REPUBLIC OF THE PHILIPPINES DEPARTMENT OF EDUCATION LEARNING GUIDE

GRADE III - MATHEMATICS

RATIONAL NUMBERS

MODULE 6: COMPREHENSION OF FRACTIONS

office wherein the work is created shall be necessary for exploitation

of such work for profit. Such agency or office may, among other things,

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

Strategy

MODELLING. This strategy explicitly demonstrates the cognitive processes and skills required of a learner for a particular task. Teachers and students can also demonstrate processes and skill to each other.

Materials

• 4 sheets of Grade 3 paper

• pair of scissors

Activity 1: “Take Parts of a Whole”

1. Organize the class into 6 groups. 2. Instruct each group to do the following:

Paper 1 Fold it lengthwise into 2 equal parts. Cut along the folds. Write the fraction for each part.

Paper 2 Fold it lengthwise into 3 equal parts. Cut along the folds. Write the fraction for each part.

Paper 3 Fold it lengthwise into 4 equal parts. Cut along the folds. Write the fraction for each part.

3. Tell them not to do anything on paper 4.

4. After which, let at least two members take any 2 pieces of papers on their outputs. Ask them to name and describe the 2 papers.

5. Then, ask one volunteer per group to share her/his answer to the whole class.

Formative Assessment

Ensure the active participation of the students in the activity.

Roundup

Students would have named and described 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, the students will identify less than one, equal to one, and/or more than one fractions.

Strategy

Materials

• pieces of papers used in Activity 1

• marking pen

• manila paper

• paste

Activity 2: “Let's Put the Right Part in Place”

Prior to the activity, let them fold the manila paper into 6 parts and copy the label of each part as shown below.

Fractions Less

Than One

Fractions Equal to

One

Fractions Greater

Than One

Directions:

1) Use the same grouping as in the first activity.

2) Instruct each group to paste accordingly the strips or pieces of paper as specified in each portion on the manila paper.

3) Then, let them describe and compare the numerator and denominator of each fraction. Note: Keep their outputs for these will be revisited on the last stage of this Learning Guide.

Formative Assessment

Ensure that each member in the group has the opportunity to share his/her ideas. Check each group's output.

Roundup

The activity gave them an opportunity to identify less than one, equal to one, and/or more than one fractions.

3. Learning Activity Sequence

Background or purpose

In this stage, students will be able to:

• order fractions less than one/equal to one/more than one; and

• change fractions to lowest terms.

Strategies

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.

MODELLING. This strategy explicitly demonstrates the cognitive processes and skills required of a learner for a particular task. Teachers and students can even demonstrate processes and skills to each other.

Materials

• Activity 3

activity sheet (refer to Student Activity 3) Task 1, page 11

Task 2, page 12 Task 3, pages 13-14

• Activity 4

activity sheet on page 15

• crayon

• manila paper

• bond paper

• marking pen

• Activity 5

activity sheet on page 16

Activity 3: “Working with Fractions”

1. Group the students by 5 or as desired. 2. Let them do the 3 tasks one at a time.

3. Instruct them to write their outputs on a manila paper. 4. After which, let them post their outputs for comparison.

5. Ask at least 2 groups with different answers to present their outputs to the class. 6. Process the activity through an interactive discussion.

Activity 4: “Which Comes First?”

1. With the same groupings, provide each group with the activity sheet (refer to Student Activity 4 on page 15).

2. Let them perform the task at a set time.

Activity 5: “What's Its Simplest Form?”

1. Organize the class into groups of 5.

2. Provide each group with the activity sheet. Refer to Student Activity 5 on page 16. 3. Give them sufficient time to perform the task.

4. After which, let them exchange outputs with the groups. Ask group volunteers to present their output to the class for comparison and discussion.

Formative Assessment

Ensure the maximum participation of the students in the series of activities for them to get the expected outputs.

Check their outputs.

Roundup

It is important to check further if students could independently order fractions less than one/equal to one/more than one, and change fractions to lowest terms. Additional exercises should be given if there are still difficulties and confusions.

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

This stage aims to check further whether the students can order fractions less than one/equal to one/more than one, and change fractions to lowest terms.

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.

Materials

• fraction strips (refer to Teacher Resource Sheet 1 on page 17)

• activity sheet (Refer to Student Activity Sheet 6 on page 18)

• manila paper

• paste

• crayons

Activity 6: “Our Fraction Tree”

1. Group the students by 5 or as desired. Provide them with a set of materials for the activity.

2. Instruct them to paste each fraction strip on the appropriate part of the tree. 3. Then, on a separate sheet, let them:

☑order all like fractions from biggest to smallest;

☑reduce each fraction which can still be expressed to its lowest form; and

☑write the fractions more than one in words.

4. After which, let them post their outputs for comparison and discussion.

Formative Assessment

Monitor the involvement of the students as they perform the activity. Check their outputs.

Roundup

The activity gave the students an opportunity to check further their understanding and skill on ordering fractions less than one/equal to one/more than one, and changing fractions to lowest terms.

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

This stage challenges the students to apply their knowledge and skills in ordering fractions less than one/equal to one/more than one, and changing fractions to lowest terms.

Strategy

GRAFFITI. This strategy encourages groups to rotate around a series of recorded ideas or issues. This can be used as a preparation or follow up activity. How can this be facilitated?

• Allocate each group an issue or aspect of a topic. Ideas are to be recorded on a large sheet of paper.

• After a set amount of time, each group rotates to the next sheet of paper. New ideas can be added.

• Ask groups to check any ideas they agree with, place a question mark next to those that need clarification, and draw a lightning bolt next to inappropriate solutions.

Materials

• task cards (refer Teacher Resource Sheet 2 on pages 19-20) • manila paper

• marking pen

• masking tape

Activity 6: “Let's Take the Parts”

Prior to the activity, post one set of cards in one side of the classroom (for group A) and the other set on the opposite side (for group B).

1. Organize the class into 2 groups, A and B. Then, reorganize each group into 4 smaller groups.

2. Assign each group on a certain task to perform.

3. Let them write their outputs on a manila paper and post it.

4. Then, using the GRAFFITI strategy, facilitate the conduct of the activity, and presentation and checking of outputs. Refer to its description and steps above. 5. Conduct an interactive discussion on points where there are question marks and

lightning bolts.

Formative Assessment

Ensure the active participation of each member in the group. Check their outputs.

Roundup

It is important to check if students were able to apply what they learned in the previous activities.

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 summarize and check what they learned through the given series of activities.

Strategy

BUZZ SESSIONS. This is a strategy where students work in small groups within a determined time limit and without a leader, to answer a question, or solve a problem and come up to some kind of conclusion.

Material

● output in Activity 2

Activity 7: “Let's Revisit the Fractions”

1. Use the same grouping as in Activity 2.

2. Give them back their output in Activity 2 and let them review, discuss, and check their answers.

3. Instruct them to give five other examples to each type of fraction.

Formative Assessment

Roundup

Students were given the opportunity to summarize and check what they learned in the given series of activities.

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.

STUDENT ACTIVITY 3

TASK 1: FRACTIONS LESS THAN ONE

Objective: Identify fractions equal to one

Directions:

1. Get a whole sheet of bond paper.

2. Fold it equally into 16 parts. Then, color the following parts as indicated.

(Note:

Color only each portion once.)

Number of Parts Color

1 2 3 4 6

red blue yellow

green brown

•

What fraction of the paper is colored with red? _______ blue? ______

yellow? ______ green? ______ brown? ________

•

Now, complete this statement.

A fraction is less than one if

_____________________________________________________

_____________________________________________________

____________________________________________________.

•

A fraction which is less than one is called

_{proper fraction}

.

•

Give other examples of fractions which are less than 1.

Note:

✔The fractions are like fractions. ✔ Each fraction is less than one. ●

✔Unlike fractions like , , and

are also less than one. 3 4

5 8

STUDENT ACTIVITY 3

TASK 2: FRACTIONS EQUAL TO ONE

Objective: Identify fractions equal to one.

Danna's sheet Kaye's sheet Kate's sheet

☑

What is the fraction that tells about all parts of each sheet?

Danna: ________________ Kaye: _________________ Kate: _________________

☑

Is each fraction equal to 1? Support your answer.

_________________________________________________________________________

_________________________________________________________________________

☑

Now, complete this statement.

A fraction is equal to one if

_________________________________________________________

_________________________________________________________

_________________________________________________________

☑

A fraction equal to one is called an improper fraction.

Danna, Kaye and Kate plan to share their sheets of paper with their classmates for their paper doll- making project.

Danna divides her sheet into 3 equal parts, Kaye's sheet into 6 equal parts, while Kate's sheet into 8 equal parts.

STUDENT ACTIVITY 3

TASK 3: FRACTIONS GREATER THAN ONE

A) Objective: Recognize fractions more than one.

Trina's Group Garden Plots

☑

_{How many equal parts are there in all? _________________________}

☑

Color the parts which were planted with mongo.

☑

What is the fraction for the shaded part? ________________________

☑

Is this fraction greater than 1? Support your answer.

_________________________________________________________________________

_________________________________________________________________________

☑

Now, complete this statement.

A fraction is greater than one if

_________________________________________________________

_________________________________________________________

_________________________________________________________

☑

Fractions greater than one are also called improper fractions.

Trina's group was assigned to cultivate 2 garden plots. In their group report, they indicated the following activities they did in a week:

- divided each plot into 4 equal parts - planted 7 parts with mongo.

B) Objectives:

•

Separate groups of objects to show fractions more than one.

•

Read and write fractions more than one in symbols and words.

Try to study the table below.

Total number of parts of green bell

peppers

In symbol

In words

4

4

4

4

3

4

11

4

1

1

3

4

2 3

4

☑

Is

11

₄

an improper fraction? Explain your answer.

☑

Another name for

11

₄

is

2 3

4

. This is a mixed number.

Now, what is a mixed number?

______________________________________________________________

______________________________________________________________

STUDENT ACTIVITY 4

ORDERING FRACTIONS

Objective:

•

Order fractions less than one/equal to one/more than one with the same

denominator.

Use the squares below to illustrate each part of the cloth used by the Paolo, Claire,

and Loi.

Paolo's cloth Claire 's cloth Loi's cloth

•

Which part is the biggest? _____________________ the smallest?

•

Who used the greatest part of the cloth? ________________ the smallest?

•

Now, arrange the fractions from biggest to smallest. _________, _________, ________

•

Compare the denominators of the fractions.

•

Complete the statement.

To order like fractions,

________________________________________________________________________

________________________________________________________________________

Paolo, Claire and Loi each had a piece of

cloth of equal size for their

banner-making project. Paolo used of his

cloth, Claire used of his cloth, and

Loi used of his cloth. Who used the

biggest part?

3

4

2

4

STUDENT ACTIVITY 5

WHAT'S ITS SIMPLEST FORM?

TASK A: Finding the Greatest Common Factor (GCF)

Directions:

1. List down the factors of the following:

9 18

•

Encircle the greatest common factor of the two numbers.

•

Complete the statement.

The greatest common factor (GCF) of two or more nonzero numbers is the

__________________________________________________________________

__________________________________________________________________

•

What is the GCF of 8, 12 and 20?

TASK B: Reducing Fraction To Its Lowest Term

2. Reduce

9

18

to its lowest form. To answer, try to complete the box in each step.

Step 1: Find the GCF of the numerator and denominator.

9

18

Step 2: Divide both the numerator and the denominator by their GCF.

9

18

=

9

÷

=

18

÷

So,

₁₈

9

=

3. Complete the statement.

To reduce a fraction to its lowest term,

TEACHER RESOURCE SHEET 1

FRACTIONS STRIPS

STUDENT ACTIVITY 6:OUR FRACTION TREE

Fractions Less

Than One

TEACHER RESOURCE SHEET 2

TASK CARDS

Directions: Reproduce each card into 2 copies and cut. You may enlarge each

problem on a manila paper.

Mother sliced all the avocados she bought into

halves.

From these, Jenny got avocados for her

fruit salad. How many pieces of avocados did she

used then for the salad?

9

2

Forty stringed instruments are displayed in the music

room.

If there are 16 harps and the rest are guitars, then

what part of the total number of instruments are

harp?

Reduce each fraction to determine what simplest part of the total

number of hours in a day does Piolo spend in each of the following

activities.

9

24

8

24

2

24

•

In what activity does he spend

the longest time? the shortest?

•

If you were Piolo,

☑

what other activities will

you do for the remaining

hours of the day?

☑

how many hours in all will

you spend taking a bath,

taking your breakfast, and

preparing yourself to

school?

4

24

Trina bought four pieces of cloth.

She divided each equally into four to make pieces of handkerchiefs. Of these, she gave to her sisters,

to her friends, to her cousins, and to her mother.

a) Who received the greatest part? the least?

b) Who among them received a part equivalent to a whole piece of cloth?

5 4

1 4 4

4

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