Three of the same pen cost £5.40. How much do six of the same pen cost?

Pete is painting the walls of his bedroom. So far he has used 5 litres of paint and covered 24 m² of wall. What area will 20 litres cover?

Pete is painting the walls of his bedroom. So far he has used 5 litres of paint and covered 24 m² of wall. How much paint will 480 m² of wall require?

Ribbon is sold at a rate of £3 per 2 m. How much would I pay for 9 m of ribbon?

Amara is going on holiday. For every £15 she exchanges, she will receives $19. How much money will she get if she exchanges £112.50?

Understanding rate quiz

﻿Hi I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on conversion rates. We're going to mainly focus on currency but there will be some other conversions in there as well for you to get your head around. Before we get started can you make sure please that you're in a nice quiet place if you're able to be free from any distractions, and that you've got something to write with and something to write on. If you need to pause the video now to get any of that sorted then please do, if not, let's get going! So, for today's try this then, you've got 8 descriptions on the screen of different rates. Some are involving mass, some are involving distance, some are involving capacity, some are involving currency. You've got to decide what's the same or what's different about them and then how would you group them? So pause the video now and have a go at this task. Excellent there's loads of different ways you could have grouped them here. You could have grouped all the ones involving distance for example, which would have meant this one here could have gone with this one here and this one here, and this one here because it's involving miles And that's it. so you could have grouped all the ones involving distance You could have grouped all the ones involving capacity so this one here would have gone with that's it, so that one would have been on it's own. So, as I said, there's loads of different ways to group them. One way that I group them was like this. So the ones that are blue so that's this one here, this one here, this one here and this one here. Those are in the constant ratio so those don't change, the number of centimetres per inch is always the same, the number of kilometres per mile is always the same, the number of centimetres per metre is always the same, and the number of litres per gallon is always the same. The other ones, the ones that are purple could change couldn't they? So the number of pounds per minute that could depend on different mobile phone companies for example. The number of dollars per Euro, well that could depend on a different bank or a different time of year. The number of people per train again could depend on the destination, so it could vary and the number of miles per hour again could vary because of the speed that you're going. So we can see here that we've got some that are in a constant ratio and some that are variable that could change, so we're going to have a look at those a bit more closely now. So the first one that we're going to look at is that 86,400 seconds equal a day. So the rate of seconds per day is there are 86,400 seconds per day. So we could also say here then we know that one day is 86,4000 seconds we could say that one second is how much of a day could you tell me that? Excellent. So one second would be one eighty six thousand four hundredth of a day. So if we look now at the miles and kilometres, five miles is eight kilometres so again these are always in a constant ratio. This could mean that five miles is eight kilometres obviously one mile is how much of a kilometre tell me now. Excellent. So one mile is eight fifths of a kilometre or conversely we could say that one kilometre is how much of a mile? Excellent. It's five eighths of a mile. So you have to notice here that we can figure out miles to kilometres or we could also do kilometres to miles it works in both directions and on the first one we could use our seconds to work out days or we could use our days to work out seconds, it works both ways. So now we are going to have a look at one that is not in a constant ratio and for this example we are going to use currency. So imagine you are going on holiday to the US and you've got some pounds that you want to exchange for dollars. You've got three banks, Bank A, Bank B and Bank C. And they are all offering you a different exchange rate. So Bank A says for every ten pounds you exchange you receive thirteen dollars. Bank B is selling US dollars at a rate of 1.274 and Bank C is exchanging your money for every one hundred pounds you will receive one hundred twenty eight dollars. I want to know which bank I should use if I want to get the most dollars for my money. So pause the video now and work that out. Excellent, so, we've got to compare these in a common way haven't we? So we can either create all of them as ten pounds, all of them as a hundred pounds, or all of them as one pound, so let's go with ten pounds. So we know in Bank A for every ten pounds we exchange we receive thirteen dollars. This one here might have been a bit tricky for you to interpret this is how you would see it if you went into a bank. This means for every one pound you will receive one dollar twenty seven and a bit cents. So we're going to just leave it like that for now because if we decide what it would be for ten pounds how would we work that out? Excellent we'd multiply by ten wouldn't we? So for every ten pounds we would get twelve dollars seventy four. And then Bank C tells us that for every one hundred pounds we get a hundred twenty eight dollars so I'm going to again convert this to ten pounds, so for every ten pounds how much would I get? Excellent, twelve dollars eighty. So which one gives me the most dollars for my pounds? Excellent, Bank A does doesn't it I get 13 dollars per ten pounds here, I get twelve dollars seventy four per ten pounds here, and I get twelve dollars eighty per ten pounds here. So you've got to just be a bit careful when you're looking at currency to make sure you're going to get the best deal. We are now going to apply your 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. Excellent effort on that independent task. Let's go through some answers then. So convert the following: 15 miles to km The first thing you needed to remember was that five miles was eight kilometres. So hopefully you went back through the video if you couldn't remember that to find it. So that means that fifteen miles will be twenty four kilometres. Then you were asked to do 48 km into miles. So if we know that 24 km is 15 miles then it makes sense that 48 km is 30 miles. And then finally we were asked to do 12 km into miles, if we know that 48 km is 30 miles, then we can use that to find that 12 km is 7.5 miles. Cala is going on a journey. The journey is 30 miles. Antoni says "this is approximately 50 km." Do you agree with Antoni and explain your reasoning. We've seen haven't we in part B above that 30 miles is equal to kilometres. So what did you say here? Did you agree with Antoni or not? I think you can argue it either way. We can say that it is approximately 50 km because 48 km rounds to 50 km to the nearest ten, or we could say that we don't agree because 30 miles is 48 km, so well done either way. Philippa went on holiday to Sweden. She exchanges some money into euros. We're told that one pound is 1.2 euros and she has to exchange 550 pounds into euros so she receives 660 euros. Then she came home with 78 euros left, the new exchange rate was 1 pound to 1.25 euros how many pounds did she get back? Now I found it helpful here to draw myself a little table where I had pounds and euros and then I've got one pound is 1.25 euros. And if you remember from our work on the rule of four, we have a relationship going across our table and a relationship going down our table. We are told that she has 78 euros left, so for me it was most helpful here to realise that the relationship here was multiplying by five quarters or five over four. So going back the other way it would either be dividing by five quarters or multiplying by four fifths. Now whichever way you did it it's absolutely fine but you should have got here that she got 62 pounds forty left. Cause obviously our relationship going across here is multiplied by sixty two point four. So our final answer is she got sixty two pounds and forty pence back. Moving on to the explorer task now then, Antoni and Cala are doing a sponsored run. Who is going to raise more money if they run the same distance? So we're told that five miles is eight km and five euros is four pounds. Antoni is raising forty pounds per mile and Cala is raising thirty euros per kilometre. Pause the video now and have a go at this task. Excellent now you've had a go at that, maybe you can think about these. They ran different distances in the end, but raised the same amount of money. How much could they have raised and how far could they have run? Pause the video now and think about that. Excellent, so, what I did here was I found it most helpful to convert them to a standard unit so I converted to pounds per kilometre. You could have converted to pounds per mile, you could have converted to euros per kilometre, or you could have converted to euros per mile, there's no right or wrong way to do it, all of them should give you the same. So the first thing I did was I started with Antoni and I knew that he was raising forty pounds per one mile. So that means that he raises forty pounds per eight fifths of a kilometre. Yeah? So that means that he raises two hundred pounds per eight kilometres and then if I divide both by eight I get that he raises twenty five pounds per kilometre. But Cala, she raises thirty euros per kilometre so I found this one actually a little bit trickier to do but maybe you found it easier. So I said that first of all I needed to work out that one euro is equal to four fifths of a pound which is eighty p. So that means that thirty euros must be equal to thirty times eighty p. So that told me that she was raising twenty four pounds per kilometre. Now who's going to raise more money if they run the same distance, well Antoni is raising twenty five pounds per one kilometre which is more than Cala at twenty four pounds per kilometre. So in the end they ran different distances but raised the same amount of money, there's absolutely loads of answers here, how much money could they have raised? One example that I came up with was that they could have both raised six hundred pounds, because six hundred pounds is a common multiple of twenty four and twenty five. And then how far could they each have run? well for Antoni I would need to do six hundred pounds divided by twenty five pounds to find out that he ran twenty four kilometres. And for Cala I would need to do six hundred pounds divided by twenty four pounds to find out that she ran twenty five kilometres. So Cala has to run a little bit further in order for them to raise the same amount of money. That's the end of today's lesson so thank you so much for all of your hard work. 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!

Fill in the gap: conversion rates are _______________.

Which of the following is an example of a conversion rate that is is a constant ratio?

Given that there are 1440 minutes in a day, how many days is 10080 minutes?

Martin went on holiday to Sweden. The exchange rate is £1 to 1.15 euros (€). He exchanges £660 into euros. How many euros should he receive?

Martin went on holiday to Sweden. The exchange rate is £1 to 1.15 euros (€). He receives 414 euros. How many pounds did he exchange?

Conversion rates quiz

In this lesson, we will learn about conversion rates that are in the same ratio, and those that change. We will model problems and solutions involving conversion rates.

Maths

Y8 Maths

Key Stage 3

Year 8

Miss

Conversion rates

Ratio, real life graphs, and rates of change

Ratio and proportion

THEME

UNIT

Understanding rate

Exchange rates with graphs

Density as rate

Speed as rate (distance-time graphs)

Calculating speed, distance and time

Displacement-time graphs (Part 1)

Displacement-time graphs (Part 2)

Amara is going on holiday. For every £15 she exchanges, she will receive $19. How much money will she get if she exchanges £112.50?

Binh cycles 80 kilometres in 5 hours. What is her average speed in kilometres per hour (km/h)?

A train travels 75 miles at an average speed of 25 mph. How long does the journey take?

Lesson overview:Conversion rates

Core Content

Ratio, real life graphs, and rates of change: