﻿Hello, I'm Mrs. Kingham, and today we're going to be looking at whether equal parts of the whole always need to look the same. So today you're going to need a few things. A pencil, some paper, if you've got some paper hanging about, and I've got some coloured pieces here which will really help us today. So if you've got some of those, that's great. And a colouring pencil or felt tip and a pair of scissors, okay? Right, so let's first of all look at the task that Mr. East left us were yesterday. So what did you think about this question? Is one quarter shaded? Now, remember, we're trying to imagine what equal parts might look like when we're looking at fractions. We have to use our heads to imagine this whole split up into equal parts. And here, we're trying to imagine if they're split up into four equal parts and that this red rectangle represents one quarter. Did you find it tricky? How did you work it out? So have a look at this. I could take my square and I could fold it in half, perfect half. What does that tell us? What do you now know about this red rectangle? So then we went that one step further and I took my whole, I folded it in half, and I folded it in half again. What can you see? Just my red rectangle. If I open it up, you can see that we proved that this red rectangle is one quarter of the whole. The whole has been split into four equal parts and one quarter of our shape is shaded. So we've seen how we did it with the paper, but now we have to think about how we visualise that in our mind. Was it like this, splitting your shape into four equal parts, and then we could see that they were equal. There are four equal parts, and one of those equal parts is shaded red. Yes, one quarter is shaded red. So here's my first question for today. What would you think if I told you that both of these shapes have the same area? They both are one half of the whole. What would you think? Do you think this is true? Or do you think this is false? Pause now and have a think. Well, let me tell you, it's true. Let's have a look and see why, and then you can challenge your whole family and ask them the same question. So first of all, we need to work out how we prove that the yellow rectangle is half of the blue rectangle. So first of all, you're going to need a couple of pieces of card or paper. And if you haven't got any coloured paper, you might want to colour one in with your colouring pencil. So I had to split this yellow one into two, into two equal parts, okay? And then I just chopped that off. But they need to be exactly the same size to start off with, okay? So I needed to fold my yellow piece of card in half. And then what do you think we could do to prove it? You're right. We could put the yellow on top of the blue. And as you can see, we can see these are now two equal parts of the whole. Therefore, the yellow is one equal part, so that's one half of the whole. And the blue is one equal part, therefore that's one half of the whole also. How about now? Is it still one half of the whole? Why? How about now? We've seen this one already, haven't we? I told you that. So how many ways could you challenge your family? So we definitely have just proved that this yellow piece of card is, when it's on top, one half of the whole, as is the blue piece of card. They're both one half. What if I put it like this? Try to, you need to make sure it's inside the whole, for a start. Is that still one half of the whole? Let's see. Yeah. Go and see if you can challenge your family. Off you go. So now we've proved that equal parts do not have to look the same. How did you get on? Did you challenge them well? Do you remember these images from Mrs. Crosier's lesson? Have a look again. What's the same and what's different? Pause now and have a think. You're right. All of them have been divided into four equal parts, and in each square, one of those equal parts is shaded in red. So therefore one quarter of each whole has been shaded red. What was different? So what was different? You're right. All of our equal parts look different. Equal parts don't have to look the same. Okay, here is a whole, and the hole is square. Have a look at this image. The whole has been split into how many equal parts? Are they equal? How do you know? Pause the video now and have a think. Yes, they are equal. So the whole has been split into four equal parts and the four equal parts look different. All right, let's have a look if this sentence can stay the same for the next image. Are there still four equal parts? What do you think? Yes, there are. They just look different. How about this one? Are there still four equal parts? Yes, they are, but they just look different. Equal parts don't have to look the same. So I think that we can all agree that we have two wholes on the page, and they're both big squares. And each of those wholes is divided into four equal parts and one of those equal parts is shaded red. Can we show that all of the parts are the same size and how might we do this? We're going to need to visualise it in our minds. I'd like you to think about how we might make the red rectangle look the same as the red square. How did you do? Okay, so did you do something like this? In my mind, I visualised myself cutting the rectangle into two. And then with my mind, I visualised one half moving upwards. How do they look now? Do the two equal parts look the same? Can we prove that both of them are the same size? Yes, we have. Let's try another one. Okay, how about this time? Well, we all know that both of our wholes have been split into four equal parts and one of those equal parts is shaded, but how can we make those parts look the same? Pause the video now and have a think what you might do. Okay, what did you do? Well, this time, I imagined myself splitting the triangle into two and I visualised it meeting the other triangle, and therefore we've proved that those two parts are the same size. Say this stem sentence with me. The whole has been divided into four equal parts. One equal part is shaded, so each equal part is one quarter of the whole. Equal parts do not have to look the same. I wonder, can we show that all the parts are the same size this time? Is it a bit more tricky? Pause the video now and have a go. Okay. Hmm, it's a bit more tricky this time. Did you do something like this? I still have to split my shape. Did you do that? There we go. Now you can see the whole was divided into four equal parts. One equal part is shaded, so each equal part is one quarter of the whole. We've proved that equal parts do not have to look the same. Well done. We're getting really good at this now. Here's a more tricky example. Have a think, what's different this time? Pause the video and have a think. You're right. This time, the whole has been divided into four equal parts. Divided into four equal parts. One of those parts is shaded. That's the same. The difference is that actually within the whole, our equal parts look different. So how can you show that all of the parts are the same size or the same fraction? Did you do it like this? There we go. We've proved it again. It's still a quarter. Okay, how about this one? How can we show that all the parts are the same size now? I'm going to show you with this one 'cause I've just cut myself out some paper. Okay, watch closely. Okay, so I started with my square, and I know how to make this into four equal parts. So I'm just going to fold it into four equal parts, and we all know we can do that. All of those parts are exactly the same size, okay? And then I cut myself out my triangle. I'll show you how to do that in a minute. There we go. Now, how am I going to make this one of my equal parts look the same as my square equal part? So I'm going to take a pencil like this, and here are my folds here. I'm just going to go along like so and make it the same. And then I'm going to chop off really carefully the bottom of my triangle. So I've still got my triangle. It's not gone anywhere anywhere. But what I'm going to do is I'm going to move it all away, turn it round, and move it into the space here. And look, my equal parts look exactly the same. I've still got one quarter and one quarter of my whole is shaded. Okay, you've done brilliantly today, so now it's your turn to try this at home, okay? To prove that equal parts don't have to look the same. I'm going to show you how to do it. So you will need your paper now, okay? So just watch this. So I've got a normal A4 piece of paper here, and I'm just going to, I know Mrs. Crosier showed you this before, actually. I'm going to fold it over here to make this shape like a triangle. I'm going to pinch at the edges. I'm just going to make some marks down the bottom so that I know where to fold my paper or where to cut it off. And to fold my paper, and now I've got my square is the whole. So now what I've done with my square is I've just folded it, folded the bottom here to represent the picture that I can see on the screen. And then I folded it this way, as well, and then drew my lines on so that I have got exactly the same as the picture that you can see there. Okay? Right, I also did the same with a red piece of paper, which meant I could cut out that quarter, as well. So do the same with a red piece of paper. Have a look at the next slide for a task that you can do at home. Okay, so now it's your turn to have a go. We've made this representation and we know now that the whole here has been split into four equal parts and that one of those parts is shaded red. We also know that equal parts don't always have to look the same, but we want you to prove that they are the same. So how many ways can you show that these parts of the same fraction of the whole. Mr. Adsen will look at it with you in the next lesson. Good luck and well done today.

In this lesson, we will look at whether equal parts of the whole always need to look the same. We will compare different representations of fractions using the same original whole.

In this lesson, we will look at whether equal parts of the whole always need to look the same. We will compare different representations of fractions using the same original 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

Understand that Equal Parts Can Look Different - Area

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 - 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

Build and compare wholes when different unit fractions represent different amounts

Lesson overview:Understand that Equal Parts Can Look Different - Area

Core Content

Working with fractions: