## 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.

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

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

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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

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

What do you observe? What do you wonder?

## Day 59: The One With Cost *and* Revenue

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Today we took the cost equation and table and graphed it. Then, we graphed the revenue equation and table for each of 2 prices onto the same graphs.

Here’s one of the first work samples that we used as a model for the class. (In grading the projects, a lot of kiddos only have one line and I need to think about how to make that clearer when we teach it again in 2 years).

What do you notice?

What do you wonder?

## Day 48: The One Where We Explain Slope to Each Other

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We’re heavily borrowing structures and curriculum from the last time we taught this course 2 years ago and I’m totally OK with that. One of those structures is the Explain to Each Other where students try to solve a problem and then explain it to a group with a different problem. The emphasis today is on finding the slope in a linear equation, given an equation and the option to make a table and a graph.What do you notice? What do you wonder?

## Day 47: The One with the Slope Triangles

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We rotate the kiddos through stations, where they take different linear graphs and calculate the slope. We are challenged at every turn by trouble reading graphs – are we counting numbers or squares? We start to make connections between different-sized slope triangles on the same line.

What do you notice? What do you wonder?