Try this game. First get them to cut out a strip of paper and tape it's ends together to make a stubby cylinder. Then, have them cut it along its equator. That'll be in keeping with their intuition.

Then, make them cut out a strip of paper and tape it's ends after a half twist. Now, make them cut along the equator. Everytime I've tried this on people who don't already know, it's always got a fantastic response. Since we - or at least kids from non math academic households - normally don't encounter such objects in our day to day lives, our intuitions are not prepared for what happens and so it's always a surprise. Trust me, as you keep making them cut along the equator, they'll be thrilled like its some alien object.