The Challenge: Create this decagon using the symmetries visible in the piece. The central images are rhombi.

Materials Needed: compass or ruler, could also use graphing software (see below!) Math conceptsyou could explore with this challenge: angles, circles, geometric construction, geometry, polygons, symmetry, vertices/intersetions.

The Challenge: Create the tessellation above using a compass and straight edge.

Materials Needed: Compass, straight edge, possibly grid paper Math conceptsyou could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, symmetry, vertices/intersections.

The Challenge: Create all of the possible “stars” given a certain number of vertices.

Materials Needed: Pencil/paper Math conceptsyou could explore with this challenge: angles, arithmetic, circles, combinations & permutations, lines, proportions/ratios, symmetry, vertices/intersections

The Challenge: (Re)create a Sona drawing. I did a couple hours of research yesterday (which is totally insufficient to fully understand it), but what I can tell you is that these drawings originate with the Chokwe people in southwestern Africa, specifically Angola and the southern part of the Democratic Republic of the Congo. The drawings are told in conjunction with a story, and the goal of most is to draw them in as unbroken a line. Please check out some of the resources below, and if you have others to add, I’d love to see them and link them here.

Materials Needed: grid, pencil, paper, perhaps graphing software. Math conceptsyou could explore with this challenge: angles, counting, geometry, graph theory, proportions/ratios, slope, symmetry, vertices/intersections

The Challenge: This is a modular origami (7 squares) spinning top.

Materials needed: 7 squares of paper. Any paper will do, it doesn’t need to be origami paper. Math conceptsyou could explore with this challenge: angles, geometry, origami, polygons, symmetry, vertices/intersections

The Challenge: Build yourself a wobbler. Wobblers are 2 circle (or 2 ellipse!) constructions that have a constant center of mass. Or rather, a center of mass that doesn’t move up and down as the wobbler rolls. Thus, resulting in a satisfyingly continuous “wobble”.

Materials Needed: cardboard, ruler, boxcutter or scissors Math conceptsyou could explore with this challenge: algebra, angles, circles, geometry, proportions/ratios, symmetry, vertices/intersections

An orange triangle with a large number of folds and lines drawn on it.

The Challenge: Create your own version of Matt Henderson’s triangle incenters.

Materials needed: Paper? Pencil? Origami? Graphing software? (There are lots of options here.) Math conceptsyou could explore with this challenge: angles, geometry, polygons, symmetry, vertices/intersections