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Hi, my name's Mr. Peters.

Thank you for learning with me today.

In this lesson, we're gonna start thinking about comparing and ordering decimal numbers.

Let's get straight on with it.

Okay, in this lesson we're gonna look at several key words.

Some you would've heard before.

These words are compare, order, place value, ascending, and descending.

So when we compare, we're looking for similarities and differences in either an object or a value.

Once we've compared things, or for example, numbers in this lesson, you can then order them by putting them in a place based on a set rule.

For example, from smallest to largest or from largest to smallest.

When we talk about place value, we're referring to the value of a digit based on where it is placed within the number.

Referring back to order, we can have an ascending order.

This is where we go from the smallest to the largest.

And we can also have a descending order.

This is where we go from the largest to the smallest.

So by the end of this lesson, hopefully you'll feel confident enough to be able to say that I can compare and order decimal numbers with tenths.

This lesson is broken down into two parts.

The first part is thinking about applying our place value understanding to compare numbers.

And the second part of our lesson, we'll focus on comparing and ordering numbers with the same whole numbers.

Let's have a look at the first part.

Throughout the lesson today, Laura and Jun will also be joining us to help us with our thinking and our learning.

So to start our lesson today, we're gonna be thinking about using these base 10 blocks.

Jun and Laura are using these base 10 blocks to help them when they're comparing their numbers.

Jun is saying that the value of his block is one whole, and Laura is saying that the value of her block is one tenth.

You're going to need to think about these blocks in this way throughout this lesson.

So first of all, I've got a question for you.

I'm wondering who's correct.

Jun is saying that his number is larger because he has more blocks, whereas Laura is disagreeing with him.

She is saying that she has a larger number, as she has two of the bigger blocks, and each of those blocks represents a one.

She has more of these blocks than Jun does.

So I think we're going to need to compare these numbers to identify who has the larger amount.

We can use inequality symbols to help us with this.

For example, this symbol says less than, and that's because the one on the left-hand side is less than the three on the right-hand side.

This symbol says greater than.

And again, this is because we have three yellow blocks on the left-hand side, which are greater than the one red block on the right-hand side.

And we can also use the equal to symbol.

This symbol represents that is equal on both sides, as you can see by the two orange blocks on the left and the two orange blocks on the right.

So thinking about these symbols, which one of those symbols do you think we're gonna have to place in the circle to represent this? That's right, we're gonna have to use the less than symbol, because Jun actually does have a number that is less than Laura's number.

The reason for this is Jun's number only has one whole, and Laura's number has two wholes, so it does not matter how many additional tenths the even number has.

So for some numbers, we can compare them just by looking at the whole numbers.

Two wholes is greater than one whole, therefore Laura has the larger number.

We can also represent this on a number line.

Here is Jun's number.

Jun's number is 1.

He had one whole and three additional tenths.

Laura's number is two.

And we can see, as Laura is saying, that two is further along to the right-hand side on the number line than Jun's 1.

Therefore, the larger the number, the further to the right it would be on our number line.

At this point, we can also start using our place value understanding to help us compare these numbers.

Here, I've got a place value chart with the headings on, and I've placed our numbers into the chart.

We can see Jun's number is at the top, and I've placed a one in the ones column and a three in the tenths column.

And for Laura's number, I've placed a two in the ones column.

Now, we don't need to have the place value headings anymore, do we? So we can replace them with a decimal point.

Now, we know that we place a decimal point between the ones and the tenths, which we have now done.

And as a result of that, we can see there's a gap in the tenths column for Laura's number.

We can place a zero there, but we don't have to if we don't have any fractional parts after the decimal point.

So as Laura is now saying, to compare two numbers, we can start by looking at the largest place value.

And in this case, the largest place value is the ones.

Jun has one one, and Laura has two ones.

Therefore, Laura has the larger number.

I know that 1.

3 is smaller or less than two because the largest place value is the ones column.

And within the ones column, Jun has one one and Laura has two ones.

Or as Laura has said, there are more ones in two than there are in 1.

Once we understand how to compare the numbers, we can start to order them.

Here, I've got three numbers for us to look at and we need to place them from the smallest to the largest.

Have a look at the numbers before I place 'em in the place value chart.

Which one do you think is the largest? Which one do you think is the smallest? Which one would go in between? Now I've placed them in the place value chart, and Jun is now reminding us to look at the largest place value first.

Well, let's have a look.

We can see that there is one number that has a 10, and the other two numbers do not have any tens, therefore this number must be the largest number.

So 12.

4 would be the largest number.

Let's look at the last two numbers.

We can't compare their tens, so we now look at comparing their one digits.

One of them has five ones, and the other number has three ones.

So which one is the largest? That's right, five ones is larger than three ones, so three ones must be the smallest number.

So the number with five ones must go in the middle, 5.

And the number with three ones must be the smallest number, so we place that at the end.

Okay, time to check your understanding.

True or false, 3.

4 is larger than 4? Take a moment to have a think for yourself.

Once you've had a think, have a look at our justifications.

Which one of these will help you to answer the question? A, four ones is larger than three ones, or B, 3.

4 has two digits and four has one digit.

Okay, so the answer was indeed false, and we can justify that by saying 3.

4 actually has three ones, and the four would have four ones, therefore four is larger than three is greater than three.

Okay, and here's another check for understanding.

I've represented it with the base 10 blocks and underneath I've written it as a decimal number.

Can you compare these two numbers? That's right, 3.

2 is greater than 2.

2 has three ones and 2.

6 only has two ones.

Therefore, we do not need to compare any of the other tenths, we can just focus on the ones.

And we know that three ones is greater than two ones, so 3.

2 is greater than 2.

Okay, time for our first practise task.

I've given you three numbers here, and I've placed them in a place value chart to help us.

I wonder, could you order them in ascending order for me? So from the smallest to the largest.

And then for your second task, could you order these numbers? This time I've given you four numbers and I'd like you to arrange them in ascending order this time.

Okay, and for the second task, I'm wondering, could you possibly order these in descending order this time? I've given you four numbers without a place value chart.

And to order them in descending order, that means you need to go from the largest to the smallest.

Good luck and I'll see you again shortly.

Okay, welcome back.

Now, the first task here then, we had to order these in ascending order, so from the smallest to the largest.

Let's have a look at what we've got.

Well, I can see a number that has a value in the tens column.

Therefore, that looks like quite a large number compared to the other two, so we'll ignore that one for the moment.

Let's look at the other two remaining numbers, the top number and the bottom number.

Both of those numbers have some ones.

The top number, 4.

2, has four ones, and the bottom number, 6.

0, has six ones.

I know that four ones is less than six ones, so that must be the smallest number.

And that would go into our box underneath, like so.

So now we're looking for the second smallest number.

Well, we already realised that one of these numbers had a digit which had a value of one ten.

So that must be the largest number, which therefore means that the six in the ones column must be the middle number.

And to the other number, which was 12.

7, must be the largest number, because although it only has two ones, which might be less ones than the other two numbers, it has a 10 and therefore it makes 12.

So 12.

7 is the largest number and it's greater than 6.

0, and it is also greater than 4.

Let's have a look at the second activity then.

This time, we had to order them in descending order.

So this time we had to go from the largest to the smallest.

Hmm, which one of these looks like the largest number? Well, they've all only got one digit before the decimal point, which means those digits have a place value of ones.

So now we need to figure out, well, which one has the most ones? So 6.

6 has the most ones as it has six ones.

The second one is five because it has five ones and it doesn't have a decimal point or any fractional part after it, which we know doesn't matter for this because five ones is less than six ones.

The next number is 3.

This only has three ones, which we know is less than five ones.

And finally the last number is 2.

0 or two, and we know that two ones is less than three ones, so this would be our smallest number.

Well done if you managed to get those.

Now we're moving on to the second part of our lesson, and we're gonna be thinking about comparing and ordering numbers, which have the same whole number.

So as we can see, sometimes the largest place value has the same amount in it for each of these numbers.

Have a look at the numbers.

How could we record these in our place value chart? Well, the first number on the left has three ones and five tenths, and the second number has three ones and two tenths.

Hmm, how could we compare these now? Well, let's remove the place value headings and insert our decimal points, and let's read these numbers correctly.

We've got 3.

5 and then we've got 3.

We could use a stem sentence to help us with our thinking here.

I say 3.

5, but I think three wholes and five tenths.

Hmm, the number underneath, how would we say that? Well, we can say 3.

2, but I think three wholes and two tenths.

So we can see if we look at the largest place value, they both have the same, they both have three ones.

So Laura is now suggesting that we need to look at the next largest place value, which would be the tenths.

Having a look at the tenths, we can see that 3.

5 has five tenths and 3.

2 has two tenths.

And therefore, we know that five tenths is larger than two tenths.

Therefore, 3.

5 is greater than 3.

2, or 3.

2 is less than 3.

Okay, let's have a look at another example.

In this example, on the left-hand side, we can see that we've got four one-tenth counters, and on the right-hand side, we've got five one-tenth counters.

If we were to write these in our place value chart, we would write them with a zero in the ones column, as neither the numbers have any ones, and then we would record the four and the five in the tenths column.

Let's place our decimal points in place to help us understand these numbers.

And we can see, that we have 0.

4 and 0.

So what is it that we are noticing about these digits then? So the ones column, there aren't any ones.

There are zero ones.

Therefore, we can't use the ones column to compare, can we? We have to go and look at the tenths column.

And if we look at the tenths column, we can see that one of them has four tenths and the other one has five tenths.

And as a result, we can say that 0.

5 is greater than 0.

4, or 0.

4 is less than 0.

Here's one more example.

Have a look at the place value counters.

You probably might be able to start thinking about which one is the largest already, just by looking.

Well, this time we can see, on the left-hand side, we have three tens counters we have a one one counter, and we have four tenths counters.

This number would be recorded as three tens, one one, and four tenths.

If we record the other number, we can see that we also have three tens, we also have one one, but this time we have five tenths.

So how are we gonna compare these numbers? What do you notice? Well, once again, the largest place value this time actually is the tens and the tens are the same.

They both have three tens.

We then look at the ones and the ones are both the same.

They both have one one.

Finally, we'll have to look at the tenths.

Four tenths is less than five tenths, and as a result of that, 31.

4 would be less than 31.

5, or 31.

5 would be greater than 31.

Okay, so again, we can also compare more than two numbers.

We can actually compare three numbers or more.

And once we've done that, we can then start thinking about ordering them from smallest to largest or largest to smallest.

Have a look at the numbers we've got so far.

You can see that all of the place value counters are jumbled up, so it's not as easy to see which number is the largest at first.

So let's record each one of our numbers into a place value chart to help us.

Now that we've recorded them, have a look at the digits themselves.

What do you notice this time? Well, once again, they all have the same number of tens and they all have the same number of ones again, don't they? So therefore, we don't need to compare the whole numbers 'cause that's not gonna help us.

We need to go and look at the largest place value we can, which would be the tenths.

So by looking at the tenths now, we can see that one number has four tenths, one number has five tenths, and the other number has two tenths.

So we can start to compare these numbers now and we can see that 31.

2 would be the smallest number, as it only has two tenths, 31.

5 would be the largest number as it has five tenths, and 31.

4 would be the number in the middle because it is greater than 31.

2, and it is also less than 31.

Okay, time for us to check our understanding again.

Have a look at the place value counters next to A, B, and C.

Which number is the largest? Take a moment to have a think.

That's right, C is the largest.

Jun's now asking, well, how did you know that? Well, we can see by looking at option A and option B, that both of those numbers only have one 10.

If we look at option C, it actually has two tens, therefore two tens is greater than one 10, and as a result, option C would be the largest number.

Here's another one for us to think about.

True or false, the larger the one's place value, the larger the number? Here are some justifications to help you think through your answer.

Which one of these will help support your answer? That's right, he answer is false.

And the justification that can help you would be justification B, which says, it depends, because if there's a larger place value to look at, then we would need to look at that column, wouldn't we? For example, that larger place value could be the tens or the hundreds or even the thousands or more.

Okay, time for you to complete task B for me now.

Here, I've got two sequences of questions.

You'll need to complete the set on the left first, and then you'll need to complete the set on the right afterwards.

You need to use your inequalities, so your greater than, your less than, and your equal two symbols, and write them into the circles when you compare each of the numbers.

Once you've completed that task, I want you to have a go ordering these numbers.

Again, there are three numbers here, and I'm looking for you to order them in descending order, so from the largest to the smallest.

And then finally, a nice activity here for us to finish on.

I've given you some empty boxes, and each pair of boxes represents a decimal number, which has a decimal point placed between them.

Your task is to use only the digits zero to five and place them all in one of those boxes to make it a true statement.

Once you found one way, Jun's then asking you, how many different ways can you find to make the statement true? Good luck with these tasks and I'll see you shortly.

Okay, let's work through these answers then.

Let's look at the first set on the left-hand side.

7 is greater than 0.

4, and we know that, because they both have zero ones and therefore, we have to look at the tenths.

Seven tenths is larger than four tenths.

7 is greater than 1.

What changed this time between the last example and this example? Ah, actually the number of ones changed, but those number of ones stayed the same, didn't they, in this example.

The previous example had zero ones, whereas both of the examples in this one had one one.

And we still know that seven tenths is greater than four tenths, therefore, the same reasoning applies, 1.

7 is greater than 1.

2 is less than 2.

Did I nearly catch you out there? What's the value of the two in the numbers? Well, the value of the two in the first example is two tenths, whereas the value of the two in the second example is two ones, and we know that two ones is greater than two tenths.

The next example was very similar to the previous one, wasn't it? 0.

4 is less than 4.

0, and it's the same reasoning that applies.

We know that four tenths is less than four ones.

And finally, the last example nine is equal to 9.

We know they're the same thing, don't we? Okay, let's look at the top of the next row.

0 or one, which one is greater? The answer to that is neither of them, they're the same.

They're equal again, aren't they? And we know, that 1.

0 is the same as saying one whole and zero tenths, which is the same as just saying one.

The next one says 0.

6 and 1.

Have a look at those examples.

That's right, 1.

6 is greater than 0.

6, or 0.

6 is less than 1.

6, because there is one one in 1.

6, and 0.

6 has zero ones.

What about this next example? Hang on, the numbers are the same.

They've just been turned around the other way.

So that means, we'll also have to turn our symbol around, won't we? 1.

6 is greater than 0.

6, or again, 0.

6 is less than 1.

2 and two.

The two in the 0.

2 represents two tenths, and the two on the other side, it represents two ones, therefore 0.

2 is less than two.

And the last example, did you look carefully at this one? The number on the left-hand side is actually 14.

That's one 10 and four ones.

And the number on the right-hand side is 1.

That represents one one and four tenths.

So we know that 14 is greater than 1.

4 because it has a 10 and 1.

4 doesn't have any tens.

Okay, let's look at task B.

Here, we had to order the numbers in descending order, didn't we? The numbers look all very similar to me.

Hmm, let's have a look.

Well, they all have three hundreds, don't they, so we can't compare them yet.

Let's have to look at the tens column.

Well, the first number has two tens, the second number has four tens, and the last number also has two tens again.

So that must mean the middle number must be the largest because it has four tens.

So 342.

1 is the largest number.

Now we just need to compare the last two numbers.

We know they have the same hundreds, we know they have the same tens, so now we're gonna have to look at the ones digits.

Well, in the first number it has four ones, and in the last number it has one one.

Therefore, 324.

1 must be the middle number and 321.

4 must be the smallest number.

Well done for spotting the differences between those numbers.

And then finally, our last task.

Here, we had to place the digits nought to five in each one of the boxes, and we could only use them once in order to be able to solve and make this statement true.

So Jun has managed this here.

He's placed a four and a zero in the first two boxes.

In the second two boxes, he's placed a two and a three.

And in the last two boxes, he's placed a one and the five.

He's only used each digit once.

And he is saying that 4.

0 is greater than 2.

3, which is greater than 1.

5, and that would be true.

Well done, Jun.

How many different solutions did you manage to find? Did you spot any patterns when you managed to do that? Did you find any strategies that made it a bit easier for you to do so? If you get a chance, share them with someone nearby to you.

Okay, that's the end of our lesson on comparing and ordering decimal numbers with tenths.

Just to summarise what we've learned today, we know that to compare two numbers, we need to compare the digits from the largest place value first.

If the digits of the largest place value are the same, we then need to look at the next largest place value.

And finally, and once we know how to compare numbers, we can then start thinking about ordering these numbers, either in an ascending order, so from the smallest to the largest, or in a descending order, from the largest to the smallest.

Thank you for learning with me today.

Hopefully you've enjoyed yourself and you feel a lot more confident with comparing and ordering decimal numbers with tenths.

Take care and I'll see you again soon.

I've finished the video