Mathematics 6

Quarter 3
Module 5
Defines a variable in an algebraic
expression and equation.
Mathematics – Grade 6
Quarter 3 – Self – Learning Module 5: Defines a variable in an algebraic expression
and equation.
First Edition, 2020

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Development Team of the Module

Writer: Jessamin L. Calubing
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Reviewers (Content and Language): Wilma P. Soriano and Teresita P. Tagulao Ed,D
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 Mathematics 6
Quarter 3
Module 5
Defines a variable in an algebraic expression and
equation.

Introductory Message
For the facilitator:

Welcome to the Mathematics Grade 6 Self – Learning Module on Defining a variable

in an algebraic expression and equation.
This module was collaboratively designed, developed and reviewed by educators from
Schools Division Office of Pasig City headed by its Officer-In-Charge Schools Division
Superintendent, Ma. Evalou Concepcion A. Agustin in partnership with the Local
Government of Pasig through its mayor, Honorable Victor Ma. Regis N. Sotto.
The writers utilized the standards set by the K to 12 Curriculum using the Most
Essential Learning Competencies (MELC) while overcoming their personal, social,
and economic constraints in schooling.

This learning material hopes to engage the learners into guided and independent
learning activities at their own pace and time. Further, this also aims to help learners
acquire the needed 21st century skills especially the 5 Cs namely: Communication,
Collaboration, Creativity, Critical Thinking and Character while taking into
consideration their needs and circumstances.

In addition to the material in the main text, you will also see this box in the body of
the module:

Notes to the Teacher

This contains helpful tips or strategies that
will help you in guiding the learners.

As a facilitator you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to manage
their own learning. Moreover, you are expected to encourage and assist the learners
as they do the tasks included in the module.

For the learner:

Welcome to the Mathematics 6 Self- Learning Module on Defining a variable in an
algebraic expression and equation!

The hand is one of the most symbolized part of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a learner
is capable and empowered to successfully achieve the relevant competencies and
skills at your own pace and time. Your academic success lies in your own hands!

This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning material while being an active learner.

This module has the following parts and corresponding icons:

Expectation - These are what you will be able to know after completing the
lessons in the module

Pretest - This will measure your prior knowledge and the concepts to be
mastered throughout the lesson.

Recap - This section will measure what learnings and skills that you
understand from the previous lesson.

Lesson- This section will discuss the topic for this module.

Activities - This is a set of activities you will perform.

Wrap Up- This section summarizes the concepts and applications of the
lessons.

Valuing-this part will check the integration of values in the learning

competency.

Posttest - This will measure how much you have learned from the entire
module.

EXPECTATION
At the end of the lesson, you are expected to define a variable in an algebraic
expression and equation.

PRETEST

Directions: Read and understand the following questions. Choose the letter
of the correct answer.

1. In the phrase “w diminished by thirty-five divided by y”, what are the

variables?
A. w and y B. w and 35 C. y and 35 D. 35
2. What is the variable from the phrase, “twenty-two increased by m”?
A.22 + m B. 22 C. m D. m + 22

3. Give the variable from this expression, 32 + x.

A. x+32 B. x C. 32 D. x2 + 3

4. What are the variables in the equation, 8(k-6)=32?

A. 8 B.8 and 6 C. k and 32 D. k

5. Find the variable from the given equation, p-9 =17 + q.

A. p-9 B. 17 + q C 9=17 D. p and q

RECAP

Directions: Read and answer.

How do you translate expressions or equations into symbols?
How do you translate expressions or equations into mathematical
statement?
Translate the following word phrases or sentences to algebraic expression or
equation or vice versa.
______1. three times the sum of x and y
______2. ten decreased by twice a number
______3. The sum of a number and six is eighteen.
______4. 4m-10
______5. r + 15 = 26

LESSON
THINK AND UNDERSTAND
Problem:
During pandemic, Sandy’s father baked 150 cookies for 9 PNP
frontliners. Sandy wanted to share cookies with her 6 friends, too. How would
she divide the cookies?

From the given problem, what is the mathematical phrase?

How will you translate the mathematical phrase into an algebraic expression?
Do you use a symbol to represent the unknown number?

The number of cookies that Sandy and his father has to share is unknown.
Let us represent n for the number of cookies.

One hundred fifty cookies were divided to 9 150 ÷ (9+6) = n 24 ÷ 6 = n 24 ÷ 6 =4

PNP frontliners & Sandy’s 6 friends.
What do you call n in the algebraic expression? (Variable)
The numbers 150, 9, and 6 are constants.

Algebraic Expression is a combination of variables, numbers, operations and

grouping symbols.
In an algebraic expression, any letter that represents a number is called a
variable. A number may replace a variable.
A specific or fixed number represents a constant. Terms are the parts of an
algebraic expression separated by the operation symbols “+” or “-”.
A numerical coefficient is a constant multiplier of the variables in a term.

Study the following examples:

Example 1: The algebraic expression, 3x + 2y – 15
has 3 terms 3x, 2y, and 15
the variables are x and y
the numerical coefficient 3 and 2
the constants are 15

Example 2: Given the algebraic expression, (a2- b2) c3

How many terms are there? (3 terms) a2 , b2, c3
What are the variables? a,b, and c
What are the numerical coefficient imaginary 1
What are the constant? None

VALUING

Directions: Read and answer the given questions.

 1. Do you share your food with your classmates, friends, or neighbors?
2. How did you feel when you gave something to the needy?
3. If you were Sandy and his father, would you do the same thing?
Why?

ACTIVITIES

PRACTICE

Directions: Write the variable/s in each expression or equation.

1. 30 + 5x ________________
2. 3y ÷ 15 ________________
𝑐+𝑑
3. 10𝑎 − ( 2 ) ________________
4. 49f ________________
5. h – 7g x 12
3 ________________
6. (2r3 + 4)- ( 5v-q)=87 ________________
7. 6s-14 =2t ________________
8. 8w + y - 25 =12 ________________
9. m (10÷n)=76
2 – ________________
10. 3d + 5 =14 ________________

KEEP PRACTICING
Directions: Identify the variable, constant and operations used in the following
algebraic expressions or equations.

Algebraic Number of terms Variable Constant

Expressions/Equations

1. 3
ab2
4

2. 8n + 5

3. (4x-2y)3

4. 𝑑+𝑒
=2
9

5. 2L + 2w =50

TEST YOURSELF
Directions: What are the variables used in the following mathematical
phrases and sentences?
 1. Twenty-seven less than the cube of a _____________
2. Four more than thrice a number is 16. ______________
3. Five less than twice x ______________
4. Twelve more than a number y is 35. ______________
5. The sum of the reciprocals of a , b, and c ______________

WRAP UP

Directions: Answer the given questions.

1. What is a variable?
2. How do you represent the unknown number in a mathematical phrase?

POSTTEST

Directions: Read and analyze the questions below. Choose the letter of
the correct answer.

1. What is the variable in the phrase, the sum of a and b subtracted from
56?
A. a + b=56 B. a and b C. 56 D.56- (a+ b)

2. In the expression 9xy, what are the variables?

A. 9x B. 9y C. xy D. 9xy

3. Give the variable from this equation, 8m = 5 +12.

A. m B. 8m C. 5 + 12 D. m=5 +12

4. From the sentence, “The square of the quotient of 20 and d equals the
difference of 50 and e”, what are the variables?
A.20÷d B. (20÷d)2 C. 50-e D. d and e

3
5.What is the variable in the equation, 𝑛 + 16 = 22?
5
3
A. n B. C. n +16 D.16=22
5
 KEY TO CORRECTION

References
Oliver G. Mariano,Sitero Francisco Memorial National Hs,Division of
Valenzuela City,Patterns and Algebra Grade 6 Page 1,2109 MTAP- DepEd
NCR Seminar Workshop and Regional Convention

Adela C. Villamayor,Amelia D. Celeridad-Wright and Eden C. de Joya

Math for Life, Wortktext in Mathematics Pages 246-247
Sampaloc, Manila, Published by Rex Book Store, Inc. 2017