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Hi, my name is Mr. Peters.
Thanks for joining me for this lesson today.
In this lesson, we're going to be thinking about how we can round decimal numbers with hundredths to the nearest tenth.
This is a skill we use all the time in our daily lives, and therefore it would be really useful for us to think about this deeply and grapple with this skill so that we have a really secure understanding for how we can use it ourselves.
If you're ready, let's get started.
So by the end of this lesson today, you should be able to say that you can round decimal numbers with hundredths to the nearest tenth.
In this lesson today, we've got four key words that we're going to be using throughout.
I'm going to have a go at saying them first and then you can repeat after me.
Are you ready? The first one, multiple.
Your turn.
The second one, previous.
Your turn.
The third one, next.
Your turn.
And the last word, rounding.
Your turn.
Let's think about what these mean in a bit more detail now.
A multiple is the result of multiplying a number by an integer.
For example, two multiplied by five is equal to 10.
So ten is a multiple of both two and five.
Something that comes before something else is known as the previous thing.
Something that comes after something else is known as the next thing.
And finally, rounding means making a number more simple to work with, however, keeping it close to the value that it was originally.
This lesson today is broken down into two cycles.
In the first cycle, we're going to be thinking about locating decimal numbers amongst tenths, and then in the second cycle we're going to be thinking about rounding decimal numbers to the nearest tenth.
Let's get started.
Throughout the session today, you're also going to meet Jun and Andeep who will share their thinking throughout the whole of the lesson as well as any questions that they might have to further our thinking.
Let's start off by thinking about where hundredths might be located on a number line.
Here you can see I have a number line, which is between zero and 10.
And what I'm interested in is looking here in a little bit more detail between zero and one.
There's a distance here between zero and one that must have some numbers between there.
So let's have a look.
That's right.
We're familiar with tenths now, aren't we? We know that between zero and one, we can divide that interval into ten equal parts and each one of those parts would represent a tenth.
So now we've got zero at one end and one at the other end, and each one of those intervals is one tenth of the whole and they increase one tenth at a time.
But what if we now took each one of those intervals and divided those again into ten more equal parts? Let's have a look here.
As Andeep is saying, our whole has now been divided into a hundred equal parts and each one of these parts represents one hundredth.
We can see here on our number line that between zero and one tenth that there are going to be ten hundredths.
So ten hundredths are equivalent to one tenth.
Let's zoom in on that one tenth again in a little bit more detail.
Now you can see that we've got ten hundredths.
On the left-hand side of our number line it starts at zero and then we can count up in hundredths, 0.
01, 0.
02, 0.
03, 0.
04, 0.
05, 0.
06, 0.
07, 0.
08, 0.
09, and then 0.
1 or one tenth.
So now the interval between zero and 0.
1 or one tenth has been divided into another ten equal parts and each one of these parts would represent one hundredth this time.
An important word for us to focus on here is this word consecutive.
Hundredths are not just found between zero and 0.
1, one tenth.
They can be found between any two consecutive tenths.
Have a look here for example, let's look at between 0.
4, four tenths and 0.
5, five tenths.
If we break this interval down into another ten equal parts, we can see here that each one of those parts would represent one hundredth again and again looking at the numbers, we can see how they're increasing by one hundredth each time.
So let's have a look at our whole again, between zero and one, we can see that our whole has not only been divided just into ten equal parts, it's actually been divided into a hundred equal parts and each one of those small interval markers represents one hundredth.
And Andeep is asking where would 0.
62 or 62 hundredths sit on our number line? Take a moment for yourself to have a think.
That's right.
We would place 0.
62 here on our number line.
Andeep's asking which tenths either side of our number would help us to identify where we would place this number? Well, we can see that 0.
62 sits between 0.
6 and 0.
7 or six tenths and seven tenths.
We can say that 0.
6 is the previous multiple of 0.
1 or one tenth and 0.
7 is the next multiple of 0.
1 or one tenth.
We know that a multiple of one tenth is any number that would be represented if we were to count up in lots of 0.
1 or one tenth.
Have a look here at this example.
We've now got the letter A.
A is between two multiples of 0.
1.
Which two multiples of one tenth is A between? Let's use this stem sentence to help us articulate this.
Maybe you could say it along with me.
Here we go.
A is between 0.
8 and 0.
9.
0.
8 is the previous multiple of one tenth and 0.
9 is the next multiple of one tenth.
Well done if you managed to get that.
Here's another example this time.
B is between two multiples of one tenth.
Have a think for yourself.
What is it between? Let's use our stem sentence again to help us.
Say it along with me if you can.
Are you ready? B is between 3.
3 and 3.
4.
3.
3 is the previous multiple of one tenth and 3.
4 is the next multiple of one tenth.
What did you notice about this one this time? That's right.
In the previous example we had zero wholes, didn't we? Whereas this time we've got three wholes and it's important that we recognise the wholes when we talk about the multiples of tenth, we don't just say 0.
3.
If we've got three wholes, then we need to say it's 3.
3.
We can also think of it like this.
If you know the multiples of one tenth a number sits between, you can estimate where that number might be placed.
For example, where would we place C? Let's use our stem sentence to find the multiples that C sits between.
C is between 4.
1 and 4.
2.
4.
1 is the previous multiple of one tenth and 4.
2 is the next multiple of one tenth.
Therefore C can be placed anywhere between 4.
1 and 4.
2.
And as Jun has said it's important to note that it can fit anywhere between 4.
1 and 4.
2 on our number line.
Okay, time for you to check your understanding now.
The consecutive multiples of one tenth, that D is between are something and something.
Take a moment to have a think.
That's right, it's A.
D is between 14.
8 and 14.
9.
Andeep's asking, "Why is it not option B or option C?" Well, D looks very close to 14.
8, doesn't it? But it's actually just a little bit after 14.
8.
And so we need to recognise that the previous multiple of one tenth is 14.
8 and not 14.
7.
14.
7 would be too far back.
And secondly, why is it not C? Well, C is 14 and 15 and technically they are multiples of one tenth, but they're also multiples of one, aren't they? And we are looking for the two consecutive multiples of one tenth either side of where D is sat.
And so D is sat between 14.
8 and 14.
9.
Okay, onto our first practise task for today.
What I'd like you to do here is look at the letters A, B, C, and D and have a think about the previous and next multiples that they sit between on our number line.
For task two, what I'd like you to do is place the letters in an appropriate place on our number line.
So I've given you the previous and next multiples that they sit between.
You just need to find a suitable place to put them.
And then task three here says that E is between 74.
1 and 74.
2.
And what I'd like you to do is circle all the possible numbers that E could potentially be.
Jun then says, can you think of any other numbers that E could potentially be? Have a go at writing these down as well.
Good luck with these tasks, I'll see you again shortly.
Okay, welcome back.
Let's run through these then.
A is between nine and 9.
1, B is between 9.
3 and 9.
4, C is between 9.
6 and 9.
7, and D is between 9.
9 and 10.
Don't forget that both nine and 10, even though they are whole numbers can also be multiples of one tenth.
Okay, let's have a look at B then.
A could be placed anywhere between 37 and 37.
1, and that would be where the first interval marker is.
B could be placed anywhere between these two intervals of 37.
4 and 37.
5.
We know that the middle interval marker would be 37.
5 'cause that's halfway between 37 and 38.
C can be placed anywhere just after that interval marker between 37.
5 and 37.
6.
And finally D can be placed anywhere between the second to last interval, so between 37.
8 and 37.
9.
And for task E, let's go through the numbers that would sit between 74.
1 and 74.
2.
There you go.
Hopefully you managed to find those three.
Jun also says that the last two remaining possible solutions could have been 74.
11 and 74.
13.
Well done if you managed to get all of those.
Okay, let's move on to cycle two then.
Rounding decimal numbers of hundredths to the nearest tenth.
Let's have a look here then.
Our first decimal number is 0.
62 and that sits between 0.
6 and 0.
7 as the previous and next multiples of one tenth.
Jun is saying let's zoom in between these two multiples of one tenth and find out which one it's closest to.
Okay, so now you can see on our zoomed in number line and that on the left-hand side we've got 0.
6 or six tenths, and on the right hand side we've got 0.
7 or seven tenths.
If we divide this tenth up into ten equal parts, each one of these intervals would represent one hundredth.
0.
62 would be placed here as Jun is saying.
And Jun is saying that 0.
62 is two hundredths away from 0.
6 and we can write that as an equation.
0.
62 minus 0.
02 is equal to 0.
6.
If we know that it is two hundredths away from one of our multiples of one tenth, then we know it must be eight hundredths away from our next multiple of one tenth.
Because we know between any two consecutive multiples of one tenth we can divide that into ten equal parts and each one of those would represent a hundredth.
This once again can be written as an equation.
0.
62 plus 0.
08 is equal to 0.
7.
And as Andeep is quite rightly pointing out, 0.
62 is closest to 0.
6.
So 0.
6 is the closest multiple of one tenth.
So this is where we can introduce our language of rounding again.
When we do this, we can say that 0.
62 rounded to the nearest multiple of one tenth is 0.
6.
Let's have a look at another example now.
Have a look, where would you place 6.
38 on our number line? That's right, 6.
38 would sit here, wouldn't it? The previous multiple of one tenth is 6.
3 and the next multiple of one tenth is 6.
4.
So 6.
38 would sit past the halfway mark up to eight hundredths.
When we think about how close this is to our multiples, well, we can see that 6.
38 is eight hundredths away from 6.
3.
And again, we can write that as an equation.
We can also say that is going to be two hundredths away from the other multiple of one tenth or in this case 6.
4.
And again, we can write that as an equation.
Which multiple is it closest to? That's right, it's closest to 6.
4.
So we can say that 6.
38 rounded to the nearest multiple of one tenth is 6.
4.
Let's have a look at one more example this time.
Hmm, what do you notice this time? That's right.
Our number sits right in the middle this time, isn't it? What number is going to sit right in the middle of 8.
6 and 8.
7? That's right, it would be 8.
65, wouldn't it? Because we know that it's five hundredths away from 8.
6 and it is also five hundredths away from 8.
7.
Hmm.
So what do we do in this situation then? It's right in the middle.
It's the same distance away from either multiple of one tenth.
Well, in these examples we always round to the next multiple of one tenth.
So here we would say that 8.
65 would round to the next multiple of one tenth, and in this case it would be 8.
7.
So I wonder if you noticed anything about all the examples that we've looked at so far.
Which digits and the numbers were you looking at to help you decide which way we had to round? Andeep's noticed that when rounding to the nearest tenth, what's really important is that we look at the hundredth digit to decide whether we round to the previous or next multiple of one tenth.
So for example, if our number has four hundredths or less, they round to the previous multiple of one tenth.
Have a look at our numbers, 8.
61, 8.
62, 8.
63, and 8.
64.
They will have four hundredths or less, so they round into the previous multiple of one tenth.
If however, our number has five hundredths or more, then we can see that they round to the next multiple of one tenth.
Again, look at the numbers, 8.
65, 8.
66, 8.
67, 8.
68, 8.
69.
All of those have five hundredths or more and they round to the next multiple of one tenth.
So we can say that if there are five hundredths or more, then we round to the next multiple of one tenth, or if there are four hundredths or less then we round to the previous multiple of one tenth.
Hopefully this really helps us to maybe not have to think about drawing it as a number line or think about representing it as a number line.
And we can just do that now by looking at the numbers themselves.
Let's have a go at that then, shall we? So 2.
47 rounded to the nearest multiple of one tenth is? Take a moment to have a think for yourself.
Well, I know that 2.
47 is between 2.
4 and 2.
5.
2.
4 is the previous multiple of one tenth and 2.
5 is the next multiple of one tenth.
And if we look at the hundredths digit in our number, we know that there are seven hundredths and therefore because seven hundredths is more than five hundredths, it would round to the next multiple.
So 2.
47 rounded to the nearest multiple of one tenth would be 2.
5.
Now that we're feeling more confident with this, we can then begin to apply this to different problems. Have a look here.
Jun is 1.
24 metres tall.
He's only just allowed to go on the rollercoaster at the theme park, which measures people to the nearest one tenth of a metre.
What was the minimum height to have a go on the rollercoaster? Well, 1.
24 is between 1.
2 and 1.
3.
1.
2 is the previous multiple of one tenth and 1.
3 is the next multiple of one tenth.
So for Jun to be allowed to go onto rollercoaster, we know that 1.
24 would be placed here and it has four hundredths, doesn't it? So four hundredths is less than five hundredths, so it would round down to the previous multiple of one tenth, which would be 1.
2.
So Jun had to be at least 1.
2 metres tall to go on the rollercoaster.
I hope he had fun and it wasn't too quick for him.
He didn't scream too much on the way around.
Okay, time for a check for understanding now.
3.
47 rounded to the nearest tenth is? That's right.
The answer would be 3.
5.
And we know that 'cause 3.
47 has seven hundredths, which is greater than five hundredths, so it would round to the next multiple of one tenth.
And here's another check.
Andeep used his watch to measure how far he swam.
He swam 1.
03 kilometres whilst in the pool.
How far did Andeep swim to the nearest one tenth of a kilometre? Well, we know that 1.
03 is between one kilometre and 1.
1 kilometres, and as we can see on the number line, 1.
03 is closest to one kilometre.
So 1.
03 kilometres rounded to the nearest one tenth of a kilometre would be one kilometre.
Okay, onto our next group of tasks then for today.
What I'd let you to do here is have a go at filling in the missing numbers, working down one at a time through the questions.
And then once you've done that, I'd like you to have a little think about how we can apply this idea of rounding to these different contexts here.
Good luck with that and I'll see you again shortly.
Okay, let's go through these then.
You can tick them off as you go.
3.
19 rounded to the nearest tenth would be 3.
2.
3.
15 rounded to the nearest tenth would be 3.
2.
3.
12 rounded to the nearest tenth would be 3.
1.
3.
09 rounded to the nearest tenth would be 3.
1.
3.
03 rounded to the nearest tenth would just be three, wouldn't it? 2.
99 rounded to the nearest tenth would also be three.
2.
95 rounded to the nearest tenth would also be three.
And finally 2.
92 rounded to the nearest tenth would be 2.
9 this time.
Well done if you've got all of those.
Okay, Andeep then doing some decorating at home and measuring the length of one of his walls to wallpaper.
2.
47 metres rounded to the nearest one tenth of a metre would be 2.
5 metres.
Therefore, Andeep would need a 2.
5 metre length of roll.
Gilbert, the gerbil weighs 39.
15 grammes.
How much is this to the nearest one tenth of a gramme? Well, 39.
15 rounded to the nearest one tenth of a gramme would be 39.
2 grammes.
And finally, Jun had a litre of water and he drunk 0.
46 litres of the water.
How much does he have remaining to the nearest one tenth? Well, if he's drunk 0.
46 litres, that means he has 0.
54 litres remaining and 0.
54 rounded to the nearest one tenth of a litre would be 0.
5 litres.
So we had 0.
5 litres or half a litre remaining.
Well done if you managed to get all of those.
Okay, that's the end of our lesson for today.
So just to summarise our learning then, decimal numbers with hundredths can be placed between any two consecutive decimal numbers with tenths.
These tenths are known as the previous and next multiples of one tenth.
And our generalisation today, if a decimal number has five hundredths or more, then we can round it to the next multiple of one tenth.
Whereas if a decimal number has four hundredths or less then we can round it to the previous multiple of one tenth.
That's all for today.
Hopefully that's made some good connections for you to think about to your previous learning about rounding.
Take care and I'll see you again soon.
