Students begin an activity in teams where they match different problems with appropriate first steps.

9th-11th Grade Math - Quadratic Functions*Barbara Shreve, San Lorenzo High School, San Lorenzo Unified School District, San Leandro, California*

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| BARBARA SHREVE: So you're going to look at a whole bunch of first steps. And on this handout I've given you quite a few problems and even more first steps. And you don't have to do the whole problem, but you do need to match each one with its first step. It's possible that there's more than one right choice for each problem but you're only going to use each one of these once. Okay? And you need to be ready to justify it. When you tell me you've done all your matching, I come over and I ask you to explain why on one of them. Does that make sense? So when you get this take a look at each first step problem and talk together. You might want to make some notes for yourself on there to show why you think what you think and be ready to explain it. Anybody in your team needs to be ready to explain when I come over. Okay? Finish the first side and call me over to check in, and then you'll get to go on to the second. I'm going to need somebody in that team to get a fast start saying, "Okay guys which one do we want to start trying to match?" And show me all of those good group conversations skills that you guys used on Wednesday. Okay? So you're going to match each problem with a first step.

STUDENT: The second one. Con la second.

STUDENT: ¿Este?

STUDENT: Yeah.

STUDENT: ¿Por qué?

STUDENT: Porque they both – they have the same numbers. Mira, like the x2 -7x+10 and next one tiene x2 -7x+10. They're both the same. You made that, the one, into zero.

STUDENT: The last one?

STUDENT: Yeah. When you're solving for x – you have to – you have to combine – you have to, like –

STUDENT: The second one?

STUDENT: No, this one.

STUDENT: So this...it can match with that correct?

BARBARA SHREVE: Yes.

STUDENT: Okay.

BARBARA SHREVE: Go for it.

STUDENT: The factor goes with the generic rectangle. You guys know why, right? You know why it goes with the generic rectangle? x2 +10? And then the factor completed goes with the one at the bottom. It's a generic rectangle too. Because 3x2, -9, -12. Yeah. And I think that the “solve for x” goes with the one up here. But I'm not quite sure though because it could go with the one above that.

STUDENT: Say where are the groups...

STUDENT: Yeah, that goes with it.

STUDENT: On the top right? That don't go up here?

STUDENT: It could go right here also. I mean, I think it go right here but it could also go here.

STUDENT: And you divide. You add and divide. Because if you get the answer here x is...

STUDENT: (Inaudible) x-5, x-3.

STUDENT: Yeah, yeah, so you're trying to find the x.

STUDENT: So you add both of the x's?

STUDENT: I guess this over here. No, wait. It's this one. Yeah, it's this one because you go from 5 to 2, and then you go inside, remember how she said it?

STUDENT: Don't that one go to this one? Right here. Don't the number line one go to this one? No, wait a minute, I think it goes to this one because it says the roots of y=x-5, x-2. So isn’t it this...

STUDENT: I think this one goes with that one because she told us to use the number line.

STUDENT: Yeah, I think it goes with that one too. You have to use the (inaudible) over there.

Watching how conversations moved forward in pairs, I see that students did not push each other to give reasons as much as I had hoped. This instead seemed to come out most as teams were questioned about their matching decisions by an adult. I periodically use the strategy of verbally “quizzing” teams or pairs after they have a chance to make sense of a problem in order to probe their thinking and better understand their reasoning. However, I recognize that while I spend time with a team others may not be getting their questions answered. In this lesson I had the luxury of two adults in the classroom to help question teams about their thinking. Students engaged with the matching activity in interesting ways. Some students were aware of which kinds of problems they waited until the end to match because they wanted to narrow the number of possible choices. As they found two problems that they thought would have the same first step, they also were able to revise some of their own thinking without intervention from a teacher.