Republic of the Philippines
Department of Education
REGION 02-CAGAYAN VALLEY
SCHOOLS DIVISION OF THE CITY OF ILAGAN
CAPUGOTAN ELEMENTARY SCHOOL
A Detailed Lesson Plan in Mathematics 4
Greatest Common Factor
I.
II.
III.
Objectives
At the end of the lesson, pupils should be able to:
a. write a given number as a product of its prime factors;
b. find the common factors and the greatest common factor (GCF) of two numbers using the
following methods: listing, prime factorization, and continuous division; and
c. solve real-life problems involving GCF of 2 given numbers.
Subject Matter
A. Topic: Finding the Common Factors and the Greatest Common Factor of Two Numbers
B. Reference: Mathematics Quarter 2 – Module 2: Greatest Common Factor PG. 1-20
C. Material: tv, laptop, slide presentation, chalk,
D. Value Focus: Helpfulness/Alertness
Procedure
Teacher’s Activity
Pupil’s Activity
A. Preliminary Activities
1. Prayer
2. Greetings
3. Checking of attendance
4. Discussing the Health and Safety
protocols of IATF
5. Discussing New Normal Classroom
rules
B. Preparatory Activities
1. Review
Take a look at these examples. Tell
whether the number is a prime or
composite number.
(I will flash a number on the screen
and call pupils to identify whether it
is a prime or composite number)
17
25
23
56
36
(Pupils will identify if the number is a prime or
composite number)
Prime number
17
25
Composite number
23
Prime number
56
Composite number
36
Composite number
Very good!
2. Motivation
We will have a game and we will
call it “Mix and Match”. In this
game, I will distribute numbers cards
to all of you. When I say “Mix”, all
of you will mix with one another.
When I say “Match” you look for a
partner who is holding a number that
when you multiply both numbers it
will give the answer that I am
holding.
Are you ready, class?
Okay! Then let’s start the game.
(I will say “Mix” and will flash
number one by one)
35
12
10
44
54
Yes, ma’am!
(The pupils will mix with one another)
5
3
1
2
8
10
4
7
9
6
4
11
16
(I will say “Match” and the pupils
will find their partner)
(Pupils will find their “Match” to get the
answer which is the teacher holding)
35
Very good!
What have you realized after the
game?
Yes, Prince?
7
5
10
1
10
54
9
6
12
4
3
44
4
11
16
2
8
Ma’am!
We have realized that we have to find the
What value do you need to possess
correct pair of the number to get the correct
in order to find the correct pair of the answer.
number?
That’s true. We need to be alert in
everything we do in order to finish
everything in time.
Just like in the game, numbers do
have their partner. Without this
partner, we cannot get the answer
that we need.
let’s see what these pairs being
talked about in our new lesson.
We need to be alert in order to find the pair of
the number.
3. Setting of Objectives
At the end of the lesson, pupils should
be able to:
a. write a given number as a product
of its prime factors;
b. find the common factors and the
greatest common factor (GCF) of
two numbers using the following
methods: listing, prime
factorization, and continuous
division; and
c. solve real-life problems involving
GCF of 2 given numbers.
C. Developmental Activities
1. Presentation
Let us read the word problem.
Arnel helps his father in their bakeshop. They
baked 48 cupcakes and 60 cookies. They plan to
pack them separately in small boxes. What is the
biggest number of cupcakes and cookies that can
be placed in boxes if these are of the same
numbers.
(Pupils will read and understand the word
problem)
What did Arnel and his father baked?
Ma’am!
Yes, Althea?
They baked cookies and cupcakes
How many cupcakes were baked?
48 cupcakes
How many cookies were baked?
60 cookies
What do Arnel and his father plan to do
with the cupcakes and cookies?
they plan to pack them separately in small
boxes with the same number.
Can you solve the problem of Arnel and
his father?
Yes, Ma’am!
Now, try to think of a way on solving
the problem of Arnel and his father.
(Pupils will think of ways on solving the
problem)
You will solve this problem by pairs.
Your seatmate will serve as your partner
in solving this problem.
You can use any method in solving it
and later on you will be presenting your
output by pair.
Now let’s see if you have found the
solution of the problem.
What are the methods you use in the
problem?
(Pupils will share their solution on the board.)
We used listing method ma’am.
We also used the prime factorization ma’am.
That’s right! Those are some ways of
solving the problem.
What are the common factors of 40 and
68?
Ma’am!
Yes, Lance?
Common factors- 1, 2, 3, 4, 6, and 12
Very good!
What factor of 48 and 60 is the greatest?
12 ma’am! (Everybody answered)
So, 12 is the greatest common factor of
48 and 60. Greatest Common Factor or
GCF is the greatest common factor to 2
numbers.
How could Arnel and his father pack the
cupcakes and cookies?
Ma’am!
Yes, Airob?
They can pack the cupcakes and cookies by 12
ma’am.
That’s right!
2. Discussion
We can find the Greatest Common
Factor (GCF) of a number in three ways.
A. By Listing Method
List down the factors of 48.
1,2, 3, 4, 6, 8, 12, 16, 24, and 48
List down the factors of 60.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
What are the common factors?
1, 2, 3, 4, 6, and 12
What is the greatest common factor
of 48 and 60?
12 ma’am.
That’s right!
B. Another way of finding the
greatest common factor of 48
and 60 is by prime factorization.
We will write 48 and 60 as a product
of its prime factors using a factor
tree.
48
60
2 x 24
2 x 30
3x4
2x2
2 x 15
3x5
What are the prime factors of 48 and
60?
Ma’am!
Yes, Angel?
48-2x2x2x2x3
60-2x2x3x5
Multiply all the common factors.
2x2x3
What is the Greatest Common
Factor?
The GCF of 48 and 60 is 12 ma’am
Very good!
C. We can also solve the problem
by using the Continuous
Division.
Here’s how we can do it.
2
2
3
48
24
12
4
60
30
15
5
To get the GCF multiply all the
divisors.
We have 2 x 2 x 3 = 12
What is the GCF of 48 and 60?
The GCF of 48 and 60 is 12 ma’am
(I will give other pairs of numbers
and let the pupils identify the GCF
of the numbers)
D. Generalization
How do we get the Greatest Common
Factor (GCF) of numbers, class?
Very good!
E. Application
Activity 1. Find the Greatest
Common Factor (GCF) by
completing the needed data.
1. 6 : 1, __, 3, 6 12 : 1, 2, 3, 4, __, 12
Common Factors
:___________________
GCF :______
2. 9 : 1, __, 9 12 : 1, 2, 3, 4, __, 12
Common Factors
:___________________
GCF :______
3. 10 : 1, 2, 5, __ 15 : 1, 3, __, 15
Common Factors
:___________________
GCF :______
4. 20 : 1, 2, 4, 5, __, 20 40 : 1, 2, 4,
5, 8, 10, __, 40
Common Factors
:___________________
GCF :______
5. 21 : 1, 3, 7, __ 35 : 1, 2, 5, __, 15,
30 Common Factors
:___________________
GCF :_____
To find the GCF of two given numbers, we can
use the Listing Method, Prime Factorization
and Continuous division, ma’am
IV.
Evaluation
V.
Assignment
Prepared by:
Checked:
JENNY MAE Q. CULALABE
Teacher-Aide/LSB
MADONNA S. PATTALITAN
Head Teacher I
Republic of the Philippines
Department of Education
REGION 02-CAGAYAN VALLEY
SCHOOLS DIVISION OF THE CITY OF ILAGAN
CAPUGOTAN ELEMENTARY SCHOOL
A DETAILED LESSON PLAN IN MATHEMATICS 4
Solving Word Problems Involving Greatest Common Factor
I.
Objectives
At the end of the lesson, pupils should be able to:
a. write a given number as a product of its prime factors;
b. find the common factors and the greatest common factor (GCF) of two numbers using the following
methods: listing, prime factorization, and continuous division; and
c. solve real-life problems involving GCF of 2 given numbers.
II.
Subject Matter
A. Topic: Finding the Common Factors and the Greatest Common Factor of Two Numbers
B. Reference: Mathematics Quarter 2 – Module 2: Greatest Common Factor PG. 1-20
C. Material: TV, laptop, slide presentation, chalk,
D. Value Focus: Helpfulness/Alertness
III.
Procedure
Teacher’s Activity
A. Preliminary Activities
1. Prayer
2. Greetings
3. Checking of attendance
4. Discussing the Health and Safety protocols of
IATF
5. Discussing New Normal Classroom rules
B. Preparatory Activities
1. Review
Pupils Activity
(Pupils will pray)
(Pupils listen attentively to the new normal
rules)
What is our lesson yesterday, class?
Yes, Alvin?
That’s right!
Who can enumerate the 3 ways on how to
find the GCF of 2two numbers?
Ma’am!
It is about Greatest Common factor ma’am.
Yes, Nicole?
Ma’am!
That’s great!
2. Motivation
Let us have first some of the concepts that
can help you understand Greatest Common
Factor (GCF).
First is the listing method. Second is Prime
Factorization/Factor Tree and the last way
in finding the GCF is the Continuous
Division ma’am!
A. Write each number as a product of its
two factors.
1. 42 = ____________
2. 43= ____________
3. 38= ____________
4. 81 = ____________
5. 50 = ____________
(I will call 5 pupils to answer the question
on the board)
Amazing Job, class!
C. Lesson Proper/Developmental Activities
1. Presentation
Our topic for today is on how to Solve Word
Problems Involving Greatest Common Factor
(5 Grade 4 pupils will answer the given
problem)
7x6
1 x 43
2 x 19
9x9
5 x 10
Let us start learning the new concept with the
help of this story problem.
Read the story problem.
Mrs. Santos is preparing emergency kits to be
given to each class in Grade 4. She has 30
bottles of water and 20 canned food, which she
would like to distribute equally among the kids
with no items left. What is the greatest number
of kits can she make?
(Pupils will Read the story problem)
What can you say about Mrs. Santos? What
kind of person is she?
Ma’am!
Yes, MJ?
Mrs. Santos love the pupils. She is
generous.
How will you solve the problem?
(pupils will try to solve the given problem)
We will find out whether you answered the
problem properly and correctly.
2. Discussion
The problem is about finding the Greatest
Common Factor because it requires us to find
the greatest quantity of equal groups that we
can make with the bottles of water and cans of
food.
So, we can use the 4-step plan in solving for the
answer.
Step 1. Understand
The greatest number of kits that
Mrs. Santos can make
What is
asked in
the
problem?
What
30 bottles of water, 20 cans of
facts are food
given?
STEP 2. Plan
How will By finding the Greatest Common
you
Factor (GCF)
solve the
problem?
STEP 3. Solve
Step 4. Check and Look Back
What is the answer to The greatest number
the problem?
of kits is 10.
Therefore, 10 is the greatest possible number of
kits that Mrs. Santos can make.
3. Application
Let us see if you already know how to solve
word problems involving Greatest Common
Factor (GCF). Read each problem and answer
the questions that follow on your notebook.
1. Cassandra is creating individual servings of
dessert. She has 16 pili nut candies and 24
chocolates. If she wants each serving to be
identical, with all food included in the servings,
what is the greatest number of servings
Cassandra can create?
a. What is asked in the problem?
b. What facts are given?
c. How will you solve the problem?
d. Show your solution.
e. What is the answer to the problem?
Are you done class?
(pupils will answer the word problem)
Yes, ma’am! (they all answered)
(we will check their answers by calling some
pupils to solve it on the board and reward them
after they solve it)
D. Generalization
What are the 4 step-plan that we need to remember
in solving word problems involving Greatest
Common Factor?
Awesome class! I hope you do not forget those
steps in solving a word problem.
These are as follow:
1. Understand
a. What does the problem ask for?
b. What facts are given?
2. Plan How will you solve the problem?
3. Solve How is the solution done?
4. Check and look back What is the answer
to the problem
IV.
Evaluation
Read and understand the problem, then answer the questions that follow.
Mrs. Perez has 45 pencils and 60 pens to be given to her pupils. Each pupil must receive the
same number of pens and pencils and there will be no pens or pencils left. What is the
greatest number of pupils in her class?
1. What is asked in the problem?
2. What facts are given?
3. How will you solve the problem?
4. Show your solution.
5. What is the answer to the problem?
V.
Assignment
What is Least Common Multiple (LCM)?
Prepared by:
Checked:
JENNY MAE Q. CULALABE
Teacher-Aide/LSB
MADONNA S. PATTALITAN
Head Teacher I
Republic of the Philippines
Department of Education
REGION 02-CAGAYAN VALLEY
SCHOOLS DIVISION OF THE CITY OF ILAGAN
CAPUGOTAN ELEMENTARY SCHOOL
A DETAILED LESSON PLAN IN MATHEMATICS 4
“Least Common Multiple”
Grade: Grade 4
Section: A
I.
Time: 10:00-10:50 AM
Objectives
At the end of the lesson, pupils should be able to:
a. find the common multiples and the least common multiple (LCM) of two numbers using the
following methods: listing, prime factorization, and continuous division; and
b. solve real-life problems involving LCM of 2 given numbers
II.
Subject Matter
A. Topic: “Least Common Multiple”
B. Reference: Mathematics Quarter 2 – Module 3: Least Common Multiple, pg. 1-22
C. Material: TV, laptop, slide presentation, chalk,
D. Value Focus: Helpfulness/Alertness
III.
Procedure
Teacher’s Activity
Pupil’s Activity
A. Preliminary Activities
1. Prayer
2. Greetings
3. Checking of attendance
4. Discussing the Health and Safety
protocols of IATF
5. Discussing New Normal
Classroom rules
B. Preparatory Activities
1. Review
Last time we discuss about
“GCF”
Who can enumerate the 3 ways
Ma’am!
of solving GCF?
Yes, Angelo?
Awesome!
Now, let us review first some
of the concepts that can help
you understand our new lesson
Find the Greatest Common
Factor (GCF) of the given pair
The 3 ways in solving the GCF are Listing
Method, Prime Factorization and Continuous
Division ma’am.
of numbers using any of the
following methods: listing,
prime factorization, and
continuous division.
(Pupils will find the GCF using any of the 3
methods)
8 and 12
7 and 14
2. Motivation
Before we start our lesson. Let’s
have “TOWER CLIMB”
Try to find the Least Common
Multiple (LCM) of 3 and 4 using
Tower Climb.
Follow the steps:
1. Copy the tower shown in a
piece of paper.
2. Write 3 and 4 in the base
blocks. 3. Climb the tower by skip
counting. Use the given numbers
to give their multiples, write the
next number in the next block
(upward direction).
Now, fill in the needed data based
from your observation.
3. Lesson Proper
1. Presentation
Our topic for today is about
Least Common Factor (LCM)
Let us start learning the new
concept with the help of this
story problem. Read the story
problem.
(they will write their answer based on their
observation)
I observed that the first 4 multiples of 3 are:
1. ____ 2. ____ 3. ____ 4. ____
I observed that the first 4 multiples of 4 are:
5.____ 6. ____ 7. ____ 8. ____
I observed that the first common multiple of 3
and 4 is:
9. ____
Their Least Common Multiple (LCM) is:
10.____
The Grade 4 pupils of Ms. Rachel participated
in the recycling activity of the school. They
collected plastic bottles and arranged them in
boxes of 4 and 6. What is the least possible
number of bottles that the class gathered?
What is asked in the problem?
Ma’am!
Yes, Ivy?
Excellent!
The least possible number of bottles that the
class gathered.
What are the given facts that
can help you solve the
problem?
Ma’am!
Yes, Althea?
boxes of 4, boxes of 6
Very good!
What can you say about the
class of Ms. Rachel?
Ma’am!
Yes, Edrian?
Very good!
They are helping restore our planet by means
of recycling.
This problem is about finding
the least common multiple
because it requires us to find
the least possible number of
bottles that the class gathered.
2. Discussion
So, Least Common Multiple
(LCM) is the smallest multiple
common to the given numbers.
You can find the answer to the
given problem using different
methods.
Method 1. Listing Method
List the multiples of 4 and 6.
multiples of 4: 4, 8, 12, 16, 20,
24, 28, 32, 36, 40, 44, …
multiples of 6: 6, 12, 18, 24,
30, 36, 42, 48, 54, 60, 66, …
Find the common multiples of
4 and 6.
Common Multiples: 12, 24,
36, …
Get the smallest or Least
Common Multiple (LCM) of 4
and 6.
LCM: 12
Method 2. Prime
Factorization
Who wants to go the board and
find the GCF of the given
(someone will volunteer to go the board and
number using prime
answer the given data)
factorization?
4
6
4 and 6
2
2
3
2
4=2x2
6=2x3
Let’s proceed to the third
method: Continuous Division
Kindly please read the steps.
Okay let’s solve.
Continuous Division is done following the
steps below.
1. Write the numbers horizontally and find a
prime number that will divide the numbers, if
possible.
2. Divide the numbers by that prime number
and write each quotient below the respective
dividends. Copy any numbers not yet divided
below the dividend.
3. Continue the process until all the quotients
are 1.
Multiply all the prime divisors
to get the LCM.
2 x 2 x 3 x 1 x 1 = 12
LCM :12
Therefore, the least possible
number of bottles that the class
gathered is 12.
Is it clear, class?
Yes, Ma’am!
Any question or clarification?
None, Ma’am.
Let us see if you already know
how to find the Least Common
Multiple (LCM) of a given
pair of numbers
3. Application
Activity 1. Find the first 3
common multiples and the
Least Common Multiple
(LCM) of each pair of
numbers. Some of the
multiples are already given.
Are you done class?
Yes, Ma’am!
Very good! You are doing
great!
4. Generalization
What is LCM again, class?
Least Common Multiple (LCM) is the
smallest multiple common to the given
numbers.
That’s right!
and how to find the LCM of
two numbers?
By using three different ways: listing method,
prime factorization and continuous division.
Awesome!
And for that, bring out 1 whole
sheet of paper and do this
activity.
IV.
Evaluation
Find the Least Common Multiple (LCM) of the given pair of numbers using any of the following
methods: listing, prime factorization, and continuous division.
1. 11 and 22
2. 10 and 20
3. 12 and 3
4. 8 and 24
5. 4 and 16
V.
Assignment
Let us try some more.
A. Find the Least Common Multiple (LCM) of the given pair of numbers using any of the following
methods: listing, prime factorization, and continuous division.
1. 8 and 12
2. 20 and 30
Prepared by:
Checked:
JENNY MAE Q. CULALABE
Teacher-Aide/LSB
MADONNA S. PATTALITAN
Head Teacher I
Republic of the Philippines
Department of Education
REGION 02-CAGAYAN VALLEY
SCHOOLS DIVISION OF THE CITY OF ILAGAN
CAPUGOTAN ELEMENTARY SCHOOL
A DETAILED LESSON PLAN IN MATHEMATICS 4
“Fractions”
Grade: Grade 4
Section: A
Time: 10:00-10:50 AM
I.
Objectives
At the end of the lesson, pupils should be able to:
a. identify proper fractions, improper fractions and mixed numbers;
b. change improper fractions to mixed numbers and vice versa; and
c. change fractions to lowest terms.
II.
Subject Matter
A. Topic: “Fractions”
B. Reference: Mathematics Quarter 2 – Module 4: Fractions
C. Material: TV, laptop, slide presentation, chalk,
D. Value Focus: Cooperating and Focus on the lesson
III.
Procedure
Teacher’s Activity
A. Preliminary Activities
1. Prayer
2. Greetings
3. Checking of attendance
4. Discussing the Health and Safety
protocols of IATF
5. Discussing New Normal
Classroom rules
B. Preparatory Activities
1. Review
What is our last lesson, class?
Yes, Ayesha?
Pupil’s Activity
Ma’am!
Our previous lesson is about Least Common
Multiple ma’am!
Awesome!
Okay class, give the fraction for
the shaded part in the picture.
(pupils raised their hands)
(pupils will go the board and answer the given
shaded picture)
Which is the numerator?
Which is the denominator?
Is the numerator less or greater
than the numerator?
2. Motivation
Take a look with this picture class.
(show picture using power-point
presentation)
Where do you think they are?
(some pupil will answer orally)
Ma’am!
They are in the market ma’am.
Yes, Prince?
That’s right!
How many of you go to the market
(majority of them raised their hands)
with your parents?
3. Lesson proper
1. Presentation
On Saturday morning, Albert
accompanied his mother to the
market to buy ingredients for
their dish. They bought ¾
kilogram of potatoes, 5/4
kilograms of chicken, and a 1
¼ kilograms of meat. Albert
carried the ingredients in going
home.
What ingredients did Albert
and his mother buy?
Ma’am!
Yes, Kenneth?
Potatoes, chicken and meat
What kind of a boy is Albert?
ma’am!
Very good!
2. Performing the activities
I will group you in to 3
working teams. Using
regions/tiles, illustrate the
fractions used in the problem
and identify the kinds of
fraction shown by the regions.
Afterwards, you will present
your output. Do that in 10
minutes. Your timer starts
now.
A helpful boy, ma’am.
Expected answers:
3. Processing the Activities
What can you say about the
first fraction?
Yes, MJ?
Very good!
Is it less or greater than 1
whole?
Can you give other example?
Ma’am!
It is less than the 1 whole
It is less than the whole, ma’am
(they all answered)
¾, 1/5
Yes, Angel?
Very good!
What can you say on the
second fraction?
It is more than 1 whole, ma’am
Can you give other example?
5/3, 6/5
What is a mixed number?
Ma’am!
Yes, Alvin?
It is the combination of a whole and a part of
whole
Excellent!
4. Discussion
So, there are three kinds of
Fractions:
Three Kinds of Fractions:
Notice that:
In the fraction 7/8, the
numerator is smaller than the
denominator. It is a fraction
less than 1. It is a proper
fraction.
In the fraction 9/8, the
numerator is bigger than the
denominator. It is a fraction
greater than 1. It is improper
fraction. A fraction whose
numerator is equal to the
denominator is also an
improper fraction. It is a
fraction equal to 1. An
example is 8/8.
The fraction 1 2/8, contains a
whole number and a proper
fraction. It is a mixed
number.
5. Application
I have here a flashcard with 3
kinds of fraction. I will choose
3 leaders to hold the signs:
Proper Fraction, Improper
Fraction and Mixed Number.
Now, I will also group you
into 3 and you need to form a
line at the center. I will flash
the cards. The first group will
go to the pupil leader to give
the answer for the card. Once
finished answering, they will
go back to their own seats.
Ex.
8/7
4 1/8
5/9
4/5
12/5
9/2
Write P if the given is a Proper
Fraction, I for Improper and M
if it is a mixed Number.
6. Generalization
What is proper fraction?
What is improper fraction?
what is mixed number?
IV.
A fraction whose numerator is smaller than
the denominator. The fraction is less than 1
A fraction whose numerator is bigger than the
denominator. It is a fraction greater than 1.
A fraction whose numerator is equal to the
denominator is also an improper fraction. It is
a fraction equal to 1
A fraction that contains a whole number and a
proper fraction. It is a mixed number
Evaluation
Write the given fractions correctly in the appropriate column in the table.
V.
Assignment
Write P if the given is a proper fraction, I if it is an improper fraction, and M if it is a mixed number.
Prepared by:
JENNY MAE Q. CULALABE
Teacher-Aide/LSB
Checked:
MADONNA S. PATTALITAN
Head Teacher I