Uploaded by VideoTSBVI on 04.02.2010

Transcript:

A TSBVI Outreach Tutorial.

APH Graphic Aid for Mathematics

a.k.a. Graph Board.

Part 8: Graphing the circle on a coordinate plane.

Presented by Susan Osterhaus,

a Texas School for the Blind and Visually Impaired Outreach Math Consultant.

Okay, we're gonna graph a circle now.

And we're gonna use our wire, one of our wires. Okay.

So we're going to decide to graph a circle, and instead of this being a more elementary circle

we're going to pretend that we're doing something called analytic geometry,

where you're actually graphing the circle on the coordinate plane again.

And we're going to pretend that this circle has the center at the origin,

which means that's going to be, it's not gonna actually be a point.

Because the circle, how we define a circle is, in this case,

we are going to say that the circle has a radius of four.

So if we start at the origin and go in any direction, four units...

One, two three, four, and place a point.

And now, we'll go... That particular one, we went to the left.

Now, we're gonna go to the right. One, two, three, four.

And, notice, I'm picking very nice distances of four.

Not once out like this because it would be more difficult for me

to count four that way diagonally.

And then I'm gonna go, one, two, three, four, up.

And then, one, two, three, four, down.

And now, I have what should be a circle if I connect the points correctly.

Well, okay. I want a circle, right?

Oh, my goodness, what happened?

I used a rubber band and...

That looks like a diamond or a rhombus or a square...

That does not look like a circle. Bad choice.

So this is not what we want because this is not really the point on there.

It's the one that's four units out.

But trying to sit here and hold this and make this look like a circle

would, kind of, be a little bit counterproductive,

especially if we're trying to take a digital picture.

So not a good choice.

So this is when we get the wire out and what you do is...

By the way, the students can do this much more easily than me.

Somehow, they tactfully, they can find that little slot.

And bottom line is you just put that right over your point, tighten it up a little bit.

And now, the students can recognize that it is a circle.

And again, the distance from the center of the circle to the circle itself

is four all the way around.

And that is a very good use of these wires.

Now, I will warn you, if you have some of the older wires,

that this particular metal rusts very easily.

So try to keep this away from any moisture.

Or as I do, sometimes I warn the students to wash their hands after they use it

if they happen to get any rust on their hands from it,

so that they're not getting it on their clothing.

But, anyway, other than that, the wires are very nice.

Now, I will tell you something else that when you get into larger circles...

Okay, let's go ahead and make the radius on this eight.

One, two, three, four, five, six, seven, eight.

One, two, three, four, five, six, seven, eight.

I hope I counted right.

I'll find out soon.

Well, uh-oh, uh-oh! What's going to happen here?

Okay, okay. As I dodge a little bit over here to the left, I have to grab another wire.

And my students came up with this. I said, "Oh, my gosh, what are we..."

I do this all the time to my students. "What are we gonna do, we can't graph this."

So they managed to come up with, put another one...

Let's see if I'm gonna be able to do this.

So, they put two together.

And what, of course, they didn't like was the fact that this little thing sticks out.

I'll show you what I'm talking about in a moment.

But anyway, so they did like this, and they're now able to make a larger circle.

Now, I happen to pick one that was nice and there's not too much of a tail there.

So I don't know if you can actually see that little bit of a tail where it's coming up.

That one... That one is very nice.

Now, there's just a little bit of a tail over here.

And that's only because I picked a circle with radius eight.

I was crafty.

But anyway, what my students say is that APH should include

these little, little clippy things that would hold that,

so that if this little tail wouldn't stick out quite so much.

So they have all kind of great ideas as to how to change the APH product a bit.

And by the way, if you have other changes, et cetera, please let me know.

Many of these things, my students and I,

we've just decided to add to the parts and so forth.

So if you come up with a great idea, please let me know

because, again, this is one of my favorite things.

So this is... Probably one of the best uses of the wires

is when you are having to graph circles.

And you saw what happened with the rubber bands,

so I think that that's something that you can all understand.

And I presume, if we wanted something bigger, we could even connect that third one

and make it even a larger circle.

Probably, that's why they gave you three. Three is about it.

Otherwise, you're gonna be off the frame of the graph.

And that's how you graph circles.

**Captions by Project readOn**

APH Graphic Aid for Mathematics

a.k.a. Graph Board.

Part 8: Graphing the circle on a coordinate plane.

Presented by Susan Osterhaus,

a Texas School for the Blind and Visually Impaired Outreach Math Consultant.

Okay, we're gonna graph a circle now.

And we're gonna use our wire, one of our wires. Okay.

So we're going to decide to graph a circle, and instead of this being a more elementary circle

we're going to pretend that we're doing something called analytic geometry,

where you're actually graphing the circle on the coordinate plane again.

And we're going to pretend that this circle has the center at the origin,

which means that's going to be, it's not gonna actually be a point.

Because the circle, how we define a circle is, in this case,

we are going to say that the circle has a radius of four.

So if we start at the origin and go in any direction, four units...

One, two three, four, and place a point.

And now, we'll go... That particular one, we went to the left.

Now, we're gonna go to the right. One, two, three, four.

And, notice, I'm picking very nice distances of four.

Not once out like this because it would be more difficult for me

to count four that way diagonally.

And then I'm gonna go, one, two, three, four, up.

And then, one, two, three, four, down.

And now, I have what should be a circle if I connect the points correctly.

Well, okay. I want a circle, right?

Oh, my goodness, what happened?

I used a rubber band and...

That looks like a diamond or a rhombus or a square...

That does not look like a circle. Bad choice.

So this is not what we want because this is not really the point on there.

It's the one that's four units out.

But trying to sit here and hold this and make this look like a circle

would, kind of, be a little bit counterproductive,

especially if we're trying to take a digital picture.

So not a good choice.

So this is when we get the wire out and what you do is...

By the way, the students can do this much more easily than me.

Somehow, they tactfully, they can find that little slot.

And bottom line is you just put that right over your point, tighten it up a little bit.

And now, the students can recognize that it is a circle.

And again, the distance from the center of the circle to the circle itself

is four all the way around.

And that is a very good use of these wires.

Now, I will warn you, if you have some of the older wires,

that this particular metal rusts very easily.

So try to keep this away from any moisture.

Or as I do, sometimes I warn the students to wash their hands after they use it

if they happen to get any rust on their hands from it,

so that they're not getting it on their clothing.

But, anyway, other than that, the wires are very nice.

Now, I will tell you something else that when you get into larger circles...

Okay, let's go ahead and make the radius on this eight.

One, two, three, four, five, six, seven, eight.

One, two, three, four, five, six, seven, eight.

I hope I counted right.

I'll find out soon.

Well, uh-oh, uh-oh! What's going to happen here?

Okay, okay. As I dodge a little bit over here to the left, I have to grab another wire.

And my students came up with this. I said, "Oh, my gosh, what are we..."

I do this all the time to my students. "What are we gonna do, we can't graph this."

So they managed to come up with, put another one...

Let's see if I'm gonna be able to do this.

So, they put two together.

And what, of course, they didn't like was the fact that this little thing sticks out.

I'll show you what I'm talking about in a moment.

But anyway, so they did like this, and they're now able to make a larger circle.

Now, I happen to pick one that was nice and there's not too much of a tail there.

So I don't know if you can actually see that little bit of a tail where it's coming up.

That one... That one is very nice.

Now, there's just a little bit of a tail over here.

And that's only because I picked a circle with radius eight.

I was crafty.

But anyway, what my students say is that APH should include

these little, little clippy things that would hold that,

so that if this little tail wouldn't stick out quite so much.

So they have all kind of great ideas as to how to change the APH product a bit.

And by the way, if you have other changes, et cetera, please let me know.

Many of these things, my students and I,

we've just decided to add to the parts and so forth.

So if you come up with a great idea, please let me know

because, again, this is one of my favorite things.

So this is... Probably one of the best uses of the wires

is when you are having to graph circles.

And you saw what happened with the rubber bands,

so I think that that's something that you can all understand.

And I presume, if we wanted something bigger, we could even connect that third one

and make it even a larger circle.

Probably, that's why they gave you three. Three is about it.

Otherwise, you're gonna be off the frame of the graph.

And that's how you graph circles.

**Captions by Project readOn**