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 conceptsyou could explore with this challenge: arithmetic, combinations & permutations, counting, knot theory, proportions/ratios.
The Challenge: Create your very own order 4 Permutohedron (see video below).
Materials Needed: Paper, pencil, patience, and if you want to go 3D, you sure can. Post-it notes work pretty well when playing with this. Math conceptsyou could explore with this challenge: angles, combinations & permutations, geometric construction, geometry, graph theory, polyhedra, sequences, vertices/intersections.
The Challenge: Can you figure out all of the ways that 3 circles can overlap and intersect with each other?
Materials Needed: Curiosity and patience. Whatever medium you like! Please watch ONLY the first 1 minute and 20 seconds of the video below. If you watch more, the answer will be given away! Don’t ruin it for yourself! It’ll be so satisfying if you do it yourself! Math concepts you could explore with this challenge: circles, combinatorics & permutations, vertices/intersections, radii