This is the Grade 6 Mathematics Quarter 4, Module 4 self-learning module, “Constructing and Interpreting a Pie Graph Based on a Given Set of Data.” It was developed by DepEd Region VI as an Alternative Delivery Mode (ADM) module, First Edition, 2020, for learners studying at home or in class. After working through it, learners should be able to turn a table of data into a pie graph and read information from one.
What learners will learn
The module states one learning objective:
- Construct a pie graph based on a given set of data and interpret it.
The module has a single lesson with the same title as the module.
What a pie graph is
The module explains that pie graphs, also called circle graphs, show the percent of a quantity that falls in each of several categories. They also make it easy to compare one category with another, because each category is a slice of one whole circle.
A full circle measures 360°. So the slices of a pie graph always add up to 100% and to 360°.
How to construct a pie graph: the module’s example
The lesson uses a survey of the most liked ice cream flavors of 40 learners. Here is how the module works it out.
- Change each count to a percent. Divide the number of learners for each flavor by the total, then multiply by 100. For example, Rocky Road: 10 ÷ 40 = 0.25, and 0.25 × 100 = 25%.
- Find the angle for each slice. Change the percent to a decimal by moving the decimal point two places to the left, then multiply by 360°. For example, Chocolate: 30% = 0.30, and 0.30 × 360° = 108°.
- Draw a circle using a compass.
- Draw each angle with a protractor to divide the circle, then label each section.
- Write a title for the graph.
The finished table from the example:
| Ice cream flavor | Number of learners | Percent | Angle measure |
|---|---|---|---|
| Rocky Road | 10 | 25% | 90° |
| Double Dutch | 4 | 10% | 36° |
| Strawberry | 10 | 25% | 90° |
| Vanilla | 4 | 10% | 36° |
| Chocolate | 12 | 30% | 108° |
| Total | 40 | 100% | 360° |
The module also gives a useful tip: if only the percents are given, multiply each percent by the total to find how many people are in each category.
How to interpret a pie graph
Reading a pie graph means answering questions from its slices. The module’s activities ask learners to:
- Find the largest and smallest categories (for example, the subject a learner spends the most or least time on).
- Change a percent back to an amount. For example, if a learner spends 8% of a 24-hour day on gadgets, that is 0.08 × 24 = 1.92 hours.
- Compare two categories, such as how much more is spent on food than on monthly bills.
The examples come from everyday life: a family’s monthly budget, favorite sports, ways of going to school, how a Grade 6 learner spends the day, favorite fruits, and summer vacation choices.
Parts of the module
- What I Know: a pretest where learners draw a pie graph of Mrs. Gonzales’s monthly expenses and answer five questions about it.
- What’s In: complete a pie graph of the favorite sports of Grade 6 pupils.
- What’s New and What is It: the ice cream example and the steps above.
- What’s More: complete a table and draw a graph of learners’ means of transportation, then answer questions about how a learner spends the day.
- What I Have Learned: a summary of the four steps.
- What I Can Do: draw a pie graph of the favorite fruits of 300 Grade 6 learners and answer questions.
- Assessment: draw graphs of a family budget and of summer vacation preferences, then interpret a graph of the time Dina spent on her modules.
- Additional Activities: draw a circle graph of your own daily schedule and of your weekly allowance budget.
- Answer Key for the activities and tests.
How to use this module
- Learners: Start with the pretest to check what you already know. Then go through each part in order. Write all answers on a separate sheet of paper, not on the module. You will need a compass and a protractor. Check your work with the answer key only after you finish, and be honest when you use it.
- Parents and guardians: Help your child prepare a compass, protractor, and answer sheet, and encourage them to ask the teacher when a task is hard.
- Teachers: The ice cream example is a ready model for class demonstration, and the Additional Activities let learners apply pie graphs to their own schedules and budgets. The module notes that the order of lessons can be adjusted to match the textbook in use.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 6 Mathematics, Quarter 4. It is Module 4 of that quarter.
How do you find the angle of each slice in a pie graph?
Change the percent to a decimal and multiply it by 360°, since a full circle is 360°. For example, 25% becomes 0.25, and 0.25 × 360° = 90°.
What tools do I need to draw a pie graph?
The module uses a compass to draw the circle and a protractor to draw each angle measure.
Does the module have an answer key?
Yes. It includes answers for the pretest, the activities, and the assessment. The Additional Activities have no fixed answers because learners use their own data.
What is the difference between a pie graph and a circle graph?
There is no difference. The module uses both names for a graph that shows each category as a part of a whole circle.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 4 – Module 4: Constructing and Interpreting a Pie Graph Based on a Given Set of Data
[illustration: students and a teacher studying with books, a globe, and a lamp under a tree]
CO_Q4_Mathematics 6_ Module 4
Mathematics – Grade 6 Alternative Delivery Mode Quarter 4 – Module 4: Constructing and Interpreting a Pie Graph Based on a Given Set of Data First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or 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.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by _____
Development Team of the Module
Writer: Prilyn S. Albarico
Editors: Mae Joy M. Tan, Susana L. Lutero, Nora B. Rebadomia, Mary Jane O. Amante, Ma. Pinky C. Arquio, Susan T. Dela Torre,
Reviewers: Ivy Joy A. Torres, Ma. Theresa L. Tabotabo, Jem Rymon S. Chien, Mae Joy M. Tan
Illustrator: Eldiardo E. Dela Peña
Layout Artists: Eldiardo E. Dela Peña, Pepe M. Tabanao, Jr.
Management Team: Ramir B. Uytico, Pedro T. Escobarte, Jr., Elena P. Gonzaga, Donald T. Genine, Adonis A. Mosquera, Clarissa G. Zamora, Fevi S. Fanco, Ivy Joy A. Torres, Jason R. Alpay, Mae Joy M. Tan, Jem Rymon S. Chien, Ethel S. Gali
Department of Education – Region VI
Office Address: Duran Street, Iloilo City Telefax: (033)336-2816, (033)509-7653 E-mail Address: region6@deped.gov.ph
Mathematics
Quarter 4 – Module 4: Constructing and Interpreting a Pie Graph Based on a Given Set of Data
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
This module was designed and written with you in mind. It is here to help you master the skills in constructing and interpreting a pie graph. The scope of this module allows you to use it in many different learning situations. The language used recognizes your diverse vocabulary level. The lessons are arranged to follow the standard sequence of your course. But the order in which you read them can be changed to match with the textbook you are now using.
- After going through this module, you are expected to construct a pie graph based on a given set of data and interpret it.
What I Know
A. Read and study the data carefully. Construct a pie graph out of it. Write the answer on your answer sheet.
Mrs. Gonzales spends her monthly income in this way.
| Expenditures | Amount | Percent | Degrees |
|---|---|---|---|
| Food | ₱4,500.00 | 37.5% | 135⁰ |
| Education | ₱3,000.00 | 25% | 90⁰ |
| Monthly Bills | ₱1,500.00 | 12.5% | 45⁰ |
| Transportation | ₱1,800.00 | 15% | 54⁰ |
| Savings | ₱1,200.00 | 10% | 36⁰ |
| Total | ₱12,000.00 | 100% | 360⁰ |
B. Use the data in the pie graph that you had constructed to answer the following questions. Write the answer on your answer sheet.
- What percent of the monthly income does Mrs. Gonzales spend on education?
- In which categories does she spend the greatest part of her income?
- How much does she spend for her transportation?
- How much more does she spend on paying for food than monthly bills?
- How much does she save monthly?
Lesson 1: Constructing and Interpreting a Pie Graph Based on a Given Set of Data
When we look for information to help us make important decisions, we often find the information in the form of graphs. One of these graphs is the pie graph. This module will focus on how to construct and interpret a pie graph.
What’s In
Complete the data in the pie graph below. Use the data found in the table. Write the answer on your answer sheet.
| Favorite Sports of Grade VI Pupils | |
|---|---|
| Sports | Percentage |
| Baseball | 12% |
| Sipa | 20% |
| Volleyball | 15% |
| Tennis | 10% |
| Basketball | 43% |
| Total | 100% |
[chart: pie graph; Favorite Sports of Grade VI Pupils]
Labels printed on the chart:
- Baseball , 12%
- ______, ___
- ______, ___
- ______, ___
- ______, ___
Values are not labeled on the chart.
What’s New
The table below shows the percentage of learners who like the given flavors of ice cream.
| THE MOST LIKED ICE CREAM FLAVORS OF LEARNERS | |
|---|---|
| Ice Cream Flavor | Number of Learners |
| Rocky Road | 10 |
| Double Dutch | 4 |
| Strawberry | 10 |
| Vanilla | 4 |
| Chocolate | 12 |
| TOTAL | 40 |
How will you construct a pie graph using the data in the table?
What is It
Pie graphs or circle graphs are used to show the percent of a quantity in each of the several categories. It can also be used to easily visualize the ratio of one category to another.
To construct a pie graph, you may do the following steps:
Step 1: Find the angle measure for each section
Step 2: Change the number of learners per ice cream flavor preference to percent form by dividing it to the total number of learners. The, their quotients is multiplied to 100; transforming them to percent form.
Rocky Road: 10 learners ÷ 40 = 0.25 x 100 = 25%
Double Dutch: 4 learners ÷ 40 = 0.10 x 100 = 10%
Strawberry: 10 learners ÷ 40 = 0.25 x 100 = 25%
Vanilla: 4 learners ÷ 40 = 0.10 x 100 = 10%
Chocolate: 12 learners ÷ 40 = 0.30 x 100 = 30%
Step 3: Change percent form to decimal form by moving the decimal point 2 places to the left. Then, multiply each decimal to 360°. (The complete rotation of a circle is equivalent to 360°.)
Angle Measure
Rocky Road: 25% of 360 = 0.25 x 360° = 90°
Double Dutch: 10% of 360 = 0.10 x 360° = 36°
Strawberry: 25% of 360° = 0.25 x 360° = 90°
Vanilla: 10% of 360° = 0.10 x 360° = 36°
Chocolate: 30% of 360° = 0.30 x 360° = 108°
Note: If the number of learners per preference is not found and only percent is given, multiply percent by the total number of learners to solve how many learners like rocky road, double dutch, strawberry, vanilla and chocolate.
Step 4: Draw a circle using a compass.
[illustration: a compass drawing a circle, with an arrow pointing to an empty circle]
| Ice Cream Flavor | Number of Learners | Percent | Angle Measure |
|---|---|---|---|
| Rocky Road | 10 | 25% | 90° |
| Double Dutch | 4 | 10% | 36° |
| Strawberry | 10 | 25% | 90° |
| Vanilla | 4 | 10% | 36° |
| Chocolate | 12 | 30% | 108° |
| TOTAL | 40 | 100% | 360° |
Step 5: Use a protractor to draw the angle measures of 90°, 36°, 90°, 36°, and 108°. Then label each section.
[illustration: protractor measuring 90° (Angle measure of Rocky Road), with an arrow to a circle labeled Rocky Road 90°]
[illustration: protractor measuring 36° (Angle measure of Double Dutch), with an arrow to a circle labeled Double Dutch 36°, Rocky Road 90°]
[illustration: protractor measuring 90° (Angle measure of Strawberry), with an arrow to a circle labeled Double Dutch 36°, Rocky Road 90°, Strawberry 90°]
Step 4: Write a title for the graph.
[illustration: protractor measuring 36° (Angle measure of Vanilla), with an arrow to a circle labeled Double Dutch 36°, Rocky Road 90°, Strawberry 90°, Vanilla 36°]
[illustration: protractor measuring 108° (Angle measure of Chocolate), with an arrow to a circle labeled Double Dutch 36°, Rocky Road 90°, Strawberry 90°, Vanilla 36°, Chocolate 108°]
[chart: pie; THE MOST LIKED ICE CREAM FLAVORS OF LEARNERS]
Labels printed in the chart:
- Rocky Road, 10 / 25%
- Double Dutch, 4 / 10%
- Strawberry, 10 / 25%
- Vanilla, 4 / 10%
- Chocolate, 12 / 30%
[chart: pie; untitled]
Labels printed in the chart:
- Sleep 34%
- Study 25%
- Doing Chores 15%
- Playing Outdoors 12%
- Playing Gadgets 8%
- Others 6%
What’s More
A. Complete the data in the table below and construct a pie graph out of it. Do it on your answer sheet.
| Means of Transportation in going to School | Number of Learners | Percent | Angle Measures (Degrees) |
|---|---|---|---|
| Bus | 10 | ||
| Tricycle | 25 | ||
| Private Car | 5 | ||
| Jeepney | 10 | ||
| Walking | 30 | ||
| TOTAL | 80 |
B. The pie chart below shows how a Grade VI learner spends his day. Refer to the pie chart to answer the following questions: (Hint: 1 day = 24 hours)
- What percent of the day is used by the learner in doing the household chores?
- In which category does the learner spend most of his time?
- How many hours of the day does the learner use gadgets?
- How many percent does the learner spend in studying the lesson?
- How many percent does the learner spend in doing other things?
What I Have Learned
Pie graphs or circle graphs are used to show the percent of a quantity in each of the several categories. It can also be used to easily visualize the ratio of one category to another.
To construct a pie graph, follow these steps:
- Find the angle measure for each section accordingly by their percentage.
- Draw a circle using a compass.
- Use a protractor to draw each angle measure and partition the circle. Then label each section.
- Write a title for the graph.
What I Can Do
Construct a pie graph based on the given data below and answer the questions that follow. Write the answer on your answer sheet.
The table shows the favorite fruits of 300 Grade VI Learners of Escalante Central Elementary School.
| Fruits | Percent |
|---|---|
| Banana | 20% |
| Mango | 50% |
| Avocado | 5% |
| Apple | 15% |
| Guava | 10% |
| Total | 100% |
- How many percent of Grade VI learners like guava fruit?
- How many learners like eating bananas?
- What is their least favorite fruit?
- What fruit is favorite by half of Grade VI learners?
- How many more learners prefer to eat apples than avocado fruit?
Assessment
A. Construct a pie graph on the following data. Write the answer on your answer sheet.
- Family budget with monthly income of ₱ 20,000.00
Education – 20% Food – 40% Transportation – 15% Rental – 15% Saving – 10%
- Summer Vacation Preference of Grade VI Learners
Beach – 24 Camping – 12 Mountain climbing – 6 Stay Home – 18
B. Study the pie graph below and answer the questions that follow. Write the answer on your answer sheet.
Dina tracked the time she spent in answering her modules for a week.
[chart: pie; untitled]
Labels printed in the chart:
- English, 9%
- Science, 12%
- TLE, 9%
- Math, 16%
- EsP, 13%
- Aral Pan, 11%
- Filipino, 18%
- MAPEH, 12%
- Which of the subjects requires a longer period of time?
- Which of the subjects requires the least period of time?
- If Dina spent 2 400 minutes in answering her modules for a week, how many minutes were spent on:
A. EsP?
B. Science?
C. Filipino?
D. Math?
Additional Activities
Construct a circle graph for the following activities. Write the answer on your answer sheet.
- Your schedule for your day’s activity in the new normal.
- Your own budget for a week allowance last school year.
Answer Key
What I Know
A.
| Expenditures | Degrees |
|---|---|
| Food | 135° |
| Education | 90° |
| Monthly Bills | 45° |
| Transportation | 54° |
| Savings | 36° |
| Total | 360° |
[chart: pie; Mrs. Gonzales, Monthly Expenditures]
Labels printed in the chart:
- Savings, 10%
- Transportation, 15%
- Monthly Bills, 12.50%
- Education, 25%
- Food, 37.50%
B.
- 25%
- Food
- ₱1,800.00
- ₱3,000.00
- ₱1,200.00
What’s In
- Basketball, 43%
- Sipa, 20%
- Volleyball, 15%
- Tennis, 10%
What’s More
A.
| Means of Transportation going to School | Percent | Angle Measure |
|---|---|---|
| Bus | 12.5% | 45° |
| Tricycle | 31.25% | 112.50° |
| Private Car | 6.25% | 22.50° |
| Jeepney | 12.5% | 45° |
| Walking | 37.5% | 135° |
| Total | 100% | 360° |
[chart: pie; Learners’ Means of Transportation going to School]
Labels printed in the chart:
- Bus, 10
- Tricycle, 25
- Private Car, 5
- Jeepney, 10
- Walking, 30
B.
- 15%
- Sleeping
- 1.92 hours
- 25%
- 6%
[transcriber’s note: this page is printed rotated 180 degrees; it is transcribed in upright reading order, with the “What I Can Do” column first, then “Additional Activities”, then “Assessment”]
What I Can Do
Chart
[chart: pie chart; Favorite Fruits of Learners in Escalante Central Elem. School]
| Fruit | Percent |
|---|---|
| Guava | 10% |
| Apple | 15% |
| Avocado | 5% |
| Mango | 30% |
| Banana | 20% |
[transcriber’s note: the questions for items 1 to 5 do not appear on this page]
- 10%
- 60
- Avocado
- Mango
- 30 learners
Additional Activities
- Learners’ answer vary
- Learners’ answer vary
Assessment
A.1.
[chart: pie chart; Monthly Family Budget]
| Category | Percent |
|---|---|
| Savings | 10% |
| Education | 20% |
| Rental | 15% |
| Transportation , | 15% |
| Food | 40% |
2.
[chart: pie chart; Summer Vacation Preference of Grade VI Learners]
| Preference | Value |
|---|---|
| Stay Home | 18 |
| Mountain Climbing | 6 |
| Camping | 12 |
| Beach | 24 |
B.
- Filipino
- English and TLE
- a. 312 minutes
b. 288 minutes
c. 432 minutes
d. 384 minutes
References
Perez, Marjoseph H. et. al., 21st Centry MATHletes 6 Textbook, Department of Education, Ground Floor, Bonifacio Building., DepEd Complex, Meralco Avenue, Pasig City, Philippines, 2014.
Jose-Dilao, Soledad et. al, Advanced Algebra Trigonometry and Statistics, JTW Corporation, 1281 Gregorio Araneta Avenue, Quezon City, 2003.
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
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