In this clip, Hillary Lewis-Wolfsen invites students to look at another problem and one strategy used by a student to answer the problem.
HILLARY LEWIS-WOLFSEN: Okay, let’s go ahead and move on to our next one… (peels back) This was another problem on your assessment, and it said, it showed, if you remember, it showed you the picture, told you this was a candy box, and can I get a volunteer to read the problem to us? It gave us these instructions, or this information on your assessment. And you are… Alyssa. Alyssa, will you read that for us?
CAROLYN DOBSON: I’m going to ask Alyssa, will you speak so loudly that I can hear you way over here? And I’m a little hard of hearing.
ALYSSA: (reading) Valerie shares some of the 12 candies from this box. She gave Cindy 1 candy for every 3 candies she eats herself. How many does she give Cindy?
HILLARY LEWIS-WOLFSEN: Thank you. Okay. I’m gonna show you… let’s see. This was the response we got on one of the assessments. Can you figure out what this student was doing? Just think. Think, Saurabh. This is going to be our routine, I’m going to ask you to think silently first, and then we’ll start sharing. First, just some private think time. Can you figure out what this student was doing? And when you think you’ve figured it out, can I get a private thumbs-up, when you think you’re ready to move on? Private, so that you and I are the only ones who see it. Keep it really close to your chest. That works well for me, thank you. Okay, so when you and your partner are ready, could you and your partner go ahead and share what you think is going on in this illustration?
Student A: For every 3. So there’s 12 candies, right? So what’s 12 divided by 4? Student B: 3. Student A: So 12 divided by 4 is 3. So, 3.
HILLARY LEWIS-WOLFSEN: What do you think about this one? What do you think? And you… are, Ashank?
ASHANK: For every, like, 3 candies that she, that Valerie has, Cindy would only get 1.
HILLARY LEWIS-WOLFSEN: Okay, so how do you think this person created this? What do you think they were thinking?
ASHANK: Like, in one column it contains, in one row it contains 4 candies. Since Valerie will get 3 candies, Cindy will get 1 of them.
HILLARY LEWIS-WOLFSEN: …..3 and Cindy will get 1 of them. Okay, I see some heads nodding. Does anybody else think about this differently? Andrew, what do you think?
ANDREW: the person counted 3 candies for Valerie and then put a C in the next candy, because Valerie gets 3 candies?
HILLARY LEWIS-WOLFSEN: Are you saying they counted 3 here, rather than thinking in rows, they did 3, and then a C, 1,2,3, oh, look at that, 1,2,3, and a C. That’s possible, too.
I like having the students read the problems to the class. There are students who are not comfortable sharing their mathematical ideas with the whole group. They want to participate. Reading the problem aloud is often the safest way for them to participate.
One of the unusual situations of being in someone else’s classroom is having to explain my own routines several times. When teaching my own class, these routines are established over time and wouldn’t need as much repeating. I use the “private thumb” because it allows me to know who is finished, but the kids who are still working are not distracted or intimidated by kids waving hands in the air.