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.

*Exploring surface area and volume in simple solids.*

**Which is Greatest?** (20 minutes)

**Materials and Prep **

*Which is Greatest?*student sheets.- iPad with Volumize app.
- Wifi access to send work to other iPads or to the online project space.

**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.

**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.

- 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: _____________

** **

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.

- 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.

- 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.

- 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.

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

Name: __________________________ Date: _____________

** **

- 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?

- 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 |

- 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?