Lesson Guide

In

Elementary Mathematics

Grade 4

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

Comprehension of Multiplication of

Fractions

INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011

Lesson Guides in Elementary Mathematics Grade 4 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 4 Region 3

Evelyn H. Magpayo Pampanga Myrna Vicente Nueva Ecija Ester Ramones Tarlac Virgie Costales - Zambales

Region 4 A (CALABARZON)

Flordeliza D. Yamo Laguna Araceli C. Montoya San Pablo City Estelita Q. del Rosario Cavite City

National Capital Region (NCR)

Remylinda T. Soriano Manila Maria Brucal Makati Lina Sea Taguig/Pateros Analee Pacaa Pasig/San Juan

Bureau of Elementary Education (BEE)

Rogelio O. Dones Leony M. Achacoso Zosima C. Ventura

Ateneo de Manila University

Eva Marie Guevarra

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, Ateneo de Manila University Carmela C. Oracion Ateneo de Manila University

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. de Robles OIC, Asst. Chief, Curriculum Development Division

Virginia T. Fernandez Project Coordinator

EXECUTIVE COMMITTEE

Jesli A. Lapus Secretary, Department of Education

Jesus G. Galvan OIC, Undersecretary for Finance and Administration Vilma L. Labrador Undersecretary for Programs and Projects

Teresita G. Inciong Assistant Secretary for Programs and Projects Printed By: ISBN 971-92775-3-x

iii

TABLE OF CONTENTS

Introduction .................................................................................................................................. iv Matrix ........................................................................................................................................ v

II. RATIONAL NUMBERS

E. Comprehension of Multiplication of Fraction Visualizing Multiplication of Fractions ............................................................................ 1 Fractional Part of a Number ........................................................................................... 5 Translating Expressions ................................................................................................. 9 Multiplying a Fraction by another Fraction .....................................................................12 Analyzing Word Problems ............................................................................................... 15 Solving Word Problems................................................................................................... 21

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 IV

COMPETENCIES VALUES INTEGRATED STRATEGIES USED MULTIPLE

INTELLIGENCES TECHNIQUES

II. Rational Numbers

E. Comprehension of Multiplication of Fractions

1. Multiply two fractions

1.1 Visualize multiplication of fraction

Generosity Concept development Modeling

Acting out, Reading, Writing, Hands-on activities

1.2 Find a fractional part of a number Cooperation Simplifying the problem Use data resources from a story

Manipulative, Imagery

1.2.1 Translate expressions such as: 1/ 2 of 2 /3 2 /3 of 1/ 6

Resourcefulness Use data resources from story and a chart

Manipulative, Completing tables

2. Multiply a fraction by another fraction Generosity Concept development Following direction Drawing pictures Looking for pattern

Games, Speaking, Cooperative groups, Hands-on activities, Illustrating

3. Application of Multiplication 3.1 Solve word problems involving

multiplication of fraction

Cooperation and Sportsmanship

Concept development Use of data resources from a story Looking back Drawing pictures

Contest, Hands-on activities, Logic, Reading, Number, Cooperative groups

3.1.1 Analyze the word problem 3.1.1.1 Tell:

- what is asked - what is/are given - the word clue/s the

operation to be used

Active participation and cooperation

Concept development Guess and check Write equation Acting out Simplifying problems

Puzzle, Reading, Writing, Speaking, Cooperative groups, Hands-on activities

3.1.2 Transform the word problem into a number sentence

Active participation And cooperation

Concept development Guess and check Write equation Acting out Simplifying problems

Puzzle, Reading, Writing, Speaking, Cooperative groups, Hands-on activities

3.1.3 Use the correct operation 3.1.4 State the complete answer

1

Visualizing Multiplication of Fractions

I. Learning Objectives

Cognitive: Visualize multiplication of fractions Psychomotor: Illustrate multiplication of fractions correctly Affective: Show generosity to others

II. Learning Content Skills: 1. Visualizing multiplication of fractions 2. Identifying a given fraction References: BEC-PELC II.E.1.1

textbooks in Math Materials: strips of cartolina with different shapes, cutouts of fractions, learning activity

sheet, crayon Value: Generosity

III. Learning Experience

A. Preparatory Activities

1. Drill

Answer the basic multiplication facts using flash cards.

3 5 4 2 3 5 x 2 x 3 x 3 x 3 x 6 x 6

2. Review

Identifying fractions using cutouts of fraction. Name the fraction for the shaded part.

3. Motivation

Acting out a problem.

Ask a group of eight pupils to stand in two rows in front of the class. Ask 43 of the group

to sit down then ask

31 of the group who sat down to kneel. What part of the whole group

would be kneeling?

What did you do to find the answer? How do we get of 43 ?

13

1

2

31 of

43

43 of the group

B. Developmental Activities

1. Presentation

a. Present the word problem.

Mayumi bought 31 metre of linen cloth. She used

21 of it to make a

handkerchief for her Mother. What part of the cloth was used for the handkerchief?

What kind of a daughter is Mayumi? Is it good to be generous? Why?

Guide the pupils in analyzing the problem. Let them give the number sentence

for 21 of 3

1. Help them visualize and interpret the multiplication sentence. Make

necessary illustrations. Give emphasis to the double shaded part.

21 of

31 is double shaded

of means x

To multiply fractions, we should multiply the numerators to get the numerator of the product and then multiply the denominators to get the denominator of the product.

1 2

1 3

1 2

1 3

1

3

3

21 of

31 =

21 x

31 =

61

Or 21 x

31 =

21 x

31 =

61

Therefore the answer is metre.

b. Give another presentation.

Draw a rectangle on the board and mark it into fourths. Then draw a line dividing the

whole rectangle into two. Shade 21 of

41 .

What part of the whole rectangle is shaded twice? (81 )

What then is 21 of

41 ? (

81 )

Show this on the board: 21 of

41 =

81

21 of

41

Therefore: 21 of

41 =

21 x

41 =

Is the double shaded part.

2. Guided Practice

(Remind the pupils to work neatly and share coloring materials.) Activity Sheets Match the picture in column A with the multiplication sentence in column B. Write only the letter of the correct answer. A B

1) a. 42 of

21

2) b. 21 of

21

1 6

1 4

1 8

1 8

4

3) c. 31 of

43

Complete the multiplication sentence appropriate for the given figures. 1) 2) 3)

___ of ___=____ ___ of ___=____ ___ of ___=____ Draw or visualize each multiplication of fractions.

1) 52 of

21 2)

53 of

31 3)

63 of

41

3. Generalization

How do you visualize multiplication of fractions?

Multiplications of fractions can be visualized by shading one factor with horizontal and the other factor by vertical lines placed over the other. The double shaded part represents the answer to the equation.

C. Application

Read and solve on your paper. Write the multiplication sentence then express your answer in lowest terms.

Rorie has 43 metre of red ribbon. She used

21 of it in decorating a gift package for

her mother. What part of a metre of ribbon was used in decorating the gift package for her mother?

What kind of daughter is Rorie? Are you like Rorie? In what way?

IV. Evaluation

1. Illustrate the following.

a. 53 of

31 c.

53 of

41 e.

42 of

21

b. 32 of

51 d.

52 of

21

2. Illustrate the following fractions.

a. 83 of

42 b.

52 of

42 c.

63 of

41

5

d. 73 of

21 e.

85 of

32

3. Visualize each multiplication of fractions.

a. 53 of

62 b.

85 of

32 c.

74 of

81

d. 94 of

43 e.

43 of

64

V. Assignment

Complete the table.

Fraction Illustration Product

a. 32 of

21 _____ _____

b. _____ _____

c. 31 of

21 _____ _____

Finding the Fractional Part of a Number

I. Learning Objectives

Cognitive: Find a fractional part of a number Psychomotor: Form sets of objects using counters Affective: Work cooperatively in group activities

II. Learning Content

Skill: Finding fractional part of a number References: BEC-PELC I.E.1.2 Materials: flash cards, cutouts of fractions, learning activity sheets, counters like buttons,

seeds, etc., number cards from 0 to 9 Value: Cooperation

III. Learning Experiences

A. Preparatory Activities

1. Drill Oral drill on basic multiplication facts using flash cards

6

3 8 7 6 4 5 x 4 x 3 x 5 x 4 x 9 x 5

2. Review

Give the multiplication sentence suited for the given illustrations.

a. b. c.

3. Motivation

a. Divide the class into groups of four. Give each group 20 counters (e.g. buttons, seeds,

etc.) and number cards from 0 to 9. b. Ask the groups to use their counters to show the following.

Example: 21 of 12 = 6

1) 31 of 15 2)

31 of 18 3)

51 of 20

Whose group finished first? Why do you think you were able to

finish first? B. Developmental Activities

1. Presentation

Ramil has 20 marbles in a jar. One-fifth of these are red marbles. How

many red marbles are in the jar?

a) Help them analyze the data in the problem. 1) What part of the marbles are red? 2) How many marbles are there inside the jar?

3) Write the mathematical sentence. (51 of 20)

4) Get 51 of 20. What is your answer?

5) How did we get the fractional part of the number? b) Let them work on more complex exercises using their counters.

Example: 52 of 10 = 4

Have them divide 10 into 5 equal parts (2 counters each), then get 2 parts (2 x 2).

c) Present it by computation.

7

Example: 83 of 16 =

To get the factional part of a number, like of 16: Express 16 as a fraction with a denominator of 1 multiplied by . X = = This is an improper fraction. Simplify by dividing 48 by 8. So the answer is 6. Therefore: 6 is of 16.

Another Example:

54 of 25 =

54 x 25 = 4 x (25 5) = 4 x 5 = 20

d) Give another example.

How will you find 43 of 32?

Ask a volunteer to solve it on the board.

43 of 32 = n 32 4 = 8 , 8 x 3 = 24

Therefore : of 32 is 24

2. Group Activity Activity Sheet

Complete the equation.

a) 21 of 20 = _____ b)

31 of 12 = _____ c)

41 of 16 = _____

Write the answer.

a) 81 of 48 = _____ b)

71 of 21 = _____ c)

32 of 9 = _____

Solve these problems. If there are 60 minutes in an hour, how many minutes are there in

a. 21 of an hour? b.

31 of an hour? c.

41 of an hour?

3. Generalization

How do you get the fractional part of a whole number?

To get the fractional part of a whole number, multiply the whole number by the numerator of the fraction then divide the product by the denominator. Or divide the whole number by the denominator of the fraction then multiply the quotient by the numerator of the fraction.

3 8

3 8

16 1

3 8

3 x 16 8 x 1

48 8

3 8

3 4

8

C. Application

Read and solve on your paper.

Joshua had 12 colored pencils. If 41 of them are broken, how many pencils are

broken? IV. Evaluation

1. Find the answer.

a. 101 of 200 = __ b.

121 of 36 = __ c.

52 of 20 = __ d.

43 of 16 = __ e.

72 of 14 = __

2. Write the answer.

a. 53 of 30 = __ b.

53 of 60 = __ c.

54 of 50 = __ d.

72 of 28 = __ e.

43 of 24 = __

3. Draw sets of objects to show the equations and solve for the answer.

Equation Illustration Solution and Answer

a. 1 of 15 3

b. 2 of 30 5

c. 5 of 16 8

d. 4 of 25 5

e. 4 of 28 7

V. Assignment A. Find the answer.

1) 42 of 16 2)

83 of 40 3)

54 of 50 4)

92 of 81 5)

32 of 18

B. Solve for the answer.

1. Ruela had 30 stamps. She gave away 65 of them. How many stamps were left?

2. Mang Jose picked 100 pieces of mangoes. He sold 54 of the mangoes. How many mangoes

were left?

3. Johnny has 12 crayons. Of these, 41 are broken. How many crayons are broken?

4. Mang Jack has 10 jars of paint. One-fifth of them are yellow. How many are yellow?

5. Anna had 9 colored pencils. He lost 31 of them. How many colored pencils were lost?

9

Translating Expressions

I. Learning Objectives

Cognitive: Translate expressions such as 2

1 of

3

2,

3

2 of

6

1 to multiplication of fractions

Psychomotor: Illustrate expressions using shaded regions Affective: Show resourcefulness in doing ones project

II. Learning Content

Skills: 1. Translating expressions such as 2

1 of

3

2,

3

2 of

6

1

2. Multiplying a fraction by another fraction References: BEC PELC II E 1.2.1 & E 2

Materials: flash cards, cutouts of fractions, learning activity sheet, chart showing illustrations Value: Resourcefulness

III. Learning Experiences

A. Preparatory Activities

1. Drill Contest on basic multiplication facts using flash cards.

3 7 5 2 6 3 x 2 x 2 x 2 x 3 x 3 x 5

2. Review Naming fractions Give the fraction corresponding to the shaded part.

3. Motivation

Get 2

1 sheet of Grade 4 paper. Fold

2

1 of your paper. What is

2

1 of a half? What word in

this sentence has an equivalent symbol in mathematics? What symbol can be replaced by the word of?

B. Developmental Activities

1. Presentation

Nancy found a piece of white cloth in an old chest of her grandmother. She cut

3

2 of it, then she used

2

1 of this for her aprons pockets. What part of the whole

piece of cloth did Nancy use for her aprons pockets?

10

a. Help the pupils in the analysis of data.

1. What kind of a girl is Nancy? 2. If you were Nancy, would you do the same? Why? 3. What part of the cloth did Nancy cut? 4. What part of the cloth did Nancy use for the aprons pockets? 5. Write the mathematical sentence.

b. Help them visualize and interpret the multiplication sentence.

2

1 of

3

2= n

1. Show them this illustration.

2. Ask them to shade 3

2 of this illustration then doubly shade

2

1 of it.

c. Present the multiplication sentence from the expression.

2

1 of

3

2 means

2

1 x

3

2= n, where n is for the answer

2

1 x

3

2 =

6

2 or

3

1

d. Present another example.

What is 3

2 of

6

1?

3

2 of

6

1 means

3

2 x

6

1= n

3

2 x

6

1=

18

2 or

9

1

2. Group Activity

a. Write the mathematical expression for the following :

1) 6

1 of

3

2 = 2)

2

1 of

4

3 = 3)

3

1 of

6

3 =

b. Translate the following to mathematical expressions then find the product.

1) 2

1 of

5

3 = 2)

3

1 of

7

4 = 3)

5

1 of

8

3 =

c. Illustrate the following expressions using shaded regions and translate into mathematical

expressions.

1) 2

1 of

6

1 = 2)

5

1 of

2

1 = 3)

3

1 of

5

2 =

11

3. Generalization

How do you translate expressions such as 2

1 of

3

2 into mathematical expressions?

To translate expressions like 2

1 of

3

2 into mathematical expression, we change

of to x symbol which means times to form the multiplication expression.

C. Application

Read and solve on your paper.

During a tooth-brushing demonstration for dental week, several Grade 4 pupils used

2

1 of the

4

3 full tube of toothpaste. What part of the whole tube of toothpaste was used?

IV. Evaluation

1. Translate the following expressions to multiplication expressions.

a. 4

2 of

2

1 = b.

3

2 of

5

1 = c.

5

3 of

3

1 = d.

6

3 of

4

1 = e.

5

2 of

3

1 =

2. Complete the data in the chart.

Expressions Multiplication Expression

a. 3

1 of

5

2

b. 2

1 of

4

3

c. 5

1 of

2

1

d. 4

1 of

3

2

e. 5

3 of

2

1

3. Name the double-shaded region by writing two fractions using the word of then translate them

into a multiplication expression.

a. c. e. _____ of _____ _____ of _____ _____ of _____

_____ x _____ _____ x _____ _____ x _____

12

b. d.

_____ of _____ _____ of _____ _____ x _____ _____ x _____

V. Assignment

Translate the following expressions to multiplication expressions.

a. 7

2 of

4

3 = b.

2

1 of

5

4 = c.

3

1 of

7

4 = d.

4

2 of

8

3 = e.

5

1 of

2

1 =

Multiplying a Fraction by another Fraction

I. Learning Objectives

Cognitive: Multiply a fraction by another fraction Psychomotor: Illustrate multiplication of fractions Affective: Show generosity to others through sharing

II. Learning Content

Skill: Multiplying a fraction by another fraction References: BEC-PELC II.E.2 Materials: chart, multiplication table, picture, rectangular regions, show-me-boards, learning

activity sheets Value: Generosity

III. Learning Experiences

A. Preparatory Activities

1. Drill

Conduct a drill on the basic multiplication facts. Present a table similar to the one below. As the teacher points to a number, the pupils will write their answers on their magic slates or show-me-boards.

X 4 8 6 3 7 2 9 0 1

6

2. Review

Review expressing fractions in lowest terms.

13

Write each fraction in its lowest terms.

a. 10

2 = ___ b.

15

6 = ___ c.

32

8 = ___ d.

15

5 = ___ e.

12

8 = ___

3. Motivation

Show a picture of a cake and say, Suppose you have a whole cake. You cut it into

halves and give 2

1 of a half to your neighbor. What part of the whole cake did you give

away? Valuing: Is it good to share food with neighbors? Why?

B. Developmental Activities

1. Presentation

a. Present the lesson by asking four groups of pupils to follow the directions written in activity sheets.

1) Ask representatives from each group to post their work on the board as he/she reports about it.

2) Teacher checks which groups have the correct illustration.

3) Ask: What then is 2

1 of

4

1?

Show this on the board : 2

1 of

4

1 =

8

1

Tell someone to change it into a multiplication sentence. What do we do with the numerators to get the numerator of the product?

How about the denominator of the product?

When we have the expression 2

1 of

4

1, what process do we use?

b. Present another method involving cancellation to simplify multiplication of fractions. Show that in cancellation, one divides a numerator and a denominator by a common factor. When all common factors have been used, multiply to find the product. The product should be in its lowest terms. Example:

1 2

5 x 14 = 2 71 153 3

ACTIVITY SHEET 1) Get a bond paper. 2) Fold it into four equal parts vertically. Shade one part. 3) Fold it again horizontally.

4) Shade 2

1 of

4

1

5) Answer this: What part of the whole rectangle is shaded twice?

14

c. Introduce cancellation using 3 fractions. Example: 1 3 1

3 x 6 x 7 = 3 4

2 7

1 12

4 8

2. Guided Practice

a. Use the picture to find the product. Express the answer in its lowest terms. 1) 2) 3)

2

1 x

3

1

2

1 x

2

1

2

1 x

5

1

b. Find the product using cancellation. Write the product in its lowest terms.

1) 8

3 x

5

4 = ____ 2)

7

5 x

10

3 = _____ 3)

15

8 x

12

5= ____

c. Multiply using cancellation. Write the product in its lowest terms.

1) 12

7 x

14

9 = ____ 2)

3

2 x

10

9 x

8

3 = _____ 3)

5

4 x

16

15 x

2

1 = ____

3. Generalization

How do we multiply a fraction by another fraction?

To multiply fractions, multiply the numerator by the numerator and the denominator by the denominator. Express the product in its lowest terms.

C. Application

Read and solve on your paper. Express the answer in its lowest terms.

1. A butter cake recipe needs 4

3 cup milk. How many cup of milk is needed to make

2

1 butter

cake?

2. A sewer made pockets for shirts. First, she cut 3

2 metre of the material. Then, she used

4

3 of

the material she had cut for pockets. How much material did the sewer use for pockets?

IV. Evaluation A. Multiply. Write the answer in its lowest terms.

a. 3

1 x

8

1 = b.

2

1 x

3

2 = c.

5

4 x

2

1 = d.

8

1 x

5

4 = e.

4

1 x

5

2 =

B. Find the product. Express it in simplest form.

a. 3

2 x

10

6 = b.

4

2 x

3

2 = c.

4

3 x

7

3 = d.

4

1 x

8

5 = e.

5

1 x

15

5 =

15

C. 1. Find the product. Shade the correct part of each region to show your answer.

a. 3

1 x

2

1 = b.

3

2 x

2

1 =

D. Multiply using cancellation. Write the product in its lowest terms.

c. 3

2 x

16

15 = d.

12

6 x

42

3 = e.

3

2 x

8

6 x

14

12 =

V. Assignment

Find the product and reduce it to lowest terms. Write the answer on te blank.

a. 3

1 x

2

1 = __ c.

3

2 x

5

2 = __ e.

5

2 x

10

1 = __

b. 5

4 x

3

1 = __ d.

3

1 x

4

3 = __

Analyzing Problems

I. Learning Objectives

Cognitive: Analyze word problems involving multiplication of fractions Psychomotor: Write the answers to the questions correctly Affective: Show active participation and cooperation in class discussions

II. Learning Content

Skill: Analyzing word problems involving multiplication of fractions References: BEC-PELC II.E.3.1.1 3.1.4

textbooks in Math 4 Materials: activity sheets, mini-boards, textbooks, strips of cartolina Values: Active participation and cooperation

III. Learning Experiences

A. Preparatory Activities

1. Drill

Have some exercises on multiplication facts in the form of a game.

16

Partners

5 x 5 6 x 3 3 x 3 7 x 3 5 x 6 9 x 5

9 x 8 8 x 7 6 x 4 4 x 8 8 x 8 7 x 4

6 x 8 9 x 7 4 x 9 6 x 7 8 x 5 5 x 4

25 21 56 24 63 45

9 72 32 64 42 28

18 30 48 36 40 20

a. Two players share the same gameboard. b. One player cuts out 36 cards and places them at random face down on the table/desk.

Player A turns over 2 cards. If these cards match, he/she takes the cards. For example, if

player A turns over two cards 8 x 7 and 56, he/she takes these cards, they match.

c. If the cards do not match, the player leaves them face-up. player B now turns over 2 more cards and matches any cards that are face up on the table.

d. Each player alternates until all the cards are turned face-up. e. The player who accumulates the most cards wins. f. The player can reshuffle the cards and play more games. g. The teacher may change the given numbers.

2. Review

a. Have a game on rearranging steps in analyzing word problems. b. The group that finishes first is the winner.

3. Motivation

Present this word problem.

Marissa bought 3

1 of a metre of cotton cloth. She used

2

1 of it to make a

tablecloth. What part of a metre was used for the tablecloth?

a. Who is talked about in the problem? b. What did she do?

B. Developmental Activities

1. Presentation

How will you find the answer to the problem? How are you going to work with the other members of your group? Why do you have to cooperate with the other members of the group?

2. Group Activities

Strategy 1 Acting out the problem a. Members of the group are to act out the problem. b. The group should follow the steps in analyzing the problem.

1) What is asked? _____ 2) What are the given facts? _____

Factors

Products

17

3) What is the operation to be used? _____ 4) What is the mathematical sentence? _____ 5) What is the answer? _____

Strategy 2 Following directions

Place the given word/s in their proper order or step.

Given data:

First Second Third Fourth Fifth -

Strategy 3 Supplying the missing data 1) The problem is asking for _____. 2) _____ and _____ are the given data. 3) The process to be used is _____. 4) The mathematical sentence is _____. 5) _____ is the final answer.

Strategy 4

Number the given data from first to fifth using the following steps:

1) The problem asks for the _____. 2) The given facts are the _____. 3) The process to be used is _____. 4) The mathematical sentence for the problem is _____. 5) The answer is _____.

Given data: 3

1 x

2

1 = n

6

1 metre of cloth

3

1 of

2

1

metre of cloth used multiplication Analysis/Abstraction What did we do to the problem? How did we analyze the problem? Did you follow the steps?

1 and 1 metres of cloth 3 2

What part of a metre was used for the tablecloth?

Multiplication

1 metre 6

1 x 1 = n 3 2

18

3. Guided Exercises

Choose the letter of the correct answer.

Esmer bought 5

3 kilo of sugar for the icing of a cake. Only

2

1 of it was used.

How much sugar was used?

1) What is asked in the problem? a. amount of sugar used c. amount of sugar in a plastic bag

b. amount of sugar bought d. amount of sugar in a cup 2) What is the process to be used?

a. addition c. multiplication b. subtraction d. division

3) What is the mathematical sentence for the problem?

a. 2

1 +

4

3 = n b.

2

1 x

4

3 = n

c. 2

1 -

4

3 = n d.

2

1

4

3 = n

Mary had 5

3 metre of lace. She used

3

2 of it for her project.

What part of the lace was used for her project?

Match column A with column B.

A B 1) What is asked in the problem? a. part of lace used 2) What are the given data?

b. 3

2 x

5

3= n

3) What is the process to be used? c. multiplication 4) What is the mathematical sentence for the problem? d. 15

6 or

3

2

5) What is the answer? e.

3

2,

5

3

4. Generalization

How do we analyze problems involving multiplication of fractions?

Analyzing word problems involving multiplication of fractions

First Second Third Fourth Fifth

19

In analyzing word problems involving multiplication of fractions, we should follow

the following steps: a. Find what is asked b. Find the given data c. Know the process to be used d. Give the mathematical sentence for the problem e. Solve for the answer

C. Application

Supply the missing words.

Roy used 3

1 of the

8

7 metre of bamboo stick for his lantern. How much of

the stick was used?

1. The problem is asking for _____. 2. The answer to the problem is _____. 3. The mathematical sentence is _____. 4. The process to be used is _____. 5. The _____ and _____ are the given data.

IV. Evaluation

Connie had 4

3 of a cake. She gave

2

1 of it to her friend. What part of the cake

did Connie give away?

Choose the letter of the correct answer. 1. What is asked in the problem?

a. Pieces of the whole cake b. Part of the cake that is given away c. Parts of the cake that were eaten d. Pieces of the cake that were broken away

2. What are the given facts?

a. 2

1 of the cake

b. 4

3 of the cake

c. 2

1 and

4

3 of a cake

d. 8

3 of a cake

3. What is the mathematical sentence?

a. 2

1 x

4

3 = n

20

b. 2

1 +

4

3 = n

c. 4

3

2

1 = n

d. 4

3

2

1 = n

4. What is the process to be used?

a. addition b. subtraction c. multiplication d. division

5. What is the answer?

a. 6

3 b.

8

3 c.

9

3 d.

12

3

V. Assignment

Write the word/s that show the steps in analyzing word problems. Write the needed facts to answer the questions below.

A. What is asked in the problem?

B. What are the given facts?

C. What is the process to be used?

D. What is the mathematical sentence?

E. What is the answer?

1. David had 4

3 can of horse manure. He needs

2

1 of it to fertilize his garden plots. What part of

the can of horse manure did he use?

2. Rennie bought 2

1 litre of paint. He used

4

3 of it for their class in Industrial Arts. How much

paint was used?

3. A chocolate recipe needs 4

3 cup of milk. How many cups of milk are needed to make

2

1?

4. Nene gave 2

1 of 1 kilo of peanuts to her sister. What part of a kilo did her sister receive?

5. Maria ate 3

1 of

6

1 of a pie. What part of the pie did Maria eat?

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Solving Word Problems

I. Learning Objectives

Cognitive: Solve word problems involving multiplication of fractions Psychomotor: Follow specific directions in solving word problems Affective: Show cooperation and sportsmanship in performing group work

II. Learning Content

Skill: Solving word problems involving multiplication of fractions Reference: BEC-PELC II.E.3.1 Materials: textbook, flash cards, charts where problems are written, learning activity sheet Values: Cooperation and sportsmanship

III. Learning Experience

A. Preparatory Activities

1. Drill

Oral drill on basic multiplication facts using flash cards Ex.

5 x 4

6 x 3

7 x 6

8 x 9

9 x 2

2. Review

What are the steps in solving word problems?

3. Motivation

Are you ready for a contest on multiplication of fractions? Using flash cards, conduct a

contest on multiplying fractions. Do this by groups. Emphasize working cooperatively and accepting their losses if some groups win. Did the members of the group cooperate with one another? How? What did the loser group do? Is it important to be a good sport? Why?

B. Developmental Activities 1. Presentation

a. Present a word problem.

Precious bought home 5

4 of a round cake. She gave her brother

3

1 of it. What part of

the whole cake did she give to her brother?

1) Help them analyze the word problem. a) What is asked in the problem?

22

b) What are the given facts? c) What operation will you use? d) Write the number sentence. e) What is the answer?

2) Show the multiplication sentence by computation.

5

4 of

3

1 =

5

4 x

3

1 =

15

4

She gave part of the cake

b. Read the problem. Answer the questions on your paper.

Virgie had 10

8 kilogram of carrots to sell. She sold

4

3 of it. What part of a kilogram of

carrots was left? 1) What is asked in the problem? 2) What are the given facts? 3) What is the word clue? 4) Determine the operation to be used. 5) Give the mathematical sentence for the problem. 6) What is the correct answer? 7) Draw a picture for the problem.

c. Present a set of problems and let them solve these by groups. Ask a representative to

explain their work. Solve for the following problems.

1) Joe jogs daily for 2

1hour. How long does he jog in a week?

2) Charisse found 4

3 of a cake on the table. She ate

2

1 of it. What part of the cake did

she eat?

3) Peter bought 2 kilos of lanzones. He gave 3

1 of it to me. What part of a kilo of

lanzones did he give to me?

2. Generalization How do we solve word problems involving multiplication of fractions?

In solving word problems involving multiplication of fractions, we must determine what is asked, what are given, and what is/are the word clue/s. Decide what operation to be used and what the number sentence is then solve the problem.

C. Application

Read and solve on your paper.

Aling Myrna divided the bibingka into five equal parts. Nardo got one slice and gave half of the slice to Gerard. What part of the whole bibingka did Gerard get?

4 15

23

IV. Evaluation

For each of the problems, write what is asked and the mathematical sentence then solve for the answer. Do these on your paper.

1. Elvira had 4

3 of a cake. She gave

2

1 of it to her younger sister. What part of the whole cake did

Elvira give away?

2. Dante had 4

3 can of horse manure. He used

2

1 of it to fertilize his garden plots. What part of the

can of horse manure did he use?

Read and solve the problems. Follow the steps in problem solving.

1. Catherine had 5

3metre of lace. She used

3

2 of it for her project. What part of the lace was used

for her project?

2. John had 5

4 of the plot vacant. He planted

4

1 of it with pechay. What part of the plot was planted

with pechay?

3. Mrs. Garcia had 10

8kg of flour. She used

2

1 kg of it for baking a pudding. How much flour did she

use?

Solve for the following problems.

1. In the hospital, 10

7 cavan of rice is cooked in a day. How many cavan of rice is cooked in

3

1 of a

day?

2. Four-fifths of Benjies garden is planted with vegetables. Of the vegetables planted, 8

7 is

cabbage. What part of the garden is planted with cabbage?

3. Jojo has 3

2 metre of string. He used

2

1 of it for tying a small box. What part of the metre was

used for tying the small box?

V. Assignment Solve for the following problems.

1. Danny and Lily packed 4

3 of the canned goods. Two-thirds of these were sardines. What part of

the canned goods packed were sardines?

2. Mother cooked fried chicken for her sons birthday party. She prepared 4

3 litre of cooking oil.

However, she used only 2

1 of it. What part of the cooking oil was used?

3. Elisa had 6

3 of a cake. She gave

2

1 of it to her friend. What part of the whole cake did Elisa give

away?