Lesson video

Hello everyone.

My name's Mr. Grattan, and thank you so much for joining me for today's lesson.

In today's lesson on place value, we'll be looking at converting and comparing between different metric units and seeing if those conversions make sense in a real world context.

We'll be using a handful of keywords.

Metric units, which are metres, grammes and litres, and the prefixes, centi, milli and kilo.

Pause here to familiarise yourself with these to keywords.

We will approach this lesson in three parts, starting with converting metric measures using place value.

We can use place value charts to visualise conversions.

You must always focus on the ones digit first no matter how big or small the number is.

The unit is metres, so I need to place the ones digit, which is two, into the metres column.

All other digits are placed in the correct space so that it matches the original number at the top.

In this case 12.

As we are converting into centimetres, we then insert placeholder zeros up to and including the centimetres column.

The decimal point goes to the right of the unit we are converting to, but because 1,200 is an integer, we do not need to keep it.

However, other conversions may require you to keep the decimal point, so this step is important to consider.

Our answer is then 1,200 centimetres.

Here is a similar example.

Note the decimal point.

It does not change our procedure at all.

We always focus on the ones digit first.

The ones digit is seven.

This goes in the kilogrammes column because the unit is currently kilogrammes.

The five goes to the right.

Because we are converting into grammes, we include placeholder zeros up until and including the grammes column.

As before, the decimal point goes after the number that we are dealing with.

But because 7,500 is an integer, we can ignore it.

The answer is then 7,500 grammes.

Looking at a place value chart is always helpful, but sometimes it's a bit impractical and long-winded.

We can also convert by looking at the prefixes of our units.

Kilogrammes means 1,000 grammes.

So 7.

5 kilogrammes means 7.

5 lots of 1,000 grammes.

The calculation is 7.

5 times by a thousand, which is 7,500 grammes.

The same answer as before.

Okay, let's check for understanding.

Which of these columns should Sam place the digit four in this place value charts? Pause here to have a think.

The answer is C.

Well done if you got that right.

Remember, you should always focus on the ones digit first, which is the number four.

You place the ones digit in the column of its current unit.

Since this is 64 centimetres, you put the four in the centimetres column.

Okay, let's finish off Sam's question.

Which of these is the correct conversion of 64 centimetres? Pause here to have a go.

The answer is 640 millimetres, as the centimetre is 10 times bigger than the millimetre.

Well done if you got that right.

Final check, Jun says, if I convert 0.

47 litres into millilitres, I get? Choose the right value to finish off his sentence.

Pause the video now to make your selection or wait a little bit to get a hint.

Okay, here's the hint.

The correct answer is D, 470 millilitres.

Whilst B also represents the same value, it is best not to have leading zeros to the left of your answer unless absolutely necessary.

Notice how all of our answers so far have gone from a smaller number to a larger number.

This is because we have converted from larger units to smaller units.

We can also do the opposite.

The process is identical with a few small adjustments later on in the process.

As with before, start with the ones digit.

Place it in the millilitres column, and grow the number out from there, to get 6,050.

We are converting into litres.

As with before, we need to place the decimal point to the right of the unit you are converting into.

In this case, I put the decimal point to the right of the litres column.

The decimal point is now necessary to keep and so the answer is 6.

05 litres.

This makes sense as 6,000 millilitres is exactly six litres.

And so slightly above 6,000 millilitres will be slightly above six litres.

6.

05 matches this.

We can also convert this using the prefixes.

So millilitre means one, 1,000th of a litre.

So 6,050 millilitres means 6,050 over a thousand of a litre.

This can be also described as a thousand times smaller than 6,050.

A thousand times smaller than 6,050 is 6.

05 litres, the same answer as before.

Okay, one last example of converting.

Let's convert 840 grammes into kilogrammes.

I'll focus on the ones digit and the unit, the zero then goes in the grammes column and I grow the rest of the number out from there.

Because I want to convert into kilogrammes, I focus on the kilogrammes column and put placeholder zeros up to and including that column.

I then have to place a decimal point after the kilogrammes column and because that decimal point is necessary, I keep it and the answer becomes 0.

84 kilogrammes.

We can also do this conversion using the prefixes.

Kilogramme means 1,000 grammes, therefore one gramme is 1,000 times smaller than a kilogramme.

I can write it like this, 840 over a thousand, which is 0.

84.

Exactly the same answer as before.

Right.

Check time again.

Complete Jacob's sentence.

I have a bottle of water that says 660 millilitres.

This is the same as? Pause the video to think what the answer could be.

Remember, when you're converting into litres, you need to include placeholder zeros up to and including the litres column and have the decimal point after the litres.

The answer is 0.

66 litres, B.

Well done if you got that correct.

Okay, similar question.

Complete Alex's sentence.

My brother drove 24,500 metres.

This is the same as driving? Fill in the place value chart yourself.

Pause the video and find out your answer.

Okay, here's the place value chart filled in.

Because I want to convert into kilometres, I have to put the decimal points after the kilo, so after the four, and so the answer is 24.

5 kilometres.

Okay, here are a few practise questions for you to try.

You can use the place value charts to help you if you want to, but you can choose not to use them if you feel confident enough.

Pause the video to do those conversions.

Okay, as with before, I've given you an even less filled in place value chart for you to use if you want.

Pause the video to attempt these conversions.

Okay, finally, on the left are three objects, a drum, a jug, and a motorcycle.

On the right hand side are a bunch of conversions, some are correct, some are incorrect.

What we'll need to do is convert each of those measurements on the right hand side to see if they match either the mass of the drum, the capacity of the jug or the distance that the motorcycle travels.

There may be more than one correct answer for every one of the objects.

Pause now to give that a go.

Good luck.

Right, let's go through question one.

If I were to convert seven kilometres into metres, I would have to multiply the number by a thousand, so the answer is 7,000 metres.

To convert from metres to centimetres, I multiply it by a hundred again, which gives me 700,000 centimetres.

To convert from centimetres to millimetres, I multiply by ten one more time, which gives me 7 million millimetres.

Well done if you got those three correct answers.

Similarly for question two, if you got 0.

425 litres, very well done.

Remember, you have to include placeholder zeros here on the left underneath the litres header.

Okay, question number three is very similar to question number two.

The answer is 0.

163 kilogrammes.

Well done if you got that right.

Notice how question four is different to questions three and two.

We are converting from a large unit capacity to a small one, making our answer 1,150 millilitres.

Well done if you spotted those details.

Right, for question number five, the mass of the drum is 6.

3 kilogrammes.

This is the same as D, 6,300 grammes.

The capacity of the jug is 630 millilitres.

This is actually less than one litre, it is 0.

63 litres.

Now the number for the motorcycle might look really big.

It is travelled 6,300,000 millimetres, but actually that is only 6.

3 kilometres or 6,300 metres, not actually that far a distance.

Well done if you've got any of those correct.

Now that we're familiar with converting into different units, let's put this into some practical use by comparing the size of different measures.

For example, Lucas and Sophia both give the distance they travel to school, but Lucas gives it in kilometres and Sophia in metres.

Who walked further? Remember, kilometre means 1,000 metres.

We can use this to convert one of the two values and we can choose either, it does not matter.

So let's do both one at a time.

First up, Lucas, converting kilometres into metres.

1.

2 kilometres means 1.

2 lots of 1,000 metres.

So we multiply 1.

2 to a thousand.

Therefore, Lucas travelled 1,200 metres and Sophia 850 metres.

Onto Sophia, converting from metres into kilometres.

850 metres means 1,000 times smaller than 850 kilometres, which is a division that gives you 0.

85 kilometres.

Either way, we can see that Lucas travelled further.

Okay, similar question.

Can this kettle of 1.

85 litres fill four 400 millilitre cups? We can convert both values as before, but I'm just gonna convert once, converting the 1.

85 litres.

Remember, millilitre means one, 1,000th of a litre.

By converting 1.

85 litres, we will avoid decimals, which is why it's my preferred methods.

1,000 lots of 1.

85 is 1,850 millilitres and that is the capacity of the kettle.

Right, if we focus on the four cups, four lots of 400 multiplied together is 1,600 millilitres.

The kettle has a bigger capacity and so it can fill all the cups with water to spare.

Okay, check time.

Which bottle contains the most liquid? Pause and figure that out.

Ah, both are equal because 0.

82 litres is equal to 820 millilitres.

So they are exactly the same capacity.

Right, which vehicle travelled further? Which one are you gonna convert? Pause and have a think.

75 kilometres is 75,000 metres.

And so the aeroplane travelled 10 times further than the speedboats.

We can find out values bigger or smaller than a measurement by converting the measures first.

So, Laura asks to find three different distances with three different units that are all longer than 20 metres.

My advice is to convert 20 metres into the other units of distance.

These are kilometres, centimetres and millimetres.

Before attempting to find the distances that are longer, I want to focus on the conversions first.

20 metres is equal to 0.

02 kilometres, 2,000 centimetres and 20,000 millimetres.

And so that conversion has basically done the whole job for us.

Any number bigger than those three values will be a suitable answer.

Here are some examples.

0.

03 kilometres is bigger than 0.

02 kilometres; 2,500 centimetres is bigger than 2,000 centimetres; and 20,001 millimetres is bigger than 20,000 millimetres.

Right, next few checks.

Select all the capacities that are bigger than 1.

04 litres.

Remember, you will have to convert the 1.

04 litres first.

There may be more than one correct answer.

Pause and give it a go.

1.

04 litres is equal to 1,040 millilitres.

So the only correct value is D.

Okay, similar question.

Select all the masses that are bigger than 40.

2 kilogrammes.

Pause to give it a go.

40.

2 kilogrammes is equal to 40,200 grammes.

So this time there are two correct answers, C and D.

Onto independent practise.

By converting the units of every animal first, find out which cat is longest, for question one, and which dog is heaviest, for question two.

Pause the video and good luck.

Convert these values first to answer the questions.

There are multiple, multiple correct answers for each.

Pause the video and good luck.

For question five.

Place these distances in order of size, smallest first.

It might help to convert them all into a common unit.

Which unit you choose is up to you.

Take your time, pause, and good luck.

For question six, the value on the left of each pair is smaller.

The value on the right of each pair is larger.

Come up with a number to make each of the descriptions correct.

Again, you'll have to do some conversions first.

Pause and off you go.

By converting all of the cats to millimetres, we see that the first cat is the longest at 1,070 millimetres.

Converting all of the dogs to grammes, we can see the second dog is the heaviest or has the greatest mass.

For question number three, 1.

3 litres is the same as 1,300 millilitres, so any number less than 1,300 millilitres is correct.

Careful on question four though, 2,300 kilogrammes becomes 2,300,000 grammes.

So any number bigger than that 2,300,000 is correct.

Question number five.

I converted all of those into metres.

Do not worry though if you converted into a different unit, like centimetres or kilos.

Regardless of the unit, the correct order is the same.

F is the shortest, then D.

B and E are equal in size.

Very well done if you spotted that.

Then C, and then A is the longest.

Right, for question six, 900 grammes is equal to 0.

9 kilogrammes.

Therefore anything greater than 0.

9 is correct.

For the second question, 7.

5 litres is 7,500 millilitres, and so anything greater than 7,500 is also correct.

And lastly, for the last one, 18,500 grammes is equal to 18.

5 kilogrammes.

But because the missing value is on the left, the smaller value, it has to be a number less than 18.

5 that gets you the correct answer.

If you've got any of those correct, very well done.

Now that you're hopefully familiar with converting and comparing, let's check if the conversions people make are sensible, especially when comparing to real world things.

Right, starting with Jun, who says his mum drove 16 kilometres to work.

Well, 16 kilometres is reasonable for someone who travels to work in a different but nearby city or town.

But Jun says that this is equal to 160 metres.

Is Jun correct? Well, 16 kilometres is equal to 16,000 metres.

Jun's thought is 100 times too small to be correct.

How do I know instantly without converting that Jun's thought was not sensible? Well, 160 metres is a short walk down the road, not a drive to work.

Right, here's a label for a kettle with the tag slightly ripped off.

Which of the following is the correct value that fits into that gap? By conversion, millimetre means one, 1,000th of a litre.

And so the 1,700 millilitres on the tag is equal to 1.

7 litres.

We can also tell instantly that this value is sensible as a normal kettle holds between one and two litres of water.

Okay, final check.

This small aircraft is 13 metres long.

This is the same as 13,000, what? Which answers, if any, look sensible? You can also convert 13 metres to confirm your answer.

Pause and give it a go.

Right, 13,000 millimetres is the correct answer as there are 1,000 millimetres in a metre.

Let's look at the other options.

13,000 kilometres is far too big.

In fact, it is the distance that nearly gets you to Australia.

13,000 centimetres is ambiguous.

You can't tell instantly if it's correct or incorrect, so it is sensible to do the mathematical conversion to check it wasn't the correct answer.

And now onto the final few independent practise tasks.

For questions one and two, using either understanding of real world measurements or by converting, I do not mind which, figure out which of these values are correct conversions for the mass of the bike and the water capacity of a full bathtub.

There may be more than one correct answer for either question.

Pause and give these questions a go.

Right, a cruise ship is huge.

This one is 0.

29 kilometres long and has a mass of 113 million kilogrammes.

By converting these values into different units, think about what missing units would go with the 290 and the 29,000, and what number goes before the grammes.

Take some time to think.

Pause the video and off you go.

And the last question.

The value on the left of each pair is shorter.

The value of the right of each pair is either longer or taller.

Come up with a number to make these descriptions correct.

Again, you'll have to do some conversions first.

Pause and good luck.

Onto the answers.

For question number one, 1.

457 kilogrammes is too light.

It's the mass of a small watermelon.

145.

7 kilogrammes is far too heavy.

It's the mass of a lion.

And so 14.

57 kilogrammes is correct.

Question number two, there are two answers here.

182 litres, which is found by dividing 182,000 by a thousand.

This might seem quite high, but remember you rarely fill a bathtub all the way to the top.

The other answer is 18,200 centilitres.

An uncommon but still used unit of capacity.

We get this by dividing 182,000 by 10, as centi is 10 times bigger than milli.

Okay, onto question three.

First, let's convert 0.

29 kilometres into metres.

This gives us 290 metres.

Converting from metres to centimetres gives us 29,000 centimetres.

And converting from kilogrammes to grammes means multiplying, multiplying by a thousand.

So 130 million multiplied by a thousand is 113 billion.

Yes, that is nine zeros after the 113.

Right.

And last question, question four.

24,400 centimetres is the same as 244 metres.

Since 225 metres is still too small, the missing unit must be kilometres.

And for Izzy's height, 0.

0017 kilometres is the same as either 1.

7 metres or 170 centimetres.

Since 16.

5 metres is too big, it must be centimetres.

And if centimetres is correct and millimetres is a smaller unit, millimetres must also be correct.

Mark your answers, and very well done for all the questions you've completed today.

And that concludes our lesson on metric units.

Today we have covered converting using place value charts and converting using prefixes.

We have also compared two or more measures using conversion and checked whether those conversions make sense in a real world context.

Right, that is all for today.

Thank you so much for joining me, and I hope to see you soon for some more maths.