digit/s in the 'part' are larger than those in the same column in the 'whole'

Which of these calculations requires regrouping?

True or false this questions has been answered correctly? 456 - 147 = 311

Has this question been answered correctly? 526 - 309 = 217

Subtracting 3-digit numbers (regrouping tens to ones)

Key Stage 2

Maths

Addition and subtraction

True or false, this calculation needs some regrouping? 54 + 23 =

Which of these calculation needs regrouping?

Check this answer - is it correct? 596 + 122 =   6118

﻿Hello, there, I'm Miss Brinkworth. I'm going to be going through this math lesson with you today. Let's have a look at our learning objective. So today what we're doing is we're subtracting three digit numbers. And today what we're going to need to regroup is involving our 10s and our ones column. So let's have a look at our lesson agenda. So we're going to start by recapping some mental strategies. It's really good practise to just get us thinking about subtraction again, but it's also going to be useful when we're subtracting each of those columns we will need to do mentally. And then we are going to have a look at some dienes. So just the blocks that we use in class to see how they can help us visualise regrouping. We're going to use column subtraction to regroup. So we're going to talk about our written method, how we write that out to make sure we get a really accurate answer. And hopefully by that point of the lesson we won't need the dienes anymore. We'll make that connection between the dienes and our column method and move on to just using the column method later on in the lesson. And then you'll have that independent work at the end where you'll have as much time as you need to practise your new skills. And then there's a little quiz just to see how many questions you can get right. Okay, so for today's lesson, pen or pencil and paper is absolutely crucial. What would be useful are some online dienes. So please ask a parent or carer to help you find some online dienes and use them throughout the lesson. Pause the video here, take as long as you need to find your equipment. Great, hopefully you're ready to get started. Let's start with our warm up then. So can you please decide which of the these questions you can answer mentally? So they're all subtraction questions but you shouldn't need column subtraction for all of them. So hopefully you can answer most of them mentally. That means you don't need to write anything down, you can do them in your head. But a couple, or one or two, will need some column subtraction. So have a go at answering them all, but think carefully about what strategies you needed to use to answer them. Pause the video for as long as you need for your warmup. Great, so hopefully you've been able to answer some of these mentally. And those questions are the ones where the part, so the amount that we are subtracting, each digit in that number is smaller than each of the corresponding digit in the whole. So we haven't had to do any regrouping. We can hopefully just use our mental strategies to do three subtraction sums. Our ones, our 10s and our 100s and get our answer. So we look at that first question, for example, 384 take away 263. So we always start with our ones, we start with the smallest unit first, so we start with ones. And so our first sum, our first mental sum that we need to do for that question is our ones, we need to do four take away three. Don't become confused about which order to do them in. We are always taking away the smaller number from the larger number, but sometimes what happens is people think that just because the digit is smaller, they get their whole and their part confused. So just make sure that you've got them in the right order and that you're taking the right number away from the right one. We'll talk about that a bit more during the lesson. So for the first question, we're doing four take away three, in the ones. So that gives us one, one in our one column, four take away three is one. We then got eight take away six. Your eight is just two more than six, I know that because of my two times table, so I've got two in my 10s column. And then I've got three take away one from two, so for that first question you should have 121. Well done as well, if you managed to answer these other questions mentally. So you didn't need to do any writing down, and you didn't need to use your column subtractions because those questions don't require any regrouping. All of the digits in the part are smaller than the corresponding digits in the whole. So you haven't had to do any regrouping. This last question, where the answer hasn't appeared yet, 361 take away 227 does require some regrouping. Hopefully you can see that that's because in the ones column we've got seven in our part and we've got one in our whole. So one take away seven requires some regrouping. Well done, if you did have a go at that question and get the answer, but if you didn't, please don't worry, because that's exactly what we're going to be learning about in this lesson. So let's go through and have a look at what we mean. Pause the video again here, have a look at these bar models and think about which one might be the odd one out. Okay, there's not really a right or wrong here. You can decide that things are the odd one out for whichever reason you like. Maybe one's the odd one out because it's all purple. Or maybe that one's the odd one out because it's got some lines going through it. The one I selected as the odd one out, going along with our learning objective about regrouping is this one here. And that's because this one requires us to regroup. And that's because we can see that in the ones we've got a six in the part and a three in the whole. So we need to regroup to complete that sum, okay? So if we look at our question that requires regrouping, 253 take away 126. We can represent it with our dienes and that's what I've done here. 253 take away 126. If we look at this again, what we need to do is exchange one ten for 10 ones. So you can see, both of those sitting on top of each other there, there's the two different representations of 253. The only difference is that one of my 10s I've split up into 10 ones. And that's exactly what we do when we're regrouping. Because we don't have enough in that column, in that place value column, in this case our ones, we use some from the next place value column, in this case our 10s. So here it is just represented again. Because I'm taking away six in the ones, in 126, I need to regroup for my 10s. Let me show you what that looks like then. So we're going to take this question really slowly. I'm going to show you what it looks like in dienes and then in column subtraction. So if this is something you know quite well, please bear with me, but it won't do you any harm to just look at how we use dienes to show us what we mean by regrouping. So firstly I need to get my dienes and if you've got some to use online then please feel free to make them as well, and go through this question with me. So I'm making 253, so I need two 100s. And then how many 10s do I need? I need five 10s for my 50. And then I just need my three ones, 253. And I'm taking away 126. And when we see it like this, represented with our dienes, it becomes really clear that it's tricky to take away six ones from three ones, okay? That's what's great about dienes, it's a real visual way of seeing things. So like I mentioned earlier in the lesson what we need to do is exchange one of our 10s for 10 ones. It's the same, I'm just representing it differently. Then I can go about taking away my six ones. One, two, three, four, five, six. The rest of the sum is quite straightforward. I need to take away two 10s and one hundred. And what I'm left with is 127. So I've just taken that amount on the bottom row away from the amount on the top row. And because I had more ones to take away in my part than I had in my whole, I exchanged one ten with 10 ones. Let's see what that looks like then with column subtraction. But here you can see I've written out the sum again. I've written it out differently now. I've put it into columns, that's what column subtraction means. So I've got my ones sat perfectly one above the other. And my 10s and my 100s. I've got my bigger number first, then my smaller number. My whole and then my parts. That means I don't get confused at what I'm subtracting from what. I know that my bottom number is being subtracted from my top number. Even if the number is bigger and I need to do some regrouping. You can see I've got my dienes representation there. And just to remind you, that the reason we are regrouping like this is because we have a bigger number in our ones column for the part than we do in the whole. So six, so we going to take away six. So how do we do it then when we're just doing column subtractions? Well, what we did was we regrouped from our 10s, if you remember, I moved one of my 10s into the ones. So that's what I do when I'm doing column subtraction. I change one of my 10s into ones. So I get rid of five 10s. I haven't got five 10s anymore. I'm going to use one of them, so I've only got four 10s. And that 10 moves over into my ones column. So instead of having three ones now, I've got 13. I've added one lot of 10 to my three. Hopefully that's clear for you. So 13 take away six. How would you work out 13 take way six? What would your mental strategy be? Well, I would do three first to get me down to 10 and then I'd do three more. I know that six is three and three, so I can take away three and then take away another three. So if I take away three from 13 I get to 10, take away another three, I get to seven. Okay, important thing to remember now when I move through to calculating my 10s, is I need to remember that I've only got four 10s, not five. Five has been crossed out, it's not there anymore, because I've used one of those 10s to calculate my ones. So just bear that in mind, it's not five take away two, it's four take away two. Four take away two is two. My 100s haven't changed, two take away one is one. And there's my answer. Okay, so what to remember is that once you've crossed out your number and written a new one, make sure that that's the number you're reading when you go through your calculation. As well you can see I've circled the one there. Just make sure that you're bearing that in mind when you're subtracting from your ones. Okay. What question do you think this bar model is showing? Well, we've got the full amount, haven't we? We've got the total there, the whole is 343. We've got a part which is 126. And what we're looking for is the other part. So this sum is 343 take away 126. So we're just going to go through one more subtraction sum again with our dienes and then with our column subtraction, so you can really clearly see how we set it out, and why we do it that way. So here's our dienes again, there's 343 and there's 126. And like I say, with your dienes it then becomes clear, "Oh, look, I've got a lot of ones in my part, and so I'm going to need to regroup to take that away from my whole." Let's have a look at what that looks like. I've got 343 take away 126. I need to exchange one of my 10s with 10 ones. I need to move 10 of those ones into my ones column. So I'm going to get rid of a 10 and exchange it for 10 ones. Okay, once I've done that, I can now complete my sum. So I need to take away six ones. One, two, three, four, five, six. Don't forget to do the rest of the sum though. Just because you've had to do that exchanging and that regrouping, sometimes we can get quite pleased with ourselves and think, "Oh, all done." We've still got to take away our 10s and we've still got to take away our 100s. So I've got to take away two 10s and one hundred. And there's my answer. So I've got two 100s, one ten, and how many ones have I got left? It looks like seven. Let's go through then and have a look at what that looks like with our column subtraction. So there it's just showing you again, why I've had to regroup. I've had to exchange one of my 10s. And then if you look at this sum, I've got three take away six. Now, a trap that some people fall into, a mistake that some people make, is that they might do six take away three, instead. And I can totally understand why people do that, it looks easier, doesn't it? Why do three take away six which involves this regrouping, when you could just do six take away three? But as long as you remember that you're always taking the bottom number away from the top number, as long as you've laid out your column subtraction properly, hopefully you won't fall into that trap. And although it might seem easier to take three away from six, it will get you the wrong answer. So do exchange when you need to, do regroup when you need to. So we need to regroup from our 10s, we need to take one of our 10s away. I've got four 10s at the moment, you can see in 343. So if I move one to those 10s inside my ones I'm not going to have four 10s anymore. I'm only going to have three 10s. And one of my 10s has moved over. So I've made the number 13. 13 take away six, well, if it was 12 take away six I'd get six 'cause I know six and six is 12. 13 is one bigger than 12, so I'm going to end up with a number one bigger than six. One bigger than six is seven. I've then got three take away two. Again, remember that you are now looking at three not four, four is gone. It's three take away two. Three take away two is one and three take away one is two. And there's your answer, okay? So that's just showing you where we've regrouped. Okay, pause the video here and see if you can have a go at this question. If you can do it just with the column subtraction which I've set up for you there, well done. But if you'd like to use your online dienes at any point throughout this lesson, please do so. Pause the video for as long as you need for that question. Let's see how you got on. Hopefully you didn't fall into the trap when you started with your ones of doing nine take away three. It is three take away nine, so you do need to regroup from your 10s. So we're going to get rid of eight and make it seven. We've then got 13 take away nine. Well, nine is nearly 10. If it was 13 take away 10 it'd be three, but it's one more than that. So it's four, and then I need to remember that it's seven take away five, not eight take away five. So seven take away five is two in my 10s. And then my 100s, two take away one, leaves one. And there's the regrouping that you've done. Really good, okay. Let's have a look at this answer then. So when you're asked to check an answer, you should go through it just like you were doing the question. So we're going to start with our ones. Now we can't see the regrouping that they've done here. So maybe they have made a mistake there as they haven't written out any regrouping, I can't see any of those ones or that crossing out. So maybe there is a mistake with the regrouping, but let's have a look. So we need to do by five take away six. So we're going to need to regroup from our 10s. So they've got rid of their six in the 10s and moved one over. So 15 take away six. Yep, 15 take away six is nine. Looks like they've got the right number in their ones column. They then should be doing five take away four, which would give them one. But I think maybe because they haven't crossed it out as they've gone through their regrouping, they've forgotten that they haven't got six 10s anymore in their whole, they've only got five. So they've made a mistake there in their 10s column, there should only be one and they've written two. The 100s looks okay. But I can see they've made that mistake there. 'Cause they haven't done this, and so they've made a slight mistake there. The right answer should be 119, not 129. Okay, time to pause the video and have a go at the independent task. Just before you do, this is what your independent task looks like. It's just a series of subtraction questions for the first part. They don't all require column subtraction. So it's up to you to choose the best method, the most efficient, that means it's accurate, but it's also as quick as possible. So have a think about whether column subtraction is needed. It might be possible for you to do some of them mentally. So pause the video here and have a go at your independent task. Great, let's have a look at how you got on. I'm going to give you the answers to these questions in a moment, so have a look through them. Really, really well done, if you've got all those questions right. And even better, if you were able to see when questions didn't require any column subtraction. Like that last question, for example, 354 take away 122. I can see that that doesn't require column subtraction because the digits in my part, one, two, two, are smaller than the digits in my whole three, five, four. So I shouldn't need to do column subtraction. Really, really well done, if you saw that. Okay, having a look here then, how did you get on? Well, the first box there for that first question needs to be a number bigger than six. As long as you wrote a number bigger than six you're fine. So you could have written seven, eight or nine in that box. The reason that number needs to be bigger than six, is because we know that we need to have three in the 10s column because we need three take away, it's only three take away three that can give us zero. So that one's got to be three. And the one in the 100s column has got to be seven. And well done as well if you saw that there was a problem here on the second question. It should have been a zero in the 10s column, not the one. Really, really well done, if you were able to see that. Okay, it's just time for the quiz now to see how well you've got on with today's learning. I'm really impressed with all that hard work you've put in. So have a go at the quiz and enjoy the rest of your learning for today.

Subtracting 3-digit numbers (regrouping tens to ones)

Subtracting 3-digit numbers (regrouping tens to ones)

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UnitMaths / Addition and subtraction

Maths