﻿Hello, I'm Mr. Johnson. And I'm going to be working with you on today's lesson. But before we look at our new learning, we're going to look at the problem that was set for you by Mrs. Bonds at the end of the last lesson, hopefully you've had a really good go and now we'll look at how you could have solved this. So the problem was, who has the most chocolate? Is it Josie or Will, so we've got our pictures here. So a third of Josie's chocolate is shown and also a third of Will's chocolate is shown. So we have Josie and Will. And in both cases, the part is a third. So that means that the whole must be three times as much. Now let's look at Josie. So Josie has got one, two, three, four, five pieces of chocolate is one third. The five pieces is her part. So that means all of the parts must be five. So then we need to do our calculation, which is three times five. So Josie had 15 pieces of chocolate. Now let's look at Will. So Will hard. Two, three, four, five, six, seven pieces of chocolate was a third. So that means that if one third is a seven, the other parts are also seven and our calculation is going to be three times seven. So Will had 21 pieces. So who had the most chocolate? The answer was Will. To help us with our learning for this week, we're just going to have a quick recap 'cause you've seen this problem before. Let's have a look what's the same and what's different. That's right, in both classes, the number of children in a part is the same. 'Cause there's four children in the fifth of class A and there's four children in the six of class B, but what's different. That's right. The size of the fraction is different. Let's also look at this problem that we've seen before. So what's the same and what's different. The same is the part, because in both classes, it's a fifth. So in both classes, the whole is going to be five times bigger, but what's different? The number of students in each part is different. So let's look at this problem. So what's the same and what's different. What's the same is, that both classes have got students in them, but what's different. Well, the number of students in each class is not the same. And also the fraction of the whole is not the same. So this problem is different than what we've seen before, but we do have the skills to be able to solve it. But rather than look at the problem as a whole, let's just look at class A. So what do we know about class E? What we know there are four students, is the fifth of the class? So if one fifth is the part then the whole is five times as much. So let's say that together. So if one fifth is the part, then the whole is five times as much. That's brilliant. So if we take five parts, and put them together, we will now have the whole. And what we know is that in each part, there's going to be how many children? That's right, there's going to be four children in every part. So to find out how many there is in the class, we need to work out what's that total is five times four students equals 20 students. That's right. That's brilliant. So that's class A has 20 students. So let's look at class F. Now, What do we know? That's right. Five children is a third of class F and if one third is the part, then the Whole is three times as much. So let's say that together. If one third is the part, then the whole is three times as much. So we thought is our part. We need to put three parts together to form the whole. And we know that five children is one third is one of our parts. So that means that every other part would also be five children. And we need to now find out how many there is in total. So if we do three times five students, we will get our answer of 15 students. So now we know how many children are in class F. So let's look at the whole problem again. So the problem was which class has more students. So in class A, four students are a fifth of the class and in class F five students are a third of the class. So let's look at our work and that we did. So for class A, if fifth is the part, then the whole is five times as much. So five times, four students equals 20 students. Let's look at class F. So if a third is the part, the whole is three times as much, three times five students equals 15 students. So 20 is greater than 15. So that meant that class E had the most students. Now here's the problem for you to have it go up. So the problem is, which class has more students. So in class G four students are a third of the class and in class H, six students are half of the class. Now two children have made a prediction about what the answer will be. So Dan thinks class G will have the most students as there'll be more parts to make the whole. And Anna thinks class H will have the most students as the more people in each part. Now, do you agree with either of them? So, I would like you to have a go show you're working and then we'll see whether we agree. So I want you to pause the video now, let's see if I agree with you. Nice, I'm really impressed that you've had a really good go with that. Now let's check your answer against mine. So the problem is which class has more students, class G or class H. So let's look at class G first of all. So in class G all students are a third of the class. So if one third is the path. Then the whole is three times as much. So let's take three parts, first of all, and put them together. So that represents our whole, and each of those paths, there's going to be some children, some students. So how many will there be in each part? That's right. There's going to be four. Now we need to work out how many there are in total. So I have got three times four students equals 12 students. Now let's look at class H. So with one half as the path then the whole is two times as much. So this time we need to take two parts and put them together. Now, how many need to go in each part? How many children? That's right, 60. And we need to now work out how many there are altogether. So two times six students equals 12 students. Oh, so in this case, class G and class H have the same number of students. So neither of the children who predicted it in the beginning were right. Now, I hope you're working looks like mine. So this is our final lesson on unit fractions. So let's check out our understanding by completing this activity. So I'm going to want you to fill in all the blanks, but I want you to think about all of the knowledge that you've acquired in the recent lessons. So I'm going to ask you to pause the video, and then we will go through the answers after that. So, good luck. If you'd please pause the video now. Let's look at the first blank. So we know the parts is one triangle and the number of equal parts in the whole is three. So that must mean that each part is one third of the whole. Small second blank, so we know that the part is a rectangle and the number of equal parts in the whole is five. So i wonder what you put, but I know that then if the number of equal parts and the whole is five, then each part must be one fifth. So on the next blank. So the path this time is five people. And the number of equal parts in the whole is four. If we look at the picture of the whole, we can see that in each part, there were five people. So that must mean if the number of equal parts in the whole is four, then each part is going to be? That's right, a quarter. So in our next blank, we know that's it the parts is aligned. And the path of the fraction of the whole is a fifth. So if the parts is a fifth. The whole is five times as much. And then the diagram, the picture of our whole is going to be five equal lines. And then we come to our final two boxes. And this is similar to the problems that we've been looking at today. So the part is for children and the part is a fraction of a whole is a seventh. So we've seven as a part. The whole is seven times as much and our whole picture. So we're going to have seven parts in each part, there is going to be four children. So it would look like that. Now, I hope you got all of those right. 'Cause that would show that you've really developed your understanding recently. So that's absolutely brilliant. So really well done on Tryon activity. It's quite tricky. Now, keep practising your skills and then will soon see you in the next lesson. So for now, goodbye.

In this lesson, we will build and compare different wholes when different unit fractions represent different amounts.

In this lesson, we will build and compare different wholes when different unit fractions represent different amounts. 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

Build and compare wholes when different unit fractions represent different amounts

Working with fractions

UNIT

Divide and describe the same whole when divided into differing numbers of equal parts

Understand fraction notation to represent a relationship between part and whole

Begin to use and understand the terms 'Numerator' and 'Denominator'

Name unit fractions and match them with the fraction notation and a representation

Embed previous fraction work using a linear model

Assign unit fraction names and notation to 3D representations

Assign unit fraction names and notation to equal parts of quantities

Recognise and reason about unit fractions in a variety of contexts

Understand that Equal Parts Can Look Different - Area

Understand that Equal Parts Can Look Different - Volume and Area Contexts

Compare unit fractions using a fraction wall

Reason about comparing unit fractions

Compare unit fractions in a measure's context

Can we compare unit fractions of different wholes?

Construct a whole from a part and identify the fraction it represents

Build and compare different wholes from the same unit fractions that represent the same length

Build and compare different wholes from the same unit fractions that represent different lengths

Build and compare different wholes from different unit fractions that represent the same quantity

Build and compare different wholes from different unit fractions that represent different quantities

Lesson overview:Build and compare wholes when different unit fractions represent different amounts

Core Content

Working with fractions: