Day Hoc Hinh Hoc Voi Su Ho Tro Cabri GeoMetry

NGUYN B KIM O THI LAI TRNH THANH HI

DY HC HNH HC VI S H TR CA PHN MM CABRI GEOMETRY NH XUT BN I HC S PHM

M s: 02.01. 65/175 H 2008

MC LC LI NI U......................................................................................................... 3 PHN 1 ................................................................................................................... 4 PHN MM HNH HC NG CABRI GEOMETRY ................................. 4

1.1. TNG QUAN V PHN MM DY HC HNH HC ........................................................................ 4 1.2. PHN MM HNH HC NG CABRI GEOMETRY ......................................................................... 5 1.3. THAO TC VI CC CNG C CA CABRI GEOMETRY............................................................ 10 1.4. VIT HO GIAO DIN CA CABRI GEOMETRY............................................................................ 23 1.5. PHN MM CABRI GEOMETRY V VIC DY HC HNH HC PHNG ................................. 23

PHN 2.................................................................................................................. 33 LM QUEN VI CC CNG C CA CABRI GEOMETRY....................... 33

2.1. S DNG CNG C CA CABRI GEOMETRY DNG HNH.................................................. 33 2.2. S DNG CNG C CA CABRI GEOMETRY DNG HNH NG....................................... 41

PHN 3.................................................................................................................. 55 DY HC HNH HC VI S H TR CA PHN MM CABRI GEOMETRY ......................................................................................................... 55

3.1. QUY TRNH KHAI THC CABRI GEOMETRY VO DY HC HNH HC ................................. 55

3.2. PHNG N KHAI THC CABRI GEOMETRY VO DY HC HNH HC .............................. 57

3.3. THI LNG S DNG CABRI GEOMETRY TRONG CC GI LN LP .................................. 61

3.4. THIT K PHIU HC TP T CHC CC HOT NG HNH HC VI CABRI GEOMETRY....................................................................................................................................................... 63

3.5. S DNG CABRI GEOMETRY TRONG DY HC KHI NIM.................................................... 65

3.6. S DNG CABRI GEOMETRY TRONG DY HC NH L .......................................................... 70

3.7. S DNG CABRI GEOMETRY TRONG DY HC GII BI TP ................................................ 79

3.8. MT S KCH BN DY HC HNH HC VI CABRI GEOMETRY ........................................... 94

TI LIU THAM KHO ................................................................................... 100 PH LC ............................................................................................................ 102

2

LI NI U

Hin nay c rt nhiu phn mm h tr dy hc ton c ph bin rng ri nh:

Geometers Sketchpad, Euclides, Mathematica, Matcad, Maple... Cabri Geometry l kt qu nghin cu ca phng nghin cu cu trc ri rc v phng

php ging dyTrung tm nghin cu khoa hc quc gia trng i hc Tng hp Joseph Fourier Grenoble (Php). Ta c th download v cp nht cc phin bn mi ca Cabri Geometry trn mng Internet ti a ch: www.ti.com/calc; www.thnt.com.vn.

Chng ti xin gii thiu ti cc bn phn mm Cabri Geometry v nhng ng dng trong dy hc hnh hc vi hy vng ng gp mt phn nh b vo vic y nhanh tin ng dng phn mm vo dy hc, gp phn i mi phng php dy hc, nng cao cht lng o to.

Ni dung cun sch gm cc phn sau: Gii thiu tng quan v Cabri Geometry. Hng dn s dng cc cng c ca Cabri Geometry. Hng dn khai thc Cabri Geometry trong dy hc hnh hc. c bit, cc tc gi ch n vic s dng Cabri Geometry trong cc tnh hung in

hnh ca dy hc ton nh dy hc khi nim, dy hc nh l, dy hc gii bi tp. c gi c th xem xt v th li cc v d c th r hn cc vn m tc gi cp ti.

Cun sch nhm phc v sinh vin cc trng i hc S phm, Cao ng S phm, gio vin ging dy hc phn l lun v phng php dy hc b mn Ton v gio vin cc trng Trung hc ph thng, Trung hc c s.

Do ln u bin son nn ni dung cun sch khng th cp ht cc tnh hung khai thc Cabri Geometry trong dy hc hnh hc. Rt mong nhn c kin ng gp, trao i ca cc bn c ni dung cun sch c hon thin hn. Nhm tc gi

3

PHN 1 PHN MM HNH HC NG CABRI GEOMETRY

1.1. Tng quan v phn mm dy hc hnh hc Trn th gii cc phn mm h tr dy hc hnh hc nh: Omnigraph, Coypu,

Mentoniezh, Cheypre, Defi, Geometers Sketchpad, Geospacw, Geoplanw, Euclides, Autograph,... c s dng, khai thc rng ri trong nh trng. Bn c c th tm hiu cc phn mm ny trn Internet.

Vit Nam, trong thi gian qua cng c cc phn mm h tr dy hc hnh hc nh Geometry, GeoBook v cc phn mm dy hc hnh hc vit theo chng trnh sch gio khoa ca SchoolNet.

1.1.1. Phn mm dy hc The Geometers Sketchpad The Geometers Sketchpad (GSP) l phn mm hnh hc ng h tr vic nghin cu v

dy hc hnh hc phng. Phn mm GSP c tc gi Nicholas Jackiw a ra phin bn u vo nm 1995 v lin tc c nng cp, n nay l phin bn 4.7. Chng trnh GSP c th download ti website: http://thnt.com.vn hoc http://www.keypess.com/sketchpad.

Trn th gii, phn mm GSP c s dng cc nc ng Nam nh Malaysia, Singapore v mt s nc khc nh M, c...

GSP c cc chc nng v, dng v thc hin cc php bin i i vi cc i tng hnh hc. Bn cnh , GSP cn c cc chc nng tnh ton, o c v chc nng hot hnh.

s dng GSP bn c c th tham kho cc ti liu ca nh xut bn Key Curriculum Press hoc ti website: http://www.keypress.com.

1.1.2. Phn mm dy hc Geometry Phn mm Geometry tr gip dy hc hnh hc c tc gi Nguyn Thanh Thu (i

hc Bch khoa H Ni) thit k theo nh hng sau: To ra mt giao din ho tr gip hc sinh pht trin kh nng quan st trc quan. a ra cc tr gip chng minh theo tng bc hoc ton b qu trnh gii bi ton. C th khai thc phn mm Geometry di cc hnh thc sau: Dng hnh v thao tc trn hnh v (tng t Cabri Geometry, GSP). Gip khai thc cc lut sn c (cc nh l, tnh cht...) vn dng trong qu trnh

chng minh bi ton (tng t nh h Mentoniezh)... C th ni v tng th phn mm Geometry c nhiu u im so vi cc phn mm

hnh hc khc. Do nhiu l do nn hin nay phn mm ny cha c a ra s dng rng ri.

1.1.3. Phn mm dy hc GeoBook Phn mm GeoBook l sn phm ca Cng ti Tin hc nh trng SchoolNet vi giao

din hon ton ting Vit. Vi GeoBook, hc sinh, gio vin c th truy cp vo cc file tm kim cc kin thc

lin quan n cc tnh cht ca cc hnh, cc ng thng, cc ng trn... v cch chng

4

minh cc tnh cht hnh hc. Gio vin c th son gio n trc tip vi GeoBook m khng cn cc phn mm cng

c khc. GeoBook cho php gio vin lng ghp cc tng, tnh hung s phm vo bi ging cng vi vic tm kim thng tin c lin quan mt cch nhanh nht v chnh xc nht. Nh vy, ta c th khai thc GeoBook trong cc khu chun b ln lp, thc hin ln lp v nh gi kt qu hc tp ca hc sinh...

1.1.4. Phn mm dy hc Euclides Phn mm hnh hc Euclides do cc chuyn gia ngi Hungari Lszl Istvn v Simon

Pter pht trin. tm hiu phn mm ny ta c c th truy cp vo website: http://www.moti.hu/euclides.

Phn mm Euclides cho php thit k v xy dng cc i tng hnh hc mt cch trc tip nh h thng cc cng c. Vi Euclides ta c th s dng chut v v thay i v tr cc hnh v mt cch d dng.

Hn ch ca Euclides ch, thao tc dng hnh phc tp, mt s thao tc khng ging vi thao tc dng hnh thng thng bng thc k v compa m hc sinh c lm quen, hn na giao din hon ton l ting Anh nn gy kh khn cho hc sinh v gio vin trong qu trnh khai thc.

1.2. Phn mm hnh hc ng Cabri Geometry 1.2.1. Khi ng Cabri Geometry

Nu my tnh ca bn cha ci t phn mm Cabri Geometry th bn c th download Cabri Geometry trn Internet ci t (xem ph lc).

gi Cabri ra lm vic ta ln lt chn cc lnh: Start/Programs/Cabri Geometry II Plus/Cabri Geometry II Plus hoc bm chut vo logo ca Cabri Geometry trn mn hnh.

5

1.2.2. Giao din ca Cabri Geometry Ca s lm vic ca Cabri Geometry bao gm cc thnh phn chnh nh: h thng

menu bar, h thng cng c v vng lm vic dnh v, dng cc i tng hnh hc (hnh 1.1).

Vng v hnh

H thng cng c

Menu bar

Hnh 1.1

1.2.3. H thng menu bar ca Cabri Geometry H thng menu bar ca Cabri Geometry gm 5 nhm chc nng chnh, mi nhm ng vi

mt h thng menu dc (PopUp). Nhm chc nng File: gm 11 chc nng (hnh 1.2)

New (Ctrl+N): M mt tp mi. Open (Ctrl+O): M mt tp lu trn

b nh ngoi. Khi xut hin ca s Open a File, ta phi chn a, th mc v tn tp tin cn m ri chn lnh Open.

Close (Ctrl+F4): ng tp tin ang lm vic. Nu ta cha lu tr tp tin, xut hin thng bo (hnh 1.3). Khi nu chn Yes th Cabri Geometry s lu tr tp tin trc khi ng. Nu khng mun lu li thng tin ta chn No. Nu chn Cancel ta s tip tc lm vic vi tp tin hin thi.

6

Hnh 1.2

Hnh 1.3

Save (Ctrl+S): Lu tr tp tin. Nu l ln lu tr u tin s xut hin ca s Save File As. Ta phi chn a, th mc

v t tn cho tp tin ny. Nhng ln ghi sau, Cabri Geometry s ghi theo thng s chn (hnh 1.4).

Save As: Lu tr tp tin c vi tn mi.

Hnh 1.4

Export figure for calcs...: Chuyn i tp tin theo nh dng ca cc my tnh in t c

chc nng ho nh TI83; TI88; TI92... Revert: Chuyn giao din lm vic v tnh trng ban u. Show Page...: Xem ni dung trc khi in (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+F4): Kt thc phin lm vic. Nhm chc nng Edit: gm 8 chc nng (hnh 1.5) Undo (Ctrl+Z): Hu b lnh va thc hin. Hnh 1.5

Cut (Ctrl+X): Xo cc i tng c la chn trn mn hnh v lu tm chng vo b m Clipboard.

Copy (Ctrl+C): Lu tr tm thi cc i tng c la chn trn mn hnh vo b

7

m Clipboard. Paste (Ctrl+V): a cc i tng ang lu tr trong b m Clipboard ra vng lm

vic. Clear (Del): Xo b cc i tng c la chn. 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 ca hnh dng. Nhm chc nng Options: gm 6 chc nng (hnh 1.6)

Hnh 1.6

Show/Hide Attributes (F9): Hin hay n bng la chn thuc tnh cc i tng. Show Figure Description (F10): n hay hin bng lit k cc thao tc dng hnh

thc hin. Preferences..: Khai bo la chn cc tham s h thng nh la chn mu i tng, ch

hin th, font ch h thng, dng phng trnh (hnh 1.7).

Hnh 1.7

Nu mun thay i cc thuc tnh ca i tng no th cn phi khai bo, la chn

8

trong danh sch cc mu sn c, ri bm chut vo : [x] Keep as defaults. Nu mun lu tr cu hnh bm chn lnh Save to file.

Language...: La chn ngn ng hin th. S c nhiu la chn nh ting Anh, Php, c, an Mch... ta cn bm chut vo ngn ng cn s dng.

Font: La chn kiu ch cho i tng ang c la chn. Nhm chc nng Session: gm 5 chc nng (hnh 1.8)

Hnh 1.8

Begin recording... (F2): Bt u ghi li chui cc thao tc v, dng hnh... v lu tr

di dng tp tin trong th mc ring. Stop playing/ Read a session (F4): Kt thc qu trnh ghi hay c mt recording c

(khi ta c th xem li cc bc dng hnh c ghi). Previous (F6): Chuyn v thao tc trc . Next (F7): Chuyn n thao tc tip theo. Print a session (F5): Ghi ni dung recording ra file. Nhm chc nng Window H thng gm cc lnh dng b tr sp xp cc ca s theo kiu dn ngang hay lp

ngi, hoc ng cc ca s ang m. Chc nng Help

Hnh 1.9

9

Nu bt chc nng Help, khi ta ch chut vo cng c no th pha di ca s s hin ln chc nng ca cng c (hnh 1.9).

1.3. Thao tc vi cc cng c ca Cabri Geometry H thng cng c ca Cabri Geometry gm 11 nhm chc nng. Biu tng ca cng c

ang c la chn s c mu sng. s dng mt cng c no , ta bm chut vo biu tng nhm chc nng ri di chuyn chut bm chn cng c cn s dng.

Phn ny chng ti ch lit k cc cng c ca Cabri Geometry. thc hnh, bn c nn thao tc da theo cc v d chi tit phn 2.

1.3.1. Nhm chc nng chn trng thi lm vic vi chut Khi bm chut vo nhm chc nng ny, xut hin danh

sch 4 cng c:

Pointer: S dng la chn, dch chuyn cc i tng hnh hc.

Sau khi chn cng c Pointer: chn mt i tng no , ta ch chut vo i tng v

bm (click), khi chut s c dng hnh bn tay v hin ln ch thch kiu ca i tng. chn nhiu i tng mt lc, ta nhn phm Shift trong khi ln lt bm chut vo

cc i tng cn chn. di chuyn mt i tng, sau khi chn i tng ta gi phm chut trong khi di

chuyn chut (drag) thay i v tr hnh v.

Rotate: S dng xoay hnh xung quanh mt im hay tm ca hnh.

Sau khi chn cng c Rotate ta bm chut xc nh tm quay sau bm chut vo i tng v gi phm xoay hnh.

Dilate: Thay i kch thc ca hnh bng mt php ng dng. Sau khi chn cng c Dilate ta cn bm chut xc nh mt im c chn lm tm

ca php ng dng sau bm chut vo i tng v gi phm ko thay i kch thc.

Rotale and Dilate: C th cng mt lc va xoay va thay i kch thc ca hnh.

1.3.2. Nhm chc nng chn cng c to im Khi bm chut vo nhm chc nng ny, xut hin 3 cng

c:

Point: To im.

Khi chn cng c Point chut c hnh dng bt ch, a u bt ch n v tr xc nh im, bm chut tri. C th xc

10

nh nhiu im m khng cn chn li cng c.

Point on Object: Ly im thuc mt i tng c.

Sau khi chn cng c Point on Object, ta a chut ch vo i tng, xut hin cu thng bo, chng hnly im ny trn ng trn... cn chn im v tr no, ta bm chut ti v tr (hnh 1.10)

Intersection Points: Xc nh im l giao ca cc hnh hnh hc c.

xc nh giao ca hai i tng no , ta chn cng c Intersection Points ri a chut ln lt bm vo hai i tng . Cng c th ch chut vo v tr l giao ca cc i tng, khi xut hin dng thng bo Ly ti giao im ta bm chut (hnh 1.11).

Hnh 1.10

Hnh 1.11

1.3.3. Nhm chc nng chn cng c v cc i tng hnh hc Khi bm chut chn nhm chc nng ny, xut hin bng 7

cng c dng cc i tng hnh hc c bn:

Line: Dng mt ng thng. Mt ng thng c xc nh bi hai im. dng mt

ng thng, trc ht ta chn cng c Line sau a chut bm chn v tr hai im trn mn hnh. Khi thay i v tr mt trong hai im th ng thng cng thay i v tr mt cch tng ng.

Segment: Dng mt on thng.

Thao tc dng on thng tng t nh dng ng thng. Ta chn cng c Segment ri sau a chu bm vo v tr ca hai u mt on thng cn dng.

t

Ray: Dng mt tia.

d c nh im gc v hng ca tia. Chn cng c ng mt tia ta phi x Ray sau b cm chut xc nh im gc ca tia, di chuyn chut chn hng ca tia v bm hut xc nh im tip theo, ta c tia cn dng.

11

Vector: Dng mt vect.

ng mt vect ta chn cn d g c Vector ri sau ln lt bm chut xc nh im gc v im ngn ca vect cn dng.

Triangle: Dng mt tam gic.

ng mt tam gic, ta chn cng d c Triangle ri sau di chuyn v bm chut ln l s t xc nh v tr 3 nh ca tam gic, ta nhn c tam gic tng ng vi 3 im chn.

Polygon: Dng a gic n cnh.

ng t nh dng tam gic, ta chn cng c

T Polygon sau a chut ln lt bm xc ta nh v tr cc nh. Kt thc bm p chut tri, c a gic tng ng vi cc im chn.

Regular Polygon: Dng a gic u (n

hay parabol, hypecbol.

1.3.5. Nhm chc nng chn cng c dng cc i tng mi c dn xut t cc i

o nhm chc nng ny xut hin bng 10 c

tng hnh hc c Khi bm chut vng c:

Perpendicular Line: Dng ng thng vung gc.

dng mt ng thng i qua mt im v vung gc v

i mt ng thng (on thng) cho trc ta chn

cng c Perpendicular Line ri ln lt bm chut chn xc nh m m ng thng s i qua v ng thng (on thng...) vung gc. Cng c th thao tc theo trnh t xc nh ng thng (on thng) trc, im sau (hnh 1.12).

i

: Dng

ng ng thng i qua mt im v song song vi m

Parallel Lineng

dsong song.

t ng thng (on thng...) cho trc: Chn

cng c Parallel Line ri ln lt bm chut xc nh ng th (on thng...) v im m ng thng song song i qua.

ng

Hnh 1.12

Midpoint: Xc nh im gia ca hai i , trm ung im ca on thng.

Sau khi chn cng c

Hnh 1.13

Midpoint, a c mhut bm xc nh hai i hoc bm chn on thng, cnh a din... ta c im cn dng (hnh 1.13).

Perpendicular Bisector: Dng ng trung tr

in ta chn cng c

c.

on thng trc t dng ng trung trc ca mt Perpe onndicular Bisector sau a chut bm xc nh hai u mt ca on thng hoc thng c.

Angle Bisector: Dng ng phn gic.

d ng ng phn gic ta chn cng c Angle Bisector ri sau a chut bm xc nhnh 3 im theo th t thuc cnh th nht, v cnh cn li ca gc.

Vector Sum: Xc nh tng hai vect.

ng vect tng ca hai vect: Chn cn d g c Vector Sum sau a chut bm

13

xc cnh hai vect thnh phn ri bm chn v tr lm gc a vect tng.

Compass: Dng ng trn vi bn knh cho trc. dng mt ng trn c bn knh cho trc: Chn

cng c Compass sau a chut bm xc nh on thng chn lm di bn knh (hoc bm chn hai im phn bit c khong cch s l bn knh) v bm vo mt v tr (im) bt k c chn lm tm ca ng trn (hnh 1.14).

c

Measurement Transfer: Xc nh mt im cch m t i

t s thc (

m

n cng c

m cho trc mt khong cho trc. thc hin chc nng ny trc ht phi c mc th l kt qu o c cc i tng, kt qu tnh

).

Thao tc dng im nh sau: Ch

ton hoc nhp trc tip t bn ph

Measurement Transfer ri a chut bm chn gi tr s trn mn hnh v im cho. Trn mn hnh xut hin mt ng chm k c di bng gi tr s chn. Ta chn hng v bm chut tri xc nh im cn dng.

Locus: Dng qu tch. dng qu tch ca mt i tng no ,

ta chn cng c Locus v sau dng chut ln lt bm vo yu qu tch v yu t gy qu tch.

V d 1.1: Cho tam gic ABC ni tip trong t

ng

metry dng hnh.

trn tm O. im B, C c nh, A thay i. G l trng tm ca tam gicABC. Tm qu tch im G.

Bc 1: S dng cc cng c ca Cabri Geo

Bc 2: Chn cng c Locus ri ln lt bm vo im G (yu t qu tch) ri bm vo im A (y n u t gy qu tch). Ta nh c hnh nh qu tch im G (hnh 1.15).

Redefine Object: nh ngha i tng hnh trong qu trnh dng hnh.

sdng th m no

(m <

Gi ta thc hin n bc dng hnh nhng mun thay i li bc

n). V d ta dng tam gic ABC v xc nh tm ca ng trn ngoi tip tam gic ABC l giao ca hai ng trung trc cnh AB v AC nhng li mun thay i li thnh xc nh tm ca ng trn ni tip tam gic ABC.

khng phi thao tc li m1 thao tc u,

14 Hnh 1.16

Hnh 1.14

Hnh 1.15

Redefine ta s s dng cng c Object. Khi chn cng c ny s xut hin danh sch n bc dng 6).

n bng gm 6

hnh, ta bm chn vo bc th m v thc hin thao tc mi (hnh 1.1 Trong v d trn ta chn Angle Bisector dng cc ng phn gic.

1.3.6. Nhm chc nng chn cng c dng nh qua cc php bin hnh Khi bm chut vo nhm chc nng ny, xut hi

cng c:

Reflection: Dng hnh qua php i xng trc. dng hnh i xng ca i tng qua ng, on thng, tia,

trc t o , cnh tam gic, a gic... ta chn cng c Reflection ri sau bm chut chn i tng ban u v i tng chn lm trc i xng (hnh 1.17).

Symmetryi xng tm.

au

: Dng hnh qua php

S khi chn cng c Symmetry ta ln lt bm chut xc nh i tng ban u v im c chn lm tm ca php i xng, ta s thu c nh ca i tng chn qua php i xng tm.

Hnh 1.17

Hnh 1.18

Translation: qua php tnh tin. dng nh ca mt i tng hnh hc qua

php t ti

Dng hnh

nh n theo mt vect: Bc 1: Xc nh vect lm c s cho php tnh tin.

Bc 2: Chn cng c Translation sau ln lt d

tnh tin v vect, ta c nh ca hnh qua php tnh ti

ng chut bm chn i tng cn dng nh qua php

n (hnh 1.18).

Rotation: Xc nh nh qua php quay. dng nh ca mt i tng hnh hc qua php

quay ta chn cng c Rotation ri tip bm chut chn i t lng xc

h

ng ban u, im chn lm tm quay v i nh gc quay. V d 1.2: t c hin php quay cung OO' xung

quanh tm O vi gc quay 600 ta chn cng c Rotation ri bm chut vo cung OO', im O v s 60. Ta nhn c nh ca cung OO' qua php quay (hnh 1.19)

Hnh 1.19

15

Dilation: Dng hnh qua php v t. dng nh ca mt i tng qua php v

t tr p v t.

c tin ta phi xc nh tm v h s ca ph

Thao tc: Chn cng c Dilation ri bm chut la chn i tng ban u, im c xc nh l v

ta chn cng

c

m tm v h s ca php t. V d 1.3: dng nh ca ng trn (O)

qua php v t tm A v h s k=2.2

Dilation ri sau ln lt bm chut vo ng trn, t s k v im A. Ta thu c nh ca

(O) qua php v t (hnh 1.20)

Inverse: Dng hnh qua php ng

m qua php nghch o: Chn cng c

hch o.

dng nh ca mt i Inverse, ri bm chut .

1.3.7.n hnh nhiu thao tc (chng hn nh

c thao tc dng hnh di dng mt Macr

cng c:

la chn im ban u v ng trn nghch o

Nhm chc nng chn cng c xy dng Macro dng mt i tng no ta thng phi ti

dng ng trn ni tip tam gic). Nu ta ghi li chui co th t ln sau ta khng nht thit phi thc hin li cc bc dng hnh m ch gi thc

hin Macro. Cabri Geometry s thc hin t ng tt c cc bc dng hnh c ghi trong Macro .

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

Initial Objects: Xc nh cc i tng ban u.

Final Object: Xc nh cc i tng thu c sau khi kt thc t c hh in cc lnh ca Macro.

Hnh 1.20

Define Macro: Cc bc to m

c tam gic ABC, hai n xc nh giao ca chng).

nh ngha tn v chn phm tt cho Macro. t Macro:

B 1: Dng hon chnh cc bc dng hnh (v d ta ln lt vg trung tuyn ca tam gic 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 ban u X (trong v d trn th ta phi bm chut vo tam gic ABC).

Bc 3: Bm vo biu tng, chn Final Objects, sau bm chut vo nhng i tng c coi l nhng i tng kt thc Y (trong v d trn ta phi bm chut vo hai trung tuyn v giao ca chng).

Bc 4: Bm vo biu tng, chn Define Macro (hnh 1.21): Bn cn t tn cho

16

Macro, nhp cc thng tin cn thit v chn OK. ta

trong v d trn ta gi Macro v bm vo mt tam g

V d 1.4: Xy d t tam gic ta tin hnh nh sau:

ng tam gic ABC; i ng phn gic xut pht t nh B, C;

a hai ng phn gic; i cnh BC.

ng d.

Chy Macro: Sau khi gi tn Macro bm chut vo cc i tng lm c s thc hin Macro, ngay lp tc ta s thu c kt qu (

ic hoc ba im khng thng hng bt k, ta nhn c hnh nh hai ng trung tuyn v trng tm ca tam gic).

Hnh 1.21

ng Macro dng ng trn ni tip trong m

Bc 1: D Dng ha Xc nh giao im O c Dng ng thng d i qua im O v vung gc v Xc nh giao im H ca cnh BC vi ng th Dng ng trn tm O v i qua im H.

Bc 2: Chn Initial Objects, sau bm chut vo tam gic ABC.

Final Objects sau bm cBc 3: Chn hut vo ng trn ni tip.

Bc 4: Chn Define Macro v t tn cho Macro l DT_N_Tiep.

17Hnh 1 22

thc hin Macro, ta bm vo nhm chc nng chn DT_N_Tiep sau a chut bm

vo tam gic MNP cn dng ng trn ni tip. Ta c ngay kt qu (hnh 1.22).

chn

Khi bm chut chn nhm chc nng ny, xut hin bng gm 5

Nh vy, chc nng Macro cho php ta m rng cc cng c ca Cabri Geometry. Ta c th xy dng mt h thng Macro bao gm tt c cc thao tc dng hnh thng dng trong

g trnh ph thng v lu li di dng file. Vic s dng chng s cho php rt ngn thi gian v hnh.

1.3.8. Nhm chc nng chn cng c kim tra thuc tnh

cng c:

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

Sau khi ch

18

n cng c Collinear ta dng chut bm xc nh ba i c n theo v uy

m n kim tra. Xut hin mt khung hnh ch nht di chuy tr ca chut. Ta di ch n khung ny n mt v tr no trn

mn hnh, bm chut. Ni dung thng bo kt qu kim tra s hin ra ng hng hay khng. cho bit ba im c th

Parallel: Kion thng... c song song vi nhau hay khng, ta

chn g

m tra hai ng thng, on thng... c song song khng? kim tra xem hai ng thng,

Parallel ri a chut bm chn hai ng thng, on thngcn c ... cn kim tra. Cabri Geometry s a ra thng bo cho bit chng c song song hay khng.

Perpendicular: Kim tra hai ng thng, on thng... c vung gc vi nhau khng?

Thao tc: Chn cng c Perpendicular ri xc nh hai ng thng, on thng...cn kim

tra.

Equidistant: Kim tra hai im c cch u mt im th ba hay khng?

Hnh 1.23

Equidistant, sau ln lt Chn cng cbm chut vo ba im cn kim tra.

Member: Ki m tra mt im c thuc mt hnh hay khng?

cc i tng khc khng?

Ch nng trn c s dng kim tra mt i tng ny c thu

Thao tc: Chn cng c Member ri ln lt la chn i tng cn kim tra v i tng c kh nng cha i tng cn kim tra.

V d 1.5: Dng ra ngoi ba cnh ca tam gic

u ABC cc tam gic u ABC', BCA' v ACB'. Gi I l giao im ca CC' vi BB'. S dng

cng c Member ri ln lt bm chn im I, on thng AA'. Cabri Geometry s thng bo cho bit im I thuc on thng AA' (hnh 1.23).

1.3.9. Nhm chc nng chn cng c o c tnh ton Khi bm chut vo nhm chc nng ny, xut hin bng cc cng c:

Distance and Length: o khong cch, di, chu vi... t on thng, mt

cung, u vChc nng ny cho php ta o khong cch gia hai im, di m ch i mt a gic, mt ng trn.

Thao tc: Chn cng c Distance and Length sau bm chut xc nh i tng cn o c, t

n cng c

a s nhn c kt qu V d 1.6: V tam gic vung ABC, vung ti

A. Dng trung tuyn AM. Ch Distance and L

t ength ri a chut bm vo ng trung tuyn

AM v sau bm chn hai im B, C. K qu Cabri Geometry cho ta s o ca on thng AM v BC (hnh 1.24). Kt qu cho thy khi tam gic vung

ABC thay i th di cnh huyn BC lun gp i di trung tuyn AM.

Area: Tnh din tch hnh trn, tam

Hnh 1.24

gic, a gic...

Chn cng c Area sau a chut bm xc nh i tng cn o din tch, t t qa s nhn c k u.

Slope: Xc nh h s gc y/x. xc nh h s gc (tan) ca mt

ng, on ay vect, ta chn cng Slope sau a chut bm xthng, tia h c ng th c nh i tng.

Angle: o gc.

Thao tc: Sau khi chn cng c Angle ta dng chut bm xc nh 3 im theo th t ln l t, nh v cnh cn li ca gc, ta s nhn c s o ca gc chn

t thuc cnh th nh(hnh 1.24).

Equation and Coordinates: Cho hin to im, phng trnh ca ng... ra mn hnh.

Thao tc: Chn cng c Equation and Coordinates sau a chut bm vo i tng hnh hc (im, ng thng, ng trn, th...). Cabri Geometry s hin ra mn hnh

19

to a ca im, phng trnh c ng thng, ng trn... m ta chn.

Calculate: Tnh ton vi s liu ng.

tnh kt qu ca biu th cng c

Hnh 1.25

c ta chn Calculate, khi mn hnh s c mt y tnh cc php ton s hc c bn (hnh 1.25).

huyn gi tr vo biu thc.

m tnh ton vi nhng s liu o c, tnh ton c trn mn hnh, ta ch vic a chut

bm vo nhng gi tr . Cabri Geometry t ng cChn chc nng =, ta c kt qu v c th a gi tr ca biu thc ny Result ra

mn hnh. Mt khc, ta c th tnh ton nh mt my tnh b ti.

Tabulate: t cc s liu tnh ton vo bng.

Tabulate sau a chut ra mn hChn cng c nh vch mt khung bng, s ct v s dng tu g, ta phi chuyn ln lt tng dng mt b u

chc nng ny, xut hin bng gm

theo ta la chn. chuyn d liu vo bnng cch ch ch t vo d liu cn a vo bng.

1.3.10. Nhm chc nng chn cng c s t tn cho i tng v xc nh yu t ng Khi bm chut chn nhm

8 cng c:

Label: To, sa tn cho i tng hnh hc.

t tn cho i tng hnh hc, ta chn cng c Label a t hin mt

khung sau chut bm vo i tng cn t tn. Xu

hnh ch nht ta nhp tn cho i tng hnh hc .

Comments: To, sa li ch thch.

Cng c Comments c s dng khi ta cn a thng tin

vic. di dng vn bn vo trang lm

Thao tc nh sau: Chn cng c Comments sau a chut ko r to thnh mt khung ch nht ta nhp ni dung vn bn.

20 Hnh 1.26

Numerical Edit : To, sa cc s thc.

Numerical Edit tSau khi chn cng c a a chut bm xc nh v tr t s trn mn hhnh. Xut hin khung c nht ta nhp gi tr ca s . Ta d dng thay i gi tr tng hoc gim bng cch bm chut vo biu tng hnh mi tn ca hp thoi lu tr s (hnh 1.26).

Mark Angle: nh du gc chn.

Thao tc: Chn cng c Mark Angle sau a chut bm xc nh 3 im tng ng t v huc cnh th nht, nh cnh cn li ca gc cn nh du.

Fix/ Free: Xc nh c nh hay chuyn ng. M i tng khi b gn thuc tnh c nhFix (kht i ta thy hnh nh mt chic inh

gim)

uc tnh c nh (t do) cho i tng no ta chn cng c

th ta khng th thay i v tr ca n. Ta ch c th thay i v tr ca mt i tng khi chng trng thi t doFree.

xc nh hay g b th Fix/Free ri bm chut vo i tng .

Trace On/Off: li vt cho i tng hnh hc khi di chuyn. t a chng trn mn

hnh

Trace cho mt i tng no th ta chn cng c

M i tng c gn thuc tnh Trace On th chng s li vt ckhi thay i v tr. Tri li nu mt i tng c gn thuc tnh Trace Off th khi thay

i v tr chng s khng li vt.

xc lp (hay g b) thuc tnh Trace On/Off ri bm chut vo i tng .

Animation: To chuyn ng. Mt i tng hnh hc c th chuyn ng theo

rng b

ta ch

Hnh 1.27

uc xc nh (v d nu ly mt im thuc ng trn (ng thng...) th ta c th cho im chuyn ng nhng vn lun thuc ng trn (ng thng...)).

Mun to chuyn ng cho i tng hnh hc no

n cng c Animation ri bm chut vo i tng . Cng c bm chut vo i tng, gi phm, ko nh (xut hin hnh l xo) ri th chut ra (hnh 1.27).

Mun dng chuyn ng ca i tng ta bm chut

th

vo v tch

rt tr

tr bt k trong trang lm vic. y l chc nng h tr dy hc ni dung quc quan.

Multiple Animation: Th ng phc tp, hn hp.

n

c hin chuyn

Multiple Animation ri ln lT g t nh trn, ta chn chc nng t la chn i tng in v phng thc chuyn ng. thc h chuyn ng, ta n phm Enter.

1.3.11. Nhm chc nng chn cng c nh dng cc i tng

21

Khi bm chut chn nhm chc nng ny ny, xut hin bng 9 cng c:

Hide/ Show: Cho n, hin cc i tng.

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.

Modify Appearance: Sa k hiu trn hnh.

Show Axes: n hay hin trc to .

New Axes: t to mi.

Define Grid: nh ngha li. nh dng:

g c la c

n

Cch s dng cc cng cKhi ta chn cng c trn, tu theo cn

Hnh 1.28

hn s xut hin mt bng cc la chn tng ng. 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 (hnh 1.28).

Cng c n/hi Hide/ Show cho php mnche (khng hin ra hnh) nhng i tng c nh du lm cho hnh v n gin, rc ri.

22

1.4. Vit ho giao din ca Cabri Geometry Cc lnh ca Cabri Geometry trong phin bn gc thng l ting Anh nhng s cu lnh

ca Cabri Geometry khng nhiu nn vic ghi nh chng khng qu kh. i km vi mi lnh l mt biu tng, gio vin v hc sinh ch cn nhn vo biu tng

cng bit c chc nng tng ng ca cu lnh. i vi hc sinh cc trng Trung hc c s vng, min cn hn ch v ngoi ng, chng

ta c th Vit ho h thng cc cu lnh ca Cabri Geometry (mt s chuyn gia nh Ng nh Tuyt, V nh Ho, Nguyn V Quc Hng Vit ho Cabri Geometry). Ta m tp USEnglish.cgl (Cabri Geometry Language) v thay i ni dung cc nhn t ting Anh sang ting Vit (hnh 1.29). Nh vy, s dng, khai thc cc tnh nng ca Cabri Geometry khng i hi nhiu gio vin, hc sinh v kin thc tin hc v thi gian chun b, ta c th trin khai vic s dng Cabri Geometry h tr dy hc hnh hc trn din rng.

Hnh 1.29

1.5. Phn mm Cabri Geometry v vic dy hc hnh hc phng Phn mm Cabri Geometry h tr c lc cho gio vin, hc sinh trong qu trnh dy v

hc hnh hc phng bi cc l do sau:

1.5.1. Cabri Geometry l mt vi th gii hnh hc Cabri Geometry l mt vi th gii hnh hc vi nhng c im c bn: C cc chc nng to ra cc i tng c bn nh im, on thng, cc mi quan

h hnh hc c bn nh quan h lin thuc, quan h gia, quan h song song, quan h vung gc ca hnh hc clt.

C cc cng c tc ng ln nhng i tng hnh hc c nhm xc lp nhng i tng hnh hc mi, nhng quan h hnh hc mi.

Khi tc ng vo cc i tng ca hnh v nh dng chut lm thay i v tr cc im, di cc on thng, ln ca gc th cu trc v mi quan h gia cc i tng vn c bo tn.

23

1.5.2. Cabri Geometry cho php to ra cc hnh nh trc quan Cabri Geometry c mt h thng cng c cho php ta v, dng hu ht cc hnh c trong

chng trnh hnh hc phng:

Dng cc i tng hnh hc c bn: im ( Point), ng thng ( Line), ng trn ( Circle)... c im chung ca cc i tng ny l d dng thay i v tr sau khi v.

Dng cc i tng hnh hc mi trn c s cc i tng c: Trung im ca on thng ( Midpoint); giao im cc hnh ( Intersection Points); on thng i qua hai im cho trc ( Segment); ng thng i qua mt im v song song ( Parallel Line) hoc vung gc ( Perpendicular Line) vi mt on thng, mt ng thng cho trc; ng phn gic ca mt gc ( Angle Bisector); ng trung trc ca on thng ( Perpendicular Bisector)... Khi thay i yu t ban u th cc i tng mi cng thay i nhng chng vn bo ton cc thuc tnh c. Tuy nhin khi xo mt i tng no th cc i tng ph thuc vo i tng ny cng b xo b theo.

Xc nh thuc tnh cho i tng hnh hc: Chn mu ( Color); chn dy ( Thick); chn kiu nt lin hoc nt t ( Dotted) cho cc ng, nt trong hnh v v chn mu cho cc phn bn trong hnh v ( Fill)... Chc nng Hide/ Show: dng n bt cc chi tit ph, cc chi tit trung gian s dng trong qu trnh v hnh.

Phin bn Cabri Geometry m chng ti gii thiu y cha phi l phin bn dng trong khng gian, nhng nu s dng cc ng nt t, ta cng c th m t c mt s hnh khng gian n gin (hnh 1.30).

Vi Cabri Geometry, trc ht ta khai thc cc cng c th hin cc yu t ca hnh v mt cch trc quan, nhanh chng, chnh xc, sau cho thay i v tr, mu sc... ca hnh v tp trung ch ca hc sinh vo mt s yu t trong hnh v.

Vi cc hnh v bng Cabri Geometry hc sinh s pht hin rt nhanh nh quan st bng mt cc quan h song song, vung gc, thng hng, bng nhau, ln hn cng nh hnh

dng ng i ca im chuyn ng... nh m hc sinh c th c lng, nhn dng, tm ra cc mi quan h hnh hc cha ng bn trong hnh v.

Hnh 1.30

Nh vy chc nng trc quan ho bin Cabri Geometry tr thnh chic cu ni gia hot ng dy v hc.

1.5.3. Cabri Geometry l phn mm hnh hc ng Cabri Geometry cung cp cc cng c to ra cc mu c bn trong hnh hc Euclide

(im, ng, on thng, ng trn...) v bin i, to chuyn ng nh thit b con tr (chut, bt quang v phm mi tn). Mt khc Cabri Geometry c kh nng m t cc tnh cht, quan h gia cc i tng hnh hc. Sau khi v hnh, hc sinh s dng chut thay i v tr

24

mt s i tng ca hnh v quan st hnh v rt nhiu gc , v tr khc nhau. Trong qu trnh ny hc sinh s pht hin c cc yu t bt bin ca hnh v v nhn bit c u l nhng thuc tnh ca hnh.

Cabri Geometry c mt h thng cc cng c thit k cc yu t ng:

Chc nng Animation: gn thuc tnh chuyn ng cho mt i tng trong hnh v. Mt i tng sau khi c gn thuc tnh ny th c th di chuyn v tr theo cc rng buc do qu trnh dng hnh xc lp nn.

Chc nng Multiple Animation: gn thuc tnh chuyn ng cho mt nhm i tng trong mt hnh v no .

Chc nng Trace On/Off : li hoc khng li vt ca mt i tng hnh hc khi thay i v tr. y l cc chc nng h tr rt tt cho vic dy hc ni dung qu tch.

V d 1.7: Trn ng trn (O) ly hai im B, C c nh v im A thay i. Gi H l trc tm ca tam gic ABC v H l im sao cho HBHC l hnh bnh hnh. Tm qu tch ca im H.

Bc 1: S dng cc cng c ca Cabri Geometry dng hnh:

Chn cng c Circle: dng mt ng trn c tm O v bn knh tu .

Chn cng c Point on Object: ly ba im A, B, C bt k thuc ng trn (O).

Chn cng c Triangle: dng tam gic qua ba im A, B, C.

Chn cng c Perpendicular Line: dng ng thng i qua A v vung gc vi BC, ng thng i qua B v vung gc vi AC.

Chn cng c Intersection Points: ly giao im H ca hai ng thng vung gc va dng trn.

Chn cng c Segment: dng on thng HC.

Chn cng c Parallel Line: ln lt dng ng thng i qua C v song song vi BH, ng thng i qua B v song song vi HC.

Chn cng c Intersection Points: xc nh H' l giao ca hai ng thng trn.

Chn cng c Segment: dng cc on thng BH, CH v HH.

Chn cng c Intersection Points: xc nh giao im I ca HH v BC.

Hnh 1.31 Bc 2: Khai thc hnh v Sau khi hc sinh ch ra c H thuc (O) v

hai im H, H i xng nhau qua I nn qu tch ca H l ng trn tm O i xng vi (O) qua im I:

25

Dng cng c Trace On/Off, xc nh thuc tnh li vt cho H.

Dng cng c Animation bm vo im A. Kt qu hc sinh s c quan st qu tch im H ng nh li gii ca bi ton (hnh

1.31).

1.5.4. Cabri Geometry bo ton cu trc ca cc i tng hnh hc Mt hnh c xc nh bi cc i tng hnh hc c bn nh im, on thng v

cc mi quan h nh quan h lin thuc, quan h song song, quan h vung gc gia cc i tng hnh hc. Tnh cu trc ca Cabri Geometry c th hin r ch nu quy trnh s dng cc cng c ca Cabri Geometry th hin ng cc i tng hnh hc v m bo c cc mi rng buc th ta c mt hnh v phn nh ng vi hnh cn th hin. Khi mc d hnh v thay i nhng cu trc ca hnh vn gi nguyn.

V d 1.8: Gi s ta s dng Cabri Geometry tin hnh cc thao tc sau: Bc 1

Chn cng c Point ly mt im A bt k trn mn hnh.

Chn cng c Line v mt ng thng a bt k trn mn hnh. Bc 2:

Phng n 1: Chn cng c Perpendicular Line sau a chut bm vo im A v ng thng a. Ta nhn c ng thng d i qua im A v vung gc vi ng thng a.

Phng n 2: Chn cng c Line sau a chut bm "ng chng" vo im A v di chuyn chut sao cho ng thng d "nhn thy l vung gc vi a".

Ta dng chut tc ng vo hnh v, chng hn cho thay i v tr im A, v tr ca ng thng a. iu khc bit r rng gia hai hnh v l:

ng thng d phng n 1 lun lun i qua im A v vung gc vi ng thng a.

ng thng d phng n 2 c nhiu lc khng i qua im A hoc khng vung gc vi ng thng a.

Hnh 1.32

S d c s khc bit nh vy l phng n 2 ta khng s dng cc cng c dng hnh ca Cabri Geometry nn Cabri Geometry khng bo ton cu trc ca hnh v (hnh 1.32).

26

V d 1.9: S dng Cabri Geometry v ba ng cao ca mt tam gic.

Hnh 1.34 Hnh 1.33

Vi ABC, ta ln lt chn cng c Triangle dng ABC sau chn cng c Perpendicular Line ln lt dng cc ng cao. Cui cng chn cng c

Intersection Points xc nh giao im ca ba ng cao.

Vi ABC ta v cc ng thng sao cho "nhn thy vung gc vi cnh tam gic" v "cng i qua mt im" (hnh 1.33).

Cho hai tam gic: ABC v ABC thay i, ta thu c kt qu: Vi ABC ta lun c ba ng cao ng quy. Vi ABC trong nhiu trng hp cho thy r cc ng khng phi l ng cao

v ba ng khng cn ng quy na (hnh 1.34). Hon ton tng t, khi s dng Cabri Geometry v ba ng trung tuyn, ba ng

phn gic, ba ng trung trc ca tam gic... ta phi s dng cc cng c v xc nh th t cc bc thao tc. Chnh dy cc thao tc v chc nng ca cc cng c xc nh cu trc rng buc gia cc yu t trong hnh v. Khi thay i mt s yu t ca hnh v, cu trc ca hnh v vn c bo ton, qua ta pht hin ra cc yu t bt bin ca hnh.

V d 1.10: Ta v ba tam gic ng: tam gic ABC c ba cnh bng nhau, tam gic DEF c hai cnh bng nhau, cn tam gic GHK bt k v cho hc sinh quan st. Hc sinh nhn thy cc yu t v v tr, v di cnh thay i nhng cc quan h bng nhau v cnh lun c

bo ton (hnh 1.35).

Hnh 1.35

Nh vy, vi Cabri Geometry ta a ra cc i tng hnh hc v cho hc sinh nghin cu chng dng ng pht hin ra nhng yu t bt bin, t dn ti cc nhn xt, d on v cc tnh cht ca i tng hnh hc .

27

1.5.5. Cabri Geometry c mt mi trng lm vic thn thin Cabri Geometry c giao din thn thin, kh nng tng tc rt cao v: H thng lnh rt d nh, d thc hin di dng menu, biu tng ho. Cho php trnh by hnh v, thng tin di nhiu nh dng khc nhau to ra nhng

hnh v rt sinh ng. Cc ch th, thao tc ca ngi s dng u c p ng trc tip ln cc i tng v

th hin qua giao din ho sinh ng. C mt h thng tr gip ngi s dng la chn i tng cn thao tc, nhn dng

chnh xc tn cc i tng hnh hc cng nh thuc tnh v cc mi quan h ca chng. Vy kh nng tng tc ca Cabri Geometry rt cao. Mi trng lm vic ca Cabri

Geometry rt thn thin, gn gi vi cc thao tc thng ngy m hc sinh thc hin. V d 1.11: Cho tam gic ABC. Gi M, N, P theo th t l trung im ca BC, CA, AB.

Cc ng cao AD, BE, CF gp nhau ti H. Gi I, K, R theo th t l trung im ca HA, HB, HC.

Ta c 9 im I, D, M, K, E, N, R, F, P cng thuc mt ng trn (ng trn le). Bc 1: V ABC, xc nh cc im I, D, M, K, E, N, R, F, P. Bc 2: V ng trn i qua ba im. Ly ra 3 im bt k trong 9 im v v

ng trn i qua 3 im .

Hnh 1.36

V trc gic cho thy ng trn ny i qua 6 im cn li.

Bc 3: Minh ho kt qu bi ton. Cho tam gic ABC thay i ta thy ng

trn lun i qua cc im cn li. S dng cng

c Member (kim tra mt i tng ny c thuc mt i tng khc nay khng?). Kt qu cho thy cc im u thuc ng trn (hnh 1.36).

1.5.6. Cabri Geometry h tr nghin cu cc hin tng mt cch lin tc Nu ch s dng cc phng tin, dng dy hc truyn thng th miu t mt qu

trnh no , chng hn nh qu tch, thng phi v mt s trng hp c th v sau khi qut ho tm ra quy lut, tuy nhin khng phi lc no hc sinh cng hnh dung ton vn v "hnh nh", "qu o" phi tm. Vi Cabri Geometry ta c th d dng th hin rt nhiu hnh v cc gc hoc cho i tng thay i v tr hc sinh quan st s bin i v v tr hay cc thuc tnh ca i tng. Ngoi ra, ta c th s dng chc nng Trace On/ Off" c mt hnh nh lin tc ca i tng khi di chuyn.

V d 1.12: Cho gc xOy bng 900. Mt im B c nh trn tia Oy, mt im A di ng trn tia Ox. Tm tp hp trung im I ca AB .

28

i vi bi ton ny, nu ch v hnh bng thc v compa th d v rt nhiu v tr ca im A, hc sinh cng kh hnh dung ra hnh nh trc quan tp hp cc trung im I ca AB nh th no.

Hnh 1.37

Sau khi s dng Cabri Geometry v hnh, dng cng c Trace On/Off xc nh thuc tnh li vt cho im I v cng c Animation gn thuc tnh chuyn ng cho im A. Hc sinh s c quan st hnh nh tp hp im I khi im A di ng (hnh 1.37).

Cabri Geometry c mt h thng cng c gip ta o c, tnh ton, tuy nhin khi hnh v thay i, cc s liu s c cp nht v hin th theo qu trnh bin i mt cch lin tc.

V d 1.13: Cho ng trn tm O ng knh AB. Gi M l mt im nm trn ng trn, tnh s o gc AMB.

Sau khi v hnh, cho im M thay i, bng trc quan hc sinh d on AMB vung. S dng chc nng Angle o: kt qu AMB = 900 (hnh 1.38).

Hn na, gio vin c th t cu hi: Khi im M thuc ng trn th AMB c vung vy nu mt im M no tho mn

l gAM gc vung th

liu M c cn thuc ng trn khng? hc sinh c th i n pht hin mi: Trong tam gic vung ABC nu c nh cnh huyn BC v cho nh A thay i ta s nhn c tp hp im A l ng trn ng knh BC.

B l

1.5.7. Cabri Geometry cung cp mt h thng chc nng kim tra cc mi quan h gia cc i tng

hnh hc

Hnh 1.38

Cabri Geometry cung cp mt s chc nng kim tra thuc tnh ca cc i tng hnh hc nh: kim tra tnh thng hng ca 3 im, tnh song song, tnh vung gc ca hai on thng, ng thng, tnh lin thuc... y l nhng cng c tt h tr hc sinh tm ti khm ph, kim tra cc mi quan h tim n bn trong hnh v.

V d 1.14: Cho gc xOy bng 900. Mt im B c nh trn tia Oy v mt im A di ng trn tia Ox. Tm tp hp trung im I ca AB .

Trong thc t, rt nhiu hc sinh ng nhn nh sau: "im B c nh, IB lun bng na AB nn tp hp im I l ng trn tm B, bn knh IB".

Nu khai thc tnh ng v cc chc nng kim tra ca Cabri Geometry, hc sinh c th

29

trnh c sai lm trn bng cch xc nh v tr im A 3 v tr khc nhau: im A trng vi im O, xc nh c im I1 l trung im BO. Ly hai im A, A khng trng vi im O. Xc nh trung im I, I' qua xc nh

ng thng II'. Trc gic cho thy ng thng II' i qua

im I1 nn hc sinh a ra gi nh: Nu im I1 nm trn on thng II' th tp hp cc im I c

kh nng l ng thng! S dng chc nng ( Member) kim tra im I1 c thuc ng thng II hay khng? Kt qu I1 thuc ng thng II' (hnh 1.39).

Mt

khc, trc gic cho thy ng thng II vung gc

vi OB! Dng cng c (

Hnh 1.39

Perpendicular) kim tra, kt qu cho thy ng thng II vung gc vi OB (hnh 1.40).

Sau khi pht hin c ng thng II' i qua trung im ca OB v vung gc vi OB, hc sinh s d on, tm cch chng minh tp hp im I l ng trung trc ca OB v xc nh gii hn ca qu tch.

Hnh 1.40

1.5.8. Cabri Geometry cho php thc hin mt s chc nng tnh ton Cc chc nng h tr tnh ton ca C

V d 1.15: Tm mi lin h gia khong cch t giao

khi v hnh, hc sinh ln lt s dng chc

nng

abri Geometry rt phong ph, chng hn: o khong cch gia 2 i tng, di 1 on thng, 1 cung, chu vi ca mt hnh hnh hc; tnh din tch hnh trn, tam gic, a gic...; xc nh h s gc y/x; xc nh s o ca gc; xc nh to ca i tng; tnh ton trc tip nh mt my tnh b ti...

Hnh 1.41

im cc ng trung trc ca tam gic n mt cnh v khong cch t trc tm n nh i din vi cnh .

Sau

Distance and Length xc nh s o ca on KE v HB; chc nng Calculate thc hin php chia. Kt qu t s HB : KE l 2.

Cho tam gic ABC thay i, hc sinh nhn c kt qu t s HB : KE khng i vn lun

bng 2 (hnh 1.41). n y hc sinh s i tm cch chng minh t s HB : KE lun bng 2.

30

V d 1.16: Cho tam gic vung cn ABC (vung ti A) v tru

Cho thay tr im o din tch ca

.5.9. Cabri Geometry to mi trng t chc cc hot ng hnh hc ng hnh hc nhm

gip h

D v

g c vn .

trung trc ca DE.

Cho im D, E di chuyn. hc sinh tnh hung c

vn t im? (hnh 1.

Hot ng 2: Gii quyt vn . r c bit: Khi

D tr

, E di chuyn ng trung trc c

Hnh 1.42

ng im M ca cnh BC. T M v mt gc 450, cc cnh ca gc ny ct mt hoc hai cnh ca tam gic E v F. Hy xc nh v tr ca E v F sao cho din tch tam gic MEF l ln nht. Din tch ln nht bng bao nhiu?

S dng cng c v hnh

Hnh 1.43

v o din tch hnh phng ca Cabri Geometry ta s nhn c kt qu din tch tam gic MEF (hnh 1.42). E, F v quan st s i v

MEF trn mn hnh. Sau mt s trng hp hc sinh s pht hin c v tr cn tm ca im E c th l chn ng vung gc h t im M xung cnh AB (khi im F trng vi im A) (hnh 1.43).

1Cabri Geometry to ra mt mi trng thun li t chc cc hot c sinh c iu kin pht huy cao tnh tch cc, kh nng sng to trong hc tp hnh hc.

V d 1.17: Cho tam gic ABC cn ti A. Cc im

Hnh 1.44

E theo th t di chuyn trn hai cnh AB v AC sao cho AD = CE. Chng minh rng cc ng trung trc ca DE lun i qua mt im c nh.

Hot ng 1: To tnh hun S dng Cabri Geometry v hnh. Gn thuc tnh li vt cho ng

Hnh nh trc quan gi cho : Mc d D, E thay i nhng c th ng trung trc

44). i qua mca DE lun

Hnh 1.45

Cho im D di chuyn n cc v tng vi B th E trng vi A nn ng trung trc

ca DE chnh l ng trung trc ca AB; Khi D trng vi A, th ng trung trc ca DE l ng trung trc ca AC. Vy c th giao ca hai ng trung trc s l im c nh? (hnh 1.45).

chng minh khi Da DE lun i qua I cn chng t im I cch u

31

hai im D v E. Hc sinh s ch ra AID = CIE (c.g.c) nn ID = IE. Hot ng 3: M rng bi ton.

C l tam gic cn ti A.

a ln lt xt tng trng hp: n n cc v tr c

bit v

AB > AC: Khi D di chuyn n v tr im B

th ta

, cho thy vi s tr gip ca Cabri

1.5.10. Mt s vn cn lu khi s dng Cabri

qu o c ca Cabri Geometry ch l cc i lng gn ng. Ta c th can thip

etry hin trn mn hnh c v gp khc (hin tng ny p

ng ng thng i qua mt im v song song (hoc

Hnh 1.46

I

Ta xt trng hp tam gic AB Nu ABC l tam gic bt k th sao? T AB < AC: Cho im D di chuy xc nh c im c nh s l giao im ca

ng trung trc ca AC v ng trung trc ca BF (F AC sao cho AB = CF) (hnh 1.46).

Hnh 1.47

I

khng xc nh c im E thuc cnh AC nn

phi xt c trng hp im E thuc cnh AC ko di v pha im A (hnh 1.47).

Qua cc v d trn Geometry, ta c mi trng t chc cho hc

sinh hot ng kin to hnh v, khm ph, tm ti v xem xt, kim tra i n gii quyt v pht trin m rng bi ton.

Geometry Cc kt vo h thng ca Cabri Geometry la chn chnh xc ca cc kt qu ny trong

phm vi m Cabri Geometry cho php. Mt s nt v ca Cabri Geomh thuc ch phn gii ca mn hnh). Cabri Geometry ch c cc chc nng d vung gc) vi mt ng thng cho, nn khi cn dng mt on thng, mt tia i qua

mt im v song song (hoc vung gc) vi mt ng thng cho ta vn phi dng ng thng trc ri dng on thng hoc tia trn c s ng thng trn.

32

PHN 2 LM QUEN VI CC CNG C

CA CABRI GEOMETRY

2.1. S dng cng c ca Cabri Geometry dng hnh

V d 2.1: Dng mt tam gic u c cnh bng 5 cm. Trnh t thao tc dng hnh nh sau:

Chn cng c Numerical Edit: nhp gi tr 5.

Chn cng c Point: ly 1 im bt k trong mt phng.

Chn cng c Label: t tn im va to l A.

Chn cng c Line: dng mt ng thng bt k i qua im A.

Chn cng c Compas: dng ng trn tm A c bn knh bng 5.

Chn cng c Intersection Points: xc nh giao im ca ng thng vi ng trn va dng (y l im B).

33

Chn cng c Label: t tn cho im B.

Chn cng c Compass: dng ng trn tm ti B c bn knh bng 5.

Chn cng c Intersection Points: xc nh giao ca hai ng trn (A, 5); (B, 5) (y chnh l im C).

Chn cng c Label: t tn im C.

Chn cng c Triangle: dng tam gic qua 3 im A, B, C (hnh 2.1).

Chn cng c Hide/Show: du cc ng trung gian.

Hnh 2.2

Hnh 2.1

V d 2.2: Dng mt tam gic vung cn ABC, vung A bit rng mt cnh gc vung bng 25 mm.

Trnh t thao tc dng hnh:

Chn cng c Numerical Edit: nhp s 2,5 (cm).

Chn cng c Point: ly mt im bt k trong vng lm vic.

Chn cng c Label: t tn cho im va xc nh l A.

Chn cng c Line: dng mt ng thng bt

k qua im A.

Chn cng c Perpendicular Line: dng ng thng vung gc vi ng thng va dng v i qua im A.

Chn cng c Compass: dng ng trn tm A, bn knh bng 2,5. Chn cng c Intersection Points: xc nh giao ca ng trn va dng vi hai

ng thng vung gc dng (y l cc im B, C).

Chn cng c Label: t tn cho im B, C.


Chn cng c Hide/ Show: du cc ng trung gian. V d 2.3: Dng mt tam gic cn bit cnh y AB = m v ng trung tuyn ng vi

cnh y l CM = n (cm). Trnh t thao tc dng hnh: V tam gic ABC cn ti nh C nn trung tuyn CM s l ng cao h t nh C xung

cnh AB nn trnh t thao tc dng hnh nh sau:

Chn cng c Segment: v hai on thng tng ng vi di cnh y AB = m v trung truyn CM = n.

Chn cng c Point: ly im A bt k trong vng lm vic.

Chn cng c Label: t tn cho im A.

Chn cng c Line: dng mt ng thng bt k i qua im A.

Chn cng c Compass: dng ng trn tm A c bn knh bng m. Chn cng c Intersection Points: xc nh giao ca ng trn (A, m) va dng

vi ng thng dng (y chnh l im B).


Chn cng c Midpoint: xc nh trung im M ca on thng AB.

Chn cng c Label: t tn cho im M.

Chn cng c Perpendicular Line: dng ng vung gc vi AB ti M.

Hnh 2.3

Chn cng c Compass: dng ng trn tm M c bn knh bng n.

Chn cng c Intersection Points: Xc nh giao ca ng trn (M, n) va dng vi ng thng vung gc dng (y l im C).

Chn cng c Label: t tn cho im C.


34

Chn cng c Hide/ Show: du cc ng trung gian. V d 2.4: Dng tam gic vung bit mt cnh gc vung bng m, ng trung tuyn ng

vi cnh y bng n. Trnh t thao tc dng hnh:

Chn cng c Segment: v hai on thng tng ng vi di cnh gc vung AB = m v trung truyn CM = n.

Chn cng c Point: ly im A bt k trong vng lm vic.


Chn cng c Line: dng mt ng thng bt k qua A.

Chn cng c Compass: dng ng trn tm A, bn knh bng m. Chn cng c Intersection Points: xc nh giao ca ng trn (A, m) va dng

vi ng thng dng (y chnh l im B).


Chn cng c Perpendicular Line: dng ng vung gc vi AB ti A.

Chn cng c Midpoint: xc nh trung im M ca on thng AB.


Chn cng c Compass: dng ng trn tm M, bn knh bng n. Chn cng c Intersection Points: xc

nh giao ca ng trn (M, n) va dng vi ng thng vung gc dng ti A (y l im C).

Hnh 2.4


Chn cng c Triangle: dng tam gic qua 3 im A, B, C.

Chn cng c Segment, ni C vi M (hnh 2.4).

Chn cng c Hide/ Show: du cc ng trung gian.

35

V d 2.5: Dng hnh thang ABCD bit y AB = 3 cm, y CD = 4 cm, cnh bn AD = 2 cm v gc D = 700.


Chn cng c Numerical Edit: nhp cc gi tr 700, cc s: 2, 3, 4.

Chn cng c Point: ly im D bt k.

Chn cng c Label: t tn cho im D.

Chn cng c Line: dng mt ng thng bt k qua D.

Chn cng c Compass: dng ng trn tm D, bn knh bng 4. Chn cng c Intersection Points: xc nh giao ca ng trn (D, 4) va dng

vi ng thng dng ta c im C.


Chn cng c Rotation: quay on thng DC mt gc 700, tm D.

Chn cng c Compass: dng ng trn tm D, bn knh bng 2. Chn cng c Intersection Points: xc nh giao ca ng trn (D, 2) va dng

vi ng thng dng qua php quay ta c im A.


Chn cng c Parallel Line: dng ng thng qua A song song vi DC.

Chn cng c Compass: dng ng trn tm A, bn knh bng 3. Chn cng c Intersection Points: xc nh giao

im ca ng trn (A, 3) vi ng thng song song va dng ta c im B.

Hnh 2.5


Chn cng c Polygon: dng hnh thang ABCD.

Chn cng c Hide/ Show: du cc ng trung gian (hnh 2.5).

V d 2.6: Dng tam gic ABC vung ti A, bit cnh huyn BC = 4 cm, gc nhn = 65

$B0.


Chn cng c Numerical Edit: nhp cc gi tr 4; 650.

Chn cng c Point: ly im B bt k.


Chn cng c Line: dng mt ng thng bt k i qua im B.

Chn cng c Compass: dng ng trn tm B, bn knh bng 4.

36

Chn cng c Intersection Points: xc nh giao ca ng trn (B, 4) va dng vi ng thng dng ta c im C.


Chn cng c Segment: dng on BC.

Chn cng c Midpoint: xc nh trung im O ca on thng BC.

Chn cng c Circle: dng ng trn tm O ng knh BC.

O

Chn cng c Rotation: quay on thng BC mt gc 650 vi tm quay l B.

Chn cng c Intersection Points: xc nh giao ca nh ca BC qua php quay v ng trn (O, BC/2) (y l im A).


Chn cng c Triangle: dng tam gic qua 3 im A, B, C.

Hnh 2.6

Chn cng c Hide/ Show: du cc ng trung gian (hnh 2.6).

V d 2.7: Dng hnh thang cn ABCD, bit y AD = 3cm, ng cho AC = 4cm, = 80

D0.


Chn cng c Numerical Edit: nhp cc gi tr 3, 4, 800, 800.

Chn cng c Point: ly im A bt k.


Chn cng c Measurement Transfer: ly mt im bt k cch A mt khong 3 cm (y l im D).


Chn cng c Line: dng ng thng AD.

Chn cng c Rotation: xc nh nh ca ng thng CD qua php quay tm D, gc quay 800.

Chn cng c Compass: dng ng trn tm A, bn knh bng 4.

Chn cng c Intersection Points: xc nh giao im ca ng trn va dng vi nh ca ng thng CD qua php quay tm D, gc quay 800 (y l im C).


37

Chn cng c Parallel Line: dng ng thng qua im C v song song vi AD.

Hnh 2.7

Chn cng c Intersection Points: xc nh giao im ca ng thng va dng vi nh ca ng thng AD qua php quay tm A, gc quay 800 (y l im B).

Chn cng c Label: t tn cho giao im l B.

Chn cng c Polygon: dng hnh thang ABCD (hnh 2.7).

Chn cng c Hide/ Show: du bt cc ng trung gian. V d 2.8: Dng tip tuyn vi ng trn t mt im A cho trc nm ngoi ng

trn (O). Trnh t thao tc dng hnh:

Chn cng c Circle: dng ng trn tm (O) bt k.

Chn cng c Label: t tn cho tm O.

Chn cng c Point: ly im A by k bn ngoi ng trn (O).

Chn cng c Label: t tn cho cc im O, A.

Chn cng c Midpoint: xc nh trung im I ca on thng OA.

Chn cng c Label: t tn cho im I.

Hnh 2.8

Chn cng c Circle: dng ng trn (I, IO).

Chn cng c Intersection Points: xc nh giao im ca hai ng trn.

Chn cng c Label: t tn cho hai giao im l B, B.

Chn cng c Ray: dng hai tip tuyn AB v AB (hnh 2.8).

Chn cng c Hide/ Show: du bt ng trung gian.

V d 2.9: Cho mt ng trn (O) v mt im P bn trong ng trn. Dng ng trn (P) sao cho ng trn (O) chia n ra thnh hai na bng nhau.


Chn cng c Circle: dng ng trn (O) bt k.

Chn cng c Point: ly im P bt k bn trong ng trn (O).

Chn cng c Label: t tn cho hai im im O, P.

38

Chn cng c Line: dng ng thng i qua hai im P, O.

Chn cng c Perpendicular Line: dng ng thng qua P v vung gc vi PO.

Chn cng c Intersection Points: xc nh giao im ca ng trn (O) v ng vung gc va dng.

Hnh 2.9

Chn cng c Label: t tn cho hai giao im l A, B.

Chn cng c Circle: dng ng trn tm l im P i qua im A (hoc B) (hnh 2.9).

Chn cng c Hide/ Show: du bt ng trung gian.

V d 2.10: Dng hnh thoi ABCD bit ng cho BD = 5cm v ng cao BH = 3cm.


Chn cng c Numerical Edit: nhp cc s 3, 5.

Chn cng c Point: ly im B bt k.

Chn cng c Measurement Transfer: ly mt im D bt k cch B mt khong 5cm.

Chn cng c Label: t tn cho 2 im B, D.

Chn cng c Segment: dng on thng BD.

Chn cng c Midpoint: xc nh trung im I ca BD.

Chn cng c Circle: v ng trn tm I i qua im B (I, IB).

Chn cng c Compass: dng ng trn tm B, bn knh bng 3.

Chn cng c Compass: dng ng trn tm D, bn knh bng 3.

Hnh 2.10

Chn cng c Intersection Points: xc nh giao im ca 2 ng trn (B, 3), (D, 3) vi ng trn (I).

Chn cng c Label: t tn 2 giao im l H, K (H(B) v K(D)).

Chn cng c Line: v ng thng DH v BK.

Chn cng c Intersection Points: xc nh giao im ca 2 ng thng DH v BK (ta c im A).

Chn cng c Label: t tn giao im l A.

Chn cng c Reflection: xc nh C l nh i xng qua BD ca A.

39

Chn cng c Label: to nhn cho im C.

Chn cng c Polygon: dng hnh thoi ABCD (hnh 2.10).

Chn cng c Hide/ Show: du bt cc ng trung gian. V d 2.11: S dng phn mm Cabri Geometry dng tam gic ABC, bit cnh BC = a, -

ng cao AH = h v trung tuyn AM = m. Bc 1: Xc nh cc gi tr h, m, a, dng cnh BC c di bng a.

Chn cng c Segment : ln lt v ba on thng h, m v a.

Chn cng c Line : dng mt ng thng d bt k. Chn cng c Point on Object: xc nh im B thuc d.

Chn cng c Compass: dng ng trn O(B, a). Chn cng c Intersection Points: xc nh giao im C ca ng thng d vi

ng trn O(B, a). Bc 2: Xc nh tp hp nhng im cch BC mt khong bng h.

Chn cng c Perpendicular Line: dng ng thng d2 bt k vung gc vi ng thng d ti im H.

Chn cng c Compass: dng ng trn O1(H, h). Chn cng c Intersection Points: ly giao im ca ng trn O1(H, h) vi

ng thng d2, ta c im R, P.

Chn cng c Parallel Line: dng hai ng thng d3, d4 song song vi d i qua im R, P.

Bc 3: Xc nh trung im M ca BC v tp hp nhng im cch im M mt khong bng m.

Chn cng c Midpoint : xc nh trung im M ca AB.

Chn cng c Compass: dng ng trn O2(M, m).

Bc 4: Xc nh im A v dng tam gic ABC, trung tuyn AM, ng cao AH.

Chn cng c Intersection Points: xc nh giao im ca O2(M, m) vi hai ng thng d3, d4, y l v tr nh A cn tm (c 4 giao im).

Chn cng c Triangle : dng tam gic ABC.

S dng cng c Segment : k ng trung tuyn AM v ng cao AH (c 4 tam gic tho mn iu kin u bi).

Hnh 2.11

Bc 5: Pht hin mi quan h gia cc i lng a, m, h.

40

Cho thay i di cc on thng m, h, qua quan st trc quan trn mn hnh, hc sinh s pht hin c bi ton ch c nghim khi h < m (hnh 2.11)

Nhn xt: Qua vic m t cc bc ca bi ton dng hnh ni trn minh ho vic s dng cc cng c ca Cabri Geometry. Hn na nh Cabri Geometry m hc sinh chuyn t vic v sang xy dng i tng, iu ny gip hc sinh nm chc cc kin thc v cc tnh cht v cc mi lin h gia cc i tng ca hnh v.

2.2. S dng cng c ca Cabri Geometry dng hnh ng V d 2.12: Cho mt gc vung xOy. Trn tia Ox ly mt im A c nh sao cho OA = a,

trn tia Oy ly im B di ng. V trong gc xOy hnh vung ABCD. Tm tp hp qu tch im D khi B di ng.


Chn cng c Ray: v tia Oy bt k.

Chn cng c Numerical Edit: nhp s 90 v mt s dng a bt k.

Chn cng c Rotation: quay tia Oy mt gc 90 xung quanh im O.

Chn cng c Compass: dng ng trn tm O, bn knh bng a (O, a).

Chn cng c Intersection Points: xc nh giao im ca (O, a) vi Ox.

Chn cng c Label: t tn cho giao im trn l A.

Chn cng c Point on Object: ly mt im B bt k trn tia Oy.


Chn cng c Segment: dng on thng A, B.

Chn cng c Perpendicular Line: dng hai ng thng i qua A, B v vung gc vi AB.

Chn cng c Circle: dng 2 ng trn tm A, B bn knh AB.

Chn cng c Intersection Points: xc nh giao ca 2 ng trn vi 2 ng thng vung gc i qua A, B ni trn.

Chn cng c Label: t tn cho 2 giao im pha trong gc xOy l C, D.

Chn cng c Segment: Dng cc on thng BC, CD, DA.

Chn cng c Hide/ Show: Cho n i cc yu t khng cn thit. Gi hng khai thc hnh v: Bc 1: S dng chut cho im B thay i v

tr v quan st quy lut ca im D d on v i n vic chng minh qu tch.

Bc 2: Minh ho qu tch.

Chn cng c Trace On/Off: gn thuc tnh li vt cho im D.

41

Hnh 2.12

Chn cng c Animation ri bm cho im B chuyn ng quan st qu tch, hoc chn cng c Locus sau ln lt xc nh yu t qu tch (im D) v yu t sinh qu tch (im B), ta nhn c qu tch nh hnh 2.12.

V d 2.13: Mt on thng AB = l chuyn ng sao cho hai mt ca n chy trn hai ng thng vung gc vi nhau. Tm tp hp trung im M ca cc on thng AB .


Chn cng c Line: v mt ng thng b bt k.

Chn cng c Label: t tn cho ng thng b.

Chn cng c Point on Object: ly mt im O tu trn ng thng b.

Chn cng c Label: t tn cho im O.

Chn cng c Perpendicular Line: dng ng thng a i qua O v vung gc vi ng thng b.

Chn cng c Label: t tn cho ng thng a.

Chn cng c Numerical Edit: nhp mt s dng l bt k.

Chn cng c Compass: dng ng trn tm O bn knh bng l. (O,l)

Chn cng c Intersection Points: xc nh giao ca ng trn (O,l) vi hai ng thng a, b.

Chn cng c Label: t tn cho cc giao im ln lt l A1, A2, B1, B2.

Chn cng c Midpoint: xc nh trung im cc on thng OA1, OB1, OA2, OB2.

Chn cng c Label: t tn cho cc trung im trn l M3, M2, M1, M4.

Chn cng c Segment: dng on thng i qua 2 im A1 v A2.

Chn cng c Point on Object: ly mt im A bt k trn on A1A2.


Chn cng c Compass: dng ng trn tm A, bn knh bng l. (A,l)

Chn cng c Intersection Points: xc nh giao ca ng trn (A,l) va to vi ng thng b.

Chn cng c Label: t tn cho mt trong hai giao im l B.

Chn cng c Segment: dng on thng AB.

Chn cng c Midpoint: xc nh trung im M ca on AB.


Chn cng c Hide/ Show: cho n i cc yu t khng cn thit. Gi hng khai thc hnh v: Bc 1: S dng chut cho im A thay i v tr n mt s im c bit:

42

Khi A A1 th B O, M M3. Khi A A2 th B O, M M1. Khi A O th B B1, B B2, M M2, MM4. Vy ta thy cc im M3, M2, M1, M4 u thuc vo qu tch ca M v v chng c nh

nn ta o cc khong cch t cc im ti O. Kt qu l chng cch u O mt khong l/2 khng i. Vy ta d on qu tch M l ng trn (O; l/2).


43

Chn cng c Trace On/Off: gn thuc tnh li vt cho im M.

Chn cng c Animation: cho im A chuyn ng quan st qu tch hoc chn cng c Locus sau ln lt xc nh yu t qu tch (im M) v yu t sinh qu tch (im A). Ta nhn c qu tch nh hnh 2.13.

Hnh 2.13

V d 2.14: Cho hnh thoi ABCD c cnh AB c nh. Tm qu tch giao im O ca hai ng cho ca hnh thoi .


Chn cng c Segment: v on thng AB bt k.

Chn cng c Label: t tn cho hai u mt on thng A, B.

Chn cng c Circle: dng ng trn tm A i qua im B: (A).

Chn cng c Point on Object: ly im D tu thuc ng trn (A).


Chn cng c Segment: dng on thng AD.

Chn cng c Parallel Line: ln lt dng hai ng thng i qua im D v song song vi AB, i qua B v song song vi AD.

Chn cng c Intersection Points: ly giao ca cc ng thng trn.

Hnh 2.14

Chn cng c Label: t tn giao im va tm c l C.

Chn cng c Segment: ln lt dng cc on thng DC, BC, AC v BD.

Chn cng c Intersection Points: xc nh giao ca cc on thng AC v BD.

Chn cng c Label: t tn cho giao

im trn l O.

Chn cng c Hide/ Show: cho n i cc yu t khng cn thit. Gi hng khai thc hnh v: Bc 1: S dng chut cho D thay i v tr trn ng trn tm A v quan st quy lut

ca im O: Hai im A, B c nh Gc AOB lun vung Vy d on qu tch ca O l ng trn ng knh AB. Bc 2: Minh ho qu tch.

Chn cng c Trace On/Off: gn thuc tnh li vt cho im O.

Chn cng c Animation cho im D chuyn ng quan st qu tch hoc chn cng c Locus sau ln lt xc nh yu t qu tch (im O) v yu t sinh qu tch (im D). Ta nhn c qu tch nh hnh 2.14.

V d 2.15: Cho hai im A, B c nh. Tm qu tch tip im ca tip tuyn qua A vi cc ng trn tm B c bn knh nh hn hoc bng on thng AB.


Chn cng c Segment: v mt on thng AB bt k.

Chn cng c Label: t tn cho hai u mt ca on thng l A, B.

Chn cng c Point on Object: ly mt im C tu trn AB.


Chn cng c Circle: dng ng trn tm B, bn knh BC. (B)

Chn cng c Midpoint: xc nh trung im I ca on thng AB.


Chn cng c Circle: dng ng trn tm I, bn knh IA (I).

Chn cng c Intersection Points: ly giao ca 2 ng trn (B) v (I).

Chn cng c Label: t tn cho cc giao im va dng c l M, N.

Chn cng c Ray: dng cc tia AM, AN.

Chn cng c Hide/ Show: cho n i cc yu t khng cn thit.

Gi hng khai thc hnh v: Bc 1: S dng chut cho im C thay i v tr. Quan

st quy lut ca cc im M, N ta c: Hai im A, B c nh

44

Hnh 2.15

Gc AMB v gc ANB l gc vung Vy d on qu tch ca M, N l ng trn ng knh AB. Bc 2: Minh ho qu tch.

Chn cng c Trace On/Off: gn thuc tnh li vt cho im M, N.

Chn cng c Animation cho im C chuyn ng quan st qu tch hoc chn cng c Locus sau ln lt xc nh yu t qu tch (im M, N) v yu t sinh qu tch (im C). Ta nhn c qu tch nh hnh 2.15.

V d 2.16: Cho ng trn (O), AB l ng knh c nh, M l im chy trn ng trn. Ni MA, MB v trn tia i MA ly im I sao cho MI = 2MB. Tm tp hp cc im I.


Chn cng c Segment: v mt on thng AB tu trn mt phng.

Chn cng c Label: t tn cho hai u mt ca on thng l A, B.

Chn cng c Midpoint: xc nh trung im O ca on thng AB.

Chn cng c Label: t tn cho im O.

Chn cng c Circle: dng ng trn tm O, bn knh OB. (O).

Chn cng c Point on Object: ly im M tu trn ng trn (O).


Chn cng c Segment: dng on thng MB.

Chn cng c Distance and Length: o di on thng MB.

Chn cng c Calculate: tnh gi tr 2*MB, a kt qu ra mn hnh.

Chn cng c Ray: v tia i tia MA.

Chn cng c Measurement Transfer: xc nh im cch im M mt khong l 2MB.

Chn cng c Circle: dng ng trn tm M c bn knh 2MB (i qua im va to).

Chn cng c Intersection Points: xc nh giao ca ng trn va to vi tia i ca tia MA.

Chn cng c Label: t tn cho giao im l I.

Chn cng c Hide/ Show: cho n i cc yu t khng cn thit. Gi hng khai thc hnh v: Bc 1: Cho im M thay i v tr v quan st quy lut ca im I d on qu tch

ca I l cung cha gc.

45

Hnh 2.16


Chn cng c Trace On/Off: gn thuc tnh li vt cho im I.

Chn cng c Animation cho im M chuyn ng quan st qu tch hoc chn cng c Locus sau ln lt xc nh yu t qu tch (im I) v yu t sinh qu tch (im M). Ta nhn c qu tch nh hnh 2.16.

V d 2.17: Cho ng trn (O) vi tm O c nh v bn knh thay i, mt im M bn ngoi (O). K cc tip tuyn MA, MB ca ng trn. Tm qu tch cc tip im A, B.


Chn cng c Line: v mt ng thng tu trong mt phng.

Chn cng c Point on Object: ly 2 im O, I bt k trn ng thng ni trn.

Chn cng c Label: t tn cho hai im O v I.

Chn cng c Circle: dng ng trn tm O, bn knh OI (O, IO).

Chn cng c Point: ly im M bt k bn ngoi ng trn (O, IO).


Chn cng c Segment: dng on thng OM.

Chn cng c Midpoint: xc nh trung im C ca on thng OM.


Chn cng c Circle: dng ng trn tm C, bn knh CO (C, CO)

Chn cng c Intersection Points: xc nh giao ca hai ng trn (O, IO) v (C, CO).

Chn cng c Label: t tn cho 2 giao im va dng ln lt l A, M.

Chn cng c Ray: ln lt dng cc tia MA, MB.

Chn cng c H khng cn thit. thc hnh v:

i v tr v qu

h.

ide/ Show: cho n i cc yu tGi hng khai

Hnh 2.17

Bc 1: S dng chut cho im I thay an st quy lut ca hai im A, B d on v i

n vic chng minh qu tch. Bc 2: Minh ho qu tc

Trace O Chn cng c n/Off: gn thuc tnh li . vt cho im A, B

Chn cng c Animation: cho im I

46

chuyn ng quan st qu tch hoc chn cng c Locus sau ln lt xc nh yu t qu tch (im A, B) v yu t sinh qu tch (im I). Ta thu c qu tch nh hnh 2.17.

V d 2.18: Cho ng trn (O; R) vi hai tip tuyn AB, AC. Mt tip tuyn di ng ca ng trn (O) ct cc on thng AB, AC ti cc im tng ng P, Q. Gi P, Q theo th t l giao im ca cc on thng OP, OQ vi ng trn (O). Tm tp hp trung im I ca PQ.


Chn cng c Circle: v mt ng trn tu trong mt phng O.

Chn cng c Label: t tn cho tm ng trn va v l O.

Chn cng c Point: ly im A tu bn ngoi ng trn (O).


Chn cng c Segment: dng on thng OA.

Chn cng c Midpoint: xc nh trung im E ca on thng OA.

Chn cng c Label: t tn cho im E.

Chn cng c Circle: dng ng trn tm E, bn knh EO (E, EO).

Chn cng c Intersection Points: xc nh giao ca (O) v (E, EO).

Chn cng c Label: t tn cho hai giao im ni trn ln lt l B, C.

Chn cng c Segment: ln lt dng hai on thng AB, AC.

Chn cng c Point on Object: ly im H tu thuc ng trn (O).

Chn cng c Label: t tn cho im H.

Chn cng c Segment: dng on thng OH.

Chn cng c Perpendicular Bisector: dng ng thng i qua im H v vung gc vi OH.

Chn cng c Intersection Points: xc nh giao ca ng thng trn vi hai on thng AB, AC.

Chn cng c Label: t tn cho hai giao im ln lt l P, Q.

Chn cng c Segment: ln lt dng cc on thng PQ, OP, OQ.

Chn cng c Intersection Points: cc nh giao ca OP, OQ vi (O).

Chn cng c Label: t tn cho hai giao im l P, Q.

Chn cng c Segment: dng on thng PQ.

Chn cng c Midpoint: xc nh trung im I ca on thng PQ.

47

Label: t tn cho im I. Chn cng c


thay i v tr v quan st quy lut ca im I d on

Gi hng khai thc hnh v: Bc 1: S dng chut cho im Hv i n vic chng minh qu tch. Bc 2: Minh ho qu tch.

Trace O Chn cng c n/Off: gn thuc tnh li vt cho im I.

Chn cng c Animation cho im qH chuyn ng uan st qu tch

hoc chn cng c Locus sau ln lt xc nh yu t qu ch (im I) v yu t sinh qu tch (im H). Ta nhn c qu tch nh hnh 2.18.

V d 2.19: Ch

t

o gc xOy bng a v mt d

p tam gic

hnh:

i l. Hai im A, B di ng trn hai cnh tng ng sao cho di AB lun lun bngAOB. Tm qu tch im I.

Trnh t thao tc dng

l. Gi I l tm ng trn ngoi ti

Chn cng c Numerical Edit: nhp hai s dng a, l bt k.

Chn cng c Ray: v mt tia Oy bt k.

Rotation: ly nh ca tia Oy qua php quay tm O gc quay bng a. Chn cng c

Chn cng c Label: t tn cho tia nh l Ox.

Chn cng c Point on Object: ly mt im bt k trn tia Ox.


Chn cng c Compass: dng ng trn tm A, bn knh bng l (A, l)

Chn cng c Intersection Points: xc nh giao ca (A, l) vi Oy.

Label: t tn cho giao im va xc nh c l B. Chn cng c

Segment: dng on thng AB. Chn cng c

Chn cng c Perpendicular Bisector: ln lt d

ng c

ng cc ng trung trc ca on thng OB, OA.

Chn c Intersection Points: ly giao ca 2

Chn cng c

ng trung trc trn.

48

Label: t tn cho giao im va xc nh c l I.

Hnh 2.18

Hnh 2.19

Chn cng c Segment: dng cc on thng I

Chn cng c

A, IB, IO.

Hide/ Show: cho n i cc yu t khng cn thit.

dng chut cho im A thay i v tr trn Ox v quan st quy lut im I d o ch

ho qu tch.

Gi hng khai thc hnh v: Bc 1: S n v i n vic ng minh qu tch. Bc 2: Minh

Chn cng c Trace On/Off: gn thuc tnh li vt cho im I

Chn cng c Animation cho im A chuyn cng c

ng quan st qu tch hoc chn

Locus sau ln lt xc nh yu t qu tch (im I) v yu t sinh qu tch (im hnh 2.19.

chuyn ng trn cung n tch ca im H.

h

A). Ta nhn c qu tch nhV d 2.20: Cho tam gic ABC ni tip ng trn (O). D l mt imBC khng cha h A. Ni A vi D. H CH vung gc vi AD. Tm qu

Trn t thao tc dng hnh:

Chn cng c Circle: v mt ng trn bt k.

Chn cng c Label: t tn cho tm ca ng trn va v l O.

Chn cng c Point on Object: ly 3 im tu trn (O).

Label: Chn cng c t tn cho cc im A, B, C.

Chn cng c Triangle: dng tam gic ABC.

Arc: dng cung trn BC khng cha A. Chn cng c

Point on Object: ly mt im D bt k trn cung BC. Chn cng c

Label: t tn cho im D. Chn cng c

Chn cng c Line: dng mt ng thng i u i q a hai m A, D.

Perpendicular Bisector: dng ng th Chn cng c ng i qua im C v vung gc vi AD.

Intersection Points: xc nh giao ca 2 ng thng trn. Chn cng c

Label: t tn cho giao im va dng l H. Chn cng c

Chn cng c Perpendicular Bisector: ln lt dng ng thng i qua im C v vung gc vi AB; i qua A v vung gc vi BC.

Intersection Points: xc nh giao im cc ng vung gc Chn cng c vi cc on AB, BC.

Chn cng c Label: t tn cho hai giao im ln lt l E, F.

Chn cng c Segment: dng on thng AF, CE, AD.


49

Gi hng khai thc hnh v: Bc 1: S dng chut cho im D thay i v tr v quan stv i n vic ch minh qu tch.

quy lut ca im H d on ng

q

Chn cng c

Bc 2: Minh ho u tch.

Trace On/Off: gn thuc tnh li vt cho im H.

Animation cho im D chuyn Chn cng c ng hn cng c quan st qu tch hoc c Locus

sau l tch (im H) v yu t sinh

n

thao tc dng hnh:

n lt xc nh yu t ququ tch (im D). Ta thu c qu tch nh hnh

2.20. V d 2.21: Cho BC l mt dy cung c nh ca

ng trn (O), A l mt im chy trn cung l BC sao cho tam gic ABC lun lun c ba gc nhn. Gi M l ing trn (O). Tm qu tch ca cc trung im I ca AM.

Trnh t

m chnh gia ca cung nh BC ca

Chn cng c Circle: v mt ng trn bt k t

Chn cng c

rn mt phng.

Label: t tn cho tm ng trn va dng l O.

Chn cng c Point on Object: ly 2 im trn ng trn (O).

Chn cng c Label: t tn cho hai im B, C.

Chn cng c Segment: dng on thng BC.

Chn cng c Perpendicular Bisector: dng cc ng thng vung gc vi BC i qua C, B.

Chn cng c Intersection Points: xc nh giao ca hai ng thng va dng vi ng trn (O).

Chn cng c Label: t tn cho hai giao im ln lt l A , A .

n cng c

1 2

Ch Arc: v cung trn A1A2 khng cha cc im B, C.

c Chn cng Point on Object: ly im tu trn cung A1A2 va to.


Chn cng c Perpendicular Bisector: dng ng thng i qua im O v vung gc v

hn cng c

i BC.

C Intersection Points: xc nh giao ca ng thng trn vi cung nh BC.

Chn cng c Label: t tn cho giao im va dng l M.

Hnh 2.20

50

Chn cng c Segment: dng on thng AM.

Chn cng c Midpoint: xc nh trung im ca on thng AM.



Bc 1: S dng chut cho im A thay i v tr v quan st quy lut ca im I.

2 (khng cha B, C). K t b :

i

khi A trng A2.

qu tch c

Gi hng khai thc hnh v:

V tam gic ABC lun c ba gc nhn nn A ch c th thuc cung A1Ahi , ta c t nh a im thuc qu tch ca I

im I1 l trung m ca A1M, khi A trng A1.

im I2 l trung im ca A2M,

im O, khi A i xng vi M qua O, do vy d on a I l cung I1I2 i qua O.


Chn cng c Trace On/Off: gn thuc tnh li vt cho im I

Chn cng c Animation cho im A chuyn ng quan st qu tch hoc chn cng c Locus sau ln h (im I) v yu t sinh qu tch (im A). Ta nhn c qu tch nh hnh 2.21.

nhBc 1: Dng qu tch nhng im M(x,y) c to tho

n

Hnh 2.21

lt xc nh yu t qu tc

V d 2.22: Xc qu tch nhng im M(x,y) tho mn y=ax2 mn y=ax2

Ta ln lt thc hi cc thao tc sau:

Chn chc nng Show Axes: cho hin h trc to

Chn chc nng

Oxy.

Point on Object: ly im X (x; 0) bt k trn trc Ox.

Chn chc nng Circle: v ng trn tm O, bn knh bng 1 (O, 1).

Intersection Points: xc nh giao im ca ( Chn chc nng O,1) vi trc Oy, v t tn cho giao im c to (0;1) l A.

Chn chc nng Circle: v ng trn tm O, bn knh OX. (O,OX).

Intersection Points: xc nh giao im ca (O,OX) vi tr Chn chc nng c Oy, v tt tn cho giao im c o (0;x) l B.

Chn chc nng Segment: ni im X vi im A ta c on thng d1

Chn chc nng Parallel Line: qua im B k ng thng d2 // d1 Intersection Points: xc nh giao im ca d2 vi tr Chn chc nng c Ox, t tn

cho giao im l C.

51

Circle: v ng trn tm O, bn Chn chc n g n knh OC (O, OC).

Chn chc nng Intersection Points: xc nh giao im ca ng trn (O, OC) vi trc Oy, t tn cho g im c tung dng l Y. iao

Chn cng c Perpendicular Line: ln lt dng cc ng thng vung gc vi trc Ox ti X, vung gc vi tr i Y. c Oy t

Chn chc nng Intersection Points: xc nh giao im M ca hai ng thng vung gc va dng. (Theo nh l Talet ta c ngay OC = OX2 hay M chnh l im c to tho mn y=x2.

Chn chc nng Trace On/Off: gn thuc tnh li vt cho im M Cho im X thay tr, hc sinh s quan st c hnh nh trc quan v tp hp cc

im biu din cc cp gi tr tng ng (x,y) ca hm s y=x

i v

2.

Chn chc nng Locus: ln lt ch vo im im X Cabri Geometry a ra qu tch ca M v

im M.

Ta cng c th chn cng c Equation and Coordinates tch

c quan, hc sinh thy r qu tch nhng im m

Pht trin kt qu): V th hm s y = ax2 t th hm s y = x

v ch vo qu m Cabri Geometry va a ra, kt qu cho thy ng cong c phng trnh: y = x2 (hnh 2.22).

Bng trM(x,y) c to tho mn y=x2 l t ng cong

nm pha trn trc honh, i qua im gc to , nhn O ltrc i xng.

Bc 2: (

im thp nht v nhn trc tung l

2

Chn chc nng Numerical Edit: nhp mt s thc a bt k.

Chn ch c nng Dilation: ln lt ch vo im Y, im O v s thc a. Ta xc nh

n cng c

c im Y1.

Ch Perpendicular Line: dng cc ng thng vung gc vi trc Ox ti X, vu tng gc vi trc Oy i Y1.

Chn chc nng Intersection Points: xc nh N l giao im ca hai ng thng vung gc va dng.

Chn chc nng Trace On/Off: gn thuc tnh li vt cho im N. Cho im X thay i v tr, hc sinh s quan st c hnh nh trc quan v tp hp cc

im 2biu din cc cp gi tr tng ng (x,y) ca hm s y=ax ; cng c th chn chc nng

Locus: ln lt ch vo im N v im X Cabri Geometry a ra qu tch ca im N.

Hnh 2.22

52

Equation and Coordinates ch vo qu t kim tra, chn cng c ch, kt qu cho thy q

l im cao nht v nhn trc tung lm trc i xng. s y=ax2 th hm s no c h

s a "dc"(Hnh

M(x,y

u tch c phng trnh y=ax2. Bc 3: Khm ph cc tnh cht ca th hm s y=ax2

Cho thay i h s a. Bng quan st trc quan hc sinh pht hin c cc vn sau: Khi h s a < 0 th ca hm s y=ax2 l mt ng cong nm pha di trc honh,

i qua im gc to O, nhn im Nu v trn cng mt h trc to nhiu th ca hmv mt gi tr tuyt i cng cao th th cng , th cng st vo trc tung Oy 2.23). V d 2.23: Minh ho qu tch nhng im ) sao cho:

( 0)a ax

= , vi a =12. y

c nng

Trnh t thao tc vi Cabri Geometry nh sau:

Chn ch Show Axes: cho hin h trc to Oxy.

Chn cng c Numerical Edit: nhp gi tr 12

Chn chc nng Point on Object: ly im X(x; 0) bt k trntrc O

Chn chc nng

x.

Equation and Coordinates: ch vo im X hin to ca im X ra mn hnh.

Chn cng c a Calculate: nhp biu thc tnh gi tr yx

= , trong x l honh im X.

ng Chn chc n Measurement Transfer: ln lt bm chn gi tr va tnh c sau ch vo trc tung Oy. Ta xc nh c im Y thuc Oy.

Chn cng c Perpendicular Line: ln lt dng cc i trc Ox ti im X

ng vung gc v, vung gc vi Oy ti im Y.

Chn chc nng Intersection Points: xc nh giao im M ca hai ng thng vung gc va dng. M s l im c to (x, f(x)).

Chn chc nng Trace On/Off : gn thuc tnh li vt cho im M. Cho im X thay i khi vt li ca tp hp cc im M s cho ta hnh nh th

ca hm s y=f(x) (hnh 2.24).

53

Hnh 2.23

L u : Bn c th a mt hm s bt k, ch cn bn ch b

tin hnh theo phng php ny v th cc tnh gi tr ca y=f(x).

54

Phn 3 DY HC HNH HC VI S H TR CA

PHN MM CABRI GEOMETRY

3.1. Quy trnh khai thc Cabri Geometry vo dy hc hnh hc Khi khai thc phn mm Cabri Geometry vo dy hc hnh hc s c mt s hot ng

ca gio vin v hc sinh c s dng my tnh in t (MTT) v Cabri Geometry, nh vy quy trnh chun b ln lp, thc hin ln lp c nhng nt c th ring v c th phn chia thnh cc bc sau (s 3.1):

Xc nh mc tiu, ni dung bi hc

La chn cc hot ng s dng PMDH

S dng PMDH thit k cc m un

Dy hc vi gio n c s dng PMDH

X l cc thng tin phn hi

Tch hp cc m un vo gio n

S 3.1

Bc 1: Xc nh mc tiu, ni dung bi hc. Gio vin xc nh mc ch, yu cu, ni dung c th ca gi dy v tin hnh son gio

n. y l gio n truyn thng, dng cho gi dy theo hnh thc thng thng cha s dng MTT v phn mm Cabri Geometry.

Bc 2: La chn cc hot ng s dng phn mm Cabri Geometry. Gio vin tm ti pht hin nhng hot ng trong gi hc c th khai thc th mnh ca

MTT v Cabri Geometry t chc cho hc sinh hot ng nhm tng cng tnh tch cc trong hot ng hc tp ca hc sinh. Cn ch n cc tnh hung khai thc c tnh trc

55

quan, tnh ng, tnh cu trc, tnh lin tc ca Cabri Geometry. c th pht huy c th mnh ca Cabri Geometry, ta phi quan tm n cc yu t sau: Yu cu pht trin t duy ca hc sinh. Trnh t ln lp. Hnh thc t chc ln lp. Hnh thc s dng phng tin MTT. Bc 3: S dng phn mm thit k cc m un. Gio vin tm hiu cc phn mm v phng tin k thut thit k cc m un ph hp

vi cc ni dung c la chn tch hp vo gi dy. Phng n th nht: Ch s dng Cabri Geometry th hin ton b thng tin nh

hnh v, li ch thch, cu hi... Phng n th hai: Kt hp vic s dng Cabri Geometry vi cc phn mm cng c

nh PowerPoint, Flash, FrontPage... son bi ging. Khi thit k cc m un cn phi cn c vo ni dung, trnh t lgc ca mch kin thc.

C th phi xc nh r ta thit k s dng Cabri Geometry nhm hnh thnh khi nim mi hay pht hin nh l hay gii bi tp, n tp, tng kt... Mt khc khi thit k cc m un cn ch n tnh hiu qu khi s dng chng. Chng hn, tit kim thi gian tnh ton, o c, v hnh tp trung vo ni dung kin thc v rn luyn t duy hoc khai thc yu t ng nhanh chng i n d on cc tnh cht (ng quy, thng hng...).

Bc 4: Tch hp cc m un vo gio n. Ta thit k kch bn ln lp trong xc nh r cc hot ng c s dng Cabri

Geometry. Mt phn ni dung ca bi ging c chuyn qua vic khai thc cc m un (gio vin thit k sn sao cho th hin c s phi hp ca cc phng php dy hc a dng v nhiu chiu).

Vic tch hp cng cn lu n tnh a dng ca i tng hc sinh. Nu hc sinh trung bnh, yu ta c th s dng tt c cc m un m gio vin chun b. Trong trng hp nhn thc ca hc sinh t mc kh, gii th ta c th b qua mt vi bc trung gian v khi hc sinh hiu bi ta kt thc chuyn sang hot ng tip theo.

Bc 5: T chc dy hc vi gio n c s dng Cabri Geometry. Trc tin, gio vin chun b phng tin k thut nh MTT, my chiu a nng v cc

phng tin dy hc khc. Nu cn, c th b tr li s ch ngi trong lp nu tit hc c nhng hot ng c t chc theo hnh thc nhm nh. Trong mt s tit dy, gio vin cn hng dn hc sinh chun b, hon thnh mt s yu cu trc tit hc.

T chc dy hc theo phng n chun b. Bc 6: X l cc thng tin phn hi. Gio vin cn cn c vo kt qu nhn thc ca hc sinh thng qua bi kim tra v cc

thng tin phn hi (nh thi hc tp, kt qu hc tp... ca hc sinh) c th iu chnh cc bc cho vic ln lp nhng tit sau.

56

Tuy nhin cn trnh xu hng lm dng Cabri Geometry trong cc tit dy, nu ni dung no s dng Cabri Geometry khng hiu qu hn so vi cc hnh thc, phng tin truyn thng th khng s dng.

3.2. Phng n khai thc Cabri Geometry vo dy hc hnh hc Trong thc t hin nay v iu kin trang thit b CNTT v trnh tin hc ca gio vin,

hc sinh ta c th trin khai rng cc phng n sau:

3.2.1. S dng Cabri Geometry trong cc lp hc truyn thng s dng Cabri Geometry trong cc tit hc vi s hc sinh t 35 n 50, ngoi cc

phng tin dy hc thng thng ca mt lp hc truyn thng nh bng en, phn trng, thc k... cn c MTT, my chiu Projector, my chiu Overhead... Cc hot ng ch yu trong gi hc bao gm:

Gio vin trc tip s dng MTT, khai thc cc tnh nng ca Cabri Geometry trnh by bi ging mt cch sinh ng.

Hc sinh quan st cc thng tin do MTT cung cp v a ra cc d on, nhn nh. C th gi mt vi hc sinh ln thao tc trn MTT kim tra mt d on, minh ho mt nhn nh no .

Nu trong phng hc c trang b my chiu Overhead, gio vin c th ra nhim v cho hc sinh thng qua cc phiu hc tp v khi hc sinh hon thnh cng vic, gio vin chiu cc phiu hc tp ln mn hnh c lp cng trao i.

V d 3.1: Gip hc sinh pht hin ra tnh cht ca hai ng thng song song: Hot ng 1: Gio vin v hnh.

Chn chc nng Line: V ng thng a bt k.

Chn chc nng Parallel Line: V ng thng b song song vi a.

Chn chc nng Line: V ng thng c ct a ti A, ct b ti B. Hot ng 2: Hc sinh pht hin hai gc so le trong bng nhau.

Gio vin cho hnh v thay i mt s v tr, cho hc sinh quan st v nhn xt v quan h gia hai gc so le trong.

Hc sinh a ra nhn nh: Hai gc so le trong "hnh nh" bng nhau! kim tra d on hc sinh chn chc

nng Angle: Xc nh s o hai gc so le trong. Kt qu hai gc c s o bng nhau (hnh 3.1).

Gio vin c th tip tc cho ng thng a hoc c thay i hc sinh kim tra mt vi trng hp khc. Kt thc hc sinh a ra pht hin: Nu mt ng thng ct hai ng thng song song th hai gc so le trong bng

nhau".

Hnh 3.1.

57

V d 3.2: Gip hc sinh pht hin ra nin m tp chun b trc v tam gic

ABC

B2 + AC2 > BC2 A 900

h l Pytago o. Gio vvung ti A v cc kt qu o c, tnh ton

(hnh 3.2) sau cho tam gic ABC thay i v yu cu hc sinh in cc du >, < hoc = vo hnh ch nht trong cc trng hp sau:

58

A

AB2 + AC2 < BC2 90A 0

AB2 + AC2 = BC2 90A 0

?

Hnh 2.69Hnh 3.2

Qua vic hon thnh bi tp hc sinh i n pht hin: Trong mt tam gic nu bnh phng mt cnh bng tng bnh phng hai cnh cn li th tam gic l tam gic vung.

3.2.2. S dng Cabri Geometry trong dy hc theo nhm Lp hc c chia thnh cc nhm nh, mi nhm c t nht mt my tnh ci t Cabri

Geometry. Nu cc my tnh c ni mng th cc nhm c th chia s thng tin vi nhau. Cc hot ng ch yu trong tit hc bao gm:

Gio vin giao nhim v cho cc nhm thng qua phiu hc tp. Cc thnh vin trong nhm 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 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 MTT v c c hi th hin, trao i nhng suy ngh ca bn thn vi c nhm, gp phn kim chng nhng nhn nh, phn on ca cc thnh vin khc trong nhm. Mi hc sinh, khng ch nghe, tp lm m cn hng dn cho bn cng lm, qua gp phn tng hiu qu hc tp ca c hc sinh c gip v nhng hc sinh gip cc bn khc. Mt khc, nhng hc sinh km s c kh nng, c hi by t v hc hi nhiu hn chnh cc thnh vin trong nhm.

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

V d 3.3: Gio vin t chc cho cc n m hc sinh s dng Cabri Geometry tm v trsao cho tng AC + BC nh nht nh sau:

Hot ng 1: V hnh, o c v khong cch t im C n A, B.

Hot ng 2: Cho hnh v thay i,kt qu o c d on v tr cn tm c(hnh 3.3).

Hnh 3.3 hch im C

tnh tng

quan st a im C

3.2.3. Hc sinh s dng Cabri Geometry mt cch c lp ti lp Lp hc c t chc ti phng my tnh, mi hc sinh c mt MTT. Hnh thc ny cho php gio vin t chc cc hot ng ph hp vi kh nng nhn thc,

nng lc ca tng hc sinh trong lp do vy hc sinh c iu kin pht huy ht kh nng ca bn thn. y l mi trng thch hp thc hin dy hc phn ho. Tuy nhin hnh thc ny i hi nng lc chuyn mn, t chc ca gio vin mc cao trnh tnh trng gi hc phn tn.

V d 3.4: Cho gc xAy khc gc bt, 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.

Phiu hc tp c thit k nh sau: Nhim v 1: Em hy s dng Cabri Geometry v hnh theo hng dn sau:

Chn cng c Ray: v tia Ax v tia Ay.

Chn cng c Point on Object: ly mt im B bt k trn tia Ax.

Chn cng c Segment: dng on thng AB.

Chn cng c Point on Object: ly im C bt k trn on thng AB.

Chn chc nng Circle: v ng trn tm A bn knh CB.

Chn chc nng Intersection Points: xc nh D l giao ca ng trn vi tia Ay. Chn chc nng Circle: v ng trn tm A bn knh AB, xc nh im D trn tia Ay (hnh 3.4).

Nhim v 2: Em hy d on v tr im c nh bng cch thc hin c

Documents

Day Hoc Hinh Hoc Voi Su Ho Tro Cabri GeoMetry