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 how we can describe rotations using the standard unit of measure of degrees in comparison to right angles.

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

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

In this lesson today, we've got three keywords we're gonna be referring to throughout.

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

The first word is degrees, your turn.

The second word is estimate, your turn.

And the third word is rotation, your turn.

Let's now think about what these mean.

A degree is a unit of measure of angles.

To estimate is to find the value that is close enough to the right answer.

Usually, there's some thought or calculation involved in that process too.

And finally, a rotation is a circular movement around a fixed point.

Have a look out for these words throughout our lesson and try to use 'em for yourself to help you with your reasoning throughout.

This lesson today is broken down into two cycles.

The first cycle is thinking about rotating things, and the second cycle is all about estimating rotations in context.

Let's get started with the first cycle.

Throughout our lesson today, we're gonna have both Laura and Lucas joining us.

As usual, they'll be sharing their thinking as well as any questions that they've got to help us with our learning along the way.

So our lesson starts with both Laura and Lucas thinking about things that rotate.

Lucas has come up an idea.

He says, "Planet Earth." Planet Earth rotates around.

It has an axis, which it spins around, doesn't it? He says, "Wheels." They also rotate around.

You could have the wheels on a bike or the wheels on a car or the wheels on different types of transport or toys.

He also says that doors rotate round.

And they do, don't they? They rotate around their hinges, don't they, as we open and close them.

Items that rotate rotate around something which is called a fixed point.

Have a look at this example here.

Laura's saying that her dad has lots of these in his house.

This item here has a fixed point in the middle, and that is what this item spins around.

Yeah, you are right, Lucas.

In fact, this object is a CD.

CDs were very common at a time, and they were used to play music for people.

They still exist today, but people don't use them as much as other forms of music.

Here's another example that Laura's come up with.

She says that a door handle rotates around a fixed point too.

However, the fixed point is hidden within the door handle itself.

We've drawn a little black dot to show you where the fixed point would be.

We can describe the amount of rotation that an object does using degrees as well.

If we draw a line to show where the handle starts and show you the rotation of the handle around the fixed point now, we can now see the size of the rotation that has taken place.

We've created an angle with the amount of rotation that's taken place and we can now begin to describe the size of this angle.

That's right, Lucas.

The door handle has rotated 1/4 turn, hasn't it? So we can say that the door handle has rotated 90 degrees 'cause we know that 1/4 turn is equivalent to a 90 degrees.

So the examples we've looked at so far, we have two objects.

One of the objects, the CD, is an example of something that rotates more than a full turn, and a door handle is an example of something that rotates less than a full turn.

Can you think of some examples for yourself that either rotate more than a full turn or less than a full turn? You might like to take a moment to think for yourself.

Here's an example of something that could rotate less than a full turn, but also it can rotate more than a full turn as well.

When it's windy, a wind turbine might only rotate a little tiny bit.

There we go.

However, when it's windier, we could say that the wind turbines continue rotating, don't they? And we can see that here, for example, this wind turbine is continuing to rotate to create energy.

Here's another example of objects that can rotate greater than the full turn or less than a full turn.

Over one minute, the hour hand rotates ever so slightly.

There we go.

Did you see that? It moved ever so slightly clockwise, isn't it? In comparison, the minute hand, over the course of one minute, rotates one place to the right.

There we go.

And then finally, in comparison to that, the second hand, over the course of one minute, rotates one full turn.

There we go.

So we can use our understanding of items which rotates more than a full turn or less than a full turn, and we can place these into a Venn diagram.

On the left-hand side circle, we're looking for objects that only rotate less than 360 degrees, and on the right-hand side, we're only looking for objects that rotate more than 360 degrees.

Any objects like the wind turbine, which can rotate less than 360 degrees, but can also rotate more than 360 degrees would be placed in the middle.

We can say that a door handle rotates less than 360 degrees.

So we're gonna place that one here.

We could say that a washing machine rotates more than 360 degrees, so it'd be placed in this circle here.

Hm, what about a garden swing then? That's a great question, Laura.

What do you think? Yep, I agree.

I say that a garden swing actually rotates less than 360 degrees.

It possibly can rotate more than 360 degrees.

However, for its use, typically, it would rotate less than 360 degrees, wouldn't it? Yeah, exactly that, Lucas.

Unless you're trying to divide gravity, it's best off placed in the left-hand part of our Venn diagram.

Hm, that's a great example as well.

The planets, they all continuously rotate, don't they? So where would we place that one then? That's right.

We place the planets in the right-hand circle, wouldn't we, 'cause they all rotate greater than 360 degrees.

Hm, what about a pizza cutter this time? That's an interesting one, isn't it? What do we think about that? Yeah, exactly that, Lucas.

That depends on how much you cut, doesn't it? If you only cut a little tiny bit, then it would be less than 360 degrees.

However, if you're cutting a long pizza, then you might rotate greater than 360 degrees.

So I think we'd have to place the pizza cutter in the middle, wouldn't we? Okay, time for us to check your understanding now.

Could you ever think about where would you place a fridge door in this Venn diagram? Take a moment to think.

That's right.

A fridge door is pretty similar to most other doors, and most other doors only rotate less than 360 degrees.

So we can place that in the left-hand side of our Venn diagram.

Yeah, nice spot, Laura.

You're right.

Fridge doors generally are able to open only up to the size of either an acute angle or sometimes an obtuse angle.

Depends if there's anything behind it or not.

Okay, and now what I'd like to do is have a think about ticking the objects here that rotate less than 360 degrees when they're used correctly.

Again, take a moment to have a think.

That's right.

We can say any of these three items here are often found in a park could be identified as objects that rotate less than 360 degrees.

The swings rotate less than 360 degrees, a seesaw rotates less than 360 degrees, and the park gate would also rotate less than 360 degrees.

A roundabout could rotate less than 360 degrees, although that wouldn't really be the purpose of its use.

Its use is to spin round and round, isn't it? So we could say that a roundabout would generally rotate greater than 360 degrees for its use.

Okay, onto our first task for today then.

What I'd like to do is have a think about going and finding some objects for yourself that rotate in your own setting, rotate less than a full turn, that rotate more than a full turn, or, in fact, could do both.

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

Okay, I wonder how you got on.

Let's see what examples that Laura and Lucas come up with.

Laura has said that sharpening a pencil would be example.

And you're right, Lucas, that depends on the amount of rotation you put into each turn.

You could do a small turn, which would be less than 360 degrees, but equally, you could do a larger turn.

You could go all the way around, which would be greater than 360 degrees, potentially.

Here's another example that Lucas has come up with.

He's talking about windscreen wipers.

Let's have a look.

Car's windscreen wipers rotate forwards and backwards, don't they, over the same distance, however, they also rotate less than a full turn, don't they? They don't go all the way around.

They go up to the edge of the window and then back down, don't they? So we can say that they rotate less than the full turn.

Okay, that's the end of our first cycle.

Moving on to cycle two now, estimating rotations in different contexts.

So let's have a look here.

Let's go back to our windscreen wipers.

Laura and Lucas are thinking about the amount of rotation that takes place by these windscreen wipers.

We know that these windscreen wipers rotate less than 360 degrees, don't we? And we know that they rotate back and forth, don't they, to wipe the rain off of the window screen.

Laura thinks that these windscreen wipers rotate the amount of an acute angle.

Let's have a look.

Hm, you're right, Laura.

So they definitely rotate less than 90 degrees, don't they? What do you think they rotate? Can you estimate the size of rotation that these windscreen wipers go through? What do you think? Laura has gone for 80 degrees for her estimate.

I wonder if you came up with something similar to that.

That's a good idea, Lucas.

We can use our angle tools, can't we, to help us estimate this.

We can replace on the 90-degree angle tool now.

We can clearly see that it's less than 90 degrees, can't we, which is brilliant.

And now we can see how far away it is from the 90 degree angle.

So let's take 10 degrees off, there we go.

We can now see what 80 degrees would look like as it would be the rotation from the dash line up to the first green line.

Hm, you're right, Laura.

It is still less than 80, isn't it? So actually, you're changing your estimate now.

It's about 75, are you? That's okay.

It's good to readjust your estimates from time to time.

Here's another example.

Here's a swing.

Let's have a look at the rotation of the swing this time.

Wow, that swing's gone quite high, isn't it? Must have been quite a push.

Here is the angle of the rotation that the swing has gone through.

Take a moment to have a think for yourself.

How large do you think this rotation is this time? Lucas thinks it's larger than a right angle.

Hm, I tend to agree with you, Lucas.

I think it is larger than the right angle as well.

So Lucas has gone for 120 degrees.

I wonder what you went for? Once again, let's check using our angle tool, shall we? Let's place on the 90 degree angle.

We can clearly see that it's greater than 90 degrees, can't we? But the question is how much more than 90 degrees is it? So let's use some more angle tools to check.

Here, I've placed another 30 degree angle, so we've now got 90 and 30, which gives us 120 degrees.

And look, it's pretty similar, isn't it? It's nearly there.

So we could probably say it's about 120 degrees, which I think, Lucas, was your estimate.

So well done you.

What a great estimate.

Here's another example.

You might be familiar with these.

This is a controller for a games console.

When we're playing games, we have to rotate the analogue stick to usually move a character, for example.

Laura's saying that when she plays her football game, she needs to hold down L1 and then rotate the analogue stick to do a skill.

Let's zoom in to the left-hand part of the controller and to the left analogue stick.

She's now gonna show us how far she rotates the analogue stick to complete the trick.

She starts the analogue stick here and she rotates it round, just like this.

So we can now see the angle of rotation that the analogue stick has gone through.

Here we go.

Take a moment to think.

What type of angle is this? That's right, it's a reflex angle, Lucas, you're right.

So we know it's gonna be greater than 180 degrees, don't we? 'cause it's greater than the angle on a straight line.

Take a moment to have a think again for yourself.

Can you come up with an estimate for how big you think this angle is? Lucas has gone for an estimate of around 210 degrees.

Hm, that's interesting, Laura.

You think it's larger than 210 degrees because it's actually nearer to a 3/4 turn.

And we know a 3/4 turn is three lots of 90 degrees, three right angles.

So that would be 270 degrees, wouldn't it? Let's check it out.

So we can use our 180-degree angle tool to show the angle on the straight line.

So we definitely know it's a reflex angle, and now we can add in one of our angled tools.

This is another 40 degrees.

So altogether so far, this is 220 degrees.

And then we can add in another 20.

There we go.

This is now 240 degrees altogether.

And are we there? I think we are just about there, aren't we? We're just about on the line.

So I think this is the most we're gonna be able to fit in to estimate our angle.

So there we go.

It's about 240 degrees altogether.

And that is only another 30 degrees away from a 3/4 turn of 270 degrees.

So Lucas's estimate of 210 degrees was actually probably a little bit too low.

to be honest, whereas Laura estimated that it would be less than 270 degrees.

And although she didn't give us an exact value, she knew that because it was slightly less than 270 degrees, it could have been in the region of 240 or 250 degrees, which would be a better estimate for this example here.

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

Can you identify the type of angle that this rotation produces? Watch carefully.

Take a moment to have a think.

That's right.

The angle rotates through an acute angle, doesn't it? And how did you know that? That's right.

We know an acute angle is any angle between zero degrees and 90 degrees.

And in fact, this time, is less than a right angle.

So you can therefore say it's an acute angle.

And then this time, can you choose the best estimate for the size of the angle that's created from this rotation? Take a moment to have a think.

Yep, we've gone for 80 degrees this time, and I think that's a good estimate.

We know it's less than 90 degrees, which is a right angle, and it's not far away from that though, is it? So we've gone for 80 degrees, and hopefully you felt that was close to it too.

Okay, time for us to practise now then.

What I'd like to do here is have a go at playing this game.

It's called the Floor is Lava.

You've got your character on the left-hand side, and you're going to need to propel your hook into the clouds to swing from stone to stone.

You need to get from the left-hand stone platform that you're on to the right-hand stone platform on the far side.

Each time you propel your hook into the cloud and swing from there to the next stone, you'll need to estimate the size of the rotation that you swing through as you go from stone to stone.

If, however, you estimate it and then once you check it and you are more than 10 degrees out on your estimation, then you'll need to start again and you'll no longer be able to use the cloud that you had just used.

I wonder if you're able to do it in less than three goes.

Once you've done that task, I'd then like to go on to thinking about finding some different rotations in your everyday context once more, and you'll need to estimate the size of those rotations that those objects go through.

Once you've done that, you can then organise them into either acute rotations, obtuse rotations, or reflex rotations, depending on the size of the angle that you've estimated.

Good luck with those two tasks.

And once you've done that, I'll see you back here shortly.

Okay, let's see.

This is how Lucas's got on.

He estimated his first swing to be roughly 90 degrees.

So here's the 90 degrees we've placed that one on now.

We can see that, in fact, it's slightly larger than 90 degrees.

So is it gonna be okay Lucas, or are you gonna be outside of the limit? Well, let's check shall we? Luckily, it was just inside the limit, wasn't it? Here's a 10-degree angle tool that we've just placed on, and we can see that it is just inside the limit.

So your first wing was a good estimate.

Well done, Lucas.

I wonder if you managed to make it all the way over.

Okay, and here's some examples of some rotations that we managed to find in our everyday context.

The first one here is opening the biscuit tin.

When you open the lid of the biscuit tin, some of you may take the whole lid off, but when I do it, I tend to just open the lid ever slightly and sneak a hand in there.

So I've roughly estimated that when I open the biscuit tin, I open it at a degree of roughly 50 degrees.

Turning on the tap is another really good example of a rotation that happens in our house.

You can see here to turn the tap on that I rotate it from this initial position on the left to the next position on the right.

That would be the tap being turned on to full blast.

So actually you can see that a full blast of the tap is roughly around 95 degrees.

And finally, here's one more example, table football.

Some of you may have played this, some of you might not have.

It's a great game though.

And you can see that the middle player here has gone through a rotation of starting in this position to then kicking the ball to then finishing in the second position on the right.

So that rotation is in fact greater than the angle on a straight line.

And I would therefore say it's an estimate of 190 degrees.

It's just more than the angle on the straight line.

Well done if you managed to find three or more of your own examples for this as well.

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

Let's summarise what we've been thinking about.

When an object rotates, it can produce either an acute, obtuse, or reflex angle.

The amount an object rotates can be measured in degrees as a number.

And it's often helpful for us to estimate the size of the rotation that an object goes through, which often helps us to make sense of the situation in which we're in.

Thanks for joining me for today's lesson.

Hopefully, you enjoyed that one.

I know I did.

Take care and I'll see you again soon.