REPUBLIC OF THE PHILIPPINES DEPARTMENT OF EDUCATION LEARNING GUIDE

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GRADE VI - MATHEMATICS

GRAPHS

MODULE 16: COMPREHENSION OF CIRCLE GRAPH

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impose as a condition the payment of royalties.

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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

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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

In this stage, the students will perform an activity wherein they will classify figures or cut-outs according to their common attributes. Then, they will explain how the figures or cut-outs will be classified.

This activity will help the students recall their prior learning on colors, sizes and shapes.

Strategy

SORTING FIGURES. This is a strategy which uses figures or cut-outs for the students to sort and classify. They will examine each figure or cut-out. Then, decide how to classify them according to their common attributes - colors, sizes or shapes.

Materials

• set of figures (Teacher Resource Sheet 1 on pages 12-13)

• envelope • manila paper • paste/glue

• masking tape • pentel pen

• pair of scissors

Activity 1: WHERE DO I BELONG?

Instructions:

1. Prior to the activity, prepare a set of figures or cut-outs. 2. Divide the class into five groups or as desired.

3. Distribute to each group the materials needed for the activity.

4. Instruct them to classify the figures or cut-outs according to their common attributes. 5. Give them a few minutes to perform the task.

6. Let them present their outputs on a manila paper.

7. Ask them to explain how the figures or cut-outs were classified.

Formative Assessment

See to it that everyone involved himself/herself in the group activity. Then, check the outputs of the students.

Roundup

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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 make a graphical presentation of the data in the first activity using any of the graphs (pictograph, bar graph or line graph) they have learned in the previous grade level.

Strategy

GRAPHS. This is a strategy which uses different graphical forms such as pictograph, bar graph and line graph to display information and data.

Materials

• ruler

• manila paper • pentel pen

• masking tape • pair of scissors

Activity 2: GRAPHING

Instructions:

1. Use the same groupings of students as in the first stage to perform this activity. 2. Distribute the necessary materials to each group.

3. Instruct them to make a graphical presentation of their output in the first activity using any of these graphs: pictograph, bar graph or line graph. See to it that the graph will be labeled properly with its important parts such as:

• title • label • legend

4. Give them few minutes to perform the task.

5. Let them present their outputs for analysis and discussion.

6. Tell them that in the next stage, they will learn another kind of a graph which is CIRCLE GRAPH.

Formative Assessment

Supervise the group activity to ensure that everyone is involved in the discussion. Then, check the outputs of the students.

Roundup

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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, the students will perform an activity which will guide them to construct a circle graph. Then, they will read and interpret the data on it.

Strategies

SURVEY. This strategy is a useful way of collecting data from other students, teachers, parents and the wider community. Administering a survey in an “interview” situation can develop student's speaking and listening skills.

INTERACTIVE LECTURE. This strategy provides students with a general outline to give them a framework for thinking about a subject and to structure their note taking. This type of lecture involves students by focusing their attention on key words. It emphasizes information transfer at the knowledge, recall, and comprehension levels of learning.

Materials

• Survey Form (refer to Teacher Resource Sheet 2 on page 14) • Consolidation Form (refer to Teacher Resource Sheet 3 on page 15) • Strip Graph (refer to Teacher Resource Sheet 4 on page 16)

• activity sheet (refer to Student Activity 3 on pages 17-18)

• Teacher's Input on circle graph (refer to Teacher Resource Sheet 5 on pages 19-23)

• manila paper • crayon

• protractor

• pentel pen • masking tape • ruler

Activity 3: DO IT RIGHT

Instructions:

1. Prior to the activity, prepare a strip graph and other materials needed for the activity. 2. Divide the class into five groups or as desired.

3. Provide each group with the necessary materials. 4. Instruct them to perform Student Activity 3. 5. Give them enough time to perform the task.

7. Conduct an interactive lecture to enhance their learning about circle graph.

For your reference in conducting an interactive lecture, you may use the attached Teacher's Input, Teacher Resource Sheet 5 on pages 19-23.

Formative Assessment

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Roundup

The students would have performed an activity on how to construct a circle graph. Then, they would have read and interpreted the data on it.

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 will enhance the learning of the students and will give opportunity for the teacher to check how much the students have understood about constructing a circle graph, and reading and interpreting the data presented on it.

Strategy

INVESTIGATION. This strategy gives opportunities for the students to make simple discoveries on the total number of each day in a year using the calendar.

Materials

• calendar (refer to Teacher Resource Sheet 6 on page 24) • activity sheet (refer to Student Activity 4 on page 25)

• manila paper • pentel pen • masking tape

Activity 4: THOSE WERE THE DAYS

1. Divide the class into five groups or as desired.

2. Provide each group with the materials needed for the activity. 3. Give them a few minutes to perform Student Activity 4. 4. Let them present their outputs for analysis and discussion.

Formative Assessment

Roam around the classroom to ensure that everyone performed the task correctly. Then, check the outputs of the students.

Roundup

This stage would have enhanced the learning of the students and gave opportunity for the teacher to check how much the students have understood about constructing a circle graph graph, and reading and interpreting the data presented on it.

5. Practice and Application

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Background or purpose

In this stage, students will be given an opportunity to apply their learning on constructing a circle graph, and reading and interpreting it in a new and real-life situation/s.

Several activities are provided in this stage as options.

Strategy

SMALL GROUP DISCUSSION. This is a strategy that involves a smaller number of participants in each group. With this strategy, it is hoped that all members of the group feel connected to each other in the accomplishment of a common goal, that each group member shares and collaborates with other members in a way that promote continued progress, and that they develop social skills with your support as their teacher.

Materials

ACTIVITY 5.A: RUN TO ME

• Record Sheet (refer to Teacher Resource Sheet 7 on page 26) • meter stick

• stop watch

ACTIVITY 5.B: TIME CHECK

ACTIVITY 5.C: MONEY MATTERS

Activity 5.A: RUN TO ME

1. Prior to the activity, prepare a running field for a 50-meter sprint. Using the meter stick, measure the appropriate distance for the race and mark the “START” and “FINISH” lines. 2. Divide the class into groups of five or as desired.

3. Distribute the materials needed for the activity. 4. Let each group assign a time keeper and a recorder.

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6. Tell them to make a circle graph showing the number of seconds each member got in the race.

a) Add the number of seconds got by all members in the group.

b) Determine the percentage of the number of seconds each member got. c) Find the average number of seconds in their group.

d) Make sure that the graph has its important parts labeled correctly. e) Interpret the graph by considering its title, sectors and sector labels. 7. Give them few minutes to perform the task.

ACTIVITY 5.B: TIME CHECK

1. Divide the class into five groups or as desired. 2. Distribute the materials needed for the activity.

3. Tell them to list down all their activities during Saturday and Sunday.

4. Instruct them to make a circle graph showing the number of hours they spent for each activity.

a) Get the total number of hours for Saturday and Sunday. b) Assign a corresponding number of hours for each activity.

c) Determine the percentage of the number of hours in each activity.

d) Find the average number of hours for their activities during Saturday and Sunday. a) Make sure that the graph has its important parts labeled correctly.

b) Interpret the graph by considering its title, sectors and sector labels. 5. Give them a few minutes to perform the task.

ACTIVITY 5.C: MONEY MATTERS

1. Prior to the activity, instruct the students to ask their parents or guardians about the monthly income of their family and how they spend it.

2. Divide the class into five groups or as desired. 3. Distribute the materials needed for each activity. 4. Let them discuss their monthly income and expenses.

a) Get the average monthly income of their families. b) Agree among themselves how they will spend it.

c) Determine the percentage of the amount for each item. d) Find the average amount spent for all items.

5. Ask them to make a circle graph showing the monthly income and expenses. 6. Make sure that the graph has its important parts labeled correctly.

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Formative Assessment

Check the outputs of the students. Ask them to cite other situation/s in which their knowledge on constructing a circle graph, and reading and interpreting a circle graph will be applied.

Roundup

The students would have applied their learning on constructing a circle graph, and reading and interpreting a circle graph in a new and real-life situation/s.

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, the students will perform an activity which will give them a chance to make a composition expressing their learning on constructing a circle graph, and reading and interpreting the data on it.

Strategy

COMPOSITION WRITING. This is a strategy which enhances students' skills in creative writing. Their learning on constructing a circle graph, and reading and interpreting the data presented on it through a song, rap, rhyme, poem or acrostic.

Materials

Activity 6: MAKE ME UP

Instructions:

Before the conduct of the activity, unlock the terms, song, rap, rhyme, poem and acrostic.

1. Divide the class into groups of five or as desired.

2. Instruct them to make a composition expressing their learning on constructing a circle graph, and reading and interpreting the data on it.

3. Let them choose from the options below.

• Option 1 – Song • Option 2 – Rap • Option 3 – Rhyme

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4. Give them a few minutes to perform the task.

5. Ask them to rehearse for the presentation of their composition. 6. Let them present their composition.

Formative Assessment

Assess the performance of the students in the activity and check also their outputs. You may use the rubric on pages 27-28.

Roundup

The students would have performed an activity which gave them a chance to make a composition expressing their learning on constructing a circle graph, and reading and interpreting the data on it.

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.

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TEACHER RESOURCE SHEET 1

SET OF FIGURES

Directions:

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Color and cut the figures below.

•

Place them in an envelope.

yellow

orange

blue

red

green

white

blue

violet

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brown

black

white

blue

green

yellow

orange

violet

red

green

yellow

orange

black

white

blue

red

yellow

orange

violet

brown

violet

red

brown

green

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TEACHER RESOURCE SHEET 2

SURVEY FORM

Directions:

•

Reproduce this form corresponding to the number of groups.

•

Then, give each group 1 copy.

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TEACHER RESOURCE SHEET 3

CONSOLIDATION FORM

Directions:

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Reproduce this form corresponding to the number of groups.

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Then, give each group 1 copy.

SUBJECT

NUMBER OF STUDENTS

Mathematics

English

Science

Filipino

Makabayan

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TEACHER RESOURCE SHEET 4

STRIP GRAPH

Directions:

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Use a cartolina or chipboard to enlarge the 100 cm by 2 cm strip shown below.

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You've just constructed a circle graph...

STUDENT ACTIVITY 3

DO IT RIGHT

Objectives:

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Conduct a survey on the favorite subject of the

students.

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Construct a circle graph.

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Read and interpret the data presented in a circle graph.

Directions:

1. Make a survey to 100 students about their favorite subject. Then, record their

responses on the survey form.

2. Consolidate the gathered data using the consolidation form.

3. Color the strip graph corresponding to the number of students per subject. Make

sure to consider the following:

➢

a part represents 1 student

➢

1 color for each subject

4. Form the strip graph into a ring. Tape both ends together. Make sure they will not

overlap.

5. Place the circular strip on the manila paper and trace the circular figure on it.

6. Mark the boundaries of the color partitions representing each subject.

7. Mark also the center point of the circle.

8. Draw a line segments to connect each boundary to the center point.

9. Color and label the sectors of the circle in the same way as you colored and

labeled the strip graph.

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Answer the following:

a) What is the best title of the circle graph?

b) What does each part of the strip graph represent?

c) What does each section of the circle graph

represent?

d) What part of the whole circle graph does each

section show?

e) What is the total of the numerical data in all of the

sections?

f) Which subject has the greatest and least no. of

percentage?

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TEACHER RESOURCE SHEET 5

CIRCLE GRAPH

Directions:

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Study the concepts about circle graph.

•

Use this sheet as reference in conducting an interactive

lecture.

WHAT IS A CIRCLE GRAPH?

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It is also called PIE GRAPH or PIE CHART.

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It is another kind of graph that is often used in presenting data specifically in

showing how a whole is partitioned into parts.

WHAT ARE THE PROPERTIES OF A CIRCLE GRAPH?

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It is a circular-shaped graph with the entire circle representing the whole.

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The circle is then divided into parts or sectors.

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Each sector represents a part of the whole.

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Each sector is proportional in size to the amount each sector represents.

Therefore it is easy to make generalizations and comparisons.

HOW TO READ A CIRCLE GRAPH?

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When reading a circle graph, we will consider the following information:

1. Title of the Graph

It gives an overview of the information displayed in the graph. The title is

written oftentimes at the top of the graph.

2. Sectors

Each sector represents one part of the whole. The size of each sector

represents its fraction/part of the whole.

3. Sector Labels

The label of each sector indicates the category of information it refers to,

and may also give numeric data (often a percentage) so we know the size

of each sector.

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Example:

HOW TO CONSTRUCT A CIRCLE GRAPH?

1. Organize the data

Gather the data, then write them in a tabular form or place them in a table.

Family Expenses

Item

Amount

Food

_{3 800}

Electricity and Water

_{2 375}

Education and Recreation

_{1 425}

Savings

₄₇₅

Miscellaneous

_{1 425}

Family Expenses

25% 15%

5% 15%

40%

Food Saving_s Electricity

and Water

Education and Recreation

Miscellaneous

Title of the Graph

Sector

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1. Add the data

Determine the “whole” or the total.

3800 + 2375 + 1425 + 475 + 1425 = 9500

2. Calculate percentages

Find the percentage by dividing each item by the whole or total. Then, the

result will be multiplied by 100.

(3800 ÷ 9500) x 100 = 40%

(2375 ÷ 9500) x 100 = 25%

(1425 ÷ 9500) x 100 = 15%

(475 ÷ 9500) x 100 = 5%

(1425 ÷ 9500) x 100 = 15%

3. Get the angle of each sector

Multiply the percentage by 360 which is the total number of degrees in a circle.

360 x 40% = 144

0

360 x 25% = 90

0

360 x 15% = 54

0

360 x 5% = 18

0

360 x 15% = 54

0

4. Draw a circle

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5. Determine the center point of the circle

Draw or place a point at the center of the circle.

6. Draw each section

Start at the center point of the circle, draw lines to show its sections/sectors

with the corresponding percentage in each item. Make sure to consider the angle

of each section/sector.

7. Complete the graph

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References:

• http://cstl.syr.edu/FIPSE/TabBar/ReadCirc/REVCIRCL.HTM

• http://cstl.syr.edu/fipse/TabBar/BldCirc/BUILDCIR.HTM

• http://www.wikihow.com/Make-a-Pie-Chart

Family Expenses

25% 15%

5% 15%

40%

Food Saving_s Electricity

and Water

Education and Recreation

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TEACHER RESOURCE SHEET 6

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STUDENT ACTIVITY 4

THOSE WERE THE DAYS

Objectives:

•

Determine the total number of Mondays, Tuesdays,

Wednesdays, Thursdays, Fridays, Saturdays and Sundays in

a year.

•

Construct a circle graph showing the data.

•

Read and Interpret the data presented in a circle graph.

Directions:

1. Count how many is each day in a year and record it.

Sunday _____ Thursday _____

Monday _____ Friday _____

Tuesday _____ Saturday _____ Wednesday _____

2. Construct a circle graph showing the gathered data.

3. Read and interpret the circle graph by answering the following:

a) What is the circle graph all about?

b) Does the title tell about the data presented in the circle graph?

Justify your answer.

c) Which has the least number of days?

d) Which has the most number of days?

e) How many days are there in all in a year?

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TEACHER RESOURCE SHEET 7

RECORD SHEET

Directions:

•

Reproduce this sheet corresponding to the number of groups.

•

Give each group a copy of this sheet.

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TEACHER RESOURCE SHEET 8

SCORING RUBRIC FOR PRESENTATION OF COMPOSITION

Directions: Indicate appropriately the points earned by the students from the presentation of composition they have made based on the given category below.

CATEGORY

P O I N T S C A L E

4 3 2 1

CONTENT Shows a full understanding of the _topic. Shows a good understanding of the _topic. Shows a good understanding of parts _{of the topic.} Does not seem to understand the _{topic very well.}

PREPAREDNESS Student is completely prepared and has obviously rehearsed. Student seem pretty prepared but might have needed more rehearsals. Student is somewhat prepared but it is clear that rehearsal was lacking.

Student does not seem at all prepared to present.

CREATIVENESS Excellent creative effort is manifested throughout the presentation.

Good creative effort is manifested

throughout the presentation. Little attempt to manifest creative effort throughout the presentation. No attempt to manifest creative effort throughout the presentation.

SPEAKS/SINGS CLEARLY

Speaks/sings clearly and distinctly all the time and mispronounces no words.

Speaks/sings clearly and distinctly all the time but mispronounces few words.

Speaks clearly and distinctly most of the time and mispronounces many words.

Often mumbles or cannot be understood.

VOICE QUALITY

Presenter's voice is loud enough to be heard by all audience members throughout the presentation.

Presenter's voice is loud enough to be heard by all audience members at least 90% of the presentation time.

Presenter's voice is loud enough to be heard by all audience members at least 80% of the presentation time.

Presenter's voice often too soft to be heard by all audience members.

LISTENS TO OTHER PRESENTATIONS

Listens intently. Does not make

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SCORE SHEET

NAME OF STUDENTS

CATEGORY

CONTENT PREPAREDNESS CREATIVENESS SPEAKS/SINGS _CLEARLY VOICE QUALITY LISTENS TO OTHER

PRESENTATIONS

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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