Thanks for the interesting web page...

Donna Endress

To answer your question, there is of course no way to make a sphere out of a piece of paper. It's important to find out how lax your son's teacher plans to be, or in fact what the fellow had in mind. Topologically speaking a cube is equivalent to a sphere, and you can easily create a cube out of a piece of 6" x 8 1/2" paper. (Just think of it as a 3x4 rectangle. Make 2" cuts from the long sides towards the center. Fold the middle 1x4 strip in a "square" or "cubic" shape; let the dangling flaps overlap.)

I would contact the teacher to find out his/her implicit restrictions on the possible shapes.

All the best,
Alexander Bogomolny