cheesemonkey wonders

cheesemonkey wonders

Monday, October 7, 2013

Teaching Mathalicious' "Harmony of Numbers" lesson on ratios, part 1 (grade 6, CCSSM 6.RP anchor lesson)

I started teaching Mathalicious' Harmony of Numbers lesson in my 6th grade classes today, and I wanted to capture some of my thoughts before I pass out for the night.

The Good — Engagement & Inclusion
First of all, let's talk engagement. This made a fabulous anchor lesson for introducing ratios. The lesson opens with a highly unusual video of a musical number that every middle school student in America knows — One Direction's "What Makes You Beautiful."

You'll just have to watch the video for yourself to see how the surprise of this song gets revealed.

What I wish I could capture — but I can only describe — was the excitement in the room as my 6th graders realized what song was being played. It took about eight measures for the realization to kick in. Imagine a room full of South Park characters all clapping their hands to their cheeks and turning around with delight to see whether or not I really understood the religious experience I was sharing with them.

Every kid in the room was mesmerized. Even my most challenging, least engaged, most bored "I hate math" kids were riveted to the idea that music might be connected to math. It passed the Dan Pink Drive test because suddenly even the reluctant learners were choosing to be curious about something in math class. My assessment: A+

We started with a deliberately inclusive activity to kick things off — one whole-class round of Noticing and Wondering (h/t to the Math Forum). Sorry for the blurry photography of my white board notes. They noticed all kinds of really interesting things and everybody participated:

From noticing and wondering, we began to circle in on length of piano strings and pitch of notes. This was a very natural and easy transition, perhaps since so many of the students (and I) are also musicians of different sorts. Five guys, one piano, dozens of different sounds, what's not to like?

The Not Actually 'Bad,' But Somehow Slightly Less Good
One thing I noticed right away was that, while the scale of the drawings on the worksheet worked out very neatly, it was kinda small for 6th graders to work with. The range of fine motor skills in any classroom of 6th graders is incredibly wide. At one end of the spectrum, you have students who can draw the most elaborate dragons or mermaids, complete with highly refined textures and details of the scales on either creature. At the other end of the spectrum, you have the students I've come to think of as the "mashers," "stompers," and "pluckers." These are the kids who haven't yet connected with the fine motor skills and tend to mash, crush, or stomp on things accidentally. Some will pluck out the erasers from the pencils in frustration ("Damn you, pointy pencil tip!!!").

This made me want to rethink the tools and scales of the modeling. It might be good to have an actual manipulative with bigger units (still to scale). Cutting things out is a good way for students this age to experience the idea of units and compatible units. Simply measuring and mentally parceling out segments is a little tough for this age group. Ironically, within a year or so, this difficulty seems to disappear. I'm sure there are a lot of great suggestions for ways to make this process of connecting the measurements to the ratios through a more physically accessible manipulative or model. But then again, I'm just one teacher, so what do I really know? My assessment: B

The Not Ugly, But Still Challenging Truth
The most difficult thing about this lesson is that 6th graders go S L O W L Y. Really slowly. My students' fastest pace was still about three times longer than the initial plan.

I am fortunate that this pacing is OK for me and my students. They need to wallow in this stuff, so I will simply take more time to let them marinate. We'll try to invent some new manipulatives for this, and I'll blog about them in a follow-up.

But the reality is that this lesson is going to take us three full periods to get through. They will be three awesome, deeply engaging learning episodes filled with deep connections as well as begging to have me play the video again (Seriously? Three times is not enough for you people???).

Even though this is a much bigger time requirement, I still give this aspect of the lesson an A+. Getting reluctant learners to be curious about something they're very well defended against is a big victory.

I'm excited to see what happens tomorrow! Thanks, Mathalicious!


  1. Yo hey -- So I'm thinking about changes that could be made to what we provide in this lesson. As you can imagine, it's tough for us to deviate from the multimedia presentation + student handout packaging. But we could, for example, put the segments-to-measure on a grid, so kids could visually estimate without having to manage a ruler. Or put the segments by themselves on a whole sheet of paper, landscaped, to make them bigger (as we sometimes put a single graph by itself on a whole sheet of paper, when the graph is referred-to throughout the lesson).

    We struggle sometimes with what we can do to make our materials accessible for everyone, and what we should leave for teachers to do, to accommodate the needs of the students in their classes. Would you say the masher/stomper/pluckers are a prominent feature in every 6th grade classroom? Or is it relatively few teachers who need to accommodate the occasional student?

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