Michelle challenges her students to individually select one grouping of representations from their chart and move them over to a poster without the justifications. Each student then writes responses to several questions, each of which has a sentence stem prompt:
MICHELLE MAKINSON: As we spent time putting together the chart of all the factual...the five ways to represent the fractions, right? And so now you're going to pick with your partner. So Michael and Jakob, uh, Nathan and Giovanni, come to the front again. You can leave your materials there, just bring a pencil. I have paper up here already. Okay. So you're going to, based upon part of the presentation we saw, based upon your work so far, um, everything you've heard about fractions, you're going to have an opportunity to share out, change or modify one grouping of your choice from your chart. So each partner is going to pick a different grouping and you're...literally, because they're on the tape loops, you can move them onto your poster. Does that make sense? So you're going to move the whole set over to your poster, but you're not going to move the gold justification cards. You're going to leave those on your chart. Does that make sense? So how many cards will you move?
MICHELLE MAKINSON: Five. Five cards without the justification cards. Okay? And you'll put them all on your construction paper, and then you're going to answer some questions related to those. Each one of the partners is going to pick one row that they want to change, modify, explain. And you're going to answer these questions: Why did you select this grouping? And so on the actual, you're basically making a poster about that row. So you're not going to write the question down but you're going to use the sentence stem “I selected this grouping because,” and then finish the thought. Does that make sense? Complete sentences.
Then the second question is: How do you know that all the cards represent the same quantity? “I know that all the cards represent the same quantity because,” and then finish that sentence. Nod your head if that is making sense. No, it's not making sense?
MICHELLE MAKINSON: So nod your head. Okay. When sharing your work with other pairs, what did you learn from the discussion? Remember when you shared your charts with another group? What did you learn from that? So when I shared my chart with another partnership, I learned "blank:" multiple things, possibly, from the discussion. Does that make sense? So you're picking a row from your own chart that you think you want to change, or modify, explain. Right? To show your thinking. Does that make sense?
MICHELLE MAKINSON: Okay. So we're going to get your charts to you. All right, so you need to be opening up your chart and looking at the different rows. And each partner will take a different row to put onto their yellow construction paper, and then answer those questions in complete sentences. Explaining your thinking. Good job, JT. Okay, so you can pick any. You can move it over so he can start working. Make sure you get your name and number on this yellow paper, please.
STUDENT: I selected this grouping because it's the first one I saw. I know this card...these cards represent the same quantity because they all have to do with one out of two equal parts. When I shared my...I'm still working on the next one.
STUDENT: I selected this grouping because it has equivalent fractions. I know that all the cards represent the same quantity because they all represent two fourths, which equals one half. When I shared my chart with other partner, partners...I'm not finished with that one yet.
STUDENT: And I know because you need to really think about what you're doing when you...when you, like, do all these answers because you don't want to get them wrong.
STUDENT: I selected this grouping because this is easy to explain. I know the cards represent the same quantity because all of them are equal to two...equal to two sixths, except the number line, and it is equivalent to two sixths. When I shared my chart I learned that the number line doesn't have to be two sixths. It can be, uh, it can be something else as long as it's equivalent to two sixths.
STUDENT: And I know that all the cards represent the same quantity because they are all eight twenty-fourths. And when I shared my chart with another partnership I learned that not all the answers were the same.
STUDENT: I selected this grouping because it is the most basic -- well, in my point of view. And I know all these match because there is five, five here that are four-sided, and it's a...and there was kind of here in total. So there's five out of ten, and right here is ten out of five, and right here is...this is zero, this is one. And right there is the middle and five tenths -- that's pretty much obvious. So, would...I'm still... So I know all of these cards match because, because they're...if you just look at them all, they mean the exact same thing, or in our case, five tenths.
STUDENT: I selected this grouping because I'm familiar with these fractions. I know that all the cards represent the same quantity because each card has the same numerator of two and the denominator of four.
STUDENT: I selected this grouping because there is great quantity fractions, and I know that all the cards represent the same quantity because (inaudible) and then I'm going to finish.
MICHELLE MAKINSON: I often encourage my students to get up out of their seats and move, to keep them from becoming frustrated. This clip is after we’d begun to do our partner sharing outside, but ultimately they were too distracted by other things that were going on, so we came back in. My thinking was, they were feeling cooped up. I like to move them around to different environments because it kept their interest. It kept them from becoming fatigued and annoyed, and when they become fatigued and annoyed they do especially disruptive things to each other, verbally. I could see the meltdown happening. It was not a very good day. I thought, "Okay, I have a little, tiny window before the younger kids come out for recess.” They’re actually more focused in this sharing than they were outside, maybe in part because they got to move.
Because of all the emotional issues and the turmoil in that class, I had to do a lot of work. Every day was a struggle. There was so much stuff. If one person would calm down, another one would pop off. There were at least 10 of them that were extremely high needs, and few of those had any official diagnosis of special needs.
I see them using academic vocabulary well here. There was some anchoring in that. Just constantly using the same academic vocabulary, insisting on it, not moving forward until they use the right vocabulary and questioning them towards it.
I'm working as a teacher trying to figure out what is the right balance. I also want to create reference books that they have organized, so then it becomes a writing thing, an organization thing, so they can look up content for math. We have a pretty well developed math journal. We're used to documenting our own thinking and then going back and seeing what you have to do in order to make the thing we created viable and useful.