Visual Patterns

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


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:


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.


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.

NCTM Conference Thoughts

My main thought at this point is just “!!!” but that’s not really a worthwhile blog post, is it?

More specifically: Boston is a really lovely city, with a great skyline, really good mass transit, and a Chinatown far less fake than the one in DC. It’s very obvious that the population is disproportionately intelligent, and nobody actually talks like Juliane Moore on 30 Rock, so that’s a relief. The NCTM conference itself was exactly as energizing and inspiring as I had hoped it would be.

The first talk I went to that I really loved was by David Peabody from the other Washington. He teaches a class entirely devoted to math in art, technology, and history, so I got some excellent ideas in my continuing quest to make my curriculum arts integrated, or at least arts enhanced. I just emailed him the link to my blog so there is at least a slight chance he could be reading this RIGHT NOW, hello if so!

Next I heard from Geoff Krall, who did an excellent talk on strategies for turning closed textbook problems into open, engaging tasks. I’m working on some ideas for “doing the dang thing” with three-dimensional design problems, possibly doing something with sketch-up. This talk made designing open problems seem entirely possible, and may inspire me to crack open a textbook for the first time in literally years. He also said it to me in a language I understand – Parks and Recreation clips.

That evening I went to Jo Boaler’s much-anticipated talk. I was so inspired that I cried, like actual tears. She showed clips too, but not funny ones, terrible ones of Disney Chanel shows implying that girls can’t be good at math. She shared that she is soon to meet with Disney to address this issue, and just continues doing everything she can to eliminate math anxiety in a fight-the-power, taking-on-the-patriarchy sort of way.

Friday I went to another great arts-integrated talk by Carole Desoe about frieze patterns and other tessellated/ grid-based designs, mainly in Islamic art and architecture. I want to go on a field study to the Freer/Sackler galleries to find some of these grid-based designs, then maybe to the Native American and African art museums to compare these intricate interlocking designs across cultures. I want students to be able to look at these tiles or paintings or cloth patterns and see the underlying grid structures. She gave us some great resources to be able to do that.

Next up was Dan Meyer’s talk, obviously great. I’m inspired to look for potential math modeling situations everywhere now. I’m envisioning a task involving mass transit payment options: here in DC it’s crazy complicated with a different rate depending on how many stops you go, and an additional $1/ride for paper cards, but a $10 up-front cost for SmartTrip cards. I can’t decide if he is more the math teacher Brad Pitt or Dalai Lama. I will admit that I soaked up his celebrity just like everybody else, and was just as starstruck as I went up to shake his hand. I asked him what to do for our new “learn what you missed week,” when kids will be back in class for 2 days AFTER final exams, so I’m eagerly awaiting a response because I’m basically one of those teens who got invited to Taylor Swift’s houses last year. As in “OMG MET DAN MEYER, I LITERALLY DIED!”

The last really exciting talk I attended was by Dan Anderson about the Mandelbrot set. I was tangentially aware of the Mandelbrot set and the Julia set because they are fractals, but I guess I assumed their generating functions were more complicated than they actually were? He has this great program that generates the set with increasing precision. The math is also approachable and involves all students in creating these stunning images. 100% using this program with my math 4 class next year, especially because all of them will have a background in complex number operations. I love being the only [non-senior] math teacher some days, it can have its advantages when it comes to prior knowledge.

So now I’m back in DC and should get to work on things like grocery shopping, writing exams, and just continuing to soak up the math that is all around me.