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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STUDENT: Look, you have to multiply here to get the missing numbers in the box.

STUDENT: But I think it's this one, but I'm not sure.

STUDENT: These two, why?

STUDENT: Yes, because this is the factor of this one, but it has zero over here, so I'm not sure. But if you factor it, if it's the same as this one, then I have to give the same answer, but for this one I don't know.

STUDENT: Like zero?

STUDENT: Mm-hmm. But it could also be this one.

STUDENT: It could be both.

STUDENT: I think it's this one.

STUDENT: Me too.

STUDENT: I think it's this one.

STUDENT: Well then, I think so too.

STUDENT: Okay, so now we just have this one.

STUDENT: If we factor this one to find the x-intercept...

STUDENT: Of this one, right? It can be with this one too -- we have this one here.

STUDENT: Okay, I'm going to copy this.

STUDENT: Come on, Elizabeth, think of something. It can be this one.

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.