In my freshman IMP 1 classes the past few days, we’ve been creating and interpreting graphs. We haven’t formally talked about slope yet, as for right now, we’re going for a more intuitive approach. I want them to understand slope as a rate of change, as opposed to thinking about slope as “m”.
It seemed only natural to toss in Dan Meyer’s Graphing Stories, so I brought it up during PLC time a few weeks ago. The other teachers loved it. Thus, Dan made an appearance in each of our classrooms this week. One teacher passed him off as her husband – she told her students they spend their weekends making math movies.
Anyway, in the instructions Dan so graciously provided he says,
“Bring kids to the board to demo their own graphs and make adjustments to their classmates’. Counting all this discussion, each video soaks up about six minutes.”
Well, as I’m not one who generally follows instructions, we spent about 15 minutes on Elevation vs. Time #2. If you haven’t seen it yet, go take a quick look.
I handed out the blank graphs (thoughtfully provided by Dan as a pdf), told them they were going to graph the story, but to just watch first. Pencils down, we’re just watching. We watched it once.
The first issue: how to scale the vertical axis. A couple of students thought the second story landing was about 100 feet high, so we had a nice discussion about estimating and reached an agreement as to the elevation of each landing.
Next we watched it a couple of times at half speed. One student volunteered to put their graph on the whiteboard. Here’s a recreation of their work:
Interesting interpretation, no? When this went up, I said “What do you guys think?”. I didn’t have to say anything else, the rest of the kiddos took it from there.
He didn’t fly down the stairs – you’ve got him going down 30 feet in 4 seconds.
You missed the parts where his height off of the ground was constant. You need a flat line at 20 feet.
And another at 10 feet.
What happened after 6 seconds? Did time just stop?
At that point, I jumped back in to help direct the conversation (some of them still try to get their points across by TALKING LOUDER). After a few minutes of discussing the first answer, we watched it a couple of more times. Then someone else volunteered to put up another:
First comment from the class: You missed the part at the end where he tried to trick us. So the sketch was corrected to include that last hop up at the end. We then compared the final student answer with Dan’s answer.
Now I’m okay with not following Dan’s directions about 6 minutes per clip. I’d rather spend more time with the students talking about what the graphs mean to them. This lets me know where they understand (and what they don’t). Also, I’ve found that students are sometimes more willing to listen to their peers. I often fear they only hear the teacher from Charlie Brown when I’m talking.
Once we had seen the final answer, I didn’t move on to the next clip. I said, “I’m confused, why is the line flat for the first three seconds?”. Well, his height off the ground isn’t changing so the line doesn’t change. “Where was Mr. Meyer going down the fastest?” They discussed it in their groups and they all agreed it was the interval from 7 to 8.5. When I asked them how they knew this, they thought it was rather obvious. Uhm, the line is going down faster there, Mrs. B. We then verified this by calculating his rate of descent at each interval.
Mission accomplished. Thanks Dan.