﻿Hi, everyone. Mrs. Sawyer here. At the end of the last session, you were left with this activity. For number one, did you have a go at drawing what the lines would look like? In this example, you can see that the parts are equal in length. But the top part represents 1/4 of the whole, and the bottom part represents 1/6 of the whole. Because there are four equal parts in the top line and six equal parts in the bottom line, then the bottom line must be longer, like this. In the second example, we were comparing the length of two journeys. Again, the length of each part is the same, but that part represents 1/3 of the top journey and 1/4 of the bottom journey. And so you need to draw three equal parts on the top line and four equal parts on the bottom line, like this. The bottom journey is longer in length. Well done if you had to go at the challenge, too, making up your own question to give to someone else in your house. Today we're going to continue to look at linear models and compare length. Look at the information you are given here. We still need to find which length is longer. But can you think about the information in this slide and how it is the same and how it is different than the information we were given in the last lesson? Pause the video to have a think, or chat through with someone else in your house. Thinking about what is the same as before, we are still given one part of a length for each line, and we still need to find the whole. However, this time the parts are not the same length. But did you notice that the fraction that they represent is the same? Both of the parts represent 1/5 of the whole. If one part represents 1/5, how many equal parts would we need to create the whole? We could use these stem sentences to help us. You will be familiar with these from the last lesson. Let's say them together. If one-fifth is a part, then the whole is five times as much. Take five parts and put them together to make the whole . If we did that, which line do you think is going to be the longest, the red or the blue? Or do you think they will give a same length? If you want, you can pause the video now to give you time to decide. Let's animate the slide to find out. Were you right? Each line needed to be made of five equal parts. If a part of the red line is shorter then the whole line is also going to be shorter. If a part of the blue line is longer then the whole line is also going to be longer. The two holes cannot be equal in length if the parts are different, and there are the same number of parts. Let's have a look at another example. This time you can pause the video and have a go at proving which is the longest line. You can start by trying to visualise what the lines would look like and then drawing each one. Remember that the parts you are given for each line represents one third but that the lengths of one third are different in line A line B. The stem sentence is there for you if that helps too. Pause the video and come back when you're ready. How did you get on? Do you agree that the top line is the longest? The parts we were given in both lines represented one third. And so the whole of each line is three times as long. Each part of line A was longer. And so the whole line was also longer. Each part of line B was shorter. And so the whole line was shorter. I wonder if you can help find John's mistake with this question. John and Abby went for a run. The whole distance that Abby ran is represented in the top line. We are also given one fifth of the amount of the distance that John ran. John completed his line like this. And he says that he ran further than Abby. What mistake has John made? You might like to use the stem sentences on the screen to help you explain. Pause the video now. And if you can tell someone else in the house, the mistake that John has made and what he needs to do to correct it. Welcome back. Did you find the mistake? John had added an extra five equal parts to his line, rather than having five parts in total. To correct this, he needed to remove one part. In actual fact, John did not run quite as far as Abby. You've seen these pictures before. They show the journey made by Kofi and Ellie from their homes to school. Can you see who has the shortest journey to school? You're right if you say Kofi. If they have to walk back from school to home as well each day, what fraction of the whole does this picture represent? It represents one half of their total journey. It represents the walk to school, but not the journey back from school. I wonder how we could represent the whole journey to show who has the longest walk each day? Pause the video now and have a go. How did you get on? This is how I represented it. Kofi's journey to school is shorter than Ellie's journey to school. And so I have made Kofi's journey to school a shorter line. For each of them, their journey to school represents a half of the total distance. And the journey to home represents the other half of the total distance. You can see from the whole lines that Ellie walked further to and from school each day. You've done really well today, comparing lengths and distances. All of the parts we have used have represented the same fraction of the whole. But the parts have not been the same length. This is sometimes hard to explain. And so your practise activity in this lesson is to answer this question by drawing a representation of the whole length of each ribbon. And then by either writing down or explaining to someone else in your house why one ribbon is longer than the other, even though each part represents 1/4 of the whole. Perhaps you could even design your own question for someone else. Good luck!

In this lesson, we will build and compare different wholes from the same unit fractions that represent different lengths. We will learn how finding out the length of one part can help you to find the length of the whole.

In this lesson, we will build and compare different wholes from the same unit fractions that represent different lengths. We will learn how finding out the length of one part can help you to find the length of the whole. 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 different wholes from the same unit fractions that represent different lengths

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 different unit fractions that represent the same quantity

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

Build and compare wholes when different unit fractions represent different amounts

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

Core Content

Working with fractions: