## The One with the Last Day

### Image

The last day of summer school comes and goes. I try to find a way to fill time with expected absences (One kiddo told me, “Why did you tell me I had to come today?” to which I had to bite my tongue and not say, “I didn’t think you’d actually listen to me!”) and no new content. I end up having kiddos draw mathematics class for their opening and then fill it by having them reflect on the year and write cards to themselves and each other.

Photo: Someone’s drawing from the opening. Quite a few have the content and language objectives.

What do you observe? What do you wonder?

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

### Image

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

### Image

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 Graphing Negatives

### Image

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?)

Photo: 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 W-Looking Graphs

### Image

Our goal for today is to practice scaling axes, which is something we kind of talk about during the school year but should probably be more explicit about.Photo: Student work. Apparently when we choose random points, they look like W’s.

What do you observe? What do you wonder?

## The One with Realish Data

### Image

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)Photo: Data and graph. Gotta revise those axes.

What do you observe? 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

### Image

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?

## The One with Individual Tangent Practice

### Image

I’m a bit more into individual practice, these days. A few years ago, I think I was more “all groupwork, all the time”, but I’m appreciating the fact that a decent culture of groupwork at our school helps support our kiddos when they’re working individually while also allowing them to spend time on what they need.

We’re still working through how reference angles are related to tangent ratios (without really calling them that – most kiddos are sticking with opposite and adjacent sides). Also trying to balance procedural work (especially with ratios) and conceptual thinking. Someone made a decision with this curriculum to round some of the tangent ratios to numbers that made it easier to solve for unknown numbers. While this may take away from the actual ratios (which are a calculator button push away, anyway), it did give a lot of kiddos access who weren’t familiar with solving ratios. Lots of struggle today and I’m hoping kiddos got something out of it.What do you notice? What do you wonder?

## Write It Out: The One with More Exponent Expanding

### Image

Student explaining which numbers are affected by the exponent. It feels like we’ve been working on this long enough that kiddos who weren’t initially into it are getting it and explaining to each other.

What do you notice? What do you wonder?