July 18th, 2015

Students familiarize themselves with the Volumize app and use basic geometric solids to build 3D models out of simple 2D pictures. This allows students to approximate real world surface areas and volumes. Using information panels within the app, students manipulate dimensions and access data and formulas to figure out which objects take up the most volume and surface area.

### Volumize Intro Activity 1: Which is Greatest?

Exploring surface area and volume in simple solids.

### Expected Activity Time

Which is Greatest? (20 minutes)

Materials and Prep

• Which is Greatest? student sheets.

### Activity Prompt

Intro: Have you ever wondered how much space things take up? Also, have you ever looked at something and wondered how much wrapping paper it would take to cover it?

In this activity, you will play around with basic solids, create models of simple objects in the room, and compare their surface areas and volumes.

Which is Greatest?: Find six objects in the room that are somewhat similar in size and match them up to the following shapes: rectangular prism, cylinder, cone, sphere, triangular prism, and pyramid. Predict their volume order from 1 (least) to 6 (greatest) and then predict their surface area order from 1 (least) to 6 (greatest). Then take pictures of the objects and create 3D models of them in Volumize. Find out how well your predictions stand up.

### To Do

Which is Greatest? (20 minutes)

Have students open the app and select “Get Building.”

To start, the class should agree on the six objects that will be modeled. (Another option is to choose the objects in preparation for your class discussion.) They should be fairly close in size and also represent one of each of the following: rectangular prism, cylinder, cone, sphere, triangular prism and square based pyramid.

• Each group should take their own pictures of the agreed upon six objects. Different pictures should still result in fairly close findings for surface area and volume of the objects.
• Exploring all six objects might require more time than one class period. Adjust accordingly. One option would be to assign to groups two or three of the shapes. Then, within each group, each student should be working directly on the iPad for at least one shape.
• Once they have a picture of their first shape in Volumize, students are ready to set the scale and create the approximate model, as overlaid on the photo.
• Help students orient their models on the photos by sharing tips with each other.
• Have students follow the student sheet which requires them to take notes of their findings and answer a few questions.
• Conclude the lesson with a discussion.

### Discussion

• Ask students to discuss the representations of 3D shapes in Volumize.
• What did they notice about the difference between the 2D image and the 3D geometric solids they were playing with?
• How did the different solids compare to one another? Which had the least/greatest volume? Which had the least/greatest surface area?
• Were students’ predictions close to their Volumize approximations? Why or why not?
• How did the app help to explore the shapes?
• Can students come up with any ideas on how to build models that represent larger, perhaps more complex, shapes?

Extensions and Inquiring Further

Start looking at other objects in the room and break them down to the simple geometric shapes that make them up. Discuss the importance and value of the skill of deconstructing objects into their component shapes as a way for approximating surface area and volume.
or

Have the students explore what happens to the surface areas and volumes of each geometric solid when one of its measurements (i.e. length, width, height or radius) is doubled.

Name: __________________________            Date: _____________

### Volumize Intro Activity 1: Which is Greatest?

Make models of six objects in the room that your class has agreed upon. There should be one of each of the following: rectangular prism, cylinder, cone, sphere, triangular prism and square-based pyramid. Make predictions about surface area and volume by ordering the objects from greatest to least in the table below. Then compare your predictions with what you find in Volumize, and with findings from other groups in your class.

### To Do:

1. Open the Volumize app and click “Get Building.” You will be prompted to take a new picture. Choose the first object and take a picture. Then you will be prompted to set the scale. Do your best to line up the grid with approximate measurements of the object in the picture.

1. Hold your finger on the object in the photograph and you will be prompted to add a geometric solid. Choose the one that best represents your object. Now you can slide the shape around, change it by using the little handles, and slide them to see how adjustments are made.

1. Once you have lined up the 3D shape with the photograph, you’re ready to check out the data in the side panel. Look at surface area and volume and make notes about them in the table in your student sheet.

1. Repeat this for each shape, taking notes as you go. Finish by answering the questions in the handout.

Name: __________________________            Date: _____________

### Volumize Intro Activity 1: Which is Greatest?

1. How would you respond to a question asking how small or large something is? Is there more than one way to measure the size of something?

1. The table below is meant to help you keep track of your predictions and findings for surface area and volume for each of the six objects.

 Shape Object Name Prediction: Least to Greatest Surface Area Prediction: Least to Greatest Volume Surface Area According to Volumize Volume According to Volumize Rectangular prism Cylinder Cone Sphere Triangular prism Square-Based Pyramid

1. What were some of the things you noticed about the different geometric solids you made models of in Volumize? What seemed to play a role in increasing volume for different shapes? Surface area?

Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

In this activity, students learn to use core tools within Volumize while exploring how surface area and volume are affected by changes to dimensions.

Students will also make predictions and compare surface areas and volumes of various objects around the room. The objects in question should be basic shapes, such as cardboard boxes (rectangular prisms), soda cans (cylinders) and globes (spheres).

#### Learning Objectives

Students will be able to access all formulas for surface area and volume and will see how values dynamically change when they alter the dimensions of 3D shapes in the app. Students will:

• Explore concepts of surface area and volume for rectangular prisms, cones, cylinders, spheres, triangular prisms and pyramids.
• Understand effects of changing dimensions on surface area and volume for each shape.

Common Core State Standards-Math

Geometry

6.G.A.1                 HSG.GMD.A.3

6.G.A.2                 HSG.MG.A.1

6.G.A.4

7.G.A.3

7.G.B.4

7.G.B.6

8.G.C.9

Common Core State Standards-Math

Mathematical practices.

MP2: Reason abstractly and quantitatively.

Students create a dance visually and then have to determine the quantitative moves before making it virtual.

MP4: Model with mathematics.

Students outline their dance using the angles of rotation and coordinate notation for the translation

#### Vocabulary

• Length
• Surface Area
• Volume
• Dimension, 2D and 3D
• Rectangular Prism
• Triangular Prism
• Cone
• Sphere
• Cylinder
• Pyramid

#### Device Strategies

Single-device implementation

Be prepared to explore surface area and volume of several basic shapes in the room. Choose objects ahead of time that match up with the shapes offered in Volumize: rectangular prism, cylinder, sphere, triangular prism and pyramid. Project the single iPad to the front of the room and have students take turns manipulating the shapes in the activity described. Frame discussions around the comparisons, manipulating the dimensions and approximating the real world values.

Multiple-device implementation

If one iPad per student is not possible, groups of two, three or four students per iPad will work well. In 1:1 situations, students can simply follow the activity as defined. For groups, be sure to assign roles for students to share tasks in the activity. For this introductory activity, each student can make their own predictions about what objects have greater surface areas and volumes. Then, they can choose which one or two objects they recreate in the app. All the students should have a turn with their group’s iPad. While one student is working on the iPad, the others should be watching and helping to create accurate representations of the objects.

#### Tips & Ideas

Getting a handle on orienting the 3D models in the app can be tricky. Here are some helpful techniques:- Tap the lock icon on the bottom left of the modeling screen to enable rotating the base shape (that's the first shape you add to the scene).- Moving your model on one axis often helps maneuver it into its desired orientation.- Try swiping up or down, or right or left, and watch how your swiping affects the orientation.- Zoom in and out on models can help to orient the scene to your liking.- Double tap at any point will return your model to the starting position. This can be very helpful for making modifications to your construction.