Detailed Lesson Plan

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DETAILED LESSON PLAN IN MATHEMATICS
School ROMBLON STATE UNIVERSITY – SFC Grade Level 10
Practice Teacher RICHMOND R. ROON Learning Areas MATHEMATICS - 10
Teaching Date and Time NOVEMBER 22, 2023 / 1:30 – 2:30 PM Quarter 1ST
I.OBJECTIVES
A. Content Standards The learner demonstrates understanding of key concepts of polynomials and polynomial
equations.
B. Performance Standards The learner is able to formulate and solve problems involving polynomials and polynomial
equations in different disciplines through appropriate and accurate representations.
C. Learning Competencies The learner proves the Remainder Theorem and the Factor Theorem
Objectives 1. Evaluate polynomial function
2. Prove the remainder theorem
3. Develop patience solving exercises involving remainder theorem.
4. Solve real-word problems involving remainder theorem.
II. CONTENT Proves the Remainder Theorem
III. LEARNING RESOURCES
A. References
1. Teachers Guide Pages pp. 51 – 54
2. Learners Materials Pages pp. 76 – 81
3. Textbook Pages
4. Additional Materials from Learning Resource
Portal
Laptop
LED TV
Downloaded images
5. Other Learning Resources Mathematics 2016,

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Worksheets and PowerPoint Presentation
IV. PROCEDURES TEACHER’S ACTIVITY STUDENT’S ACTIVITY
Preliminary Activities
A. Prayer “Good Afternoon, Class. Before we start, let us
stand up for a prayer.”
(The teacher will select a student to lead a prayer)
“Good afternoon, Sir!”
(The teacher and the students will pray)
B. Greetings
C. Setting of Class
Standards
“Good Afternoon, Class!”
“Before you take your seats, please pick up the
pieces of papers and plastics under your chair.”
(The students will clean their areas.)
“Thank you, you may now take your seats.”
“How are you today, class?”
“Alright, that’s good to hear.”
“Good Afternoon, Sir!”
“We are doing well, Sir.”
D. Checking of
Attendance
E. Presentation of
“Class Secretary, is there any absentees from the
class?”
“Very good! Since we have a perfect attendance,
give yourselves perfect clap.”
“Do you know how to do perfect clap?”
(Teacher will demo the perfect clap.)
“Class I have here class rules that I want to
“No one is absent, Sir.”
No, Sir.
(The student will do the Perfect clap)

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Classroom Rules implement during my class. Who wants to read?”
(The teacher will call a student for each rules.)
(The teacher will discuss the class rules)
“Is that clear, class?”
“Class do we have an assignment?”
(Student will read the classroom rules)
1. Be participative.
2. Listen attentively. Do not make unnecessary noise.
3. Using gadgets without the permission of teacher is prohibited.
4. Raise your hand if you want to answer.
5. Respect
“Yes, Sir.”
“None, Sir.”
Integration of 7 E’s
ELICIT
A. Reviewing
previous lesson
or presenting
the new lesson.
“Before we start to our next topic, let us have a short
review of what we discussed last meeting. Who can
still remember our topic last time?”
“Very good! Give her/him three claps.”
“According to Ms./Mr., last time, we discussed about
division of polynomials.”
“How do we divide polynomials? What methods do
we use?”
“Last meeting, we discussed about division of polynomials.”
“We divide polynomials by using the long method and synthetic
division.”

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“Exactly! Give her/him three claps.”
“Long method and synthetic division are the two
ways of dividing polynomials.”
“One last question. In what form should we write the
dividend before we divide?”
“Indeed! Give her/him three claps.”
“We need to write it in standard form, wherein we
arrange the polynomial in decreasing degree of
terms.
“Do you still have any questions regarding our last
topic?”
“That is good to hear.”
“We should write the dividend in standard form.”
“None, Sir.”
ENGAGE
B. Establishing a
purpose for the
lesson
“It seems that you have already mastered dividing
polynomials. Are you ready for our next topic?”
“That is nice to hear, but before I reveal to you our
new lesson for today, which is about a theorem, let
us have first an activity titled “GUESS ME!”.
“Who wants to read the Mechanics of the activity?”
(The teacher will explain the mechanics)
MECHANICS: The teacher will show two photos for
“Yes, Sir.”
(The student will read the mechanics.)

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the student to guess. If the student failed to correctly
guess the first photo, he/she needs to guess the
second photo correctly. However, if the student
guessed the first photo correctly, he/she has an
option whether to continue or not for the second
photo. Participants will be given strips of papers to
claim their prizes.
1.
“Who wants to guess the first picture?”
“Since you failed to guess it right, now guess the
second picture.”
The student will guess. (The student is expected to incorrectly
guess the picture, because the pictures are very hard to guess.)
The student will answer “Reminder”
IMAGE

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“Very good! Give him/her 3 claps.”
(The teacher will give strip of paper to the student.)
2.
“Who wants to guess the first picture?”
“Since you failed to guess it right, now guess the
second picture.”
(The students will clap three times.)
The student will guess. (The student is expected to incorrectly
guess the picture, because the pictures are very hard to guess)
The student will answer “Remained Deer”
IMAGE

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“Very good! Give him/her 3 claps.”
(The teacher will give strip of paper to the student.)
3.
“Who wants to guess the first picture?”
“Since you failed to guess it right, now guess the
second picture.”
(The students will clap three times.
The student will guess. (The student is expected to incorrectly
guess the picture, because the pictures are very hard to guess)
The student will answer “Remainder”
IMAGE

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“Very good! Give him/her 3 claps.”
(The teacher will give strip of paper to the student.)
“Now, do you have any idea of what our new lesson
for today is?”
“Very good!”
“Our lesson for today is all about Remainder
Theorem.”
In this lesson you will learn a new method of finding
the remainder when a polynomial is divided by x-r.”
“But before that, we will first have an activity that will
recall your lesson on evaluating polynomials. This
(The students will clap three times.)
The student will answer “REMAINDER THEOREM”

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activity is titled Message under the table.”
“I will group you into four. Grouping is according to
the color of your name tags.
“Who will read the Direction?”
Activity 1: Message under the table
Direction: Evaluate the polynomial at the given
values of x. Next determine the letter that matches
your answer. When you are done, you will be able to
decode the message. Each correct answer will earn
one point.
A. P(x) = x3
+ x2
+ x + 3
B. P(x) = x4
– 4x3
– 7x2
+22x = 18
(The students will sit with their group.)
(Student will read the direction.)

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Criteria for group activity:
3 points in team cooperation
2 points in timeliness
5 points in correct solution
5 points in presentation
Total of 15 points
“I will give you five minutes to finish the task.
The time starts now!”
“Time is up. Post your work on the board.”
(Checking of activity)
“How did you find the value of a polynomial
expression P(x) at a given value of x?”
“What message did you obtain?”
(The students will do the activity.)
“We find the value of the polynomial by evaluating the polynomial.”
“COMPASSION”
A. 17 C. -3 E. 5 I. 18
M. 3 N. 78 O. 2 O. 30
P. 6 R. 0 S. -6 T. 24

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“Alright. Class, do you have any idea what
compassion is. How will you show compassion to
your classmates or friends?”
“Wow, that is a nice answer. Give him/her “Nice one,
Baby” Clap.
“To add into his/her answer, we should be
compassionate by showing empathy to others,
especially to your co-students. We need to
understand and feel other’s emotions and have the
ANSWER KEY:
A.
B.
“Compassion is like showing pity and concern for sufferings or
misfortune of others. I will show compassion to my classmates or
friends by relating to their situation and helping them.”
(The students will perform the clap.)

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desire to help.”
“Do you understand?”
“Yes, Sir!.”
C. Presenting
Examples/Insta
nces of the new
topic
“Let us have another group activity. “
“Who will read the direction?”
Activity 2: Proving the Remainder Theorem
Directions: Fill in the blanks with words and
symbols that will best complete the statements given
below.
Suppose that the polynomial P(x) is divided by (x –
r), as follows:
𝑃(𝑥)
𝑥 − 𝑟
= Q(x) +
𝑅
𝑥 − 𝑟
If P(x) is of degree n, then Q(x) is of degree (1.)
_____. The remainder R is a constant because
(2.)____________________.
Now supply the reasons for each statement in the
The student will read the direction
ANSWER KEYS:
1. n – 1
2. the degree of x – r is 1, so the degree of the remainder has to
be less than 1, making it 0.

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following table.
Criteria for group activity:
3 points in team cooperation
2 points in timeliness
5 points in correct solution
5 points in presentation
Total of 15 points
The previous activity shows the proof of the
Remainder Theorem:
The Remainder Theorem
If the polynomial P(x) is divided by (x – r), the
remainder R is a constant and is equal to P(r).
R = P(r)
Thus, there are two ways to find the remainder when
P(x) is divided by (x – r):
1. calculate P(r), or
2. use synthetic division
Similarly, there are two ways to find the value of
P(r):
(1) substitute r in the polynomial expression P(x), or
(2) use synthetic division.

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EXPLORE
D. Discussing new
concepts and
practicing new
skills #1.
E. Discussing new
concepts and
practicing new
skills #2.
Use the Remainder Theorem to find the remainder
R in each of the following and check using synthetic
division.
(The students will listen attentively and will answer to the teacher’s
questions.)

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1. Find the remainder when 8x4
+ 3x3
-2x -2 is
divided by x – 8.
“Now, who wants to try another example on the
board and will explain?”
(Student will answer the problem on the board and will explain.)
EXPLAIN
F. Developing
Mastery
“Let’s have another example.”
On your seats, find the remainder when;
1. (x4
– x3
+ 2) is divided by (x + 2).
2. (x3
– 2x2
+ x + 6) is divided by (x – 3).
(Check your answer using synthetic division.)
“I will give you five minutes to solve the two
problems.”
(The students will solve the given problem.)

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“Time is up.”
(Who will solve the problems on the board and will
explain?)
“Did you get it class? Do you have any questions?”
(Two students will be selected to solve and explain the solution.)
“None, Sir.”
ELABORATE
G. Making
generalization
and
abstractions
about the
lesson.
“Since there is no question, let us have another
group activity. With the same grouping, I will give
each group the materials for a activity. Each group
will solve a worded problem to be solved. You will
write your solutions in a manila paper. Finish the
task in 3 minutes and post it on the board. Have
your representative to present your work. Is that
clear?
Criteria for group activity:
3 points in team cooperation
2 points in timeliness
5 points in correct solution
5 points in presentation
Total of 15 points
“Yes, Sir!”

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Group 1
Sarah baked x4
+2x3
-x2
-6x+3 cakes for a party. If she
arranged the cakes on trays, with each tray holding
x-6 cakes, finding the remaining cakes that is not
arranged on the trays.
Group 2
A school auditorium has 2x3
+ 6x2
+ x – 7 seats.
Find the remainder when the total number od seats
is divided by x – 3?
Group 3
A bookstore ordered 25x2
+ 2x - 7 copies of a
popular novel. When the books were delivered, they
were packed in boxes of x – 2, find the remainder.
“Time is up. Post your work on the board and
present your work.”
The Remainder Theorem
If the polynomial P(x) is divided by (x – r), the
remainder R is a constant and is equal to P(r).
R = P(r)
There are two ways to find the remainder when P(x)
is divided by (x – r):
(1) use synthetic division, or
(Students will do the activity.)
(Students will explain their work.)

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(2) calculate P(r).
Similarly, there are two ways to find the value of
P(r):
(1) substitute r in the polynomial expression P(x), or
(2) use synthetic division.
EVALUATION
H. Evaluating
Learning
“Since you now have full knowledge, If there are no
questions anymore, let us have another activity but
this time it is individual. This activity is good for 15
minutes and it will reserve as evaluation. Please
read and follow the directions carefully. Write your
answers in a one whole sheet of paper. You may
now start answering.”
1. (x2
– 3x + 7) ÷ (x + 5)
2. (2x3
– 10x2
+ x – 5) ÷ (x – 1)
3. (x4
– x3
+ 2) ÷ (2x + 5)
4. (x3 – x2 – 8x – 4) ÷ (3x + 2)
5. Alice bought (9x2 – 8x + 7) gift for a charity event.
If she plans to pack the gift in a box with x-3 gifts
each, what are the remaining unpacked gift?.

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EXTENDED
I. Additional
Activities for
applications or
remediation
For your assignment, have an advanced reading
regarding the Factor Theorem.
V. Remarks
VI. Reflection

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PREPARED BY:
RICHMOND R. ROON
Student Teacher