# 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.

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