Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in our maths lesson today, from the unit "Reviewing Column Addition and Subtraction." Hopefully, there'll be things in here that are familiar to you and you'll be able to revisit some ideas that you've learned about before.

So if you're ready, let's make a start.

So welcome to this lesson where we're going to be thinking about using column addition with regrouping in the ones and the tens.

So you may have been doing a lot of column addition recently, and you may have done some regrouping in the ones perhaps, but we're going to regroup in the ones and the tens today, so let's have a look at what's going to be in our lesson.

Well, we've got two key words in our lesson, column addition and regroup.

So I'll take my turn to say them and then it'll be your turn.

My turn, column addition.

Your turn.

My turn, regroup.

Your turn.

Now you may well be very familiar with these words, but let's just remind ourselves what they mean 'cause they're going to be useful to us as we go through the lesson.

Column addition is a way of adding numbers by writing a number below another.

It's a way of representing our addition so that we can keep track of what we've added and what we've still got to add.

The process of unitizing and exchanging between place values is known as regrouping.

So for example, 10 tens can be regrouped for 100, and 100 can be regrouped for 10 tens.

And you can see in our image, 10 tens are the same as 100, and 100 is the same as 10 tens.

Sometimes we want to think about that number as 10 tens, and sometimes we want to think about it as 100, and thinking in both ways will be useful as we go through our lesson today.

So in the first part of our lesson, we're going to be regrouping ones and tens, and in the second part, we're going to be solving problems with regrouping.

So let's make a start.

And we've got Alex and Lucas helping us out today.

Alex is trying to remember how to use column addition with two digit numbers.

He says, "I remember working on this in Year 3, but I can't remember exactly how to do it." He says, "What happens when the sums of the ones and tens digits are both 10 or greater?" And he's got an example here, 48 add 76.

8 ones add 6 ones have a sum greater than 10 ones, and 4 tens and 7 tens have a sum greater than 10 tens, so what would Alex do when he was adding these numbers together? Lucas says, "It's okay, we have to use regrouping in the ones and the tens." So Alex wants to use column addition, regrouping the ones and tens to help him to add these numbers.

So he says, "What is the sum of 48 and 76?" And Lucas says, "Well, 8 ones add 6 ones is equal to 14 ones." And the 14 ones is regrouped into 1 ten and 4 ones, 'cause we know that's what 14 is, 1 ten and 4 ones.

Then we can move the 10 into the tens column, so we can add it in with the tens when we get to the tens.

4 tens add 7 tens, and add the regrouped 1 ten is equal to 12 tens.

So 4 tens plus 7 tens is equal to 11 tens, plus the additional 10 is equal to 12 tens.

And 12 tens can be regrouped into 1 hundred and 2 tens.

The 100 is moved to the hundreds column, and the 2 is recorded in the tens column.

There are no other hundreds except the regrouped hundred, so 1 is written in the hundreds column because we've got that 1 hundred.

So 48 add 76 is equal to 124.

Alex wants to add three digit numbers using column addition with regrouping in the ones and tens, so Lucas sets him a challenge, "What's 257 add 186?" And Alex has set it out carefully with the columns carefully lined up.

And he says, "7 ones add 6 ones is equal to 13 ones." 13 is regrouped into 1 ten and 3 ones.

The 10 is moved into the tens column.

So there we have it, the 10 ready to be added with the tens and the 3 of the 13 recorded in the ones column.

5 tens add 8 tens, and add the regrouped 10, is equal to 14 tens.

5 tens add 8 tens is 13 tens, add another one is 14 tens.

14 tens is regrouped into 1 hundred and 4 tens, and the 100 moved into the hundreds column.

So there we have it.

2 hundreds add 1 hundred, plus the regrouped 100, is equal to 4 hundreds.

So we record that in the hundreds column.

So 257 add 186 is equal to 443.

Sometimes, regrouping the ones means regrouping in the tens.

Have a look carefully at this one.

What do you notice? Alex says, "It only looks like I need to regroup in the ones because 4 tens add 5 tens is equal to 9 tens." Lucas says, "Watch what happens!" Oh, let's have a go at adding these together.

So starting with the ones, 7 ones add 8 ones is equal to 15 ones.

15 is regrouped into 1 ten and 5 ones, and the 10 is moved into the tens column.

So there we have it.

4 tens add 5 tens, add the regrouped 10, is equal to 10 tens.

Ah, Lucas was right to tell us to watch out.

So 4 tens plus 5 tens is equal to 9 tens.

Add one more 10 is equal to 10 tens.

10 tens is regrouped into 100 and is moved into the hundreds column.

But we've got no extra tens, so we put a zero in our tens column.

3 hundreds add 3 hundreds, add the regrouped 100, is equal to 7 hundreds.

So our answer, our sum, is 705.

You only needed to regroup in the tens because you'd had to regroup a 10 from the ones column.

So, time to check your understanding.

Use column addition to add together these numbers.

488 add 219.

And there they are, set out as a column addition.

So pause the video, have a go, and we'll come back for some feedback.

How did you get on? Alex says, "8 ones add 9 ones is equal to 17 ones." 17 is regrouped into 1 ten and 7 ones.

The 10 is moved into the tens column.

8 tens add 1 ten, add the regrouped 10, is 10 tens.

8 add 1 is 9, and one more is equal to 10.

10 tens is regrouped into 100, and the 100 is moved into the hundreds column, and we've got no additional tens to record.

4 hundreds plus 2 hundreds, plus the regrouped 100, is equal to 7 hundreds.

So the answer to our equation is 707.

488 add 219 is equal to 707.

Well done if you got all that regrouping correct.

Alex tries to find two numbers with a sum of 432, and he's got to choose two of these numbers on the cards.

Alex says, "The ones digits must add to a sum of 12.

I know that 5 ones add 7 ones is equal to 12 ones." How did he know that they must add up to a sum of 12? Well, let's have a look at the numbers we've got.

We've got numbers with 5, 6, and 7 in the ones, so we can't have anything that just adds to a 2.

So it's got to be a 12 to give us that 1 in the ones digit in the sum 432.

So he says that I know that 5 ones add 7 ones is equal to 12 ones.

He says, "I can use estimation too.

275 is close to 300, and 147 is close to 150." And he wants something that's close to 432, so that's not bad is it? And he says, "300 plus 150 is equal to 450, and 450 is close to the sum of 432, so I'm going to add 275 and 147." So he set it out as a column addition.

Let's see if he's right.

5 ones add 7 ones is equal to 12 ones.

12 is regrouped into 1 ten and 2 ones, and the 10 is moved to the tens column.

7 tens add 4 tens, add the regrouped 10, is equal to 12 tens.

And 12 tens is regrouped into one hundred and 2 tens, and the 100 is moved into the hundreds column.

Can you see a problem already? What was the sum we were aiming for? 432.

I'm not sure he's quite there, is he? 2 hundreds add one hundred, add the regrouped 100, is equal to 4 hundreds.

So he's got a sum of 422.

And Lucas says, "Your answer is 422, Alex.

It's very close to 432, but it's not the same number." Time to check your understanding.

Which two numbers have a sum of 432? Now Alex has started you off on this, I wonder if you can use his ideas and help you to get the right answer.

Alex says, "Look carefully at the ones numbers and think about using estimation." Pause the video, have a go, and we'll come back for some feedback.

Alex said, "I'm gonna try 256 add 176." Ah, now the 5 plus 7 to equal the 12 didn't work, so he's looking at 6 plus 6 to equal the 12 to give him that 2 in the ones column.

I wonder how his estimation worked.

Let's have a go.

6 ones add 6 ones is equal to 12 ones.

12 is regrouped into 1 ten and 2 ones, and the regrouped 10 is moved into the tens column.

5 tens add 7 tens, add the regrouped 10, is equal to 13 tens.

13 tens is regrouped into 1 hundred and 3 tens, and the 100 is moved to the hundreds column.

It's looking good so far, isn't it? 2 hundreds add 1 hundred, add another 100, is equal to 4 hundreds.

So, yes, we've got our sum of 432.

So the two numbers were 256 and 176.

I wonder if you've got there as well.

Did you use some estimating to help you to work that out? Time to have a go for yourself now.

So you are going to calculate the sum of each pair of numbers.

So here they are and you're going to add them together, remembering to think about how you might need to regroup the ones, and possibly regroup the tens as well.

And for the second part of your task, you are going to add any two of these numbers to make each of the sums that you've been given.

And Lucas says, "Look carefully at the ones digits." And Alex says, "Use estimation.

Think about the size of your numbers and whether your answer is reasonable." So pause the video, have a go, and we'll get together for some feedback.

How did you get on? Here are the answers to the first question.

So you had to do regrouping in all of them, but did you spot in C, that we only had a two digit number that we were writing? And Alex spotted in C, that regrouping was needed in the tens because there's regrouping in the ones.

4 tens plus 5 tens, add the regrouped 10, is equal to 1 hundred, so we had an extra 100 to add in there.

And for part two, you had to choose the pairs of numbers, the correct pairs of numbers to give those sums. Did you get those correctly? Though Lucas says here, 6 ones add 7 ones is equal to 13 ones, so you can see that regrouped 10.

And for the final one, Alex said 550 plus 300 is equal to 850.

So the sum of 546 and 275 is quite close to 850.

So he used some estimation to help him.

I wonder what other things you thought about as you were choosing the numbers to add.

Did you think about, as Lucas did, thinking about adding those ones digits together to find the correct ones digit in your sum? I hope you had fun experimenting, and I hope you got the answers.

Let's move on to part two.

So we're going to be solving problems with regrouping.

Lucas is using these number cards.

He makes two 3-digit numbers.

He uses column addition to add them together.

"The sum is 403," he says, "which two add-ins did I make?" Hmm, I wonder.

Alex says, "I'm going to work out how Lucas arranged the cards." Good luck, Alex.

Let's see if we can help you out.

Alex tries again to make the sum of 403 using the cards.

He says, "I'm going to use 1 and 2 as the ones digits." Oh, 1 add 2 equals 3, doesn't it? 1 one add 2 ones.

So there we go, he's used 1 and 2 and he's crossed them out to keep track of what he's used.

So 1 one add 2 ones equals 3 ones, that's fine.

He says the tens digits must have a total of 10 because we've got that zero there, so we must have 10 tens, which will mean we've got an extra 100.

So he's going to use 7 and 3.

So 7 and 3 equals 10.

So 7 and 3 is equal to 10, and these tens are regrouped as 100, so he's got to remember that when he's finding the total for his hundreds column.

So he's got a 1 there to add in, can you see a problem here? "Oh no," he says, "there are 4 hundreds, but I've used the digit cards 1 and 2." He'd have to have 1 hundred plus 2 hundreds, plus the extra 1 hundred to equal 4 hundreds, wouldn't he? He's not got the right cards left.

I don't think that was the right way to start, was it, Alex? Can you think of another way that he could get a three in the ones of his sum? And Lucas says, "Yeah, you can only use each card once in a solution." So he can't just use the 1 and the 2 again, I'm afraid.

Alex tries to make the sum of 403 once more.

So the sum has a 4 as the hundreds digit.

He says, "I need to use the digit cards 1 and 2 as the hundreds." So he's actually gonna fix those ones there first.

How does he know he's got to have only the 1 and the 2? Why couldn't he have 1 and 3, do you think? What do you spot about that tens digit of 0? Yeah, we must have regrouped somewhere, mustn't we? So there must be a hundred being regrouped from the tens column.

So he's gonna think about the 1 and the 2 for the hundreds column this time.

"The ones digits must add to 13 then," he says.

"I'm going to start with 9 and 4 as the ones digits." So he spotted that if we've got to use 1 and 2 in the hundreds, we can't use them in the ones, so therefore, the sum of our ones digits must be 13 and not 3.

So he's got 9 and 4, 9 and 4 equals 13, and 13 ones can be regrouped into 1 ten and 3 ones.

So he's got that extra 1 in there.

Oh, now what? Hmm, last time, we had the tens digits having a sum of 10, didn't we? But I don't think that's going to work this time, is it? He said the tens digit cards must have a total of 9 tens, and then we can have the extra 1 ten to make the 10 tens.

So he says I can use 6 and 3.

6 tens add 3 tens, add the regrouped 10, is equal to 10 tens.

And these 10 tens are regrouped to 100.

And now he was right to save those cards, wasn't he? 1 hundred add 2 hundreds, add the regrouped 100, is equal to 4 hundreds, so he can use his 1 and 2 cards there.

And Lucas says, "Excellent work, Alex." And that was good work, wasn't it? I wonder if you were thinking a step ahead of Alex all the way.

But it was a good puzzle to solve, and lots of thinking about what our column addition means.

Time to check your understanding.

Can you use the digit cards to make two 3-digit numbers that sum to 625? And Lucas says, "Think about the size of the digits and whether you need to regroup in the ones and the tens." So pause the video, have a go, and we'll come back to some feedback.

How did you get on? "So here's one possible answer," says Lucas.

So Alex says, "7 ones add 8 ones is equal to 15 ones.

15 ones can be regrouped into 1 ten and 5 ones." So 7 add 8 equals 15, and we've got that 1 ten extra there, so what does that mean about our tens? Well, they've got to total 12, haven't they? So 5 tens add 6 tens, plus the regrouped 10, is equal to 12 tens, and 10 tens are regrouped as 100.

So 6 plus 6 is equal to 11, plus another 1 is 12, and that regrouped 10 tens goes into our hundreds.

So now what do we spot? We've got an extra one there.

So our 1 hundreds digits of our two add-ins have got to some to 5.

So 3 hundreds add 2 hundreds, add the regrouped 100, is equal to 6 hundreds.

You might have gone for 1 and 4 there, which would've worked as well, but Alex went for 3 and 2 in the hundreds.

So 3 hundreds plus 2 hundreds, plus the extra 1, is equal to 6 hundreds, and so that is now correct.

Our sum is 625.

Our add-ins are 357 and 268.

You may have found a different solution.

Time for you to have some practise.

Can you use these number cards and make two 3-digit numbers, and then use column addition to add them? Can you make the sums below? And you can see, you've got some regroupings in there marked in.

So can you pick the correct cards to make two 3-digit numbers to make those sums? And because we've got those regrouping ones there, Alex is saying, "Can you find solutions with regrouping in the ones and the tens?" And then can you use the number cards to make two 3-digit numbers and find three different ways of getting the sum of 843? So you may not have to use regrouping in all of these.

But Lucas says, "Can you find solutions with regrouping in the ones and the tens amongst your answers?" So pause the video, have a go, and we'll come back for some feedback.

How did you get on? There were different solutions for these, but here are some possible solutions.

So you could have had 198 add 326 to give you a sum of 524.

You could have had 769 add 148 to give you a sum of 917.

And you could have had 524 add 176 to give you a sum of 700.

And Lucas says to get 700, you had to regroup in the ones and the tens.

So here are some possible solutions with 843 as the sum.

I wonder if you found any other ones.

These ones all involve regrouping in the ones and the tens.

And Lucas says, "9 plus 4, 8 plus 5, and 7 plus 6 all have a sum of 13, which would give you that 3 in the ones." So there were different ways that you could start your calculation.

And we've come to the end of our lesson.

Thank you for all your hard work and your thinking, especially when we were finding those different ways of making a sum using those digit cards.

Lots of thinking going on there, lots of reasoning, so well done.

So what have we been learning about today? We've been learning that when using column addition, we start by adding the numbers with the smallest place value first.

Really important, especially when there's regrouping.

If the sum of the ones or tens digits is 10 or greater, then regrouping is needed when we're adding with three digits.

Any complete tens are regrouped into the tens column, and any complete hundreds are regrouped into the hundreds column.

You've worked really hard today, and I hope you've enjoyed it as much as I have.

See you soon.

Bye.