Near the beginning of the Problem String, Kim asks students to find the number of sticks in four packs. She is looking to find someone who doubled the two packs. Notice how she interacts with students as she continues to ask questions to find someone who doubled the two packs:

Kim: What if I said that Luke had four packs of gum? How many sticks would that be? How many sticks would that be? Bella, you think you know?

Bella: 48?

Kim: 48. Anyone agree with Bella? Bella, how did you do that so quickly?

Bella: Because I know how to do skip count by 12's.

Kim: Oh, so you thought about 12 and 12 and 12, that was pretty fast. Did anyone think about something that was up here, to help them figure out how many? Logan, what did you think about?

Logan: I did 4 times 12.

Kim: Okay. Is that what I'm asking you, 4 times 12? Yeah. Did anyone think about what we know about two packs and just say, "Well, if I know two packs then I can use that to help me figure out four packs"? Brooks?

Brooks: So I know that two--

Kim: Two what?

Brooks: Two times 24 equals 48. And so I got, so I used two times 24 and then for the fact 'cause I know that two times 24, you just skip count, it equals 48.

Kim: And why did you do two 24's?

Brooks: Because if you, well if you do two 24's and four 12's, you get the same answer as 48.

Kim: Interesting. So if you have two packs of gum, it's 24 sticks. Then you can just double that and say, "Well if I double the number of packs then I can double the number of sticks?" Is that true? If I double the number of packs, can you picture that? If I double the number of packs, do I need to double the number of sticks? And how many was that, how many sticks?

Brooks: 48.

Kim: 48, interesting.

Kim asks gradually more and more specific questions while still honoring what students are saying. Then she spends some time questioning about and restating the doubling relationship because she knows not many of the students were using it. And ending with "interesting," gives students the idea that she is interested in their thinking, especially when they are using relationships from the ratio table.