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
