Sets of Nets: Math Task

1.  A rectangular prism is a solid object with 6 rectangular faces, much like a box. 

If we unfold a prism and flatten it out, the resulting figure is called a “net” of the prism.

Many different nets can be formed from a given prism, depending on how you unfold it.

1.     Only one of the following figures is NOT the net of a rectangular prism.  Determine which one is not a net, and give a reason for your answer.  For each of the others, indicate where you would fold first, fold second, and so on, in order to make the prism.

2.     12 rectangles are drawn on dot paper below, but only 6 of these rectangles can be placed together in order to form the net of a rectangular prism. 

  1. Find these 6 rectangles.

  1. On the dot paper below, show how the 6 rectangles from part a. can be arranged in order to form the net of a rectangular prism.

  1. Cindy must make a rectangular prism out of posterboard for a project in math class.  She has a rectangular piece of posterboard measuring 8 units x 5 units, and she wants to use this as one of the faces of her prism.  She will need to cut the other five faces from a large sheet of posterboard. 

Cindy is your best friend and you want to help her do well on her project.  What advice would you give her about the sizes of the five pieces of posterboard she needs to cut to make the other faces of the prism?

Extension Question: 

A pyramid consists of a face that is a base and triangular faces that meet at a top vertex.  Some sketches of pyramids are shown below:

Construct nets for each of the following pyramids:

  1. A pyramid whose base is an equilateral triangle.
  2. A pyramid whose base is not an equilateral triangle.
  3. A pyramid with a square base.
  4. A square-based pyramid constructed so that the four triangular faces are NOT all congruent to each other.
  5. Describe the strategy you used in designing these pyramids.

© 2008 by Education Development Center, Inc. from The Fostering Geometric Thinking Toolkit. Portsmouth, NH: Heinemann. Reproduced with permission.