G9 variation

Specific Objectives:
1. Identify the practical
situations involving direct
variation.
2. Illustrates and translates
variation into mathematical

3. Appreciates the
importance of direct
variation in real life.

Reviewing previous
lesson or presenting
the new lesson

The longer
you shower,
the more
water you
use.

The more
water you
consumed,
the higher
the amount
you pay.

The more
hours you
play online
games, the
bigger
amount you

Establishing a
purpose for the
lesson

Strategy Used: TCP (THINK-
COMPLETE-PAIR).
Complete the statement below.
1. The more entries in a certain
raffle, the more
___________________.
2. The more water you consumed,

3. The less time you study your
lesson, the ____________________.
4. The more time I drive (at a
constant rate), the
________________.
5. The more hours you play online
games, the __________________.

Presenting
examples/instances of
the new lesson

Activity 1:
If a kilo of rice
cost 53 pesos, 106 pesos
for 2 kilos, and 159
pesos for 3 kilos.

Complete the table below:
No. of Kg of rice
(x)
1 2 3 4 5
Total Cost (y)

Questions:
1.What happens to the cost as
the length of the number of
kilogram of rice increases?
2. Using this pattern, how much
is the cost of 8 kg.?

3. How will you be able to find
the cost without the aid of the
table?
Write a mathematical statement
to represent the statement.
4. Does the change in one
quantity affect a change in the

Discussing new
concepts and
practicing new skills

There is 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” and
“y is proportional to x

are translated mathematically as
y = kx , where k is the constant of
variation.
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.
There are other direct
variations of the form y = kx as
in the case of
y = kx2. The graph is not a line
but a parabola.

Newton’s Law of Cooling states
that the rate of change (R) of the
temperature of an object is
proportional to the difference
between the temperature (T) of the
object and the temperature (t) of
the environment in which the

Write a mathematical statement to
represent the relation.
Mathematical Equation:
R = k(T-t)
*Across the curriculum

Making
generalizations and
abstractions about the
lesson

YOU COMPLETE ME!
There is direct variation
whenever a situation produces
pairs of numbers in which
their __________ is constant.

The statements:
“y varies ____________as x”
“y is ______________
proportional to x” and
“y is _______________ to x”

are translated mathematically as
_________________ , where k is
the ________________ of variation.
For two quantities x and y, an
increase in x causes an
____________ in y as well.

Similarly, a ____________
in x causes a decrease in
y.

Finding practical
applications of
concepts and skills in
daily living

Junk shops pay Php 15.00 for
every kilo of tin cans bought
from collectors. In the
following table,
c is the cost in peso and n is the
number of kilos of tin cans:

n 1 2 3 4 5 6
c 15 30 45 60 75 90

Write a mathematical statement
that relates the two quantities n
and c.
Observe the values of n and c in
the table. What happens to the
cost c when the number n of
kilos of cans is doubled?

Give the mathematical
translation of the following
situations.
1. The length L if a person’s
shadow at a given time
varies directly as the height

2. The kinetic energy K
exerted by a body is directly
proportional to its mass (m).

3. The volume V of a cylinder
varies directly as its height h.
4. The weight W of an object is
directly proportional to its mass
m.
5. The area A of a triangle is
proportional to its height h.

G9 variation

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