﻿Hi, my name is Mrs. Chambers and I'm really excited to be teaching you today. In last lesson I sent you a challenge. I asked you to find a plate and cover it with biscuits and together we discussed what fraction one biscuit would be and what fraction three biscuits would be. The next part of the challenge was to see what would happen if you used bigger biscuits. What did you find out? Yes, the bigger the biscuits, the more space it took on the plate and therefore, we needed less biscuits to cover the entire plate. Well done. Okay, what about the next question? So can you use a range of different size biscuits together and why? Can you do that? Did you find out? No, you can't. Why? Well, let's remember our stem sentence. The whole has been cut into so many equal parts. Different size biscuits would not provide us with equal parts. The parts would be unequal. I'm so glad that you've completed the challenge. Let's move on to our new learning. We're going to be learning about fractions as numbers. Have a look at this glass. What do you notice about it? Yep. It is the same size all the way up. Anything else? Yes, it has marks drawn on it. Can you see how many parts this glass has been divided into? Yes. That's five equal parts. I'm going to start to pour the liquid into the glass and I want you to say stop when the container is one fifth full. Stop. Okay. So what have I got in my glass? How full is it? Yes, it's one fifth full. Let's have a look on the screen. So here's my glass. It's been separated into five equal parts and I am going to pour water in to one fifth of those parts. And there's my notation to show one fifth. Okay. I'm going to carry on pouring now and you see if you can tell me how much water I now have in my glass or how much liquid. Okay. Let's stop just about there. How much do you think I have? Yes, I have two one fifths. Or I can say two fifths. And on the slide? There we go. And there's the notation that shows two fifths. Is this a fairly small or a fairly large part of the whole? What'd you think? Yes. It's a fairly small part of the whole because it is less than halfway up the glass. Carry on. How much liquid do I have in my glass now? Yes. Three one fifths or three fifths. Here it is on the slide. Okay. And now. Yes, I have four one fifths or four fifths. Is that a large part of the whole or a small part of the whole? Let's look on the slide and see if it helps us. Okay, there it is reaching four one fifths. We write that as four fifths. Is that a small part or a large part of the whole? Yes, I agree. It's a large part of the whole. Okay, and finally now. Okay. Yes, the glass is completely full. I left a little up at the top so it does not overflow. So this is five one fifths or five fifths. So the whole of the glass is full. Let's see on the screen. Here's our notation. Okay, so the whole of the glass is full. Okay, what is the same and what is different about these two representations? So have a look at the one on the left and the one of the right and compare them. Pause the video so you can have a little chat. Okay. So what did you find out? What's the same about them? Well, both of them the whole has been divided into five equal parts. On both of them, the fraction notation is the same as the fractions from one fifth to five fifths and the representations are the same size. So both of them are showing the same size blocks. What about what's different? Yes. There's something different in the notation. On the one on the right-hand side, there is a zero on the baseline. Okay, so on my container that would show us where the contents would come to if the container was completely empty. So it's a baseline that shows us, that zero that shows us that there are no fifths. Okay. Well done. So does this notation remind you of a maths structure that we often use? How about now? How about now? What's the same and what's different about these three representations? Pause the video and have a little talk about it. Okay. They are all the same size, they are all divided into five equal parts and they all start at zero and end with one whole or five fifths. What's different? The orientation. Two of them are vertical and one is horizontal. Let's look at this using a strip of paper. So here I've got my number line. Okay, you can see with my peg. I'm going to move up so I've got one fifth, two fifths, three fifths, four fifths, five fifths. Okay. Let me take my pack and put it back down at zero and then I'm just going to turn it around. So I didn't do anything to it, I just turned it around, change the orientation back and still continue to count. So there we've got zero, one fifth, two fifths, three fifths, four fifths and five fifths. Okay. So it didn't do anything to the number line at all. All I have to do is turn it around that way or turn it around that way. It stays exactly the same. Okay. So let's look at this number line. It's called fractions as part of a whole. It is showing a line that has been divided into five equal parts. So each one of those equal parts is worth one fifth. As we move along the number line from zero to one fifth, two one fifths, three one fifths, four one fifths and five one fifths or one whole, we can see that as we move along the number line from zero, the amount of fifths that we have increases, increases each time we move along the line. Let's have a look at the next one. So when we're using a number line, each point represents a number. The number zero, the number one fifth, the number two fifths, the number three fifths and so on. There we go. We can see those fractions on the point. Okay. So any part that is below one fifth is less than one fifth and any part that is above one fifth is more than one fifth. On the slide there are three representations of tenths. You can see them really clearly on two of the representation's but on one it's less clear. So within the circle you can see that the circle has been divided into 10 equal parts and each one of those is labelled one tenth. On the number line, you can see that the number line has been divided into 10 equal parts and each one of those has been labelled a tenth. With the shapes, it's harder to spot the tenths. So how could we do that? Yes, we could think back to all the lessons and start to try and visualise. So can you see 10 equal parts anywhere? Yes, I can too. I can see that there are 10 columns on two rows but I can see that there are 10 columns and within each of those columns there are two shapes. So for every tenth it must be at one column or two shapes. Let's see what happens to these columns and let's see what happens to the circle when we move along the number line. When we start at zero, you can see that none of the shapes is shaded and none of the parts of the circle are highlighted. That's because we're at zero. Once we move from zero and stop to travel along the number line, we should increase the amount of shapes and increase the amount of shaded parts of the circle. Let's see if that happens. Okay, so we've gone from zero to one tenth and we can see that two of those shapes have been shaded and one of the parts of our circle has been shaded too. Let's move along a bit more. Here we go. We're at two tenths. You can see that two columns of the shapes have been shaded and two parts of the circle have also been shaded. Three tenths? That's right. So we now have got three columns of the shapes. So although we've got six shapes, we have got three columns of shapes and we have three parts of our circle shaded. Okay, make a prediction. What's going to happen when I move to four tenths? Exactly. Four columns of our shapes will be shaded and for parts of our circle. Let's just check. Brilliant. Let's move to five tenths, and six tenths, and seven tenths. So we've got a larger part of our fraction now that is shaded, either in our shapes or our circle. And we are a long way along the number line. Here we go to eight tenths, nine tenths, and we know that when we get to the numerator and the denominator being the same, then the whole should be shaded. So all our shapes, all our parts of our circle and right away to the end of the number line. Let's just check that that happens. There we go. We were right. Now, here's your practise question. So can you draw your own number line to represent tenths? How could you keep the parts equal? If you're using a ruler, each part might be a centimetre long and then you could have 10 centimetres. Can you draw 20 dots? And then can you identify where four tenths would be on both of your representations? Okay, you need to be drawing your own number line to represent tenths, draw 20 dots and then identify where four tenths would be on both of your representations. Are you ready for a challenge? Can you represent four tenths in a range of different ways? Think back to some of the representations that you've seen in other lessons. It's been a pleasure being with you today and have fun with your challenge question.

In this lesson, we will represent fractions as numbers on a numberline. We determine where on a number line a unit fraction might sit, and compare fractional representations in different formats.

In this lesson, we will represent fractions as numbers on a numberline. We determine where on a number line a unit fraction might sit, and compare fractional representations in different formats. 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

Fractions on a numberline

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

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:Fractions on a numberline

Core Content

Taking fractions further: