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I can use the unit of degrees as a standard unit to measure angles.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Angles are measured in degrees
Degrees measure rotation

Common misconception

Pupils think that the larger the size of the arc between the two lines, the larger the angle must be.

Ensure pupils compare the same angle where the arc has been drawn on either closer to the vertex or further away from the vertex. Generalise that the position of the arc doesn't matter, though it is convention to draw it closer to the vertex.

Keywords

Angle - An angle is a measure of turn. It shows how far something has rotated.
Degree - A degree is a unit of measure for angles.
Arc - An arc is part of any curve. They can be used to show the angle between two lines.

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Hi there, my name is Mr. Peters, and welcome to today's lesson.

Hopefully you're having a good week so far, wherever you are, and I'm looking forward to getting involved, thinking a little bit more about angles.

In this session today, we're gonna be thinking about how we can record the measurement of angles.

I'm thinking a bit more about a common unit of measure used for angles known as degrees.

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

So at the end of this session today, you should be able to say that, \"I can use the unit of degrees as a standard unit to measure angles.\" Throughout this session today, we've got three keywords we're gonna be referring to.

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

The first one is angle, your turn, the second one is degrees, your turn, and the last one is arc, your turn.

We can define an angle as a measure of turn.

It shows how far something has rotated.

A degree is a unit of measure of angles.

And an arc is a part of any curve.

They can be used to show the angle between two lines.

This lesson today is broken down into two cycles.

The first cycle is quantifying angles, and the second cycle is common partitions of a full turn.

Let's get started with the first cycle.

Throughout the session today, you'll meet both Jacob and Alex.

As always, they'll be sharing their thinking and asking any questions along the way to help us with our thinking.

So our lesson starts here and we're asking this question, how can we decide which of these angles is the largest? Hmm, you are right, Jacob.

They do look very similar, don't they? Hmm, and we could try and cut them out and overlay them, couldn't we, Alex? But you're right, Jacob, that's something we can't do every single time, can we? If we've got them all on a piece of paper, we can't keep cutting out every angle to check which one is largest, can we? It's gonna take quite a while, and sometimes the angles aren't actually to scale.

So you're right, Jacob.

Luckily we can actually use numbers to help us identify the size of angles.

So let's have a look at these two angles now.

One of the angles is represented by 98 and the other angle is represented by 99.

So these numbers here are representing the size of the angle, aren't there? We know that an angle shows us the amount of turn that something does.

Another way we can say this is it shows the degree of turn that something does.

So we can now describe this as 98 degrees or 99 degrees.

And instead of writing the word degrees every single time, we can use a little symbol.

You may have seen it before.

The symbol looks this, and it's a little circle that we place to the top right hand side of the numbers.

Have a look at these here now.

What do you notice about these examples? Well, that's right, the angle sizes are all the same, aren't they? They all say 50 degrees, however, the arcs positioning between each of the lines is slightly different, isn't it? The first one is closer to the point and therefore a smaller arc, whereas the next two move further away from the point of the angle towards the end.

Do you think this matters where the arc has been positioned? That's right, it doesn't matter, Jacob does it.

We know that each of these represent 50 degrees, however, the placement and size of the arc in these examples don't matter.

They all show us 50 degrees.

Have a look at this example now.

What did you notice this time? That's right, Alex, the angle sizes are all the same once again.

However, the shape and the length of the lines are all different this time, aren't they? Hmm, so do we all think they all represent 50 degrees again? That's right.

They do all represent 50 degrees, don't they? As long as the lines are straight at the point at which they meet, then we know that this creates an angle.

And in this case, all of those arcs are representing the degree of turn between those two lines, and therefore represent the angles of 50 degrees each time.

Okay, time for you to check your understanding now.

The amount of turn that occurs can be measured in: A, centimetres, B, degrees, C, milligrammes, or D, litres.

Take a moment to think.

That's right, it's degrees, isn't it? The amount of turn that occurs can be measured in degrees.

Okay, and true or false, angle A is larger than angle B.

Take a moment to think.

Okay, and that's false, isn't it? And use one of these justifications now to help you reason why.

That's right, justification A will help us here, won't they? They are in fact the same size angle in these examples, aren't they? It doesn't matter the placement of where the arc is in both of these.

The lines are in exactly the same positions and therefore the angle size would be exactly the same as well.

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

Now what I'd like you to do is draw the arc for each angle and then complete the stem sentence as well.

Good luck with that task, and I'll see you back here shortly.

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

So you can see here the arcs that have been drawn on for each one of these angles here.

The first angle is 49 degrees.

So we can say that 49 degrees can be written as 49 with the circle in the air.

The same applies for the next one.

The next one is an acute angle again, so we can draw on the arc to represent that.

And this time, 78 degrees can be represented as 78 with a little circle in the air.

The next one is a reflex angle.

So therefore that's gonna be a large angle, isn't it? So we need a larger arc for that one.

We've got 235 degrees this time, and again, we can represent that as 235 with the degree symbol in the air to the right hand side of it.

And then finally, the last one is an obtuse angle.

So this is the positioning of the arc that you could have used.

And in this case it's 128 degrees.

So again, we can represent this as 128 with the degree symbol in the air next to it.

Well done if you've got all of those.

Okay, moving on to cycle two now then, common partitions of a full turn.

So Jacob here has drawn a 90 degree angle, and we know that this is a right angle because it creates a square corner.

Have a look at this one here.

This is a one degree angle.

Have a look at how you can compare this one degree angle to that of the 90 degree angle.

Look how small it is in comparison.

This is 10 degrees, this is 20 degrees, and this here is 30 degrees, and one more, this one here is 40 degrees.

It's a really good idea to get a sense of how much a degree is, and we can do that by looking carefully and comparing the size of the amount of degrees in comparison to other amounts of degrees.

All of these amounts that we've looked at so far are part of a full turn.

Let's have a look here.

This here is one degree.

We can then extend it, so it is 10 degrees, now it's 20, now it's 30, and now it's 40.

So a great question there, Alex.

If this is 40 degrees here, then how many degrees would be one complete full turn? Well, let's have a look at this in a bit more detail.

If we draw a vertical line from the centre of the circle to the top, and then mark on a 90 degree angle, we can see here that this is one right angle or 90 degrees.

We can add on another right angle that would be two lots of 90 degrees.

If we add on another right angle, that would be three lots of 90 degrees.

And then one more.

There we go.

So that'd be four lots of 90 degrees.

Each one of these right angles is 90 degrees.

So we can say that one full turn is equal to four lots of 90 degrees.

That in total gives us four multiplied by 90, which is equal to 360.

So the amount of degrees in one full turn is 360 degrees.

Let's think about that again this time.

But let's think about some common ways that people describe angles within a full turn.

Here is one right angle, and we know that one right angle represents 90 degrees.

If we increase the degree of turn by another 90 degrees, there we go, we've now got two right angles, which are both 90 degrees.

So we could say that actually this is two lots of 90 degrees, also known as 180 degrees.

So we could say that one half turn is 180 degrees.

If we take it a step further and include another right angle now, we could say that we've completed a three-quarter turn this time, that's three lots of 90 degrees, which in this case would be 270 degrees.

And then finally, if we went the final 90 degrees, we know that one full turn is equal to 360 degrees, isn't it? So these are really important common partitions for us to understand and be aware of.

90 degrees is a quarter turn.

180 degrees is a half turn, 270 degrees is a three-quarter turn, and 360 degrees is a full turn.

And that's right, Alex, if you know you're nine times table, that'll be really helpful, wouldn't it? It's 9 tens, 18 tens, 27 tens, and 36 tens, isn't it? Really good connection to make there, Alex? Well done, you.

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

True or false, this angle shows a turn of 270 degrees? Take a moment to think.

Okay, and that's true, isn't it? And which of these justifications helps you to reason why? That's right, it's A, isn't it? The amount of turn is equivalent to three right angles.

So it's a three-quarter turn, and we know that three lots of 90 degrees is equal to 270 degrees.

And another quick check, a full turn is equal to something degrees? Is it A, 10, B, 100, C, 180, or D, 360? Take a moment to have a think.

That's right, it's D, isn't it, 360? Yep, and that's excellent reason in there, Alex.

We know that a full turn is equal to four lots of 90 degrees, which is equal to 360 degrees.

Okay, and time for a bit more practise now then.

What I'd let you to do is use these angle tools here and take these angle tools into your own setting to find different angles that you can, which are approximately the similar size to the size of these angles here.

And then once you've done that, I'd like to have a go at labelling the size of each of the angles here.

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

Okay, let's have a look at examples that we came up with then.

I managed to find a range of things in my house, which were roughly equivalent to the size of the degrees from each of the angle tools.

Let's have a look here.

The degrees between two fingers in a glove here was actually 10 degrees.

For a clothes peg to help hang things up on the washing line.

When the clothes peg is closed, the amount of degrees between the two levers is approximately 20 degrees.

Here you can see between two playing cards that I've laid out that we've got an angle of roughly 30 degrees.

And then for the letter K, between my fridge magnet, I've got an angle which is roughly 40 degrees.

I wonder if you write your capital Ks with roughly a 40 degree angle.

And then finally here, a napkin.

This napkin is the shape of a rectangle, and that's really easy to identify them, that each of the corners here would be a square corner and therefore would be 90 degrees.

Well done if you manage to come up with something similar to those for yourself or something slightly different.

Okay, and then working through these ones here, you can see in the top row that the first one represents 180 degrees.

Second one is 90 degrees, the third one is 270 degrees, and the last one is 360 degrees.

In the second row, we can see that the first example is 90 degrees.

The second example is 180 degrees.

The third example is 360 degrees, and the last example is 270 degrees.

And then finally for the last row, the first example is 90 degrees.

The second example is 270 degrees.

The third example is 180 degrees, and the last one is 360 degrees.

What did you notice about the shapes around each of the examples or each row of the examples? That's right, the shapes were all different.

But did the degree of angles change each time? No, it didn't did it.

For example, if we look at the 180 degree example for the circle, the square and the oval shape, the 180 degrees still stays the same regardless of the outer shape that we've been looking at.

Well done if you managed to spot that for yourself too.

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

To summarise what we've been thinking about, you can say that you can use numbers to give an angle a value.

The size of an angle is measured in degrees.

You can use this symbol here, the small circle in the air to the right hand side of the number to represent degrees.

And we can also use common partitions of a full turn to help estimate different angles.

Thanks for joining me again today.

Hopefully you are feeling a lot more confident now with how we can talk about the measurements of angles, using the standard unit of measure of degrees.

Take care, and I'll see you again soon.

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______ °", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457704%2Fakt2lrcv490ejh05smte.png&w=640&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/70d46589acda49705579bec130ee7f69.png" }, "questionType": "Short answer", "correct": [ { "text": "90" }, { "text": "ninety" }, { "text": "90 degrees" } ], "id": "1a98cc90-51ac-1acb-20d5-9eb7849b5c5c", "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81" }, { "type": "Question", "question": { "text": "A full turn is equal to four right angles which is ___.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457706%2Fbg0e7f2nertzjtrjcppo.png&w=640&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/d9d6948bb3a8f3eec3c064610e2fd268.png" }, "questionType": "Multiple choice", "correct": [ { "text": "360°" } ], "choices": [ { "text": "90° " }, { "text": "180° " }, { "text": "300° " }, { "text": "360°" } ], "id": "2c174c93-92e7-da82-06ea-d8fe2a112052", "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81" }, { "type": "Question", "question": { "text": "The angle shown is 50° which means it is an ______ angle.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457705%2Fxo5dka4atyur5xrbjdr8.png&w=640&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/605a8cf885ac8a9fc9510dc5bd032703.png" }, "questionType": "Short answer", "correct": [ { "text": "acute" } ], "id": "d3084df6-c51a-bcb2-3c3c-ebb30a721340", "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81" }, { "type": "Question", "question": { "text": "The angle shown is 140° which means it is an ______ angle.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1712843644%2Fak7u1dcuadtdoloblo3u.png&w=640&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/85be4793a0d7fb74c3c5fe047a924034.png" }, "questionType": "Short answer", "correct": [ { "text": "obtuse" } ], "id": "fcb19307-b358-9eff-fbb9-4c170eea202a", "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81" }, { "type": "Question", "question": { "text": "What is the measurement of the angle shown here? ______°", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457706%2Febqk7wgbeivuagqqpdwv.png&w=640&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/537849bd99716d1599ec43d03b9b6e80.png" }, "questionType": "Short answer", "correct": [ { "text": "180" }, { "text": "one hundred and eighty" }, { "text": "180 degrees" } ], "id": "9a8ed37c-c943-5117-b8da-9c07310d075c", "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81" }, { "type": "Question", "question": { "text": "Which image shows an angle of approximately 30°?" }, "questionType": "Multiple choice", "correct": [ { "text": "B", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457707%2Fdgwx4zuetdggusfsagb8.png&w=384&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/3d13ffefb5dd604d645a957eaa4ed547.png" } ], "choices": [ { "text": "A", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457708%2Fg0zjchfbugrthbdj7vfp.png&w=384&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/697442c29d93247dd70419e4201eb3ea.png" }, { "text": "B", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457707%2Fdgwx4zuetdggusfsagb8.png&w=384&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/3d13ffefb5dd604d645a957eaa4ed547.png" }, { "text": "C", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1713457709%2Ffkl59oxmwcdmvmbqk1gw.png&w=384&q=75", "imageKey": "185adba7-d254-bdcc-f8af-943dc2087424/question/e3a78b6e980ee5b9664a98c44e403774.png" } ], "id": "ec31e248-43b4-9fd3-a03b-ab5c3194d9c0", "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81" } ], "lessonId": "e49e4f32-e806-c952-9943-0a314fcb2b81", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 5", "topic": null, "unit": "Angles: compare, name, estimate and measure angles", "lessonCount": "15", "age": [ 9, 10 ], "gradeId": "age_9_10", "gradeStage": "Key Stage 2", "lesson": "Use the unit of degrees as a standard unit to measure angles" } }, { "id": "88babac3-413e-7a05-8630-a732cf132a8b", "type": "Content", "contentType": "Additional material", "content": { "text": "

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