#MathArtChallenge Day 31: MÖBIUS

The Challenge: If you have a math friend in your life, they’ve probably introduced you to Möbius strips. If you haven’t been introduced, my apologies, on behalf of all math teachers, for having failed you this far. Please, follow instructions below to create and then deconstruct a möbius strip.

Materials Needed: Strips of paper, possibly a zipper (note! If you choose to use a zipper, make sure it is completely detachable. Meaning that the two sides can actually separate. Some zippers are permanently connected at the bottom and will not work for this task.)
Math concepts you could explore with this challenge: knot theory, sequences, topology.

Instructions:
1) Take a strip of paper

2) Make a half-twist

3) Tape together

How many edges?

Then cut down the middle.

Then if you want to get really crazy, get yourself a separating zipper and some sewing materials and head on over to http://woollythoughts.com/mobius.html

Reveal below, but only watch if you’ve played first!

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

7.) Look for and make use of structure. How does the edge of the paper change when you add a half twist?

8.) Look for and express regularity in repeated reasoning. As you add more 1/2 twists to the strip of paper, what happens to final shape? When you cut it down the center, what do you notice?