KiCH THICH NHU CJU VAN DUNG TUAN HDC VAD THIfC TlfN CHO HOC SINH P H 6 T H 6 N G TS H O A N G LE M I N H '''' Bin than toan hgc ed nguon goe tuthuc ti ln va phue vy thue ti ln Song viec van dyng toan hpc[.]
KiCH THICH NHU CJU VAN DUNG TUAN HDC VAD THIfC TlfN CHO HOC SINH P H T H N G TS H O A N G LE M I N H ' B in than toan hgc ed nguon goe tuthuc tiln va Trong vat li, ngudi ta can biet chinh xac van toe hay phue vy thue tiln Song viec van dyng toan gia toe eua mpt vat thechuyen ddng tai tdng thdi diem hpc vao cudc song ctia hgc sinh (HS) b) Tim tiep tuyen cua mdt dudng cong Bai toan thdng sau tdt nghiep chua tot Chinh vi vay, thupc ve hinh hpc, nhung ndeo nhdng ting dung quan PISA da dua he thd'ng danh gia nang lue toan hpc trpng khoa hgc.puang hgc la nganh ma nhieu eua HS \(ta tuoi 15 van dyng giai eae baitoan thuc nha khoa hpc cua the ki XVII quan tam nghien ciiu tiln (BTTT) Oaden lue, ehung ta can quan tam thich Thiet ke cac thau kinh la mdi quan tam dae biet cua dang den viee boi dudng eho HS kha nang van dyng Newton, Femiat, Descartes vaHuygens.be nghien toan hpc vao cudc song cdn ngoi tren ghe cuu dudng dictia anh sang qua thau kinh, ngudi ta phai nha tn/dng Cd nhieu nhiem vu, dd nhiem vu biet gdc madddtia sang dap vao thau kinh deap dung kich thieh nhu cau van dyng toan hgc vao thue tiln dinh luat khuc xa Gdc can ehii y la gde giua tia sang va (VDTHVTT) la khdi dau quan trgng Khi HS da ed phap tuyen eua ducmg cong, phap tuyen thi vuong gdc nhu cau thi hgse tich cue, ehu dgng viec n i m tri vdi tiep tuyen Oe xae dinh phap tuyen, ngudi ta phai thuc va hieu qua hpc tap se cao xac dinh tiep tuyen Mdt van de cdtinh khoa hgc khae Mot so bten phap kich thich nhu cau nua lien quan den tie^ tuyen cua mdt dudng cong la nghien ciiu ehuyen ddng Hudng chuyen ddng cua vat VDTHVTTchoHS Deed nhu cau VDTHVTT,tmdc het HS can dugc the'ehuyen dpng dbat ki diem nao cua quy dao chinh bietva hieu nguon goc thyc tiln cua cac kien thue toan la hudng cua tiep tuyen quy dao hpc Sau dd, HS phai hieu dugc y nghla va tam quan trpng cua eae kien thue toan hgc thue tiln va cudc song cua ban than hg Giao vien (G V j can giiip HS ed niem tin vao kha nang VDTHVTT ciia minh Nhu vay, nhi^m vu tiep theo cua GV la: - Thudng xuyen cho HS giai nhdng BTTT lien quan den kien thiic toan hgc dang hgc; -Tap luyen cho HS kha nang chuyen td BTTT ve BT toan hpe, ehuyen tu BT toan hpc ve BTTT; - Khai thac, xay dung he thd'ng BTTT v|n dyng toan hgc cho HS luyen tap Dudt day la mdt sd'bien phap va vidu cuthe 1) Gidi thieu cho HS biet nguon gdc tht/e tien eua cae kien tht/e toan hoe Vi dy: Salugc lich su tich phan Tich phan dugc biet den dau tien d Ai Cap vao khoang nhdng nam 1800 tn/dc cdng nguyen de tinh the tich cua cac kim tuthap cut Phep tinh vi - tich phSn dugc sang tao la nhdm giai quyet bon van de khoa hpe cua the kl XVII: a) Cho vat thechuyen dgng theo mdt cdng thdc la m^t ham sd'theo thcri gian, hay tim van toe va gia toe cua nd d mdt thdi diem bat ki; nguge lai, cho biet gia toe cua mdt vat the chuyen dpng la mot ham so theo thdi gian, hay tim van \6c va quang dudng di duae (kil-5/2013)- e) Tim gia tn cue dai va cue tieu eua mdt ham so Khi dan b i n tdsiJng than cdng, khoang each di dugc se phu thude vao gdc cua sung tao vdi mat dait Van de dat la tim gde eho vien dan di xa nhat Nghien euu suchuyen ddng cua hanh tinh lien quan den eae bai toan cue tri, vi du tim khoang each ngin nhat va dai nhait cua mot hanh tinh va mat trdi d) Tim chieu dai cua dudng cong, chang han nhu khoang each di dugc cua mdt hanh tinh mot thdi gian nao dd; dien tich cua hinh gidi han bdi cac dudng cong;thetichcua nhung khdi gidi ban bdinhung phan mat phang va mat cong Ngay nay, cting vdi su phat tnen cua khoa hpc cdng nghe, li thuyet phep tinh vi - tich phan van ed rat nhieu dng dyng quan trpng thue teeupc song va nghien cdu khoa hgc Engels d a v i ^ : "Chlcd phep tinh vi phan mdi dem lai cho khoa hgc tunhien kha nang mieu ta bang toan hgc khdng chi nhung trang thai ma ea nhung qua trinh" 2) Lam cho HS hieu ducre y nghia va tam quan trgng ctia toan hoc thuc tien Vi du: Trong ' TniDng Bai hpc sir pham Ha Noi Tap chi Giao due so 309 53 thuc tiln cudc song eung nhu khoa hoc kithuat chon CO sd I la: s';, = y l ^ snoom- [:s i k^ioiw]=275oootH' ngudi ta can phai tinh dien tieh eua nhung hinh p h ^ g cung nhu thetich cua nhung vat the phuc tap Ch^ng (dong); + Neu ehpn co sd II la: -ã -"-"""'Vr^' :ô:-i:'" han: Khi xay dung nha may thuy dien, de tinh luu (dong) lugng ctia ddng sdng ta phai tinh dien tich thiet dien Do do, Nha Hong nen chpn co sd I de cd chi phi ngang cua ddng song Thiet dien dd thudng la mot tha'p nha't hinh kha phuc tap Khi ddng tau eac kT su can xac Nhan xef Khi day ve ndi dung nay, GV nen ket djnh the tich cua khoang tau cd hinh dang dae biet hgp bai va bai vao tinh hudng day hpe hgp Tn/dc phep tinh tich phan ddi, vdi mdi hinh va tac Qua hai bai toan tren, ngoai viec ren luyen cho mdi vat the nhu vay, ngudi ta phai nghl mot each de HS phan biet cap so cdng va cap so nhan edn giiip tinh Sura ddi eua tieh phan cho Chung ta mdt phuong HS ren luyen kTnang van dyng clip socgng vaeap so phap tong quat de giai hang loat eae baitoan dien tich nhan vao cac tinh hud'ng thuc tiln Mat_khac, cung giiip HS nhan thdc dugc rang thuc tiln mdi va the'tich ndi tren 3) Thudng xuyen eho HS giai nhung BTTT phai lua ehgn can suy xet thau dao, ddi mpt yeu lien quan den kien tht/e toan hpe dang hoc Vi td'nao dd ed Igi tn/dng hap nhung lai khdng dy: Sau hgc xong bai cap so nhan, GV dua bai cd Igi tn/dng hop khac Ngoai ra, sau hpc xong hai bai toan nay, GV cd the yeu cau HS tim toan sau: BT1: Nha em can khoan mgt ealgieng cd sau thuc tien eac tn/dng hc^ tuong tunhu vay, vi du nhu bai toan ve gia taxi, mua tra gdp, 20m delay nude sinh hoat Tim hieu ve tien cdng 4) Tap luyen eho HS kha nang chuyen h/BTTT khoan gieng a hai casa khoan gieng thi duae biet gia ca nhu sau: • Casa I: Gia eua met khoan dau tien la veBTtoan hgc Vdi BT bien phap 2, GV ed SOOOOOd vaketiimet khoan thuhai,giacuamdimet the gcri md cho HS dua BTTT ve bai toan Toan khoan sau tang tfie/n SOOOOdso vdigiacih met khoan hoc da biet theo cac cau hoi sau: GV;€ec6thelua trudc dd - CasaII: Gia cua met khoan dau tien chpn duae m dt ea sd ed \q\ thi ta can biet yeu to nao? WS.'Ta can biet tong gia khoan xong gieng la 400000d va ketumet khoan thd hai, gia cua moi cua hai ca sd G V:De biet td'ng gia khoan met khoan sau tang them 8% gia eua met khoan xong gieng eua hai eo sd thi ta lam gi? WS;Tinh so tn/dc Theo em, nen ehgn edsanao degia tien \itng met khoan theo gia cua hai ea sd roi eong khoan gieng re nhat, biet rang chat lUdng va tong lai Gl^; Viec tinh gia cua tdng met khoan gieng thdigian khoan gieng cua hai ca sola nhu nhau? lien tiep gay mat nhieu thdi gian, v | y ed each ' Ldigial: Ggi u^ va v^ tuong dng la gia cua met nao tinh td'ng gia nhanh hon khdng? HS.'NghT khoan thdn theo each tinh eua co sd I va eo sd II Goi den viee tinh tong n so hang dau tien cua cap sd'cpng S„, S \ lan lugt la tong so tien cila n met khoan gieng hoae caip socgng G l / E m ednhan xet give mdc theo each tinh eua ea sd I va ca sd II chenh lech gia tien giua met khoan lien tiep ctia hai Dithay: ^u^lap cap so cdng, vdi t/|=500000; cosd? Sotien phai tra cho tung met khoan lien tiep cd u„= 500000 + 50000(n-1); fv^lap cap so nhan, dae diem gi gan gid'ng vdi kien thue toan da hpe? HS: vdi v,= 400000, v^= 400000.1,08"' Khi dd, so tien Muc chenh lech gia tien giua met khoan lien tiep eua nha em se phai tra: + Neu ehpn co sd I la: eo sd I la mdt so khong doi {50.000d), cdn dd'i vdi ca 5,„ = =2[i5ooooo+(:o-i)5oooo]=i95ooooo (dong); + Neu sd II thi m et sau b^ng 1,08 lan m et tn/dc dd => gia tien eae met khoan cua co sd I tao caip so cdng vdi choncasallla:-?,„=40oooo• 1-1.08 =-•""•••'^(ddng) I8304785({: cdng sai la 50 000, gia tien cac met khoan cua ca sd II tao cap sd'nhan vcri cdng bdi la 1,08.61'.'Vay Vay ehgn ca sd II se cd gia re hon lam the nao de so sanh va lua chpn ea sd khoan BT2- Nha Hong eung dang can khoan gieng cd gieng nao cd Igi hon? WS.Chi can tinh td'ng so tien sau 25m Thay nha em chon ca sd 11 nen Hong phai tra khoan xong gieng theo gia eua hai ca sd cung ebon casali Nhung biet chuyen, ban Nam va so sanh Gl^.'Em hay phat bieu dudi ngdn ngu lai khuyen Hong ehgn ea sd I Neu la em thi em se toan hgc ctia BT khuyen Hong ehgn easd nao? Visao? HS: Tinh tong eua n so hang dau cua cap so cdng 'Ldi gial :HS didang lap luan tuong tu S T / So Wen khoan gieng cd dp sau 25m se phai tra + Neu va caip sd'nhan, rol so sanh ehung vdi 54 Tap chi Gido due so 309 -(kil-5/2013) 5) Tap luyen cho HS kha nang ehuyen tu BT toan hgc veBTTT.Y\ dy: Xet bai toan sau: 'Choeap so nhan (uj xac dinh nhU sau: u, = 10,q = 2,1: a) Tinh so hang thd 15; b) Hdi408,4101 la so hang thd may?" Em hay gial bai toan tren Dua vao baitoan tren em hay sang tac mot BTTT, van dung ^ giai bai toan de giai quyet bai toan dd Neu HS dugc lam quen nhieu vffl eac bai toan mang ngdn ngdgan gui, ed ndi dung thuc tien thi kha nang-ssnp/a'c" cac bai loaned ndi dung thuc tien tren CO sd bai toan toan hpe cd san cua hgc sinh se cao han Dieu cho tha'y viec tang cudng dua eae bai toan condidung thuc tien vao DH la cdhieu qua vacan phat huy de nang cao chat lugng day hpe mdt so tien bang nhau" Hay xae dinh so ngucri nhdm, biet ring hg co tu 10 den 20 ngucri BT6: Cap so nhan Vat It Chu ki ban cua nguyen to Poloni 210 la 138 (tuc la sau 138 ngay, khd'i lucffig cua nguyen to Poloni eh? cdn mot nua) Em hay tinh (chinh xac den hang phan tram) khd'i lugng cdn lai eua 20 gam nguyen to Potoni 210 sau 7314 (khoang 20 nam) BT7: Bai toan dan sd;Theo ket qua dieu tra dan so, dan sd'trung binh nude Viet Nam qua mptsd'moe thdi gian (Don vj: 1.000 ngudi): N3m Sfidan 1976 49160 1980 53722 1990 66016,7 2000 77635 2010 88434,6 6) Khai thac, xay dt/ng he thong BTTT van diing toan hoe eho HS luyen tap Vi dy: Co the dua he thd'ng bai t$p sau cho hgc sinh luyen tap day hpe ve Cap sd'nhan: Gia suti le % tang dan so tnjng binh mdi nam khdng ddi mdi giai doan Neu cdduy tri tile tang dansonhudgiaidoan2000-2010thiden nam 2015 va 2020 dan so eua Viet Nam la bao nhieu? S r / ; M p t duan dau tu ddi hoi von dau tula 120 trieu d6ng va sau nSm ed the se thu lai dupc so tien la 185 tri^u d6ng Vdi lai su^t ngan hang la 12% mdt nam, hay danhgiaxem cdnen dau tuthuc hien duan hay khdng? Cac baitoan cd ndi dung thuc tien ludn tao cho HS earn giac gan gui, tao nen niem say me va thu hgc tap HS se thudng xuyen tutim hieu xem cudc song cd eae tinh hud'ng nao tuong tunhu bai toan da hoc bay khdng Td dd tieh ei/c tim hieu, trao dot detim, glal thich hay lien he cae tinh huong thue tien vdl kien thdc toan da dugc hgc BT2:Baltoan tle'tkl$m: Nam nay, nha em mud'n Cling di du Ijeh vao dip 30/4 nen tddau nam (mung1/1)boconem b^tdaubdlgn20.000d,sau cd lien tyc sau cao hon tn/de OOOd Hdl den 30/4 thi nha em CO du tien tham gia tour du Tren day la mgt so' bien phap ca ban giiip kich Ijeh dd khdng? Biet ring gia trgn gdi tour du Ijeh cho thich nhu eau VDTHVTT cho HS phd'thdng Mud'n gia dinh gom ngudi la 9.000.000d (chin trieu dong) thue hien dugc cac bien phap dd, G V can phai trang BT3: Cap sd'nhan trong trgt Nha Hoa cd bi npi dung lich su toan hpc, dpng vien va tao dieu mgt vudn cam sanh Vao mua thu hoach, nha Hoa kien cho hp dau tu chat xam cho viec thiet ke cac gid da ban cho ngudi thd nha't nda so cam thu hoach hpe ed VDTHVTT va eac bud'i hoat ddng ngoai khda dugc va nua qua cam, ban cho ngudi thdhai nua so toan hpc Dae biet can dua ndi dung VDTHVTT vao cam cdn lai va nua qua cam, ban eho ngudi thu ba ehuang trinh kiem tra danh gia • nda so cam cdn lai va nda qua cam Den ngudi thu bay thi cung ban cho ngudi dd n i ^ so cam cdn lai va nt)a qua cam thi vda het cam Hdi nha Hoa da thu hoach dddc bao nhieu qua cam? BT4: Sinh hgc: Susinh san eua tmng Am'ip: Mdt conAmipsaumdtgiayndtuphanthanh2Amipcon Va cdsau moi giay, moi Amip eon ay eung h; phan Tinh xem sau 30 giay ed tat ca bao nhieu eon Amip dugc sinh td Amip ban dau? Srs.'Sa/toanst/y/uan.Mdt nhdm khoa hgc dugc thudng mgt so tien vang Tn/dng nhdm dem so tien vangr6idenghi:''ehLingtacd the chia so tien vang theo hai each: hoae ngudi tre tud'i nhat lay dong tien vang ngudi tiep tyc lay ddng tien vang, tiep theo lay 8, tiSp theo lay 16, hoae la ehung ta la'y moi ngudi Iki MM tham khdo OECD Learning mathematics for life A perspective from PISA; 2009 Pham Van Ho^n - NguySn Gia C6c - Triln Thuc Trinh G i i o due hoc mftn Toan, NXB Gido due, H 2000 Bui Van Nghj Van dung h'lu^n vao thuc tien day hoc mfln Toan o- tnToiig phd thdng NXB Dgi hoc su phm Ha Ndi, 2009 SUMMARY The article refers to problems of teaching applied mathematics In practice The author has made five basic measures to stimulate demand for the practical application of mathematics In high school students All of the measures are based analysis, implementation and illustrative examples Tap chi Gido due so 309 55 (ki 1-5/2013)- ... tiln cudc song eung nhu khoa hoc kithuat chon CO sd I la: s'';, = y l ^ snoom- [:s i k^ioiw]=275oootH'' ngudi ta can phai tinh dien tieh eua nhung hinh p h ^ g cung nhu thetich cua nhung vat the phuc... nha Hoa kien cho hp dau tu chat xam cho viec thiet ke cac gid da ban cho ngudi thd nha''t nda so cam thu hoach hpe ed VDTHVTT va eac bud''i hoat ddng ngoai khda dugc va nua qua cam, ban cho ngudi... can khoan mgt ealgieng cd sau thuc tien eac tn/dng hc^ tuong tunhu vay, vi du nhu bai toan ve gia taxi, mua tra gdp, 20m delay nude sinh hoat Tim hieu ve tien cdng 4) Tap luyen eho HS kha nang