Daily Lesson Log of M8AL-Ia-b-1 (Week 1 Day 2)
School
Grade level
Grade 8
Teacher
Learning
Area
Mathematics
Teaching Date and
Time
Quarter
First
I. OBJECTIVES
A. Content Standards
Objectives must be met over the week and connected to the curriculum standards. To
meet the objectives, necessary procedure must be followed and needed, additional
lessons, exercises and remedial activities may be done for developing content
knowledge and competencies. These are assessed using Formative Assessment
Strategies. Valuing objectives support the learning of content and competencies and
enable children to find significance and joy in learning the lessons. Weekly objectives
shall be derived from the curriculum guides.
The learners demonstrate understanding of key concepts of the factors of polynomials
B. Performance
Standards
C. Learning
Competencies/
Objectives
The learners formulate real-life problems involving factors and solve these with
utmost accuracy using a variety of strategies.
Learning Competency: Factors completely different types of polynomials (polynomials
with common monomial factor, difference of two squares, sum and difference of two
cubes, perfect square trinomials, and general trinomials). M8AL-Ia-b-1
Learning Objectives:
1. Identify the expression that can be factored
2. Determine the process of factoring polynomials with difference of two squares
3. Show appreciation in factoring
4. Find factors of a given polynomials
II. CONTENT
Factoring polynomials with difference of two squares
III. LEARNING
RESOURCES
A. References
Curriculum guide, Teacher’s guide, Learner’s module
1. Teacher's Guide
Module 1: Pages 34-35
2. Learner's Module
Page 32-33
3. Textbook Pages
4. Additional
Materials From
Learning Resources
(LR) Portal
B. Other Learning
Resources
IV. PROCEDURES
These steps should be done across the week. Spread out the activities appropriately so
that students will learn well. Always be guided by demonstration of learning by the
A. Review previous
lesson Or presenting
the new lesson
students which you can infer from formative assessment activities. Sustain learning
systematically by providing students with multiple ways to learn new things, practice
the learning, questions their learning processes, and draw conclusions about what they
learned in relation to their life experiences and previous knowledge. Indicate the time
allotment for each step.
The teacher lets the students recall the definition of factoring and the first type of
factoring introduced to them.
Possible response:
Factoring is the reverse of multiplication. The first type was factoring by greatest
common monomial factor
He/she then ask the students if the given polynomial below has a common monomial
factor and let them also describe the given polynomial
1.
abc + abd
2. 24m2-12m
3. X2-y2
4. 25-b2
Possible response:
numbers 1 and 2 have a common monomial factor
numbers 3 and 4 don’t have any common monomial factor
The given polynomials are binomials
terms in numbers 3 and 4 are perfect squares
numbers 3 and 4 are polynomial with difference of two squares
B. Establishing a
purpose for the lesson
C. Presenting
examples/ instances
of the new lesson
The teacher lets the students realize that factoring by common monomial factor is not
applicable to all polynomials but it is necessary that greatest common monomial
factor should be use first before applying any type of factoring.
The teacher lets the students , in group of two do the Activity 5 on page 32 of the
Learner’s Module and answer the following questions:
1. How do you think the products are obtained?
2. What are the different techniques used to solve for the products?
3. What is the relationship of the product to its factor?
4. Have you seen any pattern in this activity?
Possible responses :
1.
D. Discussing new
concepts and
practicing new skills
#1
E. Discussing new
concepts and
the product are obtain by making the given numbers into sum and difference
of binomials
2. by multiplying the sum and difference of binomials
3. the factors of difference of two squares are sum and difference of binomials.
4. Students give varied answers
The teacher discusses with students using the given number pattern of activity 5 to see
the relationship of factors to product. He/she may bring back the students to
multiplying sum and difference of binomials in special product to see how factors may
be obtained. Students should realize that factors of difference of two squares are sum
and difference of binomials.
The teacher illustrate now on how to obtain the factors of polynomials with difference
of two squares. He/she can use the examples found in learner’s module at page 33.
practicing new skills
#2
F. Developing mastery
( leads to formative
assessment)
The teacher lets the students match polynomials of column A to its corresponding
factors in column B.
1.
2.
3.
4.
5.
Column A
X2-16
9-m2
X2-4
81-m2
x2- 9
Column B
a. (9+m)(9-m)
b. (x-3)(x+3)
c. (x+4)(x-4)
d. (3-m)(3+m)
e. (x+2)(x-2)
Answer key:
1.
2.
3.
4.
5.
G. Finding practical
applications of
concepts and skills in
daily living
H. Making
generalizations and
abstractions about the
lesson
X2-16
9-m2
X2-4
81-m2
x2- 9
------- c. (x+4)(x-4)
------- d. (3-m)(3+m)
--------- e. (x+2)(x-2)
-------- a. (9+m)(9-m)
-------- b. (x-3)(x+3)
The teacher summarizes the concept of factoring polynomials with difference of two
squares by asking the following questions:
1. What are the factors of polynomials with difference of two squares?
2. How to find the factors of a given polynomial with difference of two squares?
Answers shall be drawn from the students.
Possible responses:
1. It is the sum and difference of binomials
2. Get the square roots of the two squares, then write the product of the sum
and difference of the square roots
Remember:
The factored form of a polynomial that is a difference of two squares is the sum and
difference of the square roots of the first and last terms.
I. Evaluating Learning
The teacher lets the students answer individually the formative assessment.
Find the factors of the given polynomials.
1. c2-25
2. w4-1
3. 36-h6
4. k4-100
5. 1-r10
Answer key:
1. (c-5)(c+5)
2. (w2-1) (w2+1)
3. (6-h3) (6+h3)
4. (k2-10) (k2+10)
5. (1-r5) (1+r5)
J. Additional
Activities or
Remediation
V. REMARKS
VI. REFLECTION
A. No. Of learners
who earned 80% of
the evaluation
B. No. Of learners who
require additional
activities for
remediation who
scored below 80%
C. Did the remedial
lesson work? No. Of
learners who have
caught up with the
lesson
D. No. Of learners
who continue to
require remwdiation
E. Which of my
teaching strategies
worked well? Why did
these work?
F. What difficulties did
I encounter which my
principal or supervisor
Can help me solve?
G. What innovation or
localized materials did
I use / discover which
I wish to share with
other teachers
The teacher may let the students answer Activity 7 on page 34 of the Learner’s
Module to enhance more their skills in factoring polynomials with difference of two
squares.
Prepared by:
ABIGAIL Y. MUÑEZ
Labogon NHS