This is the Grade 6 Mathematics Quarter 2, Module 2 self-learning module, Defining and Illustrating Ratio and Proportion, prepared by DepEd Region VI (First Edition, 2020). It is for Grade 6 learners studying at home or in class, and for the parents and teachers who guide them. After this one-lesson module, learners can explain what a ratio and a proportion are, show them with objects or drawings, and tell when two quantities are in proportion.
What learners will learn
The module covers the competency of defining and illustrating the meaning of ratio and proportion using concrete or pictorial models (M6NS-IIb-131). After going through it, learners are expected to:
- define ratio and proportion;
- use concrete objects or draw pictorial models to illustrate ratios and proportions; and
- recognize when two quantities are in proportion.
Key ideas: ratio and proportion
The module gives two short definitions to remember:
- A ratio is a comparison of two or more quantities.
- Two equivalent ratios form a proportion.
The mango shake example
The lesson starts with a problem. Mother uses 2 ripe mangoes to make 3 glasses of mango shake. How many mangoes does she need for 9 glasses?
The ratio of mangoes to glasses is 2 : 3. Drawing three groups of 2 mangoes and 3 glasses gives 6 : 9, so Mother needs 6 mangoes. Her guide for bigger batches looks like this:
| Number of mangoes | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| Number of glasses | 3 | 6 | 9 | 12 |
| Ratio in simplest form | 2 : 3 | 2 : 3 | 2 : 3 | 2 : 3 |
All the ratios simplify to 2 : 3, so they are equivalent. When the first quantity doubles, the second doubles too; when the first triples, the second triples. So 2 : 3 = 4 : 6 is a proportion, read as “2 is to 3 as 4 is to 6.”
When quantities are not in proportion
Angelo mixes orange paint four ways: 3 red to 1 yellow, 6 to 3, 8 to 5, and 12 to 9. As fractions these are 3/1, 2/1, 8/5, and 4/3. Because the ratios are different, the amounts of red and yellow paint are not in proportion.
Solving a problem with a ratio
A dance group has 1 girl for every 3 boys and 20 members in all. The module shows two ways to solve it:
- Draw a picture: make groups of 1 girl and 3 boys until there are 20 people.
- Make a list: count up 1 : 3, 2 : 6, 3 : 9, 4 : 12, 5 : 15, checking the totals (4, 8, 12, 16, 20).
The check 1 : 3 = 5 : 15 confirms the answer: 5 girls and 15 boys.
In another example, Mrs. Galvez uses 12 cups of water with 8 cups of oats, then 6 cups of water with 4 cups of oats. Both ratios simplify to 3 : 2, so she used the same proportion for both batches.
Block models
Many activities ask learners to draw a block model: one bar of blocks for each quantity, with the actual amounts labeled. For example, white and green marbles in the ratio 1 : 3, with 4 white and 12 green marbles, give the proportion 1/3 = 4/12.
Parts of the module
- What I Know: a pretest with a salt-and-sugar proportion table and five true-or-false items.
- What’s In: a review of ratios and fractions using a block model of seashells collected by Joy and Leah.
- What’s New and What is It: the mango shake problem and the worked examples above.
- What’s More: practice tables about cars and wheels, square and heart biscuits, and males and females in volunteer groups.
- What I Have Learned: the definitions of ratio and proportion.
- What I Can Do: drawing block models for coins, money, and paint, and a cement-and-sand mixture in the ratio 5 : 3.
- Assessment: five multiple-choice items.
- Additional Activities: grouping buttons in the ratio 4 : 3, checking whether the sides of two triangles are in proportion, and a reasoning question about equivalent ratios.
How to use this module
- Learners: Start with the pretest to see what you already know, then work through the parts in order. Write your answers on a separate sheet of paper and keep the module clean. Draw the block models; they help you see the ratio. Check your work with the answer key only after you finish, and be honest when you use it.
- Parents: Help your child use everyday things, like fruits, buttons, or coins, to act out the ratios in the examples. If your child has trouble, reach out to the teacher.
- Teachers: The answer key at the end covers the pretest, the activities, the assessment, and the additional activities. Several items, such as writing proportions from a table, accept different correct answers.
Frequently asked questions
Which grade and quarter is this module for?
It is for Grade 6 Mathematics, Quarter 2. It is Module 2, Defining and Illustrating Ratio and Proportion, with the competency code M6NS-IIb-131.
What is the difference between a ratio and a proportion?
A ratio compares two or more quantities, such as 2 mangoes to 3 glasses (2 : 3). A proportion is formed when two ratios are equivalent, such as 2 : 3 = 4 : 6.
How do I know if two quantities are in proportion?
Write each pair as a ratio and simplify. If all the ratios are the same, the quantities are in proportion; if they are different, as in Angelo’s paint mixtures, they are not.
Does the module have an answer key?
Yes. The answer key at the end covers What I Know, What’s In, What’s More, What I Can Do, the Assessment, and the Additional Activities.
What is a block model?
It is a drawing that uses a bar of equal blocks for each quantity to show a ratio, with the actual amounts labeled. The module uses block models to illustrate and solve ratio and proportion problems.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 2 – Module 2: Defining and Illustrating Ratio and Proportion
[illustration: students learning outdoors under a tree and at a table with a globe and a lamp]
CO_Q2_Mathematics6_Module2
Mathematics– Grade 6 Alternative Delivery Mode Quarter 2 – Module 2: Defining and Illustrating Ratio and Proportion First Edition, 2020
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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Development Team of the Module
Author: Lalyn G. Lumandog
Editors: Ma. Portia G. Galanto and Collin G. Sales
Reviewers: Elleda E. de la Cruz, Rosemarie D. Aclan and Collin G. Sales
Illustrator: Lalyn G. Lumandog
Layout Artist: Felizardo S. Valdez III and Lee Lanie P. Manos
Management Team: Ramir B.Uytico Pedro T. Escobarte, Jr. Elena P. Gonzaga Donald T. Genine Ma. Roselyn J. Palcat Nordy D. Siason, Jr. Rowena S. Carillo Rosemarie D. Aclan Arthur J. Cotimo Felizardo S. Valdez III Marve E. Gelera
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
Mathematics Quarter 2 – Module 2: Defining and Illustrating Ratio and Proportion
What I Need to Know
This module was designed and written with you in mind. It is here to help you understand the concept of ratio and proportion. The scope of this module allows you to use it in many different learning situations. The language used recognizes your diverse vocabulary level.
The module contains lesson on defining and illustrating the meaning of ratio and proportion using concrete or pictorial models. (M6NS-IIb-131)
After going through this module, you are expected to:
- define ratio and proportion;
- use concrete objects or draw pictorial models to illustrate ratios and proportions; and
- recognize when two quantities are in proportion.
What I Know
A. The table below shows the amounts of salt and sugar in proportion.
| Amount of salt | 3 | 9 | 12 | ||
|---|---|---|---|---|---|
| Amount of sugar | 2 | 4 | 10 |
- Complete the table.
- Draw a block model that shows the amount of salt for 10 units of sugar.
- Use the table to write three different proportions.
B. Read each statement carefully. Write TRUE or FALSE.
_______ 1) 5 : 8 = 10 : 24 is an example of a proportion. _______ 2) A proportion tells us that two ratios are equivalent. _______ 3) In a proportion, the quantities can be written in any order. _______ 4) The ratios 18 : 6 and 3 : 1 form a proportion. _______ 5) When the ratios of two quantities are different, the two quantities are not in the same proportion.
Lesson 1: Defining and Illustrating Ratio and Proportion
A lot of what we do in real life involves making comparisons. Previously, you have learned how ratios and fractions are related and how they are used to compare two or more quantities. This time, you will be moving forward to understanding more deeply about ratio and proportion using concrete or pictorial models.
What’s In
The model below compares the number of seashells Joy and Leah collected one day at the beach.
[chart: block model; the model below compares the number of seashells Joy and Leah collected one day at the beach. Joy: 6 boxes. Leah: 7 boxes. Values are not labeled on the chart.]
Write at least 5 statements about the model using fractions and ratios.
Example: The ratio of the number of seashells Joy collected to the number of seashells Leah collected is 7 . [transcriber’s note: the fraction in the example appears to be missing its numerator and denominator as printed]
What’s New
One hot day, Mother uses 2 ripe mangoes to make 3 glasses of mango shake. She plans to make 9 glasses. How many mangoes does she need?
What is It
Let us illustrate the problem.
[illustration: two mangoes beside three glasses, labeled “Mangoes” and “Glasses”]
For every 2 ripe mangoes used, 3 glasses of mango shake are made.
We can also say that the ratio of the number of mangoes used to the number of glasses of mango shake made is 2 : 3.
Find the number of ripe mangoes needed to make 9 glasses of mango shake.
[illustration: three groups, each of two mangoes and three glasses, labeled “Mangoes” and “Glasses”]
The ratio of the number of mangoes needed to the number of glasses of mango shake is 6 : 9.
This means that Mother needs 6 ripe mangoes to make 9 glasses of mango shake.
The following table shows Mother’s guide in preparing batches of mango shake.
| Number of mangoes | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| Number of glasses | 3 | 6 | 9 | 12 |
| Mangoes : Glasses | 2 : 3 | 4 : 6 | 6 : 9 | 8 : 12 |
| Mangoes : Glasses (simplest form) | 2 : 3 | 2 : 3 | 2 : 3 | 2 : 3 |
What can you say about the ratios?
The ratios are the same.
[chart: equivalent-ratio diagram; number of mangoes / number of glasses = 2/3 = 4/6, with “x 2” arrows above and below; and number of mangoes : number of glasses, 2 : 3 and 4 : 6, with “x 2” arrows on both sides]
What is It (continued)
When the first quantity doubles, the second quantity doubles also.
2 : 3 and 4 : 6 are equivalent ratios. These two ratios form a proportion.
2 : 3 = 4 : 6 can be read “2 is to 3 as 4 is to 6.”
[chart: equivalent-ratio diagram; number of mangoes / number of glasses = 2/3 = 6/9, with “x 3” arrows above and below; and number of mangoes : number of glasses, 2 : 3 and 6 : 9, with “x 3” arrows on both sides]
When the first quantity triples, the second quantity triples also. The ratios 2 : 3 and 6 : 9 are equivalent. We can also say that 2 : 3 and 6 : 9 are in proportion.
From the table, what do you notice about the ratios 4 : 6 and 8 : 12? Do they form a proportion? Why or why not?
Let’s take a look at more examples.
Angelo prepares four different mixtures of orange paint. He then writes the ratio of the number of cans of red paint to the number of cans of yellow paint.
| Mixture | A | B | C | D |
|---|---|---|---|---|
| Number of cans of red paint | 3 | 6 | 8 | 12 |
| Number of cans of yellow paint | 1 | 3 | 5 | 9 |
| Number of cans of red paint / Number of cans of yellow paint | 3/1 | 2/1 | 8/5 | 4/3 |
What can you say about the fractions? They are different.
So, the numbers of cans of red paint and yellow paint are not in proportion.
There is 1 girl for every 3 boys in a dance group. There are 20 members altogether. How many girls and how many boys are there in the group?
Number of girls : Number of boys = 1 : 3 The ratio of the number of girls to the number of boys in the dance group is 1 : 3.
Method 1: Draw a picture
[illustration: five groups, each showing one dark blue circle and two light blue circles]
Method 2: Make a list
| Number of girls | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number of boys | 3 | 6 | 9 | 12 | 15 |
| Total | 4 | 8 | 12 | 16 | 20 |
Check:
[chart: equivalent-ratio diagram; number of girls / number of boys = 1/3 = 5/15, with “x 5” arrows above and below; and number of girls : number of boys, 1 : 3 and 5 : 15, with “x 5” arrows on both sides]
1 : 3 and 5 : 15 form a proportion.
Answer: There are 5 girls and 15 boys in the dance group.
Mrs Galvez uses 12 cups of water and 8 cups of oats to prepare oatmeal for her family. She mixes 6 cups of water and 4 cups of oats as extra. Does Mrs Galvez use the same proportion for both batches of oatmeal?
| Cups of water | 12 | 6 |
|---|---|---|
| Cups of oats | 8 | 4 |
| Water : Oats | 3 : 2 | 3 : 2 |
[chart: equivalent-ratio diagram; number of cups of water / number of cups of oats = 12/8 = 6/4, with “÷ 2” arrows above and below]
The ratios are the same.
The numbers of cups of water and oats are in proportion. Answer: Yes. Mrs. Galvez used the same proportion for both batches of oatmeal.
What’s More
- Carol finds a number of cars in a parking lot. Complete the following table.
[illustration: four cars in red, green, blue, and black]
| Number of cars | 1 | 2 | 3 | 5 | 15 |
|---|---|---|---|---|---|
| Number of wheels |
The ratio of the number of cars to the number of wheels is _____ : _____.
If there are 12 wheels, then there are _____ cars.
If there are 36 wheels, then there are _____ cars.
The number of ______ and the number of ______ are in the same proportion.
- Tony counts the number of square-shaped and heart-shaped biscuits in a container. Complete the following table.
[illustration: square-shaped and heart-shaped biscuits in a container]
| Number of squares | 2 | 4 | 8 | ||
|---|---|---|---|---|---|
| Number of hearts | 10 | 15 | 25 |
The ratio of the number of squares to the number of hearts is _____ : _____.
The ____________________ and ____________________ are in the same ____________.
For every 10 square-shaped biscuits, there are _____ heart-shaped biscuits.
- Members of a volunteer organization are divided into groups for different projects. The table shows the number of males and females in each group. Complete the table.
| Number of males | 9 | 12 | 18 | ||
|---|---|---|---|---|---|
| Number of females | 8 | 16 | 20 |
The ratio of the number of males to the number of females is _____ : _____.
If there are 32 females in a group, then there are _____ males.
What can you say about the number of males and the number of females?
What I Have Learned
- Ratio is a comparison of two or more quantities.
- Two equivalent ratios form a proportion.
What I Can Do
- Draw a block model to illustrate each situation. Then, write the proportion.
Example: The number of white and green marbles in a bag are in the ratio 1 : 3. There are 4 white marbles and 12 green marbles in the bag.
[chart: block model; White and Green marbles; labels 4 (above White) and 12 (below Green)]
number of white marbles / number of green marbles = 1/3 = 4/12
A. The ratio of the number of 5-peso coins to the number of 10-peso coins in a bottle is 7 : 4. There are 49 5-peso coins and 28 10-peso coins.
B. Ben and Sheila has some money in the ratio 6 : 5. Ben has ₱330 and Sheila has ₱275.
C. A painter mixed 50 ml of yellow paint with every 90 ml of blue paint to obtain green paint. She used 450 ml of blue paint and 250 ml of yellow paint.
- Ricky used cement and sand in the ratio 5 : 3 to make different mixtures.
A. Draw a block model to show the ratio.
B. Use the same proportion to fill in the table.
| Mixture | A | B | C | D |
|---|---|---|---|---|
| Number of pails of cement | 5 | |||
| Number of pails of sand | 3 |
C. Use the information in the table to write five different proportions.
D. If Ricky used 27 pails of sand, how many pails of cement did he use?
Assessment
Read and analyze each item carefully. Then choose the letter of the best answer.
- Which statement represents the following model?
[illustration: three boxes, each with green triangles above yellow parallelograms, forming a block model]
A. 12 : 6 = 2 : 1 B. 2 : 4 = 12 : 6 C. 4 : 8 = 6 : 12 D. 12 : 6 = 4 : 2
- Which block model shows 3 : 2 = 24 : 16?
A. [chart: block model; labels 24 (top) and 16 (bottom); 1st quantity 3 blocks, 2nd quantity 2 blocks]
B. [chart: block model; labels 16 (top) and 24 (bottom); 1st quantity 2 blocks, 2nd quantity 3 blocks]
C. [chart: block model; labels 24 (top) and 16 (bottom); 1st quantity 2 blocks, 2nd quantity 3 blocks]
D. [chart: block model; labels 16 (top) and 24 (bottom); 1st quantity 3 blocks, 2nd quantity 2 blocks]
- Thalia has 117 local stamps. She has 9 local stamps for every 8 foreign stamps. Which model can help find how many foreign stamps she has?
A. [chart: block model; Local and Foreign bars; 117 bracket at right]
B. [chart: block model; Local and Foreign bars; 117 (top) and ? (bottom)]
C. [chart: block model; Local and Foreign bars; ? (top) and 117 (bottom)]
D. [chart: block model; Local and Foreign bars; 117 (top) and ? (bottom)]
- In two games, the number of points scored by a basketball player for every number of shots he took were in the same proportion. Which of the following does NOT show the correct proportion?
| Game 1 | Game 2 | |
|---|---|---|
| Number of points | 12 | 18 |
| Number of shots | 14 | 21 |
A. 12 : 14 = 6 : 7 B. 12 : 21 = 18 : 14 C. 6 : 7 = 18 : 21 D. 12 : 14 = 18 : 21
- Which of the following statements is TRUE?
A. In a proportion, the quantities can be written in any order. B. When the ratios of two quantities are different, the two quantities are in the same proportion. C. A proportion is a statement that two ratios are equivalent. D. When the ratios of two quantities are the same, the two quantities are not in proportion.
Additional Activities
- Imagine you have some blue and yellow buttons.
A. Form 5 different groups of buttons. Make sure that the ratio of the number of blue buttons to the number of yellow buttons in each group is 4 : 3.
B. Construct a table to record your results in (a).
C. Use the information in the table to write five (5) proportions.
D. If there are 72 yellow buttons in a group, how many blue buttons are there?
- On a bulletin board, a teacher posted the following triangles.
[illustration: two triangles; small triangle sides 5 cm, 7 cm, and 6 cm; large triangle sides 10 cm, 14 cm, and 12 cm]
A pupil said that the sides of the triangles are not in proportion. Do you agree? Why or why not?
- Ratio A is equivalent to Ratio B. Ratio B is equivalent to Ratio C. Do Ratios A and C form a proportion? Explain your thinking.
Answer Key
[transcriber’s note: this page is printed upside down; transcribed in reading order]
What I Know
A.
| Amount of salt | 3 | 6 | 9 | 12 | 15 |
|---|---|---|---|---|---|
| Amount of sugar | 2 | 4 | 6 | 8 | 10 |
[chart: block model; Amount of salt (3 blocks) and Amount of sugar (2 blocks); labels 15 (top) and 10 (bottom)]
Possible answers:
9 : 6 = 12 : 8
9 : 6 = 15 : 10
6 : 4 = 15 : 10
12 : 8 = 15 : 10Possible answers:
6 : 4 = 9 : 6
6 : 4 = 12 : 8
3 : 2 = 6 : 4
3 : 2 = 9 : 6
3 : 2 = 12 : 8
3 : 2 = 15 : 10Possible answers:
3 : 2 = 6 : 4
3 : 2 = 9 : 6
3 : 2 = 15 : 10
3 : 2 = 12 : 8
B.
- F
- T
- F
- T
- T
What’s In
Possible answers:
- The ratio of the number of seashells Leah collected to the number of seashells Joy collected is 8 : 7.
- The ratio of the number of seashells Joy collected to the total number of seashells both girls collected is 7 : 15.
- The ratio of the total number of seashells both girls collected to the number of seashells Joy collected is 15 : 7.
- The ratio of the number of seashells Leah collected to the total number of seashells both girls collected is 8 : 15.
- The ratio of the total number of seashells both girls collected to the number of seashells Leah collected is 15 : 8.
- The number of seashells Joy collected is 7/8 of the number of seashells Leah collected.
- The number of seashells Leah collected is 8/7 of the number of seashells Joy collected.
- The number of seashells Joy collected is 7/15 of the total number of seashells both girls collected.
- The number of seashells both girls collected is 15/7 of the number of seashells Joy collected.
- The number of seashells Leah collected is 8/15 of the total number of seashells both girls collected.
- The number of seashells both girls collected is 15/8 of the number of seashells Leah collected.
[transcriber’s note: this page is printed upside down; transcribed in reading order]
What’s More
| Number of cars | 1 | 2 | 3 | 5 | 15 |
|---|---|---|---|---|---|
| Number of wheels | 4 | 8 | 12 | 20 | 60 |
The ratio of the number of cars to the number of wheels is 1 : 4. If there are 12 wheels, then there are 3 cars. If there are 36 wheels, then there are 9 cars. The number of cars and the number of wheels are in the same proportion.
| Number of squares | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|
| Number of hearts | 5 | 10 | 15 | 20 | 25 |
The ratio of the number of squares to the number of hearts is 2 : 5. The number of hearts and number of squares are in the same proportion. For every 10 square-shaped biscuits, there are 25 heart-shaped biscuits.
| Number of males | 18 | 12 | 9 | ||
|---|---|---|---|---|---|
| Number of females | 20 | 16 | 8 |
[transcriber’s note: the blank cells in this table show no values in the rendered page]
The ratio of the number of males to the number of females is 3 : 4. If there are 32 females in a group, then there are 24 males. What can you say about the number of males and the number of females? The number of males and the number of females in each group are in the same proportion.
What I Can Do
a. [chart: block model; 5-peso coins (49) and 10-peso coins (28)] number of 5-peso coins / number of 10-peso coins = 7/4 = 49/28
b. [chart: block model; Ben (₱330) and Sheila (₱275)] Ben’s money / Sheila’s money = 6/5 = ₱330/₱275
c. [chart: block model; yellow paint (250 ml) and blue paint (450 ml)] amount of yellow paint / amount of blue paint = 5/9 = 250/450
[transcriber’s note: this page is printed upside down; transcribed in reading order]
What I Can Do
a. [chart: block model; Cement (5 blocks) and Sand (3 blocks)]
b. (Answers may vary as long as the ratio for each mixture is equivalent to 5 : 3.)
c. (Answers depend on the given values in the table in (b).)
d. 45
Assessment
- D
- A
- B
- B
- C
Additional Activities
a-b. (Answers may vary as long as the ratio of the number of blue and yellow buttons in each group is 4 : 3, and that five (5) groups of buttons are recorded in the table.)
c) (Answers depend on the given values in the table in (b).)
d) 96
No. (Explanation must show understanding that the ratios of the pairs of corresponding sides are the same.)
Yes. (Explanation must show understanding of proportion by comparing Ratios A, B and C.)
References
- Department of Education 2016, 21st Century MATHletes 6, Book Media Press Inc., 82-91
- Bureau of Elementary Education, Department of Education 2010, Lesson Guide in Elementary Mathematics 6, Book Media Press, Inc., 289-293
- DepEd Most Essential Learning Competencies (MELC) in Mathematics for Grade 6
For inquiries or feedback, please write or call:
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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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