This document outlines a lesson plan on direct variation for students. It includes objectives, subject matter, procedures, and evaluation. The procedure section details how the teacher will introduce direct variation using an example of Spongebob's travel time and distance. Students will then practice determining the constant of variation and writing the equation of variation for different scenarios. They will also solve word problems involving direct variations in real life situations. At the end, students will complete a worksheet to evaluate their understanding of direct variation.

1. I. Objectives
At the end of the lesson, the students will be able to:
A. Determine a direct variation
B. Determine the constant of variation
C. Relate direct variation to real life situations
D. Create an equation expressing a direct variation
E. Solve word problems involving direct variations
F.
II. Subject Matter
Intermediate Algebra (Direct Variation
References: Teaching Guide in Intermediate Algebra
Math Time Vol. XV, no. 3
Materials: visual aids, strips of papers, marker
Values: cooperation, determination and patience
III. Procedure
Teacher’s Activity Students’ Activity
“Good morning class!” “Good Morning Sir!”
“Before we start our class, let us all stand up and
pray. __________, please lead the prayer. (One student will lead the prayer)
“Please pick up the pieces of paper under your (Students pick up the pieces of paper)
chair”
__________, kindly pass the attendance sheet to (The class president will give the attendance sheet)
me.”
“Ok, Thank you”
Presentation
Activity
As an introduction to the lesson, direct
variation, present the following story:
It is already 7 in the morning but (Students listen attentively to the story)
Spongebob is just on his way to work in The Krusty
Krab. He is supposed to be on The Krusty Krab at 8
in the morning so he immediately rode on his
bicycle and drove his way to work. His journey
from his place to The Krusty Krab is shown below:

2. “Class, what do you think? Will he come on time or
he will be late? Why did you say so?”
“He will be on time because it will only take him 50
minutes to travel from his place to the Krusty
Krab”
“Ok, Very Good, __________. In 50 minutes, he
was able to travel 2000 meters “
“What happens to the distance traveled by
Spongebob as the time goes by?” “As time goes by, the distance traveled by
Spongebob goes longer and longer.”
“So, what do you think will happen if he only
traveled for 20 minutes? How long will he travel?” “He would only travel for 800 meters”
“Correct!”
“How about if he traveled for 40 minutes? How “He would travel for 1600 meters”
long will he travel?”
“Do you see any relationship between the time
coverd and distance traveled by Spongebob during
his journey?” “Yes sir!”
“Then, what is it?” “As the time increases, distance also increases and
as time decreases, distance also decreases”
“Exactly! That is the point.”
“As a variable increases, the other variable also
increases and when a variable decreases, the other
also decreases. In this case, our variables are time (Students’ listen attentively)
and distance. And this special relationship
between variables is what we call direct variation”
“Will you please give me more examples wherein
direct variation can be seen?” (Students’ will give more examples)
“From those given examples, describe or define a
direct variation” “A direct variation is a relationship between two
variables wherein when one variable changes the
other also changes in proportion to the first.
(When a variable increases, the other also
increases and when a variable decreases, the other
also decreases )”
“Thank you __________, Very well said”
Activity
From the previous activity, put the time
covered and distance traveled by Spongebob on a
table. (Students will complete the table by posting the

3. provided pieces of paper on the posted table)
Distance 400 800 1200 1600 2000
(meters)
Time 10 20 30 40 50
(minutes)
“Class, let us try to write it in Ratio form or
Fraction Form. Who wants to give it a try? Yes,
__________”
“Very Good!”
“The variables that we used are d and t. d for
distance and t for time. Always remember that we
can use any letters as variables other than d and
t.”
“The value that you got which is 40 is what we call “The constant of variation is the ratio between
the constant of variation. Since you are the one two variables in a direct variation (Quotient of
who got it, why don’t you give it your own variables)”
definition?”
“That is correct. The constant of variation is also
the number that relates two variables”
“If used in an equation, the constant of variation
can be presented by the letter k. from the way you
solved it a while ago, how are you going to make a
formula for the constant of variation?”
“Definitely! Thank you _________”
“Ok now, using the formula , make a
formula for d. Who wants to try? Yes, _________”
d = kt
“Very good! And that formula is what we call the
equation of variation”
“Let us try the use of that equation, using
Spongebob’s data. A while ago, we solved for k
and got 40 as our answer. So our equation of
“The equation of variation will be d = 40t”
variation will be _________”
“Very Good, ________”

4. “If Spongebob traveled for 70 minutes, how long
will he travel? Why don’t you give it a try,
________ ” d = 40t
d = 40(70)
d = 2800
“He will travel 2800 meters”
“Thank you, _______. That is great”
“Those two formulas that you discovered can be
both read as “d is directly proportional to t,
because whatever happens to t happens to d ”
“Now as far as I can see, you are already getting a
hang of it. I think it is about time for our group
activity. Proceed to your groupmates and
cooperate”
“Yes sir”
Group Activity
Each group will be given different task for
them to.
Solve for the constant of variation and
equation of variation if x is directly proportional to
y.
Task 1: x = 33 , y = 3 (Students will show their solutions on the provided
Task 2: x = 9 , y = 3 manila papers and explain it later)
Task 3: x = 20 , y = 4
Task 4: x = 25 , y = 5
Task 5: x= 64 , y = 8
“Very good, class! It is so nice to see that you can
easily solve these problems. Let us see how you
are going to work with it being applied in real life”
Group work
Task 1: Patrick’s income as an employee in Jollibee (Students work and cooperate with their
varies directly as the number of hours worked. If groupmates)
Patrick earns P950 for working 8 hours, how much
will he earn for working 48 hours?
Task 2: Mica manages horseback rides in Picnic
Groove. A 2.5 hour ride costs P375. What is the
cost of a 2-hour ride?
Task 3: Michael’s car travels 75 kilometers in 45
minutes. How long can it reach a place which is
210 kilometers away?

5. Task 4: Bianca wants to drink calamansi juice.
According to her recipe, it takes 30 calamansi fruits
to make 5 cups of calamansi juice. How many
calamansi fruits will she need to make 45 cups of
calamansi juice?
Task 5: The amount of commission is directly
proportional to the amount of sales. As a car
agent, Jestelle received P90000 on the sale of car
worth P600000. How much would be Jestelle’s
commission on a car worth P750000?
IV. Generalization
A direct variation is a relationship between two variables wherein when one variable
changes the other also changes in proportion to the first.
The constant of variation is the ratio between two variables in a direct variation.
We obtained two formulas in this lesson, the constant of variation formula (k = ) and
the direct variation formula (x = ky)
V. Evaluation:
(Worksheet)
1. Lairen bought 27 pieces of intermediate paper at the canteen worth P9.00. after a while,
Krizelle asked her to buy P5.00 worth of intermediate paper. How many pices of
intermediate paper will Krizelle receive from Lairen?
2. The weight of an object in earth is directly proportional to the weight of the same object
on the moon. A 200-pound man weighs 32 pounds on the moon. How much would a
50=pound dog weigh on the moon?
3. The profit of a company varies directly as the number of product it sells. If a company
makes a profit of P4350 on the sale of 300 angry birds key chain, what is the profit when
the company sells 500 units of angry birds key chain?
VI. Assignment:
On your journal notebook, write something about the use of direct variation in
our life. You may also include your learning experiences for today.