Molly McNinch distributes example approaches by three fictional students — “Judi,” “Gerry,” and “Heather” — so that her (actual) student groups can evaluate and critique the approaches of other mathematicians’ work. Molly has color-coded the example work and asks students to look at it in a particular sequence. She asks her students to “think of them as your new groupmates who have new ideas to share, okay? You guys don't know if they're right; they don't know if they're right. So you're just taking their information and using it to help your idea go further.”

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

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MOLLY MCNINCH: I think some of you guys are getting some new insights, some of you guys are getting a little bit stuck, so I'm going to bring in some help. All right. So we are going to enlist the help of your three new friends: Judi, Gerry, and Heather. Oh, gosh. That's hard to see. Okay, so, you guys are going to ... Let me just adjust this. Okay, so you guys are going to evaluate their work. Now, you're each going to get a little sheet protector, and it has three different pieces of work: there's a red, [a] blue, and [a] yellow.

Now, look at the work actually in that order of red, blue, and yellow. So for the first 10 minutes -- for about 30 minutes, you guys are going to be looking at this work. While you are looking at it, you're going to be filling out the worksheet that you picked up at the door. So the one that's stapled is what you're going to be looking at. Answer these questions as a group, as you go along.

We will end with Judi, okay? So go Heather, Gerry, Judi; also red, blue, yellow. None of these are ... I don't want you to think of these as solutions, but rather think of them as your new groupmates, who have new ideas to share, okay? You guys don't know if they're right. They don't know if they're right. So you're just taking their information and using it to help your idea go further. Okay.

So you need your staple packet out, so you're going to be filling that in with complete sentences. Again, none of these are really -- I don't want you to think of them as solutions, but rather think of them as new groupmates with valid, valuable ideas. All right. So I'm going to hand one of these one to everyone, I -- and you need your staple packet. All right. I already said that. Okay. Keep going.

With the additional “student work” pieces, it was helpful, I think, for my students to have three separate colors. When I did it in an earlier period, I didn't tell them anything about whether they had solutions, but with this class, I emphasized that neither of these, or none of these, have the solution. It was also helpful to talk about, "Okay. You have three new group members, so we have a red, a yellow, and a blue group member. What does each group member bring to your solution or your ideas that you didn't have before?" Asking "What does each individual new group member bring that you didn't have prior?" is helpful to the students.

A note about making the sheets different colors: whenever there is an opportunity for students to clearly identify something quickly, I go for different colors. It’s easier to say, “Look at the pink paper.” than say “Look at the paper titled ‘Helen’s work.’”