Lesson video

Hi, my name's Mr. Peters and I'm really looking forward to learning with you today as we begin to think about decimals and how they link to our prior learning.

Today, we're gonna be thinking about what a tenth is and how this relates to a whole.

So by the end of this lesson, you should be able to say that I can identify tenths as a part of a whole.

Throughout this lesson, we're gonna be using two key words.

The first word is equal, and the second word is tenth.

Let's have a look a little bit more about what these mean.

I'm sure you've heard of the word equal a lot before.

So for today, we are going to define equal as exactly the same, an even amount, or a value.

And tenth is also a word that we should already be familiar with.

And so in this lesson, we'll be defining a tenth as one part of 10 equal parts of a whole.

This lesson has been split into three parts.

The first part will be to define how one tenth relates to a whole.

The second part will identify what one tenth looks like in different contexts.

And finally, the last part of our lesson will describe what it looks like when we have more than one tenth, we have multiples of one tenth.

Let's get going on our first section, defining how one tenth relates to a whole.

Throughout this lesson, you'll meet Sophia and Jacob, who will help us along our way with our learning.

Firstly, I wonder if you could have a look at these shapes for me.

Have a little think for yourself.

What do you notice about each of the shapes? What's the same about them and what's different about them? You may have noticed that the shapes are all different.

Each part is a different size, but each shape has been split into 10 parts.

Each part is equal to the others.

Now have another little look.

What do you notice this time? That's right.

One part in each of those wholes has been shaded.

Each whole has been divided into 10 equal parts, and now we have one of them that is shaded.

We call this one part one tenth.

I wonder if we could use this stem sentence together to help us with our learning.

Let's have a look at the first shape.

Here's the whole.

The whole has been divided into 10 equal parts, and one of those parts is shaded.

This is one tenth of the whole.

I wonder if you could join in for me for the next shape.

Here's our next whole.

Let's say this together.

The whole has been divided into 10 equal parts, and one of those parts is shaded.

This is one tenth of the whole.

Let's try another shape.

The whole has been divided into 10 equal parts.

One of those parts has been shaded.

This is one tenth of the whole.

And finally, one more shape.

Our whole has been divided into 10 equal parts, and one of those parts is shaded.

This is one tenth of the whole.

Well done for saying that along with me.

Let's have a look at one shape a bit more in particular now.

What'd you notice about these two shapes? Sophia has joined us and she's also asking, "How can I describe these shapes?" That's right, you might be thinking, well, they've been divided into 10 parts again, and those parts are all equal.

And this time they both have one that is shaded, although the shaded part isn't in the same place.

Is this still one tenth? Yes.

Yes, it is.

I wonder if we could use our sentence stem again to help us.

Let's start with the one on the left first.

The whole has been divided into 10 equal parts and one part is shaded.

This is one tenth of the whole.

Now let's do the same with the second shape.

All together.

The whole has been divided into 10 equal parts and one of those parts is shaded.

This is one tenth of the whole.

So both of these parts are one tenth of the whole even though they're in different places, it does not matter which one of those parts we shade in.

Each one of those parts represents one tenth of the whole.

Bar models are a really effective way to help us represent our fractional understanding, and we can use a bar model to help us understand this relationship between the wholes and tenths.

Let's have a look in a bit more detail.

At the top, you can see one whole, and underneath you can see a whole that has been divided into 10 equal parts, and each one of those parts is one tenth.

Let's say our stem sentence together again.

The whole has been divided into 10 equal parts and one part is shaded.

This is one tenth of the whole.

Now some time for us to check our own understanding.

Here's a quick question.

To show one tenth, the whole must be divided into 10 something parts.

Is it a, different, b, square, or c, equal? Take a moment for yourself to have a think.

That's right, it's c, equal.

To show one tenth, the whole must be divided into 10 equal parts.

The parts don't all need to be square, and the parts don't all have to be different.

Here's another question.

Which image shows one tenth? Have another careful look for yourself.

That's right, it's c.

C shows one tenth of a whole because the whole has been divided into 10 equal parts and one of those parts is shaded, and this part is known as one tenth.

Jacob's joined us now and he's now asking, "Well, why does a and b not show one tenth? Did you manage to spot why? Well, that's right, 'cause a actually has 11 equal parts.

So we cannot call this one tenth because it's not split into 10 equal parts.

And for b, well, there are 10 parts and one of them is shaded, but those parts aren't equal.

They're different in size.

Therefore, that is not one tenth of the whole.

So now I've got a little task for you.

I wonder, could you show one tenth in three different ways using the squares that I've divided up for you? Once you've done that, have a go at question two, where I'm then asking you to have a go at creating your own example of one tenth, maybe an example of one tenth that no one else can think of themselves.

Good luck and I'll see you shortly.

Welcome back.

Let's see how you got on.

Jacob has joined us again and showed us the examples that he's created.

Hopefully you can see in each of the pictures that each of the wholes were already divided into 10 equal parts that each have one shaded, and it doesn't again matter which one of those parts we have shaded.

Each one of those parts represents one tenth.

Jacob then created his own example.

Let's have a look at that.

Hmm.

Here's an example I've not seen yet.

Here, we've got an oval with 10 circles in it.

Now, each one of those circles are the same in size, and one of those circles hasn't been shaded.

Hmm.

So if all 10 of those circles are the whole, then the one unshaded circle is one tenth of the whole.

So one tenth of the whole doesn't always have to be the shaded part, it could be the unshaded part.

Well done, Jacob.

A great example.

Now, hopefully you're feeling more confident with what one tenth is in relation to the whole, where we begin to look at one tenth in lots of different contexts.

We're going to start here with an image that represents a one metre stick.

Now, we can use one metre sticks and think about how they relate to a whole and tenths.

However, it would take quite a while to draw one of those out each time.

So we can also use a number line to represent one metre.

Again, the whole has been divided into 10 equal parts.

At one end of the number line, we have zero metres, and at the other end of the number line, we have one metre.

Here you can see how the metre stick and the number line are very similar to each other.

So now that we're going to use a number line to represent a metre, we can now see that our whole metre has been divided into 10 equal parts.

And now one of them has been shaded.

This is one tenth of a metre.

And in this case, one metre is acting as our whole.

Let's have a look at another example.

Here, we have a jug, which, when it reaches the top of our vertical number line, is one litre.

So at the bottom of our number line on the jug would be zero litres, and at the top of the number line on our jug would be one litre.

So the whole this time is one litre.

And now we have poured in some water.

I wonder if we could use our stem sentence to help us again.

The whole has been divided into 10 equal parts.

One part has been shaded, or one part has had water poured into it.

This represents one tenth of the whole.

And in this case, the whole is one litre.

So we would say this represents one tenth of a litre.

Ah, so so far we've looked at metres and litres, and now we're gonna start thinking about kilogrammes.

Have a look at the image.

What do you notice? That's right, the scale is balanced.

And on the left hand side of the scale, we have one kilogramme, and on the right hand side of the scale, we have a kilogramme as well, but that kilogramme has been divided into 10 equal parts.

Let's use our stem sentence again to help us.

But instead of saying the whole this time, why don't we say the kilogramme? The kilogramme has been divided into 10 equal parts and one of those parts has been shaded, so that one part would represent one tenth of a kilogramme.

Okay, time for another check for understanding.

Have a look at the image below.

Sophia is asking us true or false? This picture represents one tenth of a metre.

Have a little think.

That's right, it's true.

The little blue section does represent one tenth of a metre.

Jacob's now asking, well, how did you know that? Well, we know that the whole has been divided into 10 equal parts.

And again, just one of those parts has been shaded.

This represents one tenth of the whole, which in this case is one tenth of a metre.

And we know that it doesn't matter which one of those parts is shaded in.

Each one of those parts can represent one tenth of a metre.

Okay, time for you to have a go at the second task now.

I'm wondering, in your own setting, is it possible for you to find practical examples of one tenth of a whole? I've given you some examples here below to help you along the way.

You could grab a metre stick and some paper and cut up the paper into tenths and line it up against the metre stick and shade in one of those tenths to represent one tenth of a metre, or one tenth of the whole.

You could also measure out a litre of water and then pour that up into 10 cups potentially and make sure that each of those parts are equal.

Each one of those cups would then represent one tenth of a litre.

Or potentially, you could find something that you could weigh.

I've put an example here like rice, and you could weigh out one kilogramme of rice and then divide that into 10 equal parts.

You might like to hold one of those parts in your hands and get a feel for actually how heavy one tenth of a kilo feels.

And then finally, whatever you do, don't forget to recombine your parts altogether at the end so that you can recreate the whole.

Good luck, it'll be interesting to see what you can come up with.

Welcome back.

Here are some examples that I did, and just as I suggested, here, you can see we found a kilogramme bag of rice and we held that kilogramme bag of rice and got a feel for how heavy the kilogramme was, and then we poured that kilogramme, we divided that into 10 equal parts, and then we held one of those parts as well in our hands and got a feel for how heavy that felt.

And on the right, you can see that we found a metre stick and we found some paper, and we cut out 10 equal parts that represented the whole of that metre stick, and then are shaded in one tenth.

And as you can see, that one tenth isn't placed at the beginning.

It's actually placed a little bit further along from the middle somewhere.

And we know that each one of those 10 parts each represents one tenth, and the one that shaded doesn't matter where it's lined up against the metre stick.

Well done.

That's two parts of our lesson completed.

Now we're into the final part of our lesson.

We're going to start thinking about multiples of one tenth, examples where we have more than one tenth.

Let's get going.

Okay, have a look at this shape here now.

You've seen this shape before, but something's changed slightly.

Can you notice what's changed? Can you have a think about what the relationship now is between the parts and its wholes? Have a little think for yourself.

Maybe you could use a stem sentence below to help you.

That's right, let's say it together.

The whole has been divided into 10 equal parts and two of those parts are shaded.

This represents two tenths of the whole.

In the previous example, we only had one part shaded and that represented one tenth of the whole, whereas now we have two parts shaded.

Each one of those parts represents one tenth, and together they combine to make two tenths of the whole.

Here's another example.

Have a little think for yourself.

And again, look at the stem sentence to help you.

Okay, let's say it again together.

The whole has been divided into 10 equal parts, and this time we have three parts that are shaded.

This represents three tenths of the whole.

So this whole was very different to the previous whole.

And the parts in those wholes were, whilst they were the same within the whole, they're different in shape or size, but actually, as long as the parts are equally split within the whole, then each one of those can represent one tenth.

And in this case, we have three parts that are shaded, so this represents three tenths.

Okay, going back to our bar model again, have a little look this time.

How many parts has it been divided into and how many are shaded? That's right, this time the whole has been divided again into 10 equal parts and we have seven parts that have been shaded.

This is seven tenths of the whole.

Ah, we've got the jug again here to help us see it within a context.

We know that when the jug reaches the top of the vertical number line, that is one litre.

But we haven't quite got one litre here, have we? So let's figure out how much we do have.

So let's remind ourselves that our whole this time is one litre and our whole has been divided into 10 equal parts.

And this time we have nine of them that are shaded.

So this represents nine tenths of the whole, or in this case, nine tenths of a litre.

Right, our last couple of checks for understanding.

Can you match each image of tenths to its description? Pause the video and have a little think.

Okay, how did you get on? The first image on the left is the same as four tenths.

We can see that the whole has been divided into 10 equal parts and there are four parts that have been shaded.

This is four tenths.

The middle number line on the left hand side.

Well, the whole is one metre, and that whole has been divided again into 10 equal parts.

And the jump is jumping over six tenths.

So six tenths of the whole have been covered, or jumped in this case.

And finally, our bottom example.

Ah, this is a different shape.

Well, all of the shapes are the same, they're all equal and there are 10 of them.

So the whole, again, has been divided into 10 equal parts, and this time we have five of them that are shaded.

So this represents five tenths of the whole.

Well done.

Okay, and another quick check for understanding.

Which one of these images is a non-example of seven tenths? which one does not represent seven tenths? I'll give you a moment to have a little think.

That's right, it was b.

B does not represent seven tenths.

And now Sophia is asking us, "Well, can we justify why it doesn't represent seven tenths?" Well, our whole, which is represented by all of the 10 counters would've been technically divided into 10 equal parts, 'cause the counters are all the same size, but the value of each one of those counters is different.

The value of each one of those counters is not one tenth, the value is in fact seven.

So our image is representing 10 lots of seven, which of course we know is 70.

So for it to be the correct image, what would we need to do? Well, actually, we could keep the same number of counters.

We'd need to change the value from seven to one tenth for each of the counters.

And if we wanted seven one tenths, then we would need to shade seven of those tenth counters.

Well done for keeping up there.

Let's have a look at our next activity.

Okay, onto our final task now.

I'm wondering, could you possibly draw four tenths in different ways using the tens frames that I've provided for you? Each one of those tens frames represents one whole.

Once you've done that, then have a go at drawing your own non-example of four tenths.

So hopefully you can see that I've used counters to represent one tenth.

Each one blue counter represents one tenth, and I've placed them in lots of different ways in those wholes or those tens frames that we are using to represent each whole.

We know that it does not matter where those tenths are placed, as long as there are four of them.

And altogether, each one of those images represents four tenths.

And then Jacob's come up with an example at the bottom, he says, "Do you agree that this is a non-example?" Have a look at it carefully.

Can you see what Jacob's done? That's right.

Jacob has drawn an image and he has got 10 parts, and he shaded in four of them.

But, that's right, one of those parts is not the same size as all of the others and therefore they're not equal.

So this would be a non-example of four tenths because the whole has been divided to 10 parts, but they're not 10 equal parts.

Okay, there we have it.

Great learning today, and thank you for joining me.

Let's just summarise what we've learned today.

We've been thinking about tenths and how they relate to a whole.

And we know that when a whole is divided into 10 equal parts, each one of those parts represents one tenth, which you can see on the picture of the circle.

If we then go onto shade more than one tenth, we have multiples of one tenth of the whole.

And again, in the example below, you'll see that four parts have been shaded, each one of those parts is equal.

So each one represents one tenth, but we have four of them, so that would represent four tenths.

Again, thanks for learning with me today.

Hopefully you enjoyed yourself and you learned some new knowledge thinking about tenths.

Take care and hopefully I'll see you again soon.