A close-up look as a pair solves the final problems.
STUDENT A: Caramel, f,f,c,c,c, and then f,f,c,c,c, I kept on doing that pattern, and then I got my answer. (inaudible)
STUDENT B: That’s like what I did, except I put it more square.
STUDENT A: Want to use it?
STUDENT B: I like tiles because you can build …
STUDENT A: Yellow is caramel and red is fruit, okay?
STUDENT B: Okay. Strawberry.
STUDENT A: 30 in all…
STUDENT B: Strawberry. Red is strawberries.
STUDENT A: 7,8,9,10.
STUDENT B: I’ll take all the red, you take all the yellow. Or do you want the red? You want the red? Or you want the yellow.
STUDENT A: It’s like the other one that we did. Okay, let’s count. Put them …
STUDENT B: I’ll put 2, you put 3.
STUDENT A: 3 caramels.
STUDENT B: And then 2 more.
STUDENT A: 3.
STUDENT B: And then 2 more strawberries.
STUDENT A: You mean fruit.
STUDENT B: Strawberry’s a fruit! 2 more strawberries.
STUDENT A: And 3 more caramels.
STUDENT B: 2 more fruit.
STUDENT A: 3 more caramels.
STUDENT B: and then, last, 2 more fruit. Just make it look nice.
STUDENT A: So now we count them up... Good enough.
STUDENT B: So we count ‘em. 2,4,6,8, 10, 12. 12 fruit.
STUDENT A: So there are…12 fruit centers.
STUDENT B: 12 fruit, and then, 12 30 minus 12.
STUDENT A: 1, 2,3,4,5,6 – 18. And 18 caramel.
STUDENT B: Well, you could have just done 30-12.
STUDENT A: Yeah, but same thing.
STUDENT B: Nice square!
HILLARY LEWIS-WOLFSEN: I know some of you are finishing rather quickly, I have some extra problems for you to work on. If you have time. If you need more paper, let us know.
STUDENT B: Let us do early finishers number one. There are a class of 42 STUDENTs. For every 3 …
STUDENT A: 3 + 4 = 7. So 7 * 6 = 42. So you multiply, 3 * 6 = 18, and 4 * 6 = 24. So there are, so there are 18 boys …
STUDENT B: 18 boys…
STUDENT A: …and 24 girls.
STUDENT B: 24 girls. The girls rule this class!
STUDENT B: In another class there are 12 girls. There are 3 girls for every 5 boys. How many boys…what? Okay, so, that’s 4, and then 4 * 5, there’s 20 boys.
STUDENT A: Are you sure?
STUDENT B: No.
STUDENT A: You have to just do it, then! There are 12 girls. So, 12…
STUDENT B: And there’s 22 people in the class.
STUDENT A: 3,4,5,6,7,8,9,10,11,12.
STUDENT B: Right? Because for every 3 * 5, 3 * 5 is fifteen.
STUDENT A: So you go 3, then, 5 boys. 3, 5, 3, 5, 3, 5. There’s 20 boys. 20 boys. You’re right.
STUDENT B: Isn’t there, like 32 people? Or 22?
STUDENT A: No, there’s…
STUDENT B: 22, right?
STUDENT A: 32.
STUDENT B: What? Oh, yeah, yeah, 32. Sorry.
STUDENT A: No, 42.
STUDENT B: What? Oh. What?
STUDENT A: Yeah. Because then there’s 20 boys and 12 girls. 42. I mean, sorry! 32. Yeah. 32.
STUDENT B: Yeah. Okay! We’re done.
Two very bright kids. They clearly respect each other and are comfortable working together. They question 22, 32, or 42 as the answer to the last problem but they never talk about how or why 32 is the answer they agree upon.