# Lesson video

In progress...

Hi there, everyone.

Thank you for joining me.

My name is Ms. Jeremy.

And today's math lesson is focused on rounding problems. So find yourself a nice quiet space.

Let's begin by looking at your lesson agenda for today.

So we're going to begin with a rounding recap before looking at rounding to the same multiple, and we'll finish with some rounding riddles and your independent task and quiz at the end of the lesson.

For today's lesson, you will need a pencil and some paper and a nice quiet space.

So pause the video now, to find these resources and restart when you're ready.

Let's begin looking at our warmup.

We're looking at a little recap of rounding.

So the question asks us, can you round 452,087 to the nearest multiple of 1000, the nearest multiple of 10,000 and the nearest multiple of 100,000? So we're going to have a go at doing this together.

What I'd like to do is to use a slightly simpler method than the number line method.

The number line method works perfectly well for this, but I'm going to use a slightly quicker method today, which is to look at the net digit I'm rounding and then take a peek at the digit that is to the right of the digit I'm rounding and use that to help to tell me when I'm rounding up to the next multiple or down to the previous multiple.

So let's start with looking at rounding to the nearest multiple of 1000.

In our number, the first thing I'm going to do is look at the digit that's in the thousands column.

So I'm going to underline it just so we know exactly what it is, in this case it's the two.

So that's equivalent to 2000.

In order to find out whether I'm going to be rounding up or down, I need to take a peek at the digit that's in the hundreds column.

And I can see that's a zero.

Anything that is four and below tells me that I'm going to need to round that thousands down.

Anything that is five or above tells me I'm going to need to round it up.

So in this case, we're on a zero, that tells me that I am rounding down to the lower multiple.

So in this case, the nearest multiple of 1000 is 452,000.

Next one, let's have a look at rounding to the nearest multiple of 10 thousand.

This time, I'm looking at the digits in the 10 thousands place that's the five equivalent to 50,000, and I'm going to take a peek at the thousands column, to let me know what I'm running up or down.

In this case, the digit in the thousands column is a two.

I'd like you to spend three seconds working out, whether we're going to round up or down based on that information.

So hopefully you have seen that we will be rounding down because anything that is four and below tells us that we are rounding down to the smaller multiple of 10,000.

In this case, the smaller multiple of 10,000 is 450,000 rather than 460,000.

So I'm rounding down to 450,000.

Finally, the last thing I need to do is round to the nearest multiple of 100,000.

I'm going to underline that digit and take a little peek at the next door, and I can see there, that the digit that is in the 10 thousands column is a five.

Three seconds, do you think we're rounding up to 500,000 or down to 400,000? So hopefully you should have seen it based on the fact that we've got five next door to our 400 thousands.

We are rounding up to the next multiple.

So our answer and when we're rounding, the nearest multiple of 100,000 is 500,000.

And you can see all of the answers there on the screen just like we said.

So for the nearest thousand and 10,000, we rounded down, whereas when we were rounding to the nearest 100,000, we rounded up.

Let's move on to the next type of question for today's lesson.

So let's have a look at this question, which involves rounding to the same multiple.

It says, "I wonder if I can list all the numbers "that will round to 700,000, "when rounding to the nearest multiple of 100,000." So this has a bit of a reasoning problem for us to think about.

We want to know all of the numbers or the whole range of numbers that would round to 700,000, when you're rounding to the nearest multiple of 100,000.

Now there's lots of ways that we could solve this problem.

We could decide to take an approach, which I call a random approach.

Where we just come up with as many numbers as we can possibly think of, that would round to 700,000.

So I could say, for example, I know that 729,863 rounds to 700,000.

And I could just do that for as long as I possibly can and hope that I get them all.

The problem with that method, is that firstly, it's not very logical.

It's not very systematic.

And I'm unlikely to get all of the numbers that I need.

The second issue with that, is it's going to take me a long time.

I'd probably be here until next week, if I decided to use that method.

So what I need, is a systematic logical method that provides me with all of the possible numbers, but doesn't take as long.

So the next strategy I could do, is a bit more systematic.

I could say that, if I start at 700,000 and I work my way backwards, so I list all of the numbers before 700,000, that round to 700,000, and then I list all the numbers forwards, that would also round, then I'll get them all.

So this is what I could do.

I could say, the number before 700,000 is 699,999.

Then that next number before is 699,998, then next number, and I can continue to do that until I get them all.

This is a little more systematic than my random method.

It's a little bit more logical, but it's still probably going to take me until about next week.

We want a systematic, logical, but super speedy method that allows us to see the full range of numbers.

So this is the way I'm going to do it.

I'm going to think to myself, what is the smallest possible number that would still round to 700,000? So what is the very, very first point on that number line that would still round up to 700,000? And then once I've done that, I'm going to see what I can work out, what the very largest or the greatest possible number is that would also still round back down to 700,000.

Once I know what those two numbers are, actually, what I can say is, the range of numbers between those two, all of those numbers will round to 700,000.

So what I'm going to do is think back to the very first number on my number line that would still round to 700,000.

Think to myself, what about the number 635,000? What I know that's not going to work.

635,000 runs back down to 600,000.

So what is the very first number on that number line? What is the smallest possible number that will still round to 700,000? I'm going to give you a bit of thinking time.

I'm going to give you 10 seconds.

I want you to think, what do you think the smallest possible number that would still round up to 700,000 is? How did you get on? Well I'm going to let you think that, actually I know that numbers beginning with six will round up to 700,000, but only if the next digit is five or greater.

So my digit in the 10 thousands column will need to be a five.

That's the smallest possible number it could be.

If it was a four, it would round back down to 600,000.

So it needs to be a five.

And remember I'm trying to think of the smallest possible number.

So what I'm made to do, is just fill in the rest of the numbers with placeholders, because it doesn't matter what those numbers are.

But I know that the digit in the 10 thousands column is going to determine whether this rounds up.

The smallest possible number that's still rounds to 700,000 is 650,000.

Now let's think about, the largest possible number that still rounds down to 700,000.

I'm thinking about a number that is on this side of my number line.

I know that actually a number that begins with seven, for it to round back down to 700,000, the next digit will need to be a four.

If it were five, it would round up to 800,000.

And I don't want to be doing that.

I want to around back down.

So my number's got to begin with the digit seven and four.

The rest of my number, doesn't make too much difference, but I do want to make it the largest possible number I can.

So I'm going to fill these in with nines.

Because I know then, that that is the largest possible number that will still round back down to 700,000, 749,999.

So what I can say, and this is much more efficient, much more logical than my previous methods, is any of the numbers between 650, 000 and 749,999 will all wound down or up to 700,000.

And that took me far less time than my random method or my slower method might have done.

So it's your turn to have a go.

I'd like you to have a look at this question here.

It says, what is the range of numbers that will round to 300,000 when rounding to the nearest multiple over 100,000.

So this question is exactly the same as our previous one, the only difference this time, is that we've got 300,000 rather than 700,000.

I'd like you to pause the video, to identify the range of numbers that will round to 300,000 when rounded to the nearest multiple of 100,000, and resume it once you're finished.

How did you get on? Let's have a look at this together.

So again, I'm going to use that systematic method to work out what the smallest possible number could be, that will still round up to 300,000.

And then I want to know the largest possible number that will still round down to 300,000.

So I know that this is going to begin with a two.

It's going to have a two in hundred thousands, I'm going to need to put a five in my 10,000, so it rounds up, but the rest of the numbers can be Pesos, so my lowest possible number is 250,000 that will still round up.

And the greatest possible number, it has a three in hundred thousands, but it's got to have a four next door to it, otherwise it will round up.

And then I'm going to fill in the rest of the digits with nines to make it the largest possible number it can be.

So the range that you should have identified was 250,000 all the way to 349,999.

I can also to test out the strategy a little bit.

Because what I can do is I can think to myself, let me just make sure, if I just check the digit before 250,000, which is 249,999, I know that that rounds down to 200,000.

So I know I'm correct with this one here.

I'm going to check the digit that would just be just after 349,999, which would be 350,000, that would round up to 400,000.

So I also know I'm correct just here.

And what I can do is say that the full range of numbers between those two, will round to 300,000.

Let's look at a slightly different example.

This time, we want to think about rounding to the nearest multiple of 10,000.

So we looked around into the nearest multiple of 100,000, now we want to know what range of numbers would still round to 630,000? Again, same method.

I don't want to use that random method, I don't want to use the method that takes me until next week to finish it, I want to use that really efficient method that will give you the full range of numbers that will round up and down to 630,000.

So I'm looking for the smallest possible number that will still round up, and the largest, the greatest possible number that will still round down? I need to give you 10 seconds.

In those 10 seconds, I'd like you to see if you can work out the method that we'll use.

We want to use a similar method to what we were doing, when were rounding to the nearest multiple of 100,000, but how will we adapt it this time, to round to the nearest multiple of 10,000? You've got 10 seconds.

How did you get on? Let's have a look together.

So let's have a look at this smaller multiple first of all.

I want to know the smallest possible multiple would be, that still rounds up, sorry, the smallest possible number would be, that still rounds up to 630,000.

Because this time I'm focused on those 10,000.

But I'm going to put two in my 10 thousands place, and think about what number, what digit will I have to put next to that two, for this to round up to 630,000 rather than down.

I can see that it's going to have to be a five.

Because a five or above is the only digit that I could put in there that would still make the number round up that would still make that two, round up to the next multiple of 10,000.

And then I remember I want this number, to be the lowest, the smallest possible number it can be, so I'm going to fill in the rest of the digits with placeholders there.

625,000 is the smallest possible number that will still round up to 630,000.

And I know this is the case.

Because if I think about it, if I think about the digits or the number 624,999, that would round down to 620,000.

So this is definitely the smallest possible number that will still round to 630,000.

Just think about the greatest possible number now.

So again, I'm going to start with my 600,000, that digit is not changing.

We're not focused on the hundred thousands anymore, we're focused on those 10 thousands.

And I'm going to put three in my 10 thousands, but I'm going to think, what could the rest of the number be that would ensure that we are rounding down to 630,000 rather than up to 640,000? What I know, it's going to have to be a four there.

If I were to put five there, it would round back up.

So I need to put a four there for it to work.

The rest of the numbers I'm going to fill in.

And because I want it to be the greatest number possible, I'm going to fill those in with nines.

That's the greatest digit I can put in.

So my range is 625,000 all the way up to 634,999.

The way that my strategy changed this time was that, instead of focusing on the hundred thousands digit, I focused on that 10 thousands digit.

And I was looking at what I needed to do to maintain that 10 thousands digit when I was rounding.

So you all can have a go.

I would like to know what is the range of numbers that will round to 570,000 when rounding to the nearest multiple of 10,000? Same strategy that I used, but this time the number is 570,000.

Pause the video to complete your task and resume it to once you're finished.

So remember, we're trying to get all of the numbers, the full range of numbers that will round to 570,000.

And we start by thinking about the smallest possible number that will still round up to 570,000.

So reminding myself again, we're now using our 500 thousands and we're not focused on a hundred thousands at the moment.

So they're going to stay as they are.

The next digit is going to be a six, because I would like my 60 thousands to round up.

In order for those 60,000 to round up to 70,000, the next digit, the smallest possible number it could be is a five, if it were a four it would round back down.

Filling in the rest of my number with my placeholders, because I want it to be the smallest possible number it can be, so your number should have been 565,000.

Looking at the next side, I want the greatest possible number that will still round down to 570,000.

So again, I'm dealing with my 500 thousands, so I'm not focused on those hundred thousands.

So I keep the digit as is.

We're going to keep a seven there for our 70,000, and we want the next numbers to ensure that this rounds back down to 570,000.

So the greatest possible number I can have, in my thousands column is a four.

If it were a five, I would end up rounding up to 580,000.

I don't want to do that, so I've got to make that four.

But the rest of my digits can all be nines, because I'd actually like to round this number.

I get this number as high, as great as it possibly can be, and so putting nines in for the rest of the number helps me with that goal.

So you can see here that the full range of numbers that will round to 570,000, span from 565,000 to 574,999.

So let's move on to our next activity.

So we're going to look at some worded problems involving rounding now.

And that's read this worded problem together.

It says, "my number has five digits.

"It is approximately equal to 42,300 "when rounded to the nearest 100.

"It is even.

"What could my number be?" So a little riddle here, we've got some clues which I'm going to underline as we go through.

So we know that the number has five digits.

That means it's got to have digits in the 10 thousands column, thousands column, hundreds, tens, and ones.

It is approximately equal to 42,300 when rounded to the nearest 100.

So we know that that is the key number that we need to be able to round to.

We need to know that our number is even.

So we need to know that our number ends in a zero, two, four, six or an eight.

So we've got some clues to help us out here.

We're going to start thinking about, what the number could possibly be.

So I've got some options for us to consider.

Look at number B, 42,317, is it possible for the number to be 423,193? Or could it be 42,298? What I'd like you to do, is spend the next couple of minutes working out, which of those numbers is a possibility, if any, and if one of those numbers is not a possibility, Can you explain why? Pause the video now, to have a look at those three numbers and resume it once you've identified, which of those numbers could be a possibility, if any? So let's have a look together.

Let's have a look at the first number 42,317.

If we look at this, according to our clues, it is a five digit number.

So that is correct.

Now, does it round to 42,300, when rounded to the nearest 100? Well, yes.

If I look at my hundreds column there, and ake a peak at the tens, I can see that it would.

So for that particular clue, it is also correct.

Is it even, does it end in a zero, a two, four, six or an eight? No, so that is not correct.

It couldn't possibly be that number, because it doesn't fit in with all of our clues.

Let's have a look at the next number.

The next number is 423,183.

Straight away, I can see that the big problem with this number, is it doesn't have five digits, it has six digits.

So already, even without looking at the rest of the clues, I can see this is incorrect.

The last one, the last one has five digits.

If I round it to the nearest 100, I can see when I'm looking at my hundreds column there, that a hundreds column I take a peak.

It would round to 42,300.

It is also an even number because it ends in eight.

So that is the number that could be the number this boy is thinking of.

However, if we wanted to be a bit more specific, we could look at our number line and identify exactly what the range of numbers would be, that would round to 42,300 when rounding to the nearest 100.

Remember we're rounding to the nearest 100.

So we'd like all of our numbers to have still a four in the 10,000, still a two in thousands, but it's that three and the number next to it that we need to think about.

So the first thing I'm going to think about, is the number that is going to be the smallest possible number that will still round up.

So I know it's going to have my four in the 10 thousands, my two in the thousands, but this time I'm going to have a two in hundreds, and I'm going to think about what digit needs to come next.

What is the smallest possible digit that needs to come next, so that this would still round up.

I'm going to give you three seconds to work out what the smallest digit would be.

So you should have seen, that the smallest digit that could be placed next would be a five.

Because four or below would mean that, that digit, that number would round back down again.

So we've got five and then I'm going to fill in with my zero.

So 42,250, that will still round up to 42,300.

Now, what is my greatest number that will still round back down to 42,300? Once again, I'm keeping my 10 thousands, I'm not interested in those at the moment.

My thousands are also staying the same.

I'm going to have my three hundreds, but I'm going to think about the last possible number that will still round back down.

So I'm going to have to have a four next, and fill in the next bit of my number with my highest possible number, that's a nine.

So I know that the range of numbers that could round to 42,300, span all the way from 42,250 to 42,349.

So that's a really handy tip.

I didn't need to do that to solve the riddle, but you can do that to help you out, if the question is asking you what the range of numbers that can help you out there.

A little example for you to try.

It says, "my number has four tens "and is a multiple of five." I'm going to underline some information as we go.

So it has four tens, it is a multiple of five.

"My number is approximately equal to 780,000 when rounded to the nearest 10,000.

"What could my number be?" So this time round, I want to us to have another think about this, in the context of a number line.

So we're going to think of the full range of numbers.

And then my challenge to you is to have a little think about what the number could potentially be, with regards to the initial bit of clues that we have here, which says that it has four tens and it's a multiple of five.

So first of all, let's work out the range of numbers that will still round up.

So we need to know what are the numbers at the end of my number line here, that will still round up to 780,000? And what is my greatest possible number that will still round down to 780,000? So we've done this a couple of times now, let's have a go at this particular number.

So I know that my hundred thousands, are going to stay the same, but I want the lowest possible number.

So I'm looking at my 10,000 being seven.

If that seven is going to round up to 80,000, I need to have a five that comes next.

And I'm going to fill in with placeholders for the rest of my number.

Looking at the number on the other end, my greatest possible number, again, my hundred thousands don't change, my 10 thousands are going to be eight, but I need to have a four that comes next otherwise that eight would round up to nine.

And I'm going to fill in where the greatest possible number that I can find and those are the digit nine as I go.

So you can see the full range of numbers now, range from 775,000 to 784,999.

So let's look at the next part of the riddle here.

We know it needs to have four tens, we know it needs to be a multiple of five.

So any number that is a multiple of five needs to end in either a zero or a five.

And you'll know that because if you do your five times table, you can see that all of the numbers that are in the five times table end in a zero or a five.

And it has four tens.

What I'd like you to do is spend about 10 seconds writing down two possible numbers, that this could be.

Two possible numbers that fit in with all of the clues on this riddle.

10 seconds beginning now.

Time's up.

Well done.

Let's have a look at the last thing that we're going to do today.

You've got three questions, that you're going to complete, and they're very similar to the questions that we have had a look at already today.

So what I'd like you to do for each of those questions, is to underline the key information.

If you've got this printed out.

Then I'd like you to draw out your number line, so, you know, the range of numbers these numbers could be.

And then I'd like you to write out the range of numbers, but alongside that, I'd like you to write three possibilities of what the whole number could be for each of those examples.

So there'll be a whole range of different possibilities for some of these questions, but I want you to write down three different possibilities for each one, along with a number line, showing you the range of digits or the range of numbers it could be as well.

So spend some time on that, pause the video now, to complete your task and resume it once you're finished.

You're welcome for all your hard work today.

It might be a really nice idea to ask somebody to check through the answers that you've done, and just have a look at whether your answers are plausible, if they match the clues as part of the riddle.