Lesson video

Hi, my name's Mr. Peters.

Thanks for learning with me today.

I'm really looking forward to it.

Today, we're gonna be thinking about recording tenths as decimal fractions.

Let's get going.

By the end of this lesson today, you should hopefully feel confident enough to be able to say that I can describe and represent tenths as a decimal number.

During this lesson, we're gonna need some key language.

The first one is one tenth the size, the second one, tenths column, and the third one, decimal point.

Let's find out a bit more about what these mean.

So, when a whole has been divided to 10 equal parts, we can say that one of those parts is one tenth the size of the hole.

The tenths column can be found on a place value chart and places the number of tenths that a given number has.

And finally, decimal point, this is a small dot used in a number to separate the whole numbers from their fractional parts.

Look out for how this language is used throughout the lesson.

This lesson today is gonna be divided into three parts.

The first section is gonna look at our understanding about what we mean by one tenth.

The second section, we'll look to identify tenths on a place value chart.

And the last section, we'll think about tenths and how we record these as decimal numbers.

Let's get going.

Throughout this lesson, you may see Aisha and Lucas join us as well, and they will be helping us along our way with our learning.

Okay, so just to get you started, I want you to have a look at our image here.

On the left-hand side, we have a 1, and on the right-hand side we have ten 1s.

So, I want you to have a think for yourself now, what's the relationship between the 1 on the left hand side and the full 10s frame of 1s on the right-hand side? Yeah, well spotted.

So, on the left hand side we only have one 1, and on the right hand side we have ten 1s.

So, the relationship is that we could add ten 1s together to make a 10.

We could say 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 is equal to 10.

Now, my image has changed slightly.

What would the relationship now be? The previous relationship was additive, we were adding 1s together to make the 10, but what's happened this time? It's not as easy to see this time is it? But something has happened to the 1 to turn it into a 10.

We could say that the value of the 1 has increased, it's grown, it's become 10 times bigger or 10 times the size.

And this is some language we're gonna have to carry on using in the next section.

So, if I place a value in my place value chart and we start it in the 1s column, each time it moves to the column on the left, we can say that it is grown 10 times the size.

So, if I make one 1 ten times the size, it becomes one 10.

And the same happens for one 10.

If I make one 10 ten times the size, it becomes 100.

And if I make one 100 ten times the size, it becomes one 1,000.

So, the inverse of this is when a value becomes smaller or shrinks in size.

Here, we have a counter representing one 1,000.

Now, if I move that one place to the right in my place value chart, the number will have become one tenth the size or 10 times smaller.

So, if I make one 1,00 one tenth the size, it becomes one 100.

If I make one 100 one tenth the size, it becomes one 10.

And if I make one 10 one tenth the size or 10 times smaller, it becomes one 1.

Here, you can see that I've changed the counter to a 1 this time to represent the same thing.

If I make 1 ten times the size, it becomes one 10.

If I make 10 ten times the size, it becomes 100.

And if I make 100 ten times the size, it becomes 1,000.

And likewise, if I go backwards moving to the right each time in the place value columns, then we can see that 1,000 when I make it one tenth the size becomes 100.

And 100, when I make it one tenth the size, it becomes a 10.

and one 10, when I make it one tenth the size or 10 times smaller, it becomes a 1.

So, we've established that moving a value one place to the right in a place value chart makes the value one tenth the size.

This is also the same as saying dividing that value into 10 equal parts.

Let's have a think about this in a little bit more detail.

If I have 1,000 and I divide that 1,000 into ten equal parts, each one of those parts becomes 100.

We have divided it into 10 equal parts or we have made it one tenth the size.

So, we can say that 100 is one tenth the size of 1,000.

Let's have a look again.

This time I have got 100.

And if I take that 100 and I divide that 100 into ten equal parts, each one of those parts becomes one 10.

So, we can say again that 10 is one tenth the size of 100.

And finally, let's take our 10.

If I have one 10 and I divide that one 10 into ten equal parts, each one of those parts will have a value of 1.

And therefore, I can say that 1 is one tenth the size of 10.

So, when using our place value chart, it's really important that we understand what each value represents when it is in a column.

Here, for example, we have a 1 in the 1,000s column, so this 1 would represent 1,000.

Aisha is now asking, "Well, what would the other values represent if the 1 was in their columns?" I think we could use this stem sentence to help us each time.

If we had a 1 in the 100s column, then the 1 would represent 100.

If we had a 1 in the 10s column, this 1 would represent one 10.

And if we had a 1 in the 1s column, then this 1 would represent one 1.

Time to check our understanding.

100 is 10 times the size of what? Is is a, 1, b, 10, c, 1,000? Have a think.

That's right, it's b, 10.

100 is ten times the size of 10.

Here's another one for you.

100 is one tenth the size of what? Is it a, 1, b, 10, or c, 1,000? Have another think again.

That's right, it's 1,000.

100 is one tenth the size of 1,000.

Well done if you were able to imagine a place value chart in your head as you did that.

Okay, so onto your first task for today.

Can you fill in the missing numbers from our sentences? It might be helpful for you to think about a place value chart in your head again, or to have one nearby to support you in the thinking.

Aisha is then asking, "Can you create your own missing number question to test on a friend or someone nearby to you?" Pause the video now and have a go at the task.

I'll see you shortly.

Welcome back.

Let's go through the answers together.

The first one, 10 is ten times the size of 1.

Something is ten times the size of 10.

That's right, 100 is ten times the size of 10.

Let's look at the third one now.

100 is one tenth the size of something.

Hmm, that's right, it's 1,000.

100 is one tenth the size of 1,000.

And finally the last one, something is 10 times smaller than 10.

<v ->Hmm, that's right, 1.

</v> 1 is ten times smaller than 10.

Aisha made her own example.

I wonder if you managed to make yours.

Aisha's example says, "Something is one tenth the size of 1,000." Can you get that one? That's right, 100 is one tenth the size of 1,000.

You managed to get Aisha's example correct too, well done.

Now, let's move on to phase two of our lesson.

We're going to start thinking about identifying tenths on a place value chart.

Okay, Lucas is asking, "Well, we looked at what would happen when we had 1 in the 1s column and we've been thinking about making things one tenth the size." Lucas is now asking, "Well, what would happen if we made 1 one tenth of the size?" Hmm, we've run out of space on our place value coms, haven't we? We're gonna have to add a new one in.

Now.

I wonder what the heading for this one would be.

Well, maybe our sentence stem can help us a little bit of this.

So, if 1 was divided into 10 equal parts, each one of those parts would have a value of one tenth, therefore one tenth is one tenth the size of 1.

So, we would have to call this column the tenths column as Aisha has pointed out.

Any value placed in that column represents a number of tenths a number has.

Let's have a think about the value of the 1s again each time here then.

So, if we go back to thinking about what we did earlier, we'll remember that the 1 when it was placed in the 1,000 column represented 1,000.

When it was placed in the 100 column, it represented 100.

When it was placed in the 10s column, it represented one 10.

And when it was placed in the 1s column, it represented one 1.

And then finally, if it now moves into the tenths column, the 1 this time would represent one tenth.

So, now you can see that I've made five different numbers.

I've got five rows and each row is going to represent one number.

So, in the top row, this 1 is gonna represent 1,000.

And in the second row, the 1 is going to represent 100.

And in the third row, the 1 is gonna represent a one 10.

In the fourth row, the 1 will represent one 1.

And finally in the fifth row, the 1 will represent a tenth.

But we don't always have place value headings when we write down our numbers, do we? And that's something Lucas is now wondering.

He says, "Well, if the place value headings weren't there, how would we know which each one represents?" Well, we often place zeros in the columns that don't have anything representative within it.

So, the zeros would represent either zero tenths, or zero 1s, or zero 10s, or zero 100s, or even zero 1,000s if we were looking at a bigger number.

But even now, if we look at the very bottom number, we've got a 1 there, but previously we wanted that 1 to represent one tenth.

And the row above it actually has what looks like the number 10.

But if I remember rightly, we wanted that 1 to represent the 1's column, so we wanted that 1 to represent one 1, so we need something else to help us here.

And as Lucas has pointed out, we can't just use a 1 to represent one tenth in the bottom row, can we? So, this is where we're going to introduce something new, we're gonna introduce a decimal point.

A decimal point is used to separate whole numbers from the fractional parts within a number.

Let's have a look more carefully about where they're placed.

This makes a little bit more sense.

Let's start from the top row.

In the top row, the 1 represented 1,000 when we had the place value headings.

Now, that makes sense 'cause we can see that actually our number has one 1,000 and it has a 0 in the 100s column, a 0 in the 10s column, and a 0 in the 1s column, so that number represents 1,000.

We also have a zero in the tenths column, and this represents zero additional tenths or zero fractional parts.

As we said, the decimal point separates the whole numbers from the fractional parts.

Have a look at the number underneath, that 1 represented 100, and again, we know 100 is represented as 1 in the 100s column, a 0 in the 10s column, and a 0 in the 1s column.

We also again have zero tenths.

Underneath that, we have the number 10, and we know we write the number 10 as a 1 and a 0.

That 1 represents one 10 and that 0 represents zero additional 1s.

And then again, we also have a 0 in the tenths column, this represents zero additional tenths.

And then nearly there, underneath that we have a 1 in the 1s column, and we remember that from the place value headings that we had, that one represents one 1.

And again, we don't have any fractional parts for this, so we've got 0 in the tenths column.

However, when we made that 1 one tenth the size, we know that it became one tenth.

So, the very bottom row, we have a 1 in the tenths column and this 1 represents one tenth.

Hmm, but it doesn't actually tell us how many whole numbers we have, we don't have any numbers before the decimal point.

Well, what we'd need to do here is place a zero before the decimal point.

It's important to do that so that we can really recognise that we have zero whole numbers and we have one fractional part, and that fractional part is one tenth.

You would not need to place zeros in all of the other columns, like the tens, the hundreds, and the thousands columns.

You'd be going on forever doing that, so we just place a zero in the ones column.

So, one tenth can be represented as 0.

1.

Okay, time for us to check our understanding.

The decimal point separates the what? Is it a, ones from the tens, is it b, tens from the tenths, or is it c, whole numbers from the fractional part? Have a little think.

That's right, it's c.

The decimal point separates whole numbers from their fractional parts.

Okay, one more for us to think about.

True or false, one tenth can be written as 1.

0? That's right, it's false, one tenth cannot be written as 1.

0 because the 1 represents a 1 and that 0 would represent zero tenths because we know that the decimal point separates the whole numbers from the fractional parts.

So, I wonder which justification underneath we would need to use to help us.

Is it a, the 1 represents one tenth or is it b, there is a 0 in the tenths column? Yep, that's right, there's a 0 in the tenths column.

So, if we were to help justify our answer, we might use statement b to help us justify our thinking, there is a 0 in the tenths column.

Okay, time for Task B.

I wonder, could you have a go at constructing your own place value chart and writing the headings in as well of each of the columns? Once you've done that, cover up the columns and then have a go at writing in the numbers below.

I'd like you to have a go at writing the number 1 thousand, 1 hundred, 1 ten, 1 one, 1 tenth.

and a little tip, don't forget your decimal point.

Good luck, and I'll see you soon.

Welcome back.

Yours might look a little bit like this one here.

As you can see, I've kept the place value headings at the moment, but because I've got the decimal points, I don't need those place value headings anymore so we can remove them and we use the decimal points to help us understand the magnitude of each of the numbers.

Well done for giving yours a go, and hopefully you feel confident about the position of the tenths column on your place value chart.

Okay, let's move into the third part of a lesson now where we're gonna start thinking about recording tenths as decimal numbers.

So, we've already begun to think about how we can represent one tenth as a decimal number.

We know that we need to place a 1 in the tenths column and we also need to place an additional 0 in the 1s column to represent zero whole numbers.

We would say this number as 0.

1.

So, one tenth can be written as 0.

1.

Could you say that with me? One tenth can be written as 0.

1.

But then, actually, what if we had more than one tenth? Let's have a look here.

Hmm, this time we've got three tenths in the tenths column.

How would I write that as a decimal fraction? Have a little think for yourself first.

That's right, this time we would be a 3 in the tenths column and still we don't have any whole numbers, so we'd still place a 0 before the decimal point in the 1s column.

So, one tenth can be written as 0.

1 and three tenths can be written as 0.

3.

Let's say that altogether again.

One tenth can be written as 0.

1.

Three tenths can be written as 0.

3.

Okay, let's have a look at another example.

So, we know that one tenth can be written as 0.

1, but what if we had, hmm, how many have we got this time? That's right, we've got five tenths this time.

I wonder if you can spot the connection and know how we'd write this really quickly now.

That's right, we would need to place a 5 in the tenths column.

and we still don't have a whole number at this point so we place a 0 in the 1s column.

So, if one tenth can be written as 0.

1, then five tenths can be written as 0.

5.

Let's say that again together.

One tenth can be written as 0.

1, so five tenths can be written as 0.

5.

This time we've gotta change in image.

Does that matter though? No, you're right.

It still stays the same, doesn't it? The whole has been divided into 10 equal parts and we have one of them that is shaded, so this one part represents one tenth and we know we write one tenth as 0.

1.

So, if we know we write one tenth as 0.

1, how would we write this image? Have a think for yourself first.

That's right, we've got four tenths.

So, if one temp can be written as 0.

1, then four tenths can be written as 0.

4.

Ah, another context, and this time we're looking at the jug again.

We know that one litre represents the whole this time and that litre has been separated, has been divided into 10 equal parts.

At the moment, we have one of those parts, so we would write that as 0.

1.

One tenth can be written as 0.

1.

Whereas now, oh look, what's happened this time? Ah, yeah, good spot.

There's another one tenth poured in, so now we have two one tenths or two tenths, so we would write that as 0.

2.

One tenth can be written as 0.

1, so two tenths can be written as 0.

2.

Time to check our understanding again for the final time today.

One tenth can be written as 0.

1, so seven tenths can be written as? Is it a, 7.

0, b, 0.

7, or c, 0.

07.

That's right, it's b, it's 0.

7.

Just out of interest, why isn't it a? Yeah, that's right because a has 7.

0 and that's seven before the decimal point is placed in the ones column, so that would seven would represent seven 1s.

And what about the final one, why is c not correct? Well, actually, we've got zero in the ones column and we've got a zero in the tenths column so it can't represent seven tenths because there is not a seven in the tenths column.

The last check for understanding, which image shows 0.

3? That's right, it's a.

The whole has been divided into ten equal parts and three of them have been shaded, and this represents three tenths or 0.

3.

Again, I'm gonna ask the question, why can it not be option b or option c? Well, in option b, we can see that there is a three, but it's in the 1s column, so that would represent three 1s.

And then for option c, well, we have a whole, but how many parts has it been divided into? Yeah, it's only been divided into three equal parts and not 10 equal parts, so therefore it cannot represent three tenths.

Okay, time for your task now.

I'll walk you through each of the questions I want you to have a think about.

You have to fill in the blanks for each of the sentences that have been given to you.

The first one says, "A pizza is cut into ten equal parts.

Lucas eats three pieces." And the sentence says, "Lucas eats something tenths of the whole pizza.

We write this as?" So, you'll need to tell me how many tenths that Lucas eats as well as how we write that as a decimal number.

The second question shows Aisha and she has a litre of water.

She drinks some during the morning and by lunchtime she has eight tenths of her litre left.

So, we need to ask the question, how much did Aisha drink? Again, it's up to you to fill in the gaps in the sentences.

And finally, we have a slightly different context.

We have Aisha and Lucas who have both grown flowers.

Now, Lucas's flower is significantly taller than Aisha's flower.

Aisha's flower is significantly shorter than Lucas's flower.

So, the question is, how many tenths shorter is Aisha's flower than Lucas's? So, again, fill in the blanks in the sentences.

Good luck, and we'll catch up soon.

Okay, welcome back.

I hope you got on okay with that.

Let's go through the answers together.

Let's start off with Lucas and his pizza.

Lucas actually ate three tenths of the pizza.

So, here we've got Lucas eats three tenths of the whole pizza, and we write this as 0.

3.

Aisha actually drank two tenths of the litre of her water, and as a result we would write that as 0.

2.

And well, the last question asked, well, how much shorter is Aisha's flower than Lucas's flower? Well, Aisha's flower was, in fact, five tenths shorter than Lucas's flower, and we would write that as 0.

5.

Well done for getting through that lesson with me today.

You've done some really good thinking, and I've been really, really impressed with the way you thought about your maths today.

To summarise the key points of your learning, hopefully you can feel confident enough to say that a tenth is one tenth the size of a whole, or one.

The tenths column is placed immediately to the right of the ones column, and the decimal point separates those two columns.

The decimal point separates the whole numbers from its fractional parts, and therefore would be placed in between the ones and the tenths.

Thanks for learning again with me today.

I've really enjoyed it, hopefully you have too, and I'll see you again soon.