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 conceptsyou could explore with this challenge: counting, graph theory, knot theory, vertices/intersections.

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.