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POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
Facilitator: Daniela Marie O. Apelado
I. OBJECTIVES
A. Content Standard : 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 Standard: 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.
A. C. Learning Competencies : At the end of the discussion, the students should be able to:
a. 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). Transform a statement into an equivalent if-then statement.
II. SUBJECT MATTER
Topic: Patterns and Algebra (M8AL-Ia-b-1)
A. Topic: Patterns and Algebra
B. Materials: Laptop, Presentation, Slide Decks/Visual Aids, LCD Monitor/Projector, Board,
Pen or Chalk
C. References: 1. Elementary Algebra I. 2000. pp. 200-211* 2. Moving Ahead With
Mathematics II. 1999. pp. 194-209 3. NFE Accreditation and Equivalency Learning Material.
Special Products and Factoring. 2001. pp. 11-18 4. BEAM I – Module 16: Factoring
D. Values Focus: Mutual Respect
E. Duration: 45-50 minutes
III. METHODLOGY/PROCEDURE
Teacher’s Activity Learner’s Activity
A. Preparatory Activity
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
I. Daily Routine
Good morning class!
How are you today?
It’s good to hear that. Are you excited for today’s
lesson?
All right! Before we begin with our discussion,
may I request everyone to please stand for a short
prayer.
You may now take your seats.
Is everyone here today?
Impressive.
II. Review/Apperception
Now, as a short recap from our previous lesson,
who can give a short overview of the concepts
we’ve discussed?
Very Good!
Let us see how much have you learned from our
previous discussion by this activity.
Are you ready?
Activity: Find My Factors.
Direction: Determine the factors of the following
quadratic equations.
x
2
x
2
− 7 x − 8
x
2
x
2
x
2
− 10 x − 200
Good job class! It seems that you have really
mastered our previous lesson.
Good morning Sir!
We’re doing great Sir.
Yes Sir!
(A student will lead the prayer.)
Yes Sir.
Last meeting, we talked about factoring quadratic
equations. We determined the factors of the value
of C that when added, we will get the value of B in
the quadratic equation.
We’re ready Sir!
(x+6) (x+1)
(x+1) (x – 8)
(x+3) (x+2)
(x+1) (x+12)
(x-20) (x+10)
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
What is the answer?
Very good! Everybody got the correct
answer.
√
Raise your board.
What is the answer?
Very good! Everybody got the correct
answer.
√
Raise your board.
What is the answer?
Very good! Everybody got the correct
answer.
Give yourselves a congratulations clap.
13
(raising their show me board)
11
(raising their show me board)
12
C. Explore
For our lesson, I am going to introduce to you
a song in Mathematics.
Is everyone familiar about the song Jingle
Bells?
Great! Can I hear it?
Marvelous! I can see you are wondering why
we sang the Jingle Bells, here’s why.
We will be using the Jingle Bell’s rhythm in
reciting a formula.
This formula was called the “Quadratic
Formula”.
So, this is the Quadratic Formula (writes the
formula at the board).
Yes Sir.
(sings the Jingle Bells)
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
x =
− b ±
b
2
− 4 ac
2 a
I will sing it twice then it’s your turn after. Am I
clear?
(sings the formula twice)
Now, it’s your turn.
Marvelous! You all are great singers! Now we
can proceed to the discussion.
Yes Sir.
(sings until they can sing without looking at the
board and memorizes it)
D. Explain
This morning, we will find the origin of the
quadratic formula and it is formed from the
quadratic equation to that formula.
The quadratic formula where x is isolated at
the left and the equation at the right can
determine the zeros of the equation was
derived from the quadratic equation itself.
ax
2
In finding zeros, we must find the value of x
and Mathematicians derived a formula to
isolate the x at the left and come up to a
formula that can be solved by just substituting
the values of A,B and C.
First,
Start with
ax
2
Divide the equation by a
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
x =
− b ± √
b
2
− 4 ac
2 a
Can you sing the quadratic formula song
again?
Marvelous! Now everybody sing on my count.
That’s great to hear that you can catch up to
the lesson.
So that’s how Mathematicians come up to
isolate the x.
Now, we move on to how we can determine
the value of A, B, and C.
The quadratic equation is in the form
ax
2
So, the values of a, b and c are the coefficients
and the constant for the value of c.
For example:
x
2
A=1 B=7 C=
Another example:
x
2
− 10 x − 20
A=1 B= -10 C= -
Now, can you determine the values of A, B,
and C?
Let’s test your comprehension.
Yes Sir!
(sings the quadratic formula)
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
Determine the values of A, B and C in this
equation.
x
2
Marvelous! Now we can proceed further to
the lesson.
After we mastered how to get the values of A,
B and C, we will now substitute that to the
quadratic formula to find the zeros of the
equation.
Can you all sing again the quadratic equation
one more time?
Ok! On my mark, everybody sing!
Marvelous! My heart sings also with joy
knowing that all of you can catch up! Anyway,
let’s proceed.
Given this equation, let’s find the zeros or the
values of x.
x
2
Can you determine the values of A, B, and C?
Very good!
After we get the value of A, B and C, we
proceed to substitution.
Let’s substitute it to the quadratic formula.
x =
− b ± √
b
2
− 4 ac
2 a
Substitute:
Yes Sir!
A= 1 B= 9 C= 18
Yes Sir!
(everybody sings the quadratic formula)
Yes Sir! The values are A= 1 B= 7 C= 6
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
Yes Sir!
E. Elaborate
I will divide your class into four groups. I will
designate leader each group who will pick a fruit
from the tree and solve the x values for the
equation written on the fruit.
x
2
x
2
3 x
2
5 x
2
Instruction: Solve for the values of x then report
your answer to the class?
Use the step we discuss earlier and try to answer
without erasures.
(start doing their activity)
(presenting of activities)
F. Evaluate
Prepare a sheet of paper.
Direction: Read the equations carefully. Write
POLYTECHNIC UNIVERSITY OF THE PHILIPPINES
SAN PEDRO CITY CAMPUS
the answer by following the steps in solving
for the x values using quadratic formula. Solve
it in your own.
- x
2
x
2
− 10 x − 200
You have 10 minutes to answer the activity.
(After 10 minutes)
Pass your papers.
Please stand and let’s have a closing
prayer. (Closing Prayer)
