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.

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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:

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

Oisín visualized it in a completely different way:

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

Finally, Jaclyn took yet another approach:

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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! ❤

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About katenerdypoo

Middle Years and Upper Grades math teacher in the Netherlands teaching both within the Dutch national curriculum and the IB MYP and DP.
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