Reason about comparing unit fractions

Key Stage 2

Maths

Working with fractions

﻿Okay, hello, it's me, it's Mrs. Kingham here again. I'm really pleased to be back. And today we're going to be investigating further into what you've been looking at with Mr. East, and note that the denominator, tells us how many equal parts there are, and it also tells us the size of equal parts compared to the whole. And we're going to be investigating that a little bit further today. But he got you to make some fraction walls, didn't he? Did you find some bit of that more difficult than the others? Did you're grown ups help you at home? Hopefully they did. You can use those today to help you in all different parts of this lesson. Okay, let's go. With Mr. East yesterday, you decided on that this was true. That when comparing unit fractions, now let's just remind ourselves of a unit fraction. Can you remember what it was? Can you explain to an adult what a unit fraction is? Okay, right. When comparing unit fractions, our unit fraction is where a whole has been divided into equals parts. Let's just say, for example here, two equal parts, and one of those parts is our unit fraction. So therefore, every unit fraction, our numerator is one. Okay, so a unit fraction has a numerator of one. Now, we decided that when comparing unit fractions, the greater the denominator, and the denominator here is this bottom number, how many equal parts the whole has been divided into. The greater the denominator the smaller the fraction. So, we are going to investigate that even further today. Okay, so how can this representation prove that when comparing unit fractions, the greater the denominator the smaller the fraction. How can this two representations of fractions help me? Or is there something missing? What do you think? You're right, we need to know the whole. If our rectangles weren't labelled as unit fractions, we wouldn't know what they were. So, we need to compare them to the whole, to make sure that we can label them as unit fractions correctly. And actually we are going to use some skills that we've have spoken about before, and that is our estimating and our visualising skills. Do you remember? So, think about visualising, how many of the red rectangles it would take to be the same as one whole, the orange bar. How many red ones do you think? Therefore this will give us our denominator. Have a think. You're right. I think I agree with you. I think three of this red rectangles, maybe the same as the orange rectangle. Therefore our denominator is three, because the whole would have been split into three equal parts and we have one of those parts, therefore this is the unit fraction one third. How about the blue, have a think. I think that you might have this right. How many of the blue rectangles do you think will be the same as the orange rectangle? I think you're right too. Maybe if we had split the orange rectangle into four equal parts, then we'd have four blue rectangles of which this is one of them. So, 1/4, so this is the unit fraction of the quarter. So can we see if our rule works by comparing unit fractions the greater the denominator the smaller the fraction. So, we've got 1/3, and our denominator is three, and 1/4 our denominator is four. And we are saying that the great the denominator, which is four, the smaller the fraction. And look at this, yes that's right. The blue rectangle is a smaller fraction of the whole, than the red rectangle. Well done. You may want to use the fraction wall that you made with Mr. East yesterday, to help you on this next few tasks, and that's absolutely fine. Now that we've looked at our rule again, I've poped it in the top corner for you. So I would like you to order this fractions, remembering our rule. Now, down here you can see that I've put some symbols. Now this mean that I would like you to order these fractions, from the largest fraction to the smallest fraction, which is also called descending order, the largest fraction to the smallest fraction. Off you go. So how did you get on? Did you see that 1/3 is greater than 1/4, which is greater than 1/5. Does this work with our sentence, say it with me, when comparing unit fractions, the greater the denominator, the smaller the fraction. Therefore let's have a look at this. The largest denominator is here 1/5, and actually yes that is the smallest fraction, smallest fraction and the other end this is the largest. Well done. Let's try another one. Okay, how about this one. There's something slightly different this time, what could it be? This time I would like you to order this fractions in ascending order. Ascending means with the smallest fraction first going up to the largest fraction, and that means that this mean less than. Okay, off you go. How did you get on? And what did you notice? Let's have a look. Therefore this time it says that, 1/5 is less than 1/4, is less that 1/3. They are just the other way around, aren't they? But is the rule still the same? The greater the denominator the smaller the fraction. The greater the denominator the smaller the fraction. It's true. Try this one on your own. I haven't given you any greater than or lesser than symbol this time. But this time I'd like you to order these fractions, from the smallest to largest, that's in ascending order. Okay, off you go. Pause now. How did you do? Did you use the rule? The smallest to largest so in ascending order. So the smallest fraction was the one with the largest, the greatest denominator. Did you do well? I bet you did. So, if we know that the orange bar here is one whole, then can you match the other unit fractions to the correct rectangle. Pause the video now and have a go. Okay so how did you do this? There's a few ways that we probably could have done it. So I know that all of my rectangles are descending in order of size, aren't they? But what does that mean for my denominator? Does that mean that the denominator is larger at the bottom? Yes it does, because that was our rule, wasn't it? The greater the denominator the smaller the fraction. So 1/6, where do we think that might belong? Yes, because it was my second largest denominator. How about 1/3? That was my smallest denominator, so therefore my greatest part, wasn't it? Of the whole. 1/10 and 1/4. How did you do? So let us just remind ourselves that we've got three as our denominator, four is our denominator here, six is our denominator here, and ten is our denominator here. So the greater the denominator, the smaller the fraction. We've proven this all the time. Well done. Okay, so look at this then. We're going to start to use some skills now that we did before. So we were estimating, so we were thinking about... Estimating means you're not completely accurate, you're as accurate as you can be, and visualising what part the whole might look like. So, can we estimate what this unit fraction might look like in comparison to our whole, and the orange bar there is our whole. So we want to look at 1/20 of the orange bar. Have a try. It looks like a huge denominator, so actually that means it's a small part of the whole. Have a go. How did you do? Why, I'm going to have a go at this then. I know that 1/10, what we've seen on the last slide, was about here. And I know that 1/20, even though it's a larger number, the fraction is smaller. So, I think 1/20 is going to be probably about here. I don't know, do you agree? Let's try another. Whoa that is a huge denominator. 1/100 One hundred equal parts. Wow. Pause now and you have a go, then it's my turn. Okay, right. A hundred equal parts. So, I'm going to go to my ten again I think so, and then that might be about... Remember estimating, your just kind of estimating where it might be, it doesn't have to be completely accurate. Does that look like I could get 10 equal parts of my green line, about that I think, probably yeah. So 1/100, a hundred of those tens, aren't they? I could have some images in my head. If you've ever seen a metre stick or some thing like that, they've got 100 centimetres on them, haven't they? Let's have a think. So 100 equal parts. Let's say I think that a hundred equal parts might be about this size, do we think? That might be a bit too big. What do you think? 1/64, 64 equal parts. Right, it's your turn to have a really good think about this one. What do you think 1/64 looks like compared to the whole. Have a go and reason your answer, tell somebody in your family why you think it's like that. Good luck. So, I think we've definitely proved after all of our work, that when comparing unit fractions, the greater the denominator, the smaller the fraction. So, our unit fraction here was 1/3, three 1/3 make the whole. And then we had our quarters, 1/4. Then we had our fifths, 1/5. Then we had our sixths, 1/6. Then we had our tenths, ten 1/10 make the whole. And we have definitely proved that the larger the denominator, the smaller the fraction, and we can see that pattern down here look. Let's have a look all the way down here, the parts get smaller as the denominator increases. I think that you have done so well, that you don't need the pictures anymore, that you can just deal with the fraction and notation. So, I've got my unit fraction, 1/3. Let's have a look and think about our rule. Is 1/3 greater than or smaller than 1/4? Think about the denominator. The greater the denominator the smaller the fraction, therefore 1/3 is greater than 1/4. How about this one? 1/5 1/4 say it with me. 1/4 is greater than 1/5. Well done. No pictures see. How about this one? 1/6 say it with me. 1/5 is greater than 1/6. And finally, say it with me 1/6 is greater than 1/10. And why is that? You're right. Because the greater the denominator, the smaller the fraction. Let's see the pictures to prove it. Ta ta. Well done. Let's look at all of this a different way. Okay. So, now our representations are slightly different. Is the rule still the same in a different shape? This time, what have we got that's different? Yeah, you're right, circles. So let's see, let's name this fractions to start off with. The first circle is split into or divided into two equal parts, therefore my denominator is two, and just one of those parts are shaded. How about the second one? You're right, it's 1/4. Four equal parts and one of those parts are shaded. Sixths, this is 1/6, a unit fraction of 1/6, and finally 1/3. So as you can see... Hmm how could I make this more simple to see if our rule works? Can you put them in order? Pause now and have a go. Have a look at this. Which order did you put them in? I've put them here in ascending order. So it goes from the smallest fraction to the largest fraction. Okay, so denominators, let's just have a check and see if our rule works. So we've got.. Uh, that's definitely the greatest denominator here, six. And look it's true, it has the smallest fraction, and the smallest denominator, has the largest fraction. Our rule works on circles too. That must mean it works everywhere. Let's have a look at this now in real life. Okay, so let's think about this in real life. I have got eight children coming to a party, and that means that I'm going to share my birthday cake, which I've got here, divided through for eight children. So, I'm going to have to cut it into eight equal parts. So, there we go eight equal parts, and every single child will get 1/8 of my birthday cake. Can you see? Eight equal parts. And every... Oh no, they've fallen off. Every single child will get 1/8 equal parts. And every child will get one of those 1/8. The eight equal parts and every child will get one. There we go. This time I have got four children coming to my party. So, here we go. In my children's party there are four children, so I'm going to need to split my cake into four equal parts this time. Here we go, two equal parts, and four equal parts there we go. Let's see if I could show you without them falling off. Four equal parts, and each child is going to get one of those equal parts. So here's my question, Which party, if you were feeling really hungry for cake, would you rather go to? The party where there are eight children and then you get 1/8 of the cake? Larger denominator smaller parts. Or would you rather go to the party with four children, and therefore there's a smaller denominator, and then for a larger part of the cake. Your choice. What would you choose? I hope you've enjoyed the lesson today. But to finish off with, were just going to do a bit of a game show, it's called Would You Rather?. So question number one, and remember the rules that we've spoken about today. Would you rather, 1/4 or 1/5 of you favourite chocolate bar? Have a think. And why? Tell somebody your reason. Question number two. Would you rather, 1/3 or 1/9 of one million pounds? Now the million pounds is the whole remember. So, would you rather have 1/3 or 1/9 of one million pounds? Tell somebody why. And finally, Would you rather have 1/32 or 1/9 of you plate, your dinner plate, filled with wiggly worms for dinner? Hmm, that might depend if you like eating wiggly worms or not. Talk it with your family and see what you think. I hope you've enjoyed this lesson today, and now it's your turn. So, can you make up some similar questions that challenge your family. And remember do they know the rule, do they know that when comparing fractions, the greater the denominator the smaller the fraction, or can you catch them out? Good luck. I will see you on the next lesson.

Reason about comparing unit fractions

Reason about comparing unit fractions

Lesson details

Key learning points

Licence

Video

Lesson appears in

UnitMaths / Working with fractions

Maths