Project Math Access DVD 05 - Geometry - Part 07 Transcript Start Audio Description: Part seven; using a braille compass to construct intersecting circles. TEACHER: Okay John, I would like you to make two intersecting circles using the compass that you have, and if you want to make the... circles pretty medium-sized. So increase your compass a little bit. Audio Description: John picks up the compass and adjusts it. JOHN: That should be good right about there. No, even that might be a little too small. Let’s try this. Audio Description: John will be working on a sheet of braille paper. TEACHER: Now remember you want to fit two of the circles on the piece of Braille paper that you have there. JOHN: I know, I’m going to try to go as close the middle as I can here. Audio Description: Under the braille paper, there is a piece of cardboard. JOHN: Oh, I remember, okay, I'll try it. [sound of circle being drawn] Audio Description: The compass has a small sprocket wheel that is used the emboss the paper. JOHN: Let’s see, take it from here... Audio Description: John continues to make the first circle using the braille compass. [sound of circle being drawn] JOHN: Oops, I'll retrace that section. Audio Description: The compass lifts from the paper, and John has to retrace that part of the circle. JOHN: Okay, should be good. Let’s check it out. Audio Description: The first circle is finished. John turns the paper over to check his work. JOHN: Yeah, that's pretty good. TEACHER: Okay, now you want to make one that intersects with that so that you have sections that are adjoining. JOHN: Alright, so I've got to turn it over again. This is probably the biggest problem I have with the compass is that the tracing wheel makes the design on the other side of the paper and then... when you try and make it smaller you've got to try and find this little dot right here where the other, where the pointy edge of the compass has... poked through the paper and sometimes that's really hard to find. I think I have it though. Audio Description: The point John is referring to is in the center of the circle. JOHN: So I'm going to make this one smaller. TEACHER: No, you want to make them same size circle and you want them to have intersection parts. So you're not going to use the radius at all, the center point. JOHN: Okay, so I'm going to do this then and put it right about here. TEACHER: Okay, but you're going to make that circle right in the same circle. What we want to do is you want to have this circle separate. JOHN: Okay, we'll put it right here then. Audio Description: John selects a center point for the second circle outside of the first circle, but near the edge of the paper. TEACHER: Okay, is your circle going to all fit on the paper? JOHN: Yes, it will. It'll fit because I'm far enough over. [sound of circle being drawn] Audio Description: The second circle is not intersecting the first circle. JOHN: Pretty close. TEACHER: [laughs] Audio Description: The circle is too close to the edge and the compass runs off the paper. JOHN: Yep, and then you go like right around here. TEACHER: Okay, let's try doing another one where if fits, and it didn't intersect at all with that circle either. Audio Description: The teacher points where the two circles miss. JOHN: Okay, I can feel this circle, it's right down here. Okay, so we might want to do one, let's see, yeah, this should fit all on the paper. TEACHER: Okay, why don't you try, have it go all the way around before you, and does it intersect at all? Wait, before you start tracing. JOHN: Yeah, it does, it's going to intersect right through here. TEACHER: Before you start tracing make sure that it's going to fit all on the paper. Audio Description: The camera shows that the two circles do intersect. JOHN: Yeah, it is because I went all the way around down here already, down here. It's going to be a tight fit, but it will fit. Audio Description: John demonstrates that the new, second circle will fit on the paper. [sound of circle being drawn] Audio Description: John begins drawing the second circle, and the camera shows a close up as it intersects with the first circle. Halfway through the second circle, the sharp center of the compass becomes dislodged and moves about one eighth on an inch. John is not aware of this. However, it happens after the circles intersect and it will not affect his answer. JOHN: Alright that should be good. Audio Description: John finishes the second circle and turn the paper over to check his work. JOHN: Let's see here if we have... it's pretty close. The two circles intersect like right through here and here. So there's two... TEACHER: They intersect very little. They have a very small spot that intersects. JOHN: That's okay because in Geometry sometimes they intersect a whole side and sometimes it's just points. TEACHER: Right, right. Okay, I'm going to have you do one more circle and this time I want... you to do it where it intersects to the center of the original circle that you drew. So you want, here turn your paper over. Audio Description: John starts to turn the paper over, then returns to the back side. TEACHER: Or wait, you can keep it this way. Here's the first circle that you drew, right here, and here's the center. And I want you to draw a circle that the edge comes to the center. Audio Description: John picks up the compass. JOHN: Okay, let me see here how we're going to do this. I'm going to mess with the size a little bit here. Audio Description: John adjusts the compass to make the radius smaller. TEACHER: You probably want to make your compass a little bigger. JOHN: A little bigger, huh? Let's see, I'm just going to put it by the edge and see if l go all the way around, let's see, if l put it right here, it's going over the center. Ah, I might want to make it just a tad bigger. Audio Description: John increases the radius on the compass. JOHN: I think you're right. Okay, that's good. Audio Description: John turns the paper to the front side. TEACHER: How are you going to line up your compass? Audio Description: John searches for where to place the compass. JOHN: Okay, I'm going to put it like... because if l put it right here... then it's going to intersect the center of the circle which is right about here. TEACHER: Good. So you want to put the tracing wheel part on the center of the circle. JOHN: Right, yeah, right there. Audio Description: John has the tracing wheel of the compass on the center of the circle he created in the first problem. JOHN: And I'm going to try, without moving the compass too much, and put it in. [sound of circle being drawn] Audio Description: John begins creating the new circle with the compass. John finishes the new circle. JOHN: Okay, that should be good. Audio Description: John turns the braille paper over to check his work. JOHN: Yeah, pretty close. It does come through the center here of that other circle. Audio Description: The camera shows that the new circle intersects the center of the first circle. TEACHER: Now you want to make sure that when you do this next time that you push down harder on the tracing wheel because in sections... JOHN: It's a little faded TEACHER: Okay, what are some advantages and disadvantages that you see to the compass, for you to do it? JOHN: For me doing it, well one advantage is I get a better picture of what the Geometry teacher... is talking about when she says that circles can intersect at different points. One key disadvantage, however, is that every time you use a tracing wheel, it puts the design on the other side of the paper. And therefore, if l didn't have your assistance, I might not have been able to get those circles to intersect at all because when you flip the... paper over you can kind of feel the design, you can feel the back side of it a little bit, but it's kind of hard to tell where it's... going to intersect, especially when you have to take your compass and put it here, put my... tracing wheel here, then it's going to intersect the circle you know, right here. It's kind of hard to feel that without moving the compass all around and having... your spatial awareness become all messed up, as to where you are. So that's some of the advantages and disadvantages. One other disadvantage is depending on, because the compass is kind of an odd shape, depending on where it is on the circle, sometimes it's going... to be harder and easier to push down real hard on the tracing wheel, because if it's over here... it's fine, but it's when it gets here and like here that this edge, this side wants to move around a little bit. Audio Description: John indicates that it's easier to draw the top half than the bottom half of the circle. TEACHER: And you did a very nice job today with making the circles. In the past you've had some difficulties, like you were saying where the center of the circle drifts and.... JOHN: That's because they've required it to be in a smaller area. TEACHER: Right. JOHN: We were lucky. We could use a whole piece of paper and make a big circle... but for some of these problems when you had three and four circles... it was necessary to shrink them, and then when you deal with smaller figures... it allows you less room for error, and therefore the errors appear greater. Audio Description: The teacher takes the braille paper and the compass and turns the paper to the backside. TEACHER: Some of the advantages and disadvantages that I see to this is when the students are doing it, they don't get as... hard of a tactual read out, because there's so much for them to try to concentrate on doing, and also I had mentioned before that a lot of times... the circle, the center point that they're holding the center of the compass in, tends to increase... as they're moving the compass around as it does a lot of times with sighted people. But so that then makes the circle, the hole then gets dragged out, so then the circle doesn't line up how it's supposed to line up. So then they're not getting the complete circle that they need to have. Also, the compass does not have a reading on it so you can't tell the degrees of the circle, as a sighted compass has. I did find this beneficial for when I had to make circles for his handouts and worksheets. This worked better for me than using a tracing wheel, where I would draw a circle in print first and then use a tracing wheel over it. I found that I got a better circle when I used this, but then I still had some of the same problems... where the center of the circle ended up getting larger and the circles didn't line up. The other problem is is that the type of surface that you have to do it on, when we used a rubber mat, it would eat through the rubber mat. You have to do it on some type of surface, because, otherwise, the tracing wheel that's on the compass will eat through the tables, make marks on tables. So the thing we found best it either using cardboard or using newspaper to make the circles.