The One Where the Equation Pushes the Representations

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In our abbreviated summer program, we’re going through linear functions. Kiddos are great at tables and pretty good at graphs. So now it’s on to using equations to generate those representations.

I feel like we could probably push more on what the different parts of the equation mean (slope, y-intercept) and I almost wish we were doing more with really big numbers (to make using an equation worth it rather than just counting or multiplying), but it feels important to build intuition around how to use linear functions and equations.2017-06-29 13.52.56-2

Photo: Student work. What do you observe? wWhat do you wonder?

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The One with the Extension

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Our school/summer program works with a wide range of prior student knowledge. As such, I feel like teachers sometimes talk about whether they feeling stronger supporting students with interrupted education or students who need more of a challenge (the two extremes of the spectrum). For whatever reason, I often think of myself who is (mildly) better at supporting students who are struggling.

So I’m pretty pleased with how Wednesday’s extension went. We started with a 3 Reads problem that I’ve done before (the first one I ever wrote and, surprisingly, one of the strongest ones I’ve taught). It ties in pretty well with the content we’re studying right now – linear functions and volume. Most of the class tried to figure out how many boxes there were be if a certain number of boxes kept appearing every day. The one group that was farther ahead got yardsticks and had to estimate if all the boxes would fit on the third floor, which involved actual estimating and modeling (if you think I’m letting kiddos out into the hallway to roam free during last period, you might be confused).

2017-06-28 13.58.17-1Photo: Student answer sheet and calculations: What do you observe? What do you wonder?

The One with Graphing Negatives

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One of the weaknesses of the curriculum we wrote for the school year is that it mostly focuses on graphing in the first quadrant. As I was reminded while writing and pulling activities for this summer, that’s where many of the “real world” problems are. (I know, I know. Not all math needs to be “real world”)

Fortunately (and as a reminder to my future self), problems with money and days can extend into work with negative numbers. My Summer Planning Partner also came up with the idea of using a 4-quadrant axes regardless of where the numbers fall (at some point, School Year Planning Partner and I made the decision to print 1st quadrant graphs so that kiddos could focus on bigger, more easy to see points. Maybe I regret that?)

2017-06-27 18.12.09Photo: Because we didn’t put in a table to scaffold, one (some times distracted) kiddo wrote their own work on the bottom, then made the graph without much prompting at all.

What do you observe? What do you wonder?

The One with Realish Data

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We are trying to align our curriculum to the biology curriculum, which has to do with waste management. For our Friday Project Page, we find a few interesting graphs from an actual report. One kiddo asks what MSW is and I have to google it during first period (Municipal Solid Waste, in case you were wondering). I wonder whether the tables and language might have been just a bit too academic, but #IRegretNothing (well, I don’t regret much)2017-06-23-14-50-28.jpgPhoto: Data and graph. Gotta revise those axes.

What do you observe? What do you wonder?

The One with the Linear Representations Scaffold

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One thing I’m finding, 3 weeks (to the day) into summer school, is that when in doubt, lean on your routines (I’m fairly certain I read this in Carl Oliver’s blog, to give credit where credit is due). We have about 5 weeks with 50 minute classes, so there is not much time to teach or to plan (let alone condense everything into a cohesive, project-based unit that may or may not sync with the biology class next door).

It’s taken me a while to remember this, and to get back into it.

I do recall that one of the structures that was most successful from our linear functions unit is the multiple representations paper (It says “Different Representations” on the actual paper and that is how the kiddos largely refer to it. Change it? Leave it? The eternal dilemma…)

For some reason, the kiddos love this one. There’s enough to talk about, there are different sections, and (added benefit of teaching summer school to some awesome multilinguals, many of whom I taught some portion of the year to) enough kiddos know something about the things that we’re seeing that most kiddos have some access to the content but still need to practice what goes where in the table or why we don’t just put the y-numbers from the table on the y-axis.

I’m also fairly certain that only our school talks about “Figure X” as I had to stop class and review it every time. It’s sometimes a bit too complicated for my tastes, anyway (but makes a nice stretch point).

Photo: Different Representations Paper

2017-06-21 15.35.24What do you notice? What do you wonder?

The One with the Big Numbers

We’re doing linear functions for summer school and pulling hard from last year’s curriculum. This means using CPM’s pile patterns (which I cheat and just refer to as “patterns”. Who wants to explain what “pile patterns” is to a class of (amazing) emerging multilinguals, when there’s so much else you could be teaching).

Kiddos glom on to the idea of patterns pretty readily, which is great. They’re visual and you can ask “how many?” and point without requiring too much language (my big takeaway this week).

I get to tinker with this class a bit more and we have less time (5 weeks, 5o minutes a class), so I cut some stuff.

For the patterns, we usually jump from finding the 4th and 5th figure to finding Figure 99. This has always been a bit of a jump for me, especially for kiddos with Interrupted Education who may not make connections to the idea of repeated addition and multiplication.

Photo: How many squares in Figure 15?2017-06-20 16.42.12

I spend quite a bit of time in class saying, “Sit down, Jeronimo” (not the kiddo’s real name). But he really grabbed on to this task. While many kiddos struggle to anticipate the figures beyond the ones they can see (or ones one or two our), this kiddo made his own chart to help track numbers. Pretty awesome.

What do you notice? What do you wonder?