July 17th, 2015

As a class, students select a few different objects from the Virtual Props Library and decide how to pose so that they will “fit” in the picture. After using the calipers and the data tool, they graph the data associated with each picture (object height and object distance) and analyze patterns they see.

### Size Wise Activity 5: Strike a Pose with Virtual Props

Graphing Proportional Relationships

### Expected Activity Time

Strike a Pose (40 minutes)

### Materials and Prep

• Strike a Pose Student Sheets
• Graphing Paper or Graph Sheet
• Spreadsheet software like Excel (optional)
• iPad with Size Wise for each group of 3-4
• Prep: Make sure students have ample space to take pictures at different distances (hallways are good)

### Activity Prompt

As a class, choose a set of different virtual props you want to use. Take pictures of your friends so that they “fit” in the picture with the virtual props. Collect careful data so that you can compare it to your classmates’ data.

Note: You might decide to take pictures wearing different-sized virtual pants.  Or perhaps you’ll pose so that you’re the same size as the virtual elephant and then the virtual giraffe.  Be sure to choose props that are very different in size. You’ll have to discuss what it means to “fit” with the props you’ve chosen.

### To Do

Strike a Pose (40 minutes):

Students will get their friend to appear like he/she fits with some virtual props.

Have students:

• Go into the Virtual Props library and select one of the chosen virtual props.
• Create a caliper for each of their group members.  Align the calipers carefully with their friends, from head to toe.
• Take pictures of their group members posing so that they “fit” with the prop.
• Select another chosen prop and take photos of each group member posing with it.  Repeat.
• Go to the Gallery, and select the Data tool to view four pictures of the different members of their groups posing with the same prop. Look for any relationships between distances needed to stand away for their pose to “fit” with the prop.  Have students consider: Do they notice a pattern? Can they describe what you notice mathematically?
• Collect all of the data for all group members for both props. Plot their data on a graph of Object Height vs. Object distance, using a different color for the data from each virtual prop.

### Discussion

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

• What did they have to do to ”fit” with the smallest virtual prop?  With the biggest?
• What patterns did they see in the data?
• Does the height of the person make a difference in how far away they need to be to fit with the prop?
• When they graphed the data, what did you see?
• How can these relationships be represented mathematically?

In their discourse, look for mention of:

• The size of the prop and its relationship to distances they had to stand (e.g., the smaller the prop, the farther away they needed to go)
• _% larger
• x times the height
• Taller people had to stand farther back.
• Reduce the image size, increase the distance
• the ____ increases as the ______ decreases

### Extensions and Inquiring Further

Another way to analyze the relationship between image size, object height and object distance revealed in students’ graphs is to analyze and compare the slopes. Use the Image Size Calipers and the Ratio Tool to look at relationships between image sizes on the screen. Is there a relationship between the image sizes they measured and the lines they saw in the graph you created?

The slope of each line depends on the size of the virtual prop, since the prop determines the image size.  The smaller props, will determine steeper lines with greater slope.  This is because there is an inversely proportional relationship between image size and object distance.

### Strike a Pose with Virtual Props

To Do:

Get your friend to appear like he/she fits with different virtual props.

• Go into the Virtual Props Library and select one of the virtual props the class chose.
• Create a caliper for each of your group members.  Align the calipers carefully with your friends from head to toe.  Take pictures of each of your group members posing so that they “fit” with the prop.
• Select another chosen prop and take photos of your group posing with it.  Repeat until everyone in your group has posed with each of the chosen props.
• Go to the Gallery, and select the Data Tool to view four pictures of the different members of your group posing with the same prop. Look for any relationships in distances your friends needed to stand to pose with the prop.  Do you notice a pattern? Can you describe what you notice mathematically?
• Collect all of the data for all your group members and all of the virtual props you used.  Plot your data on a graph of object height vs. object distance, using a different color for the data from each virtual prop.

### Data Sheet

After you have taken a few pictures with different virtual props:

1. Go to the Gallery, select Data, and drag in four pics of your group members posing with the same prop.
 Virtual Prop used Group Member Image Size Actual Height Distance from Camera 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
• What do you notice about the actual heights of your group members versus their distances from the camera in posing with different props? Use ratio language to describe the relationships you see.

### Graphing Sheet

 In Camera Mode, you will use: To enter and calibrate the height of students and their friends. To select among several virtual props to try on or fit in. To see how image sizes of your subjects relate to the image size of the virtual prop To see how far away students have to stand to achieve the desired effect. To reflect on the things students notice about the pictures they take. They can email these notes to themselves. In Gallery Mode, students can use: To compare data across 4 pictures (e.g., distance they stand to get different image sizes) To write ratios that they see on the photos they took.
Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

The virtual props don’t change size. In this activity students have to position themselves at the right distance from the camera so that they “fit”. In this way, the image size is held constant (i.e., everyone is the same image size since they are all aligning with the same prop).  The data collected from multiple students posing with that same prop reveals a directly proportional relationship between the actual height of each student and their distance from the camera, because taller students have to stand farther away from the camera.

Since the size of the prop affects the desired image size, it affects the slope of the plotted line (the smaller the prop, the greater the slope). Plotting all of the data from two different-sized props on the same graph reveals these different directly proportional relationships.

#### Learning Objectives

Students interact with the concepts of ratios and proportionality in two different ways:

• By manipulating the image size and distance of objects, visually and kinesthetically making sense of these relationships.
• By gathering related data and using ratios to describe the relationships at hand.
• By graphing the data and discussing the patterns revealed.

From this activity, students will be able to:

• Use ratio language to describe a ratio relationship between two quantities

Common Core State Standards-Math

Ratio and Proportional Relationships

6.RP.A.1. Understand the concept of ratio and se ratio language to describe a ration relationship between two quantities.

6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems.

7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.A.2. Recognize and represent proportional relationships between quantities.

7.RP.A.2A Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Common Core Standards-Math

Mathematical Practices

MP2 Reason abstractly and quantitatively.

MP4 Model with mathematics.

Common Core Standards-ELA

Literacy

RST6.8.3. Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

#### Vocabulary

• Increase
• Decrease
• Variables, comparison
• Image size (height)
• Object height
• Object distance
• Proportion
• Ratio
• Slope
• Direct proportion

#### Device Strategies

Single-device implementation
If you have one iPad, have a volunteer go to the front of the class and take pictures of them wearing three differently sized pants. Have classmates observe and document the position of the volunteer for each pair of pants: small, medium, and large. Share the photos and data via your smart board or projector and discuss what children notice about the image size and distance relationships between each pants picture.

Multiple-device implementation
Because this activity requires collaboration, this is a perfect activity for groups of 3-4 per iPad. Have students switch roles between being the photographer, the models, the directors, and documenters.

#### Tips & Ideas

Selecting Props: It’s best to choose props that are dramatically different sizes, but keep in mind that posing with very small objects will require students to stand very far away. 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. One measurement technique is to develop a standard idea of what it means to “fit” with the chosen props. For instance, if students want to pose with the Statue of Liberty, are they lining their picture up with the statue’s feet, or with the base? And what about the torch? In a discussion about fit, you might include a conversation about image size ratios. For instance, the class might choose to dress in different virtual pairs of pants, or different virtual shirts. In the case of Size Wise clothing, the question of “fit” isn’t really about fashion. Since the data that Size Wise collects is based on measuring things from top to bottom, the class might determine that the clothes “fit” if the height of the prop is in a specific ratio with the student’s image height. Do the pants look right if they’re in a 1:2 ratio with the student’s height? Or something else? If the students decide to standardize based on a specific image size ratio, then they should use the ratio tool to check their “fit”.Analyzing the Data: Ask a couple of students to collect some outlier data by “posing” some very short objects (e.g. a trashcan, backpack, or pencil cup) and some very tall things (e.g. the distance from the floor to the top of the blackboard) with the same virtual props.The data that the students collect can be graphed both as a group and then as a class. Plot the data on graph of object height vs. object distance, using a different color mark for each virtual prop. As long as the data was collected with some care, the graph should reveal a straight, upwardly sloping line for each separate prop. Each of these lines is a directly proportional relationship, where both values increase in proportion to each other. That is, taller students have to stand back farther to fit with the same prop.