REPUBLIC OF THE PHILIPPINES DEPARTMENT OF EDUCATION LEARNING GUIDE

GRADE IV - MATHEMATICS

RATIONAL NUMBERS

MODULE 10: COMPREHENSION OF MULTIPLICATION OF

FRACTIONS

impose as a condition the payment of royalties.

Mind Map

The Mind Map displays the organization and relationship between the concepts and activities in this Learning Guide in a visual form. It is included to provide visual clues on the structure of the guide and to provide an opportunity for you, the teacher, to reorganize the guide to suit your particular context.

Stages of Learning

The following stages have been identified as optimal in this unit. It should be noted that the stages do not represent individual lessons. Rather, they are a series of stages over one or more lessons and indicate the suggested steps in the development of the targeted competencies and in the achievement of the stated objectives.

Assessment

All six Stages of Learning in this Learning Guide may include some advice on possible formative assessment ideas to assist you in determining the effectiveness of that stage on student learning. It can also provide information about whether the learning goals set for that stage have been achieved. Where possible, and if needed, you can use the formative assessment tasks for summative assessment purposes i.e as measures of student performance. It is important that your students know what they will be assessed on.

1. Activating Prior Learning

This stage aims to engage or focus the learners by asking them to call to mind what they know about the topic and connect it with their past learning. Activities could involve making personal connections.

Background or purpose

The activity in this stage will activate students' knowledge and skills in adding and subtracting fractions.

Strategy

PUZZLE. This strategy aims to exercise one's mind. Usually, a problem is given to test one's skill or ingenuity. The end results mirror the performance of the individual member as they

Materials

• puzzle cards (refer to Teacher Resource Sheet 1 on page 10) • manila paper

• masking tape/paste

Activity 1: Garden Puzzle

Instructions:

1. Organize the students into 5 groups or as desired.

2. Give 1 set of puzzle cards and other materials to each group.

3. Instruct them to arrange the puzzle cards to form a rectangular garden.

4. Ask them to find the part of the garden that is planted with cabbage, carrots and tomatoes if

1

10 of the garden is planted with radish.

5. Then, let them paste it on a manila paper. 6. Ask them to present and justify their outputs.

Formative Assessment

Ensure the involvement of all students in the group discussions during the activity.

Roundup

Students would have activated their knowledge and skills in adding and subtracting fractions.

2. Setting the Context

This stage introduces the students to what will happen in the lessons. The teacher sets the objectives/expectations for the learning experience and an overview how the learning experience will fit into the larger scheme.

Background or purpose

In this stage, students will indicate if they agree , disagree or don't have the knowledge yet on the given ideas or concepts about multiplication of fractions.

Strategy

AGREE OR DISAGREE (RESTRUCTURED). A strategy that will help students organize data to support a position for or against an idea. It promotes students' thinking about the content. A “Don't Know” column is added to find out the concept which the students do not have prior knowledge.

Materials

• enlarged copy of Agree-Disagree Chart (refer to Teacher Resource Sheet 2, page 11) • pentel pen

• masking tape

Activity 2: Agree? Disagree?

1. Divide the class into 5 groups or as desired. Provide the needed materials to each group. 2. Motivate the students to think and recall their past learning. Let them check the “Agree”

column if they are in favor of the idea, “Disagree” if they are against to it and “Don't Know” if they don't have the knowledge yet. They will do this on the “BEFORE” columns of the chart. 3. Remind them not to place any mark under the “AFTER” columns yet.

4. When done, let them post their chart on the board for comparison. Discuss with the students the items they agree, disagree or they don't know yet as indicated on their charts.

5. Keep the charts for these will be revisited in the last stage of this Learning Guide.

Formative Assessment

Ensure the active participation of students in performing the activity.

Roundup

Students would have indicated if they agree , disagree or don't have the knowledge yet on the given ideas or concepts about multiplication of fractions.

3. Learning Activity Sequence

This stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.

Background or purpose

In this stage, students will perform activities that would enable them to acquire the knowledge and skills in:

• visualizing multiplication of fractions using visual models, • translating expressions such as:

1

2

2

3

2

3

1

6

• multiplying a fraction by another fraction, and

• solving word problems involving multiplication of fractions following the steps in problem solving.

Strategies

MODELLING. A strategy that explicitly demonstrates the cognitive process and skills required of a learner for a particular task. Teachers and students can demonstrate processes and skills to each other. For example, teacher will provide materials or may assign students to bring the materials and students will make their own model.

PROBLEM SOLVING. Teaching students how to effectively solve problems will provide them with useful lifelong skills.

CLARIFY What is the problem asking you to do or find out? CHOOSE What tools would be effective in solving the problem? USE Use the appropriate tools to give an answer to the problem. INTERPRET Is this answer reasonable? Can you check it using another tool? COMMUNICATE Communicate the answer. This maybe in a simple form ( one

sentence) or a more complex form ( a report)

Materials

Task A:

• activity sheet (refer to Student Activity 3, Task A, on page 12) • piece of paper

• crayons (blue and yellow)

Task B: activity sheet (refer to Student Activity 3, Task B, on page 13) Task C: activity sheet (refer to Student Activity 3, Task C, on page 14)

Activity 3: Do and Discover

Task A : Using model Instructions:

1. Organize the students into 5 groups or as desired. 2. Give the needed materials to each group.

3. Let them perform the task at a given time.

4. Call volunteers to present their outputs for discussion. Task B : Translating Expressions

Instructions:

1. With the same grouping, give each group the activity sheet. 2. Let them perform the task at a given time.

3. Call volunteers to present their output for discussion. Task C : Follow the Steps

Instructions:

1. Following the same grouping, give activity sheet to each group. 2. Let them perform the task at a given time.

3. Call volunteers to present their output for discussion.

Formative Assessment

Roundup

Students would have multiplied fractions and solved word problems involving multiplication of fractions following the steps in problem solving.

4. Check for Understanding of the Topic or Skill

This stage is for teachers to find out how much students have understood before they apply it to other learning experiences.

Background or purpose

In this stage, students will perform an activity to check their knowledge and skill on comprehension of multiplication of fractions.

Strategy

CONFERENCING. This involves working with an individual student or small group of students to discuss their work. This may take place at any stage of students' learning at the beginning to facilitate planning, during work to see how students are “going” and after work is completed to facilitate reflection. It provides a good opportunity to give feedback on student's learning and also to observe their achievements and understanding.

Material

• activity sheet (refer to Student Activity 4 on pages 15-16)

Activity 4: Words' Worth

Instructions:

1. Organized the students into groups of 4. 2. Give the activity sheet to each group.

3. Instruct them to analyze and answer the task assigned to them on their activity sheet. 4. When done, let them post their outputs.

5. Then, call 1 member from each group to present their outputs for comparison and discussion.

Formative Assessment

See to it that all students are actively participating in the activity. Check their outputs.

Roundup

Students would have checked their knowledge and skill on comprehension of multiplication of fractions.

5. Practice and Application

In this stage, students consolidate their learning through independent or guided practice and transfer their learning to new or different situations.

Background or purpose

Strategy

LEARNING STATIONS. A cooperative approach that enables the students to visit each station one after the other and solve cooperatively the given problem. Students will discuss within their group what the problem is all about and how to do it.

Materials

• activity sheet (refer to Student Activity 5 on page 17)

• problem cards (refer to Teacher Resource Sheet 3 on pages 18-19)

Activity 5: Problem Solving

Instructions:

1. Prior to the activity, prepare 4 learning stations inside the classroom and provide one problem card to each learning station.

2. Group the students into 4.

3. Assign first one group to each station to perform the task. Instruct them to solve the problem on each station cooperatively at a set time.

4. After performing the first task, let them move clockwise to the next station. This is done until all the groups have visited all the stations.

5. Ask one member from each group to report their output on the first task assigned to them for comparison and discussion.

Formative Assessment

Check the groups' outputs.

Roundup

Students would have solved problems involving comprehension of multiplication of fractions.

6. Closure

This stage brings the series of lessons to a formal conclusion. Teachers may refocus the objectives and summarize the learning gained. Teachers can also foreshadow the next set of learning

experiences and make the relevant links.

Background or purpose

In this stage, students will consolidate their learning on comprehension of fractions by revisiting their “Agree-Disagree” chart. This time, they will complete the chart by completing the “AFTER” columns.

Strategy

AGREE OR DISAGREE (RESTRUCTURED). A strategy that will help students organize data to support a position for or against an idea. It promotes students' thinking about the content. A “Don't Know” column is added to find out the concept which the students do not have prior knowledge.

Materials

• masking tape

Activity 6: Let's Revisit

Instructions:

1. Let the students go back to their grouping in stage 2.

2. Give them back the Agree Disagree chart they used in the second activity. 3. Instruct them to complete its AFTER columns.

4. Then, let them post and present their outputs to the whole class. 5. Clarify misconceptions if there are still any.

Formative Assessment

Monitor students' involvement in performing the task.

Roundup

Students would have consolidated their learning on comprehension of fractions by revisiting and completing their “Agree-Disagree” chart.

Teacher Evaluation

(To be completed by the teacher using this Teacher’s Guide) The ways I will evaluate the success of my teaching this unit are: 1.

TEACHER RESOURCE SHEET 1

PUZZLE PARTS

TEACHER RESOURCE SHEET 2

AGREE-DISAGREE CHART

Directions: Enlarge the chart and give a copy to each group.

BEFORE

STATEMENTS

AFTER

Know Agree Disagree KnowDon't

Multiplying fractions is the same as adding them.

To multiply dissimilar fractions, change them to similar, then multiply.

To multiply a fraction by another fraction, multiply the numerators, then the

denominators.

To multiply whole number by a fraction, multiply it with the numerator and the

denominator.

The expression

1

2

2

3

1

2

2

3

The lowest term of

5

20

1

5

be stated in its lowest term.

In solving problems involving multiplication of fractions, follow the

STUDENT ACTIVITY 3

DO AND DISCOVER

TASK A: USING MODEL

Objective:

Visualize multiplication of fractions using model.

Directions: Read and answer the problem.

To answer the problem, do the following:

1. Get a piece of paper.

2. Fold it crosswise into 4 equal parts. Color 3 parts of it with blue.

•

What fractional part of the paper is colored with blue? __________

1. Fold the same paper lengthwise into halves, then unfold.

•

Into how many parts the paper is now equally folded? ________

1. Shade

1

₂

of the colored paper with yellow.

•

What is the fractional part of the paper with both blue and yellow colors?

__________

•

So, what part of the chocolate bar did Sarah get? ____________

•

Write a multiplication sentence out of the

problem.___________________________________________

Joanne was given of a chocolate bar.

She shared of it to her classmate, Sarah.

What part of the whole chocolate bar did Sarah get?

3

4

1

TASK B: TRANSLATING EXPRESSIONS

Objectives:

1. Translate expressions like

1

2

of

2

3

,

2

3

of

1

6

to multiplication.

2. Multiply fraction by another fraction.

Multiplication Expression

Multiplication

Sentence

phrase

symbol

1

2

of

2

3

2

3

of

1

6

2

5

of

3

4

2

6

of

1

2

3

4

of

6

8

R e m em ber:

To multiply fractions by another fraction,

multiply the numerators, then the

denominators. Simplify the product.

3. Now, complete the third column of the above table by answering each

expression to have a multiplication sentence.

TASK C: FOLLOW THE STEPS

Objective: Solve word problems involving multiplication of fraction following the

steps in solving problem.

Directions: Read the problem and answer the questions below.

QUESTION ANSWER

What is asked in the problem?

What are the given facts

What word clue suggests the operation to be used?

What operation will be used to solve the problem?

Transform the problem into a number sentence.

Solve the problem using the correct operation.

Write the complete answer.

Omar's father owns a farm. Four fifths of it is a rice field.

He planted only of the rice field with rice.

What part of the whole farm is planted with rice?

2

STUDENT ACTIVITY 4

WORDS' WORTH

Objective:

Solve problems involving multiplication of fractions.

Letter Boxes:

Word

Multiplication

expression

The word is worth...

WE

₄

24

x

1

4

4

96

=

1

24

Directions:

1) Form 10 two-letter words from the given letter boxes

below. Record them in the first column of the table.

2) Using their corresponding fractions, form a

multiplication expression. Write it in the second column.

3) Then, answer each expression to complete the table.

The first one is done for you.

A 1

8

C

2

3

B

4

8

D

3

10

E

1

4 F

5

20

G

3

15

H

I

8

2

3

30

M 6

30

N

2

12

O

4

20 P

1

6

R

5

a) Find other two-letter word which has

the same value with “HE”.

b) What is the simplest form of the

product of the fractions which form

a three-letter pronoun that refers

to a “girl”?

STUDENT ACTIVITY 5: PROBLEM SOLVING

Directions: Use the guide questions on the first column of the table to answer the

word problems in stations 1 to 4. Then, complete the table.

Question

Station 1

Station 2

Station 3

Station 4

What is asked in

the

problem?

What are given

What word clue

suggests the

operation to be

used?

What operation

will be used?

Transform the

problem into a

number sentence.

Solve the problem

using the correct

operation.

State the

TEACHER RESOURCE SHEET 3

PROBLEM CARD

Directions: Reproduce and cut each card.

Ace found of a watermelon

on the table. He ate of it.

What part of the whole

watermelon did he eat?

1

4

1

3

Station 1

Anne brought 2 kilograms of

ripe mangoes. She shared

of it to her aunt. How many

kilograms of mangoes did she

give to her aunt?

1

8

There are about 20 flowering

plants in the school. One half

of these are roses. Of the

roses, are red.

How many roses are there in all?

red roses?

1

5

Station 3

Station 3

Meriam was given a cake as her

price for finishing Grade IV with

honors. She sliced the cake into 6

equal parts and gave one part to

Rose. What part of the whole

cake was given to Rose?

For the Teacher:

Translate the information in this Learning Guide into the following matrix to help you prepare your lesson plans.

Stage

_1.

Activating Prior Learning

2.

Setting the

Context

3.

Learning

Activity Sequence

4.

Check for

Understanding

5.

Practice and

Application

6.

Closure

Strategies

Activities from the Learning Guide

Extra activities you may wish to include

Materials and planning needed

Estimated time for this Stage