Lesson video

Hello everyone, I'm Mrs Crane and welcome to today's lesson.

In today's lesson we're going to be subtracting using the column method when more than one column requires re-grouping, it sounds quite complicated but don't worry if you follow everything we do today then you'll know exactly what to do.

Don't worry about getting equipment just yet.

I'll go through all of the things that we'll need in a moment.

If you can turn off any notifications on your phone, tablet, or whatever device you're using to access today's lesson on and then you can try and find somewhere nice and quiet in your home so we're not going to be disturbed in our lesson today.

When you are ready let's begin.

Let's run through today's lesson agenda, we're going to start off by what happens when we regroup in more than one column, then it'll be time for your let's explore and your turn.

Then we're going to look at regrouping, what happens when there's a 0 and what happens when regrouping creates regrouping.

They both sound quite complicated but don't worry we're going to go through some examples and see exactly what I mean when I'm going through those with you.

Then it'll be time for your independent task today which is going to be solving some subtraction equations and then we'll go through the answers together.

So, if you haven't already please pause the video now to get yourself a pencil and some paper.

Welcome back, hope you're feeling ready.

Let's get started then.

So, my first question today is how do we know if we need to regroup in more than one column.

Remember, we're talking about subtraction today.

So how do we if we need to regroup in more than one column.

Well, I know that if the number that I'm taking away from is greater.

This is my whole, sorry.

If the number that's in the column of my part is greater than the number in my whole then I know I need to regroup.

So, if we look at our bar model it helps us think about that part and that whole a little bit more.

So, here you can see my whole is 8839 and one of the parts is 5963, we don't know the other part at the moment.

If I look at my one's column I'm not going to need to regroup.

My part one, obviously it's not a one it's a three, but my ones isn't greater than my whole ones.

My part ten is greater than my whole tens so I know I'm going to need to regroup the ten column.

My part hundred 9 is greater than my whole 8 in my hundreds so I need to regroup there.

And then my part 5 is so I'm not going to need to regroup that.

So, I know that I'm going to need to regroup in more than one column, so that's going to help me when I come to answer my equation because if I've only regrouped in one column and I've already told myself I need to regroup in two I know I've gone wrong somewhere, another thing that's going to help us out is using that estimate before we make our answer.

That gives us an idea if we've gone wrong horribly or if we're on track when we get to our answer.

For an estimate I always round to the nearest thousand, so 8800 round up to my nearest thousand is 9000.

5900 round up as well is 6000.

So, 9000 subtract 6000 gives me 3000.

So my almost approximately equal to symbol goes here and I know the number that I'm looking for when I'm subtracting is about 3000.

You can kind of see here as well that it's going to roughly be 3000.

If you think, that's 6000 this is about half of that.

So, let's get started, Now, using my place value counters I have made the number 8839, I want to start with my ones.

Why do I start with my ones column? Well, if there's regrouping and I've started with my thousands I'm going to get myself in a real muddle.

So, I always start with my ones, remember my face is covering the O for ones, I am in the ones column - it's still here.

So, in the ones I have 9 and I'm taking away 3, what's 9 take away 3? Absolutely it is six, I can put that into my written method here and I can show it here, I'm going to keep going between my place value here and my written method which is over here.

So you can see here is my written method and here are my place value counters.

I want to do that so that you can see exactly what's happening if you choose to draw it out or if you choose to write it out using the formal method.

So, now I can go onto my tens column.

Now, I've already worked out that I'm going to need to do some regrouping because 6 is greater than 3 and I can't take it away without using negative numbers and I don't want to do that.

So, I need to regroup one of my hundreds from my 8, so that was 8.

I've pulled one down, there's now 7 and there's my one 8 here.

So, 100 I'm going to regroup into 10 tens because there are 10 tens in 100.

So you can see them, they've moved to here, my one hundreds moved and have become 10 tens.

I still have my three tens because I have 3 in that column already.

Now, can I take 6 away from 13? Absolutely, I can.

13 take away 6.

Before I do that, let me show you what it looks like here.

Put a line through that 8 because it's now no longer 8, there are now 7.

Here you can see them there's 7 hundreds.

And there are now 13 tens in my tens column.

It's really important that we remember to do that because if we don't remember to do that it's going to be quite tricky when it comes to subtracting, we're going to be holding too much information in our heads.

So, 13 take away 6 leaves me with 7.

Then I can do, can I, can I do 7 hundreds take away 9 hundreds, I can't.

So, I'm going to need to regroup in more than one column, to do that I'm going to look to the next column which this time is my thousands column.

I'm going to take one of my thousands to give me, this 7000 is going to be remaining.

I've taken one of them and I'm going to regroup that 1000 into ten hundreds because I know that there are 10 hundreds in 1000.

Then I can subtract, so lets see what happens.

1000 is gone and it's become ten hundreds.

So these are my new ten hundreds.

Here, you can see my remaining 7 hundreds are here.

Now, I have 17 hundreds, let's see what that looks like in our column method.

So you can see I've had to cross out my 8 because I don't have 8 thousands.

anymore, I have 7 thousands, here they are.

I now because I regrouped ten hundreds and one thousand.

I now have 10 hundreds here so I can mark that in here with my one to show that there is ten hundreds.

So I now have 17 hundreds, here are my 17 hundreds.

Now I can take away nine of them.

Take away nine of them and I'm going to be left with eight, so I can put eight into this grid.

Now, I have 7 thousands and I want to take away five.

Can I do that? Absolutely I can and it leaves me with two.

So my answer is 2876.

Is that close to my estimate? Yes it is.

I have regrouped in more than one column and I knew that I needed to regroup in more than one column so absolutely.

So my answer isn't too far away from my estimate and I know I haven't gone horribly wrong.

Now how do we then again in this equation if I need to regroup in more than one column.

If you're feeling really confident with regrouping in more than one column please pause the video now to have go at this equation here, before we go over the answer together.

If you're not feeling so confident, don't worry.

If you are going to pause it make sure you make your estimate before you work out your equation.

Okay, let's have a look at these numbers.

So 3 and we're taking away 9 from it.

Is the number we're taking away from greater than our whole? It is, so we're going to need to do some regrouping.

7 take away 2 we can do that.

4 and I want to take away 8, is the number that I'm taking away from greater than my part? Absolutely it is.

So I know I'm going to need to do some regrouping.

So, I know there's more than one column in this equation that needs regrouping.

I can do that really quickly by just lining up those columns in my head and seeing if the number that I'm taking away is greater than the whole, my part is greater than my whole.

So, let's make a quick estimate.

7400 rounds down to 7000 and 4800 rounds up to 5000.

7000 subtract 5000 gives me 2000.

So my rough estimate is going to be 2000.

Let's see then.

I've made my number, 7473.

Now I want to take away 4829.

Can I take 9 away from 3? I can't, so I need to regroup in my tens column.

I'm going to take one of my tens and put it down here.

I'm going to then take this ten and I'm going to use it to make 10 ones.

It'll give me 13 ones.

Let's see what that looks like over here.

I'm going to put a line through my 7 and mark it as 6 because I've got 6 remaining here.

Now I'm going to put 1 here because I actually now have 13 in my ones column, now can I do 13 subtract 9? Clearly I can, that leaves me with 4 so I'm going to put 4 in here.

Now can I do 6 subtract 2? I can.

And it leaves me with 4, so I'm going to put 4 in my tens column.

4 hundreds subtract 8 hundreds, can I do that? I can't, I need to regroup.

1000, I'm going to bring it down here and I'm going to regroup it into ten hundreds.

They've become ten hundreds, you can see them here.

You can still see my remaining 4 here, so I now have 14 in hundreds.

Let's have a look over here, I don't have 7 anymore, I have 6 thousand and I have 14 hundreds.

You can see that here and you can see it here on this part.

14 subtract 8, can I do that? I can indeed.

That leaves me with 6.

I'm going to put that here, you can see my six here.

Now I have 6 thousands left and I want to take away four, I can do that and it leaves me with two.

So my answer is 2644.

Put my answer here.

We knew there was regrouping in two columns and we got that right and it's not that far away from our estimate, so we know we haven't gone horribly wrong.

Okay, now it's going to be your turn.

So, what I want you to do for your turn is to estimate the answer to this calculation.

Calculate your answer and then check it back against the estimate.

Remember to look for which columns you're going to need to regroup in first and you can use this speaking frame here.

Pause the video now to have a go at today's let's explore.

Okay, welcome back.

Let's have a look at the answer.

So, which columns did we need to regroup in for our example.

Well, I know that number 9 is greater than 8 so if I line it up here I think I'm going to need to regroup in this column and I don't need to regroup in that column.

I do need to regroup my hundreds column.

So it looks like ones and hundreds at the moment.

Make a quick estimate, 7100 rounds down to 7000.

4500 rounds up to 5000, 7000 subtract 5000 is 2000.

Oh, I've estimated it as 3000.

I must've been thinking that 5000 and the 1000, they're quite large numbers.

So, let's see if it's quite close to my estimate.

8 subtract 9， we can't do that, we know that we need to borrow, to regroup our 8 we need to knock next door to find our next column.

We need to regroup one group of our tens to become 5 tens and 18 ones, 18 ones take away 9 ones leaves me with nine.

5 take away 2, can I do that? Yep, I can.

That leaves me with 3.

Oh, I got a bit carried away there.

Now, I can't do one take away 5 without going into negative numbers so I need to regroup 7 from my 7000 to leave me with 6000 and 11 hundreds.

11 hundreds subtract 5 hundreds give me 600 and I can do that.

6000 take away 4000 gives me 2000.

So, my answer is 2639, not far away from my estimate at all.

2639 is my answer.

What we're going to do now is look at an example where regrouping actually creates more regrouping.

So here if I look at the columns, in fact we'll look at the columns in a moment.

Let's look at how we estimate our answer.

Then we'll look at what will happen.

So I'm going to estimate that that's going to be about 10000 because I round 9600, it rounds up so does 4600 to 5000.

So, my estimate is going to be 5000.

Now, I'm going to be showing you in the column, I think it's just bit easier to see what I mean.

So, ones column is not going to require a grouping.

Tens column, yes it is, at the moment hundreds column is not going to, thousands column is not going to.

So, we're predicting that only one column needs regrouping.

But if we go back a section we know that regrouping will create more regrouping.

So we know that in this column here because we have to regroup it's going to cause us to have to regroup in another column, let's see what I mean by that in moment.

If you're feeling really confident have a go at doing this yourself.

If you're not feeling really confident that's absolutely fine.

So 7 subtract 3, we know we can do that because the number we're subtracting from is smaller than our whole.

It leaves us with 4, so I'm going to put 4 in here.

2 subtract 8, I know I can't do that without regrouping, so I'm going to regroup one of my hundreds so it'll leave me with 5 hundreds and 12 tens.

So let's see what that looks like over here.

So here's my 5 hundreds and here's my 12 tens.

Here are my 5 hundreds and here are my 12 tens.

Can I do 12 subtract 8? Absolutely I can, and it leaves me with 4, so I can put 4 in here.

Now originally this was 6 subtract 6 which I can do, it'll leave me with 0.

But can I do 5 subtract 6? I can't, so because I had to regroup in this column here I now have to regroup in this column here as well.

So I need to now knock next door to the column in my thousands column to regroup so that I can subtract in my hundreds column.

So I'm going to take one of my thousands from my 9000, which will leave me with 8000 and that thousand is going to become ten hundreds.

Here we go, we've been left with 8000 here then we're going to put them here.

So we're going to have our ten hundreds here, now I have got 8 left here and I have 15 here.

So you can see that here are my 15 hundreds here.

Now I can do 15 subtract 6 which is going to leave me with 9 and I can put 9 in here.

Now I have 8 thousands here and I want to take away 4000 so I am left with 4000, so my answer is 4944.

Put that in here, is that close to my estimate? It's really close to my estimate, so I know I haven't gone horribly wrong anywhere at all.

Now, remember we thought we only had to regroup in one column but because we regrouped in that one column it actually meant we had to regroup in another column because it meant that our tens had decreased, not our tens sorry, our hundreds had decreased so that we couldn't subtract that.

Sometimes that might happen, originally we didn't think that you needed to regroup that column but because of regrouping you actually do need to regroup that.

Okay, this time, what happens when there is a 0 in a column? So my equation is 9304, 0 in this column here and I'm subtracting 3128.

So, I know that there is a 0 here and there isn't a 0 in the ten columns here so I'm going to need to regroup.

We might need to regroup in other columns too, let's check.

4 subtract 8, I'm going to need to regroup in that column.

So, let's have a think about making an estimate and then we're going to work out how to do it.

If you're feeling really confident with a 0 pause the video and have a go at doing this, remember to make your estimate.

If you're not feeling super confident that's absolutely fine we're going to go through it now.

My estimate would be 9000 subtract 3000 which is 6000 because that's what the closet numbers they round to when they're rounded to the nearest thousand.

Now, let's see how this looks.

What do you notice about the tens column? We know that there are no tens in my original, whole number.

So there's nothing in that column and that's probably what you've noticed.

We do have 9 thousands, 3 hundreds, and 4 ones though.

So can I do 4 subtract 8, I can't.

Can I regroup anything from my tens? I can't.

Where do I have to go next to regroup? I need to go to my next column that there's a number in that I can regroup from which is my hundreds.

So, I'm going to regroup 100 into 10 tens and I'm going to show you what this looks like over here now.

So I now have 2 hundreds left and I have 10 tens, can I subtract now, can I work it out? Can I do 4 take away 8? No, I still can't - I still need to do something else.

I then need to regroup form my tens column into my ones column to be able to solve this part of my equation.

So, I'm going to regroup 1 ten which is going to leave me with 9 tens here and 10 ones.

Here are my 9 tens and here are my ten ones.

Let's see what that looks like here.

So I need to cross out my ten which has actually become a nine.

I now have 14 ones, can I now subtract from my ones column? Yes I can.

14 subtract 8 leaves me with 6, so I can put 6 in here.

9 tens subtract 2 tens, can I do that? I can, and it leaves me with 7 tens.

and I can put that in here.

2 hundreds subtract 100, can I do that? I can, it leaves me with 100.

9000 subtract 3000, can I do that? I can, it leaves me with 6000.

So my answer, 6176.

Is it close to my estimate? Absolutely it is.

What did we have to do then when there was that place holder? That's right, we had to just keep going until we found a column with digit that we could regroup from and then we had to regroup from a column where we had our place holder before we could regroup from our ones column.

Okay? So just remember that if there is that place holder it doesn't need to panic us, we don't need to worry.

We just might need to regroup from a different column.

So, it is now going to be time for your independent task which is solving some subtraction equations.

I'm going to hide myself for a moment.

What I'd like you to do for today's independent task, using the column method for each bar model write the subtraction equation that it represents.

Then make an estimate that you can use before you do your column subtraction to calculate the missing part.

My challenge to you today is, can you work out which columns are going to require regrouping before you start calculating.

Please pause the video now to complete your task and remember we'll go through the answers after you've resumed once you've finished.

Welcome back, I'm going to put myself back on the screen.

I might just move myself around a little bit so that you can clearly see the equation.

We're going to start with our first equation here.

Which is 6734 subtract 4782, I've made my estimate and I've estimated for it to be 2000.

I'm going to show you how I do it with my column method here.

4 subtract 2 is 2.

3 subtract 8, can I do it? No, I need to regroup.

My 700 becomes 600 and I now have 13 tens take away 8 tens gives me five tens.

6 takeaway 7 hundreds, can I do that? I can't.

Originally I could but I now need to regroup from my thousands.

Leaving me with 5000 and 16 hundreds.

16 hundreds take away 700 is 900.

5 takeaway 4 is 1.

Is it close to my estimate? Really close to my estimate, so I know I haven't one horribly wrong.

Next question then, I'm going to move myself again so you can clearly see the question.

So my number is 8063 and I want to take away 1882.

My estimate is 6000.

Let's start on our ones, can we do it, 3 subtract 2? Yes, we can and it leaves us with 1.

6 subtract 8, can we do it? No we can't.

Can we regroup from our next column? No we can't.

We need to regroup from our thousands.

My 8000 becomes 7000 and I end up with 10 hundreds.

I then need to regroup one of those hundreds leaving me with 9 hundreds and 16 tens.

16 tens take away 8 tens is 8.

900 take away 800 is 100.

7000 take away 1000 is 6000.

Is my answer 6181 close to my estimate? Absolutely, it's not too far from that at all.

Question 4, let's have look, my estimate to the equation 7943 subtract 2678 is 5000.

Let's start with my ones column, am I going to need to regroup? Absolutely, I am.

We can regroup from our tens column, leaving me with 3 tens and 13 ones.

13 ones take away 8 ones gives me 5.

3 take away 7, can I do that? I can't, I need to do some regrouping.

Leaving me with 800, I'm going to regroup one of those hundreds to give me 13 tens.

13 tens take away 7 tens is 6 tens.

800 take away 600 is 200.

7000 take away 2000 is 5000.

And is the number 5265 close to my estimate? Absolutely it is.

And last but no least question four, here's my equation and my bar model here.

7608 and I'm subtracting 2539, my estimate is 5000.

8 take away 9, can I do that? I can't.

Can I regroup from my tens column? I can't, I have to regroup from my hundreds column.

So I'm going to be left with 5 hundreds and 10 tens.

10 tens is going to be regrouped to become 9 tens and 10 ones.

18 take away 9, can I do that? I can indeed and it leaves me with 9.

9 in my tens column now take away 3, can I do that? I can, it gives me 6.

5 take away 5, can I do that? I can, it gives me 0, you must put that 0 there, it's a place holder.

7 take away 2 gives me 5.

Fantastic, today I've been super impressed.

Lot's of regrouping.

If you'd like to please ask your parent or carer to share your work from today on Twitter by tagging @OakNational and using the hashtag #LearnwithOak.

Again, as I said I'm so impressed with how you've been using this column method today especially when there's multiple regrouping and especially when there's that 0 there as a place holder, it's there to trick you - don't let it.

Don't forget to complete today's quiz because you can show off all your fantastic knowledge from today's lesson.

I hope that I see you again soon for some more maths work.

Thank you and bye bye.