Shrink and Grow

Students will use the “Caliper” tool to gather data about what happens to their friend’s image size on the screen as she/he is positioned at different distances from the camera. They will explore this relationship kinesthetically and visually, and begin to look for patterns in the data collected.

Size Wise Activity 3: Shrink and Grow

Exploring Proportional Relationships

Expected Activity Time

Part 1: Moving Away (20 minutes)

Part 2: Control Your Image (20 minutes)

Materials and Prep

Shrink and Grow Student Sheets
1 iPad with Size Wise for each group of 3-4 students
Wifi access to send work to other iPads and the online project space
Measuring Tapes (optional)
Prep 1: Make sure students have ample space to take pictures at different distances (hallways are good)
Prep 2: Assign roles for students

Activity Prompt

To use forced perspective photography well, you need to know how to control it. In this activity, you’ll experiment with how your image size changes as you move closer to the camera or farther away.

To Do

Part 1: Moving Away (20 minutes)

Students will direct their partners to move closer or farther from the camera to make them shrink or grow. They will notice what happens to your their partners image sizes on screen when they move closer and farther away.

Have students:

Open the app, choose “Take Some Pics,” and then click “Calipers.”
Select “Add New Friend Or Object” and add the name of the friend who will be in the first photo, and then their friend’s actual height.
Position the subject so that their feet are near the bottom of the screen and their head is near the top. Align the top and the bottom of the calipers so that it measures the entire image of the subject and snap a picture.
Have their partner step back several steps and repeat step 2. Repeat one more time.
As students measure people with the Calipers, tap the “Distance” tool and notice the information onscreen. The app is using the information it has to calculate how far away the subjects are from the camera. Does the data it shows you make sense?
Take a few pictures of each person in their group at different distances, each time using the calipers to measure them. (Be sure to create new calipers for each new person.)
After they’ve taken some pictures, go BACK, and tap “Gallery.”
In Gallery mode, tap “Data” and drag in the pictures they just took. Compare the measurements associated with the images.
Ask: What patterns do you notice?Part 2: Control Your Image (20 minutes)This time, students should choose an image size and direct their partner’s distance from the camera until the image is the right size.
Have students:
Tap “Calipers” and tap “Image Size Caliper”. This will let them measure image size with more precision. Adjust the caliper so that it’s 4.00 inches.
Using the Image Size Caliper, take a picture of their partner so that their image height is 4.00 inches.
Take 2 more pictures where the subjects’ image is 2.00 inches, and then 1.00 inches.
Go into the Gallery and look at the pictures. In each picture, tap the caliper to edit it and then tap the subjects’ information to connect their information to the caliper. This tells Size Wise how tall the subject is so it can calculate their distance.
Compare the data across pictures. Ask: Can they find any mathematical patterns? Note: since they’re dealing with real measurements, the mathematical relationships will be approximate, not exact.

Discussion

Prompt students to make observations and encourage students to use ratio language and reasoning while completing the challenges.

Ask students:

How is the distance of an object related to the height of the object on screen?
Is there a mathematical way to represent this relationship?

Language and discourse to listen for:

As the distance from the camera increases, the image size decreases
As the distance from the camera decreases, the image size increases

Extensions and Inquiring Further

Have students draw diagrams that show how far back from the camera they stood in a few of the pictures that were taken of one person. Can they use their diagrams to explain why the image size changed?

Shrink and Grow

Working in pairs or small groups, use the Calipers and notice what happens to your image size on screen when you move closer to and farther away from the camera.

Part 1: Moving Away

Open the app, choose “Take Some Pics,” and then tap “Calipers.”
Select “Add New Friend Or Object” and add the name of your friend who will be in the first photo, and then your friend’s actual height.
Position your friend so that their feet are near the bottom of the screen and their head is near the top. Align the top and the bottom of the Calipers so that it measures the entire image of your friend and snap a picture.
Now, have your friend step back several steps and repeat step 2. Repeat one more time.
As you measure people with the Calipers, tap the “Distance” tool and notice the information onscreen. The app is using the information it has to calculate how far away your friend is from the camera. Does the data make sense?
Take a few pictures of each person in your group at different distances, each time using the calipers to measure them. (Be sure to create new calipers for each new person.)
After you’ve taken some pictures, go BACK, and tap “Gallery.”
In Gallery mode, tap “Data” and drag in some of the pictures you just took. Compare the measurements associated with the images.
What patterns do you notice?

Part 2: Control Your Image

This time, you’ll choose an image size and direct your friend’s distance from the camera until the image is the right size.
Tap “Calipers” and tap “Image Size Caliper”. This will let you measure image size with more precision. Adjust the caliper so that it’s 4.00 inches.
Using the Image Size Caliper, take a picture of your friend so that their image height is 4.00 inches.
Take 2 more pictures where your friend’s image is 2.00 inches, and then 1.00 inches.
Go into the Gallery and look at the pictures. In each picture, tap the caliper to edit it and then enter your friend’s height to connect her measurements to the caliper. This tells Size Wise how tall she is so it can calculate her distance.
Compare the data across pictures. Can you find any mathematical patterns? Note: since you’re dealing with real measurements, the mathematical relationships will be approximate, not exact.

Part 1: Moving Away

Working in pairs or small groups, use the calipers and notice what happens to your image size on screen when you move closer to and farther away from the camera.

Create a Caliper for yourself.
Have a classmate take pictures of you at different distances.
Go to gallery and click Data tool. Drag in up to four pictures of you from the gallery and compare them.
Record your data below.
What patterns do you notice in the data? Describe the relationship between size and distance.

Distance	Image Size

Part 2: Control Your Image

Working in pairs or small groups, use the calipers and notice what happens to your image size on screen when you move closer to and farther away from the camera.

Create a Caliper for yourself.
Have a classmate take pictures of you so that your image size is 4.00 inches, 2.00 inches, and 1.00 inch.
Go to gallery and click Data tool. Drag in these three pictures of you from the gallery and compare them.
Record your data below.
Can you find a mathematical relationship in the data between two pictures? Describe.

In Camera Mode, you will use:
	To enter and calibrate the height of themselves and their friends
	To see the distance one had to stand to achieve an effect.

In Gallery Mode, you can use:
	To compare data across four pictures.
	Write ratios seen in pictures taken.

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Big IdeaThe size of an object’s image on the screen is related to its distance from the camera. When distance increases, the image gets smaller—an inversely proportional relationship. For instance, to make your onscreen image half as big, you need to stand twice as far away.
When students direct their subjects to move back and forth to change they’re image size onscreen, they are exploring this relationship.
Students interact with the concepts of ratios and proportionality in two different ways:
By manipulating an object’s image size and distance, visually and kinesthetically making sense of these relationships.
By gathering related data to create representations of the relationship at hand.
Learning ObjectivesFrom this activity, students will be able to:
Use ratio language to describe a relationship between two quantities.
Follow a multistep procedure when performing technical tasks.
Use ratios to solve real world problems that pertain to designing digital media.
Identify important quantities in a practical situation, map their relationships, and analyze the relationships.
Standards AddressedCommon Core State Standards-Math  
Ratio and Proportional Relationships 
6.RP.A.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Common Core State Standards-Math  
Mathematical Practices
MP2 Reason abstractly and quantitatively.
MP4 Model with mathematics
Common Core State Standards-ELA  
Literacy 
RST.6-8.3. Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

				Vocabulary
				Increase
Decrease
Comparison
Image size
Object distance
Ratio

			

				Resources
				SW Activity 3 Student Sheet 1
SW Activity 3 Student Sheet 2
SW Activity 3 Student Sheet 3

			
Device StrategiesSingle-device implementation
Have volunteers go to the front of the class and take pictures of them at different distances.  Have classmates observe their positions. For the group shot, ask for a volunteer cameraperson and director to take a group shot of classmates.    Share examples via your smart board or projector and discuss what your students noticed about the image size and distance relationships.
 
Multiple-device implementation
Because this activity requires collaboration, this is a perfect activity for groups of 3-4 students per iPad.  Have students switch roles between being photographers, models, and directors.  Be sure they measure the photos they take so that there is data they can compare across the groups.
 

				Tips & Ideas
				Measuring Real Heights: This activity requires that students enter heights into the Calipers Tool they create for themselves.  Since students have rapid growth spurts, we found that they often don’t know how tall they are at any given time.The act of measuring themselves and group members is useful to reinforce the idea that they are working with actual heights of objects in the real world. It is another opportunity for them to think about the different variables Measuring Real Heights: It is important that students personalize their Caliper Tool with their current height. The act of measuring themselves and group members is useful to reinforce the idea that they are working with actual heights of objects in the real world. It is another opportunity for them to think about the different variables they are measuring.  This also reinforces measuring skills for those less experienced.Measuring With Calipers:  Urge students to take care both when they take their photos and when they adjust their calipers to “fit” their subjects.  The data they’ll get is only as good as their measurement techniques.			