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Mathematics 4 Quarter 4 Module 7: Interpreting and Solving Problems Using Bar Graphs

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This is a Self-Learning Module (SLM) for Grade 4 Mathematics, Quarter 4, Module 7: Interpreting and Solving Routine and Non-Routine Problems Using Data Presented in Bar Graphs. It was developed by DepEd Region V (Bicol) for learners studying at home and in class. After the module, learners should be able to read single and double bar graphs and use their data to solve word problems.

What learners will learn

The module states these goals:

  • Interpret data presented in different kinds of bar graphs.
  • Solve routine and non-routine problems using data presented in a single or double bar graph.

Lessons in this module

  1. Lesson 1: Interpreting Data Presented in Bar Graphs. Learners read the parts of a bar graph, such as the title, axes, labels, scales, and legends. They compare bars to answer questions about single and double bar graphs.
  2. Lesson 2: Solving Routine and Nonroutine Problems Using Data in a Bar Graph. Learners use bar graph data in word problems that involve totals, differences, averages, and costs. They also try strategies such as Guess and Check.
MATH4-Q4-MOD7

Lesson 1: How to read a bar graph

The module explains that bar graphs appear in newspapers, magazines, and on the internet. To interpret one, learners are taught to:

  • look at the parts of the graph
  • find the information on the vertical and horizontal axes
  • check the labels, scales, and legends
  • compare the heights or lengths of bars across groups or categories and look for differences
  • compare categories within groups

Example: a single bar graph

A survey asked kids about their favorite Christmas Day activity:

ActivityNumber of kids
Watch movies30
Exchanging gifts25
Go caroling50
Visiting relatives/friends42

The vertical axis shows the number of kids, and the horizontal axis shows the activities. Go caroling is the most popular activity. Visiting relatives/friends comes second, watching movies third, and exchanging gifts last. Adding all the bars shows that 147 kids were surveyed.

Example: a double bar graph

A double bar graph compares two groups side by side. In the module’s example, Mike and Neo recorded the minutes they spent on four Christmas activities. Both boys spent 120 minutes watching a movie. Together they spent 290 minutes caroling (130 + 150). Neo spent 20 more minutes than Mike visiting relatives/friends (200 − 180).

The practice graphs cover empty bottles collected, favorite desserts, books borrowed by grade level, profession choices, quail eggs sold, votes for SPG president, board games, and registered scouts.

Lesson 2: Solving problems with bar graph data

Routine problems

Routine problems follow a four-step method:

  1. Understand: What does the problem ask for? What are the given data? What is the hidden information?
  2. Plan: What operation or operations will you use? What is the number sentence?
  3. Solve: Show the solution using the operations.
  4. Check: Look back and give the final answer.

For example, a graph shows T-shirts sold in a day: 8 extra large, 14 large, 20 medium, and 10 small. To find the average sold per size, the number sentence is (8 + 14 + 20 + 10) ÷ 4 = N, so N = 13.

Non-routine problems

The module describes non-routine problems as problems that need some creativity to solve. They can be solved in more than one way. Strategies include the Listing/Table Method, Guess and Check, Drawing/Diagram, and Using Patterns.

In one worked example, a table is used to test guesses. Learners try 3 rabbits and 3 birds, then 4 rabbits and 2 birds, until the total value matches. Other problems ask about seats left at rearranged cafeteria tables, tiles for a porch, and the distance between trees planted along a road.

How to use this module

  • Learners: Start with the pretest (“What I Know”) for each lesson. Then work through “What’s In,” “What’s New,” “What Is It,” “What’s More,” “What I Have Learned,” and “What I Can Do.” Finish with the Assessment and the Additional Activities. Write your answers on a separate sheet of paper, and do not mark the module.
  • Checking answers: Answer keys are provided for every activity and test. The module asks you to be honest when using them. If you score 8 to 10 on an assessment, you are ready to move on. If you score below 8, study the lesson and the activities again.
  • Parents and facilitators: Help your child read each direction carefully. Encourage them to write the number sentence before the final answer, because Lesson 2 asks for both.
  • Teachers: The module’s graphs and guide questions can serve as ready-made class drills on single and double bar graphs. Learners who have questions or trouble with the tasks are told to consult their teacher or facilitator.

Frequently asked questions

What grade and quarter is this module for?

It is for Grade 4 Mathematics, Quarter 4. The cover and file name label it Module 7.

What are the two lessons in this module?

Lesson 1 teaches how to interpret data in single and double bar graphs. Lesson 2 teaches how to solve routine and non-routine word problems using bar graph data.

What is the difference between routine and non-routine problems?

Routine problems are solved with the four-step method: understand, plan, solve, and check. Non-routine problems need some creativity and can be solved with strategies such as Guess and Check, tables, diagrams, or patterns.

Does the module have an answer key?

Yes. Answer keys are provided at the end for the pretests, activities, and assessments of both lessons.

What score do learners need to move on?

A score of 8 to 10 on an assessment means the learner understood the lesson. A score below 8 means they should study the lesson and activities again.

Full text of the module

The text below is a transcription of the PDF above, as printed.

Mathematics Quarter 4 – Module 7: Interpreting and Solving Routine and Non-Routine Problems Using Data Presented in Bar Graphs

4

[illustration: students studying outdoors under a tree, a teacher helping students at a desk, and a globe]

CO_Q4_Mathematics _ Module 7

Mathematics – Grade 4 Alternative Delivery Mode Quarter 4 – Module 7: Interpreting and Solving Routine and Non-Routine Problems Using Data Presented in Bar Graphs

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

Development Team of the Module

Writers: Nancy D. Fara-on Editors: Elena D. Hubilla Reviewers: Loyd H. Botor Illustrator: Layout Artist: Maelyne L. Yambao Management Team: Gilbert T. Sadsad Francisco B. Bulalacao Jr. Grace U. Rabelas Ma Leilani R. Lorico Monserat D. Guemo Florena M. Deuna

Printed in the Philippines by _____

Department of Education – Region V (Bicol)

Office Address: Regional Center Site Rawis, Legaspi City 4500 Telefax: 0917-178-1288 E-mail Address: region5@deped.gov.ph

[transcriber’s note: the file is named MOD7, and page 1 is labeled Module 7, but this cover and the pages that follow are printed as Module 5 with the same title. Transcribed as printed.]

5

Mathematics

Quarter 4 – Module 5: Interpreting and Solving Routine and Non-Routine Problems Using Data Presented in Bar Graphs

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

Bar graphs appear in many documents or reports. These graphs can be seen in newspapers, magazines, and internet. A good presentation of graphs can convey varied meaning or information.

In this module, we will focus on reviewing and processing the content of the data presented in a bar graph in order to solve problems and come up with well-defined decisions.

At the end of this module, you should be able to interpret data presented in different kinds of bar graphs.

What I Know

Study the graphs, and then answer the questions that follow.

[chart: bar graph; Michael’s Grade in the 3rd Quarter]

Axis labels: GRADE (%); SUBJECTS. Axis scale: 80, 85, 90, 95.

SubjectGrade (%)
Math85
Science89
English88
Filipino90
EsP92
AP91
EPP91
MAPEH93

  1. In which subject did Michael get the highest grade?
    a. AP b. EPP c. EsP d. MAPEH


  2. What is the lowest grade attained by Michael in the 3rd quarter?
    a. 85 b. 87 c. 88 d. 89


[chart: horizontal bar graph; Lengths of Colored Ribbons Sold in a Day]

Axis labels: Color; Length in cm. Axis scale: 0, 100, 200, 300, 400, 500, 600, 700.

ColorLength in cm
Pink480
Blue240
Gold660
Red250

  1. How many gold ribbons were sold?
    a. 480 b. 500 c. 600 d. 660


  2. How many more gold ribbons were sold than red ribbons?
    a. 250 b. 410 c. 660 d. 810


  3. What was the total length of all the ribbons sold in a day?
    a. 1 630 b. 1 620 c. 660 d. 810


What I Know

  1. How many pupils chose dog as their pet?
    a. 21 b. 22 c. 25 d. 29


  2. What pet is preferred by most of th pupils?
    a. dog b. cat c. bird d. none


[chart: grouped bar graph; Pet Choices]

Axis labels: Number of Pupils; Pets. Axis scale: 0, 5, 10, 15. Legend: Boys, Girls.

PetBoysGirls
Cat714
Dog1210
Bird87

[chart: horizontal grouped bar graph; Favorite Movie Types/Genres of Grade IV Pupils]

Axis labels: Movies; Number of Pupils. Axis scale: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18. Legend: Girls, Boys.

MoviesGirlsBoys
Comedy1315
Horror68
Drama1610
Action1217

  1. What is the most favorite movie type or genre of the pupils?
    a. Action b. Comedy c. Drama d. Horror


  2. How many boys like Comedy, Horror, Drama and Action?
    a. 40 b. 50 c. 55 d. 60


  3. How many more pupils like comedy than horror movie?
    a. 12 b. 13 c. 14 d. 15


Are you done answering? If yes, time to check. Please go to page 32 for the Answer Key.

Lesson 1 Interpreting Data Presented in Bar Graphs

What’s In

Read and understand the problem. Do what is asked.

The School Principal wants to know, what day of the week has the highest number of borrowers of books in the library.

He also wants to know which Grade level borrowed the most number of books for 2 weeks. He asked Ms. Pilapil, the school librarian, to give him the information he needed.

The data given by Ms. Pilapil are shown in the table below.

A. Using the given data below, make a single horizontal bar graph.

DayNumber of Borrowers
Monday14
Tuesday23
Wednesday34
Thursday21
Friday40

B. Present the given data below using a double vertical bar graph.

Number of Borrowers in All Grade Level for Two Weeks

Grade LevelIIIIIIIVVVI
Week 1233226213631
Week 2172430312533

Are you done answering? If yes, time to check. Please go to page 32 for the Answer Key.

What’s New

In a survey conducted, the following are the most favourite activities kids love to do on Christmas Day.

  • Watch movies – 30
  • Exchanging gifts – 25
  • Go caroling – 50
  • Visiting relatives/friends – 42

We can present the same information in a bar graph as shown below.

[chart: bar graph; Favorite Activity Kids Love to Do on Christmas Day]

ActivitiesNumber of Kids
Watch movies30
Exchanging gifts25
go carolling50
visiting relatives/friends42

Vertical axis label: Number of Kids. Horizontal axis label: Activities.

Look at the bar graph. What information does it tell us?

What Is It

Let us find out what information a bar graph tells us. Let us read and interpret the bar graph.

[chart: bar graph; Favorite Activities Kids Love to Do on Christmas Day]

ActivitiesNumber of Kids
Watch movies30
Exchanging gifts25
go carolling50
visiting relatives/friends42

Vertical axis label: Number of Kids. Horizontal axis label: Activities.

  1. What does the vertical axis represent?
    (It shows the number of kids.)
  2. What does the horizontal axis represent?
    (It shows the different activities.)
  3. What is the title of the bar graph?
    (Favorite Activities Kids Love to Do on Christmas Day)
  4. What are being compared on the graph?
    (The number of kids and the activities they love to do on Christmas Day.)
  5. Which activity did 25 kids choose?
    (Exchanging gifts)
  6. Which activities were chosen by more than 30 kids?
    (Go caroling and visiting relatives/friends)
  7. How many kids chose visiting relatives/friends as their favorite activity? (42)
  8. What activity is preferred by most kids? (Go caroling)
  9. How many kids were surveyed? (147)

Based on the single vertical bar graph,

  • Go caroling is the most favorite activity kids love to do on Christmas Day. Visiting relative/friends is the second. Watching movies is the third, and the last is exchanging gifts.
  • 147 kids were surveyed.

Let’s try another example. Let us study and interpret a double bar graph.

Mike and Neo spent their whole day enjoying Christmas Festivities. They kept track on how much time (in minutes) did they spend for four different activities. When they got home, they made a bar graph to show the time they spent for each.

[chart: double bar graph; Time Spent for Four Different Christmas Activities]

ActivitiesMikeNeo
watch a movie120120
exchange gift7660
visit relatives/friends180200
go for caroling130150

Vertical axis label: Time Spent (in minutes). Horizontal axis label: Activities. Legend: Mike, Neo.

  1. What is the title of the bar graph?
    (Time Spent for Four Different Christmas Activities)


  2. What are being compared?
    (The time spent by Mike and Neo for the different activities)


  3. What is found in the vertical axis?
    (The time they spent in minutes)
    In the horizontal axis?
    (The different Christmas activities)


  4. Which activity did they spend the same number of minutes?
    (Watch a movie)


  5. Which activity did they spend the shortest time?
    (Go caroling and visiting relatives/friends)


  6. What activity did they spend the longest time?
    (Visit relatives/friends)


  7. What is the total number of minutes they spent together for caroling?
    (290 minutes)


  8. Which of the two boys spent more in visiting their relatives/friends? By how many more minutes?
    (Neo, by 20 minutes)


Based on the double vertical bar graph,

  • Both boys spent the longest time in visiting relatives/friends. The shortest time they spent is in exchanging gift. They consumed the same time in watching a movie.
What’s More

Study the graph carefully, then fill in the blank to complete the statements below.

[chart: horizontal bar graph; Empty Bottles Collected by Karen in a Week]

Days in a WeekNumber of Empty Bottles
Friday60
Thursday42
Wednesday36
Tuesday24
Monday40

Vertical axis label: Days in a Week. Horizontal axis label: Number of Empty Bottles.

A

  1. _____________ is found in the horizontal axis, while _____________ is found in the vertical axis.
  2. The horizontal bar graph compares _________ and _________.
  3. On _______, Karen collected the most number of empty bottles. She collected ______ empty bottles.
  4. On _________, she collected the least number of empty bottles? She collected _______ empty bottles.
  5. She collected ________ empty bottles in a week.

[chart: double horizontal bar graph; Favorite Dessert Eaten by Children]

DessertsPrinted values (left to right)
Leche Flan35, 37
Bibingka37, 40
Jelly Roll25, 30
Ube20, 25

Vertical axis label: Desserts. Horizontal axis label: Number of Children. Legend: Girls (black), Boys (gray).

transcriber’s note: the printed values are listed in the order they appear on each row. The image does not clearly show which value belongs to Girls and which to Boys for each dessert, so no assignment is made.

B

  1. The two variables or data items being compared in the double horizontal bar graph are _____________ and _________________.
  2. _____________ is the information placed along the horizontal axis.
    _____________ is the information placed along the vertical axis.
  3. Most of the children preferred to eat __________ than any other dessert while the least preferred dessert is _____________.
  4. There are _____ children who chose leche flan as their favorite dessert.
  5. There are ______ more girls preferred to eat Ube than boys.

Are you done answering? If yes, time to check. Please go to page 32 for the Answer Key.

What I Have Learned

How do we interpret the data in different bar graphs?

To interpret different bar graphs, we have to:

  • look into the parts
  • find the information in the vertical and horizontal axes
  • look into labels, scales and legends
  • compare heights or lengths of bars across groups or categories and look for differences.
  • compare categories within groups
What I Can Do

A. Read and interpret the data presented in the bar graph. Use the guide questions below.

[chart: horizontal bar graph; Books Borrowed in a Week]

Grade LevelsNumber of Books
VI70
V60
IV40
III55
II50
I45

Vertical axis label: Grade Levels. Horizontal axis label: Number of Books.

  1. What grade level borrowed the most number of books?
  2. What grade level borrowed the least number of books?
  3. What is the total number of books borrowed in a week?

B. Study the double vertical bar graph below. Choose the letter corresponding to the statement that correctly describes or interprets the data.

[chart: double vertical bar graph; Profession Choice of Students]

ProfessionBoysGirls
Teacher2330
Nurse1532
Engineer2515
Police Officer3517

Vertical axis label: Number of Students. Horizontal axis label: Profession. Legend: Boys (black), Girls (gray).

a. Most of the girls preferred to be a nurse or a teacher rather than to be a police officer or an engineer. b. Most of the students chose to be teachers. c. There are 35 boys who want to be a police officer someday. d. Among the four professions, to be an engineer is the least preferred by the students. e. There are 53 students who want to be in the field of teaching profession.

Are you done answering? If yes, time to check. Please go to page 33 for the Answer Key.

Assessment

Study the graphs and then answer the questions that follow. Choose the letter of the correct answer.

[chart: vertical bar graph; Number of Quail Eggs Sold in a Week]

DaysNumber of Eggs
Monday215
Tuesday200
Wednesday210
Thursday200
Friday145

Vertical axis label: Number of Eggs. Horizontal axis label: Days.

  1. On which day was the sale of quail eggs the greatest?
    a. Friday
    b. Monday
    c. Thursday
    d. Tuesday
  2. On which two days were the number of quail eggs sold the same?
    a. Thursday and Friday
    b. Monday and Wednesday
    c. Tuesday and Thursday
    d. Tuesday and Monday

[chart: horizontal bar graph; Votes for SPG President]

CandidatesNumber of Votes
Danica73
Andrei112
Jazmine87
Allan90

Vertical axis label: Candidates. Horizontal axis label: Number of Votes.

  1. How many more votes did Andrei get than Allan?
    a. 20
    b. 22
    c. 23
    d. 24


  2. What is the total number of students who voted in the election?
    a. 365
    b. 363
    c. 362
    d. 361


  3. Which of the following statements best interpret the given bar graph?


[chart: bar graph; Total Number of Flu Cases]

  • Vertical axis: Cases (0 to 50, scale 0, 10, 20, 30, 40, 50)


  • Horizontal axis: Month


  • Categories: January, February, March, April


  • Values are not labeled on the chart.


    a. There was a slight decrease in the number of flu cases.
    b. The number of flu cases increased from January to April.
    c. The lowest number of flu cases was in February.
    d. The highest number of flu cases was in March.


[chart: bar graph; Favorite Board Games among Kids]

  • Vertical axis: Number of kids (0 to 30)
  • Horizontal axis: Board Games
  • Legend: Boys (black), Girls (gray)
Board GamesBoysGirls
monopoly1615
scrabble1213
chess1518
snake and ladder2518

  1. Which board game is least popular among the boys?
    a. chess
    b. monopoly
    c. scrable
    d. snake and ladder


  2. Which board games are equally popular with the girls?
    a. snake and ladder & scrabble
    b. monopoly and chess
    c. snake and ladder & chess
    d. scrabble and chess


[chart: bar graph; Number of Students in a Class]

  • Vertical axis: Classes
  • Horizontal axis: Number of Students (0 to 35)
  • Legend: Girls (black), Boys (gray)
ClassesGirlsBoys
Class D2530
Class C2222
Class B2023
class A3022

  1. In which class is the number of boys greater than girls?
    a. B & D
    b. C & D
    c. B & A
    d. C & A


  2. What is the total number of students in Class B?
    a. 43
    b. 44
    c. 52
    d. 55


  3. How many girls are there in all 4 classes?
    a. 110
    b. 100
    c. 99
    d. 97


Are you done answering? If yes, time to check. Please go to page 33 for the Answer Key.

Got a score of 8 -10? EXCELLENT! You already understood the lesson. You are now ready for the next lesson.

If your score is below 8, kindly study again the lesson and the activities.

Additional Activities

Interpret the data of the double bar graph below. Answer the guide questions that follow.

[chart: double bar graph; Registered Scouts]

  • Vertical axis: Schools
  • Horizontal axis: Number of Scouts (0 to 100)
  • Legend: Girl Scouts (black), Boy Scouts (gray)
SchoolsGirl ScoutsBoy Scouts
San Ramon ES5633
San Vicente ES5448
San Pascual ES6454
San Isidro ES9085
  1. What is the title of the graph?
  2. How many girl scouts are registered?
  3. How many boy scouts are registered?
  4. Which school has the highest number of registered scouts?
  5. Which school has the lowest registered scouts?

Are you done answering? If yes, time to check. Please go to page 33 for the Answer Key.

What I Need to Know

In this lesson, you will apply your knowledge on bar graphs in solving word problems. Understanding the problem, planning strategies, executing solutions, and writing the correct answer are positive attitudes towards problem solving.

After going through this module, you are expected to solve routine and non-routine problems using data presented in a single or double bar graph.

What I Know

The bar graph below shows the weights of five children.

[chart: bar graph; Weights of Five Children]

  • Vertical axis: Weight in kg (0 to 60)
  • Horizontal axis: Name of Children
Name of ChildrenWeight in kg
Peter47
John38
Carlo42
Joseph45
Christian48

Use the data in the bar graph to answer the following questions. Choose the letter of the correct answer.

  1. What is the combined weight of John and Joseph?
    a. 80kg
    b. 82 kg
    c. 83 kg
    d. 84 kg


  2. What is the total weight of the five children?
    a. 230 kg
    b. 225 kg
    c. 220kg
    d. 215 kg


  3. How much more is the combined weight of Peter and Joseph than the combined weight of John and Christian?
    a. 6 kg
    b. 8 kg
    c. 10 kg
    d. 12 kg


Answer the following questions for problems 4 and 5. a. What is the number sentence? b. What is the complete answer?

  1. What is the average weight of five children?


  2. What must be the weight of the sixth child to get an average weight of 42 kg?


The classes of Ms. Cruz, Mrs. Diaz, and Mr. Flores went on a field trip. The number of students in each class is shown in the bar graph below.

[chart: double bar graph; Students who Joined in the Field Trip]

  • Vertical axis: Number of Students (0 to 50)
  • Horizontal axis: Classes
  • Legend: Boys (black), Girls (gray)
ClassesBoysGirls
Ms. Cruz2342
Mr. Flores3130
Mrs. Diaz2622

Use the data presented in the double bar graph to answer the questions. Choose the letter of the correct answer.

  1. What is the total number of students who joined the field trip?
    a. 172
    b. 173
    c. 174
    d. 175


  2. What is the difference between the total number of girls and the total number of boys who joined the field trip?
    a. 13
    b. 14
    c. 15
    d. 16


  3. What is the average number of students of the three classes?
    a. 31
    b. 38
    c. 48
    d. 58


  4. How much is the total cost for all students if the cost to join the field trip is Php 450 for each student?
    a. What is the number sentence?
    b. What is the solution and the final answer?


  5. The cafeteria where Mrs. Diaz’ class ate lunch has 10 rectangular tables with 8 seats each. If they rearranged the 10 tables into two lines with equal number of tables and placed the shorter sides of the table’s end-to-end, how many seats will not be occupied? Hint: The shorter side can only have one seat.


[chart: diagram; arrangement of ten tables in two lines]

  • Line 1: Table 1 | Table 2 | Table 3 | Table 4 | Table 5


  • Line 2: Table 6 | Table 7 | Table 8 | Table 9 | Table10


    a. 14
    b. 16
    c. 18
    d. 20


Are you done answering? If yes, time to check. Please go to page 33 for the Answer Key.

CONGRATULATIONS! If you got a score of 9 or 10, you should not have any difficulty studying the lesson in this module.

If you got a score of 8 or below, you may need to study the lesson more carefully and do all the given activities.

Lesson 2: Solving Routine and Nonroutine Problems Using Data in a Bar Graph

What’s In

Study the graph and answer the questions that follow.

A. Mang Kanor sells dried fish in the market. The bar graph shows the profit he had for a week.

[chart: bar graph; Profit in a Week]

  • Vertical axis: Profits in Pesos (0 to 700)
  • Horizontal axis: Days in a Week
Days in a WeekProfits in Pesos
Sunday250
Monday300
Tuesday400
Wednesday450
Thursday400
Friday600
Saturday500
  1. On which day did Mang Kanor earn the highest profit? Has the lowest profit?
  2. On which days did he earn the same profit?
  3. What was the increase in profits from Tuesday to Wednesday?
  4. What was the decrease in profits from Friday to Saturday? What is the total profit for the week?
  5. What is the total profit for the week?

B. The double bar graph shows the attendance of the Ball Games and Track and Field Athletes in a training for 5 months.

[chart: double bar graph; Attendace of Athletes]

  • Vertical axis: Months
  • Horizontal axis: Number of Athletes (0 to 400)
  • Legend: Track and Field (black), Ball Games (gray)
MonthsTrack and FieldBall Games
January230210
February290300
March340350
April300290
May280320
  1. Which month has the highest attendance?
  2. Which month has the highest attendance?
  3. What is the total attendance of the Ball games athletes?
  4. What is the total attendance of the Track and Field athletes?
  5. What was the difference in attendance of the Ball games athletes and the Track and Field athletes?

Are you done answering? If yes, time to check. Please go to page 34 for the Answer Key.

Let us solve the problem through Guess and Check:

No. of RabbitsValueNo. of BirdsValueTotal Value
First Guess33 x 400 = 1 20033 x 200 = 6001 200 + 600 = 1 800
Second Guess44 x 400 = 1 60022 x 200 = 4001 600 + 400 = 2 000

Therefore, he bought 4 rabbits and 2 birds.

Total number of rabbits is 6 – 4 = 2, there were 2 rabbits left in the store. Total number of birds is 10 – 2 = 8, there were 8 birds left in the store.

What’s More

Study the graph and use the given data to answer the following questions.

[chart: horizontal bar graph; T-Shirts Sold in a Day]

SizesNumber of T-Shirts Sold
Extra Large8
Large14
Medium20
Small10

Axis labels: Sizes (vertical); Number of T-Shirts Sold (horizontal, scale 0 5 10 15 20 25).

  1. What is the average number of t-shirts sold in a day?
    a. What is asked in the problem?
    b. What information/facts are needed to solve the problem?
    c. What operation will you use?
    d. What is the number sentence?
    e. What is the complete answer?


  2. If a small shirt costs Php 300, a medium shirt costs Php 350, a large shirt costs Php 380, and an extra-large shirt costs Php 400, what is the total sales of the store on that particular day?
    a. What is the number sentence?
    b. What is the complete answer?


Are you done answering? If yes, time to check. Please go to page 34 for the Answer Key.

What I Have Learned

How do we solve routine and non-routine problems using data presented in a bar graph?

Routine problems follow the 4-step solving method.

Understand: What does the problem ask for? What are the given data or information? What is the hidden information?

Plan: What operation/s is/are to be used? What is the number sentence?

Solve: Show the solution by using the operations.

Check, look back and give the final answer.

Non-routine problems are those that require some degree of creativity to solve. These problems can be solved in multiple ways or using different strategies like Listing/Table Method, Guess and Check, Drawing/Diagram, Using Patterns, etc.

What I Can Do

Mario wants to tile his porch. He bought several sizes of tiles in the store. The bar graph shows the sizes and the number of tiles he bought from the store.

[chart: vertical bar graph; TILES BOUGHT IN THE STORE]

Tile Sizes in CMNumber of Tiles
8 X 812
12 X 1210
16 X 1614
24 X 2420

Axis labels: NUMBER OF TILES (vertical); TILE SIZES IN CM (horizontal).

Use the data in the given bar graph to answer the following questions.

  1. What is the total number of tiles he bought from the store?
  2. What area can be covered by 10 pieces of 12 x 12 tiles?
  3. How many possible squares can be made by 12 pieces of 8 x 8 tiles?

Are you done answering? If yes, time to check. Please go to page 34 for the Answer Key.

Assessment

A. Study the bar graph carefully.

[chart: vertical bar graph; Rico’s Water Consumption Bill]

MonthsNumber of Cubic Meters
January31
February24
March26
April32
May32

Axis labels: Number of Cubic Meters (vertical, scale 0 10 20 30 40); Months (horizontal).

Use the data in the vertical bar graph above to solve the following problems. Choose the letter of the correct answer.

  1. What is the total water consumption from January to May?
    a. 144 m3
    b. 145 m3
    c. 146 m3
    d. 147 m3


  2. What is the average water consumption bill for 5 months?
    a. 28 m3
    b. 29 m3
    c. 30 m3
    d. 147 m3


For numbers 3 to 5: Suppose the cost of water per cubic meter is Php 34.00.

  1. How much would Rico pay for the month of January?
    a. Php 1540. 00
    b. Php 1450.00
    c. Php 1054.00
    d. Php 1045.00


  2. How much would he pay for the months of February and March?
    a. Php 1700.00
    b. Php 1750.00
    c. Php 1800.00
    d. Php 1900.00


  3. What is the total water consumption bill for 5 months?
    a. Php 4309.00
    b. Php 4903.00
    c. Php 4930.00
    d. Php 4980.00


B. Marichu is the Chairman of the Committee on Barangay Beautification. She collected different kinds of seedlings for the tree planting activities. The table shows the numbers of seedlings she already collected.

[chart: horizontal bar graph; Collected Seedlings]

TreesNumber of Seedlings
Ipil-Ipil28
Kamatsile21
Agoho26
Mahogany40
Acacia35

Axis labels as printed: “Trees” (vertical axis); “Number of Seedlings” (horizontal axis, scale 0 to 45).

Answer the following questions.

  1. What is the total number of seedlings she collected?
    a. What is the number sentence?
    b. What is the final answer?


  2. What is the average number of collected seedlings?
    a. What is the number sentence?
    b. What is the final answer?


  3. If they are going to plant mahogany and acacia trees along side of the road with 4 meters interval, how many meters will it cover?
    a. What is the number sentence?
    b. What is the final answer?


  4. If the road in front of the school will be planted with 21 Kamatsile trees and the trees are 3 meters away from each other. How far is the 10th tree away from the first one?
    a. What is the number sentence?
    b. What is the final answer?


  5. If one seedling of agoho tree costs Php 100.00, how much would she pay for 26 agoho seedlings?
    a. What is the number sentence?
    b. What is the final answer?


Are you done answering? If yes, time to check. Please go to page 34 for the Answer

Got a score of 8 to 10? EXCELLENT! You already understood the lesson. You are now ready for the next module.

If your score is below 8, kindly study again the lesson and the activities.

Are you done answering? If yes, time to check. Please go to page 34 for the Answer Key.

Additional Activities

Cassandra used to save excess coins from her weekly allowance. At the end of the school year, she counted the coins in her piggy bank and graph the results.

The bar graph shows the number of coins in her piggy bank.

[chart: vertical bar graph; Coins in Casandra’s Piggy Bank]

CoinsNumber of Coins
25 cents90
1 Peso115
5 Peso100
10 peso85

Axis labels as printed: “Number of Coins” (vertical axis, scale 0 to 140); “Coins” (horizontal axis).

Use the data in the bar graph to answer the following questions.

  1. What is the total amount of her savings?
  2. She donated 20 pieces of each type of coins to the church choir.
    a. How many total coins does she have left?
    b. What is the total amount of the coins she donated?
    c. What is the total amount of coins left?

Are you done answering? If yes, time to check. Please go to page 34 for the Answer Key.

Answer Key

[transcriber’s note: this page is printed upside down; the text below is transcribed in upright reading order]

Lesson I
What I Know
ItemAnswerItemAnswer
1.d6.b
2.a7.a
3.d8.a
4.b9.b
5.a10.c
What’s In

A.

[chart: bar graph; Books Borrowed in Two Weeks]

Axis labels as printed: “Grade levels” (horizontal axis, categories I, II, III, IV, V, VI); “Number of Borrowers” (vertical axis, ticks 0, 20, 40). Legend: Week 1, Week 2.

Values are not labeled on the chart.

B.

[chart: bar graph; Books Borrowed in Two Weeks]

Axis labels as printed: “Grade levels” (horizontal axis, categories I, II, III, IV, V, VI); “Number of Borrowers” (vertical axis, ticks 0, 50). Legend: Week 1, Week 2.

Values are not labeled on the chart.

What’s More

A.

  1. Number of Bottle Days in a week
  2. Number of Empty Bottles Collected each day in a Week
  3. Friday, 60
  4. Tuessday, 24
  5. 202

Lesson 1

What I Can Do

A.

  1. Grade VI borrowed the most number of books while Grade IV borrowed the least number of books
  2. 320

B.

a,c,d,e

Assessment

ItemAnswerItemAnswer
1.b6.c
2.c7.c
3.b8.a
4.c9.a
5.b10.d
Additional Activities
  1. Registered Girl and Boy Scouts
  2. There are 264 registered Girl Scouts and 220 registered Boy Scouts.
  3. San Isidro has the highest registered scouts while San Ramon has the lowest.

Lesson II

What I Know
  1. c
  2. c
  3. a
  4. a. (47 + 38 + 42 + 45 + 48)/5 = N
    b. 44 kg
  5. a. (6 x 42) – (47 + 38 + 42 + 45 + 48) = N
    b. 32 kgs
  6. c
  7. b
  8. d
  9. a. (23 + 42 + 31 + 30 + 26 + 22) x Php 450.00 = N
    b. Php 78,300.00
  10. b

Lesson 2

What’s In
  1. Friday has the highest profit while Sunday has the lowest profit.
  2. Tuesday and Thursday has the same amount of profits.
  3. An increase of Php 50.00
  4. A decrease of Php 100.00
  5. Php 2900.00
  6. March has the highest attendance
  7. January has the lowest attendance
  8. 1470
  9. 1440
  10. 30
What’s More
  1. a. The average number of T-shirts sold in a day.
    b. 8, 14, 20, 10 t-shirts
    c. addition and division
    d. (8 + 14 + 20 + 10) ÷ 4 = N
    e. 13 is the average sales in a day
  2. a. (10 x Php 300.00) + (20 x Php 350.00) + (14 x Php 380.00) + (8 x Php 400.00) = N
    b. Php 18 520.00
What I Can Do
  1. 56 tiles
  2. 1440 sq cm
  3. 3

Assessment

  1. B
    1. a. 28 + 21 +26 + 40 + 35 = N
  2. B
    b. 150
  3. C
    1. a. (28 + 21 +26 + 40 + 35) ÷ 5 = N
  4. A
    b. 30
  5. C
    1. a. 34 x 4 = N
      b. 136 m
    2. a. 9 x 3 = N
      b. 27 m
    3. a. 26 x Php 100.00 = N
      b. Php 2600.00
Additional Activities
  1. Php 1487.50
  2. a. 310 coins
    b. Php 325.00
    c. Php 1162.50

References

K to 12 Mathematics Curriculum Guide, August 2016

Tabilang, Alma R., Arce, Ian Jay B., Pascua, Rodrigo V., Calayag, Nelma P., Dacubo, Lolita p., Borais, Diolata B., Buemia, Rafael B., collao, Myra T., Morandante, Larry G., Danao, Amado B., Gonzaga, Laura N., Briones, Isagani A., Daganta, John Antonio D., 2015, Mathematics 4 Teacher’s Guide, Department of Education

Tabilang, Alma R., Arce, Ian Jay B., Pascua, Rodrigo V., Calayag, Nelma P., Dacubo, Lolita p., Borais, Diolata B., Buemia, Rafael B., collao, Myra T., Morandante, Larry G., Danao, Amado B., Gonzaga, Laura N., Briones, Isagani A., Daganta, John Antonio D., 2015, Mathematics 4 Learner’s Material, Department of Education

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