Lesson Video: Adding Tens to Three-Digit Numbers Mathematics

In this video, we will learn how to model adding a multiple of ten to a three-digit number and investigate which digits in the number change.

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Video Transcript

Adding Tens to Three-Digit Numbers

In this video, we’re going to learn how to model adding a multiple of 10 to a three-digit number. And as we do this, we’re going to investigate which digit in the number change.

Now, let’s begin with a three-digit number, 231. And let’s imagine we want to find out what 40 more than this number is. We’re going to need to find the answer to an addition, aren’t we? 231 plus 40. Let’s think about this number that we’re adding for a moment. What can we say about it? Well, we know that if we are modeling it out of base 10 equipment, we just need some tens blocks. We’d only need tens counters if we wanted to model it out of place value counters. And if we wanted to record it in a place value grid, the only digit we’d need that wasn’t a zero would be a four in the tens place. Obviously, we’d still need a zero in the ones to show that the four is in the tens place.

So, all of these facts show us that 40 is what we call a multiple of 10. It’s a number we get by multiplying 10 or counting in tens. 10, 20, 30, 40. These numbers all end in zero. They’re all multiples of 10. And these are the sorts of numbers that we’re going to be adding in this particular video. So, with this particular question, the multiple of 10 that we’re thinking of is 40.

Now, one way we can find the answer quickly to a calculation like this is by using place value blocks to help. So, let’s start by modeling our three-digit number using place value blocks. 231 is made up of two hundreds, three tens, which are worth 30, and one one. Now, as we’ve said already, we’re going to be adding a multiple of 10 to this number. And we model 40 using four 10s. Can you see where we need to add this to our place value blocks?

We can add the four 10s to the three 10s blocks that we already have, and three plus another four equals seven. Our number now has seven 10s in it. We still have two 100s; that hasn’t changed. And we still have one one; that hasn’t changed. But our three-digit number has gone from having three 10s to seven 10s. That’s because by adding 40, we’ve added four 10s. 231 plus 40 equals 271.

Now, we don’t have to use place value blocks to find the answer to a question like this. Because we’re adding a number of tens, we could count on in tens to find the answer. And we could use a number line to help us do this. Let’s start with the number 147. And let’s imagine we want to find the sum of this number and 50. And we know that finding the sum means adding. So, we need to find the answer to 147 plus 50.

The first thing we can do is look at the number that we’re adding and see that it’s a two-digit number that ends in a zero. It must be a multiple of 10. And when we think about our times tables facts, we know that five 10s make 50. So, we need to add five 10s to 147. And because we know how to count in tens, we could skip count in tens five times from 147 to find the answer. So, we could sketch a number line.

We could mark 147 on the left because we’re going to be counting onwards. We’re going to need the rest of the number line to show what we’re doing. And we could put an arrow on both ends of the number line to show that it continues in both directions. And now, we simply need to practice counting in tens five times. So, we can say 147 and then 157, 167, 177, 187, 197. Did you notice which digit changes as we counted on in tens? The number 147 is made up of one 100, four 10s, and seven ones. And because we were skip counting by ten, it was the tens digit that began to change. Four 10s became five 10s, then six 10s, seven 10s, eight 10s. And we ended up with an answer that had nine 10s.

We started off with a number that had four 10s. We added five more 10s. And because we know four plus five is nine, we’ve ended with a number with nine 10s. And you know you can hear the tens digit change as we read the numbers. 147, 157, 167, 177, 187, 197. You actually hear it changing, can’t you? So, this is another way we could add a multiple of 10 to a three-digit number by counting on in tens. 147 plus 50 equals 197.

Now, let’s try one more example. And this time, it’s going to involve separating out the tens so that we can look at them on their own. Let’s imagine that we want to find the answer to 844 plus 30. Once again, we’re starting with a three-digit number, and we’re adding a two-digit number that ends in a zero. It’s a multiple of 10. And we know that 30 is the same as three 10s. And we know if we’re adding a number of tens to a three-digit number, it’s going to affect the number of tens in that number. So, the first thing we could do is to separate out the tens to look at them.

And what we’re about to do, you could do in your head. But we’re going to use a part–whole model just to show exactly what we’re doing. So, we’re going to take our number 844. And because we know we’re adding a number of tens, we could separate out the tens part of 844 because we know there is a four digit in the tens place; we know that’s worth 40. And the other part is the rest of the number. So, we’ve still got our eight 100s and our four ones, 804.

Can you see why we split the number up like this? We know that we want to add 30 to our number, which is worth three 10s. So, we’ve taken our four 10s out of the three-digit number so we can think about them separately. Now, we know that four plus three equals seven. And so, four 10s plus three 10s must equal seven 10s, or 40 plus 30 equals 70. The four 10s that we started off with are now seven 10s. And we just need to combine our two parts back together to find the answer. It still has eight 100s, and it still has four ones. Those digits haven’t changed, but our tens digit has changed. And by separating out the tens like this, we could find the answer quickly. 844 plus 30 equals 874.

Let’s have a go to answering some questions now, where we have to add tens to some three-digit numbers, and we’ll try putting into practice some of the different strategies we’ve talked about.

Add the two numbers 328 and 20.

In this question, we’re given two numbers to add together. We’ve got the three-digit number 328 and the two-digit number 20. Now, the number that we’re adding, 20 here, is a multiple of 10. We know this because it ends in a zero, and a multiple of 10 is a number that we can get by multiplying 10 several times. We know that two 10s are 20. Now, we know the number 328 contains three 100s, two 10s, and eight ones.

And so, one way to find the answer might be to count on from this number in tens twice. Let’s count aloud and see where we end up. So, we start with 328 and then 338, 348. Look out, the tens digit in our number has gone from two 10s to four 10s. This is because our number had two 10s to begin with, and we needed to add 20 which is the same as two more 10s, which makes four 10s altogether. We counted on to find the answer. If we add together 328 and 20, we get the total 348.

Count in tens to find the sum. 643 plus 40 equals what.

Our question begins with a three-digit number, 643. Can you see it labeled on this number line? And we need to add to it a multiple of 10. We know that a multiple of 10 is a number that we get by multiplying another number by 10. In other words, it is a number in the 10 times table. It’s a number of tens. And we can recognize the number 40 as being a multiple of 10 because it ends in a zero. And also, we know a times tables fact to help us, don’t we? Four 10s are 40. And that’s why we’re told in the question to count in tens to find the sum or we could even say count on four 10s.

Now, if we look at our starting number, we can see that it contains four 10s already. So, we’ve got four 10s and we need to count on four 10s. How many tens do you think our number is going to have by the time we finished? Let’s count on to find out, and we’ll use the number line to help us. So, we have 643 and then 653, 663, 673, 683. The number 40 is the same as four 10s. So, we counted on in tens four times to find the sum. Our starting number had four 10s. We added on four 10s, and our answer has got eight 10s. And we can see why this is, can’t we? Because four plus four more equals eight. 643 plus 40 equals 683.

Find the sum by adding the tens first. 321 plus 40 equals what.

In this question, we need to find the sum of two numbers. And we know that finding the sum means finding the total, adding together. And the two numbers that we need to add together are a three-digit number, 321, and a two-digit number, 40. And we’re told to find the sum by adding the tens first. Can you see why we might want to do that? It’s because the number that we’re adding, 40, is a multiple of 10. It’s a number of tens. We know that four 10s are worth 40. And so, we can take out the tens of our number, 321, and just add our four 10s onto this, as long as we put the whole thing back together again at the end. And that’s what the part–whole model underneath the number 321 shows us.

Let’s show what we mean using arrow cards too. So, here’s our number 321. And because we want to add on four 10s to it, we’re going to take out the tens from this number. There we go. So, we’ve split the number 321 into two parts. We’ve got our tens that we’re going to be working with. That’s two 10s, which are the same as 20. And we’ve got the other part, which is the number we’ve left behind. We’ll come back to that at the end, and that’s 301. So now that we’ve separated out the tens, we can add them.

What is 20 plus 40 or what are two 10s plus another four 10s? Well, we know that two plus four equals six. So, the answer is going to be six 10s or 60. Let’s record our answer using another part–whole model. So, two 10s plus four 10s equals six 10s. And in the other part, we’ve still got that 301 that we left behind. So, to find the overall answer, we just need to quickly put back together our two parts, 301 and 60. Can you see what the numbers are going to be? Well, we know those six 10s are just going to slot neatly into the tens place of our answer, aren’t they?

321 plus 40 equals 361. We found the sum of 321 and 40 by adding the tens first. 321 has two 10s, and we added on four more 10s. And so, our answer has six 10s. The sum of 321 and 40 is 361.

If I add together 436 and 60, what will the tens digit of the sum be?

This is an interesting question because it starts off by looking like we need to add together 436 and 60. But as we read the rest of the question, we can see that we’re not being asked for the sum of these two numbers. We’re being asked what the tens digit in the sum is going to be. And you might think to yourself, “Well, I’m gonna have to work out the answer and then just look at what the tens digit is.” But there’s a quicker way to solve the problem, and it involves us understanding what it means to add a multiple of 10 to a three-digit number. So, let’s have a go at solving this problem the quick way.

And it’s not that difficult; it just involves us understanding the place value of the numbers that we’re adding. So, if we think about the number we’re starting with, 436 contains four 100s, three 10s, and six ones. And the number that we’re adding to this contains six 10s and zero ones and, of course, zero 100s as well. Now, the really important bit about what we’ve just said is this digit here. The number that we’re adding on to 436 contains six 10s. It doesn’t contain any hundreds, doesn’t contain ones, just six 10s because six tens equals 60.

Now, as we’ve said already, our starting number 436 has got three 10s. So if we already have three 10s and we’re adding on six 10s, what will the tens digit of the sum be? Well, we know that three plus six equals nine. So, three 10s plus six 10s is going to make nine 10s. Our answer is going to have the digit nine in the tens place. So, although we don’t have to, let’s just write down what the sum would be. It’s still going to have four 100s, and it’s still going to have six ones. Those digits aren’t going to change. But the three tens that we started with are now going to become nine 10s. 436 plus 60 equals 496.

We’ve used our knowledge of place value here to work out what the tens digit is going to be. If we add 60 to a number that has three 10s — in this question, it was the number 436, but, you know, it could have been any number at all — we found that the answer will contain nine 10s. So, the tens digit of the sum of these two numbers is nine.

So, what have we learned in this video? We’ve learned how to model adding a multiple of 10 to a three-digit number. We’ve also investigated which digits change when we do this.

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