Lesson video

Hi there.

Welcome to today's lesson.

My name's Mr. Peters, and in this lesson today, we're gonna be thinking about how we can estimate both acute and obtuse angles, using the standard unit of measure of degrees.

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 estimate both acute and obtuse angles using the standard unit of measure of degrees.

In this lesson today, we're gonna have two keywords that we're gonna be referring to throughout.

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

The first word is estimate.

Your turn.

The second word is degrees.

Your turn.

Let's have a think about what these mean.

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

This usually involves some sort of thought or calculation.

A degree is a unit of measure of angles.

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

The first learning cycle is about estimating angles, and the second learning cycle is about applying angle estimates.

Let's get started with the first cycle.

In today's lesson, we've got both Andeep and Aisha.

They'll be sharing their thinking as well as any questions that they've got to help us develop our understanding as well as we go throughout the lesson.

So our lesson starts here with both Andeep and Aisha and they're playing a game.

In their game, they have to estimate the size of the angle each time.

The person who gets the closest estimate to the angle gets one point.

And if somebody estimates the angle within five degrees, then they get three points.

The first player to 10 points is the winner.

Aisha's saying it's a bit chilly today.

Hmm, Andeep's suggesting that she goes and sits in the corner because it's a bit warmer there.

I wonder why you'd suggest that, Andeep? Why would it be warmer there? Oh, because it's 90 degrees.

Very good, Andeep.

Do you know what? If it was 90 degrees in the corner, I think it'd be a bit too hot for anybody to sit in the corner.

And you know, we are not talking about degrees as the temperature, are we? We're talking about degrees as a unit of measure for angles.

Yeah, do you know what? You're not far wrong, Aisha.

Keep practising those jokes, Andeep.

So we've got a wheel here that we're gonna spin.

And I wonder if you can estimate the angle that it creates.

Are you ready? There we go.

You're right, Andeep.

It didn't spin very far.

But what do you think the size of the angle is? Hmm.

An acute angle.

Why'd you say it must be an acute angle? That's right, because it's less than 90 degrees, isn't it? Exactly, Andeep.

Okay, so after three then, make your estimates.

Are you ready? One, two, three.

There we go.

What have you gone for, Aisha? Aisha reckons it's about 38 degrees and Andeep reckons it's about 45 degrees.

Hmm, okay.

How can we check this then? Well, now we can unveil what's hidden underneath.

And here we go, and we can see that we've got a circle here that goes up in multiples of 30 degrees.

Each tiny interval is also an additional five degrees.

So each tiny interval goes up in lots of five degrees.

So let's figure out what the actual amount was here then.

As we know, each interval goes up in lots of five degrees.

So let's start from 30 and we can count up.

35.

40.

45.

Ah.

And then the arrow is between 45 and 50 degrees.

So there we go.

We know that the size of this angle is between 45 and 50 degrees.

So who was the closest then? That's right.

Andeep was the closest.

And was he within five degrees of the actual angle size? That's right.

He was, wasn't he? So we're gonna give three points to Andeep this time.

There we go.

Okay, time for round two now then.

Are you ready? There we go.

What do you think, Andeep? Well, you think it's an obtuse angle this time, do you, because it's greater than 90 degrees? That's right.

It is an obtuse angle.

So let's get ready to make our estimates again.

Are you ready? One, two, three! There we go.

What have we gone for this time? Aisha, you've gone for 110 degrees.

And Andeep, you've gone for 100 degrees.

Ooh, I wonder who's gonna be closest this time.

Let's check it now then, shall we? Here we go.

We can see that the arrow is between the 90 and 120-degree marker, isn't it? So let's count on in multiples of five degrees from 90 degrees.

Are you ready? 95.

100.

105.

And 110.

There we go.

So we can see that the arrow is pointing between 105 degrees and 110 degrees.

So we can say that we think it is slightly less than 110 degrees, can't we? Which is exactly what Aisha is pointing out.

So who got the point this time then? That's right.

Aisha would've got the point this time.

She was the closest.

And was she within the five-degree limit? That's right.

She was within the five-degree limit.

So, Aisha, you have got three points for yourself this time.

Back on level terms, aren't we? I wonder how the rest of the game's gonna go? Okay, here's the next example.

Can you tick the best estimate for this angle here? Take a moment to have a think.

That's right.

It's 145 degrees and we can check that now here to see.

We can see that the arrow is pointing between 120 and 150 degrees.

And do you know what? We could count backwards, couldn't we, in multiples of five from 150? So that would be 145 and then 140.

And we can see that the arrow is pointing between 140 and 145.

So 145 degrees would be the best estimate.

Well done if you managed to get that.

Here's another example.

Can you estimate the size of this angle this time? I wonder how you got on.

Let's check.

We can see that the arrow is pointing between the zero marker and the 30 marker.

And we can see that if we counted back in lots of multiples of five from 30 degrees and we can see that the arrow is pointing between 25 and 30 degrees.

Therefore, any estimate between 25 and 30 degrees would've been a good estimate.

Well done if you managed to get that too.

Okay, time for you to have a go now for yourself.

Could you play this game with a partner? How quickly can you get to 10 points? Once you've had a go at the game, maybe have a think about how you could make the game even more challenging.

It'd be really interesting to hear your ideas about how you do that.

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

Okay, welcome back.

I wonder how you got on.

Hopefully you've enjoyed that game and you managed to have a couple of rounds and you managed to win for yourself at some point too.

Andeep has come up with an idea for how to improve the game to make it even more tricky.

He said, why didn't you rotate the circle so the zero-degree marker isn't facing vertically? So here we go.

We can see now it's actually facing a little bit more horizontally, isn't it? Towards the top left of the screen.

I wonder how you made it more tricky.

Ask other people how they did it as well.

It might spur you on for a further challenge with your partner.

Okay, that's the end of cycle one.

Moving on to cycle two now, then, applying angle estimates.

So after school, Aisha and Andeep have gone off to play crazy golf.

Have you ever played crazy golf? I really enjoy playing it.

I often lose to my son though.

And he's only seven and he's hardly played any golf before.

So what does that tell you about my golfing ability? Hmm, I need some practise, I think.

Andeep really enjoys his crazy golf.

And he says that his Dad says that crazy golf is a game all about angles.

I wonder what he means by that? It's lucky that we've been learning about them.

Aisha, you're right.

So he's gonna have a go first.

Are you ready? He places his ball down and he strikes his first shot and the ball ends up here.

He's saying that's not his best shot so far.

Hmm, how's he gonna get the ball now towards the hole? What's gonna be the best move for him now to try and hit the ball towards the hole, I wonder? What do you think? How would you do it? Aisha says, you're gonna have to rebound it off the side, aren't you? A little bit like this.

So he's now starting to think about what angle he needs to create when he hits the ball off of the side.

Can you see the angle that he's created? How big do you think the size of that angle is? Take a moment to have a think for yourself.

Aisha thinks it's less than 90 degrees, so roughly about 70 degrees.

He's gonna give it a go.

Are you ready? Ah, so close, Andeep! It's rebounded off the wall exactly how you wanted it to, but it's fallen just short, hasn't it? So we must have got the angle bit right, roughly, mustn't we? But he just needed to hit it a little bit harder, didn't he? Unlucky, Andeep.

Right, Aisha's turn this time.

Are you ready? Aisha says, they call her Tiger.

Who? Do you not know who Tiger Woods is, Andeep? No, nevermind.

Don't worry.

Let's get on with the golf, shall we? Aisha plays her first shot.

Hmm, what did you think? Yeah, I agree.

It's a good shot, Andeep, isn't it? Where would you play your next shot then to try and get it into the hole? Oh, Aisha's going for a slightly different approach this time.

She's gonna try and rebound it off the back wall, she thinks.

She can't quite get it straight into the hole, can she? So she's gonna have to rebound it off of a wall.

Hmm, let's have a look.

What angle would be best for this then? Well, there we go.

We've now created the angle.

What do you think the size of that angle is? Hmm, again, it's definitely less than 90 degrees, isn't it? So Aisha thinks it's roughly about 40-degree angle.

Should we have a go? Go on, Aisha.

Let's see if you can get it.

There we go! Straight down the hole, Aisha! Amazing shot! Well done you! Yeah, exactly.

Fair play.

Great shot, Aisha.

Well done to you.

You weren't wrong, Aisha, when you were likening your skills to Tiger Woods, although I'm still not quite sure Andeep knows that we were referring to a person here rather than a tiger.

I've never seen a tiger play golf.

Okay, time for you to check your understanding now.

Can you estimate the angle needed to putt the ball into the hole? Take a moment to have a think.

Aisha thinks it's about 95 degrees.

We can see that it is gonna be slightly larger than a right angle.

So I think 95 degrees is a good estimate, Aisha.

Well done you.

Okay.

And now look at this shot here.

This shot gets rebounded off of three places.

So which one of those angles that's been created would roughly be 110 degrees? Take a moment to have a think.

That's right.

It'd be this top angle here, isn't it? We're looking for an obtuse angle because we know 110 degrees is greater than 90 degrees and less than 180 degrees, so therefore it would be obtuse.

And this looks like the only obtuse angle between the three of them.

Well done if you got that.

Okay, here's a slightly different golf hole now then.

Can you plan a route to putt the ball and estimate each angle size that you make as you go through? Once you've done it once, could you find a different route to go through? And again, estimate the angle sizes for those.

Once you've done that, you've then got a really tricky challenge here.

Can you estimate the route that Aisha took when trying to putt this ball? She says the first shot made a 30-degree angle.

The second shot made a 20-degree angle.

And the last shot made an 85-degree angle.

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

Okay, let's have a look then.

Here's an example of the route that Aisha took for the first one.

And let's estimate each one of these angles.

The first angle is roughly 80 degrees.

We know it's less than a right angle, but only just a little bit, so we can go for 80 degrees.

The second one is, once again, less than a right angle, but I think it's actually slightly smaller than the first one we looked at.

So we're gonna go for roughly 75 degrees for that one.

The third one is greater than a right angle.

We can see it's an obtuse angle, can't we? So we have estimated this time that it's 160 degrees.

And then finally, the last one.

Well, actually, it looks just bigger than a right angle, I would say this time.

So we've gone for 95 degrees.

Well done if you managed to come up with similar estimates to those as well.

And then for task two.

Did you manage to guess this route? You may have found a different way of doing it, but this was the route that Aisha took.

Let's have a look at Aisha's route here.

She putts it long, first of all, and then gets a short rebound off of the first piece of wood that gave her an angle of 30 degrees.

From this position, she can't putt the ball into the hole still yet, can she? So she rebounds it off of the back wall ever so slightly.

This angle creates a 20-degree angle.

And then from this position, she then putts it straight into the hole, creating an 85-degree angle from where the ball was.

Well done if you managed to find something similar to that as well.

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

Hopefully you've enjoyed yourself and it's been great to think about how we can estimate acute and obtuse angles in different contexts.

To summarise our learning, you can estimate acute and obtuse angles to help you solve everyday problems. And it is also really useful to estimate the size of the angle as to whether it is an acute, obtuse, or reflex angle before estimating an actual value for the size of the angle as well.

Well done today.

Thanks for joining me.

Take care and I'll see you again soon.