September 7th, 2016

Three spheres in Volumize with radii ratios of 2:4:8.

#### Introduction

Discuss and/or review the sizes of similar objects.  Examples could include: Baby and adult animals, architectural models and the real buildings, vegetables like pumpkins, trees and plants, etc.

Notice that the student sheets pose the question about what they would expect the surface area and volume ratios to be. In this lesson students will be guided to explore these relationships.

#### To do

1. Students will follow the instructions on their sheets.
2. The lesson guides students through creating three spheres and exploring their radii lengths, surface areas and volumes.
3. They are then prompted to find the relationship between these ratios.  Gage the amount of help they need in making the discovery of this relationship.
4. In Part 2 students are invited to create a model of a robot, building, vehicle, etc.  They’re prompted to set the scale of an approximate real world value.  Guide them to choose objects that are somewhat boxy as Volumize uses simple solid shapes as building blocks.  The modern house example, included below, might be a helpful inspiration.
5. After they record the data for their model, they are then prompted to “edit scale” and increase the height of the object by a factor of 3.
6. They are then prompted to record that data, and answer the questions.
7. Questions for both parts 1 and 2 are included below.
8. Circulate the room and check for understanding, help students as needed.

#### Sharing

1. With each lesson, spend some time allowing the students to share their work with the class. In this lesson, students can share difficulties they might be having as well as successes in…
2. You might also invite students to continue thinking about how…

#### Part 1

1) What is the ratio of radii between the three spheres? (Your answer will look something like a : b : c where a, b and c are numbers.)

2)  What is the ratio of surface area between the three spheres? (Your answer will look something like a : b : c where a, b and c are numbers.)

3) What is the ratio of volume between the three spheres? (Your answer will look something like a : b : c where a, b and c are numbers.)

4) What is the relationship between the three ratios you found?

#### Part 2

5) In your new Volumize 3D model, what is the ratio of lengths?

6) In your new Volumize 3D model, what is the ratio of total surface areas?

7) In your new Volumize 3D model, what is the ratio of total volumes?

8) What is the pattern between the height ratio, surface area ratio, and volumize ratio?

9) Define the word dimension.  Include examples of the first, second and third dimensions and the models you made in this activity.

Set of 3 ratios between 3 spheres and the data for radii length, surface area and volume as found in Volumize.

Example of a modern house made in Volumize. Notice the parts of the 3D model that aren’t exactly matched with the reflection. However, skinning the 3D model with the rectangles from the house create a slick model. To do this, take a screenshot of the original image and crop it to the size of the single rectangle. Do that for each face of the house. Solid colors can be saved and used on all the other faces. More examples of this model below.

Example of the same model above without any added skin.

Example of the same modern home without the background image.

Apps used
Duration: 40-60 mins
Challenge Level: Intermediate
Prep: Easy

#### Big Idea

Students will explore ratios across the first, second and third dimensions.  Starting with three spheres in Volumize with radius lengths in the proportion of 2:4:8, students will examine how those ratios are related to the same spheres’ surface area and volume ratios.  Then they will make something of their choosing, building, robot, vehicle, etc., and change the scale to get three sets of data for their same model.

#### Learning Objectives

From this activity, students will be able to:

• Use ratio language to describe a ratio relationship between two quantities
• Understand the relationship between length, area and volume between similar figures

#### Resources

Scale – Lesson 1 – Dimensions 1 2 3 – Full Student Handout with worksheetsA set of iPads with the Volumize app

#### Device Strategies

If necessary, have students label their iPads so they will be able to return to them for the next lessons.

These lessons are designed for students to work individually, in pairs, or in groups.  Each student should do all the work on their own sheets, and the iPad should be shared across group members as equally as possible.
We suggest that groups be no larger than four students.  Four or more students in a group will require extra attention to make sure that every group member is contributing equally.