The Challenge: To create this star.
Materials Needed: In an ideal world, you have a compass and ruler, but sans compass, you just need to do your best to divide a circle into 10 equal pieces.
Math concepts you could explore with this challenge: angles, geometric construction, geometry, islamic geometry, lines, vertices/intersections
And now is a great time to explore some polyhedra if you haven’t yet done so! Here are some websites shared by Mark Kaercher that are great.
The Challenge: Make your very own paper roll polyhedra. All inspired by this tweet from Mr. Allan shared by Clarissa Grandi
Materials Needed: Paper rolls. Can be toilet paper or paper towel rolls or you can make your own!
Math concepts you could explore with this challenge: angles, geometry, polygons, polyhedra, symmetry, vertices/intersections
The Challenge: Create your very own Golden Rectangle Icosahedron!
Materials Needed: Cardboard, markers, scissors/box cutter, string/ribbon/thread
Math concepts you could explore with this challenge: angles, geometric construction, geometry polygons, polyhedra, proportions/ratios, vertices/intersections
The Challenge: Great your very own tessellation from a small piece of cardboard.
Materials Needed: Pencil, paper, and cardboard from a cereal box or a pop box or something similarly thin but stiff enough to trace.
Math concepts you could explore with this challenge: angles, geometry, polygons, tessellations, vertices/intersections
The Challenge: Draw a polygon. Then mark the midpoint of each side. Connect the midpoints of each side to make a new polygon. Repeat. (Don’t sleep on the quadrilaterals here. They do something rather surprising and beautiful!)
Materials Needed: Paper & pencil or online graphing software like Geogebra or Desmos
Math concepts you could explore with this challenge: angles, fractals, functions, geometry, lines, polygons, proportions/ratios, slope symmetry, vertices/intersections.
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
The Challenge : Create this design from the Agra Fort.
Materials Needed: If you have a compass, use this tutorial from Samira Mian. If you do not have a compass, you can use my instructions for making this from a regular grid below that.
Math concepts you could explore with this challenge: angles, geometric construction, lines, polygons, symmetry, tesselations, vertices/intersections
The Challenge: Fold 30 identical pieces of paper to put together as an icosahedron.
Materials Needed: 30 square pieces of paper. No problem if it’s not origami paper, you can use regular paper (and you can decorate it if you want!)
Math concepts you could explore with this challenge: Geometry, graph theory, origami, polygons, polyhedra, symmetry, vertices/intersections
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 concepts you 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 concepts you could explore with this challenge: angles, combinations & permutations, geometric construction, geometry, graph theory, polyhedra, sequences, vertices/intersections.
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