Udcntt Day Hoc Toan Trinh Thanh Hai

I HC THI NGUN

TRNG I HC S PHM KHOA TON

Trnh Thanh Hi

(Ch bin)

GIO TRNH

NG DNG CNG NGH THNG TIN TRONG DY HC TON

Thi Nguyn 6/2004

ng dng Cng ngh thng tin trong dy hc ton

Li cm n

hon thnh tp gio trnh ny, chng ti xin trn trng by t lng bit n ti cc cng s thuc khoa Ton trng HSP-HTN trc tip bin son, gp v sa cha ni dung ca gio trnh.

Chng ti xin trn trng cm n cc em sinh vin khoa ton cc kho K34, K35 trong nm hc 2002-2003 v 2003-2004 th nghim hc tp v gp cho nhng bn tho ca b gio trnh ny trong chng trnh hc phn Tin hc ng dng dnh cho sinh vin ton, tin.

Chng ti xin trn trng cm n Ban gim hiu, Phng o to NCKH-QHQT trng HSP-HTN to iu kin chng ti c dp gii thiu v hng dn hn 300 cn b gio vin b mn ton ca 6 tnh. H Giang, Sn La, Bc Kn, Lng Sn, Cao Bng v Thi Nguyn lm quen v thc hnh theo mt s ni dung ca gio trnh ny.

Chng ti xin trn trng cm n cc trng THPT Lng Ngc Quyn- TP Thi Nguyn, THPT I T, THCS Th trn i T - huyn i T, trng THPT Thi Nguyn thuc HSP Thi Nguyn to iu kin cho chng ti th nghim s phm.

Xin trn trng cm n.


Li Ni u

Hin nay chng ta ang chng kin s pht trin nh v bo ca cng ngh thng tin v truyn thng (ICT). Vi s ra i ca Intemet thc s m ra mt k nguyn ng dng cng ngh thng tin v truyn thng trong mi lnh vc ca i sng x hi, kinh t,... Trong khung cnh o to v gio dc c coi l mnh t mu m cho cc ng dng ca ICT pht trin, iu s to ra nhng thay i su sc trong cng ngh o to v gio dc. Nhng cng ngh tin tin nh a phng tin, truyn thng bng rng, CD - ROM, DVD v Intemet s mang n nhng bin i c tnh cch mng trn quy m ton cu trong lnh vc o to, gio dc do s dn n nhng thay i trong phng php dy hc.

Vic ng dng cng ngh thng tin trong ngnh gio dc c ng, Nh nc v B Gio dc v o to c bit quan tm, n c:

+ Ch th s 58 ca B Chnh tr, k ngy 17/10/2000, v y mnh ng dng v pht trin cng ngh thng tin phc v s nghip cng nghip ho, hin i ho nu r: "y mnh ng dng cng ngh thng tin trong cng tc gio dc v o to cc cp hc, bc hc, ngnh hc. Pht trin cc hnh thc o to t xa phc v cho nhu cu hc tp ca ton x hi. c bit tp trung pht trin mng my tnh phc v cho gio dc v o to, kt ni Intemet ti tt c cc c s gio dc v o to".

+Quyt nh ca th tng Chnh ph S: 47/2001/Q-TTg ph duyt "Quy hoch mng li trng i hc,cao ng giai on 2001 - 2010" H Ni, ngy 04 thng 4 nm 2001 ch r: "Tng cng nng lc v nng cao cht lng hot ng th vin; hnh thnh h thng th vin in t kt ni gia cc trng tng bc kt ni v h thng th vin ca cc trng i hc, th vin quc gia ca cc nc trong khu vc v trn th gii. M cng kt ni Intemet trc tuyn cho h thng gio di i hc".

+Ch th s 29 ca B trng B Gio dc v o to k ngy 30/7/2001 v vic tng cng ging dy, o to v ng dng cng ngh thng tin trong ngnh gio dc giai on 2001-2005 nu r: "i vi gio dc v o to, cng ngh thng tin c tc ng mnh m, lm thay i ni dung, phng php. phng thc dy v hc. CNTT l phng tin tin ti mt x hi hc tp. Mt khc gio dc v o to ng vai tr quan trng bc nht thc y s pht trin ca CNTT thng qua vic cung cp ngun nhn lm cho CNTT

+Ch th s 40/CT-TW ca Ban chp hnh TW ng ra ngy 15/6/2004 v vic xy dng, nng cao cht lng i ng nh gio v cn b qun l gio dc nu r:


"Tch cc p dng mt cch sng to cc phng php tin tin, hin i, ng dng cng ngh thng tin vo hot ng dy v hc."

Mn ton l mt b mn vn d c mi lin h mt thit vi tin hc. Ton hc cha ng nhiu yu t phc v nhim v gio dc tin hc, ngc li tin hc s l mt cng c c lc cho qu trnh dy hc ton.

Vi s h tr ca MTT c bit l ca Intemet v cc phn mm dy hc qu trnh dy hc ton s c nhng nt mi chng hn:

Gio vin khng cn l kho kin thc duy nht. Gio vin phi thm mt chc nng l t vn cho hc sinh khai thc mt cch ti u cc ngun ti nguyn tri thc trn mng v cc CD-ROM.

- Tin trnh ln lp khng cn my mc theo sch gio khoa hay nh ni dung cc bi ging truyn thng m c th tin hnh theo phng thc linh hot. Pht trin cao cc hnh thc tng tc giao tip: hc sinh - gio vin, hc sinh - hc sinh, hc sinh - my tnh,... trong ch trng n qu trnh tm li gii, khuyn kch hc sinh trao i, tranh lun,... t pht trin cc nng lc t duy hc sinh.

Nh vy vi mc tiu nng cao cht lng o to, i mi phng php ging dy th mt trong cc bin php kh thi l bit kt hp cc phng php dy hc truyn thng v khng truyn thng trong c s dng CNTT nh mt yu t khng th tch ri.

Vi mc tiu khim tn l cung cp nhng thng tin ban u bn c c th khai thc cc phn mm ton hc vo cng vic ging dy, hc tp ca llluul chng ti mnh dn bin son b ti liu: ng dng Cng ngh thng tin trong dy hc ton. gio trnh gm:

Vi ni dung chnh " Hng dn s dng v khai thc mt s phn mm ph bin trong dy hc ton "

y l mt cng vic mi m v "qu ti" i vi chng ti nn khng th trnh c sai st. Rt mong c s tha th v ng gp kin ca bn c, c bit l cc Thy, C gio v cc em hc sinh, sinh vin - y s l ngun t liu qu gi chng ti hon thin ti liu ny.

Chng ti xin trn trng cm n.

a ch lin lc: Trnh Thanh Hi - Khoa Ton - Trng HSP Thi Nguyn;

E- mau: [email protected].

Gio trnh: S dng Cng ngh thng tin trong dy hc ton

Mc lc

Chng 1: DY HC TON VI S H TR CA CNG NGH THNG TIN V TRUYN THNG (ICT) .........................................................................................1

1.1. Vn khai thc s dng ICT trong dy hc ton ...............................................1 1.2. T chc dy hc ton trong mi trng ICT........................................................4 1.3. Nhn nh............................................................................................................12

Chng 2 S DNG PHN MM GRAPH ...............................................................13 2.1. Gii thiu v phn mm Graph...........................................................................13 2.2. Lm vic vi Graph ............................................................................................13 2.3. Gii thiu h thng Menu...................................................................................14 2.4. Mt s chc nng c bn ....................................................................................16 2.5. Th vin cc hm ca Graph ..............................................................................20 2.6. Khai thc phn mm Graph ................................................................................21 2.7 Bi tp: .................................................................................................................21

Chng 3 S DNG PHN MM HNH HC NG.............................................22 3.1. Gii thiu s lc v phn mm Cabri Geometry..............................................22 3.2. Cc vn c bn lm vic vi Cabri Geometry ..........................................22 3.3. Thao tc vi h thng cc cng c ca Geometry Cabri ....................................26 3.4. Gii thiu phn mm The Geometer's Sketchpad ..............................................38 3.5. V hnh vi phn mm hnh hc Cabri...............................................................46 3.6. S dng Cabri minh ho bi ton qu tch .........................................................47 3.7. Khai thc phn mm hnh hc ng Cabri h tr dy hc ton .........................50 3.8. Tho lun v bi tp............................................................................................58

Chng 4 .......................................................................................................................59 HNG DN S DNG PHN MM MAPLE.......................................................59

4.1. Tng quan chung v phn mm Maple...............................................................59 4.2. Lm vic vi Maple ............................................................................................59 4.3. Giao din ca ca s lm vic ca Maple ..........................................................60 4.4. Cc thao tc c bn trong vi Maple ..................................................................61 4.5. S dng cc lnh ca Maple ...............................................................................66 4.5. Khai bo hm t to............................................................................................85 4.6. Cc cu trc c bn c s dng trong lp trnh ca Maple ............................86 4.7. ng dng maple trong kho st hm s ..............................................................88 4.8. S dng Maple h tr kim tra kt qu tnh ton. ............................................119 4.8.2 Kim tra tnh ly tnh ca mt ma trn vung................................................120 4.9 S dng Maple h tr suy lun trong qu trnh hc ton. .................................123 4.10. Khai thc Maple trong Xc sut thng k ......................................................133 4.11. Maple vi bi ton quy hoch.........................................................................136 4.12. Khai thc Maple trong hnh hc .....................................................................140

Ti liu trch dn, tham kho.......................................................................................183


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Chng 1: DY HC TON VI S H TR CA CNG NGH THNG TIN V TRUYN THNG (ICT)

1.1. Vn khai thc s dng ICT trong dy hc ton

Cng vi s pht trin nh v bo ca cng ngh thng tin v truyn thng, vic nghin cu v trin khai cc th mnh ca ICT nhm h tr qu trnh dy hc ton c nhiu quc gia v cc nh gio dc quan tm.

Trong ti liu The free NCET (1995) leanet (Mathematics ang IT - apupils entitlement) m t 6 hng c bn trong vic s dng ICT nhm cung cp cc iu kin cho ngi hc ton, c th:

* Hc tp da trn thng tin ngc: My tnh c kh nng cung cp nhanh v chnh xc cc thng tin phn hi di gc khch quan. T nhng thng tin phn hi nh vy cho php ngi hc a ra s c on ca mnh v t c th th nghim, thay i nhng tng ca ngi hc.

* Kh nng quan st cc m hnh: Vi kh nng v tc x l ca MTT gip ngi hc a ra nhiu v d khi khm ph cc vn trong ton hc. My tnh s tr gip ngi hc quan st, x l cc m hnh, t a ra li chng minh trong trng hp tng qut.

* Pht hin cc mi quan h trong ton hc: MTT cho php tnh ton biu bng, x l ho mt n st s thay i trong cch chnh xc v lin kt chng vi nhau. Vic cho thay i mt vi thnh phn v quacc thnh phn cn li gip ngi hc pht hin ra mi tng quan gia cc i lng.

* Thao tc vi cc hnh ng: Ngi hc c th s dng MTT biu din cc biu mt cch sinh ng. Vic gip cho ngi hc hnh dung ra cc hnh hnh hc mt cch tng qut t hnh nh ca my tnh.

* Khai thc tm kim thng tin: MTT cho php ngi s dng lm vic trc tip vi cc d liu thc, t hnh dung ra s a dng ca n v s dng phn tch hay lm sng t mt vn ton hc.

* Dy hc vi my tnh: Khi ngi hc thit k thut ton s dng MTT gip tm ra kt qu th ngi hc phi hon thnh dy cc ch th mnh lnh mt cch r rng, chnh xc. H sp t cc suy ngh ca mnh cng nh cc tng mt cch r rng.

* S dng ho vi my tnh: th trn my tnh l nt mi trong cc lp dy hc ton. Kenneth Ruthven bt u la chn, nghin cu v pht trin d n s dng ho my tnh t nm 1986 (Ruthven 1990).Tuy nhin, khi nim, nh v mt mi trng m trong ngi s dng c th thay i kch thc to nh, iu tra, tm hiu s giao nhau v


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dc a phng c pht trin t lu (David Tall s dng my tnh BBC).

Tall trnh by con ng s dng ho my tnh ca ng dy hc cc php tnh t u nm 1980. Phn mm "Hnh nh my tnh" do ng pht trin ln u tin cho my tnh BBC. Phn mm ny cho php ngi hc phng to, thu nh th vi bt k phm vi no, qua hnh thnh khi nim, chng hn gradient ca th. Tall sm cng b mt lot cc bi bo v s quan h trong dy ton tp ch Mathematics Teaching, sau cc bi bo c tp hp li trong mt cun sch nh (Tall 1987). Hn na trong thi gian gn y mt vi ngi tng t Tall ng dng bng tnh, ho, cc tng ny c bo co trong Micromath (Morgan .Jones & Mcleay, 1996; Crawford, 1998; Morrison, 1998).

Mt vi nghin cu ch ra rng nu gio vin c s dng ho MTT trong qu trnh ging bi th h c th a ra cc cu hi vi yu cu cao hn so vi lp khng s dng. V d, Ring (1993) hng dn 2 gio vin lm th no vi ho my tnh phc v cho cu hi chin lc ca gio vin v phng php trnh by kin thc ton hc. Rich tr gip gio vin s dng ho my tnh v ch trng n vic kho st t m, gip hc sinh a ra phng on ca mnh. Vi s h tr ca my tnh, gio vin c th ra cc cu hi c yu cu cao hoc s dng nhng v d khc nhau, qua khai thc vai tr quan trng ca ho my tnh trong s phn tch vn . Mt khc, s dng ho cho php ta phn tch cc mi lin kt gia i s, hnh hc. tng trn v s dng ho my tnh cho hc sinh t 11 n 16 tui c trnh by trong Open Calculalor Challenge ca Open University (1993), Graham & Galpin (1998), Arter (1993), Ruthven (1992). Theo Colette, mt nh nghin cu v dy hc mn ton ngi Php, th MTT c kh nng to ra mi trng gii quyt vn (problem solving environments) cho hc sinh v mi trng c vai tr to ln trong vic kch thch hot ng tm ti khm ph v t hnh thnh kin thc mi. Theo hc thuyt kin to (cosntructivist hypothesis) th kin thc hc sinh c to nn khi hot ng trong mi trng ton hc, MTT c kh nng rt tt trong vic to ra mi trng Trong mi trng my tnh hc sinh tip thu c bng chnh hot ng, thc hnh ca mnh (learning hy doing).

John Mason (tc gi ngi Anh) nm 1992 pht trin tng cho rng cc phn mm my vi tnh v ton l mt h thng cc cng c c kh nng c s dng gii ton v gip nghin cu khi qut i n vic tm ra cc tnh cht ton hc.

Rosamund Sutherland thng qua d n "ANA" nghin cu v vic dy hc ton vi phn mm lng c c kt rng: "iu quan trng nht khi hc sinh s dng ngn ng, k hiu my tnh l c kh nng hnh thnh khi qut ho ton hc".

Cc tc gi Mark Hunter, Paul Marshall, John Monaghan v Tom Rope (nm 1993) tin hnh mt t th nghim vi vic s dng h thng chng trnh CAS trong ging dy cho i tng hc sinh THCS. Kt qu th nghim cho thy kh nng suy lun ton hc ca hc sinh do phng tin mi em li t hiu qu rt cao.

Ton hc l mt mn khoa hc tru tng, do khai thc s dng phn mm v


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MTT trong dy v hc ton c nhng c th ring. Ngoi mc tiu tr gip hc sinh chim lnh kin thc th vn pht trin t duy suy lun lgic, c tng tng sng to ton hc v c bit l kh nng t tm ti chim lnh kin thc l mt mc tiu rt quan trng.

Sn phm ca mi trng hc tp vi s h tr ca cng ngh thng tin l nhng hc sinh c nng lc t duy sng to ton hc, c nng lc gii quyt cc vn v nng lc t hc mt cch sng to. Nh vy, vic t chc dy - hc vi s h tr ca MTT v cc phn mm ton hc nhm xy dng mt mi trng dy - hc vi 3 c tnh c bn sau:

To ra mt mi trng hc tp hon ton mi m trong mi trng ny tnh ch ng, sng to ca hc sinh c pht trin tt nht. Ngi hc c iu kin pht huy kh nng phn tch, suy on v x l thng tin mt cch c hiu qu.

Cung cp mt mi trng cho php a dng ho mi quan h tng tc hai chiu gia thy v tr.

To ra mt mi trng dy v hc linh hot, c tnh m. Trong cc hnh thc t chc dy - hc c s h tr ca cng ngh thng tin th vai tr

ca ngi thy c bit quan trng. N i hi cao hn ngi thy kh nng cc hnh thc t chc dy hc truyn thng. V mt gc no , nng lc ca ngi thy th hin qua h thng nh hng gip hc sinh pht hin v gii quyt vn thng qua h thng cc cu hi. H thng cc cu hi ca ngi thy phi p ng c cc yu cu sau:

Cc cu hi phi mang tnh gi m, nh hng gip cho hc sinh con ng x l thng tin i n kin thc mi.

Cc cu hi phi tr gip hc sinh cng c kin thc mi v tng cng kh nng vn dng kin thc trong thc hnh.

Cc cu hi phi c tnh m khuyn khch hc sinh pht huy tnh sng to, kh nng phn tch tng hp, khi qut ho cc tri thc c trang b gii quyt vn .

iu khc bit so vi cc hnh thc dy hc truyn thng l qu trnh truyn t, phn tch, x l thng tin v kim tra nh gi kt qu c gio vin, hc sinh thc hin c s tr gip ca cc phn mm v MTT.


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1.2. T chc dy hc ton trong mi trng ICT

1.2.1. S dng phng tin ICT trong cc gi ln lp vi s ng hc sinh

Hnh thc ny c p dng vi quy m s hc sinh t 40 n 60. Ngoi cc phng tin dy hc thng thng ca mt lp hc truyn thng nh bng en, phn trng, thc k... lp hc c trang b thm my tnh, my chiu Project, my chiu Overhead... Trong gi hc, c lp quan st kt qu x l ca my tnh trn mn hnh ln.

Hnh thc ny c nhng c im sau:

- Gio vin trc tip ln lp khai thc cc tnh nng ca ICT trnh by kin thc mt cch sinh ng. Mt s trng hp, gio vin c th chun b sn hnh v, bng biu,... rt ngn thi gian thao tc vi my tnh.

- Hc sinh quan st v phn on theo s nh hng ca gio vin. Hc sinh t c trc tip thao tc vi my tnh. V d trong dy hc nh l, m hnh t chc lp hc nh sau:

Nh vy, lp hc thng din ra theo xu hng sau:

- Tng hc sinh lm vic gn nh "c lp" vi nhau, cng tp trung vo quan st, x l nhng thng tin trn mn hnh.

- Nhng hc sinh kh, gii cha c pht huy ti a kh nng ca bn thn v c lp cng c giao mt nhim v c th nh nhau.

- Trong lp hc gia cc hc sinh s c s ganh ua vi nhau, do vy d so snh, phn loi gio vin thng c xu hng tp trung vo ging dy v k nng thc hnh, gi


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li kin thc c v h thng li kin thc ca hc sinh.

1.2.2. T chc hot ng hc "cng tc " theo nhm nh

Hc sinh c chia thnh cc nhm nh khng qu 7 hc sinh.

Trang thit b ti thiu mi nhm c mt my tnh. Nu cc my tnh c ni mng th tt hn v cc nhm c th chia s thng tin vi nhau.

Hnh thc ny c nhng c im sau:

- Gio vin giao nhim v cho cc nhm thng qua cc nh hng gi m hoc cc phiu hc tp.

- Mi nhm hc sinh s dng chung mt my tnh, c trch nhim cng tc, chia s nhng tng ca bn thn hon thnh nhim v ca nhm cng nh ca mi bn thn. Kt qu ca nhm ch thc s c hiu qu khi ton b cc thnh vin trong nhm hon thnh mc tiu hc tp. Nh vy mi thnh vin u nhn thc c rng: Khng phi mi hc sinh lm c g m l c nhm hc c iu g. Nh vy ba yu t c bn ca hnh thc ny l: S thnh cng ca ton nhm, trch nhim ca mi c nhn trong nhm v iu quan trng l mi thnh vin trong nhm u c c hi thnh cng bnh ng nh nhau.

Hnh thc lm vic " cng tc " theo nhm nh c nhng u vit sau:

- C nhiu c hi th hin, trao i nhng suy ngh ca bn thn. Thay v ch mt mnh gio vin thao tc, trnh by, hnh thc ny mi ngi trong nhm u c th trc tip lm vic vi cc i tng hnh hc v c nhm lun sn sng n nhn nhng nhn nh, phn on ca mi thnh vin.

- Mi c nhn ngoi iu kin lm vic trc tip vi phn mm, cn c kh nng nhn c s h tr khng ch mt mnh gio vin m ca c nhm, qua lm tng hiu qu hc tp ca c hc sinh c gip v nhng hc sinh i gip cc bn. Chnh v vy kh nng thnh cng ca mi c nhn u tng. - Nhng hc sinh hc km s c kh nng, c hi by t v hc hi nhiu hn chnh cc thnh vin trong nhm. V d trong dy hc nh l c th t chc hc tp theo m hnh sau:

Hnh thc hc "cng tc" ch thc s pht huy tc dng nu ta m bo c cc yu

t quan trng sau:

- Thit lp s ph thuc tch cc gia cc thnh vin trong nhm.


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- Gio vin hnh thnh v pht trin c k nng hp tc ca mi hc sinh.

- Khng nh r rng trch nhim ca tng c nhn trong nhm.

- To c mi trng tng tc gia cc thnh vin trong nhm.

- Hnh thnh k nng giao tip, ng x cho hc sinh trong hc tp.

- Hnh thc phn chia nhm:

Tu tng ni dung m ta c th chia nhm ngu nhin hay chia nhm theo trnh ngi hc. V d: Khi lm vic vi ni dung mi c th s dng nhm ngu nhin hc sinh gii, kh c th km cp, gip hc sinh yu. Nu l gi luyn tp, rn luyn k nng th c th phn chia theo trnh ngi hc giao nhim v ph hp nhm pht huy c ti a kh nng ca ngi hc.

1.2.3. Hnh thc hc sinh lm vic c lp ti lp

- Mi hc sinh c s dng mt my tnh. Lp hc c t chc ti phng my tnh ca trng.

- Nhim v ca c lp c phn thnh cc nhim v nh giao cho cc c nhn (do vy hc sinh u thc c rng, tuy hot ng c lp nhng thnh cng ca bn thn chnh l thnh cng ca c lp v ngc li).

Hnh thc ny c cc c im chnh sau:

- Hc sinh c iu kin pht huy ht kh nng ca bn thn.

- Trong mt thi im c th gii quyt nhiu bi ton khc nhau. '

- Ph hp vi vic nhn thc chnh lch trong mt lp. Tu mc kh nng ca bn thn m hc sinh c khuyn khch m nhn nhng nhim v va sc.

- i hi trnh phn tch, tng hp vn ca gio vin mc cao (v nu khng gi hc phn tn, khng hng hc sinh c n nhng ni dung kin thc cn nm sau mi gi hc).


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Trong m hnh lm vic a tuyn, gio vin ng vai tr iu khin "t xa" bng cch nu nhim v chung ca c lp. Hc sinh trao i, phn chia bi ton thnh cc bi ton con (qu trnh ny c th c lp hoc din ra di s tham mu ca gio vin). Mi c nhn cn c vo kh nng ca mnh nhn thi cng mt m un. Trong qu trnh lm vic, c th c s trao i gia cc hc sinh. Kt qu ca hc sinh ny c th c hc sinh khc s dng. Thm ch, mt thnh vin c th yu cu mt thnh vin khc iu chnh kt qu theo hng c li cho vic k tha cho cc thnh vin khc.

1.2.4. S dng phng tin ICT dy mt ni dung ngn

Qu thi gian s dng phng tin ICT ch khong 1 n 3 pht nhm mc ch nu ra tnh hung c vn vn , gi m, kim chng nhng suy on nhn nh trong qu trnh


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i tm li gii hoc minh ho kt qu li gii. Hnh thc ny thng c s dng trong hnh thc t chc lp hc vi s ng. Gio vin cho mt vi hc sinh trc tip thao tc vi my tnh. Hnh thc ny tn dng c thi gian ln lp v ph hp hn c l cc tit hc ni dung bi mi.

V d. S dng Cabri pht hin hoc hnh thnh ng c chng minh nh l minh ho qu tch, minh ho kt qu tng qut va tm c vi nhng trng hp c th . . .

1.2.5. S dng phng tin ICT dy hc trn vn mt phn ca bi hc

Vi mc ch s dng phn mm gii quyt trn vn mt ni dung c th trong tit hc nn qu thi gian s dng phng tin c th ko di t 5 n 10 pht. Qua vic thao tc vi phn mm, hc sinh pht hin v gii quyt trn vn mt vn , v d dy hc khi nim mi. Hnh thc ny c th s dng trong c hnh thc t chc lp s ng hoc hc tp theo nhm. Hot ng s dng, khai thc phn mm c tin hnh an xen vi cc hot ng khc nn gi hc rt sinh ng ph hp vi tm sinh l ca la tui hc sinh.

1.2.6. S dng phng tin cng ngh thng tin dy trn vn mt tit hc

Trong hnh thc ny bi ging c thit k thnh mt h thng lin kt cht ch phi hp an xen cc hot ng ca thy v tr t c mc ch ca gi ging. iu c bit l bi ging c thit k sao cho khai thc ti a s h tr ca phn mm v MTT. Vi hnh thc ny, c th thi lng s dng bng en s khng nh cc gi hc khc v ni dung kin thc c thit k sn trong cc Slide v gio vin chiu ln mn hnh thay cho vit bng (ta tm gi l gio n in t). Gio n in t c bin son di hnh thc cc Slide bao gm cc n v tri thc, cc bi tp t n gin n phc tp, to iu kin cho vic lnh hi tri thc. T chin lc s phm, ta cu trc ho cc n v tri thc trong gio n. Cc ni dung trnh by bao gm cc s kin s ny sinh trong qu trnh tng tc. Cc tc ng ny thc hin theo nhng lc nht nh. Vic phn tch, nh gi cc p ng ca ngi hc thng da trn cc yu cu chun b sn. S lng cng nh ni dung ca mi Slide c xc nh sao cho th hin c tt nht ni dung bi ging cng nh s phm. Lng thng tin ca mi Slide cng khng hn ch, vi s h tr ca cc phn mm cng c th ni dung khng ch l dng text (vn bn) m cn l m thanh, hnh v, nh ng, thm ch c video. Gio n in t cho php ta trnh din mt cch trc quan sinh ng cc ni dung nh kho st hm s, dng hnh, qu tch m nu khng s dng my vi tnh th khng th no m t c vi chc nng siu lin kt (Hyperlink) cho php ta kt ni cc Slide ca bi ging thnh mt h thng, t mt v tr ta c th truy nhp n bt k mt ni dung (mt Slide) no khc trong bi ging. Mt khc, ta c th kt ni hng lot cc bi ging vi nhau thnh mt h thng hon chnh ging dy mt vn , mt chng.

V gio n in t tch hp sn mt khi lng kin thc c lin kt sn cho php ngi gio vin n tp n phn no, gio vin kch chut vo tn mc chuyn n slide ni dung ca mc . Vi gio n in t ny tin trnh ln lp rt linh hot, tin trnh n


9

tp c th r nhnh, trin khai i su vo nhng ni dung chi tit, quay lui chuyn v nhng ni dung trnh by... Hn na, khi lng kin thc c n tp li trong mt tit rt ln v gio vin tit kim c thi gian vit k, v ln bng. Nh s h tr ca my tnh v gio n in t, gi n tp chng khng cn l cnh gio vin lit k li ni dung hc m n l qu trnh lm vic tch cc ca tr di s dn dt ca thy. Vic lm vic vi "cy" kin thc gp phn pht trin t duy lgic, bin chng cho hc sinh.

Tuy nhin gio n in t c thit k theo mt kch bn ca ngi gio vin d nh trc nn vic a ra cc tnh hung l hu hn, cc gii php p ng yu cu c nh, trong thc t rt a dng v phong ph. Vy gio vin cn phi hp vi cc phng php, hnh thc dy hc khc pht huy ti a tnh tch cc, ch ng ca ngi hc nhm nng cao cht lng dy hc.

Quy trnh thit k mt gio n in t:

V d v hnh thc gio n in t


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1.2.7. S dng ICT trong kim tra, nh gi

Hot ng chnh ca ni dung ny l s dng MTT tr gip hc sinh gii bi tp, kim tra nhn thc ca bn thn, c th:

+ Giao cho cho mi nhm hc sinh hoc mi hc sinh mt my tnh. Hc sinh t s dng phn mm tm ti cch gii quyt vn v hon thnh nhim v c giao (gii c bi tp hoc hon thnh phiu hc tp ca c nhn, ca nhm).

+ Kim tra nhn thc hc sinh bng ngn hng in t: Ton b cu hi v p n c thit k np sn trong my. Mi hc sinh c my pht ngu nhin mt phiu kim tra. Hc sinh s chn phng n tr li bng cch s dng chut hoc bn phm nh du cu tr li m hc sinh cho l ng. Kt qu chm im c my tnh t ng cp nht v thng bo kt qu ra mn hnh.


11

1.2.8. Tr gip hc sinh t hc

Trong iu kin nhiu hc sinh c iu kin trang b my tnh ti nh ring th y l mt hnh thc cn c khuyn khch v khai thc s dng v thi lng hc sinh t hc ngoi mt phm vi lp hc l rt ln, mt khc n khng tri buc hc sinh v mt thi gian, a im, c th:

+ Gio vin ra nhim v, hc sinh s dng phn mm c lp tm ti v a ra cch gii quyt vn . Gio vin kim tra, nhn nh li kt qu.

+ Gio vin thit k nhim v hc tp ghi trong cc tp tin. Hc sinh m tp tin, theo hng dn v tip tc hon thnh nhim v. Gio vin c th c thit k nhim v theo tng liu (c ghi trong cc tp tin khc nhau) hc sinh c th t hc theo chu trnh r nhnh.

+ S dng cc bi ging "gia s in t". Ton b ni dung kin thc, v d minh ho v bi tp c thit k di dng Website. Hc sinh ln lt kch chn nhng ni dung cn hc v tm hiu ni dung qua cc v d km theo. Kt thc mi mc c bi tp cho hc sinh t kim tra nh gi nhn thc ca mnh. Sau khi gii song bi tp hoc c kh khn, hc sinh c th m li gii hoc hng dn tham kho.

Nh vy hiu qu ca qu trnh ny ph thuc hon ton vo tnh ch ng, tch cc

v s hng ch rt cao ca hc sinh.

1.2.9. Dy hc qua mng

Trong iu kin c s h tng cng ngh thng tin ang pht trin nhanh nh hin nay th Vit Nam cc hnh thc o to qua mng tr nn n gin. Mi nh trng u c mt trang web ring ca mnh. Hc sinh truy cp qua mng v thc hin theo phc hc tp c quy nh. Cc thc mc hoc trao i u c thc hin nhanh chng bng dch v th in t (Email) hoc trao i trc tuyn (online) vi gio vin hng dn theo cc gi quy nh.

Vi hnh thc ny, hc sinh hon ton t ch v mt thi gian, ni dung v phng

php hc tp. Hnh thc ny pht huy c tnh tch cc ca hc sinh, ph hp vi xu th


12

mi ca gio dc trn th gii.

1.3. Nhn nh

Vic khai thc c hiu qu s h tr ca ICT s tc ng mt cch tch cc ti hot ng dy v hc bi cc yu t sau:

* Tnh linh ng, mm do: ngi hc b thu ht bi nhng thng tin v qu trnh x l thng tin trn my tnh, t truy tm nguyn nhn vn .

* Tnh h thng: ngi hc c th iu chnh nhn thc ca mnh trong h thng kin thc nm c vn , iu ho mu thun gia s hoang mang bi ri trc vn mi v tnh t m ham mun tm hiu, khm ph.

* Tnh kt hp: ngi hc c lm vic trong nhm nn khai thc c nhng u im v ng vin s ng gp ti a ca tng c nhn.

* Tnh mc ch: ngi hc c gng, tch cc tp trung cao vo cc hot ng nhm tm hiu, khm ph, nhn thc cho c i tng.

* Tnh m thoi: hc l mt hot ng x hi, qu trnh i thoi gia ngi hc vi nhau s h tr c lc cho vic nm bt c kin thc khng ch trong m c ngoi trng hc.

* Tnh ng cnh: hot ng hc c t v tr c ngha c bit trong cc hot ng ca th gii thc hoc ng vai tr mi trng c s, do to ra mt ng cnh mang tnh tch cc, thc y vic hc ca sinh vin.

* Tnh phn nh: vi s h tr ca cc cng c, ngi hc kt ni li nhng g h c hc v thu nhn nhng phn nh trong cc qu trnh t my tnh i n nhng quyt nh ng n.

Vn s dng ICT trong nh trng c khng nh trong Ch th 58- CT/TW ngy 17- 10-2000 ca B Chnh tr Ban chp hnh Trung ng ng Cng sn Vit nam, Ch th 29-2001/CT-BGD&T ca B trng B Gio dc v o to, v rt nhiu vn bn khc ca Chnh ph, ca B Gio dc v o to. iu chng t tnh cp thit v hiu qu ca vic a ICT vo nh trng.

Cu hi tho lun: Khi s dng ICT trong dy hc th vai tr ca ngi Thy c g khc so vi cc hnh thc dy hc khng s dng ICT?


13

Chng 2 S DNG PHN MM GRAPH

2.1. Gii thiu v phn mm Graph

Phn mm Graph l mt phn mm h tr minh ho v gii quyt mt s vn trong b mn ton ph thng tng i gn nh c ci t trong mi trng h iu hnh Windows. Ton b chng trnh cha gn trn mt a mm 1.44 MB ca Ivan Johansen. Phn mm ny hin nay c th download min ph ti a ch: http://www.padonwan.dk. Hin nay c phin bn 3.0 c a ln mng ngy 20/1/2004.

2.2. Lm vic vi Graph np chng trnh Graph, ta thc hin dy thao tc: StartlPrograms/Graph hoc

nhy chut vo biu tng ca Graph:

Giao din ca phn mm Graph gm cc thnh phn: H thng menu, thanh cng c v trang cng tc c chia thnh 2 phn: ca s tri l danh sch cc i tng: danh sch hm (Functions), danh sch cc im (Point series), danh sch cc min c la chn (Shades) v danh sch tn cc i tng (Labels), ca s bn phi dnh hin th cc i tng nh th, ng thng, im, nhn tn i tng,...


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2.3. Gii thiu h thng Menu

H thng mnh ca Graph gm 6 chc nng c bn: File, Edit, Function, Zoom, Cacl, v Help

2.3.1. Menu File:

- M mt tp mi ( New - Ctrl + N),

- M mt tp c ( Open - CTrl+O),

- Lu tr tp ( Save - Ctrl+S, Save as),

- In n ( Print),

- Kt thc phin lm vic (Exit - Alt+F4),

- Lu tr kt qu di dng nh (Save as image - Ctrl+B), chc nng ny gip ta c c cc th p

thit k gio n in t

2.3.2.Menu Edit:

- Hu b thao tc ngay trc ( Undo - Ctrl-Z),

- Lp li thao tc ngay trc ( Redo - Ctrl+Y),

- Ct i tng lu vo b m (Cut - Ctrl+x),

- Copy i tng lu vo b m ( Copy - Ctrl+c),

- Dn i tng t b m ra trang cng tc (Paste- Ctrl+v),

- Sao chp hnh nh (Copy image),

- Tu bin h trc to ( Axes - Crtl+A),

Xc lp mi trng lm vic ( Options).


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2.3.3. Menu Function:

- Khi to mt hm mi(Insert frunction - Ins),

- To v tip tuyn (Insert tangent - F2),

- nh du mt min(Insert shade... - F3),

- V im trn h to ca trang cng tc

(Insert point series... -F4),

- V h thng im (Insert trendline-Ctrl+T),

- t tn cho cc i tng (Insert label...),

- Cp nht cc i tng ang c la chn (Edit...),

- Xo b cc i tng ang c la chn

- Chn th o hm ca hm s (Insert f'(x)).

2.3.4. Menu Zoom :

H thng cc chc nng ca menu con gm cc lnh iu khin, thay i gc hin th ca trang lm vic, trong ch cc chc nng sau:

- iu chnh theo hng thu hp khong [a,b] ca trc honh c hin th trn trang cng tc (In)

- iu chnh theo hng gia tng khong [a,b] ca trc honh c hin th trn trang cng tc (Out), Chuyn v trng thi chun ( Standard-Ctrl+D),

- Chuyn v trng thi cho php di chuyn cc i tng trn trang cng tc (Move system - Ctrl+M,

- Chuyn v ch hin th sao cho quan st c tt c cc im trn trang cng tc (All points).

2.3.5. Menu Calc:

- Xc nh di ca th f(x) trn on [a,b] no ( Length of path),

- Tnh din tch phn gii hn bi cc ng thng x=a, x=b vi th ca f(x) ( Aren),

- Xc nh gi tr ca f(x) ti mt im xo no (Evaluate - Ctrl+E),

- To bng tnh gi tr ca f(x) trong on [a,b] vi bc chia cch u ( Table).


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2.4. Mt s chc nng c bn

2.4.1. V th hm f(x)

khi to mt th mi, dy thao tc nh sau:

-> Function-> Insert function (hoc chn biu tng trn thanh cng c). Xut hin bng khai bo cc tham s:

+ Biu thc tng qut ca f(x),

+ Gii hn phm vi gi tr ca i s,

+ Kiu nt v,

+ rng nt v,

+ Mu nt v,

Khai bo xong, nhn OK hon tt cng vic.

2.4.2. Cp nht i tng

chnh sa th ca hm s c, thao tc nh sau: Trc tin la chn th s chnh sa, tip theo chn: ->Function ->Edit (hoc bm p vo biu thc ca f(x) ca s bn tri) s xut hin ca s Edit function ta cp nht li. Ta c th khai bo li gi tr on [a,b], chn li dy nt v, nhp ni dung ghi ch :cho i tng hoc mu v ca ng tip tuyn. Nhn OK hon tt cng

vic.


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2.4.3. V tip tuyn vi th f(x) ti im xo

V tip tuyn vi th hm s f(x) ti im xo trc tin phi la chn hm s, tip theo chn: -> Function -> Insert tangent. Xut hin ca s Insert

tangent. Ta nhp gi tr xo ti ca s: x=, sau chn rng, kiu ng v tip tuyn, mu v c th nhp ni dung ghi ch cho tip tuyn ti ca s: Description. Sau cng nhn OK hon tt.

iu chnh tip tuyn v, bm p vo biu thc ca tip tuyn ti ca s tri, s

xut hin ca s Edit tangent ta cp nht.

2.4.4. Chn th ca o hm f'(x)

Graph c chc nng v cng mt h trc to th ca hm s f(x) v f'(x). s dng chc nng ny, trc tin ta chn hm cn chn thm th ca o hm ca s bn tri, sau thao tc:

->Function -> Insert f'(x). Xut hin ca s Insert (fx). Ta khai bo khong [a,b], kiu nt v, dy, mu v ghi ch cho th mi ny. Nhn OK hon tt.

2.4.5. Xc nh di ca th f(x) trn on [a,b]

Chc nng Length of path cho php ta bit c ngay gi tr di ca th hm s f(x) trn on [a,b]. s dng chc nng ny, trc tin ta chn hm ca s bn tri sau thao tc: ->Calc -> length of path. Xut hin ca s cho ta nhp gi tr hai u mt a ti ca s From: v b ti ca s To:, ta s c kt qu c thng bo Length. C th nhp cc gi tr a, b khc nhau

tnh nhiu ln.


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2.4.6. Tnh din tch

Graph c chc nng tnh nhanh din tch phn mt phng gii hn bi cc ng thng x=a, x=b vi th ca f(x).

s dng chc nng tnh din tch hnh phng, trc tin ta chn hm ca s bn tri, tip theo ta thao tc nh sau: -> Calc > Aren. Xut hin ca s, ta nhp gi tr u mt a ti ca s From:, b ti ca s To., ta c kt qu din tch s c thng

bo ti ca s Area. Trn mn hnh ho s thy phn din tch tng ng s c biu din bi cc ng gch sc. Ta c th nhp cc gi tr u mt a, b khc nhau tnh din tch cc min khc nhau.

2.4.7. Tnh gi tri f(x), f'(x), f(x) ti im xo

s dng chc nng ny, trc tin ta chn hm ca s bn tri, tip theo ta thc hin thao tc:

-> Cacl -> Evaluate, xut hin ca s ta nhp gi tr ca im xo cn tnh. Kt qu c thng bo 3 ca s bn di ln lt l : f(x), f'(x), f''(x).

Ta c th thay i gi tr xo c c kt qu ti cc im khc nhau.


19

2.4.8. Tnh gi tr ca f(x) trong on [a,b] vi bc chia cch u

Chc nng Calculate table cho phn hoch on [a,b] bi mt li cc nt cch u nhau mt on dx v tnh gi tr ca hm s f(x) ti cc im chia.

lp bng, trc tin ta chn hm ca s bn tri, v thao tc: ->Cacl ->Table, xut hin ca s Calculate table. Ta khai bo khong [a,b] v bc chia dx. Nhn nt Calc ta s c kt qu cn thit.


20

2.4.9. V cc im trn h trc to .

s dng chc nng ny, ta thao tc nh sau:->Function ->insert point series..., xut hin ca s: Insert point series. Ta cn khai bo to ca im cn v. Bn tri c cc la chn

- Kiu v im: Style,

- Mu v im: Color,

- Kch thc im: Size,

- Hin to ca im Show coordinates...

Khai bo song nhn OK, ta s nhn c hnh nh cc im trn mn hnh.

2.4.10. In n kt qu

in cc kt qu, ta chn:

->File ->Print.

Xut hin ca s Page Setup ta xc nh cc thng s trc khi in. Nu cn la chn my in trong danh sch cc my in ci t; ta chn tip Printer... a ra my in, ta chn OK.

2.5. Th vin cc hm ca Graph

Trong phn mm Graph, cc hm c thit k ci t trong th vin tng i phong ph, tuy nhin cc hm sau thng c s dng nhiu trong chng trnh ph thng:

ABS - Hm ly gi tr tuyt i ca i s,


21

SQR - Hm cho gi tr bnh phng ca i s,

SQRT - Hm cho gi tr l cn bc hai ca i s,

SIN - Hm cho gi tr hm s sin ca i s,

COS - Hm cho gi tr hm s cosin ca i s,

TAN - Hm cho gi tr hm s tang ca i s,

ARCSIN - Hm cho gi tr ca hm s ngc ca hm s sin,

ARCCOS - Hm cho gi tr ca hm s ngc ca hm cosin,

ARCTAN - Hm cho gi tr ca hm s ngc ca hm tan,

LN - Hm cho gi tr logarit c s e ca i s,

LOG - Hm cho gi tr logarit c s thp phn ca i s,

PI - Cho gi tr ca s i,

Ton t ^ : dng biu din lu tha, v d 10^3 l 1000, 2^8 l 256.

bit thm chi tit, chn Help tra cu nhng thng tin cn thit.

2.6. Khai thc phn mm Graph

Graph cho ta mt cng c tng i y dy hc ni dung o hm v ng dng ca n trong chng trnh ton lp 12, c bit l ni dung kho st hm s v ni dung ng dng tch phn tnh din tch mt min.

Phng php ch yu l dng Graph minh ho v kim tra kt qu. Sau khi hc sinh hon thnh khi lng cng vic, gio vin c th s dng Graph hc sinh kim tra li kt qu tnh ton ca mnh v kho st chi tit thm hm s nh vo cc cng c ca Graph.

Ta c th s dng Graph v th sau lu tr th di dng nh a vo gio n son trn Word hoc Powerpoint.

2.7 Bi tp:

a) Kho st cc hm s

b) Minh ho vic t th hm s f(x) suy ra th cc hm s: f(|x|). |f(x)|, |f(|x|)l|

cng nh tnh cht ca hm s m, hm s lgarit.

c) S dng cc chc nng ca Graph kim tra kt qu tnh ton cc bi tp tnh di, din tch v tch phn xc nh trong sch gio khoa THPT.


22

Chng 3 S DNG PHN MM HNH HC NG

3.1. Gii thiu s lc v phn mm Cabri Geometry

Phn mm Cabri Geometry l kt qu nghin cu ca phng nghin cu cu trc ri rc v phng php ging dy - Trung tm nghin cu khoa hc quc gia - trng i hc tng hp Joseph Fourier Grenoble (Php). Hai ngi c cng ln trong vic pht trin Cabri Geometry l Laborde v Franck Bellemain. Jean - Marie Laborde bt u pht trin d n Cabri II t nm 1981 nh mt mi trng cho l thuyt th. Franck Bellemain bt u lm vic v d n Cabri II vo 1986 v chu trch nhim vit nhng phin bn u tin ca phn mm Cabri Geometry.

Hin nay phn mm Cabri Geometry II c th download min ph ti a ch http://www.ti.com/calc. Tp nn wcabri.zip c kch thc 3258 KB. Khi ci nn, chng trnh t ng to mt th mc mi th mc gc C vi tn l CABRI vi dung lng khong 5 MB. -

Giao din lm vic ca Cabri cho php chn cc ngn ng khc nhau vi ngm nh l ting Anh. Tuy nhin ta c th Vit ho cc h thng mnh ca Cabri.

3.2. Cc vn c bn lm vic vi Cabri Geometry

3.2.1. .Khi ng Cabri Geometry

Cabri l phn mm c th chy trn nn ca h iu hnh MS - DOS v Windows. Chng ti s gii thiu v phin bn Cabri for Windows.

gi Cabri ra lm vic, ta thc hin ln lt cc thao tc kch chut: -> Start ->programs -> Cabri Geometry II -> Cabn Geometry II.


23

Ta c th to Shortcut ng ca Cabri Geometry trn mn hnh vic gi c thun tin hn.

Sau khi khi ng, giao din ca Cabri nh sau:

3.2.2. H thng menu bar ca Cabri:

Cabri c h thng mnh bai gm 5 nhm chc nng chnh, mi nhm ng vi mt h thng mnh dc (Popup).

* Nhm chc nng File

- New (CTRL + N): M mt tp (mt trang hnh hc) mi.

- Open (CTRL + O): M mt tp ca Cabri c lu tr trn (ta phi chn , th mc lu gi tp tin, chn tn tp tin cn m).

- Close (CTRL + W): ng tp tin ang lm vic Nu ta cha lu tr tp tin, Cabri s nhc: Nu chn Yes: Cabri s lu tr tp tin trc khi ng. Nu chn No: Cabri s khng lu tr nhng thay i ca tp tin so vi ln ghi trc hoc khng lu tr. Chn Cancel l hu b lnh ng Cabri.


24

- Save (CTRL + S): Lu tr tp tin trn mn hnh. Nu l ln lu tr u tin s xut hin ca s Save, ta phi chn a, th mc lu tr tp tin v tn ca tp tin ny. Nhng ln thc hin lnh ghi sau, Cabri khng hi m s t ng ghi theo thng s chn.

- Save As: Lu tr tp vi tn mi.

- Show Page: Xem ton b tp trc khi in (ta c th chn vng in bng cch di chuyn khung ch nht n v tr cn thit).

- Page Setup: nh cc thng s trc khi in ni dung tp.

- Print (CTRL+P): Thc hin lnh in

- Exit (CTRL+Q): Kt thc phin lm vic.

* Nhm chc nng Edit: (bao gm 8 chc nng)

- Undo (CTRL+ Z): Hu b lnh va thc hin.

- Cut (CTRL + X): Ct b cc i tng c la chn nh du khi mn hnh lm vic v lu tm vo b m Clipboard.

- Copy (CTRL + C): Copy cc i tng c la chn nh du lu tm vo b m Clipboard.

- Paste (CTRL+ V): a cc i tng ang lu tm trong b m Clipboard ra v tr


25

con tr.

- Clear (Del): Xo b cc i tng c la chn nh du.

-Select All (CTRL + A): nh du la chn tt c cc i tng.

- Replay Construction: Xem li ton b qu trnh dng hnh.

- Refresh Drawing (CTRL + F): Ly li ho tit thao tc dng hnh.

* Nhm menu Options: (gm 5 chc nng cho php la chn thuc tnh)

- Hide Attributes: Cho hin hay n thanh cng c la chn thuc tnh cho cc i tng.

- Preferences...: Khai bo la chn cc tham s h thng nh: la chn n v mu, mu i tng, ch hin th, font ch h thng . . .

Nu ta mun thay i cc thuc tnh ngm nh ca Cabri th cn phi khai bo, la chn theo ca ngi s dng. lu tr li s la chn ta bm chn vo : [ ] Keep as defaults. Nu mun lu tr cu hnh nh mt mu ring, ta bm chn vo Sa ve to file.

- Language: La chn ngn ng hin th (c nhiu la chn nh: ngn ng Anh,

Php, c, an Mch...).

- Font: La chn kiu ch cho i tng ang c la chn.


26

* H thng menu Window

H thng menu ny bao gm cc lnh c cng dng tng t nh cc phn mm khc trong mi trng h iu hnh Windows dng b tr sp xp cc ca s.

* H thng mnh Help

H thng tr gip ca Cabri v gii thiu tng quan v phn mm Cabri.

3.3. Thao tc vi h thng cc cng c ca Geometry Cabri

Ton b h thng cng c ca Cabri bao gm 11 nhm chc nng chnh:

3.3.1. Nhm chc nng chn trng thi lm vic vi chut

Khi bm chut vo hp cng c ny, xut hin 4 s la chn:

Pointer: Trng thi s dng la chn, dch chuyn, xo b v lm cc thao tc sa i vi cc i tng hnh hc.

Rotate: Xoay mt hnh xung quanh mt im chn hay tm ca hnh.

Dilate: M rng hay thu hp mt hnh theo tm ca hnh hay mt im chn. Rotale and Dilate: C th cng mt lc va xoay va thay i rng, chiu cao ca hnh.

3.3.2. Nhm chn cng c to im

Khi bm chut vo nhm cng c ny, xut hin bng c 3 s la chn:

Point: To mt im t do. Point on Object: To mt im trn mt hnh c

Intersection Points: Xc nh im l giao ca cc hnh hnh hc. * S dng cc cng c:


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+ To mt im trn mt phng:

Kch chut vo biu tng, chn Point, xut hin hnh tng bt ch, a u bt ch n v tr xc nh im, bm chut tri c th xc nh nhiu im lin tc khng cn chn li cng c.

+ To mt im thuc mt hnh hnh hc c:

Kch chut vo biu tng, chn Point on Object, khi a bt ch ch vo i tng hnh hc c, xut hin cu hi, chng hn: "Dng im ny trn ng thng", "Qua im ny trn ng trn "... cn chn v tr no, ta kch chut vo v tr .

+ Xc nh im l giao ca cc hnh hnh hc c:

Kch chut vo biu tng, chn Intersection Points, khi a bt ch vo v tr l giao ca cc hnh hnh hc, xut hin dng thng bo tu ti giao im". Nu ng l im cn chn, ta bm chut chn im .

3.3.3. Nhm chn cng c v cc ng v cc hnh

Khi bm chut chn nhm cng c ny, xut hin bng gm 7 chc nng v cc i tng hnh hc c bn:

Line: V mt ng thng i qua hai im cho trc hoc i qua mt im vi gc nghing,

segment: Dng mt ng thng i qua 2 im cho trc,

Ray: Dng mt tia bit gc v hng, Vector: Dng mt vc t khi bit hng v 2 im mt,

Triangle: Dng 1 tam gic khi bit 3 nh, Polygon: Dng a gic n cnh, Regular Polygon: Dng a gic u (n


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+ Dng mt on thng:

Kch chut vo biu tng chn Segment, a bt ch ln lt xc nh im th nht, im th 2 ta c on thng tng ng.

+ Dng mt tia, bit gc v hng:

Ta chn chc nng dng tia: Kch chut vo biu tng, chn Ray. a bt ch xc nh im gc ca tia, sau di chuyn chut chn hng ca tia cn xc nh; bm chut tri xc nh im th 2, ta c tia cn dng.

+ Dng mt vc t khi bit hng v 2 u mt:

Ta chn chc nng dng vct: Kch chut vo biu tng, chn Vector, sau a bt ch xc nh im gc v im ngn ca vc t cn dng. Sau khi chn xong 2 im ta c vc t tng ng.

+ Dng tam gic:

Ta chn chc nng Dng hnh tam gic: Kch chut vo biu tng, chn Triangle, sau a bt ch ln lt xc nh v tr 3 nh ca tam gic, khi ta s c tam gic tng ng.

+ Chc nng dng a gic:

Chn chc nng dng hnh a gic: Kch chut vo biu tng, chn Polygon, sau a bt tr ln lt xc nh cc nh, kt thc bm p chut tri, ta c a gic tng ng vi cc im chn.

+ Chc nng dng mt a gic u:

Chn chc nng dng hnh a gic u: Kch chut vo biu tng, chn Regular Polygon. . Trc tin ta a bt ch xc nh tm ca a gic, sau di chuyn bt ch xc nh bn knh ca ng trn ngoi tip a gic u . tm xut hin s cnh ca a gic, ta dng chut xc nh s cnh cn c. Kt thc bm chut tri.

3.3.4. Nhm chn cng c v cc ng cong

Khi bm chut chn nhm cng c ny, xut hin bng gm 3 chc nng v cung, ng trn v ng cnic.

Circle: V ng trn khi xc nh tm v bn knh, Arc: V cung trn qua 3 im,

Conic: V ng conic qua 5 im, * S dng cc cng c:

+ Dng hnh trn:


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Chn chc nng dng hnh trn: Kch chut vo biu tng, chn Circle, sau a bt ch xc nh tm ca hnh trn, di chuyn chut xc nh bn knh v bm chut tri. thay i bn knh, ta tr v ch con tr, sau ch chut vo ng trn, s xut hin hnh bn tay ta thay i bn knh. Mun di chuyn ng trn, ta ch vo tm tip theo gi phm tri di chuyn hnh v.

+ Dng mt cung trn:

S dng chc nng dng cung trn: Kch chut vo biu tng, chn Arc, sau a bt ch xc nh 3 im, t hon ton xc nh mt cung trn tng ng vi 3 im chn. Mun thay i, ta a bt ch vo mt trong 3 im xc nh cung trn iu chnh. Mun di chuyn c cung trn ta a bt ch vo mt im bt k trn cung trn (ngoi 3 im) di chuyn.

+ Dng ng cnic:

Chn cng c dng cc ng cnc: Kch chut vo biu tng, chn Conic, sau ta xc nh ln lt 5 im. Tu v tr 5 im s cho ta cp hay parabol, hypecbol...

3.3.5. Nhm chn cng c xc nh im, ng, nh cc i tng hnh hc c dn xut t cc i tng hnh hc c

Khi bm chut chn nhm cng c ny, xut hin gm 10 chc nng:

Perpendicular Line: Dng ng thng i qua mt im v vung gc vi mt on thng, ng thng. . . no .

Parallel Line: Dng ng thng i qua 1 im v song song vi mt on thng, ng thng... no .

Midpoint: Xc nh im gia ca 2 im, trung im 1 on thng.

Perpenicular Bisector: Dng ng trung trc ca on thng, gia 2 im...

Ang le Bisector: Dng ng phn gic ca 1 gc khi bit 3 im. Vector Sum: Xc nh tng 2 vc t. Compass: Dng ng trn vi tm v bn knh xc nh. Measurement Transfer: Xc nh nh ca mt im cch mt im cho


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trc mt khong cho trc.

Locus : Xy dng tng bc cc i tng hnh hc, xy dng qu tch. Rederme Object: nh ngha li i tng hnh theo s ph thuc ban u.

* S dng cc cng c:

+ Dng ng thng vung gc:

S dng chc nng "Dng ng vung gc": Kch chut vo biu tng, chn Perpendicular Line, ta ln lt phi xc nh ng thng hoc on thng cho trc v im ng thng s i qua. Khi im hoc ng thng thay i th ng thng vung gc cng thay i theo.

+ Dng ng thng i qua mt im v song song vi mt ng thng hay on thng cho tr.

Ta s dng chc nng "Dng ng song song": Kch chut vo biu tng, chn Parallel Line, ta ln lt xc nh ng thng hoc on thng c v im m ng thng s i qua.

+ Xc nh trung im gia hai im:

Ta chn chc nng " Xc nh trung im gia 2 im": Kch chut vo biu tng,

chn Midpoint, sau a bt ch xc nh hai im mt. Trn mn hnh s xut hin im gia ca 2 im hoc on thng.

+ Dng ng trung trc ca mt on thng cho:

Ta chn chc nng "Dng ng trung trc ca mt on thng": Kch chut vo biu

tng, chn Perpendicular Bisector, sau a bt ch xc nh hai u mt ca on thng hoc on thng c. Trn mn hnh s xut hin ng thng trung trc ca on thng m ta va la chn.

+ Dng ng phn gic:

S dng chc nng "Dng ng phn gic": Kch chut vo biu tng, chn Angle Bisector, sau ta a bt ch xc nh 3 im theo th t thuc cnh th nht ca gc, nh v im thuc cnh cn li. Ta s c ng phn gic tng ng.

+ Dng vct tng ca 2 vct :

Ta chn chc nng Dng tng vc t ca 2 vc t: Kch chut vo biu tng, chn

Vector Sum, sau a bt ch xc nh ln lt hai vc t thnh phn v cui cng l chn im gc ca vc t tng.


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+ Dng mt hnh trn c bn knh cho trc:

Ta chn chc nng "Dng ng trn c bn knh xc nh": Kch chut vo biu

tng, chn Compass, sau a bt ch xc nh 2 im ca on thng chn lm bn knh hoc chn mt on thng c lm bn knh, tip theo chn tm ca ng trn. Ta c ng trn cn dng. Tuy nhin, khi cho on ng thng chn thay i v ln th ng trn cng thay i theo.

+ Dng mt im trn mt i tng ng thng, vi khong cch ca im ny vi mt im xc nh thuc ng l mt s xc nh (khong cch hay di ca mt cung):

xc nh khong cch, ta chn mt s xc nh trn hnh chn cng c Numerical Edit "To s" g s v n v. Thao tc tip theo bao gm: Chn chc nng

Measurement Transfer: "xc nh im vi khong cch", sau a bt ch chn im gc v a bt ch chn con s c nhp trc mn hnh; trn mn hnh xut hin mt ng chm k, ta di chuyn chn hng, bm chut tri xc nh im nh.

+ T ng xy dng tng bc i tng hnh hc (im, ng)- xy dng qu tch thng qua s chuyn ng ca im:

Ta chn chc nng: "Dng qu tch ca mt im": Kch chut vo biu tng, chn

Locus v thit lp mi tng quan gia cc im, ng vi nhau, sau cho mt s im, ng thay i xc nh qu tch.

+ nh ngha li i tng theo s ph thuc ban u ca mt nhm i tng: Kch chut vo biu tng, chn LJ Redefine Ohject. Ta s dng chc nng ny a mt i tng hnh hc ny chuyn thnh mt i tng hnh hc khc.

3.3.6. Nhm chn cng c dng nh qua cc php bin hnh

Khi bm chut chn hm cng c ny, xut hin bng gm 6 chc nng:

Renection: Dng hnh i xng qua mt ng thng, on thng ca mt hnh no .

Symmetry: Xoay hnh 1 gc 1800. Translation: Xc nh nh mt hnh qua mt php tnh tin theo mt vc t.

Rotation: Xc nh nh ca mt hnh qua mt php quay.

Dilation: Xc nh nh ca mt im qua mt php v t. Inverse: Xc nh nh ca 1 im i xng qua cung, ng trn.


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* S dng cc cng c:

+ Dng hnh i xng ca i tng hnh hc qua mt ng, on thng, tia, trc to cnh tam gic, a gic...

Ta chn chc nng "Php i xng qua mt ng". Kch chut vo biu tng, chn

Reflection, sau la chn im gc v ng chn lm trc i xng, ta c nh ca im i xng qua ng chn.

+ Xoay hnh mt gc 1800 quanh mt im xc nh:

Ta chn chc nng " Php i xng tm": Kch chut vo biu tng, chn Symmetry, sau ln lt la chn im cn ly i xng v im gc, ta s thu c nh ca im chn qua php i xng tm.

+ Dng hnh nh ca mt i tng hnh hc qua php tnh tin theo mt vc t:

Bc 1 : Ta phi xc nh vc t lm hng v khong cch cho php tnh tin.

Bc 2: Chn chc nng "Php tnh tin hnh": Kch chut vo biu tng, chn Translation, ln lt chn i tng cn dng nh qua php tnh tin v xc nh vc t c chn lm hng v khong cch cho php tnh tin, ta c nh ca hnh qua php tnh tin.

+ Dng nh ca mt i tng hnh hc qua php quay (vi mt im xc nh l mt gc xc nh)

Xc nh i tng cn quay, tm quay v cui cng l gc quay (s hin trn mn l gc).

Bc 1 : S dng chc nng Numerical Edit "g s v n v" xc nh gc ca php quay.

Bc 2: Chn chc nng "Php quay quanh mt tm": Kch chut vo biu tng,

chn Rotation, tip theo la chn hnh cn quay, im chn lm tm quay v cui cng ch vo s xc nh gc quay. Ta c nh qua mt php quay.

+ Dng mt im, hnh hay ng ca mt i tng qua mt php v t (vi mt im v mt s xc nh)

Bc l: s dng chc nng Numerical Edit g s v n v nhp mt gi tr chn lm t s ca php gin.

Bc 2: Chn chc nng "Gin i tng ": Kch chut vo biu tng, chn Dilation, tip theo la chn hnh cn gin v i tng lin quan n php gin (tm, trc) v xc nh h s ca php gin, ta thu c kt qu.


33

+ Dng im i xng ca mt im qua cung trn:

Xc nh im cn c im i xng v cung trn. Ta s dng chc nng "i xng

qua cung trn": Kch chut vo biu tng, chn Inverse, tip theo la chn im cn ly i xng v cung trn c chn lm cn c i xng, ta thu c im nh.

3.3.7. Nhm cng c xy dng macro

Khi bm chut chn nhm cng c ny, xut hin bng gm 3 chc nng:

Initial Objects: Xc nh cc i tng ban u thc hin cc lnh macro.

Final Object: Xc nh cc i tng thu c sau khi kt thc vic thc hin cc lnh ca macro.

Define Macro: nh ngha tn v chn phm tt cho macro mi. * S dng cc cng c:

Bc 1 : Dng hon chnh hnh v

Bc 2: Bm vo biu tng, chn Initial Objects, sau bm chut vo nhng i tng c coi l nhng i tng xut pht (nh ngha lc ban u X)

Bc 3 : Bm vo biu tng, chn Final Object, sau bm chut vo nhng i tng c coi l nhng i tng kt thc (Y)

Bc 4: Bm vo biu tng, chn Define Macro ghi li macro qu trnh dng hnh, ta phi t tn cho Macro.

Bc 5: Chy cc macro (ta phi xc nh cc i tng u vo (X), chy macro ta s thu c (Y)).

3.3.8. Nhm chn cng c kim tra thuc tnh


Collinear: Kim tra xem 3 im c thng hng hay khng ?

Parallel: Kim tra xem 2 ng thng, on thng... c song song khng?

Perpendicular: Kim tra xem 2 ng thng, o thng... c vung gc vi nhau khng ?

Equidistant: Kim tra 2 im c cch u 1 im khng ?


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Member: Kim tra mt im c thuc mt hnh hay khng ? * S dng cc cng c:

+ Chc nng " Xc nh thng hng ":

Kch chut vo biu tng, chn Collinear, sau chn cc im cn xc nh c thng hng hay khng. Sau khi chn im th 3, xut hin mt khung ch nht, ta a khung ny n mt v tr no trn mn hnh, bm chut, kt qu kim tra s xut hin trong khung .

+ Chc nng "Song song khng ":

Kch chut vo biu tng, chn Parallel:, ln lt xc nh cc on thng, ng thng cn kim tra, kt qu s c thng bo trong mt khung ch nht.

+ Chc nng "Vung gc khng ": Kch chut vo biu tng, chn Perpendicular:. S dng tng t chc nng kim tra tnh song song ca 2 on thng hoc 2 ng thng.

+ Chc nng "Cch u nhau ": kim tra xem trong 3 im c la chn c khong cch vi nhau c bng nhau khng? Kch chut vo biu tng, chn Equidistant, sau ln lt bm chut vo cc im, nu khong cch di 1 l nh nhau, ta c thng bo 3 im c cch u hay khng.

+ Xc nh mt i tng ny c thuc i tng khc khng:

Sau khi chn cng c: Kch chut vo biu tng, chn Member, ta ln lt la chn i tng cn kim tra v i tng c kh nng cha i tng cn kim tra. Kt qu c thng bo trong khung ch nht. 3.3.9. Nhm chn cng c o c tnh ton


Distance and Length: Xc nh khong cch gia 2 i tng, di 1 on thng, mi cung, chu vi ca mt hnh hnh hc.

Area: Tnh din tch hnh trn, tam gic, a gic...

Slope: Xc nh h s gc y/x. Angle: Xc nh s o ca gc. Equation and Coordinates: Xc nh to im hay phng trnh ca ng thng.


35

Calculate: Tnh ton trc tip (tng t nh mt my tnh b ti) Tabulate: t cc s liu tnh ton vo bng.

* S dng cc cng c:

+ Chc nng " Khong cch v chiu di ":

xc nh khong cch gia 2 im bt k, sau khi chn chc nng Distance and Length, ta ln lt bm chut xc nh 2 im cn o. xc nh chu vi ca mt hnh, ta a bt ch vo i tng cn xc nh chu vi. Kt qu s c thng bo trong khung ch nht.

+ Chc nng Tnh din tch ca a gic, hnh trn, hnh ellipse :

Ta chn chc nng Area "Din tch hnh", sau a bt ch xc nh hnh cn o din tch. Kt qu c thng bo trong khung ch nht.

+ Xc nh dc (hay tg - xc nh t s y/x) ca ng, on, tia hay vc t.

Ta chn chc nng Slope "Xc nh r ca ng thng (y/x)" sau a bt ch xc nh ng thng, on thng, vc t hoc tia cn xc nh h s gc.

+ Xc nh ln ca gc c xc bi ba im (im th hai l nh ca gc): Ta

chn chc nng Angle "Gc nghing", sau a bt ch xc nh 3 im theo th t ln lt thuc cnh th nht, nh v cnh cn li.

+ Xc nh to ca im hay phng trnh ca ng:

Ta chn chc nng Equation and Coordinates "'Hm biu din ng v to im", sau a bt ch la chn im cn xc nh to hoc la chn ng cn xc nh phng trnh hm biu din.

+ Tnh kt qu pht sinh ca biu thc:

Chn chc nng Calculate "Tnh ton ta s c mt my tnh b ti vi cc php ton s hc c bn. a kt qu ra mn hnh, ta chn chc nng INV, ta c thng bo "Result" v kt qu tnh ton.

+ t cc gi tr tnh ton, hay cc s liu vo bng:

Ta chn chc nng Tabulate "Lp bng k", sau a bt ch ra mn hnh vch mt khung bng, s ct v s dng tu theo ta la chn. chuyn d liu vo bng, ta phi chuyn ln lt tng dng mt bng cch ch bt ch vo con s hoc d liu cn a vo bng.


36

3.3.10. Nhm cng c s t tn cho cc i tng v xc nh yu t ng


Label: To, sa cc nhn t tn cc i tng hnh hc.

Comments: To, sa li ch thch. Numerical Edit: To, sa li cc s. Mark Angle: nh du gc chn. Fix/Free: Xc nh im l c nh hay

chuyn ng.

Trace On/Off: To nh cho s di chuyn ca i tng hnh hc ( li vt).

Animation: Cho i tng chn chuyn ng theo mt rng buc Xc nh trc...

Multiple Animation: Thc hin chuyn ng phc tp, hn hp. * S dng cc cng c:

+ To cc nhn cho cc i tng hnh hc:

La chn chc nng Label "nh du nhn", sau a bt ch ch vo i tng cn gn tn, s xut hin mt hp ch nht ta g tn cho i tng hnh hc .

+ Sa i hay thm li bnh, ghi ch:

Ta s dng chc nng Comments "Li bnh, ch thch", sau a bt ch xc nh v tr dng vn bn trn mn hnh, khi xut hin khung ch nht ta nhp ni dung text.

+ To v sa li gi tr s.

Chn chc nng Numerical Edit "To v sa li s", hoc n CTRL+U chn n v, sau nhp gi tr.

+ nh du gc:

Gc c xc nh bng ba im, im th hai l nh. Ta chn chc nng Mark Angle nh du gc bng nhau, sau a bt ch xc nh 3 im tng ng vi gc cn nh du.


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+ Gn thuc tnh cho im c nh, hay t do:

Ta s dng chc nng Fix/Free: "im c nh, im di ng" xc nh thuc tnh c nh hay di chuyn cho mt im.

+ li vt khi di chuyn mt i tng hnh hc:

Ta chn chc nng Trace On/Off: li du vt On/Off, sau la chn i tng hnh hc s di chuyn. Khi mi di chuyn ca i tng trn u li vt trn mn hnh.

+ T ng cho tnh tin, quay hay gin cc i tng hnh hc. Kch chut vo i tng ko v di chut, chuyn ng s theo chiu ca dy cng. Ta chn

chc nng Animation "Chuyn ng i tng", sau a bt ch xc nh i tng hnh hc s di chuyn.

+ Thc hin cc chuyn ng phc tp, c t hai i tng hnh tr ln cng lc chuyn ng:

Ta chn chc nng Multiple Animation chuyn ng phc tp, sau ln lt la chn i tng v phng thc chuyn ng. thc hin, ta n phm Enter. 3.3.11. Nhm cng c nh dng cc i tng


Hide/ Show: Cho n, hin cc hnh c. Color: T mu nt v. Fill: Chn mu bn trong hnh v. Thick: Thay i kiu nt v dy - mng. Dotted : Chn kiu nt lin hay nt t. Modifv Appearance: Sa k hiu trn hnh. Show Axes: n hay hin trc to .

New Axes: t to mi. Define Gid: nh ngha li.

* S dng cc cng c:

Nguyn l chung cho cc cng c nh dng l khi ta chn cng c, s xut hin mt bng cc la chn. Ta bm chut vo mt trong nhng la chn (v d kiu ng k, mu sc...), sau a bt ch bm vo i tng ta cn nh dng theo. Ring cng c n/hin c s dng che bt khng hin ra mn hnh nhng i tng c nh du n lm cho hnh v n gin, rc ri.


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3.3.11. Bi tp

Bi 1 : Cho ng trn (O) v hai im A, B. Dng ng knh COD sao cho CA = DB.

Bi 2: Cho gc xy v mt im A trong gc . Dng qua A mt ng thng ct Ox,Oy M v N sao cho MA=AN.

Bi 3: Cho 3 im A,B,C.Dng ng thng d sao cho tng khong cch t B v C n d bng h cho trc.

Bi 4: Cho hai ng trn (O) v (O') ct nhau A v B. Dng qua A mt ng thng d ct (O) v (O') M,N sao cho MA+NA ln nht.

Bi 5: Cho gc xOy. Ly A nm trn Ox,B nm trn Oy sao cho OA+OA=m cho trc. Ttm qi tch trung im I ca on AB.

Bi 6: Cho ng trn (O) v im A c nh,ng knh BC quay quanh O Tm tp hp I l tm ng trn ngoi tip tam gic ABC.

Bi 7: Cho gc xy c nh v mt im A nm trong gc . Mt gc vung c nh trng A, hai cnh ca gc ct Ox,Oy ti E v F (k c tia i ca Ox, Oy). Tm tp hp trung im M ca EF khi gc EAF quay quanh A.

Bi 10: Cho tam gic cn ABC (AB=AC), M nm trn tia BA, N nm trn tia i ca tia CA sao cho MB=CN. Ly BM, CN lm hai cnh bn lin tip dng hnh bnh hnh BMNI. tm tp hp I khi M, N thay i.

Bi 1 l: Th hin nh ca mt hnh H qua php tnh tin (Hnh hc 10).

Bi 12: Th hin nh ca hnh H qua php i xng trc (Hnh hc 10).

Bi 1 3 : Th hin nh ca mt hnh H qua php v t (Hnh hc 10) .

Bi 14: V hnh bi Cabri sau copy hnh v sang Powerpoint thit k gio n ni dung cc php bin hnh lp 10 v hnh khng gian lp 11, 12.

3.4. Gii thiu phn mm The Geometer's Sketchpad

Chng trnh The Geometer's Sketchpad l mt phn mm hnh hc ng h tr vic nghin cu v dy hc hnh hc rt hiu qu. Chng trnh Sketchpad c th download ti website: hp://www.keypess.com/sketchpad. (V phn mm Sketchpad, c th tm hiu su trong cc ti liu ca TS. Trn Vui HSP Hu).

lm vic vi phn mm Sketchpad, ta thao tc nh sau:

-> Sart -> Programs-> Sketchpad ->The Geometer's Sketchpad

(hoc bm chut vo biu tng trn mn hnh ).

Sau khi khi ng, giao din lm vic ca Sketchpad c dng sau:


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3.4.1.Thanh cng c

H thng cng c ca Sketchpad gm 6 nhm chc nng:

- Chn trng thi lm vic vi chut,

- Xc nh im,

- Xc nh ng trn, - Xc nh on thng, tia, ng thng,

- To text box,

Tu chn cc chc nng cng c

3.4.2. H thng cc menu chnh

* Menu File

- New Sketch (Ctrl+N): To mt bn v mi,

- Open (Ctrl+O: M mt Sketch/ Script c,

- Save (Ctrl+S: Lu tr Sketch/script,

- Save As: Lu Sketch/ Script vi tn mi,

- Close (Ctrl+W ng file hin thi,

- Docment Options...: La chn thuc tnh cho ti liu,

- Page Setup...: Xc nh thng s trc khi in n,

- Pht Preview: Chn ch in, xem ni dung ti liu trc khi in ra.

- Print: In ti liu,

- Quit (Ctrl+Q): Thot Sketchpad, tr v Windows.

* Menu Edit


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- Undo (Ctrl+Z): Phc hi li trng thi trc ,

- Redo (Ctrl+R): Lm li thao tc va thc hin,

- Cut (Ctrl+X): Xo i tng c chn v lu vo b nh,

- Copy (Ctrl+C): Copy i tng c chn vo b nh,

- Paste (Ctrl+V): Chp i tng b nh ra Sketch,

- Clear (Del): Xo cc i tng c chn,

- Action Buttons: To nt lnh thao tc vi cc i tng,

- Select All (Ctrl+A): Chn tt c cc i tng trn trang lm vic,

- Select Parents (Ctrl+U): Chn i tng c bn ban u,

- Select Children (Ctrl+D): Chn i tng dn xut,

- Split/Merge: Phn tch mt i tng hnh hc t mt i tng khc / hoc nhp gn kt hai i tng hnh hc li thnh mt h thng,

- Edit Defmition (Ctrl+E): Sa cha hm, bng tnh ton hay tham s...

- Properties (An+?): Xc nh thuc tnh ca hnh,

- Preferences...: Xc nh cc thuc tnh tu chn cho mu, n v o lng, text box...

* Menu Action Buttons:

- Hidel Show: To 2 nt lnh cho php hin th/ khng hin th cc i tng chn.

- Animation...: To lnh thc hin vic di chuyn i tng,

- Movement. . . : To lnh thc hin vic di chuyn gia hai i tng c chn,

- Presenlation...: To cc nt di chuyn, chuyn i...,

- Link: To cc nt lin kt cc hiu ng chng trnh,

- Scroll: To cc hiu ng ko trt.

* Menu Display


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- Line Width: Chn 1 trong 3 dng ng,

- Color: Chn mu,

- Text: Chn kiu vn bn,

- Text Font: Chn font ch,

- Hide Object (Ctrl + H): Khng hin th cc i tng la chn,

- Show All Hidden: Hin th tt c cc i tng ang n,

- Show Labels (Ctrl + K): Hin th tn ca i tng,

-Trace (Ctrl+X): t ch li vt khi i tng thay i v tr,

- Erase Traces (Ctrl+B): Xo b cc vt do i tng chuyn ng li trn mn hnh,

- Animate (Ctrl+) Lnh cho i tng chuyn ng,

- Increase Speed (Ctrl+[), Decrease Speed (Ctrl+]): Lnh cho thay i khong 25% tc chuyn ng ca i tng,

- Stop Animation: Kt thc cc chuyn ng ang xy ra,

- Show Text Palette (Shift+Ctrl+T): Hin hay n thanh cng c nh dng text:

- Show Motion Controller: Hin hay n hp chc nng iu khin chuyn ng nh:

thc hin, dng, lp li...

- Hide Toolbox: Chn ch n hay hin hp cng c.

* Mnh Construct

- Point On Object: Chn im trn i tng,

- Midpoint (Ctrl+M): xc nh trung im ca mt on thng hoc im gia ca 2 im,

- Intersection (Ctrl+I): Xc nh giao im ca hai i tng,

- Segment (Ctrl+L): Xc nh on thng ni 2 im xc nh cho trc,

- Line: Xc nh ng thng ni 2 im xc nh cho trc,

- Parallel Line: Dng ng thng i qua mt im song


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song vi mt ng thng khc,

- Perpendicular Line: Dng ng thng i qua mt im v vung gc vi mt ng thng,

- Angle Bisector: Dng phn gic gc,

- Circle By Center+ Point: Dng ng trn khi bit tm v mt im trn ng trn,

- Circle By Center+Radius: Dng ng trn khi xc nh tm v bn knh,

- Arc ON Circle: Dng mt cung qua 2 im trn ng trn,

- Arc Through 3 Points: Dng mt cung qua 3 im khng thng hng,

- Interior:(CTRL+P) T mu bn trong min mt a gic, hnh trn....,

- Locus: Xc nh qu tch ca mt i tng.

* Menu Transform

Transform Menu - Mark Center(Shift+Ctrl+F): Chn im lm tm ca php quay,

- Mark Mirror: Chn trc i xng,

- Mark Angle: Xc nh gc cho php quay,

- Mark Ratio: nh du t s,

- Mark Vector: Chn vect cho php tnh tin,

- Mark Distance: Xc nh khong cch,

- Translate . . . : Xc nh php tnh tin,

- Rotate ...: Quay i tng mt gc vi tm chn,

- Dilate ...: Php v t vi tm v t s cho trc,

- Refiect ...: i xng qua trc,

- Iterate: Xc nh php bin hnh.

* Menu Measure

- Length: Xc nh di mt/ nhiu on thng,

- Distance: Xc nh khong cch gia hai im,

- Perimeter: Xc nh chu vi ca mt a gic,

- Circumference: Xc chu vi ca ng trn, cung trn


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- Angle: Xc nh s o ca mt gc,

- Area: Xc nh din tch ca mt hnh kn,

- Arc Angle: Xc nh gc tm,

- Arc Length: Xc nh di ca dy cung,

- Radius: Xc nh bn knh mt hoc nhiu ng trn,

- Ratio: Xc nh t s di ca 2 on,

- Abscissa(x): Xc nh honh ca mt im,

- Ordinate(y): Xc nh tung ca mt im,

- Coordinate Distance: Xc nh khong cch gia hai i tng,

- Slope: Xc nh h s gc ca ng thng,

- Equation: Xc nh phng trnh ng thng/ ng trn.

*Menu Graph

- Define Coordinate System: Thit lp h thng mi (tu thuc vo i tng ta ang la chn),

- Mark Coordinate System: Thit lp to h thng,

- Grid Form: La chn h thng to cc hay to cc

- Show Grid/Hide Grid: Cho hin hay n h thng li to ,

- Snap Points: La chn ch di chuyn theo to nguyn hay bt k,

- Plot Points: V mt im trong to cc hay to cc

- New Parameter (Shift+ctrl+P): Xc lp mt gi tr cho bin,

- New Function (Ctrl+F): Xc lp mt hm vi i s x,

- Plot New Function... (Ctrl+G): V th ca mt hm s,

- Derivative: Xc nh o hm bc nht ca mt hm s,

- Tabulate: a cc i tng chn vo bng,

- Add Table Data: B sung thm d liu vo bng c,

- Remove Table Data: Hu b cc d liu a vo bng.


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*. To im chuyn ng qu tch vi Sketchpad

Bc 1 : Chn i tng cn cho chuyn ng,

Bc 2: -> Display -> Animate s c hp thoi iu khin chuyn ng,

Mun li vt ca i tng khi im chuyn ng, ta chn i tng , -> Display -> Trace Point, sau

mi chn lnh Animate.

3.4.3. Thit k cc Script vi Sketchpad

Trong thao tc dng hnh vi Sketchpad, c nhiu thao tc phi lm i, lm li, tit kim thi gian, ta c th ghi cc thao tc thnh mt Script v sau s dng nh mt chc nng cng c c sn ca Sketchpad.

Thao tc:

- Trc tin m mt tp mi (Sketch) .

- Thc hin thao tc dng hnh cn thit.

- Chn tt c nhng i tng c quan h hnh hc va dng m ta mun to mt Script.

- Chn Custom Tool t thanh cng c:

Xut hin bng lnh, gm cc chc nng c bn nh: to mi mt Script, tu chn cng c, n hin Script v danh sch cc Script c, ta chn tip: -> Create New Tool...

Xut hin bng chn:

Ta t tn cho chc nng cng c mi ny. Nu mun quan st ni dung ca Script, ta nh du chn vo mc [x] Show Script View. Khi xut hin ca s ca Script c dng nh sau:


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* Thc hin mt Script

Sau khi lu tr, mun s dng, ta chn Custom Tool v chn tn cng c Script m ta cn thc hin.

Nu ta copy Script ny, th trong danh sch Document s c tn v ta s dng chng nh mt lnh ca Sketchpad.

3.4.1 .Bi tp .

Bi 1: Cho ng trn (O,r) v mt im P ngoi ng trn. Mt ct tuyn thay i i qua P ct ng trn (O,r) ti hai im B, C. Gi E l im gia cung BC. Gi A, A' l tip im ca hai tip tuyn k t P vi ng trn (O,r).

Hy minh ho tp hp I l giao ca AE vi BC .

Bi 2: Gi s hai ng trn (O,r) v (O',r) ct nhau ti hai im A, B. im M chy trn ng trn (O',r). MA, MB ct ng trn (O,r) ti P v N. tm qu tch tm I l tm vng trn ngoi tip tam gic MNP.

Bi 3: Cho ng trn (O,r), v bn knh OA v dy AD c nh. V vng trn tm O, ng knh OA ct AD ti C. Mt ct tuyn thay i i qua O ct ng trn (O,r) ti M v (O,r) ti N, N'. DN ct CM ti P v DN' ct CM ti P'.

Tm qu tch P, P'.

Bi 4: Cho hai ng trn (O,r) v (O,r) tip xc ngoi nhau ti A. Mt gc vung c nh trng vi im A, quay quanh A, hai cnh ca gc ct (O,r) v (O',r) ti B v C. Tm tp hp hnh chiu H ca A trn BC.

Bi 5: Cho tam gic ABC cn ti A ni tip trong mt ng trn (O,r). M l mt im di ng trn cung AB. Trn tia CM ly im N sao cho AM = CN.

Tm tp hp im N.


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3.5. V hnh vi phn mm hnh hc Cabri

Trong ni dung ny, chng ti m t thao tc vi Cabri v hnh.

* Dng tam gic ABC, bit cnh Bc=a, ng cao AH : h, trung tuyn BD=m:

Thao tc dng hnh vi Cabri nh sau:

Bc 1 : Dng tam gic vung BDK bit cnh huyn BD = m v cnh gc vung DK = h/2 nh sau:

- Xc nh im D v k mt ng thng Dx i qua im D.

- V mt ng trn tm D, bn knh = h/2

=> Xc nh im K.

- T K dng ng vung gc vi ng thng Dx.

- T D v mt ng trn tm D, bn knh = m.

=> Xc nh c im B.

Bc 2: V ng trn tm B, bn knh = a => xc nh im C.

Bc 3: V ng thng CD.

Bc 4: Ly i xng im C qua im D => xc nh im A.

* Dng tam gic ABC, bit cnh Bc=a, ng cao AH=h, trung tuyn AM=m.

- Thao tc dng vi Cabri.

- V ng thng Ax i qua A.

- V ng trn tm A, bn knh = h => Xc nh im H .

- V ngthng vung gc vi Ax ti H.

- V ng trn tm A, bn knh = m => xc nh im M.

- V ng thng i qua 2 im H, M.

- Ly M l tm, v ng trn bn knh a/2 => xc nh 2 giao im chnh l B, C V tam gic ABC.

- Bi ton ch c nghim khi h < m (l iu kin tn ti tam gic AHM).


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* Dng tam gic vung ABC (vung ti A), bit gc B=a (O Tam gic vung ABC l tam gic cn dng.

3.6. S dng Cabri minh ho bi ton qu tch

*V d 1 : Cho tam gic ABC ni tip ng trn (O). D l mt im chuyn ng trn cung BC khng cha nh A. Ni A vi D. H CH vung gc vi AD.

Minh ho qu tch ca im H.

- S dng Cabri ta v hnh, sau cho im D di chuyn, ta pht hin c t nht c 3 im c nh thuc qu tch:

- im E (chn ng cao h t nh C n cnh AB tng ng vi trng hp khi D chy n trng vi B).

- im C (tng ng vi trng hp D trng vi C)

- im F (chn ng cao h t nh A n cnh BC, ng vi trng hp AD trng vi ng cao h t A n BC).

Nh vy, ta d on qu tch l cung cha gc.

Dng chc nng li vt s c hnh nh qu tch im H.


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* V d 2: Cho hnh thoi ABCD c cnh AB c nh. Minh ho qu tch giao im O ca hai ng cho ca hnh thoi .

Bc l: S dng chut cho hnh thoi ABCD thay i.

- Hnh thoi ABCD tr thnh hnh vung ABCIDI => Xc nh im O1 thuc qu tch.

- Hnh thoi ABCD tr thnh hnh vung ABC2D2 => Xc nh im O2 thuc qu tch.

- Hnh thoi ABCD c im C tin trng vi im B => im O trng vi im B.

Nh vy, bng trc quan cng nh bng kim tra ta thy r 3 im khng thng hng, vy qu tch c kh nng l mt ng trn i qua B. V vai tr im A v B nh nhau nn khi cho im D tin trng vi im A, ta pht hin c im A cng thuc qu tch. Ta d on qu tch im O l ng trn nhn AB l ng knh.

Bc 2: V mt trng hp bt k, ta kim tra im O c thuc ng trn nhn AB l ng knh hay khng. Kt qu cho thy "im ny nm trn i tng".

* V d 3: Trong mt ng trn (O), AB l mt ng knh c nh, M l mt im chy trn ng trn. Ni MA, MB v trn tia i ca tia MA ta ly im I sao cho MI = 2MB. Tm tp hp cc im I ni trn.

Vi Cabri ta cho v tr im M thay i, qua ba v tr c th ta c ngay d on: qu tch im I khng th l thng, nh vy c kh nng qu tch im I l mt cung cha gc. T y gi cho ta i tm yu t gc khng i.

iu c bit bi ny l: Nu s dng tnh lun t ng dng ca tam gic MBI th ch dng vic a ra kt lun gc AIB khng i. Vy qu tch l cung cha gc dng trn on thng AB. Tuy nhin, vi Cabri ta c c kt lun tng i th v. Qu tch im I l na ng trn ng knh BIO. Trong Io nm trn tip tuyn vi ng trn ti im A sao cho AIO = 2AB.

Ta m rng bi ton theo hai hng sau:

+ AB khng phi l ng knh m ch l mt dy cung ca (O).


49

+ MI = k.MB (vi k l s thc dng cho trc).

Kt qu cng rt th v. Qu tch l mt phn ca cung cha gc i qua

* V d 4: Cho BC l mt dy cung c nh ca ng trn (O), A l mt im chy trn cung ln BC sao cho tam gic ABC lun c 3 gc nhn. Gi M l im chnh gia ca cung nh BC ca ng trn (O). Tm qu tch cc trung im I ca AM.

Sau khi d on qu tch, ta phi chng minh c gc OIM khng i bng 900, im M, O c nh, suy ra I nm trn ng trn ng knh OM.

y c mt yu t gc khng tng minh ( l tam gic ABC lun c 3 gc nhn). Nh vy chc chn ta phi kim tra gii hn ca qu tch. Bng trc quan cho im A di chuyn v li vt ca im I cho php ta kim chng c gii hn ca qu tch l phn cung (mu ). T trc quan, ta d dng xc nh c hai v tr gii hn ca im A l im A1 v A2 ( tng ng vi cc ng knh CA1v BA2 ca ng trn (O)).

* V d 5: Cho hai ng thng vung gc x, y giao nhau ti im O. Tm qu tch im M bit bnh phng khong cch t im M trn ng thng y bng khong cch t im M trn ng thng x .

Xt theo gc hnh hc gii tch th qu tch im M chnh l tp hp cc im M(x, y) sao cho y = x2. Tuy nhin, vi Cabri ta da hon ton vo kin thc hnh hc l nh l Talet dng qu tch.

- Dng mt ng trn tm O bn knh bng 1 .

- Ly mt im X bt k trn ng thng x v dng ng trn tm O, c bn knh OX.

- Ni im X vi giao im ca ng thng y vi (O,1) (chn giao im v pha di ng thng xi gi l d1 .

- Ti giao im ca ng trn tm O i qua im X vi ng thng y (chn giao


50

im v pha di ng thng x) k ng thng song song vi on thng (d1) ni trn gi l d2.

- Xc nh giao im A ca d2 vi ng thng x.

- Dng ng trn (O, OA). ng trn ny ct ng thng y ti B.

- Qua X, B ln lt dng cc ng thng vung gc vi x, y. Hai ng thng ny giao nhau ti im M.

D thy MX = MB2.

- Cho im X di chuyn trn ng thng x minh ho qu tch cn tm. Kt qu cho ta mt parabol

.

3.7. Khai thc phn mm hnh hc ng Cabri h tr dy hc ton

* V d 1: Minh ho nh ca mt hnh qua php v t.

- Dng im O. S dng chc nng., G s v n v nhp mt s thc k 0.

- Dng hnh H v nh H ca n qua php v t tm O t s k (V0k).

- Khi thay i cc yu t to nn hnh H, ta c ngay s thay i tng ng ca hnh H.

- Cho thay i gi tr ca k khi hnh v cng thay i theo, c bit cc gi tr k = 1 (php ng nht) v k = -1 (php i xng tm O).

* V d 2: Minh ho "Nu php i xng trc bin hai im bt k M v N thnh hai im M', N th MN = M N ".

Cc bc thao tc vi Cabri nh sau:

- Dng ng thng d.

- Dng hai im M, N.

- Dng nh M ca M v N ca N qua php i xng trc d (d)

- Dng on MM' v NN' bng nt t

- Ni MN v M'N', o di ca hai on thng ny (kt qu c ghi vo mt khung hnh ch nht t bn cnh on cn o).


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Ta cho thay i im M hoc im N th di on MN v M'N' cng thay i nhng lun bng nhau.

* V d 3 : Minh ho "Php v t bin 3 im thng hng thnh 3 im thng hng v bo tn th t ca chng ".

Ta thao tc vi Cabri nh sau:

- Dng im O v nhp vo mt s thc k 0.

- Dng on thng AC.

- Ly im B thuc on AC.

- Dng im A' l nh ca A qua php Vok, ni OA. Lm tng t i vi B v C (nh ca chng ln lt l B', C').

- S dng chc nng "Xc nh thng hng" thy rng A', B', C' thng hng v B nm gia A' v C'.

- Cho B chuyn ng trn AC th ta thy B cng chuyn ng nhng tnh thng hng v th t ca 3 im A, B', C' vn c bo tn.

- Thay i on AC sao cho O, A, B, C thng hng, thm ch cho 1 trong 3 im A, B, C trng vi O, ta vn thy A', B', C' thng hng v B nm gia A' v C'.

* V d 4: Minh ho "Php v t bin ng trn thnh ng trn" .

Thao tc vi Cabri nh sau:

- Dng im O v g vo mt s thc k 0.

Dng ng trn (I,R), ly M thuc (I,R).

- Dng nh I' ca I qua php Vok, ni OI.

- Dng nh MI ca M qua Vok, ni OI bng nt t.

Xc nh trng thi li du vt cho im M', sau di chuyn im M trn (I,R), khi im MI cng di chuyn v vch ra qu tch ca n, qu tch nhn trc quan c v nh l mt ng trn tm I'.

T d on trn, ta gii thiu nh l v gi cho hc sinh hng chng minh: S chng minh cho im M lun cch im I' mt khong khng i. Ta ni IMv IM ri yu cu hc sinh s dng nhng kin thc hc (nh l 1 ca bi Php v t" hoc "tam gic ng dng ") chng minh.

* V d 5: Hng dn hc sinh tm li gii bi ton: "Cho 3 php i xng tm A, B, C, vi im M bt k, gi M1 l nh ca M qua A, M2 l nh ca M1 qua B, M3 l nh


52

ca M2 qua c. Chng minh rng trung im ca on thng MM3 l mt im c nh. T suy ra qu tch ca im M3 khi im M chy trn mt ng trn (O) hay mt ng thng d ". Vi Cabri c th lm nh sau:

- Dng cc im A, B, C, M.

- Dng cc im Ml, M2, M3 theo yu cu bi ton.

- Dng trung im D ca MM3

- Ni cc on MM1, M1M2. M2M3 bng nt t v cc on AB, BC, CD, DA, M3M1, MM3 bng nt lin.

Ta cho im M thay i minh ho cho kt lun ca bi ton.

Cng trong qu trnh di chuyn im M, yu cu hc sinh nhn xt v hnh dng ca t gic ABCD (l mt hnh bnh hnh c nh) t rt ra hng chng minh: Chng minh cho D l nh th t ca hnh bnh hnh ABCD.

Sau khi chng minh c D l im c nh, nu hc sinh cha gii c tip theo ca bi ton th ta c th tip tc nh sau:

- t thuc tnh " li du vt " cho im M3.

- Dng ng trn (O) hoc ng thng d i qua M.

- Cho im M di chuyn dc trn (O) (hoc d) quan st qu tch ca M3, t xc nh phng hng gii quyt.

* V d 6: Hng dn hc sinh tm li gii bi ton: "Cho hai im c nh B, C trn ng trn (O) v mt im A thay i trn ng trn . Tm qu tch trc tm H ca tam gic Thao tc :

- Dng ng trn (O).

- Dng tam gic ABC ni tip trong ng trn.

- S dng Macro "ng cao " dng cc ng cao ca tam gic ABC, t xc nh trc tm H ca tam gic .

- Cho im A chy trn ng trn (O) v theo di qu tch ca im H, ta s thy H chy trn mt ng trn i qua B, C. Chn 3 im trn ng trn ny v dng Macro "Tm ngoi tip " xc nh tm O' ca ng trn ny.

Nhn hnh v, hc sinh c th d on rng ng trn (O') c bn knh bng bn knh ca ng trn (O) (ta c th kim tra iu ny bng cch o 2 bn knh ca 2 ng trn , sau cho bn knh ca ng trn (O) thay i th s thy bn knh ca ng trn (O') cng thay i theo). T d on ny, ta c th hng hc sinh ti suy ngh rng: (O') l nh ca (O) qua mt php di hnh no , chng hn nh php i xng trc, i xng


53

tm hoc php tnh tin. C th nh sau:

- Nu l php i xng trc th trc l ng thng no? (Hc sinh d nhn thy rng l ng thng BC).

Nu l php i xng tm th tm l im no? (Hc sinh d nhn thy chnh l trung im I ca BC).

Nu l php tnh tin th vect tnh tin l g?

Cho im A chy trn (O), ta thy AH lun vung gc vi BC v di AH hnh nh khng i, t gi hc sinh chng minh rng vc t AH lun bng mt vect khng i no ( chnh l vect tnh tin cn tm) t i n kt lun: A chnh l to nh ca H qua php tnh tin ni trn.

- Ta c th a ra mt s trng hp c bit, chng hn nh cho A trng vi B hoc C v yu cu hc sinh xc nh im H

* V d 7: Hng dn hc sinh tm li gii bi ton "Cho ng trn (O) v im P c nh nm ngoi SO). BC l mt dy cung thay i ca (O) nhng c di khng i Tm qu tch trng tm ca tam gic PBC ".

th hin gi thit: Mt dy cung thay i nhng c di khng i ca mt ng trn , ta c th lm nh sau:

- Dng 2 ng trn ng tm O nhng bn knh khc nhau.

- Trn ng trn nh ly im I, dng on thng OI.

- Dng ng thng d qua I, vung gc vi OI.

- Gi B, C l giao im ca d vi ng trn ln. Dng on thng BC, sau lm n i ng thng d v ng trn nh.

- Dng im P nm ngoi (O). Ni PB v PC.

- Dng Macro "Trng tm " dng trng tm G ca tam gic PBC.

- Ni IP th d thy G thuc IP (v I l trung im ca BC).

- Xc nh trng thi " li du vt cho im G, sau cm im I di chuyn dc theo ng trn nh (ng trn nh lc ny tuy b n i nhng do cch dng im I nn khi di chuyn th I s lun nm trn ng trn ), dy BC s c di khng i v khong cch t O n BC lun bng bn knh ca ng trn nh.

- Quan st du vt ca im G li, ta d on qu tch ca G l mt ng trn. T nhn xt PG = 2/3 PI, ta thay vic tm qu tch im G bng vic i tm qu tch im I. Sau


54

khi tm c qu tch im I l ng trn nh th cho ng trn nh hin ln ri i n kt lun: 'lqu tch M chnh l nh ca ng trn nh qua php v t Vp2/3 .

Ta m rng bi ton bng cch di chuyn im P vo trong hoc trn ng trn nhn xt xem kt qu c cn ng khng? .

* V d 8: Cho im M di chuyn trn na ng trn ng knh AB. Ta dng bn ngoi tam gic MAB cc hnh vung MBCD v MAEF.

Tm qu tch cc im C v E.

Bc 1 : Ta xy dng mt Script "Dng hnh vung" (tp hvuong.gss) nh sau:

Given:

Point A

Point B

1 . Let [j] = Segment between Point A and Point B.

2. Let C = 1mage of Point B rotated 90 degrees about center Point A.

3. Let D : 1mage of Point A rotated 90 degrees about center Point B.

4. Let [k] : Segment between Point C and Point D.

5. Let [l] = Segment between Point D and Point B.

6. Let [m] - Segment between Point A and Point C.

Bc 2: S dng phn mm Sketchpad c s dng Script "Dng hnh vung" dng cc hnh vung MBCD v MAEF khi xc nh c cc im cho trc M, B v A, M. Cc bc c th thc hin nh sau:

- Dng c tam gic MAB.

- M tp hvuong.gss ( thit k trn).

- Chn A, M theo th t, n vo nt PLAY ca ca s script "hvuong.gss" va m. Ta ln lt c quan st cc bc dng hnh vung MAEF theo kch bn to sn.

- Tng t, dng c hnh vung MBCD vi hai im khi u l M, B.

Bc 3: Khai thc s tr gip ca Sketchpad trong vic d on qu tch ca C v E khi cho M di chuyn trn cung AB:

Chn E v C, vo menu Display chn nt lnh Trace Object chn chc nng li vt ca 2 im ny khi chng thay i.

- Chn im M v cung AB, vo Display chn nt Animate, xut


55

hin ca s Path Match.

- n vo nt Animate, ri quan st s thay i tng ng vi M l hnh dng bin i ca cc hnh vung MBCD v MAEF, cng s thay i v tr khc nhau ca C v E. Tp hp cc v tr C v E i qua khi M thay i chnh l tp hp im cn tm.

T quan st hnh v: C v E di chuyn theo cung trn. Vn t ra: "Cung trn c xc nh c th nh th no? ". C v E chnh l cc nh ca M qua php quay ln lt tm B v A. Do M di chuyn trn na ng trn ng knh AB nn qu tch ca C v E l hai nh ca ng trn ny trong cc php quay trn. Theo cch ny, ta cn dng thm hnh vung ABB'A'. ng cn tm l 2 na ng trn ng knh AA' v BB', bn ngoi ABB'A'.

* V d 9: Hng dn gii bi tp: "Cho tam gic cn ABC (AB=BC). Gi M l cung im ca ng cao AH, gi D l giao im ca cnh AB vi CM. Chng minh rng

ABAD31= ".

Hot ng 1 : S dng Cabri v tam gic cn ABC (AB=BC), ng cao AH, xc nh trung im M ca AH, ni CM xc nh D l giao im ca CM vi AB. Hc sinh nhn xt ng cao AH ng thi l ng trung tuyn => BH=HC.

Hot ng 2: Xut pht t yu cu cn chng

minh rng ABAD31= , th khi ta chia on AB lm 3

phn bng nhau bi hai im chia th im D phi l mt im, im cn li gi s t tn l E. D thy E phi l trung im ca on AD. Khi ta c 3 on thng bng nhau AD=DE=EA (iu c minh

ho bng kt qu con s trn mn hnh l 2 cm).

Hot ng 3: Ta ni E vi H. T trc gic thy hai ng thng HE v CD song song v s dng Cabri khng nh iu .

Hot ng 4: Ta c BH=HC v BE=ED, vy HE i qua trung im hai cnh ca tam gic CDB nn n phi song song vi cnh th ba l CD =>HE // CD => HE // MD.

Hot ng 5: Vi tam gic AEH, ta c:

AM = MH V MD // HE, vy ng thng MD i qua trung im ca cnh AH v song song vi cnh th hai l HE vy n phi i qua trung im cnh th ba tc l: AD = DE. Vy ta c AD = DE = EB => PCM.

* V d 10: Tm mi lin h gia khong cch t giao im cc ng trung trc ca tam gic n mt cnh v khong cch t trc tm n nh i din vi cnh . S dng Cabri hng dn hc sinh gii bi ton ny nh sau:

Hot ng 1 : S dng cabri v hnh.


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Hot ng 2: S dng chc nng "Khong cch v chiu di" xc nh s o ca on KE v HB. Hc sinh thc hin php chia v nhn c kt qu HB:KE l 2.

Hot ng 3 : Cho tam gic ABC thay i. Hc sinh nhn c thng bo ca Cabri: t s HB:KE khng thay i v lun bng 2. Nh vy hc sinh d on v tm cch chng minh t s HB:KE lun bng 2.

Hot ng 4: Tm ti cch chng minh: Hc sinh lin tng kin thc c: trong mt tam gic, ng trung bnh ca tam gic song song vi cnh th ba v bng na cnh . Nh vy, nu ta xc nh c mt tam gic m ng trung bnh c s o bng s o KE v cnh tng ng c s o bng s o cnh HB th bi ton c gii quyt.

Hot ng 5: K tia CK. Ta c E l trung im AC nn ta gi cho hc sinh k thm cc ng ph sao cho KE l ng trung bnh ca tam gic m A v C l hai nh. Gi nh cn li ca tam gic cn tn l Q, theo cch dng Anh KE vy hc sinh xc nh c nh Q bng cch t A k Ax // KE ct CK ti im Q. Vy vi cch dng trn th KE l ng trung bnh ca ACQ v KE bng mt na AQ .

Hot ng 6: Gio vin t vn : chng minh KE bng mt na HB, ta cn chng minh c HB bng AQ.(H5)

T B k By // KF, gi s By ct CK ti Q'. Theo cch dng KF l ng trung bnh ca tam gic CBQ' v do ta c Q'K=KC (*), mt khc v KE l ng trung bnh ca tam gic ACQ nn KC=KQ (**). T * v ** chng t Q trng vi Q' suy ra BH=AQ. n y ta gii quyt song bi ton: Kt qu hai khong cch lun t l vi nhau vi t s bng 2

* V d 11 : Cho gc xay khc gc bt, Az l tia phn gic, B l im c nh trn tia Ax, C l im chuyn ng trn on thng AB, D l im chuyn ng trn tia Ay sao cho AD=BC. Chng minh rng ng trung trc ca on thng CD lun lun i qua mt im c nh khi C, D di ng.

Trc tin hc sinh dng Cabri v hnh, sau cho thay i v tr im C d on im c nh.

Mt s hc sinh pht hin ra im c nh l giao ca tia phn gic gc vi ng thng trung trc ca on thng AB. Mt s phn hc sinh li cho im C di chuyn n nhng v tr c bit v pht hin ra c im c nh chnh l giao ca hai

ng trung trc ca on thng AB v AD'. (D' trn tia Ay sao cho AD'=AB).

Sau khi d on im c nh, c hai nhm u chng minh c iu d on ca


57

mnh l chnh xc.

n y, c hc sinh cm thy hnh nh c 2 im c nh ! . tm hiu vn ny hc sinh s dng chc nng kim tra Nm trn i tng v kt qu cho thy giao hai ng trung trc nm trn tia phn gic ca gc A. Nh vy y ch l 2 cch xc nh im c nh.

Sau qu trnh m mm, pht hin, hc sinh chng minh c ng trung trc ca on thng CD lun lun i qua mt im c nh khi C, D di ng.

Tuy nhin hc sinh cng rt kh hnh dung trn vn hnh nh im "c nh" khi C, D di ng ra sau?. Ta s dng chc nng li vt khi cho C,D di ng, hc sinh s c tn mt quan st hnh nh v hnh dung y v im c nh.

V d 12: Cho tam gic u ABC, M l trung im ca BC. V ME song song vi AB (E thuc AC), v MF song song vi AC (F thuc AB). Chng minh rng

BME = FMC . Bc 1 : S dng Cabri v hnh.

Vi gi thit M l trung im ca BC, hc sinh d dng chng minh c BME = FMC (c.c.c).

Bc 2: Gio vin nu vn : M l im bt k thuc BC, kt qu trn cn ng khng?. Hc sinh dng chut cho di chuyn v tr ca M trn BC, vi cc cng c o khong cnh v gc, hc sinh nhn thy BME = FMC v nh vy hc sinh s i tm hng chng minh bi ton m rng.


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Bc 3: Tm ti hng chng minh.

C ME//AB nn gc CME lun bng 600 (gc ng v), mt khc gc MCE bng 600 (gt) vy MCE l tam gic u nn ME=MC (*).

-Tng t ta c MBF l tam gic u nn MB=MF (**). Mt khc ta c gc FMC bng gc EMB.

-Vy BME = FMC (c.g.c). Nh vy vi Cabri gip hc sinh m rng bi ton cho v gii quyt c trn vn bi ton .

3.8. Tho lun v bi tp

* Hy a ra cc v d c th v vic khai thc phn mm hnh hc ng trong cc tnh hung in hnh ca dy hc ton:

- Dy hc khi nim.

- Dy hc nh l.

- Dy hc gii bi tp. . . .

* Xy dng mt s bi ging in t c tch hp vi vic s dng phn mm hnh hc ng theo chng trnh ton THPT v THCS.


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Chng 4

HNG DN S DNG PHN MM MAPLE

4.1. Tng quan chung v phn mm Maple

Phn mm Maple l kt qu ca nhm cc nh khoa hc trng i hc Waterloo - Canada v l mt trong nhng b phn mm ton hc c s dng rng ri nht hin nay.

MAPLE l phn mm c mt mi trng tnh ton kh phong ph, h tr hu ht cc lnh vc ca ton hc nh: Gii tch s, th, i s hnh thc... do ta d dng tnh c cc gi tr gn ng, rt gn biu thc, gii phng trnh, bt phng trnh, h phng trnh, tnh gii hn, o hm, tch phn ca hm s, v th, tnh din tch, th tch, bin i ma trn, khai trin cc chui, tnh ton thng k, x l s liu, s phc, phng trnh vi phn, phng trnh o hm ring... v lp trnh gii cc bi ton vi cu trc chng trnh n gin. Ngoi ra, vi phn mm ny ta d dng bin son cc sch gio khoa in t vi chc nng Hyperlink to cc siu vn bn rt n gin m khng cn n s h tr ca bt k mt phn mm no khc (c

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