Project Math Access DVD 05 - Geometry - Part 09 Transcript Start Audio Description: Part nine; Plotting points on a graph board. TEACHER: Okay John, we’re going to practice plotting points on a graph board. And I’m going to first set up the graph board with the x and y-axis using Wikki Stix, so then you'll know where the x and y are. Audio Description: The graph board is approximately two feet square, and is made of heavy rubber with a raised, grid pattern. TEACHER: I’m putting on the x, the y right there and then I'll do the x. Audio Description: The squares on the grid are about one half inch by one half inch. The teacher creates the x and y-axis using Wikki Stix with the intersection in the middle of the graph board. TEACHER: Okay, I am going to put a, one of our circle push pins, in the center, for (0, 0), so that you know where the center of the graph board is. Okay, so if you want to take a look at it. JOHN: Okay. Perfect. Audio Description: John's hand inadvertently moves the bottom half of the y-axis. JOHN: Oops, this one likes to move a little bit. Alright. TEACHER: Okay, and I’m going to give you some push pins and we’re just going to first practice... plotting some basic points and then I'll have you make like a square using the points or lines. JOHN: Okay. TEACHER: So here's a pin. JOHN: Okay. Audio Description: The teacher hands John a pin shaped like a cylinder. TEACHER: If you just want to plot (4, 6). JOHN: (4, 6), okay, this is (0, 0), it's right here, Audio Description: John is counting up the y-axis, when he should be counting over on the x-axis. JOHN: ...it's rise over run. Audio Description: He now counts over six on the x-axis. JOHN: It's right there. Audio Description: John pushes in a pin at the point that he located. JOHN: There we go. TEACHER: Okay, you want to remember though which number comes first, the x or the y? JOHN: It's the x first. TEACHER: Okay, and which line is your x line? JOHN: Oh, sorry. Audio Description: John realizes his mistake. He pulls out the pin and counts over four on the x-axis, and up six on the y-axis. He now places the pin at the correct point. TEACHER: Which line is your x? JOHN: It should be 4..., 3,4, 5, 6, right there. TEACHER: If you want to tell me what you did. JOHN: I went over to the right 4. I started at the origin, went over 4 places to the right and up 6. TEACHER: Good job. JOHN: I was thinking of slope there for a second, which is rise over run. TEACHER: Okay, so you want to do your x first, so you're going to go over 4 and up the 6 which is your y. JOHN: Yep. Audio Description: John demonstrates how he used the raised grid to count. TEACHER: Okay, now if you want to do (-3, -5). Audio Description: The teacher hands John a new pin. The first pin stays in the grid board. JOHN: (-3, -5)."- that's right here... oops. I'm going to go down one so that the Wikki Stix don't get in my way... but they are anyway. Audio Description: The Wikki Stix representing the lower-half of the y-axis comes loose. John realizes this, but does not replace it. JOHN: Okay, (-3, -5) did you say? TEACHER: Yes Audio Description: John uses a spherical pin at the origin as a reference for counting. JOHN: 1, 2, 3, 4, 5... Okay, I went to the left 3 and down 5 and there we go. Audio Description: John places a pin at the new point. JOHN: Oops, there we go. TEACHER: Okay, nice job. These Wikki Stix aren't cooperating. Let me fix the origin. I'll put the Wikki Stix in there and then maybe it will stay better. Audio Description: The teacher returns the Wikki Stix, representing the lower-half of the y-axis, to its correct place. TEACHER: Okay, now if we wanted to have you make a line between these two points, TEACHER: The teacher points to the pins John located on the grid board. TEACHER: you have the (4, 6) and the (-3, -5). Okay, I have a Wikki Stix here, can you show how you would combine them to make a JOHN: Yes. Let's see here. Audio Description: The teacher hands John a Wikki Stix. JOHN: It's right here, I'm going actually try and put it on the pin, so that it doesn't move. Okay and then this one right here, I'm going to do the same thing. I'm going to kind of wrap it around the pin here, so it doesn't move. Audio Description: John connects the two pins that he placed with the Wikki Stix. JOHN: Okay, that's good. We have a line now that passes, if it wasn't for that little pin thing, it would pass right through the origin. TEACHER: Good job. It would go right through (0, 0). JOHN: Yes, it would. TEACHER: And by having it with the Wikki Stix, can you tell, can you give me another point that it would pass through? JOHN: Yes. Let's see. Audio Description: John locates a new point on the raised grid board. JOHN: Where's right here? Audio Description: John uses the lines on the raised grid board to locate the new point. JOHN: 1, 2, 3... It looks like it would pass through (2, 3), over 2 and up 3. TEACHER: Nice job. It passes right through there. What else we could do is use a pipe cleaner instead of..., I'm going to have you try using a pipe cleaner, and have you tell me which one works out easier. Here's a pipe cleaner. JOHN: Okay. Audio Description: The teacher hands John a pipe cleaner. JOHN: You want me to redo the line between these two? TEACHER: Yes Audio Description: The pipe cleaner John is using is not completely straight, and has a couple of bends in it. JOHN: Okay. What if I... I'm just going to put it right here and right here. Audio Description: John connects the two points with the pipe cleaner. JOHN: See the problem with these pipe cleaners is that they don't stay put where you have them and as a result, the line moves. If you can see, I have it right here, but when I let go, the thing wants to move and it does. It in fact moves away from the origin. TEACHER: Okay. What if you bent it around the pin? Would it work that way? JOHN: It might, but then when you... oh, okay. Audio Description: The teacher wraps the pipe cleaners around the pins. TEACHER: See if that is easier. I bent it around and then I'll have you... JOHN: Yeah, that's better. TEACHER: Are you able to distinguish the line that you made easier with the pipe cleaner... because of it being different than the xy-axis, or does that not make a difference? JOHN: The pipe cleaners are good for when you have to make more than one line. Yeah, I can understand where the x- and y-axis are and then if l need to make one line with the Wikki Stix, I'll understand it. But if there's more, if there's like multiple lines, then pipe cleaners would be good to use. TEACHER: Okay. JOHN: It might also be even a little easier to tell what points the lines run across, especially if they're close together, because a pipe cleaner... is easier to sneak your finger under without moving the entire thing. Whereas a Wikki Stix, even though it's wrapped between the two pins, you still could move it a little bit more than you could this. This is pretty secure actually. Audio Description: John wiggles the pipe cleaner to show that it stays in place. TEACHER: Okay, I'm going to have you make a... quadrilateral with the points. So let's clear our graph board off. JOHN: Okay, I'll get everything off of here. Where do you have the pins at? Oh, right here, okay. Audio Description: John removes the pins from the grid board, but leaves the spherical pin that represents the origin. TEACHER: And then you'll have to... JOHN: Here, can I just take these? Audio Description: John takes the box containing the pins, and places it on his right. TEACHER: Yes. Okay, the first point is going to be (5, 3) Audio Description: John counts using the raised grid. JOHN: 1, 2, 3, okay that's (5, 3). Okay-- Audio Description: John places a pin at the point that he found. TEACHER: And then (-5, 3). JOHN: 1, 2, 3, 4, 5,... down 1, 2, 3, it's right there. TEACHER: Negative 5, 3 Audio Description: John accidentally counted negative three, instead of positive three. JOHN: Oh, I see what I did. 1,2,3... TEACHER: Okay, so negative 5 is going to be going to your... JOHN: I know, to my left. TEACHER: Yes JOHN: Negative 1, 2, 3, so it's right there. TEACHER: Okay, but I didn't say, no, it's negative 5, positive 3. So you want to go up into the second quadrant. JOHN: There we go. Audio Description: John places a pin at the new point. TEACHER: Okay, now you can do your (-5, -3). JOHN: Okay, 1, 2, 3,... Audio Description: John counts out location of the new point. JOHN: this thing keeps moving. Okay-- Audio Description: John places a pin at the new point. There are now three pins on the grid board, plus the one representing the origin. JOHN: Okay. TEACHER: Okay and then can you figure out where the last one's going to go? JOHN: Let's see, we've got one here and here and here, one here, here, here. Audio Description: John identifies the pins by using the origin as a reference. JOHN: Okay, so where is this one here, negative 1, 2, 3, 4, this one's (-5, 3). Audio Description: There is a pin in each quadrant, except quadrant four. JOHN: Okay, this one's going to be the same as this one down here. We have these two up here, this one down here, so let's see, where was that one exactly? Let's see... 1, 2, 3, that's (-5, -3)... so we need one over here at (5, -3). TEACHER: Nice job. JOHN: 1, 2, 3, right there. Audio Description: John locates the fourth point in his quadrangle, and puts a pin at that point. TEACHER: Now if they asked you to draw this, to combine the lines, to join the lines, the points, which would you prefer to use? Would you prefer to use a pipe cleaner or a Wikki Stix, Wikki Stix? JOHN: You know what, I think I'm going to try it out with a pipe cleaner. 2 JOHN: Actually, I think, because sometimes, I'm going to try this one out with a pipe cleaner, wrap it around the pin here. Audio Description: John wraps the pipe cleaner around the pin in quadrant three. JOHN: And I'm also going to do a pipe cleaner for the top line, but sometimes in Geometry they ask you,... Audio Description: John wraps the other end of the pipe cleaner around the pin in quadrant four. However, the pipe cleaner has not been pulled taught, there are a few bends in it. JOHN: I'm just going to tuck this in here, alright I'm ready for my next pipe cleaner, for the top line. Let's see, wrap this around, there we go. Audio Description: The teacher hands John another pipe cleaner. TEACHER: Don't forget, you also have to join the sides. JOHN: I was just going to say, we can use the Wikki Stix when we do that. Audio Description: John warps one end of the pipe cleaner around the pin in quadrant two, and the other end around the pin in quadrant one. TEACHER: Okay, what I would do is I would bring the pipe cleaners and wrap it around all four pegs. So you would probably need the two pipe cleaners, but, here I'm going to undo what... you've done here and bring it down so that it's wrapping on the outside of the pegs... JOHN: Okay. TEACHER: of the push pins. So then you have your square. And see if you can, how that is. JOHN: Yeah, that's good. TEACHER: Your quadrilateral, your rectangle. JOHN: Yeah, that's good. See now I would use a Wikki Stix if l had to connect this and this point,... to find, like say I had to find the line segment in between there. I would probably use a Wikki Stix to connect these two points to each other. Audio Description: John is referring to line between points in opposite corners. TEACHER: Okay, good job. Okay, one last thing I'm going to have you do is plot separate points using the different push pins that we have. JOHN: The different shaped push pins. Audio Description: John and the teacher remove the pins and pipe cleaners from this problem, and prepare for the next problem. JOHN: Here we go, oops. Here's this other pipe cleaner and... Audio Description: John makes sure that he does not remove the pin that represents the origin. TEACHER: Okay, here's one of the push pins. Do you want to do (2, 4)? JOHN: Over 2, up 4... that's good. There we go. Audio Description: John locates 2, 4 and places the pin in the grid board. This pin is a small cube. TEACHER: Do (4, 6). Okay-- Audio Description: John counts four over and six up, and places a pin that is pyramid shaped. TEACHER: And (6, 8) Audio Description: John counts six over and eoght up, and places a pin that is spherical shaped. All the pins John has placed are in the first quadrant and form a line. JOHN: Okay, here we go, that's good. TEACHER: Okay, can you tell me if all, where those three points lay? JOHN: Yeah, they all lay along the same line. TEACHER: Good. Can you say what the advantages or disadvantages of these push pins to the other push pins you were using? JOHN: Because sometimes we move from problem to problem pretty rapidly... especially when the teacher's giving notes and you know, but we still have to deal with the same figures. So sometimes, to identify what points... are for what problems, we'll used different shaped push pins. So that helps me out. TEACHER: Okay. JOHN: I'd like to point out one disadvantage. These are not the greatest when you're trying to connect the lines, like we were doing in that square. TEACHER: Yes JOHN: Their bigger shape makes it harder to wrap the pipe cleaner around or put the Wikki Stix under like I did with the other ones. Audio Description: John takes the three pins, he put in quadrant one, off the grid board. TEACHER: Okay. I'm going to have you take those out and we're going to do one more thing, with having you... JOHN: Here you go. TEACHER: label the pins, so when you're doing this in class, and you have to construct... something, that you have a way to know what the points are. I'm going to have you first label, Audio Description: The labels are plastic letters that also have braille. TEACHER: And these are just Playskool magnets that have the Braille on them... and then we've used them on a magnet board and we've also used them on this board. First have you label point (8, 3), and that's going to be A. Audio Description: John locates the point, pushes in a pin, and places a plastic letter A next to it. JOHN: Okay. Oh, I remember this stuff, okay. TEACHER: And you're just going to put that by the point. JOHN: Yeah, I'm going to put it right there. TEACHER: Okay, and then label J, is going to be (-6, 4). JOHN: (-6, 4)-- JOHN: 1, 2, 3, 4, 5, 6... Audio Description: John locates the origin, counts off negative six, but then negative four, instead of positive four. JOHN: down 1, 2... TEACHER: Negative 6,4 JOHN: Oh, down, oh, okay. Audio Description: John begins counting again, negative six, four. John places a pin at that point, and then a plastic letter J. TEACHER: Okay and here's the J. JOHN: Okay. I'm just aligning it so that it looks straight to me. okaY- TEACHER: Okay, I'm going to fix our x line real fast. Audio Description: The teacher repairs the negative x-axis line. TEACHER: Okay, do another one at (-3, -7). And that will be point B. JOHN: 4, 5, 6, 7... Audio Description: John counts off negative three, negative seven, pushes in a pin, and then adds a plastic letter D. JOHN: Okay-- Okay, where's it at? What point is this? You handed me another J. TEACHER: It's D. JOHN: Oh, okay. Audio Description: John mistook the plastic D for a J. TEACHER: Okay, so now you've graphed these points so now when your teacher in class is talking about where point A, J and D lie, you would be able to follow along with what the rest of the class is doing. JOHN: Yes. TEACHER: with this, so that you would understand where they are as she's doing it up on the overhead or up on the chalkboard.