Lesson video

Hi there.

Welcome to today's lesson.

My name's Mr. Peters.

And in this lesson today we're gonna continue to think about our understanding of angles and how we can use the language of acute, obtuse, and reflex angles in comparison to a right angle.

If you're ready to get started, let's get going.

So by the end of this session today, you should be able to say that, I can use the language of acute, obtuse, and reflex and compare these types of angles in comparison to a right angle triangle.

In this session today, we've got a couple of key words we're gonna be referring to throughout.

I'll have a go at saying them first, and you can repeat them after me.

Are you ready? The first word is angle, your turn.

The second word is right angle, your turn.

The third word is acute, your turn.

The fourth word is obtuse, your turn.

And finally the last word is reflex, your turn.

Let's have a think about what these mean then.

An angle is a measure of turn.

It shows how far something has rotated.

A right angle is a square corner or a quarter term.

And acute, obtuse and reflex angles will be defined throughout the lesson.

In this session today, we've got three cycles.

The first cycle is comparing angles visually, the second cycle will look at acute and obtuse angles, and the last cycle will be going beyond the straight line.

Let's get started with the first cycle.

Throughout the session today, we'll be joined by Lucas and Aisha, who as always will share their thinking as well as any questions that they have throughout the lesson.

So our lesson starts here with Aisha and Lucas, and they're making angles with their angle strips.

Aisha says that she's created an angle which is smaller than a right angle.

Here we go.

What do you think? Does that look smaller than a right angle to you? Lucas got an idea, "We could compare it to a right angle to check, couldn't we?" Let's do that now.

Here we go.

Lucas is using his angle strips to make a right angle.

He's folded this piece of paper twice to create the square corner, so we know that it is a right angle.

Hmm.

Lucas overlays Aisha's angle on top of the right angle.

He's lined up the pins, but he's saying he still can't quite decide whether Aisha's angle is larger, smaller, or the same as the right angle.

That's right, Aisha, isn't it? We need to line up one of the angle strips or one of the arms of the angle, don't we, so that they're in line with each other to be able to compare them.

Let's do that now.

There we go.

We can see now that the first two angle strips are now lined up with each other and we can use the second angle strips to identify the size of each of the angles.

So hopefully that's a lot more obvious, isn't it? We can see Lucas' right angle triangle, can't we, underneath, and we can see Aisha's angle on top and we can see that Aisha's angle is smaller than a right angle, isn't it? Ah, Aisha says, "Well, about this angle then?" She's created a different angle this time.

What do you think? Do you think it's larger or smaller than a right angle again? Let's check it again using Lucas' method of lining up the angles on top of each other.

Here's Lucas' right angle.

And again, we know that's a right angle 'cause we can check it's a square corner.

And now this time Lucas' lined up the arms. Hang on a minute, is that easy, for us to identify which angle is the largest? Hmm.

It's not as easy, is it? I'm not sure we've overlaid the angle strips correctly, have we? What does Aisha think? Aisha thinks we've used the wrong arms of each of the angle strips to compare them, haven't we? There we go, that's better this time.

Now both of our angles have a horizontal line, don't they? And we can compare the other arms of the angle strips to identify which angle is the largest.

Yep, and that is more like it, Aisha.

Well done, Luke, good spot.

Now we can see clearly that Aisha's angle is actually this time larger than a right angle, isn't it? And we know that because it is larger than a square corner, isn't it? Aisha's got another strategy for comparing these.

She says that we could also compare the angles by drawing on the right angle each time.

So have a look at her angle strips now.

She's saying that she knows that the right angle would be here like this.

There we go.

She's placed on the square corner and now we can mark on a dotted line to show where the right angle would be.

We can clearly see here that Aisha's angle is larger than a right angle or a square corner, can't we? Hmm.

But you're right, Aisha, sometimes that's easier to do than other times, isn't it? Have a look at your example here on this piece of paper.

We don't have a horizontal line or a vertical line, do we? So it's not as easy to identify where the right angle might be.

So Aisha's got a good idea.

She thinks maybe we could change our position in order to have a better look at this angle.

At the moment, we are looking at the angle from this point of view.

However, if we move ourselves so that we are now looking from this point of view, we'll be facing a horizontal line, won't we? And now it'll be easier to mark on the right angle and we can compare these a lot more easily, can't we? We could also, however, as Aisha pointed out, rotate the paper.

By rotating the piece of paper now we can see that we'd be facing a horizontal line straight away, which enables us to mark on the right angle, and again, we can compare as to whether it is a larger angle or a smaller angle than a right angle.

So if we revisit our right angle, there's a certain way in which we mark on a right angle, so we know that it is a right angle each time.

We can draw two small lines to show that it is a square corner.

There we go.

We've added on two small lines and now it looks like we've got a square in the corner, doesn't it? Which helps us identify that it is a square corner.

But how would we do this if we were looking at a larger angle or a smaller angle? So now you can see that our angle is larger than a right angle, isn't it? And in order to mark this, we would use what is called an arc.

Here I've marked on the arc.

This arc is a curved line which represents the angle between the two lines.

For bigger angles, the arc would look like this.

And for smaller angles, the arc might look like this.

Okay, time for you to check your understanding now.

Can you tick the angles where the arc has been marked on correctly? Take a moment to think.

Well, it is in fact the first, second and the third example.

I wonder why they've been marked on correctly.

That's right, the arc is joining the lines together to show the angle.

And it doesn't matter where that arc is drawn between those two lines as the first three examples show you.

However conventionally we usually draw a smaller arc, like for example, the first example here.

Why is the last one not correct? That's right, it's because it's not a right angle, isn't it? It's smaller than a right angle.

And we only use two smaller straight lines to mark on the square corner if it is a right angle.

Okay, onto question two now to check your understanding, can you match the angle to the description? Take a moment to have a think.

Okay, well the first one is a right angle.

Well done if you've got that.

The second one would be less than a right angle.

And the last one therefore be greater than a right angle.

Well done if you've got all of those.

Okay, time for us to have a practise now then.

What I'd like you to do is group the angle so that they are in a group which represents either smaller than a right angle, equal to a right angle, or larger than a right angle.

And then for task two, Lucas thinks that this is a right angle.

Can you explain why it isn't a right angle? Good luck with those two tasks and I'll see you back here shortly.

Okay, welcome back.

I'll give you a moment here to have a look at the way we've grouped these examples here.

So the first two examples are smaller than a right angle.

And remember we can use the dash line to represent a standard line sometimes.

So this would still classify as an angle that's been created.

The two in the middle are in fact right angles.

And remember it doesn't matter the length of the lines each time that have been used.

However, you may have noticed that we've used an arc to represent the right angle here instead of the two little lines to represent the square corner.

Actually these should represent a square corner, shouldn't they? So we should use the two lines in future.

And finally, the two examples on the right hand side represent two examples that are greater than a right angle.

Okay, and then reasoning why this isn't actually a right angle.

Aisha's saying, "Well actually if we rotate the shape slightly so that one of the lines is actually horizontal, it's easier to see as to whether this is a right angle or not." We know that the two lines that meet should create a square corner and this in fact hasn't created a square corner.

It's slightly larger than the square corner, so we would say that it isn't.

Okay, onto cycle two now then.

We're gonna start looking at acute and obtuse types of angles.

Okay, so Lucas is saying that, "We know a right angle creates a square corner or a quarter turn." However, what's the name we give to an angle which is smaller than a right angle or a quarter turn? Here, for example.

That's right Aisha.

An angle that is less than a right angle is known as an acute angle.

That's right, Aisha, acute actually means sharp, doesn't it? So I wonder why we call it an acute angle then.

Yeah, I think that's helpful, Lucas.

I think it's because of how sharp it looks at the point where it meets.

So let's have a look at a couple of examples then.

At the moment you can see that the dotted line is going to help us represent the right angle.

And any angle, here like any of these for example, would be an acute angle because they're all less than a right angle.

We know that an angle that is smaller than a right angle is known as an acute angle, should we say that together? An angle that is smaller than a right angle is known as an acute angle, even ones this small will be classified as an acute angle.

But that's right, Aisha, acute angles can look very different depending on the way that they're positioned, can't they? Here, for example, is an acute angle.

We can see that is less than a right angle still.

And we can see that because by drawing on the actual right angle, using a dotted line for the arm, helps us to identify that it is smaller than a right angle.

Here's another example.

Let's draw on the dotted line again.

There we go.

We can now see our right angle and that in fact is smaller than a right angle.

And here's one more example.

This definitely looks like an acute angle I think.

But we can draw on the dotted line to help us recognise that for certain.

And there we go.

We can clearly see that it is an acute angle.

Okay, time for you to check your understanding now.

Can you tick the acute angle? Take a moment to have a think.

That's right, it's B, isn't it? B is an acute angle because it is less than a right angle.

Yep, and that's the next logical question, isn't it Lucas? So if we know the angles smaller than a right angle are acute angles, what about angles that are larger than a right angle, like this one for example? Here we go, we've marked on the dotted line to help us represent where the right angle would be.

And we can clearly see that this angle is larger than a right angle.

Yep, that's right, Aisha, these types of angles also have a name.

They're also known as obtuse angles.

And isn't that interesting? Obtuse means blunt or not sharp.

So yeah, of course that makes sense, doesn't it? Acute meant sharp, doesn't it? So acute angles have a sharp point on them, whereas if you look at where this angle is created, the point of it is not as sharp as an acute angle, it's actually a little bit more blunt as you could say.

So if a balloon was to touch it, actually it might not burst it, it might just carry on floating up.

So let's have a look at a few examples now that are greater than a right angle.

Here you can see that the dotted line again has been put on to show where the right angle would be.

And we can now see that all of these angles here would be greater than a right angle.

So we would call these obtuse angles.

So we can say that an angle that is greater than a right angle, but in this case smaller than a straight line is known as an obtuse angle.

Let's say that together, shall we? An angle that is greater than a right angle but smaller than the angle on a straight line is known as an obtuse angle.

Yep, and once again, they look very different depending on how they're positioned sometimes.

Here's another example.

Do you think this is an acute or obtuse angle? That's right, it's definitely an obtuse angle and we can mark on the dotted line to show where the right angle would be and we can see that it is larger than a right angle or a square corner.

Here's another example.

Yep, I can mark on the dotted line this time to show where the right angle would be.

And again, we can see that it is larger than a right angle.

And one more example.

Again, notice here how the lines are different sizes, it doesn't matter does it? But we can clearly see that the right angle would be placed here.

So therefore it's an obtuse angle because it is larger than a right angle, but less than the angle on a straight line.

So Lucas is now saying that he thinks we could describe an obtuse angle as a right angle and a bit.

Let's see what that would look like.

Here we go.

We can mark on our right angle, can't we, and change the arc so that we've got our right angle and then add on the remaining bit of the arc that we had from the previous obtuse angle? So we can clearly see that this represents a right angle and a bit, which is a lovely way of thinking about it, I think Lucas, it certainly helps me remember the difference between acute and obtuse angles.

Here's another example.

Here's a obtuse angle.

Let's mark on the right angle and add on the two little lines to represent the square corner.

And now we can add on the additional part, which was the remaining part of the obtuse angle.

And again, we can call this a right angle and a bit, can't we? Okay, time for you to check your understanding now.

An obtuse angle is greater than a something and less than a something? Is it A, B or C? Take a moment to have a think.

That's right, it's B isn't it? An obtuse angle is greater than a right angle, but less than the angle on a straight line.

Okay, and on for our task for this cycle now then.

Can you draw A, an ordinary acute angle, B, a peculiar acute angle, or C, an acute angle that nobody else will think of drawing? For task two, I'd like to do the same thing, but this time I'd like to do it for an obtuse angle.

So can you draw for A, an ordinary obtuse angle, can you draw for B, a peculiar obtuse angle, and for C, can you draw an obtuse angle that nobody else will draw? And then finally what I'd like you to do is have a look at the image here and I'd like you to mark on as many acute, obtuse, or right angles that you can see in the image.

You'll also need to label each one so that we know which ones you found.

Good luck with those three tasks and I'll see you back here shortly.

Okay, welcome back.

Let's have a look through them.

Here's some examples that you may have drawn.

Here the top one is what I would call probably an ordinary acute angle.

The reason for that is because it's got the horizontal line and lots of people often draw angles based on either a horizontal or a vertical line.

Therefore that makes B, a rather more peculiar acute angle because again, this time we don't actually have a straight, vertical or horizontal line to draw the angle from.

And for C here, I've had a go drawing one that nobody else will draw.

You can see that one of the lines is incredibly long and one of the lines is incredibly short, but the lines are straight at the point that they meet and it is still less than a square corner.

So we would say it is an acute angle still.

Here are three examples of obtuse angles.

Have a look at the first one, again here you can see I've drawn a horizontal line, again, which is probably more regularly seen than other types of obtuse angles.

The second one, this time is really, really close actually to the straight line, but it is not quite a straight line, is it? And we know that anything which is greater than a right angle, but less than the angle on a straight line is still obtuse.

So this is actually probably one of the largest types of obtuse angles that you can create.

And then finally, one that nobody else will draw again.

You can see here I've changed the length of the lines hopefully, and we can see that it is greater than a right angle and less than the angle on a straight line.

So it is in fact an obtuse angle.

Okay, here's that image again then.

And here's some of the examples that we've managed to find.

Let's mark them on as we go.

So here the corner of the shelf, that would be a right angle.

Here, where the line of the bookend meets the line of the shelf, that would also be a right angle.

Hmm, where the books lean against each other, we've actually created a right angle here as well.

We've got an obtuse angle here at the top of the lampshade, and we've got another right angle here from the cubes.

Hmm, this one is an acute angle here from the plant port, isn't it? And where the plant port actually meets the shelf, we can also find another acute angle.

You may have found some other ones, which is equally great.

Well done.

Hopefully you've managed to find quite a few as well.

Okay, that's the end of our first two cycles and now we're moving on to cycle three, going beyond the straight line.

So Lucas is asking then, "How can we describe the angle on a straight line then?" Well let's create one then.

Here are two lines meeting together and they create a straight line, don't they? Here is the angle on a straight line.

Yeah, and that's right Aisha, we know that the angle is greater than an acute angle, isn't it? Because it's a right angle and a bit as we can see here.

But actually Lucas is pointing out, well right angles and a bits.

Well a right angle and a bit we would usually define as an obtuse angle.

However, here this bit actually looks like another right angle.

There we go.

It is, isn't it? So it is actually greater than an obtuse angle because it's not a right angle and a bit, it's actually two right angles, and we can say that where two lines meet together to create a straight line then the angle is equivalent to two right angles.

Have a look this time, what do you notice? That's right Lucas.

The angle is now bigger than two right angles, isn't it? We've no longer got a straight line.

The first line has changed slightly and the angle is now bigger than two right angles.

We call this type of angle a reflex angle.

If we were to mark on our right angles, there we go.

There's the first right angle we can now see.

And here's another dotted line to help represent where the second right angle would've been.

We can see that actually it's two right angles here and an extra bit, isn't it? So we can say that a reflex angle is any angle which is greater than two right angles up to a whole turn.

Let's have a look at some other examples then.

All of these here would also be reflex angles, wouldn't they? Oh, hang on, what have you noticed, Lucas? You're asking us to wait.

Ah, a good spot.

Actually this would represent three right angles at this point, wouldn't it? Is this still a reflex angle then? It is, that's right.

Anything which is also greater than three right angles up to a whole turn is also known as a reflex angle.

So we can say that any of these would also be a reflex angle.

So we can say that any angle that is greater than the angle on a straight line up to a full turn is known as a reflex angle.

We know that we have two right angles on a straight line.

Let's say this together, shall we? An angle that is greater than the angle on a straight line up to a full turn is known as a reflex angle.

You've heard that word reflex before, haven't you, Lucas? That's a great example of where reflex has been used in everyday life.

Goalkeepers when they're playing football have to make reflex saves, don't they? A reflex save might be for example, when they have to make a last ditch save to stop the ball from going into the goal.

So you're right, they have to have great reflexes to help them save the ball, don't we? That helps us maybe think about the idea of a reflex angle.

If you have great reflexes, you have to be incredibly supple and able to move into awkward positions.

So here you can see the angle that the goalkeeper has created with his body would actually be a reflex angle based on the save that he's made.

Looks like Lucas' thought of another great example for where he might find reflex angles in everyday life.

He has a roundabout.

And when a car enters the roundabout and drives around the roundabout, we can see that the car has actually driven around the roundabout creating a reflex angle.

The lines represent where the car joins the roundabout and left the roundabout.

So the journey that the car has made has included a reflex angle with the degree of turn that they have made.

Yeah, that's a bit like me to be honest, Aisha, I often miss the exit for the roundabout and have to go all the way round again, it's not just your dad, I promise you.

Okay, time for you to check your understanding again now.

Can you tick the image that represents a reflex angle? Take a moment to have a think.

That's right, it's A, isn't it? A, shows us a reflex angle because it is greater than the angle on a straight line and it's a little bit more, isn't it? And anything that is greater than the angle on a straight line up to a whole turn is known as a reflex angle.

Here are two lines here that have joined to meet each other.

Can you draw on the reflex angle for me? Take a moment to have a think.

That's right.

The reflex angle would be drawn on like this, wouldn't it? Okay, and now time to practise for the last time today in our lesson.

What I'd like to do for this first task is draw on all of the angles that you can see in each of the images.

You'll need to draw on an arc each time and label each one of the angles that you have seen.

The first one has had the arcs drawn on for you.

And then for task two, we've got a roundabout from Malaysia known as the Putrajaya Roundabout and is one of the most famous roundabouts in the world because it is the largest roundabout in the world.

It has 15 entry and exit points.

In fact, it's so big it actually has a city in the middle of it.

Our task here asks you to think about how many different reflex angles could you create by entering and exiting the roundabout at different points.

How many solutions do you think there are and how will you know that you've got them all? Here's a quick example that Aisha has come up with.

You could enter here at the bottom right hand side of the roundabout, rotate round the roundabout, and then exit the roundabout on the other side here.

This would create a reflex angle.

Good luck with those two tasks and I'll see you back here shortly.

Okay, welcome back.

Let's go through the angles here that we could find them.

So for the first one, we have a reflex angle and an obtuse angle.

The second one, we've got a reflex angle and an acute angle on the inside here.

This time we've also got our reflex angle on the outside, but we've also got an acute angle and another acute angle.

And then finally, we've got a reflex angle here.

We've got a small acute angle and we've also got a larger obtuse angle here.

So that's a really interesting observation that you've made there, Aisha.

You've noticed that the opposite angle to a reflex angle can be an acute angle, an obtuse angle, or a mixture of both.

Well done for spotting that.

Okay, and then visiting Malaysia for our roundabout.

Aisha thinks she's realised that, "Every entry point on the roundabout has either six, seven, or eight exit points for each car to have turned a reflex angle around the roundabout." I wonder how many different reflex angles you were able to find and whether you were equally able to find all of them.

Okay, and that's the end of our lesson for today.

To summarise what we've been thinking about, we should now hopefully be able to say that you can compare the size of angles visually by comparing each of the angles to a right angle.

Acute angles are angles that are less than a right angle.

Obtuse angles are angles that are greater than a right angle, but less than the angle on a straight line.

And reflex angles are angles that are greater than the angles on a straight line, but less than a whole turn.

Thanks for joining me today.

Hopefully you're feeling a lot more confident with your understanding of acute, obtuse and reflex angles and can go about estimating those in your everyday lives when you see them for yourselves.

Take care, I'll see you again soon.