The Afghan Bands amazes even adults. Just make a Mobius Strip. Ask the kids how many sides it has, and then the kids that it only has one side by drawing a line along it. Then ask them what happens if you cut it in half lengthwise (it makes one long, double twisted, loop). Then ask them what happens if you cut THAT is half! To their surprise it will form two connected loops.

Use a long strip of paper about 1.5 inches wide or more, and if you're doing this in front of a class make sure that it's big enough for everyone to see.