Primary Maths KS2

The lesson we are deconstructing is a Year 4 lesson on representing fractions, it is the first lesson of a four week unit.

Recognising fractions as different representations

Maths

﻿Hello, welcome to today's fractions lesson with me Ms. Jones. Hope your minds are ready and your thinking caps are on and let's get started. In today's lesson we'll be looking at recognising fractions as different representations. We're going to start off by thinking about what kinds of representations can we use to represent fractions. Then we're going to play a little game of fraction match. Then we're going to develop that understanding a little bit further. And do our task and our quiz. It might even be a special challenge in there today. For this lesson, all you'll need is a pencil or pen and something to write on. So a pencil on a piece of paper is absolutely fine but if you haven't got one, go and get one now and then come back. Okay, if you've got everything you need, let's get started. Okay, I'm going to start by thinking about representing a fraction using a whole. This rectangle is my whole. I'm going to divide this rectangle into four equal parts. I've divided my rectangle into quarters. I know they are quarters because I've got four parts and they're all equal size. How else could I have divided my rectangle into quarters? Pause the video now and use your pencil and piece of paper or your pen and piece of paper and jot down some other ideas. Okay, hopefully you've had a chance to jot down some other ideas about dividing this rectangle into quarters. I'm going to show you some of my ideas. So I've got my rectangle again, and I've divided it into quarters in a different way. Have I got four equal parts? Yep, four parts. And they're all equal size. So this is divided into quarters. You can do it in another way. This time I've divided into quarters slightly differently and I've got four horizontal lines. I've got four parts and they're all equal size. Some one more, you might've done some different ones and that's okay. I've started off the same way as this one so I know that this is a quarter, and I've then done this again, but then I've divided my bottom two parts in a slightly different way. Now is my shape showing quarters this time? Have a little think, but yes it is. Now although my parts do not look exactly the same shape, they are all equal size. And if we were to cut these up, these longer strips we could place part of that strip on top of each other and it would actually make this rectangle here. They're equal size, not equal shape but we're still showing quarters here. So all four of my rectangles here show four equal parts or four quarters. Let's have a look at a different shape, this time we've got a circle. Now, can you tell me which of these show quarters? Okay, and when you're doing your explanations, you can either speak out loud to the screen or you can jot them down, completely up to you. So, hopefully you've decided that this one on the left is showing quarters. Let's think about what quarters are again. We need four parts and they all need to be equal size. Here I do have four equal parts. So it is showing quarters. Now my circle on the right, we have got four parts, one, two, three, four but they are not equal size. Therefore, this isn't showing quarters. Now both of my circles here you could say are showing four quarters. If I wanted to represent one quarter, for example I might talk about how many parts are shaded blue. Here I've got one part shaded blue. One quarter is shaded blue. One part out of the whole, which is four parts. Okay, so far we've looked at a whole and we've divided it into parts. We've looked at a shape such as a rectangle or a circle. But how else can I represent fractions? Have a little think, and then we'll go through some ideas. A fraction can be parts of a whole. So this is what we've already had a look at. We've got a rectangle which represents our whole. It's divided into four equal parts. Here, three of those parts are shaded. So we could say this is representing 3/4. If we're asking how many parts weren't shaded it could represent 1/4, but let's say this represents 3/4. If we're representing 3/4 on a number line or as a number, we might represent it like this. We know that 3/4 is less than one and greater than zero. So I've put zero and one as my two end points of my number line. The middle point represents a half so I know that 3/4 would represent the points in between 1/2 and one whole. We could represent our 3/4 as a result of division. A fraction can be represented as a division problem. Here we've got three pizzas shared between four people, which we could write as three divided by four. Now three divided by four is equal to 3/4. We could also write our fraction as part of a set. My whole is four. I've got four apples, but I'm talking about or I'm identifying here three of them, three out of four. A fraction can be part of a set. Let's look at a different fraction. Here we've got 4/5. Now, if I'm representing this as part of a whole, I've got five equal parts this time, cause I'm using fifths, and I'm going to shade in four of them. My shaded part shows 4/5. On a number line, again I know that 4/5 is less than one and greater than zero. I've divided by number line into five intervals. I can count in fifths, one, two, three, four fifths would be represented here. Let's look at parts of a set. So I've got five apples. Five is my whole, and I'm going to identify four of them. I've identified 4/5 of the apples. And as a result of division, four divided by five is equal to 4/5. Okay, time for that that game I told you about. This is called fraction match. I want you to sort these cards. Now you might not have the cards with you physically so you can jot them down on a piece of paper. Now these cards either represent 3/4 or 1/5. Can you tell me which of these represented 3/4, which of these represent 1/5? Pause the video now to have a go at your task and then I'll go through the answers. Okay, you should have had a go at your fraction match, explore task. So, representing 3/4, let's have a look. We had these cards. So we have 3/4 on a number line. We've got four equal intervals here and the arrow's pointing to 3/4. This one represents 3/4 as part of a whole, three parts out of four are shaded and they're all equal parts. Here we've got 3/4 represented as division. Three divided by four is equal to 3/4 and a set. Three of these circles are shaded out of four. Then the others represented 1/5. So we've got one part shaded out of five equal parts. Here we've got another part of a whole. So we've got one part shaded out of five, a number line, this pointing to 1/5 on our number line. And finally, we've got our fraction representation here. Now there's written representation of a fraction of a numerator and denominator. We're going to have a closer look at in the next part of the lesson. Okay, so when writing a fraction the first thing we often write is this horizontal line. This is called a vinculum. It's the horizontal line that separates our top number, which is called our numerator and our bottom number, which is called our denominator. You might not have heard the word vinculum before. It's not something we use outside our math lessons. Let's have a go at saying it, vinculum, your turn. I think you've got it. Okay, the next thing we think about writing is usually our denominator. Our denominator in this instance is five and tells us the number of equal parts in the whole. So looking back at our representation we had five equal parts in our whole. Here on our number line, our number line is split into five equal intervals. Then we think about our numerator. How many of those parts are we referring to? So if we're thinking about what fraction is shaded, only one was shaded, one out of five. The numerator needs to be one. The arrow here is pointing to where 1/5 would be on the number line. Let's Look at it in a different fraction, this time 2/5. Got two representations here. Do they represent 2/5? Hmm, when thinking about it, let's think about what our denominator means and our numerator. The denominator tells us how many equal parts. Now both of these are split into five equal parts. I've got five stars, equal size. And my rectangle is split into five parts. So both of these are representing fifths. My numerator is representing, shows two. So I'm referring to two of those five parts. So if I'm thinking about the stars, I could say 2/5 of the stars are shaded. If I'm thinking about this rectangle, hmm, actually 3/5 are shaded. However, you could argue that this is showing 2/5 but only if you're talking about the parts not shaded. 2/5 of the rectangle are not shaded. How else could we represent 2/5? Or we could use a number line? So this arrow is pointing to where 2/5 would be. I've got five equal intervals here. 1/5 would be here, so 2/5 would be here. We could also think of it as a division problem. Two pizzas shared between five people, each would get 2/5 each. Two divided by five is the same as 2/5. Okay, it's time for your independent task. Now, what I want you to do here is take each fraction and represent it in four different ways. So it could be as part of a whole, part of a set, as a division problem, or it could be on a number line, okay? Or you could do multiple versions of the same type of representation. So do that for each of the fractions. Once you finished, you should find a challenge on your independent task. Pause the video now to go and do your task. When you're finished, come back here and we'll look at the challenge together. Okay, hopefully you've had a go at your independent task. Now, as the last question I sent you a challenge, I said, which does not represent 3/5? And the tricky part here is really getting that explanation correct, with the correct language. So let's look at each representation one by one. Here we've got our number line representation. Is our number line split into five equal parts? It is, and we can see we've got zero and one. So we do know that 3/5 is less than one and greater than zero. So this would be 1/5. This would be 2/5. And the arrow is pointing to 3/5. Let's look at our second representation. Got a rectangle, we need it to be split into five equal parts. Now it's split into five parts, but they are not equal. So we cannot say that this rectangle is showing or the shaded part is showing 3/5. Looking at our third one, we have five apples. Three of them have been identified. So 3/5 of the apples have been circled. So the answer was definitely this middle one, but you need to make sure you've got your correct explanation. This representation does not show 3/5 as the parts are not divided into five equal parts. Now for your independent task, hopefully you drew some wonderful representations. If you'd like to share these, please ask your parent or carer to have a look at our social media and tag LearnwithOak. It's time now to go and complete your quiz. Thanks guys, see you soon.

Which image does not show a shape divided into quarters?

Which representation shows three quarters?

What does the denominator tell us?

What does the numerator tell us?

What is the line between the numerator and denominator called?

In this lesson, we will explore different ways of representing fractions including as part of a whole, as a number, as a result of division and as part of a set.

Y4 Maths

Key Stage 2

Year 4

Miss

Fractions

Number

THEME

UNIT

Calculating unit fractions of quantities

Recognising  equivalent fractions

Recognising equivalent fractions (2)

Calculating non-unit fractions of quantities

Equivalent fractions

Fractions and division

Comparing fractions

Ordering fractions

Using mixed numbers

Using improper fractions

Converting mixed numbers into improper fractions

Adding fractions (up to one whole)

Subtracting fractions

Adding fractions (with a total greater than one)

Subtracting fractions (2)

Comparing non-unit fractions of quantities

Reasoning with fractions

How else could I write five halves?

What is the sum of the fractions?

Which is greater?

What mixed number is being represented?

Calculate:

What improper fraction has been represented?

A packet of paper has 261 sheets. Two thirds of the packet has been used. How much paper is left?

ITT: Recognising fractions as different representations

Primary Maths KS2

1. Original Oak Lesson