In this activity, students work in all dimensions by sketching 2D pictures of trees and designing a series of 3D treehouses that can “fit” in them. Using four different solids (rectangular prisms, cones, spheres and cylinders), students will mine surface area and volume data for each design to see which shaped house works best. Using the mathematical nets in Volumize, students figure out how 2D skins can wrap the 3D shapes that make up their treehouses.
Learning about scale, dimension, mathematical nets, volume and surface area through designing 3D treehouses for a 2D tree.
Treehouse Design (20-40 minutes)
For each model you will focus on surface area and volume data to help you decide how much material you will need, to determine standing and/or sleeping space inside, and to decipher amounts needed to skin each model so that the covering appears the way you would like on its surfaces. Based on your designs, you will pick the optimal treehouse for you!
Treehouse Design (20-40 minutes)
Have students open the app and select “Get Building.”
Each student or group needs to start with a sketch of a tree and then take a picture of it. Allow as much or as little time for this as necessary. (Students can sketch their trees at home and bring them in the day of the activity.) Students will then need to set the scale in fairly realistic amounts that allows them to judge if they can stand and sleep in their treehouse.
Building with 3D shapes on top of a 2D sketch that students create is a great way to frame a discussion around the concepts of moving from 2D to 3D. Ask students:
Extensions and Inquiring Further
Mathematical nets are useful for the skinning done in this activity. One possible extension is for students to create their own nets for their treehouses with paper, cut them out and fold them into shapes. Design an activity called Shape City and have students create a city populated with all the 3D shapes that your class creates. Define the scale so that there is a real world approximation.
Building 3D treehouses on top of a 2D image is a great way to introduce and to talk about the differences between these dimensions. The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott is a story about a world on a two dimensional plane and all the characters that live there. One character gets a new view of reality when it elevates off the plane and gets a view from above. This story is a classic for middle and high school math students. Assigning this novel as a reading would be a great addition to this activity.
For this activity you will be starting with a hand-drawn two dimensional picture of a tree and then, using the Volumize app, you will build a three dimensional treehouse that fits on to the branches. To get started, make a drawing of a tree in the space provided below. Then you’re ready to bring the tree image into Volumize to get building.
1. Use your drawing as the background image and set the scale in a realistic way so that you will be able to stand up and sleep inside your treehouse.
2. Create the first model, a treehouse using a rectangular prism. You can also add a rectangular prism as the roof if you wish. Fit the treehouse onto the drawing so that it looks like an actual treehouse. Rotate the model and examine your design from many angles.
3. In the space provided, draw the skin for your treehouse. What would you like to appear on each of the surfaces? Use colored crayons or markers if desired and available.
4. Once you are finished creating the rectangular prism treehouse, your’re ready to move to the next model. Go back to the homepage and create a new project and remember to save each design.
5. Repeat steps 2 and 3, creating each of the following: a tree teepee using a cone, a tree pod using a sphere, and a tree silo using a cylinder.
6. Fill in the data tables and answer the questions about your designs.
7. Be prepared to share your favorite models and engage in a class discussion about the activity.
|Example tree withspace for treehouse:||Your sketch of a tree, with space for treehouse:|
|Model||Inside Height||Inside Width||Surface Area||Volume|
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