Session 9, Part B: Nets

Session 9, Part B:
Nets (30 minutes)

In This Part: Nets with Regular Polygons | Nets with Circles

Imagine unfolding a cube so that all of its faces are laid out as a set of squares attached at their edges. The resulting diagram is called a net for a cube. There are many different nets for a cube, depending on how you unfold it. Note 2


Problem B1
Which of the following are nets for a cube? Explain how you decided. Try to imagine folding each one, or print them out to explore.


Problem B2
How many different nets for a cube can you make? How did you think about the problem, what method did you use to generate different nets, and how did you check whether or not a new one really was different?

Video Segment
Modeling objects in three dimensions as well as finding their two-dimensional representation is an important part of geometric thinking. Additionally, finding all possible nets of an object can be a challenging task in terms of ability to organize and record your testing methods. After you've completed Problems B1 and B2, watch this sequence to further explore different reasoning participants used to find all the nets for a cube.

What method did you come up with to organize and record different nets?

If you are using a VCR, you can find the first part of this segment on the session video approximately 16 minutes and 52 seconds after the Annenberg Media logo. The second part begins at 18 minutes and 29 seconds after the Annenberg Media logo.

Problem B3

Find all the possible nets for a regular tetrahedron.

Problem B4

A square pyramid has a square base and triangular faces that meet at a top vertex. Find all the possible nets for a square pyramid.

Problems B1-B4 and the Video Segment problem adapted from Connected Geometry, developed by Educational Development Center, Inc. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math

Next > Part B (Continued): Nets with Circles

Session 9: Index | Notes | Solutions | Video