A Möbius Strip is a strip with only one side.  You can make a Möbius Strip by taking a long strip of paper, making a 1/2 twist, and attaching the ends together.  

Try this.  Make a Möbius Strip and draw a line down the middle. Cut along the line.  What happens?

Try this.  Get a long strip of paper and color a band down both sides.  Make a Möbius Strip out of the paper strip.  Cut out the band.  What do you get? 

When you join two Möbius Strips by their edges, you get a Klein Bottle.  If you pour water in the bottle, it doesn't go in. (Use clay, not paper!)

Made with Bryce 3D