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 edition 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're going to look at using column subtraction with regrouping from the tens to the ones.

I wonder if you've done that before.

Let's have a look.

See what's going to be in our lesson.

We've got two key words.

We've got column subtraction and regroup.

So I'll take my turn and then you can have a practise.

Are you ready? My turn, column subtraction.

Your turn.

My turn, regroup, your turn.

Well done.

You may have come across those words before.

Let's remind ourselves what they mean 'cause they're both going to be used a lot in our lesson today.

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

It helps us to keep track of our numbers, and make sure that we're calculating efficiently, and accurately.

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 also 10 ones can be regrouped for 1 ten, and 1 ten can be regrouped for 10 ones.

Look out for that.

We're going to be doing some of this today.

There are two parts to our lesson.

We are going to be regrouping from tens to ones with 2-digit numbers in the first part, and in the second part we're going to be doing the same but with 3-digit numbers.

So let's make a start.

And we've got Alex and Lucas helping us with our learning today.

Alex has a problem with column subtraction.

Oh, Alex.

He says, "I'm not sure how to answer this question." You might be looking at that and thinking, "I think I could do that without using column subtraction." And you might well be right, but we're going to use it to help us to think about how column subtraction works.

Lucas says, "That's okay Alex, I'm here to help.

Now what's the problem?" Oh, Alex has correctly identified that he needs to start with the smallest place value digits first.

So he's looking at the ones.

And he says here, "The ones digit of the subtrahend is greater than the ones digit of the minuend.

What do I do?" So he's remembered that the number we record first is the minuend.

It's our whole, the number we are starting with.

And then the subtrahend, the number we're subtracting, is recorded below.

So here we've got 1 one, subtract 7 ones.

I don't think we can do that yet, can we? Or not in a way that's gonna help us to answer our question.

Lucas says, "Let's start by representing 41, subtract 7 using base 10 blocks." Good idea Lucas.

So there's our 41.

And Lucas says, "We need to use regrouping.

Let's regroup one of the tens as 10 ones." He's spotted we don't have enough to subtract 7 ones at the moment, but we have got lots of ones locked up in those tens haven't we? Because we know that 1 ten is equal to 10 ones.

So we've regrouped one of our tens as 10 ones.

So now it's much easier to subtract 7 ones.

So there we are.

We've subtracted 7 ones.

And Alex can now see the answer.

"That's brilliant! 41 subtract 7 is equal to 34." We can see that in the base 10 blocks.

We've got 3 tens and 4 ones as our difference.

So the answer is 34.

But Alex wants to use column subtraction with regrouping.

How do we represent what we've just done with the base 10 blocks in our column subtraction? Let's have a look.

He says, "Can you show me how to use regrouping with column subtraction?" So Lucas says again, "Yes, we need to use regrouping.

Let's regroup one of the tens as 10 ones." So just the same.

How do we record that though with our column subtraction? Well, Lucas says, "I change 1 one into 11 ones by adding 10 ones." Now there are 3 tens and 11 ones.

11 ones subtract 7 ones is equal to 4 ones.

And 3 tens subtract 0 tens is equal to 3 tens.

"Thanks, Lucas!" says Alex.

Alex wants to find the difference between 73 and 48.

He's set it out as a column subtraction.

He says, "We need to regroup 1 ten as 10 ones." He's spotted again that in our ones, 3 ones subtract 8 ones is difficult to do.

So Lucas says again, "Let's represent the problem using base 10 blocks so we can see what's happening." So here are our 73.

"Let's change 3 ones into 13 ones by regrouping 1 ten as 10 ones." We could certainly subtract 8 ones from 13 ones.

So we've regrouped one of the tens into 10 ones so that we can make 13 ones.

And we're going to record that by saying we've removed one of the tens from the tens column.

So we've got 6 tens left there, and we've moved it into the ones column.

So we've now got 13 ones.

We've still got 73 altogether, but we've regrouped it as 60 and 13.

So there are now 6 tens and 13 ones.

13 ones subtract 8 ones is equal to 5 ones.

And 6 tens subtract 4 tens is equal to 2 tens.

And you can see that happening with the base 10 blocks as well.

So Alex says, "73 subtract 48 is equal to 25." It's useful to be able to spot when there's some regrouping so let's check your understanding.

So which need regrouping from the tens to the ones? And Lucas says something to look out for, "Is the ones digit of the subtrahend greater than the ones digit of the minuend?" So pause the video, have a look, and we'll come back together for some feedback.

How did you get on? So we need some regrouping here don't we? Because we've got 5 ones subtract 8 ones.

So regrouping is needed.

What about here? 3 ones subtract 1 ones.

Is regrouping needed? It isn't.

So we don't need to regroup here.

We've got more ones in our minuend than we have in our subtrahend.

And what about the last one? This is an interesting one, because we've got 0 ones in our minuend.

We've got 80, we've got a multiple of 10.

Regrouping is needed because if we've got 0 ones, we still need to be able to subtract 7 ones.

So regrouping is needed here.

So well done if you've got those right.

So Alex is using column subtraction again.

He's calculating 67 subtract 38.

And he's spotted the ones digit of the subtrahend is greater than the ones digit of the minuend.

So our whole, our minuend, 67 has 7 ones.

And our subtrahend, the number we're subtracting, has 8 ones, which is more.

Only just, but it's still more.

He says, "I need to regroup 1 ten as 10 ones.

So there'll now be 5 tens and 17 ones." And he records that by changing the 6 to a 5, and putting that 1 next to the 7.

So we've got 5 tens and 17 ones.

"17 ones subtract 8 ones is equal to 9 ones.

And 5 tens subtract 3 tens is equal to 2 tens." So 67 subtract 38 is equal to 29.

Well done Alex.

All that working with base 10 blocks, and talking about it with Lucas, and you're being really confident now in using regrouping when the ones digit of our subtrahend is greater than the ones digit of our minuend.

So Alex uses column subtraction again.

This time he's calculating 80 subtract 68.

Does that remind you of one of the calculations in our check for understanding? Let's see what Alex does.

He says, "I think I'm really getting the hang of this.

All that practise in Year 3 is coming back to me." Oh that's good to know Alex.

He says, "I need to regroup 1 ten as 10 ones.

So they'll now be 7 tens and 10 ones." And we know that 7 tens add 1 tens is 8 tens, so 70 add 10 is equal to 80.

So even though we've got a 0 there, we still need to make sure that we've got enough ones that we can subtract the number of ones in our subtrahend.

10 ones subtract 8 ones is equal to 2 ones.

And 7 tens subtract six tens is equal to 1 ten.

So 80 subtract 68 is equal to 12.

Time to check your understanding.

Can you use column subtraction to calculate 75 subtract 37? Alex says, "You'll need to regroup 1 ten as 10 ones." Can you see that the ones digit in our subtrahend is 7, and the ones digit in our minuend is 5.

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

How did you get on? So we needed to regroup, didn't we? So 7 tens became 6 tens, and the extra 10 was regrouped with the ones to make 15.

So 75 has been regrouped as 60 and 15.

So there are now 6 tens and 15 ones.

15 ones subtract 7 ones is equal to 8 ones, and 6 tens subtract 3 tens is equal to 3 tens.

So 75 subtract 37 is equal to 38.

Well done if you got that one right.

Lucas gives Alex a problem.

He says, "Think of a 2-digit number where the digits are not the same.

Write it down, then reverse the digits, and write this new number." Hmm, let's have a go.

Alex says, "I'll start with 76.

That's a 2-digit number where the digits are not the same.

When I reverse the digits, I get 67." So he's got 76 and 67.

Lucas says, "Now use column subtraction to subtract the smaller number from the larger number." So Alex says, "I have to calculate 76 subtract 67." So he's recorded it as a column subtraction.

He says, "I need to regroup 1 ten as 10 ones.

So there are now 6 tens and 16 ones." Then we can see he's recorded it in his column subtraction.

16 ones subtract 7 ones is equal to 9 ones.

6 tens subtract 6 tens is equal to 0 tens.

So 76 subtract 67 is equal to 9.

Have a go at Lucas' challenge.

"Think of a 2-digit number where the digits are not the same.

Write it down, then reverse the digits, and write this new number." "Now use column subtraction to subtract the smaller number from the larger number." Pause the video, have a go, and we'll come back for some feedback.

How did you get on? Here's what your work might have looked like 'cause we don't know exactly which numbers you chose.

Let's start with 35, and when I reverse the digits, I get 53.

So we've got 35 and 53.

And we're going to subtract the smaller number from the larger number.

So 53 subtract 35.

So a ten has to be regrouped as 10 ones.

So there are now 4 tens and 13 ones.

13 ones subtract 5 ones is equal to 8 ones.

4 tens subtract 3 tens is equal to 1 ten.

So 53 subtract 35 is equal to 18.

I wonder what you got as your answer.

Maybe we'll come back to this later.

Time for you to do some practise.

So for Question 1, we've got six column subtractions for you to have a go at.

Remembering to start with the digits with the smallest place value.

And look carefully to see if you need to regroup or not.

And then you're going to try Lucas's challenge.

Oh I'm pleased you're going to get to have another go at that.

"So think of a 2-digit number with two different digits, write it down, then reverse the digits, and write down the new number." So you might have 31 and 13.

And then use column subtraction to subtract the smaller number from the larger number.

So you're going to set it out with column subtraction.

Try lots of different numbers.

Do you notice anything? So pause the video, have a go at your tasks, and we'll come back together for some feedback.

How did you get on? Did you spot that there was one where we didn't need to do any exchanging? So I hope you managed to do your exchanging.

Remembering to regroup a ten for 10 ones so that we could complete the calculations efficiently.

And for E, regrouping was not needed.

So you might want to pause and just check that you've got your answers correct here.

And 2, you were having a go at Lucas' challenge.

So here are some possible answers.

So 31 and 13 was the number that Lucas gave you as a suggestion.

And the difference was 18.

64 and 46.

The difference was 18.

59 and 95.

The difference was 36.

71 and 17 and the difference was 54.

I wonder if you noticed anything about your answers.

Alex noticed something I think.

He says, "You may have noticed that you kept getting the same differences, 9, 18, 27, 36, 45 and 54." Did you notice that? And Lucas says, "When you add the digits of the difference together, you always get 9." So if you had a difference of 18, and you add the 1, and the 8 together, you get 9.

If you had a difference of 36, and you add the 3, and the 6 together, you get 9.

You might have had a difference of 27.

2 plus 7 is equal to 9.

And then for 54, 5 plus 4 is equal to 9.

Really interesting.

I wonder if you found out that too.

There must be a reason that happens.

I wonder what it is.

Well I hope you've had fun with Lucas' challenge.

So let's move on to the second part of our lesson.

We're going to be thinking about 3-digit numbers.

So Alex uses column subtraction to calculate 473 subtract 128.

Can you spot anything? Ah Alex has noticed, "The ones digit of the subtrahend is greater than the ones digit of the minuend." So the subtrahend is our number that we're subtracting, and that has an 8 in the ones and our minuend, our whole, the number we start with, only has a 3 in the ones.

"I need to regroup 1 ten as 10 ones." At the moment we've got 7 tens and 3 ones so now we're going to have 6 tens and 13 ones.

So we've regrouped our ten as 10 ones.

There are hundreds in our calculation, but that doesn't matter.

We still only need to think about regrouping a ten as 10 ones at the moment.

So 13 ones subtract 8 ones is equal to 5 ones, and 6 tens subtract 2 tens is equal to 4 tens.

Our hundreds haven't changed so we can just subtract those as normal.

400 subtract 100 is equal to 3 hundreds.

So 473 subtract 128 is equal to 345.

Alex uses column subtraction to calculate 560 subtract 333.

And he's set it out.

He says, "The ones digit of the minuend is zero.

I'll need to regroup 1 ten as 10 ones." So at the moment we've got 5 hundreds and 6 tens and no ones in our minuend.

So when we regroup, we're going to have 5 tens and 10 ones.

We've still got 560, we've just regrouped one of the tens.

So now we can say 10 ones subtract 3 ones is equal to 7 ones.

5 tens subtract 3 tens is equal to 2 tens, and 5 hundreds subtract 3 hundreds is equal to 2 hundreds.

So 560 subtract 333 is equal to 227.

We need to be really careful when we've got a zero, because we have to regroup so that we have some ones to be able to subtract from.

So can you use column subtraction to calculate 381 subtract 142? So we've set it out for you.

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

So you might have to think about regrouping here.

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

How did you get on? Did you manage to do your regrouping? So we need to regroup 1 ten as 10 ones.

So at the moment we've got 8 tens and 1 one.

So when we do our regrouping, we're going to have 7 tens and 11 ones.

11 ones subtract 2 ones is equal to 9 ones.

7 tens subtract 4 tens is equal to 3 tens, and 300 subtract 100 is equal to 2 hundreds.

So 381 subtract 142 is equal to 239.

Well done if you got that right.

Alex is trying to find the missing digit.

He says, "The ones digit of the minuend is missing." And Lucas says, "To find a missing whole, add the parts together." So we know that the whole is the bit that's missing because the whole is our minuend.

So our parts are the ones digit of the subtrahend, and the ones digit of the difference.

5 plus 7 equals 12.

There must be 12 ones.

Ah, what does that mean has happened? 1 ten must been regrouped as 10 ones.

So now we'd have 7 tens and 12 ones.

So let's just check.

We know it works with the ones.

Does it work with the tens as well? 7 tens subtract 2 tens is equal to 5 tens.

You've got it.

So the missing ones digit was a 2.

So our original calculation was 382 subtract 125.

This was an interesting one, wasn't it? Our missing digit is a 2, but we can work out that it was a 2 because we must have done some regrouping.

Alex is trying to find the missing digits.

He says, "The ones digit of the minuend, and the tens digit of the subtrahend are missing." And Lucas is reminding us, "To find a missing whole we add the parts together." So if we are looking at the missing ones digit of the minuend, that is our whole.

So 8 plus 3 is equal to 11.

There must be 11 ones.

How can we get 11 ones though? What must have happened? Ah, 1 ten must have been regrouped as 10 ones.

So that's what our minuend must have looked like.

271 was regrouped into 2 hundreds, 6 tens and 11 ones.

So we know that 11 subtract 8 is equal to 3.

What about the tens? We've got a 5 as our known part in the difference.

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

So we know that that must have been 6 tens because we regrouped one of the tens into the ones.

So 6 tens subtract 5 tens is equal to 1 ten.

So our missing tens value must be a 1.

6 tens subtract 1 ten is equal to 5 tens.

So our original calculation was 271 subtract 118.

Time for you to have a go.

Can you find the missing digits in this subtraction? We've got a missing ten in our minuend, in our whole, and we've got a missing ones digit in our subtrahend, in our part.

So remember to find a missing part, we subtract the known part from the whole, and to find a missing whole, we add the parts together.

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

How did you get on? Alex spotted that 1 ten must have been regrouped as 10 ones because we had 5 subtract something is equal to 6.

So that 5 must have been 15 regrouped, with a ten regrouped from the tens.

15 ones subtract 6 ones is equal to 9 ones, we can subtract the part we know.

So our missing ones digit must be a 9.

15 ones subtract 9 ones is equal to 6 ones.

And Alex says, "I mustn't forget that I regrouped 1 ten as 10 ones." So now what can we see? Well, we can see that our two parts are 2 tens, and 1 ten.

2 tens add 1 ten, add the regrouped ten is 4 tens.

So we must have started with 4 tens.

We then regrouped a ten to give us 15 ones.

So we can now see that when we've done the regrouping, 3 tens subtract 1 ten is equal to 2 tens.

So our original calculation was 245 subtract 119.

Lots of really good thinking going on there.

I hope you got that one right.

Time for you to do some practise.

So for Question 1, you're going to complete each calculation, and you will need to regroup the ones.

Alex is saying, "In C, you need to subtract a 2-digit number from the 3-digit number." But that's absolutely fine, we just remember that there are no hundreds in our 2-digit number, but we mustn't forget to subtract the zero from the hundreds in our 3-digit number.

And in Question 2, you're going to find the missing digits.

Thinking really carefully about which is a whole, and which is a part.

And thinking very carefully because we may be dealing with some regrouping in these calculations.

So pause the video, have a go at the tasks, and we'll get together for the answers and some feedback.

How did you get on? Here are the answers to Question 1.

So we had to do regrouping in all of them.

So 222 subtract 115 is equal to 107.

450 subtract 227 is equal to 223.

And 477 subtract 49 is equal to 408.

So here are the first ones that we looked at with the missing digits.

So in A, we had a missing number of ones from our minuend, so a missing whole.

So we could see that 8 ones add 4 ones was equal to 12 ones.

So we must have had a 2 there and then a regrouped ten.

So we'd started with 5 tens.

That must have gone to 4 tens, and that then makes the tens correct.

4 tens subtract 3 tens is equal to 1 ten.

So our calculation was 252 subtract 134, and we had the same thinking in B.

Again, we had a missing whole.

But Alex says, "To find a missing part, we subtract the known part from the whole." So in C, we had to find a missing part in the tens.

We knew already that there'd been some regrouping from the tens to the ones.

So we had 8 tens because we'd regrouped.

So we must have subtracted 3 to give us our 5 tens as the difference.

So our calculation was 491 subtract 132.

So for the second set in Question 2, similar thinking going on here, it was really important to know whether you were calculating a missing whole or a missing part.

E is interesting because our missing whole was our tens in our minuend.

So we'd already worked out that some regrouping had happened to give us 15 ones.

So our missing digit was 8 tens, but it had been regrouped into 7 tens, and 1 ten had been put in with the ones to give us 15 ones.

And what about F? Ah Alex says "I think F was a trick question.

There's no regrouping needed!" So in F, we could see that we had 7 ones in our minuend, in our whole, and we had 3 ones in our difference.

And 7 subtract 4 is equal to 3.

So there was no regrouping needed there.

I hope you spotted that.

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

Well done.

You've done a lot of really good thinking today.

It's really useful to be able to spot what's happening when we are doing our regrouping, and to be able to think about what the missing numbers might be, and to really explain how that regrouping has worked.

So what have we learned? We've learned that we need to regroup when the ones digit of the subtrahend is greater than the ones digit of the minuend.

So the subtrahend is the number we're subtracting, and the minuend is the number we're starting with, our whole.

We can regroup a ten into 10 ones, and that means we can then complete the ones part of our subtraction.

And we need to change the number of ones, and tens in the minuend to record the regrouping that we've done.

I hope you've enjoyed exploring regrouping from tens to ones to help to solve subtractions.

And I hope it's perhaps reminded you of some learning that you've done before.

Thank you again, and I hope I get to work with you again soon.

Bye-bye.