**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?

SimulationCheck 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*