This lesson is the first one that the other two eighth-grade math teachers and I planned together. It’s similar to Dan Meyer’s Graphing Stories, but because so many of our students had seen those before, we needed a different set of stories to graph. One of my colleagues found a video of Kurt Vonnegut (probably my favorite author!) talking about the Shapes of Stories. He drew graphs for a few simple stories that most eighth graders would know, and he made it funny! Well, maybe I’m the only one in the classroom who found Vonnegut’s comments amusing. Don’t worry, though, because I joked about his jokes to really make things hilarious. I can’t recall if anyone actually laughed. Let’s pretend that they did. Anyway, we started the lesson by watching that video, strategically pausing it to ask students some questions and to make sure everyone understood the stories and the graphs. For the most part, students had seen Graphing Stories before, making the introduction go smoothly.

The next part of the lesson involved students graphing nursery rhymes using the same axes that Vonnegut did. We chose nursery rhymes for several reasons: (1) Many students would be familiar with them; (2) Nursery rhymes tend to be fairly short, making it easy to read through and graph a bunch of them in a class period; and (3) Nursery rhymes often feature significant changes in happiness, which made for graphs with lots of interesting characteristics. I placed each nursery rhyme in a dry-erase pocket and set them around the room. Then, I gave each student a sheet full of blank graphs on which to draw each story. As the students went around the room drawing the graphs, I had them cut out each completed graph and put it in the back of the dry-erase pocket. I chose two or three graphs for each nursery rhyme to look at as a class the next day. When we came in the next day, we started comparing the graphs I chose to see how students viewed the nursery rhymes differently. For each difference that students noticed (e.g. linear vs. non-linear), we tried to explain what might lead students to draw their graphs differently. We concluded that while mistakes caused some of the differences, the variety of interpretations for each nursery rhyme led to the majority of differences. Throughout this discussion, I listened for – and tried to point out – mathematical vocabulary like “increasing,” “line,” and “maximum.” After discussing three or four graphs, I decided we should move on, so we began formalizing the mathematical vocabulary that students had been using. Students drew examples in their notes for each vocabulary term, and thus, we achieved our goal of introducing and developing some important graphing terms.

I’ve done this lesson two years in a row, and as I enter my third year teaching 8th grade, I’m not sure if I want to use it again. I like starting the year with “intuitive” graphing. It’s a good way to help kids start thinking mathematically after a long summer, and it works well to introduce the graphing vocabulary that we use throughout the year. Also, I like the literacy connection, especially considering my district’s continued focus on literacy. That said, this lesson seems to be missing something. The discussion portion on the second day hasn’t worked as well as I’d like, and even though students usually seem engaged, I’m not sure that they’re doing as much thinking as I want them to. Part of the difficulty lies in the vast differences in prior knowledge that my students bring to the class. For some students, drawing the graphs and using vocabulary to describe them presents very little challenge. They’ve done this before and already know the terminology. For others, however, the process of analyzing the nursery rhymes and graphing the results proved extremely difficult. In many cases, struggling students did not seem to have much experience actually moving around and participating in class. I suppose the lesson ended up being a sort of compromise that worked well enough for everyone. I hope that I can come up with a way to enhance this lesson before I use it again.

Thanks for sharing your thoughts and modifications here, Daniel. You’re posing a real differentiation challenge and I only wanted to offer a couple of ways I try to extend the task in both directions.

One is to invite struggling students to graph

anything, then to repeat back in words what they’ve drawn, then to give them the chance to revise if they want. This lowers the entry point for access.The other is to encourage your advanced students towards greater degrees of precision. I’ll often put one of their graphs on the board (using Graphing Stories from Desmos) and then ask the class to offer “one thing you like and one thing you want to change.” There are almost no end to the number of ways advanced students can refine their graphs. That’s one place you might think about taking the task.

Thanks again for sharing!

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Great ideas. Thanks! I wish I had more reliable access to devices. Maybe I can replicate that using VNPS this year.

And gosh, Dan Meyer commenting on my blog…I guess I’ve finally made it!

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