Video Transcript
Halves and Quarters
In this video, we’re going to learn how to use models to investigate halves and
quarters. We’re going to explore the fact that one half is equal to two quarters. And we’re going to find out how the number of shares affect the size of the equal
parts.
Here’s a freshly baked apple pie. Now, we’re going to be cutting this apple pie up. To help us see what’s going on, perhaps it might be a good idea if we look at our pie
from above. There we go; it’s more of a circle shape now. Now, let’s imagine that we want to split this pie between two people. And we want to do it fairly so they both get an equal share. Where would you cut the pie so that they both get the same-sized piece? We can do this by making one cut down the middle. Can you see how both pieces are the same size? We’ve cut the pie into halves.
This isn’t the only way we could show halves. Hope you can see that if we cut the pie from side to side across the middle, or even
if we cut it at an angle, the main thing is that we cut it down the middle. It’s been cut into two equal parts, and each person who gets a slice of our apple pie
is going to get one half. Now, let’s imagine that we’ve got more than two people that are coming for tea. Let’s say we have four people. We don’t want any of them to think that we’ve cut the pie unfairly, so we’re going to
now have to cut it into four equal pieces.
Do you know how you do this? First, we cut the pie into two equal pieces. Remember what we call these? Halves. And then we cut each of these halves into two more pieces. And the best way to do this is to cut the pie in half across the middle like
this. Instead of two equal parts, we’ve now cut the pie into four equal parts. That’s cause we have more people coming for tea. When we divide a shape into four equal parts, we call those parts quarters. Each piece of our pie is now worth one quarter.
Let’s draw another part–whole model to represent what we’ve done here. Maybe you would better call this a part–part–part–part–whole model because this one
has been split into four parts. And each of the four people that have come for tea will have one quarter. When a shape is split into two equal parts, we call these parts halves. And when a shape is split into four equal parts, we call these quarters. Now, imagine for a moment you’re feeling really hungry. Not only that, but you love apple pie, and you’ve got a choice. You can either share your apple pie with one other person, so it’s cut into two
pieces, or you can share it with another three people, so it’s cut into four pieces
altogether. Two equal pieces or four equal pieces?
Remember, you’re feeling very, very hungry and you love apple pie. Some people might think like this. Four is greater than two. So surely, if I cut my apple pie into four equal parts, they’re going to be
bigger. But let’s stop for a moment, and let’s think about what this number four means. The number four is the number of equal parts we need to cut the pie into. So if we share the pie into four equal parts, each part will be smaller than if we
cut it into two. For example, the number 100 is a really big number. But if we’re cutting an apple pie into 100 pieces, we’d hardly get anything, would
we? The best decision is to choose this pie because one half is larger than one
quarter.
There’s something else interesting about halves and quarters, but we’ll come back to
that at the end of the video. For now, let’s practice what we’ve learned and answer some questions where we have to
understand more about halves and quarters.
Consider the given shape. Complete the sentence. The shape is cut into what. Halves or quarters? Complete the sentence. One what of the shape is shaded. Half or quarter?
We’re shown a picture of a shape here, and we need to think about it or consider it
because we’re given two sentences that we need to complete. These two sentences are quite interesting because they’re about two slightly
different things. The first sentence is about the way that the shape has been cut. So in a way, we just need to look at that black lines on the shape. And the second sentence is about the way that the shape has been shaded. So in a way, when we’re answering this part of the question, we need to just think
about the pink-shaded part.
So to begin with, let’s look at the black lines. The shape is cut into what. We’re given two words to choose from. It’s either been cut into halves or quarters. To help us, let’s sketch what’s happened to this shape. It started off as a circle, but we can see two lines have been drawn on it. These have cut it into parts. Do you remember what we call it when we divide a shape once into two equal parts? These are called halves, aren’t they? But our shape hasn’t been cut just once; it’s been cut again. So now, there are four equal parts. It’s been cut into quarters. Because the shape we’re shown has been divided into four equal parts, we can say the
shape is cut into quarters.
In the next sentence, we need to think about the part of the shape that’s been
shaded. One what of the shape is shaded, one half or one quarter? And remember, we’re not looking at the number of pieces now. We’re looking just at the shaded area. In fact, let’s make a sketch of our circle and we’ll color in the part that’s
shaded. Looks a bit like this, doesn’t it? Is one half or one quarter of the shape shaded? We can see that one half of the shape has been shaded. The shape has been cut into four equal pieces, so we can say that it’s been cut into
quarters. We can also say one half of the shape is shaded.
This rectangle can be divided into equal parts in different ways. Pick the rectangle where the equal parts are bigger. Fill in the blank. The rectangle with bigger parts is cut into what. Halves or quarters?
This question is all about a rectangle. In the first picture, we can see it. We’re told that this rectangle can be divided or split up into equal parts in
different ways. In the first part of the question that we need to answer, we’re given two rectangles
that have already been divided into equal parts. And we need to pick the rectangle where the equal parts are bigger. Shall we shade them just to help us see? This is the size of one of the parts in the first rectangle, and this is the size of
one of the parts in the second rectangle. So we can see straightaway which rectangle has equal parts that are bigger. It’s the second one, isn’t it?
Now, we’re given a sentence to complete about this rectangle. And it’s gonna help us understand why the equal parts are bigger in this
rectangle. So the rectangle with bigger parts is cut into what. Let’s spend a moment and see how many pieces these rectangles have been cut into. We can see that the first rectangle, that’s the one that’s been cut into smaller
parts, has been cut into four parts. And when we cut a shape into four equal parts, do you remember what we call them? We call these parts quarters, don’t we?
Now, if we look at our second rectangle, that’s the one with the bigger parts, we can
see it’s only being cut once down the middle. And this has only divided the shape into two equal parts. And what do we call it when we divide a shape into two equal parts? We call them halves. The shape has been split into half. The rectangle where the equal parts are bigger is the one that’s been split into two
equal parts. And we know that the more parts that you split the shape into, the smaller those
parts are going to be on. And so the opposite is true, isn’t it? If we cut the rectangle into less parts, they’re going to be bigger. And that’s why the rectangle with bigger parts is cut into halves.
True or false, half of a shape is smaller than a quarter of the same shape?
In this question, we’re given a statement, and we need to decide if it’s true or
false. There are two words in our sentence that had to do with parts of a shape. Did you notice them? We’ve got the word half and quarter. Do you remember what each one of these words means? A half is when we split the shape into two equal parts, and a quarter of a shape is
the name that we give to each part when we split it into four equal parts. So our sentence is really saying, “When we split a shape into two equal parts, it’s
smaller than if we split it into four equal parts.” Let’s try splitting the same shape into two parts and then four parts. We’ll see whether this is true.
Here is the same-sized square. First, let’s divide it into two equal parts. Just to make things interesting, let’s divide it at an angle like this. Each part is the same size, and we know that these are called halves of the
shape. And let’s shade one of them in so we can see how large it is. There we go. We’ve split our shape into two equal parts, and one of them is called a half. Now, let’s divide the same shape into quarters, so that’s four equal parts. There we go, four parts and they’re all the same size. Just like before, let’s shade one of them so we can see how large it is. There we are. Four equal parts and one of them is called a quarter.
Now, we can read our sentence again and see if it’s true. Half of a shape is smaller than a quarter of the same shape. Well, that’s not true at all, is it? Half of a shape is larger than a quarter of the same shape. The statement is false. The less equal pieces that we cut a shape into, the larger those pieces are going to
be. So if we only cut the shape into two equal parts, they’re going to be larger than if
we cut it into four equal parts. Let’s read the sentence the way it should read. Half of a shape is larger than a quarter of the same shape. The statement as it is is false.
Now, we did say we were going to come back to the apple pie at the end, so let’s do
that. Do you remember we talked at the start about cutting it into half and also
quarters? Now, let’s imagine we’re feeling really hungry when we go into a bakery, and all the
apple pies that they have for sale have been cut already into quarters. So because we’re feeling really hungry, we don’t just buy one quarter. We decide to go for two slices. How much of the pie have we got?
There are two ways to answer this question. We know that the bakery was selling slices that were a quarter each, and we’ve bought
two of them, so we could definitely say we’ve got two quarters of the pie. But can you see what two quarters are the same as? Perhaps it would help if we pushed our two quarters together. Can you see what this looks the same as? Two quarters are exactly the same as one half. So whether we eat two quarters or one half, we’ve eaten exactly the same amount. At the start of the video, we found out that one half is greater than one
quarter. And now, we’ve ended the video by finding out that one half is the same as two
quarters.
What have we learned in this video? We’ve learned how to use models to investigate halves and quarters. We’ve thought about how the number of parts a shape is shared into affects the size
of those parts. We’ve also explored the fact that two quarters are the same as one half.
