July 17th, 2015

Students will begin by sketching a scaled floor plan of a room and creating a 3D model of it in Volumize. Then they will create their dream room by rearranging furniture and redesigning the room. Designing directly with dynamic solids, students will learn about scale, dimension, volume, and surface area, along with mathematical nets.

### Volumize Activity 6: Redesign Your Room

A deep dive into surface area and volume formulas for basic geometric solids

### Materials and Prep

• Redesign Your Room student sheets.

### Activity Prompt

Intro: Have you spent any time analyzing the dimensions of the room that you spend the most time in? Are you someone who frequently rearranges your furniture? Or, perhaps, maybe it never even occurred to you that you might prefer your bed to be on the other side of the room? How much space does all your stuff take up? In this activity, you will take just a few measurements and then dive into a fun, mathematical analysis of your bedroom (or another room of your choice). Concentrating on basic shapes, you will be invited to create a:

• Direct representation of your room.
• Direct representation of your room with the furniture rearranged.

For each bedroom model you will focus on various data such as surface area and volume to help understand your space the way it is, the way it could be, and the way you wish it was.

Redesign Your Room: In Volumize, create three model rooms:

• Direct representation of your room as it is, to scale.
• Your room as it is, but with the furniture rearranged.

For each model, pay attention to the surface area and volume data, observe how solids fit together, and how to maximize space in a desirable way. Complete the data tables and answer the reflection questions in your student sheet.

### To Do

First, take some basic measurements of the desired room: length, width and height from floor to ceiling. Some other basic measurements would help too â€“ length, width and height of the bed, and other large pieces of furniture. After that, make a sketch of the floor plan and also a single wall of the room that will serve as a backdrop for the first two models in this activity. Once you have these things, open the Volumize app and begin.

• Have each group start a new project in Volumize with the image of their room wall. They should set the scale to the actual height of the ceiling. An example picture is included in the student sheet.
• The first shape to add is a rectangular prism. Have students make this first solid the floor, paying attention to the side panel so that length and width of the room are the same as their actual room. Then, students should skin the floor (top surface of the rectangular prism) with the floor plan sketch they made of the room.
• Have students add the rest of the furniture in the app. They need to pay attention to the info panels to make sure the dimensions of their furniture are as close as possible to the dimensions they measured.
• Have students draw some of the surfaces of the furniture and skin the solids appropriately. They may also use the colors and textures provided in Volumize.
• After students have completed the model of their current bedroom, have them go back and start a new project for the next model, remembering to save their work.
• Keeping the same furniture with the same dimensions that they created before, have students rearrange the furniture in the new project.
• Paying attention to how much space each piece of furniture takes up is important, but the student sheet will also direct them to think about how much free space each arrangement provides in the room.
• Part three is another new project in Volumize. Now they can draw a new wall as a backdrop, setting the scale to their liking. Breaking free of the constraints from parts 1 and 2, students are now able to build new furniture within their dream space but still need to pay attention to how much space everything is taking up.
• The student sheet will direct their attention to various data points like surface area and volume. Have students complete the data tables and reflection questions.
• Students should be prepared to engage in a class discussion following their completion of the activity.

Extensions and Inquiring Further

This activity builds a room on a background picture of a wall and floor plan but the model could include the space on the other side of the wall. That space could be another room, the front or backyard, or two new rooms. Or, the activity could involve creating a model of the entire house, or an entire dream house.

or:

Concentrate on furniture design. Have students explore designs of specific furniture pieces, recreate some of them in Volumize, and then design their own. This could be extended further and students could use these digital 3D models to build physical models.

or:

Students can explore architecture and create models of entire buildings, starting with simple geometric buildings. From those simple examples, students realize that with a handful of geometric shapes, seemingly complex structures can be designed. The famous art museum, the Guggenheim, is a great example.

### Volumize Activity 6: Redesign Your Room

For this activity you will be making models of your bedroom. Start by taking some measurements of your bedroom at home. The tables below are there to help guide you and record your data.

### To Do:

1. Along with the measurements of your room, make two drawings in the space provided. One will be of the wall of your room. This will serve as a backdrop for your model, as you will see in the example. The second drawing is of the floor plan of your room. It will be important to keep the furniture as close to scale as possible.

1. Open the Volumize app and tap â€śGet Building.â€ť You will be prompted to start with a photo. Take a photo of your drawing of your bedroom wall, and then scale it to the height of your ceiling.

Tip: Start with a cylinder and then add a rectangular prism on top of that and edit it to the floor plan. Using a cylinder as a sort of pedestal to start will allow you to easily create the floor with correct dimensions on one side of the wall.

1. Once you have your floor situated correctly in relationship to your wall, you can skin the top surface with a photo of your floor plan drawing.

1. Now youâ€™re ready to start adding the furniture. Add a rectangular prism for your bed, dresser, etc. Keep an eye on the data panel on the side and make sure the furniture youâ€™re adding is as close as possible to the actual measurements of things in your room. Record the data in the tables provided on the student sheet. You may also draw some of the surfaces of your furniture and add those drawings as skins to the solids in your model.

1. Once you have your actual bedroom modeled, answer the reflection questions and then start a new project in Volumize.

1. In the new project, create your room again, but this time rearrange the furniture. Use the same measurements of your bed, dresser, etc., but draw a new floor plan and build the new arrangement.

1. Again, record the data in the tables provided, and keep the rearranged model as a saved project. Answer reflection questions.

1. Now youâ€™re ready to build your dream room. Make a sketch of a wall of your dream room as well as the floor plan. Keep in mind that you will be using Volumize to create the 3D model of this dream bedroom. Record the dimensions of your dream room and each item of furniture in the table provided. (Note: If youâ€™d like, you can use different shapes for the floor and furniture in your dream room.)

1. Answer the remaining reflection questions, and be prepared to share your dream room with the class.

### Volumize Activity 6: Redesign Your Room

1. In the space below (or on a separate piece of graph paper), draw a wall in your room that will be the backdrop for your design in this activity. A small example is shown but use a wall that you think will best set the scene of your selected room. Next, draw the rough floor plan of your room with measurements to scale.
 Example wall of a room: Your sketch of a wall in your bedroom: Â Example floor plan: Your sketch of the floor plan of your bedroom: Â
1. The tables below are to help keep track of the data of your room.
 Dimensions: of YourBedroom Actual Measurements Volumize Data Length Width Height

 Items/Furniture in Your Bedroom Actual Measurements (Length, Height, Width, etc.) Volumize Data Bed Dresser Desk Others, list:

 Things in Your Dream Room Measurements (Length, Height, Width, etc.) Volumize Data Dimensions of the Room Bed Dresser Desk Others, list:

1. In your current room, how much empty floor space is there? Also, what is the ratio of empty floor space to floor space that is taken up by furniture?

1. What is the volume of your bedroom? How much volume is taken up by furniture?

1. When you rearranged the furniture in the model of your current bedroom, did it make you want to actually rearrange it? Why or why not?

1. Why did you choose to rearrange the furniture the way you did?

1. Aside from more space in your dream bedroom, what are some things that you added and why?

1. In your dream room, what is the ratio of empty floor space to floor space taken up by furniture?

1. What is the volume of your dream room? Why did you choose the dimensions that you did for your dream room? (Note: Donâ€™t just say, â€śTo make it bigger,â€ť what is it about more (or less) space in your dream room that is desirable?)

Apps used
Duration: 0-20 mins
Prep: Easy

#### Big Idea

This activity expands the traditional math class assignment of students mapping their rooms to scale so that they are mapping and planning with three-dimensional solids. Though in some cases it might be quicker to simply take measurements of a simple shape to find surface area and volume, Volumize allows students to build digital models and explore these concepts in ways that are meaningful to them as they develop their complex 3D designs. Using Volumize, studentsâ€™ static two-dimensional drawings become dynamic 3D models that can be spun, zoomed in on, skinned, rescaled and rearranged.

#### Learning Objectives

• Students will learn about the relationships between working in one, two and three dimensions.
• Students will understand surface area and volume for rectangular prisms, cylinders, spheres and cones.
• Students will understand how mathematical nets are related to the 3D objects that they fold into and how the nets help to understand total surface area.

Common Core State Standards-MathÂ

Geometry

6.G.A.1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  HSG.GMD.A.3

6.G.A.2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  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

• Scale
• Mathematical Nets
• Length
• Surface Area
• Volume
• Dimension
• Rectangular Prism
• Cone
• Sphere
• Cylinder

#### Device Strategies

Single-device implementation

Every student in the class can create their own drawings of their room. As assigned in the activity below, they are to make a sketch of their floor plan along with one wall that will be the backdrop. They will also draw some of the skins for various pieces of furniture in the room. Using a projector or interactive whiteboard, have the students share their designs and vote on what to use for their class model. The class will together build three models: the direct representation, rearranging the furniture, and the dream bedroom. Follow the lesson defined below as a class, giving students turns to use the app. Each student should fill out their own worksheets even as the class works together on the projects.

Multiple-device implementation

If one iPad per student is not possible, groups of two, three or four students per iPad will also work. In 1:1 situations, students can simply follow the activity as defined below. For groups, be sure to encourage students to share tasks in the activity. For this activity, each student or group can create bedroom drawings and models, and follow the lesson as defined below.

#### 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.Make sure to familiarize yourself and your students with the side panel in the Volumize app. The formulas for each solid are grouped together. Note that the total surface area subtracts the overlapping surfaces.