Keynote Video Transcript

Sean: This is one group of four. There'd be- There's only three groups, so one of those groups makes it, uh- a third- and then,

Sean: These groups each are four. There's four groups, and one of these groups would be a fourth-

Ball: Riba, are you looking?

Sean: (And-) well, I have a way to show it. Take maybe a dollar or a graham cracker. A graham cracker.

Ball: Can- Can I interrupt you again one second? There are a couple people who are still looking in their notebooks and stuff.

Ball: This isn't a time to do independent work. This is a time to think about what Riba asked, which is a very good question

Ball: And Sean is trying to explain what he's thinking. I'd like everyone looking and thinking about this. This is very important right now.

Ball: Okay. Go ahead.

Sean: Take a box-

Ball: What is that a box of? I'm sorry.

Sean: It's a box- It's a graham cracker.

Ball: Oh, it's a graham cracker, okay-

Sean: And then, um, if you cut it, like this- there'd be one, two, three- there'd be four things. There'd be four things, and one of those would be a fourth, see?

Sean: But if you take a, a graham cracker like this, and, um, make, you know, um, three, three- three things- three. One of these would be a third.

Ball: Okay, so- can I just label it again with what you said. He's saying this piece is a third and this piece is a fourth, and he's saying,

Ball: Because this has four pieces and this has three, and he's using that as another way to persuade people to agree with what he said about these pictures.

Ball: Who'd like to comment on that? Riba?

Riba: I still disagree because this one fourth, I'm just- I'm not- well, I'm not sure that I really disagree. I'm saying, um,

Riba: If you call it one fourth, could you- be four in a group?

Ball: He's telling you something different. What is he saying one fourth means to him?

Riba: ...Saying one fourth is- um, four groups.

Ball: If you cut something into four groups and one of them is one fourth.

Ball: And he showed you two different pictures of fourths. Can you find the two pictures? Where's one?

Ball: Okay. Where's the fourths? No, where are the fourths, Riba?

Riba: Right here.

Ball: There's one. Where's his other picture of fourths?

Riba: Right there.

Ball: (Okay.) And both times he cut something into four parts and called one of them one fourth. What about other people in the class? Keith?

Keith: Um, I, I think she disagrees because she think like- she thinks one-

Keith: The reason why she thinks one fourth should have four, um, crayons in it because- because of the four in the um- um-

Ball: In the bottom number?

Keith: Yeah.

Ball: When she look- when Riba looks at the four, she thinks this is telling her- excuse me, Betsy and Lucy.

Ball: She thinks this is telling her how many to put in a group. And Sean is thinking it means how many groups to make.

Ball: Now let's think about this for a minute. With one half- let's say we have six crayons, okay, one, two, three, four, five, six.

Ball: We want to have half of six. Are we going to put two in every group, or are we going to make two groups?

Students: Put two groups.

Ball: Let's try it both ways. Riba, come over here a second. Can you divide this six into two groups? Right here-

Ball: And then what does that show, half of six is what, according to that picture?

Riba: Three.

Ball: Now, let's try it again another w- your way. One, two three, four, five, six. Now put groups of two.

Ball: Two in every group.

Ball: That picture tells you that half of six is what?

Riba: Two.

Ball: Is that what you want the answer to be?

Riba: No.

Ball: So what- Can you use that to help you think?

Riba: I want it to be three.

Ball: So what if- Okay. Can you use that to help you think about what the bottom number means?

Riba: (I'm) still not sure if it should be-

Ball: Would somebody- Want to hear some more discussion?

Ball: Or do you want to say something?

Riba: I want to say something.

Ball: Okay.

Riba: If- let's say- four- three fourths- this is what I think three fourths um, is like. Um, I'm saying that, um, three fourths is like three groups of four.

Ball: And that's what Ofala was thinking, too. I don't know if Ofala's thinking that right now. You're not thinking that right now? Okay.

Sean: Can we vote?

Ball: (Maybe) you can tell Riba why you changed your mind.

Sean: Can we vote?

Ball: Why would that be a good thing to do?

Sean: Well, I just wanted to see how many people- um, I was going to say, "How many people- um- will think that my answer is correct, raise their hand, and-"

Sean: "How many people think Riba's answer is correct, raise your hand."

Ball: What would that do if we saw that?

Sean: That would prove-

Ball: (And) why would you want to know that, is what I'm saying.

Sean: That would prove it wrong.

Ball: Do people agree with that?

Students: No! Yes. No!

Ball: Keith, you're shaking your head. Why wouldn't that prove it?

Keith: Just because, like- just because somebody agrees more with one person, doesn't mean that they're right.

Ball: Other people want to comment on that- about voting and deciding what's right? Tembe, what do you think?

Tembe: I agree with Keith because if we voted, maybe the, the answer might be wrong, and the people who didn't vote- less people who voted- might be right.

Ball: Hmm. Daniel?

Daniel: Yeah, I agree because- um- like- when some people say what what's one plus one, and one person might say two and most of the persons might say three-

Daniel: And then that pers- and- and I- I agree with Keith-

Ball: So, if vo- Does anybody think voting would tell us what was right?

Students: No.

Ball: Then if voting doesn't help, what- how can you tell if something's right?

Tory: Figure it out.

Ball: Cassandra, how?

Cassandra: I don't know.

Ball: You were saying "because."

Cassandra: I don't know.

Ball: Sheena, how can we tell something's right, if voting doesn't work?

Sheena: Well, all you have to do is try and figure it out yourself, and if you think you got the right answer, then maybe you should, um, discuss it with somebody.

Sheena: And maybe they might be able to change your mind if the answer's wrong.

Ball: Sean?

Sean: Uh- I just- I just wanted to take a vote because, maybe- I wanted to see how many people would um-

Student: Agree with you?

Sean: Who got- who got- who got that answer.

Ball: What would that be good- My question to you is why would that be helpful to you? Why would you like to know?

Sean: Because I, I just wanted to know- see how many people... that- that um- got that...

Ball: (Anybody else want to comment on this) before we go back to our problem of fourths and thirds? Mei?

Mei: I don't think it would work, but it would be fun to see how many people agree with him

Mei: Because maybe some other people might come up with some other ideas.

Ball: So, you'd be curious just to know what people are thinking?

Mei: Yeah.

Ball: Anyone else want to comment about that? Is that what you were saying, Sean? Or not?

Ball: Did you hear Mei? She said it would be fun to know what- how many people think which answer.

Sean: Yeah, I agree.

Ball: She said some people might come up with other answers that wou-

Sean: Well- Look- well-,

Sean: I-

Sean: I don't- well-

Sean: That's not really- that's a hard question that Riba's asking. But why, why shouldn't there be four groups of-

Ball: Oh, you're back to talking about this now?

Sean: Three. Yeah. Because- um, because I get-

Ball: (Could we go back to) the fourths and the thirds now? Or did you really want to see what people were thinking right now, Mei?

Mei: Yeah, sort of.

Ball: Well let's see. How many people aren't sure whether fourths means four groups or four in a group? How many people are not sure about that right now?

Ball: How many people think that fourths means four in every group?

Ball: That's not what you've been showing.

Sean: No, no, no, no, no. Not four in every group.

Ball: Listen carefully, so we know what people are thinking. How many people think fourths means four in every group?

Ball: How many- She's not sure is what she said. How many people think fourths means four equal groups?

Ball: Okay, now you know sort of where people are, and you can try to make your arguments and see if we can settle this.