Square of Binomial

STAGE 3 Learning Plan No. : 1 Date : June 21 – 22, 2011 I. OBJECT JECTIV IVE ES:

At the end of this lesson/activity the students should be able to: 1. explore the process of finding the square of binomials 2. search for patterns in finding the square of binomials 3. find the special product of the square of binomials

II. SUBJEC SUBJECT T MATTER MATTER::

Lesson/Focus :

Skills

:

The Square of Binomial

Squaring a term Using special product in squaring a binomial

Essential Question

: Ho How w are are patt patter erns ns use used d to sol solve ve rea reall-li life fe problems involving the product of two binomials?

Essential Understanding : Patterns in in finding the pr product of  of  two binomials facilitates the solutions of real-life problems.

Materials :

Activity Sheets

III. PROCEDURES:

A. Prelimina Preliminary ry Activi Activities ties 1. Checking of cleanliness of classroom

2. Checkin Checking g of prope properr wearing wearing of of uniform uniform 3. Check Checking ing of of attend attendanc ance e 4. Anno Announ unce ceme ment nts s

B. Explore

Provide learners opportunities to recall mathematics concepts related to the rules in finding special product of the square of binomial

 Activity 1 Determine the square of each of the following.

 ______1.

5

 ______11. 3b

 ______2.

-8

 ______12.

-4p

 ______3.

13

 ______13.

3xy

 ______4.

-16

 ______14.

-6ab

 ______5.

0.7

 ______15.

3x

 ______6.

4.3

 ______16.

-4t

 ______7.

-2.6

 ______17.

5x2

 ______8.  ______9.

5.12 _-4_ 

 ______18.

10xy2

5

 ______19. _-3a_ 

9

 ______20. _-2t_ 

 ______10. _-2_ 

8 3

 Activity 2 Determine the indicated product in each of the following. Then answer the questions that follow. 1)

(x +3)(x +3)

2)

(x – 2)(x – 2)

3)

(3x +1)(3x + 1)

4)

(2x + 3)2

5)

(3x – 2)2

How did you find each product?

What mathematics concepts or principles did you apply to come up with each product?

How did you apply these concepts or principles in finding each product?

What observations can you make about the product?

Did you find any pattern in determining each product? Describe the pattern, if there is any.

Is there an easy way of finding each product without using the distributive property method or the FOIL method? Explain your answer.

C. Firm – up

:

How can we obtain the product of similar binomials?

Example: Multiply: (x + 5)2

(x + 5)2

=

(x + 5) (x + 5) F

O

I

=

x2 + 5x + 5x + 25

=

x2 + 10x + 25

L

Notice the patterns that appear in the example.

Here x is the first term and 5 is the second term

(x + 5)2

=

x2 + 10x + 25

x2 is the square of the first term of  the binomial (x)2 = x2

10x is twice the product of the terms 2(5x) = 10x

25 is the square of the second term (5)2 = 25

 This patterns leads to the formula for the square of binomial:

(a + b)2

=

(a + b) (a + b)

=

a2 + 2ab + b2

 To square a binomial, square the first term, get twice the product of the terms and finally square the second term.

 Activity 3 Find each indicated product then answer the questions that follow. 1)

(x + 9)(x + 9)

2)

(2x – 2)(2x – 2)

3)

(3x +y)(3x + y)

4)

(3m + 1)2

5)

(4b + a)2

How do you find each product now?

Is it easier than using the FOIL method? Why?

IV.ASSIGNMENT:

Use special product in multiplying the following. 1)

(x - 4)(x - 4)

2)

(m + 7)(m + 7)

3)

(x + y)(x + y)

4)

(m + 6)2

5)

(b + 3a)2

Learning Plan No. : 2 Date : June 23, 2011 I. OBJECTIVES:

At the end of this lesson/activity the students should be able to: 1. find the special product of the square of binomials 2. use special product in squaring binomial

II. SUBJECT MATTER:

Lesson/Focus :

The Square of Binomial

Skills

:

Materials :

Using special product in squaring a binomial

Activity Sheets

III. PROCEDURES:

A. Preliminary Activities

1. Checking of cleanliness of classroom 2. Checking of proper wearing of uniform 3. Checking of attendance 4. Announcements

B. Deepen

Provide learners opportunities to recall mathematics concepts related to the rules in finding special product

 Activity 4  Answer each of the following.

1. In finding the square of binomial, how do you find each term of the product? 2. How are the terms of the binomial being squared related to the middle term of the product? 3. In squaring a binomial, how many terms does the product have? 4. Michael says that (x + 4)(x + 4) ≠ (x + 4)2. Do you agree with

him? Explain your answer.

 Activity 5 (Worksheet in Square of Binomial) Determine the indicated product. 1) (y +8)(y +8)

2) (m – 7)(m – 7) 3) (5x +2)(5x + 2) 4) (x + 3y)2 5) (2x – y)2

IV.ASSIGNMENT:

 Answer each of the following 1)

Express your understanding on the Square of Binomial by giving 2 examples.

2)

Make an advance study on the Product of the Sum and Difference of Two  Terms.