In this problem, Hillary Lewis-Wolfsen invites the students to consider several different strategies for answering a proportions and ratios task.

5th Grade Math - Proportions & Ratios*Hillary Lewis-Wolfsen, Forest Park Elementary School, Fremont Unified School District, Fremont, California*

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STUDENT A: Well at least he got the method right.

STUDENT B: He or she got the method right, and I hope, the answer right.

HILLARY LEWIS-WOLFSEN: We have thoughts on this last one, here? Yeah, we do! Holy cow, look at the hands! Kevin, what are you thinking?

KEVIN: He’s very close to the answer, but he messed up. So 1 cream plus 2 chocolate equals 3, so 3 of them, they, they subtract, then they come out, it’s 9, then he just go on, not.

HILLARY LEWIS-WOLFSEN: 9 in all, so you’re saying they’re very close, because they added the 1 and the 2 to get the 3, kind of like, I think, Ashank was helping us with, over here?

KEVIN: Uh huh.

HILLARY LEWIS-WOLFSEN: And getting that 3, to find the 9 in all. What did you want to add, Cynthia?

CYNTHIA: Yeah. He knew that 1 cup of cream is with 2 cups of chocolate, and that equals 3, but she knew that the total cups was 9, so had to multiply 3 by 3, and so they (inaudible) 2 cups of chocolate, that would make 6 cups of chocolate.

HILLARY LEWIS-WOLFSEN: That would make 6. 6 cups of chocolate. What if I told you there was a line under all this, and the student wrote, “6 chocolates” and put a big box around it. What would you think of that? What would you think of that? Daniel?

DANIEL: I would think he’s right, because he knows that there’s 9 cups in total, and for every 1 cup of cream, there’s 2 chocolates, so he first adds them up and there’s only 3, but then the whole thing is 9, so he thinks he should do more until he reaches 9, and then if you add the chocolates, it’d be 6.

HILLARY LEWIS-WOLFSEN: Yeah. The student, yeah, did actually find 6, I just cut that off because I didn’t want you to, to see that too quickly. I’m going to go ahead and move on, because I’m going to push you to think a little bit more about the next one. Okay, Ashank?

If I’d kept the answer that was originally there (6 cups), I don’t believe we would have had as rich of a discussion about the work. I think the kids would have focused on the answer, and not the strategy. Sometimes editing the student work is just as critical as choosing which solutions to use in a lesson.