The Challenge: Create a Celtic knot, and do some wondering about why you got the number of links that you did. Can you predict how many links you’ll get? (I wrote another blog post on this a while ago, but only go there if you need more examples, because I reveal a lot of the good stuff in it: Knots, Links, & Learning)
Materials Needed: Paper, pencil. If you have grid paper, that might help, and here is some special grid paper you can use courtesy of Justin Aion.
Day18 11×15 Celtic Knot Grid
Day18 MAC 16×22 Celtic Knot Grid
(or you can just rotate grid paper 45 degrees like I do in the video below)
Math concepts you could explore with this challenge: arithmetic, combinations & permutations, counting, knot theory, proportions/ratios.
Here is a visual set of instructions, and below that is a video tutorial.
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. How many distinct links are created by an nxm grid? How do you know? What if you remove a “hole”? How does that affect the final number of links?
8.) Look for and express regularity in repeated reasoning. Through making a large number of these, can you possibly decide what the length of each link will be? For which ones can you know and for which can you not?