The Challenge: Draw an alternating knot. Then see if there’s any way to draw a looping line that cannot be turned into an alternating knot.
Materials needed: Pencil & eraser, or whiteboard, or markers?
Math concepts you could explore with this challenge: counting, graph theory, knot theory, vertices/intersections.
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!
3.) Construct viable arguments and critique the reasoning of others. Is it always possible to create an alternating knot? How do you know? Can you create a counterexample?
7.) Look for and make use of structure. How can you methodically work through your knot so you can be assured you’ve truly alternated it? Is it always possible?