> Playing devils advocate for a moment.... > > Other than for topology students in grad school, where is the mathematics > in exploring mobius strips and hexaflexagons? The mathematics comes in looking for patterns in what happens. You have to take it beyond the simple cutting of a Mobius strip and seeing how long the cut is. What happens if you twist the band twice instead of once? Three times? What if you cut it into thirds instead of halves? Where are Mobius strips used? What is the advantage of them over straight strips?
When you put two loops together at a 90 degree angle you get a geometric shape. How can you combine loops in different numbers and at different angles to get different geometric shapes? Now you are getting into some pretty complicated spatial relationships.
Baking soda and vinegar can be a gee whiz activity, but it can also be the beginning of a lot of investigation. What is the combination that will give you the maximum fizz? How are the bubbles produced related to soap bubbles? Where are bubbles like this found in nature? How do we use them?
Mobius strips, flexagons, and baking soda/vinegar are what you make them. They can be a one shot gee whiz activity or they can be the grabber that gets the student interested in something much deeper. It depends on how the teacher handles it and how imaginative the teacher is in coming up with ways to integrate it into the curriculum.