Lesson video

Hello there and welcome to today's lesson.

My name is Dr.

Rowlandson and I'll be guiding you through it.

Let's get started.

Welcome to today's lesson from the unit of 2D and 3D shape with compound shapes.

This lesson is called checking and securing understanding of converting between metric and imperial measures.

And by the end of today's lesson, we'll be able to convert between metric and imperial measures.

Here are some previous keywords that will be useful again during today's lesson.

So you may want to pause the video if you want to remind yourselves what any of these words mean before press and play to continue.

In the first learning cycle, we're going to focus on the prefixes for words for metric units and how those prefixes help us with metric conversions.

And in the second learning cycle, we're going to be looking at converting between metric and imperial measures.

Let's start off with prefixes and metric conversions.

The students at Oakfield Academy were asked to measure the length of their cat from head to tail using a metric unit of distance.

Let's take a look at those cats now.

Aisha says, "My cat is not 0.

87 metres long." Lucas says, "My cat is 79 centimetres long," and Sam says, "My cat is 682.

4 millimetres long." Andeep's listening in and Andeep says, "Wow, Sam's cat is so much longer than the other cats." Hmm, is Andeep correct here? And whether he is or isn't, how do you know? Pause the video while you think about this and press play when you're ready to continue.

Well, what makes this tricky is that Aisha, Lucas, and Sam are all using a different metric unit of measure to describe the length of their cat and each unit describes a different length.

So let's think about these different units in a bit more detail now and how each unit compares to the other.

For example, if this bar has length one metre, then let's think about how long a bar of one centimetre would be in comparison to this one.

It would be about this long.

This bar would have length of one centimetre, and that means that 100 of these small centimetre bars will be needed to describe the same distance or length as one metre.

Now the word itself, centimetre, can help us remember that there are 100 centimetres in one metre, particularly if you know your French numbers.

The metric system is thought to have originated in France, and so the prefixes in these units often have a link to the French numbers.

For example, 100 in French is cent, so a centimetre is 100th of a metre or there are 100 centimetres in a metre, however you think of it.

So centi is a prefix that means 100th, and that means that a centimetre is a length that is 100th length of a metre, and you need 100 centimetres to reach the same length as one metre.

So let's think now about millimetres.

If this bar has length one metre, how long would a millimetre be in comparison? It would be about this long.

This very tiny bar has length of one millimetre in comparison to the length of one metre above it.

1,000 of these tiny millimetre bars are needed to describe the same distance or length as one metre.

Let's think about the word millimetre now.

In the English language, we probably associate milli with million.

That's probably the closest number to the sound of milli.

But in French, a 1,000 is mil, and same in Spanish as well.

So milli is a prefix that means 1,000th.

So a millimetre is a length that is 1000th the length of a metre, or you can think of it as you need 1,000 millimetres to reach the same length as one metre.

So we can use these prefixes to convert each of the different lengths into metres, for example, and this allows us to compare how long each cat is more easily.

So let's do that.

Aisha's cat is already in metres.

She says it's 0.

87 metres long.

Lucas said it was 79 centimetres.

Well, a centimetre is 100th of a metre, so that means 79 hundredths of a metre would be 0.

79 metres.

Sam's cat is 682.

4 millimetres long.

Well, a millimetre is 1,000th of a metre, which means Sam's cat is 682.

4 thousandths of a metre, which would be 0.

6824 metres.

Now we have the lengths of each cat in the same units, it's much easier to make comparisons between them.

For example, we can see that the longest cat belongs to Aisha, which is 0.

87 metres long.

The next longest cat belongs to Lucas, which is 0.

79 metres long.

And then the shortest cat belongs to Sam, which is 0.

6824 metres long.

Andeep listens in to this and says, "Oh, I was wrong.

Sam's cat is actually the shortest." He reflects on it and says, "I should probably convert all the measurements so they're in the same units before comparing them." So let's check what we've learned.

Complete each sentence.

Pause the video while you do this and press play when you're ready for answers.

Here are your answers.

One centimetre is 100th of one metre and one millimetre is 1,000th of one metre.

So you can use these to answer the next question.

Complete each conversion into metres.

Pause the video while you do this and press play when you're ready for some answers.

Let's take a look at some answers.

Here they are.

233 centimetres is 233 hundredths of one metre, which is 2.

33 metres, and 1,002 millimetres is 1,002 thousandths of a metre, which is 1.

002 metres.

Let's now apply the same idea to some different units from the metric system.

The prefixes of centi and milli apply to all units of measure from the metric system.

One centilitre is 100th of one litre and one millilitre is 1,000th of one litre.

So with that in mind, write down a fraction calculation for each conversion into litres.

Pause the video while you do this and press play when you're ready for answers.

Here are your answers.

A 330 millilitre bottle of water is 330 thousandths of a litre, and a 75,000 centilitre pond contains 75,000 hundredths of a litre.

So with that in mind, complete each conversion into litres.

Pause the video while you do this and press play when you're ready for answers.

Okay, here are your answers.

330 millilitres is equal to 0.

33 litres, and 75,000 centilitres is equal to 750 litres.

So now let's apply this to some different units from the metric system.

One centigramme is 100th of a gramme and one milligramme is 1,000th of a gramme.

So with that in mind, complete each conversion into grammes.

Pause the video while you do this and press play when you're ready for answers.

Okay, here are your answers.

A 12 milligramme hay fever tablet is 0,012 grammes and a 50,000 centigramme bag of sugar contains 500 grammes.

Andeep says, "Millimetre and centimetre both describe lengths smaller than a metre.

But are there any prefixes that can help name lengths greater than a metre?" Well, there are many units that describe lengths greater than one metre, including a decameter which is 10 metres, a hectometer which is 100 metres and a kilometre, which is 1,000 metres.

Now decameter and hectometer aren't used very often, but kilometre is used quite a lot.

Let's look at kilometre a little bit more.

The prefixed kilo means 1,000 times larger than, so you need 1,000 metres to reach the same length as one kilometre because one kilometre is 1,000 times larger than one metre.

The prefix of kilo can also be applied to all metric units of measure.

So one kilogramme is 1,000 grammes and one kiloliter is 1,000 litres.

So going back to Andeep's question, millimetre and centimetre both describe lengths smaller than one metre.

Are there any prefixes that can help name lengths that are greater than a metre? Yes, there are, deca, hecto and kilo, but most commonly kilo for kilo, kilogramme, and kiloliter.

So let's check what we've learned.

Let's imagine that I invented a new metric unit called a florb.

Which of these statements would be correct about the kiloflorb? Is it a, there are 1,000 kiloflorbs in one florb? Is it b, there are 1,000 florbs in one kiloflorb? Is it c, 1,000th of a florb is one kiloflorb? Or is it d, 1,000th of a kiloflorb is one florb? And it might be more than one correct answer.

Pause the video while you do this and press play when you're ready for answers.

The answers are b and c.

There are 1,000 florbs in a kiloflorb because the word kiloflorb means 1,000 times larger than a florb.

And we could also say that 1,000th of a kiloflorb is one florb.

And once again, that would mean a kiloflorb is 1,000 times larger than a florb.

And actually these two statements are in fact the inverse of each other.

So now, still focusing on our brand new unit called the florb, which of these statements are correct about the florb? Is it a, there are 1,000 florbs in one kiloflorb? Is it, b there are 1,000 florb in one milliflorb? Is it c, there are 100 centiflorbs in one florb? Is it d, 1,000th of a florb is one milliflorb? Or is it e, 100th of a centiflorb is one florb? And it may be more than one correct answer.

Pause the video while you do this and press play when you're ready for answers.

The correct answers are a, c and d.

One mathematical tool that you can use to help you is a ratio table.

Ratio tables can be used to help convert from one unit to another unit that measures the same thing.

For example, convert between units of length, convert between units of mass or convert between units of volume.

What you can't do is convert from a length unit to a volume unit.

For example, convert 75,000 grammes into kilogrammes.

Well, we know that one kilogramme means 1,000 grammes, so we can set it up in a table like this.

On the left column, we have kilogrammes.

On the right column, we have grammes.

We filled in what we know about the units, that one kilogramme is equal to 1,000 grammes.

So if I wanna convert 75,000 grammes, I would put 75,000 in the gramme column.

And what I wanna know is what is in that blank box on the bottom left? Well, I know that I could times the right column by 1,000th to get the left column and that means I'll be doing 75,000 divided by a thousand, which is 75.

So 75,000 grammes is equal to 75 kilogrammes.

Here's another example.

Convert 40,632 millilitres into litres.

Well, we know that one millilitre means 1,000th of a litre.

So let's set that up in our ratio table.

We have millilitres and litres.

We've filled in that one millilitre is 1,000th of a litre.

We can put 40,632 in our millilitres column and think about how we get to where the blank box is.

Well, one times 1,000th gives us the same answer as 40,632 divided by 1,000, which is 40,632.

So 40,632 millilitres is equal to 40,632 litres.

So let's check what we've learned.

Find the values of a to c in this ratio table in order to convert 5,370 kilogrammes into grammes.

Pause the video while you do this and press play when you're ready for answers.

And here are your answers.

You are converting 5,730 kilogrammes by multiplying by 1,000 to get 5,730,000 grammes.

Here's another question.

Find the values of a to e in this ratio table in order to convert 0,809 litres into centilitres.

Pause the video while you do this and press play when you're ready for answers.

So here's what your answers should look like.

One centilitre is equal to 100th of a litre, which means you are multiplying by 100 to convert from litres to centilitres.

So 0.

809 times 100 gives you 80,9.

So in the examples we've seen so far, we've been using ratio tables to convert from one unit to another, but each time, one of the units has been a base unit, for example, metres, grammes or litres.

Multiple ratio tables can be used to help convert from one unit to another that measures the same thing where neither is the base unit.

For example, neither the units you're dealing with are metres or neither of the units you're dealing with are grammes or neither of the units you are dealing with are litres.

Let's take a look at some examples.

Convert 0.

32 kilometres into centimetres.

Now the base unit here is metres, but we are not converting into metres or out of metres within this question.

That doesn't mean we can't do it along the way though.

For example, we could start by looking at the relationship between kilometres and metres and set up a ratio table for that.

One kilometre is 1,000 metres, so 0,32 kilometres would be times 1,000 to get 320 metres.

And then we can set up another ratio table now for the relationship between metres and centimetres.

We know that 100th of a metre is equal to one centimetre.

So we can put 320 metres from our last ratio table into our new one here, and then we can convert that into centimetres.

That times 100 gives us 32,000 centimetres.

So that means that 0.

32 kilometres is equal to 32,000 centimetres.

So let's check what we've learned.

By completing both of these ratio tables, convert 0.

04 kiloliters into millilitres.

Pause the video while you this and press play when you're ready for answers, The answer is 0.

04 kiloliters is equal to 40,000 millilitres and here is how your ratio table should look.

Okay, it's over to you now for Task A.

This task contains five questions and here are questions one and two.

Pause the video while you do this and press play when you're ready for questions three, four, and five.

And here are questions three, four and five.

Pause the video while you do these and press play when you're ready for answers.

Okay, well done with that.

Here are the answers to questions one and two.

Pause the video while you check these against your own and then press play when you're ready for more answers.

Here are the answers now to question three.

Pause while you check and then press play when you're ready for more answers.

And here are the answers now to questions four and five.

Pause while you check and press play when you're ready for the next part of today's lesson.

Great work so far.

Now let's move on to the second learning cycle, which is about converting between metric and imperial units.

The units of measure that we've looked at so far that describe length are millimetres, centimetres, metres, and kilometres.

And we'll notice this for all of those words have metres as part of the word because that's our base unit of length for those units.

Now Andeep says, "But I've heard of other units that describe length as well, such as miles and inches and feet.

Are they related to metres, too?" Well, the answer is no.

These are all examples of metric units for measuring lengths and each metric unit is related by a power of 10.

That means to convert from one to the other, you usually multiply or divide them by either 10, a hundred, a thousand and so on.

They're all powers of 10.

But miles, inches and feet are all examples of imperial units for measuring length.

Now imperial units are an older unit of measurement and they do not use prefixes such as milli, centi and kilo.

This is because imperial units are not usually related to each other by powers of 10 and they are not related to any metric units by powers of 10 either.

So let's take a look at some examples of imperial measurements for length.

Inches is one imperial measurement for length.

And you might hear the word inches be used to describe the length of a pizza or the diameter of a pizza, to be more exact.

Feet is another imperial unit of length and we may sometimes give the height of a person in feet.

Yards is another imperial measurement of length, and you might hear yards be described when it comes to length of a sports field.

And miles is another much larger unit of length and that might be used to describe the distance of a journey of some kind.

Now with metric units, we often write them down abbreviated.

So for example, centimetres is often written as cm for centimetres.

We can do the same thing with imperial units as well.

You might see these units abbreviated to these things we can see here.

And now let's look at some imperial measurements for capacity.

For example, you might hear pints be used quite regularly to give the amount of milk in a bottle.

You might also hear the word gallons be used to describe the amount of petrol in a car.

Those are both imperial units of capacity.

And you might see these abbreviated to these things here.

So let's check what we've learned.

Match the imperial unit to the thing that it measures.

Pause the video while you do this and press play when you're ready for answers, Miles measures length, ounces measures mass and pints measure capacity.

So match the unit here, given in its abbreviation form to the thing that it measures.

Pause the video while you do this and press play when you're ready for answers.

And here are your answers.

A is pounds and that is an imperial unit of mass.

B is centimetres and that is a metric unit of length.

C is gallons and that is an imperial unit of capacity.

D is milligrammes and that is a metric unit of mass.

And E is foot or feet and that is a imperial unit of length.

Sometimes it is helpful to convert between metric and imperial units in certain contexts and this can also be done using a ratio table.

For example, Izzy's family go on a road trip from Oakfield to France.

The spare tyre can only travel a maximum of 60 miles per hour.

But when they arrive in France, the speed limit is given in kilometres per hour.

If they need to use a spare tyre in France, what is the maximum speed that they can travel at? One thing that makes this problem tricky is that it involves two different units of length, miles and kilometres.

So what can be helpful to know is how these units compare to each other.

Well, eight kilometres is approximately equal to five miles.

So now we know that, we can set up our ratio table with that fact in.

We have kilometres in the left column, miles in the right column, and we have so far that eight kilometres is approximately equal to five miles.

So let's look back at our problem and see what measurement is given to us.

We can see we have 60 miles, so let's put 60 in our table under the mile column and then we can think about different ways of getting the answer in that blank box in the bottom left.

One way could look at how to convert from miles to kilometres by thinking what you multiply five by to get eight and then do the same to the 60.

But because five is not a factor of eight, but it is a factor of 60, it might actually be easier to think about how to multiply five to get 60, and that is multiply by 12.

We can then do the same thing to the eight.

Eight times 12 is 84.

That means the maximum speed that Izzy's his family can travel with their spare tyre is 84 kilometres per hour.

Here's another example.

For a cake recipe, Lucas needs to buy 300 grammes of apples.

So Lucas goes to the farmer's market and buys 10 ounces of apples.

Does Lucas have enough apples for his cake recipe? Once again, what's tricky here is that we have two different units of mass, we have grammes and we have ounces.

So what would be helpful to know is how these units compare to each other.

170 grammes is approximately equal to six ounces.

So now we know that, we can set up our ratio table and we've got a few options here.

We could either put 300 grammes in our table and convert it to ounces and see if it's more or less than 10, or we can put 10 ounces in our table, convert it to grammes and see if it's more or less than 300.

Let's do the second of those.

Let's put 10 ounces in our table.

It'll be here.

Now, six is not a factor of 170, which means that my multiplier from ounces to grammes will not be an integer.

And also six is not a factor of 10, which means my multiplier from the second row, the six in to the bottom row of the 10 in will also not be an integer.

So that means it doesn't really matter which multiplier I find, one will not be easier than the other.

Let's for example, go from ounces to grammes by multiplying by 176, which would give me 283.

3 and so on.

That means that Lucas does not have enough apples, as he only has 283.

3 grammes, not 300 grammes.

He's not got enough.

So let's check what we've learned now.

For a cake recipe, Lucas needs to buy 650 millilitres of milk.

Lucas goes to the supermarket and buys one pint of milk.

Does Lucas have enough milk for his cake recipe? And you are given the conversion from millilitres to pints.

Find the values at A to C in this ratio table to help you solve this problem.

Pause the video while you do this and press play when you're ready for answers.

Okay, here are your answers.

13,070 millilitres is equal to 23 pints, which means to get from 23 pints to one pint, you could do it by dividing by 23.

That might be the easiest way to do this problem.

But there are other ways.

And if you divided 13,070 by 23, you get 568,26 and more digits.

That doesn't really matter so much.

What you know is that Lucas has bought 568 millilitres of milk and this is not enough.

He needs 650 millilitres of milk for his cake recipe.

When converting between metric imperial units of measure, there is a multiplicative relationship between the two units.

This relationship can be plotted on a straight line graph in the form y equals kx.

Let's take a look at an example.

Three stone is approximately equal to 19 kilogrammes.

That means that one stone is approximately equal to 19 thirds of a kilogramme.

Now we can plot this as a graph in the form y equals kx by plotting the line y equals 19 thirds of x where x represents stone and y represents kilogrammes.

And if we plot a graph for that, it would look something a bit like this.

We can then use this graph to estimate conversions between stone and kilogrammes.

For example, if we like to convert 10 kilogrammes into stone, well, we could go to where 10 kilogrammes is on the y axes and go across to where the line is and then go down to the x axes and c and it's equal to approximately 1.

57 stone.

Another example could be to convert 0,9 stone into kilogrammes.

Well, I'm converting from stone, so let's go to my x axes and read off 0,9.

Go up to my line and then go across to my y axes to get what that would be in kilogrammes, and that would be approximately 5.

7 kilogrammes.

So let's check what we've learned.

This graph shows the linear relationship between gallons and litres.

Could you, please estimate the number of gallons in 10 litres? Pause the video while you do this and press play when you're ready for answers.

Let's now do this together.

Litres is on the y axes and we are converting 10 litres.

If we go across to the line and then down to the x axes which has gallons, we can see that it's somewhere between 2.

1 and 2.

3 gallons.

So here's another question.

Estimate the number of litres in four gallons.

Pause the video while you do this and press play when you're ready for answer.

Okay, well, this time we're converting from gallons to litres, so let's start on our x axes and go to the four gallons, and then go up to the line and then cross the y axes to get approximately somewhere between 18 and 18.

3 litres.

Here's another question.

Estimate the number of litres in three gallons.

Pause the video while you do this and press play when you're ready for an answer.

Okay, let's do this together.

If we start at three gallons and go up to the line and then go across, we get somewhere between 13.

6 and 13.

8 litres.

So using your previous answer, estimate the number of litres in nine gallons, and what's tricky here is you can't see nine on the graph.

So pause the video while you think about how to do this and have a go at it and then press play when you're ready for an answer.

Well, we can't use the graph for this directly, but what we can do is use our previous answer.

We know that three gallons is approximately 13.

7-ish litres, so if we take our previous answer and multiply it by three, we should get somewhere between 40,8 and 41,4 litres.

Okay, it's over to you now for Task B.

This task contains three questions and here are questions one and two.

Pause the video while you do these and press play when you're ready for question three.

Okay, final question of the lesson, here is question three.

Pause the video while you have a go at this and press play when you're ready for answers.

Well done with that.

Here are your answers to questions one and two.

Pause the video while you check 'em and press play when you're ready for the answer to question three.

And here are your answers to question three.

Pause the video while you check this and press play when you're ready for today's summary.

Fantastic work today.

Now let's summarise what we've learned during this lesson.

There are lots of different units of measure.

The most common fall into two systems, imperial and metric.

Metric units can be used with the prefixes milli, centi, kilo as the measures are related to powers of 10.

That's because we are multiplying or dividing by either 10, a hundred or a thousand to convert from one to another.

Imperial units do not have powers of 10 as their multiplies, so you need to even know or lock up a conversion between 'em 'cause they're all slightly different to each other.

It is also possible to convert between metric and imperial measures if you are given the relationship.

If you're not given the relationship, you can also look that up as well online, for example.

And ratio tables or linear graphs are mathematical tools that can help you when converting between different units.

You can also only convert between units, whether within a system or between systems, that measure the same thing.

For example, you can convert between different units of length, whether that is converting from metric to imperial units of length or from one imperial unit of length to another imperial unit of length.

But what you can't do is convert from a unit of length to a unit of volume, for example.

Thank you very much.

Have a great day.