Lesson Part 4B

lesson part 4b

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Students work together on their status posters, examining and connecting to the fictional students’ work. Molly McNinch’s students consider how they need to correct the fictional students’ thinking and how that correction will help them prepare their visual representation of their group’s work. Molly’s students discuss how to label elements of the poster.

lesson part 4b

9th Grade Math - Modeling through Geometry: Circumference of a Cup’s Roll
Molly McNinch, San Lorenzo Unified School District, Woodside High School, Woodside, California


Next Up:   Lesson Part 4C
Previous:  Lesson Part 4A

STUDENT: If it’s a dead end, why would we put that on our thing? Why can’t we just say, like --

STUDENT: Okay, so, you know we can, like, say, we tried finding a conclusion for every type of situation, but then we looked at Heather’s --

STUDENT: And then did [inaudible].

STUDENT: But then we looked at the Heather page, and --

STUDENT: Then figured out what the --

STUDENT: Yeah.

STUDENT: -- missing variables.

STUDENT: And like, from there -- so we tried finding --

STUDENT: And this 99, and see how much it changes. And then, so then we'll write what that made us think. There's an orange marker.

STUDENT: Where?

STUDENT: Just right there. Okay. So you should write, extra two data points. Or, I don’t know.

STUDENT: Wait, what?

STUDENT: And then so, this -- we’ll use this one and then this one. I don't know how you want to label it. Like, extra data points.

STUDENT: Okay.

STUDENT: Yeah.

STUDENT: Extra.

STUDENT: Good. And then, use a different color. Here's a red one. And then, so just, like, the wide diameter -- so just write W, N, S, R.

STUDENT: Like, when we made the graph for --

STUDENT: Do we need to? Should we? Like, not the whole thing. Just these two. Should we write, just like, W equals, N equals?

STUDENT: Just do, like, yeah, just do W equals, N equals.

STUDENT: Okay, so, W equals -- W equals 100. N equals 99.9.

STUDENT: Should I do it below?

STUDENT: Yes. S equals one. And then, like, I guess on -- should we write it below? Or over here?

STUDENT: Just do it below.

STUDENT: Okay, right below.

STUDENT: Well, wait, are we going to write --

STUDENT: R equals 1,000.

STUDENT: -- right here?

STUDENT: Yeah, because I was just going say, like -- eh, that's good. A thousand.

STUDENT: Okay, and then, with purple, right there.

STUDENT: Why do we have to switch colors?

STUDENT: Because, it needs to be pretty.

STUDENT: Okay, what am I writing?

STUDENT: The next one is -- so W equals a hundred.

STUDENT: Here?

STUDENT: Yeah.

STUDENT: Sorry, I need to --

STUDENT: Okay.

STUDENT: N equals 99. S equals one. R equals 100. And then with this, we say what we came up with was -- the -- like, how do we want to say, like, this affects this greatly?

STUDENT: So, can I do, like, a little arrow here, and then say, like --

STUDENT: I don't know.

STUDENT: Should we do that with arrows?

STUDENT: We could just, like, write “the relationship between the --

STUDENT: What if I use a highlighter?

STUDENT: -- wide and the narrow diameter affected the roll radius greatly.”

STUDENT: Significantly.

STUDENT: Astronomically.

STUDENT: Astronomically. Significantly.

STUDENT: So, this and this, and then this and this.

STUDENT: Should I just like, circle the whole thing?

STUDENT: How do we want to do this? How about we write it first, and then we can figure it out?

STUDENT: I would just write it. I would just write it.

STUDENT: Okay, write it to the side. Okay, so, “the narrow radius compared to the” -- wait, don’t -- don't write this yet. So, “compared to the wide radius affects it greatly”? Or, like, significantly?

STUDENT: Yeah, the narrow radius, I would write the difference makes [inaudible]. “The narrow radius compared to the -- in comparison to the wide radius, had a significant effect on the roll radius.”

STUDENT: Roll radius. Great. Oh, it’s the narrow --

STUDENT: Diameter, that's what it is.

STUDENT: Oh yeah.

STUDENT: Just cross it out. Write over it. It's okay.

STUDENT: We -- so we don't know the roll radius until we calculated -- until we calculated this. We, however, before were assuming that

MOLLY MCNINCH: All right, so within --

STUDENT: -- we got a new roll radius.

MOLLY MCNINCH: -- the next six minutes you guys should start be putting your posters up --

STUDENT: I get it.

STUDENT: So should we just say the equation?

MOLLY MCNINCH: -- because it's almost done, it's almost there.

STUDENT: Yeah.

STUDENT: Do you want to write it?

STUDENT: Write it?

STUDENT: Yeah, say like -- really big, and just say, like, that's the equation. And it’s -- just, yeah, like that.

STUDENT: I'm going to draw Gerry's equation, and then be, like, “from Gerry's equation.”

STUDENT: Okay.

STUDENT: You could draw, like -- also draw an example of, like, the wide diameter and the narrow diameter, how -- did you already --

STUDENT: Just draw pictures?

STUDENT: Yeah.

STUDENT: Yeah, okay. I'll do that.

It was a little bit difficult for some students to see the similar triangles relationship, which was our previous unit. It was hard for them to go from the cup to the cone to the triangle to the circle. By helping and trying to guide them towards a, "Well what would this cone look like if you drew it two dimensionally?", I found once they had an image, it was easier for them to say, "Oh, this looks like similar triangles.”