Wk 4 - Art-ifying Mathematics

 To begin my experiment, I started simple. Based on the concentric circle representation of Binary put together by Ali and Colin, I tried my hand at representing base 4. It wasn't until I was partway through that I compared it to their base 4 representation and found many differences! 

Here is mine: 

It made sense to my brain to connect the location/size of the circle, the colour, and the number. So, in the first circle, the number 1 is represented by both the size of the circle (smallest) and the colour (red). I used the existing colour(s) until they could no longer combine in addition to create the next numbers. At this point, a new colour and layer of circle was introduced. Because there were only 4 circles, I ran into a problem at circle 15. 

While creating this, I found I had to pay close attention! I struggled to consider which circles would work together to create the number I needed. It is clear that my brain is not used to mixing art and math. When I finished, I found myself pondering many questions: 

• How could I make it so that I could use numbers multiple times? (For example, use 2 2's to make 4, rather than 3 and 1?)
• Is it necessary for the circles and colours to both represent a number? What would change if only one represented a number?

My thought, which I might try and update later, is that the circles and colours can both represent colours, so when a colour is in a specific circle, it results in those two numbers being multiplied! Things might get crazy, but I'm excited! 

Math For Love is the creator of one of my FAVOURITE math games, Prime Climb. Prime Climb is great for many reasons, but it is connected to this week's module because of the way the game board is set up. The board contains 101 circles that players move their pieces along. These circles are numbered 1 to 100 and have colours that correspond to specific numbers and circles. What students/players don't know at the beginning is that these colours represent multiplication and prime numbers. When a number is a prime number, it is denoted by a red circle. The first few numbers -- 1, 2, 3 -- are distinct colours as well. Things change when you arrive at 4, which is split into two sections of orange, representing the fact that 2 2's multiply to create it. This continues all the way up to 101! 

Here is their chart, for reference: 

Once I finished playing with my circles, I jotted down the following points to begin thinking about ways to have my students play with these ideas. 

I would love to hear your thoughts: 

• How can I bridge this over to higher-level math concepts? My Calculus 12 students are the group that would marvel at this the most, but I don't know how to take it beyond the basic operations. 
• What is the next step? Once students have played around with this, where do we go next?