A Detailed Lesson Plan in Mathematics 9
Prepared by: Daff Jeszel R. Duran
February 27, 2025
A. Content Standard
The learners demonstrate understanding of key concepts of parallelograms and triangle
similarity.
B. Performance Standard
The learners are able to investigate, analyze, and solve problems involving
parallelograms and triangle similarity through appropriate and accurate representation.
C. Learning Competency/Objectives:
By the end of the lesson, the learners are able to:
1. Multiply and Divide Integers.
2. Solve problems involving multiplication and division of integers.
I.
Content and Materials
A. Subject Matter: Multiply and Divide Integers
B. References:
C. Materials: Power point presentation, White Board, White Board Marker, Manila
Paper
D. Values: Romans 8:28: "And we know that in all things God works for the good of those who
love Him, who have been called according to His purpose." The rules of integers
demonstrate that even negative outcomes can lead to positive results, much like how God
can turn challenges into blessings in life.
Procedure:
Teacher’s Activity
A. Before the Lesson
1. Prayer
2. Greetings
3. Attendance
4. Review
Short Review: Let the learners answer the
short activity. Perform the indicated
operations on integers and give the results.
1) 6 – 12 = _____ 6) –1 – 14 + 17 = _____
2) 11 + 14 = _____ 7) 6 – 20 +15 = _____
3) –12 – 5 = _____ 8) –10 – 8 – 7 = _____
Student’s Activity
4) 5 + 13 + 6 = _____9) 3 +10 – 15 = _____
5) 1 – 13 +14 = __10) 3 – 16 + (–16) =____
Motivation:
Sing-along:
Direction: Students will sing the song
‘Multiplying and Dividing Integers’. And after
that they need to answer the questions below. (Students will sing along)
Multiplying and Dividing Integers Song
(Tune to: If you’re happy and you know it clap
your hands)
A negative times negative is positive
A negative divide negative is positive
A negative times negative
A negative divided negative
if its same sign you get
positive
A negative times positive is negative
A negative divide positive is negative
A negative times positive
A negative divided positive
if its different sign you get
negative
2x
If you have a same sign, you get positive
But if they’re different you get negative
If you have the same sign, you get the positive
But if they’re different you get negative.
Incomplete Sentence:
1. A negative times positive is ___________.
2. If you have the same sign, you get_____.
3. A negative divided negative is _________.
4. If the sign is different, you get_________.
5. A negative times negative is __________.
Answers:
1. Negative
2. Positive
3. Positive
4. Negative
5. Positive
Ask the class:
1. What do you think is the purpose of the
lyrics in the song?
2. What did you learn from answering the
incomplete sentence?
4. Do you think, based on the song you listen
to, our topic will be challenging? Why?
5. What ways can you do to overcome the
challenges in learning about it?
The purpose of this song is to teach
us and remind us about the signs of
integers in multiplication and
division.
This is new to me to learn, and
answering the incomplete sentence
helps me to know if I clearly remember
the lyrics of the song.
Yes. Because besides the multiplication
and division, which are a bit challenging
to solve, especially if there are many
numbers, there are also negative and
positive signs or integers that are added
to them.
No. Because I think if we practice, read,
and learn it again, we are capable of
resolving any problem that comes our
way
For me, I think I need to listen
carefully to the discussion so that I
can understand how it is properly
solved and confidently use my skills
in solving the problem. Also, be
determined to face new challenges,
especially in solving this
multiplication and division of
integers.
Today, we’ll dive into the fascinating world of
integers, specifically on how to multiply and
divide them properly
B. During the Lesson
1. Activity
In order for you to have a better
understanding of our topic, let us have
first an activity.
Integer Puzzle:
I will divide the class into two teams. Each
team will be given a manila paper with
incomplete mathematical equations and
cards with integers. You have to work
collaboratively with your group to put the
correct integers in the blank space in the
equation.
(Students will participate.)
Example equations:
Expected Answers:
1.
2.
3.
4.
+5 x -3 = _______
___ x +4 = +20
-6 x _____ = +18
+8 ÷ -2 = _______
1.
2.
3.
4.
-15
+5
-3
-4
Follow the guided questions that I will give,
then explain what are being asked:
1. What strategies did you use to find the
missing integer?
2. Did you notice any patterns or
shortcuts that helped you solve the
equations more quickly?
3. Can you explain the difference
between a positive integer and a
negative integer in your own words?
4. How can you use these skills with
integers in real-life situations?
Paste your work in the board, then write your
answers in the manila paper. I will give you 10
minutes to finish your work. After that, you
will report your answers in front of the class.
(Students work collaboratively with
their groupmates)
2. Analysis
Time is already up!
You may now send a representative to
explain your answers.
(Students present their answers)
Guided Questions:
1. We used inverse operations to
isolate the missing integer.
2. Yes, we noticed that when
multiplying or dividing integers
with the same sign, the result is
always positive.
3. Positive integers are greater than
zero, while negative integers are
less than zero.
4. These integer skills are crucial for
understanding and managing
finances, like tracking income
and expenses.
Nice job everyone!
3. Abstraction
What are Integers?
● The word integer originated from the Latin
word “Integer” which means whole or intact.
Integers is a special set of numbers comprising
zero, positive numbers and negative numbers.
○ Zero is neither a positive nor a
negative integer. It is a neutral number
i.e. zero has no sign (+ or -).
○ The positive integers are the natural
numbers or also called counting
numbers.
○ The negative integers are the
negative of natural numbers.
What are Multiplication and Division Integers?
● Multiplication of integers is the process of
repetitive addition including positive and
negative numbers or we can simply say
integers.
● Division of integers involves the grouping of
items. It includes both positive numbers and
negative numbers. Remember that division is
the opposite or the reverse operation of
multiplication. Just like multiplication, the
division of integers also involves the same
cases.
What are the rules for multiplying and dividing
integers? Observe the illustration below:
What did you notice?
Very good! That’s correct!
Same rules apply to both multiplying
and dividing integers.
Same signs result to POSITIVE
INTEGER
Different signs result to NEGATIVE
INTEGER
Since you already know the rules for
multiplying and dividing integers, let’s try
to solve the following problems:
1.
2.
3.
4.
+2 x +11 = _______
-4 x -6 = ______
-10 ÷ +5 = _______
+54 ÷ -2 = _______
Very Good!
4. Application
To assess your learning and understanding
of multiplying and dividing integers, you
will be doing an individual activity.
Direction: The students will solve the
problem of multiplication and division of
Integers below and write the letter of the
answer in the box.
A 15 × 2 ÷ 5 =
C -14 × 2 =
I -85 × 9 =
A 15 ÷ 15 ×15 =
E -369 ÷ 9 =
S -36 ÷ -6 =
T -40 ÷ -4 =
M 22 × 5 =
M 69 ÷ -3 =
H 3 × 3 ÷ 3=
T 16 ÷ -2 =
Expected Answers:
1. +22
2. +24
3. -2
4. -27
C. After the Lesson
1. Generalization
Do you have any questions?
If there’s none, then let’s sum up all of the
learnings you’ve learned from this lesson.
Student A, B, and C can you tell me what you
learned from today’s lesson?
Expected Answer:
Multiplying and dividing integers
follow specific rules that highlight
the interplay of positive and negative
numbers. A positive product or
quotient results when both integers
have the same sign, while a negative
product or quotient occurs when the
integers have opposite signs. These
mathematical operations reflect
balance and opposites, teaching us
that even challenging or "negative"
situations can lead to positive
outcomes when approached
correctly. Understanding these rules
not only helps in solving
mathematical problems but also in
appreciating real-life patterns and
God's purposeful design.
2. Assessment
Direction: Read and match the multiplication and division of integers questions in column A with
the answers in column B.
Column A
1. The integers are ___________________.
2. The multiplication and division integers have _______.
3. Ten divided by a negative five is equal to _______.
4. One positive multiplied by one negative multiplied by one positive equals ____________.
5. Positive five multiply by positive two multiply by ten times two is equal______.
6. Negative eighteen multiplied by positive two is equal to ________.
7. Three multiplied by eight times two is equal to _______.
8. Positive two divided by Positive two is equal ___________.
9. Positive nine divided by negative three is equal to _________.
10. The neutral number of integers is ____________.
Column B
A. Negative two
B. Negative thirty-six
C. Positive and negative signs
D. Positive forty-eight
E. Positive two hundred
F. Zero
G. The collection of whole numbers and negative numbers
H. Negative one
I. Positive one
J. Negative three
3. Assignment
I. Multiply and Divide the following Integers.
1. 15 x (-5) =
2. (-24) x (-2) =
3. 16 ÷ (-8) =
4. (-3) ÷ (-3) =
5. 10 ÷ (-2) x 5 =
II. Statement: Reflect on the lesson.
1. I learned that:________________________
2. I discovered that:____________________________
3. I realized that:___________________________________