Lesson video

Hello there, my name is Mr. Tilstone.

I'm a teacher, and today, I feel really lucky, because I get to spend this lesson with you.

We're going to be exploring imperial units.

That might be an expression that's not too familiar to you.

However, I guarantee that you'll have heard of some of these imperial units before.

So if you're ready, I'm ready.

So let's begin.

The outcome of today's lesson is: I can understand the approximate equivalence between metric and imperial units, and you are probably very familiar with metric units.

We've got two keywords today.

My turn, metric.

Your turn.

My turn, imperial.

Your turn.

So let's have a look at what those words mean.

Metric is a system of measuring based mainly around the decimal system.

So for example, kilometre or gramme.

Imperial is a system of measuring which originated in England, which has been replaced by the metric system in most countries.

But we still do use a few imperial measures.

Our lesson is split into two cycles.

The first will be what are imperial units and the second will be equivalence between metric and imperial.

So if you're ready, let's have a look at answering the question, what are imperial units? In this lesson, you're going to meet Andeep and Laura.

Have you met them before? They're here today to give us a helping hand with our maths.

Andeep has been learning about different units of measure in school, and you probably have too.

He's thinking about different units of length.

Can you think of any units of length, anything that you can measure length in? I can think of centimetres.

Yes, that's a unit of length.

Metres, yes, and kilometres.

So they're different units of length, and I'm sure you are quite familiar with those too.

Laura says, "I'm sure I've heard other units of length mentioned.

My family shared a 12-inch pizza yesterday." So inch is a unit of measure, a unit of length specifically.

"I was watching a football match on the television at the weekend, and the commentator talked about the 18-yard box." So that's a different unit of length.

The units of length mentioned by Andeep are called metric.

So these are units that are used across the world.

"Metric sounds a little bit like metre." Yes, it does, doesn't it? Metric, metre, I can see that.

"That's how I will remember it." So if you can think that metre is metric and then think about other things that are a bit like metre, that will help you to decide what a metric unit is.

The units of length mentioned by Laura are called imperial.

Imperial measures have been used for hundreds of years.

They are used in the United Kingdom and some other countries but are not used worldwide.

So our system of measurement is a little bit of a mix between metric and imperial.

Metric measures were introduced more recently in the United Kingdom and are used throughout the world.

Imperial units of length.

So let's start thinking about length.

So foot and feet, they're imperial.

Have you heard of those? The origin of the foot was the average length of an adult human foot.

It is still frequently used to describe people's height.

So have you ever heard somebody's height described in feet? So Andeep's saying, "My uncle is six feet tall." Have you heard somebody saying something like that? Maybe you've used that expression too or something similar.

And Laura says, "My mom ordered a footlong sandwich." Hmm, sounds delicious.

Have you ever heard of one of those, a footlong? Inch and inches.

An inch is exactly one twelfth of a foot.

So one foot equals 12 inches.

Some rulers have centimetres on one scale and inches on the other one.

So have you seen inches? You might have measured something in inches before.

Have you heard of inches? So here we go, look.

So look at the bar model, one foot on the top and you can see underneath 12 inches.

So one foot and 12 inches are exactly equivalent.

Andeep says, "My auntie is five feet and six inches tall, or five foot six." And Laura says, "My older brother has a record collection," as do I, "with seven-inch and 12-inch records." So they're particular sizes of records that you can get, seven inch and 12 inch.

So that language is still used.

What about this one, yard? Have you heard of yard as a unit of length? One yard is equivalent to three feet, or 36 inches.

You may occasionally see road signs which give the distances to places that are very close by in yards.

So have you seen something like this? Like a picnic area 150 yards away? So it's quite close by.

So one yard is equal to three feet, exactly equal.

Miles.

Oh, I guarantee you've heard of miles.

I guarantee you've used that word lots and lots of times.

Miles are still a more commonly used unit of measurement in the United Kingdom than kilometres.

So sometimes you will see or use kilometres, but it's much more common to see and hear miles.

So have you ever seen anything like this on a road, on a motorway, something like that? That gives you the miles.

So the numbers there, 17, 32, and 35, are miles.

And Laura says, "My grandparents live 18 miles away." Now Andeep and Laura are thinking about different units of mass.

Andeep says, "Kilogrammes must be a metric measure because they have the prefix kilo, and 1000th of a kilogramme is a gramme." So that's very clever of Andeep.

So think about some of the prefixes or some of the parts of the words that might give it away whether it's metric or imperial.

So kilo is definitely a giveaway that it's metric.

"I think I've heard of a milligramme too," he says, "so that must be a thousandth of a gramme." And you know what? He's quite right.

So that prefix milli was a giveaway that it's a metric unit.

"I've also heard of stones," says Laura, "as a unit of mass.

So I presume they must be imperial." Have you ever heard of that, people measuring their mass in stones? Let's have a look at some imperial units of mass.

So, stones.

People often discuss their mass in stones.

So Andeep might say, "My mass is around seven stone." Pounds are a smaller imperial unit of mass and can be abbreviated to lb.

One stone equals 14 pounds.

So when you see that lb, you can read that as pounds and you can say that as pounds.

Here we go, look.

So look at the bar model.

So one stone is exactly equivalent to 14 pounds.

So you could have a mixture.

So Laura might say, "My mass is seven stone and two pounds, or seven stone two." Let's do another one.

Ounces.

Have you heard of ounces before? Ounces are the smallest imperial unit of mass, often used in recipes when describing food.

One pound equals 16 ounces.

You don't have to remember all of this, but if you can, that would be a nice bonus.

Here we go.

That's one pound, underneath it 16 ounces, they're equivalent.

So Andeep says, "I had an eight-ounce steak for my dinner." Now Andeep and Laura are thinking about different units of capacity.

I wonder if you can think of any metric ones.

Andeep says, "Millilitres must be a metric measure because they have the prefix milli, and 1000 millilitres is equivalent to one litre." So well done, Andeep is quite right.

So once again, there was a little clue within that word, that prefix told us that it was a metric measure, milli.

Laura says, "I've also heard of pints as a unit of capacity, so I presume they must be imperial." Have you heard of pints before? So let's look at some imperial units of capacity, pints.

Some drinks are still commonly referred to in the United Kingdom using the imperial measure of pints.

So you might, for example, have a pint of milk.

And a pint is approximately, not quite, approximately half a litre.

So if you can picture a litre, think about half of that, and that's a pint.

Gallons.

This is not one you hear very often.

Gallons are an even bigger imperial unit of capacity.

One gallon equals eight pints.

So if you've got in your head roughly what a pint is, think about eight of them, and that's a gallon.

So that's quite a lot.

Sometimes people refer to fuel amounts in terms of gallons, so things like petrol.

So one gallon, as you can see, is the same as eight pints.

Quite a lot.

Let's have a little check.

Which of these sentences involving imperial units make sense? Two of them do, and two of them are a little bit silly.

Let's see if you can spot which is which.

So A, Andeep is four gallons tall.

Does that make sense? Hmm.

B, Laura has a tortoise which is 15 inches long.

Hmm.

Does that make sense? C, Izzy has ordered a pint of pizza.

Hmm.

Does that make sense? And D, Jacob used a quarter of a pound of butter in his cheesecake.

Which of those make sense and which don't? Pause the video.

Welcome back.

Hopefully some of those sounded a little bit silly to you and a little bit wrong.

So Andeep is four gallons tall.

No, that's impossible.

You can't measure height in gallons.

But B, Laura has a tortoise which is 15 inches long.

That's plausible.

That makes sense.

You can't have a pint of pizza.

Liquids are measured in pints.

You can't have a pint of pizza.

But Jacob used quarter of a pound of butter in his cheesecake, does make sense.

It's time for some practise.

Now if you can do the next activity in a group with big piece of sugar paper and sticky notes, fabulous, do that.

Write down as many units of measure as you can think of and add them to the table below.

So just like Andeep and Laura were doing, they were thinking about different units of measure.

So how many units of length can you think of? How many units of mass can you think of? And how many units of capacity? And it might be some of the ones that Laura and Andeep measured.

And you might also be able to think of some other ones as well.

So when you've got them, can you then sort them? Which ones are imperial? Which ones are metric? And once again, my little tip is to look at prefixes within the word.

Have fun with that.

Pause the video and I'll see you soon for some feedback.

Welcome back.

How many did you think of? Let's have a look.

Lots of possibilities.

You might have thought of these units of measure.

So units of length that are imperial are foot, yard, inch, and mile.

And units of length that are metric are metre and centimetre.

Units of mass that are imperial are stone and pound.

And units of mass that are metric are kilogramme, gramme, and milligramme.

And a unit of capacity that's imperial is gallon, and metric units of capacity include litre and millilitre.

Well done if you got those.

Are you ready for cycle B? This is looking at the equivalence between metric and imperial.

So far we've looked at the equivalence between imperial and imperial.

The imperial measure of one foot is approximately, so it's about equivalent to the metric measure of 30 centimetres.

Let's have a look at that.

So one foot is approximately equivalent to 30 centimetres.

So what about two feet? How many centimetres will that be equivalent to? Hmm.

Think about what's happening on the top.

0, 30, counting in thirties.

What's gonna come next? 60.

So two feet is approximately 60 centimetres.

So what do you notice about that double number line? What's happening with it? Hmm.

Well, the feet are going up in ones and the centimetres are going up in thirties.

So let's have a think.

Let's see if you can predict what's going to come next.

If you multiply the number of feet by 30, it gives you the number of centimetres.

So can you complete the rest of that number line? See if you can get there before I do.

So what's coming up? Well, three feet is 90 centimetres.

Four feet is 120 centimetres.

Five feet is 150 centimetres.

Six feet is 180 centimetres.

Now have you noticed that if you can count in threes, you can count in thirties? Seven feet is 210 centimetres.

Eight feet is 240 centimetres.

Nine feet is 270 centimetres.

And what about 10 feet? 10 feet is 300 centimetres, or approximately.

It's not exact.

It's very close though.

Hmm.

What could this be showing? So look at the little red notch.

What could it be showing? Look where it is.

Hmm.

How many feet could that be? How many centimetres could it be? As well as converting from whole numbers of feet to centimetres, so one feet, two feet, three feet, et cetera, a number line allows you to convert from values in between the intervals, but you've gotta do a little bit of working out, use some of your knowledge.

So that's 2.

5, two and a half, and it's halfway between two and three.

Now, 75 is halfway between 60 and 90.

So we can say 2.

5 feet is approximately 75 centimetres.

And that number line, that double number line helped us to work that out.

What about this one? What's that in between? What two numbers are feet? What two numbers are centimetres? And again, you might need to do a little bit of calculation there for the centimetres particularly.

That's showing 225 centimetres is approximately 7.

5, or seven and a half feet, because 225 is the halfway number between 210 and 240.

And I can work that out by thinking, what do I add to 210 to get to 240? That's 30, and then half it, that's 15.

And add it on to the 210.

So 210 + 15 = 225.

The imperial measure of one ounce, and that can be abbreviated to oz, is approximately equivalent to the metric measure of 28 grammes.

So one ounce is 28 grammes.

Two ounces.

What do you think that's going to be? You need to do a little bit of arithmetic here.

28 plus 28.

56.

So what do you notice this time? It's similar to the last one, isn't it, but different numbers.

The bottom numbers are going up in ones, and the top numbers are going up in steps of 28.

So a little bit harder to work out, but you can do it, I'm sure.

So if you multiply the number of ounces by 28, it gives you the number of grammes.

Can you complete the rest of the number line? Three ounces.

So adding 28 on to 56 is 84 grammes, or if you like, we're multiplying 3 by 28.

So 4 times by 28, or you could add 28 onto the 84.

Either way, it will give you 112.

So four ounces are 112 grammes.

Five ounces, 140 grammes.

Six ounces, 168 grammes.

Seven ounces, 196 grammes.

Eight ounces, 224 grammes.

Nine ounces, 252 grammes.

And finally, 10 ounces, 10 times 28, I'm sure you can do, is 280.

What does this point on the double number line represent? Hmm.

How many ounces is that and how many grammes is that? Have a look.

What do you think? That's half, or 0.

5.

So 0.

5 ounces is approximately 14 grammes because 14 is halfway between 0 and 28.

What does this point on the double number line represent? What's it in between? Think about the ounces, think about the grammes.

Again, you might need to do a little bit of calculation to get this.

Well, 196 plus 14, which is half of 28, equals 210.

So 210 grammes is approximately 7.

5 ounces.

The imperial measure of one gallon is approximately equivalent to the metric measure of 4.

5 litres.

And we've got a complete number line showing that.

So one gallon is 4.

5 litres.

Two gallons is approximately nine litres, et cetera, et cetera.

The information can be used to reason about conversions beyond that number line.

Let me show you what I mean.

For example, if 10 gallons is approximately 45 litres, and you can see that there, that must mean 20 gallons is approximately 90 litres because we've doubled both values.

If five gallons is approximately 22.

5 litres, then that must mean 50 gallons, which is 10 times more, is approximately 225 litres because that's 10 times more.

What else could you reason? You might want to have a little think about that.

But let's do a check.

So the imperial measure of one stone is approximately equivalent to the metric measure of 6.

4 kilogrammes.

And we've got a number line to show that.

So the question is this: is 20 kilogrammes more than, less than, or equal to three stone? Pause the video, have a think.

If you've got somebody to work with, share your ideas.

Off you go.

What do you think? More than, less than, or equal to? Well, that would be 20 kilogrammes, just a little bit more than 19.

2.

It'd be somewhere like that on the number line.

So you can see that's slightly more, a little tiny bit more than three stone.

Let's have a look at some other approximate equivalences between imperial and metric units.

So one pint is approximately 568 millilitres.

So it's not quite, but that's roughly how much it is.

So that means that one pint is slightly more than half a litre, and that's a bit easier to remember than the 568 millilitres.

One pint, a little bit more than half a litre.

That must mean two pints is slightly more than one litre.

So if you are asking for one litre of something, you are also asking for approximately two pints of something.

One pound, and again we're gonna use that abbreviation lb, is approximately 453 grammes.

That's quite hard to remember, isn't it? But that means that one pound is slightly less than a half a kilogramme.

That's easier to remember.

One pound, a bit less than half a kilogramme.

How else might you describe pounds in relation to grammes or kilogrammes? Have a little think.

Look at the other example for some inspiration and pause the video.

What did you say then? You might have said something like, two pounds is slightly less than a kilogramme.

Or you might have said, one kilogramme is slightly more than two pounds.

And these are easier things to remember than one pound is approximately 453 grammes.

It's just a rough equivalence.

It's time for some more practise.

Number one, one inch is approximately 2.

5 centimetres, and that's been included on that double number line.

Create a conversion line and use it to answer the questions.

So basically finish off that number line.

You're counting in ones on the bottom and 2.

5s on the top.

And if you can count in 25s, you can also count in 2.

5s.

So answer these questions.

Four inches is approximately how many centimetres? 15 centimetres is approximately how many inches? And then a question, is nine inches more than, less than, or equal to 21 centimetres? Number two, here's the first part of a conversion number line.

Use it to answer the questions below.

So we're looking at feet and centimetres here.

But the questions are this: what is half a foot in centimetres? Four feet is approximately how many centimetres? And 10 feet is approximately how many centimetres? And then number three, Andeep's older siblings are weighing themselves but have used different units.

His brother's mass is 10 stone and his sister's is 60 kilogrammes.

So they've used different measures.

One has used imperial and one has used metric.

Using the conversion that one stone is approximately 6.

4 kilogrammes, can you explain who has the greater mass? Number four, one gallon is approximately 4.

5 litres.

How much is three gallons of petrol in litres? Number five, one yard is approximately 91.

4 centimetres.

Can you think of a good way to remember approximately how long a yard is? Because I'll never remember that one yard is 91.

4 centimetres.

So can you make it a bit more approximate? And number six, circle the larger measurement for each pair.

So which is larger, five litres or five pints? Five grammes or five pounds? Five centimetres or five inches? Circle the larger one each time.

Pause the video.

Good luck.

I'll see you soon.

Welcome back.

Let's have a look how you got on.

So number one, one inch is approximately 2.

5 centimetres.

Create a conversion line and use it to answer the questions.

So one inch, 2.

5 centimetres.

Two inches, five centimetres, so on and so on.

All the way up to 10 inches is 25 centimetres approximately.

So A, four inches is approximately 10 centimetres.

15 centimetres is approximately six inches.

And is nine inches more than, less than, or equal to 21 centimetres? More.

It's more than 21 centimetres.

And number two, that's the first part of a conversion number line, feet and centimetres.

Use it to answer the questions.

What's half a foot in centimetres? That's 15 centimetres.

Four feet is approximately 120 centimetres.

And 10 feet is approximately 300 centimetres.

And then Andeep's older siblings are weighing themselves but have used different units.

His brother's mass is 10 stone, that's imperial, and his sister's is 60 kilogrammes, that's metric.

Using the conversion that one stone is approximately 6.

4 kilogrammes, can you explain who has the greater mass? Well, 10 multiplied by 6.

4 kilogrammes equals 64 kilogrammes.

64 kilogrammes is greater than, slightly greater than 60 kilogrammes.

So that must mean his brother has a greater mass.

So well done if you've got that and well done if you explained that.

Number four, one gallon is approximately 4.

5 litres.

How much is three gallons of petrol in litres? Well, if you multiply 4.

5 by 3, it gives you 13.

5, 13.

5 litres.

One yard is approximately 91.

4 centimetres.

A bit hard to remember that.

What's a good way to remember? You might have said something like, 91.

4 centimetres is very close to 100 centimetres, which is one metre.

So if you can picture a metre stick, it's just a little bit more than a yard.

I think that's helpful, don't you? And then the larger measurement, five litres is larger, five pounds is larger, and five inches is larger.

We've come to the end of the lesson.

Today's lesson's been all about understanding the approximate equivalence between metric and imperial units.

So I said at the start, you've probably not heard the word imperial before, but you've probably heard of lots of imperial units.

Hopefully you do know what the word means now.

Certain units of measure have been around for hundreds of years and are not based on the decimal system or used worldwide, but are still used in certain countries, such as the United Kingdom.

These are known as imperial and include units of length, such as inch, foot, yard, miles, units of mass, such as ounce, pound, and stone, and units of capacity, such as pint and gallon.

There are ways of converting from imperial to metric units using a basic known fact as a starting point or using double number lines.

So the big takeaway from this lesson is that in the United Kingdom, we've still got a bit of a mixture of imperial and metric units and we need to know what all different kinds mean.

I've really enjoyed spending this lesson with you and I hope see you again soon for some more maths.

But until then, take care.

Enjoy the rest of your day, and goodbye.