Lesson video

Hi, my name's Mr. Peters, and today we're gonna be thinking about column edition and column subtraction, and how we can use this to help us when working with decimal numbers.

I'm really looking forward to our lesson today.

Hopefully you are too.

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

Okay, by the end of this lesson today, hopefully, you should be able to say that you can use representations to help you think about your rounding of decimal numbers with 10ths to the nearest whole number.

Throughout this lesson, we've got several keywords that we need to consider as we go.

I'm gonna have a go at saying them first, and then you can have a go as well afterwards, okay? My turn, multiple.

Your turn.

My turn, previous.

Your turn.

My turn, next.

Your turn.

My turn, rounding.

Your turn.

Okay, so let's think about these words in a little bit more detail.

Let's start with multiple.

A multiple is the result of multiplying a number by an integer.

For example, 2 X 5 is equal to 10.

2 could be the number 5 could be the integer, and 10 would be the multiple.

So 10 is a multiple of 2 and 5.

Thinking about previous then, something that comes before something else is known as the previous thing or item.

With that thinking, something that comes after something else can be known as the next thing or, again, the next item.

And finally, rounding.

Rounding is a process we use to make numbers simpler, although keeping the value of that number close to what it was originally, okay? Let's get started with our lesson.

In this lesson we're gonna be breaking it down into 3 parts.

The first part is to locate decimal numbers amongst whole numbers, the second part is the reason about distance from whole numbers, and the last stage is to round to the nearest whole number.

Let's get started with the lesson.

Throughout this lesson, Aisha and Sam are gonna work with us and share their thinking as we go.

Okay, so let's start the lesson thinking about where 10ths can be positioned on a number line.

To start off with, you can see here that my number line is going up in multiples of 10.

(mouse clicks) If we focus between zero and 10, for example, we can zoom in here and now you can see how my number line has changed slightly from zero to 100 to zero to 10.

We're gonna look at just that little section in particular.

And if we now zoom in between zero and one, we can now look at a number line where on the left-hand end of the number line we've got zero and on the right-hand end we've got 1, and that whole, now the distance from zero to 1 has been divided into 10 equal parts and the value of each one of those parts is one 10th.

Now, 10ths don't just belong between zero and 1, they can exist between any two consecutive numbers, for example, 4 and 5.

If we zoom in between 4 and 5 we can now see that our number line starts at 4 and ends in 5, and the distance between 4 and 5 is one whole, and that whole has been divided into 10 equal parts and each one of those parts represents a 10th as well.

Sam's asking, "Where do you think 3.

4 might lie on our number line?" Well, Aisha has pointed out that 3.

4 sits between 3 and 4.

These are the whole numbers that 3.

4 sits between.

(mouse clicks) These whole numbers can also be known as multiples of 1, they would be a part of the 1 times table.

So the previous multiple of 1 would be 3 and the next multiple of 1 would be 4.

Okay, have a look at this now.

A is between which multiples of 1? Have a little think for yourself.

Okay, let's use our stem sentence to help us verbalise our thinking.

A is between 5 and 6, 5 is the previous multiple of 1, 6 is the next multiple of 1.

Now look at this example, this time we've got the letter B.

Have a think again.

What is B in between? Maybe use our stem sentence to articulate that.

B is between 21 and 22.

21 is the previous multiple of 1 and 22 is the next multiple of 1.

Okay, we can take this one step further now.

If we know the multiples of 1 that a number lies between, we could estimate what number it is.

So, for example, C is a number we're gonna be thinking about and we're gonna ask ourselves, "Where would we place C on the number line?" Let's go through our sentence stem to help us.

C is between 35 and 36.

35 is the previous multiple of 1 and 36 is the next multiple of 1.

Where would you place C on the number line? That's right.

There's an example of where we've placed C.

Sam is saying that C could be placed anywhere on that number line between 35 and 36.

It doesn't have to be placed exactly where we've put it.

That's just one example.

Okay, time for you to check your understanding now.

True or false? Have a look at where D is placed.

The previous multiple of 1 is 5 and the next multiple of 1 is 7.

What do you think? That's right, it's false.

Aisha is asking us, can we explain why it's false? Well, let's use our sentence stem to help us.

D is between 6 and 7.

6 is the previous multiple of 1 and 7 is the next multiple of one, therefore the issue here is that 5 is not the previous multiple of 1, it's 6.

I can understand why though 'cause the arrow's very close to the 6, isn't it? Which might make you think that 5 is the previous one but actually there's only a little distance to go, but it is 6 which is the previous multiple of one.

Okay, and the second question.

The multiples of 1 that F is between are something and something.

Is it A, B, or C? Have a think for yourself.

That's right, it's C.

F is between 106 and 107.

106 is the previous multiple of 1 and 107 is the next multiple of 1.

Sam's asking, "Well, why is it not A or B?" Well, the first 1 is 100 and 110, and the distance between 100 and 110 is 10, so we're thinking a little bit more about multiples of 10 here rather than multiples of 1 where we're looking at the distance being 1 between each multiple each time.

And why is it not B, 6 and 7? Well, it's easy to forget about the 100s but the number is 106 and 107 not 6 and 7, which is why it's C.

Okay, the first task then, can you identify the previous and next multiple, the A, B, C, and D all sit between on your number line? For task B, I've given you the previous and next multiples, and this time I want you to place A, B, C, and D on the number line according to the previous and next multiples that the letters might sit between.

Good luck with that task and I'll see you again in a minute.

Okay, let's have a look then, shall we? Let's have a look at our number line, first of all.

Our number line starts at 30 and ends at 40, so there's a distance of 10 here.

That must mean that the intervals are going up in ones, so A is between 30 and 31.

The previous multiple of 1 is 30 and the next multiple of 1 is 31.

Let's have a look at B.

B is between 34 and 35, it's very near the central point of our number line and we know the central point would be 35 so the previous multiple of 1 would be 34 and the next multiple of 1 would be 35.

Let's have a look at C.

C is getting towards the end of our number line, and that's right.

C is between 38 and 39.

38 is the previous multiple of 1 and 39 is the next multiple of one.

And finally D, which is positioned between the interval at the very end of our number line.

The previous multiple of 1 this time would be 39 and the next multiple of 1 is 40.

Okay, let's have a look at task two then.

We're trying to place A between 90 and 91.

Well, let's find 90 and 91 on our number line.

The number line again extends from 90 to 100 and is broken down to 10 equal parts, that must mean each interval is a multiple of 1.

90 is at the beginning of our number line, 91 would be at the end of the first interval along So A can sit anywhere between 90 and the first tick mark of 91.

B is between 94 and 95.

Well, if we're going up in multiples on 1, then we can see that B would sit anywhere here between these two tick marks.

C is between 95 and 96.

We know the middle point is 95 so that must mean the next tick mark is 96, So C can sit anywhere between these two marks.

And then finally D, between 99 and 100.

Well 100 is at the right-hand end of our number line So 99 is the previous tick mark, So D can sit anywhere between these two marks.

Well done if you managed to get those.

Okay, let's move on to the second part of our lesson, reasoning about distance from whole numbers.

So we've already looked at 3.

4 from an earlier example and we identified that 3.

4 is between 3 and 4, 3 is the previous multiple of 1 and 4 is the next multiple of 1.

Aisha is asking, "which multiple of 1 will 3.

4 be closest to?" Let's zoom in on this little section in a little bit more detail.

So here you can now see my number line.

It starts at 3 and ends in 4 and is divided into 10 equal parts, and each 1 of those parts represents one 10th.

The halfway point of our number line would be five 10ths, so 3 wholes and five 10ths, 3.

5.

Sam is saying that, "3.

4 would be placed here." He's saying, "It's four 10ths away from 3." And we could record this as a subtraction equation, 3.

4 - four 10ths or 0.

4 is equal to 3.

So the next question is, "Well, how far away is it then from 4, the next multiple of 1?" Well, if we use our number bonds of intent to help us here, we know that 3.

4 is four 10ths away from 3 and four 10ths and six 10ths would be 10 10ths, so actually it's going to be six 10ths away from the next multiple of 1.

This can also be recorded as an addition equation, 3.

4 + 0.

6 is equal to 4.

So having noticed this now, 3.

4 is closest to which multiple of 1? Well, it's four 10ths away from 3 and it's six 10ths away from 4, therefore it's closest to 3, isn't it? 3 is the nearest multiple of 1.

Let's have a look at another example.

7.

8 would be placed here on the number line.

Have a think which multiple of 1 do you think it's nearest to and how far away is it from those multiples of 1? Well we know that 7.

8 is eight 10ths away from 7.

And, again, we record that as a subtraction equation.

7.

8 - 0.

8 is equal to 7.

And, again, if we start thinking about our number bonds of in 10, well it's eight 10ths away from the previous multiple of 1 and a whole is made up of 10 10ths so it must need another two 10ths to get to the next multiple of 1.

So 7.

8 is two 10ths away from 8 and, again, we can record that as an addition equation.

7.

8 + 0.

2 is equal to 8.

So, again, have a think, which multiple of 1 is 7.

8 closest to? That's right, 7.

8 is closest to 8, it is only two 10ths away from 8 so the closest multiple of 1 to 7.

8 is 8.

Okay, here's 1 more example for us to think about.

Have a look at where the arrow is.

Aisha is asking, "What number would sit directly in between 7 and 8? That's right, that would be 7.

5.

Have a think, which multiple of 1 is 7.

5 closest to? Well, we know it's five 10ths away from the previous multiple of 1, which is 7, and we can record that as 7.

5 - 0.

5 is equal to 7, and it's also five 10ths away from the next multiple of 1.

And, again, we can record that as an equation.

7.

5 + 0.

5 is equal to 8.

So which multiple of 1 is it nearest to? What happens in this situation when it's exactly halfway between both of the multiples of 1? Well, when we think about rounding in mathematics, if the number sits exactly halfway between each multiple of 1, then we round to the next multiple of 1.

So in this case 7.

5 rounds to the next multiple of 1 and that is 8.

Okay, time for you to check your understanding again.

Can you fill in the missing number? Have a look at the number line.

That's right, the missing number is 0.

6.

8.

4 is four 10ths away from 8, and therefore it would be six 10ths away from 9.

And here's another opportunity.

True or false? 4.

5 rounded to the nearest multiple of 1 is 4.

Okay, that's correct.

That would be false, wouldn't it? And which justification helps you to reason that here, is it A or B? That's correct, it's B.

We know it cannot be A because we cannot choose which multiple of 1 to round it to here.

When a number sits halfway between two multiples, we round to the next multiple.

So in this case, when the 10th digit is 5 or more we'd round to the next multiple of one.

Okay, and onto our second task then.

What I'd like you to do is have a look at the number in each of the sentences and round those numbers to the nearest whole number, as well as also completing the sentences by considering the 10th digit and whether it is greater than, less than or equal to 0.

5.

You can use the number line to help you identify where the number sits and think about where it rounds the nearest whole number as well.

Good luck and I'll see you again shortly.

Okay, let's see how you got on.

So number one, 1.

1 would round to 1 because the 10th digit is less than 0.

5, and we can see that on our number line.

1.

4 would round to 1 as well because, again, the 10th digit is actually four 10ths here and, again, that is less than 0.

5, five 10ths.

1.

7 would round 2 this time, wouldn't it, because the 10th digit is greater than 0.

5.

We've got seven 10ths and we know that's greater than 5 10ths.

And finally 1.

5, yeah, that would round to the next multiple of 1, which in this case is 2 because, as we know, when we have five 10ths we round to the next multiple of 1, and therefore if it is equal to five 10ths we round to the next multiple of 1.

Well done if you managed to get all of that.

Okay, onto the final part of our lesson now.

We're gonna be thinking about rounding now to the nearest whole number.

So just as we've kind of been talking about already, Aisha is saying that she's noticed that when trying to round a number to the nearest multiple of 1, it depends on how many 10ths there are in the number.

(mousse clicks) For example, if a number has four 10ths or less, then we'd say it'd round to the previous multiple of one.

Let's look at some examples.

7.

1, 7.

2, 7.

3 and 7.

4.

The 10ths digits here are either 4 or less and they're all closer to 7.

They would round to 7 as the previous multiple of one.

If, however, our 10th digit is 5 or greater, then it would round to the next multiple of 1.

Let's have a look.

7.

5, 7.

6, 7.

7, 7.

8 and 7.

9 are all closer to 8, the next multiple of 1.

So, hopefully together now, we've arrived at our generalisation for this lesson.

If there are five 10ths or more, round to the next multiple of one.

If there are fewer than five 10ths, we round to the previous multiple of one.

Hopefully now we can start to round decimal numbers with 10ths to the nearest multiple of 1 without even needing a number line.

Let's have a look at this example.

2.

4 rounded to the nearest multiple of 1 is.

Hmm, let's have a think.

Can we use our stem sentence to help us with this? 2.

4 is between 2 and 3.

2 is the previous multiple of 1.

3 is the next multiple of 1.

And Sam is now saying, "2.

4 as a number has four 10ths and we know that's fewer than five 10ths, therefore this would need to round to the previous multiple of one, wouldn't it?" So 2.

4 would round to 2, as the previous multiple of 1.

Once you're feeling more confident with this, we can then start applying this to problems. Our first problem here says that Sam has walked 3.

9 kilometres over the weekend.

To the nearest kilometre, how far did Sam walk? Well, let's use our stem sentence again to help us.

3.

9 is between 3 and 4.

3 is the previous multiple of 1 kilometre and 4 would be the next multiple of 1 kilometre.

Have a look at the digit.

3.

9, that has nine 10ths, therefore we need to round to the next multiple of 1 kilometre, don't we? So 3.

9 would round to 4, so 3.

9 kilometres would round to 4 kilometres, and we can see that here on our number line.

Okay, last couple of checks for understanding now.

4.

7 rounded to the nearest 1 is something.

Have a look at the number line to help you.

That's right, 4.

7 would round to 5, the next multiple of one.

And that's because it has seven 10ths and seven 10ths is greater than five 10ths, and that is therefore closer to 5, the next multiple of 1.

Here's another example, this time it's in a context.

At the weekend, Aisha walks 6.

2 kilometres.

How far did Aisha walk to the nearest multiple of 1 kilometre? Have a look at the number line to help you as well, if you need to.

I wonder if we can say it together at the bottom.

6.

2 rounded to the nearest multiple of 1 kilometre is 6 kilometres.

That's right.

6.

2 has two 10ths and we know that's fewer than 5, therefore it'd round to the previous multiple of 1 kilometre, in this case would be 6 kilometres.

(mousse clicks) Okay, and onto our last few tasks for today.

Task 1 is asking you to fill in the missing numbers.

Try and do this without drawing a number line, as much as you possibly can.

If you need to, then do draw yourself a number line to help you.

But have a go without, try and imagine it in your head.

Here you've got some rounding problems based on different contexts to think about.

Once you've done that, come back and we'll go through the answers together.

Good luck.

Okay, let's go through these then.

I wonder if you could say them with me as we go.

2.

1 rounded to the nearest multiple of 1 is two, 3.

5.

rounded to the nearest multiple of 1 is 4, 4.

3 rounded to the nearest multiple of 1 is 4, 16.

2 rounded to the nearest multiple of 1 is 16, 5.

5 rounded to the nearest multiple of 1 is 6, 9.

9 rounded to the nearest multiple of 1 is 10 and 12.

7 rounded to the nearest multiple of 1 is 13.

Well done if you managed to get all of those.

And then task two.

Pandora the python is 4.

2 metres long.

How long is this to the nearest metre? 4.

2 metres rounded to the nearest multiple of 1 is 4 metres.

And we know that because 4.

2 has two 10ths and two 10ths is fewer than 5 10ths, so that would round to the previous multiple of 1.

Gemma the gerbil has a mass of 34.

5 grammes.

How much is this to the nearest gramme? 34.

5 grammes rounded to the nearest multiple of 1 is 35 grammes.

And, again, we know that because we have five 10ths here, don't we? 34.

5 is between 34 and 35 and we have five 10ths, which means we would round to the next multiple of 1, in this case, 35.

And finally, Samuel the snail moved 0.

5 metres one morning and moved another 0.

6 metres that afternoon.

To the nearest whole metre, how far did Samuel travel? Hmm, let's have a think.

He moved 0.

5 and then he moved 0.

6, so altogether he moved 1.

1 metres, didn't he? Hmm, what's the previous multiple of 1 and what's the next multiple of 1? Ah, the previous multiple of 1 would be 1 and the next multiple of 1 would be 2, and 1.

1 would be closer to one, wouldn't it? That's right.

1.

1 metres rounded to the nearest multiple of 1 would be 1.

Well done if you managed to get those.

Okay, that's the end of our lesson for today.

Hopefully you're feeling a lot more confident when thinking about rounding decimal numbers with 10ths to the nearest whole number.

To summarise our lesson, we can say that decimal numbers are positioned between two consecutive whole numbers, two numbers that are next to each other.

These whole numbers are known as the previous and next multiples of 1.

And, finally, our generalisation, if there are five 10ths or more we round to the next multiple of 1.

If there are fewer than five 10ths we round to the previous multiple of one.

Hopefully you've enjoyed that lesson today, I know I've enjoyed teaching that for you.

Take care, and I'll see you again soon.