Intro Quiz: Adding two 3-digit numbers (regrouping in multiple columns)

Video: Adding two 3-digit numbers (regrouping in multiple columns)

﻿Hello again, I'm Miss Brinkworth I'm going to be your teacher for this addition math lesson today. So if we look at our learning objective, what we're doing today is that we're adding together two three digit numbers and today we're going to be regrouping in more than one column. Don't worry, all of this is going to become clear as we go through today's lesson. Let's just look at what our agenda is for today. Firstly, we're going to have a look at some mental strategies. Even when we're doing written methods, we're still using mental strategies to add together the values in each column. So let's recap those strategies. You're then going to have an opportunity to have a look at what regrouping looks like when we've got dienes. As the lesson goes through, we'll try and move away from the dienes and just move on to solely column addition and regrouping through column addition, and then the independent work and the quiz at the end, will give you a chance to practise what you've learned and see how well you can get on in that quiz. See how many points you can get at the end of the lesson. So, all you're going to need is a pen or pencil and some paper. Please do make sure you have that for this lesson as it's really crucial. If you can find some square paper, that would be even better. Don't worry if you can't though. It would also be quite useful if you could find some online dienes. So dienes are the blocks that we use during lessons when we're talking about addition and subtraction and we can move things around and regroup. We're not in the classroom together, unfortunately, but it would be useful if you could find some online, so speak to a parent or carer to see if they can help you find someone online and use them during this lesson. If you can't find them, please don't worry. I will put them all on the screen for you as well. So pause the video. Take as long as you need to find your equipment for today. Okay should we get started. So here is your warm up. Now two these can be answered mentally. There's no regrouping needed and you should be able to do them all in your head. Two of them will require some regrouping. So it's up to you to decide. Can you tell by looking at it, is regrouping required or whether you can just do them in your head? So pause the video, take as long as you need to answer these questions. Let's see how you did. We're looking at that first question there 583, add 262. I can see you do need regrouping. I can see that because if I look at your 10s columns, you've got eight and six, they add up to more than 10. So you'll need to regrouping and probably to write down some column addition to answer that question. Well done, if you are able to do that and get the answer. So we've got two add three is five in our ones column. Eight add six is 14. So you can regroup, one of them into the hundreds, we've then got five add two is seven, not forgetting that we moved one over from our tens because it's 845. Where are your other answers? You shouldn't have needed regrouping or column addition for that question as the numbers don't go over 10 in each column. This one you don't either but for your final question, you needed some regrouping and you probably needed to do it with a method. So those have got the circle around. Really well done if you got those answers right. Let's move on then. Pause the video and just have a think about which of these you think is the odd one out. Bear in mind that we're talking about regrouping today. Okay, there's not really a right or wrong here. All I said was find the odd one out but I did mention that we all talked about regrouping. So the one I've highlighted as the odd one out is this question here. I wonder if you can tell why. Unlike the questions we looked at in the warmup, this question needs you to regroup in more than one column. What I mean by that is that the ones and the tens add up to more than 10. So when we add together all ones, we're going to get a number bigger than 10 and when we get out together our tens we're going to end up with a number bigger than 10. So this is what today's lesson is all about. Addition questions with three digit numbers where we need to regroup in more than one column. Shall we look at how we do that? Let's have a look at how we'll represent that with our diene. Now, it's not always possible in real life, obviously to get our dienes out, but it does help us at the beginning of this lesson to visualise why we regroup and what regrouping actually looks like. If you have managed to find some online dienes please feel free to use them alongside me in these next few questions. If you haven't managed to find them, don't worry. I'm going to put them all up for you to have a look at. So 176, how am I going to represent that with my dienes? Well, I've got 100, one 100. I then need some tens. How many tens are there in 176? Well, 70 is 7 tens. So there are my 7 tens. One two three four five six seven. I then need my ones, and there are 6 ones in 176. Okay, I've then got 247, 2 hundreds, and 1 2 3 4 tens, and 7 ones. Okay, now it's just about adding them together. Now, when we're doing addition like this, it's really important we start by adding our ones first, then our tens then our hundreds. Why do you think that might be? Well, the reason is because we're regrouping, we've got to make sure that we've got that column free to regroup into. So we start with the smallest value, which is our ones so that if we need to move those into the next place value column, we can do that. So for our ones, we're doing six add seven. How would you work out six add seven? Well, what I always think about is I love the question five add five. I feel really confident that five add five is 10. Six and seven are quite close to five. So I can use that back to help me. And what I do is I know that six has got one more than five and I know that seven has got two more than five. So if I added my five and five together I've got 10 and then I add together my two and my one, I've got 13. So six add seven is 13. Maybe you think about a different way of adding six and seven together. Maybe you do make 10, for example. So you start with six and you think, oh I need four more to get from six to 10. So I've used four, and then I've got three leftover from seven to do 13. Whichever strategy you use doesn't matter as long as you get the right answer, which is six add seven is 13. How am I going to represent the team of my dienes then? 13 is bigger than 10, I can see that 'cause it's got two digits in it. It's a two digit number 13, any two digit number while we're doing our column addition like this today requires us to regroup, move into the next place value column. So with my dienes with 13, I'm not going to represent all of them with 13 ones. 13 has got three in the ones column and one in the 10s column. So I'm going to regroup 10 from my 13. I'm going to take it out of the ones column and put it in the 10s column. What does that look like with my dienes? Well instead of 13 ones, I have three ones and one 10. Moving along to my tens column. I've got seven add four in that original question there. I've got seven in 176 and I've got four in 247. Okay, seven add four. How would you work out seven add four in your head? Well, I think about seven add four, I think seven add three. That's a fact I'm really comfortable with because that's a number bond. Seven add three is 10, so seven add four, which is one more than three must be 11. So I've got 11 tens. 11 tens, that's 110. So again, I'm going to regroup because I've ended up with the number 11, which is a two digit number, which requires me to regroup. So 11 tens, 110, what does that look like in dienes? I'm not going to have 11 green tens, I'm going to have 110 like this. 10 of my tens get to regroup into 100. I then need to add together my hundreds, There's no regrouping needed there because I've got three hundreds. Okay, let's see what that looks like for column addition then. How would we place that into column addition? So we said that six add seven is 13 and we said that 13 has got three in the ones column. So we should have I've just circled there on the dienes where I've had to regroup just so you can see that while we're doing our column addition. So 13 has got 3 in ones column. I then have got to make sure I write that one underneath my tens and I can't forget about it. I've got to add it on now that I'm adding my tens up. So if we said that seven add four is 11, but I've got my one to add on there as well, really important. So it's 12. I've then got the one coming into my hundreds and I add that together with two and one to get my final answer, 423. So that's how I do it and I can see that I needed to regroup in two columns because I've got a one sat under my tens and my hundreds. Let's go through it again with a different question. Here we've got 625 add 426. Can you take a moment to get that question out with your dienes? You don't need to do anything with it. Just see if you can get some dienes to look like that, to represent that question. Okay, hopefully you'll dienes look something like this. So 625, 420, sorry 425 and 625 and 426. Okay so let's add these together. I can see that I'm going to have to regroup in my ones because I've got five add six. Five add six is 11, I know that because five add five is 10 so five add six must be 11, one more. And that's how I'm going to represent 11, one 10 and one 1. My tens then, I don't need to regroup, I've only got four of them. But I do need to regroup my hundreds. I've got six and I've got four which is 10. 10 hundred, 10 hundred is 1,000. So I've regrouped my 10 hundreds into 1,000. So let's have a look at what that looks like in my place value columns for my column addition. So there I've got my dienes to remind me, ad I'm going to circle I have to regroup. Five add six is 11, so one in the ones and one under the tens. Two add two is four, add one more is five and then six add four is 10 which goes like this to show that it's 1,000. Okay, and there's where I've regrouped. Your turn then, I'll give you the dienes to represent 369 add 166. If you want to just for now represent the dienes, great. If you're confident to move onto column addition to answer this question, brilliant. Pause the video and take as long as you need. Let's see how you got on. Does yours look like mine, I wonder. So we've got nine add six. I'm going to have to regroup aren't I? Nine add six, how would you work out nine add six? I'm going to take one from my six and add it to the nine to give me 10 and then I've got five at left over. So nine add six is 15, To represent that in dienes I'm going to have one ten, and five ones. My tens, I've got five add six. Five add six is one bigger than five add five. That gives me 11 which means I've got 110. So that's how I'm going to represent my 110 in dienes and then my hundreds don't require any regrouping. Let's move that over then to my column addition. There's my regrouping in the ones and the tens. So five, sorry. Nine add six is 15. Then I've got six add five, add the one at the bottom, it gives me 12. And then I've got five there in my hundreds. Really, really well done if you could see that and you got that answer, that's brilliant. There's your regrouping. Okay one here I'd really like you to have a go now without using your dienes. So start with your ones and regroup what you need. If you're counting, you can see that I've given you a little bit of a clue where some regrouping is needed. So pause the video and have a go at answering that question. Let's have a go at going through the answer. So the first thing thing you should have done is eight add five or five add eight. It doesn't matter which order you want to do that in. Five add eight or eight add five. I think I prefer having the big number first. So I do eight add five and I work out eight add five as eight needs two to get to 10. So I'm going to take two from my five to get me to 10. I've got three leftover so eight add five is 13. How do I write that in my column addition though, it's important for you to see the three. Oh, I've made a mistake. It should be a three in the tens column there and not a two, so first mistake. And then a one under the tens. Then I've got three add two in my tens is five, add the one is six. Oh I got that one right at least and then seven add four is 11 which means I moved my one across to 1,000. So the right answer is 1,163. I made a mistake on that one. Okay, let's check this out so then. Let's see if I've made another mistake, Have a look and see if you can see any mistakes in this answer. Okay, well, when I look at the answer, I think that's too big. I've got 500 and something add 200 and something. I wouldn't expect my answer to go away over 1,000 so that's my first clue that there's a mistake here. Also, when I look at the numbers that they've regrouped, that they've moved across those little numbers at the bottom in red, I could see a five. We wouldn't expect to see that. So I think they've made a little bit of a mistake here. What do you think they've done? Well, instead of, well, let's have a think. We'll start with the ones and check it methodically. Seven add three is 10 and that's what they've written in. Zero in the ones, and one moved over to the tens, that's fine. Six add eight or six add eight is 14, add one more is 15. So I think they've got their five or the one the wrong way around. The five should've gone in the tens column and the one should have gone underneath the hundreds column. So here's the right answer and that looks a little bit more reasonable, doesn't it? That we would end up in the 800s when we've added together 500 and something and 200 and something. Okay, time to pause the video and have a go at your independent task. Take as long as you need and please come back together for the answers. Let's see how you got on. So I'm not going to go through the answers in huge detail. I'm hoping that you did some column addition to work these out and that you were regrouping carefully. I'll give you the answers in a moment to have a look at how you got on. Okay, well very well done if you got all of those right. We all make mistakes when it comes to column addition so please don't worry if there's one or two creeping in. The important thing is to line up your columns correctly and take your time. Okay, what could the missing numbers here be them? So we need something add six is going to give us one in the ones column. Well, the only number that can be is five because we're looking for 11 and the only number that I can add to six to get me five, sorry to get me 11 is five so that number's got to be five. Here again, I don't need to regroup. So as long as you've got, as long as you've got a number smaller than six that that's fine because you don't regroup from your tens into your hundreds. You can see that 'cause there isn't a one under your hundreds column. And then here, this number could be different. Again, it needs to be bigger than four, because we need to regroup into the hundreds, but you might have written five, six, seven, eight, or nine, and you'd have a different number at the top and a different number at the bottom there. So yours might differ. What if we look at this question then? What mistake do you think maybe we've made here? I think what they've done, they've got the three in the right place there. Six add seven is 13. I think what they've done is forgotten to move to regroup their one into the tens. So they've done two add four is six, but it should be a seven in the tens because they should have regrouped one over from the ones. Okay, time for your final knowledge quiz. Let's see how well that learning's gone in. Fantastic work today, everybody. Well done, bye bye.

Worksheet: Adding two 3-digit numbers (regrouping in multiple columns)

Exit Quiz: Adding two 3-digit numbers (regrouping in multiple columns)

Completed: Adding two 3-digit numbers (regrouping in multiple columns)

This lesson will look at using column addition when a number requires regrouping in more than one column when adding.

Maths

Adding two 3-digit numbers (regrouping in multiple columns)

Introductory Quiz

Video

Worksheet

Final Quiz

Lesson Complete