Speaker 1: All right. We’re going to work on a math problem here but I’m going to give you a chance to first start with your messy ideas. Just get out your first thoughts, your sketches, whatever helps you kind of think through the problem. Then after that, you can compare with a friend, and then that will help you to make a Less Messy Idea. We’re going to give you the chance to refine your sketch or refine your thinking about it, and then we will go from there on the problem. The problem is going to be this one:

Can you create a line (or linear equation) if you want to? Can you create a line that goes down through the point (4, 5)? I’m going to be giving some bonus if you can make it really steep through (4, 5). First start, use that messy idea box. Put down your first thoughts, your first collection of ideas. You can sketch things that can be messy. That’s totally fine to start out with. Let’s do that first.

Student 1: Pretty smart.

Student 2: Because it’s the steepest.

Student 1: It still goes through (4,5).

Student 2: Yes, and it goes through (4,5). It could start at (4,0), but it could also start at (4,-6) or (4,-5) as long as it goes through.

Student 1: That makes sense. Then it’s still steep as possibly you want to make it; that makes sense.

Student 1: Sharing my idea with my partner was good because it helps me–because at first, I didn’t really understand, like, I understood, but I didn’t understand it in a way, and she made it easier to understand.

Student 2: I think that sharing my idea with my partner was good because I also helped her, but at the same time, I helped myself go over my idea and make sure there wasn’t any flaws.

I particularly enjoy sharing my idea with my partner because it’s a good way to review without needing to just read it over and over and over again.

Student 1: I felt that going through a messy idea to a clear idea helped me because it made me clear up all the stuff that I thought I wasn’t sure about. It made me understand how it is and how it’s done.

Student 2: There is a situation where I think that going from a messy idea to a Less Messy Idea is a good idea because when I’m writing, I really like to write creatively. When I’m writing, I have to go from a draft to the actual thing, because sometimes I make grammar mistakes or I forget to capitalize something. It’s nice to just review it and be like “All right. Here’s how we can make this better.”