Box nets

What does a box with square sides and no top look like when flattened out? (Marion Walter, Boxes, Squares, and Other Things, NCTM, 1970.)

Approaches

Squash the box.

Cut along all edges and stack the pieces.

Good creative thinking. What if we want to make a pattern ("net") that can be folded into a cube with no top?

Are there any others?

Are they all different? What do we mean by different? Are there patterns of five squares that cannot be folded into open-topped cubes?

How many different "pentominoes" are there? What interesting shapes can you make out of combinations of them?

Simulation

Check out this simulation of teaching this problem to a cooperative group of virtual students.

Your experience

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

Last updated 27 September, 2008