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CHUYEN TIT NGON NGIT DAI sH SANG N G O N N G V S H HOC IRDNG VKC HUONG DJlN HOG SINH TilU HDG GlAl CHG BAl TDUN Gll III! VAN O ThS T H A I H U Y VINH" Bdng / I ng dfin cho hqc sinh tllu hqc (HSTH) kha[.]
CHUYEN TIT NGON NGIT DAI sH SANG N G O N N G V S H HOC IRDNG VKC HUONG DJlN HOG SINH TilU HDG GlAl CHG BAl TDUN Gll III! VAN O ng dfin cho hqc sinh tllu hqc (HSTH) khai ihdc cdc cdch gldl bdl todn cd Idl vdn Id mdt bl^n phdp hChj hl^u v l ^ rfin luy$n vd phdt trlln ngdn ngiJ (NN) todn hgc cho hqc sinh {HS) Gidl cdc bdl todn cd Idl vdn thyc ch^t Id chuyin h> N N thdng thudng song N N vd ki hi|u todn hqc Trong khudn khd bdl vilt ndy, chung tdl dua mdt sd bdi todn cy thl vd Irlnh bdy phuong phdp khai thdc cdc cdch gldl Bdng / khde bdng cdch ldp phuong h'inh bde nhdt dn vd h§ phuong h'inh TT at bde nhdt d'n Sou dd, chuyin djch h> N N dqi sd' song N N sd' hqc d l hudng dfin cho HSTH gldl theo N N 2 sd hqc nhdm cung cd vd phdt triin ndng lye \u duy, N N todn hqc eho 3e-x cde em I « Bdi todn (bdi todn cd d Kiu hgc (TH)): "Vua gd vua ehd, bd Igi eho trdn, ba muoi sdu eon, mgt trdm chdn chdn Hdl cd bao nhliu gd, bao nhiiu chd?" O d d y , chung tdl mudn khai thdc td't ed cdc cdch gidi dql sd bdng edeh ldp phuong Hnh bde nhd't d'n sdvd hfi phuong h'inh bde nhd't dn sd'; sou dd, ehuyen djch sang N N sd' hqc d l huong dfin cho HSTH 1) Gidi vd khai thdc bdl todn bSng cdch lip phuong trinh bic nhd't d'n vd hi phuong trinh bic nhdt dn sd' Trudc hit, ta cdn xdc djnh bdl todn cd mdy dgl lugng chua bilt? (dd Id sd' gd, sd' chdn gd, sd'con chd, so'chdn end) Chf cdn bilt Kong dgl lugng sfi Km duge cdc dqi luqng cdn Iqi 36-i ' S ThS T H A I H U Y V I N H " hfong i}ng vdl c ^ gldl bdng cdch ldp phuong h'inh bde nhd^ dn sd, cdch ehqn dn » hnhg i>ng vdl d cdch gldl bdng cdch Idp h | f r f i u ^ i ^ h-Inh bde nhdt 6n s^ (d ddy quan nl|m mSl ci^cn^ chqndnsdid cdch gidi, Kong mfil cdch ehqn an sd sfi cd nhllu cdch bllu dlln phuong Kinh hoy h$ phuong Ktnh khdc md d bdng dudi ddy chung Idl ehl mdl nfiu cdch bllu dlln si 2i< S& ae-x tOO-j 2(36->i) 100-X y X Si diAncM MX-n) lW-)i 4x "*^isiiirb2"* 2x « 4(30 •>)-100 x-22 J 2(36-«)*4i = 100 x * ( - - ) -100 x = 5e X-tL 100-y y *y =9X-22:v-44 (2x**y-tM s lx+y-36 X = 22 V > 14 l2r*>-IOO 2x > y |i-.-.100 I'22 y - ' e 100-x If*"" y 3e-x 10 To ed cdc cdch gldl bdng N N dql sd duqc Ktnh bdy bdng dudi ddy (xem bdng 1) Nhi/vqy, t>d/laSn ) c c a c h c h n Aistf 100-y x = 44;y = 56 y x = 14:v«96 'SiCtttlieiiMllHlWIi Tap chi Blip due s6 (M a n/»oi»i Tu bdi todn ndy, cd the khdi qudt cdc cdch gidl tnqt bdl todn bde nhd't bdng cdch ldp phuong trinh bqc nhd't d'n sd vd hg phuong trtnh bde nhdt dn sd nhu sou: ne'u cd n dql lugng ehua bilt thi sfi cd n edeh gldi bdng edeh ehgn dn sd vd ed C^„ cdch gidl bdng edeh ehqn dn sd, dd, to ed n -t- C^^ cdch Sd gd (I); I S d e h d n g d (II): I 1 Sdcon ehd llll): , Sd'ehdnehd(IV); ^ [ ' Tacd:(l) + {lll) = 3d;[ll) + ( I V ) = 0 Quo so dd, HS d l ddng thdy Idn sd 2) Chuyin td cdch gidl bdng NN dgt sd chd Id: 100 - (3d X 2) = 28 (con); sd chd Id: sang NN sd hgc di hudng ddn eho HSTH: 28 : = 14 (eon); s6 gd 3d - 14 = 22 (con) Cdch • Gid su d d i u Id chd ed, N h u GV ed the chuyin so dd doqn Kidng thdnh so v^y, mdi eon gd da «thgm vdo" chdn Luc dd, dd khde khdl qudt hon md khdng cdn gid su sd t^ngsdchdn Id: d x = 144 (chdn) Sdehdngd ehd ft hon hay sd gd it hon sd ehd: dd «thgm vdo" Id: 144 - 0 = 4 (chdn) Suy Bllu thj O Id sd gd thl sd chdn gd Id O O sd,gd Id: 44; = 22 (eon); sd chd Id: d - 22 = Bllu thj D Id sd ehd thi sd chdn chd Id D D D D 14 (con) ., / idv _ To ed so do: f,.^ Cdch 2: Gid si> d deu Id gd ca Khi d d , moi eon ehd dd «bdt d i " chdn Luc d d , td'ng sd' chdn Id: d x = 72 (chdn) So chdn chd dd «bdt di" Id 100 - 72 = 28 (chdn) Suy sd chd Id: 28 : = 14 (con); so g d Id: 3d - 14 = 22 (con) Cdch 3: Gid su 100 chdn deu Id chdn eh(^ dd mol gd dd "thfim vdo" chdn Vdy, tong so' vdt Id: 100: = 25 (eon) Sd' eon vdt «hyt" di Id: d - 25 = 11 (eon) Suy so gd Id: 11 x = 22 (eon); sd chd Id: 3d - 22 = 14 (eon) D i D i D n Dyo vdo so 66, HS de ddng thd'y hai hinh vudng ung vdi: 100 • 3d x = 28 (con) Mdt hinh vudng ung vdi: : = (con) Gido vidn (GV) ed t h l ed cdch li gldl khdc So chd 14 con, so gd Id 3d - 14 = 22 (con) cho HS nhu: Id'y 3d cdi hjl tuqng trung cho 3d Ti> cdch I vd cdch 2, GV hudng dan HS gid vdt vd 100 hqt ddu tuqng trung cho 100 cdi su cd so chd hodc so' gd Id mdt so n bd't ki, chdn Gid su 100 chdn deu Id chdn chd thi phdl nhidn, n phdi nhd hon hodc bdng 3d Chdng hqn, bd mol tui hqt vd bd duqc 25 hii Cdn 11 tul chua ed hqt ndo, budc phdi bdt 22 hqt d 11 Kil gid su so chd cd con, dd sd gd Id: 3d - = dd bd hqt ddu, mol hji hqt Luc d d , se cd 33 (con} So chdn ehd Id: x = 12 So chdn gd n X = 22 KJI dyng hqt ddu vd 14 tul dyng Id: 33 X = dd Td'ng so chdn gd vd chdn chd Id: hgt ddu Nhu vdy, gd cd 22 con, chd cd 14 12 + d d = 78 Sdchdn "hyt" di: 100 - 78 = 22 So' gd phdi thay bdng sd ehd Id: Cdch 4: Gid su 100 chdn deu Id so chdn gd 22 : [4 • 2} = 1 Vdy, sdeon ehd Id: + 11 = 14 thi do, moi eon chd d d "bdt d l " chdn Vdy, (con); so gd Id: 33 - 11 = 22 (con) tong sdcon Id: 100 : = (con) Sdeon "tdng Gid su sdchd Id n eon (n < 3d), to ldp bdng sou: thgm" Id: 50 - 3d = 14 (con) Suy so' chd Id 14 S i gfl dir^c vd so' gd Id: d - 14 = 22 (con) st S i chfln Ihay bin s i S6 S i 56 Si Si c h i Hoflc s i Chan ChA conga GV If gidi cho HS tuong tu nhu cdch 3: Idy 3d chd Iflng mam c n i Oirc^ tnev ( - n ) CM gi Wn a i gi cdi hji hrong hvng cho d vdt vd 100 hqt 22 72 2B 36 n IV 26 V7 74 7n ddu hjgng h'ung cho 100 cdi chdn Gid su tdt cd 22 12 24 fin 76 34 100 chdn deu Id chdn g d , bd mSl tul hqt thi 22 78 Hfi 22 33 1? cdn phdi cd tul Luc d d , thilu 14 tul vd cd 28 140 40 22 20 i f l f i 21 22 142 42 i^n hgt ddu chua duqc bd vdo tul ndo Bd mol tui 22 14 22 144 ItX) 44 n = 36 thfim hqt nua se cd 14 hjl dyng hqt ddu Suy HS ed the gid su so chd Id n, vdi ^ n ^ 3d sd chd Id 14 vd sd gd Id 22 Cdch 5: GV hudng dan HS ve so dd doqn (n = chinh Id cdch gid su d deu Id g d , n = d Id cdch gldl gid su d eon d i u Id chd cd), tndng nhusau: hodc gid siJ sd gd h> d i n 3d Gid su sd' chd it hon sd g d , to cd so dd: Tap chi Glao duc so (fcia-n/aoiai # Tu edeh gidl bdl todn bdng cdch ldp phuong ã trinh bde nhdt d'n ho^c hĐ phuong Irlnh bde nhdt d n , ta ed t h l Hm ro n h l l u cdch gldl sd hqe khde Bd I todn : Mit xe md td dg djnh dl h> tinh A din tfnh B mit ^dl glan nhdt djnh Niu xe chgy vdl vin tdc 35 km/ gid thi din nol chim gid Niu xe chgy vdl vin tdc 50 km/gid thi din nai sdm hon ] gid Tfnh qudng dudng AB vd thdi gian dt/ dinh lOc ddu [Di thl ehqn HS gldl TH Knh Ngh§ An ndm hqe 0 - 2001) Tuong ty nhu bdi todn 1, bdl todn ndy ed dql luqng chua b i l l , dd Id: qudng dudng AB, Kidl gian dl vdl vdn tdc 35 k m / g l d , thdi glan dl vdl vdn tde 50 k m / g l d , thdi glan d y djnh luc ddu vd vdn tdc d y djnh lue ddu N h u vdy, s3 cd cdch chon d'n sd, ldp phuong trinh bde nhdt d'n sd vd C ' = 10 edeh ehqn dn sd, ldp h$ phuong trinh bde nhd't d'n sd, suy cd 15 edeh gldl bdng N N dql sd D i n ddy, GV cd t h l hudng dfin HSTH gldl bdl todn bdng N N sd hqe Q u o hal bdl todn ey t h l d trgn cho thdy, ddl vdl bdl todn ed Idi vdn duqc gldl bdng cdch ldp phuong Kinh bqc nhd't d'n hode h | phuemg trinh bqc nhd't dn sd, n l u cd n dql lugng chua b i l t Kii se cd n cdch ehqn dn sd rdl Iqp phuong h'inh bde nhd't dn vd cd C^'cdeh chon dn sd sou dd ldp hg phuong trinh trinh bde nhd't d'n N h u vqy, cd tdt cd n + C„^ cdch gldl dql id Tt> cdch gldl dql sd to c h u ^ n song cdch gldl s ^ ITng dung E-leamIng (Tlip thea trang 53} - E)dnh gid vd p/idn hii ngudi hgc: Website e-leorning phdl thudng xuy6n k l l m Ko qud trinh K i p Kiu k i l n thue vd RLNVSP cOo SV, Vi§c Kinh bdy bdl gidng cdn duqc d i l u chlnh theo ndng lye vd l i l n d q hqc tqp eua SV Vua k i l m Ira thudng xuy&n, vuo x u li kjp tbdl nhijng phdn hdl cua SV v l lien vd nhung vd'n d l phdt sinh Vide ung dyng e-learning RLNVSP cho SV ngdnh su phqm todn se duo ro mqt mdi trudng ddo tqo mdl thfch hqp, uu vigt hem mdi trudng ddo tqo t r u y i n thd'ng, d d Id Iqo mdl trudng hogl ddng tieh eye, chu d d n g , sdng tqo eho SV; ddm bdo ho trg SV r6n' luy§n KNDH theo hudng phdn hod Q hqc, nghTo Id c h u y i n td N N dgl sd sang N N sd hgc d l hudng dfin eho HSTH; i>ng vdi mfil edeh gldl thl N N todn hqc duge trtnh b d y vd d i l n dqt cung khdc nhou Ddy Id mdt nhiJng bl§n phdp gdp phdn nfing coo chd't lugng dgy hqc todn dTH.Q Tdi li^u Iham khdo i Ph9m Dinh Thyc M^t c&u hdi v& d&p vi vifc d^y toiln * tiiu hpc NXB Cido dvc, H 2004 G Polya Gidi bdi todn nhir th£ ndo NXB Cido due H 1997 G Polya, Sdng t^o todn hpc NXB Cido diic, H 1997 D Trung Hi$u - VO Duong Thuy Nhiing phuvng phdp gidi todn & ti^u hpc NXB Dpi hpc su phpm, H, 1980 Tr&n Dien Hiin 10 chuyfin d£ bii diKhig hpc sinh gidl Todn • NXB Gido due H 2003 SUMMARY The solving problems in elementary school have the text Is very rich, diverse and unique So teachers have to use common knowledge ond language of higher mathematics to explore so/uflons to theproty lem then find a guide forstudents This article I raised the extraction method of solving the most - /rove me text problem by addressing the most equation of a system of equations and unknovms most two unknowns, from which teachers seeking to move from language to language algebra arithmetic to guide elementary students explore the solutions by numerical methods In accordance with the program Tdl lifu tham khdo Dko Tam (chO bifin) - Lfi Hiin Ducmg Tifp cfin cdc phuong phdp d^y hpc khOng truyin thtfng day bpc mtm Todn & trudng d^i hpc vd truong plil thdng NXB Dpi hpc suphpm H 2008 Trin Tnmg (chu biftn) - D^ng Xufin Cuong - NguySn van H6ng - NguySn Danh Nam O'ng di^ng cAng ngh^ thdng tin vdo d^y tipc mOn Todnfrtruimg phi thAng NXB Gido due Viit Nam H 201 i SUMMARY Appik:a^on e-ieaming in practice ofpedago^: cai qualification forstudents of education mathemat-: Ics at the Universtles This paper presents the role of pedagogic training activities forstudents of education mathematics at the university Also, It ^lowspos^lrty of e-ieoming and proposes a number of requirements tor the applk:atk}n of e-leamir)g in pedago0cc^ training forstudents of educatkxi mathematics In the directton ofrMerentkjtion Tap chi filao due s6 (id a - n/aoia) ... thdy Idn sd 2) Chuyin td cdch gidl bdng NN dgt sd chd Id: 100 - (3d X 2) = 28 (con); sd chd Id: sang NN sd hgc di hudng ddn eho HSTH: 28 : = 14 (eon); s6 gd 3d - 14 = 22 (con) Cdch • Gid su d... m Ira thudng xuy&n, vuo x u li kjp tbdl nhijng phdn hdl cua SV v l lien vd nhung vd''n d l phdt sinh Vide ung dyng e-learning RLNVSP cho SV ngdnh su phqm todn se duo ro mqt mdi trudng ddo tqo... ddm bdo ho trg SV r6n'' luy§n KNDH theo hudng phdn hod Q hqc, nghTo Id c h u y i n td N N dgl sd sang N N sd hgc d l hudng dfin eho HSTH; i>ng vdi mfil edeh gldl thl N N todn hqc duge trtnh b d