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: Today, courtesy of the extraordinary Mark Kaercher:
Materials Needed: Cardboard tube (toilet paper or paper towel rolls)
Math concepts you could explore with this challenge: angles, geometry, polygons, symmetry
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: 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: 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 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 concepts you 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 concepts you could explore with this challenge: angles, combinations & permutations, geometric construction, geometry, graph theory, polyhedra, sequences, vertices/intersections.
The Challenge: Create an illusion using isometric lines.
Materials Needed: Isometric Grid paper You can print some or you can create some (that just takes a bit of patience), pencil and ERASER. This challenge is best done as an exercise in erasing, changing and play. You can see in my time lapse below just how much erasing I did and I’ve done this kind of thing many times before. Be gentle with yourself.
Math concepts you could explore with this challenge: Angles, geometric construction, geometry, isometric grids, perspective
(Props to Kate Nowak who suggested this.)
The Challenge: Create as many iterations of the Dragon Fractal as you can. See below for my attempts and videos to help.
Material Needed: There are a couple options here:
-Paper and marker (sharpie?). Maybe grid paper, preferably paper that is thin enough to see through (notebook paper is normally thin enough)
-Strips of paper to fold it
-Whiteboard marker and whiteboard/window
-??? I bet you have better ideas than I do.
Math concepts you could explore with this challenge: fractals, functions, geometry, proportions & ratios, sequences
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