This is the Grade 6 Mathematics Self-Learning Module for Quarter 4, Module 5: Solving Routine and Non-Routine Problems Using Data Presented in a Pie Graph. It was developed by DepEd Region VI as part of its Alternative Delivery Mode materials for home-based learning. After working through it, Grade 6 learners should be able to read a pie graph and use its percents to answer word problems, such as finding how many items belong to one part of a whole.
What learners will learn
The module has one lesson. It targets this Most Essential Learning Competency:
- Solve routine and non-routine problems using data presented in a pie graph (M6SP-IVf-4.6)
The lesson builds on the previous one, where learners constructed and interpreted pie graphs from a given set of data.
The four-step plan for pie graph problems
The module teaches learners to solve every problem with a four-step plan:
- Understand. Know what is asked and list the given facts.
- Plan. Choose the operations to use and write the equation.
- Solve. Show your solution.
- Check and look back. Review your answer and complete it with the proper label.
Worked example: Mengie’s flower shop
Mengie’s flower shop has 350 flowers in five varieties. The pie graph shows roses at 30%, carnations at 14%, anthurium at 27%, and orchids at 13%. The percent for tulips is missing. The problem asks for the percent of tulips and the number of tulips.
- Find the missing percent. A pie graph always totals 100%. So 100% – (30% + 14% + 27% + 13%) = 100% – 84% = 16% tulips.
- Find the number of flowers. Change the percent to a decimal and multiply by the total: 0.16 x 350 = 56 tulips.
- Check. The five percents add up to 100%, and 56 ÷ 350 = 0.16.
The module then uses the same graph for follow-up questions:
| Question | Solution | Answer |
|---|---|---|
| How many are roses? | 0.30 x 350 | 105 roses |
| How many orchids and anthurium are there? | (13% + 27%) of 350 = 0.40 x 350 | 140 flowers |
| How many are carnations? | 0.14 x 350 | 49 carnations |
The example shows the two moves learners use throughout the module. First, find a missing part by subtracting the known percents from 100%. Second, find a quantity by multiplying its percent, as a decimal, by the total. To combine groups or compare them, add or subtract their percents first, then multiply.
Activities in the module
Each part of the module uses a new real-life pie graph:
- What I Know (pretest): book donations to Escalante Central Elementary School, 2,500 books in five learning areas. Five multiple-choice questions.
- What’s In: a review task where learners construct a pie graph of how Marlon spends the hours of his day.
- What’s More: how 300 Grade 6 pupils go to school, by walking, tricycle, pedicab, bicycle, or bus/jeepney. Five multiple-choice questions.
- What I Can Do: Mr. Himongala’s monthly family budget of ₱18,500.00, split among food, transportation, education, clothing, and savings. It ends with an open question on whether his savings budget is a wise decision.
- Assessment: the age groups of Barangay Matiwasay, with an estimated population of 33,500, including one group with a missing percent.
- Additional Activities: Judith’s monthly expenses from her ₱22,500.00 income, with the percent for bills left for learners to find.
How to use this module
- Learners: Start with the What I Know pretest to see what you already know. Then go through the parts in order. Follow the four steps for each problem and always label your final answer, for example “56 tulips” or “₱925.00.” Write your answers on a separate sheet of paper, not on the module. Check your work with the answer key only after you have tried each activity, and be honest when you use it.
- Parents and guardians: Help your child change percents to decimals (for example, 35% = 0.35) and check that the parts of each pie graph add up to 100%. If your child has trouble with a task, encourage them to ask their teacher.
- Teachers: The answer key covers the pretest, What’s In, What’s More, What I Can Do, Assessment, and Additional Activities. The last item of What I Can Do is open-ended, so answers may vary. The module lists the MELC in Mathematics 6, 21st Century MATHletes 6 (pp. 324–331), Hypermath 6 (pp. 399–402), and Enjoying Mathematics Workbook (p. 172) as references for extra practice.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 6 Mathematics, Quarter 4, Module 5. It covers the competency M6SP-IVf-4.6, solving routine and non-routine problems using data presented in a pie graph.
How do you find the number of items from a percent in a pie graph?
Change the percent to a decimal and multiply it by the total. In the module’s example, 16% of 350 flowers is 0.16 x 350 = 56 tulips.
How do you find a missing percent in a pie graph?
Subtract the sum of the known percents from 100%, because the whole pie is 100%. In the flower shop example, 100% – 84% = 16%.
What is the four-step plan used in this module?
The four steps are Understand, Plan, Solve, and Check and Look Back. You identify what is asked, choose the operations and equation, show your solution, then review and label your answer.
Does the module have an answer key?
Yes. The answer key covers the pretest, What’s In, What’s More, What I Can Do, Assessment, and Additional Activities.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 4 – Module 5: Solving Routine and Non-Routine Problems Using Data Presented in a Pie Graph
Mathematics
Quarter 4 – Module 5: Solving Routine and Non-Routine Problems Using Data Presented in a Pie Graph
CO_Q4_Mathematics 6_Module 5
[illustration: learners studying outdoors and at home with a teacher, a globe, and a lamp]
Mathematics – Grade 6 Alternative Delivery Mode Quarter 4 – Module 5: Solving Routine and Non-Routine Problems Using Data Presented in a Pie Graph 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 book 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
Development Team of the Module
Author: Oscar B. Mascuñana
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, Peter A. Alavanza
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
Printed in the Philippines by ________________________
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
6
Mathematics
Quarter 4 – Module 5: Solving Routine and Non-Routine Problems Using Data Presented in a Pie Graph
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
[illustration: target with arrow icon]
This module was designed and written with you in mind. It is here to help you master the skills in solving routine and non-routine problems using data presented in 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 solve routine and non-routine problems using data presented in a pie graph. (M6SP-IVf-4.6)
What I Know
Read the situation presented below. Then, refer to the pie graph in answering the questions that follow. Write the letter of your answer on your answer sheet.
The pie graph below shows the percent of book donations that Escalante Central Elementary School has received from its stakeholders. The school has received a total of 2,500 books in five subject areas.
[chart: pie graph; Book Donations from Stakeholders]
| Learning Area | Percent |
|---|---|
| Science | 25% |
| Mathematics | 35% |
| English | 10% |
| Filipino | 15% |
| Araling Panlipunan | 15% |
How many are Mathematics books has the school received?
A. 675 B. 775 C. 875 D. 975How many English books are donated?
A. 250 B. 350 C. 450 D. 550How many are Science and Araling Panlipunan books?
A. 500 B. 1000 C. 1500 D. 2000How many more Mathematics books were donated to Escalante Central Elementary School than Science books?
A. 175 B. 250 C. 375 D. 450What learning area received the highest number of books?
A. Araling Panlipunan C. Mathematics
B. English D. Science
Lesson 1: Solving Routine and Non-Routine Problems Using Data Presented in a Pie Graph
In the previous lesson, you have learned how to construct a pie graph based on a given set of data and interpret it. This time, we will focus on how to solve routine and non-routine problems using data presented in a pie graph.
What’s In
[illustration: puzzle pieces icon]
Using the information below, construct a pie graph to show how Marlon budgets his time each day. Write your answer on your answer sheet.
- In school : 6 hours
- Household chores : 5 hours
- Assignment : 2 hours
- Leisure/Sports : 3 hours
- Sleep and Rest : 8 hours
What’s New
[illustration: seedling icon]
Study the problem below.
Mengie’s flower shop has five (5) varieties of flowers. Her shop has 350 flowers in all. The pie graph on the right shows the percent of flowers in each variety. How many percent of flowers are tulips? How many are the tulip flowers?
[chart: pie graph; Varieties of Flowers in Mengie’s Flower Shop]
| Variety | Percent |
|---|---|
| Tulip | ? |
| Roses | 30% |
| Carnation | 14% |
| Anthurium | 27% |
| Orchids | 13% |
What is It
[illustration: magnifying glass with question mark icon]
To solve the above problem, a Four-Step Plan can be used.
Step 1: Understand
a. Know what is asked. The problem asked for the percent and the number of tulip flowers
b. Know the given facts: 5 varieties of flowers 350 is the total number of flowers 30% are roses, 14% are carnation, 27% are anthurium, 3% are orchids
[transcriber’s note: the given facts above say 3% are orchids, but the pie graph and the equation below show 13%; both are transcribed as printed]
Step 2: Plan
a. Plan the operation/s to be used. Addition, Subtraction, and Multiplication
b. Formulate the equation/s
Let N = percent of tulips Y = number of tulips
Equation for the first question: 100% – (30% + 14% + 27% + 13%) = N
Equation for the second question: N x 350 = Y
Step 3: Solve
Question Number 1:
100% – (30% + 14% + 27% + 13%) = N
100% – 84% = N
N = 16%
Complete answer: 16% are tulip flowers
Question Number 2:
16% x 350 = Y
0.16 x 350 = 56
Y = 56
Complete answer: There are 56 pieces of tulip flowers.
Therefore, there are 56 tulip flowers which comprise 16% of all the flowers in Mengie’s shop.
Step 4: Check and Look Back
Question Number 1: Add 30%, 14%, 27%, 13%, 16%, the answer will be 100%.
Question Number 2: Divide 56 by 350, and the answer is 0.16.
Follow-up Questions:
- How many are roses?
The pie graph shows that 30% of the 350 flowers of Mengie in her flower shop are roses.
Let N = the number of pieces of roses
30% of 350 = N
0.30 x 350 = N
N = 105
Thus, there are 105 pieces of roses.
- How many orchids and anthurium flowers are there?
In the graph presented, 13% of the flowers are orchids and 27% of the flowers of Mengie’s flower shop are anthurium.
Let N = the number of pieces of orchids and anthurium.
(13% + 27%) of 350 = N
40% of 350 = N
0.40 x 350 = N
N = 140
So, there are 140 pieces of orchids and anthurium.
Follow-up Questions (continued)
- How many pieces are carnation flowers?
The graph shows that 14% of flowers at Mengie’s flower shop are carnations.
Let N = the number of pieces of carnation flowers.
14% of 350 = N
0.14 x 350 = N
N = 49
Therefore, there are 49 pieces of carnation flowers.
What’s More
Read the situation presented below then, answer the following questions. Write the letter of your answer on your answer sheet.
The pie graph shows how the 300 Grade Six pupils go to school.
[chart: pie graph; Means in Going to School of Grade VI Pupils]
- Bus/Jeepney, 2%
- Bicycle, 5%
- Pedicab, 15%
- Tricycle, 35%
- Walking, 43%
How many Grade VI pupils go to school by foot or by walking?
A. 129 C. 149
B. 139 D. 159How many pupils in Grade VI prefer to ride on a bus or jeepney in going to school?
A. 3 C. 9
B. 6 D. 12How many Grade VI pupils go to school by riding on a bicycle and pedicab?
A. 50 C. 70
B. 60 D. 80How many more pupils prefer to ride on a tricycle than on a pedicab in going to school?
A. 45 C. 105
B. 60 D. 150How do half of the Grade VI pupils go to school?
A. by riding a tricycle and by walking
B. by riding a tricycle and a pedicab
C. by riding a bicycle and by a jeepney or bus
D. by riding a bicycle and a pedicab
What I Have Learned
To solve routine and non-routine problems using data presented in a pie graph, you may follow the 4-step plan.
- Understand – Know what is asked in the problem.
- Plan – What operation to be used in the problem and its equation.
- Solve – Show your solutions.
- Check and Look back – Check and review your answer. Complete your answer with proper label.
What I Can Do
Read and understand the situation presented below then answer the questions that follow. Write your answer in your answer sheet.
The monthly family’s budget of Mr. Himongala is ₱18,500.00. It is presented in the pie graph on the right.
[chart: pie graph; Mr. Himongala’s Monthly Budget]
- Savings, 5%
- Clothing, 10%
- Transportation, 25%
- Education, 20%
- Food, 40%
How much is allotted for food?
How much does the family save in a month?
What part of the budget has the biggest allocation? What is the least allocated?
If the monthly savings is added to the education budget, how much will it be?
How much more budget is allocated in transportation expenses than on the education budget?
Do you think Mr. Himongala’s budget for savings is a wise decision? Why or why not?
Assessment
Read and understand the given situation below. Then, refer to the pie graph in answering the questions that follow. Write your answer on your answer sheet.
The graph shows the percent of various age groups in Barangay Matiwasay. It has an estimated population of 33,500.
[chart: pie graph; Barangay Matiwasay Age Group]
- 71 yrs. old & above, ?
- 51-70 yrs. old, 15%
- 31-50 yrs. old, 20%
- 11-30 yrs. old, 30%
- Under 10 yrs. old, 25%
How many percent of the population are 71 years old and above?
How many people are in the 31 to 50 years old group?
What group has the greatest number of people? How many are they?
How many people are under 10 years old group?
If 51 to 70 years old group is added to the 31 to 50 years old group, how many will they be?
Additional Activities
Read the situation below and answer the following questions. Write your answer on your answer sheet.
Judith’s income is ₱22,500.00 a month. She makes a pie graph on her expenses.
[chart: pie graph; Judith’s Monthly Expenses]
- Bills, ?
- Savings, 25%
- Food, 35%
- House Rent, 15%
- Transportation, 10%
How much money does Judith spend for house rent?
How much is her expenses for food?
How much more money is spent for house rent than the transportation?
What percent of her total expenses is the bills?
How much does Judith save for a month?
Answer Key
[transcriber’s note: this page is printed upside down; the answer boxes are transcribed below in reading order after rotating the page]
What I Know
- C
- A
- B
- B
- C
What’s More
- A
- B
- B
- B
- B
What’s In
[chart: pie graph; Marlon’s Monthly Expenses]
- In School, 6 hours
- Sleep/Rest, 8 hours
- Household chores, 5 hours
- Leisure/Sports, 3 hours
- Doing Assignment, 2 hours
What I Can Do
- ₱7,400.00
- ₱925.00
- Food, Savings
- ₱4,625.00
- ₱925.00
- Answers may vary
Assessment
- 10%
- 6, 700
- 11 to 30 years old, 10, 050
- 8, 375
- 11, 725
Additional Activities
- ₱3,375.00
- ₱7,875.00
- ₱1,125.00
- 15%
- ₱5,625.00
References:
Most Essential Learning Competencies (MELC) in Mathematics 6
21st Century MATHletes 6 pp. 324 – 331
Hypermath 6 pp. 399 – 402
Enjoying Mathematics Workbook p. 172
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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