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Hi, my name's Mr. Peters.

Welcome to today's lesson.

In this lesson today we're gonna be thinking about how we can describe and represent hundreds as decimal numbers.

I'm really looking forward to getting started.

Hopefully you are too.

If you are, let's get going.

By the end of this lesson today, you should be able to describe and represent hundreds as decimal numbers.

Throughout the session today we've got a couple of key words that we're gonna need to refer to as we go.

I'll have a go at saying them first and then you can have a go afterwards.

Ready? My turn, hundredth.

Your turn.

My turn.

100th.

The size.

Your turn.

My turn hundredths column.

Your turn.

So let's think about what these mean in a little bit more detail.

100th is something we should be familiar with by now.

It is a part from a whole that has been divided into 100 equal parts and each one of those parts would be named 100th.

When we take this hole and we divide it into 100 equal parts, one of those parts we can say is 100th the size of the hole.

And finally the hundredths column is placed to the right hand side of the tenths column.

And here we place a number of hundreds, a given number has.

Let's start thinking about the makeup of our lesson then.

This lesson is broken down into three cycles.

The first part is to understand what we mean by 100th the size.

The second part is to identify hundreds in a place value chart.

And finally, the third part is to record hundreds as a decimal number.

Let's get started with the first cycle.

In this lesson you'll meet Jacob and Lucas and they're here to help us along the way with our thinking as we go.

Okay, let's have a look at these place value counters.

What do you understand about the relationship between these counters or these numbers? Look at the arrows to help you think about the relationships that you know between these numbers.

Have a think.

Okay, you might have said just as Jacob has, that each number to the left hand side is 10 times bigger than the number beforehand.

So for example, 100 is 10 times bigger than 10.

Another way we can describe this is 10 times the size.

So here we can see if we start at 10 and follow the arrow to the a hundred, we know that when we make 10 into a hundred, we make it 10 times the size and the same thing applies for one and 10.

10 is 10 times the size of one and also one is 10 times the size of one 10th.

Lucas is now saying that we can also say that each counter to the right is 10 times smaller than the previous counter.

Let's have a look at that.

So for example, if we start at one and follow the arrow along to one 10th, we can say that one 10th is 10 times smaller than one or one 10th the size of one.

We can say the same for 10 and one.

One is 10 times smaller than 10 or one is one 10th the size of 10 and we can say the same for 10 and a hundred.

10 is 10 times smaller than a hundred or 10 is one 10th the size of 100.

Well done.

If you remember that relationship.

Here, you can see how it works as an inverse.

If I make something 10 times the size and then make it one 10th the size after that, it'll return me back to the original value that I have.

We can also represent this in a place value chart.

Have a look here.

I've got one counter in the tenths column.

This represents one 10th.

If I move that counter one space to the left in my place value columns into the ones column, I can say that I've made this number 10 times bigger or 10 times the size.

If I continue doing this, each one jump to the left hand side is making the counter 10 times bigger or 10 times the size.

For the last one, for example, we had 100, we made it 10 times the size and it turned into 1,000.

We can also say the same when we move to the right hand side of the place value chart.

This time we're gonna start with 1,000, but instead of making it 10 times bigger, of course, we're gonna be moving one space to the right, which would make it 10 times smaller or one 10th the size.

Let's have a look.

1,000 made 10 times smaller is 100.

100 made 10 times smaller or one 10th the size is 10.

10 made 10 times smaller or one 10th the size is one and one made 10 times smaller or one 10th the size is one 10th, 0.

Now hopefully you can see how we've done it with a digit this time instead, we've replaced the counter with the digit, one, and it works exactly the same with numbers.

Here this one represents one 10th.

If I make one 10th 10 times the size, it becomes one.

And if I make it 10 times the size again it becomes one 10.

Now have a look here.

What do you notice? That's right.

We were originally jumping one place to the left, weren't we? And that was making it 10 times the size.

Whereas this time we jumped two spaces to the left and that made it 100 times the size.

So we can say 10 is 100th times the size of one 10th or 0.

That also means that if you make a number 10 times the size and then make it 10 times the size again, that is the same as making a number 100th times the size.

We can apply this as well when thinking about making numbers smaller.

Here we've got 1,000, let's make it 10 times smaller or one 10th the size, that becomes 100 and let's make it 10 times smaller or one 10th the size again, that now becomes 10.

And as we realised previously, if you make something 10 times bigger and then 10 times bigger, again it's the same as making something a hundred times bigger.

We are now making something 10 times smaller and then 10 times smaller again.

Which is the same as saying making it a hundred times smaller or 100th the size.

So we can say that 10 is 100 times smaller than 1,000.

And to make a number 100th the size or 100 times smaller, we move it two places to the right in our place value column.

Okay, time for you to check your understanding.

Which picture shows 100th the size of 1,000? Is it A, B or C? Have a think.

(no audio) That's right, it's A, and Lucas is asking, "Well, how did you know that?" Well, if we look at the place value chart and imagine we placed the one in the thousands column, we'd need to move that to make it 100th the size to the right in our place value chart.

And we'd have to do that twice, wouldn't we? We'd have to go two jumps to the right to make it 100th the size.

So moving from one in the thousands column two places to the right would take us to the tens column.

So we can say that 10 is 100th the size of 1,000.

Here's another check.

What number is 100th the size of 10? (no audio) That's right.

It's 0.

1, one 10th, isn't it? And Jacob's now asking us, well how did we work that one out? Well again, if you go back to imagining your place value chart and place it one in the tens column, we want to make it 100th the size.

That means make it 100 times smaller.

So we're going to need to move it two places to the right in our place value chart.

Two places to the right in our place value chart from the tens column would be the tenths column, therefore it would be one 10th.

Well done if you've got that.

Okay, your first task for today, I've given you two sentences here.

You are going to need a place value chart and a counter.

And what I'd like you to do is move the counter either to the right or to the left.

And I want you to to think about making two of your own examples using these stem sentences that we've got here.

The stem sentences are.

"Something is 100 times the size of something," and "Something is 100th times the size, and something is 100th the size of something." If you manage to do that and you have a partner nearby, you could have a game of fastest finger first.

Somebody could give you the first part of the sentence and then you could move your counter to the correct column as quickly as you possibly can.

So for example, you could say 100 is 100 times the size of, and then move your counter as quickly as you can to the ones column.

Good luck and I'll see you when we get back.

Okay, welcome back.

Let's have a look at what you could have done for task A.

Lucas is saying these are the examples that he came up with.

He said that 10 is 100 times the size of 0.

He also said that 1,000 is 100 times the size of 10.

Thinking about making the number smaller, he said that one is 100th the size of 100 and he also said that one 10th is 100th the size of 10.

Well done if you came up with those examples or some of your own.

Okay, now we move into the second phase of our lesson.

Identify hundredths on a place value chart.

So as you can see here, we've got a one in our 10ths column and Lucas has come up with his own mathematical question.

He's asking, 'Well what happens if we make one tenth 10 times smaller or one 10th the size?" Well, let's have a look, Lucas, if I make it one 10th the size, my one digit would move to the right hand side.

But of course we don't have a column here, do we? So we're going to need to place an extra column here, aren't we? We could say that 0.

1 or one 10th is divided into 10 equal parts and each part is equal to 100th.

100th is one 10th size of 0.

1 or one 10th.

I wonder if we could say that again together.

Ready? 0.

1 is divided into 10 equal parts.

Each part is equal to 100th.

100th is one 10th the size of 0.

So the previous column was named the tenths column 'cause that's where we house our tenths.

Well this column we're gonna call the hundredths column.

And as we've got a one in there at the moment, this one is now representing 100th.

Let's have a look at how 100th compares to one one.

Well, at the moment I've got a one in the ones column and if I make it 100th the size, it takes me to the one hundredths column.

Remember that's the same as making it one 10th of the size and then one 10th of the size again.

So if we make one 100th the size, it becomes 100th.

To help describe this, we can use our stem sentence here to help us.

I'm gonna say it first and then I'd let you to have a go afterwards.

Ready? My turn.

One is divided into 100 equal parts.

Each part is 100th.

100th is 100th the size of one.

Your turn.

(no audio) So hopefully you can see here where we've got our place value columns and in each row and each column I've placed a one.

Now at the moment we can see what these ones represent, can't we? Because it's in the correct column.

So we can see that the one on the left hand side represents 1,000 because it's in the thousands column.

However, when we write our numbers, we don't always use place value columns do we? It would take a long time to write them out each time if we had to use that to help us understand what each number meant.

So if we take them away now it looks like we've got a bit of a problem because now we're not quite sure what each one of these ones represents.

If I put place holders after each of the ones now to the right hand side, have a look at the numbers that we had previously, what they represented and what we have now.

So let's look in particular at where we had a one, shall we, originally.

Originally where we had a one, it now looks like we've got 100 and we know that's not right 'cause that one was representing one one wasn't it? So we can see at the moment by just placing in placeholders and removing the place value columns, each number looks 100 times bigger or 100 times the size than it was originally.

So we need something else to help us out here.

That's where we use the decimal point.

The decimal point helps us separate the whole numbers again from its fractional parts.

And the decimal point sits between the ones column and the tenths column as we can see right now.

So if we go back to where we had the one we can see now we've got 1.

00.

The one on the left hand side of the decimal point represents one one, and the zeros on the right hand side of the decimal point represent zero fractional parts.

But of course, if we don't have any fractional parts, we don't need to place zeros here at all.

So we can remove those just like that.

Let's have a look at our one 10th and our 100th now at the bottom of our chart.

For one 10th, we can see that we've got the decimal point and then we've got the one which represents the one 10th.

However, in this situation, if there is no whole number, we do need to place a placeholder here to be clear that there are zero whole numbers.

And then we're gonna be thinking about the fractional parts.

So right in here we would write zero to represent zero whole numbers, and then we'd put our decimal points followed by our one to represent one 10th.

The same also applies when we're working with hundredths.

Here I've got zero hole numbers, so I would need to place a zero here, but I also have zero tenths, so I'd also need to place a zero here.

So to write 100th, we would write 0.

01.

The first zero represents zero hole numbers, and that's placed to the left hand side of the decimal point.

The zero immediately to the right of the decimal point represents zero tenths, and the one now represents 100th.

Okay, time for you to check your understanding.

100th can be written as A, B or C.

Take a moment to have a think.

(no audio) That's right, it's C, 100th can be written as 0.

01.

And we know that because the zero on the left hand side of the decimal point represents zero ones or zero hole numbers.

The zero on the right hand side of the decimal point immediately represents zero tenths and the one represents 100th.

Question two.

True or false, the decimal point separates tenths from the hundredths.

Take a moment to have a think.

(no audio) That's right.

It's false, isn't it? Let's have a look at our justifications and see which one of these helps us to justify your thinking.

Is it A, the decimal point separates the whole numbers from the fractional parts? Or B, every decimal column needs a decimal point between it? (no audio) That's right, it's A, isn't it? We know that a decimal point separates the whole numbers from the fractional parts and is situated between the ones column and the tenths column.

Well done if you managed to get that.

Okay, for your next task then I've given you some digit cards with ones and zeros and decimal points on.

And what I would like you to do is to represent the following numbers using those digit cards.

I'd like you to represent 1,000, one 10th, one 10, 100 and 100th.

And whilst you've done that, I want you to think about some similarities and some differences that you notice between these numbers when you've represented them with the digit cards.

Good luck and I'll see you again shortly.

(no audio) Okay, let's have a look how we got on.

Well, here we go.

1,000 can be represented with the digit cards like this.

1, 0, 0, 0.

The one represents 1,000 and we need to place the zeros as placeholders in the hundreds, tens, and ones.

One 10th can be recorded as 0.

The zero represents zero whole numbers, decimal point is in place, and then the one represents one 10th.

10 can be written as one and a zero.

The one represents the one 10 and the zero represents zero ones.

100 can be written as 1, 0, 0.

And again, the one represents 100.

The zeros represent zero, tens and zero ones.

And then finally 100th.

100th can be represented as 0.

01.

The first zero again represents zero whole numbers or zero ones in this case.

We've got the decimal point to separate the whole numbers from the fractional parts and then we've got zero tenths and then we've got 100th.

Well done if you managed to get those.

Okay, now to the final part of our lesson, we're gonna be thinking about recording hundreds as a decimal number.

So let's have a look at our first place value columns here.

We can see we've got a one counter in the hundreds column.

And then I'm asking you here, how are we gonna represent this as a decimal number? Well, as we've already pointed out briefly before, we know that this number here has zero hole numbers or zero ones.

So we're gonna put a zero here.

We know it has zero tenths, so we're gonna place a zero here and we know it has 100th.

So we place the one here to represent 100th.

We can write 100th as 0.

01.

I wonder if you could say that with me.

100th can be written as 0.

01.

Okay, what do you notice this time? That's right, we had one count originally, but now we've got four counters.

So how do you think we'd write this number now? Well, if 100th can be written as 0.

01, then four hundredths can be written as 0.

04.

Again, should we say that together? 100th can be written as 0.

01.

So four hundredths can be written as 0.

04.

Here's another example.

What do you notice now? Ah, this time we've got six counters, haven't we? I wonder if you could say our sentence stem to help you.

That's right, we've placed a six here in the hundreds column.

And let's say that sentence stem again together.

100th is 0.

01, so six hundredths can be written as 0.

06.

Okay, let's have a look at a different representation of hundreds here then.

We've got a number line this time and we can see that on the left hand side we've got zero.

And on the right we've got one.

So the hole is one hole and it's been divided into a hundred equal parts.

So each part would be 100th.

Can you spot what the arrow is pointing at? How many hundredths do you think it's pointing at? That's right, it's pointing at the position of 0.

4, also known as four tenths or 40 hundredths.

So 100th is 0.

01.

So 40 hundreds can be written as 0.

40 or 0.

Lucas is pointing out that we can write this either as 0.

40 or 0.

We don't often write the extra zero after the four in the hundreds column if it's not needed.

Okay, another representation here.

Look carefully, try and use a stem sentence to articulate how you could represent this as a decimal number.

(no audio) Okay, so I can see 12 hundredths shaded here.

So if 100th can be written as 0.

01, then 12 hundredths can be written as 0.

12.

Well done if you manage to get that.

Jacob wants to really draw our attention to how we pronounce this here.

We write it as 0.

12 and we say it in that exact way.

We know however it is 12 hundredths because the one represents 10 hundredths and there's an additional two hundredths, isn't there? So altogether we can say that there are 12 hundredths, but when we write it and say it as a decimal number, we do that as 0.

12.

Okay, let's have a look here now then.

So we've got a stick here and this stick is one metre long and the Ladybird started at the beginning of the stick on the left hand side and crawled along.

The question to you is, how much of the whole has the Ladybird crawled? That's right, the Ladybird has crawled 48 hundredths, the length of the stick.

We can write this as 0.

48.

Right, time to check your understanding now before we tackle some more practises, have a look here.

A number has been written and it can be read as either A, B, or C.

Take a moment to have a think.

(no audio) Ah, good spot.

That's right.

It was B and C, wasn't it? The number is 0.

08 and we know that that represents 800 so we can say it and write it in both of those ways.

Have a look here.

Which image shows 24 hundredths? That's right, it's image C, isn't it? The hole, it's one litre has been divided into 100 equal parts and we can see that there are 24 of those parts that has water within it.

So we'd represent this as 24 hundredths or 0.

24.

Did you manage to spot why A or B were incorrect? Well, let's have a think about A.

A is a whole that's been divided into a hundred equal parts and actually there are six parts that are shaded.

There are two in the first column and four in the second column, which is why it might be trying to confuse us.

But actually altogether there are six parts shaded.

So that would represent six hundredths and the middle one, 2.

Well we know that on the left hand side of the decimal point would be the ones column, so that two would represent two ones and the four on the right hand side of the decimal point immediately after it would represent four tenths.

So that does not represent 24 hundredths.

Okay, onto our final task for today then.

What I'd like you to do here is look at the place value columns that I've provided for you and write the number represented using the stem sentences provided to the right hand side.

For task two, I'd like you to look at the squares that have been divided into a hundred equal parts and I'd like you to shade in the amount that's written underneath each one.

And for the third task here, we've got a couple of questions.

We can see that Jun has rolled some cars from the starting point.

The distance the red car has been rolled is 100 hundredths.

So the question we're posing here is, how many hundredths of length of the red car has the blue car been rolled? The second part of this question shows Lucas and Jacob having jugs of water.

Jacob's jug is full.

It has a hundred hundredths of a litre within it.

So again, the question is how many hundredths the amount of water has Lucas got in comparison to Jacob? Okay, off you go and I'll see you again shortly for the answers.

(no audio) Okay, let's work through this here.

The first one, this represents two hundredths and we can write this as 0.

02.

The second one, this represents 24 hundredths and we can write this as 0.

24.

And the last one, well, it has six tenths, doesn't it? Which we know represents 60 hundredths.

So we can write this as 0.

60 or 0.

Here are some examples of how you could have shaded in the second task.

On the left hand side we've got 0.

7 or 70 hundredths.

So we can see we've shaded in 70 of them or seven columns as each column would represent one 10th.

25, well, I've shaded in 25 hundredths in the bottom right hand corner there.

And then the third example, 94 hundredths.

So here I've nearly shaded all 100 hundredth of an eye, but I've not shaded six of them, so only 94 hundredths have been shaded.

And the last task there, we were asking how many hundredths the length of the red car did the blue car roll? So we can see that the blue car rolled 65 hundredths the length that the red car rolled.

And again, we can write this as 0.

65.

And here Lucas has 89 hundredths the amount of water that Jacob has, and again, we can write this as 0.

89.

Well done if you managed to get all of those.

That's the end of our lesson for today.

Hopefully you feel a lot more confident thinking about how we can describe and represent hundredths as decimal numbers.

To summarise our learning, we can say that a hundredth is 100th the size of one.

We can say that a hundredth is one 10th the size of a 10th.

We can say that the hundredths column is the column immediately to the right of the tenths column and you can write hundreds as decimals.

For example, 100th can be written as 0.

01 and 23 hundredths can be written as 0.

23.

Thanks for learning with me again today.

Take care.

I'll see you again soon.

(no audio).

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