Lesson video

Hello there, my name is Mr. Tilstone.

It's lovely to be working with you today on this lesson which is about unit conversions.

We're going to be doing some problem solving today.

Sometimes that's going to require a little bit of perseverance and determination and it's going to require a lot of thinking, but you've got that in you, I just know.

So if you're ready, I'm ready, let's begin.

The outcome of today's lesson is, I can solve problems involving different units of measure.

And we've got some keywords.

My turn, convert.

You turn.

My turn, represent.

Your turn.

My turn, calculate.

Your turn.

Let's find out what those words mean.

Convert means to change a value or expression from one form to another, such as grammes into kilogrammes.

And I'm sure you've had lots of recent experience of doing that.

Represent means to communicate mathematical ideas through models.

Calculate means to choose one of the four operations to solve a problem, and that's what you're going to be doing today.

It won't be necessarily obvious what the operation is, but you'll figure it out from reading the question.

Our lesson is split into two cycles.

The first will be visualising and representing problems and the second, calculating and evaluating in problems. So if you're ready, let's begin by visualising and representing problems. In this lesson, you're gonna meet all of these characters.

I'm sure you've met them before.

You're going to meet Sofia, Alex, Aisha, Izzy, Sam, Laura, Andeep, Jun, Jacob and Lucas.

They're gonna be here to give us a helping hand with the maths.

Izzy is having a party.

Lucky Izzy.

She is making squash and she combines 15 millilitres of cordial with 1.

2 litres of water.

How many millilitres of squash has she made? Let's represent this.

How could we do that? What sorts of models can you think of that can represent problems? What about a bar model? Here we go, so we've got a bar model.

On the top we've got the millilitres of squash and on the bottom, the millilitres of cordial and the litre of water.

Here, we're combining the cordial and the water to make the squash.

So if we add those two bottom parts of the bar together, we'll get the top bar.

Cordial plus water equals squash, and I'm sure you've made the drink lots of times before.

So we've an unknown whole that we're going to calculate, but we've got a known part and a different known part.

So we know how much cordial there is and we know how much water there is, we just gotta figure how much squash that makes altogether.

So that's an adding problem.

Known part plus known part equals unknown whole.

Izzy now pours the squash from a jug.

She pours 200 millilitres of squash from a one litre jug.

Now, have you noticed the units are different? One's in millilitres, one's in litres.

How many litres of squash are left in the jug? So the question is, how many litres of squash are left in that one litre jug? How is this problem the same as before and how is it different? You might want to have a little think about that.

Let's represent it.

So again, we can use a bar model in three parts.

This time, the top bar is going to be the litres of squash before pouring and the bottom part's going to be millilitres of squash poured and litres of squash left.

But this time, we're not doing the same thing.

It's not an addition problem.

Here, we are subtracting the squash poured from the amount in the jug before pouring.

So a subtraction problem.

Squash before pouring take away squash poured equals squash left.

And again, we can represent that with a bar model.

We've got known part, unknown part in the bottom and known whole on the top.

This time, we know something different.

Known whole take away known part equals unknown part.

And we'll focus on the actual answers to these later.

We're looking at the structure for now.

Okay, and well the problem's going to be this time, there the image has changed.

Izzy know pours an equal amount of the remaining squash into four cups.

How many millilitres of squash will be in each cup? How is this problem the same and how is it different? Do you think you're going to be using the same operations this time? Let's represent it, will the bar model look the same? No, there are more parts to it.

So the top this time is the litre of squash before pouring and the bottom part, the different cups, one, two, three, four, in millilitres.

So again, our units are different, a conversion is going to be needed.

Here, we are dividing the amount of squash equally between four cups.

So it's not an addition, it's not a subtraction, this one's a division question.

Squash before pouring divided by four equals squash in each cup.

So here we've got a known whole.

So the known is the top part this time and then we've got four different parts.

Known whole divided by four equals unknown value of part.

So we've gotta work out what one of those are and they're all the same.

Okay, let's do a check, let's see how you're doing.

So Izzy adds one quarter of a kilogramme of sugar to create a cake mixture.

She also adds 225 grammes of softened butter.

What is the mass of the cake mixture in grammes at this point? Okay, don't want to know the answer, that's going to come later, want it represented, please.

So represent that as a bar model and note what is known and what is unknown.

Think you can do that? Give that a go, pause the video.

Did you get an answer? So let's have a look or a representation.

So here we go, so we've got those grammes of cake mixture, kilogramme of sugar and the gramme of softened butter.

Here, we are combining the sugar and the softened butter to make the cake mixture.

So this is an addition problem.

Mass of sugar plus mass of softened butter equals mass of cake mixture.

Also our knowns and unknowns.

Well, the whole's unknown, but we've got two known parts.

So well done if you got that.

Okay, let's think about another problem then.

So Izzy, again, has three fifths of a kilogramme of sweets in a jar.

She saves 150 grammes for herself and shares the rest equally between six party bags.

Did you notice something there? One's in kilogrammes, one's grammes.

Later on, not now, we're going to need to do some conversions.

What is the mass of sweets in each party bag in grammes? So let's think about representing that problem.

How's it the same, how's it different? Well, this time, the top part o four bar model is the kilogramme of sweets in a jar and the bottom, we've got grammes of sweets saved and grammes of sweets for party bags.

First, we are subtracting the mass of the sweets that Izzy saved from the mass of sweets in the jar, so it's a subtraction to start with.

Mass of sweets in jar take away mass of sweets saved equals mass of sweet for party bags.

So in this case, we've got a known whole, one known part and an unknown part and we're going to use subtraction to find that unknown part.

Known whole take away known part equals unknown part.

That's the structure of that problem.

What is the mass of sweets in each party bag in grammes? Well, here we've got a bar model to represent that.

So the mass of sweets for party bags and the mass of sweets in each party bag.

Then we are dividing, so this is the second part, it's a two part.

The mass of the sweets for the party bags equally between six bags.

So the mass of sweets for party bags divided by six this time equals the mass of sweets in each party bag.

So this was a two step problem.

Two sets of operations required.

So we've got a known whole and we've got some unknown parts, they're all going to be the same.

So we need to find the value of one using division.

Known whole divided by six will give us the unknown value of the part.

Okay, over to you.

You've got some tasks to do.

So have a good read, read them carefully.

Make sure you've understood exactly what it is that you're being asked to do.

Take some time on that.

Talk it through with a partner if you've got one and then you're gonna represent each of the following problem as a bar model and know what is known and what is unknown.

So what you're not doing at this point is actually solving them.

You are representing them with bar models, okay? And then question two, a little bit more open-ended for this one.

Izzy's party is from two to five pm.

Write a question that could be represented by this bar model.

So we've given you a bar model.

In the top part's three hours and then we've got two known parts, 45 minutes, one hour and 20 minutes, what could they represent? And then we've got an unknown part.

So what could the question be that goes with that? Good luck with all that and I will see you soon for some feedback.

Welcome back, how did you get on? Bar models can be tricky, can't they? But when you crack them, they are brilliant.

So here we go, so A, Izzy's party lasts for three hours and they watch a film that lasts 85 minutes.

How much time will they have left to eat and play games? Your bar model may look something like this.

Now, it may be that your 85 minutes was on the other side and your question mark on the left rather than right, that's fine, but something like that.

So Izzy has some bunting to decorate the doors of her house.

She has four metres of bunting, each door is 75 centimetres wide, how many doors can she decorate? And will she have any bunting left over? So we've got two knowns, the four metres and the 75 centimetres and then an unknown.

We don't know how many of those 75 centimetres is going to fit in.

So it may look something like that.

It might look a bit different too, but that's the essence that we're looking for.

And then for C, Izzy has twelve pounds to spend on her six party bags.

She has bought a toy for 85 pence for each bag.

How much more money does she have left to spend? Your bar may look something like this.

So 12 pounds on the top, those 85 p's, six of them at the bottom and then one bar left, that's our unknown.

So you've got a couple things to do on that in the next cycle, but it might look something like that.

D, there is 50 millilitres of squash left in the jug.

Izzy has given cups of 250 millilitres to five people at the party.

How much was in the jug to start with? So that's kind of a bit flipped around, isn't it? So there we go.

So you've got the 250 millilitres, five times, and the extra 50 millilitres there and then if you combine those together, that will tell you how much was in the jug to start with.

So we kinda reverse that one.

And then for number two, there's lots and lots of possible questions.

What do think Izzy and her friends did at the party? Well, you know, it could be this.

Izzy's party is three hours long, so we can see there we've got three hours and that sounds about reasonable, doesn't it? They play a game for 45 minutes, could do that and watch a film for one hours and 20 minutes.

How long have they got left to eat the party food? And you might've chosen different activities or had different contexts all together, but something like that.

Are you ready for cycle two? So we're gonna think a bit more about those problems now and actually start solving them and use some arithmetic.

So Izzy is having a party.

She is making squash and she combines 15 millilitres of cordial with 1.

2 litres of water.

Right, different unit conversions.

How many millilitres of squash has she made? So we've got our bar model, we established that.

Let's start thinking about what we need to calculate.

So that's our known parts, that 15 millilitres and 1.

2 litres, what's the problem now? I need to do some converting.

To give the answer in millilitres, we must convert all measurements to millilitres.

That will be helpful.

So the millilitres of cordial plus the millilitres of water equals the millilitres of squash.

So let's do some conversions.

If I know that one litre equals 1000 millilitres, and I bet you knew that, I'm confident that you did, then I know that 1.

2 litres equals 1200 millilitres.

So that's what we can call that.

So that then gives us 1200 millilitres plus 15 millilitres, the units are the same.

And that's fairly straightforward to work out.

I don't think you're gonna have a lot of problem with that, that's 1215 millilitres.

So that was the easy bit, the hard part was the conversion.

And that's the answer.

Izzy has made 1215 millilitres of squash.

So keep in your mind all the time, are the units different? Do I need to do a conversion? Izzy now pours the squash from a jug.

She pours 200 millilitres of squash from a one litre jug.

How many litres of squash are left in the jug? Okay, so we've got our bar model.

What do we need to calculate? So that's our one litre.

So our 200 millilitres.

We need to do a conversion.

Let's convert them all to litres this time, because that is what it's asking for.

So we've got to convert 200 millilitres to litres.

How can we do that? And then the litres of squash before pouring take away the litres of squash poured equals the litres of squash left.

So if I know that 1000 millilitres equals one litre, then I know that 200 millilitres equals 0.

2 litres and then we could start working with it.

So that gives us one litre, take away 0.

2 litres and that gives us 0.

8 litres.

We could also say that's 800 millilitres, but it did ask for litres in the question.

So there we go, 0.

8 litres is the answer.

That's how much squash there is left in the jug.

So we've got this problem again.

She now pours an equal amount of the remaining squash into those four cups.

How many millilitres of squash will be in each cup.

What do we need to calculate? Well, that's our bar model.

So we've got that from the previous question.

We know we've got 0.

8 litres remaining and we've got to divide that by four.

So to give the answer in millilitres though, 'cause that's what it's asking, we must convert all measurements to millilitres.

So we've gotta convert that 0.

8 litres into millilitres and then divide it by four.

So if I know that one litre equals 1000 millilitres, then I know that 0.

8 litres equals 800 millilitres.

And 800 millilitres divided by four gives us 200 millilitres.

You could say 0.

2 litres, but again, that's not what the question asked for, although it would be correct.

So there will be 200 millilitres of squash in each cup.

Let's have another check.

So remember this one.

Izzy has one quarter of a kilogramme of sugar to create a cake mixture.

She adds 225 grammes of softened butter.

What's the mass of the cake mixture in grammes at this point? Calculate the mass of the cake mixture.

So there's a bar model.

We've already got that.

Can you do the calculation? Pause the video and give that a go.

How did you get on? Were you working with somebody else? Did you manage to compare answers and strategies and perhaps get there together? Let's have a look.

Well, that's the known information we've got, one quarter of a kilogramme and 225 grammes.

The question is asking for grammes, so we need to do a conversion.

To give the answer in grammes, we must convert all the measurements to grammes.

So the grammes of sugar plus the grammes of softened butter gives the grammes of cake mixture.

Gotta sort that kilogramme out, haven't we? That one quarter kilogramme.

Can you do that? If know that one kilogramme is 1000 grammes, and I bet you knew that one, then I know that one quarter of a kilogramme equals 250 grammes.

And then that's fairly straightforward arithmetic.

There's not even any exchanges to do there.

250 grammes plus 225 grammes, I can do that in my head, I'm sure lots of you can too, that's 475 grammes.

That's the mass of the cake mixture.

Very well done if you got that.

You are on track.

Let's return to this one.

Izzy has three fifths of a kilogramme of sweets in a jar.

She saves 150 grammes for herself, why not? And shares the rest equally between six party bags.

What is the mass of sweets in each party bag in grammes? What do we need to calculate here? So that's three fifths of a kilogrammes.

Take away the 150 grammes that she wants for herself.

It's her birthday, why not? So to give the answer in grammes, we must convert all measurements to grammes.

So that kilogramme we've got to sort out this time, that three fifths of a kilogramme.

Sweet in the jar in grammes take away sweets saved in grammes equals sweets for party bags in grammes.

So if I know that one kilogramme equals 1000 grammes, I know that three fifths of a kilogrammes equals 600 grammes.

And you might've seen lots of models where 1000 is split into five parts, you might've remembered that one part is 200 and start it from there and gone 200, 400, 600, that's what I did.

So 600 grammes, however you got there.

That gives us the calculation 600 grammes take away 150 grammes, again, I think that's doable in your head, equals 450 grammes.

Now, that's the first part.

What does that tell us? The mass of sweets for the party bags, not the mass in each bag.

That's what we gotta sort out now.

So here's our other bar model that we've already got.

We know the mass of sweets for the party bags after she's taken away her share, is 450 grammes and then we gotta do some division.

Gotta divide the rest by six.

So we've got 450 grammes divided by six.

Lots of ways you could do that.

You might've used a short division method, something like that.

That's 75 grammes anyway, however you got there.

75 grammes is the mass of sweets in each party bag, that's what six people are going to be getting.

And now it's over to you.

So the same questions as before, but this time, solve them.

Good luck and again, if you can work with somebody else, I always recommend that, but if not, you're gonna be great either way.

Off you go.

All right, welcome back, how did you get on with that? Lots of thinking to do there, wasn't there? Lots of arithmetic, lots of different operations, so well done for having a go.

So let's have a look, see if you got the answers right.

So for A, so three hours, we gonna do a unit conversion, is equal to 180 minutes, 60 minutes in one hour.

There is a missing part.

To calculate the missing part, subtract the known part from the whole.

The known part is 85 minutes, so 180 take away 85 gives us 95 minutes.

And you could, if you like, express that as one hour 35 minutes, both are correct.

And for B, this time, the unknown is how many lots of 75 centimetres there are in four metres? So the units are different.

Four metres is equal to 400 centimetres and that gives us 400 divided by 75.

Now, I think the best way to do this is to count in 75s until you get as close as you possibly can.

So 75, 150, 225, 300, 375.

You can't go any further.

So that's five lengths and you might've written those down, hopefully you did, so you can see there's five of them.

Five lengths and then 400, which is the length at the start, take away 375 equals 25.

So she will have 25 centimetres of bunting left over.

And for C, you'll need to calculate the value of the six toys.

So we've got 85 times six equal 510 p and we'd more commonly say that as five pounds 10 and then to find the missing part, you subtract the known part from the whole.

So that's now 12 pounds take away five pounds 10 and that gives us six pounds 90.

So she's got six pounds 90 left to spend.

Quite a lot going on in that question.

Well done if you got that.

And 50 mils of squash left in the jug, Izzy's given cups of 250 millilitres to five people at the party, how much was in the jug to start with? So you'll need to calculate the value of the five cups of squash.

So 250 times five, hopefully that arithmetic's not too difficult for you.

That's 1250 millilitres or 1.

25 litres.

And to find the missing whole, you just add the known parts.

So 1250 millilitres plus 50 millilitres equals 1300 millilitres, and you might've expressed that as 1.

3 litres.

They're both correct.

The jug had 1.

3 litres of squash to start with.

And then whatever problem you created in the first cycle, you're now solving.

So one hour and 20 minutes is equal to 80 minutes, so 80 plus 45 equals 125, which is equal to 2 hours and five minutes.

Three hours take away two hour and five minutes equals 55 minutes.

So whatever your context, the missing part is equal to 55 minutes.

That's the correct answer that we're looking for there.

We've come to the end of the lesson.

You can breath a sigh of relief.

You've worked really hard today.

Mathematics in problems can take on many different structures.

If we can visualise, if we can picture a problem, we can represent it using a model that reveals the structure of the mathematics in the problem, regardless of the units of measurement used.

Now, I hope you agree with me here that when you did the bar model, everything else seemed to fall into place and then it was just a case of using the arithmetic.

So give an answer to a problem in a particular unit of measurement, we can convert all measurements to that unit.

So that's really essential.

So having some known unit conversion that you can reel of off by heart and if you can also do some parts of those unit conversions off by heart as well, that's great.

Very well done, you've been amazing today.

Give yourself a pat on the back, it's highly deserved.

I do hope you enjoy the rest of your day, whatever you've got in store and I hope to see you again soon for some more maths.

In the meantime, take care and goodbye.