Lesson video

Hi there.

My name is Mr. Tilstone.

I'm a teacher.

My favourite subject just has to be maths.

So it's a real pleasure and a real delight to be with you today to teach you a lesson all about unit conversions.

Now, units of measure are everywhere.

When you get home tonight, have a look in your fridge and you might see some bottles of fizzy drink with litres or millilitres on and have a look in your cupboard, you might see a tin that's measured in grammes or kilogrammes.

So they're everywhere and it's really useful to know how to convert from one unit to another.

So that's what we're going to do today.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is "I can partition 1000 and 2000 in the context of measures." You might have had some very recent experience of partitioning 1000, well today we're still going to use 1000, but we're going to go into 2000 as well.

Our key words are, my turn, scale, your turn.

What does scale mean? Scale is the value of the divisions marked on measuring equipment or the axes of a graph.

So the scale here, is marked in 200 grammes.

Our lesson today is split into three cycles.

Three parts.

The first will be partitioning and composition of 1000 and 2000, the second, partitioning using place value up to 2000 and the third, applying composition of 1000 and 2000.

So if you're ready, let's start by partitioning and composition of 1000 and 2000.

In today's lesson, you're going to meet Izzy and Sam, have you met them before? They're here today to give us a helping hand with our maths, and they're very helpful too.

What do you notice about these scales? Have a look.

Something may be different to what you've been used to recently.

Something maybe similar as well.

Well, let's have a look at this one.

We know that one kilogramme, or 1000 grammes, must be at the halfway point of this because did you notice it goes up to two kilogrammes? So half of that's one kilogramme, that must be the halfway point.

And that's a halfway point just there.

So that's showing one kilogramme or 1000 grammes.

We know that the divisions up to 1000 grammes are multiples of 100.

There we go.

So that might be quite familiar.

That's something you might have done recently.

Splitting 1000 into 10 equal parts, that's 100 grammes.

So each of those intervals, is 100 grammes.

After 1000 grammes, we can continue to count in multiples of 100.

So it goes 1100, 1200, et cetera, et cetera, all the way up to 2000.

So they're all grammes.

We can also think of these as one kilogramme and a multiple of a hundred grammes.

So 1,100 grammes is also one kilogramme, 100 grammes, 1,200 grammes is one kilogramme, 200 grammes, et cetera, et cetera.

And you might want to count in those steps.

The scales go past one kilogramme.

The one kilogramme interval is currently unmarked, but it could be marked.

It's exactly in the middle of one kilogramme and two kilogrammes.

The scale between zero kilogrammes and one kilogramme is divided into 10 equal parts, so each part is worth 100 grammes.

What value is the arrow pointing to? Hmm.

What do you think? So we know they're in steps of 100 grammes, and it's three steps away from one kilogramme, which is 1000 grammes.

So that must make it 700 grammes.

That's 700 grammes.

Now the scale between one kilogramme and two kilogrammes, is also divided into 10 equal parts.

So each part's worth 100 grammes.

What value is the arrow pointing to this time? Hmm.

And there's two answers you could give.

You could give an answer in grammes and you could give an answer in kilogrammes and grammes.

So what do we think? Well, it's three intervals past the one kilogramme, so that's 1,300 grammes.

And as it's greater than one kilogramme, it could also be expressed as one kilogramme, 300 grammes.

So both of those are the same.

What about now? Just a bit less than two kilogrammes, isn't it? So just a little bit less than how many grammes? A little bit less than 2000 grammes.

One interval less.

Again, two ways to say it.

Can you do it in grammes? Can you do it in kilogrammes and grammes? Let's start with grammes.

That's 1,900 grammes.

So 100 short of 2000.

Or you could say one kilogramme and 900 grammes.

They're the same.

This time, the scale between zero and one kilogramme and one kilogramme and two kilogrammes is divided into five equal parts.

So have a look at that.

Each part's worth 200 grammes.

We know the middle part's one kilogramme again.

So this time it goes 200, 400, 600, 800.

But what about after one kilogramme? 1,200, 1,400, 1,600, 1,800.

And that two kilogrammes could be thought of as 2000 grammes.

And once again, it can be thought of as one kilogramme plus something.

So for example, 1,200 grammes is one kilogramme, 200 grammes.

And again, you might want to count in those steps.

So there's our one kilogramme, divided into five equal parts.

What value is the arrow pointing to this time? So remember, we're counting in 200, so 200, 400, 600, that's 600 grammes.

What about this one? Can you do it in two ways? In grammes and in kilogrammes and grammes? So it's gone past 1000 grammes and we're going up in steps of 200.

So 1000, 1,200, 1,400, 1,600 grammes.

And then in kilogrammes and grammes, you can see it's gone past one kilogramme.

So it's one kilogramme and 600 grammes.

They're the same.

What about the scale this time? What do we notice? Again, it goes up to two kilogrammes.

Let's explore.

That must be one kilogramme then, 'cause it's halfway.

Think about how many equal parts it's divided into between zero and one, or one and two.

The scale between zero and one kilogrammes is divided into two equal parts.

So is the scale between one kilogramme and two kilogrammes.

So each part is worth 500 grammes.

What value is this arrow pointing to then? Well, it must be 500 grammes.

What about this one? Can you give it in two ways? It's 1,500 grammes or, one kilogramme and 500 grammes.

Let's have a check.

This time the scale between zero and one kilogramme is divided into mhm equal parts.

Hopefully that's quite a straightforward start for you.

So is the scale between one kilogramme and two kilogrammes.

So each part is worth what? And the arrow is pointing to what or what? Pause the video and have a go.

Well, it was split into four equal parts.

That means each part's worth 250 grammes.

So we can count as steps of 250.

So the arrow has gone past 1000 grammes.

It's 250 grammes more than that, it's 1,250 grammes or one kilogramme and 250 grammes.

And very well done, if you got that right, you are on track.

This time, the scale between zero and one kilogramme is divided into just one equal part.

Hmm.

Is it still possible to estimate the mass being shown by the arrow? So that must mean the space between zero kilogrammes and one kilogramme, is 1000 grammes.

Now, "it's past the halfway point", says Izzy, "so it's more than one kilogramme or 1000 grammes." Yes, agreed.

"It's over halfway between one kilogramme and two kilogrammes, so it's over 1,500 grammes." She's getting there, isn't she? Yeah.

"It's quite close to two kilogrammes." I agree.

"Or 2000 grammes." Yep.

"I can picture the space between one kilogramme and two kilogrammes being split into four equal parts." See if you can do that with your mind, could you split that into four equal parts? Can you imagine where those intervals would go? So each part, each equal part would be 250 grammes "and the arrow will be pointing to the third interval.

So I estimate this is one kilogramme, 750 grammes, or 1,750 grammes." And we can't know for sure, but I think that's a pretty good estimate, Izzy, well done.

So Izzy says, "I can estimate the amount of liquid in this container." Have a look yourself.

What do you think yourselves? Hmm.

"There's more than one litre, but less than two litres." Okay.

Yep, that's a good start, we're narrowing it down.

So there's more than 1000 millilitres, but less than 2000 millilitres.

"If you split the distance", says Sam, "between one litre and two litres into 10 equal parts, I estimate it will be three of them, so 300 millilitres." I like that strategy of picturing those equal parts that it could be divided into.

That's really useful.

So yeah, three, 300 millilitres.

"If you split into four equal parts", which it could be, "I estimate it would be one of them, so 250 millilitres." Their estimates are pretty close, aren't they? And we can't know for sure what it is, but they seem good estimates to me.

So Sam says, "My estimate is one litre 300 millilitres, or 1,300 millilitres." And Izzy says, "My estimate is one litre 250 millilitres, or 1,250 millilitres." I think they're both good estimates.

Who do you think is right? Now, let's have a look at this number line.

We're going to estimate where 800 metres would be on this scale.

So we've changed our unit, it's a straight line.

It goes from zero kilometres to two kilometres.

What do you think could be a good starting point? What have we done before with the scales and things? We could turn it into a number of metres.

So that's 2000 metres rather than two kilometres because we're estimating in metres.

And then we could put our halfway point.

So that's one kilometre or 1000 metres.

Now, that's really helping to narrow it down now.

800 metres is quite close, isn't it, to 1000 metres? And as he says, "I can imagine the zero to 1000 divided into 10 equal parts." Yep.

So can I, I can picture those divisions.

And "800 is quite close to 1000." Yeah, so about there, I think that's a good estimate Izzy, well done.

So over to you.

Can you estimate where 1,250 millimetres would be, on this scale and explain why? Pause the video and off you go.

Did you manage to make an estimate and did you manage to do a good explanation of why? Let's have a look.

Well, Izzy says "Two metres is 2000 millimetres", good unit conversion Izzy, that's going to help out.

'cause the question is all about millimetres.

Yep.

So there we go.

"Half of that's 1000 millimetres", good.

So we've got our halfway point, we're narrowing it down.

"If you split the distance between 1000 and 2000 to four equal parts, the first interval will be 1,250 millimetres." So yeah, just about there.

I think that's bob-on.

Well done, Izzy.

And well done you, if you positioned it similarly on the number line.

So here we've got one metre, 250 millimetres or 1,250 millimetres.

It's time for some practise.

I think you're ready.

Add the missing value.

So this measuring jug goes up to two litres.

Can you add all the missing values? Think about that halfway point, is my tip.

Number two, estimate where the following values will go on this scale.

Pause the video, very best of luck and I'll see you soon for some feedback.

Welcome back.

Let's have a look.

Are you ready for some answers? Well, number one, the missing values are this.

This is how I thought through it.

This is the order that my thoughts went in.

Two litres is equivalent to 2000 millilitres.

That was my first thought.

So that was the first one that I put in.

Half of two litres is one litre, or 1000 millilitres.

So that was the second one that I put in.

And then we looked at the equal parts.

So the 1000 millilitres is composed of five equal parts.

So each part's worth 200 millilitres.

Yes.

So I started with 200 and then I started counting in steps of 200, until I got all the way up to 2000.

So well done if you got those values, they're correct.

And estimate where the following values would go on this scale.

Well, at the minute it says kilometres, it would help if we turn it into metres, wouldn't it? And it would help if we identified the halfway point, which is that.

So that's one kilometre or 1000 metres.

So that's that one.

One kilometre is halfway between zero kilometres and two kilometres.

And one kilometre is equivalent to 1000 metres.

Two kilometres is equivalent to 2000 metres.

So that's helpful.

So good unit conversion.

So 100 metres would probably go about there, quite close to the star.

If you split it into 10 equal parts, that'll be the first one.

500 metres is exactly halfway between zero kilometres and one kilometre.

So that's where that would go.

1,500 metres is halfway between 1000 metres and 2000 metres.

So that would go just here.

And then 1,750 metres is halfway between 1,500 metres and 2000 metres.

And I thought of that space between one kilometre and two kilometres, as being split into four equal parts and that being the third interval.

So it'll go just there.

Let's do cycle two.

That's partitioning using place value up to 2000.

So we've got a measuring jug here.

There's one litre or 1000 millilitres of liquid in this container.

What would happen do you think, if 100 millilitres was poured out? Is that a lot? Is that a little bit? What do you think? What about 10 millilitres? What about one millilitre? What do you think the jug would look like after those amounts were poured out? Well let's first of all turn it into 1000 millilitres because we're dealing with millilitres.

Now, look, here's what would happen if we poured 100 millilitres away from that 1000 millilitres.

So there's 900 millilitres in one container and 100 millilitres in the other.

And that's about how much 100 millilitres would be, if you split it into 10 equal parts, that would be one of them.

So we could say 1000 millilitres subtract 100 millilitres equals 900 millilitres.

We could say 900 millilitres plus 100 millilitres equals 1000 millilitres.

And I can see that in that image too.

This is what would happen if you poured out 10 millilitres.

It's not very much.

If 10 millilitres of water is poured from a one litre container, there's 990 millilitres left in the container.

1000 millilitres - 10 ml = 990 millilitres.

Or, as an addition, 990 millilitres + 10 millilitres = 1000 millilitres.

And here we've got one millilitre being poured out.

That's a very, very tiny amount, so really about a drop.

If one millilitre of water is poured from a one litre container, there's 999 millilitres left in that container.

And our equations are 1000 millilitres - one millilitre = 999 millilitres.

Or 999 millilitres + one millilitre = 1000 millilitres.

I can see both of those.

Let's do a check.

What would be left in a one litre container, if the following amounts were poured out and what do you notice? So what if 300 mils was poured out? What if 30 mils was poured out and what if three millilitres was poured out? And again, my top tip, why don't you convert that one litre into millilitres to start with? Pause the video.

Welcome back.

Let's have a look.

So, if you did 1000 millilitres, that's our unit conversion, takeaway 300 millilitres, that would give you 700 millilitres.

If you did 1000 millilitres - 30 millilitres, that's 970 millilitres.

And if you did 1000 millilitres - three millilitres, that's 997 millilitres.

We can use our knowledge of 10 - 3 = 7 and place value to help.

So 10 one hundreds - 3 one hundreds = 7 one hundreds.

That's the first one.

10 tens - 3 tens = 7 tens.

That's the second one.

And 10 ones - 3 ones = seven ones, that helps us with the third one.

There are two litres of liquid this time in this container.

What would happen if 100 millilitres was poured out? What about if 10 millilitres was poured out? And what about if one millilitre was poured out? So let's start by doing that conversion.

That's 2000 millilitres.

Now we're dealing with millilitres all around.

If you poured out 100 mills, that's what would happen.

So there's 1,900 millilitres left in that container, we can see 2000 millilitres - 100 millilitres = 1,900 millilitres.

Or we can see 1,900 millilitres + 100 millilitres = 2000 millilitres.

What about this time? This time, 10 mils has been poured out.

If 10 millilitres of water is poured from a two litre container, there's 1,990 millilitres left in the container.

And there are our equations.

And this time, that tiny amount, that drop really, of liquid is poured out.

This time there's 1,999 millilitres left in the container.

And there's our subtraction, and there's our addition.

What do you notice? The first 1000 millilitres remains untouched when subtracting 1, 10 or 100.

It's the other 1000 that we're taking it from.

Let's have a check for understanding.

What would be left in a two litre container if the following amounts were poured out and what do you notice? Pause the video.

Let's have a look.

So 2000 millilitres - 400 millilitres = 1,600 millilitres, or one litre 600 millilitres.

2000 millilitres - 40 millilitres = 1,960 millilitres, or one litre 960 millilitres.

And then 2000 millilitres - four millilitres, a tiny amount, = 1,996 millilitres, or one litre 996 millilitres.

And again, we can use our knowledge of 10 - 4 = 6 and place value, to help.

That's 10 one hundreds, take away 4 100 hundreds, is 6 one hundreds.

10 tens - 4 tens is 6 tens.

And 10 ones - 4 ones is 6 ones.

Time for some practise, use your knowledge of place value to work out the following calculations and see if you can see some patterns while you're at it.

Pause the video and good luck.

Let's have a look at some answers for task B.

A, one kilogramme, that's 1000 grammes, - one gramme = 999 grammes.

B, one kilogramme, 1000 grammes - 10 grammes = 990 grammes.

C, 1000 grammes - 100 grammes = 900 grammes.

And I hope you saw there that you could use your known facts and your place value knowledge, to help you work those out.

So now over to you to check the rest of the answers.

It's time for the final cycle, applying composition of 1000 and 2000.

So there is one litre 300 millilitres of liquid in this container.

How much must be poured in to make two litres? Hmm.

Well that will make it up to two litres, but how much is that? How much liquid is that? Sam says it's 1,300 millilitres + 700 millilitres = 2000 millilitres.

Izzy says one litre 300 millilitres + 700 millilitres = two litres.

So they're using their knowledge of compliments, to a thousand.

Let's do a check.

Izzy has run 1,400 metres of a two kilometre race.

How far has she got left? My top tip, why don't you do some unit conversion with that two kilometres? Pause the video.

Let's have a look.

Did you turn it into 2000 metres to start with? That was my first step.

So 1,400 metres + something = 2000 metres.

I'm using my knowledge of place value and 4 + 6 = 10.

So 4 one hundreds + 6 one hundreds = 10 one hundreds, or a thousand.

That's helpful.

So that's 600 metres.

Now this time there is one litre 300 millilitres in the container, or 1,300 millilitres.

If 500 millilitres is poured away, how much will be left in the beaker? So we've got a slightly different kind of question this time.

This time we are pouring it away, not adding to it.

So let's use a number line, to help with our thinking.

So we've got one litre in the middle and we've got that 1,300 millilitres here.

And Sam says "I could partition the 500 millilitres into two parts." Have you done bridging before? That's what we're doing here.

300 millilitres and 200 millilitres.

Can you see why she's partitioning it like that? Then I can bridge to and from the one litre.

So there we go.

So if we take off that 300 millilitres, that takes us to a litre and then the remaining 200 millilitres would take us to.

Or one litre is 1000 ml - 200 is 800 millilitres.

So it could say one litre 300 millilitres takeaway 500 millilitres = 800 millilitres.

That number line was really helpful there and partitioning and bridging was really helpful.

There is now 800 millilitres in the container.

If 700 millilitres is poured in, how much liquid will there be? Well again, why don't we use that number line? 'cause we're going to have to do some bridging and why don't we partition that, 700 up.

So how could the 700 millilitres be partitioned so that we can bridge through that one litre? How could we make that into two parts? What would be a useful first part to take us up to one litre? It would be 200 millilitres.

So if we had 200 millilitres, what's left of the 700 mils? 500 millilitres.

So now we can add that on.

So instead of doing it in one big go, the 700 millilitres, we've partitioned and bridged.

And that was helpful.

That turns it into 1,500 millilitres.

And you might say that's one litre 500 millilitres.

Jun's having his parcels weighed at the post office.

This is a massive parcel.

A, can you work out what it is? It's been split into ten equal parts between zero and one kilogramme and that looks like seven of them.

So what could that be? That's 700 grammes.

He already knows Parcel B has a mass of 500 grammes.

So what will the combined mass be? So he's adding on 500 grammes there.

Now if we do that, that's going to cross over one kilogrammes.

So bridging would be helpful.

So we're going to partition that 500 into 300, and 200, and bridge through the one kilogramme.

So there we go.

So that gives us 1,200 grammes, or one kilogramme 200 grammes.

Let's have a check.

Izzy has run 600 metres of her race.

She stops to tie her lace then runs 700 metres more.

How far has she run in total? You may wish to draw a number line.

Pause the video.

I think I can express that in two different ways.

In the second part of her run, Izzy will bridge through 1000 metres or one kilometre.

It's helpful therefore, to partition the 700 metres into 400 and 300.

So you could say 600 metres + 700 metres = something.

You could do that, in one, or you could partition and make it 600 metres + 400 metres + 300 metres =.

And that's a little easier now 'cause we've bridged through the thousand.

That's 1,300 metres and you might have expressed that as one kilometre 300 metres.

Time for some final practise.

You might use a known factor to solve some of these problems or you might want to use something like bridging, to help you get there.

If you can work with a partner as well, that's always helpful in problem solving.

So you've got eight different problems to work through.

Have a good think about each one before you start.

Good luck.

Welcome back.

How did you find those? Tricky, medium, easy? Well, let us have a look at some answers.

Number one, on a school trip the children need to walk two kilometres.

They've already walked 1500 metres.

So, I think of that as 2000 metres and the difference between those numbers is 500 metres.

And for me that was a known fact.

I didn't have to do any calculation there.

And then Sam's mom is painting her room.

She uses 800 millilitres of a one litre 500 millilitre tin.

How much is left? I thought of it as 1,500 millilitres.

And you might have used a number line or you might have some good recall of addition factor to 20 that was a good basis for your thinking.

But 1,500 millilitres - 800 millilitres = 700 millilitres.

Three, a 10 week old kitten has a mass of 1,100 grammes.

At 20 weeks she has a mass of two kilogrammes, or 2000 grammes.

By how much has her mass increased between those ages? So we're looking at the difference between 1,100 and 2,000.

Again, I think that's pretty automatic, hopefully.

I can do that in my head.

That's a known fact.

That's 900 grammes.

They're compliments to a thousand.

And Parcel A has a mass of 750 grammes.

Parcel B has a mass of 500 grammes.

What's their combined mass? Well, if you add those two together, it's 1,250 grammes.

And a number line might have helped you.

So there is some bridging.

You might have also said one kilogramme 250 grammes.

Number five, there's a two metre tree in Sam's garden.

Her dad prunes it taking 50 millimetres from the top.

What is the new height of the tree? Why don't you think of it as 2000 millimetres, then take away 50 millimetres and that gives you 1,950 millimetres.

You might have used some place value knowledge, to help you there.

And a 200 mil glass of juice is poured from a two litre, or 2000 millilitre, bottle of juice.

How much is left in the bottle? 2000 millilitres - 200 millilitres is 1,800 millilitres.

And you might not have needed anything like a number line for that.

That might have been a known fact.

Hopefully it was.

Number seven.

Izzy has a one litre, or 1000 millilitre, tin of paint.

She accidentally knocks it over, spilling about 30 millilitres.

How much is left? That's 1000 - 30, that's 970 millilitres.

That might have been a known fact for you.

And number eight, Izzy has some ribbon, which is one metre 250 millimetres in length.

She cuts a 750 millimetre length from it.

How much is left? Well, I thought of that as 1,250 millimetres.

And a number line was helpful there.

And if you take 750 millimetres away, it gives you 500 millimetres.

Well done if you got those.

We've come to the end of the lesson.

I hope you've enjoyed it.

Hope you've learned lots.

Today's lesson has been partitioning 1000 and 2000, in the context of measures.

So just as one kilogramme can be thought of as 1000 grammes, two kilogrammes can be thought of as 2000 grammes.

And similarly, two metres is 2000 millimetres, two litres is 2000 millilitres.

Two kilogrammes is 2000 grammes.

And these values can be partitioned in different ways on scales, just as you can partition 1000 in different ways.

You can represent the scales as number lines, to solve problems, which bridge through multiples of 1000.

Very well done on your achievements and accomplishments today, there's been a lot to think about.

I bet your brain needs a little rest.

Well, give yourself a pat on the back.

You've done it really, really well.

I hope I get the chance to work with you again, in the near future, on another maths lesson.

But until then, take care.

Enjoy the rest of your day and goodbye.