﻿- Hello, my name is Mrs. and I'm going to be leading the math lesson today. So, we're going to start today's lesson by thinking about what you've been learning about whole and parts with Mr. East and Mrs. Barker. So, we've been exploring whole and parts of shapes and we've been dividing into equal and unequal parts. And we've also been thinking about length and dividing the length into equal and unequal parts. In the last lesson, you looked at folding strips of paper. So, here we can see a rectangle and I'm going to divide it into four parts. Do you think these are four equal parts or four unequal parts and how do you know? See, yes. They are four equal parts. And we know they're equal parts because each part is the same size. So, we can use this stem sentence. I have folded my whole length of paper into four equal parts. Let's have a look at this rectangle here. Do you think this rectangle has been divided into equal parts or unequal parts? Can you explain why? Yes. So, this one is four unequal parts because the parts are different sizes. So, we can use our stem sentence again. I have folded my whole length of paper into four unequal parts. Did you have a go at the challenge from last lesson? I've set one here for you. So, I've used teaspoons. These teaspoons all the same size. So, they are equal parts. So, Zoe and Alex have equal parts because they have the same size teaspoons but who has the most parts? Do you think Zoe or Alex? You choose. You've got your answer, ready? Let's see. It's Alex. Alex has got four parts. So, the whole for Alex is bigger. Zoe only has three parts, so Alex has more parts. So in today's lesson, we're going to be thinking about a set of objects as a whole, and they're going to be splitting that set of objects into parts. So, you're going to need 12 objects for this lesson. They might be 12 of your toys or 12 pens or pencils. And you're also going to need some paper and scissors for the last part of the lesson. So, you can pause the video and fetch them now, if you want to. So, what do you notice about this picture? How many parts is the whole group of children being split into? Yes. They are five carts. One, two, three, four, five. So, are they equal parts or unequal parts and how can we tell? So, these are equal parts and I know this because the number of people in each part is the same. So, there are four children in each part. Four here, four in this part, four in this part, four in this part and four in this part. So, we can use this stem sentence to help us. The parts are equal. I know this because the number of people in each part is the same. Let's say this together. The parts are equal. I know this because the number of people in each part is the same. So, here's a picture of children on some bumper cars. The whole group of children have been split into four parts. Do you think these parts are equal or unequal? How do you know? So, the parts are unequal. And I know this because the number of people in each bumper car is not the same. You can see there's four children in this bumper car, two children in this bumper car, one in this bumper car and three in this bumper car. So, these parts are not equal. So, we can use this stem sentence. The parts are unequal. I know this because the number of people in each part is not the same. Let's say this together. The parts are unequal. I know this because the number of people in each part is not the same. Here, we have a set of cars that has been divided into three parts. What do you notice? Do you think these are three equal parts or three unequal parts? And how do you know? Yeah, these are three unequal parts because the number of cars in each part is not the same. Let's say this together. The parts are unequal. I know this because the number of cars in each part is not the same. Right. We're going to have a go at this now. We're going to try it with our six objects. I've got six cars that I'm going to use. Here we are. One, two, this is a bus. Three, four, five, six. So, here's my six cars or six vehicles. And I'm going to put them into three unequal groups. So I might have two cars in this group, one car in this group here. And then I might have three cars in this group here. So you can see, I've split my whole into three parts, but they are unequal parts because the number of cars in each part is not the same. I've got two cars in this part, one car in this part and three cars in this part. Have a go with six of your objects and see if you can move them into three unequal parts. Okay. So, let's have a look at this slide. And what do you notice? You've got some counters on the slide here and the whole set has been split into three parts. Are these parts equal parts or unequal parts? And how do you know? If they are on unequal parts, and I know they are unequal parts because the number of counters in each part is not the same. So, I want you to have a think about how we can rearrange some of these counters so that the parts are equal. What would you do to rearrange them so that the parts are equal? Lets have a look. Did you see? One of the counters from the group of four moved over to join the group of two, to make this a group of three, and this is a group of three now. So, now we have got equal parts because each part has got the same number of counters. And let's have a look again at our six cars that we put into three unequal groups and see if we can move them, if we can rearrange the cars so that they are in three equal groups. What would you do? Yeah. So I'm going to move one of the cars and I'm going to move this bus from a group of three and I'm going to drive him around to make this group two, this group is still two and now this group is also two. So, you can see I've rearranged the cars so that they only are three equal parts. Each part has got the same number of cars and they are three equal parts because they've all got two cars. So, what you could try is with your 12 objects, I've got 12 cars here. If you're outside, you might have 12 sticks, 12 stones and get your 12 things and see if you can arrange them into a different number of parts and see if those parts are equal or unequal. So you might say, right, "I'm going to get my 12 cars and I'm going to put them into two parts." These two parts are unequal, because this part has three cars and this part has not got three, it has got more than three cars. So, these two parts are not equal. And then I might think well, "Let's see if I can make them equal." So, I'm going to move some cars from this part, which has got more cars and I'm going to move them, so they have the same amount in each. Let me just check. One two, three, four, five, six in this part. And one, two, three, four, five, six cars in this part. So, now I have equal parts because they are the same number of cars in each part. Have a go with your 12 objects and see if you can make equal parts and unequal parts. So, now we're going to have a think about shapes again. You can see on the screen here that we've got four squares. You've explored dividing shapes into equal and unequal parts before with Mr. East and Mrs. Barker. And you've explored different ways that you can divide a square into four parts. Are these squares? Are they divided into four equal parts or four unequal parts? Yes. They are four equal parts because each one of those parts is one part of those four equal parts of that whole square. So equal parts, four equal parts and four equal parts. But those squares have been divided into equal parts in different ways. So now, lets have a think about one part of each shape. Here's one part of each shape that is shaded. So, we've got to think about what's the same about each part and what is different? Lets have a think about how they're different. Did you spot that they're different shapes? So, this is a different shape to this. This shaded part is a different shape to the others. So, none of the shaded parts look the same. So, they look different, they're different shapes. But what about the same? What do you think is the same about each of these shaded parts? Well, this shaded part is one out of four equal parts of this square. This shaded part is one out of four equal parts of this square. This shaded part is one out of four equal parts of this square. And here, we have this shaded part is one out of four equal parts of this square. And remember, all these squares are the same. So, the same square has been split into four equal parts and the shaded bit is one of those four equal parts. So, equal sized parts do not have to look the same. They don't have to be the same shape. So now, we're going to have a look at a square and the square is going to be divided into four parts. And you have to think about whether those parts are equal or unequal parts. What do you think about this one? Has this square been divided into four equal or unequal parts? I'm not going to tell you the answer yet. What about this one? Equal parts or unequal parts? Have a think about why you're saying equal or why you're saying unequal. What about this one? Do you think this one is four equal parts or four unequal parts? Remember what we said in the last slide? That equal parts don't have to look the same. Equal sized parts don't have to look the same. So, we're going to come back to the answers of these, after we've done a little bit of work with some squared paper. So, for this part of the lesson if you can, you're going to get four pieces of squared paper. If you've got a piece of paper like this, you can make it into a square by folding the diagonal like that. So, you can then just, by that point there and then make a mark with a pencil and mark with the pencil here and then you can draw a line. And then cut the piece of the paper off, like that and then you'll be left with a square. So, you'll need four squares if you can, for this part of the lesson. So, I've got four squares here, mine are all different colours cause I'm going to cut them in different ways and then you're going to see how I've cut them. Okay. And we can see that those pieces of paper are the same size cause I can stack them together like this. And we can see that all of those four squares are exactly the same size. So, I'm going to pause the video now and when I cut them, I'm going to cut them into four equal parts, but in different ways. So, I would just press pause and you can go and get your squares now, if you can. So, you can see here with my green square, I've cut it into four equal parts like this and ill show you them down here. Just move the camera. So you can see here, here's my four parts. I can put the four parts back together to make my whole square and here are my four equal parts. And I can show you that they're equal parts because I can stack them like this and show them to the camera, so we can see that they're equal parts. So, each one of these is one out of four equal parts of that square. So, with my blue square, I've cut them into four equal parts like this. So you can see when I put them together, they make the square again. And when I move them apart, you can see they are four equal parts of that whole square. And we can see that they're equal, if I can show you them to the camera like this. So, this is one out of four equal parts. So, with my red square, I've cut it like this, so I can show you they're four parts like this and I'll put them back together so you can see, the square. So, here's my four parts to make the square. So, these are four equal parts. Each one of these is one out of four equal parts. I can show you that that equal parts, cause I can show you there, that they all stuck together and they are the same size. And so, my last square is my yellow square and I can see these are four equal parts. I can put the parts together to make my square again. I can show you that therefore different parts here and I can show you that they're four equal parts, when I stack them together like this. They are the same size. So, these are one part of the four equal parts of the same square. And if we remember, those four square started off being the same size. So, each one of these is one out of four parts of that same size square. So, I can take one of these parts and I can start making the square, like we saw on the slide before. I might take two of my green parts and two of my blue parts and put them together to make a square, that's got four equal parts, but the parts don't look the same but they are equal in size. I could swap these two green ones for two yellow ones like this. And make my square again, but with different shaped cards. But these parts are all equal in size, but they don't have to look the same. I can swap these two blue ones, two green ones and you can see that this is a square cut into four equal parts, but the parts don't look the same. We can see that this part is the same size as this part. I can show you that, cause I could fold this part here. This green one, if I fold it in half and cut it. And if I move these two parts, so that was my original shape there. If I put this part underneath here you can see that now, it looks the same as the blue one. So, they are the same size, even though they started off looking, you see that they are different shapes but they're actually the same size. So, let's have a look at the answers to this one, where there's equal or unequal parts. Let's have a look at how our first square has been divided. Here's our first square, we had like these two greens and two yellow parts here. So, we can see that we have made the square up again, using parts from two different coloured squares. But yes, they are all equal parts. So then, look at the next one. So here, we've got two of our green parts of our square and two blue parts of the square and I can make that square shape again, that whole shape again, but using parts from the different squares, but they are equal parts. Let's have a look at the next one. This time, I've got the two blue strips here and then I'm bringing the two yellow ones to join there, to make that square. So yes, these are all equal parts, even though they don't look the same. So here's something you could try at home with your squares that you've cut into parts in different ways. You could think about how you could build in squares, using parts from of the different squares that you've cut and see if you can build the squares again, so that the four parts don't look exactly the same but we know that they are equal parts. You could also have a think about making some different shapes using the four parts. So you could say, "This shape has been divided into four equal parts." Or you could say, "This shape has been divided into four equal parts." You could even have something, where you made a strange looking shape. As long as we're joining these parts together, we can make a strange looking shape. You could say, "This shape has got five equal parts because each one of these parts is equal and I've used five parts." So, this shape has been divided into five equal parts. Have some fun with your shapes that you've cut out and make some new shapes with equal parts that don't look the same. If you want a real challenge, you could have a go at an activity like this, where we're starting with a shape like this rectangle here and have a go at splitting rectangles into equal parts in different ways and then putting them back together using those different shape, equal parts. And see if you can convince somebody that those parts are equal, even though they're not the same shape. I hope you've enjoyed the lesson and I hope you enjoy the rest of your day.

In this lesson we wil think about a set of objects as a whole, split them into parts and work out if they are equal or unequal.

In this lesson we wil think about a set of objects as a whole, split them into parts and work out if they are equal or unequal. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Maths

Y3 Maths

Key Stage 2

Year 3

Develop understanding that equal sized parts do not have to look the same

Fractions: parts and wholes

UNIT

Explore the whole and part relationship in familiar contexts, using area, linear and quality models

Explore the whole and part relationship and generalise that a part is always smaller than the whole

Explore the Concept of 'Equal' and 'Unequal' Parts

Embed the concept of equal parts and unequal parts

Compare the size of parts when the whole is defined using familiar contexts

Explore that size of part is relative to the size of the whole using familiar contexts

Consider part whole relationships within the context of quantity models

Build a whole when a part is known

Explore different contexts for building a whole when a part is known

Lesson overview:Develop understanding that equal sized parts do not have to look the same

Core Content

Fractions: parts and wholes: