Students are asked to take the words of the story and make a math picture. No question is asked yet. The story is: “Maria saved $24. She saved 3 times as much as Wayne.”
BECCA SHERMAN: Great. So I’m gonna ask, we’re gonna try some active listening. Hands are free, eyes up here. If you would like, you may quietly come to the rug. So that you can, ‘cause we’re gonna spend some time looking at some different, um, different people’s pictures.
STUDENT: Do we bring our papers?
BECCA SHERMAN:If you choose to come quietly to the rug, bring your paper. You’re not going to be writing on them. You don’t need a pencil. And here’s what we want to do. You guys already know the story, you know the words. But I’m gonna put up a picture, and I’m gonna see if we, if that picture really does tell a thousand words. If it tells the complete story. Okay? And see what you guys think about it. So right now, you’re thinking quietly to yourself about this picture.
BECCA SHERMAN:Okay. So if you think you know who this story is about, give me a thumbs-up.
STUDENT: Maria and Lil’ Wayne.
BECCA SHERMAN:Without saying anything, so we don’t distract anyone else’s thinking. If you think you know who this story is about and you know how much money Maria saved, show us with two fingers. If you think you also know, see, if you could come up here and show us this sentence, She saved three times as much as Wayne, she saved three times as much as Wayne. If you think you see that in the picture, show us with three fingers. Okay. Let’s take a quiet hand. Who can tell us. You might come all the way up and show us how you know those three things. Or one of them. You want to start us off? Come on up and show us what you know about from that picture. Are you using the picture that’s up there, hon?
STUDENT: Mm hmm.
BECCA SHERMAN:Okay, go ahead. So where is that in the picture.
BECCA SHERMAN:Did everyone see what he wrote? STUDENTS: Yeah.
BECCA SHERMAN: Okay.
BECCA SHERMAN: So where does, where is that in the picture up there. Do you see that?
STUDENT: Yeah, um. 24 dollars and then over here says she saved 3 times as much as …W…
BECCA SHERMAN: As much as Wayne? Okay. Um, so, I saw a picture, thank you. I’m gonna take that red pen, I saw a picture that showed this. So we’ll come back to this picture in just a minute. I saw a picture that showed this. Had 24 in a box. And then it had another box that was 24, And then it had another box that was 24. Um… and it said, Wayne, and all of this was 72. So I saw this—did anyone else do something like this? What do you think this means? What did you think, Thomas, about this picture? You can go ahead and have a seat, thanks. So it means this, what does it mean in the story? Can you tell us who this story is about? And where it shows that Maria saved 24 dollars, and that she saved 3 times as much as Wayne? Does someone have something to say about this picture? We’re gonna come back to this one. Did anyone have something about this one? What do you think?
STUDENT: Uh, it shows like 24 times 3.
BECCA SHERMAN: Okay, so we’re pretty convinced that these are the numbers, but this is that hard part: how do we get back to those words? How does this picture, and do these…. In one case we have $72 for Wayne, and up here it says $8 for Wayne. Can they both be right?
BECCA SHERMAN: So let’s take one more thought out loud. Ron, what do you think?
STUDENT: I think it’s 3 groups of 24.
BECCA SHERMAN: You think that it’s 3 groups of 24. You think—why is that. Go back to the story.
STUDENT: Mmmm, because it has the number 24 and 3. So if you divide 24 into 3 groups, it would equal 72.
BECCA SHERMAN: Oh, so I heard two different, I heard divide 24 into 3 groups, that looks like this to me. Here’s 24, here’s—it’s not 3 groups, here’s groups of 3, that gave 8. But you said 24 into 3 groups is, divided into 3 groups, is 72. Hmmmmm! Which one is it?
It is so hard to decide which student work to begin with. I would have shown different work in retrospect. It is also difficult to get students to think about another student’s work especially if they are still unsure of their own thinking. For this reason I might choose to establish correct idea of 3 groups of 8 before exploring different models. In particular, I noticed that one student changed his mind from a correct model to an incorrect one. Lots of decisions to make in very little time… that’s teaching. Thankfully we have many days ahead and behind.