My Favourite Math Things

 For the purposes of sharing in class, this choreography puzzle might be a fun one to try. I hadn't realized I was literally embodying math through dance since I was nine and then actually figuring these puzzles out for myself when I started choreographing more at 16. I've done this lesson four times on my short practicum/subsequent visits and it's interesting how there were new approaches to it even by the fourth time it was presented!

 

 

In terms of math puzzles/problems that are my favourite, I tend to like math contest word problems. A lot of the AMC problems are fun for me to solve so I chose one at random (#19) and actually went the wrong way with it but found my way back eventually. I thought about how sometimes students will be able to identify exactly what to do and exactly what they need right from the start but some need that extra time and further exploration before they can know what exactly is happening and what needs to be done. If I had access to scissors (I'm currently self-isolating in an apartment above my family's store and can't touch things they need), I would have physically cut out this shape and tried to figure out the properties of this cylinder and what it would look like to tape two sides together. 

One puzzle that stands out from my math journey is actually a rather simple one that I think I first came across during elementary math contests. It's the one where there are multiple triangles within larger triangles where the trick is not to just count the inner triangles but recognize that there are multiple ones built up of smaller triangles (or you could describe it as many triangles contained in one big triangle). The reason this was memorable was that I ended up being in a summer camp in which I was often doodling, and one day I was trying to recreate that puzzle from memory. I wrote down "There are 23 triangles" or something, and one of the tutors running the camp came over and said, "Oh okay so there are 23 triangles here? I thought there were only 16." I started to explain, "See we have to count the triangles that are made up of triangles-"And as I was explaining, I realized I missed some so I said, "Oh no, I missed some. But basically that's what we have to do." And he just went, "Ohhhh that's interesting. Cool!" He was a math tutor and he had absolutely seen that puzzle before, which was why he asked me about it - so I would explain my process and could catch my mistake on my own. I ended up getting tutored by him for a few years after that, and eventually working with him a few years later at that same company. He was definitely a great role model for me and I have always striven to be as inspiring and engaging as he has and continues to be when teaching/tutoring students.