﻿Hello, my name is Missus Chambers and I'm so excited to be teaching you today. In your last lesson with Missus Coxon, you were focused on finding fractions that form different parts of the whole and fractions that are equivalent to one whole, by finding a numerator that is small or large relative to the denominator. For your practise activity, you are asked to complete this table, let's have a look at it together. The table is split into four columns, there they are. And three rows, and each row contains a denominator. Let's have a look at the first of these column headings in more detail, you can check your answers as we go through. I've added the bar below the chart to help me think about this problem. I like to have a visual to help me do this. Why do you think the bar I've added has 18 equal parts? Yes, you're correct, because the denominator is 18. So the whole has been split and 18 equal parts. So the first part of this table asks me to identify a unit fraction, so just one of the equal parts. So what do I need to do to my bar? Yes I need to shade in one of the parts, I'm going to do that now and I'm going to shade it red, okay? So you can see that I have still got 18 equal parts, but one of them is shaded red. So what will the numerator be on my fraction? Yes the numerator is going to be one, this is what the fraction will look like, there we go. So the second column of this table asks me to identify a fraction that is quite a small part of the whole. I'm using the same bar because my denominator is the same, all of the denominators are 18. So this bar can remained the same. Can I use the same bar as last time with one coloured? Have a little think. Yes I think I could, I could use one, 18th, that is a small part of the whole. Is there a different fraction that I could use to answer this? Yes, there are, there's a range. So the answer could be anything between one, 18th and halfway, so nine, 18th. I'm going to choose four, 18th, but your answer might be different to mine. It needs to be between one, 18th and nine, 18th. Let's have a look and see what it looks like on my bar. Let me just check, is there a small part of the whole? Yes there is, so I'm going to put that to numerator, into my fraction so it's four, 18ths, great. Okay, the third column of this table asks me to identify a fraction that is quite a large part of the whole. Could I keep my bar the same as last time with four shaded in? Let me think, a fraction that it's quite a large part of the whole, I don't think I could, I think it needs to be greater than half. Is there a different fraction that I can use to answer this? Are there a range of different fractions? Well actually, the answer could be anything between nine, 18ths and 18, 18ths. I'm going to choose 13, 18ths, but your answer might be different to mine, but it needs to be between nine, 18ths and 18, 18ths. I'm going to show you what that looks like on my bar. Okay, let me check. Yes, it's definitely a fraction that is quite a large part of the whole, I'm happy with that. So I'm going to put 13 as my numerator, there we go. Okay, so the final column of this table asks me to identify a fraction that is equivalent to one whole. Think about the lesson that you did with Missus Coxon, when the denominator and the numerator are the same, then this is equal to one whole. It means the whole of the bar has been shaded, okay? Is there more than one answer that I could use for this one? Have a pause and have a think. No, I don't think you can, I think that that if every single part of the bar needs to be shaded, to be equivalent to a whole, then there is only one answer and that answer would be 18, 18, so let's just check. Yes, the entirety of my bar is shaded and the numerator is 18, there we go. So the next part of the table shows fractions with a different denominator, you can see that row. Okay, so this time my denominator is, yes you're right, it's seven, so I'm dealing with seventh this time. How could I use what I did with 18th to help me complete the next part of the table. What would my whole look like? I'm going to use a bar to show it, to represent this because it helps me with my thinking, it helps me to really structure my thoughts and helps me to visualise. So here's my bar. Yes, you're right, it was separated into seven equal parts. Okay, so how did I use the bar last time when I was there dealing with 18th to show a unit fraction, I shaded in just one apart and then my numerator was one of those parts, so one, seventh, okay. Other than use the bar to find a fraction, that's quite a small part of the whole. Well, I use sort of halfway and thought, oh, it must be smaller than that. So with sevenths, it could to be one, seventh, two, sevenths or three, sevenths. I'm going to use three, sevens, but you could choose any of the ones I just mentioned. And then when I was looking for a fraction, that's quite a large part of the whole, I used halfway again and thought actually it needs to be more than halfway, so I could use four, sevenths, five, sevenths, six, sevenths, could I use seven, sevenths? No you're right, seven, sevenths would be the whole. So it wouldn't be a large part, it will be the entirety of the whole. So this time I've chosen to use six, sevens, but you could use four, sevenths, five, sevenths or six, sevenths and then as I've just said, that fraction that's equivalent to a whole would be the numerator and the denominator exactly the same seven, sevenths. Okay, have a look at the next part of that table. So this time we're dealing with 30ths. Okay, so I need you to visualise an estimate 30ths. Can you do that in your head? I'm not going to use a bar this time. Okay so I can see in my head, a bar that separated into 30 equal parts. So a unit fraction would be one of those parts. So it must have a numerator of one. Okay a fraction of that's quite small part of the whole or half way would be 15, 30th, so anything that's between one, 30th and 15, 30th, I've chosen 10, 30. And so a function that is quite a large part of the whole, okay, so I need to use halfway again, which is 15, 30th and it needs to be up to, but not including 30, 30th. So if you've got a fraction between 15th, 30th, and 30, 30th, then you are correct, I chose 20, 30th. And then I now know that in order for a fraction to be equivalent to a whole, the denominator and the numerator needs to be identical. they need to be the same, so it must be 30, 30ths. Now, I would like you to use the visualise and estimating skills you've been developing in past lessons. Look at the yellow square, I wonder how much space in the oval it takes up. Is it quite a large part of the whole? Or is it quite a small part of the whole? Take a minute, I have a real big think about that. What did you think? How much space does the yellow square take up? Is that a large part of the whole or a small part of the whole? Pause the video to decide. What did you decide? At first I thought, it was quite big and then I had to relook at it and thought, oh, actually I think it's quite a small part. I think there's quite a lot of space around it, I think I could probably get another one in, what did you think? So Meg and Raz are trying to estimate what fraction of the oval is yellow. So, just identify, what is the whole? That's right, the oval is the whole. And what is the part? Yes, one of the parts is yellow. Okay, so Meg and Raz estimate what fraction of the oval as yellow, this is what they think. Meg thinks that it's a third and Raz thinks that it's a 10th. How can you use your visualising and estimating skills to help them decide? What do you think? Pause the video and have a little think too. Okay, I had a little think about this too, I was finding it really difficult to visualise what Raz's fraction look like, so, I made an oval. So here's my oval, okay? And I had my square, okay? And I tried to make it the same size, so can see that it takes up the same mass about size. And then I thought, how many squares would I need to have, if it was Raz's fraction that was correct? And it looked at the denominator and thought, actually I'd need to have 10 squares. So there's two squares, three, four, five, six. I'm not going to go any further because if you're using your visualisation techniques, do you think that Raz is accurate? Okay, and then has Mag's, so she had one square, here's my oval again, one square, two squares, three squares. Okay. So, who was more accurate and why? Pause the video and discuss? What did you think? Okay, so you think the Mag was the more accurate and why? Okay, so she has got one third that this yellow square is covering ones third of the oval and there's two-thirds that are left empty, is that what you thinking? Okay, let's just see. Who is correct then? How do you know? So you were saying before that you thought that Mag possibly, how's that it was closer? How do you know that? So how do you know that there is two thirds left and one third in the middle? Okay. I will need to visualise two of those squares onto my oval, so there's my oval and there's one square. Try and make it out of that and two squares. Now I can see that I've got some gaps around. Okay, so can I fit a full square in? But I definitely could start to visualise how it could cut out a square and then fill the rest of the shape, so I agree. I think that Mag is correct, let's see what answer was. We were right, it was Mag. So you'd need to be able to visualise two of those squares onto the oval and then see that you could caught up another square to add it around. Whereas Raz needed to have 10 squares on that and that just would be way too many squares. Okay. So here's an activity for you to do. So in your house, can you find a plate? It could be a side plate or a dinner plate, it might be better to have a smaller plate. I would like you to ask the mate, how many biscuits it would take to cover the plate and I would like you to try it. Okay, so I would like you to pause the video. I would like to go and find a plate and I would like you to cover the plate with baskets, okay? Press pause now. It's lovely to have you back. So what fraction of the plate wouldn't one biscuit cover? So have a look at your pieces of biscuits, okay? What fraction of the plate would one biscuit cover? Yes you're right, the numerator would be one, the denominator would be the total amount of biscuits on the plate. Okay, so it will be a unit fraction. What about or three biscuits? Would this be quite a small part of the whole? Or quite a large part of the whole? I think this would very much depends on the size of your plate, because if you have a very small plate, three biscuits might be quite a large part of the whole, but if you've got a really huge plate, it might be quite a small part of the whole. So, which was correct for you? Well done. So, are you ready for this challenge? I was going to ask you two questions, what would happen if you used bigger biscuits and can you use a range of different size biscuits together? Why? Okay, we'll discuss those answers or with the person teaching you next time. It's been a pleasure to be here, thank you so much and enjoy the rest of your day, thank you.

In this lesson, we will visualise and estimate non-unit fractions using a variety of visual representations.

In this lesson, we will visualise and estimate non-unit fractions using a variety of visual representations. 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

Visualising 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

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

Using Equivalence to 1 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:Visualising non-unit fractions

Core Content

Taking fractions further: