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Hi, everyone.

My name is Miss Coo, and I'm so happy to be learning with you today.

I'm also really pleased that you've decided to complete your learning with me.

It's going to be a great and super interesting lesson, and I'm so excited to be learning with you.

In today's lesson from the unit place value, you'll be learning about place value in decimals, and by the end of the lesson you'll be able to state place value in decimals, including recognising exponent and fractional representations of the column heading.

Place value in decimals is so important because we use in everyday life.

The biggest example is money.

Now throughout this lesson we'll build on past knowledge such as exponents and integers.

We're going to work really hard today, but I'm here to help and we can learn together.

In today's lesson, we'll be looking at writing a number in decimal form.

Now a number in decimal form is when there is a decimal point shown and there are digits to the right of the decimal point.

For example, 12.

475.

We have a decimal point and we have digits to the right of the decimal point.

Another example would be 395.

2905.

We have a decimal point and digits to the right of the decimal point.

Another example would be 0.

23.

We have a decimal point and digits to the right of the decimal point.

Now a non-example would be 23.

You can see we don't have a decimal point and we certainly do not have digits to the right of that decimal point.

We'll be splitting our lesson into two parts, firstly, looking at our decimals in a place value chart using exponential and fractional forms for decimals, and then we'll move on to different representations of decimals.

So let's make a start looking at exponential and fractional forms for decimals.

Well, a decimal is a number that has parts that are not whole, and the place value chart splits the whole number into tenths, hundredths, thousandths, and so on.

We use a decimal point and it's placed at the right of the ones column and each number after that decimal point is called a decimal place.

Pronunciation of a decimal is really important.

So let's have a look at this number, 792.

258.

You can see the two shows the decimal has two tenths.

The five shows the decimal has five hundredths.

What do you think the eight represents? Well done.

It shows that we have eight thousandths, so the correct pronunciation of this decimal is 792.

258.

We don't pronounce it as 792 and two tenths, five hundredths, and eight thousandths, but pronunciation can change when we're looking at money.

So how would you pronounce this amount of money, and what would it look like on a place value chart? Press pause if you want to draw a place value chart.

Well done if you pronounced it as 213 pounds and 12 pence.

Well, how does it look on our place value chart? Well, it looks like this, but we pronounce it differently.

We pronounce it as 213.

12.

So pronunciation with money is different when we're talking about decimals, you can see from this number we have one tenth and you can also see we have two hundredths.

If we link it back to our money, what does it represent? Well, we know 1/10 of a pound is 10p, and we also know 2/100 of a pound is 2p.

So this explains the 12 pence.

So it's important to remember the difference when pronouncing money with pronouncing decimals.

It's important to know place value charts have different headings but are equivalent.

Here we have fractional headings, which are exactly the same as fractional and exponential headings.

Now you can see all our column headings have exponents.

You may have also come across column headings as decimals.

This is just another way of representing the same thing.

They are all equivalent.

Some students find it helpful to copy the place value chart with the exponent column headings.

Press pause if you want to copy this down.

In addition, some students find it helpful to add the equivalent decimal column headings to the place value chart too.

This really does show the equivalence.

Press pause if you want to draw or add this to your place value chart.

Well done so far.

So we've looked at recognising exponent and fractional representations of the column headings in our place value chart.

Now let's move on to a check question.

I'll help you out with the first one.

We're asked to give an example of a decimal with exactly four hundredths.

We can use the place value chart if it helps.

I'm going to come up with the number 719.

341 and interestingly, there's an infinite number of solutions where there's exactly four hundredths, but what's important to remember is that you put a four in that hundredths column to make a decimal with exactly four hundredths.

The next question says, give an example of a decimal having exactly seven tenths and five times 10 to the three.

You can use a place value chart if it helps.

Press pause and give it a go.

Well done.

So let's have a look at an example.

I've chosen 5241.

75 and there are an infinite number of solutions, but whatever decimal you chose, just remember you've put in a seven in the tenths column and a five in the 10 to the three column as this represents our seven tenths and our five thousandths.

Well done.

Let's have a look at some more checking questions.

Here the question wants you to identify the decimals which have for part A exactly three tenths, for part B exactly five over 10 to three, for part C exactly seven over 10 squared, and for part D, exactly zero hundredths.

Drawing a place value chart might help you out.

Press pause and give it a go.

Well done.

So let's go through our answers.

For part A, the decimal with exactly three tenths is 0.

36.

Remember, tenths is in the first column to the right of the decimal point.

So we're looking for a three in the first position to the right of the decimal point.

For part B, five over 10 to the three.

Well done if you've got this one.

It's 12.

1651 because we want exactly five thousandths, and the thousandths column is the third column to the right of the decimal point.

So the five had to be in the third position to the right of the decimal point.

For part C, seven over 10 squared.

This was tricky because there were two answers.

Huge well done if you got this.

The first one is 34.

2791 and the second one is 1.

87.

Remember, we're looking for seven hundredths, so we're looking at the hundredths column.

It's the second digit to the right of the decimal point, and that's where we should see our seven.

Lastly D, exactly zero hundredths.

Really well done if you got these two answers.

The hundredths is in the second column to the right of the decimal point, so we're looking for a zero in the second position to the right of the decimal point.

6.

909 has zero hundredths, and although you can't see the hundredths in 9.

2, there are an infinite number of zeros after that two.

So there are exactly zero hundredths in 9.

2.

How did you do? If it was a little tricky, try drawing out the place value chart as it can sometimes help.

By inserting the decimal into the place value chart, you'll be able to see the correct digit under the correct column heading.

Now it's time for your task.

There are two questions for this task.

Question one wants you to fill in the gaps so that each column shows a different way of writing the same value.

The question starts off by giving us a completed column.

We know one hundredths in its fractional form, in its decimal form, and in its exponent form.

Looking at the first column, it wants us to find out what one tenth is in its fractional form, decimal form, and in its exponent form.

In the third column, it wants us to find out what 0.

001 is in its fractional form, in its exponent form, and in words.

And in the final column, it wants us to find out what 1/10,000 is in its decimal form, exponent form, and in words.

Press pause and give it a go.

Well done, so let's move on to question two.

Question two wants us to write the following in decimal form.

If it looks a bit tricky, why not try writing a place value chart to help you work these out? Press pause and give it a go.

Really well done.

So let's go through these answers.

For question one, we need to fill in the first column identifying the equivalent forms to 1/10.

So in fractional form, 1/10 is one over 10, in decimal form it's 0.

1, and in exponent form, it's one over 10.

All are equivalent to 1/10.

In the third column, we had to write the equivalent forms to 1/1,000.

In fractional form, that would be one over a thousand, in decimal form it'd be 0.

001, and in exponent form, it'd be one over 10 to the three.

All of these are equivalent to 1/1,000.

In the final column to the right, we're identifying 1/10,000.

In fractional form, it's one over 10,000, in decimal form it's 0.

0001, and in exponent form it's one over 10 to the four.

All are equivalent to 1/10,000.

Well done if you got those right.

This was a good question and helps us recognise the equivalence between fractional, decimal, and exponent form.

Now let's have a look at question two.

We're asked to write the following in decimal form.

A place value chart would've helped you out here.

So let's have a look at each calculation.

Two times 10 to the three is the same as 2,000.

Add three times 10 squared is the same as 300.

Add our four and nine times one over 10 is the same as 0.

9, or 9/10.

Summing them all together gives us 2304.

9.

Part B gives us eight times 10 to the three, which is the same as 8,000.

Add our four and our 0.

7 and our 0.

02 gives me a final answer of 8004.

72.

For part C, nine times 10 squared is 900.

Add our six, add our 0.

8, and seven times one over 10 to the three is 0.

007.

So summing these together gives us 906.

807.

Lastly, two times ten to the three is 2,000.

Add our 40, our 0.

003, four times 1/10 is 0.

4 or 4/10, and six times one over 10 to the three is 0.

006, or 6/1,000.

Adding these together gives us 2040.

409.

Well done if you got any of those right.

Moving on to the second part of the lesson, we'll be looking at place value in decimals with different column headings.

Place value in decimals can be represented in different ways using different place value charts, and it's important to understand how these place value charts work.

So let's have a look at a Gattegno chart.

Looking at each column as you move up or down a row, you'll be multiplying or dividing by 10.

And also if you look in each column, you'll see how the numbers are aligned.

Now the thousandths, hundredths, tenths, and ones, et cetera, are all aligned.

I'm going to show you this decimal.

Can you identify the decimal being represented here? Well done if you've got it.

The answer is 643.

62.

So looking at the Gattegno chart, you need to break it down into hundreds, tens, ones, tenths, so on and so forth to identify your decimal.

So let's extend this a touch more.

Here we have two different place value charts.

Which has the largest decimal value, and can you explain? Press pause if you need.

Well, if you got the answer B, very well done.

Hopefully you've identified the Gattegno chart identifies the number 286.

28.

I've just lined it up underneath the other number, 286.

82.

This is because I want you to see that the hundreds, tens, and ones are all the same for both decimals, but the Gattegno chart shows two tenths and eight hundreds, which is less than eight tenths and two hundredths.

Well done.

This was a hard question.

Now let's have a look at our next task.

Here for question one, it wants you to complete the charts to make the following decimals, 751.

15, 262.

26, and 93.

191.

Now the Gattegno chart on the right you'll notice is blank, so you need to fill in the chart.

Try and remember how the numbers are aligned.

Press pause while you complete this question.

Now let's move on to question two.

Question two shows us three students having different numbers.

We have Alex, Laura, and Sofia.

Now you need to insert the digits six, five, four, and two into Sofia's place value chart to make for part A a decimal greater than Laura's, for part B, a decimal less than Alex's, for part C, a decimal in between Alex's number and Laura's number.

As an extra extension, try to find more than one answer for each.

Press pause and complete this question.

Really well done.

So let's go through our answers, starting with question one.

We had to identify 751.

15.

Well, I have seven hundreds, I have a 50, and I have a one.

I have 1/10 or 0.

1, and I have five hundredths, which is 0.

05.

Well done if you've got that.

262.

26 is represented as 200, our 60, our two, two tenths, which is 0.

2, and our six hundredths, which is 0.

06.

Well done if you got that.

If you correctly drew the Gattegno chart here, a huge well done, especially if you've aligned these digits, ensuring to keep your tens, hundreds, thousands, all aligned.

Another huge well done will go to you if you put the numbers in ascending order from left to right.

Drawing a Gattegno chart can be quite tricky, so well done if you've managed to do it.

So let's identify 93.

191 where we have our 90, we have our three, we have our tenth, our nine hundredths, and our one thousandths.

Well done if you got those right.

Moving on to question two, it was important to firstly identify what number did each student have.

Well, Alex had 234 and Laura had 255.

2, so we had to use the digits six, five, four, and two to make a number greater than Laura's.

I put some examples on the screen.

Don't worry if you did not get my answers.

I just put up three example answers, 654.

2, 256.

4, and 645.

2.

Did you get an answer that was different to mine? It doesn't really make a difference as long as your number is greater than 255.

2.

Well done.

The next question, part B, wants a decimal less than Alex's.

Now remember Alex had 234.

There are plenty of different answers out there, and I've just put some examples on the screen.

54.

26, 26.

45, and 64.

25 were just my three examples.

Well done if you've got any of these or any more, as long as they're less than 234.

For part C, we wanted to identify a decimal in between Alex's number and Laura's number.

There are only two answers for this because we wanted a number in between 234 and 255.

2, and the two answers were 254.

6 and 245.

6.

Well done if you've got both of those.

Great work today.

We've done so much learning.

We've looked at the definition of a decimal, wrote numbers in decimal form, as well as recapped on exponent form too.

We've also compared different place value charts, for example, a Gattegno techno chart, but most importantly, we know a decimal can be represented by using exponentials in the column headings of a place value chart.

And we also know a decimal can be represented by using fractions in the column heading of a place value chart.

Finally, we looked at place value charts have different column headings, which can express a decimal in different ways.

Try and discover all the different ways we use decimals in real life.

We know we use decimals with money, but keep an eye out for all the different ways in which we use decimals and how they've become an important part of our lives today.

A huge well done.

It was great learning with you today.