Over at Hunkin's Experiments, there are a number of fascinating things to try.

The Brain Gang will be especially interested in the Mathematical Experiments section. This includes fun items such as how to prove 1=2 and 2=3, Moebius Bands (including one approach to them I've never seen before) and the classic method for making an extra square appear. The method by which this last one works has been used in many mathematical effects, including this nice version from WoodenCigars.com, which includes an amazing video demonstration.

There are also experiments which show surprising applications of mathematical theory, including how to push a cube through the middle of a cube the same size, and surprising methods for trisecting an angle and making a right angle with string. For surprising math tricks, check out what Hunkin calls Russian multiplication, which allows you to multiply any two numbers from 6 to 10, using only your fingers! Usually, when mathematicians mention the phrase "Russian multiplication" or "Russian peasant multiplication", they're usually referring to this method for multiplying two large numbers together.

Take your time, and look through the other experiments, too. You'll even find some classic magic tricks, such as mind reading with coins, telephones, hands and names.