It has few interesting properties, one of which is that mobius strip has only one surface. For example, if you start drawing line from the seam in the middle of strip, it will meet the starting point and will be double the length of the original strip of paper.
Now, here is questions:
What will happen if you take scissors and cut mobius strip along the middle (or follow the line drawn as explained in the example above)? What will happen if you do it again ?
It is easy to find answers to those questions by trying out, but try to solve in your head first and then check your solution with experiment.
Personal note, my son was amazed with results and which prompted this particular puzzle.