Lesson video

- Hi there, my name is Miss Darwish, and for our maths lesson today we are going to be solving some problems. We're going to be doing problem solving involving converting between miles and kilometres.

So, before we get started if I could just ask you to take yourself to a place where there are no distractions around just so you're ready for the lesson.

Okay, so the agenda for today's lesson is the following.

First of all, we're just going to discuss miles and kilometres and just practise converting between both.

Then we're going to have a look at some conversions and then word problems. At the end of the session, there will be of course, a quiz for you to go and complete.

So, what you will need is a piece of paper, something to write on, something to write with, pen or pencil are fine and a ruler.

If you want to go and grab those things, then we can start.

Okay, so this should be a bit of a recap.

So there are eight kilometres in five miles.

That's how I like to remember it.

Shall we say that, shall we do that together with the actions? There are eight kilometres in five miles.

That's meant to be an M.

Okay, once more, there are eight kilometres in five miles, well done.

So, let's have a look at this table and see what you can complete.

So we know there are eight kilometres in five miles.

What about in 10 miles? If in five miles is approximately equivalent to eight kilometres, then what about 10 miles? We double five to get 10, don't we? Or five times two, five multiplied by two gives us 10.

Which means we also multiply the kilometres by two.

So eight times two is equal to 16.

Okay, now we've got 40 kilometres and 96 kilometres.

Approximately how many miles is that? I'll give you some thinking time.

If you want to jot these down, and then we can go through the answers.

Okay, shall we have a look together? So, we said 10 miles is approximately equivalent to 16 kilometres, what about 40 kilometres? How do we get from eight kilometres to 40 kilometres? Eight times what is 40? Eight times five, so five times five is equal to 25.

25 miles is approximately equivalent to 40 kilometres.

Okay, what about 96 kilometres now? How do we get from eight kilometres to 96 kilometres? Eight times something is 96, or 96 divided by eight is equal to 12.

So eight times 12 is equal to 96, so five times 12.

We're looking at the miles now, let's convert five times 12, is equal to 60 miles, well done if you said 60 miles.

So I'll just leave that there for a few seconds for you to check through.

So five miles, there are eight kilometres.

10 miles is approximately equivalent to 16 kilometres.

25 miles is approximately equivalent to 40 kilometres.

And 60 miles is approximately equivalent to, 96 kilometres.

Well done.

Okay, let's have a look at this word problem.

So, Yasmin is on holiday in Egypt.

She's staying in Cairo, but she wants to visit other places in Egypt.

Work out how far each place is, both in miles and kilometres.

So Yasmin's on holiday, and she's staying in Cairo.

So she wants to know, how far all these other cities and places are, from Cairo, from where she's staying.

And she wants to know how far they are in distance.

In miles and in kilometres.

Shall we have a look? Okay, so from Cairo to Alexandria, it's 170 miles.

The distance between Cairo and Alexandria is 170 miles, so we'll need to convert that into kilometres.

The distance between Cairo and Luxor is 656 kilometres, so we'll need to know how far that is in miles.

And the distance between Cairo and Hurghada is 464 kilometres.

So we'll need to convert that in miles.

Okay, shall we have a look at Alexandria first of all? So 170 miles is approximately equivalent to how many kilometres? So, eight kilometres is approximately equivalent to five miles, we'll remember that.

What about in 170 miles? Let's have a look.

So, five times something is 170.

Or, 170 divided by five is equal to? 34.

So five times 34 is equal to 170.

What does that mean I do to the eight kilometres? Multiply it by? Also multiply it by 34.

Eight times 34 is equal to 272 kilometres.

So, let's go back to the table.

So the distance between Cairo, from where Yasmin is staying, to Alexandria is 170 miles, or in kilometres, is 272 kilometres.

Well, I don't know if you said that.

Okay, let's have a look at the next one, Luxor.

656 kilometres away this time.

So in this time, we know how far it is in kilometres, but we want to know how far it is in miles.

So the opposite basically, to what we were doing, when we were working out the distance between Cairo and Alexandria.

So, in eight kilometres, there are five, approximately five miles.

So in 656 kilometres, approximately how many miles is that? So eight times 82, is equal to 656.

So eight times 82 is equal to 656, so five times 82 is equal to 410 miles.

So five times 82 is equal to 410 miles.

So approximately, 410 miles is approximately equivalent to 656 kilometres.

Okay, let's get back to the table.

So Luxor is approximately, 410 miles away from Cairo, and that is approximately the same as 656 kilometres.

Okay, let's look at the last one, Hurghada.

So what do we know? It's 464 kilometres away.

So again, like Luxor, we've got the kilometres and we need to work out how far that is in miles.

So 464 kilometres.

If you want to go ahead and work something out before I reveal the answer, then go for it.

you jot down some notes? Okay.

Eight kilometres is approximately equivalent to five miles, what about 464 kilometres? So eight times 58 is equal to 290, or if I did 464 divided by eight, I would get 58.

So, that means five times 58 is equal to 290 miles.

Well done if you said that.

So 464 kilometres is approximately equivalent to 290 miles.

And then let's look at the table again.

There is from Cairo to Hurghada, it's around 290 miles or 464 kilometres, that's the distance.

So now we've got the distance between Cairo and Alexandria, Cairo and Luxor, Cairo and Hurghada, and we know the distance in miles and in kilometres.

Now, which one is the closest to Cairo? Alexandria.

Which one is the furthest away? Luxor definitely, okay? And we can just look at that, just by either comparing the miles or the kilometres, doesn't matter which one.

Okay, well done.

Right, we have a look at another word problem? Okay, so word problem two.

Last weekend, Antoni cycled 10 miles.

This weekend he plans on cycling a further 24 kilometres.

How far will he have cycled in total? Okay, let me read that through again.

So last weekend, Antoni cycled for 10 miles.

What did he do last weekend? He cycled for 10 miles.

This weekend, he plans on cycling a further, that means an extra, if you like, another synonym.

An extra 24 kilometres, than he did last weekend.

How far will he have cycled in total? Okay, so it's a lot conversions here.

We want to basically do 10 miles, add 24 kilometres to find out how far he plans on cycling this weekend.

So, what I like to do, is sometimes I like to grab my highlighter and highlight all the key points or the key information, and just take out the information from the word problem and put it on my notepad, just so that everything's a bit clearer for me.

So, what I've done is I've done a table.

I've split it into last weekend and this weekend.

So what do we know so far? We know, that Antoni cycled 10 miles last weekend, correct? That's down there, okay.

Now, just like the other table we saw, when Yasmin was in Egypt and she was looking at Cairo to Luxor, Cairo to Alexandria, Cairo to Hurghada, we had the kilometres and we had the miles next to each other.

And I think that's a good idea to do now, okay? So, if there are eight kilometres in five miles, then in 10 miles, there must be eight times two is equal to, 16 kilometres.

So, what about this weekend, what do we know about this weekend? We know that he cycled an extra 24 kilometres, don't we? Okay.

So, extra 24 kilometres than last weekend.

So 24 add to sixteen's equal to, 40 kilometres.

So last weekend, he cycled for 16 kilometres, and this weekend he plans on cycling for 40 kilometres.

That's a lot! Now, what did the question ask us for? How far will he have cycled in total? Doesn't say if they want the answer miles or kilometres.

So let's do both, just to be sure.

So, 40 kilometres is then approximately equivalent to how many miles? Give you some thinking time.

40 kilometres is approximately equivalent to, 25 miles.

Well done if you said that.

So now I know that last weekend, Antoni cycled for 10 miles, which is approximately equivalent to 16 kilometres.

And this weekend, he plans on cycling 25 miles, which is approximately equivalent to 40 kilometres.

That's a lot, well done Antoni.

Okay, and the question asked us for overall, in total.

So in total, 40 kilometres add 16 kilometres is equal to, 56 kilometres and 25 miles add 10 miles is equal to 35 miles.

So that's how far he cycled in total.

So the total amount is the total distance he cycled.

In kilometres, and in miles.

So we've put both because the question hasn't said.

Okay.

Right, well done.

Now it's time for you to pause the video and have a go yourself at the independent tasks I've left for you to do.

Once you've finished and you've checked through it, bring a pen to mark with, and come back and we'll go through the answers together, good luck.

Okay, welcome back.

How did you find those? Okay, let's have a look together.

So, you have to place a tick or a cross.

So tick if the conversion was correct, and a cross if it was not correct, and then to correct it.

So we've said where they've put 20 miles, 36 kilometres, 40 miles, 64 kilometres, 90 miles, 144 kilometres, 150 miles, approximate 260 kilometres.

Let's have a look.

So, did you get these right? The first one and the last one are not correct.

Okay, so these are the two that need changing.

So 40 miles is approximately equivalent to 64 kilometres, and 90 miles is approximately equivalent to 144 kilometres.

So well done if you got those right.

Now let's see what the answer should have been for the first one and the last one.

So we're saying the two in the middle are correct, okay.

So 20 miles.

Ooh, I said 36 kilometres, that's not right.

What did you get? 20 miles is approximately 32 kilometres, and 150 miles is approximately equivalent to 240 kilometres.

So well done if you corrected those.

Okay.

If you would like to share your work with us here at Oak National, then please do ask your parent or carer to share your work for you on Twitter tagging @OakNational and to use the #LearnwithOak.

Now, I just want to say before I leave you to complete the quiz, well done on all the brilliant problem solving and word problems that you've answered today.

You have worked so hard, and good luck with the quiz.