Ms. Patricia Flores
Ms. Janice Cruz
Jocelyn dela Peña
Ma. Jhoana Bulos
LINEAR EQUATIONS in one
Time Frame: 10 days
The learner demonstrates understanding of
the key concepts of first-degree equations in
The learner models situations using oral,
written, graphical and algebraic methods to
solve problems involving first degree equations
and inequalities in one variable.
Real life problems where certain quantities
are unknown can be solved using first degree
equations and inequalities in one variable.
How can we use first degree equations and
inequalities in one variable to solve real life
problems where certain quantities are
The students will know:
mathematical expressions, first degree
equations and inequalities in one variable
first degree equations and inequalities in one
properties of first degree equations and
inequalities in one variable
applications of first degree equations and
inequalities in one variable
The students will be able to:
Differentiate mathematical expressions from equations
Identify an describe first-degree equations and
inequalities in one variable.
Give examples of first degree equations and inequalities
in one variable
Describes situation using first degree equations and
inequalities in one variable
Enumerate and explain the different properties of first
degree equations and inequalities
Give illustrative examples of each property
Apply the properties of equations and equalities in
solving first degree equations in one variable
Verify and explain the solution to problems involving
first degree equations and inequalities in one variable
Extend, pause, and solve related problems in real life
Unknown quantities or variables can be
represented only by x or y.
Variable has a fixed value.
Linear equation cannot be apply in real life.
In solving equations, variables are always on
the left side.
The use of properties of equalities and the
use of relationship symbols ( or )
Use linear equations in one
variable to solve real-life
To model relationship between physical
quantities and real life situations
To apply your knowledge involving linear equations in one variable, you are to
play the role of a teacher. You are tasked to investigate the relationship
between the physical quantities that are found in the environment or find
real word problems that models a linear equation. You are tasked to write
the corresponding equations and related questions to the problem. Write
your explanation. You are to organize your work on a chart or poster which
shall include the problem/situation that you investigated, your observations,
the corresponding linear equation/model, related questions, explanations
and reflection. Your presentation will be judged by your classmates.
Category 4 3 2 1
Clarity of creativity and
on creative little or no Not clear
Presentation goes beyond
thought and creativity
Detailed and understand
Explanation Clear and several
clear but includes
written in Presented
narrative form relationship
form and are No
Conclusion and are to
supported by conclusion
supported by evidence
mathematical maybe limited
greatly add to
Questions are are difficult
the reader’s Questions are
Related somewhat to
understanding clear and easy
Question difficult to understand
of the to understand
understand or are not
related to the
Complete, Neat and easy Neat but 3 or Messy and
neat and easy to read, 1 or 2 4 items are more than 5
to read items missing missing items missing
Facets of understanding
How to solve physical quantities that are found in the
environment or real word problem that models linear equations
By recording an observation in a chart and writing the
findings and conclusion
Variety of techniques in solving real life problems involving
Self – knowledge
Solve problem through the idea of linear equations in one
You are a farmer and supplier of rice in your
community. If the approximate numbers of
families is above 45 and each family needs a
cavan of rice per month, how many cavans of
rice are needed for 2 months? 5 months? One
year? What do you think will happen if the
number of families increases by 2 per year.
Complete the table to show the demands of
Year No. of Families No. of Demands per
Based on the given information on the
table, form an equation.
How can you construct an equation to get
the number of demands for the succeeding
How can we use the first degree equation in
one variable to solve real life problems where
certain quantities are unknown?
On Properties of Equality
Say: Earlier, you were able to represent and solve the
unknown by using linear equation in one variable. For
further understanding of the topic, ask: What is
equilibrium? Solicit students’ answers.
Discuss the different properties of equality. Illustrate
each through examples and mathematical models. Use a
number line or algebra tiles whenever necessary.
Emphasize the said properties are used to simplify and
solve mathematical equations.
Let the students answer Activity # 1.
Ask them to choose a partner and discuss their work.
Let them work on Activity # 2.
You may also ask the students to access the website for
their independent study on the properties of equality.
Topic on Properties of Equality and Exercises
Let the students have a journal and answer the
question: “When do we say that equality exists between
On Solving Linear Equations
Say: In the activities that we have done, we
understand/realize the importance of having equality among
men, object, and things. Then ask: Given an equation, when
do we apply APE, SPE, MPE, and DPE. Tell the students
that in the next activity they will apply the different
properties in solving equation in one variable.
Ask the students to perform Activity # 3. Allow them to
work for 10 – 15 minutes. Ask them to get a partner, to take
turn in showing and explaining their work in front of the
class and write at least two comments on their partner’s
Discuss the reason why zero should not be
used as a multiplier [or a divisor] in
transforming equations. Differentiate between
the terms undefined and indeterminate.
Review PEMDAS. Have students
remember the order of operations in a multi-
operation expression or equation.
Let the students work by group in answering Activity
#4. Let them explain their work on the board.
Ask the students to give procedure in solving
mathematical equations. Relate the steps to the different
properties of equality.
Emphasize the importance of reading a word problem
carefully. List down the related terms of operations like
addition, subtraction, multiplication and division.
Word problems are difficult for many beginning algebra
students. It is important for students to realize that
when they need to apply mathematics to real life
problems, they must isolate or identify relevant data from
extraneous data. Emphasize that sometimes there are not
enough facts available to solve a given problem.
Let them work on Activity 5. (Word problem)
You may also ask the students to access the following
websites to answer more activities on solving equations.
Let the student do the Performance Task.
Summarize what you have learned about linear
equations and inequalities by doing the activity below.
Give the students 3 to 5 minutes and ask some students to
present and explain their answers to the class.
Can be expr essed as
Has differ ent
Ask them to answer the following questions in a
Journal to process the learning experience of the
What knowledge and skills did you learn from the
lesson that you can use in real life? What are the
attitudes of men that can be developed in the study
of first degree equations in one variable?
How can you use your knowledge of linear equations to
lessen/eliminate corruption in our government?
Linear equations can be expressed either in verbal or
mathematical manner. Properties serve as a guide in
solving equations. After performing the activity, we can
say that linear equations can help in solving problems in
real life. As we continue the lessons, you can see more
applications in our everyday life.
Identify the property used in each equation.
1. If x = 7 and y = 7, then x = y.
2. If x = 5, then x + 3 = 5 + 3.
3. If 4x = 5, then 4x/4 = 5/4.
4. If 5x = 7, then 7 = 5x.
5. If x + 10 = 5, then x + 10 – 10 = 5 – 10.
Supply the appropriate equation indicated by the given
1. If x = 3 and x + y = 4, then ________________ (Substitution)
2. (x + y) + z = _____________________ (Associative)
3. If m = n and m = 3, then ___________________ (Transitive)
4. If x + 3 = 8, then ________________________ (Addition PE)
5. If 4x = 8, then __________________________ (Division PE)
Solve the following equations.
1. x + 6 = 3
2. x – 8 = 15
3. -3x = 12
4. 1/3 x = 9
5. x + 4 = - 15
Solve the following equations.
1. 2x + 6 = x - 2
2. 2(x – 1) = 3(x – 2) + 7
3. 3x + 4 = 12 + 5(x – 4)
4. ½ (x + 4) = (x + 5)
5. 2/3x + 4 = ½ (x – 3)