School: BIRBIRA HIGH SCHOOL
Teacher: AGOSTO C. BUNSAY
Teaching Dates and AUGUST 22-26, 2022
Time:
GRADES 1 to 12
DAILY LESSON LOG
MONDAY
I.
OBJECTIVES
A.
Content Standards
B.
Performance Standards
C.
Learning Competencies/
Objectives
Write the LC code for each
II. CONTENT
III. LEARNING RESOURCES
A.
TUESDAY
Grade Level: 8
Learning Area: MATHEMATICS
Quarter: 1ST QUARTER
WEDNESDAY
THURSDAY
1. Identify the expression that can be factored
2. Determine the process of factoring using greatest common monomial factor
3. Show appreciation in factoring
4. Find factors of a given polynomials
The learners demonstrate understanding of key concepts of factors of polynomials
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
Factoring polynomials with greatest
common monomial factor
Curriculum guide, Teacher’s guide,
Learner’s module
Curriculum guide, Teacher’s guide,
Learner’s module
Factoring polynomials with greatest
common monomial factor
Curriculum guide, Teacher’s guide,
Learner’s module
Factoring polynomials with greatest
common monomial factor
Curriculum guide, Teacher’s guide,
Learner’s module
Module 1: Pages 29-33
Module 1: Pages 29-38
Module 1: Pages 29-38
Pages 27-31
Pages 27-31
Pages 27-31
Let the students recall the definition of
factoring and the first type of factoring
introduced to them.
Review previous lesson by letting the
students answer the exercises.
1. What are the two types of
factoring being discussed and
introduced to you?
2. What type of factoring can be
applied if you are given 49-n2?
What are the factors?
Factoring polynomials with greatest
common monomial factor
References
1. Teacher’s Guide pages
2. Learner’s Materials pages
3. Textbook pages
4. Additional Materials from
Learning Resource (LR)
portal
B. Other Learning Resources
Pictures of Filipino celebrities
IV. PROCEDURES
A.
Reviewing previous lesson or
presenting the new lesson
FRIDAY
Getting to know each other and Subject
Orientation
The teacher lets the students recall
about finding the greatest common
factor (GCF) of the given numbers using
flash cards.
1. 3 , 6
2. 4, 6
3. 24, 36
4. 14, 28, 35
Possible response:
Factoring is the reverse of multiplication.
The first type was factoring by greatest
common monomial factor
Factoring polynomials with greatest
common monomial factor
Curriculum guide, Teacher’s guide,
Learner’s module
5. 9, 12, 24
Possible responses:
1. 3
2. 2
3. 12
4. 7
5. 3
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
3. X2-y2
2. 24m2-12m
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
3.
How about if you are given
36t2-8t? What are the factors?
Possible responses:
1. Factoring polynomial with
greatest common monomial
factor and difference of two
squares
2. Difference of two squares,
(7+n)(7-n)
3. Factoring with greatest
common monomial factor,
4t(9t-2)
Then the teacher now ask the student :
If given this kind of polynomial a3+b3, can
we find the factor using greatest common
monomial factor or difference of two
squares? Why?
Possible responses:
No, because the given has no GCMF and
is not a difference of two squares. Also, It
is a sum two cubes.
B.
Establishing a purpose for the
lesson
C.
Presenting
examples/instances of the
new lesson
D.
Discussing new concepts and
practicing new skills #1
* State that after studying polynomials in
grade 7 which are special products, that
is, polynomials which are the results of
multiplying polynomials of particular
forms, we can now take a look at how to
determine the factors of these special
products.
* Ask the student to recall what they have
learned before about factors.
* State that factoring is the process of
obtaining the factors of a product. It is the
reverse of the process of finding the
product.
*Show pictures of celebrities performing
Superhero roles.
Start the study of factoring with a
discussion of Greatest Common
Monomial Factor. The activity presented
will be a springboard in the discussion of
factoring by greatest common monomial
factor. He/she tells the students when to
Let 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?
Discusse and illustrates thoroughly the
steps in finding the factors of a polynomial
with sum and difference of two cubes.
Give examples:
1. 8-d3
2. k6+125
use and not to use this type of factoring.
Emphasize that this type of factoring
should be use first before applying any
type of factoring.
2.
3.
4.
What are the different
techniques used to solve for the
products?
What is the relationship of the
product to its factor?
Have you seen any pattern in
this activity?
Answer key:
1. (2-d)(4+2d+d2)
(k2+5) (k4-5k2+25)
Possible responses :
1.
E.
Discussing new concepts and
practicing new skills #2
F.
Developing mastery (leads to
Formative Assessment 3)
G.
Finding practical applications
of concepts and skills in daily
living
H.
Making generalizations and
abstractions about the lesson
Illustrate now on how to obtain the
greatest common monomial factor of a
given polynomial. He/she can use the
examples found in learner’s module at
page 31.
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.
Students give varied answers
Discuss 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.
Summarize 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?
Summarize the steps in finding the factors
of a given polynomial with sum and
difference of two cubes through questions
like:
A. What are the steps in finding the
factor of polynomial with sum of two
cubes?
B. What are the steps in finding the
factor of polynomial with difference
of two cubes?
Answers shall be drawn from the
students.
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
Possible response:
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.
A. Steps in finding the factor of
polynomial with sum of two cubes
Step 1: Find the cube root of the first and
last terms.
Step 2: Write their sum as the first factor
Step 3: For the second factor, get the
trinomial factor by:
a. Squaring the first term of the first factor;
b. Subtracting the product of the first and
second terms of the first factor.
c. Squaring the last term of the first factor
Step 4: write them in factored form
B. Steps in finding the factor of
polynomial with difference of two cubes
Step 1: Find the cube root of the first and
last terms.
Step 2: Write their difference as
the first factor
Step 3: For the second factor, get the
trinomial factor by:
a. Squaring the first term of the first factor;
b. Adding the product of the first and
second terms of the first factor.
c. Squaring the last term of the first factor
Step 4: write them in factored form
I.
Evaluating learning
Find the factors of the given polynomials
1. 7r4h5+14rh6
2. 32m3-24mn5-64m2n
3. 120a2b4c7+50abc10
Answer key:
1. 7rh5(r3+2h)
2. 8m(4m2-3n5-8mn)
10abc7(12ab3+5c3)
J.
Additional
activities
for
application or remediation
V. REMARKS
Let the students answer individually the
formative assessment.
Find the factors of the given polynomials.
1. c3-d3
2. w6+1
3. 216-h9
Answer key:
1.
2.
3.
(c-d)(c2+cd+d2)
(w2+1)(w4-w2+1)
(6-h3)(36+6h3+h6)
VI. REFLECTION
A.
B.
C.
D.
E.
F.
G.
No. of learners who earned
80% in the evaluation
No. of learners who require
additional activities for
remediation
Did the remedial lessons
work? No. of learners who
have caught up with the
lesson
No. of learners who continue
to require remediation
Which of my teaching
strategies worked well? Why
did these work?
What difficulties did I
encounter which my principal
or supervisor can help me
solve?
What innovation or localized
materials did I use/discover
which I wish to share with
other teachers?