SUf DUNG PHUONG PHOP DIEN TICH TRONG DAY HOC GIAI CAC DAI TOAN HINH HOC CHO HOC SINH Tl iu HOC O TS NGUY§N IVIANH CHUNG'''' CthI hilu, phuong phdp difn Kch Id mft uong phdp gldl lodn, dung d$ gidi cdc ll[.]
Trang 1SUf DUNG PHUONG PHOP DIEN TICH TRONG DAY HOC GIAI CAC DAI TOAN HINH HOC CHO HOC SINH Tliu HOC
O TS NGUY§N IVIANH CHUNG'
CthI hilu, phuong phdp difn Kch Id mft
uong phdp gldl lodn, dung d$ gidi cdc
ll todn v l olfn Kch md khdng sii dqng hvc
tilp cdc cdng thiic tinh difn flch (1} Phuong phdp
diin Kch cung la CO sd cho vlfc gldl cdc bdi todn
v l cdt g h i p hinh Ddy Id mft pnuong phdp khd
I I I vdiliqc sinh |HS| difn dqi hd n i n SGK c6 d l
cf p nhung hjqng bdi t f p ddnh cho vdn d l ndy
cin it
1 d H & hqc, HS da duqc hqc v l difn Kch
cdc hinh nhu: hinh chO nhf t, hinh vudng, hinh
tom gidc Cdc cdng thiic v l difn Hch cOo cdc
hinh ndy chu y ^ duqc HS ling dqng gidi cdc bdi
tfp Knh lodn cd Ilin quon d ^ difn Kch D l b i t
dudng, phdt h-lln ndng Iqc gidi todn cho HS K I U
hqc thdng quo vlfc gidl cdc bdi todn hinh hqc
bdng phuong phdp difn Hch, gido vlin (GV) cdn
trong bj cho cdc em ndm vOng mft s i Knh chdt
hinh hqc sou: 1) N l u mft hinh duqc chia ra ihdnh
cdc hinh nhd thi tdng difn Hch cOo cdc hinh nhd
bIng difn Kch cua hinh Idn bgn ddu; 2) N l u g h i p
cdc hinh nhd k;i d l duqc mft hinh Idn Hil difn
Kch hinh Idn thu duqc bdng tdng difn Hch cOa
cdc hinh nhd dem g h i p Iqi; 3) N l u hat hinh cd
difn Kch bdng nhou cOng bdt di mft phdn chung
Ihl hai phdn cdn \gl cung cd difn Hch bdng nhou;
4) N l u to thim vdo hai hinh c6 difn flch bdng
nhau mft phdn chung thi to nhf n duqc hot hinh
o i difn Kch bdng nhau; 5 | Khi s i do cqnh ddy
khdng ddi ihl difn Kch vd chllu coo cua mft tom
gidc UI hoi dqi luqng K If thuf n; 6) Khi chllu coo
khdng ddi ihl sd do difn Hch vd s i do cqnh ddv
la hoi dqi luqng H If thuf n; 7) Khi s i do difn Hch
khdng d i i thi » do cqnh ddy vd chllu cao cOo
ilifl tom gidc Id hoi dqi luqng H If nghjch; 8|
Nlu hoi tom gidc cd chilu ddi cqnh ^ v d dudng
o n bdng nhou thi difn Kch cOa chOng bdng nhou;
' ) N l u hgi tom gidc cd difn bdng nhgu vd cd sd
do cqnh ddy bdng nhou thi cd chllu coo bdng
nhau; 10| N l u hot tom gidc cd diin Kch bdng
Tap chi Glao due s6 2 8 6 (w a • s/aon)
nhou vd cd chilu coo cOng bdng nhou thi cd s i
do cqnh ddy bdng nhou
2 Cdc bdi todn v l Knh d i f n Kch, so sdnh
d i f n tfch gfOg cdc hinh
VI dv I; Cho tom gidc ABC cd difn Kch bdng
200cm^ Kio ddi AB mft doqn BM bdng AB, kio ddi BC mft doqn C N bdng BC vd kio ddi CA
mft doqn AP bdng AC N l i cdc dilm I*, N , P Tfnh difn Kch tom gidc MNP (hinh 1) Gldl: Di gidl bdi todn ndy, G V c6 rill gql y
cho HS so sdnh difn Kch d o cdc tam gidc sou: ABPvdABC;BPAvdBPM
Khi dd, HS d l ddng nhdn riily: Tom gidc ABP
vd tam gidc ABC cd chung dudng coo hq
h i B v d A P = A C non vioB ^ ^Aflc "
2 0 0 c m ' ( 1 ) Tom gidc BPA
vd torn gidc BPM cd chung dudng coo hq hiPvdAB = BM nin S ^ - S , „ - S,,^^ = 200cm' (2)
Tu (1) vd (2), suy ro: S , ^ = S ^ + S ^ =
2 0 0 c m ' + 2 0 0 c m ' = 4 0 0 c m ' (3) Tuong h;, ta cd: S«N - ScN, = '•00cm' (4) Tli (1), (3) vd (4), suy ra: S ^ - SAK + S ^ + S ^ + S a , = 200cm' +
4 0 0 c m ' + 4 0 0 c m ' + 4 0 0 c m ' = 1 400cm' Bdng phip suy luf n hjong h; nhu hong cdch gidi bdi todn h i n , HS cd H i l gidi duqc bdi tadn
sou: «C/io to aide ABCD, kio ddi AB mdt doqn
BM bdngAB, kio ddi BC mdt doqn CNbdng BC, kdo ddi CD mdt doqn DP bdng CD, kto ddi DA mdt doqn AQ bdng DA Ndt cdc didm M, N, P,
Q Tfnh dt$n Hch lu gidc ABCD, bidt rdng dl$n Hch Id gidc MNPQ Id 2 0 c m "
Hinh I
•IiMi|i)ill«cMi|Bit
Trang 2cho nhfl ABCD, hin AB ^
ldydllmM,h«nCDldy
dllmN.ANcdtDMhjl
l,CMc4tBNhjiH So
sdnh difn Kch cOa hi
gidc IMHN vdl tdng Hinh 2
difn flch hai tom gidc
AIDvdHBCf/.(n/>2;
Gldl: 6 bdi todn ndy, GV cd ihl hudng ddn
HS dug difn Kch hi gidc IMHN thdnh ting difn
Hch cOa hat tom gidc ndo dd Khi dd, HS d l ddng
nhfn riidy difn Hch cOa hi gidc IMHN bdng ling
difn Hch cOa hoi tom gidc IMN vd MHN
AAf t khdc: tom gidc AND vd tom gidc MDN
c6 chung cqnh ddy DN, du<^ coo hq t^ A xudng
DN bdng dudng coo hq K> M xudng DN (do AB
song song vdl DC) nin:
, SAW, - SMB - > SAIO - S„N (">n8 bd» * ^
Hch cOa tom gidc DIN); hfong h;: S,^^^ •> S,^ - >
^ww ' ^ (cOng bdt di difn tfch cOg tom gidc
NHQ Tg suy ra: S „ ^ - S~, + S™
2 Cdc bdi lodn v l Hnhdf Hdi vd so sdnh
df ddi giOg cdc cqnh
VIA) I: Cho tom gidc
vudng cd hgl cqnh gdc
vudng Id 3cm vd 4cm
Tlnh cqnh huyln cug tgm
gidcdd
Gid/: GV hudng ddn
HS cdt 4 tam gidc vudng
bdng nhou cd cqnh gdc
vulng Id 3cm vd 4cm rli
ghip Iqi vdl nhgu nhu hinh vi bin Ijnirh 3) Khi
dd to cd: hinh vudng nhd cd df ddi cdc cqnh Id
1cm, nin hinh vudng nhd cd difn Kch 1cm'
Hinh vudng kin si cd difn Kch bdng tdng difn
Kch 4 tgm gidc vd difn Kch hinh vudng nhd Vfiy,
difn Kch hinh vudng kin Id: 4x6 + 1 - 25 (cm')
Suy ra hinh vudng Idn cd df ddi cqnh Id 5cm (vl
S:fS 25), nghTg Id cqnh huyln cOg tom gidc
vudng cd df ddi 5cm
V/(^2:Chotom
gidc ABC, hin BC Idy
dilm M soo cho MC
- 2MB, N Id dilm hin
AC soo cho AN •
4xNC Kio ddi MN
cdt BA hjii P So sdnh
df ddi hai cqnh BA F ^ * ^ ^ H(nA4
Gldl: 0 1 so sdnh BA vdi BP, GV cdn gql ^ choj
HS chuyin vl bdi lodn so sdnh difn flch ci5a hoi tom gidc ndo dd cd chung dudng cao, nhfn BA
vd BP hiong ling Idm hai cqnh ddy Ti> dd, gllp
HS hr duy vd djnh hudng hong vifc Hm kit gldl
Theo gid Hiilh AN - 4xNC nin S^^ - 4 x S_,
*d S , ^ - ^ " SQ^, ta duqc: S,!,,, - 4 X Sc^ (11;
Iql cd: MC - 2xMB nin S ^ - 2 x S ^ (2)
Ti)(l)vd(2)suyro:S,>,„.8xS « S
-7 X S~,-> BA - -7 x BP Vfy, df ddi doqn Ihdng
BA gdp 7 Idn df ddi doqn riling BP
3 Cdc bdi todn khdc
VI i>) /: Cho torn
gidc ABC cdM,N Idn luqt riiufc cqnh ABvd
AC soo cho: AB
-AM X 3, AC
At^x3lhlnh5l f , ,
g) Tfnh difn Kch ' r tom gidc A/«V>I, bilt
Hinh 3
Hinh 5
rdng tgm gidc ABC c6 difn Kch 9Ccm'
b) Tli gidc AtfCB Id hinh gl? VI soo?
Gldl: al Vdl bdi todn ndy, HS d l ddng Knh
duqc:i.„=l5„ = ixij„=90:9.10 (cnfl
b^ Ap dqng kit qud cdu a), to od:
S.«: =*»«;= T * « c VI hoi tam gidc BMC vd BNC cd difn Hch bdng nhou, c6 chung cqnh ddy
BC nln dudng cno xudt phdt Ki 2 dinh M, N xudng cqnh ddy BC cOng bdng nhou, suy ra MN//BC, hgyBMNCldhlnhthgng
V7 d^ 2: Cho lorn gidc ABC, M Id mft dilm bdt kl h«n BC (M khdc hung dilm BC) Hay vi qua M mft dudng thing soo cho dudng riiong
dd chia tom gidc ABC thdnh hot phdn c6 difn
Hch bdng nhgu [hinh dfl Gldl: Trude hit, GV hudng din HS phdn Kch
cdc gid riii^ cOg bdi lodn V I M Id mft dilm bdt
kl hfn cqnh BC, nin khdng mdt Hnh tdng qudt, to gid Sli: BM < MC Khi dd, gql N kb hung dilm
BC Tii N v i NP//AM, nil M vdl P, HS si chiing minh Aiqc MP Id doqn Hidng cdn Hm
Thdt v4y, tom gidc ABN cd difn Hch bdng -difn Hch tom gidc ABC Gqi I Id gigg cOg AN
vd MP VI NP//AM nin difn Kch tom gidc AMN bdng difn Kch tom gidc AMP, suy ra J f n Hdi hi
Trang 3Hinh 6
difn tfch lam gfdc
ANB vd bdng mft
niio difn tfch tam
gidc ABC
V/dv3(tfnhgld
hj Clio bilu thiic): F~\ P~l
Cho tom gidc ABC
c6 bo gdc diu nhqn Gqi O Id gloo dilm ciio bg
dudng ego AA,, BB,, CC, Tfnh td'ng
OAuSSi+OCi ,
M; i i :
cc;!'""'''^-Gldl: GVcdriilgqt;^choHSsiidvng phuong
phdp difn flch d l gidi, khi dd bdi todn si hd nin
don gidn hon nhilu
Nhdn xih Tom gidc OBC vd tom gidc ABC
oS chung ddy BC n i n : ^ = ^ 2 E ; luong h/, to
' BB^ SBCA CCi 5cu
Vfy:
OA, , OB, , PC,
AA, BB, CC,
Hinh 7 B„ C, Tinh td'ng:
'^ABD~'^ACE-^AOE-T^^E
xS.«c(l)=>«£«p=Vo(2) (3);S.c
T<i(l),(2|,(3)vd(4) suyraS,,^^ = S,^p,.,dodd, dudng coo xudt phdt tit
B din OA bdng dudng coo xudt phdt hi C din
OA MB-MC
Md rf ng kit qud cOo bd; (odn (, ta c6:
Hinh 8
Tuong h/ cdch
gidi bdi todn ndy,
HS si gldl duqc bdi
lodn sou: Cho tam
gidc ABC, O Id
dlim bd't kl Irong
tam gidc Kio ddt
AO, BO, CO,
diOng Idn luqt cdt
BC, CA, AB tgl A
CA.^OB, , PC,
AA, BB, CC, •
Sli dqng phuong phdp difn tfch, GV cd rill
kulng ddn HS gidi cdc bdi todn hinh hqc vl chiing
minh 3 dudng rildng ding quy, chiing minh 3
dl&n thing hdng,
4 Khoi llidc hf thdng bdi Ifp hi mft bdi
todn
Bdi lodn I: Cho tom gidc ABC, hin cdc cqnh
AB, AC Iln luqt le^ cdc dilm E, D soo cho A B
-3 X AE; AC - -3 X AD Cdc doqn rildng BD vd CE
cdt nhgu Iql O, AO cdt BC hjl M Oiling minh
rlSng:BM = MC(/ifn/iS)
Gldl: Ti gid riiilt: AB = 3 x AE; AC - 3 x AD,
tacd:
Tap chi Glao due so 2 8 6 pa »• 5/»on)
Tli (5) vd (6), to cd: S ^ = S,^ => OA - OM
(7), Tii kit qud ndy, gii; nguyIn gid riiiH bdi lodn
I vd thay kit luf n cOa bdi todn I bdng kit qud
(7), ta cd bdi todn sou:
8d/ lodn 2: Cho tom gidc ABC, hin cdc cqnh
AB, AC Idn luqt Idy cdc dilm E, D soo cho AB =
3 X AE; AC = 3 X AD Cdc doqn rildng BD vd CE cdt nhau tql O, AO cdt BC tql M Chiing minh rdng: AO = OM
Col kit qud bdt lodn I Id gid riillt vd ddo gid
riilAriidnhk^lufn,to
cd bdi lodn ddo cuo bdt lodn I nhu sou:
Bdt todn 3: Cho ,
tom gidc ABC, gqi M
Id trung dilm ciia BC,
O Id hung dilm cOo
AM BO kio dat cdt ACh9iD,COkiodai cdtABtqlE(hin/i^
Chiing minh ring:
AB-3xAE;AC = 3 xAD
G/d/: VI OA=OM, BM = MC nin S.„ = S„
Hinh 9
SAOB =—><5KJC, suy ra dudng COO xudt phdt hi C
din BD bdng 2 Idn dudng coo xudt phdt hi A dInBD
To \ql cd:
S ^ = 2xS^a>CD=2xAD^AC=AD;S^3 Tucmg h/:
(Xem Hip Irang 51 j
Trang 4Nhin chung, cd 3 PPDH trSn d6u cd chung c6c
inj dilm Id gdn If thuylit vdl thyc hdnh, tu duy vd
hdnh ddng, phdt huy tfnh ty Iyc, tfnh trdch nhlfm;
ph6t triin khd ndng sdng tpo; r^n luyf n ndng Iyc
gi6l quy^t nhOng vdn d l phuc hpjs; rdn luvfn
h'nh bin bl, kidn nhSn; ndng Iyc cfng tdc ldm
vlfc; phdt tri^n ndng Iyc D G ; cho ph6p phdn hdo
nhjp d f vd trinh a $ cOo HS Tuy nhidn, cdc
Iruong phdp ndy ddi hdi nhilu ihdl glon; ndng
li/c, nghlfp vy su phgm cOa G V ; sg ty gidc, Hch
eye COQ HS; vd'n d l tdi chfnh; phuong Hfn, co sd
vftchdt trong DH VI vdy, cdc PPDH ndy khdng
thay t h i cho phuong phdp thuylt trinh vd luyf n
l$p md Id htnh thOc DH bo sung cdn thilt cho cdc
PPDH truyin thdng D
Tii Ufu tham khdo
1 Ptian T r ^ B ^ Phmmg p h ^ gling d^y Am nhfc
NXB Guto</(ic,H 2001
2 NguyJn HOu DQng (Old bien) ti\hb hin»ng dtfl
mtfi phum^ ph^P dAo t^o vA k h i nSng itaig d y i ^
1996
3 Ph^m Minh H^c G U o dpc thf gkH di v i o th^ ki
XXI NXB Chtnh tri qu^c gia, H 2002
Am nhpc Tjlp 1 , 2 , 3 NXB Gido d^c, H 2002
5 Trdn Thi Tuyft Oanh G i i o dye hpc hifn dpi NXB
Di^i hQC suphgm, H 2004
6 Phmmg p h i p dpy hpc Iheo d y in, theo hqp ddng, theo g i c Tiki H$u Iham khdo ciia Dy dn Vi$t - BI
7 Nguyfin QuC^ Todn Phmmg p h i p gidng dpy Mi
thuft NXB Gidodnc H 1999
8 Nguyfin Qutfc Todn - Phfun Thj Ctiinh - Nguyfin Ldng Binh Ml thuft v i phmmg p h i p dpy hpc, tdp 1, 2,3.NXBGMorfiic.H.2001
9 Hodng Long - Ddm Luy^n (tdng chA bifin) Am
nhpc v i MI thuf 19 NXB Gido dftc, H 2007
SUMMAIIY
Teaching based on projects, contracts and pro-spective has been applied In many countries to Innovate teaching methods to encourage student's actlveness and creativity to match with Innovat-ing teachInnovat-ing process from beInnovat-ing 'content-ori-ented'to 'out-put oriented' In order to Improve drt In particular It Is neccessary to have good un-ing methods to have flexibility, creativity, goal-ori-entation and ellglbllty for learners We can strongly believe this Is an evitable factor to contribute to education's quality
Sv thing phmmg phap dien tich
(Tlip theo trang 47)
S = 2 x S j ; „ - > B E - 2 x A E = > A C = A E x 3
Nhu vdy, to m$t bdi todn gdc, chl cdn thay
do\ mft sd dilm trong gid thilt hodc kit ludn to
duoc cdc bdi lodn khdc nhau nhung cdch gldl
lucmg ty, dilu ndy giOp HS cd khd ndng ly v$n
dgng cdc p h ^ suyludn diin dfch, suy ludn quy
rap di khai thdc ^ n d l nhdm hilu sdu kll^n thOc
cGng nhu rto luyf n tu duy k>glc, tu duy sdng tgo
d)o minh
SI} dyng phucmg phdp difn Kch h-ong dgy
hoc todn d tilu h^c glOp HS gidi duoc nhilu bdi
todn khd, ede em hung thd trong hpc tdP/ bilt
vfin dyng kiln thuc mft cdch sdng tgo d l gldl
m6tbdl todn theo nhilu hudng khdc nhou Phucng
phdp difn tidn Id mft cdng cy khd hOu hifu trong
vlfc bdi dudng hr duy, phdt h i l n ndng Iyc gldl
todn cho HS; G V cdn hudng dSn HS bilt vdn
dgng linh hoqt phuong phdp ndy trong qud trinh
^oc t$p d l gldl quy^t vdn d l •
(1) Trdn Dien Hi^n Bdi dutfi^ bQC sinh gldl t o i n tifiu
hoc NXB Dpi hpc suphgm, H 2009
T i l llfu tham khdo
1 Nguyfin Mpnh Chung Bdi gidng mdn phuong ptidp dtfy hpc todn tliu hpc 3 (tdi lifu da duyc bO mOn
Todn - Khoa Su phpm ti^u hpc - Thidng Dpi hoc Hdng Ddc thim dinh), 2010
2 D6 Trung Hi$u D6 Dinh Hoan Va Duong Thvy
-Va Qatk Chung Phmmg p h i p dpy bpc mAn T o i n d-tiiu h9C NXB £><ii hpc sirpham H 2009
3 Dd Dinh Hoan (chd bien) T o i n 4, T o i n 5 NXB
Gido dfic Vift Nam, H 2011
SUMMARY
Ttie paper Introduces charateristics of acreage based on wtilch to tfuSd a task system to dr9l,dev^op Primary pupils'Interring and proving cAjlllty Ttirough IZspedflc examples, ttie article introduces two types
of basic math (the length and comparison of ttie lenglt); ttie cffea end canpartson of the area) ar}d some terms of advanced mcittiematics(stiowtiow two lines are parallel, three lines are regular or three-pohtllne ) u^g the area method te Improving Pri-mary pupl^'Inferring and proving atjUlty