Molly McNinch circulates among her student groups, challenging them to refine and improve their visual representations: “your diagram's really great ... it would be even better if you could see the dashes.” Molly encourages her students to connect the fictional students’ work to their group posters: how did each fictional student’s work connect to and extend their thinking?
MOLLY MCNINCH: So your diagram's really great. Oh, okay, I was just going to say, it would be even better if you could see the dashes.
MOLLY MCNINCH: So, what do we got here?
STUDENT: We're drawing.
MOLLY MCNINCH: You're still drawing. Did you guys keep going with Gerry? No.
STUDENT: We kind of stopped.
MOLLY MCNINCH: Okay, why did we stop?
STUDENT: We started doing the poster and, like, giving each other ideas.
MOLLY MCNINCH: Okay. Did we get a little bit tired? So, for Gerry, okay. Now we want to look at what Gerry brings to the group, okay? What does Gerry bring to the group? He brings this image. So, it says, “Use Gerry’s method to find the roll radius of this cup.” So, his method, he has step-by-step directions on, like, how to solve it. Now, 3b, 2d, and then he has the E.g., which is the example. Okay? So, use this. You guys can create the model super quickly, okay? It should look very similar to this. Yes? Okay.
STUDENT: And then we could label this. We could say, like -- what do we want to call it? We could call it, like, the invisible part.
STUDENT: Invisible cone.
STUDENT: How about we say triangle?
STUDENT: Invisible triangle. And we should label each of, like, the -- so, like, this is W, N, S, and -- like, like the lines on the side.
STUDENT: So, W --
STUDENT: W is here.
STUDENT: Oh right, S.
STUDENT: And, like, make the --
STUDENT: Does it matter?
STUDENT: -- line centered. Yeah. And then this whole thing equals R. You can use that if you want. That's good. Okay. And then, say, like, we have this as X. Or, like --
STUDENT: The tip?
STUDENT: R minus S on this part. R minus S, yes. And what else do we want to put on this?
STUDENT: I don't know. I think that’s fine.
STUDENT: I think we should write this -- this triangle is similar to that one. That's what we’re trying to do.
STUDENT: Like similar triangles?
STUDENT: Yeah, so we have to label more corners.
STUDENT: So --
STUDENT: Label, like --
STUDENT: Can we do A, B, C, D?
STUDENT: A, B, C, D.
STUDENT: How do you spell dimension, because I don’t want to spell it wrong.
STUDENT: It says it right there.
STUDENT: Oh, it does? I don't see- oh there it goes. M-E-N-
STUDENT: All right, I need to go give her the --
STUDENT: I can't read what that says. I think it says, S-I-O.
MOLLY MCNINCH: All right guys, so start finishing up. Start finishing up. Your posters should be taped up. I'm going to put a timer on for two and a half minutes.
STUDENT: All right, let’s put seven.
STUDENT: Seven E.
STUDENT: Okay, we're done. [Inaudible]
MOLLY MCNINCH: All right, two and half minutes. Posters need to be on the board.
STUDENT: So, we need to say, like, this big triangle is equal to the small triangle.
STUDENT: Well, it's similar, it’s not --
STUDENT: Oh, it’s similar, yeah. We can do that. R over W equals the -- like --
STUDENT: Well, I think what she meant is we have to say, like, "W is this, N is this, R minus S is this."
STUDENT: Okay. So, we can do that. So we can say that S --
There was one group in particular who was struggling with just, "How do I relate them all?", and so I set it up, I gave them the triangle, and then I gave them the values for that piece, and then I said, "Okay. We're finding this distance between the narrow diameter and the center of the circle, and then that whole piece is giving us our roll radius." Trying to focus them and make it something they've seen before to help pull that in, to guide them towards what they are producing.