# US1 GRAPHING LINEAR EQUATIONS

This eighth grade mathematics lesson focuses on graphing linear equations. It is a review lesson that followed a unit of work on this topic. The lesson is 44 minutes in duration. There are 36 students enrolled in the class.

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00:00:00(inaudible) four. One for each group of four. Okay? Or three. Okay?
00:00:06Okay guys, let's get started here. Okay, listen closely.
00:00:11To save a little time I won't bring out my overhead like you're usually accustomed to.
00:00:14Dear...
00:00:15Thank you.
00:00:16Okay? Instead, let me just tell you.
00:00:19What I'm going to give you for each group is a little three-page packet. Okay?
00:00:26What I need for you to do right now is, every one of you get out a blank sheet of paper. Every one of you needs a blank sheet of paper.
00:00:35Thank you.
00:00:38Ashley, can I have a piece of paper?
00:00:41Just put it right on the table back there, (inaudible).
00:00:43Thank you.
00:00:58Thank you Sarah. Don't leave without it, all right.
00:01:01Oh, (inaudible).
00:01:02Okay. Now- Here you go.
00:01:11All right.
00:01:13Okay, so... listen closely now. Everybody ready?
00:01:18Yep.
00:01:20Okay, everybody within your group of four or three, you need to work together. I know normally we work in pairs.
00:01:27Okay? But I figured today you have another pair of students-
00:01:33You know, a couple of extra brains there to help you get through this little lesson. Okay? We've done this plenty of times before.
00:01:41Some of you honestly are still a little shaky. So, if you look at the packet which you are all sharing as a group-
00:01:49Page one has five equations I want you to graph. Now you can graph it any way that you know how to do it, as long as you do it correctly.
00:02:00Can someone raise their hand and tell me what's one obvious thing that I can do to graph? Nick?
00:02:04The slope.
00:02:05Use the slope with the?
00:02:07Y intercept and X intercept.
00:02:08Y intercept. Right? That's probably the way you'll probably want to do it, right Nick?
00:02:11Yeah.
00:02:12Is there another way, though? Robert?
00:02:15Use the, um, tables.
00:02:16Right, to make a table for the equation, right? And then plot the points from the table. Everyone got that?
00:02:21So those are the two main ways, right, we can graph those equations? So right now I need you to get started.
00:02:27The key thing is when you're done with the first five, the first page, as noted on the paper, please make sure I check to make-
00:02:35Make sure you did it right before you move on. Okay? So go ahead and get started.
00:02:42Nick, question?
00:02:43Where's the... oh, right here?
00:02:44Yeah. You're going to graph on that. That is your result for your group.
00:02:48So everybody has to do one graph, right?
00:02:49Right.
00:02:50So someone here can assign themselves as the grapher or whatever.
00:02:54The rest of you kind of work together to make sure it's accurate. Okay? You going to do it? Good job, Nick.
00:03:01Yes?
00:03:03All right, the grid paper- All right, you know what? Hey, listen up real quick.
00:03:07Five, four, three, two, one, zero. I probably forgot 'cause I'm still a little nervous. Okay?
00:03:14But the grid paper, you have one per group. Right?
00:03:19So I'm relying on one of you in that group to be the designated grapher for the group.
00:03:25But the rest of you please help out- you know, help each other. Get the graphs done correctly. Okay?
00:03:35There you go, Robert. So while he's doing that, let's get started on this, guys. What are we going to do?
00:03:39Do we write this on our piece of paper?
00:03:40Yeah.
00:03:41Oh, okay.
00:03:42All right? This is actually the- use the ruler, Robert. Use the ruler man. Make it neat. All right?
00:03:48Mr. Ormsby, you know, when you put, like, a one in here, would you go like, times-
00:03:53Ah, see, so now you've already forgotten, right? First of all zeros are our favorite number, right?
00:03:58Yeah.
00:03:59You put in zero. Two-thirds times zero is what?
00:04:02Zero.
00:04:03Plus eight is?
00:04:04Eight.
00:04:05Eight. Now because this fraction is a two-thirds, do you remember what I told you what numbers you should pick now?
00:04:11Um, threes.
00:04:13All right. So maybe zero, three and six would be good numbers to try with this one, right?
00:04:18That way you don't have to worry about fractions and mixed numbers.
00:04:19Okay.
00:04:20Okay? All right.
00:04:22Mr. Ormsby, whoo-hoo. Okay. Mister, I forgot how to do these again. Like how do you do X and Y?
00:04:29Okay, so now wait a minute. You want to make a table then, right? So you're going to make an X Y table, okay?
00:04:36Now... the idea again is, to make our points we just pick any number we want for X.
00:04:42We can do that, right? Everybody agree? Jenna?
00:04:45Yeah.
00:04:46So it was zero, one, two and-
00:04:47Ah, that's true, except because this is a two-thirds fraction-
00:04:52You want to pick three as like-
00:04:53Exactly.
00:04:54Negative three, zero and three.
00:04:56Right, and if you want to just do zero, three, six and stay away from negatives, you can do that too. All right?
00:05:01I got six (inaudible) in the middle.
00:05:03So, zero, three, six.
00:05:04I get six.
00:05:06Right.
00:05:07Okay.
00:05:08And you think you can do it on your own now? You just want to be on the camera. Okay.
00:05:13No, that's not true.
00:05:14Okay, we're going to put in zero here, right?
00:05:17Okay.
00:05:18What's two-thirds times zero?
00:05:19Zero.
00:05:20Everybody watching, right? Plus eight is?
00:05:22Eight.
00:05:23Eight.
00:05:24So three times two is six.
00:05:26Six.
00:05:27Divided by three is two.
00:05:28Three is two.
00:05:30Plus eight is-
00:05:31Eight is?
00:05:32Ten. Okay I get it. Thank you Mr. Ormsby.
00:05:33Okay. Good job.
00:05:34So six times-
00:05:36All right, so, okay, this is what I did. I put three negative three, zero, three and six, all right?
00:05:37Okay.
00:05:41How come you have your table backwards? I've never done that before.
00:05:43Well, I did that.
00:05:44Okay.
00:05:45It's easier this way.
00:05:46It's easier.
00:05:47All right, if you say so.
00:05:48Anyways, I put negative three, so, I put two-thirds and then-
00:05:53Times negative three.
00:05:54Yeah. Negative three goes in the top, right?
00:05:56Right. Well, you- negative three, you remember, is negative three over one. There you go.
00:06:00So- so it's a one and a one. But that's a negative still, right?
00:06:03Right. That's still a negative there.
00:06:04So it's negative two?
00:06:05So it's negative two.
00:06:06Plus eight is?
00:06:08Six.
00:06:09Yeah.
00:06:10See, I knew that.
00:06:11So negative three is six, zero is eight. Now three I question, though. Try a positive three.
00:06:17Cause they're both positive so-
00:06:19Two-third so, three, one-
00:06:20Oh.
00:06:21Okay.
00:06:22One one, and then three, eight, 11.
00:06:26No, wait a minute. Wait a minute.
00:06:27Two. One is-
00:06:28And five.
00:06:29Two plus- wait a minute, no, you were "times-ing" it.
00:06:30Oh.
00:06:31It's two so-
00:06:32It's 10.
00:06:33Yeah.
00:06:34It's 10. And then six is 12.
00:06:35It's six then 10 and 12.
00:06:36Okay.
00:06:38All right. Yes?
00:06:39All right, I just totally forgot um, you know, how to do the graph.
00:06:43Okay, now what I liked- you at least remember to use multiples. Like this one- Let's try this one right here. All right?
00:06:49Okay.
00:06:50You remembered to use fives, but let's try zero. If I put in zero there, what's three-fifths times zero?
00:06:55Um... zero?
00:06:57Right. Minus 10.
00:06:59Is negative 10?
00:07:00So put a negative 10 there. So now you're going to- now try five in there, right?
00:07:05Okay.
00:07:06So just write a little five there so you can mentally see it. So if I do three times five that's?
00:07:11Fifteen.
00:07:12Now remember I'm going to divide by the five, which gives me?
00:07:14Three.
00:07:15Minus 10.
00:07:18Negative seven.
00:07:19Good job. I think you got it now.
00:07:21Oh, okay.
00:07:22All right. Finish it up.
00:07:22Mr. Ormsby?
00:07:23All right.
00:07:24Uh, how many points do you want us to plot? Three or four?
00:07:27Well that's a very good question. Obviously, how many points do I really need to make a line?
00:07:31Two.
00:07:32Two. Right? But just to make sure-
00:07:34Three.
00:07:35Plot at least three points.
00:07:37Okay.
00:07:38That way if they're all in a line you know you did it right. Okay?
00:07:41Mr. Ormsby.
00:07:42Yeah?
00:07:46Use the whole paper, man. Look at these big grid lines here. Everyone, make it count one. Okay?
00:07:53Don't we have to use- use graph- graph every single one of those?
00:07:56Yeah, you're going to graph these five. That's why I want you to use the whole paper. Make a big coordinate system.
00:08:00Oh.
00:08:01As a matter of fact- Let me give you a fresh one to save you some time.
00:08:02Oh, okay.
00:08:05All right, now I get it.
00:08:08All right. So, we have to make one big, um-
00:08:12Okay. So start over again.
00:08:15Use the whole coordinate system, that way all the lines are nicely spaced out and everything.
00:08:18All right.
00:08:19Okay?
00:08:20We're out of (inaudible).
00:08:22Okay, well how do you want to graph it? Using an X Y table?
00:08:26Yeah.
00:08:27Or do you want to lea how to use slope and Y intercept?
00:08:30X Y table.
00:08:32Okay. So you're gonna make a X Y table. Do you agree, Ben? All right.
00:08:40See, if you work with Chris side-by-side, then you can compare answers. Right?
00:08:43Mm hm.
00:08:44Don't just rely on Chris here.
00:08:46All right now, Chris, the idea is I'm gonna plug in any values I really want for X and figure out my corresponding Y. Okay?
00:08:54But because this fraction is a two-thirds, what numbers should I possibly use that would make it easier for me?
00:09:01Three.
00:09:02Numbers based on three. So like maybe negative three, zero, three, six. Or zero, three, six, would be good enough, right?
00:09:09Yeah.
00:09:10That way you can get that graph down. Okay?
00:09:17So, you need my help, or do you want to try it on your own first?
00:09:18So... to input this X do I have to put this number?
00:09:24Well, if you want, we don't have to do the negative. You want to do the negative?
00:09:31Yeah.
00:09:32Okay, here we go. Put a little negative three above there. Now you know I'm going to do two times negative three... is?
00:09:40Negative six.
00:09:41Divide by three is?
00:09:43Neg- negative two.
00:09:44Good. Plus eight.
00:09:46Six.
00:09:47Positive six.
00:09:49Oh.
00:09:50Right? Now you're going to put in a zero and do the same thing, right?
00:10:00All right? There you go. See, with zero you don't even have to bother putting it in. Right?
00:10:04You alr- you should already know that is your Y intercept. All right, try three. Now just make that a positive three.
00:10:11That's it. You got it. You got it. Ben, see what Chris did there.
00:10:15All right.
00:10:16All right?
00:10:18Okay. All right sir, it looks like you're being left out here, aren't you?
00:10:25No.
00:10:26Okay, you understand what they're doing?
00:10:27We're using slope.
00:10:30Okay. So all right, let me- let me test you here. Let's try number four. All right?
00:10:34Okay, number four.
00:10:36Okay. Oh by the way guys, I like how you labeled them, like that.
00:10:39Thanks.
00:10:40Excellent job. X minus nine, right?
00:10:45Minus nine, okay.
00:10:46So tell me how you would graph that?
00:10:49I would-
00:10:51Here we go.
00:10:53I would go... negative nine. So, one, two, three, four, five.
00:10:59Now that's negative nine for X.
00:11:01Uh huh.
00:11:02Right?
00:11:03Mm hm.
00:11:04That negative nine really is my Y intercept.
00:11:08So then... I go down.
00:11:09Ah ha.
00:11:10One, two, three, four, five, six, seven, eight, nine, 10.
00:11:14Good. Now we only want to go nine. Here you go. Hey, you guys taught him pretty well then, huh?
00:11:21(inaudible)
00:11:22And now my slope is one-fourth.
00:11:24Uh huh.
00:11:25So that means?
00:11:27One- one, two, three, four.
00:11:32Good job. Excellent job.
00:11:36Oh...
00:11:37All right.
00:11:38(inaudible) times two is six. Negative six.
00:11:41All right this is seven, 10, 13, and 16 this time.
00:11:43Okay.
00:11:44Is this right?
00:11:46I don't even know how to do this.
00:11:49I don't get it.
00:11:53Oh.
00:11:54What, are you shy or something?
00:11:55No, I just asked this guy and he said-
00:11:57I'm trying to do it too. I'm trying to figure this one out.
00:11:59Yeah, how do you do this?
00:12:01Okay, let me go to this other group, guys. Brandon. Brandon. Do me a favor, all right?
00:12:10I'll give you a choice, all right? You can pick either Ashley or Nick. Either way, I want- I want them to teach it to you. All right?
00:12:20It's called teamwork here. Okay? All right. And if they can't do it, I'll be back in a few minutes to help you. All right?
00:12:27Mr. Ormsby, this is like the same thing as I did that one, right? That.
00:12:30Okay. Let's take a look here.
00:12:31I mean, I know how to do this, but I don't know how to do the fractions.
00:12:35I mean, a lot of these tables look great, now let's get them plotted here.
00:12:38Okay.
00:12:39And we can see what it comes out to be.
00:12:40So after we write them all down, we plot them on here?
00:12:41Right.
00:12:42Every single one?
00:12:43Right. And then you're going to label them. Now if you-
00:12:46If you don't mind, since this is equation one, just put a little one at the end of it. And equation two put a two at it- at the end of it. Okay?
00:12:53All right.
00:12:54Brandon, you had a comment? Question?
00:12:56I know how to do the regular ones. I don't know how to do the one with fractions. That's confusing.
00:13:00Those are the ones that I have trouble with.
00:13:01Was he- Were you listening when Mr. Ormsby was saying this?
00:13:02Well, okay.
00:13:06Well maybe you ought to go to Nick. Sounds like Nick knows what he's doing.
00:13:09No, I said that I have trouble on it.
00:13:10Okay, then maybe we ought to go to Ashley.
00:13:12Nah, I could (inaudible).
00:13:13Okay.
00:13:14So you want- put-
00:13:15Okay. What do we got going on here?
00:13:17We're done.
00:13:19Sir?
00:13:20Well, we got done with all the (inaudible). We were going to call you but you were talking to them.
00:13:23Trying to embarrass me here or something?
00:13:24Of course not.
00:13:25Uh huh.
00:13:25You're really slow. For these ones here-
00:13:26You're such a character, Nick.
00:13:28For these- for the fractions we did the slope and then we made a table, and we're done.
00:13:32And everybody agr- here agrees, right?
00:13:33Uh huh.
00:13:34Okay. So let me just check them real quick. I like how you numbered them one, and so on.
00:13:41This one you didn't number. What number is that one?
00:13:43Uh, I think that was five.
00:13:44That was five. That one's correct, so put a five there. Okay, I can safely assume that this one must be the four, right?
00:13:45That was five.
00:13:53Uh-
00:13:54Or is this one the four? Which one's the four?
00:13:56This one's two.
00:13:58Which one's two?
00:13:59Four is this.
00:14:00Four- four is negative nine, and up one is four.
00:14:01This one.
00:14:02So that- yeah, this is four.
00:14:05Yeah.
00:14:06Because this one-
00:14:07One, two, three, four, five, six, seven, eight, and nine. Oh no. This is four.
00:14:11Ah. Right.
00:14:13This one's two.
00:14:14So let- do me a favor. Erase the two, right, and label them right near the ends of the lines. How's that?
00:14:23'Cause right there I can't tell which line you're talking about, right?
00:14:26Right.
00:14:27There I know. Hey two, that's that line. So this is the four line. Put the four right there. Okay? So both of those look excellent.
00:14:35Six minus (inaudible).
00:14:36Slope of three-fifths and number four, slope of one-fourth. That's good.
00:14:41Number one, slope with two-thirds starting at eight and this one is seven, right?
00:14:47Mm hm.
00:14:48Uh oh. I don't like equation three because look, it's going down. That's a positive three X.
00:14:58Oh.
00:14:59It should be going-
00:15:00Up.
00:15:01It should be angling up. So correct number three, and then you guys- As soon as you get that corrected just move on.
00:15:05I'll check that one later. Okay?
00:15:08Mr. Ormsby?
00:15:12Here we go. Yeah?
00:15:13We don't get number five.
00:15:15Number five. All right, first of all, you know the Y intercept is what?
00:15:19Negative five.
00:15:20All right. So put a dot on negative five.
00:15:23One, two, three, four, five.
00:15:26Good. We all agree on that?
00:15:28Yes.
00:15:29Now, this is something so simple but very important.
00:15:31See in Algebra we get lazy sometimes, right? Guess what number is in front of that X.
00:15:37One.
00:15:38A one.
00:15:39A one, right Robert? So therefore put a one there. If the slope is one, what am I going to do?
00:15:51All right, you ready Sir? Make that one a- a fraction. How do I make one a fraction?
00:15:56One over one.
00:15:57One over one. Write it- write like- let's just put it unde eath there. One over one. Something to look at. All right, that's fine.
00:16:03Now remember slope is rise over run, right?
00:16:05Mm hm.
00:16:06So one over one means I rise one and I go across one.
00:16:11There.
00:16:12That's it. That's the slope of one. All right?
00:16:17Just let me check them real quick.
00:16:22All right. Now do me a favor, guys. You labeled these really nice. As a matter of fact, this is a way- an ideal way of labeling it.
00:16:29Write the whole equation, but like for example, equation one right here, put a one next to it also.
00:16:36And this one's equation three, right? So put a three next to that.
00:16:38Okay.
00:16:39So number them, in other words, okay?
00:16:41Okay.
00:16:49Because that's how I label them. I label them by numbers. Does that make sense? All right.
00:16:55So as soon as you get that done, which you're almost done, you get them numbered, just move on to the next set of five.
00:17:01Okay.
00:17:02All right?
00:17:03Yeah.
00:17:05All right.
00:17:08So Y is three-fifths, X negative 10?
00:17:13Okay. So wait a minute. You try- you're doing negative five, right?
00:17:16Yeah.
00:17:17Three times negative five is negative 15.
00:17:18Negative 15.
00:17:20Divided by five. Negative three. Minus 10?
00:17:24Is, um, negative, um, seven- Oh, minus 10?
00:17:28Negative three and a negative 10.
00:17:30Oh, um, 13.
00:17:31Negative 13. So let's change that.
00:17:34Mm hm.
00:17:36Well negative five is going to be, not five, but negative?
00:17:39Thirteen.
00:17:40Thirteen. All right? Ben, you look like you're not- you're just coasting here, man. What's going on?
00:17:47(inaudible)
00:17:52Chris, make sure you help Ben out here, man. Ben- I just sense Ben's getting a little lost here.
00:17:58All right, this is your chance to ask not only Chris, but also Raymond here. Get some help from them.
00:18:06Okay.
00:18:08You think you got it? Now zero of course is going to be what? If I put in zero here what am I going to get?
00:18:14Uh- Zero.
00:18:17Wait a minute, what's three-fifths times zero?
00:18:20Three-fifths times zero?
00:18:21Zero. Minus 10 would be?
00:18:23Ten. No.
00:18:25Zero minus 10 would be?
00:18:28Ten.
00:18:29Not positive 10.
00:18:30Negative 10.
00:18:31Negative 10. So you want to put a negative 10 there. Okay?
00:18:34Okay. So, oh.
00:18:37Now try at least one more of five. Okay?
00:18:40Uh, Isn't that, uh-
00:18:43Now it's a positive five, right?
00:18:44Yeah.
00:18:45So it's going to be- Well, what's three times a positive five? Fifteen. Divided by five is?
00:18:51Three.
00:18:52Three minus 10.
00:18:54Seven.
00:18:55Negative seven. Don't forget the negative.
00:18:56Negative seven.
00:18:57Oh, all right.
00:18:58Okay?
00:19:00All right guys. Thanks for waiting so long.
00:19:01Okay.
00:19:02All right, you want me to just check the answers?
00:19:03Yeah.
00:19:04Now the only favor I need you to do, is because for each of these numbered equations, just number them. For example, this is one, correct?
00:19:12Yeah.
00:19:13This one was equation three.
00:19:14Yeah.
00:19:15This one was equation five. So near the end of each of these arrows-
00:19:18Yeah, put the number?
00:19:19Just put- put the number.
00:19:21And then this one, let me just make sure, because I don't have them all memorized.
00:19:26Let's see, negative nine was one-fourth. You've got the slope perfect there and this one was three-fifths, right?
00:19:32So everything looks perfect. Just number them and move on to the next five.
00:19:36Okay.
00:19:37Okay?
00:19:38Mr. Ormsby?
00:19:41We're on number six.
00:19:42I got it, guys. I got it.
00:19:44So here's all of number five.
00:19:45Look at that excellent work, man. Excellent work.
00:19:47I crossed it out.
00:19:48There's one, there's two, there's three, and there's four and there's five.
00:19:51I figured it out.
00:19:52Excellent.
00:19:53But it- they're having problems on number-
00:19:55Oh there it is. I found it. I found it. I- I- now I (inaudible) do.
00:19:58Okay. You know what? As a matter of fact I think it's time for me to address the whole class.
00:20:02Okay.
00:20:03Everybody. Ladies and gentlemen, listen up. Five, four, three, two, one, zero.
00:20:10Now, about half of you are about ready to start the next set of five, right? Starting on number six?
00:20:16Yep, that's what we're doing. We're starting (inaudible).
00:20:18Let me give you a hint. Just a little reminder, what you will notice-
00:20:24Julie, you're doing a great job but please listen, okay?
00:20:26You'll notice on equations six through 10 the slopes are negative. All right?
00:20:32Yep, all (inaudible).
00:20:33So therefore, instead of rise over run meaning you'd go up and to the right, with the negative you're going to instead go, down and to the right.
00:20:44Okay? Does that make sense to everybody?
00:20:47Yeah.
00:20:48So please keep going. Please make sure I check your first five and give you the okay to move on. Okay?
00:20:52Could you check ours?
00:20:53All right.
00:20:54Yeah.
00:20:55Actually, I'm on four.
00:20:56I'll check yours real quick. Okay. All right, good. You guys numbered them?
00:21:00Yeah.
00:21:01Yeah.
00:21:02Okay. There's one, slope. Equation three, two-thirds. Equation five looks good.
00:21:10I haven't even gotten to five. I'm already-
00:21:11Okay. Then you've got four and two. It looks perfect so far.
00:21:16Okay.
00:21:17Move on to equation six then.
00:21:18Okay.
00:21:19Now you're saying you're being left behind here a little bit? On which one?
00:21:23Well, they're obviously on five and-
00:21:27Okay.
00:21:28We're on-
00:21:29Now Robert, here, I'm sure can help you. You've got the- one of the smartest kids in class right here.
00:21:33He's tried to explain it once, but I'm not so sure.
00:21:36Okay. It looks like you made a nice table here, though. You understand what you did there?
00:21:40Yeah.
00:21:41Okay. So you- when you put in zero, one-fourth times zero is what?
00:21:45Zero.
00:21:46Minus nine is?
00:21:47Negative nine.
00:21:48Okay. Then you tried four, right?
00:21:51Yeah.
00:21:52All right. Why did you pick four and eight? Why didn't you pick like one and two and three? Numbers like that?
00:21:57Because they're divisible by four.
00:22:00Well said. Good job. So when I try four, see, what's one-fourth times four? Just one-
00:22:06Yeah.
00:22:07Minus nine is a negative eight.
00:22:09Yeah.
00:22:10And then you put an eight. One-fourth of eight is?
00:22:12Two.
00:22:13Minus nine is negative seven. So that's perfect. If you plot those three points you get exactly what is on your graph there. Okay?
00:22:20Can I see this really quick?
00:22:22Mr. Ormsby?
00:22:23All right. Guys-
00:22:25Are you sure this is right? Because you're all-
00:22:27Oh, so you want me to just check six real quick, right?
00:22:29And five.
00:22:30And five.
00:22:31Five, because that's the one we messed up on (inaudible).
00:22:33Right. Five now looks perfect.
00:22:35No three. Three was-
00:22:36Oh, three was the one we messed up on. So three is right here and the idea is that you want a positive three slope, which you did perfectly.
00:22:44All right.
00:22:45So three is good. Let's go back to six since we're here.
00:22:50Here's six, so you started at positive eight.
00:22:52Yeah.
00:22:53The slope is negative five-thirds so you went down five and over three, didn't you?
00:22:58Yeah.
00:22:59Perfect.
00:23:00All right.
00:23:01Okay?
00:23:04Okay. Ashley, how is Brandon doing here?
00:23:07I'm helping him.
00:23:08Brandon? Good. That's what I want to see.
00:23:10The rest- we're done. We just want you to check.
00:23:13All right, you keep helping Brandon. Let me meet with Ashley over here. Nick, if you want to watch you can.
00:23:17Okey-dokey.
00:23:19But I can tell you right now, five is good.
00:23:21Okay. And you see the patte in eight and 10? If I put- how many do you add for 10?
00:23:22Okay? Let me start in order here. One looks good. Hold it. Wait a minute. Let me check one again.
00:23:29Yeah, you've got to do 12.
00:23:30One, the slope is two-thirds, isn't it? Right? So first of all our Y intercept is eight.
00:23:34Wait- wait.
00:23:37Ashley, let's look at yours since you're more comfortable with yours.
00:23:39Yeah.
00:23:40You agree that zero, eight should be my first point, right?
00:23:43Mm hm.
00:23:44Two, four, six, eight. Okay. That's good.
00:23:47Hold on Brandon.
00:23:49Three-
00:23:50I made one over three. One, two, three.
00:23:54Yep, Jessie.
00:23:55All right? Now watch Ashley, you ready? When I put in three, two times the three would be six-
00:24:03Six. Oh yeah.
00:24:04Divided by three would make?
00:24:06Two.
00:24:09Two. Six divided by three is two, right?
00:24:10I know it's two.
00:24:11Okay, plus eight would make, 10. So three would be 10; well what's two plus eight? Ten.
00:24:18So if that's a 10, this one I'm sure has got to be something bigger. Okay?
00:24:23Eleven. Twelve?
00:24:25This may be 12.
00:24:26I believe it's 12.
00:24:27Yeah, see I did it on here, but I did it wrong on my paper.
00:24:28Okay.
00:24:29It's weird.
00:24:30All right, so it sounds like you guys didn't compare your answers here but I think that's your only mistake.
00:24:39Because equation three looks very good. All right.
00:24:43You know what? Equation two I don't necessarily like either. Is this supposed to be two?
00:24:50Two says we're starting at what number?
00:24:52Negative 10.
00:24:53Negative 10, right? You're not starting at negative 10 here. What's this number?
00:24:57Two, four- somehow you're starting at negative six. So what happened on equation two, guys?
00:25:06Hey, how come we didn't use your table?
00:25:08I don't know. We were looking at his.
00:25:10Okay. So if we start at 10, then-
00:25:13Oh, I know- Look what you did wrong. You copied the equation down wrong.
00:25:17That's number four.
00:25:19Oh, I'm sorry. You're right. My mistake.
00:25:22Oh yeah, it does start at six.
00:25:24I can't even read your writing. Yeah, why is that a six? That should be a negative 10, right?
00:25:27It looks like a six but it's 10.
00:25:28Okay. And five you got negative seven.
00:25:30Yeah.
00:25:31I agree with that.
00:25:32Yeah.
00:25:33Okay, and then 10 you got negative four.
00:25:37Okay, so why don't you try re-plotting those three points and move on to equation six through 10 and I'll check on number two later on.
00:25:47Okay, the rest of them look pretty good, though. All right?
00:25:49All right.
00:25:50Mr. Ormsby, whoo-hoo.
00:25:52Okay, what are we doing here, guys? Hey, how come none of these lines are labeled?
00:25:57Whoops.
00:25:58Now what I suggest you do-
00:25:59(inaudible) two lines.
00:26:00Hold on. What I suggest you do before I come back is for each of these- just call it equation one, two, three, four, and five, right?
00:26:08Put a number at the end of each of these lines.
00:26:13Oh, like number one, two, three-
00:26:14Like for example, number one- Uh oh. Wait a minute. I don't like what I see here.
00:26:23Look what you made me do. You probably thought of it wrong.
00:26:24Okay. Let's see here. Number one, I believe this is supposed to be your number one here, right?
00:26:33I think so.
00:26:34I don't know.
00:26:35How come it's going down, guys?
00:26:36I don't know, it does it.
00:26:38Aren't all these slopes positive? So all of these should be going up.
00:26:42How's it going down?
00:26:44Look at it. It's going down.
00:26:46It's going up.
00:26:47How do you read a book? How do you read a book, sir?
00:26:48Left to right.
00:26:49You read from left to right. So let's start on the left side of the line.
00:26:52Yeah.
00:26:53And as I move to the right I'm going in which direction?
00:26:56Down.
00:26:57Right. Now if you look at all the other lines, see they're all positive.
00:27:00But it's going up.
00:27:02Sir you have to read from left to right. Okay? All right.
00:27:07It's going down like that.
00:27:08So, guys, you need to make those corrections. Label the line. Correct this one, at least.
00:27:12How come we've never done this before?
00:27:13Okay?
00:27:14You made me do it (inaudible).
00:27:15Could you check our answers for (inaudible).
00:27:16Oh my gosh. Let me make sure I keep track of the time, too. All right.
00:27:22Hey you guys did an awesome job here. Okay. Let's take a look here. So here's your number six right?
00:27:29Uh huh.
00:27:31And you started at eight and the slope was negative five-thirds so you went down five and over three.
00:27:37Uh huh.
00:27:39That line looks perfect. Let's look at your number seven. Here's negative one. You went down four and over one.
00:27:47There's your line there. That looks perfect. Let's check number eight real quick.
00:27:52All right, I think I did it kinda-
00:27:54Oh, that's the eight, right? Okay? So on number eight you started at 12 and negative one-third. Looks perfect.
00:28:03Number nine is 14, which is where?
00:28:06It's all the way up here.
00:28:07Way at the very top. And negative three-halves means you went down three and over two, so there's your line right there.
00:28:16And finally number 10, we're at three, the slope is negative one. Perfect.
00:28:21Cool.
00:28:22So now, all you guys have to do-
00:28:26Is to answer these questions. Okay? The best you can.
00:28:29On this piece of paper?
00:28:31On your piece of paper, okay?
00:28:32Okay.
00:28:33On your own piece of paper.
00:28:34Okay.
00:28:36All right, how we doing here, guys?
00:28:37I don't know (inaudible).
00:28:40What's the ruler for?
00:28:41Oh.
00:28:43Look at this. Just from now on make sure- straighten out these lines and keep going.
00:28:49All right.
00:28:50And are you labeling? That's number one-
00:28:51Yeah.
00:28:53Number two.
00:28:54No that's number three. I forgot to do number two.
00:28:55Okay, wait a minute. Number three is conce ing me. You ready?
00:28:58Yeah.
00:28:59Let's try this again real quick. All right. It's three X plus seven, right?
00:29:03Yeah.
00:29:04So when I put in- Let's- let's just start with zero. When I put in zero, what's three times zero?
00:29:08Zero.
00:29:09Plus seven is?
00:29:10Seven.
00:29:11Why did you put negative seven? What's zero plus seven?
00:29:15Well I started- Oh.
00:29:17Chris, let me take a look at your table for three.
00:29:20How come you're not standing up to Raymond here and saying, hey man, look I got the right answers.
00:29:27All right, your table is correct. You've got to believe in yourself. All right?
00:29:28I didn't know it was right.
00:29:30You guys gotta start working better together and comparing answers. All right?
00:29:36Ben, I'm worried about you man. What are we doing here.
00:29:38Put away the book.
00:29:39Okay.
00:29:40And Chris, you need to work with your normal partner here a little bit better. And compare answers.
00:29:47So I mean, if you would have compared answers, guys, you would have seen on this table here, right-
00:29:54That, hey! Someone must be making a mistake because we're getting different answers here, right?
00:29:57Mm hm.
00:29:59So, either correct yours, or if you want, you can trust Chris. I would trust Chris- Chris' to be honest.
00:30:06All right.
00:30:07Okay.
00:30:08I used twos... (inaudible) threes.
00:30:10Right. Now did you have to go by twos?
00:30:12I- I don't- did I?
00:30:15Well wait a minute. Isn't this just a regular number three?
00:30:18Yeah.
00:30:19Yeah.
00:30:20So on these kind, I always told you just use, like, zero, one and two, right?
00:30:23You didn't have to go by multiples or anything because there's no fraction to divide by. You see?
00:30:29All right guys, let's see what we can do here.
00:30:31Mr. Ormsby? All right, never mind.
00:30:35Okay. Can I interrupt the whole class? Shh.
00:30:40Okay.
00:30:41I guess.
00:30:42Five, four, three, two, one, zero. Shh. Now please listen. Okay?
00:30:47The thing is I- I have to be honest.
00:30:51I'm getting a little- a little worried, maybe a little frustrated here, just because I could see that some of you have some serious weaknesses.
00:30:59Yet, you have people either across from you or right next to you, your own partner that seems most of the time,
00:31:12So, guys, I ask you, starting right now, is check your work with your partner's work. Work together.
00:31:19All right, this is not an individual kind of assignment here. Does everything I say make sense so far?
00:31:25Yes Mr. Ormsby.
00:31:26Okay. Now let me just give you a heads up. We've got roughly what? Twelve minutes left in class?
00:31:34Um, (inaudible).
00:31:35Okay. I want you to keep doing what you're doing. If for whatever reason you actually get to the last page-
00:31:41Yeah, we are at there.
00:31:42And you- you've answered these questions to the best of your ability- Now obviously today we have no time to discuss it, okay.
00:31:48We're going to pick up- we're going to pick this up again on Monday, but if you happen to ask these questions-
00:31:53Monday?
00:31:56Yeah, we're back on Monday, right?
00:31:58Yeah.
00:31:59When we- when we- after you answer these questions, if you get that far, please make sure you do this "quickwrite".
00:32:08All right. Which simply means all I want you to do is be honest with yourself and with me and just sit there for the remaining time.
00:32:15Write a minimum of two paragraphs, okay, on what we've lea ed today. What you've actually lea ed today. Okay?
00:32:25Those of you that aren't at this stage, don't worry about it yet.
00:32:28At about, let's say, four or five minutes, I'm going to make all of you do it anyways.
00:32:32You're so generous, Mr. Ormsby.
00:32:33So please keep working wherever you are. I'm still walking around.
00:32:38Yeah?
00:32:39(inaudible)
00:32:41Don't worry about that until Monday. We'll catch up on Monday. All right. Let's focus on this.
00:32:43We got done and we (inaudible) like- where's the paper at?
00:32:47Right there.
00:32:48All right, Ashley?
00:32:50Yeah, um- Okay, I don't get these two.
00:32:55All right. Does anyone in this group-
00:32:57No.
00:32:58Understand what to do here?
00:32:59No. Because, like, there's different numbers. Which one would we use?
00:33:01Okay. All right. Okay. Now you want to use slope and Y intercept or do you want to make tables?
00:33:08Tables.
00:33:09Seems like tables are the way to go here, right?
00:33:11Yeah.
00:33:12So let's- let's go there, all right? First of all, Ashley, that's a negative five-thirds, isn't it?
00:33:17Oh.
00:33:18Wait- No- the fastest-
00:33:19Okay. So now, if I plug in zero, guys- Brandon, watch. If I plug in zero, what's negative five-thirds times zero?
00:33:28Zero.
00:33:29Plus eight is?
00:33:30Eight.
00:33:31All right. That was easy.
00:33:33But I don't know what to use. Like threes?
00:33:35You would use threes. Try three and six. Okay?
00:33:40My stomach's hurting. Can I get a drink of water?
00:33:43Sir, no. You have to stay here. All right? So- all right, let's try three. Nick, Jessie, you ready?
00:33:49Two- 10.
00:33:50If I put in a three there, okay-
00:33:54It's going to be five, right?
00:33:55You're going to get negative five because the negative plus eight. What's negative five plus eight?
00:34:00Negative- Oh yeah.
00:34:02Positive three.
00:34:03Wait, (inaudible) is negative two.
00:34:04Wait, is that how you do three?
00:34:05Well you wrote it upside down. That's okay. And then the next one is going to be what?
00:34:09Negative two.
00:34:10It's going to be negative two. You got it.
00:34:12Oh.
00:34:13(inaudible) two.
00:34:15Oh no. I (inaudible).
00:34:17Yeah.
00:34:17Impressive.
00:34:18I always do my work in my head.
00:34:19Okay. So don't let the negatives scare you. Just the same idea as the front.
00:34:24Just know that when you times, you've got to have a negative, right, in your problem. That's all.
00:34:31All right.
00:34:33Why do you keep getting out of your seat, Robert?
00:34:34Well, I have to (inaudible).
00:34:35I'm coming to-
00:34:36Okay, I just kind of noticed out of the co er of my eye. So what's going on here, how we doing?
00:34:40Okay. We're doing fine.
00:34:44Okay? So have I come by to check all 10 equations yet?
00:34:49No not yet, we're just- We're on number 10.
00:34:50Not all 10. Just the first five.
00:34:51We're on number 10.
00:34:52Okay. You are on number 10. You want me to wait until you get number 10 done?
00:34:55Yeah.
00:34:56Yeah.
00:34:57Okay. All right.
00:34:59Why did I get it wrong- oh, I didn't write it.
00:35:00Ladies, you've been awful quiet over here. What's going on?
00:35:03Well, because we've been waiting for you?
00:35:04Okay, all right.
00:35:05For like a century.
00:35:07So where are you stuck? Or if you're not stuck, what would like me- Do you want me to just check your answers then?
00:35:12Yeah.
00:35:13Is that what you're saying?
00:35:14Yeah.
00:35:15Okay. So- So I've already checked the first five? Yes or no?
00:35:21No.
00:35:22No.
00:35:23Oh, really?
00:35:24Well, because you've been over there, you know-
00:35:26Yeah, I know. I've been pretty busy. All right, let's start with six through 10.
00:35:29Well, we're only on eight.
00:35:30So- Okay, so I'll do- I'll do the first eight, how's that?
00:35:33First eight- Okay.
00:35:36All right. So I agree, that's plus 12. Wait a minute, which one are we doing? Number six.
00:35:41That's plus eight, right? Two, four, six, eight. Good.
00:35:44Now negative five-thirds would mean you come down five and you go over three, right? So that one's perfect.
00:35:50Number seven. You would have started at negative one and because of the negative four slope you would have gone down four and over one.
00:35:53Number three.
00:35:58So that one is perfect.
00:36:00And number three?
00:36:01Okay. And number eight, I'm a little conce ed. See how it's slanting up? See, eight's a negative one-third.
00:36:08Yeah, but that's a plus 12.
00:36:09So are you ready? Well what does plus 12 mean? Up here. So erase number eight. Try number eight again. Okay?
00:36:20(inaudible)
00:36:22Okay. All right, wait a minute Jessica- All right, let me slow down, then. Because trust me, I'm sick and I'm also tired but we-
00:36:28We can do this, all right. You ready?
00:36:31Zero, three, and six is right, though, right?
00:36:33Zero was 12. So why did you plot down here, when zero positive 12 is up there.
00:36:42Okay, let's look at the rest of your table.
00:36:44I put a negative.
00:36:46So three. All right, if I put a three here, DeCarlos, what's one-third of three?
00:36:52Um, one.
00:36:54One, right? So that negative makes it a negative one plus 12, which was a positive- So you had these points exactly right.
00:36:59I check- I put them backwards.
00:37:00So you put them down- you plotted wrong, basically, right?
00:37:03Yeah.
00:37:04All right.
00:37:05Mr. Ormsby?
00:37:07Okay, all right. Yes? You're finally done, right?
00:37:10Yes.
00:37:11Okay. If you don't mind I'll just take a quick glance. Spot-check a few of them because I'd like you to move on to the questions.
00:37:19Okay.
00:37:20All right.
00:37:22And the ones I'm looking at right now, like for example, this one here this is number seven. That looks good.
00:37:27Number six, five over three, that looks perfect. Okay. Oh, let me see. You just finished 10, right?
00:37:35Mm hm.
00:37:36And that one's also perfect. So I can safely say that you guys seem to know what you're doing. So now please answer these questions. All right?
00:37:44That's a lot of questions.
00:37:45For example- Well, just go one by one. You're going to have more time on Monday anyway.
00:37:48All right.
00:37:49But on number one, what- what did you notice about the first five equations? When you graphed them what did you honestly notice about them all?
00:37:57They all went to the right.
00:37:59They all went up and to the right.
00:38:00Yeah.
00:38:02That's why we always said they had a positive slope because the positive number in front of X, all right? Okay.
00:38:03Yeah, they were positive.
00:38:09All right, ladies and gentlemen. Shh. Listen up.
00:38:14Wherever you are- wherever you are, honestly guys, it really doesn't matter.
00:38:20I really appreciate the effort you put in for me today. That's the important thing.
00:38:24What I'd like you to do-
00:38:28What I'd like you to do now, whether you're done or not guys, I honestly hope that all of you have lea ed something today. Okay?
00:38:36So I want everyone now, on their own piece of paper- I repeat, on your own piece of paper-
00:38:43Do this quickwrite for the remaining part of the class.
00:38:47On that same piece of paper.
00:38:48And a few hints would be like, hey did you lea - did you understand?
00:38:52Did you understand something about slope maybe a little bit better?
00:38:54Same paper?
00:38:56Or Y intercepts.
00:38:57Same paper.
00:38:58Or maybe you got better at making tables. On the same piece of paper, yes sir. Any questions on that?
00:39:05All right, quickwrite time guys. Let's get that done.
00:39:10Can you check these?
00:39:11What's this skull and bones stuff?
00:39:13Don't know.
00:39:14Nice drawing.
00:39:15Jeremy? Oh, you're waiting for me because we're done over here?
00:39:18Yeah.
00:39:19Yeah.
00:39:20Let me- let me see wh- Let me see the answers.
00:39:23They're over here.
00:39:24(inaudible)
00:39:26Okay. But where's your own work, Dell?
00:39:31(inaudible)
00:39:32I didn't know it was-
00:39:33And right now what are you supposed to be doing?
00:39:34I was doing that. He was doing this.
00:39:35I understand, but right now what are you supposed to be doing?
00:39:37We were waiting for you.
00:39:39All right. Now that I'm here, what else could you be doing right now? What did I talk about on the board there?
00:39:43This. Quickwrite.
00:39:44The quickwrite.
00:39:46All right. See, I can see quickly you haven't even finished graphing these yet, so I want you to do the quickwrite right now.
00:39:52And then I expect better results on Monday. I want you to finish this up on Monday. Fair enough? Okay Jeremy?
00:40:00Mr. Ormsby? Number six, it says, what do you notice about the intersection between-
00:40:05Ah, see now it gets a little interesting. Show me your equation two.
00:40:09Two is uh, down here.
00:40:11Show me your equation six. Now, one thing that hopefully you understand is- See a line-
00:40:18Those arrows mean they go on- lines go on forever in both directions, right.
00:40:21Oh yeah.
00:40:22So take your ruler... and let's ext- actually extend this line. Be very careful. Be precise.
00:40:29Let's extend that line straight down. Okay. Go all the way down to there somewhere. There you go.
00:40:40Good. Good. Good. Good. Now, that's good enough because the idea is, I'm asking about what? The intersection.
00:40:49An intersection is where two lines-
00:40:51Meet.
00:40:52Meet.
00:40:53Meet or cross each other, right? Look where these two lines meet or cross. What do you notice about the angles there?
00:41:00It's a right angle.
00:41:02Well said. Right? So now in mathematics, this is something I haven't mentioned yet, that's also called perpendicular.
00:41:10Have you guys heard about that before?
00:41:11Yeah.
00:41:12So these two lines, therefore you would say are? Perpendicular. They make right angles. Right?
00:41:19Mm hm.
00:41:21My pencil.
00:41:25Hi Mr. Ormsby.
00:41:26I screwed up on graph nine and-
00:41:27Okay.
00:41:29He's all-
00:41:34Have you started your quickwrite yet Brittany?
00:41:36No, because I was doing the graphing and Nathan has all the answers, so I have to write down all the answers.
00:41:41Right now I want you to stop what you're doing and let's just say one paragraph now. Just write as much as you can.
00:41:49I didn't lea anything.
00:41:50All right.
00:41:52You didn't lea - you didn't know how- lea how to make tables or understand slope or Y intercept or anything like that? Okay?
00:42:14I said (inaudible) graph, I'm not gonna do it because I got messed up on the, um-
00:42:16It looks nice. That looks nice.
00:42:18On the-
00:42:19How come you crumpled it up?
00:42:20Because I messed up.
00:42:21Oh, so you got a new one?
00:42:22Yeah.
00:42:23So on Monday you're going to redo it.
00:42:24I'm- I'm just trying to-
00:42:25Maybe even use a ruler to draw your coordinate system. Make it look professional.
00:42:29Yeah.
00:42:30Do it all the way down.
00:42:32Okay.
00:42:35I'm not going to be here.
00:42:36Okay.
00:42:37We're getting our work done here, look.
00:42:40Last time ladies and gentlemen. Five, four, three, two, one, zero.
00:42:47Okay. Here's the deal.
00:42:50Because we're running short on time and since I'm going to follow up anyways on Monday, okay-
00:42:58And we're actually going to have a little discussion about not just graphing but also what I wanted you to discover about these lines, all right.
00:43:07Please make sure you put away all your work. Do not lose any of it.
00:43:13Where are we-
00:43:14Do not tu in anything today because you're going to need it all Monday.
00:43:15What do we do- What do we do with this?
00:43:18Can I trust you- can your group trust you to fold that up and put it away somewhere?
00:43:21Nope.
00:43:23All right.
00:43:24What do we do with these?
00:43:26Keep it until Monday. Okay?
00:43:28Keep it till Monday in your backpack because if I take it, I'm going to lose it.
00:43:32Okay.
00:43:33Mr. Ormsby, I'm not going to be here all next weekend.
00:43:37Or all next week, 'cause we're going up to Seattle for um, Thanksgiving.
00:43:41Okay.
00:43:42And I'm gonna be (inaudible)-
00:43:43You're le- You're not even going to be here Monday, Tuesday or Wednesday?
00:43:45No, 'cause (inaudible).
00:43:46D-O-G.
00:43:47D- Cat. C-A-T.
00:43:50Okay.
00:43:51I will- I'll be back um, on the-
00:43:53Leave your work with another group member then.
00:43:54Hey, what do we do with this, Mr. Ormsby?
00:43:56Leave that on the desk. That will be fine. Okay, hurry up and go guys. Have a good weekend.
00:44:01You too.
00:44:02Wait, Mr. Ormsby. I'm taking off.
00:44:07That was fun.
00:44:08Did you have fun? Good.
00:44:09No.