Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you on this lesson from our unit on reviewing column addition and subtraction.

Are you ready to work hard? Are you ready to remember perhaps some things that you've learned before? Well, if so, let's make a start.

So in this lesson, we are going to be reviewing column addition again and thinking about adding numbers by regrouping the tens.

So our keywords in this lesson are column addition and regroup.

So I'll take my turn, then it'll be your turn.

So my turn, column addition, your turn.

My turn, regroup, your turn.

Well done.

I'm sure there are words you're familiar with, but let's just remind us what they mean, 'cause they are going to be useful to us in today's lesson.

So column addition is a way of adding numbers by writing a number below another, lining up the columns so that we can keep track of what we've added and what we still need to add.

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

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

And you can see below 10 tens being regrouped into 100 and 100 regrouped into 10 tens.

Sometimes it's useful to think of it as 100 and sometimes it's useful to think of it as 10 tens and to be able to go between the two is really important as you'll see in this lesson.

So there are two parts to our lesson today.

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

And in the second part we're going to be solving problems with regrouping in the tens.

So let's make a start.

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 though.

What do you notice about them? Alex says, "I'm a bit uncertain what to do here.

The sum of the tens digits is greater than 10." Hmm, I wonder if you know what to do here.

Have you seen something like this before? He says, "I know that 45 is close to 50 and 94 is close to 100, and I know that 50 plus 100 is equal to 150.

So the answer's going to be close to 150." He's done some good estimating there.

So he's got a good idea of what the answer will be.

Lucas says, "If the sum of the tens digits is 10 or greater, regrouping is needed." Lucas is going to use the base 10 blocks to represent the problem.

And Alex says, "I think I remember learning about regrouping in year three," but did you learn about it in year three? Maybe you've had a look at it as well already this year.

Lucas says, "If the sum of the tens digits is 10 or greater, then regrouping is needed." Let's start by representing the problem.

So we had 45, four tens and five ones, and we're adding 94, nine tens and four ones.

So we can see there are 45 and are 94 represented with the base 10 blocks, and they are our addends.

So we start in the ones because we start with the column with the digits of the lowest place value.

So we can see that five ones add four ones is equal to nine ones.

And then let's think about the tens, four tens add nine tens is equal to 13 tens.

Now, 13 tens is greater than 10 tens, so there are more than 10 tens.

So I'll regroup 10 of the tens as 100.

So 10 of the tens have been regrouped into 100, and the regrouped hundred is moved into the hundreds column.

There it goes.

So what have we got now? Alex says, "45 add 94 is equal to 139." He says, "I knew the answer was close to 150." Yes, well done Alex.

That was good estimating.

And we can see there that our sum in between the big equal sign at the bottom is one hundred and three tens and nine ones, 139.

Lucas uses column addition to find the sum of 45 and 94.

Alex says, "How would you use regrouping with tens when you are adding digits? You could see it when he was using the base 10 blocks, but now we've just got the digits in a column addition." So Luca says, "Well, let's calculate 45 add 94." We're gonna start with the ones again.

Five ones add four ones is equal to nine ones, five tens add four tens is equal to 13 tens, but we can't put all 13 of them in the tens.

So 10 tens are regrouped as 100 and written in the hundreds column, and our three tens are left in the tens column.

So 13 tens is 10 tens and another three tens, and those 10 tens are equal to 100.

And because we have no other hundreds to add in at the moment, we can write our hundreds straight into the hundreds column.

So 45 add 94 is 139.

We saw that with the base 10 blocks, but now we can see how that looks as a column addition.

Alex wants Lucas to show him column addition using different numbers.

So we've got a different addition to do here.

Alex says, "I think we need to regroup in the tens column in this calculation too." He's got eight tens and four tens.

I think he's right, isn't he? 'Cause eight add four is going to be greater than 10.

You are right, Alex.

Let me show you how to calculate 85 add 42.

Five ones add two ones is equal to seven ones.

Eight tens add four tens is equal to 12 tens.

What do you think we're going to to do? That's right, 10 tens are regrouped as 100 and written in the hundreds column.

And our two tens to make our 12 tens are written in the tens column.

So our answer is 127.

85 add 42 is equal to 127.

Time to check your understanding now.

Can you use column addition to add 75 and 73? And Lucas says, "Write the addends with the same value digits in the same column." You can see that's been done for you here.

And Alex says, "Start by adding the numbers with the smallest place value first." So pause the video, have a go at the addition, and we'll get together for some feedback.

How did you get on? I wonder if you used the same language that Lucas is going to use.

Five ones add three ones is equal to eight ones.

Seven tens add seven tens is equal to 14 tens.

That's 10 tens and another four tens.

So 10 tens are regrouped as 100 and written in the hundreds column.

And our four tens stay in the tens column.

So our answer is 148.

75 add 73 is equal to 148.

Well done if you got that right.

Alex is going to use column addition again now to add two three-digit numbers this time.

He says, "I'm going to add two three-digit numbers where I need to regroup the tens.

So Lucas says, "Try adding together 172 and 294." He says, "I'll write the addends with the same value digits in the same column." And that's what our column addition is all about, keeping our digits lined up so that we know exactly what we're adding together so we don't try to add together digits with a different place value.

So Alex has lined up his digits.

So we have all the ones together, all the tens together, and all the hundreds together.

And Lucas reminds us start by adding the numbers with the smallest place value first.

So we're gonna start with the ones.

Two ones add four ones is equal to six ones, seven tens, add nine tens is equal to 16 tens.

That's more than 10 tens, isn't it? 10 of the tens are regrouped into a hundred and written in the hundreds column, but this time we've already got hundreds to add in, so we're going to put our hundred at the bottom to remind us that it's there to add in with the other hundreds, but our six tens can go in our tens column.

So there are our six tens and our 100 is there because we've got other hundreds to add to it this time.

So we're gonna make a note of it there.

Now we can think about the hundreds.

One hundred add two hundreds add the regrouped hundred is equal to four hundreds.

So our answer is 466.

172 add 294 is equal to 466.

Alex is going to use column addition to add a two and a three-digit number this time.

Lucas says, "Try adding together 451 and 57." And again Alex is going to be careful with how he records his addends so that he has the same digits in the right columns.

So this time there was a three digit-number and we were adding a two digit number.

So we've only got one hundreds number in our addends, but Alex has been careful, he's lined up his ones and he's lined up his tens.

Well done, Lucas, reminding us to start with the smallest place value first.

So we're gonna start with the ones.

One one add seven ones is equal to eight ones.

Five tens add five tens is equal to 10 tens.

So the 10 tens are regrouped as 100 and written in the hundreds column, but this time we only had 10 tens, so we have no extra tens to record in our tens column.

So we're going to record a zero in our tens column.

And the 10 tens that we had from adding our five tens and five tens is going to be regrouped into the hundreds column, ready to add in with the other hundreds.

Now we've got four hundreds plus the regrouped hundred, which gives us five hundreds.

So our sum is 508, 541 add 57 is equal to 508.

Time to check your understanding now.

Can you use column addition to add 254 and 160? And Alex says, "Write the addends with the same value digits in the same column." And Lucas is reminding you again, start by adding the numbers with the smallest place value first.

So pause the video and have a go at using column addition to add those two numbers together, and then we'll look at the answer together.

How did you get on? Did your column addition look like this, with your ones in the same column, your tens in the same column, and your hundreds in the same column? Maybe you've got square paper to help you to line them up.

So then we're going to start by adding our ones.

Four ones add zero ones is equal to four ones.

Five tens add six tens is equal to 11 tens.

That's 10 tens and one more ten.

So the 10 tens are regrouped into a hundred and added to the hundreds column.

And then we've got one ten to record in our tens column.

So there's our one ten and our 10 tens, giving us our 1110s in total, and 10 of those tens have been regrouped and moved into the hundreds.

We've got lots of ones there, haven't we? Alex is saying the one in the tens column represents one ten and the one in the hundreds column represents 100.

We had 11 tens when we added five tens and six tens together.

Now we can add our hundreds.

The two hundreds and the one hundred and the regrouped hundred all add up to equal four hundreds.

So our answer is 414.

254 add 160 is equal to 414.

Well done if you got that right and if you remembered to regroup your 10 tens and move them to the hundreds column.

Time for some more practise.

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

So you've got some pairs of two-digit numbers here to add.

And you've got some three-digit numbers to add.

So pause the video, have a go, and then we'll come back and look at the answers together.

How did you get on? So here are the answers.

Lucas was looking at the tens in a.

He said, "Six tens add six tens is equal to 12 tens.

10 tens are regrouped as one hundred." And you can see that we've put the one hundred in the hundreds column underneath, and then we had no other hundreds to add in, so our answer was 126.

And you can see that we've done that for all the other examples as well.

And part two, Lucas is looking in particular at b here, we had a three digit and a two-digit number.

So the numbers aren't the same length, are they? We've got a gap in the hundreds for our second addend 'cause it's only a two-digit number.

Lucas is looking at the tens here.

We've got six tens add four tens, which equals 10 tens, and 10 tens are equal to that 100 that we need to regroup and put into the hundreds column.

So we end up with a zero in our tens column because we only had 10 tens and they all get regrouped to being 100.

So our answer was 309.

And for the final three, here are our answers.

And again, Lucas is focused in on f, where we had eight tens add two tens, giving us those 10 tens again.

And the 10 tens of regrouped is 100 and put into the hundreds column, leaving us with no extra tens in the tens column.

So our answer is 707 with a zero in the tens.

Onto the second part of our lesson, and we're going to be solving problems involving regrouping in the tens.

Alex is trying to find the missing digit.

He says there's a missing tens digit and I need to work out what it is.

What do you notice about this addition? What do you know has happened? Lucas says 10 tens have been regrouped in the a hundred column.

The tens digits have a sum of 13.

So he says that four and something must equal 13 to give us that 100 and three tens.

So there's been a regrouping, hasn't there? So what is our missing number? Four plus something is equal to 13.

So we know our whole is 13 and one of our parts is four.

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

So 13 subtract four is equal to nine.

So the missing tens digit must be nine.

You might have known that four add nine is equal to 13 without doing the subtraction.

You might have known that as a known pair of numbers.

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

He says there's a missing tens digit and a missing hundreds digit this time.

Have you noticed, was there a regrouping in the tens? Aha, there was.

Lucas says there's a regrouped hundred in the hundreds column, so the tens digits have a sum of 12.

So something plus seven is equal to 12.

Seven tens add hmm tens is equal to 12 tens, and again, we know to find a missing part.

We subtract the known part from the hole.

So our known whole is 12, so we're going to subtract seven.

12 subtract seven is equal to five.

So the missing tens digit must be five.

Five tens add seven tens is equal to 12 tens.

The hundredths digits have a sum of six, so a whole is six.

So something plus three plus one is equal to six.

Alex says, "I can subtract the known parts." So six is our whole, our known parts are three and one.

So six subtract three subtract one is equal to two.

So our missing hundreds digit is two.

Three hundreds add two hundreds, add another one hundred is equal to six hundreds, giving us our sum of 629.

Time to check your understanding and for you to have a go.

Can you find the missing digits in this column addition? Alex says, "Find the missing tens digit and the missing hundreds digit." So there's a missing 10 in the first addend and a missing hundreds digit in the second addend.

And Lucas says, "Don't forget the hundred regrouped in the hundreds column." Think about what that tells you about the sum of our tens digits.

So pause the video, have a go, and we'll come back and look at the answers together.

How did you get on? Lucas says eight tens adds some more tens is equal to 16 tens.

We know it must be 16 tens, because we've got 10 of those tens regrouped to make a hundred.

So to find a missing part, we subtract the known part from the whole, or you might know a fact here to help you.

16 Subtract eight is equal to eight, or you might have known that from your doubles.

So the missing tens digit must be eight.

Eight tens add eight tens is equal to 16 tens.

And we regroup 10 of those tens to make a hundred.

The hundreds digits have a sum of seven.

So seven is our whole, our parts are four and one.

So we need to subtract those to find the missing part.

So seven subtract four subtract one is equal to two, so the missing hundreds digit must be a two.

And we can check that four hundreds add two hundreds add another hundred is equal to seven hundreds.

So that gives our correct sum of 766.

Well done if you reasoned your way through and worked out what those missing digits were.

Alex and Lucas are using digit cards to complete the column addition.

Alex says we need to use two cards for the tens digits and a card for the hundreds digits.

And we can only use each card once in a solution.

So we can't have the same number more than once using our cards.

Alex says there are three tens in the sum.

We could use the one and the two cards as the tens digits, which are two, so let's put those in, one and two.

And we've crossed them out to show that we've used them.

One ten add two tens is equal to three tens, so that works.

There are six hundreds in the sum.

We could use the three card as the missing hundreds digit.

Three hundreds add three hundreds is equal to six hundreds.

That was quite straightforward, wasn't it? Oh, Lucas is challenging us.

Is there a solution where we need to use regrouping? Hmm, what would that mean for our tens? They're going to look for another solution.

Alex says the tens digits of the addends could have a sum of 13.

That would still give us three tens, but it would mean that we had a regrouped hundred to think about when we were looking for the hundreds digit.

Lucas says, "Well, six tens add seven tens is equal to 13 tens." 10 tens are regrouped as a hundred and written in the hundreds column.

So that would work, wouldn't it? So that would be our regrouped one hundred.

And we've used the six and the seven, 'cause six at seven is equal to 13, so six tens at seven tens is equal to 13 tens.

Now what about the hundreds? Alex says there are six hundreds in the sum.

So we could use two as the missing hundreds digit, because 300 at 200 add another 100 would give us our six hundreds.

So we could use the two.

Three hundreds add two hundreds add the regrouped hundred is equal to six hundreds, so that works, doesn't it? They're challenging you though, it's your turn.

Can you find another solution that uses regrouping? So that's Alex's challenge.

You've gotta find a different solution to the one they found, which was 365 add 272 equals 637.

So pause the video, have a go, and see if you can find a different solution.

Here's one possible answer, I wonder if it's the one you found.

Nine tens add four tens is equal to 13 tens.

10 tens are regrouped as 100 and written in the hundreds column.

So nine tens add four tens.

What do you think is gonna happen with the hundreds though? There are six hundreds in the sum.

So you need to use two as the missing hundreds digit.

And that's the same as they had before, so it's really only the tens we've changed, isn't it? So two hundreds.

Three hundreds add two hundreds add another one hundred is equal to six hundreds.

So that works.

I wonder if you found another way of doing it as well.

Time for some practise.

Can you find the missing numbers in these column additions? And if you notice, you've got to find numbers that have some regrouping here because we can see that regrouped 100 in each case.

And another set with a few extra missing numbers.

And then for part three, can you use the digit cards to complete each column addition? You can only use a card once in each solution.

How many different ways can you solve these and can you use regrouping? And for the second part of question three, you've got real blanks here.

So how many different ways can you solve these using six cards each time? And can you solve them using regrouping? Pause the video, have a go, and we'll get back together for some feedback.

How did you get on? Lucas is focused on a here.

He says seven tens add four tens is equal to 11 tens.

10 tens are regrouped as 100, and we can see the little one there waiting to be added to the hundreds, and the one ten is written in the tens column, because 11 tens is one hundred and one ten.

So our missing tens digit was a four.

In b, our missing tens digit was a six, and our missing ones digit was a four.

And in c, our missing ones digit was a five, and our missing tens digit was a three.

In two, we had some other missing numbers to fill in as well.

I wonder what we are focusing on here.

Ah, Lucas is focusing on c.

He says three tens add seven tens is equal to 10 tens.

The 10 tens are regrouped as 100, and we have a zero in the tens columns because we have no additional tens left over.

They all went to form a hundred in the hundreds column.

So our missing numbers for c were a zero in the ones, because zero ones plus six ones is equal to six ones, a seven in the tens, and a two in the hundreds.

Here are some possible answers for the first part of question three where you had some gaps to fill in.

So for a, Alex has spotted this solution doesn't need regrouping, but for the other two Lucas has looked at, they both need regrouping.

And for the second part, you had to make your own three-digit numbers, and and you have to use regrouping in order to be able to get two tens in the sum because we didn't give you a zero digit card to use in your answers.

So we had to have an answer of 12 is the sum of our tens digits, because we couldn't make a two without regrouping.

I hope you had fun reasoning about those answers and finding different ways to create those sums. And we've come to the end of our lesson.

Thank you for all your hard work.

And we've been looking back at using column addition to add two and three-digit numbers by regrouping tens.

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

Now, we weren't regrouping ones into tens today, but we were regrouping tens into hundreds.

It was useful to have added the tens up first before we thought about the hundreds.

And finally, when we have done some regrouping, any complete hundreds are regrouped into the hundreds column.

So every time we have 10 or more tens as our sum, we can regroup and put those hundreds into the hundreds column, ready to be added in with the other hundreds.

I hope you've enjoyed thinking about regrouping from the tens to the hundreds today, and I hope I get to work with you again soon.

Bye-bye.