The Challenge: How many 2 link knots can you find? See the examples above to help you get started.
Materials Needed: knot materials (these could be crocheted like I have, or shoe laces, or electrical cords which you can plug into themselves)
Math concepts you could explore with this challenge: combinations & permutations, graph theory, knot theory, topology, vertices/intersections.
The Challenge: Using a vertex description, build yourself one, two… up to all 13 of the Archimedean solids.
Materials needed: Card stock and tape (painter’s tape is great, or masking. Other stuff will work, but I’ve had more success with the paper-y tapes.) OR Magnatiles, but those can get pretty pricey.
Math Concepts: structure, polyhedra, angles, 3D structure
The Challenge: Create all of the possible “stars” given a certain number of vertices.
Materials Needed: Pencil/paper
Math concepts you could explore with this challenge: angles, arithmetic, circles, combinations & permutations, lines, proportions/ratios, symmetry, vertices/intersections
The challenge: Create a complete (all 16 spaces) 4 set venn diagram.
Materials needed: Pencil, paper, other??
Math concepts you could explore with this challenge: circles, combinations & permutations, graph theory, probability, vertices/intersections
The Challenge: Represent a pattern of permutations
Materials Needed: ??? There are so many options here. I used paint, but you could draw, use yarn, legos… anything.
Math concepts you could explore with this challenge: combinations & permutations, counting
The Challenge: Can you find the 4, 5 and 6 crossing knots?
Materials needed: Patience, creativity, paper, pencil, maybe some strips of t shirts and a safety pin?
Math concepts you could explore with this challenge: Combinatorics & permutations, counting, graph theory, knot theory, topology, vertices/intersections
The Challenge: Using a hexagonal grid, create a labyrinth using “Y” shapes.
Materials needed: hexagonal/isometric grid (you can print from the internet or obtain from a compass), writing utensil, randomizer (die, coin, etc.)
Math Concepts you could explore with this challenge: 2D, combinations & permutations, counting, isometric, probability, randomness
The Challenge: Start by making (or use mine below) a Pascal’s Triangle. Then shade in some sequence of values. I suggest starting with even/odd numbers, and then perhaps multiple of 3, 4 etc.
Materials Needed: Pascal’s triangle. You can print one or you can create your own!
Math concepts you could explore with this challenge: algebra, arithmetic, combinations & permutations, counting, functions, proportions/ratios, sequences, symmetry
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: Dave Richeson came up with a brilliant extension for Day 14
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