Order Several Non-Unit Fractions with the Same Denominator and Apply this Understanding

Key Stage 2

Maths

Taking fractions further

﻿Hello again, my name is Mrs. Ford, and I'll be taking you through your lesson today. Let's start by looking at the practise activity that I sent you last time. In the first question, you were asked to look at the models, and then complete the comparison statements. So compare one fraction with the other, which is bigger, which is smaller. Let's have a look at this first one. So we've got a diagram here and we can see that already, the denominator has been completed. Because we can see that each one of these has been divided into six equal parts. Now, remember what we said before? When we know the denominator is the same, we can use the numerators to compare the fraction. So which one is smallest? That's right, this one is smallest. How many equal parts are shaded? We have two lots of 1/6. So two lots of 1/6 is less than four lots of 1/6. And you know that same denominator, you know two is less than four, or two lots of 1/6 is less than four lots of 1/6. Let's have a look at this one. How many equal parts has the whole been divided into? That's right, both have been divided into 11 equal parts. Now, how many has this been? How many parts have been shaded in this diagram? Look, two, four, six, seven. And in this one, there are nine. So look at our comparison statement. This says, this fraction is greater than this fraction. So which one needs to go here? That's right, the biggest one. And we can use the numerator to compare because both denominators are the same. So we know that nine lots of 1/11 is greater than seven lots of 1/11, brilliant. Now, let's have a look here. We've got no parts filled in in fractions, but we know that this one is the bigger one, because it says it's more than this one. So what's that times four number of equal parts. That's right, nine. Both have nine hearts. And then here, how many are shaded? Two, and five here. So which is the greater? Yes, five-ninths. 5/9 is more than 2/9. Well done. Okay, and in question number two, you were asked to complete what you know, or use what you know to complete the missing symbol problems. So you had to put in either less than or greater than or equal to. So let's have a look. We've got 3/5 and 4/5. Now we know that when a fraction has the same denominator, we can compare by looking at the size of the numerator. We know that three is less than four. So 3/5 is less than 4/5. Let's have a look at this example, 9/11 and 4/11. Same denominator, so we can compare using the numerator. Nine is greater than four. So 9/11 is greater than 4/11. Now it says complete these boxes to make the statement true. So 5/9 is greater than, well, is it greater than 8/9? No, okay, what do we need to do? We could have lots of different answers here, but we'd have to make sure that this numerator is less than five, because 5/9 is greater than, so it could be 4/9, 3/9, 2/9, or 1/9. Similarly here, we've got 18/25. And we're not sure how many 25ths on this side. But what's missing is the greater than or less than symbol. So if you put greater than, you have to make sure that this numerator is higher than 18, because both have the same denominator. If you put less than, what do you need to make sure? That's right, you need to make sure that the numerator is less than 18. What about if you've got 18 here? What could you put in the middle? That's right, 18/25 is equal to 18/25, well done. So the children have been looking at this. Arrange these fractions in order from smallest to greatest. We've got 3/6, 2/6, 5/6, and 6/6. So the children use some models, and then they can see really clearly which fraction has the least amount of parts shaded. Yeah, 2/6. And the next one, 3/6. And then this one's got five parts shaded. So that's the next one. And that's all the parts are shaded. Six lots of 1/6, whole shape is shaded. Okay, so we know that 2/6 is less than 3/6, which is less than 5/6, and less than 6/6. Now one of the other children in the class thought she might like to represent this differently. So she's going to put the fractions on a number line. Let's think about what she needs to do. She's got zero and one. All of these fractions would be in between zero and one. Now let's think. How many equal parts does she need to divide this into? That's right, six, because our denominator for all of the fractions is six. They are all lots of 1/6. So let's think, let's count along the number line to see where they might go. So we've got zero, then we've got one lot of 1/6, two lots of 1/6, three lots of 1/6, four lots of 1/6, five lots of 1/6, and six lots of 1/6. 6/6, or one whole. Now we can see which fraction is smallest. Which one is closest to zero? 2/6, because 2/6 is less than 3/6, which is less than 5/6 or less than 6/6. And again, somebody else approached the problem like this, using the quantity model. We've got groups of six sweets. And we can show how many of those are made up with this fraction. So if the total number of parts is six, three of those parts will be three lots of 1/6 or 3/6. And here, we've got total number of parts is six. Two of those is two lots of 1/6, which we can see here. How many are we going to circle this time? That's right, five lots of 1/6. And in this one, all of them, yes. Six lots of 1/6, that's all of the sweets. Now we can arrange them in order from smallest to largest or greatest. We've done this already. 2/6 is less than 3/6 is less than 5/6 is less than 6/6. So all those different ways are representing it. But you remember last time, what we spoke about. We only looked at two fractions. This time, we've got four fractions to compare. But what do you notice about them that's the same? That's right, they all have the same denominator. So do you remember in the last lesson, we said that when we compare fractions with the same denominator, the greater the numerator, the greater the fraction. So we can arrange these fractions in order from smallest to greatest by looking at the numerator. Which one is smallest? That's right. 2/6, because I know that two is less than three, and that's less than five, and that's less than six. So 2/6, or two lots of 1/6, is less than three lots of 1/6, which is less than five lots of 1/6, less than six lots of 1/6. Excellent, so we can use what we know from the last lesson, even though this time we've got more fractions to compare. If we notice that the denominators are all the same, we can do exactly the same thing, well done. Now this time, we've got five fractions to compare. 5/20, 11/20, 10/20, 19/20, and 1/20. What do we need to notice? That's right. We need to notice that all of the denominators are the same. So what's our rule that we can follow or our generalisation? That's right, when we compare fractions with the same denominator, the greater the numerator, the greater the fraction. So we can look at the numerators and see, which one is the smallest, which one is the greatest. And that will help us to order our fractions. Pause the video now, and have a go. Write down the fractions in order from greatest to smallest. Okay, have you had a go? Fab, well, Madj in my class has done this. Okay, 1/20 is less than 5/20, is less than 10/20, is less than 11/20, is less than 19/20. Do you agree with him, is that what you wrote down? Yeah, well, it looks right, doesn't it? 1/20 is less than 5/20, and that's less than 10/20, and that's less than 11/20, and that's less than 19/20. I can hear some of you saying, "No, something's not quite right." Looks right. What's happened here? I know, he was in such a rush to show me that he knows how to order these fractions, and he does, he didn't read the question properly. What does it ask you to do this time? You're asked to arrange the fractions in order from greatest to smallest. That means we need the biggest one here. Okay, let's have another go. Now, is this the way that you did it? 19/20, that's right, that's the greatest fraction. It's greater than 11/20. And that's greater than 10/20, and that's greater than 5/20, greater than 1/20. Do you agree? Yes, this is the right way round now. Okay, how do we know that, though? Well, they are all twentieths, and we need to arrange looking at the numerator. And 19, I know that 19 is greater than 11, and that's greater than 10, and that's greater than five, and that's greater than one. So 19/20, or 19 lots of 1/20 is greater than 11 lots of 1/20. And so on till we get to one lot of 1/20. If you did it like that, well done. So, the children in my class have been making biscuits to sell at the school fete. And James made 4/15 of the total amount of biscuits. Madj made 2/15, Farah made 6/15, and Ava made 3/15. Who made the most biscuits? How do you know? Just pause the video and have a think through your thoughts, and while you're doing so, decide who made the most amount of biscuits. Okay now, what do we need to notice? We need to notice that all of the fractions have the same denominator. So now we can compare the fractions by looking at the size of the numerator. Okay, I think that I'd like to order them first. It's asking me here, can you order them? Who made the least biscuits to the most? And that will help us to answer our question. So who made the least, well, let's have a look. We just need to look at the numerators. Which numerator is smallest, four, two, six, and three? Well, I know that the smallest fraction there then is 2/15. And then 3/15, what comes next? James made 4/15 of the biscuits, and Farah made 6/15 of the biscuits. What was the question? Who made the most biscuits? That's right, write that down in a sentence. Mmm made the most biscuits. What did you say, you said Farah made the most biscuits, that's right, because she made the highest fraction of the total amount. Now this looks different. It says some children were taking part in a sponsored swim. Here is a chart showing how far they swam. So let's have a look, what have we got here? We've got name, so that's the name of the children taking part, and distance, so these are the distances that they swam. Hibba, how far did she swim? 3/10 of a kilometre, that's right. David swam 5/10 of a kilometre. Farah swam 9/10 of a kilometre, Ella 8/10 of a kilometre and Jason 6/10 of a kilometre. They all must be very good swimmers. Who swam the furthest, though, how do you know? Are these in order? No, you're right, they're not in order, are they? Okay, so what is it we need to notice? If we're going to order them, order the distance they swam from shortest to longest, what do we need to notice about these fractions? Can we compare them? Yes we can, because they're all fractions with the same denominator. So we're just going to look at the numerators and we can order them. Write them down, have a look, and you order them from smallest to greatest. Who swam the shortest distance, and who swam the longest distance? So, can we tell who swam the furthest? How do you know? That's right, we know that when we compare fractions with the same denominator, we can compare by looking at the numerator. And the largest numerator here is nine. So 9/10 of a kilometre was the furthest distance swam. Farah swam the furthest. So, can you order the distance they swam from shortest to longest? Yes, you can, and how will you do that? You'll do that by looking at the numerator, that's right, because they all have the same denominator. And when we compare fractions with the same denominator, the greater the numerator, the greater the fraction. So which is the shortest distance? Who swam the shortest distance? That's right, Hibba. The shortest distance was 3/10 of a kilometre. So what's next? Five, nine, eight, right, David at 5/10 of a kilometre. And then Jason at 6/10 of a kilometre, Ella at 8/10 of a kilometre, and Farah is 9/10 of a kilometre. Daniel also took part in the sponsored swim. He forgot to write down his distance, though. We know that he swam further than Jason, but less than Ella. What fraction of a kilometre should he have recorded? Just pause the video and have a think. What have you noticed? We know all of the other distances, and so we know it's more than Jason, but less than Ella. So let's have a look. We've got 3/10 of a kilometre, 5/10, 6/10, 8/10, and 9/10 of a kilometre. So what could Daniel's distance have been here? That's right, we need to look at the numerators. What is greater than six, but less than eight? Did you say 7/10 of a kilometre? Well done. Okay, so what do we notice about this problem? Well, I know that these fractions have been ordered. But I don't know, have they been ordered from greatest to smallest or smallest to greatest, because the inequality symbols are not there? Let me see, what else do I know? What do I know about the denominators? That's right, the denominators are all the same. We don't know what the denominator is, but it's represented by this pink star. And that pink star is the denominator in all of these fractions, so the denominator is the same. What do you notice about the numerators that might help you with deciding which way they've been ordered? Have a think, you have a go. Write down which fractions you think you could put in here to make this statement true, and which inequality symbol are you going to use? Is there only one answer or is there more than one answer? I think there's probably more than one answer. Have a go. Are you back? Have you had a go? Okay, let's have a look and have a think about what you could do here. What did you notice about the fractions? Ah, did you notice that five is less than 20, and 20 is greater than five? So our fractions, the numerators are getting bigger. Okay, does that help us? Okay, it does help us because we need to know then that this numerator must be less than five. Okay, what could it be? That's right, it's got to be any number less than five. So I'm going to choose a number less than five, let's say four. Okay, four something is less than five something. Okay, good, and what about this number here, this numerator? What must it be? Well, we know if five is less than this one, this has to be bigger than five. But this one is also less than 20 because we know that they're in order. Okay, so there are lots of different numbers that we could pick to go in here. I'm going to say 17. Let's see, is that correct? The denominators are all the same, so we're ordering by the numerator, and I know that four is less than five. That's less than 17, that's less than 20. Okay, so lots of different ways you could have answered that. Just make sure that you've used the rule that when the denominators are the same, the greater the numerator, the greater the fraction. Okay, good. And what do you notice about this one? Very similar, now we need to find these two fractions here. Okay, I'm just going to ask you to have a go. Go away and do what you think. Think about the rule that you know, and let that help you decide what you need to know about the numerators. Okay, have you had a go, let's have a look. What did you notice? Well, this numerator is 15. The denominators are all the same. So we can order using the size of the numerator. So 15 to three. Now, so if these are in order, this is the biggest fraction. So 15 is greater than something, is greater than something, greater than three. Okay, so now I just need to complete these two. So this one has to be greater than three. So give me a number greater than three. Seven, okay, that means that now this one, this missing one here, needs to be greater than seven, but less than 15, that's right. Okay, so any number that's greater than seven, but less than 15, say nine. Now, let's have a look, is that correct? I know the denominators are the same. So I'm going to order by the numerators. I know that 15 is greater than nine, is greater than seven, is greater than three. Is that the only way I could have solved this? No, there were lots of different ways, and you might have different numbers. You just need to check that it follows the rules. Now let's have a look at this one. What's different this time? Well, this time we've got the fractions completed, 8/9, 5/9, 2/9, don't have the inequality symbols, but we know they're in order. So could we work out what the inequality symbol is? Is 8/9 less than or greater than 5/9? That's right, because you know they're both ninths. So 8/9 is greater than 5/9. So 5/9 will be greater than this one. And this one will be greater than 2/9. So what could this fraction be? Just pause the video and write down what fraction you think that could be. Okay, are you back? What did you decide? Okay, so 5/9 is greater than this number or this fraction. So, could be 4/9, yeah? Hard to write with this pen. 4/9, so it should say 8/9 is greater than 5/9, which is greater than 4/9 is greater than 2/9. Could be, couldn't it? Have we got any other fraction, is that the one you wrote? Or did you do something else? Did you say it could be 3/9? Oops. Now you've been working so hard over the past couple of lessons, and I think you really, really understand now that if a set of fractions have the same denominator, we can order them by looking at the numerators, and we can compare them by looking at the numerators, and see which one is bigger and which one is smaller. So now, for your practise activity, you've got this set of fractions. 7/8, 5/8, 2/8, 4/8, and 1/8. I want you to plan some activities or questions for a friend. Think about all of the different types of activities that we've been doing. We did some word problems, some real life problems. We did some comparisons. We did some ordering. So, you plan some activities or questions for a friend. What could you ask them to do that would help them to understand ordering and comparing fractions with the same denominator? And what could you tell them? What big clue could you give them to be able to solve those questions that you set them? Okay, have fun, and we'll see you in the next lesson.

Order Several Non-Unit Fractions with the Same Denominator and Apply this Understanding

Order Several Non-Unit Fractions with the Same Denominator and Apply this Understanding

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UnitMaths / Taking fractions further

Maths