1. Objectives:-In Algebraic Expressions & Identities1. 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 methodPresentation based learning, video modules,etc…
3. Material Required:-Pencil, geometry box, notebook, pen glaze paper, scissors, pastingmaterial, 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 werepresent numbers 2, 3, 4 with some other names like a, b, c these are called variables. Variables andconstants 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. Whenwe 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 youWhy 4, 9, and 16 are called squared numbers?
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 = X2And 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 towork out arithmetic problemsIDENTITY TAKEN:-(a + b)2 = a2 + 2ab + b2Example: (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 – b2a2 = (a – b)2 +2 ab – b2=> (a - b)2 = a2 - 2ab + b2
You can also apply the algebraic identity to work out arithmetic problemsIDENTITY TAKEN:-(a - b)2 = a2 - 2ab + b2Example: (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 arithmeticproblemsIDENTITY TAKEN:-(a + b) (a –b) = a2 – b2Example: (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+2For a=2We can show LHS=RHS,(2+1)(2+2)=22 + 3(2)+212=12Let us now take a=-3Then also,(-3+1)(-3+2)=(-3)2+3(-3)+22=2Such 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 ofthe 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 squaresand products of algebraic expressions. They also alloweasy alternative methods to calculate products ofnumbers
8. Now try these questions:-1) Using the identity (1) find (i) (2x + 3y)2 (ii) 10322) Using the identity (11) find (i) (4p - 3q)2 (ii) (4.9)23) 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 = 4geometrically.2. Using identity find the value of thearithmetic problem (104)2.3. Find the product of 104 X 96 by using thealgebraic identity.