MITHIICTEP CTB O IIP
O
CBE
IIIEHII-fl
POC
CUfICKOfr on4EPAUIIU
KII
MururcrepcTBo o6pa:onaHl{f r HayKH II MOJIOAeXnOfi IIOJIIITII
KPacno4apcKoro KPafl
MynuuunaJrruoe o6paronanue Tyancuncrnfi pafion
i
MEOY COIII Jtbl4 c.KPunenKoBcnoe
PACCMOTPEHO
COfNACOBAHO
MeTOAUqecKllM
3auecrureJlb ArIPeKroPa
no YBP
pyxoBoAlrrenr LLIMO
Mamrurescxas A.f.
flporoxol
Ns 1
or (31) 08
flporoxol
Ns1
yTBEPxtAEHO
AselrsH 3.A.
or (31) 08
2023 r.
2023 r.
PAEOTIA-fl
IIPOIPAMMA
(rD roe7277)
y.re6Horo Kypca <)
4m o6yrarcull4xcr 5-6 Maccos
c. KpuneHKoBcKo e 2023
v colll
ea IrI.B.
II
O'ICHI'ITEIbHAfl 3AftI'I CKA
s 5-6 KJIaCCax f,BJLIOTCfl:
flpnopureTHbrMr,r rIeJrflMI,I O6yreuux MaTeMaTI4xe
o rrpofloJrxeHr{e QopvrupoBaFlufl. ocHoBHbIX MaTeMaT}IrIecK?Ix non'flrzfi
(uuclo,
BeJII{rILIHa, reoMerp[qecKaf,
lpeeMcTBeHHOCTb
o
kI IIepCIIeKTLIBHOCTb
o6YralouYrxcfl;
p&3BlrTLro lrHTeJrneKTy€lJIbHbIx
t4
Srarypa)' o6ecue'I[Baloqux
MaTeMaTLIqeCKoIO O6pasonanu-r
TBOprIecKrIx cuoco6nocrefi
o6yuaroqvrxcfl) [o3HaBaTelHrofi aKTI/IBHOCTII,
o
I4CCJIeAOBaTeJIb0KI',IX
yuenufi, IaHTepeca K I43yrIeHrIIo MareMaruKr;
HIIX ypoBHe K oco3HaHI{IO
rro.{Bo,qeHrre o6yraroqzxcf, Ha AocTyIIHOM Anf,
B3aIIMocBfl3IIMaTeMaTI4KI,IIIoKpyxaloI{eroMIIpa;
.
QoprvuapoBaHlre
IpaMorHocTLI:
synrquonalHrofi MaTeMaTllqecrofi
yMeHI{f, pacrro3HaBarb MareMarfiqecKple
o6rexrrr
B peaJlbHbrx xrI3HeHHbIX
ci[ITyallrlflx,[p}IMeHf,TbocBoeHHbleyMeHuf,AJI,peuIeHI{-[[paKTIIKoopI4eHT[poBaHHbIx3aTaq,}IHTep[peT[poBaTbIIoJIrIeHHbIepe3ynbTaTblI{
aKTIIqe cxofi cr4Ty a\r4vlo rIeH[B aTb rrx Ha co oTB eTCTBI/I e IIp
KJIaCCax
ocnosHrre ilvlilr4lr coAepxaHu, Kypca MaTeMaTuKlI B 5-6
pa3B1aBaIOTCS [apaJIJIeJIbHO',
apnsyreruqecKafl 14, reoMeTpuuecKaf,, KOTOpbIe
oAHaKo, He He3aBLIcIIMo oAHa OT
KaxAafl B gOSTB9TSTBLII{ C Co6cTBeHuoft JIoruKOfi,
Tarxe B Kypce MaTeMaT]IKll
Apyrofi, a B TeCHOM KOHTaKTe II B3a]IMoAeitctsuu,
oII}ICaTeJIbIrOfi cTaTI{CTI{KI{'
nporcxoAr{T 3HaKOMCTBO C sJIeMeHTaun alre6pbl I{
co c}IcTeM aTll3Aullrra 14
Irlsyl euu e ap n Qvr eTr{qe c KOIO M aTepu zuta HAriltH aeTcfl
rII/IcJIax, rlgnyqegHblx Ha ypoBHe HatIaJIbHoIo
pasBlrTofl. sHaHuft o HaTypaJIbHbIx
TeXHI'IKI{
o6qero o6pa:oranu,..fTpugTOM COBepIIIeHCTBOBaHI',Ie BblqllcJlrarelblrofi
c pa3BuTpIeM
t4 sopvrnpoBaHlre HOBrTX TeopeTuqecKI'IX Zsasuit' coqeTaeTcf,
rlpocrefiruuIvt npucuau
Bbrrrr{cJrlrremnoft KyJrbrypbr, B rracruocrr{ c o6yrenlleM
Vftzyrcnue HaTypuIJIbHbIx q14ceJl
HpIIKLIAKI4 I{ 9IIgHK}I pe3yJIbTaToB BbITIHcJIeHI'Ifi'
[oHflTI4flMI',I TeOpu]I
lpoAonx aeTcfl. B 6 KJracce 3HaKOMCTBOM C HaquIJIbHbIMIlt
AeJIIIMOCTLI.
x
Ha.ralo v:gvlrc;rror. O6rrrnosegHblx V AeCflTrzrrIHbIX 1po6efi orneceno
[po]lcxoAl4T 3HaKOMCTBO C
KJraccy. 3ro neprgfi sran B OCBOSH7U 4po6efi, ror,4a
5
o6HffiOneHHbIx
IIAeflMvl) fr1:aflTvtflMl,t TeMbI. flper STOM paCCMOTpeHI{e
LI3TIeHI{IO AecflTLIrIHUx 4po6efi' uro
4po6efi B rroJrHoM o6r6rvre npeAIIIeCTByeT
qucfloBoit' twlduw' KoIAa
qenecoo6pa3Ho C TOTIKLT 3peHIIf, JIO|I{KI4 II3JIOXeHLIf,
OCHOBH5IMI{
yxe
Aecf,TIIqHbIMI{ 4po6rrran MoxHo o6ocnonam
geitcrsutrt c o6HrnoBeHHbrMPI 4po6xrvru'
rr3BecrHbIMI{ EIJrrop}ITMaMLt BbrrroJlHeruut
IIOHI4MaHLIf,
3naxoucrBo c,4ecf,TrrlrHbrMrr Apo6.arraIa pacIIIIIpnT Bo3MOXHOCTII AJIfl
3an'vlcv [pll II3yIeHLIII ApyfIIx
o6yraroqvr:Ndvrcfl. rrprrKJraAHOrO [pIIMeHeHUf, nosofi
nropofi
npaKTr'rqecKoM I4CIIOJIb3OBAHVaI. K 6 rnaccy oTHeC€u
rrpaBI4JIa
4eficrnUfi
rrpeAMeTOB
Lr trpLr
c
3Tarr
B ,3yrc.",r4 Apo6efi, fAe
cpaB,eHrrrr
,.
IIpOICXOAI4T COBepIIIeHCTBOBaHLIe HaBbIKOB
rpe06pa30BaHr{Jr rpo6efi, ocBoeHlle HOBbIx BbIql{clI4TeJIbHbIx
aJIpOpI4TMOB, OTTaqIiIBaHIae TeXHITrKI{ ntrluUCleUUfi,
B
TOM TII4CJIS SHa'IeHI4fi
ycTaHoBIIeHI4e
BbrpaxeHufi, co4epxalqux u o6HrsoBeHHbIe, v [ecflTl4qHble 4po6u,
3aAaq na 'qpo6n' B saqale
cssgefi MexAy HvIMI4)paccMorpeHI{e npupuon peUIeHu'
IIpOIIeHTa.
6 rnacca npoucxoAr{T 3HaKOMCTBO C IOH.,ITIeM
qIICeJI
Oco6ennocTblo lI3fIeH?If, IIoJIoXI'ITeJIbHbIx vr oTpI'IUaTeJIbHbIX
qTo OHI{ TaKXe MOryT pacgMaTpuBATbcfl' B HecKoJIbKo sTaIIos' B 6
flB:1fleTCfi.TO,
y,yqe,ilfl. TeMbr <xyTKll' Cpannenue
rII'IceJI'
IlonoxureJrbHbre
qr4cqla' I4so6paxeH}Ie quceJl Ha
feoMerpllqecKaf, I{HTepnpeTapfl' MoAynt
roop4unarnofi ,prrofi.
LI oTp[qaTeJIbHbIMVqvrCJIAMr4'
Apra$rr,retuqecKue lefictp14g'C IISJI6XI4TSJI6H6IM[
Koop'4nuaTbl ToIIKLI Ha
flpxrr,royroJlbHaf, cI4cTeMa KoopAlIHaT Ha IIJIocKocTI4'
rorreK n Quryp Ha KoopAlrnarnofi
rrJrocKocr u, a6cyucca vr opAu1ara. flocrpoenpre
IIJIOCKOCT}I.
Byrnenuble BbIPalI(eHIrfl
3AIfi4Ckr MaTeMaTlIqecKI{X nsrpaNeuufi kt
Eyrneuuble BblpaxeHlds' t4
rrpeAnoxe;g{uit. Csoficrsa apnQrvretuqecKl{x 4eficmufi'
He[3BeCTHoIo
qIICJIOB6Ie [O,{CTaHOBK}I. Eyrnennge paBeHCTBa, HaxOXAeHI{e
vt IIJIoIIIaA]I [pflMoyIoJIbH]IKa'
KoMIIoHeHTa. @oprr,ryng, Soprrayng [ep]IMeTpa
KBaApara, o6t6ua [apzIJIJIenem'IleAa u xy 6a'
flpuuenenae 6yrn AJIf,
Peruerure reKcroBblx 3aAarl
Peruenrae
Peurenue TeKcroBbrx 3a4a.r apraQvetzilecKllM cnocoSorvr.
Bcex Bo3MoxHbIx BapIIaHToB'
JroruqecKllx 3aAaII. PerUenne 3aAar1 nepe6OpoM
BeJIIIq}IHbI:
3aAaII, coAepxalq[x 3aBI{cIIMocTLI, cBf3bIBaIoUII4x
Peruerrrre
cKopocTb, BpeMfl, paccToflHl,Ie' ueHa, KoJI}IqecTBo,
cTo}IMocTb,
pa6orH. EAnUnqH LI3MepeHI{f,: MaCCbI'
[por.r3BoA]rTeJrbHocTb, BpeMt, o616rr,r
Cnssr MeXAy eALIHLIIIaMLI
CTOrrMOcTlI, pac1T1fl;grvrg, BpeMeHI{, CKOpOCT}I'
raxAofi BeJI[IrILlHbr'
Peruenue 3a$aq., cBt3aHHbIx c oTHOIIIeHLIeM,
v 3MepeHI4s
BeJrr4rrIIH, IIpSII9HTaMII;
[pO[OpUUOHUyIbHOCTbIO
peuIeHIIe ocHoBHbIx 3aAaq na 4po6n u [poIIeHTbI'
oqenra u flpr{KlrAKa,
oKpyHIeHI4e pe3yJlbTaTa. coctarrenrae 6yrneunrtx
Bbrpaxeuufi no YcJIoBI'Irc 3a4aqu"
I4 AI4alpaMM' croJl6'Iarste
flpe4cmureHr{e AaHHbIX C noMoIIIbIO ra6tut\
arTeHrlre II [ocTpoeHl{e. I{renrae Kpyf oBblx ALIaIpaMM'
Ar{arpaMMbr :
HarlsAnafl reoMerPrlr
HarnsAurre npeAcTaBJleHufl
o
IlpflMas'
Qurypax Ha [JlocKocr[: TotIKa'
TpeylonbHuK'
yIoJI, JIoMaHar, MHoIoyIoJIbHLtK, uerrrpdxyroJlbH[K'
oKpyxHocrb, Kpyf.
HA IIJIOCKOCTLI' [apaJlnenbHble
Bsam\aHoe pacloJIOXeH[e AByX [pflMbIX
paccTof,Hrafi: uex4y AByMfl
rrpflMbre, [epleHAr/rKyJrflpHble IIpf,MbIe. LlsrvrepeH]Ie
Ha KBaAparnoft cerKe'
TorrKaMrr, or ronKrr Ao [pf,Moit, anutaMapllpyra
TpaHcIIOpTLIpa' BuArt
I4suepenue t4 [OCTpOeHI{e yrJIoB c IIOMOIIIbIo
ocTpoyrollnrtfi, IlpflMoylonrrrrrfi, TylloyfoJlruufi,
OTpe3OK, nyrtl,
TpeyI.oJIbHIIKoB:
IIerupdxyIoJIbHpIK' IIpI/MepbI
paeno6e4penngfi, paBHogToponnufi.
cTopoH'
?ICIIOJIb3OBaHLIe CSOfiCre
uerrrpexyfoJrbHllKor. fIpxvroyIoJIbHUK, KBaApaT:
Ha HeJII4HOSaHHofi
yrJroB, Anaronanefi. I4so6paxeHlle reoMeTpl{qecK[X o"yp
gauefixll, yIoJIbH}IKa' TpaHcIIopTVpa'
6yrraare c ?IcrIoJIb3oBaH[eM III{pKyJIs,
flocrpoeu vrt. Ha Krerrlarofi 6yuare'
flepnvrerp
MHOrOyroJIbHIIKa.
floruT}te IInonIaA]I sraryprt',
eA]IHI{IIbI
B roM rIrIcJIe
[nonlaAlr. flpu6unxeHHoe ]r3MepeH[e [noulaAra Suryp,
OKpyxHocT[' IJIOIIIaALI
,ru n"u4parnofi ceTKe. flpn6nuxennoe I{3MepeHue An}IHbI
Lr3MepeHLr,
Kpyra.
erplrfl : rIeHTp ajllbftafl., o c eB afl I4 3 epKaIIbHa{ c I{MMeTpI4I{'
flocrpoeur4e cllMMerpurrHblx Qntryp'
c
urvrrvr
[pocTpaHcTBeHHbIx Surypax:
IIpeAcTaBJIeHLIfl o
KoHyc, q]IJIIIHAp' U&P rt cQepa'
napaJrJrenellllfleA, KY6, [p]I3Ma, \:[Ipa-M][tItA,
pasndproK MHoI'oIpaHHLIKoB'
I4so6paxeHlle rpocrpaHcrBeHHblx 0,4ryp' flpurvreprr
(us 6yrr'raru'
qunr,rHApa r,r KoHyca. coeA a.Hr(e uoAenefi npocTpaHcTBeHHbIX Q"yp
Harux4nge
rlp oB oilo KLI, rlJracrl{
JI
rt Apyrux na arepual o n)'
eAI{HLIIIbI I{3MepeHI{-fl O6r6vra'
Lt:na
flonsule o6t6vra,
flaptulJlenerrurleAa, rY6a'
o6teu
IIpffMOyIOJIEHOTO
TIPOTPAMMbI
TTJIAHIIPYEMbIE PE3YJIbTATbI OCBOEHIIfl
yrrEsHoro KypcA (MATEMATI,IKb HA yPoBHE oCHoBIIoro
OEIUEIO OEPA3OBAHITfl
JII,TTIHO C THbIE PE 3YJIbTATbI
Jluqnocrnsre pe3yJrbrarbl
ocBoeHflf,
rporpaMMbl YueSuoro
KYPca
<t
)l
;t
.)I
il
:lal
6l
+l
|
OI
ol
t1 1Jl
O ql
ts
\o
14
-t
tst
\-|
..1
hl
pl
c.)l
f._l
I
l*l
r'-l
\cl
.al
rr:j-l
I
.
\o
o
E(
C)
u
A
a
4
o
C6
Ht
a
-i
E(
tr
Fr
(d
d
H
H
O
tr
Fr
o
A.
3
o
z
o
C)
c)
L4
EtF
;Ji
(J
E(
b4
tro
c--
(9ts
+i Li
x
Cg
F{
H
H
(.)
F
o
(t
x
F
o
H
()
o
o
L
o
l+(
g
xa
H
o
lJ{
H
o
fi
q
()
,!
o
ti
o
A
li
O
F
(.)
c0
cO
H
\o
o
to:
4
()
fr
d
0)q
tc f.
F{
4
SJi
aL
F
H
c)
o
g
l+
A
Cd
F
H
9E
Y9
!IO
l+
!
C)
o
ca
F
O
r!
)
F
V
trl
E]
F-l
14
o
ytIEEHo.METoA[qECKoEOEECIIEIIEHIIE
OEPA3OBATEJIbHOTO
mouBccA
OBfl3ATEJIbHbIE}^IEEHbIEMATEPIIAJIbIAJ|fl,ytIEHuKA
. Mareuaruxa (n 2uacrxx), 5 rlacc/
Burenrzn['fl", Xoxon B'I4'' 9ecnoKos
o6qecrso
A.C., AnercanAposa JI.A., ilInapu6y pA C.Vl., AxquonepHoe
<
