Lesson Video: Column Addition of Three-Digit Numbers: Regroup Ones and Tens Mathematics • 2nd Grade

In this lesson, we will learn how to add two three-digit numbers when we have to regroup ones and tens and record the calculation in columns.


Video Transcript

Column Addition of Three-Digit Numbers: Regroup Ones and Tens

In this video, we’re going to learn how to add two three-digit numbers together when we have to regroup both the ones and the tens. And we’re going to practice recording these calculations in columns.

Let’s imagine that we’ve been shown these number cards. And we’ve been asked to find the total of these two three-digit numbers: 466 plus 359. How are we going to do it? Well, seeing these two three-digit numbers sitting side by side like this doesn’t really help us too much. Can you remember how to write the calculation to make it easier to work out? If we write the digits in columns, we can make sure we add the ones, the — wait; we made a mistake here. We haven’t lined up these digits correctly. Let’s try again. That’s better.

Now we can see the ones are in a column by themselves, so are the tens digits and the two hundreds digits. And underneath our calculation, we could draw an equal sign just large enough for us to put one number card in each column because our answer is going to contain a number of ones, tens, and hundreds. We may even need a thousands digit, but we haven’t added our two numbers yet, so we don’t know that for sure.

Now perhaps you know how to find the answer using a written calculation like this. And certainly by the end of this video, this is all we’ll be using to find the answer. But being as this is our first example, let’s use some place value blocks to model the calculation. This can be quite useful in helping us understand what we need to do to find the answer: 400, 60, six plus 300, 50, nine.

Now how do you think we should add these two numbers together? Should we start with the largest-value digits first? So that’s start by adding the hundreds then the tens and finally the ones. Or should we start with the digits with the least value and add in the other direction? What do you think, left to right or right to left? Well the answer to that question is we always have to start by adding the ones digit, and we’ll see why in a moment. But to help us understand why, just take a look for a moment at our hundreds digits. Make a little prediction in your head how many hundreds do you think the answer is going to have. We’ll come back to your prediction later on.

So let’s start now by adding our ones digits together. 466 has six ones, and 359 has nine ones. What’s the total of six and nine? Well we know that six and 10 will be 16, so six plus nine will be one less than 16. The answer is 15. Six ones plus nine ones equals 15 ones.

But wait a moment; it’s all very well modeling 15 ones out of 15 ones blocks, but what digit are we going to put in the ones place of our answer? You may have wondered at the start of this question why we were using number cards. Well the reason is that number cards help us to understand that each column or each place in a number has only one digit. We can’t put two-digit cards in this ones place. We can only put one. So how can we show the number 15 if we’ve only got space for one digit? We need to regroup the 15 ones that we have.

Perhaps you can imagine a game of football and one team have just scored an amazing goal. But they know that as soon as the match restarts, the other team are going to be right back at them. So as they run back into their own half celebrating, the captain shouts, “Regroup! Regroup!” in other words, “Get back in position.” The team is still the same, but they’re just getting back in a different position. And in the same way, if we regroup a number, the number is still the same, but we’re just showing it a different way.

Do you remember how to regroup 15 ones? To do this, we need to exchange some of our ones. We know that 10 ones are the same as one 10. So we can take 10 of our 15 ones, and we can exchange them for one 10. We’ve regrouped the number 15 into one 10 and five ones. It’s still worth 15, but we’re representing it a different way.

Because our answer has five ones, we know that the digit in the ones place is going to be a five. But we can’t forget about the one 10 that we exchanged either. Now we know that our answer isn’t going to have only one 10 in it because we haven’t added the rest of the tens yet. But we do need to make sure that when we do add the tens, which we’re about to do, that we include the one extra 10 we’ve just made. Now we can write this one 10 in different places. Sometimes, it’s written at the top. But in this example, we’re going to write it underneath our equal sign. And with our place value blocks, let’s put this tiny 10 here just to remind us that we need to add it on.

Now let’s add the tens. 466 contains six 10s, which are worth 60. And in the number 359, we have five 10s, which are worth 50. Now we know that six plus five is 11, so six 10s plus five 10s equals 11 10s. But we can’t forget the extra 10 we made when we regrouped our ones. Instead of 11 10s, we need to show 12 10s. So here’re our 12 10s blocks. And we’re going to need to write 12 in the tens place of our answer.

What have we done? We’ve made another two-digit number. We can’t put two digits in the tens place. We’ve only got space for one number card. Looks like we’re going to have to regroup again. How can we regroup a large number of tens like this? We know that 10 10s are the same as one 100. So we can take 10 of these 12 10s and exchange them for one 100, because one 100 and two 10s, or 20, is the same as 120. And this is exactly the same as what 12 10s are worth, 120. The value of the number hasn’t changed at all. We’ve just regrouped it. So in our tens column, we can write the answer two. But just like before, we need to make sure that we record our one extra 100 somewhere so that we remember to add it when we add our hundreds.

Speaking of hundreds, let’s add them. There are four 100s in 466 and three 100s in 359. And we know that four plus three equals seven. Now do you remember at the start of this calculation when you were asked to predict how many hundreds you thought the answer was going to have? I wonder how many people watching this video thought, “Well, four plus three is seven. It’s going to have seven 100s.” If we’d have started by adding our hundreds digits together, we’d definitely have written seven in this place. But can you see now that our answer isn’t going to have seven 100s? We also need to include the 100 that we made when we added our tens together. Our answer is going to contain eight 100s.

And this is why every single time we add numbers using column addition, we start with the ones and go from right to left. Because we don’t know until we start whether adding the ones is going to affect the tens digit and whether adding the tens is going to affect the hundreds digit. Every time we have to regroup and exchange, it makes a difference to the next column along. And in this particular column addition, we had to regroup twice. We had to exchange some ones for one 10 and then some tens for one 100. That’s why in the title of this video it said, “regroup ones and tens.”

We don’t always have to regroup. Sometimes, we could add two three-digit numbers together and not need to regroup at all. Other times, it’s just the ones or just the tens. But if you can cope with a calculation like this where we have to regroup both ones and tens, you’re prepared for anything. And after a huge introduction like this, let’s show what we can do. We’re going to try to answer some questions now. And we’re going to need to regroup both ones and tens.

Add 266 and 547. Use place value blocks if you need to. Hint: Do you need to regroup ones or tens?

In this question, we need to add together two three-digit numbers: 266 and 547. Now, the question could just have shown us this first sentence, just two words and two numbers: add two 266 and 547. All the rest of the information that’s on the page is actually there to help us. And the way that this information has been written is really interesting. Firstly, we’re told to use place value blocks if you need to. And then we’re asked a question as a hint. “Do you need to regroup ones or tens?” It looks like these phrases are sort of saying, “You can if you need to.” But whenever we see this sort of thing in a question, we need to think to ourselves, “I need to” because they’re giving us a big hint of what to do.

Now, another really big help that we’re given with this question is that we’re shown how to set out the numbers. If we want to add 266 and 547 together, it’s a really good idea to write them on top of each other like this. It allows us to see the ones, the tens, and the hundreds digits separately. And we always start by adding the ones. Now as we do this, we can glance across to our place value blocks and see how it matches up with a written calculation. In 266, there are six ones. And in 547, there are seven ones. So what is six plus seven? Well we know that double six will be 12, so six plus seven is one more than 12. The answer is 13.

But how can we write the answer of 13 ones if we only have space for one digit? Well this is where our hint comes in handy. We’re asked whether we need to regroup ones or tens. When we regroup a number, we change it. We represent it in a different way. It’s still worth the same, but it’s just represented differently. So if we have 13 ones, we can take 10 of them and exchange them for one 10. One 10 and three ones still show the number 13. But now we can write the digit three in the ones place and write a little one in the tens column so we don’t forget to include this extra 10 when it comes to adding our tens together.

Now let’s add the tens. In 266, there are six 10s. And in 547, there are four 10s. And six 10s plus another four 10s equals 10 10s. But our answer isn’t going to contain 10 10s because we’ve already got one 10 that we’ve exchanged when we added the ones. The total of our 10s is 11 10s. But once again, we can’t write two digits in the tens place. What are we going to do? We’re going to need to regroup again. We know that 10 10s are the same as one 100. And so we can take 10 of our 11 10s and exchange them for one 100. This means our answer is going to have a one in the tens place to represent our one 10 that’s left. And we’re going to need to include a little one underneath to represent the one extra 100 we’ve made.

Now it’s time to add the hundreds. 200 plus 500 equals 700. But let’s not forget the extra 100 we’ve just exchanged. This makes a total of 800. We added 266 and 547 using column addition. And because some of the totals we made made two-digit numbers, we needed to regroup them. We exchanged 10 ones for an extra 10 and then later on 10 10s for an extra 100. The total of 266 and 547 is 813.

Find the sum. Hint: Think about whether you need to regroup. 199 plus 399 equals what.

In this question, we need to find the sum of two numbers. And finding the sum means finding the total, adding them together. And because we’re adding two three-digit numbers together, the way they’ve been written will really help us when it comes to adding them. We can see that the hundreds, the tens, and the ones columns are all labeled for us. This helps us to look at each type of digits separately and add them one by one.

Now before we start, we’re given a hint: think about whether you need to regroup. We know that we sometimes have to regroup a number when we’re adding like this. And when we do, it’s because the total of a particular column is a two-digit number. Now if this particular calculation was full of ones and twos and threes, we might think to ourselves, “I’m not gonna have to regroup in this calculation.” But if we spend a moment and look at the numbers we need to add together, there are quite a few nines in there, aren’t there? It looks like we’re going to be making some two-digit totals. And it’s certainly looks like we’re going to need to regroup, doesn’t it? Sometimes, looking at a calculation in this way before you start is a really good way to just get an idea of what you’re going to need to do.

So to begin with, let’s look at the ones column. What are nine ones plus another nine ones? Well, we know that nine plus nine equals 18. And we can’t write 18 ones in the answer as a two-digit number. We’re going to need to regroup. We can take 10 of our 18 ones and exchange them for one 10. And we need to write this little one extra 10 in the tens column somewhere. Sometimes we write it underneath the equal sign. But in this particular calculation, there’s a box for it at the top. Here we go; we’ve put it in. And we’re left with eight ones because one 10 and eight ones equal 18.

Now let’s add the tens. If we’d have looked at the calculation at the start, we’d have seen nine 10s and another nine 10s, which is 18 10s. But we’ve got one more 10 we need to include here too. So instead of 18 10s, we need to write down the answer 19 10s. Now again, we can’t write the number 19 in the tens column, but we can regroup it. We can take 10 of our tens and exchange them for one extra 100. And you can see where we can write the extra one at the top. And then we’re left with nine 10s, because one 100 and nine 10s is the same as 19 10s.

Finally, we can add the digits in the hundreds column. In the original calculation, we had one 100 plus three more 100s, which is four 400s, but we can’t forget that extra 100 at the top. This gives us a total of five 100s altogether. We found the sum of these two three-digit numbers by using column addition. And we had to regroup by the ones and the tens. 199 plus 399 equals 598.

So what have we learned in this video? We’ve learned how to add two three-digit numbers using column addition where we need to regroup both the ones and the tens.

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