Lesson video

Hi there.

Welcome to today's lesson.

My name is Mr. Peters and in this lesson today we're gonna be thinking about a really useful skill.

We're gonna be thinking about how we can measure the size of an angle using a protractor.

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

So by the end of this lesson today, you should be able to say that I can measure the size of an angle accurately using a protractor.

Throughout the session today, we've got a number of key words we'll be referring to.

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

The first word is angle, your turn.

The second word is point, your turn.

The third word is vertex, your turn.

And the last word is scale, your turn.

Just a reminder of what these words mean, shall we? An angle is a measure of turn.

It shows how far something has rotated.

It is often displayed as the rotation between two line segments.

A point is an exact location, it has no size, only position.

A vertex is a point where two or more lines meet and a scale is a number line with equal divisions for equal values.

Today's lesson's broken down to two cycles.

The first cycle is measuring acute and obtuse angles, and the second cycle is measuring reflex angles.

Let's get started with the first cycle.

For our lesson today, we're joined by Laura, Jun and Izzy.

They'll be sharing their thinking and any questions they've got to help us with our learning along the way too.

So let's start our thinking here today.

An angle describes how much something has turned, doesn't it? We could say that a door turns as it opens.

We can say that a wheel is something else that will also turn as it moves, as it moves forward or backwards.

And also a person can turn, can't they? They can turn to face a different direction each time.

So we know that angles can be measured from a point or a vertex.

If we have a look at the wheel here, for example, we've got a fixed point in the centre of it, and we can measure the degree of rotation that wheel goes through by using these lines to show where the wheel started and where the wheel finished.

We can also represent this on paper as well, and we can use two lines here.

And where these two lines meet, we create something known as a vertex.

So the size of an angle describes the amount of turn between the two lines.

And as we know from prior learning, the angles can be measured using numbers and the standard unit of measure for angles, which is known as degrees.

A protractor is an instrument that we can use to measure angles.

To measure an angle using a protractor, we need to place the middle spot on the protractor, on the vertex or the point, as we know, this is where the two lines meet.

We now need to turn the protractor so that one of the zeros is over a line that forms the angle.

Protractors have what we call a dual scale.

It means there are two scales.

There is one on the outside and one on the inside.

Before you measure an angle, you need to look very carefully to identify where your zero is and to determine whether you are using the inside or the outside scale.

Once we've done that, we can now follow that scale to the next line and read the value where the line crosses the scale.

In this example, we've measured in a clockwise fashion.

We can see here that the line is pointing to 112 degrees.

So the size of the angle is 112 degrees altogether.

So to summarise how to measure using a protractor, we need to place the middle spot of the protractor on the point or vertex.

We need to turn the protractor so that one of the zeros is over a line that forms an angle.

We need to check which scale has the zero on that line, and then we need to look for where the other line of the angle crosses the scale and then read the value.

Angles can be measured in a clockwise fashion or an anticlockwise fashion.

The direction you use depends on the position of your protractor.

As a result, this then affects the scale that we use.

If we're measuring the angle in a clockwise direction, then we'll need to use the outer scale.

If however, we're going to measure the angle in an anticlockwise direction, we'll need to use the inner scale.

Sometimes when we're measuring an angle, one of the lines doesn't actually quite make it to the scale itself.

Have a look at this example here.

Can you see both of these lines don't quite reach to the numbers that we need.

Therefore, sometimes it can be difficult to make this reading.

You may therefore decide to extend the lines in order to help you with this reading.

There we go.

We've extended both the lines in this example here.

And now we can replace the protractor and now we can go through the same process to measure the size of the angle.

And that's right, Laura, you only really need to extend the line of the angle that you are going to be reading from.

As long as the first line is lined up with the zero, then the other line is the one that we need to extend towards the numbers so we can read the scale more easily.

Okay, time for you to check your understanding now.

Have a look at the examples here, in which example has the protractor been placed correctly? Take a moment to have a think.

That's right, it's angle B, isn't it? The middle spot of the protractor needs to be placed on the point or the vertex, and one of the lines must be placed in line with the zero line.

Let's have a look at A, for example, what was the issue here? Well, one of the lines was placed on the zero line, but the vertex wasn't placed at the middle spot, was it? And let's have a look at C, what was the issue here? We've got a similar problem here, haven't we? One of the lines is also on the zero line, but again, the middle spot of the protractor wasn't placed on the vertex, was it? Okay, have a look at these examples here again now then.

Which of the protractors have been placed correctly this time? Take a moment to think.

That's right, it's both A and C this time, isn't it? We can see that the vertex is placed on the middle spot and there is a line which is lined up with the zero on both examples A and C.

Let's have a look at B, what's the issue here? We've got the vertex lined up with the middle spot, and one of our lines is lined up with the zero, isn't it? So why is this not correct? Well, the protractor isn't overlaying over the other line is it? And therefore we can't read a value in this example.

And here's one more quick check.

The diagram shows a part of the protractor, which is of course measuring an angle.

What is the size of the angle? Take a moment to a think.

That's right, it's A, it's 58 degrees.

And the reason for that we know is because the middle spot has been lined up with the vertex, we've got one line lined up with the zero.

And because we're measuring in an anticlockwise direction, we need to use the inner scale this time.

So following the zero of the inner scale all the way up and around, we can see that it takes us to 58 degrees.

Well done if you managed to get that too.

Okay, time for you to have a practise now.

Can you measure the size of each of these angles here? And then Jun and Laura are having a go at measuring this angle here.

Jun thinks the angle is 30 degrees, whereas Laura thinks the angle is 150 degrees.

Can you explain who's correct here? Good luck with those two tasks and I'll see you back here shortly.

And then also for task three, what I'd like to do is have a go at measuring the size of the angles within each of the shapes here.

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

Angle A can be measured like this and has an angle of 85 degrees.

Angle B can be measured like this and has an angle of 130 degrees.

And finally, angle C can be measured like this and has an angle of 28 degrees.

So for Laura and Jun, who was correct then? Well, that's right, Laura was correct.

Firstly, we know it's an obtuse angle.

Jun said it was 30 degrees, which we know isn't obtuse, is in fact acute.

Therefore, Laura is reading of 150 is an obtuse angle, which is more likely to be correct, isn't it? Also when we measure it, we can see that Jun has confused which scale to read from.

Jun has in fact read from the inside scale in an anticlockwise fashion, when in fact the line is lined up with the zero on the outside scale.

So we would need to measure in a clockwise fashion.

And then finally, these shapes here, angle A has a value of 40 degrees, angle B has a value of 100 degrees, angle C has a value of 80 degrees, and finally, angle D has a value of 135 degrees.

Hopefully, you manage to get all of those two.

Okay, that's the end of cycle one.

Moving on to cycle two now then, measuring reflex angles.

Okay, we know that an angle greater than 180 degrees is known as a reflex angle.

We've got a number of different methods for how we can measure a reflex angle.

Let's have a look at the ways that Jun, Laura and Izzy come up with.

Firstly, we can see that Jun has extended the zero line from where the protractor starts.

He's made this a little bit longer and said that the degree of rotation from the zero line to the point of which he's extended the line to is equal to 180 degrees, 'cause we know that the angles on a straight line sum to 180 degrees.

All Jun now needs to do is measure the remaining part of the angle.

So he is lined up his protractor now with the zero from the outside scale, and we're going to use the outside scale to measure in a clockwise direction.

So if we follow that bit round, we can now see that the line takes us to 66 degrees, therefore that additional part of the angle is worth 66 degrees or has a value of 66 degrees.

Therefore, we can now add the 180 and the 66 degrees together, which gives us a total of 246 degrees.

That's a nice strategy, Jun.

Laura knows that a full turn is 360 degrees, therefore we could measure the inside angle and then we can subtract that from the total amount, can't we? Laura measures the inside angle.

She finds that's 114 degrees.

Now that we know this part is 114 degrees, we can subtract that from a whole turn of 360 degrees to find the remaining angle.

So 360 degrees minus 114 degrees is also equal to 246 degrees.

And then finally, Izzy has actually used a different strategy completely.

She's changed her protractor to use what's called a 360 degree protractor or a circle protractor.

You may or may not have seen one of these before, and some schools are more likely to have them than others, and that's absolutely fine.

There's no right or wrong to this.

So being able to use this strategy is also useful if this is the only protractor you have to hand.

Of course, this time Izzy has lined up the middle spot with the vertex and lined up one of the lines with the zero.

And you can see here we're gonna have to measure in a clockwise direction, which takes us to 246 degrees, which we've measured from the previous two examples as well.

Nice work you three.

Okay, time to check for understanding now.

Izzy tries to use Jun's method of finding 180 degrees, then adding on the remaining angle.

Can you explain her mistake? Take a moment to have a think.

That's right, Izzy has extended it and made the 180 degree line, hasn't she? But then she's gone on to measure the wrong angle.

She's used the incorrect scale.

Looks like she's used the inside scale rather than the outside scale.

And therefore she's measured it at 70 degrees when in fact it's actually 110 degrees, the size of the extra part of the angle.

So the actual size of the reflex angle should be 290 degrees altogether.

Okay, take a moment now as well to check your understanding here, by measuring this reflex angle for me.

Izzy decided to use Laura's strategy.

So we're gonna place the protractor on and we're gonna measure the internal angle.

We can see that the internal angle in this case is 75 degrees by using the inside scale.

And then we can subtract that 75 degrees from 360, which is the size of a whole turn, isn't it? And that leaves us with 285 degrees.

Well done if you managed to get that too.

Okay, onto our next set of tasks, now then.

What I'd like to do is have a go at measuring these reflex angles using both Jun and Laura's strategy.

I'd like to write down the correct calculation for both of these, and then decide for yourself which strategy did you prefer.

Remember, Jun's strategy was to find 180 degrees and then add on the remaining angle, whereas Laura's strategy was to subtract the inside angle from 360 degrees.

Once you've done that, if you have a 360 degree protractor, what I'd like to do is have a go at using Izzy's method.

However, if you don't have one of those to hand, then you can choose your preferred method to find out the size of each of these angles too.

Good luck, those two tasks.

I'll see you back here shortly.

Okay, let's see how we got on there.

So if we start off by looking at Jun's strategy, for example one, we can extend to make the 180 degrees and then we can measure out the extra bit, which is 133 degrees, so a total of 313 degrees.

And then for Laura strategy, we need to work out the size of the inner angle, which would be equal to 47 degrees, and then subtract that from the whole turn of 360 degrees, which again leaves us with 313 degrees.

Here, we can extend the angle out to make the 180 and then find out the extra part of the angle, which is 144 degrees, in this case, 180 plus 144 is equal to 324 degrees.

So the size of the reflex angle is 324 degrees, or we can use Laura's strategy, find the inner angle, which in this case is worth 36 degrees.

And then we subtract that from 360 degrees, which leaves us with 324 degrees again.

And then the last one.

Using Jun's strategy, we can extend our line to make the 180 degree and then add on the remaining part, once we've measured that, which in this case is 75 degrees.

180 degrees plus 75 degrees gives us a total of 255 degrees.

Now that we've done that, we can work out using Laura strategy as well.

The inner angle actually gave us a value of 105 degrees, so we can subtract that from 360, which once again gives us 255 degrees.

Well done if you've got all of those.

Okay, hopefully you managed to measure these using Izzy strategy or if not, your own preferred strategy.

The size of the angles were as follows.

The first one was 259 degrees.

The second one was 313 degrees, and the last one was 233 degrees as well.

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

Let's summarise what we've been thinking about, shall we? We know that we can use a protractor to measure the size of an angle.

To use a protractor, we need to line up the middle spot of the protractor with either the point or the vertex.

You then need to rotate the protractor so that the zero line is lined up with one of the lines of the angle.

And we know that we can measure the angle either in an anticlockwise or a clockwise direction using either the inside or the outside scale.

That's the end of our learning for today.

I really recommend you continue to practise measuring your angles using protractors, and no wonder what angles you can find in a range of real life context.

Take care.

I'll see you again soon.