Uploaded by VideoTSBVI on 10.02.2010

Transcript:

A TSBVI Outreach Tutorial.

APH Braille/Print Protractor: Part 13, Measuring the angles of 2-D manipulatives.

Presented by Susan Osterhaus,

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

Okay, now we're going to be measuring angles using the APH Braille/Print Protractor.

I did the drawing first because I feel like measuring is gonna take a little more time.

And what I recommend now after I've had a little experience

is that we start out measuring angles that "have some depth."

Angles really don't have depth, but what I'm talking about

is we're gonna use some 2-D manipulatives with a little bit of depth.

They're supposed to be really be... Not have any depth.

Otherwise, now they're three-dimensional.

But this thickness is really gonna help our students, I think, learn how to measure.

So, a teacher may give a student a manipulative like this

and say, "I would like you to measure the angles."

Now, some of them will already figure out this is a square and hopefully know

that that should be, all four of these angles should be 90 degrees.

So, you might say, "What do you think the angle is?"

And hopefully they'll say, "90 degrees."

So, you'll say, "Okay, go ahead and set your protractor to 90."

So, hopefully, by now, they've gotten familiar, and they know that 90 degrees

is that those three dots right there.

They're gonna line that up, tighten it up. Again, kind of turn that protractor around.

And they're just gonna slide that manipulative in and then check it.

Is that hugging up that corner? I mean, that's what you're trying to do.

Is this fitting right nicely in there?

And, by golly, it is.

And you might even like, you know, really to make sure

that you've got that in good and snug.

And tighten it up and follow it down.

By golly, you were right, that is 90 degrees.

And if you wanna go ahead and try it on all four to make sure that they're all 90 degrees,

you've just proved that.

So, start probably with something...

They already know what the measurement of those angles are.

Then maybe move to a triangle like this, which I won't name.

It does have a particular name.

But they might spot... Right off the bat, they might say,

"Oh, I think that's a right angle or a 90-degree angle."

And confirm, yes.

And then you might say, "Well, what about those other two angles?"

Well, if you put that in there, the wand is not very snugly.

Oh, gosh, there's a huge space in there.

So, this might be the time to say, "Well, we'll start losing it up a little bit

and start moving that wand."

Start moving that wand, try to see if you can get it to be all snugly in there.

So, okay, now they feel like... Okay, I think that's in there pretty snug.

I've got it in there. I think it's snug, tightened.

And follow this down to the point.

Oh, I get three dots. And this was 90, this must be 45.

Okay, so, 45-degree angle. 45 plus 90 plus what makes 180 degrees?

Teach them for a moment again. There you go.

Oops, I moved it. I didn't make it snug again.

So, go back in there, tighten it up, follow that. Yes, we still have a 45-degree angle.

Okay, now we've got another manipulative.

Well, I will tell you this happens to be a parallelogram.

And they might know something about parallelograms.

If they don't, they're gonna get a quick lesson on some things about angles with a parallelogram.

Okay, they might have...

We're gonna pretend that they have no idea what that angle is.

And so, I'm gonna say, "Well, give me a guess."

Now, first of all, is it acute, obtuse, 90?

And they always tell you... I hope... That is acute.

What do you think? What measurement do you think that might be?

I'm gonna guess 30 degrees, so tell them to go again.

And let's turn it around like they would be looking at it.

Okay, 5, 10, 15, 20, 25, 30.

I'm gonna say it's 30.

Okay, so, they would go ahead and tighten it up to 30.

And I'll tell them, "We don't know that it's 30, but we're just gonna try that out."

Now, which side? Nope, that's the obtuse angle. It must be this angle.

Let's just try and see if we can...

Pretend that this is a little boat that's going in to dock.

Is it gonna fit? Oh, it's not gonna...

It's gonna have to... Look at that wand move. Okay, just keep going and going.

Oop. Oh, we got it all snugly in there.

Okay, this is giving you a chance to kind of see how the thing works

in trying to manipulate it and hug it up, and having this thickness really, really helps.

Okay, they've got it all snugly. Tighten, follow down.

Oh, my gosh, we've got another 45-degree angle.

Okay, so, if this one... I wanna make sure I've got that all in there snugly.

Okay, if this is 45 degrees, what is the one over here going to be?

Well, if somebody's really clever, they might think that those are supplementary

and just be really sneaky and put that over on this side.

And, by golly, it turns out that they are correct, that this happens to be...

Well, let's see. What would the supplement of 45 degrees be?

Well, we'd have to say 180 minus 45, 135 degrees.

So, now we know that these...

And if you keep going, flip it over and find out what this other angle is,

that's going to be 135, as well.

And then if we go back the other way...

Let's make sure we've got both of these.

We've got... We have...

This angle is 45, this angle is 45.

This angle is 135, this angle is 135.

And they've learned a lot about parallelograms.

That opposite angles are congruent, maybe, and other things like that.

So, again, this is good for teaching other lessons,

but it gives them a chance to manipulate it.

And I have found that by using these 2-D manipulatives with some depth,

it makes it much easier for them to measure

because it's going to become more difficult the less height the angle has.

And we're gonna... I'm gonna show you another type of medium

that angles have been drawn in in just a moment.

**Captions by Project readOn**

APH Braille/Print Protractor: Part 13, Measuring the angles of 2-D manipulatives.

Presented by Susan Osterhaus,

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

Okay, now we're going to be measuring angles using the APH Braille/Print Protractor.

I did the drawing first because I feel like measuring is gonna take a little more time.

And what I recommend now after I've had a little experience

is that we start out measuring angles that "have some depth."

Angles really don't have depth, but what I'm talking about

is we're gonna use some 2-D manipulatives with a little bit of depth.

They're supposed to be really be... Not have any depth.

Otherwise, now they're three-dimensional.

But this thickness is really gonna help our students, I think, learn how to measure.

So, a teacher may give a student a manipulative like this

and say, "I would like you to measure the angles."

Now, some of them will already figure out this is a square and hopefully know

that that should be, all four of these angles should be 90 degrees.

So, you might say, "What do you think the angle is?"

And hopefully they'll say, "90 degrees."

So, you'll say, "Okay, go ahead and set your protractor to 90."

So, hopefully, by now, they've gotten familiar, and they know that 90 degrees

is that those three dots right there.

They're gonna line that up, tighten it up. Again, kind of turn that protractor around.

And they're just gonna slide that manipulative in and then check it.

Is that hugging up that corner? I mean, that's what you're trying to do.

Is this fitting right nicely in there?

And, by golly, it is.

And you might even like, you know, really to make sure

that you've got that in good and snug.

And tighten it up and follow it down.

By golly, you were right, that is 90 degrees.

And if you wanna go ahead and try it on all four to make sure that they're all 90 degrees,

you've just proved that.

So, start probably with something...

They already know what the measurement of those angles are.

Then maybe move to a triangle like this, which I won't name.

It does have a particular name.

But they might spot... Right off the bat, they might say,

"Oh, I think that's a right angle or a 90-degree angle."

And confirm, yes.

And then you might say, "Well, what about those other two angles?"

Well, if you put that in there, the wand is not very snugly.

Oh, gosh, there's a huge space in there.

So, this might be the time to say, "Well, we'll start losing it up a little bit

and start moving that wand."

Start moving that wand, try to see if you can get it to be all snugly in there.

So, okay, now they feel like... Okay, I think that's in there pretty snug.

I've got it in there. I think it's snug, tightened.

And follow this down to the point.

Oh, I get three dots. And this was 90, this must be 45.

Okay, so, 45-degree angle. 45 plus 90 plus what makes 180 degrees?

Teach them for a moment again. There you go.

Oops, I moved it. I didn't make it snug again.

So, go back in there, tighten it up, follow that. Yes, we still have a 45-degree angle.

Okay, now we've got another manipulative.

Well, I will tell you this happens to be a parallelogram.

And they might know something about parallelograms.

If they don't, they're gonna get a quick lesson on some things about angles with a parallelogram.

Okay, they might have...

We're gonna pretend that they have no idea what that angle is.

And so, I'm gonna say, "Well, give me a guess."

Now, first of all, is it acute, obtuse, 90?

And they always tell you... I hope... That is acute.

What do you think? What measurement do you think that might be?

I'm gonna guess 30 degrees, so tell them to go again.

And let's turn it around like they would be looking at it.

Okay, 5, 10, 15, 20, 25, 30.

I'm gonna say it's 30.

Okay, so, they would go ahead and tighten it up to 30.

And I'll tell them, "We don't know that it's 30, but we're just gonna try that out."

Now, which side? Nope, that's the obtuse angle. It must be this angle.

Let's just try and see if we can...

Pretend that this is a little boat that's going in to dock.

Is it gonna fit? Oh, it's not gonna...

It's gonna have to... Look at that wand move. Okay, just keep going and going.

Oop. Oh, we got it all snugly in there.

Okay, this is giving you a chance to kind of see how the thing works

in trying to manipulate it and hug it up, and having this thickness really, really helps.

Okay, they've got it all snugly. Tighten, follow down.

Oh, my gosh, we've got another 45-degree angle.

Okay, so, if this one... I wanna make sure I've got that all in there snugly.

Okay, if this is 45 degrees, what is the one over here going to be?

Well, if somebody's really clever, they might think that those are supplementary

and just be really sneaky and put that over on this side.

And, by golly, it turns out that they are correct, that this happens to be...

Well, let's see. What would the supplement of 45 degrees be?

Well, we'd have to say 180 minus 45, 135 degrees.

So, now we know that these...

And if you keep going, flip it over and find out what this other angle is,

that's going to be 135, as well.

And then if we go back the other way...

Let's make sure we've got both of these.

We've got... We have...

This angle is 45, this angle is 45.

This angle is 135, this angle is 135.

And they've learned a lot about parallelograms.

That opposite angles are congruent, maybe, and other things like that.

So, again, this is good for teaching other lessons,

but it gives them a chance to manipulate it.

And I have found that by using these 2-D manipulatives with some depth,

it makes it much easier for them to measure

because it's going to become more difficult the less height the angle has.

And we're gonna... I'm gonna show you another type of medium

that angles have been drawn in in just a moment.

**Captions by Project readOn**