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