Republic of the Philippines

Tuguegarao City Science High School

MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

DETAILED LESSON PLAN

IN
MATHEMATICS 10

Prepared by:
ALEXANDRA P. TANGAN
Practice Teacher

Checked by:
ARLON MACARUBBO
Resource Teacher
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

Detailed Lesson Plan in Math

Mathematics 10
Quarter 4

I. Learning Objectives
At the end of the lesson, the students should be able to:
a. Define factorial notation,
b. solve factorial notations, and
c. appreciate the importance of factorial notation in real-life applications.

II. Subject Matter

A. Topic: Factorial Notation
B. Instructional Materials: PowerPoint presentation, whiteboard marker, printed IMs and printed worksheets
C. References:
III. Learning Procedures
Teacher’s Activity Student’s Activity

A. PREPARATION

Opening Prayer

May I ask everyone to pause for a while and feel the

presence of the Lord for the opening Prayer.
One student will lead the prayer.

Greetings
Good morning/Afternoon Class!
Good morning, Ma’am!

Checking of Attendance
Is there anyone who is absent today class?

None, Ma’am!
B. MOTIVATION
Before we begin with our discussion for today, we
will have an activity titled, “Pass the Product”. The
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

mechanics of the game will be as followed:

I. To fairly select only 10 students, the teacher will
ask who are born in the months of January to June.
II. A small ball will be passed around, the first
student says “1” and pass the ball.
III. Multiply and Pass: The next student multiplies
the previous number by the next counting number.
IV. If a student hesitates or gives the wrong product,
they step out of the line and is out of the game.
V. The game continues until one student remains and
is declared as the winner.

Are you ready?

Yes, Ma’am!
The game will start.

C. PRESENTATION
Let us congratulate our winner for today!
Now, did you notice how fast the number grew?
Yes, Ma’am!

What pattern do you see in how we multiplied?

Ma’am we multiplied the product of the previous
number to the next consecutive number.
That’s correct! We multiplied the number by the
integers before it all the way down to 1. This idea of
multiplying numbers in a specific sequence is called
factorial. But before delving more into our topic, let
us first read the learning objectives for today.
Everyone, please read:

At the end of the lesson, the students should be able

to:
a. Define factorial notation,
b. solve factorial notations, and
c. appreciate the importance of factorial notation
in real-life applications
FACTORIAL NOTATION
n factorial is denoted by n! It is the product of all
positive integers less than or equal to n.
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

Example:
5! can be read as “5 factorial”
It means 5 x 4 x 3 x 2 x 1 which equals to 120.
We can also write 5! in several ways,
5 x 4!. What else? 5 x 4 x 3!
5 x 4 x 3 x 2!
5x4x3x2x1

That’s correct! Let’s see this table where we have the

factorial notation of the numbers, the expanded form
and the value.
n Expanded Form n!
0! 1 1
1! 1 1
2! 2x1 2
3! 3x2x1 6
4! 4x3x2x1 24
5! 5x4x3x2x1 120
6! 6x5x4x3x2x1 720
7! 7x6x5x4x3x2x1 5, 040
8! 8x7x6x5x4x3x2x1 40, 320
9! 9x8x7x6x5x4x3x2x1 362, 880
10! 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 3, 628, 800

However, we can see that 0! = 1. Let’s try and prove

that. From our example, n factorials can be written
as:
4! = 4 x 3!
5 = 5 x 4!
7 = 7 x 6!
Therefore, we can say that n! = n(n-1)! From this,
let’s try and isolate n – 1.
�! � � − 1 !
=
� �
�!
= �−1 !
�
Now, let’s try and evaluate if n = 1
1!
= 1−1 !
1
1
= 0 !
1
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

1 = 0!
Let us evaluate some expressions:
1. 5! + 2! = = (5 x 4 x 3 x 2 x 1) + (2 x 1)
= 120 + 2
= 122

2. 8! – 5! = = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) – (5 x 4 x 3 x 2 x 1)
= 40, 320 - 120
= 40, 200
3. 4! 2! =
= (4 x 3 x 2 x 1)(2 x 1)
= (24)(2)
= 48
6!
4. 3! =
Expand first then cancel:
6x5x4x3x2x1 6 x 5 x 4 x 3!
= 3x2x1
or 3!
6x5x4x3x2x1 6 x 5 x 4 x 3!
= 3x2x1
or 3!

= 120
7!
5. (7−2)! =
7! 7x6x5x4x3x2x1 7 x 6 x 5!
= 5! = 5x4x3x2x1
or 5!
= 42

5!
6. 3!2! = =
5 � 4 � 3!
=
5 � 4 � 3!
=
5�4 20
= 10
3!2! 3!2! 2! 2

Absolutely right! Now, let’s determine whether each

of the following equation is TRUE or FALSE.

1. 5! = 5 x 4 x 3!
TRUE

2. 3! + 3! = 6!
(3 x 3 x 3) + (3 x 3 x 3) = 6 x 5 x 4 x 3 x 2 x 1
6 + 6 = 720
FALSE
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

3. 4!5! = 9! (4 x 3 x 2 x 1)(5 x 4 x 3 x 2 x 1) = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

24 x 120 = 362, 880

2880 ≠ 362, 880
FALSE
10! 10 x 9 x 8 x 7!
4. = 10 � 9 � 8 = 10 � 9 � 8
7! 7!
10 x 9 x 8 x 7!
= 10 � 9 � 8
7!

10 � 9 � 8 = 10 � 9 � 8
720 = 720
TRUE

D. Generalization
Those are absolutely correct! Again, let’s review
what we tackled today. What is n factorial?
Ma’am, it is the product of all positive integers less
than or equal to n.

Yes, that’s true. What else?

Ma’am, in getting the n factorial of a number, ee
multiply the number by the integers before it all the
way down to 1.

That’s right. And it is denoted by the symbol?

n!
E. Application
Very good! Please bear in mind that factorial
revolves the concept of product of all positive
integers from 1 to n. Now, let’s move on to the
usefulness of what we tackled. What do you think is
its significance?
Ma’am, factorial is fundamental to permutations
because it calculates the total number of ways to
arrange a set of objects.
That is indeed correct! Factorials help determine the
number of ordered selections. It seems that you did
understand our topic today. That ends our lesson for
Goodbye, Ma’am!
today. Goodbye, class!
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________

IV. EVALUATION:
A. Write T if the statement is TRUE and F if it is FALSE.
_____ 1. 0! = 0
_____ 2. 6! = 6 x 5!
_____ 3. Factorial values grow rapidly as n increases.
_____ 4. The factorial of any number greater than 1 is always greater than the number itself.
_____ 5. Factorials can be used to solve problems involving permutations.

B. Simplify each factorial expression. Show your solutions.

1. 3! + 2! =
2. 4! – 2! =
3. (6! - 3!) (2!) =
4. (5! x 3!) ÷ 4! =
5. (9! ÷ 7!) x 5! =

V. ASSIGNMENT
1. A school locker has a 3-digit passcode where each digit must be different. If the digits range from 1 to 5, how
many different passcodes can be made? Show your complete solutions.

Answer Key:
EVALUATION
A. B.
1. F 1. 8
2. T 2. 22
3. T 3. 1,428
4. F 4. 30
5. T 5. 8,640

ASSIGNMENT
60 possible passcodes.
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________
 Republic of the Philippines
Tuguegarao City Science High School
MABINI STREET, CENTRO 03, TUGUEGARAO CITY, CAGAYAN
______________________________________________________________________________________