In this clip, Hillary Lewis-Wolfsen invites students to look at the same problem, but with a different strategy used by a student to organize the information in the problem.

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

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HILLARY LEWIS-WOLFSEN: I’m going to show you another way of organizing this information. Can you figure out what this person was thinking? Private thumb when you think you’ve figured it out. And share it with your partner.

STUDENT in pair C: V, V, V, C! V, V, V, C! V, V, V, C. She ate 3, right? then she gave Cindy one, and then she ate another 3.

HILLARY LEWIS-WOLFSEN: Okay, so what did you think about this one? What’s going on here? Cynthia?

CYNTHIA: This person thought in rows instead of columns, and for every row, he had 3 Vs and 1 C.

HILLARY LEWIS-WOLFSEN: Okay, so instead of, we were thinking, this one was columns, but this one looks like they were thinking in rows. And did 3 Vs and 1 C. Yes, sir, what did you want to add to that?

SAURABH: I think that there’s maybe kind of a fraction way?

HILLARY LEWIS-WOLFSEN: A fraction way? What do you mean?

SAURABH: Like, for, in every row there’s 4 columns, I mean 4 rows.

HILLARY LEWIS-WOLFSEN: Mmm hmmm, so 4 row, okay… Oh, that’s … four items in a row? Is that what you mean? Okay. I’m understanding now.

SAURABH: So then, 1 is given to Cindy and 3 is given to Valerie, so ¼ is given to Cindy in each row.

HILLARY LEWIS-WOLFSEN: For each row, 1 of the 4 is given to Cindy? Okay, that’s possible, yeah. So, Mrs. Dobson, I don’t know if I mentioned that Mrs. Dobson teaches 4th grade, and she would like to do this problem with her 4th graders. And we were discussing which of these two diagrams might help present this information more clearly for a 4th grade class. So, remember, private think time, and then we’ll pair. So, private think time, which one of these two may be better for Mrs. Dobson to use when sharing this information with her 4th grade class. Remember, when you think you have a decision and an explanation, give me a private thumb. And then go ahead and share with your partner when you’re ready.

STUDENT (to Classroom Teacher): The second one… I think it’s the second one. Because, for each 3 that Valerie eats, she gives one to her friend Cindy. I mean, give one candy to Cindy.

MS. Liu: Excellent! …. How about the first one?

STUDENT: This first one is stopping confusing.

HILLARY LEWIS-WOLFSEN: Jake.

JAKE: I think the second one is better because…

HILLARY LEWIS-WOLFSEN: This one?

JAKE: Because if you’re looking, it’s confusing, 3 Valeries and then 1.

HILLARY LEWIS-WOLFSEN: Okay, so it’s easier to see the 3 Valeries and the Cindy, is that what you were saying? And… let me get your name… Ashank, nice and loud.

ASHANK: I think that it would be also a good thing. Because your brain, in the first one your brain is, it’s like very complicated to calculate, like, all the candies and the things that Valerie will eat, and Cindy. But in the second, it’s easy to calculate.

HILLARY LEWIS-WOLFSEN: Okay, so you think this one is a little harder to interpret?

ASHANK: Yeah.

HILLARY LEWIS-WOLFSEN: Okay. What did you want to add, Saurabh?

SAURABH: I think the first one would be easier because, because, when you put the… it will be easier for people to understand, because you can just draw the figure, and put Vs in the ones that Valerie eats, and then C in the ones Cindy eats. So then you can go in a kind of pattern, 3 for Valerie, 1 for Cindy. Then 3 more for Valerie, 1 for Cindy. 3 more for Valerie, 1 for Cindy.

HILLARY LEWIS-WOLFSEN: You see that in this one more than you see it in this one, 3 for Valerie, and 1 for Cindy. You don’t see that in this one? You think this one’s easier to see?

SAURABH: Yeah, the pattern… to understand.

HILLARY LEWIS-WOLFSEN: Okay. Okay.

In addition to having the students figure out how others solved the problem, we asked them to analyze the different strategies and decide which would be easier to understand for Mrs. Dobson’s 4th graders. We’d expected them to agree that the second method was clearer, but kids often surprise adults. Saurabh firmly felt that the first (diagonal) arrangement was more clearly organized.