Discussion Lesson Plan (Mathematics)

Class VIII

Topic

Algebraic Expressions and Identities

TIME DURATION 30-35 MINUTES

Presented By :-

AMIT KUMARROLL NO 36

SOHAN LAL DAV B.ED COLLEGE

1. Objectives:-

Knowledge:-The students will be able to know the identities in algebraic expression and will be able to represent it geometrically.

Understanding:-The student will be able to know the relationship between algebra, geometry and arithmetic's. The students will also be able to understand the relationship between the algebraic expressions.

Application:-The students will be able to generalise the algebraic expressions from the exercises based on pictures and numerical.

Skill:-The students will be able to use algebraic expressions in daily life .

2. Instructional aids to be used

1) General Teaching Aids – Pointer, chalk , duster, black board

2) Specific Teaching Aids - Power point presentation on Algebraic expressions and identities

3. Material Required for activity:-

Pencil, geometry box, notebook, pen glaze paper, scissors, pasting material

etc.

4. Previous Knowledge:-

Children have studied mathematics up to class 7th and they are aware about variables, constants and algebraic

expressions.

P.K TESTING

• Before we start I want to ask you one Interesting question. Have you ever learnt algebra, when you were very small kid?

• Your Simple flat answer is NO.

• But I say yes, you have learnt algebra when you were a small baby and your mother started calling you chikki, duggu. Do you know from where these names came?

Duggu! Where r u?

• Since you were unnamed that time and your mother wanted to interact with you, she needed some variable to address you and she started calling you by these names. You learnt that it was your name and started giving response to mother with smile.

Similarly in mathematics when we represent numbers 2, 3, 4 with some

other names like a, b, c these are called variables. Variables and

constants form a term and terms are added to form algebraic

expressions.

Your name is a variable which you learnt when you were kid.

Announcement of the topic-

Hi Students!

Today in this class of mathematics we are going to study about use

Identities in algebraic expressions .

6. Content:-

• Let us see how we can represent different numbers and algebraic expressions geometrically.

This is what we call geometrical expression of

algebraic expression. When we use variables to represent certain values we deal with

algebra.

So I must assume that you know algebra.

Let us perform one activity:

But before that one more question for you

Why 4, 9, and 16 are called squared numbers?

Because we represent them with squares

We can also represent squared algebraic terms with squares.

X2 is the area of a square with side length X.

Area of a square of side X = X2

And area of a square of side (a + b)= (a + b)2

a2 + ab + ab +b2 = a2 + 2ab + b2

(a + b)2 = a2 + 2ab + b2

ACTIVITY-1

Did U know? You can apply the algebraic identity to work out arithmetic problems

IDENTITY TAKEN:-

(a + b)2 = a2 + 2ab + b2

Example: (17)2 = (10 + 7 )2

= 102 + 2(10) (7) + 72

= 100 + 140 + 49= 289

(a – b)2 + ab + (a – b)b = (a – b)2 + ab + ab – b2

a2 = (a – b)2 +2 ab – b2

=> (a - b)2 = a2 - 2ab + b2

ACTIVITY-2

You can also apply the algebraic identity to work out arithmetic problems

IDENTITY TAKEN:-

(a - b)2 = a2 - 2ab + b2

Example: (17)2 = (20 - 3 )2

= 202 - 2(20) (3) + 32

= 400 - 120 + 9= 289

(a + b) (a-b) = a(a-b)+b(a-b)= a2-ab+ba-b2

(a + b) (a –b) = a2 – b2

ACTIVITY -3

You can also apply the algebraic identity to work out arithmetic problems

IDENTITY TAKEN:-

(a + b) (a –b) = a2 – b2

Example: (17 X 23) = (20 - 3) (20 +3)= 202 - 32

= 400 – 9= 391

What is an identity?

Consider the equality, (a+1)(a+2)=a2 +3a+2

For a=2

We can show LHS=RHS,

(2+1)(2+2)=22 + 3(2)+2

12=12

Let us now take a=-3

Then also,

(-3+1)(-3+2)=(-3)2+3(-3)+2

2=2

Such an equality, true for every value of variable in it, is called IDENTITY

7. What have we learnt?

An identity is equality, which is true for all values of the variables in the equality.The following are the standard identities:(a + b)2 = a2 + 2ab + b2 -------------------------(1)(a - b)2 = a2 - 2ab + b2 -------------------------(11)(a + b) (a –b) = a2 – b2 --------------------- (111)The above identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers

8. Now try these questions:-

1) Using the identity (1) find (i) (2x + 3y)2

(ii) 1032

2) Using the identity (11) find(i) (4p - 3q)2

(ii) (4.9)2

3) Using the identity (111) find(i) (3/2 m + 2/3 n) (3/2 m – 2/3 n)(ii) 9832 - 172

(iii) 194 X 206

9. Try at Home:-

1. Represent the identity (a + b)2 = a2 + 2ab + b2 by taking the value of a =3 and b = 4 geometrically.2. Using identity find the value of the arithmetic problem (104)2.

3. Find the product of 104 X 96 by using the algebraic identity.

Thank you