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I can recall that angles in a full turn sum to 360 degrees and use this to solve problems.

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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

There are 360 degrees in a full turn.
Use mental or written strategies to calculate with angles up to 360 degrees.

Common misconception

The largest angle that can be created is a 360 degree angle or one full turn.

Explore examples in everyday life where rotations are greater than one full turn. Discuss how multiples of 180 degrees or 360 degrees are often used to describe movements in sports and other contexts.

Keywords

Turn - To turn means to rotate about a point.
Degrees - A degree is a unit of measure for angles.

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Hi there.

Welcome to today's lesson.

My name's Mr. Peters.

And in this lesson today, we are gonna be spending some time thinking about how we can use our knowledge that 360 degrees is equivalent to a full turn, and using this to help us solve problems. If you're ready to get started, then let's get going.

So, by the end of this lesson today, you should be able to say that \"I can recall the angles in a full turn sum to 360 degrees, and I can use this to solve problems.\" Throughout this lesson today, we've got two keywords we're gonna be thinking about.

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

Are you ready? The first word is turn.

Your turn.

And the second word is degrees.

Your turn.

Thinking about what these mean then? You can say that a turn, means to rotate around a point.

And a degree, is a unit of measure for angles.

In this lesson today, we've got two learning cycles.

The first cycle, we'll think about exploring full turns, and the second cycle, we'll think about solving problems with 360 degrees.

Let's get started with the first cycle.

Throughout this lesson today, we've got four students who are gonna be joining us.

We've got Jun, Alex, Jacob, and Izzy.

And as always, they'll be sharing their thinking as well as any questions that they have to support us with our learning as we move throughout the lesson.

So our lesson starts here.

It starts with Jun and Izzy, thinking about the lessons that they've got coming up throughout the day at school.

Jun says he's really looking forward to his P.

lesson later on.

It's gonna be an opportunity for 'em to carry on practising their forward rolls.

Oh, well, that's good that you had time to practise outside the school as well, Izzy.

Here's an example of Izzy demonstrating a forward roll.

Yeah, fantastic form.

Fantastic technique, Izzy.

Yeah, and as always, when you finish, you have to make sure you point those fingers and toes, don't you? What a lovely aspiration, Izzy.

I must tell you though, every Olympian works incredibly hard to get to the standard that a performer.

A great aspiration as someone to work towards, Izzy.

So we can say that when Izzy completes a forward roll, then we can say that she rotates one full turn.

Hmm, and great question, Izzy, \"How many degrees is one full turn?\" Ah, yeah, we're reminded, Jun, we know that one full turn is equivalent to 360 degrees, isn't it? Yep, so we could say that Izzy's body turned 360 degrees from start to finish.

Let's have a look at Izzy's head position throughout to demonstrate this.

Here you can see that Izzy's head position started to rotate, and now she's in a complete standing position again.

So we can say that when Izzy completed her forward roll, she completed a full turn, and a full turn has a value of 360 degrees.

Hmm, that's an interesting one, Izzy, isn't it? What if you did two forward rolls, one after the other? How much would you have rotated then? Well, you're right, Jun.

That would be equivalent to two full turns, wouldn't it? And we know that each full turn is equivalent to 360 degrees.

So, two full turns would be equivalent to two lots of 360 degrees.

There's one lot and there's another lot, two full turns, and that's two lots of 360 degrees.

We could therefore multiply 360 degrees by 2.

So we could say 2 multiplied by 360 degrees is equivalent to 720 degrees.

So, we could say that Izzy rotates 720 degrees when she performs two forward rolls.

Ah, well, a good try, Izzy, isn't it? Izzy says that she tried to have a go at doing two forward roles in a row, but she only managed to do one and a half.

Let's have a look.

She completed one full forward roll and then didn't manage to complete the second forward roll.

So we can say that she's done one-and-a-half forward rolls.

Hmm, so how many degrees do you think we could say that Izzy's body rotated here then? Well, we know that one full turn is equivalent to 360 degrees, don't we? And as Jun is pointing out, we could also say that half a turn is half of 360 degrees, so that would be another 180 degrees.

So, we could add 360 degrees plus 180 degrees together now to find out the full rotation that Izzy's body went through, which in this case was 540 degrees.

There you go.

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

Three full turns is equivalent to how many degrees? Is it A, 180, B, 360, C, 720, or D, 1,080? Take a moment to have a think.

That's right.

It's D, isn't it? And why is it D? That's right.

We would need three lots of 360 degrees, wouldn't we? Three multiplied by 360.

We know that 3 multiplied by 300 is equal to 900, and then 3 multiplied by 60 is equal to 180.

Add those two together, that means 90 and 180 is equivalent to 1,080 degrees altogether.

Well done if you've got that.

And the second one then.

True or false? The largest amount of degrees and object can turn is 360 degrees.

Take a moment to have a think.

That's right.

It's false, isn't it? Look at the justifications here.

Choose one of these to help you to reason why.

That's right, it's A, isn't it? It is possible to turn more than one full turn, isn't it? So, if you can turn through more than one full turn, that means you can rotate more than 360 degrees, can't you? Okay, time for us to have a practise now then.

What I'd like you to do is have a go at completing the equations here.

The first one's been done for you.

It says, one full turn is equal to 1 multiplied by 360 degrees, which is equal to 360 degrees.

Once you've done that, I'd like to have a go at completing these equations here.

And once again, the first one has been done for you, just like the previous question.

And then for task three, I've got some questions here for you to think about for a diver, an athlete who dives off a platform into the swimming pool and performs a number of turns throughout.

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

Okay, welcome back.

Let's go through the answers then.

So we know that one full turn is equivalent to one lot of 360 degrees, so that is equal to 360 degrees.

Therefore, two full turns will be equal to 2 multiplied by 360 degrees, that is equal to 720 degrees.

Three full turns will be three lots of 360 degrees, that is equal to 1,080 degrees.

Four full turns, of course, is four lots of 360 degrees, so that is 1,440 degrees altogether.

Five full turns, is five lots of 360 degrees, and we can say that's 1,800.

And we jump on here, from five full turns to 10 full turns.

Well, we can work that out quite easily in a number of ways, can't we? We know it's 10 lots of 360 degrees, 10 lots of 360 degrees is 3,600 degrees, or we could have just doubled the amount of degrees it takes to rotate five full turns, because 10 is double five, isn't it? So, five full turns is 1,800 degrees, and then double that, that would be equal to 3,600 degrees.

Okay, and for task two then, once again, the first one's been done for us here.

We know that one full turn would be equivalent to 360 degrees divided by one full turn, which is equal to 360 degrees.

So, how could we work out what half of a full turn is? Well, that'd be equivalent to saying, 360 degrees divided by 2, because we are multiplying by a half, and we know that divide it by 2 is equivalent to multiplying by a half, so therefore we can say that one-half of a full turn is equal to 180 degrees.

We've then got one-third of a full turn, that would be 360 degrees divided by 3.

In this case, that would be 120 degrees.

Then we've got 360 divided by 4, for a quarter of a full turn, that's equal to 90 degrees.

360 degrees divided by 5, that would be one-fifth of a full turn, wouldn't it? That's equal to 72 degrees.

And then finally, once again, one-tenth of a full turn.

Well, if we know that 360 degrees is a full turn and we then divide that by 10, then we can say that one-tenth of a full turn would be equal to 36 degrees.

And then task number 3 then.

A diver completes a three-and-a-half front somersault before entering the water.

How many degrees does a diver turn? Well, we can write an equation for this as 3 multiplied by 360 degrees.

That's three full turns plus half a full turn, which equal to 180 degrees.

So, three lots of 360 degrees we know is 1,080 degrees, plus the 180 degrees, that gives us a total of 1,260 degrees.

Okay, for B, for their second dive, a diver completes a series of back somersaults.

Altogether, they rotate 900 degrees.

How many full turns is this? Well, to calculate this, we need to find out how many lots of 360 degrees are there in 900 degrees.

We know that there's two lots of 360 degrees makes 720 degrees, and then that would leave us with another 180 degrees.

So we can say that it's two-and-a-half back somersaults altogether.

And then finally, the diver says their best dive is an 810-degree forward somersault.

Explain why this cannot be correct.

Well, exactly that.

If a diver did an 810-degree front somersault, that means they would turn two and one quarter full turns, which would mean they would enter the pool on their stomach.

Now, in diving in particular, I don't know how much you know about the sport, you need to dive in with your hands first and try and be as vertical as possible as you enter the water to create as little a splash as possible.

If you're to land on your stomach, I'm not sure it looks so elegant, and it might hurt quite a lot as well.

Okay, moving on to cycle 2 now then.

Solving problems with 360 degrees.

In this cycle, we've got Jun and Alex who are coding for their computer lesson.

Alex is saying that he's trying to get his character to move one full turn in the air, but it keeps stopping here.

Hmm, good idea, Jun.

Jun wants to have a look at the coding to see what he's done.

And this is what Alex has done.

When he clicks the green flag, that means it starts rotating.

And you can see here that he's put a rotation in anti-clockwise of 82 degrees.

Ah, and that's what Jun spotted.

He says, \"Ah, I've realised that actually, you're only rotating it 82 degrees, Alex.\" Hmm, how much did you want to turn? Ah, Alex wants to turn it one full turn or 360 degrees.

Hmm, so Jun is saying, \"You need to turn another 278 degrees as well.\" Yeah, good question, Alex.

How did you know that so quickly, Jun? Well, Jun saying that he knows that you want the character to rotate 360 degrees.

So we're gonna use a bar model to represent this.

This is the amount of turn that we want the character to do.

And so far, we've only got it rotating 82 degrees.

So we need to find the difference then, don't we? We need to find the additional rotation required in order for it to turn the full 360 degrees.

So, we could write this as a subtraction equation because we are finding the difference.

So we've got 360 degrees minus 82 degrees, and that would be equal to 278 degrees, as Jun said originally.

So, we now know that by adding 82 degrees and the 278 degrees together, that would be equivalent to a 360-degree turn.

So, exactly that, Alex, you can add an extra instruction in, can't you, to turn it further 278 degrees, can't you? Hmm.

Yeah.

Or that's another way of doing it, isn't it, Jun? In fact, only have one instruction and change it to 360 degrees.

There we go.

Well done you two.

Good problem solving.

Well, there we go.

Jacob's cottoned on that Jun's a bit of a coding pro.

\"King Codra, when did you come up with, Jun?\" That's an interesting nickname.

I like the play on words though.

So, at the moment, Jacob's character is rotating 360 degrees.

Now he wants it to rotate 135 degrees less than that.

So have a look at the coding that Jacob's got at the moment, and here's his character rotating one full turn.

So how could we go about this then, Jun? Well, at the moment, we know that the character is rotating 360 degrees, that's one full turn.

So we're gonna represent this as our bar model.

And we wanted to rotate 135 degrees less than that, don't we? So 135 degrees would be part of a full turn, and then we need to find the remaining part, don't we? This would be the amount that we actually want it to turn.

So we've got 360 degrees and then we could therefore minus 135 degrees to help us find the amount that we want it to turn.

That of course would be 225 degrees.

So, exactly that, Jacob, we can change our coding now to be a turn of 225 degrees and it would look like this.

Ah, and Izzy has now also realised that Jun is a bit of an expert when it comes to coding at the moment.

Izzy wants some help with her character.

Izzy's saying that she wants her character to turn one full turn, however, this is what she's got at the moment.

Have a look at her coding.

How do you think we could try and tackle this? Well, let's have a think about how Jun's tackling it then.

He's once again saying that we want the character to rotate 360 degrees, and at the moment it's rotating 90 degrees, then 160 degrees, and then a further 35 degrees.

So we can see if we add all of these up together, that that gives us 285 degrees, which isn't quite a full turn, is it? So we now need to find the difference again.

We need to find out how much more turn we need to add on to this instruction here to make it turn 360 degrees.

We can do that by subtracting the amount of turn that we've done already from the full turn that we wanted to take.

So 360 degrees minus 285 degrees, that would be equal to 75 degrees.

So, that's right, Izzy, we need your characters to rotate another 75 degrees, don't we? And there we go.

We can add on that instruction.

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

Jun turns this character 165 degrees.

How much further does he need to turn his character so it rotates one full turn? Take a moment to have a think.

Okay, but let's represent this with a bar model then.

We know that one full turn is 360 degrees, and we know at the moment, the character is rotating 165 degrees, so we need to find the difference again.

We can do that by using subtraction, 360 degrees minus 165 degrees, that's equal to 195 degrees.

Okay, onto our final tasks for today then.

Well, let's do it.

Have a go at completing these questions here.

And then once you've done that, we've got a change in context here, I'd like to have a go at completing these questions here as well.

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

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

So the first question says, \"An owl's head can turn up to 270 degrees.

How many degrees less than a full turn is this?\" Well, we know that a full turn is 360 degrees, so we can minus the amount of turn that an owl's head can do, which is 270 degrees, and therefore we can say that is 90 degrees less than a full turn.

Okay, and for question B.

\"A boat turns 36 degrees, then another 84 degrees.

How many more degrees does a boat need to turn to complete a full turn?\" Well, for this example, again, we know that a full turn is 360 degrees, and if we subtract the amount of turn that it's taken so far, which would be 36 degrees and 84 degrees, that would leave us with 240 degrees altogether.

So, in order to complete a full turn, the boat needs to turn another 240 degrees.

And then finally, question C, \"A gymnast is performing a front somersault, which is a full turn.

They overrotate by 27 degrees.

How much did they turn altogether?\" Well, for this, we know that a full turn is 360 degrees, and if they overrotate by 27 degrees, that means they've gone too far, which would be 387 degrees altogether.

So we can say that the gymnasts turned 387 degrees.

Okay, and then question 2.

\"Earth turns 1 degree every four minutes.

How many minutes does it take for Earth to turn 360 degrees?\" Well, if it turns 1 degree in four minutes, then we need to multiply the four minutes by 360 degrees to find out how many minutes it takes.

So we can say that 360 multiplied by 4 is equal to 1,440 minutes.

Therefore, we could say that it takes Earth 1,440 minutes to rotate one full turn.

We know that when Earth rotates one full turn, that means that's the completion of one day, isn't it? So, a little known fact here for you then is that the number of minutes in one complete day is 1,440 minutes.

Okay, for B.

\"If Earth has turned 145 degrees, how many more minutes does it take to turn 360 degrees?\" Well, we could start here by subtracting the amount of degrees that the Earth has rotated already, that leaves us with 215 degrees.

And then of course, we know that if 1 degree is equal to four minutes, then we can multiply 215 degrees by four minutes to find the total amount of time it'll take.

215 multiplied by 4 is equal to 860 minutes.

And finally, for question C, \"It is 2:30 PM, how many degrees has Earth turned since midday?\" Well, we know that if it's 2:30 PM, that means.

and we are looking at the amount of turns since midday, then that would be two-and-a-half hours, isn't it? Two-and-a-half hours is equivalent to 150 minutes.

And now, if we take that 150 minutes and divide it by 4, that will enable us to find out the amount of degrees that it's rotated, and therefore we can see that that would be equal to 37.

5 degrees.

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

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

To summarise what we've been thinking about, we can say that the angle of a full turn has a value of 360 degrees.

Multiple full turns can be recorded as a value greater than 360 degrees.

And if you know the angle or angles for part of a turn, you can work out the remaining part required to complete the full turn.

That's the end of our learning for today.

Thanks for joining me, and take care.

I'll see you again soon.

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