Day 3 of functions today. It was time for Graphing Stories.
These videos were created by Dan Meyer, beginning with the original lesson (7 years ago!), then added to when he crowdsourced more ideas here. His final product is at the link above — 22 videos for students to graph, complete with an awesome handout. The lesson is simple. Show a video, 15 seconds, and name a quantity you want to graph against time. Show it again at half speed. Show it again to have kids refine their graphs. Then, show the answer. Wash, rinse, repeat.
I started with this story: guy climbs up a slide, and slides down.
Seems simple. The kids graphs were also simple. He goes up, then he goes back down. Thing is, the quantity we’re graphing is the height of his waist off of the ground. Watch the video yourself, see if you get it right the first time.
Answer looks like this:
The first drop is when he sits down. Then he pauses for a second, slides down the slide, and stands up. This was a great demonstration of what it means to attend to precision — and all of a sudden, kids wanted to get their graph just right.
One class struggled more with the basic ideas of graphing — and the lesson comes with its own scaffolding! Show them this video
of someone filling a pitcher of water. Simple, straightforward, and gives kids a chance to be successful before getting to the fun stuff.
There were lots of great moments here. A few more:
Dan filmed himself swinging on a swing, then jumping off. Here’s a screenshot:
There is nothing quite like showing kids the video twice, watching them sketch their graphs, and then asking how many times Dan swings before jumping off. The level of debate surprised me, and what they were really arguing about was attention to precision. They wanted to get their graphs just right, and that meant watching and recording carefully.
Next was a video of a kid sliding down a big slide, with three short flat parts on the way down. Got lots of graphs that looked something like this
Not bad. They get the idea. But it looks eerily like a side view of the slide. The actual graph looks like this:
It’s a subtle difference, but now students were thinking about how long the little girl is on the flat part of the slide, and forcing them to pay attention to the quantities at hand — time and height — and ignore what they were subconsciously imposing on the graph — horizontal distance.
Finally, there was an absolutely insane graph that my kids told me is from the video game Portal. You’ll have to go to the site to watch it yourself, but the graph looks something like this. While this is a bit advanced for my kids, it was a great example of how versatile the idea of a function can be, as well as just a really fun video to watch and try to graph.
The most important point here is that this lesson didn’t go nearly as well as I’m making it sound. I didn’t get the balance of whole-class and partner sharing right until my second class. I should’ve shown the kids the videos one or two more times before having them share their graphs to give them more chances to refine and improve their work. I struggled to get kids to stop giggling and just graph for some of the sillier videos.
But this lesson had two huge benefits for my kids. First, some kids think a function is just a weird thing we talk about where you have to draw vertical lines on a graph, and I’m doing them a disservice if I don’t give them real, concrete examples of the depth and breadth of relationships between two variables that functions can represent.
Second, they wanted to attend to precision. This wasn’t me saying “read carefully!” or “don’t fall for that trap!” or something else that makes me the annoying math teaching making life difficult for them. They wanted to have the best graph — and that meant saying that the guy on the bench press started with the weight in the air, lifted three times ending at 9 seconds, struggled to lift it as the weight went up and down a bit, before lifting again and ending at the top. And that is one mathematical habit that my students will take with them from class today.