# #MathArtChallenge Day 23: Brunnian Links

The Challenge: Build a set of 3, 4, or even 5 Brunnian links.

Materials Needed: Your call. Joey already did the 3 link one with straws. I used crocheted yarn. Shoelaces?
Math concepts you could explore with this challenge: Combinations & Permutations, counting, knot theory, vertices/intersections

And then because I realize it’s not nice to not pull apart the 4 for you:

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!

1.) Make sense of problems and persevere in solving them. To succeed here, you really do need to deeply understand the problem. What does it mean to have any single link unlink every other link? I encourage you to begin with 2 and 3 links.

5.) Use appropriate tools strategically. What tools can you use here? Joey used straws, I used crocheted snap-link knots – what can you come up with? Is there a way to simply draw this? Why or why not?

8.) Look for and express regularity in repeated reasoning. Is there a way to use the solution for 2 links to help you with 3? Can the 3 link solution help you with 4? Can you create a generalized rule or set of rules?

## Author: Ms. P

Math Teacher in Minneapolis, MN.