Detailed Lesson Plan in Mathematics for Grade 8

By Jomar I. Gregorio

I. Learning Objectives

At the end of the lesson, 75% of the students should be able to:

1. Identify the method in simplifying rational expression;

2. Simplify rational expression; and

3. Develop cooperation in group activity.

II. Subject matter

A. Topic: Simplifying Rational Expression
B. References:
Book:
Crisostomo, R.M. et al..(2013). Our World of Math 8. Davao City, Philippines:
Vibal Publishing House, Inc.
C. Materials: manila paper, pentel pen, scatch tape, envelope, printed materials (for
motivation), cartolina, chalk, board, coupon bond.
D. NCBTS: Curriculum
E. Value Focus: Coopeation
F. Strategy: Deductive Method

III. Methodology
A. Preparatory Activities
Teacher’s Activity Student’s Activity
a. Greetings

Good morning class!

Good morning sir!
b.Prayer

Before we start our lesson, let’s have first a prayer.

Our Father, who art in heaven
Hallowed be thy name,
Thy kingdom come,
Thy will be done,
On earth as it is in heaven.
Give us this day our daily bread, and forgive us
our sins,
As we forgive those who sins against us
And lead us not into temptation
But deliver us from evil. Amen.
You may now take your seats.

c. Checking of attendance
d. Checking of Assignment
e. Review of the past lesson

In the previous chapter, we discussed how to factor

polynomials. What are the kinds of factoring that we
discussed? Give one.
Factoring polynomials with common factor
Correct. What else?
Factoring quadratic trinomial
Right. Another one.
Factoring difference of two squares
Perfect. More answer.
Factoring the sum & difference of two cubes
Amazing. And the last one.
Factoring by Grouping

Very Good! Your skills in factoring polynomials are

very much needed in our lesson for today. Suppose
you are asked to factor 4x3 + 2x. What is your answer? 2x(2x2 +1)

How did you come up to that answer?

Using factoring polynomials with common
factor.
Correct. How about if you are asked to factor x2 + 3x +
2?
(x+1)(x+2)
What process did you use?
Using factoring quadratic trinomial.
Your right. How about x6 – 1.
(x – 1)(x+1)( x2 + x + 1)( x2 - x +1)
How did you arrive to that answer?
We first use the process of factoring the
difference of two squares and then use factoring
the sum & difference of two cubes.
Nice one. Last one, what is the factor of 2x2y+ 4x3y +
8xz2 + 16x2z2
(2x)(xy + 4z2)(1 + 2x)
Please explain your answer.
We first use the process of factoring polynomials
with common factor & then use factoring by
grouping.
Amazing. Any question?
None sir.

f. Motivation
Teacher’s Activity Student’s Activity
Today, we will discuss a new lesson but before that
let’s first play a game.
The first 2 rows in the left will be the group 1 & the
last 2 rows will be the group 2 while the first two rows
in the right will be the group 3 & the last 2 rows will be
the group. Here are your guidelines.
Guidelines of the Game
1. An envelope will be given to each group.
2. Each envelope contains polynomials which
you need to factor.
3. After you factor each polynomial, you need to
decode a hidden message in the envelope
through the aid of decoder.
4. The first group to decode the message
correctly will be the winner.
5. Creating noise is prohibited.

Polynomials to be factored
1. 4x2 + 2x - 2
2. 9x2 + 81x
3. 81x2 - 16
4. 27x3 + 8
5. x3 - 1
 6. 3xy + 2x + 6zy +4z
7. 4x2 - 1
8. 8x3 + 125
9. x6 – 8

Decoder(Factored form of polynomials)

SIM-(4x-2)(x+1)
PLI-(9x)(x+9)
FYING-(9x-4)(9x+4)
RA-(3x+2)(9x2-6x+4)
TION-(x-1)(x2+x+1)
AL-(x+2z)(3y+2)
EX-(2x-1)(2x+1)
PRES-(2x+5)(4x2-10x+25)
SION-(x2-2)(x4+2x2+4)

Note: It is jumbled in the envelope.

Hidden Message
SIM PLI__ FYING___
4x2 + 2x - 2 9x2 + 81x 81x2 - 16

RA TION AL_______
27x3 + 8 x3 - 1 3xy + 2x + 6zy +4z

EX PRES SION
4x2 – 1 8x3 + 125 x6 – 8

And the winner is Group __.

Let’s give them Very Good applause.
1 2 3(Clap) 1 2 3(Stamp) Very Good 1 2 3(Clap) 1 2 3(Stamp) Very Good

And for those group who also tried their best to solve.
Let’s give them Nice Try applause.
1 2 3(Clap) 1 2 3(Stamp) Nice Try. 1 2 3(Clap) 1 2 3(Stamp) Nice Try.

B. Presentation of the lesson

Teacher’s Activity Student’s Activity
Based on our activity, what do you think will be our
lesson for today?
Simplifying Rational Expression.
Correct.

C. Lesson Proper
Teacher’s Activity Student’s Activity
What is a rational expression?
It is a ratio of two polynomials. It can be written
in the form p/q where q≠0.(Gerlene’s class)
Very Good. Give me an example of rational expression.
(2x2)/(4y), (a)/(b), (27x)/(9y)
Perfect. Today we are going to discuss the steps in
simplifying rational expression.

Suppose you are ask to simplify the rational expression

(3x2 +6x)/(3x2). Our first step is?
Factor the numerator.
What is the factor of the numerator?
 (3)(x)(x + 2)
How about our second step?
Factor the denominator.
What is the factor of our denominator?
(3)(x)(x)
& our last step?
Cross-out the common factor of numerator &
denominator.
What will remain if we cross-out the common factor of
numerator and denominator?
[(3)(x)(x+2)]/[(3)(x)(x)]
=(x+2)/x
Our simplified form of the rational expression is?
(x+2)/x
Do you know now how to simplify a rational
expression?
Yes sir.
Very Good. Let’s have another example.
Simplify (x2 + 2x + 1)/(x2 – 1).
First we need to factor the numerator.
x2 + 2x + 1
Factor = ( x+1)(x+1)
Process: Factoring Quadratic Trinomial(Riza)
Next we need to factor the denominator.
x2 – 1
Factor = (x+1)(x-1)
Process: Factoring Difference of Two
Square(Niño)
And last cross-out the common factor of numerator
and denominator.
[( x+1)(x+1)]/[ (x+1)(x-1)]
What is the simplified form of the rational expression
now?
(x+1)/(x-1)
Very Good. Any question?
None sir.
If none, try to solve this in your seat.

1.(x3-x)/(x2+2x+1)
=[(x)(x2-1)]/[(x+1)(x+1)]
=[(x)(x-1)(x+1)]/[(x+1)(x+1)]
=[(x)(x-1)]/(x+1) or (x2-x)/(x+1)
2.(x3+3x2+3x+9)/(x3+27)
=[(x+3)(x2+3)]/[(x+3)(x2-3x+9)]
=(x2+3)/(x2-3x+9)
3. (x +1)/(x2 -1)
=(x + 1)/(x + 1)(x – 1)
= 1/(x-1)

D. Application
Teacher’s Activity Student’s Activity
Why do you think we need to learn simplifying rational
expression?
To easily solve problems solving involving
rational expression.
Right. For example we have this problem.
The width of a rectangle is 6x + 8, and the length of
the rectangle is 12x + 16. Determine the ratio of the
width to the perimeter. First, what is asked?
What is the ratio of the width to the perimeter?
How do we right a number in ratio form?
p/q; where p is the width and q is the perimeter.
What is our width?
6x + 8
And our perimeter?
36x + 48
How did you get the perimeter?
Using the formula 2L + 2W
Right. What is our ratio now?
(6x + 8)/(36x +48)
If simplified what is our new ratio?
1/6
Perfect.

E. Generalization

Teacher’s Activity Student’s Activity

Let us now review what we have discussed.
What is our first step?
Factor the numerator.
Next one?
Factor the denominator.
And the last one?
Cross-out the common factor of numerator &
denominator.
Any clarification?
None sir.

IV. Evaluation
Teacher’s Activity Student’s Activity
Direction: On a ½ piece of paper (crosswise), simplify the
following rational expressions.
1.(2a2-2ab)/(8a3) 1.(2a2-2ab)/(8a3)
=[(2a)(a-b)]/[(2a)(4a2)
=(a-b)/( 4a2)

2.(x2-16)/(x3+64) 2.(x2-16)/(x3+64)
=[(x-4)(x+4)]/[(x +4)(x2 -4x+16)]
=(x-4)/( x2 -4x+16)

3.(x3-125)/(ax-5a+3bx-15b) 3.(x3-125)/(ax-5a+3bx-15b)
=[(x-5)(x2 + 5x + 25)]/[(x-5)(a+3b)]
=( x2 + 5x + 25)/(a+3b)

4.(2x2-2)/(x3+1) 4.(2x2-2)/(x3+1)
=[(2)(x-1)(x+1)]/(x+1)(x2 -x +1)]
=[(2)(x-1)]/( x2 -x +1) or (2x-2)/( x2 -x +1)

5.(ax3+8a)/(x2-4) 5.(ax3+8a)/(x2-4)
=[(a)(x + 2)(x2 -2x+4)]/[(x-2)(x+2)]
=[(a)( x2 -2x+4)/(x-2) or (ax2 -2ax+4a)/(x-2)
 V. Assignment
Teacher’s Activity Student’s Activity
Direction: On a ½ piece of paper (crosswise), simplify the
following rational expression.
1. (2x3-2)/(2x2-2) 1. (2x3-2)/(2x2-2)
=[(2)(x-1)(x2 + x +1)]/[(2)(x-1)(x+1)]
= (x2 + x +1)/(x+1)

2.(9xy+3x+6y+2)/(6xy+4y) 2.(9xy+3x+6y+2)/(6xy+4y)
= [(3x +2)(3y +1)]/[(2y)(3x + 2)]
=(3y + 1)/(2y)

3. (27y3-x3)/(9y2-x2) 3. (27y3-x3)/(9y2-x2)
=[(3y – x)(9y2 + 3xy + x2)]/[(3y – x)(3y + x)]
=(9y2 + 3xy + x2)/(3y + x)

4. (6x2 + 16x + 8)/(4x2 – 16) 4. (6x2 + 16x + 8)/(4x2 – 16)

=[(2x + 4)(3x + 2)]/[(2x – 4)(2x + 4)]
=(3x + 2)/(2x – 4)

5. (2x2 + 7xy + 3y2)/(8x3 + y3) 5. (2x2 + 7xy + 3y2)/(8x3 + y3)

=[(2x + y)(x + 3y)]/[(2x + y)(4x2 + 2xy + y2)]
=(x + 3y)/( 4x2 + 2xy + y2)