Lesson video

Hello there, my name is Mr. Goldie.

Welcome to today's math lesson.

And here is our learning outcome.

I can subtract from a 3-digit number using column subtraction with regrouping.

And here are the keywords.

I'm going to say the keywords.

Can you repeat them back? So the first keywords 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 one hundred, one hundred can be regrouped for 10 tens.

And here is our lesson outline.

So the first part of the lesson is regrouping in the ones or tens.

And the second part of the lesson is regrouping in the ones and tens.

Let's get started.

In this lesson, you will meet Sam and Aisha.

And Sam and Aisha are going to be helping you with your maths today and asking you some difficult questions.

Sam is thinking about column subtraction with 3-digit numbers.

I think Sam's doing a lot of thinking about column subtraction.

"What happens when the ones digit of the subtrahend is greater than the ones digit of the minuend," says Sam.

"Why don't we find out?" Says Aisha.

"Let's start by representing 262 - 147 using base ten blocks." I think Aisha's chosen that number because the ones digit of the subtrahend 7 is greater than the ones digit of the minuend 2.

So what is 262 - 147? Here is 262 represented using base ten blocks.

And remember when we're using base ten blocks to represent a subtraction calculation, we only make the minuend.

So here is the minuend 262 represented using base ten blocks.

Aisha says, "We have to regroup one of the tens as 10 ones." 'Cause we have to subtract 7 ones, so we have to regroup one of the tens as 10 ones.

So Aisha regroups one of the tens as 10 ones.

"Now it's much easier to subtract 7 ones." Says Sam.

So Sam and Aisha subtract 7 of the ones.

So Sam and Aisha have subtracted the ones.

Now they need to subtract the tens.

"There are 5 tens left." Says Sam.

"5 tens subtract 4 tens equals 1 ten." So Sam and Aisha subtract 4 tens and Aisha and Sam have to look at the hundreds column, 200 - 100 = 100.

"262 - 147 = 115," says Sam.

Sam and Aisha use column subtraction to calculate 262 - 147.

So they're looking at the same calculation they've just represented using base ten blocks.

So Aisha says, "I've set out the column subtraction, writing the minuend first." "We always start with the digits with the smallest place value first." So you just remember that if you're doing column subtraction or column addition, we always start with the digits with the smallest place value first.

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

There are now 5 tens and 12 ones.

I change 2 ones into 12 ones by adding 10 ones." Sam says, "12 ones subtract 7 is equal to 5 ones." And then Aisha moves onto the tens column, "5 tens subtract 4 tens is equal to 1 ten." And 200 - 100 = 100.

262 - 147 = 115.

Sam and Aisha use column subtraction to calculate 386 - 278.

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

And Sam just reminding us, "We always start with the digits with the smallest place value first." So the first calculation is 6 ones subtract 8 ones.

So again, we need to use grouping.

"I regroup one ten as 10 ones.

There are now 7 tens and 16 ones.

I change 6 ones into 16 ones by adding 10 ones." "16 ones subtract 8 ones is equal to 8 ones," says Sam.

Use our knowledge of doubles there, couldn't we need to help us? "7 tens subtract 7 tens is equal to zero tens." "3 hundreds subtract 2 hundreds is equal to 1 hundred," says Sam.

"386 - 278 = 108." Now it's time for you to have a go at one on your own.

So I hope you really concentrate on what Sam and Aisha we're doing there.

Use column subtraction to calculate 275 - 247.

"Start with the digits with the smallest place value first," says Sam.

So here's the calculation written with the minuend above the subtrahend.

"Where do you need to regroup?" Says Aisha.

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

Jot down our calculation.

Don't forget to set it out correctly with the ones, tens, and hundreds digits in the correct columns.

Pause the video and see if you can work out the difference between those two numbers using column subtraction.

And welcome back.

How did you get on? Do you think you got the right answer? Let's take a look, see whether you were right.

So Aisha says, first of all, we need to "Regroup 1 ten as 10 ones.

There are now 6 tens and 15 ones." And we need to do that because the ones digit of the subtrahend is greater than the ones digit of the minuend.

"15 ones subtract 7 ones is equal to 8 ones," says Sam.

"6 tens subtract 4 tens is equal to 2 tens," says Aisha.

And finally, "2 hundreds subtract 2 hundreds is equal to zero hundreds." Just to show that they finished that calculation, Aisha and Sam have written a zero in that hundreds column.

Just remind them that the calculation is complete.

Look at how Sam has written the answer.

"275 - 247 = 28." Obviously, we don't need the zero there.

So very well done if you've got 28 as the difference, and very well done, if you've regrouped carefully in that ones column.

Sam is thinking about regrouping in the tens.

"What happens when the tens digit of the subtrahend is greater than the tens digit of the minuend?" "Why don't we find out," says Aisha.

"Let's start by representing 355 - 173 using base ten blocks." Aisha has chosen those numbers because the tens digit of the subtrahend 7 is greater than the tens digit of the minuend five.

So what is 355 - 173? Well here is 355 represented using base ten blocks.

And remember, if you're subtracting using base ten blocks only make the minuend, only represent the minuend and you can subtract the subtrahend from that.

"Let's start with the one," says Sam.

Very sensible Sam, always start with the numbers with the smallest place value first.

"5 - 3 = 2." But now we've got a bit of an issue, haven't we? "7 tens is greater than 5 tens.

We have to regroup one of the hundreds as 10 tens." So Sam and Aisha take one of those hundreds and they split it up, they regroup it as 10 tens.

"There are now 15 tens," says Sam.

"15 tens subtract 7 tens equals 8 tens." We're gonna subtract 7 of those tens and that means 8 tens.

And there are no longer 3 hundreds remaining.

There were now 2 hundred because one of the hundreds was regrouped as 10 tens.

"So 2 hundreds subtract 1 hundred is equal to 1 hundred." So here's our answer.

"355 - 173 = 182." So regrouping in the tens, very similar to regrouping in the ones, but you've got to remember the place value of the digits.

And when you are thinking about the number and talking about the numbers, remember to refer to them as tens or ones.

Sam and Aisha use column subtraction to calculate 355 - 173.

So it's the same calculation, they're gonna set it out as a column subtraction.

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

and Sam's reminding us again, "We always start with the digits with the smallest place value first." That's really important and that is because of regrouping.

We start with the numbers with the largest place value first we're gonna get in a bit of a muddle because we might need to regroup one of them.

"5 ones subtract 3 ones is equal to 2 ones," says Sam.

But of course, we've got to do some regrouping in the tens.

5 tens subtract 7 tens.

Very, very tricky to do.

We've gotta regroup one of those 1 hundreds.

So Aisha says, "I regroup one hundred as 10 tens.

There are now 2 hundreds and 15 tens." "15 tens subtract 7 tens is equal to 8 tens," says Aisha.

And then "2 hundreds subtract 1 hundred is equal to 1 hundred," says Sam.

So "355 - 173 = 182." Now here's something for you to do on your own.

Look at each column subtraction.

"Do they need regrouping in the ones?" What do you think? Remember you're looking to see if the ones number of the subtrahend is greater than the ones number of the minuend.

Or says Aisha, "Or do they need regrouping in the tens?" So is the tens digit of the subtrahend greater than the tens digit of the minuend? Pause the video and see if you can work out.

Do you need to regroup in the ones or do you need to regroup in the tens? And welcome back.

Did you work out the answer to each of them? Let's take a look, see whether you were right.

So that first calculation, 719 - 242.

So regrouping is needed in the tens.

One tens subtract 4 tens.

Let's look at the second calculation.

657 - 338.

Do we need to regroup in the tens or the ones? We need to regroup in the ones.

Regrouping is needed in the ones.

We've got the 8 ones is greater than 7 ones.

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

And that last calculation, 553 - 352.

Do you need to regroup in the ones or the tens? What do you think? Now regrouping is not needed.

3 - 2.

You can do without regrouping.

5 - 5, get the answer 0, but you don't need to regroup.

So well done if you got those right.

And well done if you spotted that last trick question.

Sam and Aisha use column subtraction to calculate 522 - 81.

So this time we've got a 3-digit number and we're subtracting a 2-digit number.

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

"Writing the minuend first." "We always start with the digits with the smallest place value first," says Sam.

Just reminding us again.

So the first calculation is going to be, "2 ones subtract 1 one is equal to 1 one." And we've got to move on to the tens, 2 tens - 8 tens.

So "I regroup one hundred as 10 tens.

There are now 4 hundreds and 12 tens." "12 tens subtract 8 tens is equal to 4 tens." And then lastly, "4 hundreds subtract zero hundred is equal to 4 hundreds," says Sam.

So Sam says, "522 - 81 = 441." Calculate 719 - 242.

So this is one for you to try on your own.

"Set out the column subtraction, writing the minuend first." "Start with the digits with the smallest place value first." So again, use pencil and paper or a whiteboard and whiteboard pen.

Jot down that calculation.

Make sure you write the numbers in the correct columns and have a go at that column subtraction.

Pause the video.

Can you find the difference? And welcome back.

Did you find the difference? Let's take a look to see whether you were right.

"9 ones subtract 2 ones is equal to 7 ones." "Regroup one hundred as 10 tens.

There are now 6 hundreds and 11 tens." "11 tens subtract 4 tens is equal to 7 tens." And then "6 hundreds subtract 2 hundreds is equal to 4 hundreds." Now we've got the difference.

"719 - 242 = 477." Very well done if you got that as your answer.

Let's move on to Task A.

So for the first part of Task A, you're going to complete each calculation.

You will need to regroup in the ones.

So that first calculation, A.

341 - 216.

You'll notice that 6 is greater than 1.

So you'll need to regroup in the ones.

Let's take a look at part two of Task A.

So again, complete each calculation, but this time you need to regroup in the tens.

So if we look at that first calculation, A.

447 - 256 or 7 is greater than 6.

So you don't need to regroup in the ones, but 4 is less than 5.

So you will need to regroup in the tens.

And then finally, part three of Task A.

Complete each calculation.

You will need to regroup in the ones or in the tens.

So have a good look at each calculation.

Do you need to regroup in the ones? Do you need to regroup in the tens? Pause the video and have a go at Task A.

And welcome back.

How did you get on? Did you manage to get to part three? Very well done if you did.

Let's take a look.

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

So after the first calculation, 341 - 216, the difference is 125.

And of course, you needed to regroup in the ones.

Let's take a look at part two of Task A.

And then finally part three of task A.

For the first calculation A, you had to regroup in the tens.

For B, you had to regroup in the ones.

And for C, you had to regroup in the tens again.

So one of those hundreds had to be regrouped as 10 tens.

Very well done for your hard work in Task A.

Excellent work if you got onto part three of Task A and had a look at those different calculations and worked out whether you needed to regroup in the ones or the tens.

And let's move on to part two of the lessons.

So part two of the lesson is regrouping in the ones and tens.

Sam wonders when regrouping is needed in both the ones and tens.

"Sometimes we have to regroup one of the tens and one of the hundreds," says Aisha.

Let's look at the calculations below.

Which ones need regrouping in the ones and tens? There are three calculations there.

Which ones need regrouping in the ones and in the tens? Sam says, "I don't think they all need regrouping in the ones and tens." So I think Sam is going to one of those in particular and he doesn't think we need to regroup in the ones and the tens.

"Let's work out the difference in each of the calculations," says Aisha.

So Sam and Aisha use column subtraction to calculate 511 - 223.

That's going to be the first calculation they look at.

"I think we need to regroup in the ones and tens," says Sam.

So you notice there's 1 one when we subtracting 3 ones.

So we need to regroup in the ones.

In the tens column, we've got 1 ten subtract 2 tens.

So we need to regroup in the tens as well.

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

There are now zero tens and 11 ones." "11 ones subtract 3 ones is equal to 8 ones," says Sam.

"I regroup one hundred as 10 tens," says Aisha.

"There are now 4 hundreds and 10 tens." Remember there was 1 ten, but we've regrouped it as 10 ones, which left zero in the tens column.

"10 tens subtract 2 tens is equal to 8 tens." And then "4 hundreds subtract 2 hundreds is equal to 2 hundreds," says Aisha.

"511 - 223 = 288." So we had to regroup in the ones and tens.

And again, that's why it's really important to start with numbers with the smallest place value first.

Got to regroup those ones if you need to first, before you group the tens.

Sam and Aisha use column subtraction to calculate 722 - 429.

Sam says, "I think we need to regroup in the ones but there are enough tens." Do you agree with Sam? I wonder, is Sam right? So Aisha says, "I regroup one ten as 10 ones.

There is now 1 ten and 12 ones." "12 ones subtract 9 ones is equal to 3 ones," says Sam.

Ah, now we've got a bit of a problem, haven't we in the tens column? We did have 2 tens and we could subtract to 2 tens.

But because we've regrouped one of those tens as 10 ones, there is only 1 ten left.

So Aisha says, "I regroup one hundred as 10 tens.

There are now 6 hundreds and 11 tens." "11 tens subtract 2 tens is equal to 9 tens," says Sam.

And then, "6 hundreds subtract 4 hundreds is equal to 2 hundreds," says Aisha.

So "722 - 429 = 293." And Aisha says, "We had to regroup in the tens because we regrouped the ones." Now here's one to try on your own.

Use column subtraction to calculate 654 - 377.

Sam says, "I think you need to regroup in the ones and tens." So again, use pencil and paper or use a whiteboard and whiteboard pen.

Jot down that calculation.

And see if you can work out the difference between those two numbers using column subtraction.

Don't forget to regroup as well.

And welcome back.

How did you get on? Did you manage to find the answer? Did you regroup in the ones? Did you regroup in the tens? Did you regroup in the ones and the tens? Let's take a look and see whether you were right.

So Aisha says first of all, you have to regroup in the ones, "Regroup one ten as 10 ones.

There are now 4 tens and 14 ones." Sam says, "14 ones subtract 7 ones is equal to 7 ones." I think Sam is making good use of his doubles again, there isn't he? Aisha says, "Regroup one hundred as 10 tens.

There are now 5 hundreds and 14 tens." "14 tens subtract 7 tens is equal to 7 tens," says Sam.

And then "5 hundreds subtract 3 hundreds is equal to 2 hundreds," says Aisha.

So "654 - 377 = 277." Very well done if you've got the right difference.

Very well done if you successfully regroup the ones and the tens as well to get the answer.

Excellent work.

Now Sam is not sure what happens when there are no tens to regroup into ones.

"I know we have to regroup in the ones but the tens digit is zero," says Sam.

Aisha says, "I can't regroup using the tens yet, so I have to regroup a hundred into 10 tens first." So "I regroup one hundred as 10 tens.

There are now 6 hundreds and 10 tens." "Now I can regroup one ten as 10 ones.

There are now 9 tens and 13 ones." "13 ones subtract 7 ones is equal to 6 ones." "9 tens subtract 5 tens is equal to 4 tens." "6 hundreds subtract 3 hundreds is equal to 3 hundreds." "703 - 357 = 346." So sometimes you have to regroup in the hundreds first.

Look carefully at that tens digit if it's a zero.

You've got to regroup the hundreds first, if you've got to regroup in the ones.

"Be careful." Says Aisha.

"You need to cross through the 10 tens so you are left with 9 tens." You can see how they've done it there.

They've actually put a line all the way through those 10 tens and left with 9 tens.

Be careful you're not left with 19 tens.

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

Use column subtraction to calculate 505 - 276.

So again, we've got that zero in the tens column.

Sam says, "How will you regroup in the ones if the tens digit is zero?" Do you need to regroup in the ones? We've got a 5 - 9.

So yes, you do need to, don't you? So again, use paper and pencil or a whiteboard and whiteboard pen.

Jot down that calculation.

Have a go trying to find the difference using column subtraction.

Think really carefully about regrouping.

Pause the video.

Can you find the difference? And again, welcome back.

How did you get on? Did you get the answer? Did you have to regroup in the tens before you grouped in the ones? Let's have a look.

Aisha says, "You can't regroup using the tens yet, so regroup a hundred into 10 tens first." "Regroup one hundred as 10 tens.

There are now 4 hundreds and 10 tens." "Now you can regroup one ten as 10 ones.

There are now 9 tens and 15 ones." And I hope you remember to put a line all the way through that 10, so you're left with 9 tens.

"15 ones subtract 9 ones is equal to 6 ones," says Sam.

"9 tens subtract 2 tens is equal to 7 tens." "4 hundreds subtract 2 hundreds is equal to 2 hundreds," says Aisha "505 - 229 = 276." Very well done if that is what you got as your answer.

Very well done indeed.

And whether if you remember to regroup in the tens before you regrouped in the ones.

Let's move on to Task B.

So complete each calculation, regrouping in the ones and the tens.

So when chose calculations, there's regrouping in the ones and tens.

Complete each calculation, regrouping in the ones and tens.

And if you look really carefully, you might notice something in common about all three of those calculations, especially that tens digit of the minuend.

What can you spot? And then finally, use each number once to complete all three column subtractions.

So you've got there six 3-digit numbers.

615, 344, 368, 249, 702, 733.

You've got to arrange each of those numbers into each column subtraction to make that difference correct.

Which number would you subtract from another to get a difference of 366? Which number would you subtract from another to get a difference of 365? And which number would you subtract from another to get a difference of 358? Do you know the difference between the two numbers is going to be about 300? It's a bit of a puzzle that one.

That's the kind of thing I really enjoy doing.

Trying to puzzle out a question.

See if you can get to part three of Task B.

Pause the video and have a go at Task B.

Welcome back.

How did you get on? Did you get onto part three of Task B? Very well done if you did.

Let's take a look at those answers.

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

So of course, we had to regroup in the ones and the tens.

It's our first calculation.

We've got 644 - 388.

The difference between those two numbers is 256, and that's regrouping in the ones and tens.

Part two of Task B.

We had to regroup in the ones and tens, but we had to do all the regrouping before we started trying to work out the difference.

Because the tens digit in the minuend is a zero, we've got to regroup in the tens first and then regroup in the ones before we can try to work out the difference.

So that first calculation 604 - 329, the difference is 275.

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

So for that first calculation, the two numbers were 615 and 249.

615 - 249 = 366.

For B.

733 - 368 = 365.

And finally for C.

702 - 344 = 358.

Very well done if you managed to get the answers to those ones.

So excellent work in today's lesson and hopefully you're feeling much more confident at subtracting a 3-digit number from a 3-digit number, including regrouping in the tens and the ones and you even know what to do when that tens digit of the minuend is a zero.

Excellent work today.

Very well done.

And finally, let's move on to our lesson summary.

Regroup when the ones or tens digit of the subtrahend is greater than the ones or tens digit of the minuend.

Regroup a ten into 10 ones.

Regroup a hundred into 10 tens.

And if the tens digit of the minuend is a zero, you need to regroup the hundreds before you can regroup the tens.