in the classroom

**VIDEO TRANSCRIPT:>> Okay, so for the last couple days we’ve been exploring percent. We figured out what percent means, how percents relate to decimals and fractions. And today we’re going to try to find a percent of a number. We talked about how in life we use percents for tests, for sales. What else did we talk about? How is percents used in the world? Angie?>> Grades.>> For grades a lot. What else? Martine?[ Inaudible comment ]When you take a certain percent off. Yeah?>> Sales.>> So sales, that’s what Martine just said. I know that one of the biggest ways that I use percent in my real life, is when I go to a restaurant and I get a bill and then I need to leave a tip. Do your parents do that too?>> Yeah.>> Figure out how much of a tip to leave? It’s all about finding a certain percent of a number. So this is a really important skill to learn in life. Today we’re going to start with small numbers and over the next couple of days we’ll get to bigger and bigger numbers. So today our question is, how do I use a model to find the percent of a number? Let’s still consider that this one grid equals one whole. How could I find 15 percent of 1?[ Background sounds ]I heard a lot about the process. Shatara [assumed spelling], turn and tell the group what did you guys come up with?>> Shade in 15 equals 15 out of the whole.>> Who agrees? Disagree? Agree? Show me with your thumbs. Okay. So we can shade in 15. That’s 10, 11, 12, 13, 14, and 15. So we’ve gone through the process. This is the part I didn’t hear about. What is 15 percent of 1? What’s it equal to?>> Fifteen hundreds.>> Show me your thinking. What is it equal to? We’ve shaded it in. Now how do we find its value? Leaving a tip and I paid a dollar and I need to find out what tip to leave them. Fifteen percent’s a normal tip to leave. So how much would I leave as a decimal? Angie, what’d you come up with?>> Fifteen hundred.>> She says 1500. Show me with your thumb what your thinking is. Show me with your thumb what your thinking is. You agree, disagree, you’re not quite sure. Okay. Troy, can you tell us why you agree with it?>> Because you shaded in 15 squares.>> And, uh-huh?>> And so it’s equal to 1500 because you shaded 15 [inaudible].>> Did you want to add on? Go ahead, Carolyn.>> Those squares are considered as hundreds.>> Mm-hmm.[ Inaudible comment ]Okay. And do you want to add on?>> I agree with it because it’s like 15 out of 100.>> Okay. So you used the model to find the 15 percent and then you need to go back to find what it’s equal to. So let’s record our thinking in our journals. –you go about finding–and go ahead and record it with me because you’ll talk about it with your group mate, 15 percent of 3?>> First, well me and Idalia [assumed spelling], she told me that since here when it was a 15 out of 1, she said maybe it would be better if it was 3 because 3 wholes. So we put the 3 wholes and then we put 15 on each one of them. So then I added up the three 10s, and got 30. And then that’s when you get two 5s over 40 and then we multiplied so it’s 45 and I got 4500.>> Okay, what’s your thinking?[ Inaudible comment ]Does what Christina did make sense?>> Yes.>> Are there any questions?>> I agree.>> You agree. Okay. Diangelo, do you want to say something? No? You agree?>> What is this called, percent?>> Percent of a number. We found 15 percent of 3 equals 45 hundreds. Did some of you–thank you Christina. Actually can we freeze that for a second? Thanks. Did some of you get 45? You got 45 but you forgot the decimal point. That’s like if something costs $3.00 and you left the waitress $45.00 for her tip.>> Whoa.>> That would be leaving over 100 percent. So you need to make sure to go back to your model to think what is this percent. Others of you, and tell me if you did this, others of you drew one whole and you did 15 percent, 15 percent, 15 percent and that equaled 45 hundreds. Who did that? Because that way worked also, right? What you did was you did 15 percent of 1 times 3. What happens when you get over 100, if your percent gets over 1? Then you have to add on another model. So you could do it that way, convert it to a decimal and do 15 hundreds three times. Or you could use three different wholes. Are you ready for your explore to go out and investigate more? [Background conversation] Yeah. And I have some grids for you to use. [Background conversation] No, they’re for you. So when you come up, each of you can take one explore paper and one set of grids. You can glue your grids to this paper. I think they’ll all fit. If not, you can use the back or another piece of paper. Questions before you go off? [Background conversation] Okay. Please remember when you go off, get straight to work talking and thinking and working together, sharing your thinking, and then recording it. Okay? Okay, off you go. [Overlapping Background conversations]>> What I heard Erin saying was why don’t we use these. What are these for?>> They’re for drawing the–I’m saying that if we use four of these to put 79 percent in each of them.>> Why?>> Because it’s 79 and 4, so that’s 79 percent of 4 of these.>> Yeah so like right here it says 15 percent of 3, so it would be like the same thing. So it would be saying a percent of 4.>> Right. And so you’re really smart to think of quarters, right? Four quarters, about 75, 75, 75, 75. But the problem is that works for 75 percent. And it can give you a pretty good estimate, right?>> And in fractions.>> Mm-hmm, and definitely in fractions relating it to fractions. But I think what the three of you are missing is coming together with your ideas because you had an idea, you had an idea but you weren’t listening to each other. Okay? So do you want to try the models or do you want to try the other way?>> Models.>> Models.>> Okay, so what’s your next step?>> Cutting them.>> Cutting them out and then?>> And then putting them in the–>> Shading them in.>> How much?>> 79 percent.>> Okay.>> And then we’re going to add them up.>> Okay. Sounds good. Okay. Go ahead. So talk to me about this number right here, 316. What’s that mean?>> Three hundred sixteen is how much the total counting. [Overlapping conversations]>> Okay. So let’s go back to the question. It says Kevin spent 79 percent of $4.00. What’s the value of that? You have to always go back to the context. What’s the value of this 316 when we’re talking about the money that he spent?>> Four dollars.>> So how did you go about finding how much Kevin spent?>> We first added them.>> And what’s the “them” you added?>> We added the [inaudible].>> You added what?>> We added 79 times 4.>> So you did 79 four times. Where’d you get the 79 from? Let other people jump in.>> From the percentage.>> The percent. So you added 79 four times and what did you get?>> Three dollars and 16 cents.>> I heard them say that they got $3.16. Does this show $3.16?>> No.>> What’s this show?>> Three hundred sixteen.>> Right. Who got 316, something like that, whether it had a decimal point or not, those are the digits that you got? [Inaudible] What about the decimal point because we’re talking about a percent. We know that Kevin spent 79 percent of $4.00. Did he spend all of those $4.00?>> No.>> Seventy-nine percent. Did he spend all of it?>> No.>> Did he spend more than the $4.00?>> No.>> Did he spend less?>> Yes.>> How do we know that he spent less than $4.00? I’m asking everybody. Go ahead Carolyn.>> He spent 79 out of 100.>> Okay. And what do you mean 100 percent? What would 100 percent be?>> A dollar.>> What would 100 percent of $4.00 be?>> You’d spend the whole $4.00.>> It’d be the whole $4.00, right Christina? So we need to go back to this context. Our answer is going to be less than $4.00, isn’t it?>> Yeah.>> So then we have to go back to this. What did 79 percent of $1.00 mean? Where does the decimal point go here?>> In the middle?>> Here? [Inaudible]>> Here? Here?>> Yeah>> Where does it go?>> Before the seven.>> Oh yeah, before the seven.>> Here?>> No.>> Here?>> No.>> Here?>> Yes.>> Okay. So you can’t forget about the context, what it means. And then where does our decimal point go in our answer?>> Right after the 3.>> So Kevin spent $3.16. What did you get for Brandon?>> Three dollars and seventy-one.>> Three dollars and seventy one. And how did you go about doing that? It was $3.71. Who spent more?>> Brandon.>> Brandon.>> Brandon spent more. So I see what a lot of you did today was you changed your percent into a decimal and you added that decimal up. You could have also multiplied it like I heard up here, 7 times.>> Yeah, that’s what I did.>> Okay? So I am ready to give you your exit slip to prove your thinking. Remember when you’re showing your work it’ll probably look something like this. Or you can draw models if you want to.**ANSWER 3 QUESTIONS:1. What are the different strategies students use to solve the problem?2. How does this fifth grade teacher scaffold the lesson so they are able to have access to the problem?3. When conferencing with students, what questions does she ask and what advice does she give?

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