## The One With the Graphing Project Page (Number 2)

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Admittedly, I’m not backwards planning this summer unit as well as I’d like to. We spend Fridays working on a summative-esque project page. Last week, we used real data to make graphs. This week was supposed to be more of a focus on using linear functions to make predictions, but we ended spending a worthwhile day making a table and then a graph from a situation. (I also wish we’d done something with equations, but that’s for another time).

Photo: Student work. This kiddo was rather stymied because the (correctly scaled) axes made her graph too small to see the change over time. So we worked to redraw the axes (growing by 5 instead of 10).

What do you observe? What do you wonder?

## 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).

Photo: Student answer sheet and calculations: 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

What 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?

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?

## The One with the Patterns

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Week 3 of Summer School, though I don’t know if the first 3 day week actually counts.

In what is maybe not the most cohesive move, we start a new unit on linear functions and graphing this week (Goodbye area and volume). I largely pull from our linear functions unit from this year which largely pulls on CPM (credit where credit is due).

Photo: Student Work on PatternsEduardo has been in my class for 2 years, which makes me somewhat wonder why he’s in my summer school class, but also thankful that he’s there to help support other kiddos as we go. He catches on to the patterns quick (and also has a helpful habit of saying “Wait, we learned this already”, which gives me some hope that what I teach may stick around for longer than the 65 minutes I usually see kiddos) and is quick to point out that the sentence structures for the opening are the same for this entire week (thanks, Estimation180).

He also carries over some unusual conceptions from the school year (that many other kiddos carry), including how to generalize figures with more squares. Admittedly not the most useful skill and probably not Common Core-approved, but it reminds me that I need to push kiddos to explain what the square represents and ground them in familiar concepts like base and height.

What do you notice? What do you wonder?

# Day 20: Too Fat, Mister

Today’s activity was on linear and exponential growth. Students had to scale a model of a human by addition and scale another model by multiplication, with the idea that there are situations when linear growth is a better model and situations where exponential growth is a better model.

The red copy is the “growth by adding” version from a student (who was then exiled to a lone table for goofing off, sigh), the black copy is my hastily drawn version of the same from when one class didn’t quite get as far as I would have liked before the debrief.

Funny how the debrief has to happen anyway.

Interesting that many students instinctively thought they were doing something wrong when their model “turned out funny”. Also curious to see how easily students doubt themselves and how hard it can be for them to defy convention.

(Note: typing from my phone in hopes that I can get these up faster at the end of the day)