Project Math Access DVD 05 - Geometry - Part 14
Transcript Start
Audio Description: Part fourteen, constructing on-the-spot tactile diagrams; method one.
TEACHER: This is the picture maker, The Wheatley Tactile Diagramming Kit... that was developed for 0&M and also for some basic Geometry.
We found it to be useful for John to construct some stuff, also to be used in the classroom for on-the-spot production of materials. It has-- comes with the black Velcro board and then lines, segments of circles, circles, and they are different textures and shapes. And then it also has squares, rectangles, triangles.
So it's great for when you have those quick, on-the- spot things that you have to make up.
Okay, first, what we’re going to do is work on quadrants and I’m just going to put down... ...xy-axis
Audio Description: The teacher creates the x and y-axis using two, long, straight pieces. She then grabs a small circle to represent a point.
TEACHER: And I’m going to put a circle, and if you can tell me what quadrant it is in?
Audio Description: John locates the origin and the circle.
JOHN: Okay.
TEACHER: Okay, here your xy-axis is right here.
JOHN: xy's right here, so... it’s in quadrant ll.
TEACHER: Great.
Audio Description: The teacher removes the circle and searches for a place to put a line.
TEACHER: Okay, now I’m going to put a line down and if you can tell me what quadrant or quadrants that the line falls into?
Audio Description: The line is in quadrants one and four.
JOHN: It's in quadrants I and IV.
TEACHER: The teacher removes the line and the xy-axis.
TEACHER: Okay, I’m going to have you construct a triangle. I’m going to give you some straight edges.
Audio Description: The teacher puts four, short line pieces on John's right.
TEACHER: They’re over to your right. And if you want to make a equilateral triangle.
Audio Description: The pieces are flexible plastic that attach to the velcro board. John has three pieces in his hand. He uses two to create the first angle. The angle might be a bit wide for an equilateral triangle.
JOHN: Okay. I don’t know if l need to make this a little bit sharper here.
Audio Description: John moves one piece to decrease the angle, then moves it again slightly to increase the angle.
JOHN: I'll move just a little bit around.
Audio Description: John puts a third line in place to finish the triangle.
TEACHER: Okay, equilateral means that...
JOHN: all sides are equal, I’m first trying to make it, and then I can see how to adjust it.
TEACHER: Okay.
Audio Description: The triangle John has made is very close to equilateral.
JOHN: Yeah, see, this needs to be moved over just a little bit.
Audio Description: John makes a slight adjustment in one of the pieces.
JOHN: Nope, it's not quite it.
TEACHER: Yep.
JOHN: No, this corner's a little off.
TEACHER: Just because you have the two squares, you have squares so they're not going to...
JOHN: Oh, okay.
TEACHER: You did a nice job. Good job, that's an equilateral triangle and you have all three strips that are the same. Okay, now,
Audio Description: The teacher removes the triangle from the board.
TEACHER: Let's see if l can confuse you.
Audio Description: The teacher gives John four more line pieces. They are longer.
TEACHER: I'm going to have you make a triangle that has an acute angle. And I gave you some different size strips. An acute angle again is?
JOHN: An acute angle is a slight angle, less than 90 degrees.
TEACHER: Yes.
JOHN: So, wait, let's see how I'm going to do this here.
Audio Description: John has two of the longest line pieces. He uses them to create an angle of about 35 to 40 degrees.
JOHN: Okay, I'm going to make this one long. Less than 90 degrees,
Audio Description: John changes the angle to about 70 or 75 degrees. John searches for another piece.
JOHN: I need to make it this way. Okay, where's another really, really long thing?
Audio Description: John finds another long piece, the same length as the first two.
TEACHER: Okay, if you're going to use three long ones, what type of triangle are you making?
JOHN: Oh, the incorrect type.
TEACHER: Well, actually, it's right. You made what I asked for, but what also type of triangle did you just make again?
JOHN: Again, that was equilateral.
TEACHER: And so on an equilateral triangle, all the angles are less than...?
JOHN: They're all less than 90.
EISEHNHUT: Yes. So how many acute angles do you have?
JOHN: All three of them.
TEACHER: Good. Can you construct me one more with using a smaller size stick?
Audio Description: John removes one of the long pieces from the board.
JOHN: Okay. I'll see what I can do with this one here,
Audio Description: John places a shorter piece.
JOHN: because I used two big ones, maybe if l use these smaller ones here.
Audio Description: John adds another shorter piece to extend the line he just created. John examines the triangle, which has the angles as the first one.
JOHN: This, see now you can tell that, because this angle does seem a little bit sharper than these two over here. This one I just made.
TEACHER: Well the two pieces that you used equal one of the longer pieces. So how about it you just use one of the smaller pieces and one of the...
Audio Description: John pulls a smaller piece off the board.
JOHN: Two of the longer pieces and one of the smaller pieces?
TEACHER: Yes
JOHN: Okay, well see there, okay, we'd have a triangle then with an extending line, if you will.
Audio Description: John pulls the other smaller piece off the board.
TEACHER: That's okay, you can explain that.
JOHN: See another thing with this is that it's not going to belong enough to make a complete triangle.
TEACHER: Okay, here, let me show you. If you put this up like that, so it's going up, and move this one.
JOHN: Move it over a little bit?
Audio Description: The teacher places the smaller piece, then moves the larger piece to create a triangle.
TEACHER: Now do it. Now you have...
JOHN: Okay.
Audio Description: John examines the triangle.
TEACHER: Do you understand how you can do it with using the different pieces... you just have to move them around until you get the size triangle that you want. Okay, we also have circle pieces here.
JOHN: That's what I can use, in this case, to label the different points of the triangle. Right? Like if she would've decided to put letters and stuff on them.
TEACHER: Yes
JOHN: I could just use different shapes to signify it.
Audio Description: The teacher hands John a small circle.
TEACHER: Here's one. Let's say this one is ABC. So what...
JOHN: So A, okay, I'm going to have A over here.
Audio Description: John places the circle at A, at the top of the triangle.
JOHN: This one is letter B. Right there on the corner.
Audio Description: John places an O at the B angle on the left side.
JOHN: And this one is letter C. Okay.
Audio Description: John places a larger circle at the C angle on the right side.
TEACHER: Good, good job. Now I'm going to... here let's take that off.
JOHN: Okay.
Audio Description: John removes the three objects he was using to identify the angles.
JOHN: Want me to take the triangle off too?
TEACHER: Yes.
Audio Description: John removes the triangle from the board.
JOHN: Okay.
TEACHER: Now I just have four sections of a circle that I'm going to have you try to construct a circle with. Okay, here are the four sections.
JOHN: Okay.
TEACHER: Do you want them one at a time?
JOHN: Sure.
Audio Description: John places the first quarter section of the circle on the board. John tries to complete the circle with another quarter section, but realizes his error.
JOHN: 1, 2, that doesn't quite make a circle, but... okay.
Audio Description: John places the second quarter section in about the right position. John moves the second piece slightly, and adds the third.
JOHN: This needs to be modified again.
Audio Description: The circle is slightly oversized, so the fourth quarter section does not complete the circle.
JOHN: Not quite.
TEACHER: Do you need another piece?
JOHN: No, I need to modify it again, because if l move them closer, they will form a circle.
Audio Description: John modifies the pieces.
JOHN: It's just a matter of what angle it is. Let's see if we can ﬁt number 4 in here. Maybe if l can move this one just over just a tad.
Audio Description: The four pieces now form an oval.
JOHN: I just need to move it over just this little bit and I can have it. That's more of an oval.
TEACHER: Good, that you were able to , but what if we were to add...
JOHN: You need to add one more piece.
TEACHER: Okay, here's one more piece.
Audio Description: John adjusts the pieces to form a larger partial circle.
TEACHER: I'm glad that you were able to tell that that's an oval and not a circle.
Audio Description: John adds a fifth quarter section to his circle.
JOHN: You know what, on second thought, make it two more pieces, and we'll have a circle.
Audio Description: John adds the sixth quarter section to his circle, however, some of his pieces do not line up end-to-end.
JOHN: Not quite, but good enough.
TEACHER: (chuckle)
Audio Description: The teacher adjusts one of the pieces.
JOHN: Close enough.
TEACHER: Okay, good job. Well, close. Do you think this would help you in class?
JOHN: This is good, because you can tell, for example, what the Geometry teacher will do is take a circle and then will shade in part of it... because it's missing or they don't have the degree measurement. So that's great. All that needs to be done is this part needs to be taken away and that'll represent the... shaded area or the area that you need to find the measurement for.
This is also great because you can move several pieces around without destroying or messing up any of the lines around you, as you might... have had to do with the board and the push pins.
One thing that's a pain about it though, as you could see, is that when we created the circle... we had to readjust the length between some of those pieces several times and you end... up having to move the whole figure around until you can ﬁt all the pieces into it. That is a little frustrating sometimes, especially when you're in a hurry or it's toward the end of class or when, you know... I know especially in those last sections of the chapter, they are trying to get, throw a lot of information at you at once. But overall, this has been a very useful and helpful tool.