QUARTER I
Week 1
Subject: MATH
Grade Level: 8
Date:
__________________
Day 2
Content Standard
Demonstrates understanding of key concepts of factors of polynomials
Performance Standard
Is able to formulate real-life problems involving factors of polynomials
Competency
Factors completely different types of polynomials (difference of two
squares), M8AL-Ia-b-1
I. OBJECTIVES
Knowledge: 
Skills: 
Attitude: 
II. CONTENT
Tells whether the given polynomials can be factored using sum and
difference of two squares or not.
Factors polynomial using sum and difference of two squares
Appreciates the importance of other people in everyone’s success.
Factoring Sum and Difference of Two Squares
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide
Pages
2. Learner’s
Materials Pages
3. Textbook Pages
4. Additional
Materials
5. Learning
Resources (LR)
portal
B. Other Learning
Resources
Teacher’s Guide (TG) in Mathematics 8, pp. 34 - 35
Learner’s Module (LM) in Math 8, pp. 32 - 33
Moving Ahead With Mathematics, pp. 196 - 197


Marker
Manila paper
IV. PROCEDURES
A. Reviewing or
presenting the new
lesson
ACTIVITY: REMEMBER ME?
The teacher will guide the students to answer the following;
Recall finding the special product in this form:
( x + 8) ( x – 8 ) = x2 – 64
( 2x + 4) ( 2x – 4) = 4x2 – 16
( 3a + 5) ( 3a – 5) = 9a2 – 25
QUESTIONS:
1. What have you observe on the product?
Expected answer: when we multiply two binomials with positive and
negative signs in between the product has two terms.
2. What do you call this product?
Ans. Binomial
3. Is there a relation between the special product and sum and difference
of two squares based on the given above?
Ans. Yes!
Teacher will process the different responses of the learners.
B. Establishing a
purpose for the
lesson
ACTIVITY: FIND MY PRODUCT!
Note: Let the learners identify the pattern.
a. (x + 1) (x – 1)
= x2 – 1
b. (x + y) (x – y)
= x2 – y2
1. What is the product of the binomials?
Ans. x2 – 1 and x2 – y2
2. Did you observe any pattern?
Ans. Yes!
3. If we are going to reverse the process, is it possible to find any
pattern?
Ans. Yes, it is possible.
Teacher must process the responses of the learners.
C. Presenting examples
of the new lesson
ACTIVITY: Let’s EXPLORE!
Examples of Factoring polynomials using sum and difference of two
squares.
1. x2 – 1
= (x + 1) (x – 1)
2. x2 – y2
=
(x + y) (x – y)
3. x2 – 4
= (x + 2)(x – 2)
QUESTIONS:
1. How many factors did you obtain?
Ans. Two factors
2. What are your observations based on the factors?
Expected ans. The factors are the positive square roots of each
term.
3. What is the operation on the first factor? How about the second
factor?
Ans. First factor- positive, second- negative
D. Discussing new
concepts and
practicing new skills
#1
(Teacher must guide every responses of the learner and discuss the topic)
ACTIVITY: COMPARE US!
Take a look of the following:
(x + 1)(x-1) = x2 – 1 = (x+1)(x-1)
1.
2.
3.
4.
5.
E. Discussing new
concepts and
practicing new skills
#2
1. What is being shown on the first arrow?
Ans. Showed the product of two binomials.
2. How about the second arrow?
Ans. Showed the factors of the product
3. What are your observation/s?
Expected ans. The factors are the positive square roots of each
term.
Teacher must guide the different responses of the learner.
ACTIVITY: Tell Me What I am?
Teacher will group the learners into five. Allow the learners find their
own group members but the leader are choosen by the teacher.
Instructions: Using the pattern you have learned, tell whether the
following can be factored using sum and difference of two squares.
F. Developing Mastery
1. x2 + 9
Ans. No
Teacher
must
correct
2. x2 – 9
Ans. Yes
immediately
every
wrong
3. 4x2 – 25
Ans. Yes
responses
of
the
learner.
4. y2 – 16
Ans. Yes
5. 36y2 + 121 Ans. No
ACTIVITY: CREATE YOUR OWN!
Let the learners formulate their own given binomials that can be
factored using sum and difference of two terms. Let them solve on the
board. (Answers may vary)
Teacher will select volunteer from the class.
G. Finding practical
ACITIVITY: GIVE YOUR OWN!
applications of
concepts and skills in Teacher will guide the students to give real situation that relates factoring
daily living
sum and difference of two squares.
Example:
A 5m x 5m landscaping is to be done in one corner of a 20m x
20m garden. Find the area of the field that was not affected by the project.
H. Making
Generalizations and
abstractions about
the lesson
(teacher will guide the learner in leading the correct answer)
Guide Questions for Generalization:



Describe a polynomial that can be factored using sum and difference
of two squares?
Ans. The sign in between is negative.
What have you observed on the first term? How about the second
term?
Ans. First term- Perfect square, second term- perfect square
What can you conclude based on your observation?
Possible answer:
(First term)2 – (Second term)2 =(First term + Second term) (First
term – Second term)
I.
Evaluating learning
Self-check!
Instructions: Factor each of the following polynomials:
J. Additional
Activities for
application or
remediation
1. a2 – 16
2. 9x2 – 4
= (a + 4) (a – 4)
= (3x + 2) (3x – 2)
3. 64c2 – 1
4. 100y2 – 49z2
5. y2 – 81
= (8c + 1) (8c – 1)
= (10y + 7z) (10y – 7z)
= (y + 9) (y – 9)
ACITIVITY: NUMBER PATTERN!
Instructions: Investigate the number pattern by comparing the products.
a. (11)(9) = (10 + 1)(10 – 1) = 100 – 1 =
Ans. 99
b. (5)(3) = (4 + 1)(4 – 1) = 16 – 1 =
Ans. 15
c. (101)(99) = (90 + 5)(90 – 5) = 10000 – 1 = Ans. 9,999
 What is the product?
 How do you think the products are obtained?
 Have you seen any pattern?
 What is the relationship of the product to its factor?
Note: Teacher will guide the students in doing the activity.
V.
VI.
REMARKS
REFLECTION
A. No. of learners who
earned 80% in the
evaluation
B. No. of learners who
require additional
activities for
remediation
C. Did the remedial
lessons work? No. of
learners who have
caught up the lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did these work?
F. What difficulties did I
encounter which my
principal and supervisor
help me solve?
G. What innovation or
localized I used/discover
which I wish to share
with other teacher?
A. ____No. Of learners who earned 80% in the evaluation.
B. ____No. Of learners who require additional activities for remediation.
C. Did the remedial lessons work? ____No. of Learners who have caught
up the lesson.
D. ____No. of learners who continue to require remediation
Stragegies used that work well:
___Group collaboration
___Games
___Powerpoint Presentation
___Answering preliminary activities/exercises
___Discussion
___Case Method
___Think-Pair-Share(TPS)
___Rereading of Paragraphs/Poems/Stories
___Differentiated Instruction
___Role Playing/Drama
___Discovery Method
___Lecture Method
Why?
___Complete Ims
___Availability of Materials
___Pupil’s eagerness to learn
___Group member’s Cooperation in doing their tasks
___Bullying among pupils
___Pupil’s behavior/attitude
___Colorful Ims
___Unavailale Technology
Equipment (AVR/LCD)
___Science/Computer/Internet Lab
ATTACHMENT
ASSIGNMENT
Instructions: Factor each completely. Example is done for you.
Factor:
Solution:
1.
2.
3.
4.
m2 – n2
Is m2 a perfect square? Yes!
m2 = m ˑ m
2
Is n a perfect square? Yes!
-n2 = -n ˑ n
The factors of m2 – n2 are (m + n) and (m – n)
M2 – n2 = (m + n)(m – n)
1. n2 – p2
2. e2 – x2
3. b2 – 49
4. c2 – 25
5. d2 – 16
6. x2 – 36
7. y2 – 81
8. 16c2 – 64
9. 4r2 – s2
10. m – 64m3