In this problem, Hillary Lewis-Wolfsen invites the students to consider several different strategies for answering a proportions and ratios task.
HILLARY LEWIS-WOLFSEN: Okay, let’s look at another response from a student. Another response. Their answer was 2, and their explanation? “The problem gives the answer.” Private think time.. Shhh, private think time, and then pair share when both you and your partner are ready.
STUDENT A: That is only 3 cups, and in all there should be 9 cups STUDENT B: Oh. STUDENT A: and the correct answer should be 6/9ths , or 2/3.
HILLARY LEWIS-WOLFSEN: We’re ready to share—we’re ready to share over here…Okay, a few of you are ready to share, over here. Okay, what do you think of this one? What’s going on with this? What’s going on, and… what’s your name. Oh, you even wrote it in a direction so I can read it! Bryan! What do you think of this one?
BRYAN: I think that the person who answered this problem didn’t read the whole problem.
HILLARY LEWIS-WOLFSEN: Oh… okay, maybe they didn’t read all the information? Okay? Any other ideas from…Daniel.
DANIEL: I think it’s wrong because if you made 2 cups of chocolate and 7 cups of cream, but the problem says for every 1 cup of cream he makes 2 cups of chocolate, so he would have 14 cups of chocolate total.
HILLARY LEWIS-WOLFSEN: Okay. So if they only had the 2 cups of chocolate here, you’re saying he would have had 7 cups of cream,
HILLARY LEWIS-WOLFSEN: But that… what was the rest of that, that you said?
DANIEL: For every 1 cup of cream he makes 2 cups of chocolate.
HILLARY LEWIS-WOLFSEN: Okay, okay. So, but if he had 7 cups of cream, then this would have to be 14. Sounds like you’re saying it’s just not logical. Just not… doesn’t make sense. I’d love to call on you, but I don’t call on the “ooo, ooo, ooo’s”. Sorry. Andrew, did you have one more thing to add?
ANDREW: The person’s wrong, because if there’s only 2 cups of chocolate, there will only be 1 cup of cream, and that equals only 3 cups of ingredients.
HILLARY LEWIS-WOLFSEN: Sounds like a lot of different ways to interpret where there’s just missing the logic. Didn’t quite use all the information correctly.
I found that there were times that I was trying to keep track of so many things, that occasionally a student gave a response that was so different from what I’d expected, or maybe I just couldn’t hear them well, that I had trouble processing what they’d said.