Dividing Shapes into Equal
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,
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
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.