CHUYEN TIT NGON NGIT DAI sH SANG N G O N N G V S H HOC IRDNG VKC HUONG DJlN HOG SINH TilU HDG GlAl CHG BAl TDUN Gll III! VAN O ThS T H A I H U Y VINH" Bdng / I ng dfin cho hqc sinh tllu hqc (HSTH) kha[.]
Trang 1CHUYEN TIT NGON NGIT DAI sH SANG N G O N N G V S H HOC
IRDNG VKC HUONG DJlN HOG SINH TilU HDG GlAl CHG BAl TDUN Gll III! VAN
O ThS T H A I H U Y V I N H "
Bdng /
Iihdc cdc cdch gldl bdl todn cd Idl vdn Id ng dfin cho hqc sinh tllu hqc (HSTH) khai
mdt bl^n phdp hChj hl^u trong v l ^ rfin luy$n
vd phdt trlln ngdn ngiJ (NN) todn hgc cho hqc
sinh {HS) Gidl cdc bdl todn cd Idl vdn thyc ch^t
Id chuyin h> N N thdng thudng song N N vd ki
hi|u todn hqc Trong khudn khd bdl vilt ndy, chung
tdl dua ra mdt sd bdi todn cy t h l vd Irlnh bdy
phuong phdp khai thdc cdc cdch gldl
khde nhau bdng cdch ldp phuong
h'inh bde nhdt 1 dn vd h§ phuong h'inh
bde nhdt 2 d'n Sou dd, chuyin djch
h> N N dqi sd' song N N sd' hqc d l
hudng dfin cho HSTH gldl theo N N
sd hqc nhdm cung cd vd phdt triin
ndng lye \u duy, N N todn hqc eho
cde em
Bdi todn 1 (bdi todn cd d Kiu
hgc (TH)): "Vua gd vua ehd, bd Igi
eho trdn, ba muoi sdu eon, mgt trdm
chdn chdn Hdl cd bao nhliu con gd,
bao nhiiu con chd?"
O d d y , chung tdl mudn khai thdc
td't ed cdc cdch gidi dql sd bdng edeh
ldp phuong H n h bde nhd't 1 d'n sdvd
hfi phuong h'inh bde nhd't 2 dn sd';
sou dd, ehuyen djch sang N N sd' hqc
d l huong dfin cho HSTH
1) Gidi vd khai thdc bdl todn 1
bSng cdch lip phuong trinh bic
nhd't 1 d'n vd hi phuong trinh bic
nhdt 2 dn sd' Trudc hit, ta cdn xdc
djnh bdl todn cd mdy dgl lugng chua
bilt? (dd Id sd' con gd, sd' chdn gd,
sd'con chd, so'chdn end) Chf cdn bilt
1 Kong 4 dgl lugng sfi Km duge cdc
dqi luqng cdn Iqi
To ed cdc cdch gldl bdng N N dql
sd duqc Ktnh bdy trong bdng dudi
ddy (xem bdng 1)
hfong i}ng vdl 4 c 6 ^ gldl bdng cdch ldp phuong h'inh bde nhd^ 1 dn sd, 6 cdch ehqn 2 dn » hnhg i>ng vdl d cdch gldl bdng cdch Idp h | f r f i u ^ i ^ h-Inh bde nhdt 2 6n s^ (d ddy quan nl|m mSl ci^cn^ chqndnsdid 1 cdch gidi, Kong mfil cdch ehqn an
sd sfi cd nhllu cdch bllu dlln phuong Kinh hoy h$
phuong Ktnh khdc nhau md d bdng dudi ddy
chung Idl ehl mdl nfiu 1 cdch bllu d l l n
T T
1
2
3
'
S
s
7
e
9
10
con at
«
2
3e-x
3 6 - i
2
2
3e-x
si 2i<
2(36->i) 100-X
y
2
2x
100-y
S&
a e - x tOO-j
X
1
X-tL
y
>
'
4
Si diAncM
MX-n)
l W - ) i
4x
100-y
* y
y
100-x
y
y
"*^isiiirb2"*
2x « 4(30 •>)-100
x - 2 2
2 J 2(36-«)*4i = 100
x * 2 ( 3 6 - - ) -100
x = 5e
=9X-22:v-44
(2x**y-tM
lx+y-36
X = 22 V > 14 l2r*>-IOO
| i - - 1 0 0
I ' 2 2 y - 5 6
If*""
x = 44;y = 56
x = 14:v«96
Nhi/vqy, t>d/laSn ) c 6 4 c a c h c h 9 n 1 Aistf ' S i C t t t l i e i i M l l H l W I i
Tap chi Blip due s6 2 9 8 (M a n/»oi»i
Trang 2gidl tnqt bdl todn bde nhd't bdng cdch ldp phuong
trinh bqc nhd't 1 d'n sd vd hg phuong trtnh bde
nhdt 2 dn sd nhu sou: ne'u cd n dql lugng ehua
bilt thi sfi cd n edeh gldi bdng edeh ehgn 1 dn sd
vd ed C^„ cdch gidl bdng edeh ehqn 2 dn sd, do
dd, to ed n -t- C^^ cdch
2) Chuyin td cdch gidl bdng NN dgt sd
sang NN sd hgc di hudng ddn eho HSTH:
Cdch 1 • G i d su 3 d con d i u Id chd ed, N h u
v^y, mdi eon gd da «thgm vdo" 2 chdn Luc d d ,
t^ngsdchdn Id: 3 d x 4 = 144 (chdn) S d e h d n g d
dd «thgm vdo" Id: 144 - 1 0 0 = 4 4 (chdn) Suy ra
sd,gd Id: 44; 2 = 2 2 (eon); sd chd Id: 3 d - 22 =
14 (con)
Cdch 2: G i d si> 3 d con deu Id gd ca Khi d d ,
moi eon ehd dd «bdt d i " 2 chdn Luc d d , td'ng sd'
chdn Id: 3 d x 2 = 7 2 (chdn) So chdn chd dd «bdt
di" Id 100 - 7 2 = 28 (chdn) Suy ra sd chd Id:
28 : 2 = 14 (con); so g d Id: 3d - 14 = 22 (con)
Cdch 3: G i d su 100 chdn deu Id chdn eh(^
khi dd mol con gd dd "thfim vdo" 2 chdn Vdy,
tong so' con vdt Id: 100: 4 = 25 (eon) Sd' eon vdt
«hyt" di Id: 3 d - 25 = 11 (eon) Suy ra so gd Id:
11 x 2 = 2 2 (eon); sd chd Id: 3d - 22 = 14 (eon)
Gido vidn (GV) ed t h l ed cdch li gldl khdc
cho HS nhu: Id'y 3d cdi hjl tuqng trung cho 3d
con vdt vd 100 hqt ddu tuqng trung cho 100 cdi
chdn Gid su 100 chdn deu Id chdn chd thi phdl
bd mol tui 4 hqt vd bd duqc 25 hii Cdn 11 tul
chua ed hqt ndo, budc phdi bdt 22 hqt d 11 Kil
dd bd 4 hqt ddu, mol hji 2 hqt Luc d d , ha se cd
n X 2 = 22 KJI d y n g 2 hqt ddu vd 14 tul dyng 4
hgt ddu N h u vdy, gd cd 22 con, chd cd 14 con
Cdch 4: G i d su 100 chdn deu Id so chdn gd
thi khi do, moi eon chd d d "bdt d l " 2 chdn Vdy,
tong sdcon Id: 100 : 2 = 5 0 (con) Sdeon "tdng
thgm" Id: 50 - 3d = 14 (con) Suy ra so' chd Id 14
con vd so' gd Id: 3 d - 14 = 22 (con)
GV If gidi cho HS tuong tu nhu cdch 3: Idy 3d
cdi hji hrong h v n g cho 3 d con vdt vd 100 hqt
ddu hjgng h'ung cho 100 cdi chdn Gid su tdt cd
100 chdn deu Id chdn g d , khi bd mSl tul 2 hqt thi
cdn phdi cd 5 0 tul Luc d d , t h i l u 14 tul vd cd 28
hgt ddu chua duqc bd vdo tul ndo Bd mol tui
thfim 2 hqt nua se cd 14 hjl dyng 4 hqt ddu Suy
ra sd chd Id 14 con vd sd gd Id 2 2 con
Cdch 5: GV hudng dan HS ve so dd doqn
tndng nhusau:
Gid su sd' chd it hon sd g d , to cd so dd:
Tap chi Glao duc so 2 9 8 (fcia-n/aoiai
S d e h d n g d (II): I 1 1 Sdcon ehd llll): ,
Sd'ehdnehd(IV); ^ [ '
T a c d : ( l ) + {lll) = 3d;[ll) + ( I V ) = 1 0 0 Quo so d d , HS d l ddng thdy ngay 2 Idn sd chd Id: 100 - (3d X 2) = 28 (con); sd chd Id:
28 : 2 = 14 (eon); s6 gd 3d - 14 = 22 (con)
GV ed the chuyin so dd doqn Kidng thdnh so
dd khde khdl qudt hon md khdng cdn gid su sd ehd ft hon hay sd gd it hon sd ehd:
Bllu thj O Id sd gd thl sd chdn gd Id O O Bllu thj D Id sd ehd thi sd chdn chd Id D D D D _ , / idv
To ed so do: f,.^
D n
Dyo vdo so 66, HS de ddng thd'y ngay hai
hinh vudng ung vdi: 100 • 3d x 2 = 28 (con) Mdt hinh vudng ung vdi: 2 8 : 2 = 1 4 (con)
So chd 14 con, so gd Id 3d - 14 = 22 (con)
Ti> cdch I vd cdch 2, GV hudng dan HS gid
su cd so chd hodc so' gd Id mdt so n bd't ki, tuy nhidn, n phdi nhd hon hodc bdng 3d Chdng hqn, gid su so chd cd 3 con, khi dd sd gd Id: 3d - 3 =
33 (con} So chdn ehd Id: 3 x 4 = 12 So chdn gd Id: 33 X 2 = d d Td'ng so chdn gd vd chdn chd Id:
12 + d d = 78 Sdchdn "hyt" d i : 100 - 78 = 22 So' con gd p h d i thay b d n g sd con ehd I d :
22 : [4 • 2} = 1 1 Vdy, sdeon ehd Id: 3 + 11 = 14 (con); so con gd Id: 33 - 11 = 22 (con)
Gid su sdchd Id n eon (n < 3d), to ldp bdng sou:
0
D
i
0
D
i
st chd
n = 36
S i conga ( 3 6 - n )
36
34
2
0
S i
CM
n
1?
i f l f i
i^n
144
5 6
gi
IV
7n Hfi
0
Chan ChA
72
76
140 ItX)
S i chfln Iflng mam 2B
26
22
40
44
S i con gfl d i r ^ c
Ihay bin s i con
c h i Hoflc s i con
c n i Oirc^ tnev
Wn a i con gi
12
20
22 S6
14
S i
22
V7
22
22
22
HS ed the gid su so chd Id n, vdi 0 ^ n ^ 3d (n = 0 chinh Id cdch gid su 3 d con deu Id g d ,
n = 3 d Id cdch gldl gid su 3 d eon d i u Id chd cd), hodc gid siJ sd con gd h> 0 d i n 3 d
#
Trang 3• trinh bde nhdt 1 d'n ho^c h§ phuong Irlnh bde
nhdt 2 d n , ta ed t h l Hm ro n h l l u cdch gldl sd hqe
khde nhau
Bd I t o d n 2 : Mit xe md td dg djnh dl h> tinh A
din tfnh B trong mit ^dl glan nhdt djnh Niu xe
chgy vdl vin tdc 35 km/ gid thi din nol chim 2
gid Niu xe chgy vdl vin tdc 50 km/gid thi din
nai sdm hon ] gid Tfnh qudng dudng AB vd thdi
gian dt/ dinh lOc ddu [Di thl ehqn HS gldl TH Knh
Ngh§ A n ndm hqe 2 0 0 0 - 2001)
Tuong ty nhu bdi todn 1, bdl todn ndy ed 5
dql luqng chua b i l l , dd Id: qudng dudng AB,
Kidl gian dl vdl vdn tdc 35 k m / g l d , thdi glan dl
vdl vdn tde 50 k m / g l d , thdi glan d y djnh luc ddu
vd vdn tdc d y djnh lue ddu N h u vdy, s3 cd 5
cdch chon 1 d'n sd, ldp phuong trinh bde nhdt 1
d'n sd vd C ' = 10 edeh ehqn 2 dn sd, ldp h$
phuong trinh bde nhd't 2 d'n sd, suy ra cd 15 edeh
gldl bdng N N dql sd D i n ddy, GV cd t h l hudng
dfin HSTH gldl bdl todn bdng N N sd hqe
Q u o hal bdl todn ey t h l d trgn cho thdy, ddl
vdl bdl todn ed Idi vdn duqc g l d l b d n g cdch
ldp phuong Kinh bqc nhd't 1 d'n hode h | phuemg
trinh bqc nhd't 2 dn sd, n l u cd n dql lugng chua
b i l t Kii se cd n cdch ehqn 1 dn sd rdl Iqp phuong
h'inh bde nhd't 1 dn vd cd C^'cdeh chon 2 dn sd
sou dd ldp hg phuong trinh trinh bde nhd't 2 d'n
N h u vqy, cd tdt cd n + C„^ cdch g l d l dql id Tt>
cdch gldl dql sd to c h u ^ n song cdch g l d l s ^
hgc d l hudng dfin eho HSTH; i>ng vdi mfil edeh gldl thl N N todn hqc duge trtnh b d y vd d i l n dqt cung khdc nhou Ddy Id mdt trong nhiJng bl§n phdp g d p phdn nfing coo chd't lugng dgy
hqc todn dTH.Q
Tdi li^u Iham khdo
i Ph9m Dinh Thyc M^t c&u hdi v& d&p vi vifc d^y
toiln * tiiu hpc NXB Cido dvc, H 2004
2 G Polya Gidi bdi todn nhir th£ ndo NXB Cido
due H 1997
3 G Polya, Sdng t^o todn hpc NXB Cido diic, H
1997
4 D 6 Trung Hi$u - VO Duong Thuy Nhiing phuvng
phdp gidi todn & ti^u hpc NXB Dpi hpc su phpm, H,
1980
5 Tr&n Dien Hiin 10 chuyfin d£ b i i diKhig hpc sinh
gidl Todn 4 • 5 NXB Gido due H 2003
SUMMARY
The solving problems in elementary school have the text Is very rich, diverse and unique So teachers have to use common knowledge ond language of lem then find a guide forstudents This article I raised the extraction method of solving the most - /rove
me text problem by addressing the most equation
of a system of equations and unknovms most two unknowns, from which teachers seeking to move from language to language algebra arithmetic to guide elementary students explore the solutions by numerical methods In accordance with the pro-gram
ITng dung E-leamIng trong
(Tlip thea trang 53}
- E)dnh gid vd p/idn hii ngudi hgc: Website
e-leorning phdl thudng xuy6n k l l m Ko qud trinh
K i p Kiu k i l n thue vd RLNVSP cOo SV, Vi§c Kinh
bdy bdl gidng cdn duqc d i l u chlnh theo ndng
lye vd l i l n d q hqc tqp eua SV Vua k i l m Ira thudng
xuy&n, vuo x u li kjp tbdl nhijng phdn hdl cua SV
v l lien do vd nhung vd'n d l phdt sinh
Vide ung d y n g e-learning trong RLNVSP cho
SV ngdnh su phqm todn se d u o ro mqt mdi
trudng ddo tqo mdl thfch hqp, uu vigt hem mdi
trudng d d o tqo t r u y i n thd'ng, d d Id Iqo mdl
trudng hogl ddng tieh eye, chu d d n g , sdng tqo
eho SV; ddm bdo ho trg SV r6n' luy§n KNDH
theo hudng phdn h o d Q
Tdl lifu tham khdo
1 Dko Tam (chO bifin) - Lfi Hiin Ducmg Tifp cfin cdc
phuong phdp d^y hpc khOng truyin thtfng trong day
bpc mtm Todn & trudng d^i hpc vd truong plil thdng NXB Dpi hpc suphpm H 2008
2 Trin Tnmg (chu biftn) - D^ng Xufin Cuong - NguySn
v a n H6ng - NguySn Danh Nam O'ng di^ng cAng ngh^
thdng tin vdo d^y tipc mOn Todn fr truimg phi thAng
NXB Gido due Viit Nam H 201 i
SUMMARY
Appik:a^on e-ieaming in practice ofpedago^: cai qualification forstudents of education mathemat-: Ics at the Universtles
This paper presents the role of pedagogic training activities forstudents of education mathematics at the university Also, It ^lowspos^lrty of e-ieoming and pro-poses a number of requirements tor the applk:atk}n of e-leamir)g in pedago0cc^ training forstudents of edu-catkxi mathematics In the directton ofrMerentkjtion
Tap chi filao due s6 2 9 8 (id a - n/aoia)