Lesson video

Hi there.

How are you today? <v ->My name's Mr. Peters.

</v> And in this lesson today, we are gonna be thinking about how we can describe static angles using the standard unit of measure of degrees and how we can compare these angles to the size of a right angle.

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

So by end of this lesson today, you should be able to say that I can describe static angles using a standard unit of measure of degrees in comparison to right angles.

Throughout this lesson today, we've got two keywords we're gonna be using.

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

The first word is degrees.

Your turn.

And the second word is estimate.

Your turn.

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

A degree is a unit of measure for angles.

And to estimate is to find an answer that is close enough to the right answer, usually with some thought or calculation involved.

This lesson today is broken down into three cycles.

Firstly, we're gonna be thinking about estimating acute angles.

Then we're gonna be thinking about estimating obtuse angles.

And finally, we're then gonna move on to thinking about estimating reflex angles.

Let's get started with the first cycle.

Throughout this lesson today, we'll be joined by both Sofia and Jun.

As always, they'll be sharing their thinking as well as any questions that they've got throughout the lesson, which hopefully will help guide our thinking.

So our lesson starts here with Sofia and Jun actually doing some artwork.

They've been asked to create some straight line artwork.

Sofia says she loves making straight line artwork because it has loads of maths in it.

Jun on the other hand, says he likes this type of artwork because he can make a mess.

Well, Jun, I'm not sure making art is necessarily making a mess each time, is it? It depends on the taste of your art, doesn't it? Let's have a look at what Sofia's produced.

There we go.

That's a really bright and vibrant piece of art, isn't it, Sofia? Hm.

I wouldn't say it's a funky mess, Jun.

I think it's really interesting.

It certainly caught my eye.

Sofia and Jun then go on to compare the different angles that they can find within the shape itself.

Let's start by looking at the acute angles then.

As we know, an acute angle is anything that is less than a right angle.

We should also know from previous learning that an acute angle is any angle between the value of zero and 90 degrees.

So we can use a number of tools to help us estimate and identify which angles are actually acute angles.

Here, we've now got some angle tools and you can see that they range in different sizes.

We've got one that's 10 degrees, 20 degrees, 30 degrees, 40 degrees, and then we've also got one which is 90 degrees, a right angle.

So let's have a look.

Can you have a look for yourself? Can you see any angles that you think might be an acute angle? Take a moment to have a think for yourself.

Here's one that's Sofia's found.

She says it's still quite large and that she knows that a right angle is 90 degrees.

And so this one is slightly less than a right angle.

So she's estimated that it's about 80 degrees.

Let's use our angle tools to help us check this, shall we? If we take the 90 degree angle tool and layer it over the top of the shape, we can see that it is, in fact, less than 90 degrees, can't we? And how much less than 90 degrees is it? Well, it's not a lot less is it? But it is a little bit, so actually 80 degrees seems to me like a good estimate, Sofia.

And I think Jun agrees.

Jun's turn now looking for a different angle.

He's found this one here.

What do you think? Could you quickly estimate how big do you think this angle is? Jun's saying that it's a lot smaller than 90 degrees and in fact, it's closer to zero degrees than it would be to 90 degrees.

So Jun has gone for an estimate of 30 degrees.

Shall we check again using our tools? Sofia says it's definitely less than a right angle.

And let's check that.

There we go.

We can now place our right angle in here and we can see that it is significantly less than a right angle.

And now let's use our 30 degree tool to check.

There we go.

Ah, look, what do you notice? In fact, it's actually less than 30 degrees, isn't it? So let's check that with a 20 degree tool, first of all, to see if it's bigger or smaller than that.

Here we go.

What do you notice here? Well, actually, it's quite a bit less than 20 degrees, isn't it? It's almost half of that.

So we can say that this angle is actually going to be roughly around 10 degrees.

Hmm, so we could probably say the Jun's estimate was slightly bigger than maybe it could have been.

So what that helps us to understand is we can get a sense of the size of each of these multiples of 10 degrees to really help us inform our understanding of the size of angles, roughly.

Let's take a moment to check our understanding.

What is the largest angle an acute angle can be? Take a moment to have a think.

That's right.

It's C, isn't it? The largest angle size that an acute angle can be is, in fact, 89 degrees.

We know that 90 degrees is a right angle.

So one degree less than that would be 89 degrees, and that is, in fact, still an acute angle.

Exactly that, Jun.

Well explained.

Fantastic thinking.

Here's another one.

Can you estimate the size of this angle? Take a moment to have a think.

Hmm.

What did you estimate then? Well, to me it looks like it is, again, just slightly less than a right angle.

So I'm gonna estimate that it's about, hmm, 85 degrees.

Hmm.

Well let's place our right angle checker on.

There we go.

We can definitely see that it's less than 90 degrees, and it is just marginally less, isn't it? So 85 degrees might be a good estimate.

And wow, that's exactly what Sofia went for as well.

Great thinking, Sofia? Hmm, I think any estimate that's over 80 and obviously less than 90 would be a good estimate to put.

Okay, time for us to have go at some practise for us now.

What I'd like you to do is to use the angle tools to estimate the size of each of the following angles.

Once you've done that, what I'd like you to do is to draw a second line on each of the examples here, which will enable you to draw an angle of the size that is written underneath each of the lines.

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

Okay, welcome back.

Let's see how you got on.

Here are some rough estimates that we came up with for each of the examples.

You may have come up with something similar to this.

As long as your estimate is something similar to this, then we can say that that was a good estimate.

So the first one we estimated to be roughly 45 degrees.

The second one we estimated to be roughly 70 degrees.

The third example we estimated to be roughly 85 degrees.

And the last example we estimated to be roughly 55 degrees.

Well done if you managed to get close to those.

And then for the second task here, you had to have a go at drawing the other line to create each of the angles that are written beneath.

Here's what we came up with.

Here's the first one, here's the second one, here's the third one, and here's the fourth one.

So your angles may have been either in the opposite direction, but also they may have been slightly smaller or slightly larger, and that's absolutely fine.

You might like to get your angle tools out and use them to check for each one as well.

Well done if you managed to come up with something similar to that as well.

Okay, that's the end of cycle one.

Now we're moving on to cycle two, Estimating Obtuse Angles.

Okay, so let's remind ourselves about what an obtuse angle looks like.

Here we can see we've got a right angle and we know that an obtuse angle is greater than a right angle.

So any of these angles here, for example, would represent obtuse angles.

We also know that an obtuse angle has to be less than the angle on a straight line.

So at this point here, we can now see that we've got a straight line and we've rotated through two right angles to get to there.

We know that a right angle is 90 degrees, and so two right angles would be equivalent to 180 degrees.

So the angles on a straight line sum to 180 degrees.

This is not an obtuse angle, we just refer to this as the size of the angle on a straight line.

So let's revisit Sofia's artwork then.

We can also use our angle tools to help us with this now and we can add on an angle tool that we now have to help us.

We could use this one here.

This is the angle on a straight line and we know that is 180 degrees, don't we? Sofia and Jun now begin to start looking for angles that are greater than a right angle and less than the angle on a straight line.

Sofia thinks she's found one.

Let's check it out.

We can use our right angle angle tool to check if it is greater than the right angle, which it is.

We can clearly see that already.

Great spot, Sofia.

So now that we know it's definitely an obtuse angle, we can take a closer look, can't we? Here we go.

This is the angle that Sofia found.

We know it's greater than 90 degrees.

How much greater than 90 degrees do we think it is? Sofia thinks it's about another 10 degrees greater than 90 degrees.

So she says she thinks it's about 100 degrees.

Hmm, Jun thinks it's actually more than 10 degrees.

He thinks it's roughly about 30 degrees more.

So he's gone for an estimate of 120 degrees.

Let's use our angle tools again to help us.

If we keep our 90 degree angle there, we can now add on a 20 degree angle to check.

Ah, look, there we go.

So now we've got a 90 and a 20 degree angle, so that would sum to 110 degrees.

However we can see that that's too much, isn't it? It's less than 110 degrees, isn't it? So that's better, Jun, you're right there.

We know it's less than 110 degrees, but we know it's greater than 90 degrees.

So I think any estimate between 100 and 110 degrees would've been a good estimate to have come up with.

Well done, Sofia, you came close, didn't you? Jun's turn now to find another example.

Here's one that he thinks he's found.

Let's check that one out then.

Zooming in a bit closer.

By isolating the angle, we can really think about the size of that angle in particular now, can't we? Sofia says, at the moment the lines of the angle that we want to look at aren't actually horizontal or vertical at this point.

Let's rotate our shape to help us with this.

There we go.

We've now kept the same angle but we've just rotated the shape slightly and we've now got a horizontal line which is gonna help us determine where the right angle would be in our example.

So as you can see, we could place on the right angle tool to help us.

And now we can clearly see that this angle is greater than 90 degrees, isn't it? So as we know it is an obtuse angle, we now need to identify how much greater than 90 degrees we think it is.

This time, Sofia's gone for 130 degrees.

What about you, Jun? Hmm.

Jun's gone slightly less this time.

He thinks it's about 120 degrees.

Well, once again, let's use our angle tools to help.

Let's add on another 30 degree angle to see.

There we go.

We've now got 90 degrees and another 30 degrees, and we know that 90 plus 30 is equal to 120.

So the size of the angles we've now got is 120.

Is it greater or smaller than the combined size of the angle tools? That's right, the angle is actually slightly larger, isn't it, still? So we know that our angle is gonna be slightly larger than 120 degrees, and because it's ever so slightly larger than 120 degrees, it's probably closer to 120 than it is to 130.

So I think you're right, Sofia, I think Jun was the closest this time with his estimate of 120 degrees.

Great work, Jun.

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

Can you tick the degrees that would represent an obtuse angle? Take a moment to have a think.

That's right.

B would represent an obtuse angle and C would represent an obtuse angle.

And why is that? That's right.

We know that an obtuse angle is an angle that's greater than 90 degrees and less than 180 degrees.

And 91 and 109 are both greater than 90 degrees and less than 180 degrees.

Well done if you've got those two.

And here's another check for our understanding now.

Can you take the best estimate of this angle? Take a moment to have a think.

That's right, I think 120 would be a good estimate for this one here as well.

I wonder what you came up with.

We know it's definitely greater than 90 degrees, don't we? And it's actually, it looks like about another 30 degrees more than 90 degrees.

So 120 would be a good estimate.

So 120 would be a good estimate I think.

Okay, time for us to practise again now then.

What I'd like you to do is have a look at these four different lines where the zero degree is marked.

What I'd like you to do is draw on the second line to show an angle of 130.

Once you've done that, I'd also like you to have a go at doing the same for these examples here.

These straight lines at the moment all represent where the zero degree would be marked.

And then I'd like you to also draw on an angle, which is the size of 130 degrees for each of these.

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

Okay, let's see how you got on then.

So as you can see here, for A, we've drawn on what we think 130 would look like.

We've also done the same for B and then for C and then also for D as well.

Hopefully you were able to think about rotating the angle each time as the zero degree mark changed position each time.

That might have helped you to think a little bit more about where each of these angles would be with regards to their size so they are consistent.

This time, we've tried to make it a little bit more trickier here, haven't we? Because the angles aren't actually horizontal or vertical at this point.

So you're gonna have to think really carefully about where maybe that 90 degree mark was each time and then add on the extra 40 degrees to make the 130.

Yours may be very similar to this, hopefully.

Well done if you managed to come up with those for yourself too.

Okay, that's the end of cycle two.

Now onto cycle three, Estimating Reflex Angles.

So Sofia and Jun are now discussing what a reflex angle looks like.

We know that a reflex angle is an angle that's greater than 180 degrees or greater than the angles on a straight line.

We know the angle on a straight line is in fact 180 degrees, which we know is also equivalent to two right angles.

So we can say that if we rotate through more than two right angles up to one whole turn, then any of these angles would be a reflex angle.

Let's have a look at some examples.

All of these examples here would be reflex angles.

And look here, we've now gone through a turn of three right angles.

If we carry on through this, all of these continue to be reflex angles all the way up to one full turn.

So a reflex angle is any angle between 180 degrees and 360 degrees.

Just to be clear, 360 degrees is actually a full turn.

So we don't classify 360 degrees as a reflex angle.

Also, we know that 180 degrees is the size of the angle on a straight line.

So this also cannot be classified as either an obtuse angle or a reflex angle.

The smallest reflex angle we could make to the nearest whole number would be 181 degrees.

And the largest reflex angle we can make to the nearest whole degree would be 359 degrees.

So, returning to Sofia's artwork again.

Sofia thinks she's found a reflex angle.

Here's one.

Let's have a look at it a bit more carefully again.

There we go.

We can see the size of the angle now that we've drawn on.

And Jun is saying it's definitely larger than the angle on a straight line, and we can see that, can't we? There we go.

There's our angle on a straight line.

So it's definitely larger than that.

So how are we gonna find out what this extra part is? Well, Sofia's got a good idea.

She thinks that actually this is less than 90 degrees away from a full turn.

So it actually has to be greater than a turn of three right angles.

We know that a turn of three right angles would be 270 degrees, so it needs to be greater than 270 degrees.

So which is why Sofia's gone for 290 degrees.

I think you're right, Jun.

I think it is quite tricky to estimate.

So we could use our angle tools also to help us here, couldn't we? Let's add on another 90 degrees like Sofia suggested.

There we go.

Now you can see that we've gone through a turn of 270 degrees.

We know that the angles on a straight line sum to 180 degrees, which is two right angles.

And now we've included another right angle.

So we've got 270 degrees altogether so far.

Question is how much more than 270 degrees is it? Jun thinks we should try using a 30 degree tool to help us.

Let's have a look.

Wow, look at that.

Spot on, Jun.

It's almost right there, isn't it? So you've got 270 degrees plus an additional 30 degrees, so that gives us an angle of roughly 300 degrees.

So what do you think about that? I agree, Jun.

I think Sofia's estimate there was a really good estimate.

290 is quite close to 300, isn't it? And I think it's quite tricky to estimate those reflex angles.

So well done if you managed to come up with something similar for yourself when you were estimating.

Okay, time for us to check our understanding again now then.

Can you tick the reflex angles? Take a moment to have a think.

That's right.

It's both B and C, isn't it? Both B and C are greater than the angle on a straight line of 180 and they are less than a full turn of 360 degrees.

Well done if you've got those two.

Okay, time for you to have a quick go at estimating now as well then.

Can you estimate the size of this reflex angle? Take a moment to have a think again.

Well, Sofia thinks it's a little bit more than 180 degrees, so she's gone for an estimate of 190 degrees.

Did you come up with something similar to that? I think 190 degrees is a good estimate, Sofia.

Well done, you.

Okay.

And now onto our final tasks for today then.

What I'd like to do is have a look at the size of all of these angles that have been written down and group them under the right heading.

The headings that we've got are acute, obtuse, reflex, or a multiple of a right angle.

So you need to place each of the sides of these angles under each one of those headings.

And then for task two, what you need to do is create your own piece of straight line art.

Once you've done that, you can then ask a friend to estimate the size of each of the angles that you have created in yours.

Equally, find a friend's piece of artwork and estimate the size of their angle too.

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

Okay, let's see how you got on then.

So the angles that were acute were in fact, four degrees and 89 degrees.

The angles that were obtuse were 108 degrees and 179 degrees.

The angles that were reflex angles were 300 degrees, 181 degrees, 359 degrees or 189 degrees.

And then finally, any angles that were multiple of a right angle.

Well, we know a right angle is 90 degrees, so we're looking for multiples of 90.

So 90, 180 degrees, 270 degrees and 360 degrees, we'd all classify as multiples of a right angle.

Well done if you've got all of those.

That's a great extension, Sofia, if you'd like to, you could have a go at putting some of your own examples under each heading as well.

And here's an example of Jun's artwork that he's created this time.

I can see a whole range of angles on here, Jun.

I think I can see acute, obtuse, and reflex angles.

How many can you see on Jun's artwork? Can you estimate the size of any of them? Okay, and that's the end of our learning for today.

Hopefully you've enjoyed that lesson and you're feeling a lot more confident thinking about the size of acute, obtuse or reflex angles and how we can estimate the size of these using the standard unit of measure of degrees.

To summarise our thinking, we can say that acute angles can have a value of anything between zero degrees and 90 degrees.

We can say that obtuse angles have a value of anything between 90 degrees and 180 degrees, and reflex angles we can say have a value of anything between 180 degrees and 360 degrees.

Thanks for joining me today.

I really enjoyed that lesson.

Hopefully you did too.

Take care and I'll see you again soon.