School
Teacher
Teaching Dates and Time
MATALAM HIGH SCHOOL
ELLEN JOY TORMIS
September 19-20, 2022
Grade Level
Learning Area
Quarter
8
MATHEMATICS
FIRST
I. OBJECTIVES
The Learners demonstrate an understanding of:
A.
Content Standards
 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.
The Learners should be able to:
B.
 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.
Performance Standards
C. Learning Competencies/
Objectives
(Write the LC code)
II. CONTENT
Daily Task:
The Learner will:
-
Identify Like and Unlike terms.
Add / Subtract Polynomials.
Apply addition and Subtraction of Polynomials on
ADDITION AND SUBTRACTION OF POLYNOMIALS (Review)
III. LEARNING RESOURCES
A. 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
Pages
Pages
e-math for grade 8 by Orlando Oronce and Marilyn Mendoza 43 - 49
IV. PROCEDURES
ENGAGE
- class can you still recall your previous lesson in your grade 7 about
‘Special Products’? How many types of special products did you have?
What are those? What operation was use to find special products
using the given patterns you had before?
A.
Reviewing previous lesson
or presenting the new
lesson
(the teacher presents the objectives of thee lesson)
-
okay so before we start our new discussion for today, let us refresh
first ourselves with the laws of exponents that we need to observe.
1. am (an) = am+n
2. (am)n = amn
3. (ab)m = ambn
4.
B. Establishing a
purpose for the
lesson
𝑎𝑚
𝑎𝑛
= 𝑎𝑚−𝑛
 Product Rule
 Power Rule
 Power of a Product
 Quotient Rule
Keywords as legends:
Double – means you have to raise it to square.
Triple – raise it to cube
Take away – cancel order / remove order
Hamburger – h
Fries – f
Cheeseburgers – c
Double hamburgers – h2
Double cheeseburgers – c2
Double fries – f2
Spaghetti - s
Suppose we are on a drive thru of a fast food chain. I am the customer and you are
the crew. You are going to list down everything as I say my orders by writing the
codes for each order.
Suppose my orders are:
2 cheeseburgers, 2 hamburgers, 5 double hamburgers, 3 more cheeseburger, 2
double cheeseburgers, take away once hamburger, add one more cheeseburger, five
double fries, 2 boxes of spaghetti and add 2 more double fries.
-
C.
Presenting
examples/instances of
the new lesson
Can you repeat the order?
What is my final order?
How did you write hem in codes?
What is the final order in codes?
How did you come up with your answer? What did you do?
What did you notice on the orders and the codes?
(discuss about combing similar orders, that is in terms of codes, you combine those
with the same codes. Recall their knowledge on Similar and Dissimilar Terms or the
Like and Unlike terms.)
- Based on our activity a while ago, do you have now any idea about what will
be our topic for today?
- Do you recognize the expressions that you just listed?
- Very good! They are polynomials!
- So today we will be talking about addition and subtraction of polynomials.
(the teacher will present the lesson)
EXPLORE
-
Just as you can add, subtract, multiply and divide numbers, you can also perform
these basic operations with polynomials.
To add the polynomials, write the sum and simplify by combining like terms.
Take note of these properties:
Commutative Property for Addition
- For any number a and b, a + b = b + a.
Associative Property for Addition
- For any number a, b, and c: (a + b ) + c = a + (b + c)
Example:
Find each sum.
1. 4a + (3a – 8)
D. Discussing new concepts
and practicing new skills
#1
b. (3x + 4) + (5x – 2)
c. (x2 + 4x – 2) + (3x2 + 7)
(solution by the teacher)
-
Addition of polynomials can be simplified particularly when three or more polynomials
are involved. This can be done by arranging the polynomial so that like terms are in
the same column.
Thus, the example in letter c can be written as:
x2 + 4x – 2
+ 3x2
+7
4x2 + 4x + 5
Another Example:
Simplify each.
1. (9x + 11y – 2z) + (8x + 7y – 8z)
2. (6a + 5b – 6c) + (14a – 4b + 7c) + (5a + 7c)
(explain the process to the students in two ways)
a. Writing them without parenthesis and grouping the like terms; and
b. Using the long method of addition (writing in column)
Word Problem application:
The lengths of the sides of quadrilateral LOVE are shown in the diagram. Find the perimeter of
the quadrilateral LOVE.
4x - y
L
O
4y
E
3x
5x + 2y
V
(solution by the teacher)
Subtraction of Polynomials
Rule: To subtract an expression from another expression, add its negative. That is,
a – b = a + (-b)
 The same rule in subtracting integers.
E.
Discussing new
concepts and practicing
new skills #2
Example:
Subtract:
1. (3x + 4) – (5x + 2)
2. (8x + 1) – (-3x + 2) 3. (8x2 – 5x + 9) – (4x2 – x – 6)
(solution by the teacher. Show the solution using subtracting in column and using
horizontal subtraction)
Another example:
Subtract 8x2 + 5x -4 from 6x2 – 4x.
(solution by the teacher)
EXPLAIN
“DE – FUN – ITIONS”
For each exercise, subtract the second polynomial from the first polynomials. Find
your answer in the answer column and notice the letter next to it. Each time the
exercise number appears in the code, write this letter above it. Keep working and
you will decode the de-fun-itions.
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
ELABORATE 1
Can you tell of some instances where you find addition and subtraction of polynomials important?
How Cite situations.
Answer the following as recapitulation of our lesson:
1. To add like monomials, add their numerical ___________ and keep
the __________.
2. To add two polynomials, combine any ______ contained in the
polynomials.
3. For any x and y, x + y = _____ by commutative property.
4. Associative property for addition states that “For any number a,y and
z, (x + y) + z = __________.
5. _________ are two or more terms that contain the same varoiables
and exponents.
6. To subtract an expression from another expression, ___________,
that is a – b = a + (-b).
EVALUATE
A. Add the following:
1. (3x – 7) + (-4x – 2)
2. (2x2 + 4x – 8) + (-2x + 3)
3. (-3x2 - 2x + 5) + (5x2 + 2x – 8)
4. (2a2 – 2a3 + 4a) + (2a2 + 6a + 3)
5. (3x2 – 7xy + 2y2) + (5x2 + 6xy -4y2)
aluating learning
B. Subtract:
1. (9x2 – 2x) – (8x2 + 4x)
2. (-4x + 2x2 – 2) – (6x + 2 – 4x2)
3. (-2 + 8x2 – 3x) – (6x + 4x2 – 8)
4. (8x3 – 2x2 + 2x – 2) – (3x2 + 4x + 7)
5. (4x2 – 2x – 8) – (6x3 + 6 – 2x2 + 3x)
J.
Additional activities for
application or
remediation
ELABORATE 2
V. REMARKS
VI. REFLECTION
8 - STEM
8-A
8-F
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 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?
Name:
Prepared by:
Ellen Joy Tormis
Checked by:
Elnorie L. Gajeto
Signature:
Position:
Teacher I
Subject Coordinator
Observed by:
Noted by:
Tita P. Raya, Ed.D
Principal II