July 18th, 2015

Students will learn how to look at objects in their world as comprised of basic solids. As students create rough 3D approximations of their objects, they start to pay attention to how much space things take up, a concept that can be described mathematically by surface area and/or volume. Through refining their 3D models to achieve better approximations of more complex objects, they will investigate specific attributes of basic solids, dimensions and scale.

### Volumize Activity 2: Make a Model

Representing an object with basic solids to approximate surface area and volume.

### Expected Activity Time

Make a Model (20 minutes)

Materials and Prep

• Make a Model student sheets.

### Activity Prompt

Intro:Have you ever noticed that almost every object in the world is made up of very basic 3D shapes? Buildings, vehicles, tools, furniture, nature and just about everything else can be broken down into simple solids such as rectangular prisms, cylinders and cones.

In this activity, you will create a rough model of an object of your choosing and you will refine your model several times, each time adding more detail. As you take your model from very basic to more complex, notice surface area and volume as meaningful data involving the amount of space your object takes up. Extend your thinking about your object in this activity to other objects in your world. Begin to recognize how your world is put together and how much space everything takes up.

Make a Model:Choose an object that you would like to use to create a model. Think about using something like your house, a vehicle, a favorite building or almost anything else. If you’re not confident in your object, it might be a good idea to run it by your teacher before you begin to build. Once you’ve chosen your object, take a picture of it and use Volumize, setting the scale and creating an approximation of the object with only two shapes. Take note of the surface area and volume of your first model and save it. Create new models of your original object with four shapes, then with six shapes, noting surface area and volume each time and saving them. Use any remaining time to create a model using as many shapes as you possibly can.

### To Do >

Make a Model (20 minutes)

To start, each student or group needs to choose the object they will be creating a model for and be prepared to either take new photos or import from the camera roll.

• Have each group begin with their selected images and set the scale as accurately as possible. They will be creating multiple projects, each based on modeling the same object. Therefore the scale in each project needs to remain as consistent as possible.
• Have students create a model that best represents their object but only using two geometric solids in Volumize.
• Students should take notes of surface area and volume once they have completed their first model. A data table is provided in the student sheet.
• Have students create a second project with the same image and same set scale.
• In this second project, students will create their best representation of the model using only four geometric solids in Volumize. Again, students will take notes about surface area and volume.
• Students will do this again with a third project, limiting the building process to six geometric solids.
• Finally, students may use their remaining time to use as many shapes as they want to create a model of their object.
• Using the student sheet, have students take notes of their findings and answer a few questions that can be followed up by a discussion.

### Discussion

Ask students to discuss the ways in which their first approximation was either somewhat close or not very close to their actual object.

• Did this first iteration reveal anything about the basic shapes they used to construct their object?
• How did the second, third and fourth models affect their understanding of their objects?
• How did surface area and volume change with each iteration? What do those values mean to them?

Extensions and Inquiring Further

The nature of many 3D modeling environments involves a basic process known as additive modeling, the conscious planning of very basic models that build toward more complex ones. You can have students explore this skill further by discussing additive sculpture (with clay, for example) versus reductive techniques (such as chiseling marble).
or

Challenge students to design their own original model of something they design from scratch or build on existing designs. There are thousands of designs of chairs, for example. You could show several different types of chairs and then challenge students to design a chair starting with a few basic shapes and then refining their ideas over time through multiple iterations and reflections on the process.

Name: __________________________            Date: _____________

### Volumize Activity 2: Make a Model

Choose an object that means something to you. Take a picture of it or find a picture in your camera roll. Then launch Volumize to create a specialized digital model.

### To Do:

1. Once you’ve chosen your object, start Volumize and tap “Get Building.” Choose your picture and be very careful about setting scale. Get the grid to be as close to the actual measurements of your object as possible.

1. Now you’re ready to create a model. Hold your finger on the image and choose where you would like to start. In this first project, you only get to use two shapes to create the best representation that you can of your object.

1. After you’ve added your second geometrical solid and edited both solids to be as closely representative of your object as you can, document the total surface area and volume as seen in the side panel. Use the table in the student sheet to record your findings.

1. Now, start a new project with the same picture and set the scale as closely to the first project as you can. Create another model that closely represents your object, this time limiting yourself to four solids. Again make note of surface area and volume as directed in the student sheet.

1. Repeat once more, this time your limit is six solids.

1. Finally, with your remaining time, use as many solids as you like to make up your object.

1. Be sure to fill in your table and answer the reflection questions on your student sheet.

Name: __________________________            Date: _____________

### Volumize Activity 2: Make a Model

1. Describe how closely your first model’s approximations were compared to the object you were trying to represent.

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

 Model Surface Area Volume Two Shapes Four Shapes Six Shapes More Than Six Shapes

1. How did the surface area and volume change with each new model?

1. What were some things you noticed about your object as you built more complex models? What did you notice about the solids that your model was made up of?

1. Take a look at your classmates’ models and fill in the table below.

 Brief description of classmate’s model. What basic geometric solids do you see the model made up of?
Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

In this activity, students learn the importance of recognizing basic geometric solids as the fundamental building blocks of almost everything around them. Giving students the opportunity to choose the object(s) that they model allows for a deeper investment and potentially deeper understanding about an object’s three-dimensional space. Attention to surface area and volume as a way to explore complex objects made up of simple geometric solids is a core function of the Volumize app. As such, this activity is central to the aim of the app as a simple 3D modeling platform, allowing students to build on top of a 2D image.

#### Learning Objectives

In building a more complex model, students will learn:

• Concepts of surface area and volume for rectangular prisms, cones, cylinders, spheres, triangular prisms and pyramids.
• How basic geometric solids combine to form complex objects

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

Choose an object that students will create a model for in Volumize. Preferably, decide as a class so that students will have more of a personal connection in the activity. Project the single iPad and have students take turns being in control of the app. As the class progresses from the basic model to a more refined approximation, facilitate discussion about going from 2D to 3D, surface area and volume, and the ways in which the editing of shapes affects the surface area and volume data in the side panel.

Multiple-device implementation

If one iPad per student is not possible, groups of two, three or four students per iPad will suffice. In 1:1 situations, students can simply follow the activity as defined below. For groups, be sure to assign roles for students to share tasks in the activity. For this activity, each student can make their own models and keep track of surface area and volume as they go. If there is only enough time for each group to make one model, then groups should plan for each member to build one iteration of the model as described in the “To Do” section. Further, while one student is working on the iPad, the others should be watching and assisting to create accurate approximations of their object of choice.

#### 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.