US2 WRITING VARIABLE EXPRESSIONS
This eighth grade mathematics lesson focuses on writing variable expressions. It is the introductory lesson to a unit of work on equations. The lesson is 53 minutes in duration. There are 31 students enrolled in the class.
| Time | Caption |
|---|---|
| 00:00:19 | Bless you. |
| 00:00:26 | Okay everybody, please put your books away. Quietly take out paper to start the warm-up. |
| 00:00:38 | Quietly have your homework out on your desk. I'm going to come around and check it please. |
| 00:00:49 | Tim, there's something under your chair. |
| 00:00:58 | Let's go, start the warm-up please. |
| 00:00:59 | Oh, sorry. |
| 00:01:11 | Yes? |
| 00:01:13 | Can I (inaudible) my backpack? |
| 00:01:14 | Yes, quickly please. |
| 00:01:19 | Yes? |
| 00:01:20 | (inaudible) |
| 00:01:21 | Yes, quickly. |
| 00:01:23 | Can I borrow a pencil? |
| 00:01:24 | Let's go. Come on. Quickly. |
| 00:01:34 | Brandon please do the warm-up. |
| 00:01:45 | Jared? |
| 00:01:47 | (inaudible) |
| 00:01:48 | Okay. Next time do it in pencil. |
| 00:01:53 | (inaudible) |
| 00:01:54 | Okay. Looks good. Keep doing your work, okay. |
| 00:02:03 | John, Adrian, please do the warm-up, okay? Let's go to the warm-up. Ryan, homework? |
| 00:02:17 | Okay. Very good. Thanks. |
| 00:02:27 | Yes Bren? |
| 00:02:28 | Can I sharpen my pencil? |
| 00:02:29 | Quickly please. |
| 00:02:35 | I didn't finish. |
| 00:02:39 | You didn't do this part? |
| 00:02:40 | No, (inaudible). |
| 00:02:44 | Okay. |
| 00:02:58 | Okay, that's good. |
| 00:03:02 | Keep doing your work, okay? |
| 00:03:07 | John, (inaudible). |
| 00:03:14 | Okay, good job. |
| 00:03:16 | Okay, take that one out, put it on my desk. Or hand it to me right now please. |
| 00:03:27 | It's right here, Rosalia. Good work. |
| 00:03:32 | Thank you. |
| 00:03:43 | Okay, you got a misplaced L there. Okay. Make that correction. |
| 00:03:50 | Oh, and here, you had to do the ones that were left, not the ones you crossed out. |
| 00:03:55 | Okay. |
| 00:03:56 | Okay. |
| 00:03:59 | Okay, good. Let me stamp it please. Good work Irabely. |
| 00:04:04 | Shaila, homework? |
| 00:04:09 | Okay. What about this? |
| 00:04:15 | I didn't get it. |
| 00:04:17 | Okay, when we go over it, make sure if you don't get it, you ask me questions. Okay. Good. |
| 00:04:26 | John, homework? |
| 00:04:31 | What about the L? Let's see, I don't- |
| 00:04:35 | Okay, make that correction. |
| 00:04:41 | Okay, John, good. |
| 00:04:49 | Andrea? |
| 00:04:55 | Okay, good. Good work. |
| 00:05:01 | Michelle? |
| 00:05:10 | Okay Michelle, good. Good work. |
| 00:05:17 | Kristy? What about the answer here? Okay, you have to write it out, okay? |
| 00:05:29 | Okay. Good. |
| 00:05:32 | Ashley did you pick up what you missed yesterday? |
| 00:05:35 | Yeah. Did we have a lesson yesterday? |
| 00:05:37 | No. There were no notes yesterday. |
| 00:05:39 | Okay. |
| 00:05:40 | Okay. |
| 00:05:44 | Tim, homework? |
| 00:05:53 | Okay, missing an E. Forgot the E. |
| 00:05:55 | Oh, okay. |
| 00:05:57 | Okay. That's very good Tim. Keep doing your homework. This is very good, keep it up. |
| 00:06:06 | Alex? |
| 00:06:14 | Very good. Good work Alex. |
| 00:06:22 | Steve, homework? |
| 00:06:31 | Okay, very good. Good Steve. |
| 00:06:38 | Jen? Oops, excuse me. |
| 00:06:40 | Sorry. |
| 00:06:41 | That's all right. |
| 00:06:45 | Very good Jen. Good work. |
| 00:06:52 | Kendra? Okay. Very good. Good work. Thank you. |
| 00:07:17 | Okay, Alex, good. Good work Alex. |
| 00:07:23 | Brandon, homework please? |
| 00:07:24 | Yeah, I didn't get how to do the bottom part. But, I did everything else. |
| 00:07:31 | What, this part here? |
| 00:07:32 | Yeah. |
| 00:07:33 | All right. |
| 00:07:36 | And I think I might have messed up. |
| 00:07:38 | Yeah, there's some letters here that shouldn't be. So when we go over it, make sure you make the corrections. |
| 00:07:43 | All right. |
| 00:07:44 | All right. |
| 00:07:46 | Thanks. |
| 00:07:50 | Diana? |
| 00:07:58 | A couple of extra letters in here. Okay. So, when we go over it, see if you can make the corrections, okay? Good. |
| 00:08:07 | Okay, good work Diana. |
| 00:08:15 | Josh, homework please. |
| 00:08:26 | That's good Josh. Good work. |
| 00:08:32 | Dave? |
| 00:08:39 | Okay, good David. Keep it up. Good work. |
| 00:08:46 | Marcus- yes it is, very good. |
| 00:08:53 | Okay Marcus, good. Good work. |
| 00:08:57 | This is my homework. |
| 00:09:00 | Oh, that's right, you were absent yesterday. Can you take that (inaudible) and make sure I get it in my book. |
| 00:09:05 | Did you pick up yesterday's homework? |
| 00:09:07 | I'm almost done with it. |
| 00:09:09 | Okay, thank you. Patrick, homework? |
| 00:09:12 | Yeah. |
| 00:09:18 | Okay, next page please. |
| 00:09:23 | Okay Patrick, good. Good work. |
| 00:09:41 | Very good, Carly. Good work. |
| 00:09:50 | Okay. Okay, Aubrey, good work. |
| 00:09:57 | Thanks. |
| 00:10:38 | Okay, let's begin our warm-up today. Number one, is that a right triangle? John? |
| 00:10:43 | Yes. |
| 00:10:44 | Yes John, why? |
| 00:10:45 | Twenty-five plus 144 equals 169. |
| 00:10:49 | Okay, where'd you get the 25 and the 144? |
| 00:10:52 | Uh, five squared plus 12 squared. |
| 00:10:54 | Good. Number two, Alex? |
| 00:10:58 | Ten point five nine one three. |
| 00:11:00 | That is correct. Ten point five nine one three. Number three, Ryan? |
| 00:11:07 | One and eight-fifteenths. |
| 00:11:09 | That is correct. One and eight-fifteenths. Marcus, how about four? |
| 00:11:14 | Four point zero zero five. |
| 00:11:15 | That's correct. Four point zero zero five. Number five, Steve? |
| 00:11:22 | Two-fifteenths. |
| 00:11:24 | What'd you have Aubrey? |
| 00:11:25 | One- one and seven twenty-ones. |
| 00:11:29 | Reduce it Jen. |
| 00:11:30 | I- I got one and one-third. |
| 00:11:32 | That's correct. Aubrey you were correct, you just needed to reduce it. Okay? Questions one through five? John? |
| 00:11:38 | Number two. |
| 00:11:40 | What did you get for your first set of parentheses? |
| 00:11:42 | Point one three four five. |
| 00:11:46 | Did you copy it correctly? |
| 00:11:48 | No. |
| 00:11:50 | Okay. Make sure you do that John. Brandon? |
| 00:11:52 | What was number two? |
| 00:11:54 | Ten point five nine one three. |
| 00:11:56 | What was the first parenthesis? |
| 00:11:57 | Nine point six eight eight three. Make sure you line up your decimals and then- |
| 00:12:04 | Oops, I added. |
| 00:12:05 | Okay. Ashley? |
| 00:12:07 | The first one was yes, right? |
| 00:12:09 | Correct. |
| 00:12:11 | I got no. |
| 00:12:12 | Okay, do you have five squared plus 12 squared? Does it equal 13 squared? |
| 00:12:17 | I had 25 plus 144. |
| 00:12:20 | That's correct, one- |
| 00:12:21 | Equals 52. |
| 00:12:22 | Oh, that's why. Okay? |
| 00:12:25 | Okay, number six, Patrick. |
| 00:12:27 | Eight divided by four equals two, and two plus two equals four, and four times six equals 24 |
| 00:12:32 | Good. Tim? |
| 00:12:33 | Six times two equals 12, 12 plus eight equals twenty. Twenty plus four equals 24. |
| 00:12:37 | Good. Josh? |
| 00:12:39 | Four minus two equals two, uh, six divided by two is three, and three times eight is 24. |
| 00:12:45 | Good. John? |
| 00:12:46 | Eight plus six is 14, 14 times two is 28, and 28 minus four is 24. |
| 00:12:50 | Very good. Marcus? |
| 00:12:52 | Uh, six times two is 12, eight divided by four is two, 12 times two is 24. |
| 00:12:58 | Okay, good. Another one Patrick? |
| 00:13:00 | Yeah. Four divided by two equals two, eight divided by two equals four, and four times six equals 24. |
| 00:13:06 | Very good. Very good. All right, how about the last one? Ryan? |
| 00:13:09 | Nine minus seven equals two, two times four equals eight, three times eight is 24. |
| 00:13:13 | Good. Alex? |
| 00:13:16 | Nine times three is 27, 27 minus seven is 20, and 20 plus four is 24. |
| 00:13:21 | Good. Ashley? |
| 00:13:23 | Seven minus three is four- nine minus eight is six- wait, no- Oops. I mean nine minus four is six- |
| 00:13:33 | What's nine minus four? |
| 00:13:35 | I got it wrong. |
| 00:13:36 | That's okay. |
| 00:13:37 | I did it right now. |
| 00:13:38 | Marcus? |
| 00:13:40 | Nine minus seven is two, eight- I mean four times two is eight, and eight times three is 24. |
| 00:13:46 | Good, Patrick? |
| 00:13:47 | Nine minus seven equals two, two times three equals six, six times four equals 24. |
| 00:13:51 | Okay. Good. Any questions on your warm up? |
| 00:13:57 | All right, please take out your homework. |
| 00:14:12 | Okay, on your homework the first page at the very top, graphing the numbers- |
| 00:14:22 | Should look like this. You simply had to fill in the numbers there. |
| 00:14:31 | Take a minute, look it over. |
| 00:14:42 | The second part, we had to list what was in between what they gave us. |
| 00:14:48 | Again, take a minute, look, see if you have any questions. Brandon? |
| 00:14:55 | Brandon? |
| 00:14:56 | What if you put on number, uh, where it says integers between negative five and negative eight. |
| 00:15:01 | What if you put negative seven and negative six? Does it matter what order you put them? |
| 00:15:05 | No, that's okay. |
| 00:15:06 | Thank you. |
| 00:15:08 | Any other questions? |
| 00:15:11 | All right, then the next section you had to graph them which they simply put a- meant to put a dot on the number line. |
| 00:15:21 | Some of you drew lines which is okay. Yes, Marcus? |
| 00:15:23 | Uh, I have a question. Well- well- |
| 00:15:25 | Okay, on the first it says like graph one through four. It's- you're supposed to graph it on the top one, right? Like on- |
| 00:15:32 | One through four? |
| 00:15:33 | Yeah, you're supposed to graph it on top, right? |
| 00:15:35 | No, I think- |
| 00:15:36 | I mean, I mean, I mean one and four, like that. Remember. |
| 00:15:39 | Here? |
| 00:15:40 | Yeah. |
| 00:15:41 | Yeah, so I just drew a dot here and here. It's okay if you put it above it. That's okay. Is that- was that your question? |
| 00:15:46 | Yeah, 'cause I... put it (inaudible). |
| 00:15:49 | Oh, that's fine too. Just so we know that it's one and four. It's pretty close to those numbers. Any other questions? |
| 00:15:58 | Okay, how about the bottom. What did it spell out? Michelle? |
| 00:16:00 | Seattle. |
| 00:16:01 | Seattle. When we make a deposit into a bank account, does that mean we put money in or take it out? Jen? |
| 00:16:11 | Put money in. |
| 00:16:12 | Put money in. Good. What happens to the balance then when we put money in? Alex? |
| 00:16:16 | It goes up. |
| 00:16:17 | So is that positive or negative Alex? |
| 00:16:19 | Positive. |
| 00:16:20 | Good. Questions on your first page? |
| 00:16:26 | All right. Let's go to the second page. |
| 00:16:31 | Can we call them out, or, are you gonna put them on (inaudible). |
| 00:16:33 | I'm going to call on people, Brandon. |
| 00:16:35 | Oh, yes. |
| 00:16:36 | All right, the first row, numbers one two and three, Patrick. |
| 00:16:42 | Greater than and- no, less than, less than. |
| 00:16:45 | Say it again, please? |
| 00:16:46 | Less than and less than. |
| 00:16:48 | No. One, two, and three. |
| 00:16:50 | Oh, greater than, less than, less than. |
| 00:16:52 | Good. Greater than, less than and less than. How about the next row? John? |
| 00:16:58 | Greater, greater and less than. |
| 00:17:01 | Yes. Greater than, greater than, less than. The next row, Michelle? |
| 00:17:05 | Less than, greater than and equal. |
| 00:17:09 | That's correct. Row beginning with 10, Ryan? |
| 00:17:13 | Less than, greater than, less than. |
| 00:17:16 | Good. Next row, Brandon? |
| 00:17:19 | Are we on, uh- |
| 00:17:20 | Number 13. |
| 00:17:21 | All right. Greater than, greater than, greater than. |
| 00:17:23 | Good. They are all greater than there. Andrea, how about the next row? |
| 00:17:27 | Less than, less than and greater than. |
| 00:17:30 | Very good. All right, we're batting a thousand. Tim, next row. |
| 00:17:34 | Equal to, less than and less than. |
| 00:17:37 | Very good. Marcus. |
| 00:17:39 | Uh, less than, greater than and less than. |
| 00:17:41 | Good. And Jen, how about the last row? |
| 00:17:44 | Greater than, greater than, greater than. |
| 00:17:46 | Very good. How many had all those right? |
| 00:17:48 | Everybody. |
| 00:17:49 | Good job class. Good job. Any questions on the second page? John? |
| 00:17:53 | Yeah, why wouldn't number three be equal? |
| 00:17:56 | Number three? |
| 00:17:57 | Mh-hm. |
| 00:18:00 | Okay, negative one and positive one? |
| 00:18:02 | Yeah. |
| 00:18:03 | Look up on the- |
| 00:18:04 | Because it's equal part, so... |
| 00:18:05 | Okay. That's a good- we're not doing absolute value though. Are we? |
| 00:18:10 | We're just simply like- look at our number line up here John. Negative one or positive one. Which one is greater? |
| 00:18:17 | One. |
| 00:18:18 | Right. That's what they were asking for. Not how far each one was apart from zero. |
| 00:18:22 | Oh, okay. |
| 00:18:23 | Okay? Any other questions? |
| 00:18:27 | Okay, third page. What does a Boa Constrictor order at the ice cream shop? Alex? |
| 00:18:35 | A snake shake. |
| 00:18:36 | A snake shake. |
| 00:18:38 | Take a minute look at the one. Some of you didn't have the correct ones circled. See if you have any questions. |
| 00:18:52 | You had to cross out the box and what was left was your answer. |
| 00:19:00 | Any questions, people? |
| 00:19:07 | How many had the entire assignment correct? That's good. Great. No questions? |
| 00:19:16 | Okay, take out your notes then please. |
| 00:19:32 | Okay. |
| 00:19:41 | What's today's date? Raise your hand? |
| 00:19:42 | The twenty-eighth. |
| 00:19:44 | Ryan? |
| 00:19:45 | The twenty-eighth. |
| 00:19:46 | The twenty-eighth. Please date your notes. November twenty-eighth. Yes? |
| 00:19:52 | Are we allowed to take notes in pen if- if we want to? |
| 00:19:55 | That's fine. That's the only thing you can do in pen in here. |
| 00:19:59 | Volunteer to read our quote of the week? Michelle? |
| 00:20:04 | "What is the best- What is best in mathematics deserves not merely to be learned as a task, |
| 00:20:10 | but to be assimilated as a part of daily thought, and brought again and again before the mind with ever renewed encouragement". |
| 00:20:21 | Very good. What does that mean, anybody? Patrick? |
| 00:20:24 | It means to not think of math as a like- as not something fun to do and only use it in school but to use it in your everyday life. |
| 00:20:34 | Very good. Anybody else? Brandon? |
| 00:20:36 | That math is around you all the time. |
| 00:20:38 | That's correct. And it means don't just learn it as a- because you have to. |
| 00:20:44 | Learn it because you want to and have it as a part of your daily life because math is? |
| 00:20:49 | Power. |
| 00:20:50 | All right. Good. Okay. |
| 00:20:53 | Today's lesson is titled, Writing Variable Expressions. So please title your notes. |
| 00:21:18 | Okay, I want you to think for a minute. I know- I know you can do this. |
| 00:21:26 | There are times throughout the day, I'm sure, where you hear words but in actuality you're talking about numbers. |
| 00:21:36 | For example, Suzie is six inches shorter than Mary. Anybody else think of an example that you hear? Ashley? |
| 00:21:46 | How old is she turning? |
| 00:21:48 | Okay. Brandon? |
| 00:21:50 | Tom is five inches taller than Suzie. |
| 00:21:53 | Okay. Anybody else? Patrick? |
| 00:21:59 | Uh, never mind. |
| 00:22:01 | Kendra? |
| 00:22:02 | Like, when you're taking a test or something and the teacher is like, you got a 20 out of like, 40. |
| 00:22:06 | Good. Good Kendra. Alex? |
| 00:22:08 | Your pizza is two-fifty. |
| 00:22:10 | Okay. Is that how much they cost here? |
| 00:22:12 | Yeah. |
| 00:22:13 | Yep. They rip you off. |
| 00:22:15 | Tim? |
| 00:22:16 | Like my shoe size is like 12 and (inaudible) are (inaudible). |
| 00:22:19 | Compared to maybe somebody else's? |
| 00:22:21 | Yeah. |
| 00:22:22 | Okay, good. Now, I want you to think of another example here. |
| 00:22:27 | Say you have an after school job. You make seven dollars an hour. But this week, you're busy, you can only work two hours. |
| 00:22:38 | But, next week you can work 10. So I'm going to put up here, seven dollars H. |
| 00:22:47 | What is H? Does anyone know? Alex? |
| 00:22:51 | Hour. |
| 00:22:52 | It's the hours. Good. |
| 00:22:55 | What is H called? Does anyone know that? Patrick? Patrick? |
| 00:23:01 | Me? |
| 00:23:02 | Yes. |
| 00:23:03 | Okay. |
| 00:23:04 | Patrick. |
| 00:23:05 | A variable? |
| 00:23:06 | Good. A variable. So writing expressions today, variable is number one. |
| 00:23:12 | It's a letter that represents a value that can change. |
| 00:23:20 | The example I gave you, that H can change. Two hours this week. Ten hours next week. Variable. |
| 00:23:33 | Yes Brandon? |
| 00:23:34 | So the numbers change, not the, uh, letter? |
| 00:23:38 | Well what goes in for the letter changes? |
| 00:23:40 | Numbers? |
| 00:23:42 | Correct. Yes? |
| 00:23:44 | Then like- so you have like eight dollars could you go like eight and like B? |
| 00:23:48 | Sure. Yes. You can use any letter. Any letter in the alphabet will work. |
| 00:23:49 | So, you can- |
| 00:24:04 | Okay, that's a variable. What I wrote on the board, seven H, is called a variable expression because it contains a variable. |
| 00:24:16 | You'll see it up there as one of the examples and the other two are also examples of variable expressions. |
| 00:24:35 | Can you see? |
| 00:24:48 | So we have variable and variable expression. |
| 00:24:55 | Say that job that I have represented up here. You get a raise. You now make seven-fifty an hour. How will that change? Jen? |
| 00:25:08 | There'll be point fifty after seven? |
| 00:25:10 | Okay, so seven point five H, right? |
| 00:25:14 | Yeah. |
| 00:25:15 | Okay. Brandon? |
| 00:25:16 | I don't- I didn't get it. |
| 00:25:18 | Which part? |
| 00:25:19 | The uh, the H, seven H and then the four- where do you get the four W's to- |
| 00:25:24 | That's just an example. That's just another example of a variable expression. Okay? |
| 00:25:30 | Okay. Another example. You're going to an Eagles game. |
| 00:25:36 | Oh. |
| 00:25:38 | Tim? I used Phillies in my other classes but for you Tim, I used Eagles. |
| 00:25:42 | First the Raiders. |
| 00:25:43 | Okay? You're going to an Eagles game. They're selling hot dogs. They're very good by the way in Philadelphia. |
| 00:25:51 | So are the cheese steaks. |
| 00:25:53 | So are the cheese steaks, you're right. |
| 00:25:54 | Okay. But, the hot dogs at Vet stadium where the Eagles play sell for three dollars. |
| 00:26:00 | I want you to give me a variable expression for N hotdogs. Marcus? |
| 00:26:11 | N, hot, over three dollars. Or- |
| 00:26:15 | Not over because that means divided. |
| 00:26:17 | Three N. |
| 00:26:19 | Three N. Three N means however many I buy I have to pay three dollars for, right? |
| 00:26:24 | Where do you get the N from? |
| 00:26:25 | That's- I just said, that's the N number of hotdogs. That's what I'm using as my variable. Jen? |
| 00:26:31 | Wouldn't that mean you have to multiply them? |
| 00:26:33 | Yes. That's right. So if I got two hotdogs how much money am I spending? |
| 00:26:37 | Six dollars. |
| 00:26:38 | Three times two. Good, Jen. Yes? |
| 00:26:41 | Can it be like any letter? |
| 00:26:42 | It can be any letter. Yes, Michelle it can be. Good question. |
| 00:26:44 | But isn't it confusing? |
| 00:26:46 | It can be any letter, Brandon. Whatever you choose. Okay, part B today. Evaluating Expressions. |
| 00:26:53 | What I just did with the two dollars for a hotdog was evaluating an expression. |
| 00:27:01 | So if I come back to my original example on the board here, seven H, and I said you worked two hours this week, |
| 00:27:12 | How much money are you going to make this week, Ryan? |
| 00:27:16 | Fourteen. |
| 00:27:17 | Fourteen. How much would you make if you worked ten hours next week? Josh? |
| 00:27:22 | Seventy. |
| 00:27:23 | Good. What we just did was we took the number of hours and did what? Michelle? |
| 00:27:31 | Multiplied it by a seven. |
| 00:27:33 | Good. But what- we actually put it in for there? Didn't we? Put it in for the H? |
| 00:27:37 | Well, that's what evaluating means. Substituting a number for a variable. Yes? |
| 00:27:47 | So for the hotdog thing, would the N be two? |
| 00:27:51 | Yes. We substituted two for the N. |
| 00:27:54 | Oh. |
| 00:27:55 | We evaluated that example. |
| 00:27:58 | Do you have to write that then? Or, can you just write like how- like however many dollars it was times two? |
| 00:28:05 | Yeah. Do you have to write what- what? This? |
| 00:28:08 | Do you have to write the N or- |
| 00:28:09 | Well normally you'll be given that, yes. |
| 00:28:11 | Okay. |
| 00:28:13 | You won't be given- like if we're just talking, of course, I'm not going to say write down, but- |
| 00:28:18 | You'll be given expressions and asked to evaluate for a certain amount of money or numbers. |
| 00:28:35 | So I'm going to give you an example- Here's what you were asking me Jen. Evaluate the expression, four H plus three. |
| 00:28:43 | Now the part four H plus three is the expression and then it says for H equals two. What are we going to do with that? |
| 00:28:51 | What are we going to do with H equals two? Marcus? |
| 00:28:57 | I guess like four times two. Four times two plus three, would be eleven. |
| 00:29:02 | Good. |
| 00:29:05 | Okay. What we- Marcus did here was, wherever he saw an H in our expression he substituted a two. So that was the first step. |
| 00:29:17 | And remember, if there is nothing in between a number and parenthesis what operation do we do? |
| 00:29:25 | Multiplication. |
| 00:29:26 | Patrick? |
| 00:29:27 | Multiplication. |
| 00:29:28 | Good. And as Marcus said then, the answer is eight because four- I mean 11- four times two is eight, we add three, and we get 11. |
| 00:29:57 | Any questions so far? |
| 00:30:16 | Okay. Now, I'm sure you often hear, probably on radio ads or- or maybe even here at school, |
| 00:30:27 | Phrases such as twice as much, three times as long, half as heavy. Yes? |
| 00:30:36 | So my answer to the question is, four times two is eight, plus three is- |
| 00:30:41 | Is 11. |
| 00:30:42 | All right. |
| 00:30:44 | Okay? So you hear phrases like that. Twice as much. You hear that at the store, right? Or, things like that. |
| 00:30:51 | Three times as long. Social Studies class is three times as long as math. |
| 00:30:58 | It is? |
| 00:30:59 | Because math class is fun, Tim. |
| 00:31:01 | Oh, no. |
| 00:31:02 | Oh, I get it. |
| 00:31:03 | I just like math. |
| 00:31:05 | No, it's not really three times as long. They're all the same, but- that was just an- |
| 00:31:09 | I thought fifth period was the longest? |
| 00:31:10 | Yeah. |
| 00:31:11 | Okay. Well we have an extra 10 minutes because we read, but that's all. |
| 00:31:15 | Okay. What we're doing there, is we're taking words and translating them into variable expressions. |
| 00:31:25 | Now, there's two parts to that. Taking words and putting them into numbers or the opposite. |
| 00:31:34 | So people, if you're sitting at your desk taking notes, write the opposite. You don't have to write both of those things up there. |
| 00:31:40 | As long as you understand. Remember, you don't have to write everything I write. |
| 00:31:45 | Take words, change them into numbers. Take numbers and change them into words. |
| 00:31:52 | You can do one of those? |
| 00:31:54 | Yeah, and then just write either opposite or vice versa. |
| 00:32:05 | I'm gonna give you an- some examples. |
| 00:32:13 | Wait- |
| 00:32:32 | Okay. Say I give you the words, a number plus negative three. How would I take those words from a word phrase- |
| 00:32:47 | Now this example is on page one-o-six, people, so you have your choice here. |
| 00:32:51 | How do I take the words, a number plus negative three and make it a variable expression? Patrick? |
| 00:33:01 | A plus negative three. |
| 00:33:02 | Okay. A plus negative three. You chose A. I chose N. Again, the letter doesn't matter. |
| 00:33:10 | So we took a word phrase and changed it from words to a variable expression. I'm going to give you another- Yes? |
| 00:33:21 | Why'd you put the parenthesis around negative three? |
| 00:33:24 | Good question. Why'd I put these here? Only because you don't get mixed up with the signs. If I put- |
| 00:33:31 | Oh. |
| 00:33:32 | Okay? I don't- That's why I do it that way. Andrea? |
| 00:33:36 | Do you have to put it down there? |
| 00:33:37 | You don't have to but I think it's- it makes it clearer to see. Okay? Tim? |
| 00:33:44 | Would it make a difference if we put it around N plus or not? |
| 00:33:48 | Well, in this case, we have two operation signs technically, so that's why we- I did it here. Marcus? |
| 00:33:56 | What if you switched it around (inaudible) negative three before? |
| 00:33:59 | Before N? |
| 00:34:00 | Yeah. |
| 00:34:01 | That would work okay. But it's- but- It's backwards here from what the words are. |
| 00:34:05 | Oh. |
| 00:34:06 | Technically in math that's not incorrect. Yes? |
| 00:34:09 | So a number means like you put a letter? |
| 00:34:13 | Yes. That's the variable part of it. Any letter. |
| 00:34:16 | So that means- oh. |
| 00:34:18 | Okay, what if I say six less than a number. Six less than a number. Michelle? |
| 00:34:31 | Six minus N. |
| 00:34:33 | Six minus N. What do you think Aubrey? |
| 00:34:35 | N minus six. |
| 00:34:37 | Why do you think that? |
| 00:34:38 | Oh because- |
| 00:34:40 | You're right. Tell me why. |
| 00:34:41 | Six is less than the number? |
| 00:34:43 | Right. Do you see the difference? Six less than a number. |
| 00:34:46 | Oh. |
| 00:34:48 | Yours was a number less than six. What you gave me. This will- that's the tricky saying right there. Questions so far? |
| 00:35:02 | Alex? |
| 00:35:04 | So then when it says "less than" in, like, a question, you always minus the number from the letter? |
| 00:35:09 | Like go, the letter minus the number? |
| 00:35:13 | I hate when I say "always", Alex. Uh, nine times out of 10, yes, but there may be like something else here. |
| 00:35:20 | Like may- it may say two plus a number then less than. So you've got to be careful. It's not always. Okay. Yes? |
| 00:35:30 | Who did- do you have to put the parenthesis around the minus six or would that be considered a negative six? |
| 00:35:37 | Well in here there's not another sign so it doesn't matter here. |
| 00:35:42 | Well, we're going to learn next week that it's- negative- this also does mean minus. |
| 00:35:47 | But we don't need to put parenthesis here because there's not another sign, okay? |
| 00:35:53 | All right. Now, we're going to do it the other way. We're going to start with a variable expression and go to words. |
| 00:36:00 | Start with the variable and go to words. So I'm going to give you this time- Yes? |
| 00:36:08 | Is this in the book too (inaudible)? |
| 00:36:10 | Yeah. This is still all page one-o-six. |
| 00:36:13 | K divided by eight. Try to write that in words without using the word divided. Can anybody do that? Jen? |
| 00:36:21 | K over eight. |
| 00:36:22 | Okay. That's- Steve? |
| 00:36:24 | K into eight. |
| 00:36:25 | Okay. Well no. That would be eight into K. |
| 00:36:28 | Oh. |
| 00:36:29 | Christy? |
| 00:36:30 | K of eight. |
| 00:36:31 | No. What does "of" mean in that? |
| 00:36:33 | Oh. |
| 00:36:35 | Times. Okay? It's okay, you're thinking. |
| 00:36:38 | All of those- what Jen and Steve were correct, I chose the big math word, quotient. |
| 00:36:45 | K divided by eight, the quotient of the number and eight. |
| 00:36:50 | What if I gave you 15 minus B? Fifteen minus B. Patrick? |
| 00:36:59 | Fifteen less than B. Or less- B less than 15. |
| 00:37:03 | B less than 15 would work. I chose an easier route. Fifteen minus a number. |
| 00:37:11 | Either one is correct. Questions so far on this, people? |
| 00:37:21 | Any questions? |
| 00:37:27 | Andrea? |
| 00:37:28 | What does quotient mean? |
| 00:37:29 | Quotient means divided. See my- my sign up there in the corner has all the math words. Okay. |
| 00:37:37 | Okay. The last thing then, variable expressions with more than one operation. Use the order of operations. |
| 00:37:45 | What does that mean? Order of operations. Alex? |
| 00:37:51 | Uh, says sub- well take- Substitute words and change them into numbers. |
| 00:38:03 | Well kind of, but I mean here. Do you remember back what order of operations means Jen? |
| 00:38:08 | PEMDAS. |
| 00:38:09 | What's that mean? |
| 00:38:10 | Parenthesis, exponent, multiplication, division and addition and subtraction. |
| 00:38:13 | Very good. And what's the saying that goes along with that? |
| 00:38:16 | I know. I know. |
| 00:38:18 | Jen? |
| 00:38:19 | Please Excuse My Dear Aunt Sally. |
| 00:38:21 | Aubrey what's please mean? |
| 00:38:23 | Oh, parenthesis. |
| 00:38:25 | No, not actually please, but I mean- parenthesis. Class. Excuse. What's that mean? |
| 00:38:31 | Exponent. |
| 00:38:32 | My? |
| 00:38:33 | Multiplication. |
| 00:38:35 | Dear? |
| 00:38:36 | Division. |
| 00:38:37 | Aunt. |
| 00:38:38 | Addition. |
| 00:38:40 | Sally. |
| 00:38:41 | Subtraction. |
| 00:38:43 | Okay. Good. So that's what we do here. An example, evaluate one point five plus two N for N equals 12. |
| 00:38:51 | How do I do that? Patrick? |
| 00:38:56 | You do the multiplication first. But put the- you put 12 in for N and then you do the multiplication and then you add. |
| 00:39:04 | Good. Alex? |
| 00:39:05 | Or you could substitute N for 12 and put quotations around- |
| 00:39:11 | Parenthesis. |
| 00:39:12 | Yeah, parenthesis around N 12 so you know how to do those first. |
| 00:39:15 | Good. Jen? |
| 00:39:16 | What about for us in the example that says, uh, a number plus a negative three. |
| 00:39:22 | Wouldn't you have to do something with those parenthesis though, 'cause that's the order of operations. |
| 00:39:26 | Right. So you would- you would have to take it out of there. |
| 00:39:30 | So, next week- we haven't gotten to this yet, but plus a negative, depending on what this is. That's a good point. Yes. Marcus? |
| 00:39:37 | I have a question. Is that one point five? |
| 00:39:39 | Yes. One point five plus two N. |
| 00:39:43 | So Patrick said put 12 N for N. Class what's two times 12? |
| 00:39:48 | Twenty-four. |
| 00:39:50 | Plus one point five gives us twenty-five point five. |
| 00:39:54 | Is this all in our notes? |
| 00:39:55 | Yes, Brandon. |
| 00:39:56 | Yes. |
| 00:39:58 | Once you've finished writing I'd like you to take out your textbooks quietly. |
| 00:40:22 | Remember, if you don't have a book please share. And open to page one-o-seven please. Page one-o-seven. |
| 00:40:45 | Okay. Above number seven, somebody raise their hand and read the directions for me please. Above number seven. Michelle. |
| 00:40:55 | Write a variable expression for each quantity. Explain what the variable represents |
| 00:41:02 | Good. Page one-o-seven. So we're going to write a variable and then explain what it is. Look at number seven. |
| 00:41:10 | Kim's height if she's six inches shorter than her mother. What would a variable expression be? Steve? |
| 00:41:19 | Like N... N minus negative six? |
| 00:41:28 | No, just N minus six. |
| 00:41:29 | N minus six. |
| 00:41:30 | Good. What does N represent? |
| 00:41:33 | Her mom's height. |
| 00:41:34 | Good. How about number eight. The number of calories in three slices of bread? Patrick? |
| 00:41:42 | Uh, C times three. |
| 00:41:44 | Or how else could you say that? |
| 00:41:46 | Three times C. |
| 00:41:47 | Andrea? |
| 00:41:48 | Three C. |
| 00:41:49 | Three C. Okay. Look at- look at number nine. Mike's age if Mike is three years older than Jill. Ryan? |
| 00:42:01 | Three X. |
| 00:42:03 | No. That would be multiply. Wouldn't it? Think- think about that one again. |
| 00:42:07 | Plus X. |
| 00:42:08 | So what would it be? |
| 00:42:09 | Three plus X. |
| 00:42:10 | Okay, good. What's X represent? |
| 00:42:12 | Jill. |
| 00:42:13 | Jill. Jill's age. Good. Go down to number 11. Twice a number. What would that be? Twice a number. Alex? |
| 00:42:22 | N two. |
| 00:42:23 | Or how could we say that? |
| 00:42:25 | Two N. |
| 00:42:26 | Two N. Alex, always put the number first. Okay? Look at number 14. |
| 00:42:31 | The quotient of three divided by W. There's that word Andrea. Quotient of three divided by W. Marcus. |
| 00:42:38 | W over three. Or three over W. |
| 00:42:41 | Three over W. Okay. And one more, 16. Seventeen less than N. Michelle? |
| 00:42:49 | N minus 17. |
| 00:42:51 | Good. N minus 17 is correct. Okay. Quietly put your books away. I'm going to pass out your homework. |
| 00:43:00 | Oh, do we- on our homework, uh- |
| 00:43:01 | Shh. |
| 00:43:06 | Brandon let me explain it. I'll tell you. Okay class, quiet please. |
| 00:43:17 | Where do you think we use variable expressions in real life? Patrick? |
| 00:43:26 | When you're trying to figure out all the problems. |
| 00:43:30 | Okay. Marcus? |
| 00:43:32 | Uh- |
| 00:43:35 | How many of you have science this semester? Where do you use variable expressions in science? Formulas. Steve? |
| 00:43:46 | When you're trying to figure out like, how much something weighs. |
| 00:43:50 | Okay. You have to substitute something in. Okay. |
| 00:43:51 | Yeah. |
| 00:43:54 | How about- Yes, Patrick? |
| 00:43:56 | When you're trying to convert uh, measurements. |
| 00:43:59 | Very good. Jen? |
| 00:44:00 | When you're trying to find the price of clothes or something. |
| 00:44:03 | Very good. That's another way. Yes. |
| 00:44:04 | Like, in science like when you try- try to find density. |
| 00:44:09 | Okay. The density formula. Good. |
| 00:44:12 | Okay, somebody raise your hand and read the homework board to me please. Andrea? |
| 00:44:19 | Page 64 from workbook, Xerox copy numbers one to 22, do all of them. And a quiz on Friday. |
| 00:44:27 | Okay, good. There are two extra. Please give to Vince and John. |
| 00:44:39 | Okay. Take a minute and look over your homework. Please do a couple and then I'll have you pack up. Yes? |
| 00:44:50 | For number one through 16, you don't have to write the answer? |
| 00:44:54 | I'm not sure what you mean. Write a variable expression- Oh. It doesn't say evaluate. |
| 00:45:00 | Oh yeah. |
| 00:45:01 | Yeah, just write the expression. |
| 00:45:02 | There's an extra (inaudible). |
| 00:45:04 | Could you pass it forward, John? Pass that forward please. Thank you John. Brandon? |
| 00:45:10 | On, uh, on number one do you have to have- do you have to put the number before you, uh, subtraction? |
| 00:45:15 | No. That one has to be accurate. So like- |
| 00:45:17 | So it would be like five subtract, uh, any number you- any letter you want to? |
| 00:45:18 | Thank you. |
| 00:45:23 | Yes. Any letter. Yes. Yes? |
| 00:45:25 | On number two it says, the absolute value do you have to put the lines in? |
| 00:45:31 | What do you think? |
| 00:45:32 | Yes. |
| 00:45:33 | Yes. |
| 00:45:34 | But do you like put an N? |
| 00:45:35 | Yeah. You put it around N. Good question Michelle. |
| 00:45:51 | Yes? |
| 00:45:52 | For number five do you have to put two expressions because it says, uh, says three more than the product. |
| 00:45:59 | Yes. Yes. No, into one expression but use- so three more than the product. |
| 00:46:06 | What would the product of eight and a number be? |
| 00:46:08 | So wouldn't it be like X- |
| 00:46:09 | Well, use a times because that looks like a variable. Okay? |
| 00:46:13 | So- What should I use? |
| 00:46:15 | Shh. Please John, please work. |
| 00:46:18 | So then eight, and equals... |
| 00:46:21 | Eight- No, plus- |
| 00:46:23 | Plus- |
| 00:46:24 | Plus three, right? Because that's three more than. |
| 00:46:27 | Okay. |
| 00:46:28 | Okay. Marcus? |
| 00:46:30 | I have a question on, like, number three. |
| 00:46:33 | Okay, I'll be right there. Josh what's your question? |
| 00:46:36 | How do you solve this? |
| 00:46:38 | What's the product of the number and negative eight? What does product mean? |
| 00:46:41 | Multiplication. |
| 00:46:43 | Okay, so how would you do that? |
| 00:46:44 | Uh... I don't know. |
| 00:46:47 | What are you multiplying here? |
| 00:46:49 | Negative eight. |
| 00:46:50 | And? |
| 00:46:51 | A number. |
| 00:46:52 | Okay, so how would we do that? |
| 00:46:53 | Negative eight N. |
| 00:46:55 | Good. |
| 00:46:56 | All right. |
| 00:46:57 | Very good. |
| 00:46:58 | What's the answer? |
| 00:46:59 | Okay, hang on. Let me get Marcus. Yes? |
| 00:47:01 | All right, I have no clue what to put first. |
| 00:47:03 | All right. What does product mean? |
| 00:47:05 | Like the answer to a number. |
| 00:47:07 | What kind of operation are we using for product? |
| 00:47:11 | Multiplication. |
| 00:47:12 | Good. So what are we multiplying here? |
| 00:47:14 | Uh, negative eight. |
| 00:47:15 | And? |
| 00:47:17 | Negative eight and... P. And the product of- |
| 00:47:22 | Well- |
| 00:47:23 | So, is it negative eight? |
| 00:47:24 | Times? |
| 00:47:25 | P. So, negative. |
| 00:47:26 | Yeah, negative eight P would be good. Alex do you have a question? |
| 00:47:34 | (inaudible) sum of the quarters. |
| 00:47:37 | Okay. |
| 00:47:38 | It would be? |
| 00:47:40 | How much is a quarter? |
| 00:47:41 | Twenty-five cents. |
| 00:47:42 | So how do we represent that in numbers? |
| 00:47:43 | Point twenty-five. |
| 00:47:44 | Okay. |
| 00:47:45 | So it would be N 25 or? |
| 00:47:48 | Point two five N. |
| 00:47:49 | Okay. |
| 00:47:50 | Yeah. Okay. Brandon? |
| 00:47:53 | Yes. |
| 00:47:58 | Right here. So, if it's five less than a number would it be five subtract X? |
| 00:48:02 | No. Because this is the number. X is the number so it has to be the other way. |
| 00:48:03 | Oh. |
| 00:48:06 | So it up here it would be 15 more than... how do I- So it would be X plus 15? |
| 00:48:13 | Just make sure you put it in absolute value of the box. |
| 00:48:15 | Oh, so that's good. So fifteen's got to be in the box? |
| 00:48:18 | Yeah- no, the number does. |
| 00:48:20 | What number? |
| 00:48:21 | Any va- any variable that you use. |
| 00:48:23 | Oh, so it would be, uh, the box, then X, then plus 15? |
| 00:48:27 | Yes. Yes. |
| 00:48:28 | And then down- |
| 00:48:29 | Wait a minute. Hang on. Okay, people you may pack up. We will go over this tomorrow. |
| 00:48:45 | Yes? |
| 00:48:46 | (inaudible) |
| 00:48:48 | Quickly. |
| 00:48:49 | Okay, please listen. |
| 00:48:51 | Johnny. |
| 00:48:52 | Tim. |
| 00:48:53 | Johnny. Give me my magazine. Give me my magazine. |
| 00:48:57 | We have about three minutes. |
| 00:48:59 | (inaudible) start. |
| 00:49:01 | No, I almost (inaudible). |
| 00:49:02 | Marcus. Jen. |
| 00:49:04 | (inaudible) |
| 00:49:05 | Yes. Marcus, you start? |
| 00:49:09 | Class we're going to finish by playing 24. |
| 00:49:12 | I get to go first. |
| 00:49:14 | No you don't. |
| 00:49:17 | Please finish your homework assignment and have it tomorrow. |
| 00:49:21 | All right. Eight, two, five and seven. |
| 00:49:31 | That was on last week's quiz. Carly? |
| 00:49:34 | Two times five equals 10. Ten minus seven equals three. Three times eight equals 24. |
| 00:49:38 | Very good. |
| 00:49:39 | Yeah, come on Marcus, you gotta make it harder than that. |
| 00:49:46 | Yeah, that is (inaudible). |
| 00:49:47 | Seven, two, one, five. |
| 00:49:48 | Shh. John. |
| 00:49:54 | Marcus. |
| 00:49:56 | Oh, seven minus two is five. Five times five is 25. Twenty-five minus one is 24. |
| 00:50:00 | Yeah. |
| 00:50:09 | All right. Eight, nine, six and three. |
| 00:50:17 | Oh I got it. |
| 00:50:18 | Andrea. |
| 00:50:19 | Okay, nine minus eight is one. One plus three is four, and six times four is 24. |
| 00:50:34 | Three, five, nine and seven. |
| 00:50:44 | Josh. |
| 00:50:45 | Five minus three is two. Two times nine is 18. Eighteen plus seven is- |
| 00:50:50 | Twenty-five. It's okay Josh. You're trying. Let's go. Who else can get this? Tim? |
| 00:51:04 | Oh I got it. |
| 00:51:06 | All right Brandon, you are next if Tim doesn't get it. |
| 00:51:08 | Nine plus- Yeah, nine plus five? |
| 00:51:11 | Fourteen. |
| 00:51:12 | Yeah, 14. And 14 plus seven is 21, and 21 plus three is 24. |
| 00:51:16 | I had nine- that 's not fair. Tim got one. |
| 00:51:19 | He had his hand up. |
| 00:51:20 | Cheater Jen. Cheater Jen. |
| 00:51:22 | That's his second one. |
| 00:51:23 | Write the same one. |
| 00:51:26 | Say it out loud. |
| 00:51:28 | Three- nine, three, two and then seven. |
| 00:51:37 | Nine, three, two, seven. |
| 00:51:41 | Got it. |
| 00:51:42 | Josh. |
| 00:51:43 | Seven times two equals 14. Fourteen plus nine equals- |
| 00:51:49 | Oh Josh. |
| 00:51:51 | I had it. I had it. |
| 00:51:52 | That's okay. Keep trying. |
| 00:52:02 | Oh, come on people. Patrick. |
| 00:52:09 | Nine, wait- quite. Seven- Nine minus seven equals two. Never mind. |
| 00:52:21 | Hey this is hard. |
| 00:52:23 | Malia. |
| 00:52:24 | Nine plus seven is 16. Sixteen divided by two is eight and eight times three is 24. |
| 00:52:27 | Finally. |
| 00:52:29 | Quickly. Quickly. |
| 00:52:30 | Run. Run. |
| 00:52:31 | Hurry up (inaudible). |
| 00:52:32 | No, they're winning. |
| 00:52:33 | Hey, Alex. |
| 00:52:35 | I refuse to lose. |
| 00:52:36 | Well, Jen added one. |
| 00:52:37 | It'll be a great win. |
| 00:52:39 | Tell Aubrey. |
| 00:52:40 | Three, seven, five, nine. |
| 00:52:52 | Oh god. Jeez. |
| 00:52:57 | Oh, I have it. |
| 00:52:58 | Brandon. |
| 00:52:59 | Uh, nine- Wait a minute. Yeah, nine plus seven- |
| 00:53:04 | Oh, my... |
| 00:53:05 | Have a great day people. I'll see you tomorrow. |
| 00:53:06 | It's the same one. Nine plus three equals (inaudible), the same one. |