This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, procedures, and reflections for lessons on factoring polynomials. Specifically, it covers factoring polynomials with common monomial factors, the difference of two squares, the sum and difference of two cubes, perfect square trinomials, and general trinomials. The procedures describe reviewing previous lessons, presenting new material with examples, discussing concepts, practicing skills, developing mastery through activities, and assessing learning. Reflections include the number of students who achieved mastery and require remediation on the topics.
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DLLWeek1_3.docx
1. DAILY LESSON
LOG
School Grade Level Grade 8
Teacher Learning Area Mathematics
Week/Teaching Dates and Time 1 Quarter First Quarter
SESSION 1 SESSION 2 SESSION 3 SESSION 4
I.OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and
inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions.
B. Performance
Standards
The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and
inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems
accurately using a variety of strategies.
C. Learning
Competencies
Orient the learners about the
subject.
Set standards and class rules.
To diagnose students' prior
knowledge on 1st quarter
coverage
-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
Subtask
-Factor polynomials with common
monomial factor
-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
Sub-task
-Factor polynomials with
difference of two squares
II. CONTENT Orientation Conduct Diagnostic Test PATTERNS & ALGEBRA
III. LEARNING
RESOURCES
A. References
1.Teacher’s Guide
Pages
32-33 34-35
2.Learner’s Materials
Pages
27-31 32-33
3.Textbook Pages Elem. Algebra pp.202-203 Elem. Algebra pp.208-209
2. 4.Additional Materials
from Learning
Resource(LR) Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing
previous lesson or
presenting the new
lesson
-Provide information on
classroom policies to create a
welcoming environment that
builds a sense of community
among the class.
-Be aware of the grading system
so that they will know how much
are they going to put forth in
order to pass.
Give the test:
Check the test
Have an item
analysis
Compute the MPS
Let the students review the GCF,
multiplication rule and quotient
rule as a prerequisite for factoring
polynomials.
Review the students with the
previous lesson through board
work.
B. Establishing a
purpose for the
lesson
The students will identify common
things that are present in the
three pictures. Then, they will
answer the guided questions.
Refer to Activity 4 page 30 of
Math LM.
LOCALIZATION:
Use at least 5 pictures of school
activities and let the students spot
the things common to the
pictures.
Investigate the number pattern by
comparing the products then write
your generalizations afterwards.
NUMBER PATTERN:
a. (11)(9) = (10 + 1)(10 – 1) = 100
– 1 =
b. (5)(3) = (4 + 1)(4 – 1) = 16 – 1
=
c. (101)(99) = (100 + 1)(100 – 1)
= 10000 – 1 =
d. (95)(85) = (90 + 5)(90 – 5) =
8100 – 25 =
e. (n – 5)(n + 5) =
This activity will help the students
understand the concepts of
difference of two squares and
how this pattern is used to solve
numerical expressions.
C. Presenting
examples/instances
of the new lesson
The next activity will give an idea
to the students on how factors are
associated with products. They
will match the factors in column A
with the products in column B to
Based on the activity, how do you
think products are obtained?
What are the different techniques
used to solve for the products?
What is the relationship of the
3. decode the secret message.
Refer to Activity 3 page 29 of
Math LM.
product to its factor? Have you
seen any pattern in this activity?
D. Discussing new
concepts and
practicing new skills
#1
The teacher will ask the students
with the following questions based
on the previous activity.
1. What are your observations on
the expression in column A?
Compare them with those in
column B.
2. Do you see any pattern?
3. Are the two expressions
related?
4. Why is it important to know the
reverse process of multiplication?
For you to have a better
understanding about this lesson,
observe how the expressions
below are factored and observe
the relationships of the term with
each other.
4𝑥2
– 36 = (2x + 6)(2x – 6)
𝑥2
– 𝑦2
= (x + y)(x – y)
Ask students to generate rule in
factoring difference of two
squares.
E. Discussing new
concepts and
practicing new skills
#2
The teacher will start the
discussion by defining factoring
first.
Then introduce the first type of
factoring which is factoring the
greatest common monomial factor
and give more examples. Based
on the examples that are
presented, ask the students when
to use and not to use this type of
factoring.
Oral Recitation:
1. What is the first term of each
polynomial?
2. What is the last term of each
polynomial?
3. What is the middle sign of the
polynomial?
4. How was the polynomial
factored?
5. What pattern is seen in the
factors of the difference of two
terms?
6. Can all expressions be factored
using difference of two squares?
Why or why not?
7. When can you factor
expressions using difference of
two squares
F. Developing
mastery(Leads to
Formative
Have a group contest. Board work
Call a student who can write as
many pairs of difference of two
4. Assessment) square as they can create.
(Note: Teachers must see to it
that students must form difference
of two squares).
G. Finding practical
applications of
concepts and skills in
daily living
Appreciate the importance of
knowing how to classify things
with common characteristics.
Apply concept of difference of two
squares in real life.
H. Making
Generalizations and
abstractions about
the lesson
How factoring Greatest Common
Monomial Factor is being done?
How factoring difference of two
squares is being done?
I. Evaluating learning Answer the following
LOTS:
Find the greatest common factor
of the following pair of
expressions.
1.) 8 & 12
2.) 3x & 6x
3.) 2xy4 & 4x2y2
MOTS:
Factor the following expressions.
1.) 4x2 – 12x
2.) 9m2 – 15m3
3.) 4a2 + 12a + 8
HOTS:
State the steps of factoring
Greatest Common Monomial
Factor.
Answer:
LOTS:
1. 4
2. 3x
3. 2xy2
MOTS:
1. 4x(x-3)
2. 3m2
(3-5m)
Answer the following
LOTS:
`Give 3 pairs of perfect squares.
MOTS:
Factor each completely.
1. 1 − 16𝑥8
2. 25𝑦2-9
3. 𝑎4
− 625𝑏8
HOTS:
State the steps of factoring the
difference of two squares.
Answer:
LOTS:
Answers’ Vary
MOTS:
1. (1-4x4)(1+4x4)
2. (5y-3)(5y+3)
3. (a2+25b4)(a-5b)(a-5b)
HOTS:
Answers’ Vary
5. 3. 4(a2
+3a+2)
HOTS: Answers’ Vary
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 who scored
below 80%.
C. Did the remedial lessons
work? No. of learners who
have caught up with 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 or supervisor can
help me solve?
G. What innovation or
localized materials did I
use/discover which Iwish to
share with other teachers?
6. DAILY LESSON
LOG
School Grade Level Grade 8
Teacher Learning Area Mathematics
Week/Teaching Dates and Time 2 Quarter First Quarter
SESSION 1 SESSION 2 SESSION 3 SESSION 4
I.OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and
inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions.
B. Performance
Standards
The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and
inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems
accurately using a variety of strategies.
C. Learning
Competencies
-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
-Factor polynomials with sum
and difference of two cubes.
Independence Day
-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
-Factor polynomials in a form of
perfect square trinomial.
Factor completely different types of
polynomials-general quadratic
trinomials using special formulas,
grouping and other techniques.
M8AL-Ia-b-1
II. CONTENT PATTERNS & ALGEBRA
III. LEARNING
RESOURCES
A. References
1.Teacher’s Guide
Pages
pp.35-36 pp.39-40 pp.41-43
2.Learner’s Materials
Pages
pp.34-35 pp. 36-38 pp.39-41
7. 3.Textbook Pages Elem. Algebra pp.209-210 Elem. Algebra 206-207 Elem. Algebra 204-205
4.Additional Materials
from Learning
Resource(LR) Portal
B. Other Learning
Resources
Student-made bingo cards
IV. PROCEDURES
A. Reviewing
previous lesson or
presenting the new
lesson
Students will give examples of
difference of two squares as
many as they can.
Review the students with the
previous lesson through board
work.
How to factor perfect square
trinomial?
B. Establishing a
purpose for the
lesson
Do you know how to factor the
sum or difference of two cubes?
What you need to just to get a
perfect score in a quiz?
Before you go to supermarket, did
you list first the items you want to
buy?
C. Presenting
examples/instances
of the new lesson
You have learned from the
previous activity how factoring
the difference of two squares is
done and what expression is
considered as the difference of
two squares. We are
now ready to find
the factors of the
Sum or difference of two cubes.
To answer this question, find
the indicated product and
observe what pattern is evident.
a. (a + b)(𝑎2
– ab + 𝑏2
)
b. (a – b)(𝑎2
+ ab + 𝑏2
)
Let the students perform activity
10 on page 37.
How to factor quadratic trinomial
with numerical coefficient of the
leading term 1?
D. Discussing new
concepts and
practicing new skills
#1
What are the resulting products?
How are the terms of the
products related to the terms of
the factors? What if the process
was reversed and you were
Discuss the rules on how to factor
perfect square trinomials.
Discuss how to find factors of a
general quadratic trinomial with
numerical coefficient of the
leading term 1 by listing possible
factors. Cite examples.
8. asked to find the factors of the
products? How are you going to
get the factor? Do you see any
common pattern?
E. Discussing new
concepts and
practicing new skills
#2
Show and discuss to the
students the step by step
process on factoring the sum
and difference of two cubes.
Give more examples for the
deeper understanding of the
students.
Discuss using the examples on
page 37-38
F. Developing
mastery(Leads to
Formative
Assessment)
Give group seat work. Board work
Call a student who can supply the
missing terms to make a true
statement:
1. m2 + 12m +36
=(m+__)2
2. 16d2-24d +9
=(4d-__)2
3. a2b2 -6abc +9c2
=(a2b__ ____)2
4. 9n2+30nd+25d2
=(___ __5d)2
5. 49g2 –84g+36
=(___ __ ___)2
Factor Bingo Game(By Pair)
G. Finding practical
applications of
concepts and skills in
daily living
What makes the task easier to
do?
H. Making
Generalizations and
abstractions about
the lesson
How factoring sum and
difference of two cubes is being
done?
How factoring perfect square
trinomial being done?
Give emphasis to students that
factoring quadratic trinomial is
easy to do if you list down first the
possible factor.
9. I. Evaluating learning Answer the following:
LOTS:
Find the cube root of the
following:
1.) 64
2.) X3
3.) 27y3
MOTS:
Factor each completely.
1. 64𝑐3
− 𝑑3
2. 8𝑒3
𝑓6
+ 125𝑔3
HOTS:
Your teacher asked Kenth to
factor 8x3-27 and his answer is
2x-3. Is he correct? Explain your
answer.
Answer:
LOTS:
1. 4
2. X
3. 3y2
MOTS:
1. (4c-d)(16c2+4cd+d2)
2. (2ef2+5g)(4e2f4-
10ef2g+25g)
Answer the following:
LOTS:
Determine a number that must be
added to make each of the
following a perfect square
trinomial.
1. X2+2x+_____
2. T2+20t+_____
3. R2-16r+_____
MOTS:
Factor the following.
1. x2+12x+36
2. a2+6a+9
3. 4n2+12nx+9x2
HOTS:
How do you describe a perfect
square trinomial?
Answer the following:
LOTS:
Give the factors of the following
numbers:
1. 4
2. 10
3. 15
MOTS:
1. x2+9x+20
2. a2+8a+15
3. y2-3y-10
HOTS:
How to factor quadratic trinomial
whose leading coefficient is 1?
J. Additional activities
for application or
remediation
V.REMARKS
VI.REFLECTION
A. No. of learners
who earned 80% in
the evaluation
10. B. No. of learners
who require
additional activities
for remediation who
scored below 80%.
C. Did the remedial
lessons work? No. of
learners who have
caught up with 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 or
supervisor can help
me solve?
G. What innovation
or localized materials
did I use/discover
which I wish to share
with other teachers?
11. DAILY LESSON
LOG
School Grade Level Grade 8
Teacher Learning Area Mathematics
Week/Teaching Dates and Time 3 Quarter First Quarter
SESSION 1 SESSION 2 SESSION 3 SESSION 4
I.OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and
inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions.
B. Performance
Standards
The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and
inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems
accurately using a variety of strategies.
C. Learning
Competencies
Factor completely different types
of polynomials-general quadratic
trinomials using special formulas,
grouping and other techniques.
M8AL-Ia-b-1
Factor completely different types
of polynomials-general quadratic
trinomials using special formulas,
grouping and other techniques.
M8AL-Ia-b-1
Solve problems involving
factors of polynomials.
M8AL-Ib-2
Students will follow the
standard operating
procedure in taking test.
Students will be able to
answer the summative test.
II. CONTENT PATTERNS & ALGEBRA
III. LEARNING
RESOURCES
A. References
1.Teacher’s Guide
Pages
pp.44-46 pp.46-47
2.Learner’s Materials
Pages
pp.43-44 pp.44-45
3.Textbook Pages Elem. Algebra pp. 210-211 Elem. Algebra pp. 212-216
4.Additional Materials
from Learning
Resource(LR) Portal
B. Other Learning
Resources
IV. PROCEDURES
12. A. Reviewing
previous lesson or
presenting the new
lesson
How to factor quadratic trinomial
with numerical coefficient of the
leading term 1?
Have a drill.
How to factor quadratic trinomial
using Grouping or AC Method?
How to factor polynomials consist
of more than 3 terms?
Recall the standard
operating procedure in
taking summative test
Distribute the test
papers.
Start the test.
Collect the test papers
Let them check their
answers
B. Establishing a
purpose for the
lesson
Do you know how to group
things?
What is your ideal group? Do you believe that every problem
has a solution?
C. Presenting
examples/instances
of the new lesson
How to factor quadratic trinomial
with numerical coefficient of the
leading term greater than 1?Try
this: 2x2-5x-3.
How to factor polynomials by
grouping technique?
Pose one problem. Then, let the
students solve it. Do this in a
group of 5.
D. Discussing new
concepts and
practicing new skills
#1
Discuss how to find factors of a
general quadratic trinomial with
numerical coefficient of the
leading term not 1by grouping or
AC Method. Cite examples.
State the steps of factoring
polynomials by grouping
technique. Give more examples
State to the students the steps of
solving problems involving factors
of polynomials. Cite examples.
E. Discussing new
concepts and
practicing new skills
#2
Teach them by group on how to
factor polynomials by grouping
techniques
F. Developing
mastery(Leads to
Formative
Assessment)
Group the students into 5 and
let them perform activity 13 on
page 44.
Famous Four Words(By Group)
With your group mates, factor the
following expressions by
grouping and write a four - letter
word using the variable of the
factors to reveal the 5 most
frequently used four - letter word.
1. 4wt + 2wh + 6it + 3ih
2. 15te – 12he + 10ty – 8hy
3. hv + av + he + ae
4. 10ti – 8ts – 15hi + 12hs
5. 88fo + 16ro – 99fm – 18rm
Have board work.
13. G. Finding practical
applications of
concepts and skills in
daily living
How important is proper
grouping in real life?
Apply concept of grouping
techniques in real life by
classifying things found in school.
Apply the process of solving
problems involving polynomials by
formulating real life problem
involving factors of polynomials.
H. Making
Generalizations and
abstractions about
the lesson
One of the methods of finding
the factor of quadratic trinomial
with numerical coefficient of the
leading term not 1 is through
grouping or AC method.
Extend learnings in factoring
through grouping techniques.
You have to group terms with
common factors.
Some problems encountered in
Algebra need to be expressed in
terms of polynomials before they
can be solved. Then, apply the
different factoring techniques for
finding correct solutions.
I. Evaluating learning Answer the following:
LOTS:
Arrange the steps of grouping or
AC method in factoring
quadratic trinomial whose
leading coefficient is greater
than 1.
___Group terms with common
factors.
___Factor the groups using
greatest common monomial
factor.
___Find the product of the
leading term and the last term.
___Find the factors of the
product of the leading term and
the last term
____Rewrite the trinomial as
four-term expressions by
replacing the middle term by the
sum factor.
____Factor out the common
binomial and write the remaining
factor as the sum or difference
of binomial.
MOTS:
Answer the following:
LOTS:
Group the terms with common
factors.
1. 7sm+35om+9se+45oe
2. 42wa+54wt+56ha+72ht
3. 72he+16we+27hn+6wh
MOTS:
Factor by grouping:
1. 3x2-2x+6x-4
2. 3ab+5b-3ac-5c
3. 5m-15+3m2-9m
HOTS:
Answer the following:
LOTS:
MOTS:
Solve the problem:
The square of a positive integer is
98 less than twice the square of
the next consecutive positive
integer. What are the integers?
HOTS:
Formulate 1 real life problem
involving factors of polynomials.
14. Factor the following:
1.) 2a2+a-15
2.) 3x2-8x-3
3.) 4x2+10x+6
HOTS:
Formulate 1 quadratic trinomial
whose leading coefficient is
greater than 1, then find the
factors.
J. Additional activities
for application or
remediation
JOURNAL WRITING:
Instruction: Reflect on the
activities you have done in this
lesson by completing the following
statements. Write your answers
on your journal notebook.
• I learned that I...
• I was surprised that I...
• I noticed that I...
• I discovered that I...
• I was pleased that I...
V.REMARKS
VI.REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
additional activities
for remediation who
scored below 80%.
C. Did the remedial
lessons work? No. of
learners who have
caught up with the
15. 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 or
supervisor can help
me solve?
G. What innovation
or localized materials
did I use/discover
which I wish to share
with other teachers?