Perplexed in Patterns

So much time has passed since I last blogged that I forgot my account/password. I think I tried at least 3 combinations of each before I cracked into my Blogger account. Hopefully I will do better in the future. I know I promised two blog posts tonight, but I forgot how difficult blogging is with my attention span.

Instead of conducting PD this week, I’m actually attending some professional development through the University of Mississippi’s Center for Math and Science Education (@UMCMSE). I’ve probably mentioned how great this group is many times before. I attended their CCSS 3-5 workshop last year and fell in LOVE with elementary mathematics. What I love most about these workshops is that it doesn’t rely on a whole lot of tech. It’s basically, “How can we teach the standards in ways that students can make meaningful connections with stuff you probably already have in your classroom.” Unfortunately, “technology” isn’t standard across the state. In some schools, cell phones are banned from campus and wifi is wonky most of the time. This is also true for several schools in my district, SO going “low- or no-tech” is a challenge for me.

This week, I’m attending the 9-12 workshop on the *cough cough* Mississippi College- and Career-Readiness Standards. On day two, Dr. Julie gave us the following patterns task (adapted from College Preparatory Mathematics).

Patterns. Ok, I got this (thanks to Fawn Nguyen and Visual Patterns). So the first thing I notice is that if I moved that top block that’s “hanging out” to the hole in the bottom right, I could make a rectangle. Badda bing, badda boom. I’m good.

** I should say here that I realize it asked for an equation and I created an expression… but I was all “celebratory” and stuff, and apparently the rest of the class was as well. We all did the same thing. Whoops. 🙂

We all went around the room and discussed how we got our expressions and there were some pretty interesting ones:

This person immediately saw the square in the center and the constant “extra” block up top. She also saw that the bottom row increased by one block for each phase and then realized it was the phase number plus an additional block.

 

I found this one really interesting because it’s one I wouldn’t have seen. This person added extra blocks to create a square. Then saw the pattern of doing that created three sets of “trains” of the same length plus the addition extra block needed to complete the square. (I am not explaining it as well as her work, haha). Still a very cool strategy.

So we all “ooooh’ed” and “ahhhh’ed” over each others strategies, how they were similar, how they were different, and how we could visualize that expression repeating for every new phase. And the question arose: “How do you know you’re all correct?” The answer: “When we all expand our expressions, we get the same thing.” “Oh really? What did you get?” “We got n^2 + 5n + 6.”

And then Dr. Julie rocked my world.

“So we could easily see the repeated pattern of each of your expressions in the phases. Here’s my question: Where do you see n^2 + 5n + 6 in each of the phases?”

 

Ummmmmmmm…..

 

But…but…but, I did the thing! AND I could justify the reasoning of the expressions created by my peers. We ALL did the thing.

 

No one had ever asked me to do this before. OH CRAP. My comfort zone was rocked.

 

Ok, wait, Hedge. You can do this.

 

Yes, I could find an n x n square in each of the phases with no problem. And I could even find six extra blocks. But the 5n? What would that even look like?

Not only that, but I have to make sure that the pattern is consistent (and not random) in each of the phases??? Oh LAWD. Let me channel my inner 4th grade Max Ray (reference this @ 1:56 – 2:00) and figure this out. This took a while.

(http://www.sticktwiddlers.com/wp-content/uploads/2014/11/time-passing-gif.gif)

Low and behold:

 

I found the n x n square, found the trains of length n on each side of the square, one additional train of length n below, and then six blocks (noted by the dots).

So you know me…

Then she gives us this:

I could do the “normal” inside my comfort zone. But this was new and initially wasn’t easy for me. So instead of following directions (sorry, Dr. Julie, if you’re reading this), I challenged myself to find the expanded pattern for each group.

And this is probably no big deal to most of you, but I’ve just never even thought to find the expanded form within the pattern before.

And I LIKE IT. 🙂

So here are my solutions to A and B. If you decide to do C and/or D and wanna compare, tweet me.

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One thought on “Perplexed in Patterns

  1. I have been attending workshops very similar to this as part of a state Mathematics Education Consortium grant and it has been so eye opening!! I still haven't been able to translate that work to teaching our students this way… sigh.

    Like

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