Lesson guide gr. 3 chapter ii -rational numbers, fractions v1.0

Lesson Guide
In
Elementary Mathematics
Grade 3
Reformatted for distribution via
DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL
DEPARTMENT OF EDUCATION
BUREAU OF ELEMENTARY EDUCATION
in coordination with
ATENEO DE MANILA UNIVERSITY
2010
Chapter II
Rational Numbers
Fractions
INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011

Lesson Guides in Elementary Mathematics
Grade III
Copyright © 2003
All rights reserved. No part of these lesson guides shall be reproduced in any form without a written
permission from the Bureau of Elementary Education, Department of Education.
The Mathematics Writing Committee
GRADE 3
Region 3
Agnes V. Canilao – Pampanga
Josefina S. Abo – Tarlac City
Alma Flores – Bataan
Region 4 - A
Cesar Mojica – Regional Office
Marissa J. de Alday – Quezon
Henry P. Contemplacion – San Pablo City
Region 4 – B
Felicima Murcia – Palawan
National Capital Region (NCR)
Laura N. Gonzaga – Quezon City
Dionicia Paguirigan – Pasig/San Juan
Yolita Sangalang – Pasig/San Juan
Bureau of Elementary Education (BEE)
Elizabeth J. Escaño
Galileo L. Go
Nerisa M. Beltran
Ateneo de Manila University
Pacita E. Hosaka
Support Staff
Ferdinand S. Bergado
Ma. Cristina C. Capellan
Emilene Judith S. Sison
Julius Peter M. Samulde
Roy L. Concepcion
Marcelino C. Bataller
Myrna D. Latoza
Eric S. de Guia - Illustrator
Consultants
Fr. Bienvenido F. Nebres, SJ – President,
Ms. Carmela C. Oracion – Principal,
High School
Ms. Pacita E. Hosaka – Ateneo de Manila
University
Project Management
Yolanda S. Quijano – Director IV
Angelita M. Esdicul – Director III
Simeona T. Ebol – Chief, Curriculum Development Division
Irene C. Robles – OIC - Asst. Chief, Curriculum Development Division
Virginia T. Fernandez – Project Coordinator
EXECUTIVE COMMITTEE
Jesli A. Lapus – Secretary, Department of Education
Teodosio C. Sangil, Jr. – Undersecretary for Finance and Administration
Jesus G. Galvan – OIC - Undersecretary for Programs and Projects
Teresita G. Inciong – Assistant Secretary for Programs and Projects
Printed By:
ISBN – 971-92775-2-1

iii
TABLE OF CONTENTS
Introduction ..................................................................................................................................iv
Matrix ........................................................................................................................................v
II. RATIONAL NUMBERS
A. Division
Identifying Fractions Less Than One .............................................................................. 1
Telling the Relationship Between Fractions Less than One ........................................... 5
Ordering Fractions Less than One Having One as Numerators..................................... 9
Identify Fractions Equal to One....................................................................................... 13
Identify Fractions More than One.................................................................................... 16
Ordering Fractions Equal to One, Less than One and More than One with the same
Denominators..................................................................................................... 20
Finding the GCF (Greatest Common Factor) of Two Given Numbers ........................... 25
Reducing Fractions to Lowest Terms ............................................................................. 29
Finding Fractional Part of a Set/Region.......................................................................... 33

iv
I N T R O D U C T I O N
The Lesson Guides in Elementary Mathematics were developed by the
Department of Education through the Bureau of Elementary Education in
coordination with the Ateneo de Manila University. These resource materials
have been purposely prepared to help improve the mathematics instruction in
the elementary grades. These provide integration of values and life skills using
different teaching strategies for an interactive teaching/learning process.
Multiple intelligences techniques like games, puzzles, songs, etc. are also
integrated in each lesson; hence, learning Mathematics becomes fun and
enjoyable. Furthermore, Higher Order Thinking Skills (HOTS) activities are
incorporated in the lessons.
The skills are consistent with the Basic Education Curriculum
(BEC)/Philippine Elementary Learning Competencies (PELC). These should be
used by the teachers as a guide in their day-to-day teaching plans.

v
MATRIX IN ELEMENTARY MATHEMATICS
Grade III
COMPETENCIES VALUES INTEGRATED STRATEGIES USED
MULTIPLE INTELLIGENCES
TECHNIQUES
With HOTS
I. Rational Numbers
A. Comprehension of Fractions
1. Order fractions less than one/equal to
one/more than one
1.1 Identify fractions less than one Sharing Modeling
Drawing pictures
Drawing (Spatial) 
1.2 Order fractions less than one Active participation Drawing pictures
Modeling
Play (Bodily kinesthetic)
Drawing (Spatial)

1.2.1 Tell the relationship between
fractions less than one
Health consciousness Simplifying the problem
Modeling
Drawing pictures
Cooperative
groups(Interpersonal) Drawing
(Spatial)

1.3 Identify fractions equal to one Neatness Modeling
Write equation
Games (Bodily kinesthetic) 
1.4 Identify fractions more than one Concern for others Simplifying the problem
Drawing pictures
Song (Musical) "Looking for a
Partner" Game(Bodily
kinesthetic)
Drawing (Spatial) Game "Giant
Step" (Bodily kinesthetic)
Cooperative
groups(Interpersonal)

1.5 Order fractions less than one/equal to
one/more than one
Health consciousness Modeling/drawing
pictures
"Giant Step" Game (Bodily
kinesthetic) Cooperative

2. Change fractions to lower forms
2.1 Tell the greatest number by which two
given numbers can exactly be divided
2.1.1 Give the GCF (Greatest Common
Factor) of 2 given numbers
Thriftiness Listing Games (Bodily kinesthetic)
Cooperative

2.2 Reduce fractions to lowest terms Sharing Simplifying the problem Illustrations (Spatial) Song
(Musical


vi
3. Find the fractional part of set/regions
e.g. 1/3 of 12
1/4 of 20
1/2 of 8
Helpfulness Acting out the problem Games (Bodily kinesthetic)
Cooperative


1
Identifying Fractions Less Than One
I. Learning Objectives
Cognitive: Identify fractions less than one
Psychomotor: Read and write fractions less than one
Affective: Practice the habit of sharing
II. Learning Content
Skills: 1. Identifying fractions less than one
2. Reading and writing fractions less than one
Reference: BEC PELC II A.1.1
Materials: textbooks, flash cards, coloring materials
Value: Sharing
III. Learning Experiences
A. Preparatory Activities:
1. Drill
Name the shaded part/unshaded part
2
1
3
1
4
2
8
3
2. Review – Parts of a fraction
1. What does 1 mean in
2
1
’
3
1
; 2 in
4
2
; 3 in
8
3
?
2. What do you call them?
3. What does 2 mean in
2
1
? 3 in
3
1
? 3 in
8
3
?
4. What do you call them?
3. Motivation
Show a cake model.
On Mary’s birthday, her mother baked a cake. She divided it into 8 equal parts to be
shared among her friends.
What do you call one of the equivalent parts? 8
1
Who can write the fraction in figure? 8
1
Write it in words. One eighth

2
Mary is a generous girl because she shares the cake to her friends. Do you also share
things to your friends and family? What are the things that you share to your friends? Your
family?
B. Developmental Activities:
1. Presentation
a. Show an illustration of the cake on the board
b. Let the pupil shade two of the eight equivalent parts.
How many parts are shaded?
The shaded parts were given to Rose and Josie.
What part of the whole cake was given to Rose and Josie?
Who can represent the shaded parts in figures? 8
2
Read the fraction.
How do we write it in words? Two eighths
Now, what part of the whole cake was left? 8
6
six eighths
Ask the pupil to write the fraction in figures and in words.
Let the pupils shade the whole region.
What fraction represents the whole region? 8
8
Is 8
8
equal to the whole region?
Write: 8
8
= 1
Is 8
2
less than 8
8
? Is 8
6
less than 8
8
?
c. Comparing parts of whole region (use cut-out of shapes)
Present the figures below.
Let the pupils observe the figures.
Ask: How many equivalent parts does each figure have?
Have the pupils write the numerals representing the number of equal parts each
figure has.
Let the pupils write the numerals representing the shaded parts in their show me
cards.
Ask the pupils to match their show me cards with the cut-out shapes.
Let the pupils compare the fraction by using the symbols >, <.
Which is greater? 4
1
or 3
2
, 4
3
or 4
1
, 5
3
or 4
1
, 3
2
or 4
3

3
4
1
or 4
4
, 5
3
or 5
5
, 3
2
or 3
3
2. Guided Practice
a. Drawing regions for the given numerals.
Let the pupils draw regions to represent the following fractions.
4
1
3
2
4
3
5
1
6
1
b. Comparing parts of a fraction (Numerator and Denominator)
What do we call? 1 in 4
1
, 2 in 3
2
, 3 in 4
3
etc.
What does the numerator represent?
What does the denominator tell us?
c. Using a number line, ask pupils to divide it into 5 equivalent parts.
5
1
5
2
5
3
5
4
5
5
Into how many equivalent parts is the line segment divided?
What do you call 2 of the equivalent parts?
Write the fraction in figure and in words. 5
2
two fifths
You can see in the illustration that 1 is equal to 5
5
, read all the fractions less than one
or 5
5
.
What can you say about the numerators of these fractions in relation to their
denominators? The numerators are less than the denominators.
We call these, fractions less than one.
3. Generalization
How do we know if a fraction is less than one?
A fraction is less than one when the numerator is less than the denominator.
C. Application
A. Play “Who Am I?”
1. I am a fraction equal to one. My denominator is 9. Who am I?
2. I am a fraction that shows 5 of 9 equal parts. Who am I?
3. I am a fraction whose denominator is 4 and my numerator is 2 of the equivalent parts.
Who am I?
B. Pair Square
1. Find all possible fractions in which the sum of the numerator and denominator is greater
than the numerator. What do you notice?
2. Find a fraction in which the difference of the numerator and denominator is 3 and the sum
is 8.

4
IV. Evaluation
A. Do what is asked.
a. Divide the following into halves, thirds and fourths.
a. Shade one of the equivalent parts.
c. Write the fraction name for the shaded part.
B. Write √ if the fraction is less than one and x if it’s is not less than one.
_____ 1)
3
2
_____ 2)
12
4
_____ 3)
3
4
_____ 4)
7
8
_____ 5)
9
7
_____ 6)
10
11
_____ 7)
11
8
_____ 8)
7
3
_____ 9)
10
12
_____ 10)
2
3
V. Assignment:
A. Circle the fractions less than 1.
1)
4
2
,
3
5
,
4
4
2)
6
6
,
10
12
,
5
1
3)
8
5
,
7
9
,
5
6
4)
2
1
,
2
3
,
3
4
5)
5
5
,
7
3
,
4
6

5
B. Draw and shade to show the fraction.
1. 2. 3.
4. 5.
Telling the Relationship Between Fractions Less Than One
Cognitive: Tell the relationship between fractions less than one
Psychomotor: Show relationship between fractions by using the symbols > and <
Affective: Practice eating the right kinds of food
Skills: 1. Telling the relationship between fractions less than one
2. Reading and writing fractions less than one
Reference: BEC PELC II A.1.2.1
Materials: cut-outs with color shaded parts, diagram showing fractions less than one
Value: Health consciousness
A. Preparatory Activities
1. Drill - Naming fractions less than one.
1. Show cut-outs of regions with shaded parts
2. Ask the pupils to name the shaded parts.
2. Review - What do you call fractions whose numerators are less than the denominators?
5
4
6
5
3
2
4
2
8
1

6
3. Motivation
Do you like vegetables? What particular vegetable do you like? Why do we eat vegetables?
Problem illustration
Corn is grown in 6
2
of a farm and vegetables in 6
1
. Which is greater, the part where corn
is grown or the part where vegetables are planted?
1. Presentation
a. Show a representation of the problem.
Ask the pupils to shade the part where corn is grown and the part where vegetables are
planted.
Write the fraction representing the part where corn is grown. 6
2
Write the fraction representing the part where vegetables are planted. 6
1
What part of the farm is not planted? 6
3
What fraction represents the whole farm? 6
6
Which of these fractions is less than one? 6
2
6
1
6
3
Why do we call these fractions less than one?
b. Have pupils compare the fractions representing the parts of the farm.
1. Which is greater, the part where corn is grown or the part where vegetables are
planted? Which is lesser the part representing where nothing is planted or the part
where corn is grown?
2. Show the relationship of the fractions by using symbols > and <.
6
2
>
6
1
6
3
>
6
2
6
1
<
6
2
6
2
<
6
3
This figure is a representation of the
farm in the problem.
Part where corn is grown.
Part where vegetables are planted.

7
c. Observing illustrations and comparing fractions less than one.
Show 2 cut-out of fractions.
Write the fractions in figures and in words. 4
1
one-fourth 3
1
one-third
Which is greater 4
1
or 3
1
?
Which expression tells correctly the relationship between the 2 fractions?
1. 4
1
> 3
1
2. 4
1
< 3
1
3. 4
1
= 3
1
d. Ask the pupils to illustrate the problem below.
One-third of Tom’s vegetable plot is planted to camote and two-sixths to mongo
seedlings? Show the relationship of the fraction by using > and <.
To what food groups do camote, camote tops and mongo belong? Go, glow or grow?
Why do we need to eat these kinds of food?
Do you eat enough of these kinds of food daily?
2. Guided Practice
a. Use of number line
Ask the pupils to divide the line segment into 5 equivalent parts.
5
1
5
2
5
3
5
4
5
5
b. Show the relationship by using > or <.
 Group pupils into learning barkadas.
 Distribute illustrations of regions and number lines representing fractions less than
one.
 Ask pupils to write the fractions in figures and in words.
 Ask other pupils to show the relationship of the fractions by using > and <.
3. Generalization
What symbols do we use to show relationships between fractions less than one?
We use the symbol > (is greater than) and < (is less than) to show relationship between
fractions less than one.

8
C. Application
A. Compare the following fractions. Write <, > on the blanks.
1)
2
1
___
4
2
3)
4
3
___
2
1
5)
5
4
___
9
8
2)
8
1
___
10
2
4)
5
2
___
9
1
B. Prove that the relationship is true or false.
1.
4
3
>
5
4
= ______ 2.
5
4
<
6
3
=______ 3.
3
2
>
6
4
= ______
4.
4
1
<
8
1
= ______ 5.
9
2
>
7
3
= ______
C. Pair Square
1. Three-eights of a class built a diorama;
20
5
built a wishing well. Which activity had more
members?
2. Mrs. Reyes has
5
3
gallon of water. Mrs. Lopez has
8
6
gallon of water. Who has more
water? Why?
IV. Evaluation
A. Look at the illustrations. Compare the shaded part. Use > or <.
1)
4
1
___
8
4
2)
3
1
___
4
1
3)
8
4
___
3
1
B. Show by illustrations the relationship of the following fractions.
1)
8
7
3
1
2)
6
5
6
3
3)
3
2
4
2

9
4)
4
1
2
1
5)
5
1
4
3
V. Assignment
A. Ring the fraction in column B which is greater than the given fraction in column A.
A B
1)
2
1
4
1
5
1
3
2
2)
4
3
8
1
10
9
2
1
3)
8
2
5
2
4
1
8
3
4)
4
1
2
1
5
4
3
2
5)
3
2
6
4
7
2
5
1
B. Write < or > on the blank to make each sentence true.
1)
6
1
______
4
3
2)
6
2
______
3
2
3)
3
1
______
6
4
4)
9
3
______
8
4
5)
8
3
______
8
4
Ordering Fractions Less Than One having 1 as Numerators
Cognitive: Order fractions less than one having 1 as numerators
Psychomotor: Shade parts of whole regions and write their fraction names
Affective: Participate actively in group activities
Skill: Ordering fractions less than one having 1 as numerators
Reference: BEC PELC II A 1.2
Materials: textbooks, fraction kit, flash cards, coloring materials, Show Me Cards
Value: Active participation in group activities

10
1. Drill: Distribute “Show me cards” to the pupils with fraction names. As the teacher
flashes the cards, the pupil shows the fraction name of the shaded part of each region.
2. Review: What are fractions less than one?
Is 2
1
a fraction less than one? Why?
3. Motivation
Introductory questions:
Do you have friends/barkada? Do you invite them in your house? What are the things you
do?
A group of friends was given a rice cake. Mary ate 2
1
, Rose 6
1
, Carol 8
1
and Camille 4
1
.
Who consumed the most? the least?
B. Developmental Activities
1. Presentation
a. Problem illustration using regions
1. Distribute fraction circles to pupils. Let them divide the circular regions by showing
the amount of cake consumed by each. Ask the pupils to shade the designated part
using crayons.
Mary
3
1
Carol
8
1
Camille
4
1
Rose
6
1
Who consumed the least? Who consumed the greatest?
2. Arrange a diagram to compare fractions less than one.
b. Observing a diagram to compare fractions less than one
1. From the diagram, write 2 fractions on the board and compare them using the
symbols > and <.
2
1
3
1
4
1
5
1
6
1
7
1
8
1

11
2. Order the fractions on the diagram from least to greatest.
c. Problem illustration using a number line
In the fable, “The Turtle and the Hare”, the hare had covered a distance of 2
1
from
the starting point to the end point before it decided to take a nap. Meanwhile the
persistent turtle has covered 8
1
.
Show the distance covered using the number line
8
1
2
1
Which is greater, 2
1
or 8
1
2. Guided Practice
a. Game – Using cut-outs and show me cards.
1. Distribute cut-outs to pupils with fractions printed on them.
2. Tell them to read the direction at the back of the cut-out.
3. Have them write their answer on their show me cards.
Directions: Order the fractions from greatest to least
Order the fractions from least to greatest
b. Cooperative Learning – group activities – contest
1. Group pupils into learning barkadas
2. Distribute cut-outs showing fractions with shaded parts.
3. Let the pupils arrange them from least to greatest and vice-versa.
4. Ask them to read the fractions as they move forward to show the regions.
5. The fastest group to form the line in correct order wins the game.
3. Generalization
How do we order fractions less than one?
When ordering fractions less than one with one as the numerators, remember that the
greater the denominator the lesser is the value of the fraction.
C. Application
1. In a pie-eating contest, Mary ate 2
1
of a pie, Lori 4
1
and Mercy 8
1
. Who ate the most? the
least?
2. Contest – Let the pupils participate in a softdrink drinking contest, Measure the amount of
liquid consumed by each contestant. Write the fraction names.
4
1
3
1
2
1
8
1
9
1
5
1
10
1
9
1
6
1
2
1
3
1
2
1
4
1
3
1
5
1
6
1
7
1
6
1
8
1
12
1
9
1
2
1
4
1
4
1
7
1
3
1
2
1
6
1
10
1
8
1
5
1

12
IV. Evaluation
1. Draw regions showing 2
1
, 3
1
, 4
1
, 5
1
and 6
1
. Color the shaded parts and arrange them from least
to greatest.
2. Arrange the fractions from least to greatest.
1)
7
1
5
1
2
1
3
1
3)
4
1
3
1
6
1
2
1
5)
9
1
8
1
10
1
4
1
2)
9
1
10
1
4
1
3
1
4)
8
1
2
1
3
1
7
1
3. Prove that the fractions are arranged from least to greatest.
Reason
1)
9
1
7
1
15
1
3
1
2
1
= ___________________
2)
10
1
8
1
5
1
3
1
2
1
= ___________________
3)
12
1
13
1
14
1
15
1
16
1
= ___________________
V. Assignment
a. Do what is asked.
1. Show the following fractions by using rectangular regions.
2
1
3
1
4
1
5
1
and
6
1
2. Color the part being considered.
3. Arranged them from least to greatest.
b. Arrange the fractions from greatest to least.
8
1
9
1
2
1
4
1
5
1
c. Arrange the fractions from least to greatest.
3
1
6
1
7
1
10
1
5
1

13
Identifying Fractions Equal to One
Cognitive: Identify fractions equal to one
Psychomotor: Read and write fractions equal to one
Affective: Develop the habit of writing neatly
Skills: Identifying fractions equal to one
Reading and writing fractions equal to one
Materials: fraction circles, fractional bars, activity sheet, coloring materials
Value: Neatness
1. Drill – Fractions less than one
Give the fractions for the shaded parts.
2. Review – Part of a fraction
What are the parts of a fraction?
Which part of a fraction represents the number of equal parts?
Which part represents the number parts being considered?
3. Motivation
Do you like fruits? What fruits do you like? Why?
Game: Pupil describes a fruit and let their classmates give the name of the fruit.
B. Lesson Proper
1. Presentation
a. Use a real object for problem illustration.
1. Show a papaya and cut it equally into halves.
Into how many parts is the papaya divided? 2
How will you write one of the equal parts? 2
1
How will you write two halves? 2
2
Are two halves equal to one? 2
2
= 1

14
2. Let the pupils write the fractions in figures and in words.
2
1
one half
2
2
two halves
3. Compare the fractions.
What kind of fraction is 2
1
? Fraction less than one
What about 2
2
? Fraction equal to one
What can you say about the numerator and denominator of 2
2
? They are the same
b. Use of cut-outs
1. Distribute cut-outs of different parts of a cake to the pupils.
2. The pupils put the parts together to form a whole.
3. Ask: Into how many parts is the whole divided? What do you call each part?
4. Guide the pupils in recognizing the whole as six-sixths.
How many 6 equal parts has the whole region? 6
The whole region is equal to 6
6
.
We say six-sixths and write 6
6
Is 6
6
equal to one?
What can you say about the numerator and denominator of the fraction? They are
the same.
c. Observing illustrations and identifying fractions equal to one.
2
2
4
4
5
5
1. Let pupils shade each part one after the other.
2. Ask them to identify the shaded parts.
3. When all the parts have been shaded, ask them to write the fraction names for the
shaded parts.
4. Is 2
2
equal to 1? 4
4
? 5
5
?
5. What do you notice about the numerators and denominators of fractions equal to
one? They are the same.
2. Guided practice
a. Let the pupils identify which fractions are equal to one.
Write the fraction name for the shaded parts and encircle the fraction equal to one. (At
this point remind the pupils to write their numbers neatly and legibly).
b. Distribute fraction words and figures to the pupils.
Call out a fraction and ask the pupils holding the fraction figure and fraction word to stand
side by side in front of the class.
2
2 Two
halv
es
4
4 Four
fourt
hs
5
5 Five
fifths
6
6 Six
sixth
s

15
c. Ask the pupils to read the numbers.
3. Generalization
How do we know that fractions are equal to one?
Fractions are equal to one when their numerators and denominators are the same.
C. Application
Ring the fractions equal to one
1)
4
4
4
2
3)
6
3
6
6
5)
3
2
3
3
2)
5
5
5
3
4)
9
3
9
9
IV. Evaluation
A. Write the fraction numerals for the following.
1. five-fifths _____
2. two-halves ____
3. four-fourths ____
4. eight-eights ____
5. six-sixths ____
B. Encircle the fractions equal to one.
1)
3
2
6
2
2
2
4
2
3)
10
7
8
5
5
4
3
3
5)
6
4
4
4
9
4
12
4
2)
7
7
6
7
8
3
6
3
4)
9
4
4
3
5
5
6
8
V. Assignment
A. Write 5 fractions having a value of one.

16
B. Write the fraction words for the following:
1)
6
6
________
3)
4
4
________
5)
9
9
________
2)
8
8
________
5)
7
7
________
C. Identify the fractions equal to one in the given set.
Set A
7
3
’
7
5
’
7
7
’
9
3
’
9
7
’
9
9
’
10
3
’
10
5
’
10
10
Set B
8
2
’
8
6
’
8
8
’
12
5
’
12
7
’
12
12
’
15
6
’
15
9
’
15
15
Identifying Fractions More Than One
Cognitive: Identify fractions more than one
Psychomotor: Read/Write fractions more than one
Affective: Be considerate to others/Work well with others
Skills: Identifying fractions more than one
Reading/Writing fractions more than one
Materials: textbooks, cut-outs, activity cards, coloring materials
Value: Concern for others
1. Drill - "Climbing the Ladder"
a. Call on 2 pupils.
b. Let them have a race in climbing the ladder by checking out all fractions less than one.
(note: The ladder should have the same fractions)
c. The first pupil to come up with the most number of correct answers wins the game (At
this point give some safety precautions to pupils like telling them not to push each other.

17
2. Review – When is a fraction less than one?
A fraction is less than one when the numerator is less than the denominator.
3. Motivation
Let the pupils sing a fraction song to the tune of "The Farmer in the Dell"
One whole, one whole, one whole
Divided into 2
One part is called 2
1
(Substitute 2
1
with other unit fraction)
And so the other too.
1. Presentation
a. Problem Illustration
1. Present the following with all parts shaded. (cut-outs)
A
C
B
Into how many equal parts is figure A divided? Figure B? Figure C?
What fractional parts are shaded?
What do you call the fractions 2
2
, 4
4
, and 6
6
?
8
2
2
3
3
4
9
1
6
2
7
3
5
5
4
8
10
3
4
1
8
2
2
3
3
4
9
1
6
2
7
3
5
5
4
8
10
3
4
1

18
2. Remind the pupils that fractions equal to one have the same numerators and
denominators.
3. Present other figures. (Cut-outs)
D E F
a. How many fourths does Figure D show?
b. How many halves does Figure E show?
c. How many thirds does Figure F show?
d. Write the fraction for the shaded parts of D, E and F.
4
5
, 2
3
, 3
5
e. Are these fractions less than one? equal to one? more than one?
f. What do you notice about the numerators and denominators of fractions
more than one?
2. Guided Practice
a. What kind of fractions are the following:
2
3
,
3
4
,
4
7
,
6
8
,
7
8
1. Are these fractions more than one? Why?
2. What do you notice about their numerators and denominators?
b. Game - "Looking for a Partner"
Distribute cut-outs of regions divided into equal parts.
a. Let the pupils find their partners by showing their cut-outs to the others.
b. Ask them to look for the regions with shapes similar to their cut-outs.
c. When everybody has found his partners, let them stand side by side and show their
regions and say the fraction represented by their cut-outs.
2
3
4
7

19
3. Generalization:
How do we identify fractions more than one?
Fractions are called fractions more than one when their numerators are greater than the
denominators.
C. Application
1. Draw regions showing the following fractions.
1)
4
6
2)
3
5
3)
2
3
4)
6
7
5)
5
8
2. Put a check mark before fractions equal to one, a cross mark after fractions more than one
and encircle fractions less than one
1)
2
2
2)
3
9
3)
6
3 4)
10
12
5)
4
5
6)
5
2
7)
6
6
8)
7
7
9)
7
8 10)
8
10
IV. Evaluation
A. Write the fraction for these names
1. Five-halves _____________
2. Six-thirds ______________
3. Five-fourths ___________
4. Nine-eighths ____________
5. Twelve-tenths ___________
B. Circle the fractions which are equal to one.
Box the fractions which are greater than one.
3
2
4
4
6
6
5
7
5
3
9
8
8
9
8
8
7
7
3
4
4
3
7
2
9
7
7
9

20
V. Assignment
Write the following fractions in words.
1)
2
6
___________
2)
4
5
___________
3)
5
7
___________
4)
6
8
___________
5)
3
9
___________
Ordering Fractions Equal to One, Less Than and More Than One with the same
Denominators
Cognitive: Order fractions equal to one, less than and more than one with the same
denominators
Psychomotor: Write fractions from least to greatest and vice versa
Affective: Practice good health habits
Skills: Ordering fractions equal to one, less than and more than one with the same
denominators
Writing fractions equal to one, less than and more than one from greatest to least
and vice versa
Materials: textbooks, fraction circles, activity cards, cut-outs
Value: Health consciousness
1. Drill – Identifying fractions equal to one, more than and less than one
1. Play “Giant Step” (Pupils play in pairs)
2. The teacher flashes the cards containing fraction numerals. (equal to one, more than one
and less than one)
3. Tell whether the fraction is equal to one, more than one or less than one.
4. The contestants beat each other in giving the correct answer.
5. The first pupil who gives the correct answer takes one step forward.
6. The first pupil to reach the finish line wins the game.

21
2. Review:
Circle all fractions less than one, box all fractions more than one and cross all that are equal
to one.
3. Motivation
Do you eat your breakfast before going to school?
How many meals do you eat everyday?
(Show picture of Go, Grow and Glow foods)
Which of these food do you eat everyday?
Are these foods good for the body? Why?
1. Presentation
a. Problem illustration
Are fruits good for the body?
Show two apples, an orange and papaya cut in fourths.
Into how many equal parts is the orange divided?
Get 2 pieces of the equal parts and show them.
How many fourths are there? 2
Write the fraction for the pieces. 4
2
2
?
Into how many equal parts is the papaya divided?
Get all the pieces and show them.
What fraction names the parts? 4
4
4
?
Into how many equal parts are the apples divided?
Get 5 pieces of the sliced apples and show them.
Can we get one whole from these pieces?
What fraction names the pieces? 4
5
5
?
Which is greater, 4
2
or 4
4
? 4
5
or 4
4
? 4
2
or 4
5
?
Arrange the fractions from greatest to least.
4
3
5
7
4
3 2
2
12
10
9
1
10
4 17
8
5
5
8
12
5
6
11
11
6
8
9
4
5
2

22
4
2
4
4
4
5
b. Use the regions
1. Write a numeral for the shaded parts.
A =
4
2
B =
4
5
C =
4
4
D =
4
7
2. Compare the fractions by using > or <
4
2
<
4
4
,
4
5
>
4
4
,
4
5
<
4
7
3. Arrange the fractions from least to greatest.
4
2
4
4
4
5
4
7
4. Arrange the fractions from greatest to least
4
7
4
5
4
4
4
2
5. How do we order fractions with the same denominators?
c. Use number lines.
0
5
1
5
2
5
3
5
4
5
5
0
5
1
5
2
5
3
5
4
5
5
0
5
1
5
2
5
3
5
4
5
5
5
6
1. Observe the distances covered in the number line.
2. Compare the distances covered by using > or <
5
3
<
5
5
,
5
6
>
5
5
,
5
6
>
5
3
,
5
5
>
5
6
A B C D

23
3. Arrange the fractions from greatest to least.
5
6
5
5
5
3
4. How do we order fractions with the same denominator?
2. Guided Practice
a. Cooperative learning – group pupils into learning barkadas (triads)
1. Show flashcards with fractions arranged from least to greatest and vice versa.
2. Using their show me cards, the pupils will write More if the fractions are arranged
from greatest to least and Less, if arranged from least to greatest.
3
2
3
3
3
5
3
8
3
10
less
9
2
9
5
9
9
9
12
9
15
less
5
6
5
5
5
4
5
2
5
1
more
7
2
7
4
7
6
7
7
7
9
less
8
1
8
4
8
5
8
8
8
10
less
10
9
10
7
10
5
10
3
10
1
more
C. Application
A. Write the fractions in order from least to greatest
1)
8
2
8
4
8
1
8
8
8
10
______________
2)
5
1
5
8
5
5
5
3
5
4
______________
3)
10
3
10
10
10
15
10
4
10
1
______________
B. Read, analyze and solve.
Marlyn bought 3 whole buko pies. Each buko pie was divided into 8 equal parts. She gave
8
4
to Ken,
8
8
to a friend,
8
7
to her brothers and sisters and ate the rest. Who got the biggest
share? Who got the least share?
C. Work with a partner. Pupils will be paired with learning partners. Write the fractions in order
from smallest to biggest and vice versa
Pupil 1 Learning Partner
Greatest to Least Least to Greatest
1)
8
2
8
4
8
1
8
8
8
6
______________ _______________
2)
5
1
5
5
5
3
5
4
5
8
______________ _______________

24
3)
6
7
6
4
6
5
6
6
6
1
______________ _______________
3. Generalization
How do we order fractions less than one, equal to one and more than one?
When ordering fractions less than one, equal to one and more than one with the same
denominator, remember that the greater the numerator, the greater is the value of the
fraction.
IV. Evaluation
A. Draw regions to represent these fractions. Arrange the region as directed.
1)
2
1
,
2
2
,
2
3
2)
3
2
,
3
5
,
3
3
3)
9
4
,
9
9
,
9
12
B. Which sets of fractions are written in order from greatest to least?
1)
5
2
5
1
5
4
5
6
3)
4
5
4
4
4
3
4
2
5)
6
9
6
6
6
5
6
2
2)
8
7
8
5
8
4
8
3
4)
7
7
7
6
7
8
7
5
V. Assignment:
A. Answer the problem
Karen bought 2 whole big pizzas. Each pizza was divided into 12 equal parts. She gave
12
3
to Karie, 12
12
to her friends, 12
5
to her brothers and sisters and ate the rest. Who got the
biggest share? Who got the least share?
B. Inside the boxes are fractions and shaded portions of regions representing fractions. Arrange the
fractions from least to greatest by writing numbers 1 to 7 on top of the boxes.
8
7
8
5
8
1
greatest
to leastleast to
greatestgreatest
to least

25
C. Arrange the following fractions from greatest to least
1)
6
3
6
1
6
4
6
5
6
6
6
8
6
2
2)
9
4
9
9
9
1
9
6
9
5
9
2
9
8
3)
7
2
7
4
7
7
7
9
7
1
7
3
7
8
Finding the GCF (Greatest Common Factor) of Two Given Numbers
Cognitive: Find the GCF (Greatest Common Factor) of two given numbers
Psychomotor: Tell/Write the GCF of two given numbers
Affective: Spend money wisely
Skills: Finding the GCF (Greatest Common Factor) of two given numbers
Telling/Writing the GCF of two given numbers
Materials: Learning Activity Sheets, cut-outs
Value: Thriftiness
1. Mental Computation
There are 56 boxes with 8 crayons in each box. How many crayons are there in all?
2. Drill: Games
a. The pupils give the product as the teacher points to the combinations in the number
wheel.
b. The teacher gives a product and the pupils give the factors.

26
3. Review – Term used in Multiplication
a. Write a multiplication sentence on the board.
9 x 8 = 72
b. Pupils read the sentence.
c. What do we call 9 and 8, the numbers that we multiplied? Factors
d. What do we call 72? Product
4. Motivation
Julie has 3 piggy banks. If she has 8 in each bank, how much does she have?
Who among you have piggy banks at home?
What do you do if you have extra money from your baon?
Do you put them in your piggy bank?
Is it good to save money for the future? Why?
1. Presentation
a. What shall we do to solve our problem? Multiply
3 x P8 = 24 3 and 8 are factors of 24.
24 is the product of 3 and 8.
b. Distribute cut-outs to pupils.
1. Aside from 3 and 8, what 2 numbers when multiplied will give a product of 24?
2. Call on the pupils holding the cut-outs to compare the numbers and come up with a
pair of cut-outs which are factors of 24.
6 x 4 = 24 2 x 12 = 24 1 x 24 = 24
3. Who can give all the factors of 24? 1, 2, 4, 6, 12, 24,
How many factors has 24? 6
c. Listing of and comparing factors of given numbers.
Ask the pupils to list the factors of 12.
What are the factors of 12? List them from least to greatest.
1, 2, 3, 4, 6, 12
Tell the pupils to compare the factors of 24 and 12 on the board, you can see the factors
of 12 and 24.
6
2
4 12
1
24

27
24 12
1 1 1. How many factors has 12? 24?
2
3
4
6
8
12
24
2
3
4
12
2. Look at the list and find the common factors of the
numbers. Circle the factors.
3. What are the common factors of 24 and 12? 1, 2,
3, 4, and 12
4. From the common factors, put a check mark beside
the greatest number common to both 24 and 12.
5. What is the greatest common factor of 24 and 12?
12
6. 12 is the greatest common factor of 12 and 24.
7. 12 is the GCF of 12 and 24.
2. Guided Practice
a. Use of cut-outs
 Distribute cut-outs of petals of flowers with printed numerals.
 Group pupils into 3’s.
 Ask them to form a flower from the petals and post the petals around the circle cut-
outs posted on the board.
 The numeral on the circle cut-out is the pupils’ cue for the products. The pupils will
select petals with numerals that are factors of the number on the circle cut-out.
 Ask pupils to select 2 products and write the GCF on the show me cards.
 Let them say: The GCF of 15 and 20 is 5.
The GCF of 10 and 15 is 5.
b. Use of activity cards
 Form 2 teams. Distribute activity cards. Two cards per group.
2
9
6
3
5
18
1
7
4 18 18
1
3
2
4
7
8
6
12
9
36
10
36
24
5
6
7
2
3
12
4
8
1 24
5
40
1
9
8
3
4
7 40
 In each card, circle or ring all the factors of the given numbers.
 Then ask the pupils to supply the missing data on the board.
Number Total no. of
factors
Common
factors
GCF
18
36
8
6
1, 2, 3
6, 9, 18
18 18 is the GCF of 18
and 36.

28
Number Total no. of
factors
Common
factors
GCF
24
40
8
6
1, 4, 8 8 8 is the GCF of 24 and
40.
3. Generalization
How do you find the GCF of 2 given numbers?
What are the steps in finding the GCF of 2 given numbers?
a. List down the factors of each number.
b. Find the common factors of the given numbers.
c. Look for the greatest factor common to the numbers.
C. Application
A. Use the number in the box to answer each of the questions.
1 2 4 6 9 10
12 14 15 24 27 28
1. Which pair of numbers has a GCF 5?
2. Which pair of numbers has a GCF 6?
3. Which pair of numbers has 12 as GCF?
B. Read, analyze and solve
1. Jenny has two pieces of ribbon. One is 8 dm long and the other is 12 dm long. What is
the longest length wherein she can cut both pieces into equal length without wasting any
part of the ribbon?
2. Henny has two pieces of rope with lengths of 24 m and 27 m. How long will he cut each
piece to get pieces of equal length and the longest possible without wasting any rope?
IV. Evaluation
A. Find the GCF.
1) 6 and 12 2) 12 and 18
3) 15 and 21 4) 12 and 16
5) 10 and 20
8 dm
12 dm
24 m
27 m

29
B. Match Column A with Column B by drawing a line.
A – Given Numbers B - GCF
1) 24 and 12 a. 25
2) 28 and 32 b. 5
3) 25 and 50 c. 8
4) 10 and 15 d. 4
5) 8 and 24 e. 12
V. Assignment:
A. Find the missing pair of each number:
Pair of Numbers GCF
1) 2 and _____ 6
2) _____ and 10 10
3) 24 and _____ 8
4) 48 and _____ 6
5) _____ and 15 5
B. Write the GCF of the following pairs of numbers on the blank.
1) 8, 12 _______ 2) 56, 48 _______
3) 32, 24 _______ 4) 64, 16 _______
5) 18, 36 _______
Reducing Fraction to Lowest Forms
Cognitive: Reduce fractions to lowest forms
Psychomotor: Express/write fraction in lowest forms
Affective: Practice the habit of sharing
Skills: Reducing fractions to lowest forms
Writing fractions to lowest forms
Materials: textbooks, cut-outs, activity sheets, coloring materials
Value: Sharing
1. Drill – Giving the common factors of 2 given numbers.
Show a flash card one at a time. Ask the pupils to give the common factors of the
numbers.
12 and 16 15 and 18 10 and 20 27 and 1818 and 24

30
2. Review – Writing the GCF of 2 given numbers.
Distribute cut-outs of fruits with printed numerals, each having a pair of numbers.
Ask the pupils to show their cut-outs and give the GCF of the pairs of numbers.
3. Motivation
Song
(Tune: The Farmer in the Dell)
One whole, one whole, one whole
Divided into 2
One part is called 2
1
And so the other too.
1. Presentation
a. Present a problem
Aling Beatriz bought a whole piece of buko pie.
She cut it as shown on the picture.
given to Alice
given to Zeny
What part of the buko pie did Alice receive? 2
1
What part was given to Zeny? Both girls received parts of the buko pie. If you
were Zeny and Alice would you share your buko pie to others? Why?
b. Analysis of the problem
Did both girls receive the same size of buko pie? Yes
Do 2
1
and 4
2
have the same size?
Since 2
1
and 4
2
have the same size, they are called equivalent fractions. What do we call
fractions showing the same size? Equivalent Fractions
A fraction can be expressed in lowest terms.
2
1
is the lowest term of 4
2
Observe how 4
2
is reduced to lowest term in the example below:
4
2
÷ 2
2
= 2
1
What is the GCF of the denominators?

31
What is done with the GCF to find the lowest terms of the fraction?
The numerator and denominator are divided by the GCF.
c. Problem Illustration
Look at the pieces of sticks.
How is the 2
nd
piece of stick divided?
Do 3
1
and 6
2
show the same parts?
What is the GCF of the denominators?
Using the same pattern above let's see how 6
2
is reduced to 3
1
6
2
 2
2
= 3
1
What did we do with the fraction and the GCF to reduce it to lowest terms?
d. Use of fraction bars
2
1
2
1
4
1
4
1
4
1
4
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
How many fourths are there in 2
1
?
Are 4
2
and 2
1
the same?
How many eights are there in 2
1
?
Are 8
4
and 2
1
the same?
How many eights are there in 4
1
?
Are 8
2
and 4
1
the same?
Show how 8
2
, 4
2
and 8
4
are reduced to lowest terms.
8
2
÷ 2
2
= 4
1
4
2
÷ 2
2
= 2
1
8
4
÷ 4
4
= 2
1
2. Guided Practice
a. Divide the class into triads. One of the pupils will read the fraction. The second pupil
will give the GCF and the third pupil will give the lowest term of the fraction. Each
correct answer merits one point. The team with the highest no. of points wins.
Ex. 6
3
GCF = 3 LT = 2
1
b. Group the class into dyads.
Each player takes turn in answering questions about the exercises.
Which is the lowest term of the following fractions?
1) 6
3
= ( 2
1
, 4
3
, 6
2
)
2) 8
2
= ( 4
2
, 3
1
, 4
1
)

32
3) 10
2
= ( 2
1
, 4
1
, 5
1
)
4) 20
5
= ( 3
1
, 10
2
, 4
1
)
c. Try these:
1) 8
6
÷ 2
2
= ___
2) 12
9
÷ 3
3
= ___
3) 15
10
÷ 5
5
= ___
3. Generalization
How do we reduce fractions to lowest terms?
To express the lowest terms of a fraction, divide both the numerator and the
denominator by the GCF.
C. Application
Read the problems and answer the questions.
1. Linda bought 12 eggs. She boiled 6
2
of the eggs and fried 8
2
of them. What are 6
2
and
8
2
in lowest terms?
2. Mother cooked 2
1
kg of chicken and 12
4
kg of beef. Did she cook the same amount of
meat? Why?
3. Aling Rosa cut a large squash into 6 equal parts. She gave 6
3
to her neighbors and kept
2
1
for family use. Did she keep the smaller part of the squash? What kind of person is
Aling Rosa? Is she generous to her neighbors? Do you also share some food to your
neighbors and friends?
IV. Evaluation
A. Express each fraction in lowest terms by supplying the missing number.
1) 12
4
=
 
3
3) 24
9
=  
3
5) 24
8
=
 
3
2) 12
3
=  
1
4) 15
6
=  
2
B. Write the missing number in each box.
1) 4
2
÷
 
  = 2
1
3) 15
3
÷
 
  = 5
1
2) 14
7
÷
 
  = 2
1
4) 10
2
÷
 
  = 5
1
C. Solve the following:
1) Express 20
15
as a fraction with a denominator of 5.
2) How many fifths as there in 15
9
?

33
3) How many fourths as there in 100
25
?
4) Change 18
3
to sixths.
5) Three twenty-fourth is equal to how many eights?
V. Assignment
A. Copy the fractions that are not in the lowest form. Then find the GCF and change them to lowest
terms.
3
2
, 3
1
, 10
4
, 4
2
, 5
2
, 8
4
, 9
6
, 18
5
B. Choose the lowest terms of the given fractions.
1) 15
6
a. 5
2
b. 3
2
c. 2
1
d. 3
1
3) 24
8
a. 4
1
b. 3
1
c. 2
1
d. 10
2
5) 12
9
a. 5
3
b. 8
3
c. 4
3
d. 2
1
2) 15
10
a. 3
2
b. 5
2
c. 5
3
d. 8
3
4) 21
7
a. 6
1
b. 5
1
c. 4
1
d. 3
1
Finding Fractional Part of a Set/Region
Cognitive: Find fractional part of a set/region
Psychomotor: Write the fractional part of a number
Affective: Help do household chores
Skills: Finding fractional part of a set/region
Writing the fractional part of a number
Reference: BEC PELC II.A.3

34
Materials: textbooks, set of real objects, geometric regions activity sheets, coloring
materials
Value: Helpfulness
1. Drill – Basic Division Facts (Flash cards) Game "Giant Steps"
a. Call 2 or 3 contestants at a time.
b. Flash the cards.
c. The pupil who gives the correct answer first gets a point.
d. The first pupil to reach the finish line wins the game.
Review - Naming the shaded parts of figures. Writing the fractions in words
e. Call on 2 pupils.
f. One of the pupils will name the shaded part of the figure.
g. The other one will write the fraction word on the board.
2. Motivation
What are the things that we use when eating our meals?
Show sets of glasses, saucers, cups, spoons, forks, etc.
Do you help in washing the dishes at home?
Who among you help in the household chores at home?
What are the household chores that you do at home?
1. Presentation
a. Using Fractional Parts of Set (Real Objects)
1. Arrange 14 glasses on the table.
2. Let the pupils fill 7 glasses with water.
3. Present this problem: One-half of the 14 glasses are full.
How many glasses are full?
4. Write 2
1
of 14 = ___
5. How many glasses are full?
2
1
of 14 = 7
6. Let pupils arrange 16 saucers on the table. How many saucers are there?
7. Let them put candies on 8 saucers.
8. Ask: How many saucers have candies?
9. Write 2
1
of 16 = ___ 2
1
of 16 = 8
10. Do the same procedure with the cups.
What is 3
1
of 9?

35
b. Grouping Elements of Sets
1. Group pupils into learning barkadas.
2. Distribute activity sheets to the groups.
Group by 5s 5
1
of 15=3 Group by 6s 6
1
of 18 = 3
Group by 8s 8
1
of 24 = 3 Group by 4s 4
1
of 16 = 4
. Group by 7s 7
1
of 21 = 3
Group by 4’s 4
1
of 20=5
3. Ask the pupils to group the elements as directed.
4. Let them observe the number of group formed.
5. Ask: How many groups are formed after grouping the hearts by fives?
6. 5
1
of 15 = 3
7. Do the same procedure with the other sets.
2. Guided Practice
a. Let the pupils observe the number sentences.
1) 2
1
of 14 = 7
2) 2
1
of 16 = 8
3) 5
1
of 15 = 3
4) 4
1
of 16 = 4
5) 7
1
of 21 = 3

36
b. In the first example, what is the whole number? the denominator? What did we do with
the whole number and the denominator to get the answer?
c. Use the same procedure in analyzing the other number sentences.
d. Group pupils in dyads.
e. The pupils take turn in writing the answers on the output column.
Find 5
1
of the input Find 4
1
of the input
Input Output Input Output
15 3 12 3
25 8
30 20
10 16
f. Game - "Come and Get Me"
1. Call on 3 contestants at a time.
2. Arrange fractions & whole numbers written on cut-outs of shapes on the table.
3. Ask pupils to select cut-outs which will produce a number sentence and post
them on the board.
The pupil with the most number of sentences wins the game.
3. Generalization
How do we find the fractional part of a number?
To find the fractional part of a number, divide the whole number by the denominator.
C. Application
Read the problems and answer the questions that follow.
1. Aling Dolores buys 20 oranges for her children. 2
1
of them are ripe. How many are ripe?
_________
2. Raymund had 30. He gave 2
1
of it to his brother. How much did he give his
brother?_________
3. Thirty-six children went to the resort. 6
1
just watched the others swim. How many children
did not go swimming?________
10
2
1 =5 3
1
21 =7
4
1 20 =5 6
1
18 =3
of of
of of

37
IV. Evaluation
A. Complete the tables by finding fractional part of a number.
Fraction 10 8 6 16 24 28
2
1
Fraction 9 12 15 21 27 30
3
1
B. Find the missing numbers.
1) 5
1
of 15 = ____
2) 4
1
of 20 = ____
3) 2
1
of 12 = ____
4) 3
1
of 30 = ____
5) 6
1
of 24 = ____
C. Read, analyze and solve
1. Mr. Contemplacion had 360. He spent 3
1
of his money in movie ticket. How much money was
left?
2. There are 50 children in a park. If 5
1
are boys, how many are girls?
3. Of 90 glasses, 9
1
were used by the visitors in audio-visual room. How many visitors came?
V. Assignment
A. Find the missing numbers.
1) 8
1
of ___ = 2
2) 3
1
of ___ = 3
3) 10
1
of 50 = ___
4) 4
1
of 100 = ___
5) 6
1
of ___ = 8
B. Write the answer on the box under output. Follow the rule.
Rule: Find 4
1
of the input
Find 2
1
of the input.
1. Input Output 2. Input Output
16 18
20 6

Lesson guide gr. 3 chapter ii -rational numbers, fractions v1.0

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Lesson guide gr. 3 chapter ii -rational numbers, fractions v1.0