LESSON PLAN IN MATHEMATICS V
DATE:__________________
Objective: Solves real life problems involving GCF and LCM of 2-3 given numbers.
Value Focus: Helpfulness and thriftiness
Prerequisite Concepts and Skills:
 Mastery of the basic multiplication facts
 Writing a number as a product of its prime factor.
 Finding common factors and Greatest Factor of 2 -3 given numbers
 Finding multiples and Least Common Multiple of 2-3 given numbers
Materials: cards with numbers pairs for the drill activity, problem written on the chart.
References: Mathematics Teacher’s Guide 4,
Code: M5NS-Ie-71.2,
XL Excelling in Mathematics 5
New High School Mathematics Elementary Algebra Chapter 2 page 71-74. (In LM)
http://www.k5learning.com/sites/all/files/GCF-and-LCM-word-problems-2RGr5.pdf
http://www.summit.k12.co.us/cms/lib04/CO01001195/Centricity/Domain/445/GCF
%20and%20LCM%20WORD%20PROBLEMS.pdf (in LM)
Instructional Procedure:
A. Preliminary Activities
1. Drill
Have a drill on:
 Finding common factors and Greatest Common Factor of two to three given numbers
 Finding common multiples and Least Common Multiple of 2 -3 given numbers
You can use the following exercises
Find the common factors and GCF of the following number pairs
15, 20 and 30
12, 16 and 48
120 and 100
42 and 105
120, 75, and 150
Answers: (5,4, 20, 21, 15)
Find the common multiples and LCM of the following numbers.
12 and 15
27 and 48
2
16 and 9
6, 12 and 32
14, 21 and 28
Answers: (60, 432, 144, 96, 84)
28
2. Review
Conduct a review on how to express a number as a product of its prime factors. Provide
examples example for this.
3. Motivation
Present a picture of a boy helping her mother in a flower shop. Ask the pupils to tell
something about the picture. Elicit the value of helpfulness.
B. Developmental Activities
1. Presentation
Present each problem to the class.
Elmer wants to cut as many pieces of wood of equal lengths from three pieces with lengths
35dm, 49dm, and 56 dm. What is the longest that he could cut each piece? (Answer: 7dm)
Have the pupils read the problem. Then ask: What is Mang Dencio planning to do?
Two lights blink at the same time at 6:00 am. One light blinks every 15 minutes. The other
blink every 12 minutes. At what time will both lights blink together again?
(Answer: 60 minutes or 1 hour)
Have the pupils read the problem. How will you solve for the answer to each problem.
2. Performing the Activities
Group the pupils into six working teams and have them perform the task.
Problem A.
Solution 1: Finding the Greatest Common Factor (GCF) by listing the factors of 28 and 14
The factors of 28 are 1, 2, 4, 7, 14, and 28
The factors of 14 are 1, 2, 7, and 14
Common Factors: 1, 2, 7, and 14
Greatest Common Factor: 14
Solution 2: Finding the Greatest Common Factor (GCF) of 28 and 14 by prime factorization.
28 = 2x2x7
14 = 2x7
GCF = 14
3. Solution 3: Finding the GCF of 28 and 14 by continuous division
2
14
28
2
7 14
7
1
2
GCF: 2X7 = 14
3. Processing the Activities
 We used the 4 step plan in solving problem involving GCF and LCM of two to three numbers:
Understand, Plan, Solve, and check and look back.
 We solved for the answer by listing method, prime factorization, and continuous division.
4. Reinforcing the Concept and Skill
Discuss the presentation. On page ____of LM Math Grade V,
Have the pupils solve the following problems.
1. There are 48 cups of mango juice and 72 cups of orange juice to be arranged in equal rows. Each row
should have only one kind of juice. What is the greatest number of cups that can be in one row?
(answer: 8 cups)
5. Summarizing the Lesson
Summarize the lesson by asking: How do we solve problem solving GCF and LCM of two or three given
numbers?
 We use the 4 – step plan in solving problems involving GCF and LCM of two to three given numbers.
Understand, Plan, Solve, and Check and Look Back.
 We solve for the answer by listing method, prime factorization, and continuous division.
6. Applying to New and Other Situations
Have the pupils do the exercises under Apply your Skills on page 99 LM Math Grade V. Encourage
some pupils to show and discuss the answers.
C. Assessment
Read and solve each problem. Write your answer on your answer sheet.
1. Mrs.Dela Cueva’s class is composed of 20 boys and 30 girls. If she is going to make groups of boys and
groups of girls for the activities. What is the biggest number of children in the group if they are of the
same number? (answer: 5 in each group)
D. Home Activity
Remediation
Provide more practice on finding the GCF and LCM of two numbers. Then, give problems similar to
those given in the lesson.
Enrichment
Read and solve each problem. Write the answer in your notebook.
1. Sharon has 15 oranges, 9 peaches and 18 pears. She wants to put all of the fruit into baskets with
each basket having the same number of pieces of fruit in it. Without mixing the fruit, what is the
greatest number of pieces of fruit Sharon can put in each basket?
(Answer: 3 pieces)
2. Cups are sold 5 to a package and plates are sold 10 to a package. If you want to have the same
number of each item for a party, what is the least number of packages of each you need to buy?
(Answer: 20)
LESSON PLAN IN MATHEMATICS V
DATE:__________________
Objective: Solves real-life problems involving GCF and LCM of 2-3 given numbers
Value Focus: Fairness
Prerequisite Concept and Skills:
 Finding common factors and the GCF o 2-4 numbers using continuous division
 Finding common multiples and LCM of 2-4 numbers using continuous division
 Steps in problem-solving
Materials: Problem Charts, popsicle sticks/marbles/bottle crowns to be used as counters
References: K to 12 Grade 5 curriculum (M5NS-Ie-70.2); Lesson Guides in Elementary Mathematics 5 pp 36, 47;
Realistic math 5 p. 49; Soaring 21st Century Math 5 pp. 107, 112-113
Instructional Procedure:
A. Preliminary Activities
1. Drill:
Have a drill on finding GCF and LCM.
2. Review:
Conduct a review on how to find GCF and LCM of 2-4 numbers using continuous division.
3. Motivation:
Who among you have brothers and sisters? When mother buys candies for you, do you divide them
equally? (Stress on the importance of fairness when dividing.)
B. Developmental Activities
1. Presentation
Present this situation to the class.
The Pineda Family has 24 apples and 36 oranges to be given to street children;
They want the same number of fruit of each kind in each bag. What is the greatest
number of each fruit can be given to each child?
2. Performing the Activities
Group the pupils. Let them work on counters to come up with the answer to the given problem.
Materials: manila paper, counters
Mechanics:
a. Each group will represent the numbers of apples and oranges using counters.
b. They will work on the counters to find the answer to the problem.
c. Each group will present their answer on the board when done.
3. Processing the Activities
After all the groups have presented their answers on the board, their answers will be processed.
Ask: How many possible groups can be formed using the 24 apples? 36 oranges?
-24 Apples-by 2’s (12), 3’s (8), 4’s (6), 6’s (4), 8’s (3), 12’s (2), 24’s (1)
-36 oranges-by 2’s (18), 3’s (12), 4’s (9), 6’s (6), 9’s (4), 12’s (3), 18’s (2) 36’s (1)
What number of possible groups are the same for the apples and oranges?
-1, 2, 3, 4, 6, 12
Which is the greatest? 12
Having the greatest number of groups, how many apples/oranges can be in each group? 24 ÷
12 = 2 apples; 36 ÷ 12 = 3 oranges
4. Reinforcing the Concept and Skill
Working in Groups
Each group will be given a problem card to solve and present accordingly.
A group of 45 dancers will march behind a group of 30 clowns in a parade. You want to arrange
the two groups in rows the same number of people in each row, but without mixing groups. What
is the greatest number of people you can have in each row.
Group 1: Using counters
Group 2: Using an illustration or drawing
Group 3: Using common factors
5. Summarizing the Lesson
How do we solve real-life problems involving GCF and LCM of 2-3 given numbers?
-Using counters, illustrations, factors/multiples
6. Applying to New and other Situations
Solve this problem.
1. Elsa has 27 violet marbles, 54 blue marbles, and 72 white marbles. She wants to divide the
marbles into groups so that each group has the same number of each color. What is the
greatest number of group that Elsa can make? Explain.
2. Two buses left the station at the same time. Bus A stops after 3 kms while Bus B stops
after 5 kms. At what closest distance will both buses stop?
C. Assessment
A. Solve the following word problems.
1. The blue light of a Christmas light blinks every 2 seconds, the red light every 3 seconds and the
yellow light every 5 seconds. Every how many seconds will they light at the same time?
2. Three bamboo sticks with length 36 cm, 45 cm and 54 cm are to be cut into equal lengths to build
a pen. What is the greatest possible length to cut so as to leave no remainder?
D. Home Activity
Remediation
Directions: Solve these word problems using representations.
a) Danny has a rectangular piece of paper 28 cm by 32 cm. She wants to cut into squares of the
same size without wasting any part of the paper. What is the longest side of a square can she
make?
Enrichment
Directions: Solve these word problems:
a) Tony cleans the hall every 5 days. Martin cleans the same every 4 days. They worked together
on June 4, when will they work together again?
LESSON PLAN IN MATHEMATICS V
DATE:__________________
Objective: Create problems (with reasonable answers) involving GCF and LCM of 2-3 given numbers.
Value Focus: Using spare time for hobbies
Prerequisite Concepts and Skills:
 Mastery of the basic multiplication facts
 Knowledge on finding the GCF and LCM of two to three given numbers.
 Knowledge on creating problems with reasonable answers.
Materials: flash card, drill board, chart
References: Mathematics Teacher’s Guide 4, Code: M5NS-Ie-71.2,
Excelling in Mathematics 5 page 38-41
ttp://www.k5learning.com/sites/all/files/GCF-and-LCM-word-problems-2RGr5.pdf
http://www.summit.k12.co.us/cms/lib04/CO01001195/Centricity/Domain/445/
GCF%20and%20LCM%20WORD%20PROBLEMS.pdf
Instructional Procedure:
A. Preliminary Activities
1. Drill
Have a drill on solving problems involving finding the GCF and LCM. Provide exercises on
this.
You can use the following exercises
Find the common factors and GCF of the following number pairs
18, 36, and 90
120, 200 and 100
6, 12, and 30
Answer: (9, 20, 6)
2. Review
Have a review on how to find the GCM and LCM of two to three numbers.
3. Motivation
Talk about their favourite collection?
What do you collect for your hobby?
Instill the value of “using spare time” for a favourite hobby.
E. Developmental Activities
1. Presentation
Present each problem to the class. Ask the pupils to give some question about the problem.
Problem A:
Magellan has decided to make party baskets for the fund raiser. Balloons are
sold in bags of 20, party horns are sold in bags of 10, and there are 8 candy
bars in a package. How many of each should he buy so there are an equal
number of balloons, horns and candy bars in each basket?
Problem B:
Cups are sold 5 to a package and plates are sold 10 to a package. If you want
to have the same number of each item for a party, what is the least number of
packages of each you need to buy?
Discuss with the class each problem.
Ask: How will you solve for the first problem? second problem?
Ask: Can you create problem similar to these problems?
5. Performing the Activities
Group the pupils into five working teams. Ask the groups to create a problem similar to the
ones given. Give them enough time to perform the task.
6. Processing the Activities
Let the groups present and discuss the problem they have created.
Ask: How did you come up to that kind of problem?
Expected Answers:
 We familiarized ourselves with the concept and its application to real-life situation.
 We read some word problems related to the lesson.
 We thought of the type of problem we wanted to create.
7. Reinforcing the Concept and Skill
Discuss the presentation. On page ____ of LM Math Grade V.
Then, give the following exercises.
A. Have the pupils create a problem similar to the one below.
Tony needs to ship 12 comedy DVDs, 24 animated DVDs, and 30 musicals. He can pack
only one type of DVD in each box and he must pack the same number of DVDs in each box.
What is the greatest number of DVDs Tony can pack in each box?
B. Ask the pupils to work on exercises under Get Moving on page ____. Check their Answers.
C. For more practice, let them answer the exercises under Keep Moving on page ______ of
LM Math V. Check on the pupil’s answers.
8. Summarizing the Lesson
Summarize the lesson by asking: How do we create problem involving GCF and LCM of two or
three given numbers?
 Familiarize oneself with the concept, and its application in real – life situations.
 Think of the type of problem you want to create.
 Read some problems and study their solutions.
6. Applying to New and Other Situations
Have the pupils do the exercises under Apply your Skills on page _____ LM Math Grade V.
2. Assessment
Create a problem involving GCF and LCM for each set of information given below.
1. 50 apples, 15 oranges and 25 bananas, packages of different fruits biggest number of fruits in a
box.
2. 8 ball pens, 12 pad papers and 2 erasers, smallest number of school supplies in a pouch.
3. Home Activity
Remediation
Complete the problem by making a question.
1. In preparation for a party, Brent is putting desserts onto platters. The chocolate cake is cut
into 15 pieces, strawberry cake cut into 30 pieces and the cheesecake is cut into 6 pieces.
He wants to prepare identical platters without having any cake left over.
2. Wilma is thinking of a number that is divisible by both 17 and 8. Think of the smallest
possible number.
Enrichment
Create 2 problems involving Finding the GCF and LCM in two to three numbers.
LESSON PLAN IN MATHEMATICS V
DATE:__________________
Objective: Creates problems (with reasonable answers) involving GCF and LCM of 2-3 given numbers
Value Focus: Pride in own creation
Prerequisite Concept and Skills:
 Finding common factors and the GCF o 2-4 numbers using continuous division
 Finding common multiples and LCM of 2-4 numbers using continuous division
 Solves real-life problems involving GCF and LCM of 2-3 given numbers
Materials: Problem Charts, word/number cards
References: K to 12 Grade 5 curriculum (M5NS-Ie-71.2); Lesson Guides in Elementary Mathematics 5 pp 36, 47;
Realistic math 5 p. 49; Soaring 21st Century Math 5 pp. 107, 112-113
Instructional Procedure:
A. Preliminary Activities
1. Drill:Tell whether the third number is the GCF or LCM of the first two numbers.
a. 5, 7, 35
2. Review:
What is GCF? LCM? How do we find each?
3. Motivation:
Have you experienced creating something on your own? What did you feel when you were able to do it?
B. Developmental Activities
1. Presentation
Today we will create our own problems involving GCF and LCM.
2. Performing the Activities
a. Go back to the problems used in Lesson 13.
b. Ask pupils if the problems looked for GCF or LCM.
c. Put together the problems that involved finding GCF on the left and finding LCM on the right.
3. Processing the Activities
Ask: What do you find similar/the same among the problems involving finding GCF? LCM? What will
we need to form our own problem?
4. Reinforcing the Concept and Skill
Working in Groups
Each group will be given an envelope with number and word cards in it. Using the given
information, they will be askes to create their own problem involving GCF/LCM.
5. Summarizing the Lesson
How do we create real-life problems (with reasonable answers) involving GCF and LCM of 2-3 given numbers?
6. Applying to New and other Situations
Use the following details to create your own problem involving GCF/LCM.
1. GCF- 24 girls, 18 boys, form equal rows, greatest number of rows
2. LCM- 6 cm ribbons, 8 cm ribbons, 12 cm ribbons, form the shortest equal length
C. Assessment
Create 1 problem each involving GCF and LCM. Use any of the information from the box.




A 36 cm by 42 cm cartolina cut into squares
2 alarms: Alarm 1 rings every 4 hours, Alarm 2 rings every 6 hours
30 mangoes and 18 papayas to be places in baskets
3 ribbons to be cut into equal lengths: 48 cm, 40 cm and 56 cm
D. Home Activity
Remediation
Directions: Copy 1 problem each involving GCF and LCM. Replace the given facts to form a new
problem and solve.
Enrichment
Directions: Create 2 problems each involving GCF and LCM of 2-3 given numbers and solve.
LESSON PLAN IN MATHEMATICS V
DATE:__________________
Objective: Adds fractions and fixed fractions without and with regrouping
Value Focus: Recycling used materials
Prerequisite Concept and Skills:
 Adding similar and dissimilar fractions
 Renaming improper fractions to mixed numbers
 Simplifying fractions to lowest terms
Materials: flash cards, number cards, problem chart
References: K to 12 Grade 5 Curriculum (M5NS-Ie-84); Lesson Guide in Elementary Mathematics 5, pp 79-115;
Soaring 21st Century Mathematics 5, pp. 143-148; Realistic Math 5, pp 75-85
Instructional Procedure:
A. Preliminary Activities
1. Drill: Conduct a drill on adding similar fractions using flash cards.
2. Review: Review how to add dissimilar fractions using the Least Common Denominator (LCD)
3. Motivation
What do you do with old newspapers, used papers and empty bottles you have at home? (Emphasize
that these materials maybe recycled.)
B. Developmental Activities
1. Presentation
Present the problem.
Carlo collects old newspapers and empty bottles from his neighbors and brings them to the nearby
junkshop. He collected 3 1/4 kilograms of newspapers and 2 2/5 kilograms of empty bottles. How many
kilograms of recyclable materials did he collect?
Ask: What is given? What is being asked? How do we solve the problem?
2. Performing the Activities
Group the pupils into working teams. Let them think of ways to solve the problem. Let them present
their work on the board.
3. Processing the Activities:
Ask: How did you find your answers? How do we add fractions in mixed forms?
4. Reinforcing the Concept and Skill:
Discuss more examples. Let pupils volunteer to show solutions on the board.
a)
7
1
c) 7
1
+
=
+ 4
=
15
5
8
4
b)
2
1
d)
5
2
+
=
7
+ 8
=
8
6
12
9
5. Summarizing the Lesson
Lead the pupils to give the following generalization by asking: “How do we add fractions and
mixed fractions without and with regrouping?”
5
To add fractions:
a) Similar Fractions-add the numerators, copy the denominator. Reduce the
answer to lowest term.
b) Dissimilar Fractions- rename the fractions as similar fractions and add.
To add mixed forms:
a) Add the fractions.
b) Add the whole numbers.
c) Reduce the answer to lowest term if possible.
6. Applying to New and other Situations
Find the sum. Express your answers in lowest term if needed.
a)
2
1
c) 2
5
+
=
+ 7
=
5
3
3
9
b)
2
6
4
+
5
=
9
d)
3
8
8
3
4
+
9
3
8
15
=
7
+
12
9
3
4
=
C. Assessment
Add and reduce the sum in lowest terms.
a)
2
3
c) 9
+
=
+
8
4
10
b)
10
5
6
7
=
8
+
d)
11
=
C. Home Activity
Remediation
Fill in the box with the correct number.
a) 2
7
7
+
=
+
=
5
10
10
10
10
b)
c)
4
5
6
+
7
8
=
4
24
+
24
=
4
24
=
5
24
1
1
+ 9
=
6
+ 9
=
4
3
12
12
12
In the following squares, add across and down and write your answers in simplest forms.
Enrichment
In the following squares, add across and down and write your answers in simplest forms.
6
6
1/5
8/15
3 4/5
9/10
7 3/8
2 1/4
9 5/6