Lesson video

Hi there, my name is Mr Tilston.

I'm a teacher and I'm feeling very lucky today because I get to spend this maths lesson with you learning all about unit conversions.

Unit conversions are a really important part of everyday life.

For example, I've just been into my cupboard, and we've got this cocoa powder, and you might notice it's measured in grammes.

So, the mass is in grammes on that one and I've got this plain flour, and you might notice that the mass of that is measured in kilogrammes.

So, it's really useful to be able to convert between one unit to measure and another.

Today's lesson specifically is going to involve problem solving in relation to unit conversions.

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

Let's begin.

The outcome of today's lesson is I can use efficient strategies, and common measure conversions to solve problems in a range of contexts.

Hopefully, by now you've got lots of unit conversions memorised and you can apply them today.

Our keywords, we've only got one.

My turn, convert.

Your turn.

What does convert mean? To convert is to change a value from one form to another such as converting one metres into 1000 millimetres.

So, that's one of our useful unit conversions.

Our lesson is split into two cycles.

The first will be representing the problems and the second solving problems. So, let's start by representing the problems. In this lesson, you're going to meet Jun and Snowy.

Who could Snowy be, I wonder? Ah, there's Snowy.

Jun has a West Highland white terrier called Snowy.

Very cute.

When she first came to the family as a puppy, Snowy had a mass of______ something.

Over the next two months, her mass increased.

Have you heard that word before? Increased by______ What was her mass at the end of the two months? Now, we're not going to use any values because I want us to look at the structure of that problem, what it means and what we might have to do to solve it.

First of all, what sort of problem is it? What kind of operations do you think you might need to solve it if a mass is increasing? It's an addition problem.

We're going to be adding.

And here's a bar model to represent what's happening.

So, we've got two addends and a sum.

So, addend plus addend equals sum.

And that's what we're looking for.

We need to find the sum.

And we could say that one addend is the initial mass.

The second addend is the mass increase.

And if we add those two addends together, we've got the new mass.

So, that's the sum.

So, we're looking to find the new mass.

What about this problem? Jun and his mum take Snowy for a walk.

They walk_____ in the morning and_____ in the afternoon.

How far do they walk all together? What sort of problem is this? Well, it's another addition problem, but with a different context.

This time, it's about distance.

And again, we can use that same structure, that same bar model to represent it.

We've got two addends.

And when we add them together, it will give us a sum.

So, can you think, what would the addends be this time? What two things are we adding together? Well, if we add together the morning distance and the afternoon distance, it will give us the total distance.

And that's what we're looking to find.

How about this one? Jun is trying to give Snowy the right amount of water.

For her current mass, she should be drinking ______in total each week.

So far this week, she's drunk________.

How much more water should Jun give her? Now, what kind of problem is this? What do we think? I think that's got a different structure, don't you? I think it's asking for something different.

It needs a different approach.

And it's a difference problem.

We're looking to find out the difference between two things, that how much more water was a clue that it was a difference problem.

So, this time, we've got a minuend and a subtrahend and a difference.

So, we'll subtract the subtrahend from the minuend, and it will give us the difference.

Or we'll add the difference onto the subtrahend, and it will give us a minuend.

Now, what are those three parts in this context? Well, the weekly water amount, take away the water given, will give us the water needed.

Or if we add the water needed onto the water given, it will give us the weekly water amount.

Either way, we're looking to find out the difference, which is the water needed.

So that's the structure of this problem.

We've got another problem.

Jun gives Snowy a bath.

Have you ever tried to bathe a dog? It can be fun.

It can be chaos.

Snowy is not happy.

There is already three litres of water.

Jun adds another______.

Snowy splashes around, as dogs often do, and spills about_______.

Approximately how much water is there now? Right, so have a think about this one.

What kind of problem is this, do you think? There was a little more to this problem, wasn't there? This was a two-step problem.

The first step involves addition.

So, what are we adding together here? We're adding together the water at the start, and the water added by Jun.

And that gives us a new water amount before the splashing.

And the second step involves subtraction.

So, if we start with that new water amount, and we take away the amount spilled by Snowy, it's going to give us the final water amount.

And that's what we're trying to determine, the final water amount.

So, a two-step problem.

Let's twist that about a little bit.

See if you can spot the difference.

This is similar, but not quite the same.

This time, Jun gives Snowy a bath.

Again, Snowy's not happy.

Again, there's already three litres of water.

Snowy splashes around again, and spills about____.

Jun then adds another_______to top it back up.

Did you see the difference? Approximately how much water is there now? What kind of problem is this, do you think? Well, it's another two-step problem.

The steps aren't quite the same.

This time, the first step involves subtraction.

This time, Snowy splashes about before the water's added.

So, we've got a subtraction.

We need to find a difference.

We've got the water at the start, take away the water spilled, and that gives us a new water amount.

But that's not the end of the problem.

The second step involves addition, because we're going to start with that new water amount, going to add some more water.

That's what Jun adds.

And that's going to give us the final water amount.

And that is what we're looking to find in this problem.

The final water amount.

It's time for a little check.

What type of problem is this, and can you explain why? Can you draw a bar model to represent the problem? The problem is this.

Jun has a_______ bag of dog food.

He pours______ of food into Snowy's bowl.

How much is left in the bag? Is that problem an addition problem? Is it a subtraction problem? Or is it a two-step problem? If you can, chat to the person next to you, see if you can come up with an agreement.

And I'll see you soon.

Well, what do you think? It's actually a subtraction problem.

We're trying to find out the difference between how much food there was in the bag at the start and how much there is in the bag at the end.

So that's difference.

It's subtraction.

Well done if you got that.

Here's a bar model to represent that.

We've got the food in the bag at the start.

And if we take away the food used, that will give us the food left in the bag.

That's what we're trying to determine.

It's time for some practise.

For each of these problems, put a tick to show which steps it follows.

So read it very carefully.

Have a really good think about it.

Don't rush into it.

And then for each one, decide is it an addition problem, a subtraction problem, or is it two-step? And if it's two-step, do you add then subtract or subtract then add? When you've done all that, draw a bar model to represent each one.

Six problems. Off you go.

Welcome back.

So the first one there, that was a subtraction.

We're looking to find the difference.

The second one was multi-step, two-step.

First, we're going to add and then subtract to find the difference.

The third one is a subtraction.

We're finding the difference.

The fourth one is a subtraction.

It's another difference one.

The next one is an addition one.

We're combining those together.

And the final one, we're subtracting first and then adding second.

So well done if you got those.

And the bar models might have looked a little bit like this.

Those might have looked a bit different too, but this is just an example.

That's representing the first problem.

So, we've got the Tuesday walk.

And then take away the difference between the walks gives us a Monday walk.

And the second problem, we're combining week one food, week two food to give us the food eaten over the first two weeks.

That's the first step.

And then the second step is finding out the difference between the food eaten over the three weeks, and the food eaten over the first two weeks to give us a week three food.

The next one, we're finding out the difference between Jun's height and Snowy's height.

And we can do that by subtracting Snowy's height from Jun's height or working out the difference.

That gives us a height difference.

You might not like that.

And then the next one, we're looking to find out the difference between the weekly food and the food eaten so far.

So that's what that bar model might look like.

Next one, we're combining those two.

So, week one water drunk plus week two water drunk gives us a total water drunk.

And the last one was two steps.

So, we're looking to find out the difference between the water in the bath at the start and the water spill.

That will give us the water left over.

And then if we combine the water left over with the top of water, it gives us the water in the bath at the end.

So well done if your bars looked a little something like that.

It's time to solve those problems. Let's add some values to that.

So when she first came to the family as a puppy, Snowy had a mass of, let's give it a number.

Let's use bar models to help solve the problems and then some values.

So, we've got 2,500 grammes, for example.

Over the next two months, her mass increased by two kilogrammes.

Now, what do you notice to start with? Well, one's in grammes and one's in kilogrammes.

Could we do something about that? Could we change that? Could they both be grammes? I think so.

So, the units are different, so a conversion is necessary.

Let's say 2,000 grammes.

It means the same, but now that looks easier to work out.

It's an addition problem, so we need to calculate the whole.

And if we combine those together, that gives us 4,500 grammes.

That was her mass at the end.

Snowy's mass at the end of two months was 4,500 grammes.

You could even say 4 kilogrammes, 500 grammes as well.

Let's add some values to this problem.

John and his mom take Snowy for a walk.

They walk, let's say, 750 metres before school in the morning.

Maybe that was a journey to school.

And then after school, they've got a bit more time.

They're going to go a bit further, 3,500 metres.

Is a unit conversion required this time? No, they're both already in metres.

How far do they walk altogether? So, we're going to combine those two values.

You may need a method to do this.

We may need to partition that 750 metres into two parts so we can use bridging.

And this is what that would look like.

So, start with that 3,500.

And what would it be sensible to split the 750 into? What two parts? What would the first part be to take us to 4,500? That would take us to 4,000.

And then what's left of the 750? 250.

Add that on and that gives us 4,250.

So that bridging strategy and partitioning that number was really helpful.

So how far do they walk altogether? 4,250 metres.

Let's have another problem and let's put some numbers to it.

Jenny's trying to give Snowy the right amount of water for her current mass.

She should be drinking two litres in total each week.

So, he's monitoring that.

So far this week, she's drunk 750 millilitres, right? First things first.

Do we need a unit conversion? Yes, we do because they are different.

The units are different.

What could we do, do you think? Could we turn the two litres into something? I think so.

So, let's turn that into 2,000 millilitres.

Now that looks more doable, right? How much more water? Now, remember, we're looking to find out the difference.

Now, this is a known fact, I think, hopefully.

You can solve this by recalling your complements to 1,000 and then to 2,000.

So, if you think what goes with 750 millilitres to make 1,000? 250.

And then another 1,000 would make 2,000.

So that gives us 1,250 millilitres.

In this case, I didn't need to use any written method, but you might.

You need to make that decision.

Let's add some values to this problem.

Jun gives Snowy a bath and Snowy's not happy.

There's already three litres of water and Jun adds another, let's give a value to it, 500 millilitres.

Do you think we're going to need a unit conversion? Yes, they're different.

Snowy splashes around and spills about 750 millilitres.

So, can you see we've got litre, millilitre, millilitre? It would be sensible if they were all in millilitres, wouldn't it? Approximately how much water is in now? It's an addition and subtraction problem.

We determined that at the start.

Since the other values mentioned are in millilitres, let's convert the three litres into millilitres.

Can you do that? One litre is 1,000 millilitres.

Three litres is 3,000 millilitres.

So, if we combine those two values together, it gives us 3,500 millilitres.

And now we can subtract that 750 millilitres from 3,500 millilitres to give us the difference.

Now, that's not too straightforward.

That's going to involve bridging.

So, let's do that.

So, there's 3,500 millilitres.

We're going backwards this time.

If we start by turning that 750 millilitres into 500 millilitres, that takes us to 3,000.

And then subtract the other 250 millilitres.

That takes us to 2,750 millilitres.

And that's the answer.

There's now 2,750 millilitres of water in Snowy's bath or 2 litres, 750 millilitres.

I think that number line there in bridging and partitioning was definitely helpful, don't you? Over to you.

Let's see if you can solve this problem.

John has a 2-kilogram bag of dog food and he's used 200 grammes of food.

How much is left in the bag? Think to yourself, do I need to do a unit conversion here? Give that a go.

Did you manage to get it? Let's have a look.

Yeah, we do need to do a unit conversion.

That's 2,000 grammes instead of 2 kilogrammes.

Now it's more workable.

And he's used 200 grammes of that.

Now, we know, hopefully, that 1,000 is composed of five lots of 200.

And we're taking off one of them.

So, 1,000 take away 200 equals 800.

Therefore, 2,000 take away 200 equals 1,800.

So, there's 1,800 grammes of food left in the bag.

You might have said 1 kilogramme, 800 grammes as well.

Very well done if you got either of those two answers.

John has been recording the amount of food eaten by Snowy to check that she's getting enough food.

So we've got that information in a table.

There's one value missing you might notice.

That's a week 2.

So, we've got two columns, the week number on the left, and the food eaten on the right.

Snowy ate 2 kilogrammes of food during week 1 and week 2.

How much food was eaten in week 2? Now, in week 1, we can see that's 1,100 grammes.

And in week 1 and 2, it tells us Snowy ate 2 kilogrammes.

So, we have got different units.

So, we do need to do a unit conversion.

Let's do that now.

Let's make that 2,000 grammes.

So, let's say Snowy ate 2,000 grammes.

Now we need to work out the difference.

1,100 plus something equals 2,000.

Now, I think I can work this out by thinking what goes with 11 to make 20.

That would be a good start.

And that's 9, so that makes that 900.

So, 1,100 grammes or 1,100 grammes plus 900 grammes equals 2,000 grammes.

So that's how much food was eaten in week 2.

And now our table is complete.

In which weeks did Snowy eat more than 1 kilogramme of food? Now, looking at those values, some are in grammes, some are in kilogrammes.

Why don't we make them all grammes? That would be easier.

And then in which weeks did Snowy eat more than 1,000 grammes of food? Weeks 1 and 5 are the ones that have values over 1,000 grammes.

So, week 1, 1,100 grammes.

And week 5, 1,300 grammes.

What was the difference? A difference problem this time between the smallest and largest amounts of food eaten by Snowy? So, find the smallest, find the largest, then work out the difference.

The smallest amount is 800 grammes.

That was in week 4.

Not very hungry that week, clearly.

And the largest amount in week 5 was 1 kilogramme, 300 grammes.

Very hungry that way.

Maybe did lots more exercise, something like that.

Okay, so now we need to find out the difference between them.

At the minute, they are using different units, but we'll need a little conversion.

And we need to convert that week 5 into grammes.

So that's 1,300 grammes.

Take away 800 grammes.

Or we could count on from 800 grammes to get 1,300 grammes.

From 800 to 1,300, you might think.

So, let's think of it that way.

What do you add to that to get that? That's 500 grammes.

Time for some practise.

You're going to solve those problems from task A.

So, we've got the same problems, but this time some values have been added.

So, think very carefully.

Think about the strategy that you might need.

Is it an instant recall fact? Might you need something like a number line and do some partitioning and bridging? Same questions as before.

And then when you've done that, number 2, there are some questions related to this table.

And I will see you very shortly for some feedback.

Let's have some answers, shall we? So, for 1A, you might have used your knowledge of place value.

So, we're taking away from the hundreds.

So, 4,000 metres.

Take away 500 metres is 3,500 metres.

Or 3,500 metres.

You might have thought of it that way.

And for B, we need to add together what's snowy 18 weeks 1 and 2 for our first step.

That gives us 1,750 grammes.

And then we can find the difference between those two.

You might have used a strategy like bridging for that.

Start with 1,750 and then split the next number up.

So, 250 grammes would take us to 2,000 grammes.

Another 500 grammes would take us to 2,500 grammes.

Add them together and we've got 750 grammes.

So that's what snowy ate in week 3.

And then for C, you might have applied a known fact here.

So, we turn that 1 metre into 1,000 millimetres.

And the difference is 700 millimetres.

And then for D, again, you might have used that conversion.

Hopefully, you did.

You might have made the 1 kilogramme 1,000 grammes.

Subtract the 600 grammes from it.

And that gives you 400 grammes.

And then for E, you might have used 25 plus 22 as your starting point to work out that 2,500 plus 2,200 equals 4,700 or 4,700 millilitres.

You might have also expressed that as 4 litres 700 millilitres.

And F, the bath problem, 3,000 millilitres, which is what 3 litres is.

Take away 750 millilitres equals 2,250 millilitres.

That's only our first step.

That's after snowy splashed around and spilled some.

And we're adding some more water back into that value, and that gives us 2,750 millilitres.

You might have expressed that as 2 litres 750 millilitres.

And the table, A, what do you add to 1,200 to get 3,200? 2,000.

Which days did they walk over 2 kilometres, Friday, Saturday, and Sunday? On all of those days, the values were over 2,000 metres.

How far did they walk at the weekends? That's Saturday and Sunday.

Saturday, that's 3,000 metres.

And Sunday, 2,225 metres.

We've got to add those two together, and that gives us 5,225 metres.

That's how far they walked at the weekend.

You might have said 5 kilometres, 225 metres.

That's also true.

And the difference between the longest and shortest walks of the week, Thursday was the shortest walk at 900 metres.

Saturday was the longest at 3,000 metres.

And the difference between those two is 2,100 metres.

You might have expressed that as 2 kilometres, 100 metres.

We've come to the end of the lesson.

In today's lesson, we've been using efficient strategies and common measure conversions to solve problems in a range of contexts.

It can be easier to understand problems if they are first represented using bar models, like in the example here.

This can help to see which operation, or in the case of multi-step problems, which combination of operations is needed.

It's then important to consider what strategies might be used.

Are there any automatic known facts that can be applied? Can knowledge of place value be used? Is a written method, such as partitioning and bridging, helpful? Sometimes a unit conversion will be needed.

I always say to the children in my class, when you're solving problems, look before you leap.

Have a really good think before you solve that problem.

You've been amazing today.

Give yourself a little pat on the shoulder.

You've achieved so much.

Well done on your accomplishments.

I hope I get the chance to spend another maths lesson with you in the near future.

But until then, take care and goodbye.