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Detailed Lesson Plan MATH 9
BS Secondary Education (Mindoro State College of Agriculture and Technology)
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Detailed Lesson Plan
In Mathematics 9
Content Standard: The learner demonstrates understanding of key concepts of
variation and radicals.
Performance Standard: The learner is able to formulate and solve accurately
problems involving radicals.
Learning Competency: Illustrates situations that involve the following variations: (a)
direct; (b) inverse; (c) joint; (d) combined.
I. Objectives
At the end of the lesson, the students should be able to:
a. Illustrates situations that involve direct variation
b. Identify the equation that expresses a direct variation
c. Solve problems involving direct variation using y=kx as the
mathematical equation of direct variation, where k is a constant of
variation
d. Appreciate the concept of direct variation in real life situations
II. Subject Matter
A. Topic
Direct Variation
B. References
Mathematics Learner’s Material for Grade 9, pp. 194-203
Mathematics Teacher’s Guide for Grade 9, pp. 132-134
www.slideshare.net/mobile/jmpalero/mathematics-9-lesson-4a-direct-
variation
C. Materials
Laptop, Projector/TV, Manila Paper, Marker, Tape, Illustration Board
D. Subject Integration
Science, Values, English
E. Values Integration
Cooperation, Participation, Enthusiasm, Teamwork, Discipline
F. Teaching Strategy
Guided Discovery Approach, Cooperative Learning Approach
III. Procedure
TEACHER’S ACTIVITIES STUDENTS’ ACTIVITIES
A. Daily Routine
1. Prayer
Everybody stand. (Students will stand.)
_______, kindly lead the prayer. (Let us bow our heads and feel the
presence of our ALMIGHTY GOD. In
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
the name of the Father, and of the
Son, and of the Holy
Spirit…..AMEN)
2. Greetings
Good morning class! How are you Good morning, Ma’am! We are
today? That is good to hear. feeling great Ma’am!
3. Classroom Management
Class, before you take your seats, (Students will pick up the pieces
kindly pick up the pieces of papers of papers or plastics around them
or plastics around you and arrange and arrange their chairs silently
your chairs silently and properly. and properly.)
You may now take your seats. Thank you Ma’am.
4. Checking of Attendance
_______, is everyone present Yes Ma’am except those in
today? different learning modality.
Very good!
I know everyone is aware that we
are still in the midst of pandemic,
so we have to be extra careful and
let’s practice social distancing and
wearing of facemasks all the time.
For your classmates with special
educational needs because of their
geographic location, likewise for
those who are working, they
already have the modules for
today’s topic.
B. Review of the Previous Lesson
Class, last meeting, we discussed and
solved problems involving quadratic
functions. (One volunteer student will solve
Here is a problem and let me ask one the problem on the board and
volunteer to solve it. Yes ________. others will answer on their
papers.)
Problem:
From a 96-foot building, an object is Solution:
thrown straight up into the air then
follows a trajectory. The height S(t) of
the ball above the building after t
seconds is given by the function .
1. What maximum height will the object The vertex is ( , 100) thus the
Address: San Agustin, Naujan, Oriental Mindoro, 5204
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
reach? maximum height reached by the
object is 100 ft from the top of the
building. This is 196 ft from the
ground.
Yes Ma’am.
Alright, do you get the correct answer
as well?
Good job class!
It seems that you understood our
previous topic, let us now proceed to
our new lesson.
C. Motivation
Class before we start our new lesson, I
have prepared an activity for you titled
“RELATED OR NOT?”.
I will divide you into five groups. It will
be your permanent group for the
entire period. Each group will receive
pictures and you will be given 2
minutes to study its features and
another 3 minutes to identify their Yes Ma’am
related quantities. Paste the pictures None Ma’am
and your answer on the manila paper
and kindly post it on the board.
Are the instructions clear?
Do you have any questions?
If there’s none, kindly proceed to your
group and form a circle.
(pictures will be given to the students
and will be shown on the TV screen)
Group 1 (Possible answers)
Wall and Paint
The wider the wall, the more
amount of paint to be used.
If the wall is narrow, less paint will
be used.
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Group 2 The more money you have, the
Groceries and Money more groceries you can buy.
The less money you have, the less
groceries you can buy.
Group 3 Doing more activities can result to
Nature of Activity and Heartbeat higher pulse rate.
Doing less activities can result to
lower pulse rate.
Group 4 The faster speed you go, the
Speed and Distance longer distance you can reach.
The slower speed you go, the
shorter distance you can reach.
Group 5
The more hard work you do, the
Hard work and
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Success more chance you can be
successful.
The less hard work you do, the
less chance you can be successful.
Yes Ma’am!
Do you like the activity class?
Before you go back to your seats, let’s
form a word using this equation of
pictures. Direct Variation!
I think our lesson for today is
about Direct Variation.
D. Presentation of the Lesson
Class, from the activity you had a while ago,
what do you think will be our lesson for this At the end of the lesson, the learners
day? must be able to:
Yes, ______________________. a. Illustrates situations that
involve direct variation
Good job! b. Translate into variation
statements a relationship
E. Presentation of Objectives involving direct variation
Before we start our discussion, you need to c. Solve problems involving
know first what you should accomplish at the direct variation as a means
of valuing the concept in
end of the lesson.
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Okay, kindly read the objectives. real-life situation
Yes ________.
F. Discussion
The activity earlier is connected to the
topic we have today. There is a man cutting down a
Class let me show you a photo: tree.
What can you observed in the photo? Yes/No Ma’am.
That’s correct! And did you know that
an increase in demand for paper
contributes to the destruction of trees
from which papers are made? If waste
papers were recycled regularly, it
would help prevent cutting down of
trees and other adverse effects that
could destroy the environment.
So do you think the decrease in
production of paper contribute to the
decrease in the number of trees being
cut?
The question can be answered using
the concept of variation. So let us
familiarize ourselves to Direct
Variation through the following
examples.
Example 1:
The SSG of San Agustin National High
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
School launches a recycling campaign
of waste materials in order to raise
student’s awareness of environmental
protection and the effects of climate
change. This is in connection with the
celebration of Science Month. Every
kilogram of waste materials earns
points that can be exchanged for
school supplies. Paper, which is the
number one waste material collected, The number of points also
earns 6 points every kilo. doubled.
The table below shows the points
earned by Grade 9 Lavender class for
every number of kilograms of waste 100 kilograms
paper collected.
y=kx
Questions: Answers may vary.
1. What happens to the number of
points when the number of
kilograms of paper is doubled?
2. How many kilograms of papers will
the Grade 9 Lavender class have in
order to raise 600 points? Number of 1 2 3 4 5
3. What mathematical statement will Kilograms
relate the two quantities involved? (n)
4. In what way are you able to help Points (P) 6 1 1 2 3
clean the environment by collecting 2 8 4 0
these papers? What items can be
made out of these papers?
Class, there is a Direct Variation
whenever a situation produces pairs
of numbers in which their ratio is
constant.
The statements:
“ y varies directly as x”
“y is directly proportional to x”
“y is proportional to x” Yes Ma’am!
Are translated mathematically as
y=kx, where k is the constant of How many kilograms of papers
variation, x is the independent will the Grade 9 Lavender class
variable and y is the dependent have in order to raise 600 points?
variable.
For 2 quantities, x and y, an increase
in x causes an increase in y as well.
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Similarly, a decrease in x causes a
decrease in y. 6=k(1) Substitute the given
Did you understand? values.
k=6 6 is the constant of
So in the example given above, we variation
can solve for the number of Y=kx
kilograms needed to raise 600 points 600= 6(x)
by using the formula:
Y=kx
Let x be the number of kilograms X= 100kg will be needed to raise
Let y be the number of points 600 points.
Who can solve it on the board? Yes
_______.
Very good!
Using the formula, you can find the
number of kilograms without the aid Ma’am it also increases.
of the table.
Example 2:
Using his bicycle, Jericho travels a
distance of 10km/h on a steep road.
The table shows the distance he has
travelled at a particular length of
time: The answer is 80 km.
Time(h) 1 2 3 4 5
Distance(km 10 20 30 40 50
)
What happens to the distance as the
length of time increases? Yes
_________.
That’s correct.
Using this pattern how many
kilometres would he have travelled in
8 hrs?
Who can try to solve it on the board?
Yes ____.
Very good!
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Contact No.: 0917-6768-724 / Email Address: sanagustinnhs301651@gmail.com
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Example 3
If x varies directly as y and x = 35
when y = 7, what is the value of y
when x = 25
Solution 1.
Since x varies directly as y, then the
equation of variation is in the form x =
ky. Substitute the given values of y
and x to solve for k in the equation.
35=k(7)
K=
K=5
Hence, the equation of variation is x =
5y.
Solving for y when x = 25,
25 = 5y
Y=
Y=5
Hence, y=5.
G. Application
Now let us apply what you have
learned. We will have another group
activity. Each group will get a
cardboard with happy face in front and Yes Ma’am!
sad face at the back. I will post
statements on the screen, raise the (The students will go to their
smiley face if you identify it as direct group and form a circle.)
variation and sad face if not. You have
20 seconds to think and once you hear Yes Ma’am we are ready.
the buzz, raise your answer. You’ll get
one point for each correct answer. The 1.Sad Face
group who will gain the highest score
will be the winner and will receive a 2.Sad Face
prize. For those who receive printed
modules, they will have the same
activity but they have to work 3.Smiley Face
individually.
Are the instructions clear? 4.Sad Face
Alright, you may now go to your group 5.Smiley Face
and form a circle.
6.Smiley face
Are you ready class?
7.Sad Face
1. The number of hours to finish a job
to the number of men working 8.Smiley Face
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
2. The amount of water to the space
that water did not occupy in a 9.Sad Face
particular container
3. The area of the wall to the amount 10.Sad Face
of paint used to cover it
4. The time spent in walking to the
rate at which a person walks
5. The time a teacher spends Group ____
checking papers to the number of
students
6. The amount of money raised in a
concert to the number of tickets
sold
7. The age of a used car to its resale
value
8. The distance an airplane flies to the We have learned about direct
time travelling variation.
9. The number of visitors to the size
of chairs in the venue There is a direct variation
10. The number of persons typing a whenever a situation produces
manuscript to the time spent in pairs of numbers in which their
typing ratio is constant.
Who got the highest score?
Let’s give them Good job clap! Ma’am it also increases.
And for the rest of the group, give
yourselves five claps.
No Ma’am. Because we defined
H. Generalization earlier that direct variation
This time, let me ask what have you happens for two quantities x and y
learned in today’s lesson? where an increase in x causes an
increase in y as well. Similarly, a
How can we say that there is a direct decrease in x causes a decrease in
variation in a certain situation? y.
Very good! Yes Ma’am. That real life situation
is an example of direct variation.
When one variable increases, what
happens to the other variable?
That’s correct!
Can we say there is a direct variation (Students will share their insights.)
when a variable increases and the other
variable decreases? Why/ why not?
Address: San Agustin, Naujan, Oriental Mindoro, 5204
Contact No.: 0917-6768-724 / Email Address: sanagustinnhs301651@gmail.com
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Very well said!
Now, going back to the question we
have earlier, do you think the decrease
in production of paper contribute to the
decrease in the number of trees being
cut?
I. Valuing
Why do you think it is important to
learn direct variation? Is it essential to
our daily living?
Direct variation is always visible on
our lives. From the simplest things
that we do, to the most complicated
actions that we take. After we learned
the concept, we are now aware of the
consequences of our actions, like for
instance, if we do not help in recycling
papers, we are contributing to the
destruction of tress/ecosystem. Thus,
whenever we do good things, think
that it will also contribute to the
betterment of others.
Easy Round
IV. Evaluation
Quiz Bee
Mechanics: 1. F=kd
1.Write your answer on your 1/8
illustration board. 2. C=kw
2.For every correct answer on the
Easy Round, you’ll get 1 point. 3. S=kd
For the average round, you’ll
get 2 points. And for the difficult
round you’ll get 3 points. Average Round
3.20 seconds will be given to the
easy round, 30 seconds for the
average round and 60 seconds 1. Y=4x
for the difficult round 2. Y=8x
4.Record your own score, be
honest. Difficult Round
1. Y=1107 letters
Easy Round
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
Write the mathematical equation to
the following statements:
1. The fare F of a passenger varies
directly as the distance d of his
destination.
2. The cost C of fish varies directly as its
weight w in kilograms.
3. An employee’s salary S varies directly
as the number of days d he has
worked
Average Round
Write an equation where y varies
directly as x
1. Y=28 when x=7
2. y = 48 and x = 6
Yes, ma’am.
Difficult Round
1. A mailman can sort out 738 letters (L) None Ma’am.
in 6 hours (h). If the number of sorted
letters varies directly as the number of (The students will stand.)
working hours, how many letters can Goodbye Ma’am. Thank you for
be sorted out in 9 hours? teaching us.
V. Assignment
Do you remember the Parable of
Talents? What do you think God
expect us to do with the talents we
received? Now, complete the
statement of relationship.
The more talents you are given,
________________________________
.
Answer it on ¼ sheet of paper and
submit it on our next meeting.
Is the instruction clear?
Do you have any questions
regarding your assignment?
If there’s none, everybody stand!
Goodbye class!
Prepared by:
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lOMoARcPSD|15566548
Republic of the Philippines
Department of Education
MIMAROPA REGION
Schools Division of Oriental Mindoro
SAN AGUSTIN NATIONAL HIGH SCHOOL
SAN AGUSTIN, NAUJAN, ORIENTAL MINDORO
LIRALYN D. LEUTERIO
Teacher I
Address: San Agustin, Naujan, Oriental Mindoro, 5204
Contact No.: 0917-6768-724 / Email Address: sanagustinnhs301651@gmail.com
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