Lesson video

Hi there, my name is Ms. Lambell.

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

Let's get cracking.

Welcome to today's lesson.

The title of today's lesson is "Converting Between Metric and Imperial Measures of Speed".

And this is within the unit Compound Measures.

By the end of this lesson, you'll be able to convert between metric and imperial speed measures.

Keywords that we'll be using in today's lesson are metric, imperial, speed and direct proportion.

Metric units are based around the standard units of metre, gramme and litre.

Imperial is a system of units for measuring which was created in the early 1800s during the British empire.

Speed is the rate at which something is moving.

It is measured as the distance travelled per unit of time.

Two variables are in direct proportion if they have a constant multiplicative relationship.

Splitting today's lesson into two learning cycles, in the first one, we will look at reviewing metric and imperial units of measure 'cause this is something that you may not have done for a while, so I think it's really useful to recap that.

And then in the second one, we will concentrate on using what we've learnt in the first learning cycle to convert between metric and imperial speed measures.

Let's get going with the first one.

We're gonna review our knowledge of metric and imperial units of measure.

Estimate the average mass of a newborn baby.

Sam says, I think it's 3.

2 kilogrammes and Sofia says, I think it's seven pounds and four ounces.

Can both of their estimates be correct? Yes, they've just decided to use different units of mass.

Sam has chosen to use kilogrammes.

Is this a metric or imperial unit of mass? Right, it's a metric unit of mass.

Kilogrammes are metric units and the clue there is that kilo part, that often helps us remember if it is a metric unit or not.

Estimate the capacity of this jug.

Sam says, I think it's five pints.

Sofia says, I think it's three litres.

Who has used a metric unit this time? Sofia has used a metric unit.

Sam has used an imperial unit.

Litres are metric, pints are imperial.

Now that I've reminded you of the difference between metric and imperial units, I'm hoping that you can now sort these units of measure into the correct columns, metric or imperial.

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

Let's check our metric units, and you may have these in a slightly different order, are metres, kilogrammes, millilitres, centimetres, kilowatts and metric tonnes.

And imperial are inches, miles, feet, hands, acres and tonnes.

Did you manage to get them all in the right columns? Well done, for this lesson, we need to be confident with converting between different metric units and converting between metric and imperial units.

I'd like you to pause the video and fill in the blanks.

You should be really confident and be able to recall these really quickly.

So pause the video, I expect to see you back super quick.

Let's check those, one kilometre is 1000 metres.

One metre is 100 centimetres and one centimetre is 10 millimetres.

How would we use this place value chart to convert 6,050 millilitres into litres? Our unit of measure is millilitres, so we start with the ones digit in the millilitres column and then we can place our other digits.

We want to convert it into litres, therefore we need to put our decimal point after the litres, given us that 6,050 millilitres is equal to 6.

05 litres or we know that millilitre means 1000th of a litre, which means 6,050 millilitres means I've got 6,050 thousandths of a litre, which is 6.

05 litres.

We can see that either way we end up with the same answer.

How could we use the place value chart to convert 840 grammes into kilogrammes? This time our unit is grammes and we need to put the ones digit in the grammes column.

Then we can place our other digits into the place value table.

We are converting this into kilogrammes, therefore our decimal point goes at the end of the kilogrammes.

There is no digit in the kilo column, so therefore we need to put our placeholder of zero and then our decimal point goes after that kilo column.

840 grammes is equal to 0.

84 kilogrammes or we know that kilogramme means 1000 grammes, therefore one gramme is 1000 times smaller than a kilogramme.

This means 840 over 1000, which is 0.

84 kilogrammes.

Your turn now, Jacob says I have a bottle of water that says 660 millilitres.

This is the same as which of those four options? Pause the video, make your decision, and then come back.

And the correct answer was B.

Alex says, my brother drove 24,500 metres.

This is the same as driving A, B, C, or D.

Make your decision and come back when you're ready.

We were looking at metres, we put our ones digit in the metres column, place all our other digits and we can clearly see that this is 24.

5 kilometres.

So the correct answer was A.

Since variables, which are directly proportional to each other, share a multiplicative relationship, we are able to use a ratio table to find other information.

Aisha says, my dad has a really good way of remembering the miles and kilometres conversion fact.

Jacob says, oh please tell me when I run, I measure it in kilometres, but my mum always wants to know what it is in miles.

Aisha says if you had a five mile weight in kilometres, it would be eight.

Oh, that's good, isn't it, 'cause it rhymes.

Always find things that rhyme much, much easier to remember.

And Jacob says, that's brilliant.

How far did you run this weekend, Jacob? I ran five kilometres on Saturday and four kilometres on Sunday.

How far did Jacob run this weekend in miles? He wants to tell his mom how far he's run, but he knows that she'll want to know what it is in miles.

We know that if we had a five mile weight in kilometres it would be eight.

We also know the total that Jacob ran over that weekend was nine kilometres, the sum of five and four.

I'm looking for my multiplicative relationship, which is multiplied by 1.

125.

If I multiply the kilometres by that, I need to multiply the miles by that, giving me 5.

625.

Jacob ran 5.

625 miles at the weekend.

Well done, Jacob.

Oh, do you remember this guy? Anybody remember what his name is? It's Pedro.

Pedro the panda.

Got another rhyme for you.

This time it's gonna help us remember the metric imperial conversion for mass.

A kilo of Pedro Panda's bamboo when measured in pounds is 2.

2.

Yeah, nice.

A kilo of Pedro Panda's bamboo when measured in pounds is 2.

2.

Now you say it, I bet you didn't.

Aisha says, Jacob, do you know how heavy you were when you were born? I was eight pounds, seven ounces.

Let's see what Jacob says.

Jacob says, yes, I was 4.

09 kilogrammes, who was heavier at birth? Now I don't know about you, but because they're given in different units, I would not be able to say who was heavier at birth at the moment.

We need to do some conversions.

We know that a kilo of Pedro Panda's bamboo when measured in pounds is 2.

2.

That's our conversion we're going to use.

We also know that Jacob's weight was 4.

09 kilogrammes.

We're gonna convert that into pounds.

This time I've decided that I'm going to go from left to right and it's just to remind you that in our ratio table, we can move vertically or horizontally.

My multiplier is multiplied by 2.

2, so I multiply the kilogrammes to pounds, I multiply by 2.

2 and I get nine pounds.

This means that Jacob was nine pounds at birth, so Jacob was heavier.

Your turn now, using our little rhyme, which of the following is correct? Pedro says, I eat 110 pounds of bamboo in a day.

How many kilogrammes is that? Make your decision and come back and see if you're right.

And your answer was, should have B, 50 kilogrammes, 110 divided by 2.

2 because this time we're going from pounds to kilogrammes was 50 kilogrammes.

I'm sure you got that right, now for task A, you're gonna fill in the gaps.

Pause the video, no calculators here because we're gonna be multiplying or dividing by 10, 100 and 1000 and you don't need a calculator for that.

I'll be here waiting to reveal the next question when you get back, you can pause that video now.

Question number two, I'd like you please to place the distances in order of size, starting with the smallest first.

You'll need to choose a unit to convert them all into, I'm not gonna tell you which one.

Okay, you can make that decision, but some of them will make it slightly easier than others.

Pause the video again, no calculators on this one please.

And then I'll be waiting for question three when you get back.

And question number three, note here that these images are not to scale.

You're gonna write the following in order from the shortest to the tallest and you need to use the conversion fact that one metre equals 3.

3 feet.

Again, you'll need to decide to convert them all into feet or all into metres.

I'll leave that up to you, when you've got your answer, come back and we'll check those three questions for you.

Question one, A, 23 metres is equal to 2,300 centimetres.

B, 1,750 metres is equal to 1.

75 kilometres.

C, 45 centimetres is equal to 0.

45 metres.

D, 23.

4 kilometres is equal to 23,400 metres, and E, 235 metres is equal to 23,500 centimetres.

Now obviously if I went too quick whilst I was going through those, pause the video and check them at your own pace and then come back and we'll look at question two.

Question two, shortest to longest you should have F, D, then B and E were actually exactly the same size and then C and the longest was A.

And finally question three.

The correct order from the shortest to the tallest was the garage, elephant, teepee, bus, and then the tallest was the giraffe.

Okay, let's move on then.

We're now gonna look at converting between metric and imperial speed measures.

We know how to convert between metric and imperial units, but we are looking now at speed measures.

And remember speed is a compound measure because it's made up of two units, it's made up of time and distance.

The speed limit on UK motorways is 70 miles per hour.

The speed limit on French motorways is 130 kilometres per hour.

On which motorway can you legally drive faster? What do you think? Right, have you made your mind up? Now we're going to check.

We can convert 70 miles per hour into kilometres per hour or 110 kilometres per hour into miles per hour.

Using our rhyme, if we had a five mile weight in kilometres, it would be eight.

I'm going to convert 70 miles per hour into kilometres per hour.

I'm looking for that multiplicative relationship.

Multiply by 14, five multiplied by 14 is 70.

I need to therefore multiply my kilometres also by 14.

Giving me 112, 70 miles per hour is equal to 112 kilometres per hour.

You can drive faster in France or we could have converted, like I said, the 130 kilometres per hour into miles per hour, using my same conversion, if I had a five mile weight in kilometres it would be eight and I'm converting this time my 130 kilometres into miles.

My multiplicative relationship this time is multiplied by 16.

25.

I multiply the miles by the same, giving me 81.

25, 130 kilometres per hour is equivalent to 81.

25 miles per hour.

And then we can see again that we can drive faster in France.

Using the fact that one mile equals 1.

6 kilometres, which is faster, 45 miles per hour or 70 kilometres per hour? Here I want you to think, will it be easier to convert 45 miles per hour or 70 kilometres per hour.

As we have a unit ratio in miles, it's going to be easier to convert 45 miles per hour into kilometres per hour.

We could do it the other way around, this is just about efficiency and ease and we know that one mile is equal to 1.

6 kilometres, meaning that ratio table is going to be much easier to use.

Here is my conversion.

One mile is equal to 1.

6 kilometres and we are going to convert 45 miles per hour into kilometres per hour.

My multiplier is multiplied by 45, multiplied by 45, gives me 72, 45 miles per hour is equal to 72 kilometres per hour, 45 miles per hour therefore is faster than 70 kilometres per hour.

Remember that we can also move horizontally.

Let's now do that to double check our answer.

And this is a really good thing to remember, to do it both ways, if you get the same answer both ways, you can be pretty confident you've got it right, can't you? My multiplicative relationship between miles and kilometres is multiplied by 1.

6, 45 multiplied by 1.

6 is 72.

I can now be confident that my answer is correct.

Let's do one together and then I'd like you to have a go at one independently.

We're going to stick with using that fact that one mile is 1.

6 kilometres, which is faster, 30 miles per hour or 50 kilometres per hour? Here is my ratio table.

I'm multiplying by 30 giving me 48, 30 miles per hour is equal to 48 kilometres per hour.

So we can see that 50 kilometres per hour is faster than 30 miles per hour.

Now your turn, again using the fact that one mile is 1.

6 kilometres, I'd like you please to find out for me which is faster, 55 miles per hour or 90 kilometres per hour.

Pause the video and come back when you've got your answer to this question.

Here is our ratio table.

Our multiplier is multiplied by 55.

1.

6 multiplied by 55 is 88.

55 miles per hour is equal to 88 kilometres per hour.

Therefore 90 kilometres per hour is faster than 55 miles per hour.

So Sofia's dad drives to a meeting at an average speed of 80 kilometres per hour for two hours and 15 minutes.

We need to work out the number of miles he drives.

Here is Aisha's working and here is Jacob's workings.

What is the same and what is different about Aisha and Jacob's methods? Pause the video, have a look at both methods and decide for me what's the same and what is different.

And I'll be waiting to hear what you've got to say when you come back.

What was the same? Yeah, and what was different? Perfect, they both used the conversion of five miles equals eight kilometres.

They've got to do that because the average speed was in kilometres, but we wanted to know the number of miles he drives.

Aisha has converted the speed, 80 kilometres per hour, into miles per hour first.

Whereas Jacob calculates the distance travelled in kilometres first and then converts that to miles.

Either of those gets us the same answer.

You may have a preference as to which of those methods that you prefer.

Don't worry if you've not got preference as long as you can use one of them confidently.

Using the fact that one mile equals 1.

6 kilometres, you will know that fact by the end of this lesson if I keep repeating it enough, acar travels at an average speed of 40 miles per hour.

How many seconds does it take to travel one kilometre? We know that one mile is equal to 1.

6 kilometres and we know that we are travelling at an average speed of 40 miles per hour.

We need to convert miles into kilometres because the question asks how long does it take to travel a kilometre? The multiplicative relationship here is multiplied by 40, 1.

6 multiplied by 40 is 64.

40 miles per hour is equal to 64 kilometres per hour.

Now we've got our speed in kilometres per hour, but we want to know how long it takes to travel one kilometre.

So let's find one kilometre, divide by 64.

60 divided by 64 is 15/16.

I've decided to leave that as a fraction.

Remember you could have written that as a decimal.

Just take care if it's not a terminating decimal, make sure you use the exact fraction.

One kilometre then, we need to know how many seconds it asks for.

I need to know how many seconds does it take.

To get from minutes to seconds, I multiply by 60 because there are 60 seconds in a minute.

15/16 multiplied by 60 is 56.

25 seconds.

The car will travel one kilometre in 56.

25 seconds.

Your turn now, using the fact that one mile equals 1.

6 kilometres, told you you're gonna know that by the end of this lesson, a car travels at an average speed of 55 miles per hour.

How many seconds does it take to travel one kilometre? And here I'd like you please to give your answer to the nearest integer.

Pause the video, if you need to go back and re-watch that example we've just been through, obviously that's fine.

But if you feel you're ready, have a go at this question.

Like I said, pause the video now and when you come back we'll check that answer for you.

Let's take a look then.

I've converted 55 miles per hour into kilometres per hour and that's 88 kilometres per hour.

And you can see my ratio table there.

I'm then converting into kilometres per minute and then kilometres per second.

So the correct answer, correct to the nearest integer was 41 seconds.

It was option C.

Is that what you got? Of course you did.

Now we can have a go at task B.

This sign shows the speed limit on a road in the UK.

In the UK signs use the units MPH, miles per hour.

Which of the following would break the speed limit? You must show how you get your answer.

So we've got A, a zebra running at an average speed of 68 kilometres per hour.

B, a coyote running at an average speed of 65 kilometres per hour.

C, a dolphin swim at an average speed of 64 kilometres per hour.

And D, a giraffe running an average speed of 60 kilometres per hour.

Pause the video, draw out your ratio tables and come back when you've got those answers.

Question two, Sofia's dad drives to a meeting at an average speed of 55 miles per hour for one hour and 45 minutes.

Work out the number of kilometres he drives.

Again, pause the video and I'll be waiting when you get back.

Question three, using the fact that one mile equals 1.

6 kilometres, a car travels at an average speed of 25 miles per hour.

How many seconds does it take to travel one kilometre? Pause the video now.

Great work on those questions, let's check those answers.

Question number one, the correct answers were A and B.

Now I'm wondering if you use the most efficient method here.

Once you'd converted 40 miles per hour into 64 kilometres per hour, the question was dead easy, wasn't it? We just needed to see any that ran faster than 64 kilometres per hour.

If you didn't spot that you could do that, maybe you converted all of the running speeds and swimming speeds into miles per hour, but you could have saved yourself a lot of time.

Question two, Sofia's dad drives 154 kilometres.

55 miles per hour is equal to 88 kilometres per hour.

And that means that in one hour and 45 minutes, which is 105 minutes, we travel 154 kilometres.

That's how far he drives.

And question number three, it will take the car 90 seconds to travel one kilometre.

Our conversion, our first conversion, 25 miles per hour is equivalent to 40 kilometres per hour.

We then know that we do 40 kilometres in 60 minutes, one kilometre and 1.

5 minutes, which is one kilometre in 90 seconds.

Well done with those, how did you get on? Yes, of course you got them all right.

Now we can summarise our learning from today's lesson.

It is very important you are able to recall and use facts about metric units.

So for example, that one centimetre is 10 millimetres.

A ratio table is an excellent way to solve problems involving units of measure.

The order in which you do the conversions does not matter as long as the proportional relationship remains the same.

And there's the example that we looked at where one person decided to convert the speeds first and one person decided to work out the distance and then convert that into the other unit.

Great work today, well done.

Hopefully I'll see you again really soon to do some more maths.

Take care of yourself.

Enjoyed working alongside you today, goodbye.