The Shadow Knows

I believe this is by the great cartoonist and puzzler A.W. Nugent (about whom we will be hearing more).

I like this for a few reasons.

First, as a creativity exercise it brings in new and unusual shapes and gives the students open-ended instructions in how to deal with them.

Second, it helps build intuition about geometry (particularly projective geometry).

Third, it looks like fun.

The one change I would make would be to get different shapes from the same crumpled piece of paper by moving the light source.

Make your own Platonic Solids -- let the conspiracy theories commence

(Via Google, I found these at the Philalethes Society site, so active members of the Anti-Masonic Party might want to skip to the next post)

Here's another chapter in the ongoing playing with paper series. There are any number of interesting lessons you can build around the five Platonic Solids (as usual, Martin Gardner has some clever suggestions), but the best place to start is probably by building intuition by letting the kids make and manipulate them.

Depending on the age and sophistication level of the class, try one or more of the following:

1. Decorate then assemble these patterns;

2. Use these patterns to make dice. Try playing familiar games (chutes and ladders, Parcheesi, etc.) with the new dice;

3. Make mobiles using Platonic solids and paper tubes;

4. Make sculptures with the condition that attached sides have to match (this gives you three types of sculptures -- cube-based, dodecahedron-based and everything else);

5. Measure the surface area of each solid;

5b. Use fine Styrofoam pellets to estimate and compare the volumes of the different solids.

6. Using clear plastic for the outer shell, create dual polyhedron.