﻿We will begin today's lesson by going through the practise questions where I left you during the last lesson. You're asked to look at these four questions and decide if each one is true or false. And also to explain why. I wonder what you decided for each one. Let's go through them. One question at a time. Question 1, answer should have been false. The reason why that is false is because we know the greater the denominator the smaller, the fraction. So we know 1/5 is less than 1/3. Question 2 is true. Again, it's using that statement that we know the greater the denominator the smaller the fraction. So one 1/8 we know is less than 1/4. Question 3 is true because we know the greater the denominator the smaller the fraction. So 1/14 is less than 1/13. Question 4, now this one needed a little bit more extra thinking. I wonder what you decided on this one. The answer is false. The fractions and the inequality symbol is correct. It's correctly placed between the two fractions to compare them. 1/6 is less than 1/2. However we need to remember the whole is not the same. When we compare fraction, the whole has to be the same. Right, we are now ready for today's learning. So today we are going to look at the position of unit fractions on a number line so we can compare different unit fractions and see what they look like. First, we are going to recap on some previous learning. You've come across these images before in your lesson where you were filling different unit fractions up the bars. Let's look at the first container. This one is half-full. What I'd like you to do is point to where you think the fluid would roughly come to. Check if you are right, where you've roughly pointed to this position. Well done if you were. Now, let's look at the second container. The second container is 1/3 full. Again, what I'd like you to do is point roughly where you think 1/3 might be, off you go. Fantastic, this is where 1/3 full would be. Is that where your fingers pointing to? Well done, you getting much better at this. Let's try the next one. The next container is 1/4 full, roughly point away where 1/4 might be. Is that where you were pointing? You are getting much more fluent now. Let's move on to the last container. The last container is 1/10 full. Point to where you think 1/10 might be. Right job. I bet you're getting more accurate each time. Well done. Now I'm going to show you what these containers would look like represented on a vertical number line. So here we have vertical number lines. I have marked each number line with 0 and 1 representing one whole container each time. As you can see, half is halfway between 0 and 1. How would you describe where 1/3 is? Think about that. Yes, you're right. 1/3 is 1/3 of the way up between the 0 and 1 number line. How would you describe the position of the 1/4? Sweppy, yes. 1/4 will be 1/4 of the way from 0 to 1. So that means 1/10 will be 1/10 of the way between 0 and 1 from 0 and 1, Well done.

Now we are going to look at unit fractions on a horizontal number line. That's like this first number line. It's marked 0 one end and 1 on the other. This line represent one whole. Now I want you to use information from what we've just done and consider where you would put one whole on this number line. How would you describe the position of 1/2? You would be correct if you said the number 1/2 is halfway along the number line. So it would be right in the middle, right in the centre. When we place half on the number line how many parts is the line divided into? The answer is two. Did everyone get that answer? Well done. The line is now divided into two equal parts. Okay, let's think about our next fraction then, which is 1/3. I'm going to use the sentence stem to help me this time. What I want you to do whilst I'm using the sentence stem is look at the empty number line above and place your finger where you think 1/3 would be positioned on this number line. So the whole is divided into three equal parts and we have one of them. Let's have a look. This is where the 1/3 would be on the number line. Now we move on to our next fraction which is 1/4 when you're thinking about the quarter and visualising where it would be on the number line. Would it be closer to 0 or to 1? Pause the video and tell someone next to you. Hey, let's look at the sentence stem to help us again. The whole is divided into four equal parts this time, and we have one of them. Paste your finger on the empty number line above the position where you think 1/4 would rest, would be closer to 0 than 1/3. Here is 1/4 positioned on the number line where you write. You say that 1/4 would be close to 0 than 1/3. What have you been noticing as we've been positioning these fractions on the number line? Have you noticed that the denominators are getting bigger and the fractions are moving closer towards 0? What generalisation can you come up with here? The greater the denominator, the smaller the fraction and the smaller the fraction becomes, the closer to 0 it will go. In front of you now, you can see a single number line with all the fractions that we have looked at, positioned on it. I want you to pause the video and think about what is same and what is different and anything else that you may notice. Pause the video now and have a go. Let's check then. What is the same? Did you spot that all the numerators were the same? They're all one that is because we are comparing or we have been comparing unit fractions. And what is different? All the denominators are different. We have got 4, we've got 3 and we've got 2. The fractions are 1/4, 1/3 and 1/2. What else did you notice? I wonder if anyone noticed that 1/4 is closest to 0 and 1/2 is more closer to 1. Did you also notice that a quarter has a larger denominator and half as a smallest denominator in the three fractions that we've got positioned on a number line? Well done if you did. We go back to our generalisation now because when we are comparing unit fractions the greater the, the smaller the fraction. 1/4 is the smallest fraction that we have in front of those. 1/2 is the largest fraction. The one with the largest denominator is closer to 0 because it is the smallest fraction. We've done some work together. Now it's your turn to have a practise. I've given them five fractions 1/5, 1/6, 1/7, 1/8, and 1/10. I would like you to position them on a number line like this. I want you to draw five individual number lines and represent each of these fractions on one of the number lines. So start with 1/5 and position it accurately. You have a sentence stem to help you. The whole thing for the first one is divided into five equal parts and we have one of them. So now position the 1/5 on the number line, pause video and complete offline. Okay, so let's look at the 1/5 together now. We know the whole is divided into five equal parts and we have one of them. This is where 1/5, will be positioned on the number line. The next fraction is 1/6. We know the whole is divided into six equal parts and we have one of them. The next fraction is 1/7. The whole is divided into seven equal parts. And we have one of them. Is this what yours looked like on the number line? Is this what your number line started to look like? What were you noticing as you were going through working through each fraction? Let's do 1/8 and then we'll discuss what you may have noticed. Again, the whole has been divided into eight equal parts and we have a lot of them. And this is where we positioned the 1/8. What did you notice about the 1/8 compared to 1/5? You would be right if you said 1/8 is closer to 0 than 1/5 is, because we know 1/8 has got the greater denominator and we know the greater the denominator, the smaller the fraction 1/5 has got a smaller denominator compared to 1/8. So we know 1/5 would be larger as a part than 1/8. So well done if you spotted that I have taken all the fractions or I asked you to place an individual number lines and I'm now going to place them on a single number line so we can start to notice clearly what is going on. So the first fraction was 1/5. Second one was 1/6, the third one was 1/7, fourth one was 1/8, and the final one is 1/10. What do you notice there? Probably you can see that 1/10 is closer to 0 than 1/5 is. And we can go back to our generalisation the greater the denominator, the smaller the fraction. 1/10 has got the largest denominator. So it is closer to 0. 1/5 has got the smallest denominator. So it's furthest away from 0.

We are now going to look at what all the fractions we have previously positioned on the number lines, look like placed on one single number line. So we just start with 1/2, 1/3, 1/4 1/5, 1/6, 1/7, 1/8, 1/9, 1/10. What do you notice about all these fractions? If you spotted that the one with the greatest denominator is closest to 0. You would be accurate, so well done. The one furthest away from 0 is the one with the smallest denominator. So we go back to our generalisation the greater the denominator, the smaller the fraction. So bearing that in mind, this is what I want you to think about. Where would you position these fractions that I am about to give you on this number line. You have got 1/20 1/327, 1/1000, and 1/1,000,000, pause the video and decide where you would place them on this number line. I would also like you to think about. What made you decide on placing them as you did also which fraction would be closest to 0 from the four that you are about to position. Okay, so the fraction that would be closest to 0 would be 1/1,000,000. And then all of the other three fractions would be positioned between 0 and 1/10. So all four of these fractions would position between 0 and 1/10. Where would 1/20 be? You'd be right if you said it would be halfway between 0 and 1/10. That is where 1/20 would lie. So well done. We know the fraction with the greatest denominator will always be closest to 0. So in this case it would be 1/1,000,000

It's time for us to finish. Well done everyone. You've worked really hard today, but before we go I would like to leave you with a task to complete before we come together for next lesson. You've got three parts to this task. The first one is a missing symbol problem. You have got pairs of fractions to complete. Using equality symbol to compare the pairs. You may want to draw a number line to show your depth of learning. For the second part, you're asked to audit a set of fractions from smallest to largest. Again, you may want to draw a number line to support your developing understanding. Always remember our generalisation the larger the denominator, the smaller the fraction. The ones with the largest denominator will sit closer to 0. And in the last one you're asked to fill in a missing number. So you're asked to fill in the missing digit to make each statement true. Have a go.

In this lesson, we will compare several unit fractions by placing them all together on a number line. We will make generalisations around the denominators of unit fractions.

In this lesson, we will compare several unit fractions by placing them all together on a number line. We will make generalisations around the denominators of unit fractions. 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

What do you notice when comparing two unit 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

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?

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

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

Core Content

Taking fractions further: