!̂gl len piiru Khoa hpc Giao d^c THIFC NGHIEIVI DAY HOC TI/CHQN CAC CHU DE NANG CAO Of MON TOAN LOP 6 Day hpc tu chpn d l dUpc chinh thdc dUa vao chUdng trinh trung hpc cd sd (THCS) d nude ta tdnamhpe[.]
Trang 1-Khoa hpc Giao d^c
THIFC NGHIEIVI DAY HOC TI/CHQN
CAC CHU DE NANG CAO Of MON TOAN LOP 6
Day hpc tu chpn d l dUpc chinh thdc dUa vao
chUdng trinh trung hpc cd sd (THCS) d nude ta
tdnamhpe 2001-2002 bIng quyet dinh so 03/2002/
QD-GD&DT ngly 24/1 /2002 eua Bd trudng Bp Gilo
due va DIo tao va chi dupc thUc hien d ele Idp 8
va 9 Theo quylt djnh dd, day hpc tU chpn d mdn
TolnTHCS dupe thUc hien bang d c chu de tuehpn
theo 3 loai: bim sat, nlng cao v l dip Ung Den nam
hoc 2006-2007, day hpe tU chpn d mdn Toln THCS
da dupe thue hien d toan d p hpc, ke cl d c Idp 6
v l 7, nhUng gidl han d hai loai chu de bIm sat v l
nang cao.Tuy nhi§n, vlec thuc hien day hpc tUehpn
d mdn Toln THCS, tren thuc tien, van cdn khd khan
Tai edng vIn hudng dan thUe hien nhiem vu nam
hpc 2009-2010, Bp GD&DT da lUu y rang "trong
dilu kien chua ban hanh dupe t l i lieu chCi 6i nlng
cao, can dinh thdi lUpng day hpe tU chpn de thUe
hien chu de bIm sat nham dn tap, he thong hda,
khIc sau kien thUc"(Bp Giao due v l Dao tao, 2009)
Bli viet nly gidl thieu mot thue nghiem nham gili
quyet khd khIn ve tai lieu day hpc tuehpn eho chu
de nlng cao d mdn Toln Idp 6
1 / Noi dung thiTc nghiem
1.1 Nghien culj cua Nguyen HQu Chlu v l edng
su (Nguyin HCfu Chlu 2005 a, trang 42) da md t l
kha rd v l muc tiiu, npl dung, d u true chung ve tai
lieu day hpc cho ehu di (theo loai bai hpc va loai
bai tap) va d c h thdc tiln hanh day hpc tU chpn d
THCS Vdi mdn Toan, nghien cCfu nay d l chi ra mdt
danh sach d c chu de nang cao d mdn Toan Idp 8
va Idp 9
Nghiin cCfu tiep theo ve day hpc tUchpn mdn
Toln THCS (gdm d c Idp 6,7,8 va 9) do Vien Chiln
lupe va ChUdng trinh gilo due, nay la Vien Khoa hpe
gilo due Viet Nam thuc hien, d l gldi thieu eae chu
de nang cao d mdn Toan Idp 6 gdm lOchudela:
Chu di 1: Day so tu nhien viet theo quy luat
Chu de 2; So sanh hai luy thUa
Chu di 3:Tim sd tan cung cua mot luy thCte
Chu d l 4: Cac van de nang eao ve tinh chia het,
Ude va bdi
ChCi de 5: Mdt so dang bli tap ve sd nguyen td
TS.LEVANH6NG Trung tam Nghien cihj Cong nghe Giao dye
ChU de 6: So sanh hai phln sd
Chu de 7: Day cle phan sd viit theo quy luat Chu de 8: Mdt so phUpng phap gili toan sd hpc
Chu de 9: Tinh sd dilm, sd doan thang, sd dUdng thang
ChCide 10:Tinhsddogdc
Do danh mue d e ehu 6i tren chua dugc phe
duyet v l tli lieu day hpe kem theo ehua dupc bien soan chinh thUe, nen khi tiln hanh nghien eC^, chung tdi lua chpn xay dung tai lieu day hpe cho 4
chU di vdi ten gpi nhu sau;
Chu de 1: Dly sd Chu d l 2: Chia hit
Chude3:Phansd
ChCi de 4: Tinh sd dilm, sd dUdng thing v l so doan thang
Cd the thay, ten 4 chu de ma chung toi lUa chpn gan gui vdi tin ele ehu de 1,4,7 v l 9 ma Vien Khoa
hpc Gilo due Viet Nam d l 6i xuat nIm 2007
1.2 Hai loai tai lieu day hpe eho 4 chCi d l tren dupc thuc nghiem II:
-Tli lieu dung ehung eho hpc sinh va giao vien (eho hpe sinh II chfnh)
-Tai lieu danh rieng cho gilo vien
a) Tai lieu dung ehung cho hpc sinh v l giao vien dUdc ehung tdi xay dUng theo hinh thUe he thdng
d e bai tap Sau khi thUe hien cac bai tap dd theo hudng dan cua gilo vien, hpe sinh se dat duac kien
thdc, kT nlng v l thai dp dat ra
Co sd cho viec xay dUng ndi dung chu de bang
he thdng bai tap dupe ehung tdi xle djnh d n cCf vao eae luan diem ve chUe nang cua bai tap Toln hpc trong day hoc Trude hit, la elc luan dilm ve
eae ehUe nang day hpe, giao due, phIt trien va kiem
tra dinh gil cua bai tap Toln da dupe cle tac gil Nguyen BI Kim v l Vu Duong Thuy nghien edu td nam 1980, gldi thieu d nam 1992 (Nguyen BI Kim
va Vu DUdng Thuy 1992, trang 206) va sau nly dupc Nguyen Ba Kim nhin nhan lai theo quan diem hoat
Trang 2ddng: eoi bai tap Toan ed vai trd I I " g i l mang hoat
ddng cua hpe sinh"va cd the khai t h i e vai trd cCia
bai tap tren nhieu binh dien day hpc nhU: mue dich
day hpe, npi dung day hpc va phUdng phap day
hpc, (Nguyen Ba Kim 2002, trang 384) Chung tdi
eung dua vao nhUng nghien eUu va thUe nghiem
trong q u i trlnh thUe hien de tai d p Bp"BUdc dau
thCf nghiem hinh thUc t u chpn d trung hpe cd sd;
m l so B 92-45-01 Vdi de t l i tren, dUpe nghiem thu
nam 1995, ehung tdi da xay dUng d c c h u y i n de
day hpc cho hinh thUe t u chpn dudi dang he thdng
d c bai t i p T o l n hpc
b) T l i lieu danh rieng cho g i l o vien nham giup
g i l o vien sd dung dupe tai lieu dung chung cho
hpc sinh va g i l o vien (neu tren) de t d ehUe, hUdng
dan hpe sinh cd dupe kien thdc, kT nang va thai dp
ma d c ehCi di nay mudn neu ra
Di thUe hien d i l u dd, tai lieu n l y ed hai phan
ehfnh: (1) Idi giai h o l e gpi y ve Idi giai c l e bai tap
trong he thdng va (2) gpi y ve tien trinh day hpe
ele bai tap d l neu theo thdi gian d l quy djnh eho
moi chu de 4 t i l t T r o n g phan thU hai cd gpi y d c h
t d ehUe day hpe, eleh thUe giao nhiem vu eho hpe
sinh v l to ehUc hudng dan, danh g i l k i t qua edng
v i l e hpc sinh da thuc hien Dae biet, phan n l y luu
y mot sd diem g i l o vien can nhac n h d hpe sinh ghi
n h d k i l n thdc, kT nang cd dupc tU bai tap d d hay
m d t sd bai tap da l l m de van dung g i l i c l e bai tap
sau do v l van dung lau dai NhUvay, tai lieu nay
n h u I I b i n ke hoach t o ehUe edng viee cho hpe sinh
de giao vien se t i l p tuc cu the hda chung cd the
b I n g d u hdi gpi y hay ehu y n I o do di hpe sinh
h o l n t h I n h elc bai tap da dat ra
1.3 Dudi day I I mdt sd bai t i p t d eae ehCi d l t r I n
n h u I I vi du de hinh dung t h e m ve loai t i l lieu thU
nhat da dupc thue nghiem
Chu de 7 v l d l y so dupc thiet ke vdi mong
mudn hpc sinh se cd dugc k i l n thdc ki nang ban
dau ve quy nap de k h I i q u i t tinh quy luat eua d l y
sd thanh d c edng thUe so hang tong q u i t v l sCf
d u n g chung trong giai m d t so b l i toan khdng qua
phCfc tap Mot so bai tap trong chu de nay I I :
Bai tap 1: Hay d u doan edng thUe tinh sd hang
t o n g q u i t eua d c day sd:
a ) 2 , 4 , 6 , 8 , 1 0 ,
b ) l , 3 , 5 , 7 , 9 ,
e ) 1 , 4 , 7 , 1 0 , 1 3 ,
B l i tap 13; Djnh nghTa: Ta gpi n! la tfeh eua*n sd
t u n h l l n dau tien
Khdng diJng m I y tinh h l y tfnh:
1!.21,31, 7!
Bai tap 15: Hay d u d o a n edng thdc tinh so hang
t o n g q u i t eua c l e d l y sd:
1 , 4 , 2 7 , 2 5 6 , 3 1 2 5 , 3,6,29,258,3127,
0 , 3 , 2 6 , 2 5 5 , 3 1 2 4 ,
Chu dS 2 dupe \Ua chpn n h I m giup hpe sinh
p h I t t r i l n k i l n thOfc kT n l n g v l chia h i t d l hpc 6
m d t sd kT nang edng cu ve b i l n ddi bleu thu'c chiJa
ehU N h u vay, se cd d c bai t i p 6i hpc sinh c6 kl
n l n g edng cu ban dau v l b i l n doi bleu thdc chiJiS chUva d c bai tap sUdung chung trong g i l l t o l n ve chia h i t Cu the, cd mot sd bai tap nhU:
Bli tap 1 :ThUc hien phep t o l n : a)a(x-i-y) e) 3(a-b) b)b(x-i-1) g ) 5 ( x - y ) c) a ( x - 3 ) h) 2(a-4)
d ) x ( a - b ) i ) 7 ( 2 - c ) Bai tap 7 : Chdng minh r a n g :
6 ^ ^ 6 e ) 1 2 ' » M 4 4
7 ^ ' ^ 4 9 g ) 2 ^ ' ' M 6
8 ^ N 6 4 h)3«^N81
1 3 ^ ' M 6 9 i ) 5 i ^ « M 2 5 Bli tap 15: Chdng minh rang 1-1-3-1-3^-1- -|-3«M3
Chu de3 duge x l y d u n g n h I m p h I t t r i l n e^e kT
n l n g tinh t o l n ve phan sd nhUng vdi yeu d u b i l t
sd dung dupc kT thuat p h I t hien quy luat Mdt b l i
tap trong chij di n l y :
B l i tap 1: (trieh 2 d u d i u )
a ) — - + h — - I - + 1.2 2.3 3.4 999.1000
5.7" +
-1.3 3.5 Bli tap 2:
J_ _1_
1.2"^ 2.3 n(rt + l ) Bai tap 8:
1
9 101
1
3 13.22
9 66.31
40
9331
Trang 3Chu d44 bao gdm eae bai tap vUa eung eo d c
kiln thu'c kT nang da cd theo yeu d u eua chuong
trinh VLfa phIt trien chung de dip Ung khi nang
va hdng thCi eua hpc sinh HPn nUa, mot vai bli t i p
cdn dupc lUa chpn nhIm eung cd phIt trien ve khIi
quit, ve quy nap da hinh thInh, ren Iuyen tU d c
chCi d l d l cd Cd 11 trong tong sd 22 bai tap cua
chu d l nly II:
Bli 1 / Cho 3 diem phan biet
Hly ve 3 diem va dat kf hieu eho chung
Hly ve cac dudng thang di qua 2 trong 3 diem
do Hdi cd t h i cd may dudng thang?
Bli 2/ Cho 3 diem phan biet Hay ve cac doan
thing di qua 2 trong 3 diem dd Hdi ed the cd may
doan thing?
Bli 3/ Cho 4 diem phan biet Hay ve d c doan
thing dl qua 2 trong 4 diem dd Hdi cd the cd may
do?n thing?
Bli 4/ Cho 4 dilm phln biet Hly ve cac dudng
thing dl qua 2 trong 4 diem dd Hdi ed the cd may
dudngthing?
Bli 5/ Mdt gill bdng da "TU hung" cd 4 dpi bdng
d l , ki hieu II A, B, C, D thdng nhat to chu'c dau vdng
trdn c l lupt di va lupt ve de chpn dpi Vd djch Hly
lap bIng md t l mdt d c h quy dinh thu" tU ele tran
diu cCia gili Neu gili dau quy djnh chi thi dau mdt
lUdt thi gili dd se cd bao nhieu tran dau
Bai 8/ Cho 5 dilm, trong dd khdng cd 3 dilm
nIo thing hang Tfnh so dudng thing di qua 2
dilm trong 5 diem da eho
Bli 9/T6ng quit bli toln 8 cho n diem
Bai 14/ Ba dudng thing cd 1 dilm chung dupe
gpi II3 dudng thing ddng quy Cho 5 dUdng thing
ddi mdt d t nhau m l trong do khdng cd 3 dudng
nIo dong quy Hay ve hinh va cho biet ed t h i ed
bao nhilu glao diem?
Bli 15/ Diln vao d trdng trong bIng
S6du'ejngthangd6l
m^tcSt nhau, nhung
khfing c6 3 di/dng
d6np quy
2
4
S
6
S6 giao
diem
1
6
10
So giao tang them
0
Qu/ luSt cOa day so glao diem
1 3=1+2 6=1+2+3 10=1+2+3+4
Bli 16/ Hay ve hinh tUdng ijfng vdi moi ddng
trong bIng tren
Bli 17/ Hay md rdng them d c so trong bIng va
ve hinh tUdng tfng
2/ T 6 chuTc thUc nghiem va ket qud ban
dau
2.1 Thue nghiem nay dupe ehung tdi tiln hanh hai lupt tai trudng PTCS Thuc nghiem thudc Vien KHGDVN Lupt thU nhat thuc hien trong nam hpc 2008-2009 vdi 3 chu de dau tien LUpt thU hai thUc hien trong nIm hpc 2009-2010 vdi d 4 chu de d l neu Chung tdi eCing gpi y giao vien phIt trien mdt
so kT thuat chi tilt d l dU kien trong til lieu gilo vien nhu dung may ehilu, phan mIm powerpoint, hay dung phieu hpc tap de djnh rd nhiem vu cCia hpe sinh
Qua thue nghiem lUpt thU nhat, ehung tdt dieu chinh bo sung v l tli lieu thUe nghiem hole bIng nhIc nhd giao vien hole bIng bd sung tren tai lieu
ehung eho hpc sinh v l gilo vien dupe lam rd hdn
ve npi dung kiln thUe ma eae bai tap the hien di
hpc sinh cd chCi y sd dung chung lau dai; cdn vdi tai lieu giao vien dupc chung tdi trinh bay kT hdn ve muc tieu gid day va dieu hinh hoat dong nhdm Chung tdi chap nhan thUe nghiem mdt dch tU nhien trong d e gid hpc ma nha trudng bo trf de day tang cudng moi tuan 2 tilt cho mon Toln theo
d c trinh dd cua hpc sinh.Trinh dp hpe sinh d nhdm thuc nghiem la khi trong Ian thUe nghiem thUnhat
v l II gidl trong Ian thUe nghiem thU hai 2.2 Kit qui ban dau cho thuc nghiem lUpt thd hai dupe md t l theo hai phUdng dien quan sat gid hpc va danh gil kit qui bai kiem tra sau thuc nghiem
a) Ve quan sit gid thUe nghiem, chung tdi thay; (1) Gilo vien d l tuin thu d c tai lieu day hpc ml chung tdi dUa ra nhU he thdng d c bai tap, djnh hudng to chUe, hUdng dan giai, phan bd thdi gian cho 4 tilt theo tirtig cap 2 tilt (Bd GDStDT quy dinh day hpe tU chpn 2 tiet/tuan)
(2) Giao vien d l cu t h i hda dupc dinh hUdng thiet k l trong tai lieu dinh rieng cho giao vlen bIng neu ra philu hpc tap, sif dung phUPng tiln edng nghe thdng tin ho trp, cu the hda ele gpi y day hpe bing khich le hay danh gia
(3) Hpc sinh hlo hUng hpc tap trong d c gid thuc nghiem va nghiem tuc vdi bli kiem tra danh gil cudi dpt thuc nghiem,
(4) Viee to chUc cle hoat ddng nhdm trong day hpe elc chu de nlng cao dupc thiet ke theo phucmg phap he thdng bai tap dan xen vdi cac hinh thdc, phUdng phIp day hpc khie nhu phat van, neu van
di la cd the chap nhan dupc
Trang 4(5) Ndi dung thUe nghiem ve4chu de nang eao
mdn Toan vdi he thong bai tap d l di ra dupe nhdm
hpc sinh thUe nghiem tilp nhan vdi sU ham thich
b) Vl kit qui kiem tra cudi dpt thuc nghiem,
ehung tdi xin neu ra de bai kiem tra, kit qui va mdt
sd nhan xet nhu sau:
(l)Debdi (thdi gian lam bli 60 phut)
(thdi diem kiem tra: 15/5/2010, sau khi kit thuc
thucnghiem 1 tuan)
Bdi 1 (3 diem) Du doln edng thUe tong quit
eho day so sau
1;4;9;16;25;
2;6;12;20;30;
4;10;28;82;244;
Bdi2 (2 diem) Chdng minh ring:
5100 5 « + 598 1^21
ed/3(1,5diem) ChoS-1-H2-i-2^-t-2^+ -1-2""
Tfnh sdsd hang eua S
Chdng minh S chia hit eho 7
Bd/4(2dilm)
TTnhS^-—+ + + -+
1.5 5.9 9.13 97.101
Timxbiet + + -I- + =
1.6 6.11 11.16 x.(x + 5)
56
Bffl5(1,5diem)
Cho 7 diem phln biet bat ki, khdng ed 3 diem
nao thing hIng Ndi hai diem bat ki de tao thanh
ele doan thang Hdi cd bao nhilu doan thang dupe
taothinh?
(2) Ve kit qui (Xem bang 1 va bIng 2)
Bdng 1- Tong hep
Ng en y
(3) Vai nhan xet ve kit qui bai kilm tra 1/ Dilm toan bli td diem 7 trd len ed tl le 703
% va dilm trung binh eua d nhdm thUe nghilm
la 7,22 eho thay bai kiem tra phu hpp vdi hpe sinh kha, gldi
2/ Chenh lech diem toln bli Idn (diem eao nhat
10, diem thap nhat 3,5), vay ed phan hda cao ve ket qui kilm tra du hpe sinh dupe chpn ban dau deu kha gidl
3/ HS biet dUdoan quy luat day so (bai 1), biet van dung edng thC^c cho ddi tUpng hinh hpc (bli 5) vdi mUc dp chae chin, the hien khi nang eua hpc sinh khi gidl
4/ HS da bude dau vIn dung suy luan v l chUng minh (qua elc bai 2; 3 va 4), t h i hiin mijfe dp eao eua hpe sinh khi gidi ve mdn Toln Tuy nhien, hoc sinh chua the thanh thao vdi suy luan va chdng minh nhu d l thanh thao ve tfnh toln v l dU doan
(so sanh eae bai 2 bai 3 v l bai 4 vdi cac bli 1 v l 5)
Kit qui thuc nghiem neu tren cho thay cd the
thUe hien dugc viee xay dung npi dung day hpe tu!
chpn ehu de nang eao bIng hinh thUe he thdng bli tap va tli lieu the hien phUPng phIp nay cd tinh khi thi
Thuc nghiem do cung gpi y mdt sd nhu d u ve nghien eCru mde dp khd cho cle bai tap trong tli lieu day hpe va do vay eung dat ra yeu d u cdn phli holn thien ca hai loai t l i lieu day hpc d l cd (bao gdm c l he thdng bai tap, nhat la bli t i p mang tfnh gidi thieu kiln thdc mdi v l gpi y bo sung de giao
theo diem todn bdi
Oiem
So bai
• n i ^ %
10
8
29,6
9,5
1
3,7
9 7,4
8,5
3 11,1
8 3,7
7,5
2 7,4
7 7,4
6,5
1 3,7
6
0
5.5
1 3,7
5 11,1
4,5
1 3,7
4
0 3,5
2 7,4
Bang 2 - Tong hap theo diem trung binh
Ket q u i diem cOa 27 hoc
sinh
Olem toi da
O i l m toi thleu
O i e m t r u n q binh
Lech so vcn toi da
T I I e l e c h s o v c f i t 6 l d a ( % )
Olem toan bai
10 3,5 7.22 2,78 27,8
Olem t i f n q bai
1 /
3
2 2.74 0.26
9
2/
2
0 1.37 0.63
31
3 / 1.5
0 0.98
0 3 2
34
4 /
2
0
1 3 5 0.65
33
5/ 1.5
0 1.24
026
17
(Xem tiep trang 22)
Trang 55.4 Cde logi dudn hoc tap (Project works):
Day hpc d u I n cho phep ngUdi hpe lam viee
mot each ed tfnh hop t i e vdi cac ban hpc va ngudi
hudng dan eua mlnh trong mot mdi trudng lay hpe
sinh lam trung tam, ndi ma hpc sinh dUdc khuyen
khfch kham pha elc chCi de khae nhau ma chung
quan t i m Cle dU I n ed e h i l u s l u , cd giai doan va
ed tfnh phUe tap se thue day ehung x l y dung k i l n
thCfc
N h U v a y , d a y h p e k h l m p h l e d 5 dang khie nhau
Moi dang ed nhCfng dac diem, yeu t d rieng nhUng
chung deu ed nhCfng diem ehung I I giup hpe sinh
k h I m p h i tri thUe eua n h i n loai d l bien thanh tri
thUc eua rieng minh Day hpe theo ele dang k h I m
p h i I I xu hudng eua nen giao due hien dai, dua
tren sUtham gia eua ngUdl hpe v I o viee g i l i quyet
van de v l nhCfng suy nghT ed tinh phe phan (tu
duy phe p h l n dupe p h I t huy) t r o n g hoat ddng
m l hpe sinh thay phu hpp va hUng t h u
TAI L i f U T H A M KHAO
1 Bd G i l o due va Dao t a o Dgy kJnang tuduy
H I Ndi, 2000 (Tai lieu cua d u an Viet Bi "Ho trp day
hpetCfxa")
2 David WJohnson & RogerT Johnson Learning
Together and Atone: Cooperative, Competitive, and
IndividualisticLearning.JhWd edition Prentice Hall,
Englewood Cliffs, NewJesey 076323(1991)
3 Phd Diic Hda Dgy hgc tich cue vd each tlep con
trong dgy hoc tieu hgc NXB DHSR 2009
4 J Samuel Barkin Realist Constructivism:
Rethinking international Relations Theory,
Cambridge University Press, UK 2010
SUMMARY
Constructivism Theory allows learners building
knowledge for themselves through testing ideas from
available experience and knov\/ledge, then apply
this knowledge to other situation relating to new
knowledge Learning with forms of Inquyry teaching
is trend of modern education, based on participation
of learners in solving problem and critical thoughts
(critical thought is promoting) in activity that pupils
find relevant and interesting
THirC NGHIEM
(Tiep theo trang 26)
vien cu the t h e m t l i lieu eho rieng hpe sinh nhu phieuhpetap)
TAILI|UTHAMKHAO
1 / Bp Giao due va D I o tao, Hudng ddn thuehien nhiem vu Gido ducTrung hgc nam hgc 2009-2010.Hh
Ndi, 2009
2/ Nguyen HQu C h l u (2005a, chu bien), Mdt
so vdn de ve dgy hoc edc chCi de tu chon trong chuang trlnh tdp 8 trudng THCS, NXB G i l o dye
Ha Ndi 2005
3/ Nguyen HOfu C h l u (2005b), NhUng vdn died bdn ve chuang trinh vd qud trinh dgy hgc, NXBGD,
2005
4/ Nguyen Ba Kim (chO bien) - Vu DUdng
Thuy(1992), Phuong phdp dgy hoe mdn Todn (phan
dai eUdng), NXB G i l o due, H I Npi, 1992
5/ Nguyen B I Kim (2002), Phuang phdp dgy hgc mon Todn, NXB Dai hpc SU pham, H I Npi, 2002 6/Trung t i m Cong nghe g i l o due, Bdo edo tong kit di tdi cap Bg "Budc ddu thCl nghiem hinh thdc tU ehgn d trung hoc ca s&', ma sd B 92-45-01, H I Npi,
1995
7/ Vien Khoa hpe Giao due Viet Nam (2007),
Chuang trinh dgy hgc tu chon mdn Todn THCS (lUu
hanh npi bd), H I Npi, 2007
SUMMARY
This paper introduces an experimental instructionfortwokindsofthe&^grademathematlcs materials to meet a demand on the self-selected teaching materials with the appropriate enhanced topics Pupils' handbook is developed in the form of selected system of mathematical exercises to make full use of the role of exercises as pupils' activities holder and meeting the aspects of purpose, content and teaching method Teacher's guide lets him/her help pupils ta do the above activities with a view
to achieve the demand of knowledge, skills and attitudes of teaching topic