If you've never heard of flexagons you're in for a treat. Flexagons are flat paper constructions, some of which are really easy to make, that are tremendously fun to play with because you "flex them", hence the name, to reveal more than the two sides that you would expect to see. Some flexagons are even related to the Mobius strip.
Wikipedia has a nice article about flexagons but my very favorite flexagon site is The Flexagon Portal. The portal has a number of patterns that you can print out, preferably on a color printer, cut out, fold, then flex to your heart's content. The site has easy flexagons and others that are harder to make.
Flexagon projects are great for the kids because they can color them and create their own flexagon masterpieces. Also, they can make original flexagon Christmas cards with their own messages on them. Different parts of the greeting can be revealed on different sides of the flexagon.
While you're on the Flexagon Portal don't miss the FAQ page. There are only three FAQ items but the tips for cutting, folding and pasting are definitely worth a read. Also, check out the video on how to fold a flexagon.
You Tube has a few videos about flexagons. Here's a nice one: