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Lesson Video: Dividing Shapes into Equal Parts Mathematics • 2nd Grade

In this video, we will learn how to divide shapes into halves, thirds, and quarters and describe why equal parts can have different shapes.

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Video Transcript

Dividing Shapes into Equal Parts

In this video, we’re going to learn how to divide shapes into halves, thirds, and quarters. And we’re going to describe why equal parts can have different shapes.

Here are some shapes to begin with. Let’s have a go at splitting them into halves. When we divide a shape into half, how many parts does it have? When we split a shape into half, we split it into two. Does this mean that we’ve split our shapes into half? No, each part needs to be equal. It needs to be the same size.

Let’s try dividing our shapes again. And this time we’re going to make sure that they’re in equal parts. Let’s start with our circle. We’re going to shade half of it orange. That’s better. Now, each part is exactly the same size. We’ve split the shape into two equal parts, and we’ve shaded one of them orange. You know, we could’ve shown half a circle in a different way. This is half a circle too, so is this. What matters is that both parts are equal. And so we might divide our shapes like this, like this, or like this. What matters is that we’ve divided our shape into equal parts, in other words, parts that are the same size.

When we divide a shape into thirds, we split it into three equal parts. Is this rectangle divided into thirds? No, it’s not. Each part isn’t equal. This is better. Each of the three parts is exactly the same size.

When we divide a shape into quarters, we split it into four equal parts. Here’s a square. Now, here’s an interesting question. Has it been divided into quarters? Now, a lot of people would look at this shape and say, “No, some parts are different shapes.” We can see some triangles and some smaller squares in there, can’t we? Quarters need to be the same shape, don’t they?

Let’s divide a square in exactly the same way. And this time we’re going to talk our way through it as we divide it. First of all, we’ll draw a line down the middle. Are you happy that we’ve found half of this square? You should be because we’ve divided it into two equal parts. Now, if we drew a line across the whole square like this, we’d have divided the whole square into four equal parts. So are you happy that these two squares here are quarters? Well, they are.

Now, let’s think for a moment about this half of our square. We’ve already split one-half into two equal parts. So, for us to divide the whole square into quarters, we just need to split this half of the square into two equal parts too. Now, at the moment, we’ve got a line going across, and this would be a way to show quarters. But what if we draw this line instead? We’ve still divided this half of the square into two equal parts. It’s just that this time they’re triangles. Each of the triangles is a quarter of the shape too. We know this because we could’ve divided the whole square into triangles if we’d wanted to. And so this is a really important fact to learn. Equal parts do not always look the same. They’re the same size. We could say they have the same area. But they’re not always the same shape.

Let’s try answering some questions now, where we practice dividing shapes into halves, thirds, and quarters. And as we answer them, we’re going to be careful because we know that equal parts do not always look the same.

Are the orange shapes equal to one-half of the square?

In the picture, we can see a square, and we can see it drawn twice, once here and once here. Now, this square is the same square in both of the pictures. But it’s just been divided in two different ways. And it’s been divided to make these two orange shapes underneath. And the question asks us, are the orange shapes equal to one-half of the square?

Now, to make sure we answer this question correctly, let’s remind ourselves what one-half of the square means. Half is when something is divided into two equal parts.

Let’s look at our first square. Have we divided it into two parts? Yes, we have. And are both parts equal? Are they both the same size? Yes, they are. A good way to see this is to turn your head slightly, and you can see that that dotted line goes down the middle of the shape. So we can definitely say that our first shape, which is a triangle, is half of a square. But what about our second shape? It’s a rectangle.

Let’s look at our second square to see where the rectangle came from. Has the square been split into two parts? Yes, it has, the two rectangles, aren’t they? And are those two rectangles the same size? Yes, they’re equal. So this rectangle is also a way of showing half of the square. We can divide a square into two equal parts or halves in different ways. Although they’re different shapes, the orange triangle and the orange rectangle are actually equal. They’re both worth one-half. Are the orange shapes equal to one-half of the square? Yes, they are.

James and Natalie both partitioned the same rectangle into quarters. Pick another way to divide the rectangle into quarters.

At the start of this question, we can see two pictures of rectangles. In fact, they’re the same rectangle. They’ve just been partitioned or split up in different ways. James and Natalie have split their rectangles into quarters. Now, remember, when we split a shape into quarters, it’s divided into four equal parts.

Natalie’s perhaps chosen the way that you might decide to split a rectangle into quarters. She’s drawn a line across the middle and then a line down the middle. She split the larger rectangle into four smaller rectangles. We know they’re quarters because there are four of them and they’re all equal in size.

James has chosen a slightly different way to divide his rectangle into quarters. He started off with a line across the middle, splitting the shape into half, just like Natalie did. But then, he’s drawn two lines that split his two smaller rectangles into triangles. These are different shapes than Natalie’s small rectangles, aren’t they?

So has James got the wrong answer? No, he split the rectangle into four parts, and they’re all the same size. So both Natalie and James have found different ways to show quarters of the same shape. And now it’s our job to find another way to divide the rectangle into quarters.

We’re given four possible answers. So let’s go through them one by one. How many parts has the first shape been split into? One, two, three, four, five, six parts. For us to show a quarter, we want our rectangle to be split into four parts. So this rectangle hasn’t been divided into quarters. Are there any other rectangles with more than four parts? Yes, the last rectangle has been split into six parts too. This isn’t divided into quarters either. But our two middle rectangles have both been split into four parts.

Now, we know to show quarters, each of the parts needs to be equal. It needs to be the same size. We know already from looking at Natalie and James’s rectangles that a quarter can look like a different shape. But it must be equal. Let’s look at our two possible answers. You know, there’s a few similarities between our rectangles. They’ve both been divided in half with a line across the middle. And then the top part of the rectangle has been divided into two rectangles, just like Natalie did. So we know the orange and the blue parts are both quarters.

Now, when we look at the bottom half of the rectangle, it’s been divided in two slightly different ways. Which one shows quarters? It’s this one. The bottom half has been split into two triangles, just like James did. And as we’ve already said, James split his rectangle into quarters. So, although our four parts aren’t exactly the same shape, they are equal. The correct rectangle is the one that uses a little bit of what Natalie did and a little bit of what James did. It’s the rectangle that’s been split into four equal parts.

Liam has drawn this flag on squared paper. He says that the different colors each show one-quarter of the flag. Is Liam correct?

In the picture, we can see the squared paper that Liam’s drawn his flag on. It’s a rectangular flag, isn’t it? But he split it up into a green part, a red part, a blue part, and an orange part. So there are four parts there. And Liam says that the different colors each show one-quarter of the flag. We need to think about whether Liam’s right here. Is he correct?

To help us answer the question, let’s remind ourselves what one-quarter is. A quarter is when something is divided into four equal parts. In this case, it’s a flag that’s being divided. Now, we could look at Liam’s flag and say to ourselves, “He’s colored the orange section as a big long stripe. Then, the green section is like a block. The red section is almost like a backwards letter C. There’s almost like a zigzag or a step that’s colored blue.” Yes, Liam’s divided his flag into four parts, but they’re all different shapes.

We know better than that. For a shape to be divided into quarters, it needs to be divided into four equal parts. These parts don’t look equal at all, do they? But there’s only one way to find out. Because Liam’s drawn his flag on squared paper, we could count the squares that make up each shape. The green shape takes up seven squares of the flag, so does the red shape. This is looking interesting. The orange stripe along the bottom is also made up of seven squares, and so is the zigzag blue shape. Each shape is different, but they’re all the same size.

Liam has divided his flag into four equal parts. They’re not all the same shape, but they are all the same size. Is Liam correct when he says that the different colors each show one-quarter of the flag? Yes, he is.

What have we learned in this video? We’ve learned how to divide shapes into halves, thirds, and quarters. And we’ve also learned something very interesting. Equal parts can have different shapes, even though they’re the same size.

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