The Challenge: Create a visual (or audio?) of the Recamán sequence, created by a Colombian mathematician, Bernardo Recamán Santos (who seems to have very little biographical information out there??). I was first introduced through Alex Bellos and Edmund Harris’s book.
Materials Needed: Straight edge, maybe a compass, maybe a ruler. Paper, riting utensil. Math conceptsyou could explore with this challenge: algebra, circles, counting, functions, proportions/ratios, randomness, sequences
The Challenge: Today’s math art challenge is to play the chaos game, and was inspired while I was perusing the excellent Power in Numbers by Talithia Williams. Her chapter on Fern Hunt indicated one of her research interests as Chaos Theory – something that always grabs kids attention, and leads to one of the more fascinating probability related math-art creations.
Materials Needed: randomizer (die, coin, etc.), paper, pencil, possibly graphing software. Math conceptsyou could explore with this challenge: fractals, probability, randomness
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
Materials Needed: Paper, pencil, something to randomize (die, coin, whatever) Math conceptsyou could explore with this challenge: probability, randomness, expected value
I rolled a 6 sided die to determine how many branchings and an 8 sided die (octahedron) to determine the kind of plants on each branch. It was a little loosey-goosey, and my plant is a bit more fantastical than hers, but it was fun! #mathartchallenge
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
1.) Make sense of problems and persevere in solving them. What is the expected length of each plant…arm? (Branch, they’re called branches, I remember now)
8.) Look for and express regularity in repeated reasoning. Under what circumstances is the plant going to continue forever? What conditions make for small plants? What conditions make for huge ones?
The Challenge: Using grid paper, assign each row/column a 0 or a 1. Then “stitch” both ways. You could assign the 0s and 1s as you prefer, or with a coin, or you could code something in binary!
Materials Needed: Grid/dot paper (You can print some or make some without too much trouble), or if you have the stitching materials… Math conceptsyou could explore with this challenge: binary numbers, randomness, probability, symmetry
The Challenge: Use something like a die or a coin to get random outputs. The probabilities don’t need to be equally spread! Assign a design to each output, and then get to designing. I have two examples for you below.
Materials Needed: Honestly, whatever you want. There are endless possibilities on this one. Some examples: paper & pencil (like above and in the video below), yarn (friend ship bracelets or crochet), legos… See the examples of other people’s work below! Math conceptsyou could explore with this challenge: Probability, probability distributions, randomness