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Hi, I'm Mr. Peters.

Thank you for choosing to learn with me today.

In this lesson, we're gonna be thinking about how we can count in tenths in lots of different ways.

Are you ready? Let's get going.

By the end of this lesson today, you should feel confident in counting in tenths and doing so in a variety of ways.

Throughout this lesson, we're gonna keep referring to some of the key vocabulary here that you can see.

The first one is decimal number and the second one is decimal point.

A decimal number has a decimal point followed by digits that show the fractional part.

A decimal point is a small dot that is used to separate whole numbers from their fractional parts.

Watch out for this language in the lesson and use it for yourself where you can.

This lesson is broken down into two parts.

The first part is where we'll be counting and representing tenths up to one whole.

And in the second part we'll be thinking about counting and representing tenths beyond one whole.

Let's get started over the first part.

Throughout this lession you'll meet Aisha and Alex and they're gonna be helping us along our way.

So we should already be quite familiar with what one tenth is and we know that one tenth is a whole that can be divided into 10 equal parts, and one of those parts would represent one tenth.

Now Alex is here and he's got his own whole and he's asking, can you estimate where you think one tenth might be against that whole? Have a little think for yourself.

That's right.

One tenth would sit just about there.

Look at the size of that one tenth compared to the whole.

Can you see that we would need 10 of those parts to make the whole? In fact, let's test that and count in tenths together.

Are you ready? One tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, 10 tenths, and 10 tenths is equal to one whole.

As we've already identified, this small white block is representing one tenth of the whole and the whole in this case is the orange block.

We can say this as 0.

1, or we can write this as 0.

Where the zero represents zero wholes.

The decimal point is used to separate the whole numbers from the fractional parts and the one is representing one tenth.

When we write a number like this, we have written it as a decimal number.

So, this time we're gonna do some more counting, but we're gonna use that language of how we might say it as we write it.

So for example, here we have one tenth and we can write that as 0.

Let's carry on counting together.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

90, zero point ten.

Oh, hang on a minute here.

We don't write 10 tenths on the right hand side of the decimal point like that.

'cause we know, as Alex has pointed out here, that 10 tenths is equal to one whole.

So we'd have to exchange those 10 tenths for one whole and we'd then represent that as 1.

So we wouldn't say zero point 10, we would in fact say one.

So now we've got a couple of ways that we can count in tenths.

We're gonna carry on counting, but we're gonna use a different representation this time.

So let's count starting off with how Aisha has suggested that we do so, counting in tenths, ready? One tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, 10 tenths or one whole.

Let's try a different way.

We've just counted in tenths, but we can count like we would say the decimal number.

Let's do it this way round.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, 1.

0, or just simply one.

Now when we count in different ways, for example, we've counted in tenths and we've counted using our decimal number language.

This is called dual counting.

It means we're counting in more than one way and we're gonna continue to do so throughout the rest of this lesson as well.

Now our representation has changed onto a number line, and hopefully you can see our whole, which is resting along the top of the number line.

Our whole starts at zero and it finishes at one.

This time we're gonna count using tenths.

Are you ready? One tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, and 10 tenths or one whole.

Should we count backwards this time? Here we go.

One whole, nine tenths, eight tenths, seven tenths, six tenths, five tenths, four tenths, three tenths, two tenths, one tenth, zero tenths, or zero.

Right, one more time, however, this time we're gonna use our decimal number language.

Are you ready? Zero, 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

One whole.

And backwards.

One whole, 0.

9, 0.

8, 0.

7, 0.

6, 0.

5, 0.

4, 0.

3, 0.

2, 0.

1 and zero.

Well done if you manage to keep up and count along with me.

Aisha, this time has suggested we try and use a Gattegno chart to do our counting.

This is a very different representation, but also one that's really useful to help us think about our counting.

Aisha is suggesting we use our decimal number language.

So we're gonna start with 0.

Are you ready? 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, 1.

0 or one.

And let's count backwards as well.

0, 0.

9, 0.

8, 0.

7, 0.

6, 0.

5, 0.

4, 0.

3, 0.

2, 0.

And then we'd be back at zero, wouldn't we? Alex has suggested that we could count in tenths.

Let's do the same again.

Are you ready? One tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, and 10 tenths or one whole.

Aisha has just suggested that we should also count backwards as well.

Why don't we start counting back in tenths and then change to the other way where we can use our decimal language.

Are you ready? 10 tenths or one whole.

Nine tenths, eight tenths, seven tenths, six tenths.

Why don't we change now? 0.

5 and 0.

It's also important to be able to count from different positions as well, and not just starting at zero or 0.

So this time we're gonna start from 0.

Are you ready? And even Alex has popped up and he suggested that we use our decimal language.

Here we go.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, 1.

0, or just one.

Now let's go back to Aisha's language and use Aisha's language of four tenths, five tenths.

Are you ready? Four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, 10 tenths or one whole.

And then of course Aisha has now pointed out that we can count backwards as well.

Let's just do that one more final time using the language that she's been using of tenths.

Are you ready? So 10 tenths, all one whole, nine tenths, eight tenths, seven tenths.

I know, why don't we swap and go back to what Alex was saying earlier.

Let's carry on from seven tenths.

Ready? 0.

7, 0.

6, 0.

5, 0.

Again, well done for keeping up.

Okay, time to check our understanding.

Complete the sequence below.

It starts with 0.

5, 0.

6, 0.

7 and then there are three gaps.

Can you tell me whether it's A, B, or C? Have a little think.

That's right.

It's B.

It continues from 0.

5, 0.

6, 0.

7, 0.

8, 0.

9 and then one whole.

And as we talked about earlier, when we write one whole, we write that as 1.

0, don't we? Or just one.

We don't write it as zero point 10 or 0.

10.

Now, time for your first task.

Here I've asked you to choose two representations that you can practise your dual counting on.

So you might decide to use number line, you might decide to use your base 10 blocks.

You could use a Gattegno chart or you could use some place value counters.

Good luck and I'll see you shortly.

Welcome back, Aisha is demonstrating one of her representations that she chose to use.

She's chosen to use the place value counters and she counted them both ways.

Let's have a go and see what Aisha did as well.

Here we go.

One tenth or 0.

1, two tenths or 0.

2, three tenths or 0.

3, four tenths or 0.

4, five tenths or 0.

5, six tenths or 0.

6, seven tenths or 0.

7, eight tenths or 0.

8, nine tenths or 0.

9 and 10 tenths or one whole or simply one.

Okay, great.

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

So, so far we've been counting in tenths, haven't we? And let's count up from zero one more time.

Are you ready? We'll use our decimal number language.

Zero, 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, 1 whole.

Hmm.

But now Aisha is asking, well, what would come after one and how might we describe that? What's the arrow pointing at? Can you have a think for yourself? What do you think would go there? That's right.

It'd be 1.

1 because we've reached the whole and we've got another tenth to go past.

So it'd be one whole and one other tenth.

So Aisha's asking, well, why is it not two then? Well the reason for that, which Alex is pointing out is that actually it's only gone along another one tenth.

It's the same size parts as the other parts before.

And to get to the next whole, which would be two, we would need another 10 tenths.

So hopefully you can see that another 10 tenths after that would take us to the right hand end of our number line, which would be two.

So as Alex has said, again, the arrow is pointing at 1.

1, which represents one whole and one additional tenth.

Now we're gonna carry on and we're gonna use our base 10 blocks again.

But this time I think we're gonna have to count above one.

Let's get going.

Are you ready? One tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, 10 tenths, or one whole.

Hmm, now that we've got to one whole, we can now start counting towards the next whole.

Remember, one whole is equal to 10 tenths.

So now that I've got another tenth, I'm gonna have 11 tenths.

Are you ready? 11 tenths, 12 tenths, 13 tenths, 14 tenths, 15 tenths, 16 tenths, 17 tenths, 18 tenths, 19 tenths and finally 20 tenths.

Great work.

Good counting.

Now we're gonna do the same again, but this time we're going to use our decimal language.

Are you ready? 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, one or 1.

0, 1 whole, 1.

1, 1.

2, 1.

3, 1.

4, 1.

5, 1.

6, 1.

7, 1.

8, 1.

Hmm, have a think now, what do you think might happen here? That's right.

It wouldn't go to 1.

10.

It would change 'cause we've got another whole again.

And now we've got two wholes altogether.

So we'd write that as 2.

The two represents two wholes and the zero represents zero additional tenths.

Hmm.

We've been using this language of whole quite a lot and Aisha now suggests that she can count it in one more way.

Let's have a go at Aisha's new way.

She's suggesting that we could say it has zero wholes and one tenth.

I wonder if you could count this with me.

Zero wholes and one tenth, zero wholes and two tenths, zero wholes and three tenths, zero wholes and four tenths, zero wholes and five tenths, zero wholes and six tenths, zero wholes and seven tenths, zero wholes and eight tenths, zero wholes and nine tenths.

Hmm.

Now we've got to 10 tenths, haven't we? And we now know that 10 tenths is the same as one whole.

So we would say one whole.

Now when we add on one more tenth, we're gonna have one whole and one tenth.

So let's carry on from here.

One whole and one tenth, one whole and two tenths, one whole and three tenths, one whole and four tenths, one whole and five tenths, one whole and six tenths, one whole and seven tenths, one whole and eight tenths, one whole and nine tenths.

And again, remember when we add one more tenth here, that means we'll have another 10 tenths, which makes another whole.

So altogether we will have two wholes.

I've changed the representation again here, this time we've got our number line back and as you can see, each one of these intervals represents one tenth and I've placed a base 10 block tenth to represent that for you between the first two intervals.

Let's count up in tenths again starting on zero.

Are you ready? We're gonna use our decimal number language first.

Are you ready? Zero, 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 0.

7, 0.

8, 0.

9, one whole, 1.

0, 1.

1, 1.

2, 1.

3, 1.

4, 1.

5, 1.

6, 1.

7, 1.

8, 1.

9, 2.

0 or two wholes.

Let's do it one more time, however, we're gonna use our language of tenths here.

Zero, one tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, 10 tenths, 11 tenths, 12 tenths, 13 tenths, 14 tenths, 15 tenths, 16 tenths, 17 tenths, 18 tenths, 19 tenths, 20 tenths.

Aisha is now saying that we've got 20 tenths all together or two wholes.

Hmm, Alex is then wondering, I wonder how many tenths would be three wholes altogether? Have a little think.

That's right.

It would be 30 tenths, wouldn't it? Each whole represents 10 tenths and we would have three of them, so that'd be 30 tenths.

Aisha is now gonna answer Alex's question.

She says that we can count up in tenths and find out how many tenths would make three wholes.

Here she goes.

She now has 10 tenths.

Aisha now has 20 tenths.

And finally Aisha now has 30 tenths, which would be the same as three wholes.

So three wholes are equal to 30 tenths.

Finally, for today, we can use our Gattegno chart again to count and this time we're gonna count over one.

Let's use our decimal number language again.

And if you'd like to, you might like to gently tap along as we go.

Are you ready? 0.

1, 0.

2, 0.

3, 0.

4, 0.

5, 0.

6, 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 two.

Let's do it one last time.

And this time we're gonna use the language that Aisha suggested where we talk about the wholes and the number of tenths.

So we've got zero wholes and one-tenth, zero wholes and two-tenths, zero wholes and three tenths zero wholes and four-tenths, zero wholes and five tenths zero wholes and six tenths, zero wholes and seven tenths, zero wholes and eight tenths, zero wholes and nine-tenths, one whole or 10 tenths, one whole and one tenth, one whole and two tenths, one whole and three tenths, one whole and four tenths, one whole and five tenths, one whole and six tenths, one whole and seven tenths, one whole and eight tenths, one whole and nine tenths and finally two wholes or 20 tenth.

So when we start thinking about how we can write these decimal numbers, we know that we can use a decimal point to separate the whole numbers from the fractional parts.

Let's have a look here.

Our base 10 blocks are showing a one and six tenths.

So we can place a one to represent the one in the ones column, and then we can place a six to represent the six tenths in the tenths column.

Now if you remember, we don't need to have to place value columns here so we can remove them and we can place a decimal point in between the wholes and the fractional parts to represent our number of 1.

Okay.

Have a look at it this time, have a look at our base 10 blocks.

Has there been a change in them at all? Ah, yeah, that's right.

Well spotted.

We actually still have the same amount of ones, but we have one extra tenth this time, don't we? So we actually have one whole and seven tenths.

And again, we will record that as one whole in the one's column and a seven in the tenths column and we would separate those with a decimal point.

Have another quick look, what you notice this time? Yep, you spotted it.

This time we actually have two wholes and we've gone back to the original amount of tenths that we had to start off with.

So to represent this, we would place a two in the ones column.

This represents two ones, and we'd place a six in the tenths column.

This represents a six tenths, and once more we would separate it using our decimal point.

Have a look at our final example.

What's changed this time? Ah, yeah, well actually the wholes have stayed the same, but we don't have any tenths this time.

So how would we record this? Well, you'd place a two in the ones column and you could place a zero in the tenths column to represent zero tenths.

We could separate them with a decimal point.

However, we know that we don't always have to record whole numbers with a decimal point and any tenths after it if there aren't any there.

So we could simply just write the number two.

Okay, time to check your understanding.

6 can also be read as, is it A, 1.

6 tenths, B, 16 tenths, or C one tenth and six wholes.

Have a little think for yourself.

Yep.

Good spot.

It was B, 16 tenths 'cause we know that one represents 10 tenths and the six would represent six additional tenths and six tenths and 10 tenths would make 16 tenths altogether.

Have a look at our images again, which one of these represents 1.

3? You can see that there's a whole that's been shaded in and that represents 10 tenths or one whole and there is also three additional tenths that have been shaded in, so altogether that would represent 13 tenths or 1.

Have a look at A quickly, why is it not answer A? Ah, that's because our image shows one tenth and three ones and they've been swapped around.

Now we know it doesn't matter which ways round they've been swapped, but we can see here that we would have to write that as 3.

1 because the three represents the ones or the wholes and the one would represent the one tenth that you can see.

Okay, time for you to have a go.

Your task here is to fill in the blanks and I've given you sentence stems to help you.

You need to record each image that you can see using the three different ways that we have been able to count them.

That means you can represent it as wholes and tenths.

You can represent it simply as tenths.

And finally you can represent it as a decimal number.

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

Okay, welcome back.

Let's go through the answers together then.

So the first image represents one whole and six tenths.

We can write that as 16 tenths or we can write that as 1.

The second image represents two wholes and four tenths.

And again, we can represent that either as 24 tenths or 2.

And finally, the last image represents three wholes and seven tenths.

And we could write that as 37 tenths, or we could record that as 3.

7 using our decimal notation.

So just to summarise our learning from today, you can count in tenths using a variety of different ways.

We could use the language of wholes and tenths.

For example, there is one whole and four tenths.

You could use it just counting up the number of tenths there are.

So for example, there are 14 tenths.

And finally, you could say or write the number as a decimal number using a decimal point.

And we would say this as 1.

Thanks for learning with me today.

Hopefully you learn something new and you're becoming really confident with counting forwards and backwards in tenths in lots of different ways.

Take care and I'll see you again soon.

I've finished the video