## Visual Patterns

We’re doing a unit on formulae in MYP4 Math Extended now, and the textbook has a section on formulae by induction, which is full of really challenging problems but I thought it’d be more fun to start with Fawn Nguyen‘s Visual Patterns

I put one up on the beamer and after we’d done one together, I suggested that the students take out their cell phones (ah, the forbidden fruit!) and go to the site and pick some that appealed to them and if they found a really nice one, I’d put it on the beamer for more to try.

Two girls found this really rich one and were so excited about it that I shared it with the class.

It was fascinating to see the three different ways the students came up with the rule. The first to crack it was Fabiënne. She thought of it like this:

Therefore, she wrote her rule as $H = (n+1)(n+2) - 1$.

Oisín visualized it in a completely different way:

So he wrote his rule: $H = (n + 1)^2 + n$.

Finally, Jaclyn took yet another approach:

Her rule was therefore $H = n(n + 2) + n + 1$.

I wish I had seen it coming because then I would’ve been a bit better prepared. As it was, I told the students that all three rules were correct and that really they were all the same. If I’d been quicker on my feet, I would have told them to all individually simplify each rule to prove they were all the same. Instead, we did it as a whole class.

Still, it was really cool to see how their different minds work. Also really nice to finally have a real concrete example of the “no one right way to approach a problem” idea for them! We also talked about how it’d be pretty hard to come up with a rule like $n^2 + 3n + 1$ algebraically, which was good because I feel like the coursework (and my own approach) is too focused on algebra all the time. I loved this hearts problem! ❤