An entertaining thing to do with your paper moebius strip is to cut it in half along its length. Use a pair of scissors to pierce the paper at any point and then start cutting along the strip until you reach the point where you started.

I would love to tell you what you'll create, but I believe it is more rewarding to do this for yourself.

/msg me if you are too lazy to try it or if you think I should include the 'answer' in this writeup.