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Hiya.

My name's Ms. Lambo.

Really pleased that you've decided to join me today to do some maths.

Come on, let's get started.

Today's lesson, the title of today's lesson is Ordering Decimals and this comes within our unit, comparing and ordering fractions and decimals, including positives and negatives.

By the end of this lesson, you'll be able to compare decimals using the greater than and less than symbol.

Here are some keywords that we are using throughout today's lesson.

So here's a quick reminder of what they are.

They should be familiar to you.

The value of a digit in a number based on where it's placed is known as its place value.

We are going to be looking at place value a lot during today's lesson.

Also, a number is in its decimal form, it's when the number has a decimal point and there are digits to the right of that decimal point.

We're going to split today's lesson into three separate learning cycles.

In the first we are going to look at comparing decimals using a place value chart.

This is a really useful tool when we are comparing decimals.

We'll then have a look at putting decimals onto a number line and then we'll finish up with actually ordering decimals.

So we've got a list of decimals, being able to write those in order, mostly from smallest to largest, but do always check whether it's asking for smallest to largest or largest to smallest.

Let's get started on that first learning cycle then, which is comparing decimals using a place value chart.

Like I said in the introduction that these are a really useful tool for being able to compare decimals.

Here's a reminder of what our place value chart looks like.

So we've got the column headings at the top and then we've got those in exponent form underneath.

I want you to think about is it always necessary to use a place value chart? Is it always necessary? No.

Now you may have said yes, that's okay, but actually sometimes we do not need to use a place value chart because some comparisons may be obvious and we've looked at that during previous lessons, I've called it number sense before.

Which is greater? 3.

4792 or 4.

4791.

And here you might be tempted to use the grid as the decimal parts are very similar.

They both start with a 479.

However, the second one is obviously the greater as it has a four in the ones column and the first one only has a three in the one's column.

So here it's not necessary to use that place value chart because starting from the left we can see which one has the bigger digit in that first column.

We're going to now compare these two numbers.

So again, we are looking for which is greater, 4.

125649, and 4.

125459.

Right, so this is not so obvious.

This was where our place value chart can sometimes be invaluable.

Here's my place value chart.

Now here I've missed out the column headings.

That isn't going to matter.

I just need to make sure that I line my decimal points up so that my ones are in the same column and my tenths, hundreds, et cetera.

So here it's my first number and here is my second number.

We'll always remember start from the left when we are looking at numbers and comparing the size of them, you will have done this with integers, it's just the same with decimals.

So we look at the first column and we can see in the ones column they both have a four.

So here we cannot tell the size of each of those numbers compared to the other.

So we go to the tenths column.

They both have one 10th, so we need to move to the hundredths column.

They both have two hundredths.

We'll move then to the thousandths column.

And again, we still have the same digit, we still have five thousandths.

So we move then on to the 10 thousandth column.

Now here we have a difference.

The top one has tip, sorry, six 10 thousandths and the bottom one has four 10 thousandths.

So we can now see that the top one is larger.

125649 is greater than 4.

125459.

Remember we could write that the other way round.

We could switch the numbers around and then turn our inequality symbol around.

Let's have a look at another pair of numbers.

Which is greater? So again, we are looking at which is greater.

Here's my place value chart.

And remember I don't need those headings as long as I make sure my decimal points line up.

We'll put our numbers into our place value chart and we're going to repeat what we did on the previous slide.

So we're gonna start at the left and we're going to compare the digits in each column and we need to keep going until we have digits that are not the same.

That's when we can make a comparison between the two as to which is greater.

We can see that they all both start with 0.

000.

So I'm gonna jump straight to the 10 thousandth column.

They both have six 10 thousandths.

So I go to the hundred thousandths column and they've both got four in that column.

So I go to my next column, my millionths column, and I can see here that we've got a five and a three.

Now I know that the top number is larger than the bottom number, 'cause five millionths is more than three millionths.

So we can write it with our inequality symbol and remembering that could be written the other way round.

But if we're changing the direction of the symbol, we must make sure that we've switched our numbers over.

Here we have Aisha and Jacob, and they're playing a game.

They're lucky.

Aisha's score is 1542.

12.

I'm not sure what sort of game where they're playing, where the decimals maybe you know.

Jacob's score 1542.

Aisha says, "I've won.

My score is higher as it is longer." I give you a moment to think about that statement.

I've won because my score is higher as it is longer.

Now Jacob disagrees.

Jacob says, "No, my score is higher." Here I'm telling you Jacob is correct.

Isn't that kind of me? What I'd like you to do is, I'd like you to write a sentence to convince someone or convince me that Jacob is correct.

So pause the video, have a go at writing that sentence.

Don't forget to start with a capital letter and finish your sentence with a full stop, and then when you're ready, come back.

You can pause the video now.

Super well.

Well done.

Let's have a look then.

Here is an example of something that you may have written.

Yours should be fairly similar, this was my example.

Up to the tenths column, their scores have the same value, but Jacob has a larger digits in the tenths column.

So until the tenths column, they each have the same digits, 1542.

But when we get to that tenths column, we can see that Aisha has one 10th and Jacob has two-tenths, or two-tenths is greater than one 10th.

So even though Aisha's score was longer, it wasn't greater.

And that's a really important thing.

And often people get confused, they look at the length of a number because remember when we're looking at integer, if they don't have a decimal part, that's true.

So it's understandable that sometimes people can get a little confused.

This is why we must compare each column separately and use that place value chart if we need to.

Sort these decimals into the correct group.

This is the number we are going to be comparing, 0.

2572.

And what we're going to do, I'm going to do it together, but I may stop and pause and ask you to think about where you think it goes first.

And we are going to put them into two groups.

Less than 0.

2572 and larger than 0.

2572.

Let's have a look at our first decimal.

So like I said, I'm gonna get you to do some work.

I'd like you to think before I go through it where this is gonna go less than or larger than.

So here we need to go to the hundredths column to find something that is different.

Here we can see that our number has a two.

The number we are comparing two has a seven, so therefore it is less than, two thousandths is less than seven thousandths.

Let's take a look at another one.

Again, I'd like you to think about where you think this is going to go before I go through it.

We've got 0.

2648.

This time the digit is different and the first time it is different is in the hundredths column.

We've got six hundredths, five hundredths.

So six hundredths is greater, so therefore it needs to go in the larger than.

Let's look at the next one.

Which column is the first digit different? It's the hundredths again.

So we've got four hundredths and five hundredths.

Four hundredths is smaller, so therefore it's gonna go in the less than.

Take a look at this one.

So remember you're gonna identify in which column the digits are different.

The first time that occurs, then you can make that comparison.

And here it's in the thousandths column, we've got zero thousandths and seven thousandths.

Zero thousandths is clearly less, so it's going to go in here.

And one final one, give this one again, where is it going to go? Which column is the first time the digits are different and that is this time the hundredths column, nine hundredths is obviously more than five hundredths, so it's going to go in the larger than.

Let's just recap them.

So we compare, we start from the left and we keep going until we find a column in which the digits are different.

And then the larger of those digits will give us the larger of the two numbers.

What I'd like you to do now in a moment, you're gonna pause the video and you're gonna complete the boxes with examples and non-examples of numbers that are greater than 25.

781, and you are going to use the digits one, two, five, seven, and eight.

So examples of greater than, so in your examples, you can prepare anything that would be bigger than 25.

781.

And then non-examples would be ones that are not bigger.

So ones that are less than, so very similar to the task we've just done.

But this time I've given you some digits and I've referred to exercise, sorry, I will refer to it as examples and non-examples, right? You're ready now pause the video.

Good luck with this.

Come back when you're ready, get as many as you can in each column.

You can pause the video now.

Super work.

Let's have a look.

So here are some examples and remember they're just examples you may have of the ones we've got set, sorry, 57.

128, 25.

817, 25.

871, and 125.

78.

And now for some non-examples, these are just examples, you may have others.

I've got 21.

578, 25.

178, 25.

187, 1.

2578.

Well done with that, you are now ready to have a go at an independent task.

In this task you need to work out which of the following are true and then you're going to rearrange the letters of the true statements to make a word.

So you need to go through each of the boxes and if it's true, you could write it down and then you'll need to write down the letter that's on the left hand side of that box.

Good luck with that.

Pause the video, come back when you are ready.

That's superb work, well done.

Did you manage to rearrange the letters to make a word? Let's see how you got on.

So here were my ones that were true.

I had 5.

68 is less than 5.

8, which gave me an L and then I'm gonna go down.

972 was greater than 0.

927, which gave me an E.

567 is less than 0.

576, which gave me an I.

2611 is less than 2.

611, which gave me a U.

I'm not gonna carry on reading out those answers.

What I'm going to do is suggest that you pause the video, check that you've identified all of the true ones, and then you can come back when you're ready.

So did you manage to rearrange letters to make a word? The word was inequality.

Superb work if you managed to do that, but don't worry if you didn't, as long `as you identified those true statements, that's absolutely fine.

Now we can move on to our next learning cycle.

We're going to be looking at putting numbers, sorry, decimals onto a number line.

Here's a number line.

I want you please to write down a number between the two numbers on the number line.

Great.

Here are some examples of things that you may have written.

18, 0.

42, 0.

805.

Basically as long as your number starts with zero point something, then it is right.

Well done.

Okay, now again, I'd like you to write down a number that is between those two numbers that are shown on the number line, have a go.

Some examples I've got 0.

2, 0.

05, 0.

49 and there are many, many others.

As long as it starts zero point and goes to 0.

4 something and doesn't move into 0.

5 something, then it's right.

What about this one again? Can you please write me down a number that is between those two numbers.

Super, some examples again, 0.

09, 0.

003, 0.

0145.

As long as it starts 0.

0, then you know that your answer is correct.

Well done.

And these two, same thing.

Can you write me down a number that's between those two please? Well done.

Here are some examples again, 0.

04, 0.

025, 0.

00478.

We're now gonna think specifically about what number an arrow is pointing to.

So in the previous tasks I was just asking you to write down any number that was between those two numbers.

I now want us to specifically know what number an arrow is pointing to.

Here's our number line, so we can see, sorry, on here I've marked zero one.

I want to know what number that arrow is pointing to.

Jacob says, "It's pointing at four," and Aisha says, "How can it be pointing at four? Because it's between zero and one." Oh well spotted Aisha.

Jacob now says, "Of course, I just counted the number of lines." So Jacob went, oh, it's four lines after zero, therefore it must be four.

So Aisha's reminding him that one is split two 10 equal parts.

If we count the number of parts between zero and one, there are 10.

And so each interval is one 10th, so it is 0.

Each interval here is 0.

1, not one.

So it's 0.

Do you think Jacob's right now? He was.

And like you to have a think about this question, is the arrow still pointing at 0.

4? This time each unit is split into five parts and in the previous example it was split into 10 parts.

So therefore it cannot be point into the same number.

Here we need to take our unit and we need to divide it by five to split it into those five equal parts.

This means that each part is worth 0.

2 on this number line, not 0.

1, therefore the arrow is pointing at 0.

If we count along 0.

2, 0.

4, 0.

6, 0.

So it's really important that we check the scale of our number line.

We're now going to have a look at putting these numbers onto the number line.

Now what I'd like you to do is to pause the video and have a go at doing this before I go through it with you.

Okay, well done if you've managed to put those on the number line, let's see if you've got them right.

If you didn't, don't worry because we can go through it together now and you'll be fine once we've gone through it.

Firstly, we need to work out what each interval is worth.

So here we've got 10 parts between the zero and the one.

So each unit is split into 10 parts.

So we take our one, split it into 10 parts, so each part here is worth 0.

So now we can use that to put our numbers on the number line.

So 0.

8 will be here.

We can either go eight above zero or two below one.

3 is three above one, so that's 1.

And then we've got some a little bit more challenging.

So let's think first about where 0.

2 is.

So here's 0.

2, here's 0.

So 0.

25 is halfway between those two.

So here's 0.

25.

Now with the next one, we need to identify first where 0.

6 is.

So 0.

6 is here.

Ah, and then 0.

7, it sort of almost goes off my number line.

That doesn't matter.

And then we know that 0.

65 is halfway between the two, so here's my 0.

65.

Did you get those all in the right place? Like I said, if you didn't, I'm sure you understand it now.

Let's take a look at another one.

Put these numbers in order on the, sorry, put these numbers on the number line.

We need to put them in the right places.

Have a think about it first.

Again, the first thing that we need to do is to work out what, sorry, is to work out what each interval is worth.

This time our unit is split into five parts.

Let's take our unit, which is one, and divide it by five, each part now is worth 0.

Now we can place our numbers onto the number line.

So zero point, sorry, 4.

8 would be here.

4, well let's mark worth five is on the number line and then 5.

7, hmm, if it's going up in 0.

2s, each of my lines is actually going to be an even digit on the end and this is an odd digit, so it's very similar to what we did in the previous one.

Let's find 3.

6 and find 3.

8, and we know that 3.

7 is halfway between the two.

And then 5.

9, same thing, there's 5.

8, there's six, 5.

9 is halfway between the two.

You are now ready to have a go at some of these questions independently.

So in this first task, what I'd like you to do in this check for understanding, is just match each of the number lines to the correct interval.

Pause the video, come back when you've got your answers, and I'm going to allow you here for the first time to use a calculator to do your working out if you need to.

Okay, good luck with that.

I'll see you when you come back.

Well done.

So we should have them matched up like this.

A was matched with three, B with four, C with 2, D with one, E with six, and F with five.

Now we can do that.

We can now work out what number the arrows are pointing to.

So you'll need to do the same thing.

Think about what each interval is worth and then you can work out the value of the arrows.

A, B, C, and D.

Pause the video, come back when you're ready.

Well done.

Let's have a look and see how you got on with that, although I'm sure you got 'em all right.

A was 5.

6, B, 7.

3, C, 2.

7, and D, 3.

25.

Well done with that.

You should now be ready to work on some more independent tasks.

In task B you are going to work out please what number the arrow is pointing to on each of the number lines.

You're gonna pause the video and then come back when you're ready.

Good luck with that.

Let's check those answers then.

So A, 0.

7, B, 4.

8, C, 17.

25, D, 0.

025, and E, 0.

24.

Did you get all of those right? You did.

Well done.

Let's now then move on to our final learning cycle for today's lesson, we've done brilliantly up until now.

Let's just keep it going for one more learning cycle.

If we can compare the size of decimals, we can also order them, so we now know which is bigger or which is smaller.

So that means that we can actually put a list of numbers into or decimals into order.

We're gonna write these numbers in ascending order.

We've met this word before ascending, just remember it's a way of saying smallest to largest.

Here are our numbers.

88, 0.

878, 0.

87, 0.

078, and 0.

808.

Now when I do this, I like to put them all underneath each other.

I just think it makes it clearer to see which digits are in the same column.

So remember, we start from the left, left column, all of the digits are the same, so therefore we cannot determine which is larger from this column.

So we move to the tenths column here.

Let's have a look which has the smallest number of tenths and we can see it's 0.

078, that's going to be my smallest.

Now we'll check again, in that column were all of them have eight tenths, so we need to move on to the hundredths column.

Look at our digits, which one of those is the smallest? And we can see we've got eight, seven, seven and zero.

Zero is obviously the smallest, so that's going to be our next one in our list of decimals.

808, let's pop that one in our list, right? Do I need to move on now to the next column? No, I don't just yet, because what I've got is two of them which have seven hundredths, so two of them.

So I'm now looking at just comparing these two.

Now I need to go to my thousandths column.

Hmm, there's a blank box.

What goes in that blank box? Yeah, well done.

You're right, it says zero, isn't it? That placeholder.

So that has zero thousandths, so therefore that is smaller than one number that has eight thousandths, so we're gonna put that one next.

Now we can go back to our hundredths column.

We can see that eight hundredths and seven hundredths, seven hundredths is smaller, so that's our next one, and then finally our last one.

Really important then that we start from the left and we compare the digits as we go, moving from column to column.

Here's Sam, Sam is going to write these numbers in ascending order and he says, "I always use a place value chart when I order decimals." Would you use a place value chart to order these numbers? Did you say you wouldn't? No, I wouldn't either.

And the reason for that is, they're all fairly different, so there's probably no need to.

I'm now gonna ask you to arrange those numbers in ascending order.

Remember that smallest to largest, try your hardest not to use a place value chart.

But remember you can if you need to.

So you're gonna pause the video and then when you decided which is the correct answer, A, B, or C, you can come back.

Good luck with that task.

Well done.

Let's have a look and see if you've got the answer right, I'm sure you did.

The correct answer was B.

We're gonna do one more example together now just to make sure that we've really, really got this.

And then you are gonna have a go at one independently that we're gonna check quickly and then you'll be ready to finish up on our final independent task.

We're gonna write the numbers in ascending order.

So here I might choose to write them all down in columns underneath each other, but I've tried not to here, but you could do remember.

So I'm first looking at the ones that start with zero in the ones column.

I'm then looking at my tenths column and I can see that one has zero tenths, so it's the smallest.

I'm sticking with these two because they have zero ones, whereas the other two have one, one.

So I'm now still looking in the tenths column and we can see that the one on the right hand side has two tenths and the one on the left has three tenths, so that this one is smaller.

And then we've got like the next number, and then we're comparing these two.

They've both got one, one, but the second one, the one on the right has zero tenths compared to two tenths, so this is the order that they go in.

And now it's your term, have a go at these ones.

Remember it may be easier to write them in a column, but just if you're doing that, remember to line at those decimal points.

Good luck.

You can pause the video now.

Good, well done.

Let's check your list.

You should have 0.

065, 0.

556, 0.

6, 5.

06, and 5.

065.

Great work on that.

We are now ready to tackle our final task for today's lesson, and you are going to do just what we've been doing in this final learning cycle, and that is order those numbers from smallest to largest.

So they start off a little bit easier and then they get harder as we move down.

But you'll be fine, I know you will.

You can pause the video now.

I'll look forward to seeing you when you come back.

Well done.

Let's take a look at those answers then.

So I'm not going to read all of these out because I'm gonna get very tongue tied with all the zeros and things.

So what I'm gonna do is suggest that you pause the video and then you check your answers carefully.

And then when you're done, unpause the video and we'll move on to look at our summary for today's lesson.

Well done.

I hope you've got all of those right.

Let's summarise them, what we've done during today's lesson.

When comparing decimals, a place value chart can help.

When comparing decimals compare the digits starting from the left.

When considering the position of a decimal on a number line, you must firstly work out the scale being used.

Well done.

You've worked really hard on today's lesson and I've really enjoyed working with you today, and I look forward to seeing you the next time.

Thank you.

Bye.

I've finished the video