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THIET KE TINH HUONG DAY HOC QUY TRINH XAC DJNH THIET DIEN CUA HINH C H 6 P CAT Bdl MOT MAT PHANG Tlif GIAO TUYEN GOC 6 TRUNG HOC PHO THONG O PGS TS BUI V A N N G H ! '''' ThS NGUY§N TI^N TRUNG" Xdc dinh[.]
THIET KE TINH HUONG DAY HOC QUY TRINH XAC DJNH THIET DIEN CUA HINH C H P CAT Bdl MOT MAT PHANG Tlif GIAO TUYEN GOC TRUNG HOC PHO THONG O PGS TS BUI V A N N G H ! ' - ThS N G U Y § N TI^N T R U N G " X dc dinh thilt dl$n (hgn hinh bllu dlln) Id dpng todn phd blln, chllm H l | khd Idn hSn tdng sd cdc bdi todn hong cdc sdch gido khoa, sdch bdl tdp hinh hpc 11 (cd ban eo bdn vd ban ndng cao) Theo thdng kg cuo chung tdl, sdch gido khoa co bdn cd bdi, hong sdch bdl ldp cd bdi; h-ong sdch gido khoa ndng eoo cd bdl, sdch bdl tdp cd 24 bdi Nhu vdy, ed bdi todn xdc djnh hinh hSn tdng sd bdi ldp (H l | 22,8%) Xdc djnh ihllt d l | n Id m^t dpng todn khd dd'l vdl hpc sinh (HS) vi nd ddl hdl ede em phdl cd hf h/dng tupng khdng glan vd phdi ndm vung ede khdl nl^m vd tinh ehdl co bdn cOo hinh hpc khdng gion Ody cung Id mdt dpng todn then chdt, vl n l u khdng xdc djnh dupe ihllt d i | n thi s3 khdng Knh dupe dl^n lich cOa ihllt d l | n , t h i h'ch khdi dl#n md thiet diSn Id mpt mdl eua nd Bdl vpy, rfen luy#n kT ndng gidf todn lien quon d i n ihllt dl§n Id mdt nhi#m vy quon h-png hong dpy hpc phdn Hinh bgc cho HS Idp 1 Bdl vilt h'lnh bdy mdl Hnh hudng dpy hpc v l : Xdy dvng quy trinh xdc dinh thiit dl$n cOa hinh r^dp cdt bdl mdt mdt phdng nhd giao tuyin gie (edn gpi Id phucmg phdp glao hiyln gdc, phuong phdp v l l ) Thiit di$n vd bdl k>dn xdc djnh thilt d i | n N l u cdt hinh chdp (H) bdng mdt mdt phdng (a) th) phdn mdt phdng (a) gdm cdc d i l m ihu^c vd ndm hrong (H) too ndn mot da gidc, gpl Id thilt dign eOa (H) cdt bdl mdt phdng (a) M^t phdng (a) dupe gpi Id mdl cdl Thilt dl|n ed cdc cpnh dupe xdc djnh bdi ede gioo hiyin cuo mdt phdng (a) vd mdt sd mdt cda (H|, ed cdc dinh Id glao dllm cOo mdl phdng (a) vdl mdt sd cpnh Clio (H) Nhu vdy, bdi Iodn xdc djnh thilt di^n quy v l hoi bdi todn co bdn Id xdc dfnh gioo Tap chi Glao due s6 (ki a - 7/aoia) tuyln giCra hoi mdt phdng vd xdc djnh glao dllm cuo dudng thdng vdl m£^l phdng Y hjdng cOo phuong phdp glao hjyIn gdc Id: D l xdc d)nh thilt dlSn eik] htnh chdp (H) cdt bdl mdt phdng (a), hude hit, to xdc dinh gioo tuyen euo mdt phdng (a) vdl m^t ddy cua (H) Tr6n m^t phdng ddy, xdc dinh glao dilm ciJo gfoo h;yln vua Hm dupe vdi cdc dudng thdng chua cpnh ddy cOo (H) Td cdc gioo dllm ndy s3 xdc djnh dupe glao tuyin cdo mdt phdng (a) vdl cdc mdt khde cOo (H) Glao toyln glDo mdl phdng (a) vd mdt phdng ddy cdo (H) dupe gpl Id glao hjy&i gic {hay edn gpl Id v^ cOa mdl phdng (a) trin ddy cuo (H) Trong cdc bdl todn xdc djnh thilt dlSn, mdt phdng (a) thudng dupe xdc djnh bdi dilm khong thdng hdng, hai dudng thdng cdl nhou, hofic bdt dudng thdng song song Quy trinh xdc djnh ihllt d l | n cdo hinh chdp cdt bdi mdl mQt phdng (quy h'lnh xdc djnh ihi^l diSn h> glao hiyln gdc hoy phucmg phdp glao hiyin gdc) Quy hinh gdm ede hopI ddng sau: Hogtd^ng 1: Gido viin (GV) ti diuc eho HS gidl mdt si vi dv nhdm binh ihdnh quy trinh xdc dinh thiit dl^n (tinh hudng hopt ddng): Vidv 1: Cho hinh chdp S.ABCD cd ddy ABCD Id hinh binh hdnh (binh / / Gpi M , N vd P Idn lupt Id A i m cua cdc cpnh AB, AD vd SC Xdc djnh thid dl§n cOa hinh chdp cdl bdl mdt phdng (MNP) ' GV cd t h i ddm thopi vdl HS thdng quo nhung cdu hdl nhu: Ta cd t h i xdc djnh dupe ngoy glao tuyln cua mdt phdng edt vdi mdt ndo cOo hinh chdp? Ta cdn phdl xdc djnh glao hiyin cOo mdt cdl vdl cdc mdt phdng ndo khdc cda * TnMag B9i hgc sM pb?!! Hi K(i *-NUnitUi69ilioc$fpNM hinh chdp? TrSn cdc mi^t dd, da xdc d|nh dirge xdc dinh ihlSt dl$n cua hinh chdp (tinh hudng glao cdc didm chung ndo? Tt> dl^m chung dd, cd t h i tllp, tinh hudng xdc nhdn) tim ihgm dllm chung ndo nQa khdng? TCr dd, Trong qud trinh gidl bol bdl todn trin, GV xdc djnh ihldl dl^n da hudng ddn HS thvc hl$n cdc hogt ddng l§p • tdl gIdt: Trong mijt phdng (ABCD), ggl 1, J dl l^p Igi Iheo mdt quy trinh nhdt d|nh, bdt ddu Idn lut;(t Id glao didm cOa M N vdl BC, CD Trong ti> vl^c xdc d|nh glao tuyln cdo mdt cdt vdl mSI mat phdng (SCD), k i PJ cdt SD Igl F; irong m()l phdng ddy cuo hinh chdp Cdu hdl dat cho phdng (SBC), kd IP cdl SB Igl E Khi dd, ngO gidc HS Id: To cd i h l duo ro mdt quy trinh cd tfnh MNFPE Id ihllt dl$n cua hinh chdp cdt bdl mt^t thudt todn d l xdc djnh thilt dl|n cua hinh chdp phdng (MNP) cdl bdi mdt m$t phdng khdng song song vdl ddy cda hinh chdp hoy khdng vd quy trinh dd nhu i h l ndo? VIdu 2: Cho hinh td d i j n ABCD (hinh 2) Ggi M Id Irung dllm cOa cgnh AB vd G Id irgng tdm cua tam gidc ACD N Id mdt dllm bd't ki thudc cgnh BC Xdc djnh ihlll didn cdt tu dl^n bdi mat phdng (MNG) ' Tuong t\f vi du h GV cd t h i ddm thogl vdl HS nhu sou: Vdl bdl todn ndy, to dd xdc djnh dugc gioo tuyln vdl mgt mdt phdng ndg chuo? M^t phdng ndo cd khd ndng xdc d|nh gioo tuyen nhllu hon, hdy chgn mgt m phdng (BCD) thi to xdc djnh glao tuyln nhu t h i ndo? TO glao iuyin dd, cd xdc dtnh ihim dugc cdc glao tuyln khdc khdng vd nlu dugc ihl xdc djnh nhu t h i ndo? ' Lit gtdl: Budc 1: Trong mat phdng (ACD), kd A G cdt CD tgl F Trong m0t phdng ABF, M G cdt FB tgl Khi dd, thudc mat phdng (BCD), nghTa Id Nl Id glao luyin cda (MNG) vdl mdt phdng (BCD); Budc 2: Trong m(>t ddy (BCD), k i Nl cdt CD iql P (dogn NP Id glao luyin cda mfll phdng (MNG) vdi m«l phdng (BCD); Budc 3: Trong mat phdng (ACD), k i PG cdt AD tgi Q (dogn PQ id glao tuyln gISa m$t phdng (MNG) vdi mat phdng (ACD)) Trong m ^ phdng (ABD), ndi M vdl Q ta dugc M Q Id glao iuyIn giOo m$l phdng (MNG) vdl m?t phdng (ABD) Khi dd, ihllt dl$n cdo Id dl^n cdt bdl m^t phdng (MNG) Id td gidc MNPQ Hogt d j n g : Phdt hlin, S xudt quy Irinh Vdl cdu hdi ndy, HS cd t h i d l xudt nhOng quy trinh iheo sg Iv cuo cdc em, sou dd ihdo ludn, kllm chung Knh dung ddn, ifnh hi$u qud cOa quy trinh Cudi cOng Id hodn thl^n quy trinh GV cd I h l hudng ddn HS phdt bllu quy Irinh dd nhu sou: Budc 1: Xdc djnh giao tuyln d cuo m0t phdng (a) vdl m^t phdng ddy cua hinh chdp; BuiSc 2: Xdc djnh glao d l l m cuo mt^ phdng (a) vdl cdc cgnh cuo ddy (gioo vdi cdc cgnh cuo m ^ phdng dd); Budc 3: Xdc djnh cdc glao t u y ^ cOo mj^t bin hinh chdp vdi m$t phdng (a), ti> dd xdc djnh thill dl$n Hogt d^ng 3: Sou kht dd hinh thdnh vd phdt btSuquy trinh xdc dinh thiS't dt$n theo phuong phdp glao tuyin g&:, GV td chiic cho HS gtdt ba bdt todn sau (Hnh hudng xdc nh^n): HlnltS Bdl t0p I: Cho hinh chdp S.ABCD, dd, ddy ABCD cd AB khdng song song vdl CD Dllm C Ihudc cgnh SC (hinh 3) Xdc djnh iblll dien cda hinh chdp cdt bdi m^t phdng (ABC) ' Idi gtdl: Budc 1: Oi ihdy rdng AB chinh la gioo luyin gdc; Budc : Trong mdt phdng ABCD, k i AB cdt CD tgi I; Budc 3: Tiong mdt phdng (SCD), k i I C cdt SD Igi D* Ttiilt di#n Id tu gidc ASCD' Bdf ^ : Cho Id d l ^ ABCD Ggi I, J Idn k)Dt Id Irung dllm cuo AB vd CD AAdt m ^ phdng (a) quo U vd dilm M lhu$c cgnh BC (BM = 3MC) Xdc djnh Ihllt d l ^ cuo iu diin vdi mdt phdng (a) • Phdn tich: - To cdn xdc djnh glao dllm ci5a mdt phdng (a) vdi cgnh AD Oa cd glao hiyln Tap chi Slao due so (n » T / M H I gdc ndo chuo? (d ddy cd i h l ed hal gioo hjyen gdc Id MJ hodc IMtoj^vdo vifc ehon m^t phdng ddy Id (BCD) hodc (ABC); - N l u chpn MJ Id gioo hjyIn gdc thi to cdn xdc djnh glao dllm cuo MJ vdl dudng thdng chua cpnh ndo cOa mdt ddy (BCD)? (dudng thdng BD) Td dd, xdc dinh dupe thilt difn; - N l u chpn IM Id gioo hiyin gdc thi ta cdn xdc djnh glao dllm cua IM vdi dudng thdng chOa cpnh ndo cdo mdt ddy (ABC)? (dudng thdng AC) Ti> dd, xdc djnh thill difn Htnh • Ldl gidi: Cdch 1: Budc 1: Chpn mdt ddy Id m$t phdng (BCD) Trong mdt phdng (BCD), k l MJ cdt BDtolK; Budc 2: Trong mdl phdng (ABD), k l IK cdt AD tal N ; Budc 3: Nhu vdy, thilt dl|n cua td difn cdt bdl mdt phdng (a) Id h> gidc MJNI (xem hinh 4) chdp cdt bdl m^t mdt phdng d h-gn, HS da gidi mdt sd bdl tdp CO bdn, qua dd hinh thdnh dupe cdc hi thuc phuong phdp mdl GV cdn td chi>e cdc tinh hudng dpy hpc xdc djnh thilt difn mdt cdch llnh hopt d l rfen luyfn cdc kl ndng gidl hsdn xdc djnh thiet difn cho HS Q Tdi li$u tham khdo Bhi Van Nghj Gido trinh Phuong phdp day hgc nhOng nOi dung cu (tii mdn Todn NXB Dpi hgc su p/j(im.H 2008 C6eh2:Budc /.Chpn ddy Id mdt phdng (ABC) NguySn Ti^n Trung Rin luyin kl ndng gidi cdc Khi dd, hong m^t phdng (ABC), ta cd IM Id glao bdi todn thiit difn ciia cdc hinh khdng gian hjyIn gdc; Budc 2: Trong mdt phdng (ABC), kS chuong trinh hinh hpc 11 trung hpc phd thdng Lujn IM cdl AC toi E; Budc 3: Do E thudc (ACD) nSn v&n th^c si khoa hpc gido dye, Tnidng D^i hQc su hong mdt phdng (ACD), k l EJ cdt AD tol N Tu ph^mHa NOi, 2006 Annie Bessot - Claude Comiti - Le Ttij Ho^i Chau gidc IMJN Id thilt difn cuo h/ difn edt bdi mdl Le V ^ Tlin Nhdng yj^a ttf cv bin cda didactic todn, phdng (a) [hinh 5\ (sdch song ngO Vift - PhSp) NXB Dpi hpc qu6c gia, Bdl t^p 3: Cho hinh chdp SABCD, ed ddy TP Hd Chi Minh, 2009 ABCD Id hinh binh hdnh Trong mdl phdng (ABCD), Guy Brousseau Theory of Didactical situations in vg dudng thdng d dl quo A vd khdng song song mathematics Volume 19, Kluwer Academic vdl cdc cpnh cdo hinh binh hdnh ABCD Gpi M Id Publishers, 2002 Trin Vdn H90 (ting chii biCn) Hinh hgc 11 NXB m$l dllm ndm h'gn cpnh SC Xdc i^nh ihllt difn Gido rfjicH 2007 cuo hinh chdp cdt bdi m^t phdng (a)toobdl SUMMARY dudng thdng d vd dllm M Defbingpianesectionpfc^^emisconvnonprotil&Ti • G V hudng dSn HS: Cdn cu vdo vj hi cdo h Geometry !'• grade 5kff& In soMng above prot^lem dudng thdng d,tocd cdc cdch xdc i^nh thilt difn Is Important for students This article focuses on Gaining skills In defining plane through creating an algortthm nhu sou (xem binh 6) to define puramld's plane (originc^ line of intersection Nhu vdy, tuy' vdo vlfe li/o chpn ddy cDa h> method) In solving somes simple educational difn,tasS ed cdc cdch xdc djnh khdc nhung problems, students wis experience somes repeated steps of an algorithm By the way of the above vdn ihu dupe cdng m^l kit qud teacNng situation, students fi^ay role of knowledge creators through situations and appling that kno)A^edge to sc^e some same problems Trong quy h'lnh xdc ^ n h thilt difn cuo htnh Tap chifilaodue so (fci a - 7/aoia) ... xudt quy Irinh Vdl cdu hdi ndy, HS cd t h i d l xudt nhOng quy trinh iheo sg Iv cuo cdc em, sou dd ihdo ludn, kllm chung Knh dung ddn, ifnh hi$u qud cOa quy trinh Cudi cOng Id hodn thl^n quy trinh... quy trinh Cudi cOng Id hodn thl^n quy trinh GV cd I h l hudng ddn HS phdt bllu quy Irinh dd nhu sou: Budc 1: Xdc djnh giao tuyln d cuo m0t phdng (a) vdl m^t phdng ddy cua hinh chdp; BuiSc 2: Xdc... hinh chdp phdng (MNP) cdl bdi mdt m$t phdng khdng song song vdl ddy cda hinh chdp hoy khdng vd quy trinh dd nhu i h l ndo? VIdu 2: Cho hinh td d i j n ABCD (hinh 2) Ggi M Id Irung dllm cOa cgnh