Video: Compare unit fractions using a fraction wall

﻿Hi everyone, Mr. . I'm going to take you through today's lesson and we're going to start off by thinking about the practise activity I asked you to do at the end of the previous lesson. Now I said, for this whole which is a square, can you identify what fraction is red? What fraction is yellow? What fraction is blue, and what fraction is green? If you didn't have a chance to do that, pause the video and have a go at that now. So, did anyone do this? Did they count the number of parts? One part, two parts, three parts, four parts, five parts, six parts, seven parts, eight parts, nine parts. Does that mean the red part has one of those nine parts? So that's 1/9. Does that mean that the yellow square is 1/9? The green part is 1/9. The blue part is 1/9. Can they all be 1/9 at the same whole? Are they all equal in size? They're not, are they? I can see that this red rectangle is not the same size as this yellow square. So they can't all be 1/9 of the same whole. So, we need to go back to the sentence scaffold that we've used before. The whole has been divided into equal parts. Now we're going to have to use some visualisation, using our mind to try and see those equal parts. So let me start with this yellow square. I can see one part here and I can see that there will be another equally sized part here. That would be two parts, another one of the equally sized parts here, three parts and another one here, four equal parts. So let's go back to our sentence. The whole has been divided into four equal parts. One of these parts is 1/4 of the whole. The numerator one is the number of parts that's been coloured in yellow, the denominator four is the number of those equally sized parts that we've had to visualise from this diagram. So, let's think about the red rectangle. Now I can see a red rectangle there and a white rectangle there. There's two parts so far. I have to continue to visualise the rest of the whole being made out of those equally sized rectangles. One, two, three, four, that I've counted so far. If there's four on top, there must be another four underneath. That would be five. That would be six. That would be seven. That would be eight equally sized rectangles. How many of them are coloured red? One, so let's go to our sentence scaffold. The whole has been divided into eight equal parts. One of these parts is 1/8 of the whole. Now, in the previous lesson, we also spoke about how parts can look different but they can still be an equal fraction of the whole. Now I think this might be true for our blue triangle and our red rectangle. So we started off by looking at this yellow square. I can see this red rectangle is 1/2 of the yellow square. I can also see this blue triangle is 1/2 of this. This is the same size as our yellow square. So I think this would be the same fraction, 1/8. So let's see if we can visualise eight of those triangles in the whole. This is one and two triangles. Here there would be another two, so three and four. Here, there would be number five and number six. Here there would be number seven and number eight. Yep, there would be eight triangles in total. One of them shows in blue, so that would be 1/8. So, final one. Let's think about this green square. How many of these green squares do you think would fill the whole of my square? In this top corner, I can see four. In this top left I can see, imagine there'd be another four, four plus four is eight. And this bottom left, I could imagine another four. So that would be 12. And then here there'd be another four, 12 plus four is 16. So there would be 16 squares in total. One of them is shaded in green. Let's go back to our sentence for the final time on this slide, the whole has been divided into 16 equal parts. One of these parts is 1/16 of the whole. Now I also said is a challenge to think about what fraction is white but we're not going to talk about that now, because actually that wouldn't be a unit fraction with one as the numerator, it would be a different kind of fraction. So we'll come back to that in a few lessons time. Okay, now on to some new learning here, I've got some different coloured strips of paper, and I'm going to ask you quite a simple question, which coloured strip has the most equal parts. What do you notice about the parts, is the second part to the question. So, shout out for me, which coloured strip has the most equal parts? The purple strip. Hopefully you said the purple strip. Let's see how many parts the purple strip has been split into, one, two, three, four, five, six, seven, eight, nine, 10. There's 10 parts there. They're all equal in size. So the purple strip has been split into the most equal part. Now, what do we notice about those parts? How big are those parts compared to the other parts of the other coloured strips of paper? Are they bigger? Are they smaller? They're smaller, aren't they? So, we've learnt this. I've just shown you when the whole is the same size, the greater the number of equal parts, the smaller each equal part will be. So let me show you that. So here we have the same sentence and I'm going to show you some examples that proves this. To start with, my whole has been split into three equal parts. Now, I'm going to split the same sized whole into a greater number of equal parts. This time, it's been split into four equal parts. So here is the size of each part, is it smaller? Is this part smaller than this part? Yeah, of course it is. So, that sentence is true. Let's look at our next row, has the number of parts increased? Yep, there's now five equal parts. Has each part becomes smaller? Yep, we can see that as well. Again, has that happened how many parts this time? Six, is each part smaller? Certainly is. This one, is there seven equal parts? No, if you check one, two, three four, five, six, seven, eight, nine, 10, 10 equal parts. And are the parts smaller? Yes, they are the smallest so far. And that is the first thing that we said that for the purple strip, it has the greatest number of equal parts and each of the equal parts is the smallest, really important that we are saying that the whole is the same size. The left-hand side of each whole and the right-hand side of each whole lines up. So I know the wholes are the same size. Very similar question, but slightly different, which coloured strip has the fewest equal parts. That means the smallest number. What do you notice about the parts this time? Is it still the purple strip? No, the red strip has the fewest equal parts. How many equal parts it have? It's got three equal parts and this time, what do you notice about these parts? Are they still smaller? No, if we've split the same whole into a smaller number of parts, the parts are larger. So, a very similar sentence with some slight differences. This time we can say, when the whole is the same, the smaller the number of equal parts, the bigger each equal part is. Let me show you that again with our strips of paper. So, I've started off with the purple strips. Let's go back to the sentence. When the whole is the same, the smaller the number of equal parts, the bigger each equal part is. So I've reduced the number of parts. In the purple strip, there are 10 equal parts, in the green strip, there are six equal parts. The number of parts has become smaller and has the size of each part grown? Yep, we can see that each of the green parts is larger than the purple part. Same for our next row. This time we've got five yellow parts, well done if you could see them without counting them. There's five yellow parts and is each part larger than the green and the purple? Yep, can see that they are definitely larger in size. Same for our blue. We've reduced the number of parts again, this time there are four. So each of our parts has become larger. Same for our red. Again, this is what we said, this is the smallest number of parts because there's only three, the fewest I should have said and they are definitely largest in size. Okay, now I've added a new coloured strip. We've got an orange strip. Now I'm going to call this orange strip one whole. And if I call this one whole, we can think about the other strips of paper and the other parts as fractions. We're going to use the same sentence that we've used previously. The whole has been divided into mm equal parts. One of these parts is one of the whole. So the red strip of paper, say this with me. The whole has been divided into three equal parts. I hope you said that with me. Let say the next part, one of these parts is 1/3 of the whole. So if that first red part is 1/3, what's the next red part. That's also 1/3 and the final one, also 1/3, that all 1/3 because they are all equal in size. So, let's look at the next strip. These 1/3 as well? No, we've increased the number of parts. This time there are four parts. And we said before that each of the parts is smaller in size, but let's think about what fraction each part is. Say it with me again. The whole has been divided into four equal parts. One of these parts is 1/4 of the whole, how do we write 1/4? It's one as the numerator, four as the denominator. So if that's 1/4, what's the second blue rectangle? That's also 1/4 and that must mean that each of these is 1/4 and we've then got four 1/4 within our whole. Now, the next strip of paper say it together, the whole has been divided into five equal parts. One of these parts is 1/5 of the whole. Again, if the first strip is 1/5 then the second strip must also be 1/5, all of them are 1/5. Almost there, the green ones. Again, let's just count quickly, okay. And now I'm going to say, say it with me, the whole has been divided into six equal parts. One of these parts is 1/6 of the whole. This part is 1/6. This part is 1/6. All of our parts are 1/6 because they are equal in size. Final row, we've got our purple parts. Remember I said there were 10 parts. So now let's say there's two sentences together without stopping. The whole has been divided into 10 equal parts. One of these parts is 1/10 of the whole. This is 1/10. This is 1/10. They are all 1/10. Now, I've only coloured in the first of the parts in each strip of paper. The whole, the orange strip is still one. That then means that the red strip is still 1/3, the blue strip is still 1/4, the yellow, the green and the purple, the fractions that are coloured still the same. Now I'm going to remove the other parts. Bit of a memory test, can you remember what we said each one was? The whole, the orange strip is orange. Now again, some visualisation, the red, how many would fit into the whole? Three of them, so that was 1/3. You might remember the blue one but why is it that fraction, so 1/4, why is it 1/4? Because one, two, three, four of them would split, would fits into the whole sorry. The yellow one 1/5, again, I'm picturing in my head. Five of those yellow strips making the whole because five is a number of equal parts that strip of paper was split into. What was the green, can you remember? Well done, if you said 1/6. Imagining those six in our head, really important to see that picture in your mind, see it grow as you move across. What was the purple one? Remember I said it's not just following the same pattern, it's not 1/7, it's 1/10. It's 1/10 because 10 of those equal parts make our whole. Now in this lesson and the next few lessons, we're going to be comparing fractions and at the top of the page I've got two symbols that we can use to compare numbers and fractions. This symbol and this symbol. Can you remember what these symbols are? The first symbol is smaller than. So the next symbol is greater than. Well done if you remember those. Now, we're going to use these symbols to try and compare these fractions. We said that the red strip was 1/3 of our whole. And when the whole state the same, our blue strip was 1/4 of the whole. Which is larger, is the red rectangle larger or is the blue rectangle larger? The red rectangle is larger, isn't it? We can see in size, this is definitely a larger rectangle than this one. So which symbol would we use? We use a smaller than symbol or a greater than symbol. I'll read this through and I'll leave a pause for you to say what symbol you think goes in the gap. 1/3 is 1/4. What did you say? I'm going to say, hopefully it's the same that you said. 1/3 is greater than 1/4. Okay, let's look at two more fractions. I've introduced the yellow strip. We said the yellow strip was 1/5 because five of these equal parts made a whole. So, which is greater this time? Is the blue strip greater or is the yellow strip greater? The blue strip is greater, isn't it? So this time let's say this sentence together. 1/4 is greater than 1/5. The green strip of paper. Again, we said before, smaller in size, isn't it. So again, let's say the sentence together. 1/5 is greater than 1/6, and there was one more coloured strip on our fraction wall, that was 1/10. Again, remember we're comparing this green strip with this purple strip. Is the green strip larger or smaller in size than the purple? It's greater, it larger, isn't it? So, let's say that final sentence together. 1/6 is greater than 1/10. Now, we can actually say all of these together combined into one sentence. I'm going to say join in when you see the pattern. 1/3 is greater than 1/4 which is greater than 1/5 which is greater than 1/6 which is greater than 1/10. That means if we focus on this, this means 1/3 is greater than 1/6. So here is a sentence that summarises what this page shows. When comparing unit fractions, the greater the denominator the, what word you think goes there? See if you can say it, when comparing unit fractions, the greater the denominator, the smaller the fraction. Now this is a strange concept 'cause normally when we count a larger the number we say, the larger number becomes but for fractions, we have 1/3, 1/4, 1/5, 1/6 and 1/10. The larger the denominator becomes, the smaller the fraction because that's the number of equal parts it's been split into. Goes against what we might think but really important to get our head around this concept. For today's practise activity, I want you to make your own fractional wall. I want you to make a fraction wall which shows the same whole divided into equal parts where each part on each row is 1/2 then 1/4 then 1/5 then 1/10 and then 1/20. Now the easiest way I think you should do this is to find some squared paper if you have it at home. If you have some squared paper, I want you to make them 20 squares across, and then have enough rows so that you can do those five fractions and one whole. So let me show you what I mean. I've got my square piece of paper on the screen. I'm then going to draw six rectangles which are each 20 squares long. That's what I've done here. Then I'm going to start off by labelling my top rectangle as one whole. And then I'm going to show you how I would draw the next row so that it has equal parts where each part is 1/2. So I said 20 squares. Now, I know that 1/2 means splitting into two equal parts. That means I need to divide 20 by two, which is 10. So I can start off by drawing a line that splits my 20 squares into 10 squares each side, they're equal in sizes two parts. So then I can label the left part 1/2, and the right part 1/2. So, see if you can do the same to show 1/4, 1/5, 1/10, and a 1/20. If you don't have squared paper home, you can still try to do that. If you have a ruler, you could draw some rectangles that are 20 squares long. And then think about in the same way how to make one row a whole, one row 1/2, 1/4, 1/5 or 1/10 and 1/20. If you don't have access to ruler or squared paper, or short on time, I still want you to do this activity. I want you to use either the fraction wall that I've got on the screen here, or the fraction wall that you just made, and I want you to write some of your own inequalities. So I want you to use the scaffold I've got, and then you're going to say a fraction and then say is larger than another fraction. So, I'm going to say the first one and obviously you could write this down on a piece of paper as well. So, I'm going to talk about 1/3 first, and this sign means is larger than. So I can choose any fraction that is larger than. so one whole, it's not larger than, but all of the other fractions my 1/3 is larger than, and I going to keep unit fractions. So an example could be 1/3 is greater than 1/6. So have a go at writing some of those down. See how many different ones you can write. If you want to challenge, you could try and take a whole piece of paper, and fold it into strips so that you still create fraction tiles or a fraction wall of your own but with these fractions. Now, knowingly a piece of A4 paper is just a little bit smaller than 30 centimetres. It would be nice if it was because then we could measure them. But here I've taken an A4 piece of paper, and I've cut it into a strip. I'm then going to try and make 1/2, okay. 1/2, that means two is the denominator, two equal parts. I think if I fold it in like that from end to end, and then I open it up, I could then draw a line, I going to to do that on my piece of paper, using a ruler. I can draw a line to show where I folded, can you see that on the screen? Lights a bit bright, there it is. So now I could write 1/2 on each side, that one was easy. The next one's a bit more tough. So, I've got another piece of paper, the same length as before. Remember we said we're keeping the whole as the same. Now I've got to try and fold it into 1/3. I'm going to have to fold this in a clever way so that the middle comes like that. Ooh it's going to be hard to be accurate. I think I've got it. I've done it. I'm going to open it up. I know that that is correct because when I put them on top of each other, each of my parts is of equal length. So now I can write on each of these 1/3 because I've split it into thirds. Let me do that for you. Draw my line down there, the ruler. And then I can write 1/3 on each of my parts, 1/3, 1/3, 1/3. And now I can, you can see hopefully on my strip of paper I've got one third on each of my parts and they are equal in size. I could if I wanted to, use my rule to help me to work it out, but depending on the length of your piece of paper, you might go into some more difficult numbers when you try and divide that whole into three. So good luck. Have a think which ones you find easy and more difficult, and in the next lesson, there I'll talk about those difficulties you have.

Lesson summary: Compare unit fractions using a fraction wall

In this lesson we will compare unit fractions using a fraction wall.

Maths

Y4 Maths

Key Stage 2

Year 4

Compare unit fractions using a fraction wall

Working with fractions

UNIT

Divide and describe the same whole when divided into differing numbers of equal parts

Understand fraction notation to represent a relationship between part and whole

Begin to use and understand the terms 'Numerator' and 'Denominator'

Name unit fractions and match them with the fraction notation and a representation

Embed previous fraction work using a linear model

Assign unit fraction names and notation to 3D representations

Assign unit fraction names and notation to equal parts of quantities

Recognise and reason about unit fractions in a variety of contexts

Understand that Equal Parts Can Look Different - Area

Understand that Equal Parts Can Look Different - Volume and Area Contexts

Reason about comparing unit fractions

Compare unit fractions in a measure's context

Can we compare unit fractions of different wholes?

Construct a whole from a part and identify the fraction it represents

Build and compare different wholes from the same unit fractions that represent the same length

Build and compare different wholes from the same unit fractions that represent different lengths

Build and compare different wholes from different unit fractions that represent the same quantity

Build and compare different wholes from different unit fractions that represent different quantities

Build and compare wholes when different unit fractions represent different amounts

Compare unit fractions using a fraction wall

Video

Lesson summary: Compare unit fractions using a fraction wall

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