Mathematics Activity Sheet Quarter 2 - MELC 1: Illustrating Situations That Involves Variations
Mathematics Activity Sheet Quarter 2 - MELC 1: Illustrating Situations That Involves Variations
Mathematics Activity Sheet Quarter 2 - MELC 1: Illustrating Situations That Involves Variations
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This Learning Activity Sheet is developed by DepEd Region 6 – Western
Visayas.
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Introductory Message
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Quarter 2, Week 1
• The learner illustrates situations that involve the following variations: (a) direct;
(b) inverse; (c) joint; (d) combined. (M9AL-IIa-1)
This Learning Activity Sheet is about variations. You will find out the relation
between quantities. You will also learn how a change in one quantity could correspond
to a predictable change in the other. In this lesson, you will be able to illustrate
situations that involve direct, inverse, joint and combined variation.
A. Direct Variation
There are situations in real life which illustrates direct variation. Both variables
in the situation produces the same changes.
Examples:
Points (P) 5 10 15 20 25 30
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This situation clearly illustrates an idea of direct variation between two
quantities. The higher the number of kilograms, the higher the points to be
earned. The points vary directly to the number of kilograms or points and
number of kilograms illustrates direct variation.
2. Helen and Joana walk a distance of one kilometer in going to the school where
they teach. At a constant rate, it takes them 20 minutes to reach the school in
time for their first class. One morning, the two became so engrossed to discuss
an incident that happened inside the school that they did not notice that their
pace of walking slowed down.
Questions:
a. How will they be able to catch up for the lost number of minutes? Cite solutions.
b. How are the quantities like rate, time, and distance considered in travelling?
c. Does the change in one quantity affect the change in others? Explain.
This situation illustrates a direct variation with two pairs of variables: time and
distance, and distance and rate. As time increases, the distance also increases; and
as rate decreases, distance also decreases.
B. Inverse Variation
Examples:
1. A rectangle has a width (w) of 2 cm and a length (l) of 18 cm. Keeping its area
(36cm2) constant, what happens when the width is increased to 3cm? 4cm?
The table below shows the relation between the length and the width of the
rectangle given a constant area.
Width (w) 2 3 4 5
Length (l) 18 12 9 7.2
Area (A) 36 36 36 36
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2. Anna lives 40 km away from the office of ABC Corporation where she works.
Driving a car, the time it takes her to reach her workplace depends on the car’s
average speed. Some possible speeds and the lengths of time it takes her are
as follows:
Time in hours 1 4 2 4 1
5 3 7 2
Speed in kph 40 50 60 70 80
The situation illustrates an inverse variation. The speed varies inversely as its
time. As time decrease the speed increases.
C. Joint Variation
This lesson deals with another concept of variation, the joint variation. Some
physical relationships, such as area or volume, may involve three or more variables
simultaneously.
Joint variation is closely the same with direct variation, but joint variation
involves 3 or more variables.
Statement a varies jointly as b and c means a = kbc, or k=abc, where k is the
constant of variation.
There are statements which compose of 3 or more variables that illustrates a
joint variation.
EXAMPLES:
1. The area of a triangle varies jointly as its base and its altitude.
The statement illustrates joint variation. It involves three variables which are area,
base, and altitude.
2. The volume of a pyramid varies jointly as the area of the base and the altitude.
The statement illustrates joint variation. It involves three variables which are
volume, base, and altitude.
D. Combined Variation
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Examples of statements that illustrate combined variations:
1. The electrical resistance of a wire varies directly as its length and inversely as
the square of its diameter.
2. The maximum load of a beam varies directly as the breadth and the square of
the depth and inversely as the length.
1. Directions / Instructions:
For further information about this lesson, please refer to Mathematics Learner’s
Material pages 194 - 220, Intermediate Algebra textbook pages 101 – 112.
2. Exercises / Activities
Exercise 1:
Direction: State the variation being illustrated in the given situation.
1. The current varies directly as the electromotive force and inversely as the
resistance.
2. The amount of gasoline used by a car varies jointly as the distance travelled
and the square root of the speed.
3. The number of persons sharing a pie to the number of slices of the pie.
4. The volume of a right circular cylinder varies jointly as the height and the
square of the radius.
5. The number of hours to finish a job to the number of men working.
Exercise 2:
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3. Guide Questions
4. Rubrics
SCORE DESCRIPTION
5 The illustrated situation demonstrates a thorough
understanding of the topic and the idea was clearly
presented.
4 The illustrated situation demonstrates a satisfactory
understanding of the topic and the idea was clearly
presented.
3 The illustrated situation demonstrates a satisfactory
understanding of the topic and the idea was not clearly
presented.
2 The illustrated situation demonstrates a incomplete
understanding of the topic and the idea was not clearly
presented.
1 Show lack of understanding of the topic.
V. Reflection
Complete the statement.
I have learned that_______________________________________________
___________________________________________________________________.
I have realized that _____________________________________________
___________________________________________________________________.
I will apply _________________________________________________________________
_________________________________________________________________________________.
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V. Answer Key