SCALE CITY
The Road to Propor tional Reasonin
g:
Sky-Vue Drive-In Lesson
TABLE OF CONTENTS
Click on a title to go directly to the page. You also can click on web addresses to
link to external web sites.
Overview of Lesson
Including Kentucky Standards Addressed............................................................2
Instructional Strategies and Activities
• Day One: Hands-On Activities Involving Shadows
and Indirect Proportions .................................................................................... 3-5
• Day Two: Performance, Open Response, and
Multiple Choice Assessments............................................................................... 6
Writing for the Lesson ................................................................................... 7
Adaptations for Diverse Learners/Lesson Extensions ...................... 8-9
• Shadow Puppet Performance
Applications Across the Curriculum .........................................................9
Extension ............................................................................................................9-10
Performance Assessment ............................................................................ 11
Open Response Assessment ....................................................................... 12
Multiple Choice Assessment ...................................................................... 13-15
SKY-VUE DRIVE-IN: Inverse Proportions
SKY-VUE DRIVE-IN: INVERSE PROPORTIONS
Grades 6-8
Essential
Question:
Length:
1-2 days
What is the difference
between inverse and
direct proportions?
Materials
light bulb on a lamp
without a shade or
classroom movie
projector
measuring tape, rulers
1 large sheet bulletin
board paper or large
dry erase board
markers
Concept/Objectives:
Students will develop an
understanding of inverse
proportions and methods
of calculating inverse
proportions. Students
will distinguish the differences between direct
proportions and inverse
proportions.
Activity:
Students will observe the
relationship of shadow
size relative to the distance from a light source
such as a flashlight or
projector. Students will
view a video, explore a
computer model, and
participate in a simple
classroom experiment to
explore the concept of inverse proportion. Students
will solve problems using
proportional reasoning
and related mathematical
skills.
Resources Used in This
Lesson Plan:
Scale City Video:
Greetings from the
Sky-Vue Drive-In
Online Interactive:
Drive-In Shadow
Puppets
Assessments (included
in this lesson)
Classroom Handouts
(PDFs)
All resources
available at
www.scalecity.org
Technology
computer
computer projector
Internet connection
computer lab for
individual or paired
exploration
overhead projector
calculators
Vocabulary
constant (k)
direct proportion
inverse proportion
inverse relationship
ratio and different
methods of expressing ratio (1:4, 1/4 and
1 to 4)
scale
scale factor
variables (x and y)
Instructional Strategies and Activities
NOTE TO TEACHER:
You may want to send an email to parents to let them know about the Scale City
web site and encourage them to have their children access the site at home for
additional practice.
Sample email to parents:
Our mathematics class is studying inverse proportions. This concept is important in
algebraic thinking and mathematical reasoning. Kentucky Educational Television has
created a web resource with videos, interactive exercises, and other resources to help
students explore this concept.
We will be using this web site in class instruction. Your child may also access the site
www.scalecitiy.org from home for additional practice.
Sincerely,
Teacher
SKY-VUE DRIVE-IN: Inverse Proportions 2
DAY ONE: HANDS-ON ACTIVITIES INVOLVING
SHADOWS AND DIRECT PROPORTIONS
TEACHING TIP:
This lesson explores how an object’s distance from a projector or some similar
light source affects the size of its projected shadow on a wall or screen. In
contrast, the lesson and interactive for “Greetings from the Louisville Slugger
Museum” explore how to determine an unknown height outdoors using the
shadows cast by the sun. If questions come up or if you think your students are
confused, you may want to discuss the differences between these two types of
shadows. When a shadow comes from a light source such as a strong flashlight,
overhead, or computer projector, the distance from the light source is critical.
However, shadows outside on a sunny day are not related to distance—we’re not
farther from the sun at 11:00 am or 1:00 pm when our shadows are short nor
are we closer when they are long. Instead, it is the angle of the sun that alters the
size of these shadows.
Before the Lesson
Before class, arrange for a classroom wall projector, lamp, or strong flashlight to be
placed in a stationary position opposite a wall. Make sure the angle of the light
produces shadows of measurable heights. Measure the distance between the light
and the wall. Place a chalk mark on the floor close to the projector where a person
might stand to create a very large shadow on the wall. Double the distance from the
light and place another mark. Triple the original distance and place a third mark.
Quadruple the original distance from the light to place a fourth mark.
If you can direct the light to shine toward a white board, you’ll be able to mark
directly on the board to measure shadows. Otherwise, post a large piece of white
bulletin board paper or butcher’s paper on the wall. Provide markers for student use.
Equations
x/y = k where x and y are
two related variables
and k is a constant
(direct proportion)
x • y = k where x and y
are two related
variables and k is a
constant
(inverse proportion)
Kentucky
Academic
Expectations
2.7
2.8
2.12
Kentucky
Program of
Studies
Grade 6
MA-6-NPO-U-4
MA-6-NPO-S-NO3
MA-6-NPO-S-RP3
Grade 7
MA-7-NPO-U-4
MA-7-NPO-S-RP2
MA-7-NPO-S-RP3
Grade 8
MA-8-NPO-U-4
MA-8-NPO-S-RP1
1. Post these questions on the board:
• How is the height of a person’s shadow affected as he or she moves farther
from
the light source?
• How could you use mathematical evidence to support your answer?
2. With the projector set up as described in “Before the Lesson” above, call students
up two at a time. As one student poses at each of the four marks, his or her partner
will mark and label the height of the resulting shadow. As students experiment with
SKY-VUE DRIVE-IN: Inverse Proportions 3
3. Discuss students’ responses to the activity.
4. Use an Internet projector to watch the “Greetings from Sky-Vue Drive-In” video at
www.scalecity.org.
5. Use the Internet projector to explore the online interactive simulation, “Drive-In
Kentucky Core
Content for
Assessment 4.1
Grade 6
MA-06-1.3.2
MA-06-1.4.1
Grade 7
MA-07-1.3.2
MA-07-1.4.1
Grade 8
MA-08-1.3.2
MA-08-1.4.1
MA-08-5.1.5
© KET, 2009
Shadow Puppets,” at www.scalecity.org. This activity allows students to see how shadows are influenced by distance from the projector light. You can use “Handout 1: Scale
City Drive-In Projector Shadows” so students can fill in the blanks and do the calculations as you work on the problem. If you use the handout, initially have students
complete only the y values in the table.
Review the term proportion. Remind them that a proportion is two equivalent ratios
or fractions. All the proportions that they may have encountered in the earlier interactives are direct proportions. In a direct proportion, as one variable increases, another
variable increases, and the value of each ratio or fraction is a constant (k). So, 10/5 =
20/10, and the value of both ratios is 2.
After examining the pattern, students will explore how inverse proportions are calculated. Questions to consider:
• How does the distance from the light influence the height of the shadow? The
farther the figure is from the light source, the shorter the shadow.
• Jax is half as tall as Kelli. How does the height of the shadows reflect this? How
much taller is Kelli than Lily? (6 ÷ 5 = 1.2) How do the shadows reflect this? Jax’s
shadow is also half as tall as Kelli’s at the same distances. And Kelli’s shadow is 1.2
times as tall as Lily’s at the same distance.
• Where would the graph of the shadow of a seven-foot basketball player be
relative to the other graphs? Of a mouse? Of a 12-foot dinosaur? (The basketball
player’s would be above Kelli’s, curving in a similar way. The mouse’s curve would be
considerably under Jax’s, since a mouse is only an inch or two high. The dinosaur’s
curve would be above the basketball player’s.)
• The basketball player is a foot taller than Kelli, just as Kelli is a foot taller than
Lily. But he is only 1.17 times taller than Kelli, not 1.2 times taller. Why? The dinosaur is double Kelli’s height, so how would his shadow compare to hers?
How would the dinosaur’s shadow compare to Lily’s?
• How would you describe the shape of this graph of inverse proportions? Why
might other graphs of inverse proportions also look like this? (As x increases, y
decreases. As y increases, x decreases.)
• Why is neither value ever equal to 0? (The product of x times y always equals the
same constant, k, and k is never equal to zero.)
• Would you expect a graph of a direct proportion to look like the graph of the
inverse proportion? If your students haven’t seen a graph of a direct proportion, you
might sketch a simple one for them on the overhead or whiteboard, so they can see
that it would be a straight line going through the point of origin.
6. Discuss how direct proportions are solved through equivalent fractions. Inverse
proportions are the inverse of division, that is, multiplication. A proportion is represented by x/y equals k. An inverse proportion is such that x • y is equal to k. (Algebra
students can manipulate these equations, i.e., direct proportion: y • k = x, k/x = 1/y
and inverse proportion: k/x = y, k/y = x, etc.) Use the online interactive graph table
to examine if x times y equals a constant number in each column. If not, check the
answers and discuss how measurement issues can influence numbers.
SKY-VUE DRIVE-IN: Inverse Proportions 4
7. Give students additional practice with the concept of two variables being
inversely proportional by having them complete charts beginning with
x = 32, y = 2 and k = 64. The numbers in bold should be completed
by students.
x
y
k
32
2
64
16
4
64
8
8
64
4
16
64
2
32
64
Ask students, what happens to y as x gets larger? As x gets smaller?
Another example for student practice with the x times y concept begins with x = 5, y = 20 and k = 100.
x
y
k
5
20
100
10
10
100
15
6 2/3
100
20
5
100
25
4
100
8. Assign the practice problem for discussion and/or group work. “Handout 2: Shadow Math: Inverse Proportion”
is in a multiple-choice format. If you’d prefer to have students work on the concept differently, use only the sample
problem. The underlined values should be calculated as part of the class exercise.
Practice problem
A teacher set up a demonstration using a classroom movie projector and a 4-inch doll. The shadow of the doll was
measured as the doll was moved in a straight line from the light.
x (doll’s distance from light)
y (height of doll’s shadow)
15 inches
17 inches
20 inches
12 3/4 inches or 12.75
25 inches
10.2 inches
30 inches
8 1/2 inches or 8.5
35 inches
7.2857 inches
40 inches
6.375 inches or 6 3/8
Questions for discussion:
• What are the values for the height of the shadow at 20 and 30 inches?
• When x is doubled, how is y influenced?
• What kind of relationship is happening between the x and the y?
• What is the constant?
• How would we express this relationship using variables?
• Given the data on the chart above, do you have enough information to calculate other values for y given
x values between 15 and 40?
9. Assign “Handout 3: Practice Problems” for homework or class work.
SKY-VUE DRIVE-IN: Inverse Proportions 5
DAY TWO: PERFORMANCE, OPEN RESPONSE,
AND MULTIPLE CHOICE ASSESSMENTS
NOTE TO TEACHER:
There are a variety of activities you could use on Day Two. Below is a brief
explanation of three possible choices to introduce individually or in combination.
Project/Performance Assessment (see page 11)
Using a projector and an understanding of inverse proportion, students create silhouettes of one another’s profiles.
Open Response (see page 12 )
Students observe and describe what happens to width as the length increases as they calculate various combinations of
the square feet of a given area.
KEY for Open Response
Mary and her family want to plant a big vegetable garden in their backyard. They want the garden to have an area of
120 square feet.
Length
Width
Area
30
20
15
10
5
4
6
8
12
24
120 ft2
120 ft2
120 ft2
120 ft2
120 ft2
A. Fill in the table with five different possibilities for the dimensions of the garden. See one possibility above. There are
many correct answers.
B. As the length increases, what happens to the width? The width decreases as the length increases.
C. Explain the relationship that exists between the length and the width. The length and width of the garden are inversely proportional. As one increases, the other decreases, but their product—the area of the garden—remains constant, so x • y =
k.
Multiple-Choice Assessment (see pages 13-15 )
Fifteen questions formally assess concepts related to direct and inverse proportion.
Key to Multiple-Choice Assessment
1. B, 2. A, 3. D, 4. D, 5. B, 6. D, 7. A, 8. C, 9. C, 10. B, 11. A,12. C,13. B, 14. C, 15. B
SKY-VUE DRIVE-IN: Inverse Proportions 6
Writing for the Lesson
A swimming pool membership is $180 per family for the summer. The more
frequently the family uses the pool, the less they spend per visit.
A. Complete the following chart:
Name of Family
Smith
Jones
Miller
Lee
Stuart
Number of
Times Used
60
45
30
15
10
Cost Per Use
Cost of
Membership
B. Describe how this is an inverse proportion using examples from the chart. What is the constant?
C. Caleb Stuart’s family is thinking about not buying a membership again; however, Caleb wants his family to buy a
membership. The cost for his family to go to the pool one time is $20 with no membership. Last year, the Stuarts went
to the pool ten times. Write a persuasive e-mail from Caleb’s perspective to his parents. Use math for support.
KEY for “Writing for the Lesson”
A. Complete the following chart:
Name of Family
Smith
Jones
Miller
Lee
Stuart
Number of
Times Used
60
45
30
15
10
Cost Per Use
3
4
6
12
18
Cost of
Membership
180
180
180
180
180
B. Describe how this is an inverse proportion using examples from the chart. What is the constant?
The membership fee is a constant $180. The cost per use is determined by dividing the membership by the number of times the
pass is used. The relationship of use and cost per use is an inverse proportion. The more times the pass is used, the less the cost
per use of the pass.
C. Caleb Stuart’s family is thinking about not buying a membership again; however, Caleb wants his family to buy a
membership. The cost for his family to go to the pool one time is $20 with no membership. Last year, the Stuarts went
to the pool ten times. Write a persuasive e-mail from Caleb’s perspective to his parents. Use math for support.
The e-mail should include the fact that Caleb Stuart’s family saved $20 by purchasing a pool membership. Caleb may argue
that he would like the option of going more times to the pool and a pool membership would increase the economic feasibility
of this.
SKY-VUE DRIVE-IN: Inverse Proportions 7
Adaptations for Diverse Learners/
Lesson Extensions
Use construction paper and craft sticks to create simple shadow puppets of a
dragon, plant, and a rabbit. The rabbit and the dragon should be the same size.
Students may create more scenery (forest, rocks, owl) to enhance the background.
Set up a flashlight or movie projector with a screen. As students listen to the
following story, have them move their figures closer and further from the light source to match the size of the characters in the story. Practice several times before giving a performance. Students might enjoy performing the puppet show
for younger children to help them begin to understand inverse proportions.
“The Dragon and the Bunny”
Once upon a time there was a tiny dragon. He was walking through the forest when he spied a green vegetable
growing at the edge of the forest. The dragon began to eat, but since he didn’t like healthy food, he ate very little.
The green vegetable was a magic growing plant, and even though the dragon didn’t eat very much, he started getting
bigger and bigger. The dragon was now a big dragon twice his original size.
Along came a teeny, tiny little rabbit. The rabbit was afraid of the enormous, ferocious dragon and was shaking all
over. The rabbit crouched down to hide and saw the last of the magic growing plant. The rabbit nibbled and nibbled.
(Rabbits love to eat green vegetables.)
When the dragon saw the bunny, it ran to attack. But the bunny was growing tall very fast and soon he was twice as
tall as the dragon. The dragon ran away terrified of the giant bunny.
Moral: Eat your greens, they’re healthy. You’ll grow strong.
Teacher Questions for Rehearsal of “The Dragon and the Bunny”
Once upon a time there was a tiny dragon (How can you make the shadow of the dragon the smallest?) He was
walking through the forest when he spied a green vegetable growing at the edge of the forest. The dragon began to
eat, but since he didn’t like healthy food, he ate very little.
The green vegetable was a magic growing plant, and even though the dragon didn’t eat very much, he started getting
bigger and bigger. The dragon was now a big dragon twice his original size. (How can you make dragon’s new shadow
twice the size of his first shadow?)
Along came a teeny, tiny little rabbit. (How can you make the rabbit’s shadow very small?) The rabbit was afraid of the
enormous, ferocious dragon and was shaking all over. The rabbit crouched down to hide and saw the magic growing
plant. The rabbit nibbled and nibbled. (Rabbits love to eat green vegetables.)
When the dragon saw the bunny, it ran to attack. But the bunny was growing tall very fast and soon he was twice as
tall as the dragon. (How can you make the rabbit twice the size of the dragon?) The dragon ran away terrified of the giant
bunny.
Moral: Eat your greens, they’re healthy. You’ll grow strong.
SKY-VUE DRIVE-IN: Inverse Proportions 8
Applications Across the Curriculum
For “The Dragon and the Bunny” Lesson
Visual Art
Students create shadow puppets with construction paper and craft sticks.
Explore the art of paper cutting by providing various cutting tools. Provide
a projector so that students can see the shadow projection as they create.
Drama
Use the elements of performance to enhance the storytelling of “The Dragon and the Bunny.” As students rehearse,
pose mathematical questions: Where should we place the projector, screen (white sheet), audience, etc.? Where can
we mark the locations of the small animal, an animal twice the size, and an animal four times the size? Use labeled
masking tape to mark positions for the story.
Music
The elements of music make excellent expressions of the following terms: tiny, walking, eat, enormous, ran. How
could the dynamics of loud and soft be used to convey size in telling a story? If something doubles in size, how
can music illustrate this? How can tempo be used to enhance the elements of the story? Choose simple percussion
instruments to enhance the story of “The Dragon and the Bunny.”
Science
Explore the topic of what to do when the numbers of an experiment are inconsistent. Begin with “Handout 4: Enrichment: Does Movie Projector Math Work at Home?” As students analyze the data, they will see that x times y often veers
from a steady constant. After students complete this sheet, introduce the concept that different types of light sources
produce different qualities of shadows. The teacher might demonstrate using candlelight, an incandescent light bulb,
a movie projector, and a flashlight. Students may then conduct experiments using the data from the enrichment to
measure shadows of several distinct objects using movie projectors, light bulbs, and flashlights. Discuss the differences
in light projection that influence the experiment.
Interactive Workshop from the Annenberg Series “In the Shadows of Science”
www.learner.org/workshops/sheddinglight/highlights/highlights1.html
This lesson focuses on the science behind shadows.
Social Studies
Search for drive-in theatres close to you. Examine how the number of drive-in theatres started small, increased considerably, and then decreased considerably from 1948 to 1998. Examine the current status of drive-in theaters locally and
in the state.
Drive-In Theaters in the US
www.driveintheater.com/drivlist.htm
This web site includes a list of more than 500 operating drive-in theaters and 3000 plus “dead” ones.
Extension
Use “Handout 5: Extension: What Is Happening to the X and Y?” Discuss the meanings and differences between direct
proportion, inverse proportion, and inverse relationship. A proportion is defined by x/y = k. An inverse proportion is
defined by x • y = k.
SKY-VUE DRIVE-IN: Inverse Proportions 9
This comparison provides an opportunity to discuss inverse operations and
relationships. Direct proportion, inverse relationship, and inverse proportions are
terms used to discuss patterns in the data. Students should be able to distinguish
between an inverse relationship where one variable decreases while the other
increases, inverse proportion where one variable decreases while the other increases,
and x ÷ y = k. The goal of this extension is to understand the terms inverse
relationship, direct proportions, and inverse proportions. While all the terms
describe mathematical relationships, only two of these terms define the relationship
as equal to a constant.
Challenge students to analyze and identify direct proportions, inverse proportions, or inverse relationships. You might
ask them, are there direct relationships that are not direct proportions? (Answer: Yes, there are. Sometimes both
variables increase or decrease together, but at different rates. For example, the price of gas usually goes up when the price of
oil increases, but not necessarily proportionally. Other factors, such as demand, supply, and ease of distribution
affect the price of gas at the pump.)
SKY-VUE DRIVE-IN: Inverse Proportions 10
SMENT
S
E
S
S
A
E
C
N
A
M
R
PERFO
NOTE TO TEACHER:
Note to teacher: Use “Handout 6: Creating Silhouettes” to provide extra
guidance to students through this work.
SCALE CITY
For this activity, you will need the following materials for each group:
• classroom projector
• 2 pieces of 8.5-inch by 11-inch white construction paper for each group member
• 1 piece of 8.5-inch by 11-inch black construction paper for each group member
• 1 piece of 17-inch by 22-inch white paper
• 1 piece of 17-inch by 22-inch black or dark paper
• measuring tape
• pencil
• chalk
Use an overhead projector to create silhouettes of profiles.
Directions
Using the classroom projector and projected shadows, determine a procedure to create profile silhouettes
of each member of your group for a school carnival fundraiser or for display. Given an 8.5 by 11-inch piece
of paper, determine the best distance for the subject to stand or sit between the projector and the screen
or wall and the height at which to place the paper. Measure the distance between the projector and wall.
Record the point at which the subject should be placed to achieve the best silhouette.
Using what you’ve discovered and your group’s projected shadows, create profile silhouettes of each group
member on 8.5-inch x 11-inch white paper. Cut out the silhouette and use it as a pattern to draw a matching silhouette on black paper. Mount the black silhouette on a piece of white paper.
When you are done, predict where the subject should be placed to create an image twice as large on a
17-inch by 22-inch piece of paper. Test your prediction.
PERFORMANCE SCORING GUIDE
4
•The student efficiently completes all steps of the performance assessment.
•The student’s work reflects excellent under
standing of inverse proportions and shadows.
•The student exhibits exemplary teamwork and mathematical understanding through work on this project.
3
•The student efficiently completes at least three steps of the performance assessment.
•The student’s work reflects good understanding of inverse proportions and shadows.
•The student exhibits suf-
ficient teamwork skills.
•The project work shows appropriate application of mathematical ideas.
2
•The student completes at least two steps of the performance assessment.
•The student’s work reflects basic understand
ing of inverse proportions and shadows.
•The student exhibits teamwork with limited supervision required.
•The project work shows some application of mathematical ideas.
1
•The student completes at least one step of the performance assessment.
•The student’s work reflects
limited understanding of inverse proportions and
shadows.
•The student required disciplinary supervision or extensive guidance in following directions and working on the project.
•The project work shows minimal application of mathematical ideas.
SKY-VUE DRIVE-IN: Inverse Proportions 11
0
•No participations.
NT
E
M
S
S
E
S
S
A
E
S
N
O
OPEN RESP
SCALE CITY
Mary and her family want to plant a big vegetable garden in their backyard. They want the garden to have an
area of 120 square feet.
Length
Width
Area
120 ft2
120 ft2
120 ft2
120 ft2
120 ft2
A. Fill in the table with five different possibilities for the dimensions of the garden.
B. As the length increases, what happens to the width?
C. Explain the relationship that exists between the length and the width.
OPEN RESPONSE SCORING GUIDE
4
•The student completes the chart with no math
ematical errors.
•The student accurately observes what happens to the width as the length increases.
•The student demonstrates excellent understanding of inverse proportions. 3
•The student completes the chart with no mathematical errors.
•The student accurately observes what happens to the width as the length increases.
•The student demonstrates good understanding of inverse proportions, with some gaps in reasoning. 2
•The student completes the
chart with few mathemati-
cal errors.
•The student observes what happens to the width as the length increases.
•The student demonstrates inaccurate understanding of inverse proportions.
1
•The student completes the chart with mathemati-
cal errors.
•The student inaccurately describes what happens to the width as the length increases.
•The student demonstrates little understanding of inverse proportions. SKY-VUE DRIVE-IN: Inverse Proportions 12
0
•Blank or no attempt made at a response
ENT
M
S
S
E
S
S
A
E
IC
O
H
MULTIPLE C
Name:
Date:
1. As the number of movie-goers increases, the number of boxes of popcorn sold increases. Based on sales
records, the staff should prepare one box of popcorn for every four customers. Since one variable increases as
another variable increases, this is
A. an inverse proportion
B. a direct proportion
C. a multiplicative inverse
D. an improper fraction
2. As Kim moves further away from the light source of the projector toward the screen, her shadow becomes
smaller. As the distance increases, the shadow size decreases. This is
A. an inverse proportion
B. a direct proportion
C. a prime number
D. an improper fraction
3. When Lu was 10 feet from the projector, her shadow was 12 feet tall. When Lu stands 15 feet from the projector, her shadow will be
A. 15 feet tall
B. 12 feet tall
C. 10 feet tall
D. 8 feet tall
4. Sally found that when she dug for clams alone, it took 4 hours to find the number she needed for a recipe.
If she works at the same rate with three other friends, it should take
A. 16 hours to find the number of clams needed for the recipe
B. 4 hours to find twice as many clams needed for the recipe
C. 2 hours to find the same number of clams needed for the recipe
D. 1 hour to find the same number of clams needed for the recipe
5. Tory’s club washes a nursing home’s vans as a volunteer project each year. When three people work, it takes
90 minutes to wash and polish three vans. When six people work, it takes 45 minutes to wash three vans. If
nine people work, they will finish in
A. 40 minutes
B. 30 minutes
C. 20 minutes
D. 15 minutes
6. Jordan gets paid five dollars from a local pizza place for handing out 100 coupons after the basketball game.
It takes him 30 minutes to hand out the coupons. When two friends helped, all the coupons were handed out
in
A. 20 minutes
B. 15 minutes
C. 12 minutes
D. 10 minutes
SKY-VUE DRIVE-IN: Inverse Proportions 13
Multiple Choice Assessment
7. Each student was given 24 building blocks and told to build a rectangular structure. The x and y represent the
dimensions of the sides.
x
24
12
8
6
y
1
2
3
4
4
3
2
The unknown values for y would be
A. 6, 8 and 12
B. 2, 1, and 0
C. 5, 6, and 7
D. 8, 6 and 4
8. Find the missing value if x times y = k.
x
y
k
2
16
32
4
8
32
4
32
A. 2
B. 4
C. 8
D. 16
9. Find the missing value if x times y = k.
x
y
k
5
10
50
10
5
50
2
50
A. 15
B. 20
C. 25
D. 30
10. x/y = k represents
A. an inverse proportion
B. a direct proportion
C. multiple proportion
D. squared proportion
11. x • y = k represents
A. an inverse proportion
B. a direct proportion
C. a prime number
D. an inverse square
SKY-VUE DRIVE-IN: Inverse Proportions 14
Multiple Choice Assessment
12. When Kelli stood 20 feet in front of the projector at the drive-in theatre, her shadow was half the height of the
screen. When Kelli moved so that she was 40 feet from the projector, her shadow would probably be
A. the height of the screen
B. half the height of the screen
C. one-fourth the height of the screen
D. one-eighth the height of the screen
13. Anne and Kit were setting up for a shadow experiment in the school auditorium. x is Kit’s distance from the
projector. y is the height of Kit’s shadow.
x
y
k
10
20
200
15
200
20
10
200
25
8
200
30
6 2/3
200
A. 18.426
B. 13 1/3
C. 12.325
D. 8.359
14. Consider the table below.
x
y
k
10
24
240
15
240
20
12
240
25
9.6
240
30
8
240
When x is 15, y should be
A. 20
B. 18
C. 16
D. 14
15. A good way of describing what happens to the y value in number 14 above is
A. as the x value increases by 5 the y value decreases by 3
B. when the x value is tripled, the y value is one third
C. when the x value is doubled, the y value is doubled
D. when the x value is 10 more, the y value is ten less
SKY-VUE DRIVE-IN: Inverse Proportions 15