NGHIEN CUU & UNG DUNG Id do thay ddi thi the tich se ihay ddi nhu the ndo? Trong trudng hgp ndy co hai yeu to quyet dinh den the lich do Id cgnh day vd cgnh ben Nhu vdy HS se cd hai hudng de mo mdm vd[.]
NGHIEN CUU & UNG DUNG Din Luuin nHnc uic TIT DUU SHHG THO CHO HOC SIOH OOH VIEC SHRG TOO BfJI TOHO Cl|C TR! HJIIH HOC KHOHC GIHO ThS Biii Thdnh Trung Trudng Cao dang Kinh te - Ky thuSt Diin Bien SUMMARY Train capacity for creative thinking high school students through innovative problem extremum stereometry This article presents a summary of some operators towards common geometric problems to create the problem of extremum stereometry This problem helps teachers guide students creative problem in extremum stereometry lo formation and development capacity for creative thinking in students Keywords: Creative thinking capacity: Creative problem; extremum stereometry Nlt^n bdi ngay: 15/5/2014 Ngay duy^t dSng: 30/5/2014 \ Dat vin dl Sdng tao bdi todn mdi Id mpt bude quan trpng eua qud trinh gidi todn, mgt phuong thde ren luyen nang lye sdng tao todn hpc, mdt nhUng myc tidu chinh eua hgc tap sdng tgo Viec phat hien, khai thdc vd de xudt bdi todn mdi giup HS rgn luyen khd ndng khdi qudt hda tri thdc cung nhu phuang phdp; rgn luy^n cho HS nhin nh§n mpt edeh tdng qudt edc tri thde dd hgc, phdt triln nang lyc vdn dyng linh hogt cde thao tdc tri tu§ td dd phdt triln nang lyc tu sdng tgo cho HS Bdi bdo sS trinh bdy mpt sd hudng sdng tgo bdi todn eye tri hinh hpc khdng gian nhdm hinh thdnh vd phdt trien ndng lyc tu sang tgo cho HS nhu sau: II Nghien cuu sdu bdi todn da biet bdng cdch biln si hda Tir nhirng bdi loan dinh lugng don gidn da biet cdch gidi ta cho mgt so dgi lugng bien thien de dugc bdi loan eye iri hinh hgc khdng gian Vidu 1: Ta xit bdi todn dinh lugng sau Cho hinh ehdp dlu SABC cd cgnh ddy AB - BC = CA = a cgnh ben bang b tinh the tteh hinh ehdp Ddy Id mdt bdi todn rdt quen thupe, vigc giai bdi todn ndy rIt don gidn phii hgp vdi hdu het HS THPT HS tfnh duge thl tfch hinh ehdp Id thay ddi thi the tich se ihay ddi nhu the ndo? Trong trudng hgp ndy co hai yeu to quyet dinh den the lich Id cgnh day vd cgnh ben Nhu vdy HS se cd hai hudng de mo mdm vd du dodn ta Hudng 1: Cho a ed djnh, b bign thign cd hdm s6 V,(b) -a 12 HS cd the su dyng dao hdm dg kilm tra xera hdm sd cd eye trj theo biln b hay khdng Do V hdm ddng bien theo b tren ^ ;-l-co ngn V khdng ed GTLN vd GTNN Do dd ta khdng cd bai todn cue tri ndo Hudne 2: Cho b cd dinh cdn a biln thign dd ta cd ham sd V -a HS cdthe sir 12 dung dgo hdm d6 xgt xem V cd eye tri theo a hay khdng hoac cd the su dyng bat ddng thue cdsi nhu rSO.S., 12 Tir bai todn dan gian nguai thdy co the dinli hlt^ng cho HS khai thac de sdng tgo cdc hdi todn c^tc Iri hinh hQC khong gian mdi Trtrdc het BS cdn nhin thdy bdn chdt ciia vdn de dd la The lich cua hinh ehdp ph\t thudc vdo yiu Id ndo? Khi cdc yiu 12V2 (6b'-2a') ap dung ib^ - 2a^ ta duoc: 2b ^ala'.(6b'-2a') =>a'.a-.(6b'-2a')^2a^2a^(3b'-a^) giup HS ed khd nang md mim du dodn, ed kha ndng tdng hgp kiln thdc, nhin nhdn duge bdn chat van dg c= (a^ + b ' y > 2a^2a^(3b^ - a' ) dd Id nlu hinh ehdp tam gide dlu cd cgnh bgn cd dinh thi sg cd thl tieh Idn nhdt, td HS bude ddu dupe tir M ta c6 V < — k ^ Ichi di5 GTLN sang tao bdi todn mdi, gdp phin hinh thdnh vd phdt 24 triln ndng lyc tu sang tgo cho HS k^/k >/2k Ddi vdi HS cd kha ndng tu tdt hon ngudi ,,x = khia = b = 24 thiy cd thl hudng din cho HS khai thdc bdi todn theo ! • TAP CHi THIET BI GIAO DUC-S6106-6/2014 NGHIEN CUU & UNG DUNG Nhir v$y vdi vi§c bi€n s6 h6a cdc dai lirgmg quen > Sina5inp5mX • thuOc (canh bin, canh (My, gcSc ) du4i Sir din dSt 3x/3 cua ngudi thiy HS kh6ng nhChig dtrgc rfen luy§n ky nftng tinh thd tich hinh ehdp mS c6n du^c trvc tidp ddu bdng xdy Sina = Sinp = SinX hay OA = s ^ g tao bai toSn mdi TCr d6 HS dugc hinh th^nh OB = OC Tit ddy ta cd bdi todn sau: va rin luy^n nSng lyc tu sang t ^ Bdi todn I: Cho td di?n OABC cd OA, OB, OC Tir dSng thue hinh hpc chuyin sang bit ddi mgt vudng gdc Ggi a , P, X lin lupt Id gdc giiia ding thDt; OA, OB, OC vdi mat phing (ABC) Tim GTNN ciia Xudt phdi lit cdc bdi todn ddng thitc hinh hoc, la bilu thde dp difng cdc bdt ddng thirc quen ihudc vd tit phdi T = Sina.Smp.Siia bieu thdnh cdc bdi todn ctfc tr] hinh hoc Villi/ 2: Ta xit bai toan sau: Cho til dien OABC Ap dyng bat ding thde bunhiacopxki cho vl trdi c6 OA, OB, OC ddi mOt vudng gdc Gui a , |3, X lin eiia(l)taed: lugt la gdc giaa OA, OB, OC vdi mjt phSng (ABC) (Sin^a-i-Sin^p-i-Sin^>.)^ OH' Sina = SinOAH => Sin V = °0A' Ddu bing xdy Sina = SinP = SinX Hay OA = OB = OC Tir ddy ta cd bdi todn sau: Bdi todn 2: Cho td di§n OABC cd OA, OB, OC Smp = Sin6BH=>Sin'P= ° ^ ddi m$t vudng gdc Ggi a,p,X lin lupt Id gde gida OA, OB, OC vdi m$t phing (ABC) Tim GTNN eua bilu thde T = Sin''a + S!n''p + Sm*l OB' SinX = SinOCH=>Sin'X = Sin'a+Sin'p-i-Sin'X = Otf(- OH' OC Lgi dp dung bit ding thirc bunhiacopxki ta ed: (Sina + SiAp-t-SinX)' 3VV2OA.OB.V2OB.OC.V2OC.OA O AB + BC -1- CA > V2 VOA.OB.OC AB.AC diu bing xdy OA = OB =OC Ta nhdn thiy vl trdi eua bit ddng thde chinh Id chu vi tam gide ABC, vl phdi OA.OB.OC lien hp vdi cdng thdc thl tich v^y Vgy dien tieh tam gide ABC ludn nhit bing ta lai cd bai todn sau: Bdi todn 2: Cho td dign OABC ed OA, OB, OC AB = AC= V dd tam gide ABC vudng can ddi mdt vudng gde, ehu vi tam gide ABC bdng t c6 dinh A dinh Tim GTLN eua thl tich td dign Ap dung bit ding thdc bunhiacopxki ta dugc: NIU cho tdng cdc cgnh eua td di?n la mdt s6 1 ^ 1 khdng ddi ta sg ed bdi todn sau AB' AC' AB AC Bdi todn 3: Cho td dign OABC ed OA, OB, OC ddi mgt vudng gde Tim GTLN the tich td di^n bilt Vdy GTLN cda T = y/l khiAB=AC=V2 tdng dp dai cdc cgnheda td dien Id mdt sd khdng dli S Trudc hit ngudi thiy cdn cho HS thdy dugc sy Vdi vipe dp dyng phep tuong ty hinh hpe phSng tuong ty hinh hgc phing vdi hinh hgc khdng gian: vdi hinh hgc khdng gian ngudi thdy khdng nhttng Tam gide phdng chinh Id td di?n khdng ren luygn dugc cho HS kha nang bilt ddt cdi da bilt gian, cde tinh chit eua tam gide d-ong phdng cung vdo hoan cdnh mdi( tam gide dugc dat khdng tuong tu cde tinh chit cua til: dign khdng gian gian) ma cdn ren luyen cho HS kha ndng tu Tam gide vudng dudng eao c6 dinh cd didn tieh Idn tuong tu (hinh hpc phing vdi hinh hpc khdng gian) nhat thi td dien vudng dudng eao cd dinh eung cd thl Tir dd hinh thdnh va phdt triln ndng lyc tu sdng tich Idn nhit Tam giac vudng ed tdng nghich ddo ede tao cho HS cgnh gde vudng cd GTNN thi td dien eung vgy Tu dd HS cd thl phat bilu dugc bdi todn sau: Tdi lifu tham khdo ^AB.AC>2^S„,cal Bdi todn 1: Cho td didn OABC cd OA, OB, OC ddi mdt vudng gdc, cd dudng eao OH = a Tim td dien ed thl tieh Idn nhdt b Tim GTLN ciia bilu thdc T=- OA OB OC Nlu dp dung pitago cho eac mat OAB, OAC, OBC taduge AB-HBC-HCA = 70A' + OB' + VOB' ^ OC + V o C + OA' t>V HI r t n n n i i r zt{^(\e fi/7ni A G.polya, 1976, sdng tgo todn hgc tgp 3, NXBGD Nguyin Hihi Diln (2001) Phuang phdp gidi cdc bdi todn eye tri hinh hgc NXB Khoa hpc ky thuat Phgm Gia Due - Phgm Dire Quang (2007) Gido trinh ddi mdi phuang phdp dgy hgc mdn todn a trudng THCS nhdm hinh thdnh vd phdt trien ndng lyc sdng tgo cho HS NXB DHSP Bui Thdnh Trung (2009) Phdt triin tu sdng tgo cho HS qua dgy hgc cdc bdi todn eye tr\ hinh hgc khdng gian, Lu^n vdn Thgc sy GDH, DHSPHN ... ta duge kgt qua V/^ Nhu vdy ta thdy dupe hinh chop tam gide deu ed cgnh bgn cd dinh thi thg tich hinh chop sg cd GTLN vi the ta ed the phdt bigu bdi todn md nhu sau: Bdi todn 2: Cho hinh ehdp... luygn dugc cho HS kha nang bilt ddt cdi da bilt gian, cde tinh chit eua tam gide d-ong phdng cung vdo hoan cdnh mdi( tam gide dugc dat khdng tuong tu cde tinh chit cua til: dign khdng gian gian) ma... dli S Trudc hit ngudi thiy cdn cho HS thdy dugc sy Vdi vipe dp dyng phep tuong ty hinh hpe phSng tuong ty hinh hgc phing vdi hinh hgc khdng gian: vdi hinh hgc khdng gian ngudi thdy khdng nhttng