c.floJlTaBqenctroe.
Mvuu
K
rr€trlbHoe 6ro
o6ueo6
EBCKOTO
erHoe o6
OBATEJIbHAfi
PASOI{Afl NPOTPAMMA
BneypoqHofi AesreJlbHocrn
flo
npaKTtrrcYMY rlo reoMerDrrrr
Yponenr o6pasonaHzx (rnacc)
Konll.recrBo qacoB 34
Ywtenr-.IleBa HoBa 14 pnxa Cepreeena
flporparvrnra pa.apa6oraHa B coorBercrBhrLroroc
ooo
c yrreroM rpolpaMMbr
rro feon'retprau'
ocHoBHoro o6qero o6pasonanus.Peanu3allnt Kypca >: yre6no-naeroA14qecKoe rocodue. lroA peA' E'H'
fEoy
I{PO KpacHo4apcKoro Kpat. - 2021., c yleroM mlaHl4pyeMoro
rrcnoJlb3oBaHlllo
K
yMK feolaerplu:7-$ rn. / JI' C' AraH-acxn, B' @' Eyrysoa' C'
B. Ka4onrIIeB u Ap.
-
M.: flpocBelrleHrle' 20L5'
1
. Il"rra unpyeM ble pe3yJIbTaTbI ocBoeH
Ilfl 3JIeKTIIBIIoTo Kypca.
I4syrenne reoMerplrr ro AaHHofi rporpaMMe croco6crByer QopnrupoBaHHlo y
o6yraloulaxcs JrrirvHocrHbrx, MeralpeAMerHhrx n [peAMerHbrx pe3yJlbraroB
o6yrenux, coorBercrByurlnx rpe6onannxrr,r Qe4ep€ulbHoro rocyAapcrBeHHoro
o6paaonareJrbHoro craHAapra ocHoBHoro o6qero o6paso Barrwl. u npurvrepnofi
4porpaMMe BocnlrTaHHf, .
JIu.rHocrHbIe p$ynbrarbr :
naTp[oTr.rrlecKoe Bocrr]rTaHr4e - rrpoflBJleHl{e I{HTepeca K }IcTopl',ln u
coBpeMeHHoMy cocrorHuro poccufi crofi MareMaTllqecrofi HayKI4 ; IIeHHocrHoe
orHorueHrre K AocruxeHuf,M poccuficrcrrx yrenrtx-MareMaruron (OcnoBHbIe
HanpaBJIeHI/ut Boc[HTareJlbHofi 4effenbHocrl4 ]t{b 2) ;
SCTeT[qeCKOe BocfrLITaHI,Ie - BocilpqrsrTlire gCTeT]IqecKHX KarIecTB reoMeTpnu' ed
rapMoHtlrrHoro trocrpoeHl{.f,, crpofocrll, TorlHocrrl, JIaKoHLtqHocrrI (Ocnonnue
HanpaBneHr4t BoclurareJlbHofi .4esrelbHocrn N +)t
rleHHocrr{ HayqHoro rro3HaHr{.f, - QoprvttpoBaHlle u pa3Burlre [o3HaBareJIbHbIX
MorLtBoB, HarrpaBJreHHbrx Ha rronfreHue HoBbIX sHaHufi no reoMerplrll
neo6xo,ulrMbrx AJrr o6ucnenus Ha6rroAaeMbrx [poqeccoB lt tBJIeHufi (OcnoBHbIe
4errelbHocTrl
-
i
HanpaBJIeHLlf, BocluraTeJlbHofi
Ns 5); gKo;torllqecKoe BocIILITaHue opneHrallutr Ha npHMeHeHHe
reoMerpgrrecKr.rx gHanrafi Anr peruenufl,3a1a'l-e o6racru oKpylKarorqeft cpe4rr,
noBbrrueHl{e ypoBr{fi groJron{qecrofi KyJIlTypbI (OcHonnrre HaIIpaBJI enIns'
Bocnr4Taretgrofi AeflTeJrbHocrlr Ne 8); 7 otsercrBeHHoe orHorlreHlile K )HeHlrIo'
roroBHocrb r{ cnoco6nocrr o6y.rarounxcs,K caMopa3BLIT}rIo n ca"uoo6pzBoBaHl4ro
Ha ocHoBe MorrlBalrzu r o6yreHnlo H rlo3HaHrlrc;
yMeHLre KoHTpoJrlrpoBarb npoqecc u pe3ynbrar yre6nofi n uarervraru'Iecroft
AetTenbHocTll;
KpUTurrHOCTb M6IIIIJISHIII,
MaTeMaT[qecKI[X 3aAaq.
I4HI1II{1'ATI/rBa, H€XOAqI4BOCTb, aKTIIIBHOCTb
npI'I peIUeHHH
MetaupeAMerHble p*ynbrarbr :
yMeHr4e caMocrorreJrbHo orrpeAelrxrb rlenq cBoero o6yyeruu, QTaBr4Tb 14
I4 rlHTepecbl
QoprvrynupoBarb Nts, ce6s HoBbre 3a4a'rrvt n yr66e, pa3BuBarb MorLrBbI
csoefi rlo3HaBarenurofi ,ueflTenbHocru;
yMeHr4e coorHocrrrb cBorr Aeficrsu.s c nnaHi4pyeMblMll pe3ynbraraMrl,
ocyqecrBJrflTb KoHTpoJrb csoefi AesrerbHocrll B rlpoqecce Aocrl{lt( e}Jufl'
pe3ynbrara, onpeAeJrf,Tb cnoco6rr Aeficrnr,rfi B paMKD( npeAnoxeHnbrx ycnorzfi u
rpe6onanuft, roppeKTr{poBarb cBoH Aeficrerlr B coorBercrBl{u c lr3MenflK)Irlefics
cnryaqzefi;
yl![eHr{e onpeAeJrflTb rroHflTlrf,, co3AaBam o6o6ulen,vtfl.,ycraHaBJlrrBarb
analorull,
xraccu$ullupoBarb;
yMeHr4e ycTaHaBJrr4BaTb npHqr4HHo-cneAcTBeHHbIe CBfl3V\ CTpOHTb JIOTHIIeCKOe
paccy)KAeHr{e, yMo3aKJrroqeHlre (nn4yrulBHoe, AeAyKTI{BHoe I{ no aHaJloruu) w
AenaTb BbIBoAbr;
OCTII
II [CIIOJIb3OBATb
---qbl,
CXeMbI I,I Ap.)
(rpaQuru, raoJILIl
IOHI{MATb
VMEHI,IE
J -'- -
-
lrx
apryl\deHTa\trr4;
3AAAq' [oHr.Marb HeooxoAr4Mocrb
peileH.vrvr "anaq.
IIpu *arrro,'rtrrtr
ErrloTe3br
BbTABI{raTb
yMeHrle
rpoBepKrr;
ilpeAflucaHllfi u yN[eH[e AeficTBOBaTb
B
aJIropI',ITMIIqecKI[X
[oHrrMaHrre oyTTIHOCTI{
cooTBeTcTrlv]frcIIpeAJIox(eHIIbIMaJIrop}ITMoM.
l#:flHff.':#TlHffi:*".recKr*
r'r3BrreKarb
reKcroM (a'anusupoBarb,
rreo6xoAun,rytourrQoprvraurrro),rorrrou|paMoTIIoBblpaxaTbcBOI,IMbIcJI}IB
TepMHI{oJIoII{lI u
*u"t*'ai"oecrofi
IIplIMeHeHueM
c
yctrofi nn ru'CbMennof pequ
cI{MBOJII4KI4,IIc[oIIb3oBaTbpa3JII{tIIIbIe'3bIKI{M-aTeMaTI{KI,t'qpoBoAI{Tb
MareMarrrtqecKnx
o6ocnosaHl4f, AoKa3arerlbcrBa
ruaccuQur"""",
;;;";#.
'
yrBepxqegvtit;
rrarrur-rr. u'cro'fMo'TaJrb'brx ag'rncreHufi;
oBnaAeHIIeHaBbIKaMI[ycTHbIX,II?lcbMeHHblx,I{HcTpyMeHTaIIbHbIx,
ero AJI' oll,ncu',:
yMeHI4e
reoMeTp[qec*EM
".,,oo"'oBaTb
oBJIaAeHIIe
'3bIKoM'
[peAMeToBoKpy)KalootergMI{pa,pa3BI{TIIe[pocTpaHcTBeHHbIxnpeAcTaBl|eHlv|v|14
HaBbIKoB reoMeTpfltlec*I[I
ueo6perar.o""io yuenuft , rrp"odp.teHl4e
Berrr**r'br yr'roB' rrcrrorrb3onats QopMyrlbr
neplrMerpoB reoMerprdqecKl'rx &nryp;
AJII H€D(ox,ueHrrf,
ilffiTtrLn"r"
ArrHHbr orpe3KoB,
yMeHI{e[pI4MeHflTb}I3yIeHHbIefloH.flTllfl,p$yJIbTaTbI,MeToAbIAnflpel[eHl{.f,
3aAaIIilpaKTl{itecKoroxapaKTepavg',{iaqll3cMeXI$IxAI{OIII4IIJIIfiIc
KaJIbKyJIflTopa'
c[paBoqHbD( MareppraJroB'
neo6xoA'rMocrrr
npu
[crroJrb3oBarr[eM
KoMrlbrorepa;
nnneftnb]x sJIeMeHTOn
HaxoAr4Tb 3HaqeHIIf, AnI4H
*rrrr-rnr u
OTHI
I{X orHolfieHr{fl,
$uryp il rix
rpaAycHytoMepyyIJIoB,IIp?IMeHfltronpeAenen^,)csoficreaI4npI43HaKuQurypu
rrx 3JIeMeHToB, PaBeHcrBo QuryP;
ucfloJlb3osarrcsoficTBaI{3Mepi"jHI4fl'AJIHH,yrnoBIIpupeile}ilIll3aAaa[Ha
HaxoxAeHIIeAJII,II{bIoTpe3Ka,AJII4HbIoKpyxHocTII'AJII{HII4yrrro$pyxHocTl{'
y'ffi;ff;:If#Jffi
efi
''xeneMeHrapn'xsurypurry'YrJlbLHcnorlb3vn
QoprvrynrrAJII{HbIoKpyXHoITL,_V|AJIIIHbIAyII{oKpyXI{ocTI,1;
BbIqHcJIf,TbAnI,IHyoKpyXHocTI{,AJII4HyAyruoKpyiKIIocTI4
perlaTb npaKTuqecKr{e 3a,4.a!''}r, cBf,3aHHbre c H€xo)r(AerrHeM leoMeTpl{qecKux
BeJrrrqHH, r{c[oJrb3yt npu HeodxoArrMocrrr clpaBorlHuKavr TexHr,[qecK]Ie cpeAcTBa.
8 O6ytalor4uitcxHa) rurct:
. onepnpoBarb Ha 6asosoh,r ypoBHe rroHrru.rMlr reoMerpr{rrecKr,rx Q"typ;
. ra3BJreKarr rauQoprr,rarlurc o reoMerpuqecKux Surypax, [peAcraBJrerrHylo Ha
.
rrepTex(€x B rBHoM BuAe;
. [plrMerrrrb AJrfl perueHrrfl 3aAaq reoMerpuqecKue Sarrrr, ecJln ycnoBl,lfl Irtx
rrp[MeHe Hvs, ga4atrrrr n seHofi Soprr,re;
. peurarb 3rya'au Ha Haxox(AeHue reoMerpuqecKux BerurruH no o6paaqaM TIJITI
aJrfoprrTMaM;
. onepnpoBarb Ha 6a^:oeoNd ypoBHe rroHf,TlrflMv: paBeHcrBo {uryp, paBHbIe
Qnrypu, paBeHcrBo rpeyrcnbHuKoB, napa[nenbHocrb rlp.f,Mbrx,
HeprreHA[KyJrflpHocTb npsMhrx, yfJlbr Me]K.4y rrprMhrMr{, uepneHl{}IKyntp,
HaKJTOHH€Ifl , IrpoeKrlr{t ;
. BbrrroJrHrrb r{3MepeHrre AJrI{H, paccroflnnfi, nerny}rH yrJroB, c noMolqbr)
uHcrpyMeHToB AJrr rrcMepeuufi AirrrH rr yrnoB;
. [pI{MeHmr Qoprvrynbr pacarera nep}rMerpa Qurypbr npu Bbrrrprcneurrtx:
. rpl,lMeHflrb reopeMy fln$aropa Arrs BbrqHcneHHA NruH Her{3BecrHbrx cropoH
TpeyronbHrrKa, paccroflHuiq v npocrcfirunx cJrfrarx;
. uso6paxarb rr4[oBbre nJlocKne Snrypbr or pyKrr r{ c rroMorqbrc I4HcrpyMeHToB;
' nrrOnparb noAxo,qflulufi MeroA AJI{ peilIeHns LI3BecrHbD( THnoB MaTeMarrIrIecKHx
3a.4aq.
B nonce4HeeHofi xu3Hr.r r{ rrpu r,r3freH}r}r Apyrux npeAMeroB:
. r{crroJrb3oBarb csoficrsa reoMerpnqecKrD( Q"ryp Ans peruerrut Tr.InoBbrx 3aAaq,
Bo3HuKarouU,IX B cI{TyaIIHtx noBceAnesHofi )Ku3Hrr, 3aAarl npaKTl4qecKoro
coAepxaHI4r;
.
cllTyaqrux, B
npocrefiurrax ciDrrraf,x, rrpnMeHsm Soprwynbr B [pocrefirunx crlTyarrrilrx
-
BbrrrrrcJrflTb paccTorHlaf, Ha MecTHocTrr B cTaHAapTHbrx
noBce.{HesHoft xr43HI4
.
BbIIroJIHfiTb
B
;
npocrefiuue rrocrpoenvrfl
Ha MecrHocrn, neopxogr,rMbre B pearsHofi
xfl43HI,I.
o6yuarouluilcn noryvum 6o3rvro JrcHo cmb :
. oenadema uemodaaau peurcHuf eadaq Ha ebtrtucJteHun u dorcasamenbcmaa:
uemodou om npomunHozq uemodou nepedopa nqpuaHrnos;
. npuo6pecmu onbtm rypuMeHeHun anzefipauuecKo?o u mpuzoHoMempu4ecKozo
annqpama npu pet/ueHuu eeoMempuvecKux sadau.
2. CoqeprrcaHrre Kypca
Pargen L" Yrarr. Tpeyro.urnrrnrr (14.racon)
Benrrznayrnra. fpa4ycnar Mepa yrna. Cuexnue rr BeprrrKairbHbre yrhu.
flpusnaru u csoficrea napalneJrbHrrx rrpf,Mbrx. Vrnsr rlplr napaJrneJrbHbrx rrpf,Mbrx
LI ceKyrrlefi. Cyrranra yrnoB TpeyronbHnKa. BneruHue yrJrbr rpeyroJrbHrrKa.
Euccerrpl4ca, Bblcora, MeALraHa rpeyroJrbHuKa. Panno6e4pennnrfi TpeyroJrbHlrK.
PannocropoHnprfi Tpeyronbnur. IIprcHErKr{ paBeHcrBa rpeyroirbHr{KoB.
IlpxlaoyromHrrfi Tpeyronbnur. Te opeua ffta S arop a. Cp e4nxx rrunkrs.
TpeyroJlbHuKa. HeparencrBo rpeyroJrbnuKa. TpeyronrHr,rKn Ha Krerrrarofi 6yrvrare.
MnoroyroJrbnuKu (8 uacon)
MnoroyroJlrHrlK, ero gJreMeHTbr lr ero csoficrna.
Par.qe.n 2.
yrnoB BbrrryKJroro
MHoroyroJrbHLIKa. 9erupexyroJrbHrrKn. flapanneJrolpaMM, pona6, [pflMoyroJrbHnK,
KBaApar, Tpafleqr{fl, panno6e4pennas Tpaneuur. Csoficrsa r,r npr{3HaKlr
Cyrrarvra
rrapaJrneJrolp€rMMa, porra6a, rrpf,MoyroJrbnrrKa, KBaApara.
Cpelnsr
rrnmvrfi.
Tpaneqrrrl. rlerrrpexyroJrbHr.rKr{ Ha KJrerqarofi 6yrraare.
Pasge"rr 3. OrcpyxHocTb. Kpyr (12 vacon)
OrpyxHocrb, Kpyr, HX gJreMeHTbr u cnoficrea. KacarerbHas r,r ceKyrr{afl K
oKpylKHo crrr, vD(. csofi crea. Xop4u n xyru. I{enrpzurrHbre yrnbr. BuncanHrre
yrJrbr. Bnr,rcarrnbre r{ onuc€ilrrrbre orpy}KHocrrr AJr.fl TpeyrcnrH[KoB,
qerbrpexyroJrbHrrKoB, npaBHJrLHbrx MHoroyroJrbHLrKoB. lftema oKpyxrHocrvrvl
rnoulaAb rpyra. 9
3. TervrarllqecKoe nJraH[IDoBarrHe sJleKT[rBrrCIro
MarepuarrbHo -
OcHonHbre
BHAbI
TCXHHqECKOE
AeflTeJrbHocTpr
ocHarrleHHe
(o6opyAoBaBHH
o6yramulrrxcn
(na ypoBHe
yre6nbrK
VnneepcalrbHbre yreSuue
Aeficruvrfr, (YYD, npoercrbr, HKT-
OcHonH
bIe
KOMrreTeHrIHH, MeXnpeAMeTHbre
HarpaB
NOH^'ITH'I
JIeHItg
e)
BOCIII{T
ATEJIbH
Aeficrnnfi)
ofi
AeflreA
bHOCTH
CrvrexHble
O6rgclrtrb, tITo
I,I
BepTHKzurbrrbre
yfirbr
TaKOe
yroJr
H
rpaAycHafl, Mepa
yHIa, KaKHe
yrnbr
Jlnquocrrrsre : QopnnnpoBauue
)
KJracc)),
|FOY
I4PO
KpaclroAapcKoFo
23
i llpoBepoquran pa6ora
OoptotynldpoBarb
(pI4IIH
JlnqnqcrHhle : $opueryoBanue
NOIIflTI,Ifl
V.{e6HOe rrocoSue
OTBETCTBEHHCITO OTIIOUIEHHtr K
rleHTpuIbHoro
yrJla H
nnfr o6yrarotqprxcfl
r,
S'
,
|EOY
HPO
KpacnoAapcKoro
Kpar,2A2l
33
,
@T4NH
Vqe6Hoe Roco6ne
flponepoqnafr pa6ora
Arn o6yraronlrD(cr
to'"
Knacc)),
|EOY
HPO
KpacHoAapcKoro
xipffi, 2021
34
IrlroroBbrfi ypor
OHNH
Vqe6Hoe rroco6ue
.u;lfi o6yrarolurx,cf
<
