Clip 6/10: Lesson 2, Part C
Students continue to create sets of cards that match each other (Green: Set or Area Model, White: Verbal Representation, Dark Blue: Contextual/ Word Problem, Yellow: Justification). Michelle asks pairs of students to explain the connections between the cards. She challenges students to persevere in grappling with a scenario working with 22/12. The class works with incomplete sets of 12 and incomplete wholes, recognizing that students seek to make connections to real life and become confused about how an improper fraction works in reality. The students create connections between the representations based on their observations of patterns and structures.
MICHELLE MAKINSON: There would be no purpose to having the discussion if everything matched in only one way. There was a reason why there were multiple ways to see it, even within the same type of card, and that gives you that rich conversation, forcing them to have a conversation, forcing them to debate about things and hash it out. If they knew there was a one-to-one correspondence, they would simply line them up and be done with it. It would have been a flatter activity, and this forced them to think outside the box.
As I walked around, I was listening for math conversations. Over the years, you start to be able to tell the difference between on-point conversation and off-point conversation; you don't want to cut them off from being excited about what they're doing, because that is the measurement of their interest and their engagement. I also saw that there were people where that discourse was never going to happen between them. That's something that tells me we needed to work on that, and that that partnership is not the most productive one, but I didn't hesitate to put together ones that would also produce problems that we could talk about later on. Because we're not just doing math, we're doing life, and so there's definitely going to be some rich conversations that come out of maybe some of the things that I saw that I wish we’d done a little bit better.
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