Transcript b 2 - e-CTLT

Model Lesson Plan
(Mathematics)
Class VIII
Topic
Algebraic Expressions and Identities
Sub Topic
Identities
TIME DURATION-45 MINUTES
Prepared & Presented
By
Mr. nagesh.M.S
K.V.Hassan,
Karnataka
1. Objectives:In Algebraic Expressions & Identities
1. The child will know about the identities in algebraic
expression and will be able to represent it geometrically.
2. He will be able to know the relationship between algebra,
geometry and arithmetic.
3. He will also understand the relationship between the
algebraic expressions
4. From the exercises based on pictures and numericals he
will generalise the algebraic expression.
5. He will be able to use it in daily life etc...
2. Teaching Method:1) Art Integrated Learning (AIL)
This process involves learning through
integrating various subjects with different
modules of art such as painting, drawing, clay
modelling, paper-cutting, theatre, dance etc...
2) Interactive method
Presentation based learning, video
modules,etc…
3. Material Required:Pencil, geometry box, notebook, pen
glaze paper, scissors, pasting
material, learning kit, power ppt etc.
4. Previous Knowledge:Children have studied mathematics up to
class 7th and they are aware about
variables, constants and algebraic
expressions.
5. Introduction:Hi Students!
Today in this class of mathematics we
are going to study about use
Identities in algebraic expressions .
• 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.
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
ACTIVITY-1
a2 + ab + ab +b2 = a2 + 2ab + b2
(a + b)2 = a2 + 2ab + b2
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
ACTIVITY-2
(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
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
ACTIVITY -3
a(a-b)+b(a-b)
= > a2-ab+ba-b2
(a + b) (a –b) = a2 – b2
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
