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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HILLARY LEWIS-WOLFSEN: Okay, okay. Okay, let’s go ahead and look at the next one. Thank you. This was another problem on that assessment. And I need another volunteer to read this. Kevin, could you read this for us?

EVIN: Anthony makes candy…

ILLARY LEWIS-WOLFSEN: Nice and loud.

EVIN: First he mixes 1 cup of cream with 2 cups of chocolate. In all he uses 9 cups of the two ingr..dients.

ILLARY LEWIS-WOLFSEN: Ingredients?

EVIN: Ingredients.

ILLARY LEWIS-WOLFSEN: Yeah.

EVIN: How many cups of chocolate does he use in his candy recipe?

ILLARY LEWIS-WOLFSEN: Do you remember that one? Yeah. It was one you spent a lot of time thinking about. No? Okay. What I want you to do right now is have some private think time to re-think about this problem, to remember what was going on with this problem. You can use your think sheets. Go ahead and work this problem again, see if you can remember this one from Monday. Refresh your memories. You’re welcome.

ILLARY LEWIS-WOLFSEN: I see a few of you showing me you’re remembering our system of the private thumb when you’re ready to move on, I appreciate that, thank you.

ILLARY LEWIS-WOLFSEN: Okay. I’m going to go ahead and show you one of the responses we got, let’s see what you think. One student said “9. The problem said that in all, he used 9 cups of each ingredient.” What do you think of that solution? Again, private think time. What do you think of this solution?

ILLARY LEWIS-WOLFSEN: I see some private thumbs… and when you and your partner are both ready, go ahead and you may share.

air 1: TUDENT A: So he thinks each one is 9 cups—he forgot the “in all” TUDENT B: Yeah, he didn’t write the (inaudible) TUDENT A: Yeah, he saw it. Yeah. Because he thinks every cup is 9 cups, but he forgot the “in all”.

air 2: TUDENT A: So he used 3 cups in one ingredient, and then to make it 9 cups, he had to add that ingredient 2 more times. So it makes 3 + 3 + 3, which equals 9.

ILLARY LEWIS-WOLFSEN: Still talking…

ILLARY LEWIS-WOLFSEN: So, what do you think? What do you think about this one? Some of you had a lot to say about this. What do you think? Andrew. What do you think?

NDREW: I think the problem is long and he misunderstood the question, I think he only thought that it was both cups combined.

ILLARY LEWIS-WOLFSEN: Okay, So the student misunderstood this part. Osi, what did you want to say? Really loud, I can barely hear you.

SI: He’s wrong, because he thought both the chocolate and the cream were 9 cups, which means in all, it had 18 cups. But the question said that in all, they had 9 cups only.

ILLARY LEWIS-WOLFSEN: Okay, a total of 9 cups! It seems that there was a misunderstanding here. Okay. So how many of you thought that there was maybe a misunderstanding of the problem. Okay. Does that ever happen to you? No? Maybe sometimes? Okay. No? Okay. We’re like Mary Poppins, we’re practically perfect in every way. All right.

Many of the kids in this class had been together since kindergarten. They were very comfortable together, which probably explains why they were so confident even with all of the adults in the room.