Direct Variation Lesson for Math 9

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Detailed Lesson Plan MATH 9
BS Secondary Education (Mindoro State College of Agriculture and Technology)
Studocu is not sponsored or endorsed by any college or university
Detailed Lesson Plan MATH 9
BS Secondary Education (Mindoro State College of Agriculture and Technology)
Downloaded by Cleofe Tomas-Undo (clayowfaiye@gmail.com)
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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.
_______, kindly lead the prayer.
(Students will stand.)
(Let us bow our heads and feel the
presence of our ALMIGHTY GOD. In
Address: San Agustin, Naujan, Oriental Mindoro, 5204
Contact No.: 0917-6768-724 / Email Address: sanagustinnhs301651@gmail.com
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2. Greetings
Good morning class! How are you
today? That is good to hear.
3. Classroom Management
Class, before you take your seats,
kindly pick up the pieces of papers
or plastics around you and arrange
your chairs silently and properly.
You may now take your seats.
4. Checking of Attendance
_______, is everyone present
today?
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.
Here is a problem and let me ask one
volunteer to solve it. Yes ________.
Problem:
From a 96-foot building, an object is
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 name of the Father, and of the
Son, and of the Holy
Spirit…..AMEN)
Good morning, Ma’am! We are
feeling great Ma’am!
(Students will pick up the pieces
of papers or plastics around them
and arrange their chairs silently
and properly.)
Thank you Ma’am.
Yes Ma’am except those in
different learning modality.
(One volunteer student will solve
the problem on the board and
others will answer on their
papers.)
Solution:
The vertex is ( , 100) thus the
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reach?
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
related quantities. Paste the pictures
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
Wall and Paint
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.
Yes Ma’am
None Ma’am
(Possible answers)
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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Group 2
Groceries and Money
Group 3
Nature of Activity and Heartbeat
Group 4
Speed and Distance
Group 5
Hard work and
The more money you have, the
more groceries you can buy.
The less money you have, the less
groceries you can buy.
Doing more activities can result to
higher pulse rate.
Doing less activities can result to
lower pulse rate.
The faster speed you go, the
longer distance you can reach.
The slower speed you go, the
shorter distance you can reach.
The more hard work you do, the
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Success
Do you like the activity class?
Before you go back to your seats, let’s
form a word using this equation of
pictures.
D. Presentation of the Lesson
Class, from the activity you had a while ago,
what do you think will be our lesson for this
day?
Yes, ______________________.
Good job!
E. Presentation of Objectives
Before we start our discussion, you need to
know first what you should accomplish at the
end of the lesson.
more chance you can be
successful.
The less hard work you do, the
less chance you can be successful.
Yes Ma’am!
Direct Variation!
I think our lesson for today is
about Direct Variation.
At the end of the lesson, the learners
must be able to:
a. Illustrates situations that
involve direct variation
b. Translate into variation
statements a relationship
involving direct variation
c. Solve problems involving
direct variation as a means
of valuing the concept in
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Okay, kindly read the objectives.
Yes ________.
F. Discussion
The activity earlier is connected to the
topic we have today.
Class let me show you a photo:
What can you observed in the photo?
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
real-life situation
There is a man cutting down a
tree.
Yes/No Ma’am.
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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,
earns 6 points every kilo.
The table below shows the points
earned by Grade 9 Lavender class for
every number of kilograms of waste
paper collected.
Questions:
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?
3. What mathematical statement will
relate the two quantities involved?
4. In what way are you able to help
clean the environment by collecting
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”
Are translated mathematically as
y=kx, where k is the constant of
variation, x is the independent
variable and y is the dependent
variable.
For 2 quantities, x and y, an increase
in x causes an increase in y as well.
The number of points also
doubled.
100 kilograms
y=kx
Answers may vary.
Yes Ma’am!
How many kilograms of papers
will the Grade 9 Lavender class
have in order to raise 600 points?
Number of
Kilograms
(n)
1 2 3 4 5
Points (P) 6 1
2
1
8
2
4
3
0
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Similarly, a decrease in x causes a
decrease in y.
Did you understand?
So in the example given above, we
can solve for the number of
kilograms needed to raise 600 points
by using the formula:
Y=kx
Let x be the number of kilograms
Let y be the number of points
Who can solve it on the board? Yes
_______.
Very good!
Using the formula, you can find the
number of kilograms without the aid
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:
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!
6=k(1) Substitute the given
values.
k=6 6 is the constant of
variation
Y=kx
600= 6(x)
X= 100kg will be needed to raise
600 points.
Ma’am it also increases.
The answer is 80 km.
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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
sad face at the back. I will post
statements on the screen, raise the
smiley face if you identify it as direct
variation and sad face if not. You have
20 seconds to think and once you hear
the buzz, raise your answer. You’ll get
one point for each correct answer. The
group who will gain the highest score
will be the winner and will receive a
prize. For those who receive printed
modules, they will have the same
activity but they have to work
individually.
Are the instructions clear?
Alright, you may now go to your group
and form a circle.
Are you ready class?
1. The number of hours to finish a job
to the number of men working
Yes Ma’am!
(The students will go to their
group and form a circle.)
Yes Ma’am we are ready.
1.Sad Face
2.Sad Face
3.Smiley Face
4.Sad Face
5.Smiley Face
6.Smiley face
7.Sad Face
8.Smiley Face
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2. The amount of water to the space
that water did not occupy in a
particular container
3. The area of the wall to the amount
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
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
time travelling
9. The number of visitors to the size
of chairs in the venue
10. The number of persons typing a
manuscript to the time spent in
typing
Who got the highest score?
Let’s give them Good job clap!
And for the rest of the group, give
yourselves five claps.
H. Generalization
This time, let me ask what have you
learned in today’s lesson?
How can we say that there is a direct
variation in a certain situation?
Very good!
When one variable increases, what
happens to the other variable?
That’s correct!
Can we say there is a direct variation
when a variable increases and the other
variable decreases? Why/ why not?
9.Sad Face
10.Sad Face
Group ____
We have learned about direct
variation.
There is a direct variation
whenever a situation produces
pairs of numbers in which their
ratio is constant.
Ma’am it also increases.
No Ma’am. Because we defined
earlier that direct variation
happens for two quantities x and y
where an increase in x causes an
increase in y as well. Similarly, a
decrease in x causes a decrease in
y.
Yes Ma’am. That real life situation
is an example of direct variation.
(Students will share their insights.)
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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.
IV. Evaluation
Quiz Bee
Mechanics:
1.Write your answer on your 1/8
illustration board.
2.For every correct answer on the
Easy Round, you’ll get 1 point.
For the average round, you’ll
get 2 points. And for the difficult
round you’ll get 3 points.
3.20 seconds will be given to the
easy round, 30 seconds for the
average round and 60 seconds
for the difficult round
4.Record your own score, be
honest.
Easy Round
Easy Round
1. F=kd
2. C=kw
3. S=kd
Average Round
1. Y=4x
2. Y=8x
Difficult Round
1. Y=1107 letters
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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
Difficult Round
1. A mailman can sort out 738 letters (L)
in 6 hours (h). If the number of sorted
letters varies directly as the number of
working hours, how many letters can
be sorted out in 9 hours?
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!
Yes, ma’am.
None Ma’am.
(The students will stand.)
Goodbye Ma’am. Thank you for
teaching us.
Prepared by:
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LIRALYN D. LEUTERIO
Teacher I
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