This is the Grade 4 Mathematics Self-Learning Module (SLM) for Quarter 3, Module 6: Finding the Missing Number in an Equation. It is from DepEd Region V’s Alternative Delivery Mode series (First Edition, 2020) and is written for Grade 4 learners studying at home, with help from a parent or facilitator. By the end of the module, learners should be able to find the missing number in an equation by using the properties of operations.
The module builds on the previous quarter, where learners found missing terms in a sequence of numbers or figures and stated the rule behind them.
On this page 6 sections
What learners will learn
The module has one learning objective. At the end of it, learners should be able to:
- find the missing number in an equation involving properties of operations.
Key ideas: equations and the properties of operations
The module defines an equation as a mathematical sentence that states the equality of two expressions separated by an equal sign. The properties of operations help you find the missing numbers. You can check, or evaluate, an equation by doing the operations on each side and making sure both sides give the same answer.
The module reviews five properties, each with its own example:
| Property | What it means | Example from the module |
|---|---|---|
| Commutative Property | Changing the order of the numbers does not change the sum or product | 2 x 3 = 3 x 2 |
| Associative Property | Changing the grouping of the numbers does not change the sum or product | 2 + (4 + 5) = (2 + 4) + 5 |
| Distributive Property of Multiplication over Addition | Multiplying a sum is the same as multiplying each addend and then adding | 3 x (2 + 4) = (3 x 2) + (3 x 4) |
| Identity Property | Multiplying a number by 1 gives the same number | 1 x 5 = 5 |
| Zero Property | Multiplying a number by 0 gives 0 | 0 x 1 = 0 |
Worked examples
The module shows how a property tells you which number belongs in each blank:
- Distributive: (10 x 2) + (10 x 5) = ___ x (___ + 5). The missing numbers are 10 and 2. Check: 20 + 50 = 10 x 7, so 70 = 70.
- Commutative and Associative: (40 + 5) + (___ + 15) = (___ + 15) + (40 + 30). The missing numbers are 30 and 5. Check: 45 + 45 = 20 + 70, so 90 = 90.
- Associative Property of Multiplication: (8 x 5) x 4 = 8 x (5 x 4). Check: 40 x 4 = 8 x 20, so 160 = 160.
- Commutative Property: 32 + 59 + 8 = 32 + 8 + 59, and both sides equal 99.
Word problems
The module also uses everyday situations:
- The Francisco family’s poultry house: They gathered 48 big bamboos and 28 small bamboos. Both 48 + 28 and 28 + 48 equal 76, which shows the Commutative Property of Addition.
- Facemasks in Brgy. Katipunan: Purok Magalang got 9 boxes and Purok Masigasig got 8 boxes, out of 45 boxes in all. Purok Matapang gets 28 boxes. Both 9 + (8 + 28) and (9 + 8) + 28 equal 45, which shows the Associative Property of Addition.
- Rene’s weekly earnings: He earns ₱120.00 a day as a dishwasher and ₱250.00 a day as a cook, and he works 5 days a week. Both (5 x 120) + (5 x 250) and 5 x (120 + 250) equal ₱1,850, which shows the Distributive Property of Multiplication over Addition.
Parts of the module
- What I Know: a five-item pretest on missing numbers in number sentences, such as 5 + ___ = 55.
- What’s In: naming the property shown in five equations.
- What’s New and What is It: the definition of an equation, the worked examples, and the word problems above.
- What’s More: five practice items. Learners fill in the missing numbers and name the property used.
- What I Have Learned: a short summary of the lesson.
- What I Can Do: five more equations to complete using the properties.
- Assessment: five items where learners name the property and write the missing numbers.
- Additional Activities: five equations, each with a hint showing which property to use.
- Answer Key: answers for every activity and test.
How to use this module
- Learners: Start with the pretest to see what you already know. Then go through the parts in order. Write your answers on a separate sheet of paper or in your notebook, not on the module. After each activity, check your work with the Answer Key, and be honest when you do.
- Parents and facilitators: Help your child read the directions carefully. After the Additional Activities, use the module’s scoring guide. A score of 4 to 5 means your child may go on to the next lesson. A score of 2 to 3 means they should review what they missed. A score of 0 to 1 means they should repeat the whole lesson with your help.
- Teachers: The module draws on the Mathematics 4 Teacher’s Guide (pp. 304-307) and Learner’s Material (pp. 171-172), both from 2015, so you can pair it with those materials for review or remediation.
Frequently asked questions
Which grade and quarter is this module for?
It is for Grade 4 Mathematics, Quarter 3. It is Module 6 in the series.
What properties of operations does the module cover?
It covers the Commutative, Associative, Identity, and Zero Properties. It also covers the Distributive Property of Multiplication over Addition.
Does the module have an answer key?
Yes. The Answer Key covers the pretest, What’s In, What’s More, What I Can Do, the Assessment, and the Additional Activities.
What is an equation, according to the module?
An equation is a mathematical sentence that states the equality of two expressions separated by an equal sign. You can evaluate it by doing the operations in each expression.
Where should learners write their answers?
The module asks learners to use a separate sheet of paper or their notebook. They should not put unnecessary marks on the module itself.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 6: Finding the Missing Number in an Equation
[illustration: students learning at home, outdoors and indoors, with a teacher, a globe, and a student with a lamp]
CO_Q3_Mathematics 4_ Module 6
Mathematics – Grade 4 Alternative Delivery Mode Quarter 3 – Module 6: Finding the Missing Number in an Equation 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
Writer: Marjorie Ann F. Deramas Editor: Elena D. Hubilla Reviewer: Loyd H. Botor Illustrator: Layout Artist: Joan T. Briz 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
Office Address: Regional Center Site, Rawis, Legazpi City 4500 Telefax: 0917-178-1288 E-mail Address: region5@deped.gov.ph
4
Mathematics Quarter 3 – Module 6: Finding the Missing Number in an Equation
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
From the previous quarter, you have already learned how to find the missing term/s in a sequence of numbers/figures and give/state the rule in determining the missing term/s in a sequence.
As you explore this new lesson, you will learn about finding the missing number in an equation involving properties of operations. Read on and explore to see how your knowledge in the properties of operations would help you solve the equations in every activity in this module.
At the end of this module, you should be able to:
- find the missing number in an equation involving properties of operations.
What I Know
Find the missing number in a number sentence involving operations of whole numbers.
- 5 + _____ = 55
- _____ – 12 = 20
- 3 + _____ + 5 = 15
- 15 x 3 = _____
- _____ + 7 = 13
What’s In
What property of operation is expressed in the following equations? Choose your answer from the box on the side.
- 0 x 1 = 0
- 2 x 3 = 3 x 2
- 1 x 5 = 5
- 2 + (4 + 5) = (2 + 4) + 5
- 3 x (2 + 4) = (3 x 2) + (3 x 4)
Commutative Property Associative Property Zero Property Identity Property Distributive Property of Multiplication over Addition
What’s New
An equation is a mathematical sentence that states the equality of expressions.
Look at these equations. Could you give the missing number/s?
A. (10 x 2) + (10 x 5) = _____ x (_____ + 5) B. (40 + 5) + (_____ + 15) = (_____ + 15) + (40 + 30)
How will you make each equation correct? Try to evaluate each equation.
In the first equation, you will use the Distributive Property of Multiplication over Addition:
A. (10 x 2) + (10 x 5) = 10 x (2 + 5) 20 + 50 = 10 x 7 70 = 70
In the second equation, you will use the Commutative Property and Associative Property of Addition:
B. (40 + 5) + (30 +15) = (5 + 15) + (40 + 30) 45 + 45 = 20 + 70 90 = 90
Note:
The properties of operations help us find the missing numbers in an equation. We can evaluate an equation by performing the operations in each expression.
What is It
READ AND LEARN MORE
Let us take a look at some other examples.
Example #1:
(8 x 5) x 4 = 8 x (5 x 4) 40 x 4 = 8 x 20 160 = 160
Here, we use the Associative Property of Multiplication which provides that you can multiply numbers regardless of how they are grouped and get the same product.
32 + 59 + 8 = 32 + 8 + 59 99 = 99
Here we use the Commutative Property which states that the order in which the numbers are added does not affect the sum.
Example #2
Filipinos are known for being resilient. That is why, even if many people lost their jobs during this pandemic, many have find ways to earn a living for their family to survive. Francisco family thought of raising chickens as their source of income, so they gathered 48 big bamboos and 28 small bamboos for their poultry house. How many bamboos did they gather? Show the addition sentence in two ways.
How many big bamboos did they gather? How about the small bamboos?
- They gathered 48 big bamboos and 28 small bamboos.
Number sentence
- 48 + 28 = 76
- 28 + 48 = 76
Does the sum changes? Why?
- No, because based from the Commutative Property of Addition, changing the order of the addends does not change the sum.
Example #3
Brgy. Katipunan distributed facemasks in three different Puroks namely Magalang, Masigasig, and Matapang. If the first two Puroks received 9 and 8 boxes of facemasks, respectively, how many boxes of facemasks will Purok Matapang gets if the total number of boxes of facemasks is 45? Write the number sentence in two ways and solve it.
- How many boxes of facemasks did Purok Magalang receive? How about Purok Masigasig?
- Purok Magalang received 9 boxes of facemasks while Purok Masigasig received 8 boxes.
- Write the number sentence.
- 9 + (8 + 28) = 45
- (9 + 8) + 28 = 45
- Does the sum changes? Why?
- No, because based from the Associative Property of Addition, changing the grouping of the addends does not change the sum.
Example #4
Rene earns ₱120.00 per day by working every morning as a dishwasher at Linda’s Café and ₱250.00 a day by working every afternoon as a cook at Gloria’s Diner. If he works for 5 days a week in both places, how much is his earning in a week?
- What are the jobs of Rene?
- Dishwasher and Cook
- How much does he earn as a dishwasher? As a cook?
- He earns ₱120.00 per day as a dishwasher and ₱250.00 per day as a cook.
- How many days does he work in a week?
- 5 days
- What is the number sentence?
- (5 x 120) + (5 x 250) = 1 850
- 5 x (120 + 250) = 1 850
- What property is used to solve the problem?
- Distributive Property of Multiplication Over Addition
What’s More
Find the missing number/s that would make the equation correct then identify the properties of operation involved. Write your answer in your notebook.
- 12 + 24 + 34 = 34 +12 +
_____ - 2 x (15 +20) = (
_____x 15) + (2 x_____) - 8 x 7 =
_____x 8 - 24 +
_____= 5 +_____ - (
_____x 5) x 4 = 8 x (_____x 4)
What I Have Learned
What is an equation? What should you remember in finding the missing numbers in an equation? Is there a need to evaluate an equation?
An equation states equality of two expressions separated by an equal sign. The Properties of Operations help us find the missing numbers in an equation. We can evaluate an equation by performing the operations in each expression.
If you are done answering the activity, please go to the Answer Key and check if your answers are correct.
Thank you for your honesty in answering and checking your work. Hope you will do this until the end of this module.
What I Can Do
On a separate sheet of paper fill in the blank with the missing number/s that will make the equations true using the properties of operations.
_____x (4 + 8) = (2 x_____) + (2 x_____)- 6 + 10 + 12 + 24 = (
_____+_____) + (6 + 24) - (7 x 1) + 0 =
_____x (1 +_____) - 12 x
_____=_____x 15 _____+ 240 = 460 +_____
If you are done answering the activity, please go to the Answer Key and check if your answers are correct.
Thank you for your honesty in answering and checking your work. Hope you will do this until the end of this module.
Assessment
Give the property of operations used in each equation. Then, write the missing number/s.
- (6 + 12) + (5 + 7) = (5 +
_____) + (_____+ 12)_________________ - (7 x 6) x 5 =
_____(6 x_____)_________________ - 20 +
_____= 40 +______________________ - 24 + (36 + 50) = (
_____+_____) + 50_________________ - 7 x (10 +5) = (
_____x 10) + (7 x_____)_________________
Additional Activities
In a separate sheet of paper, fill in the blank with the missing number/s to make the equations correct. Use the hint provided.
- (3 + 2) + 20 =
_____+ (_____+ 20) (Associative) - 6 x (5 + 10) = (
_____x 5) + (6 x_____) (Distributive) - (45 + 0) + (1 x 50) = (
_____+0) + (1 x_____) (Identity/Zero) - 9 x
_____= 5 x_____(Commutative) - (8 x
_____) x 5 =_____x (6 x 5) (Associative)
Check your answer with the answer key. If you get…
- 4- 5 Excellent! You may now proceed to the next lesson.
- 2- 3 You need to review the processes you missed.
- 0-1 You need to repeat the whole process. Ask your teachers or parents to help you.
Check your answers with the Answer Key.
If you get all the items correctly, you may now proceed to the next module.
Otherwise, review the lessons and ask the guidance of your teachers or parents.
transcriber’s note: this page is printed upside down in the source; it is transcribed in upright reading order. Entries marked [?] are hard to read.
Answer Key
What I Know
- 5 + 50 = 55
- 32 – 12 = 20
- 3 + 7 + 5 = 15
- 15 x 3 = 45
- 6 + 7 = 13
What’s In
- Zero Property
- Commutative Property
- Identity Property
- Associative Property
- Distributive Property of Multiplication Over Addition
What’s More
- 12 + 24 + 34 = 34 + 12 + 24 – Commutative Property
- 2 x (15 + 20) = (2 x 15) + (2 x 20) – Distributive Property of Multiplication Over Addition
- 8 x 7 = 7 x 8 – Commutative Property
- 24 + 5 = 5 + 24 – Commutative Property
- (8 x 5) x 4 = 8 x (5 x 4) – Associative Property
What I Can Do
- 2 x (4 + 8) = (2 x 4) + (2 x 8)
- 6 + 10 + 12 + 24 = (10 + 12) + (6 + 24)
- (7 x 1) + 0 = 7 x (1 + 0)
- 12 x 15 = 15 x 12
- 460 + 240 = 460 + 240 [?]
Assessment
- (6 + 12) + (5 + 7) = (5 + 7) + (6 + 12) – Associative Property [?]
- (7 x 6) x 5 = 7 x (6 x 5) – Associative Property
- 20 + 40 = 40 + 20 – Commutative Property
- 24 + (36 + 50) = (24 + 36) + 50 – Associative Property
- 7 x (10 + 5) = (7 x 10) + (7 x 5) – Distributive Property of Multiplication Over Addition
Additional Activities
- (3 + 2) + 20 = 3 + (2 + 20) – Associative Property
- 6 x (5 + 10) = (6 x 5) + (6 x 10) – Distributive Property
- (45 + 0) + (1 x 50) = (45 + 0) + (1 x 50) – Identity/Zero Property
- 9 x 5 = 5 x 9 – Commutative Property
- (8 x 6) x 5 = 8 x (6 x 5) – Associative Property
References
Tabilang, Alma R. et. al, 2015, Mathematics 4 Teacher’s Guide pp. 304-307, Department of Education
Tabilang, Alma R. et. al, 2015, Mathematics 4 Learner’s Material pp. 171-172, Department of Education
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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