BOI DUONG WDUYSANO TAO CHO HOC SINH TRONG DAY HOC TOAN d TRUNG HOC PHO THONG O TS, NGUYEN THANH H U N G '''' TRAN XUAN T H A N H " T duy sdng tgo (TDST) Id mfit dgng tu duy nhfim tgo ro y tudng mdi, gidl[.]
BOI DUONG WDUYSANO TAO CHO HOC SINH TRONG DAY HOC TOAN d TRUNG HOC PHO THONG O TS, N G U Y E N THANH H U N G ' - TRAN X U A N T H A N H " T sdng tgo (TDST) Id mfit dgng tu nhfim tgo ro y tudng mdi, gidl phdp mdi " i gidi quylt vd'n d l Mfii sfi dfic Hung co bdn cua TDST nhu; tinh mim dia (chuyin tu hogt dfing Hf tad ndy song hogt dfing Hf tad khde, nhfin ro vd'n d l mdi Irong nhi7ng d i l u ki^n quen ihugc, ), ffn/i nhudn nhuyin (Km nhilu gidi phdp Hen cdc gdc vd Hnh hufing khde nhou, nghidn cOu d l i tugngdnhilu khfa cgnh, ), tinh nhgycdm (nhanh chdng phdt hidn vfin d l , Km mdu thufin, dy dodn hudng gidi quyll vfin dl, ), Hnh die ddo (tim ro cdc m i l lidn hd, nhung gidi phdp mdi kp, ) vd Hnh hodn rfi/dn (khd ndng lfip ke hogch, phd'i hgp giOa 'y nghXvd hdnh dfing, phdt Hiln y tadng, kilm tro vd kilm chung y tadng, ) Trong dgy hgc mdn Todn phfin Hinh hgc d trung hgc thdng, theo chung Idl, cfin boi dudng TDST cho HS theo mfit so bidn phdp sou: Tdp luyfin cho HS bll^l vdn dyng cdc ihao ldc hr (so sdnh, phdn Hch, tfing hgp, ln>u tugng h d a , khdi qudi hda, ) mfii cdch nhufin nhu/Sn, m I m cJdo vd linh hogt Bidn phdp ndy glup HS Km hudng gidi cdc bdi H;>dn hodc dy dodn cdch gidl, phdt hidn vd'n d l mdi, fim Hifiy sy lidn h# glua cdc vd'n d l vdi Nhd dd, HS cd t h l md rfing, nghidn cuu sdu ndi dung kiln Hide md GV dua d l gidi quylt van d l , hodc xet nhffng H-udng hgp dde bi#t cOa vd'n d l , mfit so hudng khoi thdc Hong bi^n phdp ndy Id: J Hudng ddn HS nghiin cOu sdu, md ring bdi todn: Ta xud't phdt ta bdi todn sou: Bdi todn /: Cho tam gidc ABC Ggi O Id dilm ndm frong tam gidc ABC, S,, S2, 63, S lfin lugt Id di^n Kch cdc tam gidc OBC, O A Q OAB, ABC {hinh 1) Chung minh rfing: Si.cw+53.o5 + s,.oc = o (1) ^^Lt^il^:Ad-^AB*^ACc=>Ad = ^AB*^:AC {]) S S S S S ' ' De ehung minh (1), ta chf cfin ehi>ng minh (1') Thfit vfiy, dyng hinh binh hdnh A M O N nhfin A O Idm dudng chdo nhu hinh vd, iheo quy tfic hinh binh hdnh: '^ = ~AM-^~AN = xAB + yAC (Hongdd: AN AM J: = - ^ > , J' = - ^ > ) D I c h u n g m i n h ( r ) t a c f i n I , , L S, S, T - AM ON KO chung minh " f , y - ^ T a c o : (Hong dd O , , B, lfin lugt Id hinh chilu vudng gdc cua O , B ldn AC) Mdt khde: S^ = duoc y \O dudi nhiiu khia cgnh khde Chfing hgn, ta S , < m ^ xdt bdi lodn sou: 7M=(m-x.-y),lN = i-x,\-m~y)=> -k^7N = {hr.-k{\-m-y)) Bdi todn 5: Trong khfing gian Oxyz eho hai dudng thfing: Vl ' ^ = * ' IM ^° IN ngugc h u d n g nen trye O x , O y soo cho OM + OM=} [hinh 4) Tim tap hgp diem I thudc M N cho "777 = * (k Id sfi lM = -k^lN c/; I " [~y='-k{l-m-y) [{k + l)y = ~km + k Thay m = kx + x vdo phuang trinh (k+ 1)y » km+k, ta cd: (k+1)y = • „ k(kx+x} + k o(k+1)y=-klk+1}x +k - vd V i l t phuong trinh thorn s^ (A) dudng vudng gdc chung cOa J v d d Ta thd'y, dudng thdng d d l quo A(0; 1; d) vd nhdn vecto a(i;2;3) Idm vectochi phucmg Dudng thdng ddi quo B | l ; - ; 3) vd nh^n vecio 4(1;1;-1) ^y = -kx+-—, Tdp hgp ldm vecto chi phuang Gpi ^ Id vecto chi phuong dilm I can Hm Id mgl phfin dudng thfing cd phuong Htnh y = -kx+—— ^ n f i m Hinh todn ndy, GV nen hudng dSn HS gidl theo cdch Phuong Wnh chhh lac t —H g trinh wing quM Tdp luy^n cho HS gidl q u y l l vdin d l ddt bong n h i l u cdch Uidc mdt cdch nliufin n h u y i n , h> dd lifo chpn cdch ttfl uu d l Ihvc hl8n Ta b i l t rang tinh nhuan nhuyin cuo TDST dupc d ^ c trung t d i khd ndng tpo ro Tap chi Blao due s6 nhu sou: Cdch I: LSp phuong Irinh mdt phdng (P) qua A v d cd vecto phdp tuyen n^ =[c,a] = (14;14;~l4) Phuong trinh cua mdt phdng (P) Id: x + / - z + = Ldp phuong trinh mdt phdng (Q) dl quo B vd cd vecto phdp tuyln n^ = [c,b] = (-3;-6;-9) Phuong trinh mdi phdng (Q) Id: x+2y+3z-6 = Oudng thdng (A) = (P) n (Q| Tu d d suy ro x=-l6+5l phuong trinh ihom s^ Clio (A) Id J'-""'" Cdch 2: Ldp phuong trinh (P) (nhu cdch I): x + y - z + = Tpa dp gloo d i l m C cOo d ' vd (P) Id nghiSm hS phuong trinh: j Vectochlphu Phuong tilnh vd clft.Dodd: - = [ - , j I = (-5;4;-l|.Vdlbdl miln gdc xOy Tdp luyfin cho HS hd ihd'ng hdo k i l n ihdc d a hgc, h> d d , hodn ihi^n M thuc phuong phdp gidl todn Bien phdp ndy glup HS cd o x h nhin tdng t h l v l k i l n thuc Hong chuong Hinh, t h ^ dugc mdi lidn hd giua cdc phan d d hgc, h> dd HS se ndm vung k i l n thue Hong SGK vd phuong phdp gidi cdc bdi tdp H>dn, gdp phfin rdn luydn TDST cho cde em Di minh hga cho bidn phdp ndy, ta xet vf c/y: Sou dgy xong bdi: «f^ucmg trinh dudng thdng' (Hinh hgc 10), GV cd t h l hudng dfin HS h$ thd'ng hdo k i l n thuc thdng qua so do: DU0ng thAng cuo dudng vudng gdc chung (A) thl ^ ^ ^ »i i • T / M » ) l''' ' Gidl h^, la duoc: [x + >'-z + = ' •» , ' _ r-f2 '.'»! Dudng Hifing (A) cfin fim di qua d i l m C, nhfin c Id vecto chi phuang cd phuong Irinh tham sfi ABC V § y , M Id ldm cOo dudng trdn nfii tilp lam gidc ABC thi jj^*j^*-^ 6^/3 nhd't Id ' Id: Cdch 3: Lfip phuong trinh mijit phdng (Q) nhu cdch 1: |Q); X + 2y + 3z - - Chuyin phuong trinh cua dudng thdng d v l phuong Irinh thorn sd: Gpi D = d r i ( Q ) = » f l ( - l : - l ; ) f u d n g t h d n g ( A ) cfin Hm dl quo D vd nhfin ^ ldm vecto chi phuong vdi phuong trinh tham sfi Id: \y—'*i Q d l cdc bdt tfip lodn mfit cdch sdng t p o vd dfic ddo Tinh d$c ddo cOa TDST Id tim ro nhung h l ^ tupng, cdc mfii quon h$, gidl phdp mdi, Do dd, v i ^ lim cdch gidi hoy, dfic ddo cho mfit bdi todn Id v l ^ Idm rot bfi (ch vd cfin thilt vdl HS fid/ todn d: Cho tom gidc d l u ABC cd cpnh bdng a, M Id d i l m ndm tom gidc Gpi M D , ME, MF Ifin lupt Id dudng coo kfi l u M d i n cpnh BC, C A , A B Xdc dinh vi t r i ciio d i l m M d l tr! nhd nhfil d d Cdch gidl: Gpi /) Id dudng cao Irong lorn gidc ^^ g i d trj nhd Trong d p y hpc todn d trung hpc phfi thdng, vi$c rfin luyfin TDST ddng vol trd rat quan trpng nhdm phdt t r i l n tu cho HS; n l u G V thudng xuyfin bfil dudng TDST cho cdc em thl hi0u qud dgy hpc sfi dupc sfi dupc ndng coo Q Tdi ll^u tham khdo Alexfiep M - Onhisuc V - Crugliac M - ZabOtin V Vecxcle X Ph&t Iriln lir b^c sinh NXB Gido rf(ic,H.1976 Hoikng Chung Rin luyfn khd nfing s^ng t^o toia hpc d tnidng phi Ihdng NXB Gido due H 1969 Ton Than Xdy difng hf thd'ng cdu hdi vd bdi t^p nhdm bdi duffng m^t sdyCu td'ciia tuduy sdng Ipo cho hgc sinh khd gidi d trudng trung hQC casd Vift Nam Lu^n in ph