- Student reads first word problem printed in the Word Generation book.

- The problem includes a chart with the grades of athletes.

- Teacher emphasizes use of "previous."

- Class reviews "mean" as a math word.

- Teacher distinguishes median and mean.

- Teacher reviews the method of finding an average and asks which data set is appropriate to average.

- Students share and demonstrate methods for computation.

[clip length—12:48]

TEACHER: Regina, please read the first problem for me. “Parents and teachers…”

STUDENT 1: “Parents and teachers at Orange Tree High School were— were worried about how school sports affect the students’ grades. Many adults wanted to make good grades a…

STUDENT 2: Prerequisite

STUDENT 1: “Pre—” Ugh.

STUDENT 2: Prerequisite.

TEACHER: It’s hard. It’s a tongue twister. Pre-re-qui-site.

STUDENT 1: “Prerequisite…

TEACHER: Very good.

STUDENT 1: “… for playing school sports. This year, a new rule was made. Students had to maintain a B average to be eligible for sports. Below are— below are the math grades of the five starters on the girls’ basketball team. The second column shows the math grades during the year after the rule was made and the first column shows the math grades the previous year.”

TEACHER: So previous means before or after?

STUDENTS: Before.

TEACHER: Before. Isaiah, what’s the first three letters of previous?

STUDENT: Um, previous? P-R-E?

TEACHER: P-R-E. And what do you notice, previous and prerequisite, they both start with…?

STUDENTS: Pre.

TEACHER: Pre. Which means they happen when, Isaiah?

STUDENT: Before.

TEACHER: Before, very good.

STUDENT: Before.

TEACHER: So here are the math grades before the rule and the math grades after the rule. So I’m gonna even write the word previous here.  So here are the kids’ math grades. Here’s the proof. Right? We’re gonna see if— if the parents were right. ’Cause sometimes parents are right, sometimes they’re not; sometimes teachers are right, sometimes they’re not. What was the mean math grade for the five starters before the rule was made? What is the math word in this question?

STUDENT: Ooh! Ooh! Ooh!

TEACHER: Come on Keisha

STUDENT: Mean.

TEACHER: What is the math word? What is the math action we’re gonna take?

STUDENT: Can you come back to me?

TEACHER: How ’bout you call on somebody to help you out?

STUDENT: Jolane

TEACHER: Jolane. 

STUDENT: Mean.

TEACHER: Mean. Everybody circle the word mean.

STUDENT: Mean.

TEACHER: This is all the way back to September. Who remembers what the mean means? What does the mean mean? Sarah?

STUDENT: Average.

TEACHER: The average. So I remember— ’Cause sometimes— what are the two— what are the two terms we sometimes get confused in here.

STUDENTS: Mean and median.

TEACHER: The median. The median is the long line and it’s the—

STUDENT: The— the middle number.

TEACHER: The math— the math midpoint, very good. This is the average. Huh. How do I find the average of something?

STUDENT: [gasps]

TEACHER: All right. Josetti

STUDENT: You add all the numbers and divide it by the amount of them.

TEACHER: The amount of numbers. Okay. So Catherine which set of numbers am I gonna use to answer this question? Which set are— which section— which section of the— Which section are they asking you to work on?

STUDENT: The previous

TEACHER: The previous. So which set is it? Is it this set or this set?

STUDENT: The left.

TEACHER: The left set, okay. So I’m actually gonna circle this set because if I didn’t, if I was rushing, I might add the other numbers first. So who can give me a good strategy to add these numbers? ’Cause I’m gonna show my work on the side, and I expect everybody to do the same. This is good review from September. Owen? What do I expect?

TEACHER: Thank you, Perry, for helping him out. So here are my numbers. Josetti says I’m gonna add them all up. And there are lots of different ways we can add numbers. You can put them in order.

STUDENT: You need both sets in this one.

TEACHER: Or we can just add them. Where should we start?

STUDENT: On the right side

STUDENT: 80 plus—

TEACHER: I could start with the eighties. Okay.

STUDENT: 80 could be 1

TEACHER: So you wanna split it? 80, 80, 80, 90, 90, and then one, eight, two, and then two zeros?

STUDENTS: is this out of ?? 

TEACHER: It looks like its out of ?? but we’re not gonna work with that. We did separate the ones. Why would you separate out the ones and the tens if you’re adding?

TEACHER: [Whispers:] Easier. Why is it easier? Right of the bat, I have three sets of 80; how much do I have?

TEACHER: Give you— give you a minute? Nestor[sp?] what do you think?

STUDENT: Nah, I got the answer.

TEACHER: How?

STUDENT: I added it all up.

TEACHER: What’d you start with? Did you add with the one first or the tens?

STUDENT: The ones.

TEACHER: Okay.

STUDENT: And then I got eleven.

TEACHER: Oh, you got eleven? Okay, and then what did you do?

STUDENT: Then I carried the one…

TEACHER: Okay.

STUDENT: …then I knew nine plus one equals ten.

TEACHER: Ah, so you took this one and one of the nines and made ten? Okay.

STUDENT: Yeah. Then I knew nine and seven equals seventeen.

TEACHER: Nine and seven?

STUDENT: I mean nine and eight. [laughter]

TEACHER: Okay. So over here, you’re telling me in my little save box I’ve got ten, and I’ve got seventeen. Okay.

STUDENT: And then eight plus eight equals sixteen.

TEACHER: Okay. And then what’d you do?

STUDENT: Then I added them all up.

TEACHER: So seven plus six is?

STUDENT: It’s, uh— it’s thirteen.

TEACHER: Thirteen. And then I’ve got the thirteen plus 30 is 43. And then I just add it up from there. So now I’ve got 431 is my— what is— what’s the answer to a addition problem?

STUDENT: Sum.

TEACHER: Sum, thank you. So a sum— the sum is 431.What’s the next step?

STUDENT: Divide.

TEACHER: 431 is not one of my answers.

STUDENT: Divide.

TEACHER: Divide. Yanellis?

STUDENT: Divide

TEACHER: What would I divide by? Josetti told me to find the average. I need to add up all the numbers and divide by how many numbers I added together. How many numbers did I add together?

STUDENT 1: Five.

STUDENT 2: Two numbers.

TEACHER: I added two numbers together?

STUDENT: Five.

TEACHER: How many numbers in that set?

STUDENT: Five.

TEACHER: Ssh. How many?

STUDENT: five

TEACHER: I added 80, 81, 98, 92, and 80. Five, there we go. Who wants to volunteer to do the long division?

STUDENT: I’ll do some long division

TEACHER: Yay, Quiada. All right, Quiada, what do I do first?

STUDENT: Um, you multiply?

TEACHER: Multiply what?

STUDENT: [inaudible]

TEACHER: Okay. With what? You have to give specific numbers.

STUDENT: Five?

TEACHER: You know what, Jolane? That really wasn’t polite. She’s trying to work through it on her own. I’m gonna be respectful and let her do it. Thank you.

STUDENT: I would put the eight between the four and three.

TEACHER: I disagree. I disagree. Why don’t you take a minute to work it out on your paper? Maybelle?

STUDENT: You have to find if five can go into fourty three because four can’t go because five can’t go into four

STUDENT: You can just—

TEACHER: Okay, so I’m gonna listen to one person at a time. I know you’re all excited because you’ve conquered long division this year, and I appreciate that. Okay? If I need to tap on from somebody for Maybelle, I will choose you next, okay? So Maybelle said—and I’m gonna repeat what she said, ’cause sometimes you’re a little soft spoken. Maybelle said five can’t go into four, so she’s using the 43. And then what did you say?

STUDENT: and then I want to see if five can go into 43.

TEACHER: Okay.

STUDENT: And I know that five can’t go into 43, ’cause it’s not gonna be an even number. So I know that five times eight equals forty.

TEACHER: Okay.

STUDENT: And I put the eight on top of the four.

TEACHER: Oh, you put the eight on top of the four? I disagree. Pedria, would you put the eight on top of the four? If we’re doing 43, where would you put the eight?

STUDENT: Um, on top of the three.

TEACHER: On top of the three. Okay. Because this is the number I’m working with. I’m pretending that one doesn’t exist, right?

STUDENT: Yeah.

TEACHER: So Maybelle said that that was 40. So I spent 40. Gada?, how many do I have to bri— bring down? If I’ve spent 40, how many extra do I have?

STUDENT: Three.

TEACHER: Three. Can five go into three evenly without going over?

STUDENTS: No.

TEACHER: Oh, I need a hand. I can’t hear everybody. Regina?

STUDENT: You have to carry the one

TEACHER: Okay. So you bring the one down and you make the new number of 31. Can five go into 31 without going over, Kim?

STUDENT: No.

STUDENT: Yes.

TEACHER: Ssh. Can five go into 31?

STUDENT: No.

STUDENT: Yes, it can.

STUDENT: No, it can’t.

TEACHER: Five— I can’t divide 31 into five groups?

STUDENT: Yes, you can.

TEACHER: How many?

STUDENT: Five.

TEACHER: Watch. ’Cause I’m called on Kim, so we’re gonna look at Kim and we’re not gonna argue between each other. Kim. How many groups of five can I make if I’ve got 31 things?

STUDENT: Seven.

TEACHER: Seven?

STUDENT: Six.

TEACHER: Why did you say six?

STUDENT: Six, because it’s— Well, because if there’s one and it goes over, so I didn’t count the one.

TEACHER: Oh. So if the one— it’s seven groups, but one group only has…

STUDENT: One.

TEACHER: …one thing in it? Okay. So it has to be six. ’Cause I have to have even groups. So I’ve now got— how many things have I used— how many in those five groups of six?

STUDENT: laughter

TEACHER: I really am not appreciating today the way that children are taking answers away from other people that are trying to work out the math. I’d like a little more patience— Tiara, help her out. If I have five groups of six, how many do I have total?

STUDENT: Thirty?

TEACHER: Thirty.

STUDENT: And then one times one.

TEACHER: So I’ve got one left over. Can I make any more groups?

STUDENTS: No.

TEACHER: Mm-mm. But guess what I can do?

STUDENT: Remainder.

TEACHER: So I’ve got a remainder of one. So here’s my 86, remainder one. So that’s one out of a group of how many?

STUDENT: Five.

STUDENT: Five.

TEACHER: What’s one-fifth? But these were in decimals[?].

STUDENT: One-fifth is 20%.

TEACHER: Oh, one-fifth is 20%. 86 and twenty-over-100. But I don’t have two decimals. I don’t have two decimal places; I only have tens. What’s the equivalent form I have to do with that? Nestor.

STUDENT: [inaudible]

TEACHER: Josetti. I’m waiting for you — you know

TEACHER: I know you’re upset that I don’t always call on you, but I have 24 people that need to learn.

STUDENT: [inaudible]

TEACHER: Look at me. Look at me. Now is your time. So you have 86 and one-fifth. Somebody said that’s 20%, which is 20 out of 100. But I only have what place value in my decimal places here in the answers?

STUDENT: Ten.

TEACHER: Ten. So what’s equivalent to 20/100ths?

STUDENT: 2/10ths.

TEACHER: 2/10ths. So Josetti, what’s my answer? You can say the answer.

STUDENT: 86 and 2/10ths

TEACHER: 86 and 2/10ths. I know that makes you happy

TEACHER: All right, so 86 and 2/10ths. So see? No matter where we go, we are always working with equivalent forms. Make sure you have your work shown. ’Cause then we need to use— most Word Generation problems, when we have one problem, we have to use a correct answer here to solve the next problem. If you’ve already written down your work, you’ll need to preview question two, and see if you can solve it on your own. And then we’re gonna take a vote and see if you voted A or B. You’re gonna solve question two on your own…

STUDENT: Okay.

TEACHER: …using the correct answer to problem one. [Whispers to student: Right. I know that you like to share, and I know that you know

 

 

Math Problem of the Week