chapter3 equations grade 10

GIÁO ÁN TOÁN TIẾNG ANH SONG NGỮ LỚP ) CHƯƠNG 2 Chapter 3. EQUATIONS, SYSTEMS OF EQUATION Preparation date: Teaching date: Period 17. OVERVIEW OF EQUATION I. Objectives: By the end of the lesson, Students will be able to: To realize some concepts as equation with one unknown, condition of an equtions, equation with multiple unknowns and parametric equations To understand the condition of an equations II. Teaching aids: Teacher: lesson plan, text book Student: review about equation that learnt at grade 9 III. Method: Raising and settling problems IV. Procedure: 1 Orginization. 2 Review: Student 1: given an example about equation with one unknown? Student 2: given an example about equation with two unknowns? 3 New lesson: Vocabulary

Chapter 3 EQUATIONS, SYSTEMS OF EQUATION

Preparation date:

Teaching date:

Period 17 OVERVIEW OF EQUATION

I Objectives: By the end of the lesson, Students will be able to:

- To realize some concepts as equation with one unknown, condition of an equtions,equation with multiple unknowns and parametric equations

- To understand the condition of an equations

II Teaching aids:

- Teacher: lesson plan, text book

- Student: review about equation that learnt at grade 9

III Method: Raising and settling problems

IV Procedure:

1- Orginization.

2- Review:

Student 1: given an example about equation with one unknown?

Student 2: given an example about equation with two unknowns?

3- New lesson:

Vocabulary

Equation: Phương trình Right side: vế phải

System of equation: Hệ phương trình Set of roots: tập nghiệm

Root/ solution : Nghiệm Condition: điều kiện

Activity 1 BASIC CONCEPTS

Teacher’s activities Students’ activities

Request Students doing  1

Introduce the concept of Equations with one

unknown

Given ex 1 in order to aks student to

determine Left side and right side

Compte the value of each side when x = 2 ?

Left side : 3.2 – 2 = 4Right side: 2 + 2 = 4

Thus, x = 2 is a root of this equation.Solution :

Teacher’s activities Students’ activities

Given ex 2 and aks student to find the roots

Comment about each side ?

Given ex 3 and aks student to find the roots

Request students convert the roots to

demical

Given notes

3x – 2 = x + 2 <=> 3x – x = 2 + 2 =>2x = 4 <=> x = 2

EX 2: solve the following equation:5x + 1 = 5x – 3

<=> 5x – 5x = –3 – 1 <=> 0x = – 4

No value of x that satisfy this equation

So the equation has no real equationEx3:Solve the following equation:2x = 3 <=> x =

866 , 0 2

3 ≈

Activity 2 CONDITIONS FOR AN EQUATIONS

Teacher’s activities Students’ activities

Request students doing  2

Remark and correct the solution?

Given the concept of condition for an

equation?

In order to find the condition of equation

1 2

The equation:

1 2

1 = −

−

x x

) \ {2}

Activity 3 EQUATION WITH MULTIPLE UNKNOWNS

Teacher’s activities Students’ activities

Introduce about Equation with multiple

unknowns

Given example about Equation with two

unknowns x,y

Compte the value of each side when x =

3)Equation with multiple unknowns:

Exa) 3x + 2y = x2 – 2xy + 8 is an equationwith two unknowns ( x and y )

( x ; y ) = ( 2 ; 1 ) is a root of the equation

2, y=1 ? compare ? conclude?

Given example about Equation with

three unknowns x,y,z

Compte the value of each side when x =

-1c, y=1, z=2 ? compare ? conclude?

b) 4x2 – xy + 2z = 3z2 + 2xz + y2

is an equation with three unknowns ( x ,yand z )

( x ; y ; z ) = (–1 ; 1 ; 2 ) is a root of theequation

Activity 3 CONDITIONS FOR AN EQUATIONS

Teacher’s activities Students’ activities

Introduce about parametric equations

Given example about parametric

equations

Remark

4) parametric equations

Ex : a) 3x + m = 0b) (m – 2 )x2 + 5x – 6 = 0

4- Consolidate

Request student recall the main point of the lesson

5- Homework:

Memorize the lesson

Do the exercise 1,2 text book page 57

Preparation date:

Teaching date:

Period 18 OVERVIEW OF EQUATION

I Objectives: By the end of the lesson, Students will be able to:

- To realize some concepts as Equivalent equations, Resulting equations,

- To understand the Equivalent transformation

- applying the Equivalent transformation to solve equations

II Teaching aids:

- Teacher: lesson plan, text book

- Student: review about equation that learnt at last lesson

III Method: Raising and settling problems

IV Procedure:

1- Orginization.

2- Review:

Student 1: recall the concept of equations with one unknown, given example?

Student 2: definite the condition of an equation ?

3- New lesson:

Vocabulary

Equivalent equations: phương trình tương

Resulting equations: phương trình hệ quả Sign: đổi dấu

Transform: biến đổi PT Extraneous solution: nghiệm ngoại lai Equivalent transformation: biến đổi tương

Changing sides: chuyển vế Polynomial: đa thức

Activity 1 EQUIVALENT AND RESULTING EQUATIONS

Teacher’s activities Students’ activities

Request student doing  4

Given concept in textbook

Nominate student find the set of roots of

each equations, then compare them

Remark

II-Equivalent and resulting equations.

1) Equivalent equations.

a Concept 1 : ( text book)

b Ex : given two equations :3x + 2 = 0 ( 1 )2x + 3

4

= 0 ( 2 )

Given concept in textbook

Nominate student find the set of roots of

each equations, then compare them

Remark

S1 = S2 = { 3

2

−} so ( 1 ) and ( 2) areequivalent

2 resulting equations

a Concept 2 : ( text book)

b Ex : given two equation ( 1 )

( 2 )S1 = { 3}

S2 = { 3;8}

S1 ⊂ S2

so ( 1 ) and ( 2) are resulting equations

Activity 2 EQUIVALENT TRANFORMATION

Teacher’s activities Students’ activities

Introduce the concept of Equivalent

transformation:

Introduce the symbol: equivalent

Request student doing  5

Remark

2) Equivalent transformation:

a- concept : ( text book )b- theorem : ( text book)c- notes ( text book )

* symbol : “⇔

”

Activity 3 RESULTING EQUATIONS

Teacher’s activities Students’ activities

Introduce the concept of resulting

equations

The concept of extraneous solution

Request student doing EX 3

Nominate student go to write down the

142

Compare the value which have found

with the condition

remark

Conditions for the equations : x ≠ ±2

2

12

142

0

x x

So, the equation has a unique solution: x =0

Ex 4:

a the equation has unique solution: x=1

b set of the roots: s={2.3}

4- Consolidate

Request student recall the main point of the lesson

5- Homework:

Memorize the lesson

Do the exercise 3,4 text book page 57

(satisfy)(no satisfy)

Preparation date:

Teaching date:

Period 19: EQUATIONS CONVERTED INTO LINEAR AND QUADRATIC

EQUATIONS

I Objectives: By the end of the lesson, Students will be able to:

- Consolidate the way to solve and argue the linear equations, quadratic equations,

biquadratic equations, redical equations

Solve the linear equations, quadratic equations, biquadratic equations, redical equations

Find the condition of equations, eliminate extraneous solutions that not satisfy the

condition

II Teaching aids:

- Teacher: lesson plan, text book

- Student: review about equation that learnt at grade 9

III Method: Raising and settling problems

IV Procedure:

1- Orginization.

2- Review:

Student 1: recall the way to solve and argue the linear equations

Student 2: state the Vieta’s formulas ?

3- New lesson:

Vocabulary

Converted into: đưa về (dạng) Vieta’s formulas: định lý viet

Co-efficient: hệ số Absolute – value bar: giá trị tuyệt đối True roots with every x: có nghiệm với mọi x Eliminated; loại ( nghiệm)

Solve and justify: giải và biện luận Squaring both sides: bình phương 2 vế Radical equations: phương trình chứa căn Positive/ negative: dương/âm

Activity 1 REVIEW OF LINEAR EQUATIONS

Teacher’s activities Students’ activities

Recall the method to solve and jusify the

linear equations

Applying to the ex 1:

Determine a,b in equations

Remark and consolidate

1 Review of linear equations

Summarized in the table (text book)EX1: solve and jusify the following equation: (1)

Solution: (1)

• (1) becomes ( has no real roots)

• (1)

Activity 2 REVIEW OF QUADRATIC EQUATIONS

Teacher’s activities Students’ activities

Recall the method to solve and jusify the

linear equations

Applying to the ex 2:

Determine a,b and c in equations

Remark and consolidate

2 Review of quadratic equations

Summarized in the table (text book)EX1: solve and jusify the following equation: (1)

Solution: (1)

• (1) becomes ( has no real roots)

• (1)

Activity 3 RADICAL EQUATIONS

( ) 0 ( ) ( ) ( ) ( )

( ) 0 ( ) ( )

Find the codition of that equation

Guiding students to square to sides

Check the result: if x=1, x = 8 was a root

x = 8 is a root of this equation

so, the root of equation: x = 8

4- Consolidate

Request student recall the main point of the lesson

5- Homework:

Memorize the lesson

Do the exercise 7,8 page 62

Preparation date:

Teaching date:

Period 20 : REVIEW

I Objectives: By the end of the lesson, Students will be able to:

- Consolidate the way to solve and argue the linear equations, quadratic equations,

biquadratic equations, redical equations

Solve the linear equations, quadratic equations, biquadratic equations, redical equations

Find the condition of equations, eliminate extraneous solutions that not satisfy the

condition

II Teaching aids:

- Teacher: lesson plan, text book

- Student: review about equation that learnt at last lesson

III Method: Raising and settling problems

IV Procedure:

1- Orginization.

2- Review:

Student 1: recall the way to solve and argue the linear equations

Student 2: state the Vieta’s formulas ?

3- New lesson:

Activity 1 : solve EX 1/ text book page 62

Teacher’s activities Students’ activities

Guiding student to recognize the form

of each equations

Request student to solve equations

Nominate 4 students go to write down

x≠ −4(x2 + 3x + 2) = (2x – 5)(2x + 3)

=> 16x + 23 = 0 <=> x =

23 16

Guiding student to compare the value

of root with condition, then eliminate

x≥

3x – 5 = 9 <=> x =

14 3

d) 2x+ =5 2

condition :

5 2

x≥ −

2x + 5 = 4 <=> x =

1 2

−

Activity 2 : solve EX 7/ text book page 63

Teacher’s activities Students’ activities

Guiding student to recognize form of

each equations

Request student to solve equations

Nominate 4 students go to write down

the solution

Guiding student to compare the value

of root with condition, then eliminate

Remark and summarize

x≥ −

=> 4x2 + 2x + 10 = 9x2 + 6x + 1

=> 5x2 + 4x – 9 = 0 => x1 = 1 ( satisfy )x2 =

9 5

−(not satisfy )thus : x = 1

Activity 3 : solve EX 8/ text book page 63

Teacher’s activities Students’ activities

Guiding student to compute the value

of

Appying the Vieta’s formulas

EX 8: given the equation:

3x2 – 2(m + 1)x + 3m – 5 = 0Determine m such that the equations has a solutionthree times as larger as the other solution Find thesolutions in this case

Solution: let x1, x2 be the roots of equations .applying the vieta’s formulas, we have

2( 1) 3

=> m = 3 ; m = 7

+ if m = 3, then : x1 = 2 ; x2 =

2 3

+ if m = 7, then : x1 = 4 ; x2 =

4 3

Preparation date:

Teaching date:

Period 21: Equations and system of linear equations with multiple unknowns

I Objectives: By the end of the lesson, Students will be able to:

- Review the concept of quadratic equations and systems of to linear equations with two

unknown

- Solve and jusify systems of quadratic equations

- solve systems of three linear equations with three unknown

II Teaching aids:

- Teacher: lesson plan, text book

- Student: review about systems of equation that learnt at last lesson.

III Method: Raising and settling problems

Linear equations: Phương trình bậc nhất Triangular form: Dạng tam giác

System of linear equations with multiple

unknown:hệ phương trình bậc nhất nhiều

ấn

Substitute + into: Thay( giá trị)

Not all equal to 0; Không đồng thời bằng 0 Eliminated: khử ẩn

0rdered pair: cặp số

Activity 1 : Linear equations with two unknowns:

Teacher’s activities Students’ activities

Introduce the concept of liner equations with

two unknowns

Given examples and guiding student

determine the value of a,b,c

Request student doing  1

Nominate students go to write down the

solution

Remark

I- Review of equations and system of linear

equations with two unknowns:

1.Linear equations with two unknowns:

a) concept : ( text book)form : ax + by = cb) Ex :

3x – y = 2 (a = 3 ; b = – 1 ; c = 2) –2x = 6 (a = –2 ; b = 0 ; c = 6) 5y = –2 (a = 0 ; b = 5 ; c = –2)

Activity 2: NOTES

Teacher’s activities Students’ activities

In case a and b equals 0, then what’s the set

of roots of that equation

Determine the set of roots

Read the notesDrawn the line 3x – 2y = 6 in thecoordinate plane Oxy

Activity 3 :SYSTEM OF LINER EQUATIONS WITH TWO UNKNOWNS.

Teacher’s activities Students’ activities

Introduce the concept of systems of liner

equations with two unknowns

Take examples

How many methods two solve systems of

liner equations with two unknowns

Request student applying to solve systems

of liner equations in  3

Nominate students to solve that system of

equation by using exchange method

Nominate students to solve that system of

equation by using adding two side method

remark

Nominate students to solve system of

2 System of linear equations with two unknowns.

a) concept ( text book)

- Request student recall the main point of the lesson.

- Do exercise 1/ text book page 68

5- Homework:

- Memorize the lesson

- Do the exercise 2,3,4/ text book page 68

Preparation date:

Teaching date:

Period 22: Equations and system of linear equations with multiple unknowns

I Objectives: By the end of the lesson, Students will be able to:

- Review the concept of quadratic equations and systems of to linear equations with two

unknown

- Solve systems of liner equations and system of linear equations with two unknown

II Teaching aids:

- Teacher: lesson plan, text book

- Student: review about systems of equation that learnt at last lesson.

III Method: Raising and settling problems

IV Procedure:

1- Orginization.

2- Review:

Student 1: is the pair of number (2;0) a root of equation: 2x-3y=4

Student 2: solve the system equation:

Activity 1 : Linear equations with three unknowns

Teacher’s activities Students’ activities

Introduce the concept of liner equations

with three unknowns

Take some examples and request student to

determine co-efficient a,b,c,d in each

equation

II Linear equations with three unknowns

1 Linear equations with three unknowns

a) concept: (text book)form : ax + by + cz = d

b) example:

x + 2y – 3z = 5( a = 1; b = 2; c = – 3; d = 5)5y + 2z = 0

( a = 0; b = 5; c = 2; d = 0)3z = 15

( a = 0; b = 0; c = 3; d = 15)

Hoạt động 2: systems of linear equations with three unknowns

Teacher’s activities Students’ activities

Introduce the concept of Systems of

linear equations with three unknowns

State the form of a root?

Introduce the system equation in triangle

form

2 Systems of linear equations with three unknowns

a) concept: (textbook)form :

Given some examples about Systems of

linear equations with three unknowns

Activity 3 : gauss’ method.

Teacher’s activities Students’ activities

Guiding student to solve the systems

equations in triangle form Given

example

Nominate students to solve that system

of equation

Remark

Guiding student to solve the systems

equations that not in triangle form Given

4 3 4 3 2

z

z x

y z



 + − = − + − = −

4- Consolidate

- Request student recall the main point of the lesson

5- Homework:

- Memorize the lesson

- Do the exercise 5,6,7/ text book page 68,69