Lesson video

Hi I'm Miss Kidd-Rossiter and I'm going to be taking your lesson today on understanding rate.

It's the first in our series of real-life graphs and rate of change.

And it's a really great unit.

Before we get started, please make sure that you're in a nice comfortable place, free from any distractions and that it is as quiet as possible.

You're also going to need something to write with and something to write on.

So if you need to pause the video now to get any of those things, then please do.

If not, let's get going.

So, starting today's lesson with a try this activity.

First of all, write an example of when each rate could be applied, as Xavier has.

So Xavier whose chosen to write a statement for minutes per mile, and he has written, when athletes train they measure how fast they are by seeing how many minutes it takes them to run each mile.

So it's your job to write an example of when each rate could be applied.

And then when you've done that, what other examples of rates can you think of? And can you think of any non-examples? Pause the video now and have a go at this task.

Excellent, so you could have said lots of different things here.

So a couple of examples, you could have said, "When cars are driving, they measure how fast they are going by seeing how many miles they drive in every hour." Or you could have said something like, "The pounds per minute, when mobile phone companies charge customers for phone calls, they charge them in a certain amount of pounds per minute." We're going to look some more examples together.

But before we do that, I want you to write down this definition, because it's really important.

Rate is the relationship between two measurable quantities.

So pause the video here and write that down.

Excellent, well done! So here's our first example, then.

Yasmin is going on holiday to Italy.

She goes to exchange her money.

So our rate here, is for every 10 pounds, we receive 13 euros.

So that's our rate, for every ten pounds, we receive 13 euros.

We could write this in a ratio table, pounds and euros.

And we know that for every ten pounds, we receive 13 euros and really I don't need to write my pound symbol here, do I? Because I've written it in the title of my table.

So, what about then, if Yasmin was exchanging 100 pounds? How much would we expect her to get? Pause the video now and work that out.

Excellent we're going from ten to 100 pounds, so we've multiplied by ten there, which means that we also must multiply by ten here.

So for every ten pounds, Yasmin gets 13 euros.

For every 100 pounds, Yasmin gets a 130 euros, because we've multiplied also by ten.

What about, if Yasmin was this time exchanging her euros back to pounds, when she comes back from holiday? And she had 520 euros left.

How would we workout how many pounds that was? Tell me now.

Excellent! Go from 13 to 520, we would multiply by what? Excellent, 40! So that means that we also need to multiply our ten pounds by 40 as well to get 400 pounds.

So remember, we can go in both directions, here.

From pounds to euros and also from euros to pounds.

Second example then, the average car uses 10.

8 litres of petrol per 100km it travels.

So we could say that our rate is 10.

8 litres per 100 kilometres.

We could use this then to work out how many litres of petrol it would use for different amounts of kilometres, or the opposite way around.

So if we were given the amount of litres, we could work out the amount of kilometres.

So let's do one example together.

So we've got our litres and we've got our kilometres.

We know that our litres is 10.

8 and our kilometres is 100.

If we were working out what 1000 kilometres would be, how would we work out how many litres there? Excellent, we would multiply by ten, so we'd get a 108 litres per 1000 kilometres.

What about if it was 5.

4 litres of petrol that we used? How many kilometres would we expect to have travelled, then? Excellent, 50.

And so you can see that the relationship here is also between litres and kilometres and kilometres and litres.

Thirdly then, Antoni is painting the walls of his bedroom, so far he has used five litres of paint and covered 24 metres squared of wall.

So we're going to put in our ratio table, five litres used, and 24 metres squared covered.

How many metres squared would he cover if he uses ten litres of paint? Work that out.

Excellent, 48 metres squared.

Because we've multiplied by two here, so we would also multiply by two here.

What about if Antoni used 30 litres of paint? What area would he cover here? Excellent, 144 metres squared.

Because from here to here, we multiplied by six, so from here to here we would also multiply by six.

What about if he covered 240 metres squared of wall? How many litres of paint would he have used, then? Work that out.

Excellent! We've multiplied by ten there, haven't we? So we would also multiply by ten here to get 50 litres of paint used.

Now those have all been fairly straight forward, because it's been nice numbers to multiply by.

But do you remember from our work on the Rule of Four, that we also have a relationship going down the table here.

So what have I multiplied five by to get 24? Now that one isn't so intuitive to me.

But if I look at ten and 48, what would I multiply ten by to get 48? I can see that it would be 4.

8.

So I have the same relationship going down my table here.

So if I have seven litres of paint, I could multiply that by my constant of 4.

8 to get how many metres squared it would be.

Work that out now.

Excellent.

33.

6 metres squared of wall would be covered.

Well done.

We're now going to apply this learning to the independent task.

So pause the video here, navigate to the independent task, and when you're ready to go through some answers, resume the video.

Good luck! Excellent work! Well done.

Let's go through the independent task then.

So, we've got some statements there about buying ice creams. How much will ten ice creams cost? Well if we think about our ratio table, we've got number of ice creams and we've got the cost.

So we know that five ice creams cost seven pounds 50.

So we know that ten ice creams must cost double that.

So ten ice creams will cost 15 pounds.

Then we set the charge for the ice creams as 18 pounds.

So how many ice creams were bought? Well there were 12 ice creams bought.

So well done on that.

Second one then, Mr. and Mrs. Smith work for the same company.

They receive the same hourly rate.

Mr. Smith works 17 hours and is paid 212 pounds 50 per week.

Mrs. Smith works 34 hours per week, how much is she paid? Well she's paid 425 pounds per week.

And one week, Mr. Smith does some overtime and earns 362 pounds 50, how many hours did he work this week? He works 29 hours in this week.

Good work.

This one then, the record for the women's 100 metres is 10.

49 seconds.

How long would it take this athlete to run one kilometre, assuming the same speed was maintained? So we know, that one kilometre is 1000 metres.

So if you didn't know that, you might want to pause this video now and have another go at that task.

Excellent, so we know that in 100 metres, so we've got distance and we've got time.

So we know that in 100 metres, it was 10.

49 seconds.

So in 1000 metres or one kilometre, it would be 104.

9 seconds.

So, let me show you the answer there.

So it would take 104.

9 seconds or one minute and 44.

9 seconds if you decided to convert to minutes.

Why is the answer to part A not realistic? Well we know that the 100 metres is a sprint race, so it's unlikely that this athlete would maintain the same pace for a full kilometre.

Moving on to the explore task now, then.

A swimming pool can be filled at a rate of n litres per second.

The capacity of the pool is 90,000 litres.

Put the statements in ascending order of how fast they describe the pool being filled.

Pause the video and have a go at this task.

Excellent.

There were loads of different ways to go about this.

So I'm just going to show you one way, but if you did it differently, that's absolutely fine.

So what I'm going to do is I'm going to see how many minutes for each of these it takes to fill the pool.

So for the first one, I'm told that it's filling at a rate of five litres per second.

So the first thing I need to work out is how many seconds it will take in total.

So to do that, I do 90,000 divided by 5 and that gives me, that is 18,000 seconds.

I can now convert that to minutes, because I know that there are 60 seconds in a minute.

So I would do 18,000 divided by 60, which tells me that it's 300 minutes, it's taken to fill the pool.

The second one is slightly more straight forward, because we're told the pool is filled in three hours.

So three hours, I know, is how many minutes? Excellent.

There are 60 minutes in an hour, so three times 60 gives me 180 minutes.

So three hours is a 180 minutes.

The first 20,000 litres were filled in 50 minutes.

So I can work out how many 20,000 litres it takes to get to my full 90,000.

So 90,000 divided by 20,000 gives me 4.

5, so that means it's 4.

5 lost of 20,000 to get the 90,000.

So that means it will be 4.

5 lost of my 50 minutes, which is 225 minutes.

So which is the quickest then to fill the pool? Excellent, this is our first one.

It takes 180 minutes, which is our next quickest.

Excellent, this one takes 225 minutes and then thirdly, our rate of five litres per second is slower.

Now as I said, there's lots of different ways you could've worked this out.

You could've worked out the rate in litres per second for each of them, you could have worked out how many hours it would take.

There's lots of different ways to do it, but that's just one way that you could get the solution.

Well done.

That's the end of today's lesson, so thank you very much for all your hard work.

I hope you've enjoyed it.

Please don't forget to go and take the end of lesson quiz, so that you can show me what you've learned.

And hopefully I'll see you again soon, bye!.