GIÁO ÁN TOÁN SONG NGỮ ĐẠI SỐ 7 CẢ NĂM - Chuẩn

Preparing date: 26/8/2016
Teaching date: 01/9/2016
Chapter I - RATIONAL NUMBERS. REAL NUMBERS
Period 1. THE SET OF RATIONAL NUMBERS Q

A-Objectives:

- Knowlegde: Students understand concept rational numbers, know how to
perform and understand the relationship between the sets N ⊂ Z ⊂ Q.
- Skill: know how to present rational numbers on a number line.
- Attitude: training thinking skills for students.
B- Preparations:
1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books ( sách tham khảo)...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:
Find the numerator, the denominator of the following fractions(4 sts):

a)

b)

3=

3 ... ... 15

= = =
... 2 3 ...

− 0,5 =

− 1 1 ...
= =
2 ... 4

c)

d)

0=

2

0 0 ...
= =
1 ... 10

5 19 ...
38
=
=
=
7 7 − 7 ...

III/ New lesson:

Activities of students and teacher
T : The equal factions are the different ways
for writting,this number is rational number .

Content
1. Rational numbers :


5
T:Are the 3; -0,5; 0; 2 7 rational numbers ?

- Students must do ?1;? 2.

Eg:
5
a) 3; -0,5; 0; 2 7 are the rational numbers .

Gv: How are the rationship of the sets N, Z,
a
Q?
b) Rational number can be written b
- Students must do exercise 1(7)
- Student must do ?3
T: Similar to integers , we also present the
rational numbers on a number line (T show
the steps)

(a, b ∈ Z ; b ≠ 0 )
c) The set of rational numbers is denoted by Q.
2. Representing rational number on a number

line:

2
5
T :Request S to represent − 3 on a number * Eg: Represent 4 on a number line
line.
0

1 5/4

2

- T : Request S to do exercise 2(work book
Step1: Divide a unit segment into 4 equal parts;,
-P3)
taking each part as a new unit,it is equal to 1/4 old
unit
5
Step2: 4 represented by point M is placed to the
right of point 0,and the distance from M to 0 is 5
new units.

2
Eg 2: Represent − 3 on a number lines.
2
−2
=
3
We have: − 3
-1

-2/3

0


IV. Consolidation:
EX: Represent following numbers on the number lines:

V. Homework:

- EX; 1; 2(textbook);
- EX 1; 2; 3 (workbook).

--------------------------------


Preparing date: 29/8/2016
Teaching date: 7/9/2016

Period 2. THE SET OF RATIONAL NUMBERS Q

A-Objectives:

- Knowlegde: Students understand concept rational numbers, know how to
perform and understand the relationship between the sets N ⊂ Z ⊂ Q.
- Skill: know how to present rational numbers on a number line.
- Attitude: training thinking skills for students.
B- Preparations:
1/ Teacher: Text book, lesson plan, ...

2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:


Represent the following numbers on the number lines:

T: requests 3 Ss go to the board.
T: corrects the results.
III/ New lesson:

Teacher’ and Students’ activities

Contents
3. Comparison of two rational numbers:
1
−2

- T: requests St do ?4
T:How to compare two rational numbers ?
-Eg: request Ss reading text book

a) Eg: compare -0,6 vs
b) The way of comparison

T: How is the negative,positive rational
Write the rational
numbers ?
denominator

number

- T :requests Ss do ?5

IV. Consolidation:
- T: requests st do ex 2(7), st do yourself
- T: requests st do ex (7): + Convert to the same denominator
- Ex: Compare the following rational numbers by the fastest way :

represent the numbers on the number lines:

into

the

same


V.Homework:

- Do ex; 1; 2; 3; 4; 8 (P8-workbook)
−1
1
1

−1
<0
>0⇒
>
1000 5
- Guide : Ex8: a) 5
and 1000
− 181818 − 18
=
313131
31

d)

---------------------------------------------------------


Preparing date: 29/8/2016
Teaching date: 8/9

Period 3. ADDITION AND SUBTRACTION OF RATIONAL NUMBERS

A-Objectives:


- Knowlegde: Students understand the rule of adding and subtracting rational
numbers, and the rule of “ side moving” in the set of rational numbers.
- Skill: add and subtrcact rational numbers quickly and correctly.
- Attitude: have skill applying the rule of “ side moving”.
B- Preparations:

1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:
St 1: present the rule of adding and subtracting fractions which you learnt ingrade
6 ( the same denominators).
St 2: present the rule of adding and subtracting fractions which you learnt
ingrade 6 ( different denominators).
St 3: present the rule of “ side moving”.
III/ New lesson:

Teacher’ and Students’ activities
−3
Exercise: x=- 0,5, y = 4

Calculate :

x + y; x - y

- T comment:
T: Write rational numbers into fractions with
positive denominators ?

Contents

1. Adding and Subtracting Rational Numbers
a) Rule:
a
b
;y=
m
x= m

a b a+b
+ =
m m
m
a b a −b
x− y= − =
m m
m
x+ y=

T: Apply properties of operations in Z
T: requests 2 Sts go to the board.

b)Eg: Calculate


?1
T: requests sts to comment
T: requests Sts to do ?1

T: presents the rule of “ side moving” which Sts
learnt in grade 6 ⇒ grade 7.

− 7 4 − 49 12 − 37
+ =
+
=
8
7
21
21
21
3 − 12 3 − 9
 3
. − 3 −  −  = −3 + =
+ =
4
4
4
4
 4

2. The Rule of “ Side Moving”
a) The Rule (Textbook)
x + y =z
T : Requests Sts to show how to find x.
T: requests 2 Sts go to the board doing ?2

2
3
−x=−
4

Note: 7

⇒ x=z-y
b) Eg. Find x, given that :
−

3
1
+x=
7
3

1 3
→x= +
3 7
16
→x=
21

2 3
+ =x
7 4

?2

c) Note
(Textbook)

IV. Consolidation:
- T requests Sts represent all basic knowledge in the lesson.

- Do exercise 6a,b; 7a; 8
Guide 8d:

9c:


2
6
=−
3
7
6 2
− =x
7 3

2  7   1 3  
− − − + 
3  4   2 8  

−x −

2  7 1 3
− − − −
3  4 2 8 
2 7 1 3
= + + +
3 4 2 8
=

V. Homework:

- Exercises 6c, 2b; 8c,d; 9c,d;
Guide Ex 10: calculate correctly!

Preparing date: 3/9/2016
Teaching date: 10/9

Period 4. MULTIPLICATION AND DIVISION OF RATIONAL NUMBERS

A-Objectives:

- Knowlegde: Students understand the rule of multiplying and dividing
rational numbers, and ratio concept of 2 rational numbers.
- Skill: multiply and divide rational numbers quickly and correctly.
- Attitude: Sts have careful and corect personality.
B- Preparations:
1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:


Calculate:
−3 1
.2

• St 1: a) 4 2
 2
−0, 4 :  − 
 3
• St 2: b)
III/ New lesson:

Teacher’ and Students’ activities

Contents

- Through warm- up, T ask: present how to 1. Multiplying Two Rational Numbers
multiply and divide rational numbers?
a
c
x= ;y=
b
d
Given
a c a.c
x. y = . =
b d b.d

T: Build the formula to calculate x, y.

+ All properties of integer multiplication are *Properties :
satisfy rational number multiplication. T: represent + Commutative: x.y = y.x
properties of rational number multiplication.
+ Associative: (x.y).z = x.(y.z)
+ Distribution properties

x.(y + z) = x.y + x.z
T: Show the formula to calculate x:y?

+ Multiply with 1:

x.1 = x

2. Dividing Two Rational Numbers
T: requests Sts to do ? in group

Given

x=

x: y =

a
c
;y=
b
d

a c a d a.d
: = . =
b d b c b.c

?: Calculate
a)

(y ≠ 0)

 2  35 −7
3,5.  −1  = .
 5  10 5
7 −7 7.( −7) −49
= .
=
=
2 5
2.5
10

T: Give the note.

−5
−5 −1 5
: (−2) = . =
23 2 46
b) 23

T: Compare the difference between ratio of 2 * Note: Textbook
numbers and a fraction.

−5,12
* Eg: The ratio of -5,12 and 10,25 is 10, 25
Or: -5,12:10,25
- The ratio of two rational numbers x and y (y
x
≠ 0) is x:y or y

IV. Consolidation:

- T request Sts to do ex: 11; 12; 13; 14 (P.12)
- Exercise11: Calculate (4 sts go to the board)

−2 21 −2.21 −1.3 −3
. =
=
=
7 8
7.8
1.4
4
−15 24 −15 6 −15 6.( −15) 3.( −3) −9
b)0, 24.
=
.
= .
=
=
=
4
100 4
25 4
25.4
5.2
10
a)

−7 (−2).( −7) 2.7 7
 7
c)(−2).  −  = (−2).
=
=
=
2
12
12 6
 12 
−3 1 (−3).1 (−1).1 −1
 3 
d)−  : 6 = . =
=
=
25 6 25.6
25.2 50
 25 

a)

−5 −5 1
=
.
16
4 4

b)

−5 −5

=
:4
16
4

- Exercise 12:
- Exercise 13 : Calculate (4 sts go to the board)


−38 −7  3 
. . − 
21 4  8 
−38 −7 −3
= −2.
. .
21 4 8
(−2).( −38).(−7).(−3) 2.38.7.3
=
=
21.4.8
21.4.8
1.19.1.1 19
=
=
1.2.4
8

b)(−2).

−3 12  25 

. . − 
4 −5  6 
−3 (−12) (−25)
= .
.
4
5
6
( −3).( −12).( −25)
=
4.5.6
−1.3.5 −15
=
=
1.1.2
2
a)

- Exercise 14: Sts discuss in group
−1
32

x

4

=

−1
8

:
x

-8

:

−1
2

:

=

16

=
=
1
256

V. Homework:
- Lern follow textbook.
- Exercises: 15; 16 (P.13);: 16 (P.5 - Workbook).
Good sts 22; 23 (P.7- Workbook)
Guide Ex5:

4.(- 25) + 10: (- 2) = -100 + (-5) = -105

Guide Ex6:

Applying distribution properties , we have:
 −2 3  4  −1 4  4
+ : + + :

 3 7 5  3 7 7
 −2 3   −1 4   4
= 
+  +  +  :
 3 7   3 7   5

Preparing date: 20/8/2016

x

-2

−1
128


Teaching date:

Period 5. ABSOLUTE VALUE OF RATIONAL NUMBERS.
ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION OF DECIMALS

A-Objectives:

- Knowlegde: Students understand the absolute value concept of the rational

number.
- Skill: know to determine the absolute value concept of the rational number,
and have skill adding, subtracting, multiplying, dividing decimals.
- Attitude: Sts apply operation properties of rational numbers to calculate
reasonably( hợp lý).
B- Preparations:
1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:
Calculate:
2 3 −4
+ .
• St 1: a) 3 4 9
4
3

 − 0, 2  0, 4 − 
5

• St 2: b)  4
III/ New lesson:

Teacher’ and Students’ activities

Contents
1. The Absolute value of a rational numbers
?1


T: present absolute value concept of an integer?
T: requests Sts to do ?1 in group.
T: discuss in group
T: the groups show solutions

Fill in the blank

−4 4
−4
x =
=
7
7
If x = 7 then

T: writes down outline.

x =x

b. If x > 0 then
T: give some examples

x = 3,5 = 3,5

a. If x = 3,5 then

If x = 0 then
If x < 0 then
* We have:

x

x

=0

x = −x
=

x If x > 0

-x If x < 0

T: requests Sts to do ?2
* Comment:

x ≥0
x = −x

T: corrects mistake.

∀x ∈ Q we have :
?2: Find
a) x =

since

x

x ≥x

, given that :

−1
1
 1 1
→ x = − = −−  =
7
7
 7 7
−

1
<0
7

b)

T: give a decimal.

1
1
 1
c ) x = −3 → x = −3 = −  −3 

5
5
 5
1
1
= 3 vi − 3 < 0
5
5


d )x = 0 → x = 0 = 0
T: we can do the same as integers.

T: requests Sts to do in group ?3

2. Adding, subtracting, multiplying, dividing
decimals
- Decimals is written as decimal fractions
without denominator.
* Eg:
a) (-1,13) + (-0,264)
= -(

−1,13 + −0, 264

)

= -(1,13+0,64) = -1,394
b) (-0,408):(-0,34)
=+(

−0, 408 : −0,34

)

= (0,408:0,34) = 1,2
?3: Calculate:
a) -3,116 + 0,263 = -(
T: presents the result

−3,16 − 0, 263

)

= -(3,116- 0,263) = -2,853
b) (-3,7).(-2,16) = +(

−3, 7 . −2,16

)

= 3,7.2,16 = 7,992
IV. Consolidation:
Requests Sts to do exercises: 18; 19; 20 (P. 15)
Exercise 18: 4 Sts go to the board
a) -5,17 - 0,469 = -(5,17+0,469)
= -5,693
b) -2,05 + 1,73 = -(2,05 - 1,73)
= -0,32

c) (-5,17).(-3,1) = +(5,17.3,1) = 16,027
d) (-9,18): 4,25 = -(9,18:4,25) =-2,16


Exercise 19: Sts discuss in group.
Exercise 20: Sts discuss in group:
a) 6,3 + (-3,7) + 2,4+(-0,3)
= (6,3+ 2,4) - (3,7+ 0,3)
= 8,7 - 4 = 4,7

=

[ 2,9 + (−2,9) ] + [ (−4, 2) + 3, 7 ] + 3, 7

= 0 + 0 + 3,7 =3,7

b) (-4,9) + 5,5 + 4,9 + (-5,5)
=

c) 2,9 + 3,7 +(-4,2) + (-2,9) + 4,2

[ (−4,9) + 4,9] + [ 5,5 + (−5,5)]

=0+0=0

d) (-6,5).2,8 + 2,8.(-3,5)
= 2,8.

[ (−6,5) + (−3,5)]

= 2,8 . (-10) = - 28

V. Homework:
- Exercise 1- P.15 Textbook, Exercises 25; 27; 28 – P.7;8 Workbook
- Good Sts do more exercise 32; 33 P. 8 Workbook
Guide exercise 32: Find max value of A, given that: A = 0,5 since

x − 3,5 ≥
x − 3,5
0 hence A max where
min → x = 3,5

MaxA =0,5 where x = 3,5

x − 3,5


Preparing date: 10/9/2016
Teaching date: 16/9


Period 6. PRACTICE

A-Objectives:

- Knowlegde: Confirm the absolute value concept of the rational number.
- Skill: training skill compare rational numbers, compute expression value,
find x.
- Attitude: develop students' thinking in the form of finding the maximum and
minimum value of expression.

B- Preparations:
1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:
* St 1: - Show the formula calculating the absolute value of the rational number x.
- Do exercise 24a,b-P7, workbook.
* St 2: - Do exercise 27a,c-P8, workbook.
III/ Practice:

Teacher’ and Students’ activities

T: asks St to read request of exercise 28

Contents

Exercise 28 (P8 - workbook )
a) A= (3,1- 2,5)- (-2,5+ 3,1)

T: show the rules out brackets ( quy tắc phá
ngoặc)?

= 3,1- 2,5+ 2,5- 3,1 = 0
c) C= -(251.3+ 281)+ 3.251- (1-281)

=-251.3- 281+251.3- 1+ 281


T: asks St to read request of exercise 29

T: If

a = 1,5

find a.

= -251.3+ 251.3- 281+ 281-1 = -1

Exercise 29 (P8 - workbook )

a = 1,5 → a = ±5
T: How many cases are there in the problem?

* If a= 1,5; b= -0,5
M= 1,5+ 2.1,5. (-0,75)+ 0,75
3
3  3 3
+ 2. .  −  + = 0
2  4 4
= 2

* If a= -1,5; b= -0,75
T: asks Sts do continue N, P at home.

M= -1,5+ 2.(-1,75).(-0,75)+0,75

3
 3  3 3
= − + 2.  − .  −  +
2
 2  4 4
3
1
= =1
2
2

T: requests Sts to discuss in group

Exercise 24 (P.16- Textbook )

a ) ( −2, 5.0, 38.0, 4 ) −[ 0,125.3,15.( −8) ]
= ( −2, 5.0, 4).0, 38 −[ ( −8.0,125).3,15]
= −0, 38 − (−3,15)

T: comments, note the order you do the
operations ( lưu ý thứ tự thực hiện phép tính)

= −0, 38 + 3,15
= 2, 77


T: Which numbers whose absolute values are Exercise 25 (P.16- Textbook )
2,3
x − 1, 7 = 2,3
a)

→ How many cases?
→ x- 1.7 = 2,3 → x= 4
1
T: Which numbers that minus 3 equals 0?

x- 1,7 = -2,3

x=- 0,6

3
1
b) x + − =
0
4
3
3
1
→+
x
=
4
3

T: guiding how to use calculator for Sts

→

x+

3 1

=
4 3

x+

3
1
=−
4
3

→

x=

5
12

x=−

13
12

IV. Consolidation:
- Sts repeat rules out brackets, absolute values, additing, subtracting, multiplying, dividing
decimals.
V. Homework:
- Eercises 28 (b,d); 30;31 (a,c); 33; 34 P.8; 9 workbook.
- Review power of numbers.
.

Preparing date: 16/9/2016
Teaching date: 23/9

Period 7. POWER OF A RATIONAL NUMBER

A-Objectives:

- Knowlegde: Sts understand power with a natural number exponent concept
of the rational number x, and rules of calculating product, quotient of 2
power with the same base, rule of the power of power.
- Skill: having skill apply rules to calculate.
- Attitude: training careful and correct personality for Sts, scientific
resentations (trinh bay khoa hoc)
B- Preparations:
1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:
Calculate:
3 3  3 2
a) D = −  +  −  − + 
5 4  4 5

* St 1:

* St 2:

b) F = −3,1. ( 3 − 5, 7 )

III/ New lesson:

Teacher’ and Students’ activities

Contents

T: Give the n-th power definition of natural 1. Power with a natural number exponent
number a ( nêu đn lũy thua bậc n của số tự
nhiên a)?


T: Similar to power of natural numbers,
power of rational numbers are defined as
follows:

a
T: when x is written as x= b
n

a
 
then xn =  b  ,how can be computed ?.

*Convention: x1= x; x0 = 1.

- The n-th power of rational number is xn.

x is called the base , n is the exponent.
a
x = 
b

n

n

=

a a
a an
. ............... = n
b 4b 4 2 4 43b b
1
n.thuaso

n

an
a
=
 
bn
b

?1 Calculate:
T: asks Sts to do ?1

2

2
9
 −3  (−3)
=
=
 
2
4
16
 4 
3

3
−8
 −2  (−2)
=
=
 
3
5
125
 5 

(-0,5)2 = (-0,5).(-0,5) = 0,25
(-0,5)3 = (-0,5).(-0,5).(-0,5)

= -0,125
T: a ∈ N; m,n ∈ N

(9,7)0 = 1

And m > n , compute:

2. Multiplication and division of two powers with
the same base:

am. an = ?

Where x ∈ Q ; m,n ∈ N; x ≠ 0

am: an = ?

We have: xm. xn = xm+n
xm: xn = xm-n (m ≥ n)

We also have formulas:

?2 Calculate:

xm. xn = xm+n

a) (-3)2.(-3)3 = (-3)2+3 = (-3)5

xm: xn = xm-n

b) (-0,25)5 : (-0,25)3= (-0,25)5-3

= (-0,25)2

T: asks Sts to do?2

3. The power of power:
Exercise 49- P10 workbook

?3

( ) = ( 2 ) .( 2 ) ( 2 ) = 2
3

a) a 2

Sts disscus in group

2

2

2

6

5

  −1  2   − 1  2  − 1  2  − 1  2
b)     =   .   .   .

 2    2   2   2 

T: asks Sts to do?3

T: Base on above result, find the relationship
between 2; 3 and 6;

 −1 
. 
 2 

2

 −1 
. 
 2 

2

10

 −1 
= 
 2 

2; 5 and 10

We obtain: (xm)n = xm.n
?4
T: asks Sts to do?4

2

T: give a true or false problem form

a )23.2 4 = (23 ) 4

  −3  3   3  6
a )    =  − 
 4    4 
2

4
8
b) ( 0,1)  = ( 0,1)



* Comment: xm.xn ≠ (xm)n

b)52.53 = (52 )3
?So xm.xn = (xm)n or not?

IV. Consolidation:
Exercise 27;(P.19 - Textbook)
Exercise 27: Asks 4 Sts go to the board
4

(−1) 4 1
 −1 

=
 
34 81
 3 
3

3

 1   −9  −729
 −2  =   =
64
 4  4 

(−0, 2) 2 = ( −0, 2).(−0, 2) = 0, 04
(−5,3)0 = 1


- The power of the negative rational number :
+ If the exponent is even number then the its result is positive number.
+ If the exponent is odd number then the its result is negative number.
V. Homework:
- Learn by heart definition .
- Exercises 29; 30; 31 (P.19 - Textbook)
- Exercises 39; 40; 42; 43 (P.9 - Workbook).
-------------------------------------------Preparing date: 24/9/2016
Teaching date: 30/9

Period 8. POWER OF A RATIONAL NUMBER( continue)

A-Objectives:

- Knowlegde: Sts understand 2 rules : the power of product and the power
of quotient.
- Skill: having skill apply rules to calculate.
- Attitude: training careful and correct personality for Sts, scientific
resentations (trinh bay khoa hoc)
B- Preparations:
1/ Teacher: Text book, lesson plan, ...
2/ Students: Textbooks, notebooks, reference books...

C- Procedures:
I/ Class organization:

- Greeting
- Checking attendance

II/ Warm-up:
Calculate: