Visual Patterns

Have you seen this excellent website? It was like nondenominational math teacher Christmas when I happened upon it!

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I definitely blogged last year about the Rectangle Pattern Task, which I’m in love with. I love the mix of linear and quadratic patterns, and the low floor high ceiling aspects. So great! This website has over 200 similar things, aka I do not have to create my own. I emailed Fawn Nguyen who created the site just to say THANKS, and she emailed me right back with the answer key. I did not think I would need it, because I’m super conceited when it comes to my own high school math knowledge, but a couple of those threw me for a loop. I was actually having a ton of trouble with the third one!

This year I decided to use that Rectangle Pattern Task as a springboard into differentiating between linear and quadratic growth. We took some notes which you can kind of see in the background of the next picture, behind some of the visual patterns:

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We’re going to do linear modeling as the very next topic, plus we do a ton with quadratic factoring and quadratic modeling later on, so it was really important for them to know what the graphs look like, what the growth is like, and what the equations are like. I’m glad we’re starting with this because we’ll keep referring back to this.

Today I had them in pairs sorting the patterns into a pile for linear, a pile for quadratic, and a pile for neither (the “neither” was a fractal, which is exponential growth). Then they wrote the equations for the linear ones. I was going to start having them write the equations for the quadratic ones, but it was too many objectives for one day. We’ll get to that later when it actually makes sense. Although honestly the linear ones have a clear procedure that always works, and the quadratic ones do not, at least not one which is obvious to me. I’ll keep puzzling with it.

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I’m going to see how things go on the assessment, but I felt like I was seeing some breakthroughs. And if they aren’t ready for the assessment, I can give them like 200 practice problems. YAY.

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