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Hi there.

My name's Ms. Lambell.

You've made such a super fantastic choice deciding to join me today and do some maths.

Come on, let's get started.

Welcome to today's lesson.

The title of today's lesson is Checking Understanding of Rounding, and that's within our unit estimation and rounding.

By the end of this lesson, you'll be able to round to the nearest 100 or 10 or whole number, or to one or two decimal places.

Let's get going.

Keyword that we are going to be using in today's lesson is rounding.

Rounding means to change a number into another number that is approximately the same but is easier to work with.

round 561 to the nearest 10 would be 560.

Don't worry if you're a little confused by this at the moment.

We'll be going through this at various stages in today's lesson and then you'll be fine, I'm sure.

Today's lesson, I've split into three separate learning cycles.

Learning cycle one, we will look at rounding to the nearest 10, 100, 1,000.

In learning cycle two, we will round to the nearest whole number and then we'll move on to looking at one and two decimal places.

Let's get started with that first learning cycle.

Rounding to 10 100, 1,000.

Rounding is useful for showing the approximate value of something without it being exact.

That's what we mean when we talk about rounding in maths.

the number of people living on a street.

It's not always necessary to know the exact number, but by rounding we can get a good idea of the size of the street.

Another example, the number of pupils at a school.

If somebody said to you how many pupils are at your school, you may have an idea but you might not know an exact figure.

Maybe even your teacher doesn't know the exact figure.

Next example, the distance between your home and school.

Here, you might have an idea about it, but I doubt very much you know the exact distance between your home and school.

The attendance at a pop concert.

We do not need to know the exact figure to give us a sense of the size of the number of people at the concert.

And the distance between the earth and moon.

It'd be really difficult to measure that exactly, I'm sure.

I'm sure scientists can, but actually do we need to know the exact figure to give us a sense of the size? So when we're talking about rounding, it's approximate value that gives us an idea about the size.

Also, when we start to look at estimation, it allows us to work with numbers that are easier to deal with.

Rounded values make them easier to work with.

The number of people living on a street is 72.

Giving this to the nearest 10 gives us an idea of the size of the street, but it doesn't need to be exact.

Just as I mentioned when we went through those examples.

When rounding to the nearest 10, firstly we identify the multiples of 10 either side of the number and the multiples of 10 either side of 72 are 70 and 80.

Now let's put 72 onto our number line and 72 goes here.

Now we're going to consider how far away 72 is from our two multiples of 10 we've chosen to put on our number line.

And remember, the reason we chose those multiples is because it was the multiple below 72 and the multiple of 10 above 72, which was 80.

We can see clearly that 72 is two away from 70 and if we look at how it compares to 80, we can see that it is 80 away.

It makes sense then that we round 72 to 70 because it is closer.

72 is closer to 70, therefore 72 to the nearest 10 is 70.

The number of people attending a pop concert is 68,562.

Again, we don't need to give that as an exact figure to give us an idea of the size of the attendance of the concert.

Here, it would be sensible to round this to the nearest thousand.

Let's take a look using our number line how we would go about doing that.

When round to the nearest thousand firstly we identify the multiples of 1,000 either side of the number.

In this case, that would be 68,000 and 69,000.

Now we put 68,562 onto our number line.

We can see that it would be roughly here.

On the previous example, I could place it exactly but actually here I can't place it exactly, but I know it's slightly more than halfway between the two.

I know that 68,500 is halfway between 68,000 and 69,000, so I know it's roughly there.

I don't need to know exactly.

Now we can take a look at the distance from each of our multiples of 1,000.

We are 562 away from 68,000 and we are 430 away from 69,000.

Therefore, it's closer to 69,000 and that means that 68,562 to the nearest thousand is 69,000.

Here we've got Lucas and Laura.

What is 135 rounded to the nearest 10? You have a think about that moment.

Here's our number line.

We're rounding to the nearest 10, so we need to identify the multiple of 10 that is below and above 135.

That's 130 and 140.

Now let's place 135 onto our number line, which is here.

Now we're going to consider how far 135 is from our two multiples.

Here we can see that it's five away from 130 and we can see that it is five away from 140.

Lucas says, "What happens when the number is exactly the same distance from both?" Do you know what happens in this situation? You do? Let's see if you agree with Laura.

I think Laura's got the answer to this.

Let's take a look and see what she's got to say.

Let's see if you agree.

"When the number is exactly halfway between the two multiples, we always round up to the larger." Is that what you said? Fantastic.

Well done.

You've remembered that really, really well for some previous learning.

Well done.

Lucas says, "So, 135 is 140 to the nearest 10." Yes.

That's right, Lucas.

We can actually use Laura's fact to help us round numbers without having to work out the distance from each multiple.

And actually we did look at that in that second example, we started to sort of plant that seed a little bit.

What do I mean by that? We're going to look at this question.

What is 3,587 to the nearest a hundred? We identify the multiples of a hundred either side of 3,587, which is 3,500 and 3,600.

We know that if the value is exactly halfway between, then it is going to round up to the larger value.

Otherwise it is going to round down if it is lower than that halfway point.

So we're going to find the halfway point between these two values on our number line.

So we find the halfway point which is 3,550.

Now we can put our number onto the number line 3,587.

Now it doesn't need to be exact, we just know that it's to the right basically of 3,550.

So I've put it to the right.

Now we can see it is closer to.

Which one is it closer to? Yes, you're right.

It's closer to 3,600.

So 3,587 rounded to the nearest 100 is 3,600.

So we identify the multiples, we find the halfway point, and then basically we're going to decide whether our number is to the left of the halfway point or to the right of halfway point.

If it's to the right, we round up to the higher multiple but don't forget if it's exactly in the middle, we're going to round up to the higher multiple.

I'm sure you are ready now to have a go at this check for understanding.

It's a true or false and remember with true or false I always want you to tell me whether it's true or false, but also to justify your answer 'cause I don't want any guessing.

You know that by now.

True or false, 5,672 to the nearest 10 is 70.

Don't forget, you're gonna pause the video, decide on your answer, but I really do want that justification.

So read those justifications through really carefully and when you're ready, come back and we'll check that answer.

Well done.

What did you decide? Let's take a look.

It was false.

So it was false.

5,672 to the nearest 10 is 70.

That's not true.

Remember when we're rounding, we're changing our value to something that is very similar.

70 is certainly not similar to 5,672.

If you have 5,672 pounds in your savings account and somebody says I'll give you 70 'cause it's roughly the same, pretty sure I know what you'd say.

Now we'll take a look at the correct justification and that was B, the thousands and hundreds digits have been missed off.

You must make sure that you include those digits in your rounded answer.

To show that we have rounded numbers, we can use an approximately equal to symbol.

Have you seen the approximately equal to symbol before, I wonder? For example, if we ranked 15,865 to the nearest 10, we could write it like this.

We could write it as 15,865 and then we've got those two squiggly lines which mean approximately equal to.

Maybe pause the video and have a go at practising drawing that new symbol, particularly if it's something that's not familiar to you.

And we've rounded it to the nearest 10, so it is only approximately equal to hence the reason we've not used that equal symbol and it's approximately equal to 15,870.

You might see what a number has been rounded to written after the rounded number.

So for example here, we've written what it's been rounded to, it's been rounded to the nearest thousand.

Now you're ready to have a go at this task.

I'd like you please to find the incorrect statement in each row.

So there are three in each row.

I told you on the left hand side what I've rounded them to or at least tried to.

Two of them I've done correctly but unfortunately, in one I've made an error.

I'd like you to identify the one that is wrong.

You're going to record what letter that is and at the end you will have seven letters and you'll rearrange them to make a word that is associated with what we are doing in today's lesson.

Have a go at these, pause the video now, and then when you're ready, come back.

Remember, if you can't rearrange the letters, that's not really important.

The most important thing is that you can spot my incorrect one.

Good luck.

I'll see you in a moment.

Now let's check those answers.

First one, it was the middle one and then the first, third, first, middle, middle, and then the last or the third.

And if you rearranged those letters correctly, you would've got the word roughly.

How did you get on? You got roughly? Amazing.

Well done.

Now let's move on then to look at this something that may be a little bit more challenging, but actually we've got all of the skills we need to be successful at it, and that's rounding to the nearest whole number.

And you'll notice here that actually the processes what we go through are exactly the same as what we've just been doing.

So if you found that easy, you're gonna find this super easy too.

"The average body temperature is 98.

6 degrees Fahrenheit." Laura states that for us.

And Lucas says, "What is that to the nearest degree?" So Lucas wants that, but he doesn't want it exact.

He just wants to know what it is to the nearest degrees Fahrenheit.

Like I said, this is the same as we were doing previously.

We need to identify the whole numbers that are either side of 98.

6 and that would be 98 and 99.

We find the halfway point, which is 98.

So halfway between 98 and 99 is 98.

If you're not sure, what I tend to do is think of that as money.

What's halfway between 98 pounds and 99 pounds? And that would be 98 pounds 50.

But I don't need to put the zero on.

I could if I wanted to.

Now we locate our value and we can see that it is to the right of the midpoint.

We're gonna decide which one it's closer to so we can see it's closer to 99.

So 98.

6 degrees Fahrenheit rounded to the nearest degree is 99 degrees Fahrenheit.

Lucas says, "I bought a T-shirt at the weekend and it cost me 20 pounds." Do you think that Lucas's T-shirt was exactly 20 pounds? What do you think? Often people round values when they're talking about money.

Not very often do you go in a shop and it's an exact number of pounds to buy something.

So I think Lucas probably has done some rounding here.

Actually he paid 20 pounds and 25 pence for his T-shirt.

So he decided actually to give people an idea of what his T-shirt cost.

He was just going to round it and we can use a number line to help us to do this to round to the nearest whole number and we looked at that in the last example.

But let's take a look at it with Lucas's T-shirt.

So the T-shirt cost 20 pounds and 25 pence and Lucas rounded it to the nearest pound.

So we identify the whole numbers either side of the price that Lucas paid, which is 20 pounds and 21 pence.

We find that halfway point.

And then we locate where our value is going to go and we know that it's going to go to the left of 20 pounds and 50 pence 'cause 20 pounds and 25 pence is less than that.

Now we can see which value it's closer to, we just make that decision.

And so we can see now why Lucas said his T-shirt costs 20 pounds because actually it rounded to 20 pounds to the nearest whole number or to the nearest pound.

"I think I could round the nearest whole number without drawing a number line." Oh, Laura's getting a little bit cocky here so she thinks I don't need to draw a number line.

Let's take a look and see what Laura thinks.

Lucas also believes that he can also do that and he suggested let's try this one.

346 pounds 38, and we're going to round that to the nearest pound.

This means rounding it to the nearest whole number 'cause we've got a whole number of pounds, which is in our ones column, remember.

So here's our place value grid.

Let's put our 346 pounds 38 into our place value grid.

Here it is.

Now, we are going to round to the nearest one.

So we identify the ones column and we identify our digit in the ones column.

We need to look to the right 'cause remember, we were looking at halfway between two, which was the next basically column to the right.

Halfway would've shown us a five in that column and as three is less than five, therefore we are going to round down to the lower whole number.

In this case, that would be 346 pounds.

You can imagine your number line still, but you may prefer to not draw it out.

You may prefer to think of it in a place value grid.

You could have a place value grid and actually write these down or you might be able to just memorise what that looks like and use the method without necessarily drawing out place value grid.

So Laura says, "We identify the column we are rounding to." And Lucas says, "Yes, and then we look at the digit in the column to the right." "If it's less than five, we round down to the lower value." And Lucas says, "Yes, and if it's five or more, we round to the higher value." Remember earlier we looked at the fact that if it was exactly halfway between the two, what are we going to do 'cause it's the same distance from both? So we use the higher value to represent this.

Now let's have a go at this one.

Round 706.

51 to the nearest whole number.

Here's my place value grid with the number written in already.

We're going to round to the nearest whole number, remember that's the ones column.

So we identify the ones column and we identify our digit.

The most important number though that informs us what to do is this column to the right, immediately to the right that is.

This digit is a five, so therefore we are going to round up to the higher whole number.

And the higher whole number and if we imagine our number line would've been 706 would be the lower and 707 would be the higher.

We therefore, 706.

51 is 707 to the nearest whole number.

I think we're ready now to have a go at just maybe one more together, but I'm sure you'll probably do this one with me and then you'd be ready to have a go at one independently.

Going to start by rounding 109.

55 to the nearest whole number.

I'm going to place it in my place value grid and here I've got a shortened version of it but I've got enough of the columns to make sure that I can fit my number in.

I'm going to identify the ones column 'cause remember that's my nearest whole number and there's my digit.

And we look to the number immediately, in the column immediately to the right and that's a five.

So what do we do here? You're right, yeah, we round up to the higher integer or whole number which is 110.

So we'll round up to the higher whole number giving us 110.

Here's your one to have a go at.

Pause the video and come back when you've got that answer which I know is gonna be right.

Good luck.

Great work.

Now let's check your answer, which I said I know is going to be right.

I place value grid.

You may have chosen to draw a place value grid, you may have chosen not to, you may have even gone back and drawn a number line.

Any of those is absolutely fine.

Remember in maths, sometimes there are more efficient ways of doing things, which we try to use if we possibly can.

But actually it doesn't matter if we use a slightly different method to the person sat next to us or the person behind us, or the person that we might speak to about this a bit later on in a day.

We're going to place our number 85.

28 into our place value grid.

We're going to identify the ones column and the digit in the ones column.

Then we're going to look immediately in the column to the right, it's less than five, so therefore, we round the lower of the two integers, which is in this case 85.

85.

28 the nearest whole number is 85.

Is that what you got? Superb.

Well done.

When rounding identify the column you are rounding to.

So we're just gonna summarise what we've been doing.

So when rounding, we identify the column we are rounding to.

We look at the digit to the right of this column and remember that's the digit immediately to the right.

If it's less than five, we round down and if it's greater or five we round up.

And we do need to be careful when we're using these words round up and round down.

Remember we're rounding up or down to the nearest, in this case integer or the nearest 10 or the nearest hundred.

So, this is a summary of how we round.

If you want to, you could pause the video and make a note of that and then when you're done come back.

If not though, we'll move on.

Laura and Lucas are each given a different number to round to the nearest 10.

I'd like you please to decide who you agree with and don't forget, I want that why.

Laura has 269 and Lucas has 264.

Laura says, "My ones digit is more than five so I round up to 270." And Lucas says, "My ones digit is less than five so I round down to 250." Pause the video and come back when you can tell me who is correct, so who you agree with, but not only that, why? Good luck and I'll see you in a moment.

Super.

Let's take a look.

Laura was correct.

Did you come up with Laura as well? If you did, I hope you didn't guess.

I hope you came up with the reason as well.

And the reason here, and like I said on the previous slide actually we need to be careful when using the phrase round down as we do not change the digit, it stays the same.

So for example here, 123, if we round it to the nearest 10 is 120.

Remember.

we are looking for the multiple of 10 below 123, which is 120, and above 123, which is 130.

These are the only two values.

Lucas has actually changed his tens digit and he's changed it to a five.

Remember we can leave it the same if we've got a number that is less than five.

If not, if it's five or greater then we increase it by one.

Laura and Lucas are each given the same number to round the nearest hundred.

And again, I'd like you to decide who you agree with and why this time they both have the same number.

Let's take a look at what they've got to say.

It ends in two so I need to round down to 400.

Lucas says, "The tens digits five, so I need to round up to 500." Again, pause the video and when you've got the answer come back and don't forget I want that why.

That why is so important to show me that you really understand what you're doing.

Good luck.

I'll be here when you get back.

Super.

Let's take a look.

This time Lucas was correct.

When considering rounding up or down, we must look at the digit in the next column to the right of what we are rounding to.

And if you remember on the previous slides, I did highlight that, that we are looking to the column that is immediately to the right of the column we are rounding to.

Now you're ready to have a go at this task.

Now, don't worry if you've not managed to get this printed out.

You could draw out the grid if you wanted to.

But anyway, you could still have a go at the questions even if you don't fill in the number grid.

In this task, you are going to round all numbers to the nearest whole number and I've done the first one for you.

318.

29 to the nearest whole number.

So, the eight is in the ones column, we look to the right, it's a two so it stays as an eight.

So 318.

And you can see how I've placed those numbers into my grid, one digit in each box.

Each time you should have one digit in each box.

Pause the video and then when you come back we'll check those answers for you.

Good luck.

Super work.

Let's check those.

Here we go.

I'm gonna ask you to pause the video and then check these, a little bit difficult for me to read them out so pause the video, check them, and then when you're ready come back and we'll move on to that final learning cycle.

You've done fantastically well so far, so let's just keep it going for a little bit longer.

Great.

How did you get on? You've got all of them right? I knew you would.

Now then, now we're ready to move on to our final learning cycle.

Let's get going.

We're going to be looking now at rounding to one and two decimal places.

Again, this is only just one more step further than what you've been doing so far and you've done that so well you're gonna find this super easy.

Let's get going.

Laura and Lucas.

Laura says, "Sometimes I see questions that ask you to round to one decimal place." Lucas says, "The first decimal place is in the tenths column." Let's just pause a moment and think about that.

Is Lucas right? Yeah, the first column after the decimal point is the tenths column.

Yeah, well done Lucas.

This is gonna mean then that we round to the nearest tenth.

So if we think about it, we looked when we round to the nearest hundredth, we looked at the number that was in the hundredths column.

So if we are rounding the first decimal place, that's the tenths column.

So it just means we're rounding to the nearest tenth.

Like I said, nothing different to what we've been doing previously, we're just going to be looking at different column.

This time I think we probably don't need to be drawing out those number lines.

So here, which you're going straight into using the place value grid.

Here's my number.

We are going to round this to one decimal place, 145.

66 and we're going to round it to one decimal place.

We know we're around the nearest tenth so let's identify the column and the digit we'll be looking at.

But remember it's the number or the digit to the right of that that's going to inform what we do.

Here we can see, remember halfway would be five and six is clearly greater than five.

We are going to round up to the higher value.

Now here you can imagine drawing out your number line.

What two values would we have put either end 145.

6 and 145.

That's our answer here.

Remember, if you need to draw your number line, absolutely fine, no problem at all.

Round 54.

96 to one decimal place.

Identify the digit in the first decimal place.

So here's my number and here's the digit in the first decimal place.

We look to the right.

This is greater than five 'cause remember halfway would be showing a five in this column.

Therefore, we're going to round to the higher value.

What would be the higher value here? I know my lower value on my number line, I'm imagining my number line now would be 54.

But what would be higher value on the number line have been? The lower value would've been 54.

9 like I said.

And we need to increase that by 1/10.

And we know that 1/10 is equivalent to 0.

We can do 54.

9, add 0.

1 and we get 55.

We must include that zero because we want it rounded to one decimal place.

So we need to show a digit in the first decimal place.

54.

96 is 55.

0 to one decimal place.

So you just need to take care particularly if there is a nine in that column that you've identified as the first one.

That's the one that sometimes can trip us up a bit, but it won't trip you up, I'm sure.

Let's have a go at one together on the left hand side and then you can have a go at the one on the right.

65.

83.

Now we're gonna round that to one decimal place.

It's my place value grid.

One decimal place.

It's my tenths column.

So I look at my digit here, it's an eight.

I highlight the digit to the right of that, which is a three.

It's less than five so we round down to the lower value, meaning my answer is going to be 65.

Now your turn.

Round 875.

26 to one decimal place.

Pause the video, come back when you have got an answer.

Remember, you can use your place value grid, you might not use it at all, or you can stick with using that number line if you feel more confident.

Good luck.

I'll see you in a moment.

Super.

Let's take a look at the answer.

So, you may have used a place value grid like I have here.

You would've highlighted the two, then you would've looked at the column to the right to decide what we're going to do with that two.

Is it staying as a two? Am I changing it to a three? What did you get? You're right.

It's greater than five in the hundredths column, therefore 875.

26 to one decimal place is 875.

Well done.

I know you've got that right.

Now, let's have a look at two decimal places.

Two decimal places.

Here's my number.

And identify the hundredths column this time 'cause that is in the second decimal place.

I'm literally counting the columns after the decimal point to work out where my decimal place is.

In this case, it's the hundredths.

Process is the same, remember.

We're gonna consider the digit in the thousandths column 'cause that's to the right and that is greater than five.

So therefore we're going to round up to the higher value.

So it is going to be 2.

46.

The only difference for what we've been doing throughout today's lesson is changing that first column that we are highlighting.

That rest of the process is exactly the same.

So as long as you can identify the correct column to start with, you can be super good at any of this rounding stuff.

Another one, 1.

9037 to two decimal places.

Let's put it in our grid.

Two decimal places.

So count after the decimal point, that's the hundredth column.

And then we look at the thousandths column to decide what we're going to do 'cause that is immediately to the right of the hundredths column.

Here we can see that it's less than five, so therefore we're going to leave the digit in the hundredths column.

So my answer we're gonna round down to lower value is 1.

90.

Notice I've put the zero there.

That shows that I've considered what value needs to be in that hundredths column.

If I didn't put it there, it would might mean that actually the exact answer was 1.

Now you can have a go at this check for understanding.

Which of the following have been correctly written to two decimal places.

Pause the video and when you've decided which are the correct ones, come back and we'll check those answers.

Super work.

Let's have a look and see which ones were correct.

B and D.

Did you get B and D? Fantastic.

The others were not quite right.

A should have been 0.

07.

We can see here they've done it to three decimal places.

And C should have been 8.

46 here.

They've just done it to one decimal place.

Now you're ready for your independent learning within this cycle.

You're gonna pause the video, you're gonna round each of those to one decimal place, and then when you're ready, come back and we'll check those answers.

Good luck.

Off you go.

Great.

Now question two.

This time you're gonna be rounding to two decimal places.

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

Great work.

Question three, have a go at this one.

A little bit more challenging this one so give it your best shot.

I'm sure you'll be fine.

And the next part, C and D of question three.

Great.

And finally, the last questions in this lesson.

Good luck with these and then I'll be here when you get back.

We'll check those answers and then we can summarise our learning today.

You've done fantastically well.

So just stick with me for another couple of minutes.

Well done.

Thank you for coming back and joining me and we'll now check those answers.

One a, 3.

B, 3.

C, 13.

D, 13.

E, 134.

F, 135.

Remember we want that 0.

0 'cause it says one decimal place.

And G, 2,345.

Question two, a 4.

36.

B, 4.

35.

C, 24.

75.

D is also 24.

75.

E, 224.

91.

F, 224.

10.

And again that zero needs to be there.

And g, 5,224.

10.

And then onto those challenging questions.

I'm really pleased that you decided to give these a go.

Now here I'm just giving you some examples of answers.

Here my example for a, 3,556.

B, 345.

67.

So they're examples.

You may have something different that also works.

C, I've got 6.

4357, and D actually was totally impossible as there is not a nine, a one, or a zero card.

And then moving on to E and again it's an example of something that would be correct, 3.

7654.

F, c had the most possible answers as there were three different starting points.

And then we've already really mentioned g, haven't we? D had the least? 'Cause actually it was totally impossible.

Thank you so much for sticking with me throughout today's lesson.

We can now summarise what we've done.

So rounding is useful for showing the approximate value of something without it being exact.

A number line is useful when rounding and there you have an example of what that might look like.

We also looked at using a place value chart and we know that also this is a really useful way of making sure we can round successfully.

Like I said, throughout today's lesson, you've done fantastically well.

I'm really pleased that you decided to join me today and I look forward to seeing you again some other lesson.

Goodbye.

I've finished the video