Detailed Lesson Plan
Learning Area:
Mathematics
Quarter:
Third
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.
I.
Learning Objectives:
At the end of the lesson, 75% of the students are expected to:
a. Illustrates situations that involve direct variation
b. Translates into variation statement a relationship between two quantities
given by a table of values,a mathematical equation, a graph and vice versa
c. Solve problems involving direct variations
II.
Content:
Topic:
Direct Variation
III.
Learning Resources:
References:
a. Learner’s Material in Mathematics 9, pp. 195-202
b. Learner’s Module (LM)- Mathematics Quarter 2: Week 1 Direct Variation
Materials:
a. PowerPoint Presentation, TV, Chalk and board
IV.
Teaching Procedure
Teacher’s Activity
A. PRELIMINARY ACTIVITIES
1. GREETINGS
Good Afternoon Class
Student’s Activity
Good Afternoon ma’am
2. CHECKING OF
ATTENDANCE
-Do we have absentees
today?
-Okay, very good
3. CLASSROOM RULES
- Before we go on to
our new lesson for
today. I want us to
have an agreement
for us to have a
harmonious and
organize flow of
discussion.
Here I have 5 rules
that you must and
mustn’t do inside our
class, understood?
1st rule- listen to the teacher
2nd rule – don’t sleep in class
3rd rule- don’t use your mobile
phones in class
4th rule -don’t stand up without
permission
And the last rule- raise your hand to
speak
Okay class,
understood?
B. ACTIVITY
-Before we discuss the
topic, I would like first
to test your prior
knowledge regarding
None ma’am!
Yes ma’am!
Yes ma’am!
the topic that I will
introduce afterwards. I
would like to know if
some or all of you has
some stock knowledge
on direct variation. So I
would like all of you to
bring out your
notebooks and try to
answer the following
questions that I’ll flash
on the screen.
Are you ready class?
Yes ma’am!
(Flash questions on the screen)
Are you done answering?
Okay class, let’s check.
And to make our checking fun, could
you please arrange your chairs
making sure that you can easily stand
and sit as fast as you can.
So for the direction, if I’ll clap once,
you must sit and if I’ll clap twice you
need to stand. Anyone whom I will
caught as the last one to stand or sit,
will be the one who’ll read and
answer the problem. Is that clear
class?
Okay for problem number 1.
Yes ma’am!
Yes ma’am!
(Clap, Clap Clap)
Okay Julius, please read and try to
answer.
Student will read problem #1:
A jeepney travels a distance of d km
in t hours. The equation that relates d
to t is d = kt. What kind of variation is
it? a. Direct
b.inverse
c.joint
d.combined
Expected Answer: A
Now for number 2
(Clap, Clap Clap)
Okay Sarah please read item number
2 and try to answer please.
Student will read problem #2:
Which of the following represents the
statement, an employee’s salary (s)
varies directly as the number of days
(d) he has worked? a. k = sd
𝑘
c. d = 𝑠
𝑘
b. s = 𝑑
d. s = kd
Expected Answer: D
Now for number 3
(Clap, Clap Clap)
Okay Jane please read item number
3 and try to answer please.
Student will read problem #3:
Which is an example of a direct
variation?
3
a. xi = 5 b. y = 𝑥
2
c. y = 4x d. 𝑦 = x
Expected Answer: C
And for number 4, be ready.
(Clap, Clap Clap)
Angel, please read the problem and
try to answer.
Student will read problem #4:
If y varies directly as x and y = 24
when x = 3, then k is _____.
a. 4 b. 6 c. 8 d. 10
Expected Answer: C
For item number 5, ready yourself
(Clap, Clap Clap)
All right Shane please read and
Student will read problem #5:
answer.
If y varies directly as x and y = 32
when x = 4. Find the constant of
variation.
a. 8 b. 36 c. 28 d. 128
Expected Answer: A
And for the last number…
(Clap, Clap Clap)
Okay Janella please read then try to
answer.
Student will read problem #6:
What mathematical statement
describes the graph below?
a. T = 10k
d. T = 10n
b. T = 10/n c. n = 10t
Expected Answer: D
All right class who got 6?5?4?3?2?1?
Students will raise their hands
according to their score.
Since majority of the class got scores
4, 5 and 6. I presume then that most
of you will easily follow our
discussion.
C. ABSTRACTION
So for today, we’ll be tackling
about Direct variation. So I
have here the definition of
Direct Variation, can anyone in
the class read the definition?
Student will read the slide.
Yes Miriam?
Thank you Miriam
It is stated there that it is a Direct
Variation when a quantity is equated
to a constant multiplied to other
quantity written in a mathematical
equation y=kx where k is our constant
of variation.
We can also read there the three
statements that tell us that
“ y varies directly as x”
“ y is directly proportional to x” and“
y is proportional to x”.
But what does this three mean?
Students’ answer may vary
Anyone?
Thank you for your answers, those
are mostly correct.
So basically, the three statements
mean that for two quantities, x and y,
an increase in x causes an increase in
y as well. Similarly, a decrease in x
causes a decrease in y.
Did you now understand direct
variation?
Very good!
D. ANALYSIS
To further understand Direct
Variation, let us try to analyze this
scenario.
Scenario:
Jello plans to buy rice out of
his own savings. He wants to
help his mother whose work
has been affected of the
community quarantine
implemented by the
Yes ma’am
government due to the
pandemic. The variety of rice
he decides to buy cost Php40 a
kilo. Let x be the number of
kilos and y be the cost of
rice.Complete the table below
showing the relationship
between the number of
kilos(x) of rice bought and the
total cost(y) of rice.
In the given scenario, what are our
quantities?
And what did you observe regarding
the two quantities?
Very good, now in the given table,
we can see that there are two missing
values. So in order for us to attain the
desired outcome, let us first get our k
which is our constant. And in order
to do that, may I ask what is our
mathematical equation regarding
direct variation?
Expected Answer:
Number of kilos(x) and Total cost (y)
ma’am
Expected Answer:
As the number of kilos(x) increases,
the total cost(y) also increases.
Expected Answer:
y=kx
Alright, from that equation let us
derive the formula for k. So we need
to divide both sides by x to cancel
out x and that would leave us the
formula for k which is k=y/x
Okay with that formula, let’s now get
the value of our constant of variation
(k). So in the given table, please give
me a pair of x and y?
(Discussion; refer to the attachment
Expected answer:
(1, 40), (2, 80), (3, 120)
below)
Students will respond
Did you understand class?
Okay, very good
E. APPLICATION
At some point, you might have asked
yourself why we need to study direct
variation? But the answer for that is
simple, it’s because direct variation
can be seen in real life situations.
With that example of mine, can you
tell me another real situation or
scenario that involves direct
variation?
F. EVALUATION
Now that you have a grasp on the
discussion and you’ve already
understand direct variation to the
point that you can easily relate it
to real life situations. And you’ve
told me a while ago that you’ve
understood our discussion on how
to find missing values. So I have
here a scenario and I want you to
answer the questions that follows.
Yes ma’am
Students’ answer may vary
Expected Answer:
1.
2. When time in hours (t) increases,
the distance in km (d) also increases.
Thus, expresses direct relationship.
3.
350
280
distance (d)
A great example of this is the
relationship between fuel and
distance travelled. So if you have lots
of fuel, therefore you can travel long
distance. Isn’t it?
210
140
70
0
0
1
2
3
4
5
6
𝑑
4. The ratio 𝑡 = 70 is constant
5. k=
d
t
70
k= 1
k= 70
6. d=70t
Congratulations everyone, your
scores shows how much you really
understood the discussion.
So before I bid my goodbye.
Please pick up any piece of paper or
trash under your chairs
Students will comply
Goodbye ma’am
Let’s call it a day, Goodbye class
D. REFLECTIONS
A. No. of students who earned
80% in the evaluation
B. No. of students who require
additional activities for
remediation
E. Which of my learning
strategies worked well? Why did
this work?
F. What difficulties did I
encounter which my principal or
C. Did the remedial lessons
work? No. of students who have
caught up with the lesson
D. No. of learners who continue
to require remediation
Cooperating teacher can help
me solve?
G. What innovation or localized
materials did I use/discover
which I wish to share with other
teachers?
Prepared By:
LOVELYN JOYCE A. MALAZZAB
FS Student
Checked By:
JOANA MARIE P. GALBIS
FS Cooperating Teacher
Approved By:
BERNADETTE E. GOROSPE PhD
Principal I
ATTACHMENT
Content: Transforming Quadratic Function from its standard form to its vertex form.
DISCUSSION
y=kx
Mathematical statement showing that “y
varies directly as x”
y/x=kx/x
Divide both sides by x to cancel out the
other x
k=y/x
Leaving us the formula for k
k=40/1
Substitute a value of x and y
k=40
Constant of variation
y=40x
Derived mathematical equation
PowerPoint Presentation