Lesson video

Hi, and welcome to today's lesson.

Thank you for coming along.

Today, we're gonna be thinking about describing and writing decimal numbers in lots of different ways.

I'm really looking forward to getting started.

Let's go.

There are a number of key words we're going to need for our learning today.

Some of them, you'll have heard before.

The first one is 10th.

The second one is decimal number.

The third one is fraction.

And the last one is mixed number.

So a 10th is the name that you can give to a part from a whole that's been divided into 10 equal parts.

A decimal number is a number that has a decimal point in it, and that decimal point helps to separate the whole numbers from the fractional parts, which come after the decimal point.

A fraction is certainly something that we should be familiar with by now, and it shows us how many equal parts a whole has been split into.

And finally, a mixed number.

Well, a mixed number is a number that combines both whole numbers and fractions.

So the outcome by the end of today's lesson, is hopefully, that you feel confident enough to say that, I can describe and write decimal numbers with 10ths in different ways.

This lesson has been split into three parts.

The first part will think about 10ths and how they can be used to label a part of a whole that has been divided into 10 equal parts.

The second part of this lesson, we'll think about 10ths again and how they can be placed on a number line.

And finally, the third part of our lesson, we'll consider how 10ths can be recorded as either fractions or decimal numbers.

Let's get going with the first part.

Throughout this lesson, Andeep and Izzy are going to join us to help us with our learning.

So we know that a 10th is the name that we give to a part from a whole, and that whole would've had to have been divided into 10 equal parts.

As we can see here, we have one whole, and that whole underneath has been divided into 10 equal parts.

And each one of those parts we can term as one 10th.

And we can write that as a decimal number, 0.

1.

We could also write 0.

1 as a fraction.

And as you can see now, each of our parts has also been labelled as a fraction, and we write that as one over 10, where the bar in the middle, the vinculum, represents the division of the whole.

The denominator 10, tells us how many equal parts the whole has been divided into.

And the numerator, one, tells us how many parts we have.

As a number of 10ths grows, we start to count them together.

So as you can see, we now have 1/10 shaded in, and we can write this as 0.

1 or 1/10.

When we have another 10th, we can write this as 0.

2 or 2/10.

And if we have one more 10th, we could write this as 0.

3 or 3/10.

So you can see we've started to count these 10ths in two different ways already.

We also need to become more confident with counting in 10ths from lots of different positions, not just starting at zero or 1/10.

So here we're gonna start counting from 4/10.

Let's count using our decimal number language of zero point something.

Are you ready, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, 1.

0, or one whole, 1.

1, 1.

2, 1.

3, 1.

4, 1.

5, 1.

6, 1.

7, 1.

8, 1.

9.

And finally, 2.

0 or two wholes.

As we've already looked at as well, we can count it using our fractional language of 10ths.

Are you ready? Let's start again from 4/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10 and 10/10 or one whole.

13/10, 14/10, 15/10, 16/10, 17/10, 18/10, 19/10, and finally again, 20/10.

Whilst we've been counting these cumulatively, the number of 10ths have been growing in size each time.

We also still need to know that each one of these 10ths represents one 10th, and that's what Andeep is pointing out to us.

And this is still 0.

1 or 1/10.

Let's carry on our counting.

But this time we're gonna start from 7/10.

And again, let's use our fractional language of 10ths that we've been using so far.

7/10, 8/10, 9/10, 10/10, 11/10 12/10, 13/10, 14/10, 15/10, 16/10, 17/10, 18/10, 19/10 and 20/10ths.

It doesn't matter that the image change slightly.

We still have a whole and have divided each one of those wholes into 10 equal parts.

Let's count up again.

And this time let's use our decimal number language of zero point something.

Are you ready? 0.

7, 0.

8, 0.

9 1.

0 1.

1, 1.

2, 1.

3, 1.

4, 1.

5, 1.

6, 1.

7, 1.

8, 1.

9.

And finally two, 2.

0.

And remember, it doesn't matter about the representation being slightly different.

These representations are still showing wholes and how they've been divided into 10 equal parts, and each one of those parts has a value of 1/10.

Okay, time for you to check your understanding.

Have a think, which one does not represent 14/10? That's right, it's B.

B does not represent 14/10.

And Izzy's now asking, well, why does it not represent 14/10? Well we actually have a decimal as the numerator, and that's not really mathematically correct to write it like that.

But also, we would need 14 to be the numerator and not 1.

4, so we know that B is incorrect.

Okay, onto our first task then.

What I'd like you to do is label the images here and show me how each part has a value of 1/10.

You can either do that on the left hand side using decimal numbers, and then on the right hand side, you can do that using fractions.

Good luck and I'll see you shortly.

Okay, welcome back.

On the left hand side, you can see our pentagon.

Our pentagon has been divided into 10 equal parts.

And we know that each one of those parts is worth 1/10, or in this case 0.

1.

And we have six of them that have been shaded.

So the six shaded 10ths represent 6/10.

On the right hand side, we have got, whoa, we've got two wholes here.

And they've both been divided into 10 equal parts.

One of them has been completely shaded 'cause that represents 10/10.

But we were asked to find 12/10.

We, therefore we had to get another two, 1/10 from the second whole, and therefore we shaded those two 1/10.

And altogether we have 12/10.

Well done.

Okay, let's move on to our second part of the lesson where we start to think about 10ths and their position on a number line.

So just like any other number, 10ths also have a place on a number line.

Here you can see on my number line, on the top row, we've written it as a decimal number.

And on the bottom, we've written it as a fraction, and we know that they are both the same.

Now, I wonder, could you have a quick careful look at the number lines that I've put here? I've placed one above the other.

Have a look.

What do you notice that's different about them? Yeah, good spot.

The first one starts at zero and finishes at one, and the second number line starts at one and finishes at two.

Is there anything that's the same about these number lines? Yeah, again, that's right.

They've both been divided into 10 equal parts.

So the whole in the top number line is between zero and one.

And the whole on the second number line is between one and two.

And both of those wholes have been divided into 10 equal parts.

Now I've added a bit more to them.

Have another careful look.

What do you notice this time? What's the same about them and what's different about them? I wonder if you spotted what Izzy spotted.

She noticed that the number of 10ths on both the number lines have stayed the same.

However, it's the number of ones that have changed.

On the top number line, we have zero wholes until we get to the last interval where we reach one whole.

And then on the second number line, we have one whole until we, again, we get to the end of that number line, and then we suddenly have two wholes.

Did you notice anything about the fractions as well? The ones stay the same in the fractions from the top number line and the bottom number line.

But again, on the bottom number line, we then have an extra one.

That one represents a 10 for the 10/10 that we've already counted.

Okay, I've changed my number line again this time.

Have a really careful look, what do you notice? Ah, yeah, well done, you may have noticed that the second number line, actually this time doesn't start at one and go to two.

It starts at two and goes to three.

Yeah, that's exactly what Izzy spotted.

And again, what's the same and what's different? Well, the 10ths digits have stayed the same on the top and the bottom number line, but again, it's the ones digit that's changed.

On the top number line, we have zero ones.

And on the second number line, we have two ones until we reach the end where we get to three.

Right, last one.

Can you spot the difference this time? What do you notice? Again, our whole has changed on the bottom number line.

This time it's gone from nine on the left to 10 at the other end.

And that whole has also been divided into 10 equal parts.

So again, the 10ths digits have stayed the same and the ones have changed this time, the top number line has zero ones until we reach the end and then we get to one, one, and the bottom number line has nine ones until we reach the end and then we get to 10 ones.

And Izzy is asking us a really interesting question.

She wonders, can any two consecutive numbers, any two numbers that are next to each other always be divided into 10 equal parts? I wonder what you think.

We'll have a further look at this later on.

Okay, time for you to check your understanding.

Have a look at Andeep's number line.

Andeep thinks there's a mistake on it.

Can you have a look? Can you spot the mistake that Andeep has made? Yeah, that's right.

We've got from 0.

9 to 0.

10, and we know we don't represent one whole as 0.

10, do we, those 10/10 need to be exchanged for one whole and therefore we would write it as 1.

0.

Let's count it up just to double check.

Zero, 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, 1.

0 or one, 1.

1, 1.

2, 1.

3, 1.

4, 1.

5, 1.

6, 1.

7, 1.

8, 1.

9, and two 2.

0.

Here's another quick check.

Can you fill in the missing numbers? That's right.

The first missing number is 7.

1.

The second missing number is 7.

5.

And the last missing number is eight or 8.

0, but we're just gonna use eight.

Izzy said asking, well, how did you work it out? You have everything for yourself, what did you do? Well, I looked at my whole number line and realised that there were gonna be 10 equal parts, so chances are we're going to be working in 10ths.

I then looked at the distance between 7.

2 and 7.

3 and just double checked whether that was a 10th.

And indeed it was.

It went from 7.

2 to 7.

3.

So I then went back to the beginning and the first number was seven.

So seven, adding on one more 10th would be 7.

1, which fills the first gap, the middle gap, I could do it two ways.

I could look at 7.

4 and think, what's one more 10th than 7.

4? Or I could look at 7.

6 and work backwards.

What's one less 10th than 7.

6? I did it the latter way actually.

So I started on 7.

6 and went back 1/10 to 7.

5, which filled in the middle gap.

And then finally at the end, well, I got to 7.

9 and I realised that I needed one more 10th to jump on.

And when I have 9/10, if I add one more 10th, that makes the next whole and the next whole would be eight or 8.

0.

Izzy's now asking, well, how could I write these as fractions as well? Well, I know that 0.

1 can be written as 1/10.

So 7.

1 could be written as seven wholes and one 1/10, 1/10.

And the same for the middle row.

I know that 7.

5 is seven wholes and 5/10, therefore I could write this as seven and 5/10.

Okay, time for you to have a go now, here is a number line with lots of missing boxes on it.

I wonder, could you fill in the missing boxes? On the top row, writing them as decimal numbers and on the bottom row, writing them as fractions.

For your second task, I'd like you to have a look at this blank number line, and I'd like you to pick two of your own consecutive numbers and place them at either end of the number line, and then write in the decimal numbers on the top of it and the fractions on the bottom to show that you understand how we can record both of these as decimal numbers and fractions.

Good luck and I'll see you shortly.

Okay, welcome back.

Let's have a think about how we did this then.

Well, the first missing number was 0.

1.

And again, we knew that 'cause we're working in 10ths and we're gonna start on zero and add on 1/10 which will make 0.

1.

Okay, and the next one, the previous one is 0.

8, and I know that 1/10 on from 0.

8 is 0.

9.

The next one is one, and there's a gap after that.

So I know that one add another 10th is one whole and 1/10, which we write as 1.

1.

The next gap along is between 1.

3 and 1.

5.

If I go 1.

5 and count back one, that would be 1.

4, and then finally 1.

9.

Well, just similar to our example we had a minute ago, if I'm on 1.

9, that means I've got one whole and 9/10, and if I add on an extra 10th, that means I'm going to get to my next whole, which will be two wholes or 2.

0.

Okay, and for the fractions underneath, well zero, how would I write zero as a fraction? Well, we don't usually record it like this, but we could record it as 0/10 like this because we don't actually have any parts.

Our next one is 0.

4.

Well, underneath that I know 0.

4 can be written as 4/10, so I'm gonna write it as 4/10.

The next one? Now I could either look at the fractions either side of it or I could look up at the top.

So for this one I'm gonna look at the fractions either side of it, we've got 10/10 and then the other side I've got 12/10.

That must mean in the middle would be 11/10.

And again, 12/10 add on one more 10th, that would make 13/10.

And then for this one here, I'm gonna start thinking about the decimal numbers.

At the top it says 1.

5.

I know that as one whole and 5/10, I know that one whole is made of 10/10.

And obviously we've got these extra 5/10.

So altogether that must mean 15/10.

And finally 2.

0, two wholes.

How do I write that into 10ths? Well, we know that one whole is equal to 10/10, so two wholes must be equal to 20/10.

Well done if you managed to get all of that.

On the second task, I asked you to think about our number line and choose two of your own consecutive numbers.

Here's an example that I tried.

You may have tried this one too.

I chose between eight and nine, and as a result, I wrote the decimal numbers on the top, 8.

1, 8.

2, 8.

3, and so on.

And on the bottom I would have to write the fractional notation.

Well, I had to think about this.

I need to know what eight wholes would be as 10ths.

Now we know that one whole is 10ths and two wholes is 20/10.

Three wholes would be 30/10.

So eight wholes would be, that's right, 80/10.

and nine wholes would be 90/10.

And then in the middle of those we can place in the additional 1/10 each time.

So 80/10, 81/10, 82/10, 83/10, 84/10, and so on.

I hope you came with a really interesting idea too.

Okay, into the last part of our lesson now, and we're gonna carry on focusing a little bit more about 10ths and how we can write these as fractions and decimal numbers.

If you remember in the previous cycle, Izzy asked the question, could any two consecutive numbers be divided into 10 equal parts? Well, the answer to that is yes.

And Andeep is now asking, well, how would I write the next interval along? Look at our number line.

Our number line is starting at 340 and it finishes at 341.

So the whole between those two numbers has been divided into 10 equal parts.

So we have 340, and we know that that next interval along is one additional 10th.

So altogether we would have 340 and one additional 10th.

So we could write that as 340.

1, or this time we could write it as 340 and 1/10.

Have a look at our number line again now.

This time it's changed slightly.

It starts at 342 and finishes at 343.

Have a think for yourself.

What would you think the arrow would be pointing to here? It would be 342.

1 or 342 and 1/10.

Let's have a look how we could write this in our place value chart.

Here, we've got the place value headings written down as well, and we know that we can't keep those, so we replace those with a decimal point to help us identify the value of the number.

This number is 342.

1 or 342 and 1/10.

Here's another example for you.

This time a different representation.

Can you ever think, what number do you think this is representing? Well, I can see four 100 counters.

I can see three one counters and I can see five 1/10 counters.

How would we record this then? Well, I've used my place value headings here again, and I've placed the four under the hundreds column.

We don't actually have any tens, do we? So I need to place a zero in the tens column.

We've got three ones, so I've placed a three there and I've placed five in the 10ths column.

And as we know, we can replace the place value headings with our decimal points to help us understand what this number is.

So we can say that this number is 403 and 5/10 or we could also say it as 403.

5.

Okay, so we're now gonna think about a bit more about how we can write these as decimal numbers as well as a mixed number.

On the left, you can see I've written it as a decimal number, and on the right you can see I've written it as a mixed number, where a mixed number has a whole and a fraction written together.

We can use a sentence stem to help us with this.

I say 342.

1, but I think 342 wholes and 1/10.

Using this language helps us to convert from using the decimal number to the mix number.

Okay, here's another example.

Have a look at the number carefully, what do you notice? Yeah, just like Andeep has spotted, we actually have a zero digit in our number, so we need to be really careful about how we pronounce this number and make sure we get the correct value.

The number is 403.

5, so I say 403.

5, but I think 403 wholes and 5/10.

Now time to check our understanding a bit more.

Here's my turn and then you can have your turn.

I'm gonna say the first part of the sentence stem, and then you'll be able to say the second part of the sentence stem.

Here we go.

My turn, I say 6204.

3, but I think, can you fill in those gaps? Well done, let's do that together.

Starting from the beginning.

I say 6204.

3, but I think 6,204 and 3/10.

Well done, okay, into our last practise task now.

Can you write the numbers represented as both a decimal number and a mixed number? There are three numbers to write in each row of the place value columns.

Once you've completed that task, I've got two questions here for you.

So, can you write the amount as a decimal number and again as a mixed number? And then finally, the last task.

Can you complete the table? You'll see that some of the numbers have been written as a fraction or a mixed number, and some have been written as a decimal number.

You need to convert between the two.

Good luck and I'll see you soon.

So let's go through this together.

We can use our stem sentence to help us.

I say 312.

4, but I think 312 and 4/10.

The second one, I say 304.

4, but I think 304 and 4/10.

Did you spot the missing gap in the tens? Well done.

And finally, I say 300.

2, but I think 300 and 2/10.

Again, there are some gaps there in the tens and the ones this time, we have to be really careful with how we say those numbers, don't we? Okay, onto task two, we had to write this as a decimal number and as a mixed number.

After a party, there are three whole pizzas and 4/10 of a pizza left.

How would we record this? Well, let's use our stem sentence again.

I say 3.

4, but I think three wholes and 4/10.

Andeep drinks two litres and 8/10 of a litre of water.

Well, I say 2.

8, but I think two wholes and 8/10.

Well done if you managed to get those.

And then finally into the last task here.

We need to convert between either the fraction and mixed number to the decimal number or the other way around.

The first one says 3/10.

And we know that 3/10 can be written as 0.

3.

I say 0.

3, but I think 3/10.

The second one is 0.

7.

I say 0.

7, but I think 7/10.

Well done, third one is 2.

0.

Well, we know that's also two wholes, don't we? And one whole is 10/10, so two wholes must be 20/10.

Okay, now we've got a mixed number, 408 and 8/10.

Well that would be represented as 408.

8.

I say 408.

8, but I think 408 and 8/10.

And then finally the last one, 1037.

9.

I say 1030 7.

9, but I think 1037 and 9/10.

Okay, just to summarise what we've been learning today then.

Hopefully you feel confident enough to know that each part of a whole that has been divided into 10 equal parts can be labelled with the term 1/10.

10ths also have their own place on the number line and will always have a place between any two consecutive numbers.

And finally, we hopefully now know that 10ths can be written in many different ways.

We can write them as decimal numbers, we could write them as fractions, or we could even write them as a mixed number.

Thanks for learning with me today.

I really hope you enjoyed yourself and have got something to take away from this lesson.

Keep working hard and I look forward to seeing you again soon, bye.