Modeling Prompt

Students may forget that length, volume, and area do not scale in the same way. For example, if two objects are scaled copies of each other and the larger one is 2 times as tall as the smaller one, it will have \(2^2 = 4\) times the surface area of the small one and \(2^3=8\) times the volume. If students try to rush through the calcuations, remind them to justify their steps.

After students have completed the task, display the pages they created or have a gallery walk, so that all students can see what each group did.

Imagine that you’re writing a children’s book and you want to help readers understand the relative sizes or amounts of some things by comparing them to more common objects that they would be familiar with. Choose several related objects or amounts that you want to compare, such as the sizes of animals, and choose one or more objects to use to compare them. Here are some questions to think about:

• How many of an object would be needed to represent each thing you want to compare?
• If you scaled an object to different sizes, how big would it have to be to represent each thing you want to compare?

Your final product will be:

1. A display showing what this part of the children’s book will look like. Include illustrations and text explaining how all of the things you’re comparing are represented.
2. A summary of your reasoning for the publishing company that shows how you know your calculations are correct. Make your explanations as easy to follow as you can, since your audience might not be comfortable with math.

In this version of the task, students are explicitly instructed to make a table to keep track of their calculations. If it would be more useful for students to use a different tool to reason systematically, the task can be changed accordingly.

Students may forget that length, volume, and area do not scale in the same way. For example, if two objects are scaled copies of each other and the larger one is 2 times as tall as the smaller one, it will have \(2^2 = 4\) times the surface area of the small one and \(2^3=8\) times the volume. If students try to rush through the calcuations, remind them to justify their steps.

After students have completed the task, display the pages they created or have a gallery walk, so that all students can see what each group did.

Imagine that you’re writing a children’s book and you want to help readers understand the relative sizes or amounts of something by comparing them to a more common object that they would be familiar with. Choose several related objects or amounts that you want to compare, such as the sizes of animals, and choose an object to use to compare them. Here are some questions to think about:

• How many of the object would be needed to represent each thing you want to compare? For example, if a marble represents the size of a cat, how many marbles would represent an elephant?
• If you scaled the object to different sizes, how big would it have to be to represent each thing you want to compare? For example, if a normal-sized marble represents a cat, how big would its diameter have to be to represent an elephant?

As you work, make a table that summarizes the results of your calculations.

Your final product will be: 

1. A display showing what this part of the children’s book will look like. Include illustrations and text explaining how your object represents all of the things you’re comparing.
2. A summary of your reasoning for the publishing company that shows how you know your calculations are correct. Make your explanations as easy to follow as you can, since your audience might not be comfortable with math. Include the table you created.