Student:
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Ratios and rates
Student Activity Sheet 2; use with Exploring “Direct variation”
1. You used your camera to take a close
up picture of a giraffe at the zoo. The
height of the picture and the giraffe
in the picture are both 3 inches. The
width of the picture is 4 inches.
a. How can you use a coordinate graph and the corresponding coordinate pairs to find
the dimensions of a picture that is proportional to the original?
b. List the dimensions of at least three pictures that are proportional to the original
image. Determine at least one picture that has a dimension that is not a whole
number.
2. In the giraffe photo situation, the height (y) equals the constant of proportionality,
times the width (x):
y=
3
,
4
3
•x.
4
The camera shop makes pictures into posters with a width of 12 inches. How tall will the
giraffe be in the poster?
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Student Activity Sheet 2; use with Exploring “Direct variation”
3. The photograph is 4 inches wide and represents 16 feet in actual distance. In the
photograph, the height of the giraffe is 3 inches. Write an equation that determines the
actual height of the giraffe.
4. R
REEIINNFFOORRCCEE If the actual height of a giraffe
15 feet, what is the distance represented
the width of the photo?
is
by
5. R
REEIINNFFOORRCCEE In a different photograph of a 12-foot-tall giraffe, the width of the scene
covers 15 feet. If the height of the giraffe in the picture measures 4 inches, how wide is
the photograph?
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Student Activity Sheet 2; use with Exploring “Direct variation”
6. Consider the illustration showing a naturalist using a scope to view an animal.
a. Write a proportion that you can use to determine the giraffe’s actual height.
b. Find the ratio of the diameter of the end of the scope to the length of the tube.
c. Using this constant of proportionality, what is the height of the giraffe?
Copyright 2012 Agile Mind, Inc. ®
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Center, The University of Texas at Austin
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Student Activity Sheet 2; use with Exploring “Direct variation”
7. The dimensions of different scopes are given. The variable a represents the diameter of
the scope, and b represents the length of the scope. Fill in the values for the variables c
and d, the height of the animal and the distance of the naturalist from the animal.
Scope 1:
a = 2 inches
b = 5 inches
d=
feet
c=
feet
Scope 2:
a = 2 inches
b = 10 inches
d=
feet
c=
feet
Scope 3:
a = 4 inches
b = 5 inches
d=
feet
c=
feet
Scope 4:
a = 4 inches
b = 10 inches
d=
feet
c=
feet
Scope 5:
a = 1 inches
b = 7 inches
d=
feet
c=
feet
Scope 6:
a = 2 inches
b = 7 inches
d=
feet
c=
feet
Copyright 2012 Agile Mind, Inc. ®
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Center, The University of Texas at Austin
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Student Activity Sheet 2; use with Exploring “Direct variation”
Now that you have had a chance to see the results of using scopes of different dimensions,
try solving these problems.
8. You are standing 120 feet away from an animal. Looking through scope Type A, the
animal's image fills the scope's opening exactly. Explain what you need to do to look
through a Type B scope and see the full image of the same animal fill the opening of that
scope.
9. You are standing 60 feet away from an animal. Looking through scope Type D, the
animal's image fills the scope's opening exactly. Explain what you need to do to look
through a Type A scope and see the full image of the same animal fill the opening of that
scope.
Copyright 2012 Agile Mind, Inc. ®
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Center, The University of Texas at Austin
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Student Activity Sheet 2; use with Exploring “Direct variation”
10. You are standing 120 feet away from an animal. Looking through scope Type C, the
animal's image fills the scope's opening exactly. Exactly where would you need to stand
to see the full image of the same animal fill the opening of the Type A scope?
11.R
REEIINNFFOORRCCEE You have four different-sized scopes, as shown. You are standing 50 feet
away from an animal. Looking through Scope 1, the animal's image fills the scope's
opening exactly.
a. Explain what you need to do to look through Scope 2 and see the full image of the
same animal fill the opening of that scope.
b. Explain what you need to do to look through Scope 4 and see the full image of the
same animal fill the opening of that scope.
Copyright 2012 Agile Mind, Inc. ®
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Student Activity Sheet 2; use with Exploring “Direct variation”
c. Suppose you have a Scope 5 that is 3 times as long as Scope 1 and the diameter of the
opening of Scope 5 is twice the diameter of Scope 1. Exactly where would you need to
stand to see the full image of the same animal fill the opening of Scope 5?
12.R
REEIINNFFOORRCCEE You have a calibration scope and you sight a giraffe in the distance. The
image of the giraffe fills your view. Determine the missing values for each sighting below
if a inches is the diameter of your scope, b inches is the length of your scope, c feet is
the height of the giraffe and d feet is the distance you are standing from the giraffe.
Sighting 1:
a = 2 inches
b = 7 inches
c = 12 feet
Sighting 2:
a = 3 inches
b = 8 inches
c=
Sighting 3:
a = 4 inches
b=
Sighting 4:
a=
Sighting 5:
Sighting 6:
feet
d = 33 feet
inches b = 7 inches
c = 14 feet
d = 56 feet
a = 2 inches
b = 9 inches
c = 11 feet
d=
a = 3 inches
b = 9 inches
c=
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feet
feet
d = 42 feet
c = 11 feet
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
inches
d=
d = 48 feet
feet
Student:
Class:
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Ratios and rates
Student Activity Sheet 2; use with Exploring “Direct variation”
13. Some tourists are on safari on an African
plain. There is an elephant standing still on
the other side of the river. The current of
the river is swift and they cannot cross it.
They have some scopes of different lengths
and diameters. They would like to
determine the height of the elephant.
Since you don’t know the actual
distance across the river, you need to
use more than one scope. Use a
method that involves using two
related scopes, scope Type A and
scope Type D. Type D has the same
length as Type A, but twice the
diameter.
Remember, when we used the Type A
scope, we had to be twice the
distance from the animals as when we
used the Type D scope.
Choose a length and diameter for the Type A scope and explain how you can accurately
determine the elephant's height.
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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