It is a common theme that at some point in time students in a math class will create 3D shapes from 2D pieces of paper. This is a great exercise for students and I would encourage anyone to do it before they begin a lesson on volume or surface area (it also makes for a light homework assignment). However, the purpose of this exercise is to deconstruct 3D shapes to properties of 2D (see note below about 2D/3D) to show the connection between both dimensions.

__What You Will Need:__

- Pre-assembled 3D shapes (cereal boxes, cubes, or square based pyramid will work just fine)

- tape

- Something to cut with (either scissors, or a childproof utility knife)

- Groups work best if you don't have a lot of 3D shapes

- You could also ask the students to bring in a shape from home made out of cardboard

__Goal:__

The goal of this exercise can be two-fold, depending on the skill level of your students. At the minimum we want students to recognize that their 3D shapes are composed of 2D shapes. However, if you wanted to couple this exercise with surface area you could have them calculate the surface area of the 3D cube or square-based pyramid prior to deconstructing it and then calculate the sum of areas of the 2D shapes after it is deconstructed.

__After Activity Q & A__

Why is it helpful to think of 3D shapes as 2D shapes

What is the difference between the 2D shape and the 3D shape

What is the difference between the formulas for each

Is the 2D shape really 2D or does it have a small height?

Are there any 2D shapes?

What would a 4D shape look like

__Note Regarding 3D & 2D__

It may or may not be true that an actual two dimensional object can exist, after all, even atoms are composed of three dimensions. However, this is not the point of the exercise. For example, are shadows, electrons, TV pictures, etc, 2D? These are great questions for a physics forum or post-project discussion but beyond the scope and purpose of this lesson. The purpose is to connect the concepts of 2D and 3D in a manner that grade school students can understand

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