Equivalent fractions in context

Key Stage 2

Maths

Equivalent fractions

﻿Hello everybody. My name is Mrs. Holmes. I am here today to teach you about equivalent fractions. This is the second lesson in the series, and the first lesson was brought to you by Mrs. Lambert. And I know that she sent you a little task. I believe the task was something like this. She asked you to show a third with 15 items, she asked you to draw a shape to represent a third. She asked you to draw one-third on a number line, and she asked you to write a fraction, that was the same as one-third. Now, I decided it was only fair, I joined in with this task. So, I would try my house, as you must have done, to find some objects. And I decided I would use some teddy bears, as we had quite a few around the same size, had been collected over the years. And I lined them in a straight line, and had to look at them, and then thought, hmm, it's really tricky. How am I going to work out? How many are in a third? Without having to try and count them in different groups, and things like that. So then I said, I know, why don't I use the fraction one-third to help me? Which means that it would be in three equal parts. So I put them into three groups. And I checked that I had the same number in each group, and this is what I ended up with. Yeah, they're really cute aren't they? Very fluffy. So as you can see, they're lined up in three rows, and they are my three equal parts. The first one, this is easy. There you go, there's my one third. But then I went, ah! Not exactly what I was asked to do, is it? Because I was asked to use 15 items for a reason. Because I was trying to find, another fraction that was the same as one-third. I could then write down. I thought oh, I know, how about I use the total number of bears, as my denominator? So, it looked like this! So in my one third part, I had already found, I now had five bears, so five out 15. Which fraction would five-fifteenth? This sounds like I might have done the right thing. So, then moved on to the next part, which was to draw a shape, to represent a third. I decided I would use a rectangle because that's easier. And here's my rectangle, with the yellow part showing the one-third. And then I drew an identical, equal sized rectangle underneath. But this time, I divided it into 15 equal parts. Because that would be the same model, as the bears. Now as you can see, one-third is exactly the same size, as five-fifteenth. Final task, was to draw a number line wasn't it? Now I find those so hard to do. I always have to measure them properly, to make sure that they're equal for the parts. Third isn't too bad though. This was my third number line, these three equal parts. And then I had to draw another one underneath, the fifteenth, and this is what it looked like. And again, you can see, that five-fifteenth, seems exactly the same size as one-third. So therefore one-third, is equal to five-fifteenth. Now we're going to move on to today's lesson. And we all again going to be looking at, fractions that are the same size. But this time we're going to use, liquid really to show our fractions. So later on, I'll be asking you, to find yourself a container, with straight sides, that you can see through, something like a vase, or tall glass or something like that, plastic container, and then a big jug of water, so that we can measure out, by estimating our fractions. You can, if you want to, pause the video now, and go and grab those things, ready for the session a bit later on. If not, that's fine. We'll carry on, and move on to the next part, to show you what we're going to do. So let's look at a model, some different glasses here. What do you notice about these glasses? Hmm, we could count them, we could say, well they're six of them isn't that? What else can you say? What do you think about how they look? Are they all the same? Are any of them different? What's that? Yes you're right. The three at the bottom, are identical, aren't they? So if you think of those like our part whole, they are the whole, and they are the same size. So if I was going to put some liquid, in these top ones here, let's do that. There we go! How much liquid is in those? You don't know? No I don't know either. You're right, because they're not the same, are they? So we can't compare them. We can't see if they've got the same amount in or different. What we could do though, is transfer them into the other container and see. And there you go. I actually had exactly the same amount too. Even though, in the original containers, they look really different, don't they? And if you filled them up further, those original containers you wouldn't be able to estimate, would you? A part of it's full up, which would mean that they would have, all the parts in there, it'd be really difficult to say how much, how many parts they would be, if you're comparing the two glasses together, unless they're completely full. So that's a really important point with fractions. You need to compare them, with the whole of the same size, because then you can look at them, divided into equal parts, and then that's when it works, as far as comparing fractions. Okay, now let's move on to today's lesson. We have a straight sided container here, so this is the thing that I'm talking about, that you would need. Something like this, a bit later on, and then a jug of water. So let's say we were trying to look at fifths. And then we said, let's say where would one-fifth be? Where do you think? It would be near the top? Near the bottom? What's up? Think it'd be less than half? Yeah, I agree with you. It'd be less than half. Would it be close to half though? Hmm. Hmm, it's a difficult one isn't it? There you are. One-fifth, is actually quite near the bottom really, isn't it? And if you think about it, that's because the whole would be divided, into five equal parts, and that's just one of them. What of four-fifths? Would that be near in the middle? You don't think so. Okay. Well, could we try and say that, well I think, when we looked at one-fifth, that was near the bottom, but looking at four-fifths, that's almost all of it. That must be near the top, mustn't it? Let's have a look. There you are, there's four-fifths, just leaving the one-fifth to go. We'd already seen one-fifth. So we'd need to leave that amount, in our whole to find four-fifths. Then there's two-fifths. Hmm, we know what one-fifth is, we could find two-fifths, couldn't we? It's less than half, but it's not too far less than half. Finally three-fifths. Now that's a lot more tricky. It's more than half, but you're having to try, and measure more parts, aren't you? And there you are. This is three-fifths with two parts left, in that container. Excellent! Now, we are going to do some measuring of our own. So hopefully you have already got your water jug, and your straight sided container. But if you haven't pause your video now, and go and grab those things. Did you get it? Brilliant! Well, I have also got a jug, and in my jug I have some orange water. Just because it makes it easier for you to see on the video. And I've also got a vase I found in my cupboard. So we're working on thirds now. Can you use your jug of water, to measure out one-third. Now just need to say, be really careful not to spill the water everywhere. Make sure mom and dad, know that you've got water, and maybe do it in somewhere like the kitchen. Where if some water went a little bit on the side, it wouldn't be too much of a big deal, but that means get in trouble. So we're only doing our maths. Okay, so if I pour this, I'm going to estimate as I go, I'm looking the whole time, in fact, I'll take the lid off, that makes to lift it easier. I'm looking in, I'm thinking, oh! It needs to be in three equal parts. And I just need one of those. Now I think it's going to be about there. That's my estimation. Now, to make things a little bit easier, I did get a ruler and I marked, I measured the whole vase, and then I marked a third on it. So, I need to put it inside, and I need to have a little look. Now if you can see, I've gone a little bit too far, over a third. Now a third, is more like here. So Mrs. Holmes has got a little bit too generous there. Okay. Bearing that in mind, I need to be a little bit more cautious, when I put some more in for two thirds, don't I? How did you do with your measuring of a third? Were you a little bit over, do you think you're a little bit under? In the moment we are just estimating, but I was just showing you, how I find it quite difficult too, to estimate when you're trying to compare the shape, or size of something. Okay, so now am going to have a go at two-thirds. So, pause the video if you want to, and have a go first, or you can watch me and then have a go after, and pause the video. I think it's going to be about there. Let's see if I do any better, this time hopefully. Pop that in, there we go, ooh! Really close! So there's just a little bit above, about here this time, so a little bit above where I have marked, with the water. So it's a bit better, my estimate in that time was not, how did you do? Well done if you got close to estimating. It really isn't easy at all. Okay, but just make sure you put those to the side, so you don't get them everywhere. And let's have a look at the next bit we want to see. Okay, we're now going to look at some of other fractions, that are the same in size, as one-third. Since we've just measured out one-third, we know what that looks like in size, in a water container, don't we? So eight-twenty fourths, and three-ninths, are also the same size as one-third. Can you see a pattern there? Can you notice anything, as to why it might be? Have a little look. It might be easy to see on one, than, more than the other. I will tell you. Don't worry if you don't see the connection, because next lesson is all about that. Okay, here's a container again, showing one-third, and then the other fractions are the same, in size as one-third. Now against that one non unit fraction, which is because it's more than one part, of the whole unit fraction being one third, one sixth and so on. So five-sixth is a non unit. I'm sure you knew that, but I just wanted to recap. And the same size fractions, as five-six, is fifty-sixtieth, twenty-twenty fourths. That means that they're the same size part of the whole. We can see that quite clearly in this diagram, can't we? Again, can you see why that might be? What do you notice? Why do they represent the same part of a whole? Hmm. And here we have two number lines. One is vertical, that's going up and down, isn't it? The other is horizontal. Well, what you call different orientations, different directions. But that doesn't make any difference. You can see that one-third, on the number line whether it's vertical or horizontal, is less than half, isn't it? Along that number line. But those other fractions, the eight-twenty fourth, and a third ninth, three-ninth, are the same size, so they are exactly the same point on the number line. They're not bigger, and they are not smaller. Just because, it's shown as different fractions, what that means is, that that part, is cutting to more parts, than the one-third. So, in the same area, same size as one-third, instead of being in one piece, eight-twenty fourth has eight pieces, and three-ninth has three pieces. And the whole, for each of those, you can tell how many parts they have, for those two fractions, because you use the denominator. So in eight-twenty fourth, that means there would be 24 pieces. Here is the number lines again, you can see that for these fractions they're closer to one aren't they? Because they're five parts, out of the whole six parts, and 50 parts out of the whole 60 parts, and so on. So that shows you the difference between them, on the number lines. Okay finally, just moving onto the language that we've used, so, just to recap then, before we move on to your task for today, these are all equivalent fractions. That means, that they are the same part of the whole. We've talked all the way through about this, and the word we use for them is equivalent, or equal in size. That's what we're trying to get across. So it means that they take up the same space. Let's have a little look. Now your task is, if you can show me, you understand what we've covered so far. If I need this, lets have a little look at this. Can you see the dots above, at the top of the slide there? How many are there? A quick count, you got it? Yeah, there's 12 isn't that? Well done. And how many are circled? was that? Two, yes. So, this could be seen as a fraction, as two-twelfths, couldn't that? How else could we then see that? What other fraction could we say that, that was equivalent to? Hmm, quite hard isn't it? Right, who does imagine, that the circled group of two, is one part? So if every two is one part, how many parts would there be in total? You got it? Six, well done. So if the denominator is six, by having circled around two, that would be one part out of six. So, either two-twelfths, or one-sixth. Now look at the bottom one. Yeah, how many parts can you count? Well done. Six, yes. So six could be your denominator with two. What else could we have it as? Think back when we were measuring, what fraction were we using? That's right. One-third. Well done. And here is your task for next time. So, you might want to pause now and draw these, or you can have a go at them on the screen, and be ready for next time. I want you to find two equivalent fractions, for each of these shapes. And I'll go through those with you, in the next lesson. And thank you so much for listening. Look forward to seeing you next time. Bye.

Equivalent fractions in context

Equivalent fractions in context

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UnitMaths / Equivalent fractions

Maths