Lesson video

Hello there.

My name is Mr. Tilstone, I'm your teacher.

It's a real pleasure to see you and to be working with you today on this maths lesson, which is all about unit conversions.

Specifically we're going to be doing some problem solving today.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can solve problems involving converting units in different contexts.

We've got one keyword today, my turn, convert, your turn.

I think you might know what that means by now, but let's have a look anyway.

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

Can you think of any other examples? Our lesson is going to be split into two parts.

The first will be representing problems and the second solving those same problems. So if you're ready, let's start by representing problems. In this lesson, you're going to meet Andeep and Laura.

Have you met them before? I bet you have.

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

Okay, let's have a look at the problem.

Laura and her family are going on holiday, lovely.

They are spending (vocalising) weeks in Italy and (vocalising) days in Sicily.

How long are they away for altogether? First of all, what did you notice about that? What do you need to know or do to solve the problem? What's known or unknown? Well, let's have a look at our part, part, whole bar model.

You would need to use multiplication to convert, so that the units of measure are the same, 'cause at the minute, one's in days and one's in weeks.

And then add together the known parts.

So this is an adding context.

So we've got on our bar model time in Italy, time in Sicily, add them together, and that's how long they're away for altogether.

What useful conversion could be used here? So what do you know about days and weeks? How many days in a week? Here we go.

So in 1 week, there are 7 days, and that's going to be helpful.

Let's look at a different problem, and we'll come back to that one later.

Andeep's parents are keen marathon runners.

Very good.

If his dad runs a London Marathon in (vocalising) hours and his mom runs it (vocalising) in minutes, who is faster and by how much? Hmm.

What do you need to do to solve this problem? Again, we've got a part, a part, and a whole.

So think what's the part, what's the other part, and what's the whole.

Well, the shorter time is one part.

So whoever's got the shorter time, we don't know yet.

And the longer time is whoever's got the longest time.

We don't know yet, that's the whole.

And then we're looking for the difference between those.

You would need to use multiplication to convert, so that the units of measure are the same.

Just like before.

Then use a subtraction strategies, such as counting on to work out the difference.

So this one is a different problem.

What useful conversion could be used here? Well think about the hours and minutes.

Hmm.

Do you know how many minutes there are in one hour? I bet you do.

60.

So 1 hour is 60 minutes is our useful conversion, and we'll come back to it later.

What about this one? Laura's mom has a (vocalising) gallon petrol can.

She pours (vocalising) litres of petrol into her car.

You notice gallons and litres? How much petrol is left in the can? What do you need to do to solve this problem? Again, we've got our bar model.

What's known and what's unknown? Well the amount poured is one part.

The petrol at the end is the other part.

And the petrol at the start is the whole.

So we're looking to use a multiplication strategy to convert the units again, so that they're the same.

And then use a subtraction strategy, such as counting on to work out the difference.

So this is another difference problem.

What useful conversion could be used here? Well again, we've got gallons and litres.

This is one that you might not remember off by heart.

So here's a reminder.

1 gallon is 4.

5 litres, and we're going to work with that later.

Another one, Andeep lives (vocalising) miles away from his grandparents, and Laura lives (vocalising) kilometres away from her grandparents.

Again, different units, miles and kilometres.

How much further away does Laura live? Okay, so here's our part, part, whole model.

One part is the distance Andeep lives from his grandparents.

The whole is the distance Laura lives from her grandparents.

And we are looking for the other part, the difference between the distances.

So it's another difference problem.

But what's the conversion that you're going to need to solve this problem? Well, one's miles and one's kilometres.

You may remember this conversion, you may not.

It's useful to know this, and it's this.

5 miles is approximately 8 kilometres.

That's going to be our starting point.

Jun is making a cake.

The recipe says he needs to use (vocalising) grammes of sugar.

He only has a 1 ounce measure.

How many 1 ounce measures will he need to use? Do you notice again? One's grammes, one's ounces.

So what do you need to do solve this problem? You would need to use multiplication to convert, so that the units of measure are the same.

Just like before, all of the problems involve that same skill of converting.

Then use a division strategy this time, such as counting on in groups until the answer is reached.

So we don't know how many groups yet, could be one measure, could be two measures.

The bar model might look like that.

Could be three measures.

The bar model might look like that, we don't know.

Could be four measures.

Or any number of measures.

We need more information first.

But the question is, the important question is, what useful conversion could be used here? Again, this is one that you may not have committed to memory yet.

I suspect you have, and you might need a reminder, and that's absolutely fine.

It's this, 1 ounce is approximately 28 grammes.

That's going to be helpful when solving that problem.

Let us have a check.

What steps would you take to solve this problem? So Andeep has a mass of (vocalising) kilogrammes and Laura has a mass of (vocalising) stone.

So different units.

They step into a lift together.

What is their combined mass in the lift? Their combined, that's a little clue.

Is this multiplication then addition? Is this multiplication then find the difference? Is this multiplication and then division? Have a chat if you can with the person next to you, and see if you can come up with an answer.

Pause the video.

Welcome back.

Let's have a look.

Well, for all of these you have to multiply first, because you've got to convert the unit, so that they are the same.

So we're going to do multiplication and then it's addition, we're combining the two converted amounts together.

It is time for some practise.

Explain the steps that you would take to solve each of these problems. So let's have a look.

A, Laura and Andeep are competing against each other online to beat a tricky level on Space Blasters.

Laura clears that in exactly (vocalising) hours and Andeep takes (vocalising) minutes.

Who is quicker and by how much? Laura and her family are going on holiday.

They are spending (vocalising) weeks in Spain and (vocalising) days in Portugal.

How long are they away for altogether? C, Andeep lives (vocalising) miles away from a theme park, and Laura lives (vocalising) kilometres away from the theme park.

How much further away does Laura live? D, Laura's mom has a (vocalising) gallon petrol can, which she accidentally knocks over.

2 (vocalising) spills out of it.

How much petrol is left in the can? And E, John is making a cake.

The recipe says he needs to use (vocalising) grammes of sugar.

He only has a (vocalising) ounce measure.

How many measures will he need to use? So remember, we have no numbers yet, all you are doing is deciding how you would solve that.

Pause the video, good luck.

Work with somebody else if you can, and swap strategies.

Off you go.

Welcome back.

So your challenge really was to understand those problems. Let's see if you did.

So for A, we're going to use multipling to convert one of the units and then use a subtraction strategy to find the difference.

So that's multiplying and then subtraction.

B, we're gonna use multiplying to convert one of the units and then use adding to find the total.

So multiplication then adding.

And then C, we're going to use multiplying to convert one of the units as before, and then it's a subtraction strategy to find the difference.

D, that's using multiplying to convert one of the units, and then a subtraction strategy to find the difference again.

And for E, we're using multiplying to convert one of the units, and then a division strategy this time to work out how many groups are needed.

Right, let's tackle those problems, shall we? Let's put some numbers into them.

We're gonna solve those problems. Laura and her family are going on holiday.

They are spending 2 weeks in Italy and 5 days in Sicily.

How long are they away for altogether? Well first of all, let's convert the weeks into days.

We're gonna make them the same.

We know that 1 week is 7 days, so 2 weeks is 14 days.

So therefore, that's 14 days and 5 days.

That's nice and easy arithmetic.

14 days and 5 days, it's 19 days.

They're on holiday for 19 days.

You could say that in a different way as well.

You could say they're away for 2 weeks and 5 days.

Let's have a check for understanding.

So Laura and her family are going on holiday.

They're spending 3 weeks in Italy and 6 days in Sicily.

How long are they away for altogether? Draw a bar model and solve that problem.

Off you go.

And as you get on, right? So here's your bar model.

So in Italy, they are there for 21 days and they're in Sicily for 6 days.

So we converted 3 weeks into 21 days.

Add them together, and you've got 27 days.

Well done, if you've got 27 days, you're on track.

Andeep's parents are keen marathon runners.

If his dad runs the London Marathon in (vocalising) hours and his mom runs it in (vocalising) minutes, who is faster and by how much? Let's have a look.

So we've got our useful unit conversion.

We're going to use a table for this.

So hours and minutes.

So his dad runs it in 3 hours and his mom runs it in 170 minutes.

Who's faster? So we need to do some conversions.

Let's convert those hours, those 3 hours into minutes.

So we're multiplying 1 by 3, and we're going to use the same factor to multiply the 60 minutes.

So 60 minutes multiplied by 3 as well gives you 180 minutes.

So instead of saying that his dad runs in 3 hours, we could say he runs in 180 minutes.

And that's our information, that's the faster time.

That's the slower time.

And the difference is what we're looking for.

And the difference is 10 minutes.

So mom is 10 minutes quicker than dad, go mom.

Right, let's change the values a little bit.

Andeep's parents are keen marathon runners.

If his dad runs the London Marathon in 4 hours and his mom runs it in 250 minutes, who is faster and by how much? Draw a bar model and solve that problem.

Pause the video.

How do you get on? Okay, well there's our use for unit conversion.

1 hour is 60 minutes.

And at this time, we're going to multiply the 1 by 4, because it's 4 hours.

So we've got to do the same to the 60.

60 times 4, it's 240.

So that's 240 minutes.

So mom's time is 250, dad's time is 240.

And then we need to work out the difference.

We could subtract them, but it would be easier, because they're so close together to count on from 240 to 250.

I can do that in my head really easy.

I don't need to do any written calculation for that.

That's 10 minutes.

There's a difference of 10 minutes.

Meaning dad is 10 minutes faster than mom this time.

Laura's mom has a (vocalising) gallon petrol can.

3 gallon, let's give it a number.

3 gallons.

She pours, let's say 10 litres of petrol into her car.

How much petrol is left in the can? Okay, so again, we've got our information in the table.

That unit conversion, 1 gallon is 4.

5 litres, and we know that we are looking at 3 gallons.

So let's convert the gallons into litres.

What do we times 1 by to get 3? 3.

What are we going to do to that 4.

5? Multiply by 3.

4.

5 multiply by 3.

You might want to use 45 times 3 as a starting point for that, or you might be confident just counting in decibel steps.

But either way you get 13.

5.

So the capacity of her petrol can is approximately 13.

5 litres.

Now we can use that information, we're only halfway there, but it's useful information.

So that is the whole.

10 litres is the part, and we are looking at the difference between 10 and 13.

5.

Again, no need to do any written calculation surely for that.

That's hopefully in your head.

The difference between those is 3.

5 litres.

So that's how much petrol left in the can after 3 gallons has been poured out, 3.

5 litres.

Let's have a check.

Laura's mom has a 2 gallon petrol can.

She pours 5 litres of petrol into her car.

How much petrol is left in the can? Draw a bar model, solve the problem.

Off you go.

How did you get on? Let's have a look.

So this time, we're turning 1 gallon to 2 gallons.

That's doubling, multiplying by 2.

So we do the same for the 4.

5.

Double 4.

5 is 9.

So we can use that, that's 9 litres.

Take away 5 litres, that's how the bar model looks.

We're looking at the difference between them.

And that's 4 litres.

9 litres take away 5 litres equals 4 litres.

That's the difference.

That's how much petrol is left in the can.

Tricky one.

So well done if you've got that, you're really doing well.

Okay, Andeep lives 10 miles away from his grandparents, and Laura lives 17 kilometres away from her grandparents.

How much further away does Laura live? Let's convert the 10 miles into kilometres, so the two can be compared.

We've got that basic fact that 5 miles is about 8 kilometres, and we're gonna use that number 10, that's 10 miles.

What have we done to 5 to get 10? Double it, multiply it by 2.

What do we do to 8? Double it, multiply it by 2.

Double 8 is 16.

So we can say instead of Andeep lives 10 miles away, we can say he lives 16 kilometres away.

And Laura lives 17 kilometres away.

Then that's a really, really, really easy piece of arithmetic for you to do.

You're just working out the difference between 16 and 17, which is 1 kilometre.

So Laura lives 1 kilometre further away from her grandparents than Andeep does from his.

Let's have a check.

Andeep lives 15 miles away from his grandparents.

Laura lives 30 kilometres away from her grandparents.

How much further away does Laura live? Draw a bar model, solve the problem.

Off you go.

Let's have a look.

Well let's turn that 15 miles into kilometres.

So 5 goes into 15, 3 times.

So we do the same to the 8.

8 multiplied by 3 is 24.

So let's say Andeep lives 24 kilometres away rather than 50 miles.

They're both equal.

The bar model would look like this.

That's 30 kilometres, that's how far Laura lives away.

That's Andeep's distance, that's 24 kilometres away.

And then that leaves us just with a nice piece of simple arithmetic working out the difference between those two values.

And it's 6, 6 kilometres.

Very, very well done if you got that.

Jun is making a cake.

The recipe says he needs to use (vocalising) grammes of sugar.

He only has a (vocalising) ounce measure.

How many measures will he need to use? So that's a reminder of our useful unit conversion.

1 ounce is about 28 grammes.

So if he needs to use 280 grammes of sugar, and he only has a 1 ounce measure, how many measures will it need to use? Well let's convert the grammes into ounces.

So the information that we've got from the problem is that it needs 280 grammes of sugar.

So let's have a think this time.

How many times does 28 go into 280? What do we multiply in 28 by to get 280? Hopefully you can see that straight away.

You don't need to do any written calculation to see that.

That's 10 times bigger.

So that's multiplying by 10.

So we go to do the same to the 1.

1 multiplied by 10 is 10.

So he will need to use 10 of the 1 ounce measures for this recipe.

Well let's have another check.

Jun is making a cake.

The recipe says he needs to use 140 grammes of sugar.

He only has a 1 ounce measure.

How many measures will he need to use? Pause the video.

Let's have a look.

So we need to work out how many times 28 goes into 140 this time.

That's not as straightforward as some of the arithmetic that you've been doing, but you might notice that 140 is half of 280.

That might be a little clue for you.

Or you could count in steps of 28 until you reach that number 28, 56, 84, 112, 140.

But either way, that's 5 times.

So that's our scale factor, that's what we're multiplying 1 by 1, multiply by 5 equals 5.

So he will need to use 5 of the 1 ounce measures for this recipe.

And that's what that looks like as a bar model.

Right, time for some practise.

So you already understand those problems. Let's put some numbers in, and let's have a go at solving them.

Pause the video, and off you go.

Welcome back.

How did you get on? Let's have a look, shall we? So Laura and Andeep are competing against each other online to beat a tricky level on Space Blasters.

Laura clears it in exactly 2 hours and Andeep takes 130 minutes.

So we need to convert those hours into minutes.

60 minutes is 1 hour.

So 120 minutes equals 2 hours.

130 take away 120 equals 10.

So that's a 10 minute difference.

Laura is quicker by 10 minutes.

Laura and her family are going on holiday.

They're spending 2 weeks in Spain and 3 days in Portugal.

How long are they away for altogether? So we could say they're spending 14 days in Spain and 3 days in Portugal.

Then they're the same units.

So 1 week equals 7 days.

2 weeks equals 14 days.

14 plus 3 equals 17.

They're away for 17 days altogether.

Andeep lives 20 miles away from a theme park, and Laura lives 35 kilometres away from the theme park.

How much further away does Laura live? And we've got that hint, that 5 miles is approximately 8 kilometres.

So you could draw a table just like this.

And the other information we've got is that is 20 miles, so we're converting.

5 times 4 is 20.

So 8 times 4 is 32.

It doesn't quite answer it yet.

We need to work out the difference.

35 take away 32, which I would do by counting on from 32 to 35, 'cause the difference is close.

And that's 3.

So Laura lives 3 kilometres further away from the theme park.

Laura's mom has a 2 gallon petrol can, which she accidentally knocks over, 2 litres spill out.

How much petrol is left in the can? 1 gallon's approximately 4.

5 litres.

So 2 gallons, we're doubling 1 to get 2.

So we double 4.

5 to get 9.

So we're looking at the difference between 2 litres and 9 litres, which is 7 litres.

So there's 7 litres of petrol left in the can.

Jun is making a cake.

The recipe says it needs to use 200 grammes of flour.

He only has 7 ounces left.

Has he got enough flour? 1 ounce approximately 28 grammes.

So 1 multiplied by 7 is 7.

28 multiplied by 7.

And do you mind, you needed to use a written method to do that or you might have partition into 20 and 8, and multiplied each part.

Whatever you did, the answer was 196.

7 ounce is equivalent to 196 grammes.

196 grammes is a little bit less, but only just so he's not quite got enough flour, but he might just get away with it.

4 grammes isn't a lot of flour.

I think he can manage, don't you? We've come to the end of the lesson.

We've been solving problems involving converting units into different contexts.

If problems have mixed units, for example, one's given in imperial and one's in metric, it's helpful to convert one of the units of measurement so that it's the same as the other.

A calculation can then be applied such as adding, subtracting, or counting in groups to solve that problem.

Bar models are a helpful way to represent the problem, and tables are a useful way of helping to convert the units.

You've been amazing today.

You've done so much maths.

I'm really proud of you.

Give yourself a little pat on the back.

I really hope we get the chance to work together again in the near future to do some more maths together.

But until then, enjoy the rest of your day.

Take care and goodbye.