Lesson video

Hello, there, my name is Mr. Tilstone.

I'm a teacher, and it's my great pleasure and great delight to be with you today teaching you a lesson all about unit conversions.

So if you're ready, I'm ready, let's begin.

The outcome of today's lesson is, I can convert between miles and kilometres, and between pounds and euro.

We've got some keywords.

My turn, kilometre, your turn.

My turn, mile, your turn.

My turn, approximate, your turn.

My turn, pound, your turn.

My turn, euro, your turn.

You might know some of those words already, or you might not, but let's have a look what they mean.

A kilometre is a metric measure of distance equal to 1,000 metres.

It can be abbreviated to km.

A mile is an imperial measure of distance.

If a value is not exact but is close enough to be used, it is approximate, so it's roughly the same.

The currency used in the United Kingdom is pounds sterling, and the currency used in most European countries is the euro.

Our lesson today is split into two cycles, converting between miles and kilometres, and converting between pounds and euro.

So let's start by converting between miles and kilometres.

In this lesson, you're going to meet Izzy.

Have you met her before? She's here today to give us a helping hand with our maths.

Here she is.

Every Saturday morning, Izzy does a five kilometre park run.

So do I.

They call it a 5K park run.

Five kilometres is a metric measure equivalent to exactly 5,000 metres.

So 5K, 5,000.

Kilometres are a commonly used unit of measurement in most countries across the world.

So nearly everywhere you go, if you travel abroad, they will use kilometres for their main measure.

In the United Kingdom, distances are usually measured in the imperial unit of miles.

So there are a few countries in the world, United Kingdom being one of them, that still use miles.

So every Saturday morning, Izzy does a five kilometre park run.

How far does she run every Saturday morning in miles? Let's explore that.

Well, there's an equivalent, an approximate equivalent between miles and kilometres.

If you've gone five miles, you've gone approximately eight kilometres.

So five miles is approximately equivalent to eight kilometres, and you can see that on the bar model.

The top row is split into five equal parts, and that's the same length as the bottom row, which is split into eight equal parts.

So once again, five miles is approximately equivalent to eight kilometres.

That's a useful fact.

The model can be used to give approximate conversions between miles and kilometres.

So let's have a look at this.

So five miles is about eight kilometres, as you can see.

What does this mark show? So what do you notice? Look where the red mark is.

It's exactly on a value.

Where is it exactly? So it's exactly on four kilometres.

And four kilometres you can see is approximately two and a half miles.

It's halfway, look.

So two miles have gone, but not three miles.

It's halfway in between them.

What about this one? What can we say here? How many kilometres is that? And how many miles would you say? Two kilometres is just over one mile, and we could maybe give it as a fraction or a decimal, maybe say something like it's approximately 1.

25 miles, but I think it's enough to know that it's just over one mile.

What about that? What's that showing? Think about the miles, think about the kilometres.

That's one kilometre, and we can say it's less than a mile.

You could say it's a little bit over than half a mile as well, something like that.

Oh, okay, this is different.

What's it showing this time? It's not showing the exact number of kilometres, is it? So what is it showing? That's showing one mile.

And one mile, as you can see, is approximately 1.

5 kilometres.

It's just over halfway.

What's about this one then? We've got again an exact number of miles.

What's the number of miles? That's two miles.

And that's just over three kilometres.

These are very approximate values.

How about this one? What have we got now? Three kilometres.

So we could say three kilometres is just under two miles.

It's time for a little check.

So use our bar model to give the approximate number of miles that Izzy runs at the 5K park run.

So five kilometres is, pause the video.

Five kilometres is what? Let's have a look.

Well, it's just over three miles, isn't it? Just over three miles.

So Izzy runs just over three miles every Saturday morning.

Okay, we've got a double number line.

On the bottom, we've got the miles, on the top, we've got kilometres.

So Izzy and her family are going to France to visit her pen friend.

Have you been to France? I have, it's very nice.

In France, distances are measured in kilometres.

So when you look at road signs, they're not showing miles, they're showing kilometres.

This double number line represents the information in the bar model.

So just like before, but it's in a different form this time, we can see that five miles is equivalent or approximately equivalent to eight kilometres.

But Izzy and her family are going further, so we need larger values on this number line.

We know that five miles is approximately equal to eight kilometres.

What other equivalences between miles and kilometres can you see here? Pause the video and see what you can come up with.

Welcome back.

Well, here's some examples that you might have found, but there are many.

So you might have said 50 miles is approximately 80 kilometres.

You might have said 100 miles is around 160 kilometres.

You might have said 100 kilometres is just under 65 miles.

You might have said 40 kilometres is approximately 25 miles.

You might have said 70 miles is just over 110 kilometres.

All sorts of answers.

So here's Izzy again.

She says, "Are we nearly there yet?" Izzy's mum says they have 115 kilometres left to go.

"How far is that in miles?" she says, well, here's 115 kilometres on our number line.

What would you say? How many miles approximately do you think that is? Hmm, well, it's more than 70, it's less than 80, it's less than 75.

So a bit more than 70, a bit less than 75.

115 kilometres is approximately 74 miles.

"Not too far then," she says.

We have 45 miles to go.

What is that in kilometres? A table can be used to explore approximate equivalences between miles and kilometres, so you don't have to use that number line.

We know already that five miles is approximately eight kilometres, so we're going to add that to our table.

We've got one other piece of information as well.

In this case, the number of miles is known, it's 45.

And that can be added to the table, so that's what we've done.

So look at the miles column.

We've added it today.

Now, here's where your times tables knowledge is going to come in handy.

Five times something equals 45.

How many fives make 45? Nine.

So if five times nine equals 45, what do you think we're going to do to that eight? The number of kilometres must be multiplied by the same factor.

So we're also going to multiply that by nine.

So what's eight times nine? Hopefully that was the fact that came to you straight away, that's 72.

So we can say that 45 miles is approximately 72 kilometres.

We have 72 kilometres to go, so as you see.

So that table can be used to explore the approximate equivalences between miles and kilometres.

So there we are, five miles, eight kilometres.

Now, this time Izzy says, "We have 160 kilometres to go.

What is that in miles?" In this case, the number of kilometres is known, and it can be added to the table.

There we go, in the kilometres column.

Now, just like before, we're going to use our times tables knowledge, but we're going to extend it a little bit.

Eight times something equals 160.

Well, let's start by thinking about eight times something equals 16.

That would be a good starting point.

Eight times two equals 16, so therefore eight times 20 equals 160, because it's 10 times larger.

So if we're multiplying eight by 20, what do you think we're doing to the five? The number of miles must be multiplied by the same factor, and that's 20, again.

So five times 20, 20 times five.

Hopefully you got that pretty quickly.

That's 100.

So we can say that 160 kilometres is approximately 100 miles.

We have 100 miles to go.

Let's do a check for understanding.

Give an approximate conversion from 400 kilometres to miles.

So we've got that key fact that five miles is approximately eight kilometres, and we're looking to convert that 400 kilometres.

Pause the video and have a go.

What did you get for that one? Well, let's start thinking about what we multiply eight by to get 400.

And I'm going to start by thinking what I multiply eight by to get 40, which is five, so therefore that's 50.

So eight times 50 equals 400.

We're going to do the same for the five.

Five times 50 equals 250.

So 400 kilometres is approximately 250 miles.

Very well done if you got that, you're on track.

If five miles is equivalent to eight kilometres, 250 miles is equivalent to 400 kilometres.

It's time for some practise tasks.

So number one, give each approximate value in both miles and kilometres.

So use your double number line, your conversion line.

Number two, Izzy and her family are travelling to Lille in France where they will visit Izzy's pen friend Rochelle.

The sign tells them how far in kilometres they have left on their journey.

And if you go to France, the signs do look a little bit like that with the same colours.

Use a table to convert approximately into miles.

And each time, you've been given that key fact that five miles is approximately eight kilometres.

Have a go at that.

Remember to use your times tables knowledge is my tip there.

Number three, Rochelle and her family are visiting Izzy in Birmingham.

The sign tells them how far in miles they have left on their journey.

So these road signs might look a little bit more familiar to you if you live in the United Kingdom.

So we've got, yeah, Birmingham is 100 miles, Birmingham, 75 miles, getting closer.

And then finally Birmingham is 60 miles away.

So can you convert all of those into kilometres, which will be helpful to Rochelle.

Good luck with that.

Pause the video.

Use those times tables skills, and off you go.

Welcome back.

Are you ready for some feedback? Let's do it.

So number one, the approximate value in miles and kilometres.

Well, A, that's 50 kilometres, that one was the easier one to do.

And that's just over 30 miles.

You might have been a bit more specific than that.

And B, that's showing 85 kilometres.

And that's just over 50 miles.

And again, you might have given it a different value.

C, that's showing 125 kilometres, right in the middle of 120 and 130.

And that is just under 80 miles.

And once again, you might have said something like 78 miles.

And 140 kilometres, that's what D is showing.

And that is just under 90 miles, and you might have given a more specific value than that.

And question two, let's convert these kilometres to miles.

So we've got that unit conversion, that five miles is approximately eight kilometres.

How many times does eight go into 320? 40.

So we're going to multiply five by 40 as well, and that gives us 200.

240 kilometres, eight goes into 240 30 times.

Five times 30 is 150.

And finally, 88 kilometres, eight times 11 is 88, and five times 11 is 55.

And then they're doing the return visit in England.

So these are the English road signs.

Let's convert them into kilometres.

So five miles is eight kilometres.

100 miles, so five goes into 100 how many times? 20.

So eight times 20 is 160.

And then five goes into 75 how many times? 15.

So eight times 15 is 120.

And then five goes into 60 how many times? 12.

So eight times 12, one of our key times tables facts is, hopefully you got this instantly.

96.

Well done if you got those.

Are you ready for the next cycle? I think you are.

Let's go.

This time we're looking at converting between pounds and euro.

So France and many other countries in Europe use euro, not pounds.

Izzy has some euro to spend in France.

Five pounds is approximately six euros.

Now, that changes as well day to day.

The exact conversion, unlike kilometres and miles, does change.

What other values can you fill on the double number line? So something euros is approximately something pounds.

So let's have a look at that.

What could you say? What are we saying here then? We could say 12 euros is approximately 10 pounds.

What about this? What are we saying here? Three euros is approximately 2.

50 pounds.

What about this one? We've got the number of euros.

What would you say that is in pounds? It's halfway between seven and eight, so it's 7.

50 pounds.

Nine euros is approximately 7.

50 pounds.

Well, let's have a check.

What approximate values would you give to the remaining marks? Pause the video, off you go.

Let's have a look then.

So here are some examples of the statements that you might have made.

You might have given slightly different values, that's fine too.

So one euro is just under one pound.

Four euros is approximately 3.

30 pounds.

You might have said maybe just a little bit over three pounds as well, that's acceptable.

Eight pounds is approximately 9.

50 euros.

And finally, six pounds is just over seven euros.

You might have given a specific number.

The number lines can become the axes of a graph.

Let's have a look at that.

Here we go.

So on the bottom, on the x-axis, we've got the pounds, and on the y-axis, we've got the euros.

So that's the same number lines as before, but just in graph form.

And Izzy says, "I think we can draw a neater graph than this." I agree, Izzy, I agree.

So here is a neatened up graph with grid lines to help us, pounds for the x-axis and euros for the y-axis.

Here is some information that we found before.

So zero pounds is zero euros, five pounds is approximately six euros, and 10 pounds is approximately 12 euros.

Let's plot those in.

I'm gonna plot those in on the graph.

Let's start with this one.

That goes right here.

What about this one, so five pounds, we're gonna go long to five pounds, and then up to six euros.

Put an X there.

And this one, 10 pounds.

Let's go across the 10 pounds on the x-axis.

We're going up to 12 euros.

I'm going to put an X there too.

She says we can join the points with a line.

You can, they make a nice straight line.

And you can extend through it.

So now we've got a handy graph.

So we can convert any number of pounds into any number of euros and any number of euro into any number of pounds.

So let's do a check.

Plot the points that represent converting three euros into pounds, nine euros into pounds, and 10 pounds into euro.

Pause the video and give that a go.

Okay, so here we are.

So that's three euros.

So we're going across from the three euro and down to the pounds.

And you can see that's about 2.

50 pounds.

But that's where that would go.

And here, that's nine euros, so we're going along from the nine euros down to the pounds on the x-axis.

That's just a little bit over seven pounds, a bit less than 7.

50 pounds, I would say.

And then 10 pounds into euro, so start with the 10 pounds on the x-axis, go up to the y-axis, and across from it, and you can see that's very close to 12 euro.

And Izzy says, "I can now read off the values to convert these amounts of money." So here we've got that graph then, converting between pounds and euros.

And Izzy says, "I can use the line to do more conversions between pounds and euro." A sandwich costs five euro.

Izzy wants to know how much that will be in pounds so she can decide if it's good value.

That's a good idea, Izzy, I like that.

So we go, that's a five euro.

Along that axis and down to this, and that takes us just here on the x-axis.

So I'd say just a little bit over four pounds.

Just over four pounds, around 4.

20 pounds.

Izzy thinks that's rather expensive for a sandwich.

I think it is as well.

So she keeps looking, very shrewd.

Let's do a check.

A teddy costs 14 euro.

Izzy would like an idea of how much that will be in pounds.

Again, she's very conscientious about value, isn't she? And I like that.

Help her to convert.

Pause the video.

Let's have a look, so 14 euros.

So let's go along from the 14 euro on the y-axis, in the horizontal line, to meet that line, the diagonal line that goes through the graph, and then down from there to the x-axis where the pounds are.

And you can see it's just a little bit less than 12 pounds.

It's more than 11 pounds, less than 12 pounds.

Probably about 11.

60 pounds, something like that.

Gives you a good approximate idea though, just over 11.

50 pounds.

Time for some practise.

Use the graph to give approximate conversions between pounds and euro.

So we've got 1.

50 pound, how many euro is that? 12.

50 euros, how many pounds is that? 7.

50 pounds, 7.

50 euro, and then 15 pounds.

Can you do some conversion? Use the graph to help.

And then number two, draw a graph to give approximate conversions between miles and kilometres.

So we've got some key information on there already.

As you can probably imagine, zero miles is zero kilometres, but we knew from earlier on that five miles is approximately eight kilometres.

So you can plot that onto the graph.

And then when you've got a bit more information, you can join the dots up just like before to create a diagonal line.

Good luck with that, and I'll see you soon for some feedback.

Welcome back.

How did you get on with your graph work? Let's have a look.

So now these are approximate conversions, so your values may differ slightly, but we're looking for something around this.

So we know that's 1.

50 pounds, and that is about 1.

80 euro.

And then we've got 12 pounds, 12.

50 euro, beg your pardon, and that is just over 10 pounds, but less than 10.

50 pounds, probably about 10.

40 pounds.

Now, 7.

50 pounds, let's go up from there and across.

And that is about nine euro.

And then 7.

50 euro.

Let's go across and then down this time.

Just a bit over six pounds, isn't it? What do you think about 6.

25 pounds, something like that? And then 15 pounds.

If you go up from there and meet the diagonal line and go across from there, that takes across to about 18 euro.

And then your graph should look a little something like this.

So very well done if it did.

Then you can use that to complete all of the other information.

So zero miles, zero kilometres, five miles, eight kilometres, 10 miles, 16 kilometres, 25 miles, 40 kilometres, 50 miles, 80 kilometres, 75 miles, 120 kilometres, and 100 miles, 160 kilometres.

And maybe you've found some other values on there too.

We've come to the end of the lesson.

Today's lesson has been converting between miles and kilometres and then pounds and euro.

So five miles is approximately equivalent to eight kilometres.

This fact can be memorised and used as a starting point for other conversions between miles and kilometres.

And that's what I've done.

That fact is locked and loaded up here.

So if I need to convert from miles to kilometres or vice versa, I use that as my starting point.

And that's really helpful if you're travelling in a different country.

A double number line or a conversion graph can be used to convert from one unit to the other.

For example, from euro to pounds or pounds to euro, or miles to kilometres, or kilometres to miles.

Hopefully one day in the future you'll get the chance to travel to a country like France or somewhere else where you can use and apply these skills.

I've thoroughly enjoyed being with you today.

Thank you for your hard work.

Give yourself a little pat on the back to celebrate all of your accomplishments and achievements, and hopefully I will see you again soon for some more maths.

But until then, take care, enjoy the rest of your day, and goodbye.