#MathArtChallenge Day 22: Extending Day 14…

The Challenge: Dave Richeson came up with a brilliant extension for Day 14

While walking the dog I had the idea for this modification of @anniek_p’s #mathartchallenge activity. Randomly generate zeros and ones and use them to determine which of the four knot tiles to put in the corresponding cell. Alternate joining the end along the outside. I 1/2 pic.twitter.com/E2nufNHxMf

— Dave Richeson (@divbyzero) April 5, 2020

Materials Needed: paper (grid?) and pencil!
Math concepts you could explore with this challenge: combinations and permutations, knot theory, probability, randomness

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. Why is it that the loops are always disconnected? Will they always be? Is it possible to get them to intertwine?

8.) Look for and express regularity in repeated reasoning. How many different paths are possible given a 3×3 grid? A 4×4 grid? Can you find a generalized pattern?