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Hello, and welcome to today's lesson, all about representing decimals.

For today's lesson you will need, some paper and something to write with.

Take a moment now to make sure that you've cleared away any distractions, including turning the notifications off on any apps that you have running.

Try to find a quiet place that will help you with your learning, so that you won't get distracted.

I'm miss Sew, and let's begin our learning today.

Can you show me your thumbs up and show me that you are ready.

Today, we are going to be representing decimals.

We will be using dienes and place value counters to represent the value of different numbers, which today are going to be decimals.

First, we're going to start with a warmup and think about our place value.

Next, we'll be looking at using dienes to represent decimal values.

After this, we'll be representing decimals, and I'll be showing you how to do your independent learning task.

At the end of the lesson, you'll be learning on your own, trying out my challenge, and also having a go at our quiz.

Let's get started, so that we can try and do really well independent work today.

For this lesson, you will need some paper and something to write with.

If you don't have those things, pause the video and go get them now.

Make sure you're ready for our learning today.

First, I want you to think about the words place value.

What do you think of when you hear the words place value? Do you think of the equipment that has this name? Have you heard about it in other maths lessons? I need to give you 30 seconds to think about it.

Pause the video to help you think and write down everything that the words place value make you think of.

You might have thought of a few different things.

When I thought of place value, I thought of this place value chart.

A place value chart shows us digits of different values.

In the place value chart, this time there are place value counters to show the value of each column.

There is one thousands, four hundreds, no tens, and two ones.

In this place value chart, I have got some numbers in the digits columns.

The number is 1,402.

There is one thousands, four hundreds, zero tens and two ones.

They have the same value, but in one of these I'm using place value counters, and in the other I'm using digits to represent the number.

Today, we'll be looking at the place value of decimal numbers.

We are learning how to represent decimals, using the place value chart, to show how many tenths, hundredths, and thousandths we have.

It can be a bit tricky sometimes to say that, let's try saying it together.

My turn, then you'll turn.

Tenths.

Let me show you that chart there.

Tenths, hundredths, thousandths.

Great work team.

On my screen here, I have got one dienes block.

One diene has a value of one, it says the value next to it.

Next, I have a 10 stick.

The value of this is 10 times greater than the ones block.

I can fit 10 tens inside this 10 stick.

Next, I'm going to times this by 10 again.

This next image is 10 times greater than a 10 stick.

If I multiply my 10 stick by 10, I will have this hundred square.

The value of this is 100.

If I times my hundred square by 10, the answer will be 10 times greater, again, I will have 10000, this is 1000s cube.

You are probably really familiar with these dienes.

You've seen them and you've used them, and you know their values are one, 10, 100 and 1000.

Each of these is 10 times greater than the other.

Now, pause the video to complete this task.

Is this true, or is this false.

Great job, A is true and B is false.

B is 100 times greater, not 10 times greater.

Now, I've got the same values we had again.

Let's look at them this time.

Here I have my 1000s cube and I'm going to divide them to get 10 times smaller.

If I divide 1000 by 10, I will have 100.

If I divide 100 by 10, I will have 10.

This is 10 times smaller.

And if I divide 10 by 10 again, I will have one.

Now, this is where we're going to be learning something new.

Using our division, we're going to zoom right in to this one's block.

Pay really close attention.

Imagine that we as zooming into this one, all the way zooming into it.

And if we zoomed into our one here, let's repurpose and revalue our dienes block.

Instead of this one being worth one, it is now, we've zoomed into it, now, we've zoomed right into that dienes block, it is now worth one whole, and we're going to explore the decimal place value.

Goodbye one's block, we've zoomed into you, and we now have 1000 cube.

We are going to reassign the value of a dienes on the screen, and instead of 1000, the orange cube now has a value of one.

I have written the fraction one whole, and there's also one whole in this place value chart.

If the value of the orange cube is one whole, then the blue square now has a value of one tenth.

10 tenths are equal to one whole.

If I divide one whole by 10, I would have one tenth or 0.

1.

You can see that 10 of these blue squares would fit into this one orange cube.

There are 10 tenths in one whole.

Next, our green stick now has the value of one hundredth.

100 hundredths are in one whole, how many hundredths would be in one 10 tenth? There would be 10 of these green sticks in our blue square.

From this, I know that there are 10 hundredths in one 10 tenth.

I say this decimal number 0.

01.

Now, I am back to my individual yellow block, and this is now not just worth one, it is worth one thousandth.

If I took 1000 of these, I could fit them into the orange cube, which represents one whole.

I want you to say this number with me.

Let's read it digit by digit.

Remember, when I say this number, I read out every digit individually 0.

001.

This is one thousandth or 0.

001.

Take two minutes to check you understand what we've done so far.

Pause the video to read the questions and have a go.

If you need help, I will share a clue in the next five seconds.

Pause it now and try it yourself.

This is our representation of one tenth.

How many of these are equal to one whole? How many would fit inside the orange cube? This is our representation of one hundredth, which is the same as 0.

01.

What would I multiply this by to equal one whole, Hmm, our orange cube.

Are you ready for the answers? Great work.

Our answers are 0.

001 or one thousandth.

And how many tenths are in one whole? There are 10 tenths in one whole.

And if I had 0.

01, I would multiply it by 100 to equal one whole.

Great work.

Let's look on and carry on with our learning.

So, let's explore this number.

Now that we're feeling confident with our representation of our decimal digits, let's explore how to represent an entire decimal number.

First, let's practise reading this number.

I'm going to read it digit by digit.

This is 1.

23.

Some of the people get a bit confused and say that this is one point 23.

Now, there are no tens, so, this is not 20.

These are tenths and these are hundredths.

So, I say digit by digit 1.

23.

I can represent this with dienes.

I have got 1.

23, and here I'm going to represent it with my dienes.

I have got one whole, two tenths and three hundredths.

This is the same as one whole, at two tenths, at three hundredths.

I have no thousandths in this number.

All together, this is 123 hundredths.

I can show you my place value chart with my counters.

I can add up the decimal values equals 1.

23.

One, at no point two, at no point no three, is equal to 1.

23.

Right, we're now going to play a game.

I can't read you the number, but which one of these is the correct way of saying the number in my question.

Which of these represent that number? The answer is, the purple one, it's 0.

24 Next.

Which of these represent 0.

24? Think about what the value of each of our dienes are, now that we've repurposed them.

Is it the purple one, is it the pink one? It is the pink one.

This pink one shows one, two, three, four hundredths, and two tenths.

Two tenths is 0.

2, four hundredths is worth 0.

04.

Together, this is worth 0.

24.

Now, which of these fractions represents 0.

24, 24 hundredths or 204 thousandths? It is the pink one, 24 hundredths.

Good work team.

If you found that a bit confusing, rewind the video and try the learning again.

Make sure you understand why these are the answers.

So, I'm now going to take you through your independent task.

Let's have a look at this number.

I am going to represent this number in a variety of ways.

This number is 1.

321.

I need to write my number into the place value chart.

I need to write the addition equation for this number and also write it with fractions.

One whole is my cube, these my tenths, my hundredths and my thousandths.

So, I knew this number is 1.

321.

That helps me and I'm going to do my place value chart first.

One whole, one, three tenths, two hundredths, and one thousandths.

This is the same as my dienes.

That was really easy, and I can look at my dienes to help me.

Next, I'm going to expand the whole number, including the decimal point.

1.

321, I can read the number and write it down.

I know this is the same as one whole at 0.

3 at 0.

02, and the last number is here for me, 0.

001.

If I write this as fractions, I can represent it as three tenths, I've already added my whole, add two hundredths, add one thousandths.

Put together, this is equal to one 1321 thousandths.

And I finished one question in my independent task.

Now, it's your turn to have a go.

Listen to my example again if you need help, otherwise, it's time to pause the video, go to the independent task and have a look at having a go yourself.

Hello, have you finished your independent work? Well done Oak Academy students.

I'm really excited to show you the answers.

Let's have a look together and see what we got correct.

Remember, if we've made some mistakes, let's look at them again, rewatch our video and try and see if we can make our mistakes better.

Here are the answers for you to check your independent work.

Take a look through and check your answers.

Here are the answers for question two.

Here are the answers for question three.

Pause the video, and check that you've marked all your work.

Otherwise, rewind the video and let's watch it again.

That might help you see if you can understand your mistakes.

Thank you so much for joining in with your lessons today.

Share work with Oak National.

If you'd like to, please ask your parent or carer, to share your work on Twitter, tagging @OakNational and #LearnWithOak.

It's now time for you to go and complete your quiz.

Well done, for a fantastic piece of learning, representing decimals today.

Great work.

Bye, remember to go to your quiz.