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7RiQĈk\OjPӝWQӝLGXQJNKyWURQJFKѭѫ

Tốn trong nhà trѭӡQJYӟLWKӵFWLӉQFӫDÿӡLVӕQJF

7ӯQKӳQJOtGRÿyW{LÿmFKӑQQJKLrQ
³

7uPKL͋X
QăQJO͹F[͵O
thơng

WLQFͯDK͕FVLQKWK{QJTXDKR̩Wÿ͡QJNK

O˱ͫQJͧP{Q7RiQOͣSWKHRP{KuQKWU˱ͥ
2. 7әQJTXDQFӫDÿӅWjL

&iFÿӅWjLYӅQăQJOӵFGҥ\KӑF7RiQ

ÿmÿyQJJySPӝW
SKҫQTXDQWUӑQJWURQJYLӋFJLiRG
ĈӅ

FұSÿӃQQăQJOӵFFӫD+6WURQJGҥ\KӑFWK

SKiFNJQJÿmFyPӝWVӕÿӅWjLYjWjLOLӋX

- ĈһQJ7ӵỈQ

0{KuQKWU˱ͥQJK͕FPͣLW̩L
9L͏W1DP
1;%*LiR

9LӋW1DPFXQJFҩSFiFFkXKӓL
±ÿiSWKҳFPҳFYӅP{KuQKWUѭ
ÿiSYӅQăQJOӵFFӫD+6

- 1JX\ӉQ3K~/ӝF


³'̩\
K͕FNKiPSKi
±P͡WSK˱˯QJSKiS

QkQJFDRWtQKWtFK F͹FFͯDK͕FVLQKWUR
: ÿmÿѭDUDFiFN

SKѭѫQJSKiSYӅGҥ\KӑFNKiPSKiWURQJGҥ

- +jQ9LӃW7KXұQ

+͏WK͙QJWK{QJWLQWURQJ
, NXB ĈҥLKӑF

.LQKWӃ4XӕFGkQ+j1ӝL
ÿmSKkQWtFKVѫOѭӧFYӅWK{
thông tin.

- &QJPӝWVӕFiFWiFJLҧQKѭ7KiL
±SK˱˯QJSKiSG̩\

PͣL
9NJ4XӕF&KXQJ
±3K˱˯QJSKiSG̩\K͕F7RiQͧ7L͋
3*63761*Ѭ7

Phan Tân ±.KiLQL͏PY͉WK{QJWLQYjFiFWKX͡F

&iFWjLOLӋXWUrQFXQJFҩSFKR

FK~QJW{LQKӳQJQӝLGXQJ

YӅNKiLQLӋPQăQJOӵF
NKiLQLӋPGҥ\KӑFNKiPSKiYj

FKѭDFyÿӅWjLQjRQJKLrQFӭXYӅPҧQJWu

TXDKRҥWÿӝQJNKiPSKiWURQJGҥ\KӑF
7RiQӣ7LӇXKӑF9uYұ\

W{LÿmGӵDWUrQQKӳQJWjLOLӋXÿӇWLӃQK
2


3. 0өFÿtFKQJKLrQFӭX

7uPKLӇXYӅQăQJOӵF
[ӱOt
WK{QJWLQFӫDKӑFVLQKWK{

WURQJGҥ\KӑFÿҥLOѭӧQJYjÿRÿҥLOѭӧQJ

7ӯÿyÿӅ[XҩWPӝWVӕELӋQSKiSQKҵPQkQ
[ӱOt
WK{QJWLQFӫD
sinh

trong Gҥ\KӑFÿҥLOѭӧQJYjÿ
RÿҥLOѭӧQJWKHRP{KuQKWUѭӡ
4. *LҧLWKX\ӃWNKRDKӑF

7URQJGҥ\KӑFQӃXJLiRYLrQSKiWKX
[ӱOt
WK{QJWLQ

KӑFVLQKWK{QJTXDKRҥWÿӝQJNKiPSKiWU

WUѭӡQJKӑFPӟLWKuVӁWҥ
RÿѭӧFVӵKӭQJWK~VD\PrKӑF

WtFKFӵFYjKLӋXTXҧKѫQWURQJKӑFWұS
P{Q7RiQFKRKӑFVLQK7L
5. 1KLӋPYөQJKLrQFӭX

- 1JKLrQFӭXFiFYҩQÿӅOêOXұQYjWKӵF
[ӱOt
thông

WLQFӫDKӑFVLQKWK{QJTXDKRҥWÿӝQJNKi

ӣP{Q7RiQOӟSWKHRP{KuQKWUѭӡQJKӑF

- 7uPKLӇXYӅQăQJOӵF
[ӱOt
WK{QJWLQFӫDKӑFVLQKWK{

WURQJGҥ\KӑFÿҥLOѭӧQJYjÿRÿҥLOѭ
ӧQJӣP{Q7RiQOӟSWKHR

- 7KӱQJKLӋPWtQKNKҧWKLFӫDÿӅWjLTX

6. ĈӕLWѭӧQJYjSKҥPYLQJKLrQFӭX
6.1. ĈӕLWѭӧQJQJKLrQFӭX

9LӋFYұQGөQJQăQJOӵF
[ӱOt
WK{QJWLQFӫDKӑFVLQKWK{

WURQJGҥ\ÿҥLOѭӧQJYjÿRÿҥLOѭӧQJӣP{
6.2. 3KҥPYLQJKLrQFӭX

1JKLrQFӭXYӅYLӋFYұQGөQJQăQJOӵF
[ӱOt
WK{QJWLQFӫDKӑFV

ÿӝQJNKiPSKiWURQJ
Gҥ\KӑFÿҥLOѭӧQJYjÿRÿҥLOѭӧ
WUѭӡQJKӑFPӟLWҥLWUѭӡQJ7LӇXKӑF
Hịa Phú ±WKjQKSKӕĈj1ҹQJ
7. 3KѭѫQJSKiSQJKLrQFӭX

7URQJTXiWUuQKQJKLrQFӭXÿӅWjLQJ
-

33SKkQWtFKYjW͝QJKͫSWjLOL͏X
: Ĉӑ
c tài liӋ
u, tӯÿySKkQWtFKYj
әng hӧp các

thơng tin cҫ

n thiӃ
WFKRÿ
Ӆtài.

- 33TXDQViWV˱SK̩P
: 'QJÿӇJKLQKұQWKXWKұS

ÿӝQJTXiWUuQKJLiRGөFQKҵPNKDLWKiF
YjÿӅ[XҩWELӋQ
SKiSWѭѫQJӭQJ
3


- 33ÿL͉XWUDJLiRGͭF
: Dùng hӋthӕng câu hӓLÿ
Ӈthu thұ
SWK{QJWLQO
ӣ
thӵc tiӉ
QFKRÿ
Ӆtài.

- 33QJKLrQFͱXFiFV̫QSḴPKR̩Wÿ͡QJ
: 1JKLrQFӭXWjLO
YӅP{KuQKWUѭӡQJKӑFPӟL
- 33ÿiQKJLiYj[͵
OêN͇WTX̫
: ĈiQKJLi
phân tích và xӱlí sӕliӋ
u kӃ

t quҧthu
ÿѭ
ӧc sau khi thӵc nghiӋ
m.
- 33WK͹FQJKL͏P
: Thӵc nghiӋ
Pÿ
ӇkiӇ
m tra tính khҧthi cӫDÿ
Ӆtài.
8. &ҩXWU~FÿӅWjL

1JRjLSKҫQPӣÿҫXSKҫQNӃWOXұQYjG
FӫDÿӅWjLJӗPFySKҫQ
&K˱˯QJ&˯VͧOêOX̵Q
FͯDÿ͉WjL

&K˱˯QJ7uPKL͋XQăQJO͹F
[͵Ot
WK{QJWLQFͯDK͕FVLQK

NKiPSKiWURQJG̩\K͕Fÿ̩LO˱ͫQJYjÿRÿ
K͕FPͣL
&K˱˯QJ7K͹FQJKL͏PV˱SK̩P

4


1Ӝ,'81*
&+ѬѪ1*

I: &Ѫ6Ӣ/é/8Ұ1
&Ӫ$Ĉӄ7¬,
1.1 ĈһFÿLӇPWkPVLQKOêKӑFVLQK7LӇXKӑF
[18][19]
1.1.1 1KұQWKӭFFҧPWtQK
1.1.1.1 Tri giác

- Tri giác OjWѭGX\QKұQWKӭFFӫDFRQQJѭӡL

+67+PDQJWtQKÿҥLWKӇWRjQEӝYjtWÿL

+67+FNJQJEҳWÿҫXFyNKҧQăQJSKkQWtFK

- 7ULJLiFWKѭӡ
QJJҳQYӟLKjQKÿӝQJYӟLKRҥW
ePSKҧLFҫ

QҳPVӡWKҩ\VӵYұWWKuWULJLiFVӁWӕW

FӫDFiFHPEҳWÿҫXÿѭӧFFөWKӇYjVkXVҳ
1.1.1.2 &̫PJLiF

- /jKuQKWKӭFQKұQWKӭFFҧPWtQKSKҧQ
FiFWKXӝFWtQKULrQ

KLӋQWѭӧQJNKLFK~QJWiFÿӝQJWUӵFWLӃS

- ӢOӭDWXәLWLӇXKӑFFiFFѫTXDQFҧP
WKtQKJLiFNKӭX

[~FJLiFÿӅXSKiWWULӇQYjÿDQJWURQJTX
WKLӋQ

1KұQ
WKҩ\UҵQJFK~QJWDFҫQWKXK~W+

VҳFWtQKFKҩWÿһFELӋWNKiFOҥVRYӟLE
JLiFWtFKFӵFYjFKtQK[iF
1.1.2 1KұQWKӭFOêWtQK
1.1.2.1 7˱GX\

- 7KHR7kPOtKӑFWѭGX\FӫD+67+PDQ

WKDRWiFVDQJWѭGX\WKDRWiFWӯWѭGX\

ErQQJRjL4XDTXiWUuQKKӑFWұSFiFHP

Khi khái quát, HS tiӇ
u hӑ
FWKѭ
ӡng dӵa vào chӭFQăQJYjF{QJG
ө
ng cӫa sӵvұ
t hiӋ
QWѭѫQJ
WUrQFѫV
ӣnày chúng tiӃ
n hành phân loҥ
i, phân hҥ
ng. Hoҥ

Wÿ
ӝng phân tích tә
ng hӧp cịn
Vѫÿ
ҷ
ng nên viӋ
c hӑc Tốn sӁgiúp các em biӃ
t phân tích và tәng hӧp.
1.1.2.2 Chú ý

- ӢOӭDWXәLKӑF
VLQK7LӇXKӑFFK~êFyFKӫÿӏ

ÿLӅXFKӍQKFK~êPӝWFiFKFyêFKtFKѭD

FѫJҫQWK~Fÿҭ\7X\QKLrQKӑFVLQKӣFi
5


WUuQJD\FҧNKLFyÿӝQ
JFѫ[DFiFHPFK~êYjRF{QJ

WK~YuNӃWTXҧQyFKӡÿӧLWURQJWѭѫQJOD
.
- Trong lӭa tuә
i hӑc sinh TiӇ
u hӑc, chú ý khơng chӫÿ
ӏ
QKÿѭ
ӧc phát triӇ

n. Nhӳng
gì mang tính mӟi mҿ
, bҩ
t ngӡ, rӵc rӥNKiFWKѭ
ӡng dӉdàng lôi cuӕn chú ý các em. Vì vұ
y,
giáo viên cҫ
n sӱdөng nhӳQJÿ
ӗdùng dҥ
y hӑFÿ
ҽ
p, mӟi lҥ
, ít gһ
p, gӧi cho các em cҧ
m
xúc, hӭng thú.
1.1.2.3 7˱ͧQJW˱ͫQJ
- 7ѭ
ӣQJWѭ
ӧng là mӝ
t trong nhӳng quá trình cӫa hӑc sinh tiӇ
u hӑ
Fÿѭ
ӧc hình thành
và phát triӇ
n trong hoҥ
Wÿ
ӝ
ng hӑ
c và các hoҥ

Wÿ
ӝ
ng khác cӫ
a các em. 7ѭ
ӣQJWѭ
ӧng cӫ
a các
em còn tҧ
n mҥ
n, hình ҧ
QKWѭ
ӣQJWѭ
ӧQJFzQÿѫQJL
ҧ
QFKѭDE
Ӆ
n vӳng. Càng vӅnhӳng lӟp

hӑc cuӕ
i cҩ
SWѭ
ӣQJWѭ
ӧng cӫ
a các em càng gҫ
n hiӋ
n thӵFKѫQFiFHPÿm
Ӄ
t dӵa vào

ngôn ngӳÿ

Ӈxây dӵQJKuQKWѭ
ӧng mang tính khái quát và trӯXWѭ
ӧQJKѫQQK
ӡÿmOƭQKK
ӝ
i
ÿѭ
ӧc nhӳng tri thӭc khoa hӑc.

1.1.3 1J{QQJӳWUtQKӟYjVӵSKiWWULӇQQKұ
[13]
- Ngơn ngӳcó vai trị hӃ
t sӭc quan trӑQJÿ
ӕi vӟi q trình nhұ
n thӭc cҧ
m tính và lí

tính cӫ
a trҿ
, nhӡcó ngơn ngӳmà cҧ
PJLiFWULJLiFWѭGX\
ӣQJWѭ
ӧng cӫa trҿphát triӇ
n
dӉGjQJYjÿѭ
ӧc biӇ
u hiӋ
n cөthӇthơng qua ngơn ngӳnói và viӃ
t cӫa trҿ
. Mһ

t khác, thơng
qua khҧQăQJQJ{QQJ
ӳcӫa trҿta có thӇÿiQKJLiÿѭ
ӧc sӵphát triӇ
n trí tuӋcӫa trҿ
.
- Trí nhӟӣlӭa tuә
i tiӇ
u hӑ
c là loҥ
i trí nhӟtrӵFTXDQKuQKWѭ
ӧng chiӃ
PѭXWK
ӃKѫQ
trí nhӟtӯngӳ- lơgic
*LDLÿR
ҥ
n lӟp 1, 2, 3 ghi nhӟmӝt cách máy móc, phát triӇ
QWѭѫQJÿ
ӕi tӕt và chiӃ
m
ѭXWK
ӃKѫQVRY
ӟi ghi nhӟêQJKƭD
*LDLÿR
ҥ
n lӟp 4, 5 ghi nhӟFyêQJKƭDYjJKL
nhӟtӯngӳÿѭ
ӧFWăQJFѭ
ӡng. Ghi nhӟ

có chӫÿӏ
QKÿmSKiWWUL
Ӈ
n. Tuy nhiên, hiӋ
u quҧcӫ
a viӋ
c ghi nhӟcó chӫÿӏ
nh cịn phөthuӝ
c
vào nhiӅ
u yӃ
u tӕQKѭP
ӭFÿ
ӝtích cӵc tұ
p trung trí tuӋcӫ
a các em, sӭc hҩ
p dү
n cӫ
a nӝ
i
dung bài hӑ
c, yӃ
u tӕtâm lí tình cҧ
m hay hӭng thú cӫ
a các em.
- Nҳ
PU}ÿѭ
ӧFÿL
Ӆ
u này, các nhà giáo dө

FOX{QWuPKѭ
ӟng giúp các em biӃ
t cách
NKiLTXiWKyDYjÿѫQJL
ҧ
n hóa vҩ
Qÿ
Ӆ
JL~SFiFHP[iFÿ
ӏ
nh trӑng tâm bài hӑ
c và nӝ
i dung
quan trӑ
ng cҫ
QKѭ
ӟQJÿ
Ӄ
Qÿ
Ӈcác em dӉhiӇ
u, dӉnҳ
m bҳ
t, dӉghi nhӟvà ÿ
һ
c biӋ
t hình
thành ӣcác em tâm lý hӭng thú và ghi nhӟkiên thӭc mӟLOkXKѫQ
1.1.4 1KkQFiFKKӑFVLQK7LӇXKӑF
1.1.4.1 7tQKFiFK+67L͋XK͕F
6

1ӃXWtQKFiFK
FӫD+67LӇXKӑFPӟLKuQKWKjQK
QrQFKѭDәQÿӏQK

FiFHPPDQJWtQK[~FÿӝQJFDREӝWSKiW
FzQWKҩS7tQKFiFK

QKLrQFҧWLQYjWKtFKEҳWFKѭӟFKjQKYL
1.1.4.2 1KXF̯XQK̵QWKͱF

1KXFҫXQKұQWKӭFFӫD+67LӇX
KӑFÿmSKiWWULӇQNKi
ӯQKXFҫX

KLӇXQKӳQJVӵYұWKLӋQWѭӧQJULrQJOҿ
QKXFҫXSKiWKLӋQQKӳQ

OXұWYjFiFPӕLOLrQKӋTXDQKӋ1KXFҫ

WKjQKQKXFҫXQKұQWKӭFFKRFiFHPWӯVӟ
1.1.4.3 Ĉ̿FÿL͋PÿͥLV͙QJWuQKF̫P

ĈӕLWѭӧQJJk\[~FFҧPFKR+67LӇXKӑ
YұWKLӋQWѭӧ

QrQ[~FFҧPWuQKFҧPFӫDFiFHPJҳQOLӅ

7LӇXKӑFUҩWGӉ[~FFҧP[~FÿӝQJYjNKy

FҧPFӫDFiFHPFzQPӓQJPDQKFKѭDEӅQY
yVӵFKX\ӇQK
xúc nhanh.

1.2 ĈһFÿLӇPYӅGҥ\KӑFWKHRP{KuQKWUѭӡQ
[1]
1.2.1 *LӟLWKLӋXYӅP{KuQKWUѭӡQJKӑFPӟL

0{KuQKWUѭӡQJKӑFPӟL9LӋW1DP91(1
- YLӃWWҳWWKHRWLӃQJ

1DP(VFXHOD1XHYD
OjNLӇXP{KuQKQKjW
KLӋQÿҥL0{KuQK

NӃW TXҧ Yj WKjQK WӵX ÿәL PӟL JLiR GөF F

&RORPELDPӝWFiFKViQJWҥRSKKӧSYӟL

9LӋW1DP0{KuQKQj\ÿmÿѭӧF81,&()81
ӃJLӟL:%


YjÿiQKJLiFDR0{KuQKWUѭӡQJKӑFPӟL

WUѭӡQJKӑFWUX\ӅQWKӕQJYӯDFyVӵÿәLP

WUuQKWjLOLӋXKӑFWұSSKѭѫQJSKiSGҥ\
±KӑFFiFKÿiQKJLiFiF

KWәFKӭFTXҧQ
FѫVӣYұWFKҩWSKөFYөFKRGҥ\
±KӑF

0{KuQKWUѭӡQJ7LӇXKӑFPӟL9LӋW1DP
-91(1WKӵFKLӋ

QJXӗQNLQKSKtFӫD4Xӻ*LiRGөFWRjQFҫX

KLӋQWKtÿLӇPWӯQăPKӑF
- WҥLWUѭӡQJWLӇXKӑF

WKӵFKLӋQWKtÿLӇPYjRQăPKӑF
- ӣWUѭӡQJWLӇX

WURQJFҧQѭӟFQăPKӑF
±P{KuQKÿѭӧFiSGөQJWK

WLӇXKӑFWUrQFҧQѭӟFQk
QJVӕWUѭӡQJWLӇXKӑFWKtÿLӇP

WUѭӡQJWURQJQăPKӑF
- FҧQѭӟFFyJҫQ
7


WUѭӡQJWKӵFKLӋQP{KuQK
WUѭӡQJKӑFPӟL
. 9jQăPP{KuQK

PӟLVӁÿѭӧFWULӇQNKDLGL
ӋQUӝQJKѫQWUrQÿӏDEjQ7SĈ

1.2.2 3KѭѫQJSKiSYjKuQKWKӭFWәFKӭFGҥ\K
[2][6]

1.2.2.1 3K˱˯QJSKiSG̩\K
͕FWKHRP{KuQKWU˱ͥQJK͕FPͣ

0ӑLêWѭӣQJFDQKWkQKD\ÿәLPӟL
PPDH VX\FKRFQJÿӅXOjW

WUuQKWKX\ӃWWUuQKPӝWFiFKiSÿһWFӫDQ

SKiFӫDQJѭӡLKӑF7URQJÿyVӵNKiPSKi

KӑFFyYDLWUzKjQJÿҫX1KӳQJQӛOӵF
FiQKkQFӫD+6OjWUXQJ

GөF1JѭӡLKӑFSKҧLWӵWҥRGӵQJVӵKLӇX

ÿѫQJLҧQOjWLӃSWKXPӝWFiFKWKөÿӝQJW

OpRÿһWYҩQÿӅYjWәFKӭFP{LWUѭӡQ
JVѭSKҥPFKR+6WӵWuPW

WURQJÿyFRLWUӑQJYLӋFKӑFKӧSWiFOjP

éWѭӣQJFKӫÿҥRFӫDP{KuQKWUѭӡQJKӑ

WKӭFNƭQăQJFӫD&KѭѫQJWUuQK7LӇXKӑF
ҩXWU~FOҥLQӝLGXQ

FKR+6WӵKӑF7LӃQWUuQKWӵKӑFFӫD+6
sau:
- +RҥWÿӝQJNKӣLÿӝQJ
- 1KұQELӃWWrQPөFWLrXFӫDEjLKӑF
- +RҥWÿӝQJFѫEҧQ
- ĈiQKJLiWLӃQÿӝ
- +RҥWÿӝQJWKӵFKjQK

- 7ӵÿiQKJLiFyVӵJL~SÿӥFӫDWKҫ\F

- /LrQKӋYjӭQJGөQJNLӃQWKӭFÿmKӑF
ÿuQKYjÿӏDSKѭѫQJ
FӫD+6

1ăPEѭӟFJLҧQJGҥ\WKHRP{KuQKWUѭӡQ

Có nKLӅXNLӇXFҩXWU~FPӝWEjLKӑFWUR

JӗPEDEѭӟF1JKHJLҧQJOtWKX\ӃW
±7KHRG}LEjLWұSPүX
±/X\ӋQWұS7X\

*9VӱGөQJNK{QJKӧSOtVӁGүQÿӃQOӕLG

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