﻿Let's begin today with going through the practise activity that you were left with at the end of last lesson. You were asked to look at this set of fractions and to plan some question or activities for a friend. What could you ask them to do that will help them to understand ordering and comparing fractions with the same denominator? I'm sure you've all worked really hard and have come up with some brilliant questions and activities. I'm going to share with you some of my examples. I wonder if they are similar to yours. Here are a few of the examples that I recorded. The first one is in the context of a word problem. I've put all the fractions that were given into a word problem. Sally ran 2/8 of a one kilometre race. Jo ran 1/8 of the kilometre. Ryan ran 5/8 of the kilometre. Maj ran 7/8, and Salma ran 4/8. Order the runners from the shortest to the longest distance ran. The next one, I asked my friends to order them from the smallest to the largest, looking at the denominators, they're all the same, and then they have to really pay attention to the numerator in order to order these. In the next one I asked them to order them from the largest to the smallest. I'm sure you had plenty of other ideas as well. Well done for having a go. Time to focus on today's learning now. We are going to compare fractions where the numerators are the same. We are going to do this by using area models. You've got two area models in front of you. I would like you to write down the fraction notation that is represented by these area models, then I would like you to use the inequality symbol to compare the pair of fractions that you've written down. I would also like you to reflect on these two questions as you are doing this. What do you notice about the wholes? And what do you notice about the parts? Pause the video now and have a go. Let's check then. Did you write down 1/9 for the first area model? The whole is divided into nine equal parts and one part is shaded. Did you write 1/6 for the second area model. The whole is divided into six equal parts and part is shaded. Is this how you positioned your inequality symbol, 1/9 is less than 1/6? Well done if you did. What did you notice about the wholes? I wonder if you spotted that the wholes are identical, because when we compare fractions, the whole has to be the same. What did you notice about the parts? Did you notice, in 1/9, the parts are smaller, in 1/6 they are bigger? Now I want you to consider these two questions. What can you tell me about the numerator? And what do you notice about the denominator? Well, when you look at the numerator, they are both ones, because we are comparing unique fractions. When you look at the denominator, you've got one denominator that is larger than the other. 1/9 has got a larger denominator than 1/6. Well done for spotting that. Here is another pair of area models that I want you to look at now. Again, I want you to look at the area models and write down the fraction notation that each of them represents. I would also like you to use the inequality symbols to compare the pair of fractions that you've written down. I want you to reflect on these two questions again and consider what do you notice about the wholes, and what do you notice about the parts? Pause the video now and have a go. Again, let's check. Did you write down 1/4 for the first area model? The whole is divided into four equal parts and one part is shaded. Did you write down 1/5 for the second area model? The whole is divided into five equal parts and one part is shaded. I wonder how you positioned your inequality symbol. Did it look like this? Well done if you did. 1/4 is greater than 1/5. Again, what did you notice about the wholes and what did you notice about the parts? Yes, you'd be right in saying that the wholes are exactly the same size. Well done. And what did you notice about the parts? Yes, the parts in 1/4 are larger than the parts in 1/5. Well done for spotting that. Again, we have unit fractions that we are comparing. We can see the denominators are different. We have got four in 1/4 and five in 1/5. Now we can start to think about a generalisation. When we compare unit fractions, the greater the denominator, the smaller the fraction. Here is another example for you to work through to make sure you are really developing fluency in this learning today. You've got two area models in front of you. What I would like you to do is write down the fraction notation that each area model represents. I would then like you to use the inequality symbol and compare the pair of fractions that you've recorded. Again, I'd like you to reflect on these two questions. What do you notice about the wholes, and what do you notice about the parts? Pause the video now and have a go. Time to check. Did you write down 1/6 for the first area model? You would be correct, the whole is divided into six equal part and one part is shaded. Did you write down 1/3 for the second area model? The whole is divided into three equal parts and one part is shaded. And is this how you positioned your inequality symbol? Fantastic if you did, because 1/6 is less than 1/3. What did you notice about the wholes and what did you notice about the parts? You'd be correct in saying the wholes are the same size and the parts, in the 1/3, the parts are larger than the parts in the 1/6. What do you notice about the denominators again in these two fractions that you've written down? Yes, 1/6 has got the larger denominator and 1/3 has got the smaller denominator. Again, we can consider the generalisation. When we compare unit fractions, the greater the denominator, the smaller the fraction. And we can see that the 1/6 has a greater denominator and the fraction parts are smaller than 1/3. Now here's ones for you to do on your own. You have got pairs of fraction here. What I would like you to do is look at the denominator, compare the fractions, and fill in the missing symbols. You have got the symbol less than, greater than, or equal to. Pause the video and have a go. Remember your generalisation statement. When we compare unit fractions, the greater the denominator, the smaller the fraction. Pause the video now and make start. Let's go through the answers. How confident were you in comparing these pairs of fractions? Let's look at the first one. 1/6 with missing symbol and 1/9. Well, which one has got the greater denominator? It's 1/9. We know the greater the denominator, the smaller the fraction. So the inequality symbol for that one should have looked like this. We know 1/6 is greater than 1/9. Let's look at the second fraction. 1/8 and 1/3. Which one is smaller? Did you position your inequality symbol like this? If you did, you are accurate, because eight has got the larger denominator and we know the larger the denominator, the smaller the part, therefore the smaller the fraction. Now let's look at the next one. 1/10 and 1/4. 1/10 has got the larger denominator, so we know that is a smaller fraction and this is what the inequality symbol should have looked like there. The next one, we have 1/7 and 1/12. Comparing these two fractions, we can see that 1/12 is the larger denominator, therefore we know it is less than 1/7, so 1/7 is greater than 1/12. If you got all four of these right, you have become really fluent with this and you should be very proud of yourselves. Well done. It's almost time for us to finish. Well done, everyone, for working so hard today, but before we end this session, I want to leave you with some practise questions. These are true or false questions. I want you to go through each one and consider whether they are true or false. Think about all the learning that you have done today and remember the generalisation. The greater the denominator, the smaller the fraction. Go back on the video if you need it to help you and try your best.

In this lesson, we will compare two unit fractions using an area model. We will make generalisations around the denominators of unit fractions.

In this lesson, we will compare two unit fractions using an area model. 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 using an area model?

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 on a numberline?

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 using an area model?

Core Content

Taking fractions further: