Lesson video

Hi, my name's Mr. Peters.

Welcome to today's lesson here.

We're gonna be thinking about how we can compare and order decimal numbers with up to three decimal places.

I'm really looking forward to this lesson today.

It's a great opportunity to extend our thinking about comparing and ordering with a range of decimal numbers.

When you're ready, let's get going.

So by the end of this lesson today, you should be able to say that you can use your place value understanding to help you compare and order the decimal numbers with up to three decimal places.

Throughout this session today we're gonna have three key words that we're gonna be referring to.

I'll have a go at saying them and then you can repeat after me.

The first one is compare your term.

The second one is place value your term.

And the last one is order your term.

When you compare, you're looking for similarities and differences within an object or a value.

The value of a digit in a number based upon where it is placed is known as place value.

And when you order things or order numbers, you put them in a certain place based on a set rule.

Watch out for these words throughout our lesson today and use them where you can to support your understanding.

So this lesson today is broken down into two cycles.

In the first cycle, we're gonna compare and order decimal numbers with thousandths.

And in the second cycle we're gonna compare a range of decimal numbers.

Let's get started.

Throughout this lesson today, you're gonna meet Sam and Andeep.

Both of them are gonna share some great questions and some good thinking to develop us with our understanding as well.

So Sam and Andeep are playing a game.

They have a bag and they have lots of place value counters within the bag.

What they have to do is pick eight place value counters out from the bag at a time, and then they have to write down the number that they will have made with the place value counters that they received.

They then compare their numbers and the person with the largest number is the winner of this round.

And then for the next round they get one fewer counter than they had.

So let's say if Sam won the first round, then Sam in the second round would only have seven counters and Andeep would still have eight counters.

The winner is the first person to reach zero counters.

Here are the counters they pulled out after the first round.

Have a look carefully.

Who do you think won the first round? Let's record this in place value chart, shall we? Sam have three ones, one 10th, two hundredths, and two thousandths.

Whereas Andeep had two ones, two tenths, three hundredths, and one thousandth.

So we can record this as 3.

122 or 2.

231.

Sam's reminding us that when we compare numbers, we must start by looking at the largest place value.

So the largest place value is the ones, and it will be that throughout the whole of the game, Sam has three ones and and E only has two ones.

Therefore we can say Sam's number of 3.

122 is larger than Andeep's number of 2.

231.

Therefore, Sam is the winner of the first round.

Sam now receives one less counter.

Sam has got seven counters and E has now got eight counters.

Have a look carefully this time.

Who do you think won this around? Let's record the numbers in our place value charts again, Sam has two ones, three tenths, two hundredths and zero thousandths.

Whereas Andeep has two ones, zero tenths, three hundredths, and three thousandths.

Hmm, who'd you think won this time? Well, as always, we start with the largest place value, don't we? However, if you have a look here, both Sam and and Andeep both have two ones, don't they? That now means we need to look at the next largest place value, don't we? In that case it would be the tenths.

Have a look at the tenths.

Who has the most tenths here? Well, Andeep's pointing out that he only has zero tenths and Sam has three tenths, doesn't he? So again, Sam would be the winner of this round because Sam would got three tenths more than Andeep does.

So we can say that Sam's number of 2.

32 or 2.

320 is greater than Andeep's number of 2.

033.

Just quickly, what'd you notice about Sam's number compared to Andeep's number? Well, that's right.

Sam's number was 2.

320.

And actually we don't need to record the zero on the end of that.

So Sam's number only had two decimal places compared to Andeep's number, which had three decimal places and Sam's number was still greater, wasn't it? So even though Sam's number got less decimal places, his number was larger than Andeep's.

And the reason for that is because they had the same number of ones and they had to compare the tenths to identify which one was larger.

Well done if you spotted that.

Okay, a quick check for understanding now.

On the next turn, Sam picked out these counters Andeep won the round.

Which numbers could Andeep have had? A, B, or C? That's right, Andeep could have had A or B.

Sam's number was 2.

301.

Therefore Andeep could have had B because it has more ones, it has three ones.

Or Andeep could have had A, because it has one more tenth than Sam's number does.

Okay, moving on to round four.

Now these are the numbers they got this time.

Remember Sam has two counters less and Andeep is one one round now.

So he has one counter less.

Let's record these in our place value chart.

Sam's number is 1.

221 and Andeep's number is 1.

213.

Hmm, who won this round then? Well as always, let's stop the largest place value.

We can see they're both the same here.

They both have one, one, don't they? So we then go to the next largest place value.

Hmm, again, they both have the same again, don't they? They've both got two tenths, so that means we're gonna need to go to the next largest place value to compare these.

In this case, that would be the hundredths, wouldn't it? Have a look at the numbers.

Who has the largest number? That's right.

It's Sam, isn't it? Sam has two hundredths compared to Andeep who only has one hundredth as Andeep is saying.

So we can say that 1.

221 is greater than 1.

213.

Andeep's a bit disappointed by that.

He thought he was just getting back into the game and now Sam's going ahead again onto round five.

Then here are the counters that they pulled out.

Let's have a look at how we can record these then.

Gosh, it looks similar, don't they? Hmm, how are we gonna compare these? Where do you notice the numbers differ? Well, to compare them as always, we should start with the largest place value.

Both Sam and Andeep have the same number of ones.

They both have the same number of tenths and then they both have the same number of hundredths.

So we're going to need to look at the thousandths to be able to compare these two numbers.

Who has the most thousandths? That's right, Andeep has the most thousandths.

So Andeep has won the round, Andeep has got five thousandths compared to Sam who only has three thousandths.

So we can say that 1.

103 is less than 1.

105.

Okay, and I'm gonna check for understanding.

In round six, Sam made 2.

003.

Andeep who now gets to pull out six counters, pulled the first five counters out and made this number here.

Can you explain why 0.

001 or 1000th is the smallest value counter that Andeep needs to win the round? Take a moment to have a think.

Andeep is saying that they both have the same number of ones, but neither of them have any tenths or hundredths.

So it comes down to comparing the thousandths and Sam has three thousandths and at the moment Andeep also has three thousandths.

So if he pulls up one more thousandth, then he will also win the round.

Okay, once Andeep and Sam finished their game, they then decide to order the first three numbers that they made from the first three rounds and see who made the largest and smaller numbers.

As you can see, the purple numbers are Sam's numbers and the green numbers are Andeep's numbers.

Let's think about how we could go about ordering these.

Then Sam's saying let's start with the largest ones.

He can see out the six numbers.

There are two numbers with three ones.

So we need to compare these two here.

Andeep has noticed that he thinks he could do this even quicker than how we've been doing it so far.

He says that instead of comparing column by column, we could just look at the decimal numbers.

We could break down the tenths and the hundredths into thousandths and say the three digits after the decimal point as thousandths instead.

So Sam's first number 3.

122 is three ones and 122 thousandths.

Whereas Andeep's number of 3.

050 is three ones and 50 thousandths.

We know that 122,000 is larger than 50,000.

So 3.

122 would be the largest number followed by 3.

050.

We've now got four numbers remaining and we're looking for the next largest number.

All four of these numbers have two ones, don't we? So to compare these, we're going to need to look after the decimal point using Andeep strategy.

We can say that 2.

32 has 320 additional thousandths.

We can say that 2.

301 has 301 additional thousandths.

We can say that 2.

231 has 231 additional thousandths and we can say that 2.

033 has 33 additional thousandths, therefore 2.

32 or 2.

320, which is two ones and 320 additional thousandths would be the next largest number.

That would then be followed by 2.

301 'cause that has 301 thousandths, that's the next largest.

And then finally it'd be between these two here, one of them has 231 thousandths, and the other one has 33 thousandths, therefore 2.

231 is the next largest leaving two ones and 33 thousandths or 2.

033 to be the smallest number.

A final check for understanding for this cycle then can you order these numbers from largest to smallest or in descending order? Take a moment to have a think.

So I can notice that each of the numbers have four ones, don't they? So we can't compare them there and they all have three tenths, don't they? So we can't compare them there either.

Well we could say that the number on the left has an additional 82,000.

The number in the middle has an additional 28,000, and the number on the right has an additional 83 thousandths.

Therefore 4.

383 would be the largest number.

4.

382 would be the second largest number.

And finally 4.

328 would be the smallest number.

Well done if you managed to get that okay onto our first task for today, then can you use your inequalities, your greater than less than, than equal to symbols to compare the following numbers.

Once you've done that, what I'd like you to do is order the following numbers from largest to smallest.

Good luck with that and I'll see you again shortly.

Okay, welcome back.

Let's work through these then.

0.

178 is equal to 0.

178, 0.

177 is less than 0.

178, 0.

187 is less than 0.

188.

What did you notice change that time? Yeah, both numbers increased by one hundredth, didn't they? What about the next time? Well, both of them has been increased by one one this time, haven't they? So it still remains that 1.

187 is less than 1.

188.

And then finally, what's happened this time? Well, we've lost the additional tenths and hundredths from both of our numbers, haven't we? But on the left hand side we've now got eight thousandth and on the right hand side we've now got seven thousandth.

So 1.

008 is greater than 1.

007.

Let's have a look at the next column.

6.

002 is less than 6.

003.

What do you notice has changed this time or the value of the two is no longer 2000, it's two hundredths, therefore this number is gonna be larger.

6.

020 is greater than 6.

003.

And what do you notice this time? So we've increased the value of the three this time and away from three thousandths to three hundredths.

So we've now got 6.

020 is less than 6.

030.

What do you notice this time? That's right, the value of the two has changed again, it's now become two tenths.

So 6.

200 is greater than 6.

030.

And finally, and finally the last one.

What do you notice the value of the three in the hundredths on the right hand side has changed, isn't it? It's no longer three hundredths.

It's now three thousandths.

And is that still smaller? It is, isn't it? So 6.

200 is greater than 6.

003.

Well done if you've got all of those.

Okay, and ordering these numbers, then I'm gonna put these into the correct order for us now.

So 2.

060 is the largest, then it was 2.

051, then it was 2.

042, then it was 2.

033 and then it was 2.

006.

Again, well done if you've got all of those right.

Moving on to cycle two of our lesson.

Now compare a range of decimal numbers.

Sam is decorating her room with her mum.

They've bought a new desk to put into her room next to her bed and they've also decided to buy a photo frame to put above the desk.

They decide it would best to start by putting the photo frame up on the wall.

Sam saying we're going to need some screws to put this photo frame up.

So when people use screws in their everyday lives, they can often refer to them by the length in which they're measured in millimetres, and you can see the lengths of these screws underneath them here.

Sam's mom has a selection of screws in her toolkit.

Which screws could they use? Sam's saying that the instructions mentioned that we shouldn't use a screw that's longer than 0.

05 metres.

So the question is, which screws could we possibly use then Take a moment to have a think.

Whilst all of these screws are written millimetres, Sam saying that we can convert them all to be written in metres instead to help us compare.

So 24 millimetres can be written as 0.

024 metres.

32 millimetres can be written as 0.

032 metres.

45 millimetres can be written as 0.

045 metres.

60 millimetres can be written as 0.

06 metres or 0.

060 metres.

And finally 74 millimetres can be written as 0.

074 metres.

So I'm saying that 0.

05 metres is the same as saying 0.

050 metres or 50 millimetres.

So it's these three screws here that we could use, couldn't we? I say all of them are smaller than 0.

05 metres or 50 millimetres.

Okay, now they've put the photo frame up on the wall.

The next task is to put the desk in place.

The space to put the desk next to Sam's bed is 1.

4 metres long.

The length of the desk says it's 1.

358 metres on the box.

Sam's concern that the desk will not fit in the space should she be concerned.

She's saying that 1.

358 metres has more digits in it, therefore it's a larger number than 1.

4 metres.

So she doesn't think it's gonna fit at that moment.

Andeep is visited to see how the decorator's going.

Andeep saying, don't worry Sam, the desk will fit.

Let me show you why.

Andeep has recorded both the numbers in a place value chart.

And again, notice how the place value headings have changed here to the unit sizes for each measurement that we're working with Andeep saying, let this green bar represent one metre.

When we compare numbers, we look at the largest place values.

So we're gonna start by looking at the metres and deep saying that both of these numbers both have one metre in length, don't they? So we can't compare them yet.

We need to look at the next largest place value, which would be attempts.

Andeep saying that 1.

4 has four tenths of a metre compared to 1.

358, which has three tenths of a metre.

Therefore 1.

4 would be larger than 1.

358, therefore the desk would fit.

Sam thinks she's got an idea now she's noticed that we don't need to worry about any of the digits after the tenths place, do we if we've managed to compare the digits at the tenths place, 'cause there's a difference in the size of these digits.

As we pointed out, 1.

4 has four additional tenths and 1.

358 has three additional tenths and 1.

4 is larger than 1.

3.

And deep says we could look at this at a slightly different way as well.

It says by looking at the ones column, we can see again that they're the same, but instead of looking at the tenths then the hundredths and then the thousandths, we could just look at them all as thousandths, couldn't we? By breaking down the tenths and the hundredths into thousandths.

So we could say that the first number has 358 thousandths, and then we could say that the second number has an additional 400 thousandths by placing a zero in the hundredths column and then a zero in the thousandths column.

So 1.

358 again would be smaller than 1.

4 because 1.

4 has 400 additional thousandths and 1.

358 has 358 additional thousandths.

Sam is now really relieved.

She's grateful that Andeep has showed her that the desk will fit and she's looking forward to getting started to using it.

Okay, a couple of checks for understanding now, which is the longest length, A, B, or C.

That's right, it's C, isn't it? Five metres is the longest length as it has more metres compared to the other two numbers, which both only have four metres.

And true or false, 2.

6 metres is shorter than 2.

512 metres.

That's right, it's false.

And look at these justifications again, which one of these helps you to answer it? That's right, it's B isn't it? We know it's false because 2.

6 metres has 600 additional thousandths compared to 2.

512, which has 512 additional thousandths.

Therefore 2.

6 is greater than 2.

512.

Well done if you've got those.

Okay, onto our last task for today then.

If you can have a go at playing Sam and Andeep's game, you might like to use place value counters if you have them available to you.

If not, you might just like to cut up some pieces of paper and write the place values from the digits onto those pieces of paper instead.

I suggest that you use five ones, 10 tenths, 10 hundredths and 10 thousandths.

Once you've had a go at that, have a think about how you can make the game even more challenging.

And once you've had a go at that game, I'd like to use your inequalities again to compare each of these numbers in each of the columns.

Good luck, I'll see you again shortly.

Okay, welcome back.

Hopefully you had a good go at playing that game.

We came with a couple of ideas for how you could have changed the game slightly to make it even more challenging.

Andeep suggested putting more thousandths counters into the bag as that would change the kind of numbers that we kept on getting.

And Sam also suggested introducing a one free swap token.

So at some point throughout the game you could swap one of your counters for a different counter in the bag.

That might change it slightly might, isn't it? Hopefully you enjoyed playing and came up with something new for yourself to change the game and make it even more challenging.

Okay, and finally, using our inequalities to compare these numbers then starting on the left hand side, 0.

004 is less than 0.

006.

0.

006 is greater than 0.

004.

0.

006 is less than 0.

04.

Notice how the four has changed place value there and then 0.

004 is less than 0.

06.

Notice again how the digits have swapped sides and the value of the six has changed.

One is equal to 1.

000.

It doesn't matter how many zeros go after decimal point.

If the ones digits are the same and there is no additional tenths or hundredths or thousandths, then they would be equal on the next column.

0.

25 is less than 0.

3.

So even though there are less digits on the left hand side, because it has only two tenths and the number on the right hand side has three tenths, then this number is larger, even though it has less digits.

0.

008 is less than 0.

010.

That's the same as saying 8,000 is less than 10,000.

0.

110 is greater than 0.

101.

Again, we could read this as 110 thousandths is greater than 101 thousandths.

Five is greater than 4.

999 even though it's got all of those nines in it.

Again, as we said, the value of the ones is the important value here to look at.

We have five ones on the left hand side and we've got four ones on the right hand side.

So five is greater than 4.

999.

And then finally 5.

001 is less than 501.

Yeah, good spot there.

Actually, there's no decimal point on the number on the right hand side.

So we've got only a whole number.

So that five and zero in the one is representing 501, which of course is a lot bigger than 5.

001.

Well done if you manage to get all of those.

Okay, that's the end of our learning for today, and hopefully you're feeling a lot more confident once again thinking about comparing and ordering numbers up to three decimal places.

To summarise our learning, let's have a think.

So to compare two numbers, we start by comparing digits from the same place value.

And as always, we must start with the largest place value.

You can compare numbers with tenths hundredths and thousandths by converting both the tenths and the hundredths into thousandths and just reading them as thousandths only if the digits are the same in the largest place value, then we should always look at the next largest place value.

And of course finally, if we can compare decimal numbers up to three decimal places, then we can order these numbers as well by using as set rule.

And that could be from largest to smallest or smallest to largest.

Thank you for joining me for today's lesson.

I've really enjoyed teaching that one, and hopefully you're feeling good about your maths too.

Take care, and I'll see you soon.