH 06 H3MeHeHHH npoH3BeeHHH H qaCTHOro H 3aBHCHMOCTH OT'H3MeHeHHH OHoro H3 KOMnOHeHTOB. Iia- npHMep: Hao 84 YMHO>KHTb Ha 5. YBeJIHtlHM MHO}l{HTeJlb B 2 pa3a, rof.lla llaJto 6Y.llCT YMHO>KaTb Ha 10, tlTO JlerKO CAeJl8Tb: 84 · 10 = 840. raK KaK MHOJKHTe.'1b YBeJlHtJHJIH B 2 pa3a, TO H npOH3Be.lleHHe nOJIYQH- JlOCb B 2 pa3a 60.rlbIlle, qeM npoH3Be.neuHe qHCM 84 H 5. 3HatJHT, 'ITO- 6b1 nOJIYtJHTb HCKOMoe npOH3Be.lleHHe, Ha,ltO 840 YMeHbllIHTb B 2 pa3a, no.nYtJHTcH 420. OrclO.na BblTeKaeT npHeM YMHO>KeHHH Ha 5: qTOObl YMHO>KHTb tJHcno Ha .5, MomHO Yl\1HO}KHTb ero H 10 H nonytJeHHbIH pe3)'JIbTaT pa3.l1.eJlHTb H8 2. -TaK me 060CHoBbIBalOTcH H JJ.pyrHe npHeMbl YMHO>KeHHSI H J1eJ1eHHSI. . 10. 3HaHHe H3MeHeHHH pe3YJlbTaTOB apH<I>MeTHtJecKHx ,neHcTBHH B 38BHCHMOCTH OT H3MeHeHHH OHoro H3 KOMnOHeHTOB MO}KHO HCnOJIb30" B3Th AJIH OoocHoBaHHSI BbIBO,nOB 0 npHMo Ii o6paTHo nponopnHoHanb- HOM 3aBHCHMOCTH BlHtJHH. HanpHMep, 3HaSl, tJTO CTOHMOCTb eCTb npo- H3BeeHHe ueHW TOBapa Hero KOJIHtJecrBa, yqll{HeCSI JIerKO cenaWT OOoGw.eHHe: eCJIH KOJIHtJecTBO KynJIeHHOrO TOBapa (COMHO}l{HTeJlb) YBe- nHtIUTb H,rIH YMeHblllHTb B HeCKOJIbKO pa3, TO CTOHMOCTb (npOH3Be,AeHHe) YBe,,1HtlHTCH HJIH YMeHbllIHTCH BO CTOJIbKO >Ke pa3 npH OHHaKOBOH ne- He ( COM HO>KHTeJI b ) 1. 3,ltecb nO.llp06HO pacKpbITa MeTO,AHK8 pa60TbI no $opMHpoBaHHIO Y TpeTbeKJIaCCHHKoB SHaHH" 06 H3MeHeHHH CYMMbI B 3aBHCHMOCTH OT H3MeHeHHSI O.llHoro M3 cnaraeMWX. HsyqeHHe HSMeHeHHH peYJIbTaTOB JlpyrHx apH<pMeTlltJecKHx ,lJ.eHcTBHA CTpOHTCSl COBepweHHO aHaJIOrHtJHO. CHCrMa H MIJOAY H.''I8HHA 811eMeHTOB anre6pw B I " 11\ KJIaCCaX BeJIaCb paooTa no cpOplIipOBaHHIO y yqaIIHXCSI npeJ(cTaBJIeHHH 0 paBeHCTBe, HepaBeHCTBe, <PYHKUHOHaJIbHOH 3aBHCH- MOCTII, a Tal{>Ke <pOpMHpoBanHcb YMeHHH onepHpOBaTb 6YKBeHIIoH CJiMBOJlHKOiL B I I I KJlaCCe Bce 9TH BonpOCbI nOJIytJalOT aJIbHeHlllee pJ3BHTHe, H, KpOfe TOfO, S,l{eCb paCClaTpHBaIOTCH HOBbIe: pemeHHe C nOMOInblO ypaBHeHHH COCT8BHblX 3a){atJ H paCKpblTHe Ha KOHKPCT- HblX npHMepax npSlMO II ot5paTHo nponopUHOH8J1bHOH 3aBHCIIMOCTM DenHtIHH. PacKpoeM CHCTeMY H MeTO,l{bl" H3yqeHIIH Ka1KJ}.oro 113 Ha3BaH- HbIX BonpOCOB. 1 CM. nOAP06Hee B naparpa4Je o() HsyqeHHH npSlMO H 06paTHO nponopLlKOH8J1blIoA: saBHCHMOCTH BeJJHqHII. 210
PaieHCTsa.. Hep.. B pa60Te H3,A paBeHCTBafH H H"epaBeHCTBaMH npe- seHCT.. ,AYCMaTpHB3eTCSI nO)ij3eCTH YtlaIUHXCH K o606eHHlo u 3THX nOH..SJTHH, npOJtOJI>K3Tb npaKTMllecKoe onepH- pOBaHHe paBeHCTBaMH H HepaBeHCTBaMH, npeJ{JIara5I CneIU'JaJlbHbIe YD-, p3.>KHeHHH, B TOM IIHCJIe pellleHHe HepaBeHCTB BH){a 24-a < 10. npH H3ytIeHHH HYMepaUHH MHOr03HatIHblX IIHCeJI cJle,nyeT OTBecTH CnCUHaJlbllblH YPOK Ha o606w,eHue 3HaHUU yqalUHXCH 0 paBeHcTBax' If HepaBencTBax. C 9ToH UeJIblO {O>KHO npe,nJIO}KHTb ,neTHM cpaBHHTb qHC- JIa HJIH BbJpa}J{eHH5I H nOCTaBHTb Bh-feCTO 3Be3J.lOQeK 3uaK «panHo». «60JIbIIIe» HJIM «Me HbWe». HanpHMep: 702 * 702 254 * 250.+ 4 68.4*4.68 540 * 538 870 * 870 - 90 840 : 2 * 840 : 3 Yllalll.HeCH 3aMeQaIOT, liTO B nepBOl\i1 CToJI6HKe coe.llHHH.'1H 3HaKOM «paBHO» ,lJ.Ba IIHCJIa, lIHCJIO H Bblpa}KeHHe H..'1M ){Ba Bblp3*eHHH. YtlHTeJIb CO 06I.lJ.a eT, liTO 910 pa8eHCmeO; tIHCJIO HJIH BbIpaJKeHMe, KOTopoe Haxo- ,lJ.HTCS1 CJIeBa OT 3HaKa paBeHCTBa, Ha3blBaeTCSI /leeou 'laCmblO paBeHCTB3, 8 cnpaBa - ero npasou tlacmblO. PaCCMOTpeB BTOpOH CTOJl6HK, J1eTH BII- .AS1T, lITO s.n.eCb ABa qHCJIa HJIH ABa BbIpa1KeHHH HJIH 1JHCJIO H BbIpa1KeHlfe COe){HHeHbI 3HaKaMH «60J1bUIe» HJIH «MeHbIIIe». YIIHTeJlb rOBopHT, qTO 3TO H£paBeH£m8a. YqaHeCSI cardH H33bIB31OT npaBYIO H J1eBYIO tlaCTU llepaBeHCTB. B ,AanbHeiillIel\f npH BbITIOJIHeHHH pa3J1HIIHbIX ynpa>KHeHHii C paBeHCTBaMH H nepaBelICTBaMH Ha){O nOCTOHHHO IIOJIb30BaTbCSI HO- SbIM" Tepl\fHHaMH. Ha npOTH}KeHHH Bcero nepHO,Aa H3YQeHHSI HYl\fepanHH naJ{o BbInon- H5ITb ynpIDKHeHHH Ha npaKTHlleCKoe onepHpOBaHHe paBeHCTBaMH H HepaBeHCTBaMH C neJIblO 3aKpenJIeHHH 3HaHHH 06 OTHOllleHHSlX, S8BH- CHMOCTHX, CBoHcTBax H T. n. 3TH ynpa)KHeHHS1 HMelOT MeCTO TaM t rJ{e npHXOAHTCSI cpaBHHBaTb 1JHCJIa HJIH BblpaJKeHHH. npH H3YQeHHH HYMepau.HH, eCTeCTBeHHO, 60JIbIllee MecTO Jt0JI}KHbl 3aHHMaTb ynp8>KHe- HHH Ha cpaBHeUHe qHCeJI OTBJIelleHHblX H HMeHonallHblX (CM. B Ylle6HHKe l N2 108, 174, 228, 201 H .ltp). nOJIe3HO BKJIlOtlHTb H TaKHe ynpaJKHeHHH: I) nO.AOepHTe nO,l{XOAHw.ee tlHCJIO: 72 099 < CJ 804 560 > CJ H T. n. 2) nO.!l-OepHTe BMeCTO 3Be3,nOtIeK TIO,AXo,nSlllJ.He Il.H<PPbl: 20 000 > * 9 999 54 907 < 5 * '" 07 il T. n. 3) npoBepbTe, npaBHJIbHO JIM nOCTaBJIeHbI 3H3I{H >, ,< HJlll =: 50 001 = 49 999 + 2 800 000 < 799 999 H T. n. 1 3,lIeCb H B )),aJIbHeHlIIeM 6y.ztYT YKa3aJlhl HOMepa yn pam HeHHA H9 YQe6HHK.a no M3TCMaTHKe Ji.;uJ. III KJ1aCCa, 1971 (aBTopbI A. C. ntJe.'1KO , 1\\. A. BaHToaa, M. Hi Mo- po, A. M. nblwKano). 211
AHanotHtlHble 3aABHHH MOJKHO BKJllOtlaTb H C HMeHOBaHHbIIH tlHC- naMH. npH cpaBHeHHH OTBJIeqeHHLIX qHCM yqalUHeCS1 ,ltOJDKHbl nOJlb30- BaTbCS! )J.BYMH cnocooaMH: YCTaHaBJIHBaH MecTO Cp8SHHBaeMblX qHCeJI B HaTypaJIbHOM pRJ{Y (7 328 6JIHme K H8t1any pSl,Aa, tJeM 7 428, 3HatlHT, 7 328 MeHbwe, IteM 7 428) HJIH >Ke paccMaTpHBaH HX .necHTHlIHbIH COC TaB (B tJHCJIaX 7 328 H 7 428 O,ltHHaKOBoe ttHCJIO e,AHHHLl TbICSItt, a ttHC- JIO COTeH B nepBoM qHCJle MeHbwe, 3HatIHT, nepBoe qHCJIO MeHblIIe Bro- poro). npH cpaBHeHMH HfeHOBaHHbIX tlHCeJI 06a tlHCJIa BbIpa}KalOT B O,ltH'" lj"KOBbIX C,[1HHHuaX H3fepeHHH, 8 aaTeM cpaBHHBalOT nonyqeUHble qHC... ita TaK LKe, KaK OTBneqeHHbIe. HanpHMep, npH cpaBHeHHH tlHCeJI 5 m 6l{ l-f 57 l{ MOiKHO nepBoe qHCJIO BbIpa3HTb B u.eHTHepax H cpaBHHTb ero co BTOpbJM (56 II < 57 4) HJIH }Ke BTopoe tlnc.no BbIpa3HTb B TOIIHax II ueHTHepax, nOCJIe qero cpaBHHTb ero c nepBbIl\f I.IHCJIOM (5 m 6 It < <5 m 7 ). . KpoMe cpaBHeHHH 1Jnce.'1, BKJIlOtIaroTCH ynpCUKlleHHH Ha cpaBHeHHc ,IJ.BYX Bblpa>KeHHi\ HJIM qHCna H BbIpa>KeHHH (CM. N2 96, 120, 137 II p.). BbinonHHH 3TH H nO){06HbIe JIM ynpa>KHeHHH, yqaHeCH--:3aKpeII- JIHIOT Cct>OpMHpOBaHHble paHee 3HaHHH 0 CBOHCTBax apH<pMeTHtIeCKHX .neHcTBHH (720 + 90 * 90 + 720 - BMeCTO aBe3,ltotJKH CT8BHM 3HaK paBeHcTBa t TaK KaK OT nepecTaHoBKH CJIaraeMbIX CYMMa He H3feHHeT" CH)t 06 H3MeHeHHH peaYJIbTaroB apH<j>MeTHtieCKHX J{eHcTBHH B 3aBHCH- l\10CTH OT H3MeHellHH o)tHoro H3 KOMnOHeHTOB (540: 6 * 540 : 9 - nepBoe ttaCTHoe (SOJIbWe, tleM BTopoe, TaK KaK ,lteJIHMble o):tHHaKOBbIe, a eJII1Te.wTIb B nepBOf ,BblpameHHH feHbllIe, tJeM BO BTOpOM)t 0 COOTHO'" meHHH le}K.ny I{OlnOHeHTaMH H pe3YJIbTaTaMH apH<pMeTHtteCKHX J{eu- CTBHH (600-375 * 600 - CTaBHM BMeCTO 3Be3J{OQKH 3HaK «leHbIlle»t TaK KaK pa3HocTb rrrCHbllIe y{eHbllIaeMoro). TaKMM oopa30M, BblnOJI- HHH YKa3aHHbie ynpa)KHeHHH, yqaW.HecH .nOJl>KHbI npHMeHHTb COOTBeT- CTBYlOlIJJie 3HaHHH, H TOJIbKO B OT)teJIbHbIX CJIYQaS1X MO>KHO )tonycKaTb npe,ltBapHTeJIbHOe HaXO>K;teHHe pe3YJlbTaT8. OAHaKo nOCJIe nOCT8HOBKH 3HaKa OTHomeHHH none3HO speMH OT BpeMeHH BnonHS1Tb npOBepKY, BbIQHCJ1HTb pe3YJlbT8TbI H cpaBHHBaTb HX. B KaqeCTBe nO,ltrOTOBKH K pacKpblTIUO KOJIUtteCTBeHHblX H3MeHeHHH pe3YJlbTaToB CJIO>KeHIiH H Bbl- qHTaHHH B 3aBHCHMOCTH OT H3MeHeHHH OJ{Horo H3 KOMnOHeHTOB 9THX .D.eHCTBHH nOJIe3HO nOCJIe cpaBHeHHS1 Bblpa>KeHHH npocne)tHTb, Ha CKOJIb- {O e.D.HHHU YBeJIHQHJICSI HJIH YMeHblliHJICS1 peaYJlbTaT H Ha CKOJIbKO eAH- HHII. 60JIbille UJIH A-feHbllIe O,ltHH H3 KOMnOHeHTOB. HanpHMep, YtJauU1ecH nOCTaBHJIH Me>K,ny BbIpaiKeHHRMH aHaK «6o.nb- me»: 790 + 80 > 790 - + 70. Y1JHTeJlb npe.ll.JlaraeT BblnOJIHHTh npoBep- KY, BblQHCnHB pe3YJlbTaTbi. l{eTH BbfnOJlHSlIOT: 870 > 860. - Ha CKOJIbKO ej:lHHHU nepBaS1 cYMMa 6oJIbwe, qeM BTopaH? (Ha 10 eJ{HHHU.) - CpaBHHTe CJJaraeMble. (nepBble CJlaraeMble O.ltHHaKOBble, 8 Bro- ¥oe CJIaraeMOe B nepBOM Bblpa>KeHHH 60JIbwe U8 10 eAHHHL\, qeM 80 BTOpOM.) 272
- CnaraeMoe OOJIbWe Ha 10 eJlHHHI.( H CYMMa 60JIblIle Ha 10 eAHHHIt, eCJIM .ztpyroe CJIaraeMOe TaKoe me. np"lepHO B TaKOM >Ke nJIaHe neJ(eTCH pa60Ta no cpaBHeHHIO ABYX pa3HocTeH, a n03,nHee npoM3Be,lteHHH H qaCTHbIX. . HepaBeHcTBa C HeH3BeCTHbIM tlHCJIOM peuHllOTcH nH60 nYTeM 3aMeHbI HepaBeHcTBa paBeHcTBoM, JlH60 cnocoooM no,n60pa, KaK DO II KJIaCCe (CM. N2 197 H ,np.). npH 9TOM HepaBeHcTBa 3aJ{aIOTCH no-pa3HoMY: B OHHX CJIyqa.Slx Ha,no H3 .naHHoro pHJ(a qHCeJI BbIOpa'Fb Te 3HatteHHSI 6YKBbI, npH KoropbIX HepaBeHcTBo 6YJleT BepHblM, a B JlpyrHx CJlyqaHX yttarnllecH caMH no,n6HpalOT TaKue 3HatIeHHH 6YKB. B TOM H .ApyroM CJIY" qae pemeHHe OJI)KHO BblnOJIHHTbCH B o6w.eM BH)te. PaCCMOTpHM KOHKpeTHbIe npHMepbI: I. 113 pHJla tIHCeJI 34, 35, 36, 37, 38 BbI6paTb Te 3HatteHHSI 6YKBhI a, npH KOTOpbIX 6y;teT BepHO HepaBeHcTBo a - 25 > 10. P e ill e H H e. nO,l{CTaBMM QHCJ10BbIe 3HaQCHHH 6YKBbI a, BbIlIHCJIHM pa3HocTb H cpaBHHM pe3YJ1bTaT C lIHCJIOM 10. 34 - 25 = 9 35 - 25 = 10 36 - 25 = 11 37 - 25 = 12 38 - 25 = 13 9 < 10 10 = 10 11 > 10 12 > 10 13 > 10 o T BeT: 36, 37, 38. Tenepb BbIHCHHeTCH, QTO 6YKBe a MomHO npH,l{aTb JIIOObie 3HaQeHHSI, KOTOpble 60JIbllJe, QeM 35. 3anHcb peweHHH BbinOJIHHeTCH B o6rneM BH,Ae: a > 35. 2. HaRTH 3HaqeHHH 6YKBbI c, npH KOTOpbIX Bepno HepaBeHcTBO: 60 c > 20. Pew e H H e. CHaqaJla HaH.neM 3HatIeHHe 6YKBbI c, npH KOTOpOM 60 - c = 20. 3ro qHCJIO 40. 4TOObI pa3HocTb 6bIJla 60JIbWe, qeM 20, Ha,no, tIro6bI BbIttHTaeMoe c 6bIJlO MeHbwe, qeM 40. o T BeT: C < 40 (0, 1 f 2, ..., 39). _ .l{JlB npoBepKH .neTH nOJ{CTaBJIHIOT HeKOTopble H3 3UaQeHHH 6YKBhI C H y6eiK.l1alOTCH, qTO perneHHfI npaBHJlbHbI: c = 0 60 - 0 = 60 60 > 20 c = 8 60 - 8 = 52 52 > 20 c = 39 60 - 39 = 21 21 > 20 PeUJeHHe HepaBeHCTIJ CHa 1 Ia.Fla ObInOJIIIHeTCH nOJ{ PYKOBOJtCTBOF\f yqHTeJIH t a n03,lIHee caMOCTOHTeJlbHO. Yp88HeHN. B II I KJlacce o606I1{alOTCB 3HaHHH )teTe" 06 ypaB- HeHUSlX, BBO;{HTCH 6o.nce CJIOJKllbIe yp8BHeHHH C u n.eHCTBHHMH YfHO>KeHHH H lteJIeHMH, a TaK}Ke pemeHHe npOCTblX H coc- u TaBHblX 3a.ll.aQ c nOMOIIJ.b1O COCTaOJIeHHH ypaBHeHHH. 0606U1,llJl. 3H8UHSI llereH 06 ypaBlJeHH SIX, yqHTeJIb BBO}J.HT oIIpeJtene- HHe ypaBHeHliSl KaK paBelicTBa, cOAeplKaw.cro HCH3IJeCTuoe (CM. N2 170, 273
-- 171). K onpeAeJIeHHIO MO)KIlO no)tBeCTH llepe3 cpaBHeHHe nap paBcHcTB BH,n'a: 35 + 27 == 62 H 35 + x == 62. Yqall(HeCH no,nMeTHT t qro 3TH paBeHCTBa OTJlHlIalOTCH TeM, lITO D nepBOf H3 HHX Bce qHCJIa H3BeCTHbl, a BO BropOM OHO H3 tJHCeJI Hen3BeCTHO Hero Tpe6ye-rCfl Y3HaTb. YlIlI" Te.Hb rOBopHT, llTO pafJeHCf1Z80, coiJepJ/caw.ee HeU36ecmHoe, 0603Ha t leHHoe 6YKOOU, flQSbt6atOfll ypaBHeHueM. PelllHTb ypaBHeHHe - 3Ha1lHT HaHTU neU3BeCTHoe tIH:CJIO. lla.nce yqarnHecH caMH Ha3blBaIOT npaBYK> H JIenyro tIaCTH ypaoHeHHH. YtlHr1b n05ICHHeT, llTO BO BCHKOI ypaBHeHHH 3aK- JIlOqeH Bonpoc, HanpH1\fep: «Kal{oe 4HCJIO HaAO npH6aBHTb K 35, tIT06bl nOJIytlllTb 62?» B ,naJIbHeHIUeH pa60Te ytlHTeJIb H ,neTH ,ltOJI}KHbI noc.. TOHlIHO nOJIb30BaTbCH HOBblMH TepMHHaI\.tH: «ypaBHeHHe», «pewalO ypaBHeuHe», «B rrpaBoH lJaCTH ypaBIleHHH» H T. n. B I I I KJlaCCe, KaI< 11 ao II, peweHHe ypaBHeHMH BblnOJlH5IeTCH Ha OCHOBe B3aHMOCB5I3H 1\feLKJty KOMnOHeHTaMH H peaYJlbTaTaMH: apHMeTH- u u " qeCKHX ,neUCTBHH, npHtle"f CTpYKTypa ypaBHeHHH HeCKOJIbKO YCJIO./KHH" eTC51 - nKJIlOqalOTCH ypaBHeHHH BH,na: 42 - 5 · x = 27. KpoMe Toro, B nopSIJI.Ke nOI3TOpeHHH BKJllOtlalOTCH " ypaBHeHHH Y)Ke H3BecTHOH ll.e- TJlM CTPYKTYPbl: 45 - (x + 9) == 22, 72 : x == 33 - 9 II T. 11. 06'bHCHeHUe peweHHH ypaBHeHHH BbInOJlH5IeTCH npHMepHo TaK ./Ke, Kal{ H: DO I I KJIaCce. Hal1pHMep, pewaH ypaBHeHHe 42 - 5 · x = 27, ytleHHKM paccY}K)laIOT: B 3TOM ypaBHeHHH H3BeCTHbl yleHbllIaeMoe (42) H pa3HOCTb (27), HeH3BeCTJloe HaXO,lUfTCn B BbIQHTaeMOM; tlTo6b1 HaUTH BbIQHTaeMOe, H8)10 H3 YMeHbwaeMoro BbllIeCTb pa3HocTb: 5. x = = 42 - 27, BbInOJIHlO BbIqHTaHHe: 5 · x = 15 H T. ,n. OJJ.HoBpeMeHHo BeeTCH oGyqeHHe peweHHIO 3a,zr.all cnOCOOOM COCTaB- neHHH ypaBHeHHH. npH 9TOM npe,nYCMaTpHBaIOTCH TaKHe 3TanbI pa60Tbl: CH311ana BBO)tHTCH peIIJeHHe HeCKOJlbKHl\lH cnocooaMH npOCTblX 38Aa1l, u 3aTeM perneHHe COCTaBHbIX 3a,naQt KOTopble aIOTCH 8 «np03paQHOH» <jJOPMYJIHpOBKe, ,nOCKa3bIBalOlUeH COCTaBJleHHe ypaBHeHHH, fI, H8KOHeu;, pewalOTCH aa,nallM C HCnOJIb30BaHHeM COOTHOWeHH5I paBeHCTBa, 33,A8H- HhIM YCJ10BHeM sa;tatJH. POJlb peweH!lH pa3HblMH cnocooaMH npOCTblX 3a,natl qpesBbltJaii- HO BeJIHK3, nOCKOJlbKY B 3TOM CJIytJae paCKpbIBaeTCH rJlaBHaH H,zr.eSl co- CT8BJIeHHSI ypaBHeHHH - 9TO COCTaaJIeHHe no YCJIOBHIO 38,naQH pa.. BeHCTBa. nO,npOOHee 0 MeTOHKe peIlIeHHH 33,natJ cnOCOOO1\1 COCT3BJIeHHH yp8B- HeHHfI CKa3aHO B «OOYtIeHHH perneHHIO 3a,naQ B I I I KJlacce» (CTp; 284). B I I I K,TIaCCe C>YKBeHHaH CMMBOJlHKa HcnOJlb3yercSi rJlaBHblM oc>pa30M KaK cpe,nCTBO oooomeHHH 3HaHHH YtlaInHXCH. npn H3YQeHHH HYMepanHH MHOr03HatlHbIX lIHCeJ! nOBTopHIOTCB Te BonpocbI, Koropble ObIJIH: pacKpblThI BO II KJl3cce: paooTa C MaTeMaTH" 1ICCKMMH Bblp3JKeHHSIMH (CM. N 104, 118 H .np.) H perneHHe saAaq C 6YK- neHHbJMH ,naHHbIMIi (Ci. N295, 117, 222 H ,np.). npH BblnOJlHeHHH ynpa}K- HeHHH C M8TeM3TI1qeCKflMH Bblpa>KeHHHMM Ii npH pelIIeHHH sanaQ c 6YK- BeHHblMH ,naHHbIMH OQeHb Ba>KHO Ka:mAbJi% pa3 B TOM HJlM HHOA cpopMe OOpaInaTb BHHMaHHe ;teTe" H3 CMblcn 6YKBbI KaK CH'MBO..18 ,lJ)IH b603Ha- 6YKBeMMa,. CHMBonHHa '274
leHHH HeKOTOpOrO qHCJIOBOrO iHOJKeCTBa. C 3TOH 1l.e.,1blO npH HaXO}K,lJ.C" IIRH tlHCJlOBOrO 3HaqeHHH- BblpaiKeHHH Ha,nO npHJtaBaTb GYJ{Be lie O,AHO 3HaQeHHe, a HeCKOJIbKO. ECJlH qHCJIOBbIe 3HaqeHHH 6yJtYT Y>Ke sa)taHbI , TO cneyeT cnpOCHTb eTeH: MOJKeT JIM 6YKBa npHHHlaTb llpyrHe 3H8- qeHHH? KaKHe? Ha30BHTe erne 2 (3, 4) 3Ha1JeHHfI. OqeHb B3>KIIO npOCJIeiKHBaTb, KaK H3MeHSleTCH 3H3qeHHe BbJpa}f{e.. HHH B 3aBHCHMOCTH OT H3MeHeHHH 3HaqeHHH 6YKB. C 3TOM l1eJ1blO npe.. Jlar810TCH CnellHaJIbHbIe 3a)t3HHH, HanpHMep npH)t3Tb 6YKBe d nHTb 3H3qeHHH T8K, 1JTOUbJ pa3HocTb 60-d y6b1BaJIa (Bo3paCTaJla). B 3TJrlX >Ke neJISiX B3>KIIO HaYLlHTb )teTeH YCTaHaBJIHBaTb HaHfeHbwee Ii HaH.. 60JlbUJee 3Ha1JeHHH, KOTopble MO>KeT npHHHMaTb 6YI{Ba Ii Bblpa>KeHHe, a TaK)Ke HaXO;UiTb oo.nacTb 3Ha t leHHH 6YKBbI It Bblpa>KeHHS1. 1) Ha30BH HaHr.,feHblIJee H HaH60JIbUJee 3HaQeHH5I, KOTopble MOJKeT npHHHMaTb 6YKBa. 2) Ha30BH 3HatIeHHH, Koropble MO>KeT npHHHM3Tb 6YI{Ba. 3) H330BH HaH60JlbIllee H H3MleHbwee 3HaQeUH5I 13blpa}KeHHH 4) Ha30BH 3HatICHMH, KOTopbIe MO}KeT npHHMMaTb Bblpa>Keluie. HCCJle.noBaHHe BbIpaLKeHMH ,L{eTH ,l{OJI>KHbI BblnOJlHHTb B COOTBeTCTBHH C 3THMH 3aHHHMH. _ PaccMoTpHM npHMep. Yq3mMMCH npe.l{Jlarae1'CH 3anHcaTb pa3HOCTL QHCeJl k M 26 (CM. N2 1-18) H noo6paTb TPH 3HaqeHHH 6YKBbl. npe>K;:te qe1 no6HpaTb 3HaQeHMH, Ha,n:o BbIHCHMTb, KaKoe HaHMeHbillee 3HaqeHHe ft,10jKHO npM,n:3Tb 6YKBe k (H3HfeHblIJee 3HaqeHHe 26), l<aKoe Hal100J1bWee 3HaqeHHe MO}KHO npH,n:aTb 6YKBe k (HaHOOJIblllerO 3HaqeHHH HeT). Yqa.. lUHeCH 3aKJII01JaIOT, liTO 6YKBe k MOLKHO npHaBaTb 3HaQeHHH, paBHbIe HJIH 60JIbLllHe, 1JeM 26: 3anHchIBaeTcH 9TO TaK: k = 26 "JIM k > 26. Tenepb yqaw.HecH JIerKO BbInOJIHHT 3a,ll,aHMe, npH,ll,aB 6YKBe JII06bIe TP" 3HaqeHMR, KOTopbIe He MeHbwe, tleM 26. 3aTeM MO}KHO BbIHCHHTb, KaKoe >Ke HaHMeHbLllee 3HaqeHHe f\10>KeT npHHSlTb Bblpa>KeHHe M npH KaKOM 3HaqeHHH 6YKBbl k. .neTH YKa3bIBaIOT, 1JTO HaHMCHbIlIce 3HaqeHHe BbI- pa}KeHHH paBHO HYJIIO npH k26, a HaH60JIblIJerO 3HaqeHHH HeT. DIe,n:o- naTeJlbHO, BbIpa}KeHMe 6y,n:eT npHHHMaTb 3HaQeHHH, paBHble HYJIIO liJiK 60nbWHe HYJIH (He feHbwe HYJlSI). 3anHCb: k - 26 = 0 HJIM k - 26 > >0. CHaqaJIa HCCJIe,ll,oBaHMe BbInOJIHeTCH no,lt PYKOBO)tCTBOM Y1JHTeJIg, a 33TeM .AeTH BblnO.'IHSlIOT ero caMOCTOHTeJIbHO. npH pemeHHH 3aaq C 6YKBeHHbIMH )taHHblMM, no,n6Hpan 1.IHCJlOBble 3HaqeHHSI, H3O 06paraaTb BHHMaHHe Ha HX }KH3HeHHYIO cHTyau.H10, Ha peaJIbHOCTb qHCJlOBbIX aHHhIx (HeJlb3S1, HanpHMep, B3Tb qHCJlO yqa- IUHXCH B KJIaCCe 150 Lle.noBeK). B CBH3H C M3yqeHHeM apHMeTHqeCKHX .AeHcTBHH Han MHOr03HaQ- HbIMH tJHCJIaMH CJIeyeT npem,ne Bcero o506tnHTb 3HaHHH )teTe" 0 B3aR... u v MOCBH3H Me-iKy pe3YJIbTaTaMM Ii KOMnOHeHTaMH ,ll,eHCTBHH, a TaK}f{e Me}K){Y caMHMH ,lteHCTBHHMH. C I KJIaCCa ,neTH 3HaIOT, qro ecJIH H3 CYMMbI BblqeCTb O)tHO 83 CJI8- raeMblX, TO nonyqHTCH )tpyroe CJlaraeMoe. Ha OCHOBe 3TO" B33HMOCBSI- 3H n I I I KJlaCCe )teTH nO,l{BO,ltHTCSI K o606rneHHIO. C 9TOA D.eJIblO nocne 275
paCCMOTpeHHfI COOTSeTCTBYIOW.HX qHC.nOBbIX COOTHOmeHHA (eCJIH 12+ 7 =:2 = 19, TO - 19 - 12 = 7 H 19 - 7 = 12) BKJIlOtlafOTCH ynpamHe- . HHH BH,na: 1) ECJIH k + m == n, ,t lIeMY paSHO n - k? n - m? npOBepbTe 113 tlnCJlax. 2) npOBepbTe, liTO (a + b) - a = b " (a + b) - b = a. 06bC-. HHTe, nOqet.IY TaK nOJIYllaeTcH. C nOIOIIJ.b1O 6YKBeHHOH CHMBOJIHKH oooomalOTCSI 3HaHHH AeTeH 06 H3MeHeHHH pe3YJlbTaToB apH4>MeTHIlecKHx JteHcTBliH B 3aBHCHMOCTH OT H3MeHeHHH O.llHoro H3 KOMUOHeHTOB (CM. cooTBeTcTBYIOInHfJ naparpa 9TOH KHHrH). BYKBeHHa'H CHl\.fBOJ1HKa Hcnonb3yeTcfl, KaK BO II KJlaC- ce, ,lJ.JIH 3aUHCH CBoiicTB apH<pfeTHqeCKHX )J.eHcTBHH. B I I I KJIaCCe B nepHo,lt H3Y1leHHH YMHO}Ke.HHB H npJlMO "06paTHo ,nCJIeHHH pacKpblBaeTcH Ha KOHKpeTHbIx npHMepax ",onopL\HOHanIaHaR OAHU H3 BH){OB <PYHKlJ.HOlIaJIbHOH 3aBHCHMOCTH- ..MCMMOCTIt .en"""H npHMO H 06paTHO nponopUHOHaJIbHaSl 3aBHCH-. tOCTb eJ1UqHH. B MeTO-AHKe pa60TbI Ha)t npHMO UJ1" 06paTHO nponopUHOHaJ1bHOH 33BHCHMOCTblO BeJUllIHH npe,nYC,faTpHBalOTCH TPH OCHOBHbiX 3Tana. I-Ia nepBOM 3rane yqaLI..lHeCH 3HaKOMHTCH C BeJIHqHHaMH (HanpHMep: ueHa, 1{<1I1UqecTBO, CTOHMOCTb; BpeUI, CKOpOCTb, paCCTOHHHe H )J.p.) H B3aHMOCBH3blO le}K.llY HHr-.IH. TaK, ao II KJlaCCe npH H3ytJeHHH YMHO- >KeHHH H .lleJIeHHH JteTH YCBOHJIH: eCJIH H3BeCTHbI ueHa KynJIeHHOrO TO- u u Bapa Hero KOJIHtleCTBO, TO MOiKHO HaHTH CTOHMOCTb )J.eHCTBHeM YMHO- }KeHH; eCJIH H3BecTHbI CTOHMOCTb H KOJIHqeCTBO t TO MomBO HaUTH IleHY ,neHCTBlieM ,l(eJIeHHH; eCJIH IKe H3BeCTHbI CTOHl\{OCTb H u.eH8, TO MO:>KHO Y3HaTb KOJlHtJeCTBO )teHCTBHeM ){e.'1eHHH (TO )Ke MO}KHO CKa3aTb H 0 APY. rHX BeJIHtJHHax). B I I I KJIaCCe OHH nocreneHIIO 3HaKOl\t5lTCH C HOBblMH rpynnal\fH BeJlHtJHH H B3aHMOCBH3bIO le)K,Ay HHMH: CKOpOCTb, BpeMB, paccToHHHe (Ng 358-374); ,AJIHHa npHMoyro.'1bHHKa, ero lliHpHHa H nJ10ma)l,b (N2 927, 928, 936-938, 950-952). Ha BTOpOM 9Tane YllaInHecH 3HaKOMHTCH C npHMo H o6paTHo npoI1op- UHOHaJIbHOii 3aBHCHMOCTblO OT,neJIbHbIX rpynn BeJIH1.IHH. OnblT nOKa3an, 1JTO YllalI(HeCH npHXo,AHT K o606w.eHIHo (nepeHocHT 3l1aHHH 0 npHMo H o6paTHo nponoPIlHoHbHOH 3aBHcn1<?cTH BeJIHqHH Ha Jllo6ylO rpynny BeJIlltJHH) B pe3YJIbTaTe nO,ApOOHOro paccMoTpeHHH TO.J1bKO Tpex rpynn BeJIHtJHH: I rpynna: ueHa, KOJIHlIeCTBO, CTOH{OCTb; I I rpynna: CKOpOCTb, BpeMH, paccToHHHe; I I I rpynna: )tJIHHa, IllHpHHa, ilJIom.a,Ab npHl\foyro.nbHHKa. eTo.llHKa pacKpwTHH npHMoH H o6paTHoH nponOplJ.HOHanbHoH3a- BHCHMOCTH MeLK.llY BeJIHqHHal\iH KaiK,AoH H3 rrpHBe-AeHHblx rpynn CTpOHT- CH aHaJlOrHIIHO. OTHOCHTeJIbHO KaiK,noH rpynnbl BMUIIHH paccMaTpH" B310TCH TPH TaMunbI, B KOropbIX JtaHbI 3HaqeHHH 9THX BeJIHqHH. npH- tJeM TaOJIHIlbI OT.nHqaIOTCH O)J.Ha OT -Apyroii TeM, 1JTO B HHX AalOTCH pa3- Hhle nOCTOHHHble B'1HqHHbl (HanpHMep, B O)J.HOH Ta6.nHue He H3MeHSIeTCH ueHa, B .npyroH - KOJlH'lJeCTBO, B TpeTbeH - CTOHMOCTb; CM. Ng 505, 276
525, 537). PaccMoTpeHHe TaMHl{ nOMoraeT YCBOellHIO Toro $aKTa, liTO nocTORHHOH BeJlHIIHHOii MO>KeT 6bITb npH onpC,lI.e.neHHbIX. YCJlOBHRX nlO6aH H3 Tpex ,AaHHbIX BeJIHqHH. KpoMe Toro, yqaInHeCH 3HaKOMHTCR c pa3J1HqHbIMH aaBHCHMOCTSlMH Me>KJ(Y BeJIHqHlIal\iIH O,nHOH H TOR me rpynnbI: np" O){HHX YCJ10BHRX 3aBHCHMOCTb npHMo npOnOpu.HOHanbuaH, 8 rrpH -ApyrHx - 06paTHO nponopnHOHaJIbHaSl (3TH TepMHHbI ,neTfIM HC C006InaIOTCH). HatJJlIO)leHHe 3a 1I3MeHeHHeM BeJlHlJHH no Ka*)lOH TaMHLle 110- foraeT yqaInH1\fCH BHJ(eTb, KaK C YBeJIHlJeHHeM HJlH .YMeHbllIeHHeM u O,nHOH BeJIHqHHbI B HeCKOJIbKO pa3 ,lI.pyraR BeJIHqHHa YBeJIHqHBaeT- CH HJlH YMeHbwaeTCH BO CTOJlbKO Me pa3. PaCCl\tl0TpeHHe B3aM03aBH- CH{OCTeH leLK.llY IIepeMeHHblMH nOMoraeT ,neTSIM YCBOHTb B3aHMOO()- paTHOCTb KaK npSIMOH, TaK H 06paTHOH nponopHOHaJlbHOH 3aBHCHMOC- TJi (ecJlH, HanpHMep, npH o.nHHaKOBOH eHe C YBe..TIHtleHHCM KQ.,1H1IeCTBa B HeCKOJlbKO pa3 CTOHMOCTb YBeJIMtIMBaeTCH BO CTOJIbKO >Ke pa3, TO H oupaTIIO - C YBeJIHtleHHeM n HeCKOJlbKO pa3 CTOHfOCTH KOJIH1IeCTBO YBTIHqHBaeTCH BO CTOJlbKO LKe pa3). <l>OpIHpOBaHHIO Y J{eTeH YMeHHH YCTaHaBJIHBaTb 3aBHCHMOCTb Me/K- JJ.Y BeJlHqHHaMH nOMoraeT pemeHHe 3a.naq: 3a,naq-BOrrpOCOB, npOCTblX 3a.naq nOBbIllleHHOH TPY,lI.HOCTH H 3a)latl, pewaeMbIX cnocoOOM OTHO- rneHHH. B LleJIHX OpMHpOBaHHH npaBH"TJbHbIX o606IneHHH 0 npSIMOH H 00- paTHOH rrponopUHOHa..TIbHOH 3aBHCHMOCTH BeJIHqHH HaJ{O nOKa3aTb lJ.e- THM, 1ITO He BCer){a C YBeJlHqeHHeM O)lHOH H3 BeJIHtlHH B HeCKOJlbKO pa3 .l{pyraH YBeJlH1IHBaeTCH HJIM YMeHblIIaeTCH BO CTOJIbKO >Ke pa3, T. e. OHa MO)KeT IIpOCTO YBeJIH1IHBaTbCH HJlM YMeHbwaTbCH, HO He BO CTOJlbKO >Ke pa3. __ Ha TpeTbe1 9Tane Y1laInHeCSI nepeHOCSIT Cq,opMHpOBaHHbIe y HHX YMeHHH YCTaHaBJIHBaTb npHMO H 06paTHO nponopnHOHanbHYro 3aBH- CHMOCTb Me}K,l\Y Be.,1H1IHHa1.fH Ha J(pyrHe rpynnbI, KOTopble ellle He pac- CfaTpHBaJlHCb, HanpHMep: Bec oJ(Horo npe)lTa, 1IHCJlO npe.l{MeTOB. 06mHH Bec H ,np. . I1HbIMH CJIOB8MH, Ha 3TOM 3Tane Y1IaInHeCH caMOCTOHTeJIbHO YCTa.. HaBJIHBalOT COOTBeTCTDYIOHe 3aBHCHMOCTH Me}K,ny BeJIHqMlIaMH Oe3 CneUHaJIbHOrO paCCMOTpeHHH C yqHTeJIeM. PaCK poeM nop06Hee MeTO)lHKY pa60TbI no YCTaHOBJ1eHH npSIMoH H 06paTHoH nponopHOHaJIbHOH 3aBHCHMOCTH Mey BeJIHqHHaMH: u.eHa, KOJIHqeCTBO, CTOHMOCTb. B3aHMOCBH3b Me}K.lJ.y BeJIHqHHaMH 3TOH rpynnbI (I 9Tan) 6blna pacK- pblTa BO I I KJl8Cce. PacK;>bITHe 3aBHCHMOCTH (II 9Tan) Ha1lHH8eTCR c nOJ{roTOBHTeJlbHOH patJoTbl, KOTopaH "'npoBOAHTCH BO BpeMR H3Y1leHHH H3MeHeHHSI pe3ynb- TaTOB J.,teHcTBHH YMHO>KeHHR H J{e.n:eHHH B 3aBHCHMOCTH OT H3MeHeHHH o)tHoro H3 KOMnOHeHTOB 9THX ,ZJ.eAcTBHH (CM. Ng 408). YqaInHMCSI npe)l.JIaraerCH 3a,naqa: «CKOJIbKO CTOHT 6 M TKaHH ue- nolO no 4- py6. 3a MeTp?» nOCJIe KpaTKoH 3anHCH 3TOM 3a,l1aQH 8 TaMHlle yqalllJIMCH npe;vIaraeTCH peWHTb ee H CKa3aTb t KaKHM J(eHCTBHeM Ha. 277
XO,llHT CTOHMOCTb, eCJIH H3BeCTHbl UeHa H KOJIH1JeCTBO. nOJlyqaeTCH CJle. AYJOmaH 3anHCb: UeH3 KOJlHQeCTDO CTOHMOCTb 4 py6. 6 M x py6. !laJIee npe,lJ.JIaralOTCH BOnpOCbl: . - CKOJIbKO SanJ1aTHT, eCJ1H KynHT TaKoH >Ke TKaHH B 2 pasa 60Jlb- we? B 3 pa3a feHbllJe? . - CKOJIbko 3anol'laTHT sa Ta]{Oe }Ke KOJIHtIeCTBO TKaHH, eCJIH l1.elIa (5y,lleT B 3 pa3a 60JIbllIe? B 2 pa3a feIlbllIe? Pa30HpalOTcH anaJlOrHtIHbIe ynpa}KHeHHH H C BMHqHHaMH JtpyrHx rpynn (CM. N2 415, 426). TaKHe ynpa/KHeHHH nOMorYT B ,llaJIbHeAweM caMHM AeTHM «OTKpbITb» npHMO H o6paTHo nponopUHoHanbHYIO saBH- CHMOCTb BeJIHqHH, onHpaHcb Ha 3HaHHH 06 H3MeHeHHH pe3YJIbTaTOB AeH- u CTBHH YMHO>KeHHH H ,neJIeHHH B 3aBHCHl'rIOCTH OT H3MeHeHHH O.ll.Horo li3 KOlvlnOHeHTOB. Cnel..{HaJIbHble ypOKH nOCBHmalOTCH paccMoTpeHHlO npHMo H 06paT- u u HO nponopl..{HoHaJIbHOM 3aBHCHMOCTH Mey BenHHHaM no Ka*AoH 83 Tpex Ta6JIHn. 3TH ypOKH CTpOHTcn npHMepHO no O,nHOMY nJiaHY (Cl\f. . Nv 505-508,.525-528, 537-540). - YqaIII.HecfI 3anHCblBalOT Ta6JIHUY (CM. Nt 505) B TeTpa,Ab H caMOCTOH- TeJIbHO 3anOJIHSlIOT ee. TaOJlHna npHo6peTaeT BHA: Ue..a KOJJH'IeCTBO CTOHMOCTb 2 Kon. 2 T. 4 Kon. 2 Kon. 8 T. 16 Kon. 2 KOB. 12 T. 24 Kon. 2 Kon. 16 T. 32 Kon. 2 Kon. 24 T. 48" Kon. Ha3B8B 3HaQeHHSI KaJK.AoA BeJ1H1JHHbI, yqaU\I,leCH 3 a MellalOT, 'ITO ' u.eHa He H3MeHHeTCH, KOJIHqeCTBO YBeJIHqHBaJIH H CTOHMOCTb YBeJlJf1JH- JIaCb. - PaCCMOTpHM, KaK H3MeHHeTCH CTOHMOCTb 8 3aBHCHMOCTH OT YBe- . JIHQeHHSI B HeCKOJlbKO pa3 KOJIHtleCTBa npH HeH3MeHHoH ueHe. CpaBlIHTe, . BO CKOJIbKO pa3 OOJIbllle/"TeTpa,lleii KynHJI BTOpOH nOKynaTeJlb, tJeM nepBblH. (B 4 pa3a.) . - CpaBHHTe CTOHMOCTH: 80 CKOJlbKO pa3 60JIbIlle AeHer ynJlaTHJI STOpOH nOKynaTeJlb, qeM nepBblH? (To>Ke B 4 pa3a.) - LITO MO}KHO CKa3aTb 0 neHe? (O,llHHaKoBaSl.) - lI.a. STOPO" nOKynare.nb KYIIHJI TeTpa.A ell no TaKO" me u.eHe. K3K 'm nepBblA, B 4 pa3a OO.,'1bWe H 3anJIaTHJI 3a HHX B 4 pa3a 60JIbwe. 't - 'CpaBHHTe Tenepb caMH nOKynKY BToporo ITOKynaTeJlH H nSlToro. :, (nSlTbllf nOKynaTenb KynlfJl TeTpaeii B 3 pa3a 60JIbWe, qeM BTOPO", 278 . t " 'f . ! .
H ynnaTHJI 3a HHX ){eHer B 3 paaa 60JlbWe, tJeM BTOpOH. TeipCUtH OblJlH no oAHHaKoBoH l.(eHe.) YtlHTeJlb npe)tnaraeT npHBecTH ,npyrHe npH- Mephl, n0J1b3YHCb Ta6J1HIleH. - KaKoM me BbIBO MOJKHO C<jx>pMYJlHpOBaTb? (ECJIH KOJIHlIecTBO YBeJlHtJHTb B HeCKOJIbKO pa3, TO npH OAHHaKOBOH ueHe CTOHMOCTb YBe- JlHIJHTCH 80 CTOJlbKO :me pa3.) TaK >Ke nOBOHTCH Y4alUHeCH K ,npyrHM BbIBo,naM: eCJIH CTOHl\-IOCTb YBeJlHqHTb B HecKOJIbKO pas, a l.leHY OCTaBHTb 6e3 H3MeHeHHH, TQ KOJlHlIeCTBO YBeJlHlIHTCH BO CTOJIbKO me pa3; ecJIH KOJIHqeCTBO YMeHbWHTb B HeCKOJIbKO pa3, TO npH HeHSMeHHOH ueHe CTOHMOCTb YMeHbWHTCH BO CTOJIbKO >Ke pa3; ecJIH CTOHMOCTb YMeHbIllHTb B HeCKOJIbKO pa3, TO npH o,nHHaKOBoA lleHe KOnHqeCTBO YMeHbIllHTCH BO CTonbKO me pa3. npHMeHHIOTCH nO.lIyqeHHbIe 3HaHHH 0 nponopUHOHaJIbHOH 3aBHCM- MOCTH BeJIHqHH npe>KJle Bcero npH peIlleHHH 3a.naq-BOnpOCOB. HanpHMep: «B Mara3JfH npHBe3JIH no OHHaKOBOH lleHe HMOKH H rpYillH. HOJlOK npH:Be3JIH B 3 pa3a OOJIbIlle, qeM rpYlll. qTO MO}KHO CKa- 3aTb 0 CTOHMOCTH H6JIOK H rpyrn?» YqeHHK pacCY>K;:\aeT: u.eHa HMOK H rpYlll O;:\HHaKOBa, HO HMOK 6blJlO 8 3 pa3a 60Jlbllle, qeM rpyw, 3HatJHT, H CTOHTb OHH Oy.nYT B 3 pa3a 60JIbllle, qeM rpYWH. anee BKJIlOqalOTCH npocTble 3a,naQH nOBblweHHoii Tpy,nHOCTH, T. e. TaKHe, npH perneHHH I{OTOPbIX Ha,lJ.O HCnOJIb30BaTb BbIBO){bl 0 nponop- l.lHOHaJlbHOM 3aBHCHMOCTH BenH4HH. HanpHMep: «1!JIH YtIarnHXCH I KJlaCCa KynHJIH no o;:\HHaKoBoH ueue TeTpa)tH B KJleTKY If J1HHeHKY. 3a TeTpa;:\H B KJIeTKY ynJIaTHJIH B 2 pa3a OoJIbme )teHer, qeM 3a TeTpa,nH B J1HHeAKY. CKOJlbKO reTpaeH B KJleT- KY KYOHJIH )tJIH nepBOKJIaCCHHKoB, eCJIH B JIHHeHKY KynHJlH 36 TeT- p a){eH?» YqeHHKH TaK 06'bHCHHIOT perneHHe: eCJIH TeTpaJ{H B KJIeTKY CTOHJlH B 2 pa3a oOJlI.Ile, qef B JIHHeHI<Y, a Te H ,npyrHe TeTpa;\H ObIJI" no OAR- lIaKOBOH l.leHe, 3HaqHT, TeTpa,nCH B KJleTKY KynHJlH B 2 pa33 60Jlbllle, qef B JIHlleHKY; Ha,no 36 YMHO)l{HTb H3 2, nOJlYQHTCH 72; KynHJIH 72 TeTpa,ltH B KJIeTKY. HaKOHel(, BKJIlOqalOTCH 3a.nalln, peiliaeMbIe cnoco60M npHBe,neHHH K e)J.HIIHu.e, KOTopbIe Tenepb. MorYT 6blTb pellIeHbI H cnoco6oM dTHollIeHHit HanpHMep: «3a 5 oM rOJIyooH I.IleJIKOBOH MaTepHH ynnaTHJIH 35 pyo. CKOJIbKO 6y.nYT CTOHTb 10 At 3eJIeHOrO WeJlKa no TaKO" }Ke ueHe?» YqarnHeCH caMOC'rOHTeJIbHO 3anHCbIBalOT 3ajtallY KpaTKo B TaMHu.e: I.J;CH3 , Ko..1"'IIC'CTBO I CTOHMOCTb O,l1HllaI{OBa S1 5M 35 pyt5. 10 At x P yt5. I YqHTMh npeJVIaraer peWHTb 3TY 3a;:\aQy pa3HblMH cnoc06aMH. Yqall.lHMCH YJKe 3HaKOM crioc06 npHBe;leHHH K e,ltHHHue (x =35 : 5.10), 2J9
110, nO.7Jb3YHCb paHee C,AeJlaHlIblMH BbIBOJ{aMH, MHOrHe M3 HHX CaMO- CTOHTenbHO HaHJ{YT J{PYOH cnoc06. PemeHHe 9THMH cnoc06aMH Hao 3anHcaTb C nOHCHeHHHMH: 10 : 5 - BO CTOJIbKO pa3 60J1bWe KynHJIH 3eJ1eHOrO meJIKa, qeM rOJIY- 6oro, 35 · (10 : 5) (pyo.) - CTOHMOCTb 3eJIeHOrO WeJIKa, x .35 · ( 1 0 : 5); x == 70. o T Ble T: 70 pyoJleH. BbloHpaH BTopoe J(eMcTBHe, YlIal.IJ.HeCSI CCblJIaJOTCH H3 BbIBo;t: BO CKOJlbKO pa3 OOJIblile KO..'IHlIeCTBO 3eJIeHOrO llleJIK3, 80 CTOJIbKO pas 60JIbllle 6y JteT ero CTOHMOCTb, eCJIH u.ena OJ{HHaKOBaH. PeweHHe J(pyrJM cnoc060M 6y,neT CqHTaTbCH npOBepKoH pemellHH ncpBbIM cnoco(SoM. Ha nOCJIe..nYfOII.{HX ypoKax BKJ1I01IalOTCH aHaJIOrHIIHbIe ynp3>KlleHHSI, "PH BblnO.nHeHHH KOTOpbIX 6y,nYT npHMeHSITbCSI BbIBOJ(bI 0 nponoplU10- H3J1bIIOH 3aBHCHMOCTH Me>KJty KOJIHlIeCTBOM H crOHMOCTblO npH nOCTOHH- 110M u.eHe. npnMepHo B TaKOM >Ke nJlalle paccMaTpHBaeTcSI npHMo npOnOpl.lHO- HaJlbH3H 3aBHCHMOCTb Me}K,ny I.(elloii H CTOHMOCTblO npH nOCTOHHHOM Ko..rUlqeCTBe (cf. N2 525-528) H 06p3THO nponopUHOHaJlbH3H 3aBHCH- MOCTb Me}KJl.Y LleHoH H KOJIHqeCTBOM npH nocToHHHOH CTOHMOCTH (eM. N 537-540). H3 9THX ypoKax ,nOJI}KHa 6blTb npe){OCTaBJleH3 yqamJiM- CH 60w'1bWaH C3MOCTOHTeJIbHOCTb: nycTb OHH cOBepmeHHo caMOCTOHTeJlb- no CcpopMYJlHPYIOT BbIBObI, a 3aTeM «J{oKa}KYT» HX cnpaBe,nJlMBOCTb, npHBo,nH no T30nHl.le npHMep. KaJK,nylO HOBYIO Ta6J1Hl.lY Ha,no cpaBHHBaTb C npebI,nyrnHMH. TaK, epaBHHBaSl, HanpHMep, TpeTblO Ta6J1Hu.y C nepBoH H cooTBeTcTBYlOll1He BbIBO,ZI.bI, yqeHHKH OTMeqaIOT, liTO 3eCb BeJlHIIHHbI 0,lJ.HH3KOBbIe, 110 B nepBOH Ta6JIHu.e He H3MellHeTCH ueH3, a B TpeTbeH - CTOHMOCTb; BbI- BO,nbl Tome pa3HbIe: B nepBOM cJlyqae np YBeJIH1IeHHH HJlM YMeHbWeHJ1H B HeCKO.TIbKO pa3 O,nHOH Be.TIHIIHHbl ,npyraH TO>Ke YBeJIHqBaJI3Cb HJIM YMeHbWaJI3Cb BO CTOJlbKO >Ke .p33, BO BTOpOM cJlyqae npH YBeJIH1JeIH1H HJlH YMeHbIlleHHH O,nHOH H3 BeJlHqHH B HeCKOJIbKO pa3 pyraH, Ha060- pOT, YMeHbWaJl3Cb HJlH YBeJlH1IHBaJl3Cb BO CTOJIbKO me pa3. _ B ,lJ.3J1bHeAmeM no Mepe BKJIfOqeHHH ,npyrHx rpynn BeJlHqHH Ha,no cpaDHHBaTb K3JK,nylO HOBYIO Ta6J1Hu.y H BbIBO,nbI C paHee p3CCMOTpen- HbIMH TaOJlHl.laMH H BbIBO):\-aMH, CcJ>OPMYJIHpOB3HHbIMH no 3THM T36J1HU3M. 06Y'l8HH8 peweHHtO a8A8'1 Bill KnaCCe CYII1-eCTBeHHYIO qaCTb co,nep>K3HHH nporpaMMbI no MaTeMaTHKe I I I l{J1aCCa, K3K H .ltPyrHx KJl3CCOB, COCTaBJIHeT peIlleHHe 38J{atl. BOJ1bWaH pa60Ta no Q>opMHpoBaHHIO YMeHHH pemaTb S3J{allH npo- Be,neHa B I H II JUl3Ccax. TaM H3yqeHbl Bce BH,lJ.bl npocTbIX 3a,n3q, CB513aHHbIe C Ka*JJ.blM H3 qeTbIpeX apH<pMeTHqeCKHX AeHCTBHA, TaM 80
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4ro MOlKlIO CKa3aTb 0 CTOHMOCTH nOJIOTHa H CHTua?» 5ICHO, liTO ,llJ1H OTBeTa H3 BOnpOC 3a,ll.aQH JlOCTaTOqHO 311aTb TOJ1bKO 3aBHCHMOCTb Me}K- AY u.eHOH M CTOHMOCTblO npH O,llHHaKOBOM KOJIHlIeCTBe. 3aBepruaeTC5I o6DHcHeHHe TaKHX 3a,llaQ ynpa>KHeHHeM B peWeHHH COCTaBHblX 3a,naQ H npHTOM pa3HblMH cnOC06-aMH. B03bMCM, HanpHMep, 3aAaqy NQ 540: «8 At ,lI.pana CTOHT CTOJ1bKO. >Ke, CKOJ1bKO 24 M rneJIKa. . lJ.eHa rneJIKa 7 py6. MeTp. HaHTH u.eny Jlpana». ' ':, npH pa360pe 3a,ll.aQH BbIHCHHeTCH, liTO B Hee BXO,nHT BeJIHqHHbl - 1 u.eH3, KdJlHqecTBO, CTOHMOCTb, BbIHCHHeTCH, 3Ha1leHHH KaKHX_BeJ1U- qHH H3BecTHbI, 1JTO Tpe6yeTcSI Y3HaTb. nOBTOpSIETCSI 3HaHHe 3aBHCHMOC- ;; TO Me>K.nY l.{eHOH, KOJlHlIeCTBOM H CTOHMOCTblO H Ha OCHOBe TaKoro pa3- 'l 60pa YCTaHaBJIHBalOTCSI cnOCOObl perneHHSI. HanpHMep: J I. X =- (7 . 24) : 8. I I. x = 7 . (24 : 8). Ill. 7 . 24 :.= x · 8. I Ka>K.llOMY cnoco6y cooTBercTBye-r oco6oe paccYiKeHHe, DbITCK3Kr lIlee: a) H3 311aHHSI B3aHMOCBSl3H .lI.aHHblX BeJIH1JHH (nepBblH cnocoo); : 6) 83 3HaHHH, KaK H3MeHHIOTCH lI.eHa H KOJIHqecTBO npH nOCTOHHHOH , CTOHMOCTH u(BTOpOH cnoco6); B) H3 3HaHHH Toro, \ITO pa3HbIe BbIpaJKeHHH I ., O)UlHaKOBOH CTOHMOCTH MO}l{HO npHp3BHHTb O.l1HO I{ .npyrOMY Ii COCTa- BIITb ypaBHeHHe (TpeTHH cnoco6). _ 311aHHe )leTbMH 3aBHCHMOCTH MeJK,lI.Y BCJIHlfHHaMH .naeT B03MO>KHOCTb ' , , npH aHaJlH3e 38,l1.aQH C nOJIHbIM OCHOB3HHeM CTaB:b /onpOCbl HMellHO TaK: . J ' KaKHe BeJIHtlHHbI BXO,ll.HT B 3TY 3aJlaqy, B Kal{OH CBH3H OHH HaXOJ(HTCH, K8KHe 83 9THX BeJlHtlHH 1i3BecTHbI H -KaKYIO Tpe6yeTcH HaHTH, KaK HaH- te' TH Y BeJlHqHHY no ,llBYM ,naHHbIM. BOT 9TO H ecTb nOJlJ1HHHbIH aHaJIIl3 .} COAep>KaHHH 3aJ\aQH, oCHoBaHHblH Ha npHo6peTeHHbIX YtlaI.l{HMHcH 3H8I1HSlX. : 113 3a,llaQ C nponop",Hona,,'1bHbIMH B1HtlHHaMH B HOBbIH Y'leOHHK . ,lI.JlH III KJIaCCa BOlliJlH 3a,ll.aQH, pernaeMble cnOC060f\1 npHfiloro H o6paT- f lIoro npHBe,ll.CHHH K eJ\HHHue, cnocoooM oTHollIeuHH. 3a,llatlH Ha npo- .. ;.. nopUHOHaJlbHOe ,lI.eJ1eHHe, H3 HaXO>K,lleHHe HeH3BecTHoro no J(BYM pa3- .. HOCTSlM, pa3JIH1JHhle 3a.ll.aqH Ha .lI.BIUKeHHe (BcTpeqHOe, B npOTHBOrIOJIOJK- ', HYX HanpaBJIeHHHx), reOMeTpHQeCKHe 3anaQH Ha BbIqHC.neHHe nJIOrnaJl-H. t OHH pewalOTc 6 H Ha OCHOBe 3H3HHH 3aBHCHMOCTH MelK,ay BeJ1HlIHHa 6 Mu. .\ \.JU'bHCHHH cnoco bI HX peweHHH, paHblIIe OnHpaJlHCb r JIaBHbIM 0 pa- , : 30M Ha HarJlHJ(1I0CTb, Ha pa3JIHQHOrO pOJ(a H4I'IJIIOCTpaI.{HH co.nep>KaHHH 3aJJ.aQ. Tenepb npH oG'bHCHeHHH eCTb B03MO>KHOCTb onHpaTbCSI He TO.flb- : KO ua pa3JIH1IHbIe cpe,llCTBa HarJIHJ(HOCTH (cxeMbI, qepTeiKH, PHCYHKH), HO H Ha 3HaHHe YQarnHf\fHCH 3aBHCHMOCTH MeiK.ny Be.ilIPIHllaMH. OCHOBa- II IHleM )lJISI 9Toro CJ1YJKHT npe,llYCMOTpeHHoe nporpaMMOH CneUHaJlbHOe O.1HaKOMJIeHHe YtleHHKOB c npHMepaMH TaKOH 3aBHCHIOCTH. B KatleCTBe .neHCTBeHHoro cpe,nCTBa HarJIH.l1HOCTH "PH peweHHH TaKHX 3aq HCnOJIb3yercH H KpaTKaH 3anHCb 3?.natlH B ma6AUI{e. 3anHcb 3JJLaq B Ta6J1Hl.{e ",eIIHa TeM, liTO OHa nOMOraeT yqeHHKY QTQeTJlHBO H sicno npe,nCTaBHTb ce6e Te BeJlHtlHHbl, KOTopbIe BXO,llHT B 3aJ1-aQY, B TOM \(nene H Te, KOTopbIe B YCJlOBHH 3a.l{aQH npe.lJ.craBJleHbl neHBIIO, YHCHHTb EaHMOCBH3b Me>K,ny BeJInqHHaMH H OT,lJ.aTb ceGe HCHbIH QTqeT B TOM, Ka- 286 ""
KaH BeJ1H1JHH8 npHHHMaCT B ,lI.aHHOH 3a.llaQe OHHaKOBbIe 3HaqeHlfH H Ka KaH pa3JJHtlHbIe lIHCJ10Bble 311a qeHHH. nYCTb, HanpHMep, Tpe6YeTCH peIllHTb 3a,ll.at.Jy Ha npOnOplJ.Ho- H3JIbHOe .neJIeHHe: «B OHOM KYCKe 5 M TKaHH, B .npyroM no TaKOH )Ke ueHe 7 M. 06a KYCKa CTOBT 36 py6. CKo.nbKo CTOHT Kam,l1blH KYCOK?» (N'2 624). npH 03HaKOMJJeHHH C cOAepmaHHeM 38AaqH BbUICHHeTCJI, t.JTO B 33- ,nalle rOBopHTCH 0 J{BYX KYCKax TKaHH no O,LtHHaKOBOH ueHe, 0 TOM, qTO 06a 9TH KYCKa BMecTe CTOHT 36 pyG., 0 KO..'1HtJecTBe MeTpoB B Ka>KAOM KycKe, no,ntJepKHBaeTCH Donpoc 3a.naQH - CKOJJbKO crOHT KalKJUit KYCOK TKallH. qToGbI,ltaTb yqeHHKaf\ npeJI.eJIbHO HCHoe npeJI.CTaBJIeHHe 0 TOM, KaKHe BeJ1HqHHbl BXO,l1HT B 9TY 3a.naqy, KaKHe H3 HHX H3BecTHbI H KaKHe He- H3BecTHbI, a r.TIaBHoe - KaKaH Be.nH1JH1I8 npMHHl\iaeT 3,l1eCb O,LtHHaKO- BbIe 3Ha 1 IeHHH, COCTaD,,r)fleTCH Ta6J1Hu.a: UCHa Ko..1H'Iel:TIIO CTOHMOCTb OJUJHaI<OB3$J 5..u 7 M X 1 } 36 pyo. X2 ::0 Ha OCHOBe co,nep)KaHlfH 3a,l1aQH, KpaTKO 3anHcaHHO D TaOJIHue, ,l{aJIee npoHcxoAHT npHMepHO CJleJJ-YlOaH 6ece,ll.a B BonpOCO-OTBeT- HOM opMe. . Bon p 0 c. KaKHe BeJJHqHHbI BXO,nHT B STy 3aallY? o T BeT. eHa, KOJIHqecTBO, CTOHMoCTb. Bon p 0 c. KaKHe H3 9THX BeJIHtJHH H3BeCTHbI, KaKaH HBJUleTCR HCKO:VI0H? o T BeT. H3BeCTHO KO.,'IHQeCTBO MaTepHH B K8>K,l\01v1 KYCKe (5 AI If 7 M), ux OOInaH CTOHMOCTb (36 pyG.). HY1KHO Y3HaTb CTOHMOCTb Ka)K- ,noro KYCKa B OT,l1eJIbHOCTli. . Bon p 0 C. 4TO HaJlO 3HaTb, QTOObI HaMTH CTOHMOCTb nepBoro KYC- Ka? BToporo KycKa? o T BeT. KOJJHqeCTBO MaTepHH 8 Ka>KAOM KYCKe (OHO H3BecTHO) H n.eHY (OHa HeH3BecTHa). Bon p 0 c. KaK HaHTH ueHY MaTepHH? o T BeT. HymHo_ OOW.YlO CTOHMOCTb (36 py6.) pa3)1eJ1HTb Ha o6m.ee KOJIHQeCTBO MaTepHH (5 + 7) M. Bon p 0 c. PaccKaiKHTe nJIaH pemeHHB Haweii 3aJI.aQH. o T BeT. CHa1laJIa Y3HaeM, CKOJIbKO MeTpOB B ,l(BYX KYCKaX t nOTOM u.eHY MaTepHH, ,naJlbllle Haitnel\f, CKOJIbKO CTOHT nepB1>IH KYCOK H CKOJlb- 1,0 CTOHT BTOPO" KYCOK 1 . 1 3ror nJ1aH MomeT 6b1'Tb 3anHcaH TaK: 1) CKOJIbKO MeTpOB TK3HH B ,ltBYX KycKax? 2) CKOJIbKO CTOHT O,ltHH MeTp TK8HH? 3) CKOJIbKO CTOHT TKaHb B nepBoM KycKe? 4) CKonbKo CTOHT TKaHh BO BTOpOM KycKe? 287
ne 9TOro CJle.aYIOT 3anHCb J1eHCTBHH H BblQHCneHHR: 1) 5 + 7 = 12 (oM) 3) 3 · 5 = 15 (pyG.) 2) 36 : 12 = 3 (py6.) 4) 3 · 7 = 21 (py6.) o T BeT. O){HH KYCOK CTOHT 15 pyo.; APyroH - 21 py6. n p 0 n e p K a. 15 + 21 = 36 (Pyo.). . , BblllIe 6bIJIO CKa3aHO, qTO B I I I KJIaCCe pemeHHe pSJ){a sa,naq 3anH- CblBaeTCH qHCJIOBOH <PoPMYJlOH (ypaBHeHHeM). Ho TaM >Ke 6bIJIa CJ,l.e.nana orOBopKa: ecJIH cI>oPMY.'1a CJIOJKHa HJIH rpOM03){Ka t TO ee MOH<HO He CQC- TaBJUITb H peIllaTb sat\aqy C 3anHCblO TOJIbKO ,nefiCTBHH. 3To 3aMeQaHHC UY>KHO OTHecTI;f H K.3a;{aQaM Ha nponopLlHOHaJIbHOe .lI.eJIeHHe. <l>opMYJIa v peweHHH HarneR 3aj{allIi TaKOBa: Xi = 36 : (5 + 7) · 5 X 2 = 36 : (5 + 7) · 7 CJIO}KHOCTb SaKJIIOqaeTCSI B TOM, llTO HCKOMaH BeJlUqlfHa 3)J.eCb HMeeT ABa QHCJIOBblX 3HaqeHHR H n09TOMY npHxo,nHTCH BBO,!(HTb ,nBa HeH3BeCT- HblX - Xi Ii x 2 , npnqe1 Kam){Oe H3 HHX HMeeT CBoe MaTeMaTHlreCKOC BbIpameHHe. Ha6JHOJ{eHHH nOKa3bIBalOT, llTO y HeKOTopbIX YQHTeJ1eH .lI.CTH npeO,llOJIeBalOT 9TY TPY,lUIOCTb, Y ApyrHx - HeT. n03TOMY perneHHe Bonpoca, COCTaBJIHTb HJIH He COCTaBJIHTb q>OPMYJIY J{JIH 9THX 3a.llaQ, u.e- Recoo6pa3HO npeJ{OCTaBHTb Ha YCMorpeHHe yqHTeJIH. . MHoroe H3 Toro, tffO CKa3aHO 0 sa,l\aqax Ha nponopnHOHaJlbHOe AeJIeHHe, OTHOCHTCH H K MeTo,nHKe pemeHHR 3a){aq na HaXO}K,.neHHe He- u H3BecTHoro no JtBYM pa3HOCTHM, H K 3a.natla1 Ha ,ltBHmeHHe C TOll To.nb- HO pa3HHl{eA. liTO B noc.nej{HHX .l1BYX BH,l\ax 3aj{all oco6eHHO 6oJIblIIOe 3HaqeHHe HMeeT HarJIH,nHOCTb. Cnoco6 perneHHH 3a,naQ Ha HaXO>K,AeHHe HeH3BecTHoro no ,l\BYl'v1 pa3HOCTHM cpa3Y CTaHOBHTcn HCHbIM, Korl(a ,naeTCH qepTe>K HJ1H PHCYHOK, Ha KOTOpOt H.nJIIOCrpHpyeTcH HHBHO 3a- AaHHaH pa3HOCTb. OYCTb, HanpHMCp, pelllaeTCH 3a.lI.atIa: «B O.lJ.1I0M KycKe 4 M TK8HH, B APyroM 7 oM TaKoH me TKaHH. BTOpOH KYCOK CTOHT AOpo}Ke nepBoro Ha 18 pyo. CKOJIbKO CTOHT KablH KYCOK TKaHH?» Cnoco6 peweHHH 9TOH 3a){aqH XOpOlliO pacKpbIBaeTcH I<paTKOii 3a- nHCblO 3aJlatlH D TaOJIHue H npOCTbIM qepTemOM (pHC. 2): , I . _ - - ___ I 1-" IIQ 18 pytJ. OO/lblll.e - PHC. 2. f ltCH8 I KOJIliqeCTnO f <.noatMOCTb , I KYC 01lHilaKODaSI 4 M- x pyt'i. II KYC. 7M XI JlbWe x . ria 18 py6. 288
nOcJle pa300pa 3a,l1aQH cocrawuleTCH. nJlaH ee perneHHH. ECJIH AaH- HaH 3aJ\aqa O,l1Ha H3 nepBblX, TO IlLrtaH COCTaBJUleTCH KOJlJleKTHBHO H fO}l{eT OblTb 3anHcan: 1) Ha CKOJlbKO MeTpOB TKaHH 60JlbUIe 80 BTOPOM KYCKe, qeM B nepaoM? 2) CKOJIbKO CTOHT O)J.HH PwfeTp TKaHH? . . 3) CKOJIbKO CTOHT ncpBbIH KY-COK TKaHlI? 4) CK04/TIbKO CTOHT BTOpOH KYCOK TRaHH? P e ill e H H e: 1) 7 - 4 = 3 (At) 2) 18: 3 = 6 (py6.) 3) 6 · 4 = 24 (py6.) 4) 6 · 7 = 42 (pyo.) o T BeT. nepBbIH KYCOK CTOHT 24 pyo. t BT0t10i{ - 42 pya. n p 0 B e p K a. 42 - 24 = 18 (pyo.) B I I I K.,1acce pernaercH Mlloro pa3Hoo6pa3Hblx 3B)J.atl Ha ,ltBH>KeHHe: Ha ABH}KeHHe O)1HOro TeJIa, Ha JlBH/KeHHe JlBYX TC.TJ H npHToM B pa3Hbix HanpaBJIeHHHX - HaBCTpeqy, B npOTHBOnOJIO>KHblX HanpaBJIeHHHx. C pa3HbIl\.IH nanpaBJIeHHHMH ABH>KeH'HH H C xapaKTepHbIMH ,l{JUI 3Toro BIf)J.a 3aJ{aq TepMHHaMH (OHOBpCMeHHoe H HeO)J.HOBpeMeHHoe HatlaJIO ABH}KeIlHH, CKOpOCTb ,llBHmeHHSI, paCCTOHHHe H ,l1p.) nOJIe3HO n03HaKO- MHTb yqaHXCSI na KOHKpeTHI.JIX npHMepax ,l1BHiKeHHSI B KJIaCCe "JIH ell(e Jlytlrne na OTKpbITOH MecTHOCTH. TpH BHAa 3aJtaq Ha BCTpetlHOe ,l1BH>KeHHe, a nOTOM TPH BIIAa aa,llaq Ha JlBH>KeHHe B npOTHBOIlOJIO}KHbIX HanpaBJIeHHHX u.ecnecooopa3HO nOKa- 3blBaTb KaK 3a,llaQH B3aHMoo6paTHble. HCnOJIb3YH r.pa<pHtleCKHe H.T'(JIIO- CTpal.lHH H COCTaBJIHH qHCJIOBble OPMY JIbl pemeHHH HJIH BbIpa>KeHHH. nOKa>Kef\f npHMepbl penleHHH TaKHX 3a,lla1.l. nYCTb, HanpHl\fep, HY>KIIO pellIHTb 3aJtaQy Ng 520: «,LLBa newexo,lta DbIlII.nH o.aHoBpervleHHo HaBCTpeqy ,llpyr ,npyry H3 JlBYX CM H BCTpeTH- JIHCb tlepe3 3 1.Iaca. OJ{HII nemeXO,llIlleJ1 co ..CKOPOCTblO 4 KM B 1.Iac, ,l1py- rOM - 5 KAt B 'lac. HaHTH paCCTOHHHe Me>K,l(Y CeJIaMH». rpacpUtlecKaH HJIJIIOCTpalJ.HH 3a,ll81.1H (pHC. 3). 1 npH aHaJIH3e rpaq>HlfecKoH HJIJIIOCTpalI.HlI YCTaHaB..rIHSaeTCH, qTO paCCTOHHHe Me>KJlY CeJlaMH COCTOHT H3 ABYX OTpe3KOB. OJl-HH OTpe30K u u U )10 MeCTa BCTpe1.lH npOHAeH O,llHHM nemexoAo:\l, ,l(pyroH - nHOHJleH APY- rHM nellleXOJl,Of\1. 4KM 8 ..ac 1 . r ,r ,r r- V XHM PHC. 3. 5KM 8 ac .. ,r '-r "- ..I 10 3aKa3 694 289
l.J:r06b1 HaHrH see paCCTOHHHe Mem.ny ce.,1aH,. HY>KHO HaHTH paCCTOR- v HIiH, npOHJJ.eHHble KaJK.llbIM ncmeXOJ\OM, H CJIO)KHTb HX. PerneHHe 3aJla1JH MO>KHO 3arrHcaTb TaR: x KM - paCCTOHHHe MY CeJIaMH 4 · 3 (KAf) - pacCToHHHe, npOMJleIlHOe rrepBblM rreIlIeXOJ{OM · 5 · 3 (leM) - paccToHHHe npOHJleHHOe BTOpbIl\f rremeXO,lJ.OM x=4.3+5.3 x = 27 o T BeT. PaCCTOSlIHHe Mem.ny CeJIaMH 27 ICM. .BTOpoA cnocoo peweHHH. 1)_ Y3HaeM, Ha CKOJIbKO KHJIOMeTpOB c()JIH>KaIOTCSI 06a newexoJla B O,nHH \lac. 2) KaKoe paCCTOHHHe npoH.nYT 06a nernexo,na 3a 3 qaca? Tor.na nOJIyqHM: x = (4 + 5) · 3 ' x=9.3 x = 27 o T BeT. PaCCT05IHHe M€>K,llY ce.'1aMH paBHo 27 «..tl. Jla..'1ee COCTaB."IHeTCH H pelllaeTCH oopaTHaH 3a.naQa: «llBa newexo,na BblWJIH oJI.HoBpeMeHHo HaBcTpe\lY ,npyr ,npyry H3 .lI.BYX ce.n, HaXO,lUIInHX- CH Ha paCCTOHHHH 27 leM. OJlHH H3 HHX WeJ1 co CKOpOCTblO 4 KM 'B \lac, ApyroA - 5 "Ai B qac. 4epe3 CKOJIbKO qaCOB nellleXOJlbI BCTpeTH.TJHCb?» rpaq>lIqecKaH HJlJlIOCrpaUHH 3TOH 3aAatlH (pHC. 4). YSHaeM, CKOJlbKO KHJIOMeTpOB IIpOHJlYT 06a neIlleXO,lla B O)lHH 'lac, IiJJ.H H8BcTpellY ,llpyr JJ.pyry (4 + 5) K.M. , J!aJIbWe paccY>K,ltaeM TaK: rremexoJlbl6YJl.YT B nYT(-f .IlO BCTpetIH CTOJIb- KO lIaCOB, CKOJlbKO pa3 paCCT05JHHe (4 + 5) KM COAep)KHTCH B 27 KM. OrclOJla IIo..'I)'qaeTCH paBeHCTBO: x = 27 : (4 -1- 5). x = 27 : 9 x==3 o T BeT. neweXoAbt BCTpeTHJIHCb lIepe3 3 qaca. ,Qalnee COCTaB..'IHeTCH H peWaeTCH BTopaSI o6paTllaH saJtaqa: «j!Ba newexo,lla BblWJIH oJl-HoBpeMeHHo HaBCTpeqy ,npyr ,npyry H3 .llBYX cellI, HaX(),lUlmHXCH Ha paccToSIHHH 27 KAt, H ncrpeTHJIHCb tlepe3 3 qaca. OJlHl-I H3 HIIX men co CKOpOCTblO 4 K.M B tlac. C KaKoH CI<OpOCTblO lllCJI JJ.pyrofi newcxo,l{?» 4 KM B "IBC .. X4 A 5KM B ac 'l IIC , a x... A " r "- v -" 7KM PHC. 4. 290
rpacj>HqeCKaH HJlJIIOCTpaUHH 33JI-aqH (pRC. 5). 4TOObl Y311aTb CKOpOCTb BToporo newexo.na, "ymHo Y3HaTb, KaKoe paCCTOHHHe OH npOUIeJI 3a 3 qaca. ,QJlH 9Toro "ymHo H3 o6ero paccToH- I-IHSI - 27 K..4t BhItieCTb pacCToHlIHe, rrpOHJleHHOe nepBblM neUIeXoJlO. Do..'1yqHM BbIpameHHe: 27 - 4 · 3. 3aTeM, pa3.neJIHB 910 Bblpa>KeHHe Ha 3, nOJIYQUM 3HalfeHHe CKOpOCTH BToporo nernexo,ll.a. nOJlyqaeTCH cpop- MYJIa: x = (27 - 4 · 3) : 3: PelHHB 3TO ypaBHeHHe, HaH.!teI, qTO x = 5. o T BeT. CKOpOCTb nernexoa 5 KJot B qac. III. B Y1Je6HHKe no l'vlaTeMaTHKe )J.JHI I I I KJIaCCa eCTb cpaBHHTeJIbHO OOJlbmaH rpynna 3a,l{aq (cBblwe 60 ), K KOTOpbIM ,llaeTCH 3a;J.aHHe: «Pe- IllHTe sa.zr.aqy, COCTaBHB ypasHeHHe». TaKHe 3aaHHH rOBopSiT 0 TOM, liTO CJIeJtYlOlIlHe 3a HHMH 3a,naQH HymHo pernaTb MeTO.llO1 cocraBJIeHHH ypaBHeHHH. DpH OJlH}I{aH1l1eM paCCMOTpeHHH 9THX 3a,naQ OKa3b1BaCTCH t liTO OHH pa3.,'(H1JHbI no CBoeMY MaTeMaTHtiecKOMY COep>KaHHlO, a pewe- HHe HX npHBO)J.HT K ypaBHeHHHl\f pa3HOH CTPYKTypbl. n03TOMY. lleJ1eco- 06p83HO pa36HTb HX lIa OT)teJ1bHble rpynnbI H nOKa3aTb noxo K COC- TaBJIeHHIO ypaBHeHHH B K8>K)lOH rpynne 1 . nepB)'fO rpynny 3a,ltaQ, pelllaeMblX BIll KJIaCCe c nO!Ylow.blO ypaBHeHHH, COCTaSJlHIOT 3MatlH Ha HaXO:>K.l1euHe HeH3BecT- HblX KO....\fOOHeHTOB .!teHCTBHH. npOCTble 3MallH TaKora pO,lJ.a pernaJIHCb B I II I I KJIaCcax. B I I I K.nacce TaKHe 3a)\aqH pewalOTcH n nopHKe nOBTopeHHH II 33KpenJIelIHH rrpOH)\eHHoro. -" KpoMe TOfO, 3)1.eCb yqaWJlecH BIlepsble 3HaKOMHTCH C peweHHeM npocTbIx 3aJJ.aQ HeCI{Oel1bKHMH cnocooaMH, COCTaBJIS1H no YCJIOBHIO 3a,lta- t.JH HeCKOJIL1\O ypaBHeHHH. ):{JIH 3TOH l.le.'1H OqeHb YJ{06HbI npocTbIC 3a- ,na1JH na pa3ocTHoe H.1H KpaTHoe cpaBHeHHe. HanpHMep: «HeH3BecTHoe QHCJlO "MeHbWe, tleM IB, H3 3. HaHTII HeH3BecTHoe UHCJlO». .no YCJIOBHIO 3TOH 3aJ{atlH yqamHeCH COCTaa.HS1IOT TPH ypaBueHHS1: 18 - x == 3 - no YCJIOBHIO 3aaqH pa3HocTb I B H X pasHa 3. x + 3 ==:I 18 - ecJIH HeH3BeCTHoe (MeHbme) QHCJIO YB1H1JHTb Ha 3, TO nOJIyqHTCSI 18. 1 nOp06HO 0 MeTOJJ;HKe pemenHSI 3a)l,aQ cnoco60M COCTaBJleHHSI ypaBHeHHH CKa38UO 8 CTaTLe M. A. BaHTOBOA H f. B. 5eJJbTIOKOBOH «¥paBueHHR B HaqaJlbHOM Kypce MareM8THKHt, ony6nHKoBaHHOH 8 >KypHaJle «I-IaqaJlbllaR rnItOJIa:t, N9 5 3a 1969 r. B iTOA CTaTbe aBTopbl BnepBblc HaMe1'HJlH npHMepHYIO KJl8CcHq.HKaLtHIO SBASq, peUlaeMblX cnocol5oM ypaBHeHHR B HaqaJIbJ1blX KnacC8X. C HX It03HlUiA pacCM8TpHBaeT- CSI Donpoc 0 peweHHH 38Aaq cnocoooM COCT8BJ1eHHH ypasHeHHA II B AaHHoA rnase. 10* 291
]8 - 3 = x - ecJIH OOJ1bIllee 1.IHCJlO (18) YMeHblllHTb Ha 3, TO no.'1Y- 1JHTCSI MeHblllee II HCJIO, T. e. x. Ha 9TOM 9Tane paCCl\taTpHBaIOTCSl H COCTaBHble 3a)J.allH, no KOropb1M cocraBct1HIOTCH ypaBlleHHS1 B npHMoM COOTBCTCTBHH C YCJIOBHeM 3a.n-a1.JH. HanpHMep, 3aa1.Ja NQ 308: «OK0J10 lliKOJ1b1 pOCwTJH .nepeBbH. OceublO noca.nHJIH eme 2 pH.Lla .n.epeBbeB no 14 B Ka>l\nOM, H TOfJ{a CTaJIO Bcero 55 )].epeBbeB. CKOJIbKO ,nepcBbeB poc..TlO )].0 oceHHeH nocaKH?» <l>oPMYJ1HpOBKa 9TOH 3aa1.JH nOCKa3bIBaeT npolI.ecc cocTaB.neHHH.. yp3BHeHH. «nYCTb .n.o oceHHeH noca.n.KH pOCJIO x ,nepeBbeB». CocTaB- JlHeM Bblpa*eHHH: 14 · 2 (,lJ.epeBbeB) nocaH.'1H oceHblO; x + 14 · 2 (.nepeBbeB)' CTaJIO nOCJIe nOCa,l1KH. 113 YCJIOBHH 3aJ{allH H3BeCTHO, tITO HX CTaJIO 55. COCraBJ1HeM ypaB- - HeHHe: x + 14 · 2 = 55. npH COCT3BJIeHHH TaKHX ypaBHellHH paccYJK,l1eHHH - BeYTcH YCTHO, a nOJI)"lJaeMble BbIpameHHH H ypaBHeHH 3anHCbIBalOTCH no XO,lJ.y pac- CY>K,l1eH nfl. B TOp Y 10 f P Y n n y 3 a ,n a tI, pernaeMbIX C nOtOIII.blO ypaB- HeHHM, COCTaBJIHIOT 3a,l1allH, <PoPMYJIHpOBK8 KOTOpLIX nOMoraeT ytleHHKY COCTaBHTb ypaBHeHHe, TaK KaK B TeKCTe 3a)1atIH npHMO YKa3blBaerCH HeH3BecTHoe lIHC..7JO, YKa3bIBaIOTC H ,neHCTBHH, KOTopble Ha,lJ.O BbInOJl- H8Tb Ha.n HeH3BecTHbIM, ,lJ.aeTCH H pe3YJlbTaT. TIpHMepoM Ta!<DH sa;J.a1lH MO}KeT CJIy.mHTb 3aJJ.alla N2 289: «Ec.,Tf" HeH3BeCTHoe tIHCJlO YMHO)KHTb Jfa 7 H K no.rlytleHHoMY npoH3Be,Z{cHHIO npHoaBHTb 16, rro.rIYIIHTcH 58. lleMY paBHO HeH3BeCTHoe 4HCJIO?» 0603HallHI\f HCH3BeCTHoe lIHC.fJO 6YKBOH x H BblnO.J1HHM Te ,lI.eHCTBHH, KOTopble YKa3aHbI B 3a.n.a 1.Je. Y MHO)l{HM x Ha 7, no.TlY4HM npoH3Be.nelIHe QHCeJl x II 7 (x · 7). Ilpl16aBHM K HeIY 16; no.nY4HM CyrvIMY: x · 7 + 16, B KOTOpOH nepBoe c.naraCl\10e x · 7, BTopoe c..'13raefoe 16. H3 YCJIOBHH 3a;la4H M3BeCTHO, tITO OHa paBHa 58. npHp3BHHBael\1 Harne Bblpa)KelIHe K 58 H no..'1ytlaeM ypaBHelIHe: x · 7 -l- 16 = 58. 3a,natlH, OTHeceHHbIe 3,Zl,eCb I{ nepBoH H BTOpOH rpynne, npoxo,l1SlT lIepe3 BeCb YQe6HHK Ii pemalOTcH n3 npOTH>KeHHH Bcero Ytle6Horo ro.n.a. B pe3YJIbTaTe Y4eHHKH HaYlJaTCH pernaTb ux BnO.TIHe caMOCTOHTe.TJbHO C He06xo,lJ.HMbIIH 3anHCH1H H conYTcTBYlOW.HMH HM YCTHblMH paccY>KJ].c- HHSlMH. T peT b 10 r p y n n y 3 a ,l1 a 1J, pernaeMbIX C nOMOInblO ypan- JleHHH, COCTaBJIHlOT 3a,natIH, Q>OPMYJIHpOBKa KOTOpbIX He no,nca3bIBaeT' npHMO OTHOlllelIHe paBeHCTBa, HO B YCJIOBHH KOTOpbX np" BHHMaTeJ1b- HOM 1.1TeHHH HeTpy.n.HO 3aMeTHTb H BbI4.TJeHHTb TY BeJ1H1.JHHY, KOTopaH B 3aAatle <PHrypHPyeT JlB3iKabi npH 9T01v1 HMeeT o,nHHaKOBble tJHCJ10Bble 3IJa1JeHH. TaKYIO BeJIH1JHHY H MOJKHO nO.nO>KHTb B OCHOBY COCTaBJIeHHH paBeHCTBa (ypaBHeHHS1). K tlHCJlY TaKHX 3a,na1.J OTHOCHTCH 3a,ll.31JH no,1J. N! 404,405,414,451 H ,np.; 3TH 33)1alJH BO II KJ1aCCe pemaJIHCb cnoc06oM npHMoro H o6paTHoro npHBeeHHH K e)1HHHQe. 292
npHBe,lleM ,llJISI npHMepa TeKCTbI HeKOTopLIX H30 YKa33HHblK 3a,ll3Q. 3a,l1aQa N2 404. «EaoywKa KynHJIa 3 MOTKa 6eJIOH IllepcTH 3a 15 py6. H no TaKOH >Ke u.eHe 6 MOTKOB CHHeH wepcTH. CKOJIbKO CTOHJta CHHHH wepcTb?» 31I.ecb !.lena OeJIOR H CHHeH IllepCTH OAHHaKOBaSl. 3a.naQa N2 414. «TnJIoxo.l{, .l{BHraJ!.cb no TeqeHHlO peKH co CKOpOCTblO 30 K.,U B qac, npOilleJI rrYTb Me)l{-ny ABYI'vUI npHCTallHMH 3a 4 qaca. Ha 06paTHoM nYTH TO >Ke paCCTOHHHC OB npOWeJI 3a 5 1JaCOB. C KaKOU CKO- pOCTbIO WM TenJlOXOA Ha 06paTHO1 nYTH?» 3){eCb nYTb TY Aa H oopaT- IIO O,!lHHaKOB. TaKoe YCJIOBHe BCTpellaeTCSI B 3aAaQax HepeAKO. HanpH- Mep: «3a 6 CTOJIOBblX JIO}l{eK ynJlaTH.HH CTO.'1bKO, CKOJIbKO 3a 10 tlaHHblx. 4aHHaH JlO)KKa CTOHJIa 30 Kon. CKOJIbKO CTOHJla O){Ha CTO..TJOBaH J10JKKa?» 3,lJ.ecb HMeercSI npHMoe YKa3aHHe Ha TO, liTO CTOHMOCTb LTIO}l{eK CT0J10BbIX H qaHHblX OAHHaKOBaH. KaK >Ke HcnO.Hb30BaTb 9TY 0HHaK6BYIO BeJIHtIHIIY ,It.TJH COCTaB.neHHH ypaBHeHHH? nOKa.>KeM Ha npHMepe peIllHHH 3a,lJ.atlH N2 710: «rpyi1na TypHCTOB oTnpaBHJIaCb B noxo,l(. TYAa OHH lliJJH 18 qac. co CKOpOCTblO 4 Kl1 B lIac, a Ha 06paTHoM nYTH TO >Ke paCCTOHHHe OIlH npoexa.nH ,Ha aBTo6yce 3a 2 qaca. HaHTH CKOpOCTb aBT06yca». AHaJIH3HpyeM co,ltep>KaHHe 3a,natlH: BbIHCHHeM, 0 tleM rOBopHTCSI BI" 3aaqe, KaKue BeJIHQHHbI BXO,l(HT B Hee, KaKHe H3 HHX H3BeCTHbI H KaKaH HBJlHeTCH HCKOMOH, Kal\ 1\fOmHO ee HaHTu, KaKaSl BeJIH4HHa cpHrYPHpyeT ABa>Kjlbl, lIO npHHHMaeT OJ{HHaKOBble tlHCJlOBbIe 3HatleHHSI. 0603HatIHM HCKOMYIO Be.lIH4HHY 6Yl{BOH x: «IlycTb aBTo6yc WM co CKOpOCTblO X KM B qac». CoCT3BJ1HeM Bblpa>KeHH:H: 4 · 18 (KM) - TypHCTbl npOWJIlI nelliKOM. x · 2 (KM) - TypHCTbI npOeXaJIH Ha 8BTo6yce. TaK KaK no YCJ10BHID 3aaqH paCCTOSlHHH TyAa H 06paTHo HMeT O)l.HHaKOBbIe 3UaQeHHH, TO nOJ1YQeHHble HaMH BbIpa}KeHHH MO>KHO np- paBHHTb O,!lHO K ,ltpyroIY. OOJIYQHTCH ypaBHeHHe: 4. 18 = x o. 2. HeKoropble 3aaqH 3TOH rpynnbI MorYT pewaTbcH cnoco6oM COCTaBJ1e.. IIH5I ypaBHcHHH II Ha OCIlOBe paseHcTBa OTHOllleHHH. ClOjla oOTHOCHTCH sa,nallH nOJ{ NQ 508, 516, 528, 540. 658, 668, 68.3, 710 H JJ.p. 06bI'IHO 9TH 3a.LtaQH pelllalOTCH HecKP.,'1bKHl\IH cnoco6aMH. - nOKameM 3TO Ha npHl\lepe pewenHn 3ajlallH Ng 508: «3a 15 At TKaHH ynJlaTHJIH 45 py6. CKOJ1bKO MeTpoB Tal{OH TKallH MomHO KynHTb Ha 9 py6.? - . llcHa I O.nHH3KOoa \I {I Ko..lltQeCTRO CTOHMOCTb 15 M x tC 45 py6. 9 py6. nOCJIe aHaJIH38 co;tep>KaHHH 3a.llallH H KpaTKOH 3anHCH ee B Ta6JIHne YCTaHaBJIHBaeM nYTeM COOTBerCTYIOw.HX paCCY>K,lleHHU H sanHCH OfJ{eJIb- .,,- 293
HbJX nbipa)KeHH"J t{TO aa,naqa MO>Ker Ob1Tb pemeHa necKO.'1bKIiMH cnoco- (jaMH. HanpHfep; , I. 9 : (45: 15) - enocoo OopSTHoro npHBe,AeHHg K e,l(HHHlte: ueHa MeT- pa 45: 15 (pyo.); H3 9 py6. l\iO>KHO KynltTb CTO'1bKO , MeTpOB, CKOJIbKO pas (45 : 15) co,n.ep}J.{HTCH B 9. II. 45: 9= 15 : x-ypaBHeHHe t BblTeKalOI.qee "3 nponopllHOHaJIbHOH saBHCUMOCTH MeJKJty CTOHIOCTblO H KOJIHlIeCTBOM npH O.ll.HHaKOBOH neHe. Bblpa>KeHHS1 3TOH 3aBHCHMOCTH: 45 : 9 - BbIpa>KeHHe, nOKa3bIBalOw.ee, BO CKO..J)bKO pa3 9 py6. MeHbwe 45 py6. 15 : x - Bblpa, >I<elIHe nOKa3bIBalOIII.ee BO CKOJIbKO pa3 I<OJIH- lIecTBO x At MeHbllIe 15 .M. A T3K KaK H3BeCTHO, tI-ro npH oJtuHaKoBoH ueHe BO CKOJlbKO pa3 MeHbme CTOHMOCTb, BO CTOJIbKO pa3 MeHbwe U KOJUI, lIeCTBO TO nOJIyqeH- Hble OTHomeHIlH MO>KHO npHp3BHHTb. B Pe3Y.,1JbT8TC nOJIYtIHl\f ypaBue- HHe, 3anHcaHHoe Bblille. 4 e T B e p T Y 10 r p y n n y COCTaB.nHIOT 3aa4H, perneHHe KOTOpbIX npHBo,lJ.HT J{ ypaBHeHHHM BH,Aa x + a · b = C (HanpHMep: «YqeHIIK KYIIHJI KHHry H 4 }<apaH,l.\allIa no 3 Kon. 3a KapaHJtalli H 3a BCIO nOKynKY ynJIaTHJI 32 Kon. CKOJIbKO CTOHJIa KHHra?») H&llH BHJta: a · x + b ,. C = =d (HanpHfep: «noe3Jt wen 4 qaea co CKOpOCTblO 60 lOt B \lac H He- CKOJIbKO qaCOB co CKOpOCTblO 65 ICM B qac. 3a Bee 9T0 BpeMSI OH npOllleJI 70 ICM. CKOJlbKO 'laCOB n0e3,A WeJI co CKOpocrblO 65 KM n lIac?» ). H, 'aKoHeu, no YCoJ10BHIO' HeKoropbIX 3a,naQ l\iO>KeT 6bITb COCT3BJICHO lIeCKO1bKO ypaBHeHHif, eCJIH JIlo6oe 3HaQenUe Be,,1HQHHbT, ,naHHOH B 3a- 1{3Qe, BbIpa3HTb lIepe3 J\pyrne, a 3aTCM nOJJYlleHHOe BbIpa>KeHHe npnpan- HHTb K cooTneTcTBYlOrneMY tJHCJIY. nYCTb, HanpHMep, .peIll3e-rcH 33,na- tJa: «B Mara3HH npHBC3J1H H3 l'ilalliHHe 180 1(,2 ane..TJbCHHOB. KOfJI.a BLlf- PY3HJIH HeCKOJlbKO Hll\HKOB aneJIbCHHOB, no 6 1(,2 B K3>K,ZtOM, TO Ha Ma- WHRe erne ocra.nOCb 60 1C2. CKOJIbKO HI.qHKOB BblrpY3H.'1U?» nOCJle TOfO KaK J.(eTH YCBOHT cO;:lep>KaHHe 3a){atIU, CJ1'IaIOT KpaTKYIO 3anHCb YCJIOBHH, 06'bSICHHT, liTO nOKa3hlDaeT Ka}l{,noe 'IHCJlO, H 0603Ha- qaT HeH3BecTHoe IIHCJIO 6YKBOH (<<nYCTb BblfPY3HJIH x HInHl{OB»), Moryr 6WTb COCTanJIeHW TPH paBHeHHH: I. 6 · x + 60 = 180 II. 180-6.x=l30 I I I. (180 - 60) : x = 6 IV. B YlleoHHKe I I I KJlaCCa npeACT8BJIeH pSlA saAaq c 6YKBeHHblMu oaflHbl.Jwu, HX cpaBHHTeJ1bIlO HeMHOfO - OKono Tpex .lI.eCHTKOB. rCM OOJIbWerO BHHM3UHH Tpe6YeT K ceoe KaN(){3H U3 HHX. npOcTeulllHe H3 Ta- KHX' 3aJl,alJ YiKe peW8JIHCb BO I I KJ1aCce. I I I KJIHCC npO.ll.OJIiKaer 9TY JIH- HHIO, It yme Ha nepBblx CTpaHHijaX yqeOHHKa lIMeeTCSI pH,lI. T8KHX 3a- 294
,naq (CM. HOMepa: 95, 117, 136, 187, 222, 294, 348 H Jtp.). )J.aJlbWe, no- CTeneHHO YCJIOiKHHHCb,. OHH npoxo.llHT lIepe3 BeCb yqeOHHK. npHBe.u.eM TeKCT. HeKOTopbIX H3 HHX. HanpHMep, 3aAaqa N2294: «nepBoe qHCJIO a, BTopoe tlHCJIO b, a TpeTbe H8 k MeHbwe CYMMbI nepBblx JJ.BYX. 4eMY paBHa CYMMa nepBblX ,nBYX?» 3a.naqa N2 337: «3a 6 M CYKHa ynJIaTHJIH b py6. CKOJIbKO MeTpOB TaKoro CYKHa f\{OiKHO ynHTb H3 a pyo.? 3anHIlIHTe Bblpa>KeHHH, nOJJ.6e- paTe qHCJlOBbIe 3HaqeHHH H peIlIHTe 3a.IJ.aqy». Y>Ke H3 co,nep>KaHHH npHBeJleHHbIX 3a){aq BH){HO, liTO C HX nOl\fOl.I.\blO o6oorualOTcH 3HaHHH Yt.JaI.UHXCH 00 apHcpMeTHtICCKHX ,AeiiCTBHflX, 00 HX cBofiCTBax, oooom.alOTCH H cnOCOObl peweHHH 3a,natl. KpOMe Toro, perneHHe 3a.n.aq C OYKBeHHblMH JJ.aHHblMH 3aKpenJIHeT H COBeprneHcTByer 3HaHHfI yqaHXCH 0 MareMaTHqeCKHX BwpaiKeHHHX, ){aBaH MarepHaJl )J..llH pa3BHTHSI y ,neTeH YMeHHfI COCTaBJIflTb Bblpa>KeHHH, qHTaTb HK, Ha- XO):(HTb HX tlHCJIOBOe 3HaQeHHe. n03TOMY, npe){JIaraH ,neTHM pelllHTb TaKYIO 3a)taqy, u.e.necooopa3HO )l.aBaTb 3aJlaHHe: «COCTaBbTe no YC..TJOBHIO 9rOH 3a.naqH Bblpa}KeHHe». TaKHMH BbIpa>KeHHHMH 6YJJ.YT: a - C K 3a- ,Aa4e ]\"2 95; a · k K 3aAaqe NQ 117; a - b K 3a}].aQe Nt 136; a : (b : 6) K 3a}].a qe N2 337 H T. )I.. HaKoHell, pellleHHe 3a.natJ C 6YKBeHHblMH ,A8HHbIMH cnoco6crByeT <j>OpMHpoBaHHIO Y ):(eTeH nepBOHaQaJlbHblX npeJtcTaBJleHHH 0 <PYHKllHO" HaJIbHOH 3aBHCHMOCTH Me>K}.(Y BCJIHlIHH8MH. Ha HHX JIerKO nOKa3aTb, qro 1.J:HC.TJOBOe 3HaQeUHe Bblpa}f{eHHfI 3aBHCHT OT 3HaqeHHH OYKBbI; rrp" H3MeHeHHH 3UaQCHHH 6YKBbI H3MeHHeTCfI H 3HaqeHHe BbIpaJKeIlHH: Ka}K- ,AOMY 3I1atJCHHIO 6YKBbl cOOTBeTcTByeT orrpeJJ.eJIeHHOe 3HalleHHe Bblpa- >KeHUSI, a B 9TOM H COCTOHT CYTb 4>YHKltHOHaJIbHOH 3aBHCHfOCTH. .aJUI JJ.OCTH>KeHHH 9TOH ueJIH OC06eHHO nOJIe3HbI BblpIDKeHHH C oYKBellHblMH j\aHllblMH, KOTOpblM npe){WecTBYIOT 38,naHHH, I1anpHMep, TaKoro pO.Aa: «npHJlaHre 6YKBe b qeTblpe TaKHX 3UaqeHHH, lITOObl cYMMa b + 150 YBeJ1Ht.JHJJaCb ,Ha _ ?O». I1.11H: «nO){OepHTe lJeTbIpe 3HaqeHHH OYKBbI k, Ta"Klie, qTOObl l{aJK,ltOe CJIe,1J,YIOee 3HaQeHHe lJaCTHOro 320 : k 6b1J1o B,LtBoe 6o.n b we n pe}].bl,nymero». Y npa>KHeHHSI no,n06Horo pOJJ.a npoxo,u,HT lJepe3 BeCb YQeOHHK. I1TaK, cnoc06b1 peweHIIH 3a,AaQ B III KJIaCCe pa3HOO6pa3I1bl: B 3aBH- CHMOCTH OT CTPYKTYPbI 3a,1J,aQH H HX M3TeMaTHQeCKOrO cO,Aep>KaHHSI, OT CneL(HaJIbHbIX 3a,l{aHH H K HHM pH)]. 3aJJ.aQ pemaeTCH cnoco6oM COCTaBJIe.. HHH ypaBHeHHH, no YCJIOBHIO HeKOTopblX 3a,nall (npeHMYllleCTBeHHO C 6YKBeHHblMH ):(aHHbIfl1) COCTaBJIHIOTCH Bbfpa>KeHH; peweHHe 3HalJHTeJIb" HOH lIaCTH 33,ltaQ 3aI1HCblBaeTCH lJHCJlOBOH PMYJlOH; pH,A 3a,naQ pewaeTCH nocJle aIiaJIH3a H COCTaBJIeHHH nJlaHa C 3anHCblO TOJIbKO JteHcTBHH H BbI I IHCJ1eHHH. I Bce TaKHe 3a,AaQH pellialOTCH C TeMH HJIH HHblMH 3anHCHMH. Ho ,ltJlH BbIpa60TKH Yl\'leHHSI pewaTb 3a.naQH OOJIbWOe 3HaqeHHe HMeeT H ycmHoe pemeHHe 3aJlaq C He60JIbwHMH lIHCJlaMH H C HeOOJIbWHM KOJIHqecTBOAt ,neHcTBHH, Kor):la I1HKaKHX 3nHceH He npOH3BO){HTCH (3a' HCKJIIOt.JeHHe1 3anHCH na KJ18CCHOH ll.OCKe HeKOTopblX qHCJIOBbIX .llaHHbIX) Ii Bce BHH- MaHHC yqellHKa COCpe){OTOqUBaerCH Ha MaTeMaTHQeCKOH CYHocrH 3a- 295.
)1a1.l, H8 HCnO..'1b30BaHHH JlOfHqeCKHX npHeMOB lbIlll..leHHR, 3HaHHH CBOHCTB .nefICTBHH II 3aBHCHMOlTeH MeJKY BeJIHtJHllaMH. B npaKTHKe YIlHTe.neH YCTIIOe perneHHe 3a,naQ OJ1>KHO 3aHHTb BH)1.HOe MeCTO, H npHTOM He TOJIbKO npOCTblX, HO II COCT8BHblX 3a.natl, pernaeMblX ,llBYMH-TpeMH J1eHCTBHHMH. ( B KaKOM COOTHOllIeHHH )1.0JI->KHbI BblcTynaTb nepellHC.TJeHHble BbIwe cnOCOObl -peweHHH 3a,na1.l - 3TO onpe.lle..lIHCTCfI Y1.Ie6HHKOM H B 1i3Be- CTHOH Mepe TBOplJeCKH1 onbITOM yqHTeJIH, ero. MeTO,ltHtIeCKHM MaCTCp" CTBOM. v. Pa3Ilooopa3lIe _ cnOCOOOB pellIeHHH 3a.natI, npHMeHHeMblX B I II KJIaCCe, TpeOYeT HcnO.llb30BaHHH pa31HqHblX MeTO)1.HtlecKHX npHeMoB K3K npH o()'bHCHeHHH cnoco()oB HX peweHHH, TaK H npH 3aKpen.neHHH YMe- , HHH pernaTb 3a.llatiH. ",. CpeAH 3THX npHeMOB ocooeHHo 60..T'fbWOe 3HatIelIHe HMelOT npHeMbI cpaBHeHHH 3a.lta4, npHeMbI HX npe06pa3QBaHHH (r..'1aBHbIM o6pa30 COCTaB..rIeHHe 06paTHblx 3a.n.aq) H COCT3BJIellHe 3a.llaQ caMHMH yqaInHMHcH no pa3JIHtIIIbiM 3a.naHHHM YQHTeJIH. HOBblf1 Ylle6HHK C03aeT 6JIarOnpHHTHbTe YCJlOBHH AJIH peaJIH3au.uH npHeMa cpa8fieHUJl; B HeM c6.'1H)KeHO DO BpeMeHH paCCMorpeHHe CXOA- · HblX 3aJ(alJ - 3a,aaQ n3 BCTpetJHoe JI.BIDI<eHHe II 3aA8 1 1 H3 ,nBHJKeHHe D npoTHOnOLTIO)({BbIX HanpaBlIeHHHx, 3a,lJ,aq 113 npOnOplI.HOHa..TIbHOe A1eHHe If 33j\aq Ha HaXO>K){eHHe neH3BeCTHoro no )1.BY1 pa3HOCTSlM. TaKoe COJlH}{{eHHe nOMoraeT npoBeJ(eHHIO cpaBHeHIIH, BbI){eJIeHHIO c' nOMOInblO a1la...1H3a cyrnecTBeHHblx npH3HaKoB 3a,l(aQH, IIX aOCTparHpo- BaHlflO If 0006meHHIO. BOJlbWOe MeCTO oTBe.neHo B YQe6HHKe COCTaB.rreHIIIO H perneHHIO. .o6paTHbIX 3aJl.alJ. 3HaKofCTBO co cnoco6aMH pellleHHH 3a.naQ Ha BCTpeQ- Hoe ,lJ,BH}I{eHHe, 3a,AaQ H3 BbIqH'1ellHe BpeMeHH, 33,naQ Ha Bb!\lHCJIeHHe n.rl0rua.1J.H, pellIeHHe 3a,aall K3>K,noro H3 3THX BHAOB 06'bHCHHeTCH cpa3Y H3 Tpex B3aHOCBH3aHHbIX 3aJI.allax, H3 KOTOpblX O)l.Ha HBJlHeTCH HC- XO,llHOH, a .npyrlIe Be - 06paTHbIMH K Hefl, a Bce TPH COCT3BJISIIOT rpynny B3aHfoo6paTHblX 3a)1.all. TaKOH TIpHeM 06'bHCHeIIHH cnoco6- crByeT YCBoeHHK> H 3aKpenJIeHHIO 3HaHHH B3aHMOBH3J{ BeL1JMQHH, BXOJ1.H- W.HX B 3TH 33.natlH. <J>OpMHpOB8HnIO YleHIIH pewaTb 3a,!latiH cnoc06CTBYlOT ynpa>KHeHHH He TO.'1bKO B pcrneHHH rQTOBbIX 3a)1.aQ, JlaHHbIX B YlIeOHHKe, HO H B COC- T3BJleHlIH YlJaMMHCH CBOHX 3aAatJ no pa3JIliQHbI1\.1 3aAaHIISlM: COCTa- BMTb 3a)1.aQy no .l1aHHOMY lJepTe}KY, no cxeMe, no KpaTKOH 3anHCH ee YCJIOBHH, no ,l(al!HOH <PopMYLTIe (ypaBHeHIIIO), faTeMaTHqeCKOMY BhIpa- >KeHHIO II )J.p. ' Oco6eHHO nOJIe3HbI YIIpaiKHeHHH B COCTaBJleHHH 3a.llaQ no ,llaHHOA <Jx>PMYJIe, KorJ\a DMecTe C TeM Yl<a3bIBaeTCH, C KaI{HMH B1]HQHHaMH ]10.'1- >KHa ObITb COCT3R.'1eHa 3aJ(atJa. HanpHMep: «l1cnOJIb3YH B1HQHllbI-- u.eHY, KOJlHlIeCTBO, CTOHMOCTb»t COCT8BbTe 3a,lJ,aQH no ct>oPMYJIaf\1: 1) x = (36 : 12) · 4 x = 36 : (12 : 4) 2) x = 80 : (15 : 3) x = 21 · (80 : B) 296
HJJH: «COCTaBbTe 3a)1aqH no IIX pellleHHIO, HCnOlIb3YH BeJIHtJHUbI CKOPOCTb. BpeMH, paCCTOHHHe» (no YIle6HHKY N2 672): I) x = (180 : 3) · 6 2) 120: (60 : 2) TaKHe ynp3iKHelIHH, K8K HHKaKMe J1.pyrHe, cnocoocTBYIOT YCBoeHHtO B3aHMOCBH3H MemJlY YK33aHHblMH BeJIHqHHafH. , HOB3H MeTOAHKa OTpa>KaeT nepe){OBble B3r JIH,nbl Haillero BpeMeHH Ha npOIJ.ecc peweHHH 3a){aIlH, YTBep}K)l.aH, liTO 3TOT npOIJ.ecc OT Hatla- Jla .no KOHU.3 JlOJI>KeH 6blTb TBOplleCKH, - nOHCKOBbIM, onHpalOll(HMCH Ha caMOCTOHTeJIbHOCTb YQeHHK3, Ha ero TBOptIeCKOe Bo06pa:H<eHHe H 3J{THBHoe HCnOJIb30BaHHe p3.11H411blX MblCJIHTeJIbHbIX onepal.(Hii. .o.POfiH nepBOnaqa..TIblIble cne.l\ellHH 0 )(OJIHX e){HHHI.J.bl nO.TIyqeHbI ytIa1I.(HMR- CH BO I I K.nacce. TaM OHH n03n3KOlvIHJIHCb co cnOC0601\f nO.;'IYlleHuH ,no.nH BeJ1HIIHHbl H ,nOJIH IIHC.na (e.ll.HIIHIJ.bl), cpaBHRBa.J1H pa3.,1HlIHble )10- JIM, npH06peTaJlH YMeHHe IIHTaTb H 3anHCbIBaTb HX, H3XOHTb ,nOt/THO QHC.n3 H QHCJ10 no ero )l.OJIe npH peIlleHHH npOCTbIX 3a.Z{aq. B I I I K.nacce CBeAeHHH 0 ,nO.lIHX e,nHHHIl.bI 3HaIlHT'IbHO pacIllHpH- IOTCH. 3Jt.ecb Y1l3InHecH, nOBTopHH TOT }Ke, liTO H BO I I KJIaCCe, cnoc06 nO.lIYQeHHH OT,lleJIbIlblX .nOJIeH, BleCTe C TeM 3H3KO'fHTCH C npoueccoM 06pa30BaHHH )l.P06H, COcTOHlll.eH H3 HeCKO..TlbKHX ,noL'1efl C,ZlHHHIJ.bl; Ha 3TOM OCllone y HHX nOJIJlIHTCH npeJlcTaBJIellHe 0 )],pOOH KaK cOBoKyn- HOCTH HeCKOJIbKHX JloeH e.Z{HHUnbl. npH 3anHCH .l\p06efi BBOHTCH Tep- MHHbl «tlHCJlHTeJlb» H «31IaMeHaTeJIb» JlP06H. B co,nep>KaHHe pa60TbI Ha)J.,npo()HMH B I I I KTJacce BXO)JJIT cpaBHeHHe Jlp06eii C O)J.HHaKOBbIMH H pa3HbItH 3HaMeHaTe.nHfH (KaKaH H3 BHX 60fJblIJe, KaI<aH - MeHbllle), 3 TaK)l{e HX npeo6pa30BaHHe, T. e. cpop- MHpOBaHUC YMeHHS1 KpynHbIe .nOTIH Bblpa3HTb B 60v1ee MC.TIKHX H, Haooo- pOT, leJIKHe )l.O.;'1H Bblpa3HTb B 60.nee KpynuLlx ,nOJIHX. CYll.J,ecTBeHHYIO CropOHY pa60TbI Ha.ll.,ll3HHOH Te10H COCTaBJIHeT OOY4e- Hue ,lleTeH YMeHHIO H3XO)l.HTb )1p06b llHCJIa (HHalle rOBopH, YMeHJ;UO Haxo,!1HTb OAHY HJIH HeCKO..'1bKO paBHbIx tIaCTeH OT IIHCJ1a); 9TO YMeHHe TOT\laC }J.{e no.nYllaeT 3,necb CBoe npaKTHlIeCKOe npHl\leHeHHe npH pe- llJellHH 3aJI.311 He TOJIbKO npOCTbIX, K3K 3TO OblTIO BO I I K.TJaCCe, 1I0 H COCT3BHbIX. OTJIHtIHTeJIbHOH oco()eHHocTblO leTO){HKH H3YlleHHH )l.8HHOH TeMbI HBJ1Hel'H ee IWHKpenlHocrrlb J HQZA..WHOCtnb. Har.TIH.lI.HOCTb JlO"l>KHa OblTb HCnOJlb30B3Ha 3}{eCb B C8MbIX lIlHpOKHX pa3Mepax If conYTCTBOB3Tb <p<>p- MHpOBaHHIO Bcex npe,ncTaBJIeHHH, BXO,lU1IlJ,HX B CO)l.ep>K3HHe 9TOA TeMbl. Ka>KJJ.aH onepaUMH-6y,nb TO 06pa30BaHHe .llP06H, H.,TIH cpaBHeHHe ,llpO- t5eii"HLTIH HX npeoop830BaHHe, HJlM HaXO}K,neHHe.){p06u qHc.na)l.OJI}Kna onH paTbCH Ha qYBCTBeHHYIO OCHOBY, Ha pa60TY C npe)l.MeT3IH, PHCYH KaMH, 1.IepTemaMH. ll.JeIlHKaMH ,nOJl>KHO 6blTb npOAe.naHO 3Ha\IHTeJJb- 291
. Hoe I{O..'IHtJCCTBO npaKTHtleCKHX ynpa>KHeHHH B ,AeJIeHHH Ha paBHble qac- TH pa3Hooopa3,HbIX PraJIbHbIX npeJJ.MeToB (6YMa}l{HbIX nOJlOCOK, BbIpe- 3aHHblX 113 : KapTOHa HJIH nJtOTHOH 6Y1\larJ.f, KpyroB, np5lMoyroJlbHHK KBa.np8TOB), yrrpIDKHeIlHH B neperH6aHHH JIHCTa 6Yft,larIf, a TaK>Ke B AeJleHHH HrYJ>' KOTopbe BbIqeptlHBalOTCH yqaIUHMHCSI B CB,OHX TeT.. pa.L1HX (OTpe3KOB, npHMoyrOJIbHHKOB, KsaJ{paTOB); AOJl1KHO 6bITb npo. BeAeHO J\OCT8TOtlnO MHoro Ha6JIIOHHH paBHblX AOJIeH Ha QepTe1KaX, aHHbIX n YQe6HHKe. npOBOJUI yqeHHKOB no Bce TyneHHM KOHKpeTHOrO ooyqeHHH, HY>K- HO lleJIaTb o606rueHIfH H .lI.o6HBaTbCSI Toro. qTOt)bl ,l{eTH Mor JIH paOOTaTb c .nPO()HMH H B OTBJIeqeHHOM n.J1aHe, no npe.!XCTBJleHHIO. Y qeHHK I I I KJI8C- u 3 ca On}l{eH H TO.TJbKO YMeTb HaHTH 8' AaHHoro OTpe3Ka Merpa, ,ne- - 3 lUI MeT P a) , lIO H 3H8Tb, KaK Boo6me HaHTH - BlHqHllbI HJlH tlHC.TIa. - 8 41. OH .llOJIiKeH YI'ileTb cpaBHHTb - H -, nOJlb3YHCb He TO.lIbKO Te1 H.lIH HHbIM 82' HarJUI,ItHblM nocooHeM, HO H f5e3 onopbl Ha HarolTJH)].Hoe noco6He Ha oc- HOBamm YMeHHSI BblpamaTb KpynHble ,lJ,o.m: (+) B 6o.'1ee Me.n:KHX ,lJ,o JHIX (8 Jl8HHOM CJIytlae B BOCbfbIX JtOJIHX). YqeHilK OJI>KCH YMeTb npa- I 1 I 1 1 . BH.TJbHO paCnOJlO>KHTb AO.7JH -, -, -, -, - B nopH,nKC HX nOCTe- , 4 7 238 neHHoro y6b1BaHHJ1 H8 OCHose 3HaHHH OTHOCHTeJIbHbI pa3MepOB AOJIeH, a 9TO B CBOIO Otlepeb OCHOBbIB8e-rCfl Ha 3H8HHH Toro, lITO qeM 60JIbIIle u tIHCJIO paDlIbIX qaCTeH, Ha KOTopbIe e..'IHTCH e.nHHHlI.a, TeM MeHblIIaH ):{o- JlR lloJIYQaeTCH. TaKHe o606rneHHbIe 3HaHHS1 nOJlyqalOTCH B pe3YJIbTaTe 06'bfIcHeHH'H, onHpalOmHXCH Ha'TY H.nH HHYIO HarJIH,nHYIO OCHOBY, H OCTaTOqHOrO KOJIHqecTB8 ynp8iKHelUt,, COnpOBOjl{.lI.aelbIX: o606me- HHHMH. PeweHHe 3aJlaQ, CBH3aHHbIX C HaX01KJ{e"HHeM Apo6H qHCJI, B I I J KJIaCC HMeeT CBOIO O06eHHOCTb; OHa 3aKoi11OtlaeTCSI B TOM. qro ,np06b 3 tJlIc.aa (HanpHMep, qHCJIa 60) Haxo,ltHTCH 3,neCb He YMHOJKeIlHe1 'IHC- 4 lIa Ha p06b, K8K 3TO 6yeT B CJle,nYIOI.UHX Kllaccax, 8 ,ABYMH eHCTBHH- 1\U1 - ,neJleHHeM H YMHO>KeHHeM. n 6 0 3 u YCTb, HanpHMep, Tpc ye-rCH HaHTH 4 nOJlOCKR, HleIDlI.\eH ,nJIHHy 1 . 3 24 CM. CHaqa.na HaXO,llHT - or 24 CM, nOTOM - H 3anHCblsalOT 4, 4 BbltlHCJleHHe CJIeYIOInHM oopa3oM; 24 : 4 = 6 (CM) 6 . ,3 = 18 (CM) O 3 24 T BeT: - OT CM paBHbl 18 CM. 4 298
CHaqa.na TaKaS! 3a,lJ.a'la pewaeTCH rpaHqeCKH, a 3ateM J{eTH HaXQ- ,lUIT OTBeT BblqHC1JeHMeM. npH 3aUHCH pelIleHHSI B BHAe ,lJ.BYX AeHCTBHI1 Y'lHTenb A06HBaeTCH qeTKOro pa3rpaHHQHBaHHH yqeHHKaMH BYX 3Ta- v .nOB: HaXO)KJleHHH CHaqaJla OHOH ,ltOJIH tlHCJIa, nOTOM UeCKOJ1bKHX .noJle . OAHaKO Ha TaKOH 3anHCH peweHHSI Ao.nro aa,Aep>KHBaTb yqeHHKOB He cJleAyeT; nOJIaHO nOKa33Tb yqeHHKaM aanHCb ABYX ,AeHCTBHH- YMHOJKeHHH H )teJIeHHH - 8 OHY CTpOtIKY B BHe O.ll.HOfO BbIpa}KellHH. 3 J HanpHf\'lep, perneHHe 3aJlalIH Ha HaXO}l{)teHHe - nOJ1OCKH, paBHOH.24 CM, 4 MomBO 3anHcaTb TaK: 24: 4 · 3. n r u -,",JIH npHMepa pellIHM 3a.u.aQy C 3anaCblO BbIQHC1eHHH. .3a,naQa. «KHOCK npo,na.n 3a ,neHb 1 200 Terpa,neii; H3 HHX : 6b1JIH 2 · u 6 u B K..1JeTKY, 5 B O)J.HY 1JJiHeHKY, a OCTaJIbHbIe bV1H B Be ..TJHIteUKH. CKOJIbKO npoaHO TeTpaeH B ABe HHeHKH?» KpaTKaH 3anHCb 3aa4H: { I 200 : 8 · 3 (TeTp.) - 8 KJleTKY 1290 TeTp. 1 200 : 5 · 2 (TeTp.) - B JIHHeHKY . x (TeTp.) - B ,l(Be 7]HHeHKH 3aa'-la pernaeTCH C 3aIIHCblO AeHcTBHH: 1) 1200 : 8 = 150 (TeTp.); 150 · 3 = 450 (TeTp.) B KoJ1eTKY; 2) 1200: 5 = 240 (TeTp.); 240 · 2 = 480 (TeTp.) B .TJHHeHKY; 3) 450 + 480 = 930 (TeTp.) B K,,1eTKY H JIHHeHKY; 4) 1200 - 930 = 270 (TeTp.) B Be JIH1HeHKH. o T BeT. B ;tBe JIHHeHKH 270 TeTpa,Aei%. n P 0 B e P-K a: 450 +_480 + 270 = 1'200 (TeTp.). B Bbl1JHCcJ1eHHHX YM HOiKeH He' M Ae.J1eHHe JlaHb! nOJ{ OJlHHM HOMepOM, TaK K3K nOcpeJlCTBOM 3THX )tBYX ,lJ.eHCTBHH pernaeTCSI O,ll,HH Bonpoc: «CI{OJIbKO npO,AaHO TeTpaJleH B KJleTKY?» HII1H «CKOJIbKO TerpaJleii npo- .lI.3HO B O,nHY .nHHCHKY?» Bnoc.ne.nCTBHH, KOf,na nO,LJ.06Horo po.na 3aaqH 6YJlYT pernaTbCH np" H3YtICHHJr CHCTefaTH'leCKOrO Kypca ,llp06efl, BbJtlHCJIeHHe OT 1 200 8 TaKiKe 6y eT COCTaBJlHTb O,LJ.HO ,l{eHcTBH-e. B xo,ne H3YQellHH 9TOH TeMbl nOTIe3HO npeJlaraTb .n-eTHM 3aaHHe: «CocTaBHTb 3a,Qatly no BblpaiKeHHIO: x = 60 : 4 · 3». l{o CHX nop no T3KOMY Bb!pa:>KeHMIO yqeHHKH COCTaBJIJIH 3aJlatlH, pellI3eMbIe °11 pHBe- ,neFlHeM K e,AHllHue. Tenepb no 9TOMY BbIpa.>KeHHlO aHK MorYT COCTaBHTb 3' 3a,naqy H Ha HaXO)KAeHHe - OT QHCII'Ia 60. 4 HanpHMep: «nOe3Jl 3a OAHH qac npoxo,llHT 60 ICM. KaKoe paccToHHHe e u 3? npoHeT noeaA npH TaKOH CKOpOCTH 3a - qaca.» 4 KpaTKa.H 3-anHCb 3aAaqH: 60: 4 · 3. 299
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paBHocropOHHQX TpeyrOJIbHHKOB H ,npyrHx cpHryp. Yqnrenb ,llO.71>KeH 06paTHTb BHHMaHMe Ha nOCreneHFOe YCJIO)f{HeHHe 3aaq. HanpHMep, npe)l{e qeM npHQrynaTb K peWeHHIO 3anatJH N2 249, HeOOXO.llHMO ,no 3TOro paccfoTpeTb 3aAaqy N2 226. Ee peweHHe MO}Ker 6bITb BblnOJl- HellO c nOMOInblO ypaBlIeIlHH: 2 . (x + 4) =.;. 12; x = 2. PerneHHe 3anaqH N 249 MomHO CBeCTH K HaXO}KAeHHIO B03MO}KllbIX 3HaqeHHH 6YKB a H b, ecJlH a + b = 6, r,ne a H b - HCKOMbIe ,nJlHH8 H wHpHHa npHMoyronbHHKa. - we,nyeT 06paTH'lb BHHMaHne Ha 33,natJY N 189. 3Ta H aHaJIOrHtJHbIe 3a;J.allH n03BOJIHIOT CBH3blBarb reOMeTpHtleCKHe qnfrypbI (TOtlKH, OT- pe3KH) C qHCJlaMH H HanpaBJIeHHeJ\.1 OTCqeTa (no.n.roroBKa K 3HaKoMcTBY c KoopHHaTHbIM MeTo,noM). OCHoBHaH >Ke -. ueJIb 3a.naQU - HanTH 'IHCJIO KBapaTOB (KJIerOK IIHCTa 6Yl\'larH), Ha KOTopble pa3eJ1eH npH- Moyro..'1bHHK. no cYW.ecTBY 3,neCb YtJaw.lj.ecH rOTOBHTCH K HaXO)K,lteHHIO n..TJOll.{a.llH MlloroyrOJIbHHKa. 113YQeHHe Mep .lI..71I1HbI CB5I3bIBaerCH C npaKrH4eCKI11 HMepeHHeM Orpe3KOB _Ii C nOC'fpOeHUeM OTpe3KOB 3a.llaHHoH ,nJIHHbl. npH 9TOM HC- nOJlb3YlOTCH 6YKBeHHble 0003HaQeHHH, n03BOJlHIOInHe KOpOTKO 3anli- CBaTb pe3YJIbTaTW H3MepeHHH HJIM cpaBHeHHB oTpe3KoB.HanpHMep: oTpe30K AB = 3 CM HJlH AB > OK H T. n. He06xo.llHMo 06paTliTh BHHMallHe Ha oTpaoorKY HaBbIKOB npHMeHeHHH l1HpI<YJIH .lI.,TIH cpaBHe- . u HHH OTpe3KOB H nHpKYlIH H ,TIHHeHKH JIH lIX H3MepeHHH. npH peweUHH reOMeTpHtJeCKHX 3a.llaQ MO}KHO npllMeHHTb OT,neJ1bHble Ka.npLI .lI.HB<pHJ1bMOB «K ypOKaM MaTeMaTHKH BO II JIacce» (reOMerpH- 'leCKHH MaTepHaJI), «npHMoyro..TJbHHK, ero nepHMeTp II n.710mab». 3a- .naQH Ng 47,-48 (AonOJIHHTeJlbHWe ynpa>KHeHHH) nOCBHeHbl norOTOBKe reOMeTpHlIecKoH HnJIIOCTpau.HH OCHOBHbIX npe,ncTanneHHH, Jlc*aIl.{HX B OCHOBe nOHHTHH p06H. reoMeTpHIIecKHH faTepl1an, paccMaTpHsaeMblH B CBH3H C H3yqeHHeM CJ10/l{eHHH Ii BbItIHTaHHH MHOr03HaQHblX qnceJl, COep>KHT 3a,Z{aQH, peweHHe !{OTOPbIX rpeoyeT 6o.71ee qaCTOf,O npHMeHeHHH UHPKYJIH H .71H- HeHKH. 3.necb YtJaw.HecH 3HaKOMHTCSI C ,lteJIeHHeM OKPY>KHOCTH (H KPy- ra) Ha paBHbIe qaCTH C nO:'vIOmblO nHpKYJlH. ,aeJ1eHHe oKpymHocTH H8 6 paBHbIx qacTeil (cnoBo «,Z{yra» npHMeHHTb He 06H3a'fe.J1bHO) CBH3b1- naerCH C nocTpoeHHeM npaBHJIbHOrO (paBHOCTopOHHero) lllecTuyrOJIb.. HHKa, a Ha 3 QaCTH - C nocrpoeHHef paBHocTopoHHero TpeyrOJIbHMK3. Ba>KHO, I.:J.rOObI YCBoeHHbIH npHeM JI.eJIeJUIH OKPY>KHOCTH Ha paBHble QaCTH CHCTeMaTHqeCKU npHMeU5iJICH YQal$itHCH npH peweHHH .n.pyrnx reOMerpHqeCKHX 3aaQ, CBH3aHHbIX, HanpHMep, C AeJIeHHerwf Kpyra Ha paBBble qaCTH, c nocTpOeHHel\.f KBa.llpaToB, paBHocropoHHHX TpeyroJlb- HHKOB If T. n. C l.\e.HblO yrOQHeHHH CBOHCTB oKpymHocTH paccMarpHBalOTcH sana- tJH N9 311, 339 H T. n. B HHX 9J1el\feHTbI, onpe.ne..'1HlOmHe nOHHTHe 01\,- PY'JICHOCmb, paccMaTplfBalOTcH B CBH3H C orpe3KOM, CBOHCTBa KOToporo B 3HaqHTP...,1JbHOH Mepe Y>Ke H3BeCTHbI YIlaII.J.HMCH. TaK, npH peweHHH 3a)J.atJH -N9 311 AeTH yGe>K,naIOTcH, 'ITO B 3TOM CJ1yqae paAHYc OI<PY)KHOCTH 301
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4. cl>opMHpOB3IIHe npe,LlCTaBJleHHR 06 e.IlHHH'-IHOM KBaJ1paTe, c nOMOIII.blO KOToporo IO}KHO Bcer,l{a o6HapY)KHTb, KaKaH H3 cf>Hryp HMeeT 66JIbIIIYlO nJlOrna,llb. 3HaKoMcTBO C KBaApaTHblM callTIfMer- pOM. 5. HaXO}K,llelllie nJIorn.a,llH pa3"TJlfllHbIX ,q>Hryp D KBa,apaTHbIX caHTH- MeTpax. na71CTKa (B I I I . KJIaCce). 6. BbltUiCJleHHe n.'10ma.n.H npH10yrOJlbHHKa B KBa.n.paTHbIX caUTH- IvteTpaX (B I I I KJIaCce) . 7. BbltlHCJIeHHe nJIOmaH B KBapaTHbIx AeHMeTpax (B III KJIaCce). 8. BbIQHCJIeHHe n.nOrnaH B KBa,npaTHbIX l\feTpaX (B I I I I{JIacce). 9. BblllHCJIeHlle nJlOIUaH 3Cfe.'lbHbIX yqaCTKOB (B apax H reKTapax B IV KJIaCce) . OCTaHOBH1\fCH u Ha KpaTKoH xapaKTepHCTHKe KaiK,noro H3 9TanOB. CpaBHeHHe arpe31{OB aeT B03MO}l{HOCTb Y311aTb, CDOpMMpolaHH8 KaKOH H3 OTpe3KOB .60.TIbllJe HJIH MeHbllIe t\pyroro. 06114NX npe.qCTal. Cf\fblqI 3THX OTHOIlleHHH ,llJIH OTpe3KOD onpee.lIHeT- ft8HWM 0 nnoaqaAN CH ,llOBOJIbHO tleTKO OH03HaqHO M H3f.'1HJ(HO. ClJNrypw nepe npOBe.n.eHHeM 6CCe)bI, r.l\e BnepBble 6y- ,neT MCn0J1b30naH TepMHII nAoU{aab £f>lIrypbI, Bail{IlO o60611JJiTb lIaKOnHB- llIHecH CBe,neHHH 0 cpaBHeHHII OTpe3KOB, OTIlOIllCHHHX «60JIbllIe», «MCHb- we», «paBHbI» ,llJ]H OTpe3KOB. YqHTeJIb HanOIHHaeT (npHB.neKaH OTBeTbl yqall.lHxcfI), KaK HX cpaB- HHTb. B pe3YJIbTaTe cpaBHeHHSI JII06bIX t\BYX OTpe3KOB Y3na1OT, KaKOH H3 HHX t5obllle (MeHbwe) H.,'IIi, MO)l{eT 6blTb, OHn paBHbI. 31'0 BbInOJl- HHeTCSI nYTeM Ha"T}O>KeHHSI O){HOrO OTpe31<a H3 ,npyroH (nOKa3). 3aTeM yqeHHKH HaYllaTCH H3MepHTb OTpe3KH. B pe3YJIbTaTC H3MepeHHH (c nOMOrnblO et\HHHqHOrO OTpe3Ka - e,aHHHUbI H3MepeHlIH) JIH Ka}KOrO OTpe3Ka OHH no.nYlIaT onpeeJleHHOe lIHC.no (npIlBo,aHTCH npHMepbI ,,'lH HeCKOlIbKHX orpe3KOB, H306paiKeHHblx Ha ,nocKe). 31'0 lIUClIO Ha3blBaeTCH aAUHOU OTpe3Ka. npH cpaBHeHHH, nanpHMep, ,LlBYX MHoroyrOJIbHHKOB M..'IH KpyroB yqarn.HMcH HCHO, tITO CJIOBa «60JIbllIe», «I\feHbllle» B 3TOM cnyqae HlelOT ,npyroH CMbIC"TJ, tleM B npHleHeIIHH K OTpe3J<al'ti1. ,[leHcTBHTeJlbHO, lITO l\fO,lliHO CKa3aTb, HanpHMep, 0 npHfoyroollb- IIHKax, H306pa)l{eHHblX Ha pUCYHKe 6? KOTOpbIH H3 HHX OOJIbllIe? OHn 6YYT YTBep)K.n.aTb, lITO ncpBbIH npHfoyrOJIbHHK 60..'IbIlle BToporo, TaR KaK OH ,1I.,,1HHHee. PyrHe npH,LlYT K npOTHBOnOllOJKHOMY BbIBOAY. OHH CKaJKYT, 4TO BTOpofl npH1'vtoyrO.JlbIIHK 601l'lblIIe - OH Bblille (H,lIB lllHpe). B o60nx CJlyqaHX ,lleTH T]H cpaBHeHHH npHMoyro..TIbHHKOB (MHO- . royroJlbHHKOB) npHMeHHJI,H OTHorne- HHH, YCTaHOBJIeHHbIe ,aJIH OTpe3KOB. B03t1MKaer He06xoHMOCTb cf>OPMU" pOBaTb npeCTaB.neHH 0 cncTcrvle HO- BbIX OTHOIlIeHHH l\teIKJJ.Y Mlloroyroollb- HHKaMH, BblpaiKeHHbIX 'ymc H3BeCTHbI.. fH TepMHHaMH - 60JIbllle, feHbwe II paBHbl. - 1 PtH;. 6. 304 2
A to PHC. 7. '%I 1.' . 'I. 1" '//. PrIC. 8. Ha6.rIIOa5I <l>Hrypbl, MO}l{HO 33MeTHTb, QTO O,nHa H3 JlHX, HanpHMep Kpyr A (pRC. 7), 3aHHMaeT 60JIbme MeCTa Ha n,,10CI{OCTH, qe{ qe!b1pex- yrOJ1bHHK B. ECJIH Mbl BblpemeM TaKO" qeTblpexyrOJIbHHK H3 6y- MarH, TO OH BeCb nOl\feCTHTCH BHYTPH Kpyra. , , B TaKOM CJIyqae rOB?pHT, 1JTO n.nOIl{ab Kpyra 60lbllIe n.'1oa. ,AH QeTbIpexyrO.,1bHHKa HJIH llJIOIl(a,llb qeTblpexyrOJIbHHKa 1\IeIlLWe llJIOrna.LlH Kpyra. PaCCMaTpHBaeTCH HeCKOJIbKO aHaJIOrHlIHblX npH. MepOB. 3aTeM paCCT\.faTpHBalOT C.TJyqaH, KOr,na CpaBHHTb n.TIOIna,nb (pHryp Ha rJ1a3 TPYHO HJlH npOCTO HeB03MO/KIIO. HanpHMep, nOIlbITKH no- leCTHTb O)lHY H3 Hryp BHYTPH (pHC. 8) JJ;pyroH (3TO MOiKHO npo)leMoH- CTpHpoBaTb Ha 6YMa}KHbIX l\{O,LleJISlX) He JI.aIOT OTBeTa Ha nOCTaBJIeHHbIH Bonpoc. <PHrypa I He nOMel1l.aeTCH nOJIHOCTbk) BHYTPH BTOpOH, a rpnrypa II HC nOMemaeTcSI DlIYTPH I. KaK >Ke 6blTb? KaK BbIHCHHTb, n.TJOma)l.b KaKoro n.pHl\foyrOJ1bHHl<a (cf. pHC. 9) 6oJIbwe? BOT 3,ZteCb H npHrOHTCH H3BbiKH (n'pHo6peTeH- HblC erne BO II KJlaCce) .neJIeHH5I cpHryp Ha paBHble <t>HrypbI (HanpHMep, Ha paBUb1e KSaJ1paTbI). Pa3e.,'HM Ka>K.lI.bIH H3 np5lMoyrOJIbHHKOB na paB- Hble <l>HrYPbl. ECJ1H MbI 3TH np5lMoyrollbHHKH p3CnOJIO)KH1 na KJICTqa. TOM 6YMare, TO TaKHfH paBlIbIMH cpHrypa!\.IH 6Y,LlYT KBa,npaTbI-KJIeTKH. Ta 113 4>Hryp 6y.neT HleTb 66,,1bIllYlO nJIOa,llb, KOTopaH COJ{ep>KHT 60JIblIIee, tIe:'vt Y JI.pyroH cpHrypbI, qHCJIO I{Ba.npaTOB-KJIeTOK. I-fl npHfoyrOJIb- HHK COACp>KHT (yqaw.HeCH YIKe lIaYQHJIHCb HCnOJIb30BaTb Ta6JIuu.y YM- HO}KeHI1H .n151 HaXOiK,neHHH QHCJIa K.fJ'eToK) 27 KBalI.paTOR, a 2-ii - 40 - . // % . " Z, / I'; 'f h- / - - '/ /. '/ '/./ '/ 'l -:/: .- -- -- -/ / /. // /. -- - 1 - '/ -I- 2 - >- - - /. ,,- / '/ I- - ! 1 PHC. 9. PHC. 1 u. 30&
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nJIOllI.aH 4'Hryp TaKIKC MO>KHO H3lepHTb. L!JUI 3TO- fa HY*Ha eAHllltu.a H3Me- peHHH. Y CJIOBHJIHCb ,lVISI H3Me- peHHH n..TIOw.a,neH <t>Hryp npHMeHHTb e;U1I1HQHble KD3J(- paTbi. 3TO TaKHe KBa.ApaTbI, CTopOHa KOTOpbIX paBHa e,l\H"HUC. 'f aKIUvll\iOJKeT 6bITb KBa,lJ.p3T co CTOpOHOH B 1 CM, HJIH KBaJtll3T co CTOpOHOH B 10M, HJlH KBapaT co CTO- pOHoA B 1 M. 3TOT KBa.ApaT npHHHTo {coOTI3eTCTBeHHo) Ha3LIBaTb KfJaiJpamftblM caflnllJ,telnpOM, Kl3aOpamHbl.lw ael{u,UempOAt, KBaOpamHblM MempOM. E){HHHlIHbIM KBaJJ;paToM MO>KeT OblTb H .nlO60H JJ;pyroH KBaJl.paT, HanpHMep OHa KerKa KeTqaTOll 6YMarH. Y tIalll.HeCH BbIqepllHBalOT KB3JJ;paTHblH CaHTHMeTp H .AJIH cpaBHeHHH PSl){OM - CaHTHMeTp. 11M cooow.aeTC!!! 1JTO 3anHCb «3 K8. CM» IIHTaeT'" CH: TPH KBa,npaTHbIX CaHTHMeTpa. IlpeJlJIaraeTcH HaqepTHTb 3 CM M 3 1\8. CM. OHM 3TO BblnOtlTIHHIOT no-pa3HOMY. TaK Cna1J3JIa HCKJnOqaeTCH B03{O>KHOCTb CMellIHBaTb 3TH pa3.nH1JHbIe nOHHTHH, MOO OHH YCBaHBalOT. CH He cpopMaJIbHO, a CBH3bIBalOTCH C peaJlbIlb[MH 06pa33MH. , Bblno.JlHHCTC7I pH.A ynpa>KHeHHH, r){e cpHrypbI pa36HBalOTCH Ha KaaA. pSTHble caHTHMeTpbI HJIH COCTaBJIHIOTCSI H3 KBa.ztpaTHbIX CaHTHMeTpOB. J1.JIH 9Toro Ka>K.lI.blH YlIeHH K ,ZJ.OJIiKeH H3fOTOBHTb Haoop H3 15-20 K8. CM. YqaHeCH Y3HaIOT, liTO eCJIH nJIOma)I-b O)I-Horo KBaJtpaTHoro caH- THMeTpa npHHRTb 3a e.ztHHHUY n.;rlorn.a){H, TO MO>KHO HaHTH n..T10ll(a.D.b .ZI.an- HOH ct>HrypbI B KBaJ{paTHbIX caHTliMeTpax. J1.JIH 3Toro HY>KHO COCqH- TaTb, CKOJIbKO KB3.u-paTHbIX caHTHMeTpOB COJl.eplKHT 3Ta <pHrypa. Ta- KHM 06pa30M, nJlorn.ablO Hrypbl (B KB3)J.paTHbIX caHTHMeTpax) Ha- 3blBaeTcH "lUCAO K9aapamHblX caHlnUMempOfJ, Ha KOTopoe 9Ta cpHrypa MO>KeT 6blTb pa3AeJIeHa (pa3pe3aHa). BbIHCHHeTCH, liTO H3MepHTb nJIO- lllMb cpHrYPbI - 3HaqHT HaHTH qHCJIO KBaJI.paTHbIX caHTHMeTpOB, na KOTOpbIe MO}KeT 6b1Tb pa3t1-e.neHa <j>Hrypa. Henocpe,l1CTBeHHbIM nO,Acqe- TOM IIHCJla KBaApaTHbIX CaHTHMeTpOB (pHC. 13) HaxO,l1HT, tlTO nJIOa;J.b I-H <pHrYPbl - 10-K8. CM, 2-11 - 12 1\.8. CM, 3-H - 15 K8. CM, a 4-H - 24 K8. CJt. npH BBe)J.eHHH nOHSlTHH 0 naJIeTKe CJIe.ztYeT BOC- HaXOHC.qeHHe nno- nOJIb30BaTbCH aHaJIOrHeH C MaCllITa6HOH JIHHeHKOH. aq8A" «I*rYDbI c no- M MOlqltlO naneTKJf «J. LI BbIHCHHJlH, qTO nJI011la.Ab cparypbI MO>KHO "3- MepHTb. D.JIH 9Toro Y Hac ecTb eAHHHua H3MepeHHH (KBa,apaTHb[H caHTHMeTp). .LlJlH H3rviepeHHH JI..'1HHbI OTpe3Kon HMeeTCH Cneu.l1a.'lbHulH HHCTpYMeHT. l\\bI C HHM XOpOlllO 3HaKOMbI. 31'0 MacwTa6- Pue. 13. 307
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npHMepHoe nnaHHp008HMe Y86HOrO MITepHana no M8T8MaTHK8 8 III KII8cce I TwcS1lfa (12 qaCoB) \1'2 YPOKa COAf'P >K3HHe ypOK3 nEPBAji 4ET8EPTb 1. PemeUHe npHMepOB na C..'I0>KeIlHe H BbltJUTaJUte B npe.ne- Jl3X 100 c ItCnOJlb30BaHHeM npaBH.rla npU6aBJH:\HHR ttucJla K cyt1e H BbllJHTaUHH tIHC..T1a "3 CYMMbI. HaXO>KAeIlHe HeH3- BeCTHbJX KOMnOHeHTOB .n-eACTBHH C.,10}f{eUIUI n DhllIHTaHHR. 0603HaQeIlHe 6YKBaMH Ii '1TeHHe TOlJeK t OTpC3KOB H JI.pyrHx reoteTpHlJeCKHX cJ>Hryp ...... ........ PelUeHHe IIpHMepOB H 3a.n-311 B npe)].{,l(aX 100 C HcnO,,1b30- B3HIICM npaBHJI npH6aB..'1eHHS1 CYIMbl K lIHC,,1Y II BLJlHITaHHS1 CY11bJ 113 lIHC.rIa. YJlpa>KIIeHIHI B CpaBHeHHH ltMeHQB3HllblX lIHCe..'I. BLllIUC,,'1eHHe neplfMPTpa TpeyrO..T1bHHKa. PeWeHHe ypaBHeHHH RHJJ.a: x + 7 = 18 H X - 16 = 35 . . . . . . PerneHHe npHMepOB C HCnOJlb30BaHueM npHE:'\1a nopa3pH):l- Horo 710>KeHHH H BblqHTalJHH Jl.BY3HalJllbIX tIHCeJl. Ynpa>KHe- HHH B 3annCH H tlTeHHH 6YKBeHHblX Bblpa}f(elll1i\ H BbltJHCJIe- HUH HX 3Ha(leHHH. npH .n-8HHblX tHJCoIl08blX 3HaqeHIHIX 6YKB. } la6Juo,41.eHHR 3a U3MeHCHUeM pe3YJlbTaTOB .lJ.eHCTBHSI CJlo}l(e- HIHI H Hb(qlfTallHSI B 3aBHClfMOCTIi OT H3MeHCHHH KOMI10HeU- TOR. COCTao.,1eHHe 06paTIIOH 3a,!J.atJH . .. .. .... IloBToprHHe Ta6..ruPHlblX c..'IyqaeB YMlIO}f{eUlf H lIHCeJl 2, 3, 4 I 5 Ii COOTBeTCTBYlOlIUi x '1yqaeB )J.eJleIlHS!. PCluellHe ypaB- HeHHH BlJ.!I.a: x. 3 = 18; 18: x = 3. nepeMeCTHTeJIbHoe CBoiicTBO YMHO>KeHHSI. COCTaBJIeHHe H pewelIHe 06paTllbIX 3a.a.aq. BbIlIeptJHBaHHe OTpe3KOB 3a.n-aHHOH ,a,,1UHbl . .. . . PemeHHe npHMepOB C IICnOJlb30BaHHeM npaBHJIa YMHO>Ke- UHB eYMbI na tlHc..'10 fI qHC..'1a Ha CYMMY. T aO,,1HtHlble c..'1yqaH YMHO>KeHHH qUCM 6, 7 , .8, 9 H COOTneTCTBYIOw.He CJIyttan .n-eJIe- HHH. PellleUHe npHMepOB H3 Bce ,aeHCTBHH B npe.n-c.nax 100. PellleUHe ypa HHellUM BH,aa: x · 3 =---: 12 + 6. PeweHHe 3a.n-a(j C npOnOpu,HOHa..'1bIlblMH He.lIH1JHHaMH H COCTaB.nCHHe K HHM 06paTHblx 3a.D.all ..... . '. .. ....... PerneUHe npHMepOB C HCOOJlb300alIHeM npanuoI,a JI-e,,"1eUHSI CYMl\fbJ na tlHCJlO, npHeMbI 8HeTa6..1HtJHoro YMHomeHUH H .n-e- ..TlenHS! B npe.n-e.,1 ax 100. PelIIeuHe 3a,!J.a II C npOnOpll.HOnanbHbI- MH Be,,1H t IHH3MII. BbIqeptlHOallHe OTpe3KOB H ynpa>KHeHHH n HaXO>K.n-eHHH tlBCTH no ueJIO1Y H u,e.,10ro no ero tlaCTH. nORTopeHHe YCTUOH II nHC"b\1eHIIOH HYMepaUHH B npe):\e- Jlax 1 000. CnyqaH CJIOmeHHH H BLflIHTaHHH KpyrJIblX tlHCe.n 8 npe,lJ.e.1ax 1 000 H CJJyaH C..'IO}l(eHHSI H BbltlHTaHHH, OCROBaH- Hble H3 SHaHHH HYMepaUHH. Ynpa>KllenHSI 8 YMeHbweHHH H YB1"qeHHH QHCJJa Ha neCKOJIbKO e):\HRHU H n HE:'CKOnbKO pa3, B pa3HOCTHOM H KpaTHOM cpaBlleHHH qnceJl. BbltfepllH- BaHMe TPf}TOJlbHHKOB pa3HblX aH.n-OB (no yrJlaM). .. . . . . Y CTHblC IIpHeMLI BbJ1Ufc..'IeIlHA KpyrJlblx qHeen (ace lJeTbJ- pe ,ZJ.eHCTBHH B npe;e..lax 1 000). PeUleJIHe. 3a.n-a'l 118 YMeUb- weHHe (yneollH'IelBte) tJnc..'Ia Ila. HeCKOTlbKO e)J.HIIUIJ. H B He- 2. 3. 4. 5. 6. 7. 8. CTp. yQe6HHKa 3-4 4-5 5-6 6-7 7-8 9-11 11-12 317
.. I n pOOOA3ICeItUe Nt Co CTp. ypoKI AepaaHHe YPOKa y'le6HRK8 CKOJJbKO pa3.. Ha<5..'IIO,AeHHe 33 H3MeneHHeM CYMMb( B CBH3H C H3MeHeHHeM O)J.HOrO '03 C.naraeMblX. KnaCCl-l(I>HKau.HH Tpe- yrOJIbHUKOB no yr.naM . . . . . . . . . . . . . . . .. 12-13 9. npHeMbl nOpa3pH.D.1I0rO c..10>KeHHSI H BblqHTaHHSI Tpex- SH8'1HhIX IIHCeJl.' HaOJ1IO.l1eHHSI 3a H3eHeHHeM pa3HOCTH B S8BHCHMOCTH OT lJ3MeHeHHH YMellbwaeMoro HnH BbJlIHTaeMO- roo PeweHHe sa,aaq lIa npHBe;!.l.eHOe K e.ZU1HMue. BblIIHCJ1eUHe ,l1JIHllbi CropOHbI KBaJlpaTa no ero nepHMeTpy. PeweHHe ypaB- HeHHR BH,AS: x: 6 = 43-37 . . . . . . . . . . . . -: . 13-14 10. nHCbMeHHoe CJ10>KeHHe H Bbl4HTaHHe B npe.l1eJ1ax 1 000. PeweHHe H cocraBneHHe 3a.n.aq Ha ,l1BH>KeHHe. PerneuHe ypaB- ueHHH EUJJJ.a: x. 12 = 72 ............... 14-15 11. CJlYllaH nHCbMeHuoro CJlO>KeHHSI H BhI'IHTaHHSI C ABOARblM nepexoAoM Qepe3 pa3psuJ.. Cnocoobl npQaepKH CJJO>KeHHSI I{ Bbl4HT8HHH. PeweHHe aa,u.aq na 118XO.>KAeHHe TpeTbero c.na- raCMoro no CYMMe H ,ltBYM U3BeCTHblM CJIaraeMbiM. Bb1Qep4H- BaHIIe KBa,lJ.paTa no ,l1allHblM TOttl<8M .......... 15-16 12. CnYllaH nHCbMeHHoro Bb(l[HTaHHB TpeX3Ha'lHbIX LJHce.1 - npH HanH1JHH B YMellbwaeMoM 1-2 Hy..'1eA H CJIO)KeHHe B cnY'IaJlx BHM: 254 + 146. PeweuHe Sa;;tatl C HcnO..rrb30naHH- eM npa8HJl8 ,lJ.eJIeHMB CYMMbI nB 'IHCJlO ........., 44-50 13. KQHTponbH8S1 pa6OTa, BKJlI01J8.IOw.aB npHMepbl Ha CJIO>Ke- UHe H Bblt{HT8HHe B npeAenax 1 000. C"nyqaH Ta6fIHtlHOrO H BHeTaMUqHOrO YMHOJKeHHSI H .o.e.neHWI. PeweHHe 38,Aa t 1H, BKnlO"I81OUJ.eA . nponopUHOHaJIbHWe _ BeJlHttHHI;i. PeweUHC ypaBHeHHH BH,l1a: x - 120 = 160 "' 318 1. HYMepaltHR MHorosHa'lHhlX '1UCeJI I , 3HaKoMcTBO c nOH.sITHeM CMaCC). BBeJJ.ellHe nOHBT-HSi «Mace TLlCR'I) H ynpaJKHeHHR 8 YCTaHoaneHHH BSaHMOCBSl3H Me>K)J.Y KJI.aCCaMH H paSpH.AaMH 'IHCJla. 3H8KOMCTSO C Mac- CHblMH ClIeT8MH H ynpa.>KHenHR C HX nOMobIO B no.nYlJeHHH H '1reHJIH 'tIempeX3H811HbJX, nRTH3Ha'lHblX H rneCTH3HaQHblX qHee.n. HaXO>KAeHHe IIHCJJO.BbJX 3Ha t (eHHH oYKBellllblX Bblpa- ,)KeHd. BW'IHCJIeHUe nepHMeTpa npSlMoyroJlbHHKa . . . . . Ynpa)KBeHHSI 8 06pS30B8HHH, qreHHH, 3anHCH qucen JUlaeta Tb1CJlQ. npneMbi YCTHoro YMHO>KeHHB KpyrJJOro QHCJla lIa OJl.H03HatfHOe QHCJ10. CnO>KeHHe H BbltfHTaHHe TpeX3HatfHhlX QHCeJl. COCT3BJ1eHHe 3a,l1aQ no AaHHblM $opMYJ1aM. 3anacb 6YKBeHHblx Bpa)({eHHH H HaxoJK,AeHKe ex \(liCJ10BblX 3UaQe- HHH .......... . . . . . . . . . . . . . . . 3HOMCTBO "C o6p830aaHHeM H qTeHHeM weCTH3Ha'IHblX qHCM, B KOropblx o(5a KJIaCCa COep)KaT e,D.HHHUbi Rcex HJUt ueKOTOpblx pa3pHl1oB. Y CTHoe peweHHe npaMepOB ua ace AeHcT8HfI C 'lMCB.8MH KJlacca TbiCgtl.. PeweHHe 8a.a,aQ c 6YK- BeHHblMH ,lJ.auHblMH, n0..:J.6op I.J.HCJJOBblX 3HBt)eHHH K UHM. nOA60p QHCJI08YX 3HaqeHHH H HB.XO>K)J.eHHe aHaqeHHH Bblpa- >KeHHA c 't5YK8eIIJIblMH J1aHHhlMH .................. YnpaH<HeHMH B QTeHHH H saUHCR MHOr03U8tU1WX tfHCeJI H B OTKJJaAhlBaHHH HX ua ctleTax, B pa3JJO>KeHHH HX Ha pa3pHA- 2. 3. 4. 17 -19 19-21 21-22
n pOaOA",eHUe HI ypoKa Co,Aep>K8HHe ypOKa 5. HbJe CJlaraeMbJe. BneAeHHe nOH5tTHSI cpaaeHCTBa) H «HepaBeH- CTBB». PeWeHHe npHMepOB H8 CJI0>KenHe H Bb(qHTaHHe B npe- JleJIa I 000 c npOBepKOA. BhItJHCJreHJfe nepHMeTpa paBHO- CTopOHHero TpeyronbHHKa . . . . . . . , . . . . . . Ynpa:>KHeHHH B sanHCH.H tJTeHHH MHOr03HaQHblX qHCen, B H83b103HHH 'IHCeJI, npe.z:tbIAym.HX ,naHHoMY H CJle,ltYJOw,HX 38 HHM. YCTHhIe BhlqHCJleHHH e MJIOr03Ha t lHblMH 1JHCJlBMH, OCHOB8HHble Ra SHaRHH .nec5tT8t1HOrO COCTaB3 tJHCeJl U HY- MepaUHH. PemeUHe sa)1a'l C QHCJ10BbIMH H "6ykBeHHblMH )J.8H- HblMH. Ynpa>KHeHHft B pa3JIH'leHHH paseHcTB H HepaBeHCTB. HaXO>K,neHHe nepHMeTpa npBMoyrOJlbHHKa .....1.. 3HaKOCTBO c npaeMOM YBenHqeHHB H yeHbweHHH qHC- Jla B 10, 100 H 1 000 pa3. PeweHHe npHMepoB H 3aaq C HC- no.nb30BaHHeM 9Toro npHeMa. PellIeHHe ypaBHeuHH. Pewe- Hue aa,n.atl cnOCOOoM npHse.neHHSI K eJUUIHue. Ynpa>KHeHUSJ B 3aKpen.neHHH 3HaHHJI pa3pAAHoro COCTaBa MIIOr03IJaQUblX tIHCe.'l H nOHSlTHB CKJIaCO .............. 06'bBClJeHHe cnoc06a BbJpa>KeHHH OTBJIeqetlHhIX H HMeHO- oaHHblX qHeeJI B 60J1ee MeJIKHX HnH 60J1ee KpynHhIx e)1HHH- uax. PeweHHe IIpHMepOB Ha YMHO>KeHHe H ,lleJIeHHe TpeX3Haq- HblX qHCeJJ C npHMeHeHHeM cnoc06a yaeJIH'IeHHSI H YMeHb- llJeHH5t qHCtI,a. B 100, 10 pa3. PeweUHe ypaBHeHHA BH)J.a: 42 : 3 - b = 9 . . . . . . . . . . . . . . . . . . . . 6. . 7. 8. 3HaKOMcTBO co cnoco60M BbJ,AeJleHHH H3 sa,lJ.2HHoro 'IHC- ..1]a Bcex eHHHU YKssBHHoro pa3pSl){a. HCDOJIb30BaHHe Toro cnoc06a npH pa3ttp06.lJeHHH H npeBpaw.eHHH HMeHOBaHHbIX ttHCeJJ. COCT8BJ1eHHe no 'IepTey 3a){aqg H8 BCTpeqHoe ABH- )f{eH He. , . . . . . . . . . . . . . . . . . . . . . 9. npn nOMow,H K.naCClIbiX C'IeTOB 3HaKOMCTBO e KJ1aCCOM. MIIJIJJHOHOB u ero paapH,A3MH. I.ITeHHe- \!HC'1 KJlaCCa MHJIoi1HO:- HOB. BbPIHCJIeUHe nepHMeTpa npSlMoyroJlbHHKcl ABYI\UI cno(;o- 6a 11{ ,....................... 10." Ynp3>KHE.1UISJ B ttTeHHH, 3anlfCH H onpe,AeJJeHHH paspn- Horo COCTana ,ll,eBlITH3HaQHbJX qHCen pa3110fl CTpYKTYPb1. 3naKoMcTBO C onpeAeJleHHeM ypaBHeHU5t H TepMHHoM epe- WHT& ypaBHeHHe). PeuleHHe sa,naq Ha npHBe,aeHHe K e){HHHI.J.e C Hcnonb30RaHHe1 YCTHbIX npHeMOB Bb[qHCJJCHHA n npe)J.eJI8X 1 000. PeweHHe ypaBHeH"" BHna: x · 3 + 12 = 27 ... 11.. Ynpa>KHeHUH B sanHCH H qTeHHH ){eBSlTH3Ha t IHhlX tlHCeJ1 B YCBoeHHH nOMeCTHoro 3UaQeH.HSI nH€j>pbl t B pa3J10>KeHHH MlIOr03Ha\IHb1X 'tHCeJ1 H3 pa3psUJ.Hlile CJlaraep..uJle. COCT8&'Je- HHe H peweHHe 3aJlaq. COCTaBJJeUHe 06paTHhlx saJ¥1q. Pewe- HHe HepaBeHcTB enoc06oM nOA6ppa.. . . . . . . . . . . 12. KOHTpo.'1bHaSi pa6oTa. npoBepKa 3H8HR5t HYMepanHH MHor03HatJHbJX qMeeJJ, YMeHHR YBeJlHqHBaTb H YMeHbwaTb tJHCJJO B 10. 100. 1 000 pa3 13. PeweHHe 3a.n.aQ cnoc06oM COCraRJIeHH.SI ypa8HeHHA e npH- MeHeHHeM npHeMa ypaBHHBaIlHSI. YnpamHeH!HB B YCBOeHHH HYMc:::paUHH .l1eBATli3Ha'Ulh1X qucen H nOMeCTHoro 3HaQeHHSI JJ.Hcppbf B 4Hc.ne. PeweHHe npHMepOB C' HCOOJIb30B8HHeM · ",pHeMOD YCTHbiX If UKCbMeHHblX BbltfHCJleHHA B npeAeJlax I CTp. )"IeC5RBK8 22-25 25-26 26-27 27-29 29-30 30-32 32-33 44-50 319
Nt ypoK 8 2. 3. 4. 6. 6. 7. 320 n pOaO1:JIC£-HU COAepmallHC ypoK8 100 H 1 000. OU06w.euHe 3HaHHSI 06 H3MeneHHH CYMfbl H pa3HocTH B 3aBHCMMOCTH oT,H3MeHeHHSI O,lJ.HOrO H3 KOMnOHell- TOB' . . . . . . . . . . . . . . . . . . . . . . . . . 1. Mepbl AJlHHbI H Beea nOHTopeHHe H3YQellHblX MCp' .lI.JlHllbl H COCT3BJ1enHe Tau- J1HLl.b1 Mep. 3HaKoMcTBO C npHeMo H3MepeHMSI AJlHHbI CTOpO- Hbi npSlMoyro.1JbHHI<:a c nOMOlD.blO U.HPKYJlSI H C npHeMoM epaB- lIeHHH ,lJ.JIHH oTpe3KoB c nOM'Ow.bJO UHPKYJUJ. COCTaBJleUHe 3a,l181J H8 Bb1I1HT8HHe IIHMa H3 CYMMbI H CYM1bl H3 qUCJ1a no ,l13UHb1M <lK>PMYJIaM. PerneHHe npHMepoB Ha Bee ,l1eACTBHH B npe,l1eJIax 1 000. PewenHe HepaBeHCTB cnocoooM no,a60pa. Y npa>KHeHH SI 8 Bb1pa>KeUHH OTBJlelleHHb1X H HMeHOS8HHblX 'IHCeJl B ooJlee MeJlKHX H S 60JIee KpynHblx e.n.HIIHu.ax H3Mepe- IUIH. PellJeHhe 3aJJ,aQ cnoco6ot COCTaBJIeHHH ypaoHeHHH. Ha6JIJO){eHHH 3a H3MeHeHHeM CYMMbI 9 3aBHCHMOCTH or H3:-'1e- HeHHSI OAHoro li3 CJJaraeMblX. BbtlJHCJleliHe lllHpHHbJ npSlMO" yronbHHKa no ero nepHeTpy "HHe . . . . .. .. - nOJlyqeHHe B pe3YJIb.raTe npaKTHlJeCKHX H3MepeHHA lJH- cen C OJ!,HHM H ABYMSI HH:\teHOsaHHSlMH. 3H3KOMCTBO C Tep- MHHaMH cnpocroe HMeHOBaH.Hoe qHCJlO), «COCTaBHoe HMeHO- B8HHoe IIHCJlOt. Ynp8>KHeJlHH B pa3.z(p06neHHH H npespam.e- HHM HMeHOBaIlHb1X IIHCM. Ynpa>KHeHHSI s cpaBHeHHR Bblpa- >KeHHA (pB3110creA) lIa OCHoRe, 3HaHHSI 3asHCHMOCTH Me>Kl(Y KOMnoneHTaMH H pe3}'JlbTaTaMH J1eACTBHSI BbIQHTaHltSi. Pe. rneHHe 3aJla'l cnOCOOOM COCTanJleHHH ypaBHeHUSI . . . . . . 3H8KOMCTOO C HOBblMH eAHHHU3MH H3MepeHHH Beea: ueHTHepOM H TOHHOH, COCTaBJIeHHe Ta6.'HUb1 Mep Beea. Yn- pa>KHeHHSI B BbIpa>KeHHU COCT313HbtX HMeUOBaHHb1X qUcen B 60nee MeJlIf1.lx Mepax ,C HCnOJIb30BaHHeM B sanHCH HyneA. 3naKOMCTBO c ypaBHeHHeM BJJAa: x · 3 + 12 = 27. Pewe- HHe saJJ,aq Ha c.nO)l(eHHe, Bb1pa)f{eUIIblX B I<OCBeBHOA ctx>pte. npeSpaw.eHHe H pa3Apo6,.neHHe HMeHoaBHHbIX 'IHCM, 0603HqaIOUJ,HX MephJ Beca. npaKTHtieCKHe_ ynpa>KHeHHH DO B3BeWHS8HHH pa3J1HlJHblX npeJlMeTOR " 3anHCb pe3YJlbTaTOB B3SeWHBaHIHI. PellleHHe 3aaq cnoco60M npHBe,!l,enHSI K eAH- HHne. PeweUHe npHMepOB Ha YBeJlHlJeUHe H YMeHbllJeHHe 'IHC- na S 10, 100, 1 000 pa3 . . . . . ". . . . . . . . . . . npeBpaw.euHe H pa3Ap06..'IeHlie UMeHQBaHHblX 'tHCe.", 0603HallalQLU.Hx Mf?pbI Beca. PeUJeHHe 3a.n.aQ Ha HaXO>KAeHHe CJlaraeMOro no CYM1 H )1BYM c.naraetbJM, O)1HO H3 KOTOpblX H3BeCTHO, 3 BTOpOC HeT. Ynpa>KHeHHH B pa3J1HQeHHH BHAOB TpeyrOJlbHHKOB no yrJI8M H no CToponaM, BblqHc.neHlte nepu- MeTpa. nOBTopeHue cnoc060R BblqHTaHHH QHc.na H3 CYMMbl "H CYMMb1 H3 lJHCJla ua 6YKoeHHbJX BhJpa>KeHHHX . . 6 . . . . npe8paw.eHHC U pa3Ap06J1eUHe HMeHOBaHBblX qHCJI, 060- 3HaQalOtU.HX Mepbl CTOHMOCTH. COCraBJIeHHe H peweUHe aa.!la- - qH nQ Ta6J1HLl.e C HCnOJlb30BaHHeM Be.'lUIIHU: ueHa, KO..'tUqeCT' 80, CTOHMOCTb. COCT3BJJeHHe sa;J.aq, o6paTubix eA. nocTpoe- Hlte npHMoyroJlbHHKa no 3a,l1aHH.OMY nepHMcTpy . . . . . CTp. YQe6SHK8 . , 44-50 33-35 36-37 37-38 38-40 40-42 2-43 43-44
YpoK8 8. 9, 10. 1. 2. 3. 4. 5. 6. 7. 8. IV. COA e IM{8UHe YP<?K3 /' nOBTOpeuHe Mep .l1J1HHbI. 8eca, CTOHMOCTU, ynpa>KUeHHSI B npeBpaIUeHHu H pa3Ap06JJCHHH H1eHOBaHHblX qHCeJ1, B ux cpaBHeHHH. 3aKpenJleHHe 3HaHHH HYMepaUHH MHOr03UaQ. IIblX qucen H pa3pR,n,Horo COCTaaa 9TH X QHCeJI. PeweHHe 3a. .lI.aq, H3YQeHHblX BHAoa Cl1oco6oM COCTaBJ1eHHSI ypaBueHHH. PeweHHe npHMepOB na Bce .neHCTBHSI B npe.l1eJlax 1 000 . . KOHTpOJlbllaR pa6OTa.. npoaepK3 IIOJIYllellllbiX 3H8HHH no TeMe «Mepbl J1JIH HbI, Beca, CTOHMOCTH). CnoMeHHe H BbI'IHTaHHe MHOr03HaQHhlX ItHCeJI 3HaKoMcTBO c nHCbMeHHblM CJIO>KeHHeM H BblqHTaHHeM MHOr03HaQHblX qucen. COCTaBJIeHHe pa3JIH t lHblX BIt,ZJ.OB npo- CTblX sa.ztaq no Bblpa>KeHHIO x = a + b. PeweHHe ypaBHeHHH BUM: C - 3486 = 52 872 . . . . . . . . .. .... B3aHMOCBR3b .lI.eACTBHH CJIO>KeHHH H BbltUlTaUHR. BbJlIHCJIeHHe 3HaqeHHH 6YKBeHHblX Bblpa>KeJlHH Ha OCHOBe SHaHUH B3aHMOCBH3H Me>KJ1Y CJ10>KeHHeM H BblttHTa- IIHeM. CocraMeHHe IIpOCTbl" saAaq no Bblpa>KeHHIO: x=a-b. PeweHHe COCTaUHblX 3aA8 1 1 Ha YBeJlHqeHHe (YMeHbweHHe) ff3 HecKOJIbKO eAHHHU H H3 H8XO>KAeHHe CYMMbI. BblQHCJ1eHHe .lI..I1"HbI .nOM8HOA nHHHH ............... 3H8KOMCTBO co cnocoOoM BblqHTHHSI MIIOr03HaQHblX qH- ceJl B CJIyqaSIX 8H.!J.a: 6 000 - I 375. PellleHHe HepaBeHcTB BH;J.a: a > 14. PeJJ(eHHe 3a;J.alJH C Be.'1H'IHHaMH: ueHoH, KOJIH. qeCTBOM, CTOHIOCTbIO, cnoc060M COCTaBJIeHHSI ypaBueHHH. npeBpalI1eHHe ". p83J1p06..,eHHe HMeHOBaUllblX qHCeJl ... YnpaJKHenHH B CJI01KeHHH MHOr03HaQHblX quceJl nplt Ha- nHtlHH 60JJee ,ZJ.BYX CJlaraeMblX, B BbltlHTaHHH C nynHMH B YMeHbwaeMoM. D.Ba cnoco6a npoaepKH CJIO>KeHHR H BbltlHT8- HHH. PeweHHe 3a,AaQ Ha HaXO>K,lJ,eHHe HeH3BeCTHoro YMeHb- lllaeMoro. HaXO>KJ1<:'HHe HaHMeHbWHX QHCJ10BblX 3HaqeHHH 6YKBellHbiX BDlpa>KeUHa BH4a: 9 + k, 15 - k. BblqHCJleHHe nepHMeTpa LJeTblpexyrOJ1bHHKa . . . . . . . . '0 · '.' · 3HaKoMcTBO C J1.ByMSI CI10C06aMH IIHCbMeHHoro CJlO/KeHHH COCTaBHblX HMeHOBaHHblX qHCM. CpasHeuHe ,AeAcTBHu Ha,A HMeH08aHHblMH 'IHC..'1afH. PeweHHe aa,Aaq C HCnOJlb30B8HHeM HMeHOBaHlibIX qHCeJl. Ynpa>KHeHHH B pa3JIO>KeHHH MHoro. 3Ha'IHblX qHCeJI Ha pa3pSIJJ.Hble CJlaraeMbie. 1J0BTopeuHe HY- Mepa1J.HH MIIOr03HaQnWX t(RCeJI . . . . . . . . . . . . . 3H3KOMCTBO C ABYMSI cnoco6aMH 8bl4HTaUHH COCTaBHblX KMeHOnaHHbUt 'IHCeJI. PeweHHe 3a,ZJ.aQ Ha BblqHTaHHe HMeno- BaHHblX qHCeJJ. Ynpa>KHeUHSI 8 COCTaBJIeHHH H peWCHHH ypaBHeHHA. BblQepQHBaHHe OKPY)KKOCTH no 3a)J.8HHOMY pa- J1HYCY . . . . . . . . . . . . . . . . I . . . . . . . nepeMeCTHTe.'JbHoe CBOKCTBO CYMMbI B CJlyqae CJlO>KeHHH 60J1ee .lI.BYX c.'1araeMblX. ,neJIeHlfe OKPY>KHOCTH Ha 3 H 6 pas- HbiX qacreii C nOMOInblO lI.HpKynR. PeweHHe" 3a,AaQ H8 CJlO- )KeHHe H BbItlnTaWfe. PeweHHe 3a,lJ,aQ c 6YKBeHHblMH .lI.aHHbI- MH ........................ COqeTare..'1bHoe C80HCTBO CYMMbI np" CJIO>KenIHI HecKOJlb- KHX CJJaraeMblX. npHeMhI C.T10>KeHHR H BblttUTaHHH MHoro- 11 3aK43 694. n pOaOjtJICeHll8 Corp. y\(e6KHK8 44-50 50-51 51-52 53 64 54-56 56-57 57-58 321
Nt ypoKI 10, 11. 12. ---- J 3, J 4 . IS. 16. 17. 1 8, 19. I. 322 CoAe pJK8HHe YPOI(8 9. SH3lJHhli qHCe.n Ha C'leTax (JlerKHe cJlyqan). CnO>KeHHe H BbI- 1JHT8HHe HMeHonaHHblX ttHCeJI. PeweHHe sa.naq H8 ,nOHJKeHHe PeweHHe sa,naq cnoco6oM COCTBBJJeflHH HecKOJILKUX ypaa- lIelluA. CnOH<eHHe H BbltlRT8HHe MHOr0311SQHbJX tlHcen. Ynpa)f(- ,BeHHe Ha OnpeAeJleUHe B3aHMOnOnO}l(eHHSI OTpe3Kct H OKPY>K- HCJCTH . . . . . . . . . . . . . . . . . . . . . . . . Ha6nJOAeHHH 3a H3MeHeHI1eM CYMbI B 38BHCIJMOCTH OT H3MeHeHHH O.llHoro H3 CJlarae1b1X. opMynHponKa npaBMJlC1 H HcnO..'1b300aUHe ero npH peweHHH npHMepoB U 3a.n.aQ. [lpl-l- Mepbl na CJlO>KenHe U BbltJHTaune MHor03H3tJHblX QHCeJl. PeweHHe HepaBeHCTB H yp8SHeUHA OHM: (410 - b) · 3 = = 60 ........................ Ha6.7Ilo,neHH Sf S3 H3MeHeHHeM pa3HQCTH npH H3MeHtHHH YMellbwaeMoro_ C1>OPMYJUJpOBK3 npalUIJJ8 H3MeHeH}t pa3HO- CTH H UCnOJIh30nailHe era npH peweHHH 3A)J.a'l. PeweHHe HepaaeHCTB cnocoOOM nOJJ.t5opa. BY'Iep'lHBaHHe npJlMoyro.'1b- HHKa no S8A1tHHblM cropoHaM. npHMepbl Ha Bee AeAcTBHSI C MJJOrO&H8'1HhlMH QHCJl8MH ............... Ha6nJoJteHHR sa H3MeHeHHeM PS3.UOCTH B .satJKCHMOCTH OT HSMeHeBHJJ BLLqHTaeMoro H 4k>PMYJ1HpoBKa 9TOH 38811C8- NOCTH, npHMeHeHHe nOJlyqeHHOrO BblBOA3 npH peweHMH npH- Mepoa H 98A&1I. PeweHHe saA8q. Ha odp8THoe npHBe,D.e!IHe K e)UlHIlQe. CJIO)f(eHHe H BblqHTaHHe COCTaBHblX HMeUOBaHHblX qlU:e.llr- Pemeaile aepaBeIJCTB. PeweHHe 31A-a'l cnoco(5oM cOcTaaneHHR ypaBHeHHR . . . . . . . . . . . . . . . . 3HaKOMCT80 C npHeMOM oxpyrJleHHH '1HCen H HCnOJlb30.. B8HHe ero JUI paUHOH8J1H3au.MH npHeMOB YCTHYX BblQHCJ1e- HH:A. PeweHHe sa.na'l Ha CJIO>KenHe H BbI'lHTaHHe C 6YKBeJlHhI MH J(aHHhlMH. nOCTpoeHHe npBMoro yr na Ha He.JIHHOBaHHOH t5yM are . . . . . . . . . . . . . . . . . . . . . . . . 3H8KOMCTBo- co cnocOOoM CJlOJKeHHR B BhlqUTaHHB H3 CIJeT8X B CJJyqae JIepeXOJJ.3 Qepe3 pa3pHA. CnO}J(eHHe H BbI'1H- T8HHe OTBJleqeHJlblX H COCTaBIWX HMeHOBaHJlblX IfHCeJI. Co- CTaBJJellHe 3U8Q no A8KHbIM 4>oPMYJIaM H ypaBHeHHH no )l.aH- HblM SaJI,aqaM. YnpU<HeHHSI no pa3BHTHIO npe.aCT8BJ1eHHH 0 B38HMHOM nOJlO1KeHHH reOMeTpHLJecKHX 4>Hryp (KBaApaT H Kpyr) ........................ nOCTpoenHe npH!\toyrOJJbHMKa (KBaJtpaTa) fa HeJlHHOBaHHoft 6Y:Mare. PeweUHe 3aJ.laQ pa3HblMii cnocoOaMH. nOBTOpeHHe l-I3MeHeHHJI pa3Hocm 8 380HCUMOCTH OT M3MeHeHHB BbI'lHTaeMOro KOJITpOJlbHaJi pat50Ta " BTOPAJI lIETBEPTb CKOpOCTb, BPeMB, paCCTORHHe PaCKpblTHe 83aHMOCBSl3H Me>KY aenHtJHHaMH: CKOpOCTb, BpeMB, pacCTOSlHHe. COCTanneHHe, peweHHe H ssnHCb B Ta(S. Jume sa.aaq C 3TUMH BeJJUqUHaMH. PeweHHe YPSBlleHH:A. CpaBHeHHe CYMMU H pasHocTH H8 OCHOBe 3J1aUMR H3MeHenHn pesynbTaToB 3THX AeHcTBHA. B 3aBliCHMOCTH OT H3MeHeJJHH KOM nOllellTOD . .. .. .. -. . . . . . . . . . . . n pOOOAxenue I CTP · yq(hJJ'Ka 58,59 59,60 61-63 63-64 64-66 66-67 67 68-69 75
Nt . YPOK8 Co,ltep Ht8t:I He .ypoKa n pOiJoA:J1CeHUe CTp. YlJe6UHK8 2. 3. 2. 3. 4. 5. 6" 11. 3H8KOMCTBO ,CO CnOCooOM tlaO)J(AeHHft paCCTOHHHft ne H3BeCTHbiM tKOpOCTH H npeMeHH. PeWeHHe COCT8BHblX 3a,A81J lIa H8XO)KAeHHe paCCTORHHfI. PeWeHHe S8AaQH H8 HaXO)l(- ,!J.ellHe CKOpOCTH no paCCTORHHIO H BpeMeHH. Ynpa>KHeHHe B H3MelleHHH 3UaQeHHfI 8pa>KeHHR B CBH3H C H3MeHeHHeM 3HaqeHHR OYKBhI. Ynpa}KHeHHe 8 1(eJ1eHHU 4>HrYPbI 113 qaCTH ................,....... 3H8KOMCTBO co cnoc06oM HaXO>K,AeHIISI npe\1eHH ABHJKeHHfI no H3BecTHblM CKOpOCTH H paCCTOSlI1H10. 0606I.D-eHHe B3aHMO- CBR3H . Mf>Kl1.Y CKOpOCTblO, speMeHeM H paCCTOHHHeM. Pe- weHHe npliMep08 Ha CJ10JKeHHe H BbltlHTaHHe MHOr03fIa1.lUb(X qHcen. rnpa>KUe(fHe, nOArOT3BJ1HBaJOUJ,ee K paCCMOTpeUHIO nJIOllI.a.lI.H " . . . . . . . . . . . . . . . . . . . . . . 1. YMH01KeHJ.te HI O,l(H03I1a4Hoe 'IHCJlO Onpe,Ae.neflHe .lteHCTBHH YMHO>KeHHH Ira aCROBe 3HaHHn B3aHMOOBR3H Me>K.L\Y CJIO>KeHHeM H YMHO>KeHHeM. COCTaBJle. Hsfe npOCTblX 33,Lt8t1 Ha .YMHO>KeHHe no Bblpa>KeHHIO a · b. nOBTOpeHHe oc06b1X CJlyq8eB YMHO>KeHusr C HYJleM H e.ltUHR- LleH. CocTaa.nenHe H pemeHHe S8,lJ.aQ 1Ia .l18H>KeHHe C BeJIHt(H- lIafH: . CKOpOCTb', BpeMH, paccToHHHe .......... nHcbMeHHoe YIHO}{{eHHe MRor03HatjHoro ttRCJIa Ha O)l,Ho- 3UaQHoe. PeUJeHHe npHMepoo H 3aAaq. nOBTOpeHHe np3SI'Ina YMH01KeHHSI CYMMbI H8 tfHCJlO. CJlrttaH .l].e.'1eHIIH c HYJlM H e,AHHHneA. Ynpa>KHeHHH H3 onpe,neJJeHHe B3aHMOnOJlO>Ke- nHSI reOMeTpHQeCKHX Hryp npSlMO}TOJlbHHK8 H TpeyrOJIb- HHKa ........................ nHCbMeHHoe YMHOJKeHHe MHor03HaHHblX qucen aa O,nHO- 3KatfKoe. OcOr;b(e CJlyqaH - HYJJH B cepe,D.HHe MHO>KHMoro. COCT8BJIeHHe H peweHHe 3a,naQ C BeJIHqHHaMH: Bblpa60TKa B qac, apeMH pa<5OTbl H 8CH Bblpa6oTKa. nOC1'pOelIHe npHMo- yrOJIbHHKa no 3a,D.aHHhlM cTOpOna'-{ Ha HeJIHHOBtHHOH 6YMare. . Hawuo.aeUHR 33 H3MeHeHHeM npOH3BeAeHHSI B 3aBHCIIMO-, CTH err H3MeHeImSi O)J.Horo H3 COMHO>KHTeJlelf. cJ>opMynHpoBKa COOTBeTCTBYlOlUero Bbl:BO,na. PeweHHe npHMepOB C HCnOJIb30- B3HHeM npHeMOB nHCbMeHHoro CnO>KeHHH, Bb[qHTaHHSI H YMHOJKeIIHSI. PcweHHe COCTaBllblX 3a,AaQ. BK.'1I0 l lalOIUHX npo- CTble 38.l].atlH, Ha }'MHO)KeHHe, BbIpa>KeHHble B !{OCBeHHOA opMe . Ynpa>KHeHHH. nOlJ.rOTaBJII1B31Ow.He K BbltlHCJIeHHIO nJlo- w.a.ltH npaitoyro,,1bHHKa ................ 3H3KOMCTBO co cnOCOOoM COCT38JJeHHH ypanneuHSI npH, peweHHH 3a.n;aq. Ha6J1IO.l1eHHSI 33 H3MeHCHHCM npOH3BeAellHSI B 3aOHCHMOCTH OT H3MeHeHH H o,lUtoro H3 COM HO>KHTeneH . Pe- weHHe npHMepOB C Hcnonb30BaHHeM npHeMOB nHcbHHOro CJlO>KenHH, BhlqHTaH}JSI H YMHO>KeHHH . . . . . . . . . . 3H8KOMCTBO c nOHHTHeM cn.rroU(a,D.bl. CpaSReUHe nJIOIlla- AeH npRMoyronbHb(X cj>Hryp cnoco(5oM nO,D.CqeTa KJIeTOK, H3 KOTOpblX OHH COCTaBJIeHbI. PeweliHe 3a,!J.a1J Ha nponopURO- HaJlbUYJO 3aBRCHMOCTb. Me>KY BeJlHqHHaMB cnoco60M co- 76-77 77-78 78-79 79-80 81 82-83 83-84 ' 323
Nt y poK.:1 10. 11. 12. 13. 14. 15. 324 n poOo/l3lteHUe COAep>K3HHe YPOK3' CTp. YQe6HHK8 7. CTaBJIeHHB ypaBHeHHJI. nHCbMeHIIOe CJlO)KeHHe, B-blqUTaHHe H YM HO)f(ell Ke MHOr03H81JHblX qHCM . . . . . . i. 85-86 Y M HO>KeHHe HS OAH09Ha'iHOe '!MCJlO B CJJyqaHX, KOr.na -MHO>KHMOe OKaHtfHBaeTCB HYJlSlMH. Ynpa}KHeHHSI, nOllrOT8s- nHBalOlUKe K BbltlHCJleHHIO nJIOlijaJ1H. PellJeHHe 38)1.8 1 1 H8 Ha- XO>KAeHHe TpeTbero cnaraeMoro. COCTan..1JeUHe H pemeHIJe 38AalJ. 06paTHbIX HM . . . . .. . . . . . . . .. 86-B7 nOBTopeHHe H saKpen.neHHe npOH.AeHHoro. COCTaBneHHe ct>OPMYJIbI npH peweHHH 3a.n.all. PellleHHe 3BAall H8 B38HMO. CBfl3b MeiK.llY CKOpOCTblO, BpeMeHeM H paCCTOHHHeM. I1cno.1Jb- 30B8HHe nepeMeCTHTeJlbHOrO CBOHCTB8 npOH3BeAeHHH npH YMHO)KeHHH. PeweHHe ypaBHeHHH. CpaBHeHHe nJ10w.a.n.eJ.. q.Hryp nYTeM nO,ACqeTa I<BalI.pTODt HS KOTOpblC paa6HTa ct>H. rypa . '" ......... .... i .. 88-89 3HaKoMcTBO C KBBn.paTHbIM caHTHMeTpOM KaK e,.l:lHHHuen H3MepeHHH nJlow.aJI.H. H3MepeHHe nJlow.a.lUf cpHryp npHMO. yro.1JbHOH Opbl cnoc060M nOlI.C4eTa KBaApaTHbIx C3HTHMeT- pOB. CpaBHeHHe IJJlOUJ,a.lI.H H nepHMeTpa O.lllloR reOMeTpHlfe. CKoA c»HrYPbJ. Ynp(j)KHH"H B nHCbMeHIlOM YMHO>K.eHHK H3 OllH03H84Hoe lJnc..1JO (Bee H3Y4eHHbJe CJlY48H). Ynpa>KHeHHH B npeBpaw.eHHH H pa3lI.p06JIellHH HMeHOBaRHb1X qHCen. 89-90 3H8KOMCTBO C npHeMOM YMHO>KeHHSI COCTaBHoro HMe.. HOBaHHoro qHCJla Ha OJl.H03HalJHOe tlHC.'10. Ynpa>KHeHHH B H3XO>K.lI.eHHH 3HaqeHHA: 6YKBeHHblx Bblpa>KeHHH C Hcnonb30' BaHHeM 3H3HHH H3MeHeHHSI npOH3BeJIeHHS1 B 3aBI1CHMOCTH OT H3MeneUIIH O.llHOro H3 COMHO)f(HTe..1efl. Bbl4HCJleHHe nn0lI13- AH reO1eTpHqeCKlfx ct>Hryp nYTeM no.n.C 1 leT8 I<Oa.lI.paTHbIX c3HTHMeTpoB . .... .. .. 91-92 PemeHHe npHMepOB H 38lI.aQ Ha YMHO)l(eHHe COCTaBHoro HMenOBaHlloro 4HC.TJa Ha O.llH03Ha t lHoe tJHC.ll0. BblqHc.neHHe" cpaBHeHHe nJlolll.altU K nepHMeTpa O.llHHX H Tex me npKMo- yrOJ1bHHKOB. Bbl'lHCJleHHe lJHC..'JOBblX 3HaqeHlfH 6YKBeHHbix Bblpa>KeHH" npH ".naHHblX 3Ha i lCHHSlX BXO,lUHll.HX B HHX 6YKO. 92-94 BblBe.lI.eHHe «t>9PMYJlbI BbI4HcJleHHH nJIOma,lJ.H npSlMo- yrOJIbIlHKa: S = a · b, BbJ11 HC.TfCHHe nJlOl11.3JUI Ha OCHonc Cct>OPMYJlHpoBaHHoro npaDHna. PemeHHe 3a.n.aQ cnoco6ot COCTaB..TJeHHfl ypaBlIeHHH. Ynpa)KHeUHH D ytIlO>KeHHH co- CTaBHoro HMCHosaHHorQ tlHCna H3 0.D.H03H8 t IHoe 11 HCJlO, B CJlO>KeIlHH H BbllIHTBHHH MHor03H8 1 )HbIX 'Hlce.TJ. . . 94-95 3H3KOMCTBO co cnocoooM npH6J1H>KeHHOrO H8XO)KAeHHSI nJIom.a.nH Hryp pa3J1HIIHOf; ctJOpMLI c nOMOllJ,blO na.neTKH. I Ynpa:>KHellHSI B flHChMeHHOM YMHO>KenHH l1a OltIl03HaQnOe IJHCJIO, B CJlO>KeHHH H BbJLJHTaHHH MHOr03HaQHblX ttHCeJl 95-96 YnpaiKHellHS1 D DL1'IHCneHHH nJlO1ll3ltH npJlMoyro.nbHHK(1 no <lJopMYJIe: S = a · b. CpaBHeHHe n.TJOlI1a,lJ,H npH)foyrO.Tlb. HHKB C ero nepHMeTpOM. PerneHlIe 3B.lla4 C nOMolllblO cor. TaBJJeHKSI ypaBHeHHH. PeUJeHHe npHMepon Ha YMlJO>KeUne. ,l\e.neHHe, cnomenHe " DLl4UT3HHe MJlOr03UaQllbJX qHCM 115-123 BhllJHCJleHHe n.nowaJUi npSlMoyro.'1bHHK3 no c»opMY.'1e S = a · b H BbltIHC.YJeHHe nJtoaH .npyrH"5 reOMeTpHlIeCKHX 8. 9. ,
n pOdOAJlCeHUa Nv YPOK3 COAep >K3HHe ypoKa CTp. y'.((6HHKa 16, 17. 2. 3. 4. 5.' 6. 7. 8. <t»Hryp C nOMOll1blO naJleTKp. COCTaBJHHHe 3a,ltaq no cl><>PMYJle. BbJ'IHCJIeHHe QHCJl08bJX 311aqenHA 6YKBeHHblx Bblpa>KeHHH npH A8HHblX 3HaqeHHSlX BXO,ltHUJ.HX B HUX tsYKB. PeweHHe npHMepoB H8 see AeAcTBHH . . . . . . . . . . . . . . l(oHTponbHaH pa6oTa.. npoBepKa YMeHHH yqalltHXCH pewaTb 3a,l1aqH H npHMepbl Ha YMHO}({enHe MHOr03Ha'iHOra tJHCJla Ha OJlH03HaQHOe, YMeHHSI BbI'IHCJlHTb nJI01l18,ltb H nepH- MeTP npSlMoyronbllHKa, 3HaHHSI 3aBHCHMOC-TH npoH3aeenHR OT H3MeHeHHSI oAHoro H3 COMHO>KHTeJleA. PaooTa Ha,lt OWH6- KaMlt I. AeneHHe Ha OAH03HaHoe qHCO B3auMocBSl3b ,l1eJ1eHHH H YMHO>KeHHH. COCT3BJ1eHHe npo- CTbJX 3aaq Ha ,l1eJ1eHHe no Bblpa1KeHHIO a: b. Ynpa>K- HellHSI JJ.JIH aaKpenJIeHHSI 3H8HHSI B3aHMOCBSl3H Me>KAY KOMnOHeHTaMH H pe3YJlbT8TOM AeiiCTBHH AeJleHHH. Pewe- HHe 3aAaq C BeJlH'IHHaMH: CKOpOCTb, BpeMH, paccToRHHe npHeMbi YCTHoro ,AeJIeHHH MHOr03Ha\IHblX tJuceJJ lIa O.aHO- 3HaQHoe. PeweHHe 38,ltaq H8 YMHO}({eHHe H ,lteJJeHHe. Ha6JJIO- AellHH 93 H3MeHeHHeM 3UaQeHHA CYMMbI flpH H3MeHeHHH qnc- nOBOro 3HaqeHHR O,ltHoro H3 CJJaraeMblX H 3a H3MeHeHHeM 3HaQeHHH pa3HOCTH npH H3MeHe((JUI BblQRTaeMOro, 3a.a8HHoro Bblpa>KenHeM BHAa (52 + a) .............. 3H8KOMCTBO c nHCbMeHHblM AeJIeHHeM MHor03Ua t lIJOrO tlHCJIa Ha 0,lt1l03HaIJHoe. PeweHHe 33,AaQ Ha eJ1eHHe. BblqHC- JleHHe M0ll18,lU1 npHMoyrOJIbHHK8 no 4»oPMyne S = a · b. nHcbMeHHoe ,lteJIeHHe MHOr03HaQHblX QHCeJJ H3 0,l1n03HaQ- Hoe (CJJYQall AeJIeHHB C HyneM B cepe,ltHHe HJlII 8 KOHne qaCT- Horo). BhlQHc.neHHe nJIOl1{a,AH H nepHMeTpa npSlMoyrOJlhHH" Ka. PeweHHe 3,AaQ Ha BCTpeQHoe ,l1BH>KeIIHe; 3HaQeHHe repMHHa «O,AHOBpeMeHHO) ............... Ha6.nlO,lteHHJI 3a H3MeHeHHeM qaCTHOro B 3aBHCHMOCTH OT H3MeHeHHSI ,lte.1JHMoro. nHCbMeHHoe ,lte.neHHe MHOr03na\fHblX qHCM H3 O,ltH03HatJuoe. PeweH1ie S3AaQ cnOCOOOM COCTaBJIe- HHH yp8BHeHHSI. BblllHCJJeUHe nnOw.8JlH H nepHMeTpa npSl- Moyr()JJbHHKa .................... 0606ll1eHHe Ha6J1lO.,AeHHH 3a H3MeHeHHeM 1.JaCTIIOro 8 sa- BHCHMOCTR OT H3MeHeHHR .lteJIHTeJ1H. $>pMYJlHpOBKa BblBOJ:t,a. KpaTK3H 3anHCb nHChMeHHoro AeJIeHHH. Ha6Juo,Ae1IHSI 33 H3MeHeHHeM pa3HOCTH B 3aBHCHMOCTH OT H9MeHeHHR BhlqHTae. Moro. J:{eACTBHR C MHoro3HaQlIblMH QHCJIaM H ...... PaCKphlTHe nponopllHOH3JIbHOH SaBHCHMOCTH (6e3 Bse- ,lteHHJI repMHHa) Mey neHoA, KOJIHQecTBOM, CTOHMOCTblO. CnO>KeHHe. BbJ1IHTaHH, YMHO>KeHHe H ,AeJleHHe MHOr03HaQ- (fblX qHCeJI . . . . . . . . . . . . . . . . . . . . . . 3H3KOMCTBO C ,AeJleHHeM cocTaBHoro HMeHoa8HHoro "IHC- na Ha OAH03Ha q}{oe. PemeHHe npHMepOB H sa,ztaq HB AeJleHHe cOCTaBHoro HMeHOBaHHoro QHCJJ8 H8 0JJ.H03HaqHoe ClHCJlO. CocraBJIeHHe 3aJ(aq no KpaTKoA sanHCR Ha 38BHCHMOCTb 115-123 96-98 98-100 100-101 101-102 103-104 104-105 105-107 325
n pO OO/lJICe HUe Hi ypOK8 COAep HlaHHC ypoH.8 1 CTp. yqe(SIfBKa 12. 13. 14. 15. 16. 17,18. 326 9. Me>K).\Y nellO" , KOJJHtJeCTBOM, CTOHMOCTbJO. PeweHHe ypaRHe- IIHH 8H,aa: a + 16 · 10 = 320 . . . . . . . . . . . . . 3HaKOMCTBO co enoe06oM peUJeHHSI Tpex BII.lI.OR 3o.u.aQ HB BCTpeQHoe )J.BH)I{eHHe B HX B3aHMOcnH3H. BbJBe,lJ.eHHe 4>oPMY- JJhI peWH"H 3a;J.aQ KB>K)).oro BH,lJ.a. Haxo>KJJ.euue 3UaQelHiH Bblpa}KellHA t B KOTOpble BXO.u.SlT OIIepaUUH C lJaCTHb1M (YBeJUI4eHMe H YMeHbUJeHHe) . . . . . . . . . . . . . . PeWCHne H COC.TaDJIeHHe 33Aaq Ha 38RHCHMOCTb MeJl(JJ.Y u.eHOH, KOJIHttecTBOM, CTOHMOCTbIO. Ha6JII0.l1eUIHi 3a H3Me- neUHeM CTOHMOCTH B 3aBHCHMQCTU OT H3Mene1lHS1 uellbl npH HeH3MeHJJOM KOJJH\feCTBe. JI.eJJeHHe COCTaBHoro J.tMe]]OnaHIIOro 'IMCJla UC1 0,nn03Ha4Hoe "'MeJlO ............ I-JaXO>KAeJlHe CTOpGH npSlMoyro.nbHHKa no .LI.311HOH n.no- m.a.ll.H H OAliOH 83 ero CropOH (JtJlHHe HJlM mHpHHe). Co- CTt1BJ1eIlHe Ii peweHHe 3a.naQ na nponopllHOHaJlbHYlo 38HHCH- MOCTb Me>K,ny ueHoH. KOJI, HIJecTBOM CTOHMOCTblO. COCT3llJ1e- HHe H pewenne 38JJ.8lJ, 06paTHbix H .......... Ha6JIIo.neHHSI 3a H3MeHCHIHM ueabJ B 3aBHCHHOCTH OT H3' MeHeHHH KOJJHtleCTBa H KOJIHQeCTB3 B 3aBHCHMOCTU OT H3Me- HeHHH lleHbl npH HeH3MeHUOCTli CTOHMOCTH. nponepKa YMC- .nHR 8bJnOJlHSlTb nHcbMruHoe ,n€'JleHHe COCTaBlloro HMenOB3H' noro qHCJJa. YMJlO>f<eHHe H )).eJleHne MHOr03Ha\IHblX '1HeeJJ lIa OAH03HaQHoe qHcnO . . . . . . . . . . . . . . . . . . nOBTOpeHHe npOnOpLtHOnaJJbllOA 3annCHMOCTH Me>KAY ue- HOW, KOJlHqeCTBOM H CTOHMOCTbIO. PewellHe n38HMoo6paTHbiX sa,naq. CBR38HHblX C BbJ1JHCJJeHHeM nJlOw.a,nH npHMoyro.b- JlHK3. PellleHHe ypanneuHU BHAa (x + 70) · 4 = 320. Pe- meHHe CJJOJKHblX npHMepoB H3 Bee IJeTbJpe .n.eACTBHSI. YCTlJOe AeJJeHHe MHoro3IfaQllOrO 1JHc.na Ha 0.D,1I03na\IHoe C onopoii Ha npaRIIJ10 J1,eJ1eIJHH eYMMbJ Ha tJHCJ10 . . . . . . . . . " Y npa)J< IleHHe 8 pelilCH HH Tpex BH.D,OB S8.n.3tJ ua BCTpeq Hoe )).BIt>KeHHe. PeweHHe 38Aaq . c nOMOIlJ,blO COCTaMCHliSl He. CKOJJbKHX ypaBlJennA. PewenHe CJlOJKllblX npnMepOB Ha occ 1.JeTbIpe .lI.eHCTBIUI. BbJ\HI'1ell He n_10m3,lI.H npHoyrOJJblIbiX <pH- 10. 11. ry p . . . . . . . . . . . . . . . . . . . . . . . . . PemeHHC npHMepOR H8 YMHO>l{eHHC H .lI.eJ1eHHe MHor0311a.Q. HbiX QHce.'1 na OJ{H03HaQuoe IJHCJlO. YMHomeHHe H JJ.eJJeHlie COCTaBHblX HMenOB81IJJLJX queeJJ na O,nH03113'1noe. PemeJHle sa)J.a" H3 3aBHCHMOCTb Me>K.lJ.Y CKOpOCTbJO, BpeMeneM H pac, CTOHHHeM. PerueHHe HepaBeHCTI3 BUJ{a x + "25 > 40 H ypaB- HeHHfl BHA3 90 · 4 + x · 9 = 540 ........... HaXO>K.lleHHe 3HaqeHnH BblpaJKeHHH, B l\oTopbIe BXOAHT OnepaLtHH C npoH3BeJJ.eHHeM H II3CTnblM (yneJIH'IeHHe Ii YMeHb- meHHe). BbittHCJleUHe nJIow.aJJ.H H nepHMeTpa npHMoyro..1b' HHHOB C nOMOIlJ,blO q.OPMYJJbJ H nJlom.a,lJ.H )I.pyrHx «t>nryp eno- co6o1 nO}J.CtJCTa KJleTOK. Ynpa)f(HeHHSI B Bbl l Jep1.JHBaUliH OKPY>KHOCTH. COCTanJlCHne 3a;'J.()I' no opMYJlaM . . . . . . KOHTponbllaH pa6oTa. IlpoBepKa YMeHHH pellJaTb S8)I.a- LJH, YMelfHe lIaXO,l1HTb J1JJHny (WHPHUY) npHMoyrOJJbHHK3 no ero nJlOU\8.l1H 11 llllipHHe (AnHHe). YMeHHe AeJlHTb MIIOro3Hlt1 "hie '1HCJla HB oAH03HaIJHble, BhI'IHCJlBTb SHaqeHHH Bblpa}K. 107-108 108-110 110-111 "111-112 1]2-113 113-114 114-115 1] 5-123 115-123 I
M I ypoKa 19. 20, 21. 3, 4. 5, 6. 7. 8, 9. 2. CoAp)Kalnie ypoK8 HHH, Koropble BKJIIOqalOT OnepaItHH c qaCTKb[M (YBeJUltteHH- eM, YMeHbweHHeM) PaOOT8 Ha.n OWROKaMH YpOKH OTBO,D.SlTCH NUl pa60Tbl no M3TepHanaM ,AnSI 11.0- Uo..'lHHTeJ1r.HblX Yf1pa)K[[eHJfH . . . . . . . . . . . . . . . 1. TPETb.A LfETBEPTb Ap06H 3HaKoMCT80 C oopa30naHHeM .npotSeA. TepMHHbI «t{HCJlU- Tew1b» (f «3uaMeH a Te,,1 b». 4TellHe H 3anHCb )1po6eiL PeweHHe 3a)J.aQU Ha «npHBe.neHHe K e,lUfHluJ,e» pa3HblMH crroco6a).Hf. PelllHHe Hep aaeHCTB ................. rrpaKT{tlecKoe nOJIyqeHHe .npotSeif co 3H8:\1eHareJHIMIi 2, 4, 8. YrrpaJKHeHHH B cp3BIIeHHH .npo6eA. PemeHHe YP3BHeHH nUlJ.a: 642: x + 57 = 63 H 3aal.J H3 COOTllorneHHe Me1K.ll.Y "' CKOpOCTblO, BpeMeHeM It paccToSlHHeM . . . . . . . . . . npaKTHlJecKoe nOJJYlleHue .l1po6eH co 3HaMeHaTe.nSlMH 3, 5, 9, 10. Ynpa>KHeHHH B Bblpa>KeHHH MeJ1KHX J{OJIeA B 6oJ1ee KPYrIHblX H KpynHblx B 60nee MeJ1KHX. PeUJeHHe 33,L\aQ lIa HaXO>K,tJ.eHHe qHc.na no ero )1OJIe. BblqHCJleHHe qHc.nOBhlX 311alfeHHK t5YKBeHHblX Bblpa>KeHHR npH ,!J.aHHblX 3UaQeHHSlX BXO.ASlUU{ 8 HHX 6YKB. PelUeHHe 3a"aqH Ha npOTHBOnOJlO>K- Hoe 3HaQeUHe H COCTaBJIenUe 06paTublx eH ....... PeweHHe 33,aaQ Ha HaXO>K.neHHe AO.1JH IIHCJla H tfHCJla no ero .none. Ynpa>KHeHHSI B CpaBHeJU{H ):\Oneii. npOBepKa Bep- HOCTH paBeHCTB H aepaaeHCTB. l1.eAcTBH R C MHor03ua QHblMH 4HCJlaMH ... . . . . . . . . . . . . . . . . . . . . . Ynpa>KUeHHSI B nOJlyqeUHH, tlTeHRH R 3anHCH AP06eA. PeweHHe 3a,lJ.aq ua HaXO}f(,U.eHHe .nOJUI I.JHCJla H ttHc.na no erO ,lJ.'1e. CnO>KeHHe, Bblt{HTaHHe, YMHO>KeHHe H ,lJ,eJleHHe Muora- 3HattnwX IIHCeJ1. PeweUHe HepaBeHCTB. YMHO>KeHHe U3 10, 1 00 , I 000 . . . . . . . . . . . . . . . . . . . . . . KOHT(10.rlbH3S1 pa60T. nponepKa Yl\feHRSI pernaTb 3a.ll.aQU ([a HaXO>KAeHHe .nOonH (!HCJla, )'MeHHe cpaBHHBaTb ,lJ,OJlH. Pa60Ta HaA olllHtSKaMH 2. /' 1. )'MH01K.eHHe " JJ,e,,'1eHHe Ha MHOr03HaQHOe IfHCJlO Ynpa>KHeHHSI B YMHO}f(eHHH nJ060ro 'IHc.'1a H3 10, 100, I 000. YMHO>KeHlfe 10, 100, 1 000 HS nlOOOe LfHcno c HCnOJlb- 30BaHHeM nepeMecTHTeJlbHOra CBocTBa npOH3Be,lJ,eHHH. ,Qe- JlelfHe Ha 10, 100, 1 000 ttRCen, OKaHQHB31OHXCSl Hy.nSlMH.. PeUJeHHe 3aM II Ha ,ZJ.BH>KeHHe B npOTRBOnOJlO>KROM HB npaBJIe- HHH. PewHH npHMepoB'Ha .neneHHe MHOr03HaQHblX ttRCen lIa 0)1H03HBIIHoe C OCT3TKOM . . . . . . . . . . . . . . 3H3KOMCT80 c npHeMo).{ Jl.eJIeUHSI nlOtSoro '1HCJIa Ha 10, 100, 1 000 C OCT8TKOM. Ynpa>KHeHHH B YMHO>KeHHH H ,lJ,ene- HHH JJoooro QHCJIa H8 10, 100, I 000. PeweHHe ypaBHe. UBA DHAa: 18. x = 15 · 6. COCT8BJ1eHHe Sa,AaQH no ypaB- n pOaOA3ICeHue -cTp ycaeCSaRKa 115-123 124-125 125-127 127-130 .130-133 133-134 134-136 321
oM ypoKa n pOaOA3IlCHUe COAep)II:SHlfe YPOK3 CTp. Y'leC5HBK 10. 11. 12. 328 3. HeHHIO. PeUJClIHe SaJlaQH H3 HaXO>K,l:t€'IIHe IJIiCJIa no ero ,l:tO- Jle. . . . . . . . . . . .. . .- . . . . . . . . 3HaKOMCTBO co cnoco6oM pemeHHH sa.aB'I H8 nponopUHO- HBJlbHOe .aeJ1eUHe. Ynpa>KHeUHSI B YMHO>KeHHH H JleneHHH JlloOoro HCJIa ua JOt 100. I 000 6e3 OCT8TKa H C OCTaTKOM. 3anHCb H HaXOiK,l:teHHe QHCoIl0BblX 3HaqeHH.. 6YKBeJlIIblX Bwpa- '>KeHHft npH ,l:tBHHbIX 3naQeHIUIX 6YKB. ......... 3HaKOMCTBO C npaBHJlOM YMHO>KeHHH 'IHc.na Ha npOU3Be- JleHHeH ncnO.'1b30BaHHe 3Toro npaBHJla npn peweHRH np"MepOB H SB,l:ta4. PerneUHe 3aJ1,aQ Ha nponopu,HOHanblloe .ae..'1eHHe c BeJ1R1.IHHaMH: CKOpOCTb, apeMH. paCCTOHHHe. D.eAcTBHS{ C MHor03nattHblMH t{HcnaMH .............. 3H3KOMCTBO c peUJeHHeM YCJIO>KHeHHL1X aaJ1,3 1 ) Ha nponop" UHOH3JlbHOe .l1eneHHe no 4>OPMYJl8M: Xl = a : (a + b) : c; X2 = b : (a -f- b) : c. Ynpa>KlleUHSI 8. YMHOiKenHII QHCJ1a Ha npOH3BeJ1,eHHe. YuIO)KeHHe R .l1eJleHHe Juo60ro qHCJIa H8 1 0 . 1 00, I 000 .................... PeweHHe 3a,Aa4 ua HaXO>Kl1.eHHe J1,p06H QRCJI8. YnpB>J<ue- HHSI B Bblpa>KeHUH MeJlKHX ool']el\ B 6o.nee KpynHblx H Kpyn- HbiX B oo.'1ee MeJlKtI"X. PelueHRe HepaneHCTB BHa: 40 : a > 3. YnpB>KHeHHH, CB$)3aHllbJe c pa3BHTHeM reOMeTpHQecK}IX npeJlCTaBJIeHHH r. . . . . . . . . . . . . . . . . . . 3HaKoMcTBO co cnoc06oM "HCbMeHHoro YMHO>KeHIHI liB KpyrJlbIe QHc.na. PemeHHe ypaBHeHHA BRAS: 900 - x : 5 = 800 . . . . . . . . . . . . . . . . . . . . . . . . 4. 5. 6. 7. 8. 3HaKOMCTBO c nOIISlTHeM «nponOpLI.HOnBJlbHaH aaBJiClt- MOCTb» Me)K,lty BeJlH4HHafR: CKOpOCTb, BpeMSI, paccToflHRe. Ynpa>KHeHHSI B YMHO>KeHRH MHor03HattHbrX qucen na Kpyr- Jlble '1HMa. Ynpa>KHeHHSI, CBH3anllble C pa3BnTHe:\f reO\1CT- pnqeCKRX npe.l1.CTa1elutH ............... npReM flHCbMeHHoro YMHO>KeHHSI qHCe." OJ<.aHlIHBaIOWHX- CSI HYJJHMH. Pel.UeHHe S8,AaQ C neJJR'IHH8MH: CKOpOCTb, BpCMSJ H paCCTOHI1Re-pa3HbrMH cnoc06aMH. Ynpa>KHeHHR 8 cpaB- HeHHH 1JHCJIOBLlX Bblpa>KeHHR Ha qCHoBe pa3JIHtleHRB npaBH.'} YMHO>KeHHB "'-t{Hc.'1a H8 C)'MMY R IJHCJJa H3 npOH3BeeHHe YMHO>KeHHe \JHceJl, OKanqHBal01ll.HXCSI nyng:\1H. PerneHRe S8,ZtaQ HB nponOpUl10Ha",1blloe .l1eJ1eHHe C BeJlHttHlIaMH: ueHB, KO..'1HIJecTBO, CTORMOCTb H CKOpOCTb, BpeMH, paCCTOSlHHe. HaO..'IIO.L\eHRSI 3a. H3MeHeHHeM CYMMbI, pa3110CTH, npOH3BeJ1,e- HHSI H 4aCTHoro B COg3" C }t3MeHeHHeM KOMnoneHTOB AeAcT- BUn. HaXO>KJJ.fHHe lIHcnOBblX 3HalleHHH 6YKBeHIlblX Bblpa>Ke- Ii II H . . . . . . . . . . . . . . . . . . . . . . . . . 3HaKOMCTBO C npaBHJlOM .aeJ1ell IUI QIlCJIa Ha npOH3Bce- HHe, HCI1OJ1b30naUHe ero liP" pcrneHHH npHMepOB. PerneHHe 3a.l1aT..lR H3 H8XOil<,neuue AP06H IJ}tcJla. Ha6J1IO,a,eHHH sa H3' MeHenueM pa3HOCTU n cnn3H C yne.'IHlleHHeM BbltlHTaeMOro B HeCKO",lbKO pa3 . .- . . . . . ./. - . . . . . . . . . . Ha6Juo.n.eHHH no TaOJ1Hu,e sa H3\teHeHHe:\t paCCTOSlIJUH B 3aBHCH10CTIt OT H3MeHeHHH CKOpOCTH (opeMH 110CTOHHlIoe) H 3a 1:f3McHfHHeM CKOpOCTU B 3aAHCliMOCTH OT H3MeHeHHSI paCCTOHJIRH (BpeMH IJOCTOJIHIJOe). Ynpa)t{HeHHH B pernCHHH 9. 136-137 137 138 . 139 140 141 142 143-144 1'45 146 1 ".
Ny ypoKa 13. 14. 15. 16. 17, 18. 1 9 t 20. 21. 22. 23 Co.ltep)K8HHe YPOK8 .npHMepOB c npH:\1eneHHeM npaBRJ]8 .n.e.neHHH qlfCJJ8 Ha npo- H3Be.ll.elnte. Y n paiKHeuHB, HanpaBJIeHHble H3 pa3RHTI;le reo- MerpH qeCKHX nOH SlrHA . . . . . . . . . . . . . . .. . . 3HaKoMcTBO C npHeo1 lle..1eHUB MHOr03HaQUblX qHCen Ha KpyrJlble QHCJ13 003 OCTaTKa H C ocraTKOM npH O.l1l103HalJ- HOM qaCTHOM. COCTaMeHHe n pe1JJeHHe pa3IIbIMH cnoc06aMu 33A8q 118 38BnCHMOCTb paccronuHSI OT CKOpOCTlI npH nOCTOHH- HOM apeMen". BbitIepQHBaHHe OKPY>KHOCTH no ;J.aHHOMY pa- llHYCY . . . . . . .. ...... ....... 3H3KOMCTBO co cnoc060M nHCbMellHoro .1J.e..'leHUB MHoro. 3HattHOro qHCJIa H3 Kpyr.rrble .n.eCBTKH npH MHOr03UaQnOM Q8CTlIOM. PellleHHe ypaBHeHHil BH)J.a (x · 9) : 24 = 3. Pewe- HHe S8.naQ 118 38BHCHMOCTb Me>KllY CKOpOCTblO, BpeMeHeM H paCCTOHHHe:-.t . . . . . . . . . . . .. ....... ,[leJleHHe MUOr03HatIHblX IJHCeJ1 lIa Kpyrol1b1e IIHc..la, BK.THO' qaH ,lI.eJ1eHHe lIa KpyrJ1b1e COTHH U TblCBlln. npOBepKa ;J.eJIe- HMSI. COCraBJIeHHe sa.n.aq Ha BCTpe4Hoe U npOTHBonOJ]O)({IlOe ;1.BHmeUHe no qepTe>KaM. nOBTopeHHe npaBHJ] YMHO>KeHHSI Ha CYMMY H YMHO>KeHUe qHCna Ha npOH3Be;1.eHue. H3YlleHHe B3aHMOn0J10)({eUHB HB nJ]OCKOCTH OTpe3Ka H OKpY>KHOCTH Ha6J]IO;J.eHHSI no 'l"atSJluue sa H3feHeHHeM BpeMeHH B 3a. liHCI1MOCTH OT H3MenelHtH CKOpOCTH H H3MelIenueM CKOpOCTH A 38BHCHMOCTH OT H3MeneHHSI BpeMenH (paCCTOHHHe nocTO- Sill Hoe). HCnOJIb30BaUue 3TOA saBHCHMOCl'H npH peWCHHH 3aJl,a q . . . . . . . . . . . . . . . . . . . . . . . Ynpa>KHeHHH B nHCbMeHHOM YMHO.>KeHHH H ;1.eJleHHH MHO' r03H8tJHblX qHCe' lIa KpyrJJh1e QUCJl8. PeweHHe 3a.nall lIa 3aSHCHMOCTb Me1KA}' BpeMeHeM H CKOpOCTbJO (paCCTOHHHe nOCTOSlHHoe). PeweHHe sa,ZJ.aQH H8 nponopUHOHa..FJbHOe ;J.eJleHHe Ha6JIIOAeHHSI 3a H3MeHeHHeM CYML1 npH "3MeHelHH 0;1.' Horo 1I3 c.JIaraeMbIX H 3a H3MeHenHeM qaCTHOro B 3aBHCH1\10CTH OT H3MeHeUHH ;1.eJlIiTeJJSI ............... KOHTp0J1bIl3R paOOT3. npOBepKa YMeHHH peUl8Tb 33;1.8lJU Ha nponoplIOlla.mHoe lleJ]eHue, Ha 3aBHCHMOCTb Me}l(Jl.Y CKOpOCTbJO H BpeMeneM (paCCTORHe nOCTOHHHoe). npOBepKa YMeHHJJ YMHO}KaTb H lleJ1HTb l1a KpyrJ1b1e IIHc.na. PaOOTa HaA OWH6K8MH YpOK MO>KeT 6b1Tb HCnOJIb30B3H AJ1S1 pa60TbI C M3TepHa- nOM llJlR ,lI.onOJlHHTeJlbHblX ynpaiKHeHuA . . . . . . . . . 3H3KOMCTBO c nHCbMeHHblM npHeMOM YMHO>KeHHSI ,ZJ.BY- 3HailHoro tlHCJIa H8 ;1.BY3Ha4Hoe. I1cnoJIb30B8HHe 3TOfO npHe- Ma npH pewellHH npHMepOB H sa;1.atJ. nOBTopeHHe HYMepa- UUH MHor03HatJHWX 'IHcen. Pa3JJo*eUHe MHOr03naQHbiX qU- CM Ha pa3pSlllHble CJ]araeMbie . . . . . . . .. . . Ynpa)({HeHHSI B nHCbMeHHOM YMHO}f{eHHH MHOr03HatlHOrO QHCJIB Ha llBY3Hal(HO. PeUJeHH sa;1.a'l c npH'eHeHHeM npHe- Ma YMHO)f{eHHSl tHOr03HaqHOrO qHC'1a H8 )lBYSHatlHoe. Pewee HHe ypaBHeHuii BHAa: 96: c + 72 : 12 = 10. PellleHHe 33- AatlH c (5YKBeHHLIMlf Jl8HHblMH. BbInOJlHeIlUe rOMeTpHl{eC-- KHX ynpam})eHllii ..... ... . . 1 npOaOAJICeHUe CTp. }''1e6HHKa 147 148-149 150 151-152 152.153 153-154 154-159 159-161 161-162 329
M ypoKa 24. 25. 26. 2. 28. 29. 30. 31. 82. 33G Co,ltep)l(aHHC ypoKa , , 3HaKOMCTBO c nHCbME'HHhIM npUeMOM YMHOJKeHHH H3 TpeX3Ha'lHOe QHCJIO nYTeM Cp3BHeUJ1S1 C YMHO>KeHHt Ha ;l.BY- 3UaQUQe 'lHCJlO. 'COCTaMeHHe 33A3q no «PoPMYJI.aM: x = =a. b+c. PeilIeHH.e HepaneHCTB BHAa: 300:c = 20 H ypaBHe. lIHH BHA3: 3872 - (1698 -l- x) = 87 . . . . . . . . . . . 3H3KOMCT80 C AHarpaMMofi Kal< co cnoc06oM rpa<!tH1Jec- }{oro H306pa>KeHHSI aeJlHlIHH, nOAJJe>Kaw,HX HarJlSl,AHoMY cpaBHeHRIO. MacwTa6 It ero npHMenenue npH tlTeHHll H no- CTpOeHHH )1.HarpaMM. Ynpa>KHeHHSI B nHCbMeHHOM YMHO>Ke- ItHH H3 ,A0Y3Ha t uloe M Tpex3H3'IHoe tJHCJ10. PerneHHe -3a,ZJ.aQ (I a npOTHBOnOJlO>KHOe H BCTpeqHOe ABH}I{eHHe . . . . . . . Bse.n.eHHe 0t506U\eHHOrO cnoco6a YMHO>KeHHH lIa MHoro. 3ua'tHoe \UICJlO nYTeM conOCT8BJJelIHSI YMHO>KeHHH na OAHO. 3EI3'1HOe, ABY3HaQUoe. TpeX3HattHoe H QeTb1pex3H8tJHoe qH- no. PeweHHe 3aJ\aqH lIa 3aBHCHMOCTb Me>K,AY l(eHOH, KOJIH- 'leCTBOM . H CTOHMOCTbJO cnoc060M COCTaBJIeHHSI neCKOJ1bKHX ypaBHenHR. Ynpa>KHeHUH B qTeHHIi ,llHarpaMM . . . . . . npHeMbI YMHO>KeHHst Ha MHor03HallHble 4HCJ1a, n Cepe,AH- lie KOTOpbIX HMelOTCSI HYJ1H. PeweUHe 3a!J-aq C npOnOpIJ.Ho' lIaJlbHblMH BeJ1HlIHH8MH cnoc060M COCT3B,,1eHHH ypaBHeuHH H ,lJ.pyrHMH cnoc06aMH. nOCTpoeHHe «erHneTCKoro:t TpeyrOJJb- IUIKa. (CTOpOHbI 3 CM. 4 CM, 5 CM.) . . . . . . . . . . 3H8KOMCTBO co cnoco60M )'MHO>KeHHH COCTaBHoro HMeHO- BaHHoro QHcna Ha ABy3HaQHOe H Tpex3HaQHoe. nOBTopeHHe Mep ,lJ.nHHbI 1-1 Mep Beca. Pe1lleHHC 33,lJ.aQH lIa npSlMo nponop- HOnaJJbIlYIO aaBHCHMOCTb . . . . . . . . . . . . . . Ynp>KHeHHSI B TIHCbMeHHOM YHfO>KeHHH na TpeX3HaQHOe tjHCJlO OTMelleHlIblX H COCTBBHblX HMeHOB8HRblX t{HCeJl. YM- HO>KeHHe CYMMbI ua qHCJIO ,AB}'MSI cnoc06aMH. Haxo>K,lJ.enHe LlHCJJOBOrO 3HatfeHHH BblpS>KeHHR npn A8UHblX 3HaQeHHHX DXO,lJ.SlInHX B Hero (5YKB. PeweHHe ypaBHeHHH BMAa: (c - 8) : 60.. 30 50. lJTeHHe AHarpaMMbI . . . . . . Ynpa}KUellHSI B BblqHCJleHHH nJlom.aAH npHMoyrOJlbHHK3. 3H8KOMCTBO C KBaApaTHblM AeHMeTpoM Hero OTH01lleHHeM C KBaApaTHbiM C8HTHMeTpOM. PS3,lJ.po6JIeHHe -KBaApaTHbiX .l1eI{HMeTpOB B K88ApaTHbIe C8HTHMeTpbl H 06paTHaH onepsLlHH. PeweHHe 3a.na1.J H8 RbltlHCJlenHe nJIOaAH C 6YKBeHllblMH A8HHblMR H C 1JHCJlOBblMH. YMHO>KeHRe COCTaBHblX HMeHOBaH- HbiX 'IHCM H8 TpeX3HaqH QHCJlO . . . . . . . . . . . BhllUtCJIeHHe nJJOlU8AH H nepHMeTpa KB8ApaTa. PerneHHe aa.l18QH H8 BblQHCneHHe nJJoID-aAH npRMoyrOJJbllHK3, COCTaB- neHHe H perneHHe sa,lJ.aq. ()p8Tnblx eA. YCTHoe peweHHe npHMepoB C HcnonbOBaHHeM nepeMecTHTenbHOro H COQeTa- TeJlbHOrO CaoACTB YMHO)l(eHHH. ¥npa>KUeHHH 8 pa3,Apo6JIe- HHH KBaApaTHLIX AeUHMeTpOB B KB8;q>aTHwe CaHTRMeTpbl H 06paTH8R. nponopUHB . . . . . . . . . . · · · . . . . PeweHHe 3a.AaQ H3 nponopUIiOHaJ1bHOe .l1eJIeHHe H HI Bbl- qHCJlIHHe nnoa.AH (8 KB8,lJ.paTHblX C8HTHMeTpax). 11 npa>K: HeHHH B YMHO>KeHHH MHOr03HaQHhlX qHCen H8 ABY3HaQHble H TpeX3HaQHble. lITeHHe ,AHsrpSMMbI . . . . · . . . . . " pOaO.AeHue' CTp, YIIHHK8 162-163 163-165 165-166 166-167 167-168 169-170 170-171 171-173 173-174 /
. )' POKa 33, 34. 35. 36. 37. 38, 39. 40. 41. 42. 43. 44. 45. 46, 47. 48. , Co,Aep»caHHe ypottlt -. KOHTpOJlbH8H paOOTa. npOBepK8 YMeHHSI peW3Tb 3aAa- '1H sa naXO)J(AeHile CYMMbI ABYX npOH3BeAeHKR. npOBepKa YMeHHJI YUIIO>KaTb OTBJJeqeHHble If COCT80HbIe HMeHOBaHHble IJHCJl8 Ha ,lJ.SY3I1aQHOO H TpeX3HaQHOe QHCJlO. npOBepK3 YMe- IIUH BhJlJJ1C'JJI1Tb nJlOw.a)l.b H nepHMeTp npB:\foyrOJlbHHKa. PaOOT3 H8J1 OlUH6K3MU YpOK MO>KeT 6hITb HCnOJJb30B8H Jl.JJSI pa60Tbl C AO- 1I000HHTeJlbHblM Ma-repHa..'10M .............. npHeM nHCbMeHHoro AeJleHHSI MHor03HallHbJX IJHCe.n H8 nY3Ha'lHoe. PeweUHe 3a,lJ.att cnocooo.\f OTHoweHHH. Ha6JJIO- ,l!eJJHSJ 3a H3MeHeHHeM npOR3BeAeHHft B 3aBHCHMOCTH OT H3- MeneUUH COMHO>KHTe.l1eA H 38 H3eHeH"eM qaCTHOro npH H3- MeHeHHH ,l!eJJHMOrO .................. nUCbMeHHoe ,ae.neHHe MHOr03Ua1JHhlX QHCeJI Ha ABY3H3 t l- lIoe qHC..'10 (TPY,l!llble ClIYllaH). PeweUHe 3aAaIJ H3 Ae.neHHe. Ynpa>KlleHHH B IJTeHHH AHarpaMMbI H B HaXO)K,l!eIlHH ee Mac- wTa6a .. . . . . . . . . . . . . . . . . . . . . . . Y CTHoe H nHcbMeHlloe AeJIeHHe H8 AQySHa'iHOe .'1HCJlO. Ynpa>KHeHHH B COCTaBJIeHHH ypaBHeHHH Ha OCHoae 3HaHHH B3aHMOCBSl3H MeJf<,lJ.Y ,l!eJJHMhlM, .lteJJHTeJleM H '1aCTIIbIM. flpo- BepK3 ,l!eJJeHHH }MHO.>KeHHeM. nO;U-OTOBKa K peweHHJO S3,l!aQ H8 HBXOAeHHe HeH3BeCTHoro no BYM pa3HOCTHM 3H8KCMCTBO c pemeHHeM 3a.aaQ Ha HaXO)f()1eHHe HeJt38eCT- norD no ,ABY" pa3JlOCTBM. YMHO}Ke({})e H AeJleHHe MHor03Ha l l- HblX IJHCeJJ. 1..JreHHe ,nHarpaH.1. Hat5.TlIo,neHHB S3 H3MeHellHeM npOHSBeAelUUJ B S3BHCHMOCTH OT H3MeHeHHH MHO:>KH'I'eJUI. PeWeHHe 3BAaq H8 HaXO)K,l1eHHe HeH3BeCTHoro no )l.BYM pa3HOCTHM. COCTBBJlelJRe H peweUHe saAaq 9TOro Tuna no KpSTKOH 3anHCH B TaMHue. PerneHRe 3aAaq na naXO>K,ZJ.eHHe HeCKOJlbKHX qaCTCH OT tlHCna. YMHOJf<eHHe MHOr03lfaQHblX IjJtCe.JI ......... & . . . . . . . , . . . . . . CnY'laH ,ne.neUHB MHOr03HaQHLIX qHCen H8 ,ARY3Ha l JHoe. P,lIJellHe S8j\aQ Ha 3aBHCHMOCTb Me>KAY KOpOCTblO, BpeMe- HeM " paCCTOSlHHeM: PeweHHe HepaBeHCTB . . . . . . . . npHeM nHCbMeHHoro ,l!e.neHHSI Ha ABY3HallHOe qHCJlO C OCT8TKOM. PemeHHe 3a,J.att ua H8XO>KAeHHe HeH3BeCTHOrO no ABYM pa3HOCTHM . . . . . . . . . . . . . . . . . . 3HaKOMCTBO co cnocot50! AeJleflHSI npOCToro H COCTaBHoro HMenonaHlloro tJHCna lIa ,l(BY3HatfHoe. HCnOJJb30B8HHe 9Toro cnoco(5a npH peUJeHliH 3allaQ. ):leHcTBHSI C MIIOr03HatlHbJMH qHCJJ3MH. PeweHHe sa,l!atl. BWqeptJHBaHHe AHarpa:\1MbI YnpaJKHeHHH B AeJleHHH npOCTbIX H COCTaBHblX HMeHOB3n- HblX 'IUCM, BKJlIOQaH CJIy t l3H ,lteJleHHH HMeHOB3HHoro llHClIa lIa HMeHOB8HHoe. nOBTOpeHHe nopa3pSlAHoro COCTBBa MHO- 3H a QHblX qHCeJI . . . . . . . . . . . . . . . . . . . . nOBTOpenHe H saKpen,,1eHHe npOHJ1.eHHOrO MarepHaJl8 KOHTpOJlbHaH pa60Ta. npOBepKa YMeHHH pewaTb 3aAallH Ha HaXO»<J1.eHHe Hen3BeCTHOrO no ABYM p3HOCTHM, YMeHHSl ,ZJ.eJlHTb MHOr09HaQllble qflcna Ha ,l(BY3UaQUble, YMeHHH HaATH 1fHCJlOBOe 3Ua t JeHHe 6YKBeHHoro Bblpa>KenHSl np" AaHHYX SHaqeHHHX BXOJ\Hlll.HX B nero 6YKB. Pa60Ta BaA oWH(5xaMH. n pOaOA3ICeHue I CTP. y-.eCSJlIIH8 174-1 181-18 182-183 183-1 185-186 186, 181 187. 188 189-1 190-191 '.,. \ .j' ,.,./ " ,I' . "",,"
M YpoKa 49. 50. 51. 332 n po aOIl3ICeHlI.e Co,1.ep>KaHHC ypoK8 CTp. yqe(jUKKa 3uaKOMCTtiO C KDa.l1paTHLI MeTpOM. COOTHOllleHHe KaB,A- paTHOrO MeTpa C KBa1l.paTHblM .lI.eUHMerpOM H KBa,ApaTHbiM C8HTHMeTp0),f. BldqHC.,1eHHe lInow.aA" C "OMOblO KBaApaT- Horo 1eTpa. YMHO}f(eItHe H Ae.T(eHHe MHOr03HaQnblX QHCeJI. PenleHHe ypaBHeHHH RH,na: 87 · x - 78 · 18 = 78 . . . . 'Cuoc06 3aMeHbI KpynHLlx KBa.zr.paTHbix tep (jOJlee MeJlKH- MH H MenKHX oo.nee KpynHblMH. PeweHHe npoCTbI;J H CJI0>K- HblX 3a,l1,att na BLlqHCJleHHe n..10w.aAH. Ynpa>KHeHHst B YMHO- >KenHH H' ,a,e.'1eHHH MHOr03HaQHblX qHCen. BblqHCJJeHHe nepH- MeTP8 npHMoyronbHHKa . . . . . . . . . . . . . . . . PeweHue 3a.n.3lJ H8 BbPIHcneHHe n..'10w.aAH. HMelOw.eA: tPoPMY K Ba .l1paTa. PeweuHe sa.ll.atfH H8 HaXO>K,neHHe HeH3BCCT' Horo no ..l10YM pa3HocTHM.. PeweHHe ypaBHeHU" BHn.a: 5 · x - 215 = 678 + 267 .. ...... . . · · qETBEPTA QETBEPTb 192-193 193-194 194-195 ,AeJleHHe Ha TpeX3Ha'lHoe IIHCJJO 1. 3HaKOMCTBO C "pHeMOM .zr.eJleHHH TpeXSHaQHOrO qHcna Ha TpeX3Ha'lHoe. PeweHHe sa.ll.atlH H8 HaXO>K)J.eHHe AOJlH 'Inc- na. J!e.1JeUHe MHOr03HatlHblX qucen H8 KpyrJlble C OCTaTKOM. 195-196 nHcbMeHHoe AeJJeHHe MHOr03HaQHblX I.JHCeJI Ha TpeX3HaQ- Hoe "p" O,JlH03HaQHOM H ABY3Ha'lHOM '18CTHOM. CpaBHeHHe HMeHOBaHHblX qucen, Bhlpa>KeHHhlX APo6HblMH H lleJIblMH 'IHCJJaMH. nOBTopeHHe S8BHCHMOCTH Me>KAY KOMnOHeHTaMH AeAcTBUH Jl.eJJeHHfl. Ynpa>KHeHHe, CBflsaHHoe c pa3BHTlfeM reoMeTpH'IeCKHX npeAcTasneHHA . . . . . . . . . . . .. 196--197 npHeM I1HCbMeHHoro .n.enellHH Ha TpeX3HaqHO QHCJlO (CJJYtlaM. Kor)J.a B qaCTHOM fiOJlyqaeTCfl Tpex- HJlH 'IeTbipeX- 3HaQHOe 'IHCJlO). npoBepKa .lI.eneHHH YMHO)l{eHHeM " }J.eJle- HHeM. PeweHue cnO)l(HbiX 3a)J.a'l Ha COBMecTHYIO paooTY. BbI'IHCJleHHe JIJlOll\aJl.H " nepHMeTpa npHMoyronbHHKa. .BbI- QepQHB8HHe ero no AallHblM pa3MepaM cropop. PeweHue ypaBHeHHA BH;J.a: 8 · x-I 0 = 22 . . . .. . . . . . .. 198-199 CnyqaH Jl.eJleHHSI H3 TpeX3Ha4Hoe 4HCJlO. KorAa B AeJJHTe- ne qHCnO COTeH paBHO eAHHHD. H uu4»pa qaCTHoro HaXO..l1HTci nYTeM HeCKOJIbKHX npo(5. PeweUHe 3a.n.aq na COBMeCTHYIO pa- 6ory. nOCTpoeHHe npHMoyroJlbHoro TpeyrOJlbHHKa. BbI'IHC. neHHe nJlOma.ll.H KBaApaTOB. nOC1"poeHHblX Ha CTopOHax Tpe- yrOJlbHHKa . . . . . . . . . . . . . . . . . . . . .. 199-200 YnpaHeHHn B peweHHH ypaBHeHHA H aa)J.a'l cnoc66oM COCTaBJIeHUfl ypaBHeHHSI. CocTasneHHe 3a.ll.a'lH. no A3HHOMY ypaBHeHH. PeweHHe npHMepoB'Ha ;J.eneHHe MHOr03HaQHYX "Hcen H8 TpeX3HaQUOe 'IHCJlO. OpOBepKa pe3YJlbTaTOB YMHO- )KeHHH AeJIeHHeM. PeweHHe SaAaQH H8 BbI'IHCJleHHe nnow.SAH npHMoyroJlbflHKa .. . . . . . . . . . . . . . . _. .. 200-201 Ynpa>KHeHHB B nHCbMeHHOM lteJIeHHH lIa Tpex3HatJHoo QHCno. Hcno..Tfb30aaHHe AeAcTBHfI AeneHHst npH peweHHH saA8'1, "PH HaXO)l\.!teHHH 'IHC.1IOBblX' 3HaqeHHH: npH )J.8HHblX 3H8'1eHHftX OYKB. 41eUHe J;tHarpaMMbI ........ __. 201-202 2. 3. 4. 5. 6.
3aAaqH " npHMepW H3 Bce AeHCTBHR 1. PeweHHe npHMepOB H3 nopH.nOK AeHCTBHK. PeweHHe sa.n.aq c nOMObl0 COCTaaneHHH OPMYJ]b1. HaOJllo.neHHSI 3a 83Me- nellHeM CYMMbI 8 SBBHCHMOCTH OT H3MeHeHHA O;J.HOro 83 CJla- raeMbiX ....................... 210-211 2. nOBTopeHHe 3aBHCHMOCTJI MeiKJlY .D.J]UUOH, WHpHHOH H nJlou\a,lJ.b1O npHMoyroJlbHHK8. PeWeH}Je 38Aatt, CBH33HHblX C 9TOH 3aBHCHMQCTbJO. PelueHHe npHMepoB C MHoro3HaQHblMH qHCJlaMH Ha Bce AeHcTBIiH . . . . . . . . . . . . . .. 211-212 3. Peweu8e npHMepoB co cKooKaMH Ha Bce QeTb1pe .neHcTBIlH. CocTaa.,1eHHe H peweHHe 3a;J.aQH na 3aSHCHMOCTb Me}l<AY .n.. 1 HHOH, WHpHHOH H nJlOllJ,a,i1.b1O npHMoyrOJIbHHKa. COCT8BJle- HHe H peuIeHHe 3aj),8'1, 06paTHblx eli. .......... 212-213 4. nootopeHHe 33BHCHMOCTH Me>KAY AJlHHOH, WHpHHOH 8 nJlOw.a)l.blO npSlMoyrOJIbHHKa. PeweHHe npHMepOB Ha Bee AeHCTBHSI. PeweHHe npHMepOB co cK06KaMH. Ynpa>KUeHHH, HanpSBJJeHHble H8 pa3BHTHe reOMeTplllJeCKHX np e .D.CT8BJleHHit 213-214 5. Ynp-a}f(HeHHH B peweHHH npHMepoB H 38Aa'l HS ace AeH- CTBMA. nOCTpoeHHe npHMoyronbHHK8 no AaHHblM cropoHaM H KBapaTa no aHHOMY nepHMeTpy . . . . . . . . . .. 214-115 6. nOBTOpe}ute 38BHCHMOCTH Me>K.l1Y ,lJ...'1HHOH. WHpHHoA 8 11J1011aJ1.blO npSll\toyrOol'JbHHK8. PeweHHe 3a,A3 t l pa311bIMU cno- co6aMH . . . .. . ..... _ . . . . . . . . .. 202-210 7. 8. 9. KOIITpO..'JbH2S1 pa60Ta. nponepKa YMeHHSI pewaTb 3B.naQH na HaXO>KJJ.eUHe nnOw.a,lJ.H ,npSlMoyrOJIbllHKa 8 3a;r.aQ H8 3a8H- CHMOCTb Me>KJ.lY BeJlHtt8HaMH: K0JI8'1eCTBOM npOAYKUHH, H3rOTOBJleHHOH B OJlHH lI.eHb, KOJIH'IeCTBOM AHeH II 06UHM qHJIOM npo,nYK1.1HH. npOBepK8 YMeHHH }J;eJJHTb MHOr03Haq- Uhle '{HCJIa lIa .llBY3HaQHoe H TpeX3HattHOe QHCJIO, pew3Tb ypaBHeHHH H HepaBeHCTB3. Mepw apeMeHH COCT3BJJeHHe Ta6..1Ul{bI Mep apeMeHH. PellIeHHe 3a,Il.3tJ Ha BbJ'IHCJIeUHe BpeMellU. COCTaBJIellne 33.n.aQ na 33BHCH- MOCTb Me)K,lJ.Y Jl,JlHUOH, WHpHHOH H nJIo1.U.8AblO npHMoyroJlb' HUKa. PellleHHe npHlepOB Ha Bee )l.eHCTBJHJ C MHOr03HaQHblMH LlHC,,18\!H . . . .. ................. 215-217 3naKOMCTBO C Ta6eol'1b-KaneHlI.apeM. BblQUCJleliHe BpeMe- HH no Ta6e.flb-Ka."1eU,lJ.aplO. ,QencTBHSI C HMenOnaHHbJMH 4Hcna- MH. Ynpa>KUeHHSI B nHCbMeIlHOt .D.e..'1eHHH HB TpeX3Ha t lHoe IIHCJlO ....... ................. 217-218 Ynpa>KHeHHH B Bblpa>KeHHM KpynHblx Mep BpeMeHH B oonee MeJlK8X H MeJIKHX B 60Jlee KpynHb1x. COCTaBJIeHHe H pellIeHHe 3a,llaq ua 3aOHCUt.{OCTb Mem.ny AJlHHOA, WHpMHOH H nJlOllJ,aAblO npSlMoyro.."1bHHKa. PelIIeulfe npHMepoB Ha Bee .n.eHCTBHH C MHor03Ha l lHbJMH YHCJ18MH. Pel1leHHe 38,naQ H3 BbllIHCJlCHUe speMeHM. Ynpa>KHeHHH B cpaBHeHHH 8MeHOBaH- HblX QHCeJI. CB513aIlJlldX C nOHHTHeM CMepa BpeMeHH». . -.. 218-220 Nt }'P<>K8 I. 2. 3, 4. , ,P np080A:NCtHue CoAep>JCBJJHe ypOK8 CTp. YQe(SHBH8 ) 333
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