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Lesson Video: Estimating Sums of Two-Digit Numbers: Rounding Mathematics • 3rd Grade

In this video, we will learn how to estimate the sum of two-digit numbers by rounding to the nearest ten.

17:39

Video Transcript

Estimating Sums of Two-Digit Numbers: Rounding

In this video, we’re going to learn how to estimate the sum of two-digit numbers by rounding to the nearest ten. This is a word that’s going to crop up again and again in this video. Do you know what it means? If we estimate an answer in maths, we find a value that’s quite close to the exact amount but not the exact amount. When we estimate, we use words like about or around. The answer is going to be about this much or around this much. Now, let’s imagine that we’ve got two packets of sweets. One weighs 29 grams, and the other has a mass of 52 grams. And let’s imagine that we want to put these sweets into a parcel to send to a friend.

So we’re standing in the queue at the post office and we think to ourselves, “I wonder how much my parcel is going to weigh!” We want to know how heavy these sweets are going to be all together, so we want to add together 29 grams and 52 grams. But we’re standing in the queue at this post office and it’s going down and down and time is running out. So we need to do a quick calculation. Instead of working out the exact amount, we might quickly estimate the sum of these two numbers. We might say to ourselves exactly what this girl is saying, “I don’t need an exact answer, so I can estimate it.” And you know, one way we can estimate the sum of two numbers like this is by using rounding to help. And we can do this in two steps.

In step one, we round each number to the nearest ten. Do you remember how to round two-digit numbers to the nearest ten? There are two ways to do this. The first way is to use a number line to help. So if we think of our first packet of sweets, which weighs 29 grams, we know that the multiple of 10 that comes before 29 is 20 and the multiple of 10 that comes after 29 is of course 30. In other words, 29 is in between 20 and 30. But which of these two multiples of 10 would we round it to? Which is it nearest to? When we’re using a number line like this, it’s often a good idea to mark the midway point, and that’s about here. And halfway between 20 and 30 is 25, and this can help us think of the position of 29 on this number line now. We know that 29 is greater than 25. In fact, it’s very nearly 30, so we’d probably mark it around here on our number line, and so we can see that the nearest ten to 29 is 30.

So as we’re in the queue at this post office, we’d look at our first packet of sweets and say, “that’s about 30 grams.” Another way that we can round a two-digit number to the nearest ten is by looking at the ones digit. So if we think of our second packet of sweets, 52 grams, the number 52 is made up of five 10s and two ones. Now we know that 52 comes somewhere between 50 and 60. But which one of these two multiples of 10 are we going to round 52 to? Do you remember the rule for rounding two-digit numbers to the nearest ten? If the ones digit of our number is a four or less — so that’s four, three, two, or one — we round it down. And if the ones digit is worth five or more — so that’s five, six, seven, eight, or nine — we always round up.

The digit five is the interesting one in this list because five is the halfway point as we’ve said already. So it can sometimes be confusing to look at a number that ends in a five and think, “What do I do? It’s in the middle!” We always round numbers that end in a five up. Anyway, our number doesn’t end in a five, does it? It ends in a two, 52. And if we follow our rounding rule, we can see that we need to round this number down. So 52 rounded to the nearest ten is 50. And as we stand there in our post office queue and it’s getting smaller and smaller, we can look at our second packet of sweets and say, “that’s about 50 grams.”

Now, by rounding both of our amounts to the nearest ten, we’ve made these numbers a lot easier to work with. It’s much quicker to find a total of 30 plus 50 than it is to find 29 plus 52. So step one was to round each number to the nearest ten, and I’m sure you can guess what step two is going to be. In step two, we add these new numbers to quickly estimate. In other words, we need to find the total of 30 and 50. Now we know that three and five go together to make eight. So three 10s, which is the same as 30, and five 10s go together to make eight 10s or 80. So we’ve quickly done all of this in our heads, and the lady calls us to the desk and we can say, “Can I send these packets of sweets, please? I think they’re about 80 grams.”

We know that when she puts them on the scale, they might not be exactly 80 grams, but we’ve estimated the amount. And just to show you how well estimation like this works, as soon as the lady in the post office puts these sweets on the scales, they’re actually going to weigh 81 grams. So can you see how close our estimate was to the exact amount? If ever we’re in a situation where we don’t need the exact amount, using rounding to estimate like this is really useful. Let’s have a go at answering some questions now and put into practice what we’ve learned. We’re going to be given some pairs of two-digit numbers. But instead of being asked to find the exact amount, we’re going to estimate.

Which number is nearest to 30 plus 19? 30, 40, 50, or 80.

This is a really interesting question because it contains an addition. Now normally in a question like this, we’d see the addition and we’d be asked to find out the answer. What is the total of 30 plus 19? Which number is the same as 30 plus 19? But in this question, we’re not actually being asked to add together 30 and 19 at all because if we read the question carefully, it asks us which number is nearest to 30 plus 19. We’re not being asked for the exact answer, but just an answer that’s near to it. We’re being asked for an estimation.

An estimation is an answer that is near to the exact answer but isn’t the actual answer. It’s just close to it. So once we’ve solved this problem, we could use the word about to describe what we found. We might say 30 plus 19 is about 30 or about 40 or 50 or 80. A good way of estimating the sum of two-digit numbers like this is to use rounding. And usually, we’d be thinking about rounding both of our numbers to the nearest ten because adding two multiples of 10 is really quick to do. But if we look at our first number, it ends in a zero. It’s already a multiple of 10. So the number 30 is going to be quite quick to add. We just need to think about rounding the number 19, don’t we? One way to do this might be to use a number line.

Now, the two multiples of 10 that 19 lives between are 10 and 20, and the midway point between these numbers is 15. Now you probably didn’t need to draw a number line to work out which multiple of 10 19 is nearest to. We know it’s greater than 15. In fact, it’s very, very close to 20, isn’t it? So if we were to round 19 to the nearest multiple of 10, we’d round it up to 20. And so, instead of thinking of 30 plus 19, we can cross through 19 and imagine it was 20. What is 30 plus 20? Well, we know that three and two go together to make five. So three 10s or 30 and two 10s or 20 must go together to make five 10s. 30 plus 20 equals 50.

As we’ve said already, this isn’t the exact answer to 30 plus 19, but it’s a good estimation. Did you know if you add together 30 and 19, you get 49? Our estimation was 50. This is really near to the exact answer, isn’t it? And it’s often a lot quicker to round numbers and add multiples of 10 than to try and think what the sum of two two-digit numbers is. To find the number that’s nearest to 30 plus 19, we rounded one of our numbers to the nearest ten. 30 plus 19 is near to 50.

Estimate 23 plus 36 by rounding the two numbers to the nearest ten using the number line.

In this question, we’re given two two-digit numbers to add, 23 and 36. But we’re not asked to find the sum of these numbers. We’re asked to estimate it, in other words, come up with a value that’s quite close to the exact amount but not exactly it. Now if our question just stopped there, we might look at it and think to ourselves, “Well, how am I going to estimate this amount? What am I gonna do?” But thankfully, our question doesn’t stop there, and it goes on to tell us how to estimate the answer. We need to round both of the numbers to the nearest ten, and we’re given a number line to help us do this.

Have you ever wondered why we would want to round a number to the nearest ten like this? Well, numbers that are multiples of 10 — and you can see these marked with blue dots on our number line, 20, 30, 40, and so on — they end in zero. But when it comes to working with them, and in this case we’re going to add them, we don’t need to think about the ones digit. They’re already zeros. We just need to add together the tens. If we want to estimate the sum of two numbers really quickly, changing them into multiples of 10 is a good thing to do. It makes the whole thing a lot easier.

So let’s begin by writing out our addition as it is at the moment, 23 plus 36. And we’re gonna make this easier to work out. So we’ll take our first number 23 and we’ll see where it lives on our number line. Can you see it? It’s here, isn’t it? It’s in between 20 and 30. But which of these two multiples of 10 is it nearest to? Where would we round 23 to? Would you round it down to 20 or up to 30? You could probably see just by drawing those dotted lines which multiple of 10 it’s nearest to. But it’s often useful just to mark in the halfway point between 20 and 30, and that’s 25. Can you see that 23 is less than 25? It’s nearest to 20, isn’t it?

So the first thing we can do to our calculation is to change 23 to a much easier number to deal with, 20. It’s not gonna give us the exact amount anymore, is it? But it’s gonna give us a good quick estimate. Our second number is 36. Can you see where this is on our number line? It’s here; it’s in between 30 and 40. But again, which of these two multiples of 10 is it nearest to? Let’s mark in the halfway point again. Halfway between 30 and 40 is here, 35. And we know that 36 is just larger than 35, isn’t it? We’re going to need to round 36 up to 40. So let’s change the second number in our addition, 40.

Now we can find our estimate. We need to add together 20 and 40. Now, we know that two plus four equals six, and we can use this easy fact to help us now. Two 10s or 20 plus four 10s or 40 is going to give us six 10s or 60. We rounded both the numbers in the calculation 23 plus 36 to the nearest ten. And this didn’t give us an exact answer, but it did give us a good estimate. Did you know the actual answer to this addition is 59? So you can see how close our estimate is. Our estimated answer to 23 plus 36 is 60.

Estimate the sum by rounding each number to the nearest ten: 54 plus 28 equals what.

In this question, we’re given two two-digit numbers, and they’ve been written as a column addition. Now, you might be forgiven for looking at this and thinking, “Oh! I’ve gotta work out some column addition here.” But you know, we don’t have to do this. We are not asked to find the exact sum of these numbers. We need to estimate it. In other words, we need to find a total that’s around about the right answer — doesn’t have to be exact though. And we’re told that we need to estimate the sum by rounding each number to the nearest ten.

Let’s start by looking at our first number 54. Can you think which two multiples of 10 54 comes between? It’s between 50 and 60. But which one of these two multiples of 10 are we going to round it to? Which is it nearest to? To help us, we can look at the ones digit of this number. It’s a four. Do you remember the rule for rounding? If the ones digit of a number is a four or less, we round down. And this ones digit is a four, so we’re going to round down to 50. So let’s erase 60 from the screen, and we’re going to change then 54 into 50. By rounding this first number to the nearest ten, we’ve made it a lot easier to work with.

Our second number 28 comes somewhere between 20 and 30. But again, we need to ask ourselves, “which is the nearest ten?” This time, the ones digit in our number is an eight. And if numbers with a four or less in the ones place, we round down. This means that numbers with a five or more round up. Of course, eight is more than five, isn’t it? So we need to round this number up. 28 is nearest to 30. So instead of thinking of our calculation as a column addition that shows 54 plus 28, we’ve made the numbers so simple. We don’t even need to think of it as a column addition at all. We just need to find the answer to 50 plus 30, or if we think of it another way, five 10s plus three 10s.

But we know that five plus three is the same as eight. So five 10s plus three 10s will be eight 10s, and 50 plus 30 is the same as 80. And you know the interesting thing about our estimate is how close it is to the actual answer. And if we’d have worked out the exact answer at the column addition, we’d have got the answer 82. So our estimation is really close, isn’t it? It’s a good method to use. We’ve estimated the sum of 54 and 28 by rounding each number to the nearest ten. Our estimation is 80.

What’ve we learned in this video? We’ve learned how to estimate the sum of a pair of two-digit numbers by rounding to the nearest ten.

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