Lesson video

Hello, there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is our learning outcome.

I can subtract from a two-digit number using column subtraction with regrouping.

And here are the keywords for today.

I'm going to say the keywords.

Can you repeat them back? The first key words are column subtraction and the next keyword is regroup.

Let's take a look at what those words mean.

Column subtraction is a way of subtracting numbers by writing a number below another.

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

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

And here is our lesson outline.

The first part of the lesson is regrouping in the ones.

And the second part of the lesson is subtracting two-digit numbers with regrouping.

Let's get started.

And in this lesson, you will meet Sam and Aisha and Sam and Aisha are going to be asking you questions and helping you with your maths today.

Sam is thinking about column subtraction.

"What happens when the ones digit of the subtrahend is greater than the ones digit of the minuend?" Asks Sam.

I think Sam's really enjoying this column subtraction.

He'd like to know exactly how it works.

"Why don't we find out," says Aisha.

Let's start by representing 62 subtract five using base 10 blocks.

So here is 62.

Aisha says, "We have to regroup one of the tens as 10 ones." Now Aisha and Sam want to subtract five from 62.

But it's a bit difficult to do that at the moment, isn't it? So Aisha says, "Let's regroup one of the tens as 10 ones." So one of the tens has become 10 ones.

"Now it's much easier to subtract five ones," says Sam.

62 subtract five equals 57.

Sam uses regrouping with column subtraction.

So I start with 62, I regroup one 10 as 10 ones.

So here's 62 and Sam regroups one of the tens as 10 ones.

"I've set out the column subtraction writing the minuend first," says Aisha.

So Aisha has written the column subtraction.

Now notice 62 is written first because that's the minuend.

Five is written underneath, that's the subtrahend.

Five represents five ones.

So it has to be written in the ones column.

So it's written underneath the two, the two ones of 62.

"I regroup one 10 as 10 ones," says Aisha, so that there are no longer six tens, there are now five tens.

And Aisha adds those 10 ones to the two ones in the ones column.

There are now five tens and 12 ones.

It's still 62, but it's been regrouped.

I changed two ones into 12 ones by adding 10 ones.

"12 ones subtract five ones is equal to seven ones," says Sam.

So Aisha does the same.

12 ones subtract five ones is equal to seven ones and then five tens subtract zero tens is equal to five tens.

62 subtract five is equal to 57.

Aisha uses column subtraction to calculate 53 subtract eight.

"I start with 53, I regroup one 10 as 10 ones," says Sam.

So Sam's going to be using base 10 blocks to represent the problem, Aisha's going to be setting it out as a column subtraction.

There is 53, represented using base 10 blocks and Sam regroups one of the tens as 10 ones.

"I've set out the column subtraction right in the minuend first," says Aisha.

We've got 53 subtract eight.

Now we need to regroup because the ones number of the subtrahend is greater than the ones number of the minuend.

Three subtract eight, it's tricky to do without regrouping.

"I regroup one 10 as 10 ones," says Aisha.

So there are now four tens left and she adds those 10 ones to the ones column.

So there are now four tens and 13 ones.

"13 ones subtract eight ones is equal to five ones," says Sam.

So 13 subtract eight equals five.

Aisha also completes the column subtraction.

13 ones subtract eight equals five ones.

Four tens subtract zero tens is equal to four tens.

So there are four tens in the minuend.

There aren't any tens in the subtrahend, so we're still left with four tens.

So 53 subtract eight is equal to 45.

Now here's a problem for you to look at on your own.

Which calculations need regrouping? Now here's Sam, Sam's saying, "Look carefully at each calculation.

Which need regrouping in the ones?" How will you know which ones will need regrouping? Aisha says, "Is the ones digit of the subtrahend greater than the one's digit of the minuend?" That might be a bit of a clue.

Pause the video and see if you can work out which ones need regrouping.

Welcome back.

Did you work out the answer? Which calculations need regrouping? Let's take a look.

So that first calculation, 67 subtract six, because there's seven ones, subtract six ones, regrouping is not needed.

Seven subtract six equals one.

Look at our second calculation.

We've got 72 subtract seven, regrouping is needed.

We need to regroup one of those tens as 10 ones.

And that last one, we have got eight subtract eight.

Is regrouping needed? Regrouping is not needed.

Eight subtract eight equals zero.

So regrouping would not be needed.

Very well done if you solved that problem correctly.

Sam uses column subtraction to calculate 71 subtract nine.

Though Sam is only going to be using column subtraction.

There's no base 10 blocks this time.

If you still want to use base 10 blocks to help you, that is fine.

"I regroup one 10 as 10 ones," says Sam.

There are now six tens and 11 ones.

So you see there, the ones digit of the subtrahend is greater than the ones digit of the minuend.

Nine is greater than one, so Sam needs to regroup.

Sam takes one of those tens, so there are six tens left and adds it to the ones.

So there are now 11 ones.

That one ten has been regrouped as 10 ones and then Sam can complete that column subtraction.

11 ones subtract nine ones is equal to two ones.

So two is written in the ones column Six tens subtract zero tens is equal to six tens.

So six is written in the tens column.

71 subtract nine is equal to 62.

Aisha wonders what happens when the minuend has zero ones.

How would we calculate 80 subtract eight? Here's 80 subtract eight set out as a column subtraction.

Sam says, "I regroup one 10 as 10 ones." There are now seven tens and 10 ones.

So one of the tens is regrouped as 10 ones.

They're now seven tens and that extra 10 is added to the ones column to make 10 ones.

There were zero ones, now there are 10.

10 ones subtract eight ones is equal to two ones.

So two is written in the ones column.

Seven tens subtract zero tens is equal to seven tens.

So seven is written in the tens column.

80 subtract eight is equal to 72.

Use column subtraction to calculate 64 subtract seven.

So here's one for you to try on your own.

So there's 64 subtract seven set out as a column subtraction.

How would you work out the answer? Remember to regroup a 10 as 10 ones.

So you'll need pencil and paper or a whiteboard and whiteboard pen.

Jot down that calculation.

So pause the video and see if you can work out the answer.

Welcome back.

Did you manage to solve the problem? Let's see if you were right.

So Sam says, "Regroup one ten as 10 ones.

There are now five tens and 14 ones." Now we can complete the calculation.

So 14 ones subtract seven ones is equal to seven ones.

Five tens subtract zero tens is equal to five tens.

So 64 subtract seven is equal to 57.

Very well done if you've got the right answer.

And let's move on to Task A.

So part one of Task A, you're going to complete each column subtraction and you'll need to regroup one of the tens as 10 ones each time.

Here's part two of Task A.

Complete each column subtraction.

Now think carefully about whether you need to regroup.

Is the ones digit of the subtrahend greater than the ones digit of the minuend? If it isn't, you don't need to regroup.

And here is part three of Task A.

Use these number cards.

So you've got the number cards 1, 2, 3, 4 and 5.

Arrange any three of them to make each calculation correct by subtracting a one-digit number from a two-digit number.

Say for a, you've got a two-digit number you need to make using those number cards and then using a different number card, what single-digit number or one-digit number would you make? And the difference between those two numbers has got to be 28.

So what two-digit number subtract what one-digit number ends up with 28? You've also got to have 37 as the difference and 49 as the difference.

So a bit of problem solving.

So pause the video and see if you can complete Task A.

And welcome back.

How did you get on? Did you manage to complete all three parts of Task A? If you did, that's brilliant work.

Let's take a look, see whether you've got the right answers.

So here are the answers for part one of Task A.

So each of those column subtractions did need regrouping.

So 44 subtract eight is equal to 36.

54 subtract seven is equal to 47.

And 60 subtract six is equal to 54.

Here are the answers for part two of Task A.

So you have to complete each column subtraction and think carefully about whether you need to regroup.

Now you need to regroup in a, because there are only three ones and you had to subtract eight ones.

In b, you did not need to regroup.

Eight ones subtract seven ones is equal to one one.

And then again c, you had to regroup as well.

And here are the answers for part three of Task A.

Now here are some possible answers.

You may have answered some of those questions in a different way.

To get a difference of 28, you could do 32 subtract four that is equal to 28.

42 subtract five is equal to 37.

And 53 subtract four is equal to 49.

Very well done if you managed to get onto to part three and you managed to answer some of those, 'cause they were quite tricky, some of those problems. And let's move on to part two of the lesson.

So part two of the lesson is subtracting two-digit numbers with with regrouping.

Sam wants to calculate 62 subtract 25.

So this time, there's a two-digit number and we're subtracting a two-digit number.

I start with 62, I regroup one 10 as 10 ones.

So why is Sam going to regroup? Well, the ones digit of the subtrahend is greater than the ones digit of the minuend.

Five is greater than two.

"I've set out the column subtraction right in the minuend first," says Aisha.

So Aisha set it out as a column subtraction.

62 subtract 25.

"I regroup one 10 as ten ones," says Aisha.

There are now five tens and 12 ones.

So that one 10 has been regrouped as 10 ones.

"We always subtract numbers with the smallest place value first," says Sam.

12 ones subtract five ones is equal to seven ones.

Aisha also subtract five ones.

12 ones subtract five ones is equal to seven ones and then five tens subtract two tens is equal to three tens.

So using the base 10 blocks, two tens are subtracted and then Aisha completes the column subtraction as well.

Five tens subtract two tens is equal to three tens.

So Sam says, "62 subtract 25 is equal to 37." Sam uses column subtraction to calculate 72 subtract 29.

So here's 72 subtract 29 set out as the column subtraction.

Sam says, "I regroup one ten as 10 ones." Why did he do that? Because the ones number of the subtrahend is greater than the ones number of the minuend.

So there are now six tens and 12 ones.

So one of those tens had been regrouped as 10 ones.

There are now 12 ones altogether.

12 ones subtract nine ones is equal to three ones.

Six tens, remember it's not seven tens anymore, one of the tens has been regrouped, there are six left.

Six tens subtract two tens is equal to four tens.

72 subtract 29 is equal to 43.

Now here's a problem for you to look at on your own.

Which calculations need regrouping? So Sam is saying look carefully at each calculation.

Which need regrouping in the ones? Oh, here's Aisha, just to remind you, is the ones digit of the subtrahend greater than the ones digit of the minuend? So look at each calculation.

Which of them need regrouping? Pause the video, see if you can work out the answer.

And welcome back.

Did you manage to work out the answer? Let's take a look, see if you are right.

So our first calculation 90 subtract 36.

We've got the zero subtract six, regrouping is needed.

The ones number of the subtrahend, six, is greater than the ones number of the minuend, zero.

So at the second calculation, we got there seven subtract seven.

Is regrouping needed? Regrouping is not needed.

Seven subtract seven is equal to zero.

So it's possible to do that without regrouping.

Our last calculation, we've got 81 subtract 13.

Is regrouping needed? We've got one subtract three.

Yes, regrouping is needed.

One of those tens would need to be grouped as 10 ones.

Very well done if you got that correct.

Sam uses column subtraction to calculate 90 subtract 36.

So I think Sam's interested in what happens when we've got a zero as the ones digit of the minuend.

The ones digit of the subtrahend is greater than the ones digit of the minuend.

Six is greater than zero, so Sam needs to regroup.

"I regroup one 10 as 10 ones.

There are now eight tens and 10 ones." We got eight tens remaining and one of those tens is regrouped as 10 ones and added to the ones column.

And now Sam can complete the column subtraction.

10 ones subtract six ones is equal to four ones.

Eight tens subtract three tens is equal to five tens.

90 subtract 36 is equal to 54.

Now here's one to try on your own.

Use column subtraction to calculate 81 subtract 13.

So there's 81 subtract 13 set out as a column subtraction.

"Remember to regroup a 10 as 10 ones," says Aisha.

We just identified this a while ago that regrouping is needed for this calculation.

So you'll need to regroup one of those tens as 10 ones.

You need to use paper and pencil or a whiteboard and whiteboard pen, jot down that calculation, see if you can work out the answer.

Pause the video and have a go at trying to calculate 81 subtract 13 using column subtraction.

And welcome back.

How did you get on? Did you manage to get the answer? Did you remember to regroup? Let's take a look.

So Sam is saying, "Regroup one 10 has 10 ones." there are now seven tens and 11 ones.

11 ones subtract three ones is equal to eight ones.

And then seven tens subtract one 10 is equal to six tens.

81 subtract 13 is equal to 68.

Very well done if you've got 68 as the answer.

Aisha has these number cards.

So she's got the number cards 1, 2, 3, 4 and 5.

She has to use four of them to make the calculation correct.

So the calculation is a two-digit number subtract another two-digit number is equal to 16.

16 is the difference between the two numbers.

"The two numbers I choose must have a difference of 16," says Aisha.

"There must be regrouping in the ones," says Aisha.

And the only way to get a six in that one's column is if regrouping is being used somewhere.

So I know 11 ones subtract five ones is equal to six ones.

I'm going to start with 51.

So Aisha used it as the one digit in the ones column of the minuend and chooses the five in the tens column of the minuend.

I regroup one 10 as 10 ones.

There are now four tens and 11 ones.

11 subtract five equals six, but I can't use five because I've used it already.

So Aisha can't put five there.

She's already used the digit card five already in 51.

That can't be the correct solution.

Aisha cannot start with 51.

"I'm going to try again," says Aisha.

She's very determined isn't she? "I know 11 one subtract five ones is equal to six ones." So she's not going to use the five.

She's going to use that as the ones number of the subtrahend.

"This time I'll start with 41." So Aisha uses the ones digit in the ones column of the minuend and she uses the four in the tens column of the minuend.

I regroup one 10 as 10 ones.

There are now three tens and 11 ones.

11 subtract five equals six.

So Aisha can use that digit card five in the ones column of the subtrahend.

11 subtract five is equal to six.

What number is she going to use in the tens column of the subtrahend? Three tens subtract two tens is equal to one 10.

So Aisha uses the number card two as the tens digit of the subtrahend.

This time, Aisha has solved the problem.

Aisha was very determined to solve that problem and she wasn't ready to give up, was she? So here's a problem for you to try on your own.

Use four of the number cards to make the calculation correct.

So a two-digit number subtract a two-digit number equals 17.

Can you solve that problem? Can you solve that puzzle? That's the kind of thing I really enjoy doing.

The two numbers have a difference of 17.

So can you work out what two-digit number you can subtract from another to get a difference of 17? Remember, you can use each number card once in the calculation.

Pause the video, see if you can solve that problem.

And welcome back.

Did you manage to solve the problem? Did you get a difference of 17 between the two numbers? Let's take a look to see how Aisha did it.

So Aisha says, "Here is one solution." You might have solved this problem a different way, but this is Aisha's solution.

She says, "Start with 32." So two goes in the ones column of the minuend and three goes in the tens column of the minuend.

Regroup one ten as 10 ones.

There are now two tens and 12 ones.

12 subtract five is equal to 12.

So Aisha uses the five as the ones digit of the subtrahend and two tens subtract one 10 is equal to one 10.

That's how Aisha solved the problem.

I wonder if you did it the same way.

I wonder if you found a different solution.

But very well done if you managed to solve the problem.

And let's move on to Task B.

So for the first part of Task B, you're going to complete each column subtraction.

So look really carefully.

Do they all need regrouping in the ones column, I wonder? So have a really good look.

So our first calculation, 63 subtract 26.

What's the difference between those two numbers? Do you need to regroup? I think you might do.

Let's look at part two of Task B.

So you're going to use the same number cards as you used earlier, so 1, 2, 3, 4 and 5.

You're going to arrange any four cards to make each calculation correct.

And can you find two different solutions? So you use different number cards and can you find two different answers to the problem? Can you find two solutions that have a difference of 19 and two solutions that have a difference of 28? So once you found one, can you find two? And it might be helpful to have the number cards 1, 2, 3, 4 and five available to you and be able to actually move them around, change around.

That might help you count the answer.

That looks to me like regrouping will be needed.

So think really carefully.

How would you get a nine as the ones digit of the difference? How would you end up with that? So pause the video and have a go at Task B.

And welcome back.

I hope you got on really well with that.

I wonder, did you get some to part two? Did you manage to find different ways of making 19 or 28? Let's take a look.

So here are the answers for part one of Task B.

So 53 subtract 26, you did need to regroup.

The difference between those two numbers is 37.

52 subtract 28 is equal to 24.

So have a good look at those.

Did you get them all right? You did? Brilliant work.

And let's move on to part two of Task B.

Here are two different ways of getting the difference of 19 and two different ways to get a difference of 28.

So you could have had 34 subtract 15, that is equal to 19.

51 subtract 32, that is also equal to 19.

You could have had 51 subtract 23, that is equal to 28.

And 43 subtract 15, that is equal to 28 as well.

So very well done, you got onto to part two and you found some different ways of making those differences.

That's excellent work.

And hopefully today, you're feeling much more confident with subtracting a two-digit number from a two-digit number, including regrouping in the ones.

Excellent work today, very well done.

Let's move on to our lesson summary.

So regroup when the ones digit of the subtrahend is greater than the ones digit of the minuend.

Regroup a 10 into 10 ones and change the number of ones and tens in the minuend.