Lesson video

Hello there.

My name's Miss Brinkworth.

I'm going to go through this maths lesson with you today, all about subtraction.

Let's have a look at our learning objective for today.

So it's quite wordy.

It's the subtracting of 3-digit numbers, and we need to regroup in multiple columns.

We are now getting to the stage where you, at the end of this lesson, will be able to subtract any 3-digit number from any other 3-digit number.

So I'm hoping by the end of the lesson, you'll feel really confident with this super-useful technique of column subtraction.

So, the lesson agenda.

We are going to recap our mental strategies, that will really help us get our minds back into everything subtraction, and it will help us as we move through the columns in our column subtraction.

Column subtraction doesn't do all the work for us, there are still times we need to do some mental working out, so we're going to recap what that looks like.

Then we are together going to have a look at dienes and what that means when we need to regroup in more than one column.

Then we're just going to move on solely to column subtraction, and how we regroup when we're just writing it out, not using the dienes to help us.

And the final part of the lesson will be where you have some independent work to really consolidate what you've learned, have a practise of your new skills.

And then the exit quiz at the end of the lesson will give you that opportunity to see how many points you can get, how many right questions you can get.

So, for this lesson you will definitely need a pen or pencil and some paper, that's because this lesson is all about focusing on that written method.

So please make sure you do have a pen or pencil and some paper.

What would be useful would be online dienes, so if you could ask a parent or carer to help you find some online dienes that would really help you, especially at the beginning of the lesson, but if you can't find them please don't worry, I will put everything up on the screen for you.

So pause the video here and take as long as you need to find your equipment.

Okay, well done.

Let's get started now that you've got everything together.

Here's a little warm up for you.

One of these questions has been answered correctly, and in one there's a mistake.

So I'd like you to spot the one which has made a mistake.

And for your challenge, why do you think that mistake has been made? Pause the video and have a go.

How did you get on? Were you able to see which subtraction question they've made a mistake in? Now let's go through them together.

Hopefully, you were able to see that there is a mistake here on this subtraction question.

When we check a question, we check it just like we're doing it.

So we would go through it and we would look at how we would answer that question and see whether they've answered it in the same way.

So if we look at the ones column for that question, we need to do 7 - 6.

So they've put the right number 1 there in the ones column.

And then for the tens column we actually need to do 3 - 4.

I think what this person's decided to do is 4 - 3.

So there was some regrouping needed in this question that they didn't do.

So they needed to go into the hundreds, take one of the hundreds into the tens column to give you 13 - 4 which would have given 9.

And then of course that would have affected the hundreds column as well, because it wouldn't have been 7 - 1, it would be 6 - 1.

So the right answer in the hundreds column would be 5.

So you can see if you don't regroup it does have that impact throughout the question, you carry on getting the columns wrong.

The second question is fine, they've answered that one really well.

Okay, so a really, really quick start here for some really quick mental strategies.

So pause the video, and have a go at answering these questions, but what I'd like you to do because they are really easy, is think about how you know the answer.

You shouldn't have to write anything down, but what does your mind actually do when you see these simple subtraction questions? Okay, so if we look at 9 - 5 I'm sure.

Well, I gave you a little bit of a clue at the beginning there, but I'm sure you all know that 9 - 5 = 4.

I'm sure you can do that really quickly in your head, but how do we know that? Where does our mind go when we look at 9 - 5? Well, if I let you know what I do, if you use a different strategy that's absolutely fine, as long as you've got the right answer.

But I'm going to talk through in this lesson, what I do, what I'm thinking when I solve even these really simple subtraction questions.

So when I think about 9 - 5, I think about my known fact which is that I know 5 + 4 = 9.

9 is just one less than 10.

I'm really confident with the fact 5 + 5 = 10.

So I can use that to remember that 5 + 4 = 9.

So if I'm doing 9 - 5 the answer's got to be 4.

For the next question 7 - 6, well, we know that 7 and 6 are right next to each other.

1, 2, 3, 4, 5, 6, 7, they're right next to each other.

There's only one difference.

So if I've got 7 and I take away 6, the difference is 1.

Well done if you could see that.

For 13 - 7, well I know that 6 + 7 = 13.

I suppose I know that when I think about it, because I know that 6 + 6 = 12 so if I've got one more, 6 + 7 is going to be one more than 12.

So 6 + 7 = 13, so 13 - 7 = 6.

And 18 - 9, well, I know my two times table, 9 x 2 = 18, so 18 is made up of two nines.

So if I've taken away one of those nines, I've got a nine left.

Like I say, if you use a different strategy in your head to answer those questions that's absolutely fine.

In fact, it's great.

I'm just telling you what I use.

So we need to do subtraction questions like this all the way through the lesson, as we're doing our column subtractions.

Because what column subtraction does is it allows us to break down big numbers into simpler ones, and allows us to use our mental strategies to answer them.

So remember as we go through this lesson that subtraction makes numbers smaller.

All the questions you're going to look at today are subtraction so as you check your answer, a really good idea is to check that they've got smaller.

We're going to use those known facts like I just explained to you, these could be number bonds or near number bonds, and they could be the doubles that you know, you can utilise your times table knowledge.

Use all those known facts to help you with those mental strategies today.

And also remember the order.

It's really important when we look at subtraction that we get the order right.

We know that when we're adding it doesn't matter which order we add them in, but subtraction doesn't work in the same way, the order is very important.

Okay, pause the video here and have a think about what this image shows you.

Can you see anything different about the type of calculation that's being shown here? Well, hopefully, you can see from this bar model that it is a subtraction question.

We know that because we've been given the whole, that yellow bar, 423, and we've been given one part.

The unknown is the other part.

So this is a subtraction question, 423 - 185 will give us that unknown part there.

Also what's interesting about this question is that regrouping is needed in two columns.

How do you know that? Well, if we look at 185, 8 and 5, the tens column and the ones column, have got larger values than the tens column in our whole.

So 8 is bigger than 2 and 5 is bigger than 3.

So we're going to have to regroup in more than one column to answer this question.

And that's what our learning objective is about today.

So let's look at how we're going to do it.

Here's some dienes to represent that question, 423 - 185.

Hopefully, when you see it in dienes like this, you can see why regrouping is needed.

We need to take away more ones than it appears that we have.

We do have those ones, we just need to move them, regroup them from other columns.

And same with our tens.

It looks like we don't have enough tens to take away those 8 tens in 185, so we need to find them in our hundreds column.

Let's do that together then.

As we go through what's a really important thing to remember is that we can exchange.

So we just need to remember that 100 is 10 tens.

So if we're looking for tens, if we need extra tens, we get them from our hundreds column.

And same if we're looking for extra ones, we know that we're going to have to regroup here, and so we can exchange 1 ten for 10 ones.

So, I'm going to show you this question with the dienes.

This is the only question this lesson I'm going to go through in this amount of detail.

But I think it's really useful to show you with the dienes what regrouping and exchanging actually looks like.

So we'll take this question quite slowly.

I'm sorry if that means that I'm going a little bit slowly for you but it won't do you any harm to remember what it actually looks like when we regroup and exchange.

So let's get our dienes out.

If you've got some online dienes you can use, please get them so that you can see this question 423 - 185.

If you haven't don't worry, we'll go through it together.

So we've got 4 hundreds.

How many tens do I need for 423? I need 2 tens and I need my 3 ones.

There I go, 423.

And I need to make 185.

And again, hopefully, you can see why that exchanging, that regrouping is needed for this question.

So let's get started.

We start with our ones and I can see I need to take 5 away from 3.

Now that looks like we can't do it because I don't have enough ones to take 5 ones away.

So what I do is I go to my next column, I go to my tens and I exchange 1 ten, so I'm going to get rid of one of those tens and I'm going to replace it with 10 ones.

Is that 10 ones? Yup, there we go, 10 ones.

Then I can take away 5 ones.

There I go, taken away my 5 ones.

Fantastic, now I move onto my tens.

Oh, again, I can see I've got more tens in my part than I have in my whole.

So I need to get some tens.

Where can I get tens from? Well, I can exchange one of my hundreds for 10 tens.

So bye-bye one of my hundreds and hello 10 tens.

Then I can take away those 8 tens that are in my part.

So I get rid of 8 tens.

Final thing to do is not forget the hundreds.

I don't need to regroup to take away my hundreds.

I do need to get rid of one of those hundreds.

And there's my answer.

So just to recap what I've done there, where I've needed to regroup because the value in my part is larger than that in the column of my whole.

So where at the bottom I've got my parts and my whole at the top, I've found my extra ones or my extra tens in the next place value column.

So I'd exchanged one ten for 10 ones, and I've exchanged one hundred for 10 tens, and that allows me to subtract accurately.

So moving on then there's my diene there in the top left, but here's column subtraction.

Here's how we do it when we write it out in this written method.

Now remember, like I said column subtraction is just a way of breaking down a more complicated, a bigger number into smaller chunks.

But it's really important when we do column subtraction that we do have those columns.

So we line up our ones, our tens and our hundreds, we draw a line underneath and that allows us to remember really clearly what we are taking away from what.

So the number underneath comes away from the number at the top, even if that's a bigger number.

Sometimes it's tempting, like if I look at my ones here, sometimes it's tempting to do 5 - 3.

But that's not going to get me the right answer.

So do when you see that make sure that you're subtracting in the right order, and that when you do need to regroup, you do it.

So I can see here that I need to do 5 - 3.

I need to regroup.

I need to get some more ones from my tens column.

So by 5, 5, 2 tens, you're only one 10 now and the other 10 has moved over into my ones column.

So I've taken a 10 from my tens column into my ones column.

So I've got an extra 10.

So 3 has had an extra 10 added to it, so 3 + 10 = 13.

Now I've got a number that I can subtract 5 from, 13 - 5.

How would you do that question? Well, let me think, 13 - 5.

Right, I'm going to take 3 away first, that gets me down to 10.

And I know the 5 that it is 3 + 2.

So I've already taken away my 3, I've got 2 left to take away, 10 - 2 = 8.

I know from this question and my diene, that I'm also going to have to regroup my tens.

I've got one 10 left now and I need to subtract 8 from it.

So I need to get some more tens.

I get those tens from my hundreds column.

So I don't have four hundreds anymore, I have only got three hundreds in my hundreds column, and that hundred has moved into my tens column.

Now, there's a really important thing to remember here.

I've got rid of two, I've only got one 10 left.

So when I moved the other 10 over, I've now got 11.

Be careful not to fall into the trap of thinking that you've got 12.

So this is the lesson where we are regrouping in more than one column.

So it can become a little bit complicated, but when you've crossed a number out, you can't go back to it again.

So do actually cross it out and make sure you remembered that that's gone.

I haven't got two tens anymore, I've got one.

And then when I move the hundred over, I've got 11.

So in my tens column my question is 11 - 8.

How would you do 11 - 8? Well, I would think that I know 10 - 8 = 2, 11 is one bigger than 10, so my answer will be one bigger than 2, my answer is 3.

In my hundreds column I just need to remember that I've got rid of the 4, it's gone.

I've only got 3.

Another mistake that people fall into is they've done all their regrouping perfectly, they've exchanged, they've crossed things out, but then when they get to the end, they forget that that 4 or whatever it is, has gone.

The 4 has gone.

It's not 4 - 1, it's 3 - 1.

And in my hundreds column I've got 2.

And now I've answered that whole question.

The final thing I would do is just look at my question, and look at my answer.

I had 400-something - 100-something, I've ended up with 200-something.

That seems like a reasonable answer, and the number's got smaller.

I would just have one more check just to make sure I haven't made a silly mistake.

Okay, let's go through another one together then.

Here are the dienes that represent 313 and 154.

The dienes again, make it really clear that I'm going to have to regroup in my ones and my tens to answer this question accurately.

Let's see what that looks like with column subtraction.

So for my first question, obviously, I'm starting with my ones.

I need to do 3 - 4, I know I need to regroup, I know I need to find some more ones.

I need to find those in my tens column.

So I take one ten every time but I take one hundred every time.

But I've only got one in that column.

So that one is going to move into my ones.

And my 1, if I've got 1 and I take 1, I've got 0 left.

And my 3 has become 13, and in my tens column I've got 0.

I know that is going to become an issue when I move onto my tens column, but don't worry about it for now, just answer the ones column.

So I've got 13 - 4.

Let me think, 13 - 4.

Well, 13 - 3 would have been 10.

One more gets me to 9.

Okay, in my tens column I've got 0 and I have to take away 5.

Where am I going to get some extra tens? I've got to get them from my hundreds column.

So bye-bye three hundreds, I've only got two hundreds now because one is moving over into my tens column.

10 - 5, well, I can do that one.

I'm really confident in that 10 - 5 = 5 because I know that 5 + 5 = 10.

And then again, just in my hundreds column, I'm going to just be really careful and remember that it's not 3 - 1, it's 2 - 1 = 1.

And again, I would just check the answer carefully.

I had 300-something, I had 100-something I was taking away, I've got 100-something of my answer, that looks reasonable, it's got smaller.

Okay, your turn, pause the video here.

Use dienes if you would like to, but even better if you can just do your column subtraction.

Take as long as you need.

Let's see how you got on.

Hopefully, you saw that you needed to regroup from your tens, to get 12 - 3.

Oh, that's my three times table, isn't it? 12 - 3 is in my three times table, I need to go back one in my three times table.

So what comes with before 12 in my three times table? It's 9.

Right, I need to regroup again into my tens.

So 9 hundreds go and change the 8, and then I've got 13 in my tens.

13 - 6, well, I can split 6 into 3 and 3.

Take away the first 3 gets me to 10, Take away the second 3 gets me to 7.

I've got 7 in my tens column.

And then just remember for my hundreds that it's not 9 - 5, it's 8 - 5.

Really well done, everybody, if you got that right answer on your own, 379.

Okay.

Let's check this answer together.

Let's go through and have a look at what's happened here.

So, the first question should be 2 - 3.

What do you think they've done instead though? I think instead they've fallen into that trap of thinking, I think it'd be easier if I did 3 - 2, instead of the right thing which would have been 2 - 3 and doing some regrouping.

So straight away there when I check in the order I would do it in, I can see they've made a mistake in their ones column.

So that will be impacting the tens as well.

So let's have a go at doing this properly.

We need to regroup from our tens.

We've got 12 - 3 = 9.

We then need to regroup from our hundreds.

Okay, we've got 11 - 8 = 3 and then 8 - 5 = 3.

Okay, have a look at this question.

This sometimes gets called regrouping to regroup, which seems quite wordy but can you see what we might need to do to answer this question when it comes to column subtraction? If we start in our ones we know that we need to regroup because we need to do 2 - 1.

But then if we look at our tens column there's nothing to regroup from, there's nothing in the tens column.

So I'd have to go to the hundreds and regroup from there.

Now that's perfectly fine you can do that, and a lot of the time you will get the right answer.

So let's have a look at what this looks like.

Like I said, I need to regroup in my ones but there's nothing in my tens, so I need to go all the way to my hundreds.

So 400 goes and turns to 3.

I can then move that hundred into my tens.

You can't skip your tens and move it straight into your ones.

The ones is where we want it, but it has to come via the tens.

You can only move them one column at a time.

So my 0 becomes 10, I've added 10 tens to it, so now I've got 10 in my tens column.

Then I can cross that out and make it 9, so that I have one to move into my ones.

Now that might seem quite involved, you've got to do a lot of crossing out and rewriting.

And when we do that there's opportunity for errors to creep in.

I don't mind doing it this way, but I know some people would prefer to use a different method and that's absolutely fine.

I can then go through and answer the question quite accurately, 11 - 2 = 9, 9 - 2 = 7, and 3 - 1 = 2.

But you might feel like when you see a question like this, maybe where you've got zeros when you know you need to regroup, you might want to look for a different strategy to answer the question.

So here's the question, 401 - 122.

One strategy you might use to answer this question instead of using column subtraction might be like this.

If you don't like this strategy that I'm going to show you, please feel free to ignore it.

I just want to show people that there are different strategies.

So the first thing I did was change the numbers a little.

Instead of 401 I just took it down to 400.

I can't forget that 1, I'm going to need to add it back on at the end.

But just to make it a bit easier for myself, I'm going to take it down to 400.

400 - 100 = 300.

I can then do 300 - 20 = 280.

I then can take away my other 2, so now I've got 122, I've split up my part into 122, I've subtracted them all separately.

And then the final thing is I can't forget that there needs to be that 1.

I ignored the 1 at the beginning, 401, I just need to put it back on again at the end.

And again, that gets me the right answer.

Common subtraction is a tool, you use it when it's useful to use it.

If you find, when you have a question like this, that you don't think it's useful, that's up to you to pick the most efficient strategy.

Okay, on that note, complete your independent work.

Make sure that you're picking the most efficient strategy to get the questions answered.

Okay, I'm going to give you the answers here for Part A.

I'm not going to go through them in too much detail, but well done if you used some column subtraction on some of those questions, there's certainly a lot of regrouping needed in some of them.

But some of them don't require any regrouping.

And well done if you could see that.

So for example, 923 - 513, really well done if you did that one mentally, or if you used a slightly different written strategy to work that one out.

Okay, Part B, again, for that question, you might have decided that actually column subtraction was not quite the right strategy.

You have wanted to change the numbers a little, and then readjusted them to do that subtraction question.

Any strategy you've used is absolutely fine, as long as it gets used to the right answer.

Okay, and finally, can you spot the mistake here? What mistake do you think was made in answering this question? Well, they've done really well, they've done regrouping in their ones and their tens to make sure they have got the right number answered in their ones and their tens.

What's frustrating for this answer is it's actually, when it comes to the hundreds that they've made the mistake.

The 2 should have been crossed out and written as a 1, and then the answer would be 0, 1 - 1 = 0.

So like I mentioned earlier in the lesson, sometimes people lose concentration when it comes to the last parts of these column subtraction questions.

So well done if you spotted that error.

The right answer is just 89 not 189.

Okay, finally time for you to complete your exit quiz, so see how well you got on with today's learning.

Really well done, everybody.

Bye-bye.