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.

*Exploring Proportional Relationships*

**Part 1: Moving Away **(20 minutes)

**Part 2: Control Your Image **(20 minutes)

- 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

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.

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.