#MathArtChallenge Day 5: Probability designs!

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 concepts you could explore with this challenge:  Probability, probability distributions, randomness

Huge thanks to Emily Lynch Victory for the inspiration for this challenge. She’s a fantastic mathematical artist that I met a few years ago at a math teacher conference, who had a piece like (but far superior!) to my first one below.

Example 1: Roll a die, design a grid!

I assigned a design to each of the 6 outputs of a regular die, and then rolled the die to figure out how I should color in a 6×6 grid.

Example 2: Crochet!

Here I flipped 2 coins and assigned each of the permutations a type of crochet stitch. I made each row 10 stitches long, and switched stitches each row. In the end, I made it into a möbius strip, because that’s just cooler.

HH: single crochet

HT: half double rochet

TH: double crochet

TT: Triple crochet

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Great example here from Joel Bezaire

#mathartchallenge pic.twitter.com/Xa7XGUZmk7

— Joel Bezaire (@joelbezaire) April 20, 2020

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!

2.) Reason abstractly and quantitatively. Once you’ve finished a piece, what do you notice about the distribution of values? How does that compare with the relative size of your piece?

5.) Use appropriate tools strategically. What methods make it easiest to explore the probability of values? What are the benefits or drawbacks of using a square grid? Would a 3D model make the chosen values easier or less easy to see?

8.) Look for and express regularity in repeated reasoning When completing with a class, what patterns do you see as you look over all the designs created by the class? How does the distribution of number change?