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 in this lesson, we're going to be looking at using column addition including regrouping the ones.

We've got two keywords in our lesson, column addition and regroup.

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

So my turn, column addition.

Your turn.

My turn, regroup.

Your turn.

I wonder if you've come across those terms before.

I'm pretty sure you'll have heard of column addition, but let's just have a think about regrouping as well.

Let's have a look at what they mean.

They're going to be useful in our lesson.

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

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

For example, 10 ones can be regrouped as 1 ten.

And 1 ten can be regrouped for 10 ones.

And you can see there in the images, 10 ones are the same as one ten, and 1 ten is the same as 10 ones.

And sometimes it's useful to be able to think of it as ten and sometimes it's useful to be able to think of it as 10 ones, and you'll see that through the lesson today.

So let's make a start.

We've got two parts to our lesson today.

In the first part, we're going to be regrouping ones with two and three-digit numbers.

And in the second part of the lesson, we're going to be solving problems involving regrouping in the ones.

And we've got Alex and Lucas helping us in our lesson today.

Alex has been adding numbers using column addition.

He's unsure about the sum of these two numbers.

Have a look.

Why do you think he might be unsure? Alex says, "I'm a bit uncertain what to do here.

I know the sum of the ones digits is greater than 10." So he's looked at the ones digits, eight and seven, and realised that when you add them together, they're going to have a sum that's greater than 10.

There, we can see them.

Lucas says, "Listen Alex, how do you think you'll find the answer?" Hmm, I wonder.

Well, Alex is being sensible here.

He's going to do a little bit of estimating.

So he said, "48 and 47 are close to 50.

And I know that 50 + 50 = 100, so the answer must be close to 100." Good thinking, Alex.

It's always good to have a rough idea in your head of what the answer's going to be.

But Alex then says, "When I add them together, this happens.

8 ones add 7 ones is equal to 15 ones." There's the 15.

"4 tens add 4 tens is equal to 8 tens." Hmm.

"This gives me the answer 815, which I know can't be right." And he knows that because he did some estimating.

Can you see what he's done wrong? Can you help him out? Lucas says, "No, it's definitely not right." He says, "You've forgotten to regroup." Ah, had you spotted that Alex has forgotten to regroup? Let's have a look again.

So they're going to represent 48 add 47 using base ten blocks.

So we can help Alex with his regrouping.

He says, "I think I remember learning about regrouping in Year 3." Did you learn about regrouping in Year 3, I wonder.

I wonder if you're going to be able to help Alex.

Lucas says, "If the sum of the ones digits is 10 or greater, then regrouping is needed.

Let's start by representing the problem." So there's 48, 4 tens and 8 ones, and we're adding that to 47, 4 tens and 7 ones.

"8 ones add 7 ones is equal to 15 ones." That is 15 ones.

But how else can we think about those 15 ones? Lucas says, "There are more than 10 ones, so I'll regroup 10 ones as 1 ten." Ah, so there they are.

So 10 ones have become 1 ten.

And then the regrouped ten can be moved into the tens column.

It doesn't belong with the ones anymore.

It's going to become a ten and we're going to count it in with the other tens.

Now we can think about the tens.

4 tens add 4 tens add the regrouped ten is 9 tens, so there are 9 tens.

So we've got 9 tens and we've got the 5 ones from the 15, which was 1 ten and 5 ones.

So our answer is.

Ah, there we go, 95.

And Alex says, "48 add 47 is equal to 95.

I knew the answer was about 100." So he was right and his estimate showed him that something was going wrong, and Lucas was able to show him what happened with the regrouping.

Alex wants to use column addition with regrouping.

So how would you use regrouping when you're adding digits? Lucas says, "Let me show you.

I'm going to calculate 46 add 39." So he set it out as a column addition with his ones in the column and his tens in the column, so 46 add 39.

And Alex says, "46 and 39 are close to 40, both of them.

So 40 plus 40 is 80." So he reckons the answer is going to be quite close to 80.

Good thinking again, Alex.

So we start with our ones.

6 ones plus 9 ones is equal to 15 and 15 is going to be regrouped into 1 ten and 5 ones, and the ten is moved into the tens column.

So there are our 5 ones, and now we can represent our 1 ten with a little one at the bottom there, under the big equals sign, just to remind us that we've put another one to add in with the tens.

Now we can add the tens, 4 tens add 3 tens add the regrouped ten equals 8 tens.

So we've got our answer of 85.

46 add 39 is equal to 85.

That is quite close to 80.

Time to check your understanding.

Can you use column addition to add 36 and 26? And Lucas says, "Write the addends with the same value digits in the same column." And Alex is reminding you to start by adding the numbers with the smallest place value first.

Quite important in case there might be some regrouping to do.

So pause the video, have a go at using column addition to add 36 and 26 and then we'll get together for an answer.

How did you get on? So there's our column addition, 36 and 26.

And the addends with the same value digits in the same column as Lucas suggested.

"36 is close to 40 and 26 is close to 30.

40 + 30 = 70.

I estimate the sum to be 70." So that's Lucas's estimate of what the answer's going to be.

And as Alex reminded us, we start by adding the digits with the smallest value, so we're starting with the ones.

6 + 6 = 12.

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

So where we've got our 2 ones, we've got our 1 ten, which gives us 12 in total, but we can't put them all in the ones column, so we put the regrouped ten into the tens column.

Now we can add our tens.

3 tens add 2 tens add the regrouped ten is equal to 6 tens.

So our answer is 62.

36 add 26 is equal to 62.

62 is quite close to Alex's estimate of 70, so he wasn't far off.

It was a good estimate.

I hope you estimated well and I hope you've used your regrouping well as well.

Alex wants to use column addition to add two 3-digit numbers.

He says, "I'm going to add two 3-digit numbers where I have to regroup the ones." Lucas says, "Try adding together 256 and 227." And Alex says, "I'll write the addends with the same value digits in the same column, like we've done for all our column addition." So there, we've got it set out as a column addition.

256 + 227, with everything lined up correctly.

Start by adding the numbers with the smallest place value first, so we're gonna start with the ones.

6 + 7 = 13.

13 is regrouped into 1 ten and 3 ones, and the ten is moved into the tens column.

So there are 3 ones and our 1 ten, giving us 13.

And the ten is there underneath the equal sign to remind us to add it in with the other tens.

I think Alex is getting the hang of this now, are you? Let's look at the tens.

5 tens add 2 tens add the regrouped ten is equal to 8 tens.

And then we can think about our hundreds.

2 hundreds add 2 hundreds is equal to 4 hundreds.

So there's our answer.

256 add 227 is equal to 483, and we did have to regroup in the tens.

Time to check your understanding.

Use column addition to add 357 and 118.

And Alex is reminding you to write the addends with the same value digits in the same column.

And Lucas is reminding you to start by adding the numbers with the smallest place value first.

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

How did you get on? Did you write your numbers out in a column addition like this? So 357 add 118.

And then we start with the ones.

7 + 8 = 15.

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

So there's our 5 ones and our ten in the tens column.

Then we can look at our tens.

5 tens add 1 ten add the regrouped ten is equal to 7 tens.

7 tens.

And then with our hundreds, 3 hundreds add 1 hundred is equal to 4 hundreds.

And there's our sum.

357 add 118 is equal to 475.

Well done if you got that right, and if you remembered your regrouping of your ones into 1 ten and 5 ones.

Time for some practise.

You're going to calculate the sum of each pair of numbers.

So we've got three pairs of two-digit numbers for you to add.

And then in question two, we've got six pairs of two-digit numbers for you to add.

And to think, do you need to do some regrouping in the ones? So pause the video here, have a go at those calculations, and we will come back together for some feedback and some answers.

(object faintly rattles) How did you get on? So here are the answers.

And we did have to do some regrouping each time.

Each time, the sum of our ones digit was greater than 10, so we had to regroup into 1 ten and the ones, and then remember to add the 1 ten in with the tens column for our adding.

So Lucas is looking at c.

He says, "5 + 5 = 10.

So 45 add 35 has a 0 in the ones column of the sum." So 5 + 5 = 10.

So we had no ones to add in, but we did have 1 ten to regroup and add in with the tens in the tens column.

And again, Lucas is spotted in c.

Four add six in the ones.

4 ones add 6 ones is equal to 10 ones, and we could regroup that for 1 ten and zero in the ones column.

So the sum of 464 add 216 has a zero in the ones column of the sum.

And here are the answers to d, e, and f.

Is there another one where there's a zero? There is, isn't there? It's e.

So in e, 7 ones add 3 ones is equal to 10 ones.

So we needed to regroup the 10 ones into 1 ten and add it in with the tens column.

So 517 add 143 has a 0 in the ones column of the sum of 660.

Okay, time for the second part of our lesson.

This time we're going to be looking at some problems with regrouping in the ones.

We've got a missing digit and Alex is trying to find the missing digit.

He says, "There's a missing ones digit, I need to work out what it is." I wonder how you'd work out what it is.

What do you notice about the addition that we've been given? Ah, Lucas has spotted it.

There's a regrouped ten into the tens column.

So the ones numbers must have a sum of 13.

Can you see that? That we've got a three in our ones, but we've got that extra one reminding us that we've got a one to add in with our tens digits.

So 6 add something must equal 13.

And Lucas says, "To find a missing part, we subtract the other part from the whole." So our whole is 13, so we need to subtract 6 from 13.

Alex says, "13 - 6 = 7.

The missing ones digit must be seven." So 6 ones add 7 ones is equal to 13 ones.

So 3 ones and our regrouped ten.

And then 4 tens add 1 ten add the regrouped ten is equal to 6 tens, so that's right.

Alex wants to find the missing digits in this column addition.

What do you notice this time? Alex says, "There's a missing ones digit and a missing tens digit." Lucas says, "Let's start with the numbers with the smallest place value first." So let's look at our ones.

So we've got four add something is equal to.

Well, is it zero? No, it isn't, is it? There's a regrouped ten into the tens column.

So the ones numbers have a sum of 10.

So 4 add something is equal to 10.

And to find the missing part, we subtract the known part from the whole.

But you might know this 'cause this is a number pair to 10, isn't it? So 4 add what equals 10? Ah, there we go.

Alex says, "I know that 4 add 6 is equal to 10.

So the missing ones digit must be a six." 4 add 6 is equal to 10.

The tens digits have a sum of eight.

So Lucas says, "Something plus one must equal eight.

So the missing tens digit is seven." Is he right? Hmm.

Oh, Alex has spotted it.

"Lucas, you missed the regrouped ten.

Something plus one plus another one is equal to eight." We've got that extra one to add in as well, haven't we? And Alex says, "I can subtract the known parts." We know that eight is the whole and we know that we've got one to subtract and another one to subtract.

So eight subtract one subtract another one is equal to six.

So our missing tens digit must be six.

Time for you to have a go.

Can you find the missing numbers in this column addition? Alex says, "Find the missing ones and tens digits." And Lucas, he's learned from his last example, "Don't forget the ten regrouped into the tens column." So pause the video, have a go at working out those missing numbers and then we'll come together for some feedback.

How did you get on? So let's have a look.

Lucas says that five add something must be equal to 14.

He's spotted the regrouped 10 there, hasn't he? 5 plus something is equal to 14.

To find a missing part, we subtract the known part from the whole.

So 14 - 5 = 9.

So the missing ones digit must be a nine.

9 ones add 5 ones is equal to 14 ones, and then we've got our regrouped ten and our 4 ones.

Now let's look at the tens.

"The tens digits have a sum of six.

So something add two add one is equal to six." Well done Lucas, you've remembered that we had a regrouped ten there this time.

So Alex says he can use subtraction again.

The whole is six, the known parts are two and one, so 6 - 1 - 2 = 3, so the missing tens digit must be three.

And there we are, 335 + 229 = 664.

Well done if you got those right.

Alex is playing a computer game.

He's played it twice and he adds his scores together.

He says, "I got a total of 73.

What were my two scores?" Ooh.

So something add something is equal to 73.

These are Alex's possible scores.

I wonder if you can work out which were Alex's two scores, that when he added them together, they equaled 73.

Hmm.

Well, Lucas says, "I'm going to start by looking at the ones digits.

I know that the ones digits add to equal either 3 or 13." Hmm.

Well, he's got that three in the ones, hasn't he? So they might have equaled three, but then you could also get a three if they equaled 13.

Which do you think it's likely to be? Lucas says, "The ones digits cannot add to three, so they must add to 13." If we look at the possible scores, we'd need a two and a one or a three and a zero, wouldn't we? To equal three.

And there aren't any of those numbers in the ones digits of the possible scores.

So Lucas is right, the ones digits must add to 13.

So can you find a pair of ones digits in there that will add to 13? Lucas says, "6 + 7 = 13, but there are no numbers with a seven as a ones digit, so Alex's scores can't be 36 or 46." Oh great thinking, Lucas.

You'd need a 7 to add to a 6 to equal 13 and there is no digit with a seven in the ones, so it can't be 36, it can't be 46.

Hmm, what else could it be? He says, "18 is close to 20, and I would have to add more than 50 to get close to Alex's total.

And it's too small." There is no other score that's around 50 that he could add to the 18, so it can't be 18.

So it's got to be two of the other scores.

Lucas says, "I'm going to add together 35 and 38." So let's see if that works.

35 + 38.

5 ones add 8 ones is equal to 13 ones, regroup the 10 ones as 1 ten, and our three in the ones, so we're looking good so far.

And then 3 tens add 3 tens add the regrouped ten is equal to 7 tens.

Ah, so that works.

Alex's two scores were 35 and 38.

Well done, Lucas.

(chuckles) Alex says, "Spot on, Lucas.

You're really good at this." Over to you.

Can you be as good at reasoning as Lucas was? Can you work out Alex's two scores in the computer game? He says, "I got a total of 84 points when I added them together." So something adds something is equal to 84.

And there are Alex's possible scores.

Think about the size of the numbers, look really carefully at the ones digits too.

So can you use those two ideas, thinking about the size of the numbers and looking at the ones digits, to work out what Alex's two scores were? Pause the video, have a go, and we'll come back and talk about it.

How did you get on? Lucas says, "18 is close to 20, and we've got to get to a score of 84, haven't we? You'd have to add on more than 60 to get close to Alex's total so that 18 is too small." So it can't be 18.

"The ones digits cannot equal four." Ooh, how does he know that? Oh look, yes, they're all bigger, aren't they? They're all fives, sevens, and eights.

"So they can't add to equal four, so they must have a total of 14," he says.

"The only numbers that have a total of 14 in the ones are 37 and 47." He's right, isn't he? Nothing else will give you a total of 14, so the scores must be 37 and 47 and we can add them to check.

"7 ones add 7 ones is equal to 14 ones.

10 ones are regrouped as 1 ten.

3 tens add 4 tens add the regrouped ten is equal to 8 tens." Which gives us our 84, so Alex's two scores were 37 and 47.

Great thinking again.

Time for you to have some practise.

So for question one, you're going to find the missing numbers in these three column additions.

And then you're going to find the missing numbers in these column additions where we've got three-digit numbers, and each time we've got a regrouping of 10 ones for 1 ten, so think carefully about that.

And then for question three, Alex and Lucas each play a computer game twice.

They add their scores together to get a total.

Oh, Alex says, "I scored 93 points." And Lucas says, "I scored a total of 86 points." Can you work out their two scores from the possible scores there in the box? So pause the video, have a go at the tasks, and we'll come back for some feedback.

How did you get on? Here are the answers to the first three, adding those two 2-digit numbers and those missing boxes.

And Alex says, "9 ones add 4 ones is equal to 13 ones." He's looking at b, I think, isn't he? So we know that 9 add 4 is equal to 13.

And then in our tens, we knew that the whole was six, we knew about the three, and we knew about the one.

So three add two add one is equal to six.

So our missing digit had to be a two.

And here are the answers to the missing numbers in our three-digit additions.

How did you get on with these ones? Oh, Alex is looking at c here.

He's looking at the tens column.

3 tens add 3 tens add the regrouped tens is equal to 7 tens.

So the missing tens value in that second addend must be a three as well.

I hope you use thinking like that to complete your answers as well.

So for question three, we had to work out what Lucas and Alex's possible scores were.

Alex had a total score of 93 and Lucas had a total score 84.

And Alex says, "79 is too large to use as one of the scores." So 79 wasn't going to work.

There wasn't a number small enough to add onto it to make either 93 or 84, so we could cross out 79.

And Lucas says, "23 cannot be one of the scores because there are no other numbers that will add to it to equal 3, 4, 13, or 14." Which were the numbers that we needed to get the three or the four in the ones digits of those totals.

So I hope you did some estimating and some reasoning to get to your answers.

So Alex must have scored 36 and 57 and Lucas must have scored 35 and 49.

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

Thank you for all your hard work today reviewing using column addition to add two and three-digit numbers by regrouping ones.

What have we learned about today? We've learned that when using column addition, we need to start by adding the numbers with the smallest place value first.

And that makes real sense, doesn't it? Because we have to regroup into the tens column and if we've already added the tens, then we won't have had a chance to add them in, so it makes real sense to start with the digits that have the lowest place value when we're doing our column addition.

If the sum of the ones digits is 10 or greater, then regrouping is needed, and any complete tens are regrouped into the tens column, so we can add them in with the tens in our addends as well.

Well done for all your hard work and all your great mathematical thinking in this lesson, and I hope I get to work with you again soon.

Bye-bye.