Lesson video

Hello there.

My name is Ms. Co, and I'm really looking forward to learning with you in this unit all about place value.

I know that you are going to really enjoy these lessons and work really, really hard to deepen your understanding.

So if you're ready, let's begin.

The outcome of today's lesson is that by the end of the lesson, you will be able to say that you can compose and decompose 100 in 50s, 25s, and 20s.

Let's get going.

Our keywords today are compose and decompose, and I would like you to say these after me.

My turn.

Compose.

Your turn.

Great job.

My turn.

Decompose.

Your turn.

Let's have a look at what these words mean.

You can compose larger numbers from smaller numbers, so 100 can be composed in different ways using smaller whole numbers, and that's what we're going to look at today.

We already know that 100 can be composed from 10 10s, and you can see that in the bar model there.

You can decompose whole numbers into smaller numbers.

So we know that 100 is composed of 10 10s, and so it can be decomposed into 10s.

And it can also be decomposed into ones.

Today's lesson has three parts.

The first part, we're going to look at the fact that 100 can be composed of 50s.

Then we're going to look at how 100 can be composed of 25s, and then finally, we're going to look at how 100 can be composed of 20s.

All of that is going to help our learning outcome today.

So let's get started in the first part of our lesson.

In this lesson, you are going to meet Andeep, Jacob, and Izzy.

They are going to be helping you with your learning, but they're also going to be asking you some questions that will deepen your understanding of the ideas in this lesson.

Let's get going.

Now, you may already be familiar with the fact that 100 can be composed of 10 10s.

So we can see in our hundred square here that there are 10 groups of 10 in 100.

We know that 10 groups of 10 is equivalent to 100, or that we can compose 100 of 10 10s.

And you may also be aware of the fact that 100 can be composed of 100 ones.

There are 100 groups of one in 100, so in this hundred square there are 100 individual smaller squares that make up 100.

Today, we're going to think about what other ways can we see that 100 can be composed of when it comes to equal parts.

So we're thinking about equal parts today.

Just remember that equal means the same.

So if we're thinking about equal parts, we had 10 parts of 10, all of the parts were equal, because they all had 10 in them.

So that's what we're going to focus on today.

Andeep is saying that 100 can be composed of two equal parts.

Each part is 50.

So on our 100 square here, we have two clear equal parts.

Each part is made up of 50 individual smaller squares.

There are two parts.

Each part has a value of 50, so 100 can be composed of two equal parts of 50.

Here is one part, and here is the other part, and together they make 100.

We can also see this in a different way on our 100 square.

So this time, we have gone horizontally across and divided the hundred square into two equal parts.

Each part still has a value of 50.

We can also show this as a bar model.

So you may have seen bar models before.

Here is our bar model to show that 100 can be composed of two equal parts, with a value of 50.

The top bar represents our whole, which is 100.

The bottom bars are equal.

They are the same size, so they represent two equal parts, and each part has a value of 50.

They are the same.

So 100 is composed of two equal parts of 50.

Time to check your understanding.

Andeep has shaded in this 100 square, and he thinks that this 100 square shows that 100 is composed of two equal parts of 50.

Do you agree with Andeep? Pause the video here, have a think, and talk to your partner.

How did you get on? Well, I think this is a tricky one, Andeep, because I can see 10 groups of 10.

So I can see that 100 is composed of 10 equal groups of 10.

But can we also see that it's composed of two equal parts of 50? Wow.

Yes! Because 50 of the squares are shaded, and 50 are not shaded.

So even though the 50 shaded squares are not all grouped nice and neatly together, we can still say that there are two equal parts in this 100 square, and we can still say, therefore, that it shows that 100 is composed of two equal parts of 50.

Well done if you spotted that.

We can also represent this composition of 100 with equations.

So we've already talked about the fact that 100 can be composed of two equal parts of 50, and we can represent that in lots of ways, but we've represented it as a 100 square, and as a bar model.

We can also represent it with equations.

So we can say that 100 is equal to 50 plus 50.

If we add the two parts of our bar models together, it will find the sum, the total will be 100.

We can also write it as 50 plus 50 equals 100, because remember, it doesn't matter which side of the equals sign your addends and your sum go on, they still mean the same thing.

We can also write this as a multiplication equation.

So you may have seen multiplication before, and we know that multiplication means groups of.

So the first equation there says 100 is equal to two multiplied by 50.

Now what this means is, we can read this as 100 is equal to two groups of 50.

The second equation, well we know that multiplication is commutative, so we can write 50 and two either side of the multiplication sign and it will still make sense.

But we can also think of this as 100 is equal to 50, two times, or 50 twice, and we can see that in the bar model and the 100 square representation.

So we can represent this relationship as an addition equation, but also as a multiplication equation.

We can also use a number line to show that 100 can be composed of two equal parts.

So here my number line goes from zero to 100, and the divisions show that it has 10 equal parts.

The arrows show that we have two equal parts.

The arrows are the same length.

Each of those parts has a value of 50.

So this part there is made up of five 10s, and that part is made up of five 10s, and we know that five 10s is equivalent to 50.

So we can say that 50 plus 50 is equal to 100.

We can also say that two groups of 50 make 100.

And we can write that as a multiplication and an addition equation.

We can also think about this relationship in different contexts.

So, how many 50 pence coins would you need to make 100 pence? Well, we know that 100 can be composed of two equal parts of 50, so we know therefore that 100 pence can be composed of two 50 pence coins.

Here we are.

50 pence plus 50 pence is equal to 100 pence.

We can also write this as a multiplication equation.

50 pence twice, 50 pence multiplied by two, is equal to 100 pence, or two groups of 50 pence, two multiplied by 50 pence, is equal to 100 pence.

These all mean the same thing, and they all tell us that 100 can be composed of two equal parts of 50.

Time to check your understanding.

Jacob needs 100 crayons.

Crayons come in boxes of 50, like the one you can see on the screen.

How many boxes of crayons does Jacob need? I would like you to think about that question and say the following sentence.

"100 can be composed of 'mm' equal parts of 'mm'." Pause the video and have a go at this question.

Well, we know that 50 plus 50 is equal to 100, so Jacob will need two boxes of crayons, and we can also say our stem sentence.

100 can be composed of two equal parts of 50.

Well done if you said that.

Time for your first practise task.

For the first part of the task, I have a 100 square for you, and I would like you to show how 100 can be composed of two equal parts by colouring in or shading that 100 square.

Now, you could use two different colours, or you could just use a pencil to leave one part shaded and one part unshaded.

Either is absolutely fine, but my challenge to you is, can you find an unusual way to do that? Could you show that 100 is composed of two equal parts by colouring in the 100 square in a way that you think nobody else will have thought of? Once you've done that, can you use your model to complete the following equations? 50 plus "mm" equals 100.

50 multiplied by "mm" equals 100.

And "mm" equals two multiplied by 50.

Pause the video here, and have a go at that task.

How did you get on? Well, we know that there are lots of ways of colouring in that 100 square, but let's look at one possible option.

Now, this is one possible way.

We know that 100 is composed of two equal parts of 50.

So that means we have to have 50 shaded squares and 50 unshaded squares.

You might have used two different colours.

So here, we've got three rows of 10 that I can easily see, so that's 30.

Then sort of in the middle, we've got a row of 10, and then we've got two groups of five, which I know make 20.

So altogether, we have 50 shaded squares, and 50 unshaded squares.

So that's my unusual way, but there are lots and lots of different ways.

So check.

Do you have 50 shaded squares and 50 unshaded? Or do you have 50 squares in one colour and 50 in another colour? If you have, you can give yourself a tick.

And then the equations are as follows.

50 plus 50 equals 100.

50 multiplied by two equals 100.

And 100 is equal to two multiplied by 50.

Well done if you wrote all of those equations correctly.

Let's move on to the second part of our lesson.

So we've learned that 100 can be composed of 50s.

Now we're going to look at how 100 can be composed of 25s.

100 can be composed of four equal parts.

So our 100 square has been divided into four equal parts, and if we counted each of the smaller squares in each of those parts, there would be 25 smaller squares in each part.

So 100 can be composed of four equal parts, and each of those parts has a value of 25.

We can also show this composition of 100 using a bar model, like we did before with two parts.

So this time, our whole is 100, and in the second row of bars, we have four equal bars now.

Each one has a value of 25.

And we know that those altogether make 100.

Time to check your understanding.

Andeep thinks that this 100 square shows 100 composed of four equal parts of 25.

Do you agree with him? Pause the video here, have a think.

So what do you think? Do you agree with Andeep? Do you disagree with Andeep? Wow, Jacob is saying that actually, he noticed that there are 25 squares in each of the four equal parts, so he could say that yes, although it looks a bit different, there are four equal parts of 25.

So we can say that this representation does show that 100 is composed of four equal parts, each with a value of 25.

Well done if you said that.

We can also represent this composition of 100 using equations.

So we can say that 100 is equal to 25 plus 25 plus 25 plus 25.

There are four 25s that make up 100.

We can also write that the other way.

So 25 plus 25 plus 25 plus 25 is equal to 100.

These all mean that 100 can be composed of four equal parts of 25.

Now these are our addition equations, but we can also represent this with multiplication equations.

So we can say that 100 is equal to four groups of 25.

So we can say that 100 equals four multiplied by 25.

We can also see in our models 25 four times.

So we can say that 100 is equal to 25 multiplied by four.

So there are lots of different ways to represent the idea that 100 can be composed of four equal parts of 25.

We can also show this on a number line.

Hmm, how can we use this number line to show that 100 can be composed of four equal parts? Well, in this example, we've divided our number line into 20 parts.

Each part has a value of five.

And so this part here is made up of 25 ones, shown by the arrow.

So 25 ones there, and there are 25 ones in each of those four equal groups.

So Jacob can see that there are four groups of 25 that make 100.

And remember, we can also represent this using our addition and multiplication equations.

We can also think about this in different contexts.

So let's think about cakes.

Always a good start.

Cakes at the school fair cost 25 pence each.

Andeep has 100 pence, and he wants to know how many cakes can he buy for 100 pence? So we know that 100 can be composed of four equal parts of 25.

So that means Andeep can buy four cakes for 25p each, because we know that 25 plus 25 plus 25 plus 25 is equal to 100 pence.

So we can say that because 100 is composed of four equal parts of 25, Andeep can buy four cakes.

Time to check your understanding.

Izzy has shaded in a 100 square, so we can see all the numerals here from one to 100.

I would like you to take a moment to describe it in different ways.

So think about the ways that we have described our 100 so far.

Pause the video, have a go.

How did you get on? Now there are lots of different ways that you could talk about this, but here are some that I chose.

I can say that 100 can be composed of four equal parts of 25.

So that's our key word, isn't it? This idea of being composed.

And I can see that because of the shaded and unshaded parts in my 100 square.

I can also say that there are four groups of 25 in 100, and I can also write some equations or say some equations.

So you might have said something like "25 plus 25 plus 25 plus 25 is equal to 100." Well done if you got any of those.

Time for your second practise task.

This time, I would like you to take our 100 square and compose 100 from four equal parts by colouring it in again.

Again, I want you to think about an unusual way, something that nobody else will have thought of.

And then I would like you to use your model to complete the following equations.

25 plus "mm", plus 25 plus "mm" equals 100.

25 multiplied by "mm" equals 100.

And "mm" equals four multiplied by 25.

Pause the video here, have a go.

Good luck.

How did you get on? So, as before, there are lots of different ways that you could have coloured in your 100 square to show that 100 is composed of four equal parts of 25 this time.

Now, yours might not have looked like mine, but one good way to check is to count the squares.

In each group that you've coloured in, do you have 25 smaller squares? If you do, in each of the four groups, then you can give yourself a tick.

Doesn't matter if it doesn't look like mine.

There are lots of different ways.

For the equations, you should have written the following.

"25 plus 25 plus 25 plus 25 equals 100." "25 multiplied by four equals 100." And "100 is equal to four multiplied by 25." Really well done if you coloured in your 100 square in an unusual way and you managed to complete those equations.

Great job.

Let's move on to the final part of our learning, where we're thinking about how 100 can be composed of 20s.

So we already know that 100 can be composed in lots of different ways.

This time, we know that 100 can be composed in equal parts of 20.

So Andeep is asking, well, if he shaded in 20, and then another 20, and so on and so forth, how many equal parts would he shade in if he shaded in 20 at a time? Hmm.

Well, we can see that 100 is composed of five equal parts of 20.

So there are five equal parts here, and if we counted the smallest squares in each part, each part would have a value of 20.

There are five parts, and each part has a value of 20.

As before, we can show this in lots of different ways, and we can show it using a bar model.

So we know now that the top bar is the whole, and it's worth 100.

And the bottom bars, there are five bars there, they're all the same size, because they are equal, and each bar has a value of 20.

So this bar model shows us that 100 can be composed of five equal parts, with a value of 20.

Time to check your understanding here.

Izzy and Jacob have represented the composition of 100 with different equations.

So we've represented it with equations before, with different parts.

What do you think? Do you think that Jacob and Izzy have got this correct? Use the bar model to help your thinking, and think about the way we've written equations earlier in the lesson.

Pause the video, and have a think.

Do you agree with Izzy and Jacob? Well, let's take a look at Izzy.

Izzy is correct.

She said that 100 is equal to 20 plus 20 plus 20 plus 20 plus 20.

Now we can skip count in twenties to check.

So we use our bar model.

We can say 20, 40, 60, 80, 100.

We had five groups of 20, and we can skip count and know that they make 100.

So Izzy is correct.

What about Jacob? Jacob has said 100 is equal to five multiplied by 20.

Well he's also correct, because in our bar model, we can see five groups of 20, and we know that the multiplication symbol can also be read as groups of.

So Jacob has written 100 is equal to five groups of 20.

Remember, these are all ways of showing that 100 can be composed of five equal parts of 20.

They might look different, but they all represent the same thing.

Well done if you agreed with both Izzy and Jacob.

We can also use a number line to show that 100 can be composed of five equal parts.

So this time we have jumps.

We have 20, 20, 20, 20 and 20.

And we can skip count in our 20s.

20, 40, 60, 80, 100.

We have used five equal jumps of 20, and we've reached 100.

So we can say that this number line shows that 100 can be composed of five equal parts of 20.

We can also use different contexts.

So here we can say that 100 pence is composed of five equal parts.

Each part is 20 pence.

So we can use our coins here.

We can say that we have five equal parts, and they make 100 pence.

So it doesn't matter if the context looks a little bit different.

If you have five equal parts of 20, then you have 100, because 100 can be composed of five equal parts of 20.

We can also skip count in our 20s to check.

Now you've heard me doing this a couple of times, so let's see if we can do that together.

Are you ready? 20, 40, 60, 80, 100.

Great job, well done.

So we can see that there are five parts, they're all the same, they have the same value, and they make 100.

So how many 20 pence coins would you need to make 100 pence? Well, Jacob knows that 100 pence can be composed of five 20 pence coins.

So we can say that this is equivalent, they are the same.

We can also write this as multiplication equations.

Five groups of 20 pence is equal to 100 pence.

So five multiplied by 20 pence is equal to 100 pence.

Similarly, 20 pence multiplied by five is also equal to 100 pence.

These are all different ways of representing the fact that 100 can be composed of five equal parts of 20.

Time to check your understanding.

Izzy needs 100 crayons.

Crayons come in boxes of 20.

How many boxes of crayons does Izzy need? I also want you to say the sentence, "100 can be composed of 'mm' equal parts of 'mm'." Pause the video here, and have a go.

How did you get on? Well, Izzy says that five groups of 20 make 100.

So Izzy would need five boxes of crayons.

And let's say our sentence together.

100 can be composed of five equal parts of 20.

Great job if you said that.

To our final tasks of the day.

First of all, I would like you to complete the missing numbers.

A is a bar model, and we've seen that before.

B looks a little bit different, but it's definitely something that we have encountered in the lesson.

So see if you can work out the missing numbers.

And then C is an addition equation.

20 plus "mm" plus "mm" plus "mm" plus "mm" equals 100.

Then I would like you to think about the following problem.

100 can be composed of five equal parts of 20.

I would like you to represent this idea in your own way.

You could use a 100 square.

You could make a number line.

You could use a hundred objects, or a bead string.

The possibilities are endless, so use your imagination to represent it in your own way.

Pause the video here and have a go at these two tasks, and I'll see you shortly for some feedback.

So how did you get on? Here are our missing numbers.

For A, our bar model shows that 100 is composed of five equal parts, and each part has a value of 20.

So the missing numbers are 20.

For B, we were skip counting in our 20s.

So remember, we go 20, 40, 60, 80, 100.

And then for C, it's very similar to A, but we're representing the idea that 100 can be composed of five equal parts of 20 as an addition equation.

So we have 20 plus 20 plus 20 plus 20 plus 20 is equal to 100.

Question two asked you to compose your own way.

So showing that 100 can be composed of five equal parts of 20, in any way you want it to.

Now there are loads of different ways you could have done this.

You could have found 100 objects and made five equal groups of 20.

You could have found some money and shown that five equal groups of 20 pence make 100 pence.

You could have drawn a number line, or a bar model.

Well done if you found your own way of representing this idea.

So we've come to the end of our lesson, and I have really enjoyed working with you today.

Let's summarise our learning.

So we now know that 100 can be decomposed or split into equal parts in lots of different ways.

We know that there are two 50s in 100, there are four 25s in 100, and there are five 20s in 100.

And we also know that we can represent those compositions in lots of different ways.

Thank you so much for your hard work today, and I look forward to seeing you for another lesson.