Lesson video

Hi there.

My name's Ms. Lambell.

You've made a superb choice deciding to join me today to do some maths.

Let's get going.

Welcome to today's lesson.

The title of today's lesson is following a bearing, and that's in the unit bearings.

By the end of this lesson, you'll be able to identify the position of point B given its bearing from point A.

You may not be familiar with what a bearing is.

A bearing is an angle measured in degrees from north in the clockwise direction and written with three figures, e.

g.

an angle of 82 degrees is written as a 082 degrees.

Today's lesson is split into two separate learning cycles.

In the first one, we will just concentrate on what a bearing is, because this may be the first time that you've come across them.

And in the second one we will look at actually following a bearing.

Let's get going with that first one, understanding bearings.

Andeep says, "Hey Sam, please can you give me directions from school to your house?" Sam says, "Sure, Andeep.

Turn right out of the gates.

Turn left at the traffic lights and then mine is the fourth house on the right." Lucas says, "Listening to you talking has made me think.

How do boats and helicopters get to the right place? There are no roads and traffic lights to describe directions." Do you know how boats and helicopters get to their destinations? Bearings and distances are used to ensure that boats and helicopters get to their exact destination.

As with many areas of maths and science, conventions are used to ensure that information is shared in a clear and consistent way.

When working with bearings, we use the following conventions.

They are measured from north.

North is north no matter where you are in the world.

They are measured in a clockwise direction.

Clockwise is the same throughout the world.

Doesn't matter whether you are in England or Australia, the clock goes in the same direction.

And they are always given as three figures.

The angle marked shows the bearing of the helicopter from the plane.

From is a really important word here.

From shows us the starting point, and we can see that we are going from the plane to the helicopter.

The plane travels along this bearing.

Anywhere along that line, the plane is travelling on exactly the same bearing.

It's travelling at the same angle.

True or false, the marked angle is the bearing of the diver from the boat.

Make your decision, true or false, but also remember to give me a reason.

Pause the video and then come back when you're done.

Okay, let's check your answer and hopefully you said it was false.

And the reason it is false is looking at that word from.

It says of the diver from the boat.

From shows the starting point, and we can see that the north line is drawn from the diver and the marked angle shows the bearing of the boat from the diver, not the diver from the boat.

It's really important we get those two round the right way.

Andeep says, "I understand why bearings are measured from north." Sam says, "I understand that bearings are measured in a clockwise direction." Lucas says, "Why do they have to be given as three figures? If the angle is 35 degrees, why would you need to say the bearing is 035 degrees?" Do you know why bearings are always given as three figures? Andeep does.

Andeep says, "I know why they are always given as three figures." Lucas says, "Why are they Andeep?" Andeep says, "Sam, help me illustrate this please." Sam says, "May day, may day! my boat has run out of fuel.

I'm on a bearing of 2, 3 degrees and 3.

5 kilometres from the shore.

Please send help." Andeep's response is, "Sam, I only heard two digits.

Please repeat your location." Sam says, "I am on a bearing of 2, 3, 8 degrees and 3.

5 kilometres from the shore.

Please send help." And Lucas says, "I see why now.

I would've travelled on a bearing of 23 degrees to save Sam! Not the correct bearing of 238 degrees." Have a go at this check for me.

Which diagram shows the bearing of 120 degrees of B from A? Make your decision and come back when you're done.

Okay, what did you decide? Well, a is incorrect.

This is the bearing of A from B.

We can see our starting point is B.

b was the correct one, and c was incorrect because the direction is anti-clockwise and not clockwise.

True or false, the bearing of the boat from the diver is 45 degrees.

Is that true or false? And as always, don't forget, I want a justification as to why you've chosen what you've chosen.

Pause the video and come back when you've got your answer And you decided false, I hope.

And the reason was the angle has not been given as three figures.

The bearing of the boat from the diver is 045 degrees, not 45 degrees.

We must give them as three figures.

And another check.

Which diagram shows the bearing 200 degrees of B from A? The correct answer was b.

If we look at a, we can see that the starting line is actually pointing to east not north.

b was correct.

And then c, we can see that the angle is being measured from south and not north.

Task A.

I'd like you please to complete the following.

I've given you a diagram and then I've given you some sentences.

The bearing of something from something is 050 degrees.

You need to fill in the gaps.

Pause the video and then come back when you've got your answers.

And same thing c and d.

And here are the answers.

1a, the bearing of A from B is 050 degrees.

b, the bearing of B from A is 082 degrees.

c, the bearing of B from A is 009 degrees.

And d, the bearing of B from A is 240 degrees.

Let's move on to the second learning cycle.

We're going to be following a bearing.

Point B is 7 kilometres away from point A on a bearing of 060 degrees.

Mark point B with a cross.

And we've been given here a scale that the side of a triangle is 1 kilometre.

The grid is made up of equilateral triangles.

How many degrees is an interior angle of an equilateral triangle? And that's 60 degrees from north, 060 degrees.

And then we're gonna measure 7 kilometres, 7 of the triangles, and then we can see that that is where point B is.

Point B is 3 kilometres away from point A on a bearing of 120 degrees, and point C is 5 kilometres away from point B on a bearing of 240 degrees.

Which is the correct position of point C? Is it a, b, or c? Pause the video and then when you've got your answer come back.

What did you decide? Was it a, b or c? Let's take a look.

It was c.

If we go on a bearing of 120 degrees for 3 kilometres and then 240 degrees for 5 kilometres, we end up at point C.

The boat needs to pick up the diver.

The length of each square on the grid represents 1 kilometre.

Describe how the boat gets to the diver.

3 kilometres east and 5 kilometres north.

Andeep says, "That's not very efficient.

Surely you would want to go directly to the diver." What do you think? We could use bearings to go directly to the diver.

Join the boat to the diver, and then we can measure the angle.

We measure that angle, we can see that it is 32 degrees.

The boat needs to travel on a bearing of 032 degrees to get to the diver.

Andeep says, "Anywhere along that line the boat is travelling on a bearing of 032 degrees." What else do we need to know so that the boat gets to the exact position of the diver? We need to scale and a distance.

The scale is 1 centimetre equals 1 kilometre.

We can measure the length of our line.

The boat needs to travel on a bearing of 032 degrees for 5.

7 kilometres.

A diver is 3.

5 kilometres away from a boat on a bearing of 120 degrees.

We need to mark the position of the diver with a cross.

We start by drawing in our north line from the boat 'cause that's our starting point.

We then need our protractor.

We need to make sure we are measuring in a clockwise direction.

And so my protractor needs to look like this.

I need my zero on my north line and I'm going clockwise, so my protractor is to the right.

I'm now going to mark 120 degrees.

We know that the diver is 3.

5 kilometres away from the boat on a bearing of 120.

Anywhere along this line I've lined up the position of the boat with 120 degrees, anywhere along that line is on the bearing of 120 degrees, but we know the distance is 3.

5 kilometres and we've got a nice straightforward scale.

1 centimetre is 1 kilometre, so we need to mark the point 3.

5 kilometres away, which is here and that's where the diver is.

And we could join those points together if we wanted to.

But this angle here was 120 degrees, a bearing of 120 degrees.

And the length of that line was 3.

5 centimetres, which represented 3.

5 kilometres.

A diver is 6.

2 kilometres away from a boat on a bearing of 255 degrees.

Mark the position of the diver with a cross.

Drawing our north line from the boat, and we put our protractor on.

And Lucas says, "How am I going to draw a bearing of 255 degrees? My protractor only goes up to 180 degrees." Sam says, "Lucas, you can either mark 180 and then mark 75 from there, or go anti-clockwise 105 degrees." So either of those two would give us an angle of 255 degrees or a bearing of 255 degrees.

My north line, and I'm going to mark 105 degrees.

I've decided to go anti-clockwise.

Notice that's the same as marking where 180 is and then 75 on.

We'll put our ruler on.

And this time we need to mark 6.

2 centimetres, and that is where the diver is.

And again, we can join those points together and we can mark that bearing of 255 degrees.

That was 6.

2 kilometres.

Simon is following a bearing of 065 degrees.

Which diagram shows the protractor positioned correctly? And it is c.

Starting from north, make sure your protractor has zero on the north line and that you're moving clockwise.

A buoy is on a bearing of 070 degrees from boat A and a bearing of 285 degrees from boat B.

Mark the position of the buoy with a cross.

Let's start with the first piece of information.

It's on a bearing of 070 degrees from boat A.

Let's mark 070 degrees.

We know that it's anywhere along that line.

So I've just extended that line because I think I probably need to draw it longer than the point that I've made with my protractor.

I also know that it's on a bearing of 285 degrees from boat B.

Boat B, I'm going to now work out where that needs to be.

So I'm going to do 360 subtract 285, and that gives me 75.

So I'm going to mark 75 degrees here.

Remember you're going to be using the red scale, the inside scale because that is the scale that starts at zero on north.

I can then draw the line through, and the buoy is at the point where the two lines intersect.

So that is where the buoy will be.

A boat is on a bearing of 112 degrees from a lighthouse and a bearing of 257 degrees from a rock Mark the position of the boat with a cross.

Bearing is 112 degrees, so we need to mark 112 degrees and we're gonna draw a line.

And the bearing from the rock is 257 degrees, and so we need to mark 257 degrees.

Remember we're going clockwise or here anti-clockwise 103 degrees, and then extend the line until the two lines cross.

The boat is at the point where the two lines intersect, so that is where the boat will be.

Now for task B.

Question number one, you're gonna follow the bearings to decide what is reached at the end of the journey.

You're going to start at the tree and then you're going to travel on a bearing of 060 degrees for 4 kilometres.

Then you are going to travel along the other bearings for the given lengths, and then you should end up at one of the locations.

If you don't end up at a cross, then you know you've made a mistake and you can go back and check your working.

So pause the video, follow these bearings, and then come back when you've got your answer.

Well done.

Question number two, mark point B with a cross.

So a, point B is 7 kilometres away from point A on a bearing of 055 degrees.

And for b, point B is 2.

8 kilometres away from point A on a bearing of 315 degrees.

And you are going to use the scale 1 centimetre equals 1 kilometre.

Pause a video, give this a go.

Make sure you line up your protractor really carefully and also make sure you use a pencil and a ruler.

Good luck, and I'll be waiting when you get back.

And question three.

A boat is on a bearing of 075 degrees from a lighthouse and a bearing of 275 degrees from a rock.

Mark the position of the boat with a cross.

Pause the video and then come back when you've got your answer.

Well done.

Let's check the answer then.

You should end up at the volcano.

And you can see here the dotted lines show you the bearings and the distances that you should have travelled to get you to the volcano.

Well done if you did end up at the volcano.

Question two, you should have a line of 7 centimetres in length and it should be 055 degrees from the north line.

And for B, you should have marked either 135 degrees after 180 or 45 degrees from north anticlockwise, and your line should be 2.

8 centimetres in length.

And then question three, you should have marked an angle of 075 degrees, so 75 degrees on the protractor, and then you should have marked also an angle of 275 degrees, and the boat is at the point where the two intersect.

How did you get on? Well done.

Summarising the learning from today's lesson.

Bearings and distances are used to ensure that boats and helicopters get to their exact destination.

When we work with bearings, we use the following conventions.

They are always measured from north.

And remember that's because north is north no matter where you are in the world.

They are always measured in a clockwise direction.

And that's because clockwise, again, is the same throughout the world.

It doesn't matter where you are, whether you're in England or you're in America or you're in New Zealand, the clock goes in the same direction.

And they are always given as three digits.

For example, an angle of 7 degrees written as a bearing is 007 degrees.

To find an exact position, you also need a distance and a scale, unless you are given the bearings of an object from two separate points.

Well done, you've done fantastically well today, and hopefully I'll see you again really soon to do some more maths.

But until then, please do take care of yourself.

Goodbye.