﻿Nice to see you again, my name is Mrs. Coxon, and I'm going to take you through today's maths lesson. I hear you've been doing really well with your fractions work. So to begin with, let's just recap our learning from last time. I know you've been really busy last lesson, looking at examples like this, let's compare these two fractions. Now, if we have a whole and we've divided it into five equal parts and we have all of them, this is the same as one. And if we have another whole and we've divided it into nine equal parts and we have all of them, then this is also equivalent to one. Can you remember what this also tells us about the relationship between five fifths and nine ninths? That's right. We can say that five fifths is equivalent to nine ninths. And when the numerator and the denominator at the same, it has the same play position on the number line as one. So these two fractions are equivalent and they both share the same place on the number line as one, okay. Let's see how you got on with the practise questions from last time. So here we've got some questions with some missing numerators, missing denominators. So let's have a look at the first one. One is equal to how many fifths? How many fifths is equivalent to one? Five fifths, well done if you got that one, right. And the next one, 10, and we've got a missing denominator is equivalent to one. 10, what is equivalent to one? 10 tenths is equivalent to one. The next one, seven sevenths is equal to how many eighths? How many eights is equivalent to seven, sevenths? Eight eighths, well done. And the last one, seven sevenths is equivalent to six, sixths. So give yourself a pat on the back if you've got all of those right. Well done for that. We also gave you a little bit of a challenge to do. Now I'm thinking about this. I can think there'd be so many different answers, you can have where you were asked to complete these questions. I bet you thought of loads of ways you could think to complete these expressions. So I'm going to have a go myself and I could say four quarters is equal to five fifths. I could say that four quarters is equal to 18 eighteenths. I could say four quarters is equal to 91 ninety first. I could say that four quarters is equal to 47 47ths. So long as you've the numerator and the denominator are the same, then you have got all of those right so well done for that, super. Okay, we're going to move on with our learning. Now I've got some other fractions for us to compare, but this time they might not be equal. So here's the first pair. Can you think what sign we could put in the circle to compare these fractions to make this statement correct? It's going to be one of these here. Can you choose which one would need to go into the circle? That's right, one is equivalent to three-thirds. Now one and three- thirds share the same place on the number line. This is my number line showing one, and it also shows three-thirds. What about this pair of numbers, which sign is needed here? That's right, 10 tenths is equivalent to one and here they are on the number line as our 10 tenths, which is equivalent to one. Remember if the numerator and the denominator are the same, they share the same position on the number line as one. Now let's think about this pair of numbers, which sign is needed here? I want you to think about your reasoning this time. So let's think about the correct answer. Four-fifths is less than one. Did you get that right? So what's your reasoning and how can you convince me? So I want you to pause your video and think about what you could write or draw. You could think about where if each of those numbers is on the number line, or perhaps you could use a reasoning sentence, or perhaps you could draw a diagram. So pause the video now and we'll see what you've come up with. Well, I have three friends who shared their reasoning with me about this question. This is what they did. So first of all, this is Will, and Will decided to draw a diagram, to show how four-fifths is less than a whole. He's used a lovely bar model to compare those two numbers. And next we have Ella, this is Ella. And she has decided to imagine where four-fifths and one are on a number line. And she uses this to prove that four-fifths is less than one. And finally, this is Hannah, and she uses a reasoning sentence. And she says that, one whole is made of five-fifths. And four bets is less than five-fifths. And that means that four fifths is less than one. I wonder if you used any of those methods to show your reasoning. Little bit different this time, what about this one? I wonder if you could use your reasoning again, to decide on the missing symbol. We have to think, okay. Yeah, so we've got one eighth and one eighth, and one eighth is less than one. And that's because one is made up of eight to one-eighths and three one-eights is less than this. So three one eighths is less than one. Well done if you got that. Okay, this time I have a fraction story for you. Here's a word problem. And I wouldn't use it again to think about your reasoning to decide if there is any cake left. Here's the story. So here's Will, and Will, it's one fifth of the cake. Hannah and Ahmed eat one fifth of the cake each. Ella eats one fifth of the cake, and Daisy also has one-fifth. I want you to think about, is there any cake left? You might want to pause your video and think about how you can show that your reasoning with that one. Okay, so here's my answer to that one. I looked at one-fifth and one-fifth, one-fifth and one-fifth and one-fifth, which makes it one. So there are five fifths, which is equivalent to one, so the whole of the cake has been eaten and there is no cake left. Did you show that, well done. Okay, we've got a different style of question. Now let's try these. For each path, I want you to think carefully, if each statement is true or false and think carefully about what reasoning you will use for your answer. So you need to pause your video whilst you work through each and remember to justify your answer each time. We'll see how he got on in a moment. Okay, let's have a look at the first one. We've got three-thirds is less than six-sixths. Do we agree with that? No we don't agree with that. What sign should be between those two, do we think? Three-thirds and six-sixths. Well, we know when the numerator and the denominator are the same, it's equivalent to one. Both of those fractions are equivalent to one and that equal to each other as well, okay. But so we'll look at the next one. Eight-eighth is less than two halves. Do we agree? No, we don't agree, do we, no, 'cause eight-eighths again is equivalent to one and two halves is equivalent to one, and eight-eighths is equivalent to two halves, okay. Let's have a look at the third one. One is less than five-sixth. How many six would there be in one? I think six, six would be equivalent to one. Did you get that too? Well done. So that one's correct, because one is bigger, it's larger, it's greater than five- sixth, 'cause one would be six, sixth. And the last one we've got a quarter, add a quarter, add a quarter , add a quarter is greater than one. Do we agree? No, that's not correct either. You should have an equal sign. We've got all four quarters and all four quarters would be equivalent to one. How do we do with that? I bet you did great, super. Okay, fantastic work today. I think you are ready for a challenge. So here it is. We have some fraction statements with missing digits, missing numerators or missing denominators. Can you use the numerals for 10 and nine to make these statements correct? You can only use each digit once, and I want you to pause your video whilst you have a go and we'll see how you got on in a moment. Okay, let's see how we did. Okay, let's have a look at the first one here. We've got eight and we've got a missing denominator. So eight something is less than one. Let's have a look at the first digit, eight quarters is less than one, would that work? No, that wouldn't work. So it's not going to be for there. Let's have a look at the next digit. We've got eight-tenths is less than one? Yeah, that would work. So it could be 10. Let's just check to see if nine would work as well. Eight-ninths is less than one. Hmm, that works as well. So we don't know which one's going to go in there yet, so we're going to have to leave that one. Let's move on to let's do the middle one, okay. So we've got one is greater than so many six. One is great to than four six? Would that work? Yeah, that would work for six, would work in there. What about one is greater than 10 sixth? No, that wouldn't work, that would make that correct. And one is greater than nine six. No, that wouldn't work either. So we know that four has to go in there, correct. So let's have a look at the last one here, one is greater than nine was not going to be four 'cause we've already used that one. One is greater than nine-tenths, would that work? Yeah, one is greater than 9 tenths that would work. What about the nine? One is greater than nine ninths? No, that wouldn't work 'cause one is equivalent to nine-ninth, so we know that 10 has to go there, so our number nine, you will would have to go over here. Let's just check it. Eight-ninths is less than one, that fits as well. Well done, super. Well, it's almost time for us to finish, you've been amazing today. And I'd like to give you one last task to complete before we come back together next lesson. So here we have Yonis and this is his sister Iklan, Yonis has one quarter of an orange and his sister Ikran has three-quarters of an orange. What I'd like you to do is I'd like you to think carefully about showing and convincing me and as many ways as possible, Ikram has more orange than Yonis. And then we'll look to see how you got on in our next lesson, so be ready to convince me. So that's the end of our lesson today and I'll see you next time. Bye.

In this lesson, we will compare two fractions using knowledge of equivalence to 1 whole.

In this lesson, we will compare two fractions using knowledge of equivalence to 1 whole. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Maths

Y4 Maths

Key Stage 2

Year 4

Using Equivalence to 1 to Compare Non-Unit Fractions

Taking fractions further

UNIT

Building wholes

Building and comparing wholes

Building and comparing wholes from different unit fractions

More building and comparing wholes from different unit fractions

Representing non-unit fractions

More representing non-unit fractions

Non-unit fractions in different contexts

Fractions equivalent to one whole

Visualising non-unit fractions

Fractions on a numberline

More fractions on a numberline

Counting fractions

Repeated addition of unit fractions

More repeated addition of unit fractions

Fractions equal to one whole

Beginning to compare non-unit fractions

Use Several Methods to Compare Two Fractions with the Same Denominator

Can We Easily Compare Two Fractions With the Same Denominator?

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

What do you notice when comparing two unit fractions using an area model?

What do you notice when comparing two unit fractions on a numberline?

Use What You Know to Compare Two Non-Unit Fractions With the Same Numerator

Lesson overview:Using Equivalence to 1 to Compare Non-Unit Fractions

Core Content

Taking fractions further: