﻿Welcome back everybody, it's Mrs. Coxen again and I'm here to take you through today's lesson. So today's lesson, you will need a pencil and a paper. But before we start today's lesson, let's begin with the task I left you with last lesson. You have this fraction story and I asked you to find as many different ways as you could to show that Ikran has more orange than Yonis. I wonder how you got on, and if you've found all the different ways you could show this. Well, let's see if we can find out. Okay, well here's one method. You could have drawn two circles to represent the orange. and shaded in one, one quarter to show what Yonis had. And and three one quarters on the other one to show what Ikran has. And this will visually prove that one, one quarter is less than three, one quarters. Now, we can now put in the inequality sign symbol between the two fractions, to show that one quarter is less than three quarters. Now, if you didn't draw a diagram, you might have chosen to use a number line so that you could draw a number-lined position, one quarter and three quarters. And we've shown fractions on a number line before. So let's read the fractions on the number line together. We have zero. We have one quarter, we have two quarters, three quarters, and four quarters, which we know is equivalent to one. So what do you notice about one quarter and three quarters? Yeah, 'cause one quarter is closest to zero and three quarters is further along the number line. We can also see, that the further along the number line we go, the numerator gets larger. And this helps us compare the fractions by looking at the numerator. We know that three is larger than one. Therefore, one quarter is less than three quarters. Now some of you might have used your verbal reasoning to help prove and convince me. So I'm going to use this STEM sentence to help me. You might want to join in with me. So one quarter, is one lots of one quarter and three quarters is three lots of one quarter. Now I know that one is less than three. So that one quarter is less than three quarters. Well done. Did anyone use this model? This is called the quantity model. We have drawn four one quarters. Three, one quarters have been circled to show what Ikran has. And one, one quarter has been left to show what Yonis has. Three quarters of an orange is more than one quarter of an orange. And again, we can use our inequality sign to show that one quarter is less than three quarters. So we've looked at using method one, method two, method three, and we used our quantity model. For the examples that follow, I think we will have a look at using these three methods to show our understanding of which fraction is greater and which is less than the other. So we're going to use these three methods, to be able to compare our fractions and prove and disprove. Okay, let's have a look at another fraction's story here. So, Polly has done three eighths of her homework and Ola has done five eighths of her homework. Who has done more? You need to show that Ola has completed more of her homework than Polly has. Well let's look at those fractions for a moment because can you spot something that's the same and something that's different? Yeah, they've both got the same denominator, haven't they? They've just got different numerators. So can you see my diagram there? I wonder if you could copy that down, and pause your video so that you can sketch in and colour in on there to show that Ola has competed more of her homework than Polly has. Just pause your video while you do that. Okay, how did you get on? Well, my diagram looks like this. Does yours look like this or does it look a bit different? It might look a bit different, and that's okay. Some of you might have collared in different parts. So as long as you've coloured in one bar with three coloured in total and the other bar with five coloured in total, that doesn't matter which parts you've coloured in. So what do you notice about the numerators? Yes, we've said that, you were right. Three is less than five. So three eighths is less than five eights. Can you put their missing equality symbol between your two fractions to show this? Well done. Now let's show the same pair of fractions on a number line. So I have marked the number line for you. What I want you to do is to pause the video and place the arrows to show the position of the two fractions, okay? So you might want to sketch the number line in front of you. And pause the video while you do that. Okay, have you marked them on there? Let's see how we did. So we've got three eighths there, we've got five eighths there. So we can see that three, one eighths and five, one eighths. And we need to put in the missing inequality symbol to show this, so which one do we need to put in there? Three eighths is less than a five eighths, fantastic. So what part of the fraction tells you this? Yeah, so that's correct, it's the numerator. So, 'cause I know that three is less than five. So three eighths is less than five eighths. And finally we've got our method three, our verbal reasoning method. So, here we have our statement. "Polly has done three eighths of her homework and Ola has done five eighths of our homework." I wonder if you can pause the video now to see if you can fill in the missing part of our STEM sentence. So just pause your video while you fill in the missing bits. Okay, how did we get on? Let's have a look. So we can see, that three eighths, is three lots of one eighth. Five eighths is five lots of one eighth. And I know that three is less than five, so three eights is less than five eighths. Well done. Then we've got one more fraction story here. "Maya has read two sixths of her book and Zak has read five sixths of his book." What's the same and what's different about those two fractions? That's right, the denominators are the same. They are both six. We've just got different numerators, okay. So pause the video now, while you can use a diagram to show that Zak has read more of his book than Maya. You might want to think about a verbal reasoning sentence. You might want to use a number line. See if you can do all of those. Okay, here's my diagram. I've used a bar or a rectangle for mine, 'cause I find it easier to divide them into equal parts. Now you might've drawn two circles or two rectangles to represent the fractions and that doesn't matter. But have you shaded in two one sixths on one of them, and five one sixths on the other. So this really proves that two sixths is less than five sixths. And we can now put the inequality sign in to show that two is less than five. So we also know that two sixths is less than five sixths. Now let's look at the same pair of fractions on a number line. I've marked the number line here for you. See if you can pause your video now, if you haven't done this already, to place the arrows to show the position of the two fractions. Did you get them in the right place? Right, let's see what we've got. So that's correct, we've got two, one eighths here and we've got five, one eighths. So what do you notice about the numerator as you go further along the number line? That's right, as the numerator gets bigger, the fractions get closer to one. And finally, our method three. So, if you haven't done this, you can pause the video now to see if you can fill in the blanks for our STEM sentence. So does your completed STEM sentence look like this? Well done. So, we'll read the STEM sentence through together. So, two sixths is two lots of one sixths. Five sixths is five lots of one sixths. I know that two is less than five. So two sixths, is less than five sixths, well done. Wow, it's time for us to finish now. So well done today. You've done a fantastically well, worked really hard. And I'd like to leave you with just one last task for you to complete before the next lesson, so I want you to consider that the methods that we've used today, to allow us to compare fractions. And really helped us with our understanding of deciding which fraction is larger and which is smaller. So, each question, you've got four questions here. On the first question, we have a diagram and you need to fill in the fractions and put the inequality symbol within the circle. On question two is a number line. We have two eighths is less than seven eighths. You need to plot those fractions on the number line to show that. We've got verbal reasoning with question three. Again, fill in the missing parts of the STEM sentences and put the missing symbol in between those two fractions. And lastly, use your verbal reasoning to think about the STEM sentences and complete the fractions and the inequality symbol. So well done with all of that today. It's been lovely to spend some time with you and I'll hopefully see you again soon. Take care.

In this lesson, we will use a variety of methods to compare two fractions with the same denominator. We will use mathematical vocabulary such as greater than and less than.

In this lesson, we will use a variety of methods to compare two fractions with the same denominator. We will use mathematical vocabulary such as greater than and less than. 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

Use Several Methods to Compare Two Fractions with the Same Denominator

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

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:Use Several Methods to Compare Two Fractions with the Same Denominator

Core Content

Taking fractions further: