﻿Hello everyone my name is Mrs. Dawling and I will be teaching you your math lesson today. This lesson is on fractions and it's lesson number six. First of all let's review the practise activity that you had at the end of the last session which model shows three fifth shaded? Did you have a go at this activity? Which one did you think had three fifth shaded? Well, the triangle and the circle are not divided into five equal parts so they are not showing three fifths shaded. The square has been divided into five equal parts and three of them are shaded, did you get that at home? The square is showing three fifth shaded the triangle and the circle are not because they have not been divided into five equal parts. Well done if you've got that at home, in today's session, we will be using similar representations as used in some of the previous lessons. You might remember seeing these representations in the lesson with Mrs. Sawyer a few weeks ago. Don't worry if you haven't seen this lesson though she was sharing 12 biscuits, the whole between three plates, on each plate there was one-third of the whole, each plate had four biscuits. Let's go through this first question together, it says what fraction is shaded? First of all, we have to count how many equal parts we have I count one two, three, four, five, six, seven, eight, nine, 10, 11, 12 I count 12 equal parts, so the whole is divided into 12 equal parts. How many of the parts are shaded? How many of the hearts are pink? I count nine of the hearts are pink so nine of the parts are shaded. That is nine twelfths of the whole, nine 12th of the hearts are shaded in pink. Let's do this next question together it's the same question, what fraction is shaded? We have the same image of the hearts, but this time it's been divided into a different number of equal parts. Let's see how many equal parts it's been divided into this time, one, two, three, four, the whole has been divided into four equal parts. How many of the equal parts have been shaded in? Well, I can see three of the equal parts are shaded in that is three quarters of the whole three quarters of the hearts are shaded in pink. Now let's look at both of these representations alongside each other, what is the same and what is different? On the left we have nine twelfths and on the right, we have three quarters. Well, what is the same Is that in both representations there are 12 hearts. There are also nine hearts shaded in pink in both representations, that is also the same. Now let's think about what is different and let's use our STEM sentences to help us in the representation on the left the whole has been divided into 12 equal parts in the representation on the right the whole has been divided into four equal parts. That's why the denominators are different in nine 12ths, nine of those equal parts have been shaded in pink and the representation on the right three of the equal parts have been shaded in pink. That is why the numerators are different, look at the flowers there are 15 flowers what is the value of each flower? What do you think 12 15th of the flowers would look like? Can you imagine it? Can you draw it? Have a go now, pause the video and have a think about what 12 fifteenths of the flowers would look like. Let me show you what I came up with for 12 15th of the flowers. Each flower is worth one 15th so I circled 12 of the flowers to make 12 15ths. Now you may not have circled the same flowers but as long as there are 12 circled it is correct. Your practise activity now is to circle four fifths of the flowers. There are the same number of flowers but this time I would need to show me four-fifths. If you need to circle four-fifths what is the denominator? How many equal parts should there be? Have a go at pausing the video now to circle four-fifths of the flowers. Here's my example of four-fifths of flowers I have circled four fifths, I have five equal parts and I've circled four of them. Now you might not have circled the same exact flowers but as long as you divided the whole into five equal parts and circled four of those parts, you have circled four-fifths of the flowers. Now let's look at these two representations of flowers alongside each other. What is the same and what is different? On the left we have 12 15ths on the right we have four-fifths have a look at the STEM sentences to help you. What is the same and what is different? Pause the video now to think about or write down or draw what is the same and what is different? Did you have a go at that? Let's go through it together now, first of all, what is the same? Well, in each representation there are 15 flowers that has stayed the same. There are also 12 flowers that have been circled in each representation. Now let's think about what is different in the representation on the left in 12 fifteens, the whole has been divided into 15 equal parts and 12 of them have been circled in the representation on the right in four fifths the whole has been divided into five equal parts and four of them have been circled. That is why the fractions are different that is why numerator and the denominator are different. Let's have a look at this image together what fraction is shaded? Is there more than one way to express what fraction is shaded? Have a go now, pause the video and write down what fraction it is that you see. Did you have a go at that? Let's go through it together now, one way you could have written the fraction is three quarters because if you see the whole divided into four equal parts you have three of those equal parts or you could have written down six eighths because if the whole is divided into eight equal parts then you have six of them shaded. Well done if you had both three quarters and six eighths written down, they are both correct. Let's go through this last question together what fraction is shaded? Which of the fractions on the right matches the representation on the left? Well, if I was to divide my whole into four equal parts I see that three of those equal parts are shaded. So the fraction that matches my representation is three quarters but let's have a look at the other fractions. Let's think about why someone might have thought those fractions matched this representation. Let's go through four 16ths why might someone have thought that four 16ths matched this representation? Well, there are 16 equal parts and four of them are not shaded but the question asked what fraction is shaded so that is not correct. Now let's have a look at three 16ths someone might've thought three 16ths was correct because you could see the whole divided into 16 equal parts and they might've gotten confused because when my whole is divided into four equal parts, three of them are shaded the three 16ths does not match this representation. Let's look at the last fraction, 12 quarters well, some are might've written 12 quarters because 12 of the squares are shaded and four of them are not. But this representation definitely isn't showing 12 quarters shaded in. Your practise activity for after this lesson is this question, take the fraction being represented so look at the image of footballs and look at the ovals and work out which fraction on the right matches those representations, are you ready for a challenge? If you want to take your learning further think about these things explain why the incorrect fractions do not match the representations. Try to explain why someone might think the incorrect fraction is correct, what do you think they might've gotten mixed up with? So that is your practise activity for the end of this lesson I hope you enjoy and I will see you soon.

In this lesson, we will represent different non-unit fractions in the same given whole. We will compare the relative size of each non-unit fraction.

In this lesson, we will represent different non-unit fractions in the same given whole. We will compare the relative size of each non-unit fraction. 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

More representing non-unit fractions

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

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?

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:More representing non-unit fractions

Core Content

Taking fractions further: