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QUARTER I
Week 1
Subject: MATH
Grade Level: 8
Date: __________________
Day 5
Content Standard
Demonstrates understanding of key concepts of factors of
polynomials (general polynomial)
Performance Standard
Is able to formulate real-life problems involving factors of
polynomials (general polynomial)
Competency
Factors completely different types of polynomials
(general polynomial), M8AL-Ia-b-1
I. OBJECTIVES
Knowledge: 
Skills: 
Attitude: 
II. CONTENT
Illustrates general polynomial
Factors completely general polynomial
Displays cooperation in group work activity
Factoring with common monomial factor
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. 32 – 34
Learner’s Module (LM) in Math 9, pp. 30 – 32
Our World of Math (Textbook) in math 8, pp. 15 - 17,
Moving Ahead With Mathematics 8, pp. 202 - 206
Elementary Algebra, pp. 185 - 187
Cardboard
IV. PROCEDURES
A. Reviewing or
presenting the new
lesson
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ACTIVITY: TILE ONCE MORE!
The teacher will:
a. Group the students into five.
b. Prepare cut outs of cardboard with the following
measure 3x3 (4pcs) and labeled x2 as its area,
3inx1in (8pcs) and labeled x as its area, and 1x1
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(10pcs) labeled 1 to represents its area.
Instructions:
Form a rectangle using the algebra tiles. Use only
tiles that are required in your group.
GROUP 1: 1 big tile, 5 rectangular tiles, and 6 small
square tiles.
GROUP 2: 1 big tile, 6 rectangular tiles, and 8 small
square tiles
GROUP 3: 2 big tiles, 7 rectangular tiles, and 5 small
square tiles.
GROUP 4: 3 big tiles, 7 rectangular tiles, and 4 small
square tiles
GROUP 5: 4 big tiles, and 7 rectangular tiles, and 3 small
tiles.
Questions:
1. How did you find the activity?
(Answers may vary)
2. What is the total area of each figure?
(Answer may vary)
3. Using the sides of the tiles, write all the
dimensions of the rectangles.
(Answer may vary)
B. Establishing a
purpose for the lesson
C. Presenting examples
of the new lesson
Motive Questions:
Based on the previous activity;
1. What is being formed when you combined all the
dimensions of each tile?
Ans. Three
2. What have you observe on the figure formed?
Ans. The figure forms a square.
3. What is the degree of the polynomial formed?
4. Is it possible to find the unknown quantities in
geometric problems?
(Answer may vary)
ACTIVITY: Let’s Analyze.
Note: teacher will guide the learner.
Factor x2 + 7x + 12
Solution
We need to fill in the blanks with two numbers whose
sum is 7 and whose product is12.
(x __ ___)(x ___ __)
This can be done by setting up a table showing possible
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numbers.
Product
1(12) = 12
2(6) = 12
3(4) = 12
D. Discussing new
concepts and
practicing new skills
#1
Sum
1 + 12 = 13
2+6=8
3+4=7
Questions:
1. What are the two numbers?
Ans. 7 and 12
2. How the two terms obtain?
Ans. through finding the product and sum of the
two numbers.
3. What have you observe on the numerical
coefficient of the quadratic term?
Ans. the numerical coefficient of the quadratic
term is1.
4. What about if the numerical coefficient of the
quadratic term is greater than 1?
ACTIVITY: HELP!
John factored 3x2 – 12x – 15 as (x + 1)(x-5). Edwin told
him that her answer is wrong.
Help John find the correct factors.
(Note: teacher will guide the students to find the correct
answer.)
E. Discussing new
concepts and
practicing new skills
#2
Questions:
1. Where did John’s solution go wrong?
Ans. Factors must not be ommitted
2. What is the correct answer?
Ans. 3(x + 1)(x – 5)
3. How factors of general trinomial obtain?
DISCUSSION
The teacher will discuss the definition and other
concepts of factoring perfect general trinomial. (Refer to
Worksheet –Discusssion)
F. Developing Mastery
For developing the mastery of the learner please refer
worksheet-developing mastery
The teacher may elaborate responses of the learners.
G. Finding practical
applications of
concepts and skills in
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Ask each group to give example where the concepts of
factoring applied in real situations.
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daily living
H. Making
Generalizations and
abstractions about
the lesson
I.
Evaluating learning
Note: teacher must lead the student’s concept.
Questions:
1. Illustrates general trinomial?
2. How general trinomial factored?
3. In real life situation, does the concept of
factoring general trinomial can be applied?
ACTIVITY: INDIVIDUAL WORK
Factors each expressions.
1.
2.
3.
4.
5.
J. Additional
Activities for
application or
remediation
V.
REMARKS
VI.
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?
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x2 - 16x + 64
16x2 - 56x + 49
25x2 + 20xy + 4y2
2x2 + 12x + 10
3x2 - 6x - 72.
Possible Answer
= (x – 8) (x – 8)
= (4x -7) (4x-7)
= (5x + 2y) (5x +2y)
= 2(x + 5)(x + 1)
= 3(x + 4) (x – 6)
Note: For additional activities, please refer to attachment
worksheets.
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
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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?
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___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
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ATTACHMENT
DISCUSSION
FACTORING GENERAL TRINOMIAL
To factor general trinomial, transform the expression as a product of two binomials.
Discuss on how to factor general trinomial.
Example: factor 4x2 + 5x – 6
Solutions:
1. Multiply the coefficient of x2 and the constant term.
4(-6) = -24
2. Find the factor pair whose product is the number obtained in step 1, and whose sum
is the coefficient of x, the middle term.
It can easily verified that by listing the factor pairs of -24 and finding the pair
whose sum is 5, the required number pair is 8 and -3 since 8(-3) = -24 and 8 + (-3)
= 5.
3. Rewrite the given expression by replacing the coefficient of x with the number pair
from step 2.
4x2 +5x – 6 becomes 4x2 + 8x – 3x – 6
4. Using the last expression, factor the first two terms and the last two terms. Note
that an expression with common binomial factor is obtained.
4X2 + 8x -3x – 6 = (4x2 + 8x) + (3x – 6)
= 4x(x + 4) - 3(x + 2)
= (x + 2) (4x - 3)
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ATTACHMENT
DEVELOPING MASTERY
TEACHER…
To further develop the understanding of the leaner on this factoring technique,
you can do the bingo game. Write on a strip the polynomials below and place them on
container. Draw the strip and read it in class, give the students time to factor the
polynomials.
1. n2 – n – 20
2. n2 + 5n + 6
3. n2 – 4n – 32
4. n2 – n – 42
5. n2 + 9n + 18
6. n2 + 11n + 18
7. n2 + 17n + 72
8. n2 – 12n + 35
9. n2 – 8n – 48
10. n2 + 14n – 32
11. n2 – 17n + 72
12. n2 + 9n + 8
13. n2 + 10n + 24
14. n2 – 2n – 48
15. n2 + 11n + 24
Note: this can only be used if needed.
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ATTACHMENT
WORKSHEET
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