Which of these calculations requires regrouping?

Adding two 3-digit numbers (regrouping in one column)

Key Stage 2

Maths

Addition and subtraction

Does this look like a good estimate? 720 - 30 = 500

Does this look like a good estimate? 575 - 159 = 415

What is an estimated answer here? 604 - 350 =

What is this number rounded to the nearest 10? 996

﻿Hello! I'm Miss Brinkworth. I'm going to be going through this maths lesson all about addition today with you. Let's have a look at our learning objective. We are adding two 3-digit numbers, and that means we're going to be regrouping in one column. So what this means is, we're going to have two 3-digit numbers, and we're going to be going through a written method of adding them together. So we're not going to be doing them mentally in our heads, we're going to be writing them down, and while we're going to be writing down our answer what's going to happen is when we get to one column, there's going to be a number in it which adds up to more than 10. We're going to need to regroup that I into the next place value column moving left, and that's what today's lesson is all about. Don't worry it will all become clear as we go through, I promise. So let's have a look at what we need for today's lesson. We're going to do the agenda first. We're going to start with some mental strategies just to get you thinking about adding again, get your head into the right place. We then going to use the Dienes to visualise what we mean when we talk about the regrouping, and why we need to regroup, and hopefully when you have that practise with the Dienes, you can just move on to doing your column written addition, and you won't need the Dienes for the second part lesson, and then you will have that time for your independent work. You can take as long as you need I have got those questions on your own come back together for the answers, and then you'll have the exit quizzes to see how many questions you can get right, right at the end of the lesson. So you will need paper and pencil that's absolutely crucial for today's lesson as we are doing those written strategies. So please make sure you've got a paper, and pen or pencil and some paper. What would be quite useful as well is online Dienes. Now if we were together in the classroom we would have the Dienes, the little cubes that we use when we're adding and subtracting. Unfortunately, we're not together in the classroom today. So it will be really useful if you could find some online games. So speak to a parent or carer, see if they can help you find them, and use them throughout the lesson. If you can't find them please don't worry, you will be able to see mine on the screen. I'll pause the video here, take as long as you need to get your equipment together. Okay, let's move on to a warm up then. So here are some addition questions which I'm hoping you can do mentally, which means without having to write down any working out, hopefully you can work them out in your head. So there is six questions there. One of them I'm going to give you permission not to answer at this stage as I think it will be tricky for you to work out in your head. So that's the odd one out, can you find it? Have a go answering the other ones, so pause video here, and take as long as you need for that. Okay, let's see how you got on. So I'll just go through the first question with you, and then we'll talk about which one was possibly a little bit trickier. So the first question, 455 add 123. It's good to get into the habit at this stage of starting with your ones. So we add together five and three, that gives us eight, they are ones. Then we add together our tens, five and two gives us seven in our tens column, and then we've got four add one is five in our hundred columns.I hope you got 578. Well then if you were able to use your mental strategies to answer these other questions as well. This one in the middle here, this fifth question, is the one that was a little bit trickier. So that was the odd one out, it doesn't matter if you can get that question at this stage and there is the last one. So that question was the odd one out cause it did require some regrouping. It was probably tricky to do in your head. Don't worry if you found that one hard, that's exactly what we're going to be learning about in the rest of today's lesson. So it needed some regrouping, and that's our learning objectives of today. So let's have a look at this question together. One Sunday, in Edinburgh castle car park, there were 153 coaches and 366 cars. How many vehicles were in the car park altogether? Right. What kind of question is being asked there? Let's have a little drill down, and see if we can find the important information. What I really like to do when I'm thinking about word problems, is get a picture in my head. I'd like to see the car park, oh it's full, isn't it? There's 153 coaches. I don't know if I've seen that many coaches altogether, and 366 cars maybe it's a really hot, sunny day, and everyone's decided to go to the castle. So I want to see that. I want to see people driving around maybe trying to find a car parking space. I'm going to get that picture in my mind, and that makes it easier for me to work out what the question is asking. So if we have, the question is asking us, that we have these two amounts, and how much there're all together, well, I might draw out a bar model to help me as well. There are my coaches they are 153, and there are my cars, and in the green, and 366. Those are my two amounts, my two parts. That's my known information. I know how many coaches there are. I know how many cars there are. The unknown, the thing that I need to work out, the answer to the question, is the whole. How many were there altogether? So that's what I need to work out. How many were there altogether? So hopefully you can see that this is an addition question. Now I can write it out like this 153 add 366, or I could write it out in the other order it doesn't matter with addition, and in today's lesson feel confident to move them around. If you feel happier doing 366 add 153. That's perfectly fine. You're going to get the same answer no matter what order you do with them. Okay, so what's our strategy for today? So this is a point in the lesson where it would be useful if you got those online games. If you haven't been able to find them, just have a look at mine it's absolutely fine. So here's our question again, and I'm going to have a go representing it with my Dienes. So 153, so I'm going to have one of my hundred blocks, and then I need some pens to represent 153. 50 is five pens. So that's my five pens, and then I need three, three runs. There's 153 in green blocks. Now I need 366, and there it is, 366. So there's a total amount of things I need to add together to pull altogether to answer my question. Let's have a look at how we're going to do that then. Remember that we're regrouping, so really focus on that as I'm going through adding these things together. So let me add together my ones. Well, I've got three and six, now I'm going to end up with one two three four five six seven eight nine ones. No regrouping needed in my one, and then I've got my tens, and as you look at my pens hopefully you can see that five add six is 11. I'm going to have 11 tens. So what's happened there is that we group them, rather than having 11 green sticks, I regroup them into one ten and 100 because 11 tens is 110. So I've added my greens together, and I've changed 10 green sticks 10 tens or 100, and I also got one 10 left over, and then I add together with my hundred, and I've got one two three four hundreds that I need to add together, that is after one add three. So here's how I do an addition question with things, and there is my regrouping in the middle where I had 11 tens and instead of keeping them all in the green sticks, I've regrouped them, I've moved some from 10s to hundreds. Let's see what that looks like when I write it out. So there on the screen you can see my Dienes in the top left, and here's what it looks like for column addition. Now remember the column addition, it's really important that they get lined up brilliantly. So I've lined up my ones, my tens, and my hundreds. If they're not lined up perfectly, I make mistake every single time. So just make sure you're lining them up perfectly, and like I said at the beginning of the lesson, it's really important that we start with the ones. That's because if we regroup, we need to regroup into the next biggest place value column, and if we start in the other direction we're not going to be able to do that. So let's have a look what we need to do first. So my first question adding together my ones, three add six. What's three add six? Hopefully you can see that three add six is nine. It's my pen, wasn't it? It was in my pens I needed to regroup, and that's because five add six gives me a number bigger than 10. Five add six is 11. Remember I had 11 green sticks, so I need to write in 11, so I write in one in my tenth column, and one goes under my hundreds column, because 11 tens is 110. So I've got one in my tens column, and one goes into my hundreds column. I'm not finished there, I need to add together my hundreds, and this is where people sometimes make a mistake. They forget that they've got that 100 waiting underneath to get added together, and they just add together the three and the one. Though they ignore they're regrouping. So the answer isn't four in the hundreds column, It's five! Cause it's three and one and one. It was our pens there where we needed to regroup, and it's that, that I really want us to focus on today's lesson. That's where people if you make a mistake, if you get something wrong that will be where it is. So just focus really carefully on your regrouping today. Let's have another guide. Here's another question which requires some regrouping. I wonder if you can see straight away which column needs regrouping. Let's bring out Dienes out again. So we've got 207, four five six seven. my other number is 124. There we go. Where is regrouping needed in this question then? It's not the tens this time, is it? We've hardly got any tens, you can see the green sticks representing the tens there's not very many at all. It's the ones where we need to regroup in this question, and that's because seven add four gives us a number bigger than 10. So let's have a look at what that regrouping looks like with our Dienes. So we've got seven add four. Do you know what seven add four is? Well, I know that seven add three is 10. I know my number bonds to 10. So if seven add three is 10, seven add four or four is one more than three, say seven add four is one more than 10, it's 11. I'm not going to have 11 little yellow cubes though. I'm going to regroup into my pens. I'm going to have one pen and one one to represent my 11. I then need to add together the rest of my number, so I just pull down those two tens as there's no tens in 270 altogether, and then I add together my hundred to give me 300. Okay, what does that look like when we lay it out then in column addition? So there's my Dienes to remind me. So it was my ones this time which needed some regrouping, so seven add four we worked out as 11. So we've got one in the ones column and one less under the tens. With any section we add that together carefully. So two add zero is three, add the one is three, and then we get just anything different with hundreds just two add one. Okay, and you can see that that's where we have to regroup in our ones. Okay, your time I'm going to be nice, and give you the Dienes 356 add 126. Pause the video here, and take as long as you need to work out the answer to this question. Okay, let's have a look at what it looks like without Dienes, and if this as far as you got that's absolutely fine. So we've got six add six in our ones column that's going to give us a number bigger than 10. What is six add six? That's quite an easy one, isn't it? A lot of people know those and doublings. So it's six times two, isn't it? Six times two is 12. What does 12 look like with Diene? We're not going to have 12 little ones. I'm going to have one ten and two ones as my 12 altogether my ones. Then I'll pull my tens down altogether, and have my hundreds together too. Right there is that picture of Diene, if that's as far as you got, if you got Dienes that look like this, on that bottom row, well done. If you got this far, and started thinking about what that looks like in column addition, incredible, really really good work. Six add six 12. Let's look at where that goes. So in 12 two is in the ones column. So in our ones column we're going to have our two. The one meanwhile goes under the tens, and then we need to remember that carefully when we add our numbers together. Oh no! I've made a mistake. Five add two is seven, I've got to pull my one up. There should be an eight there, not a seven, and then three add one is three. No! Three add one is four. I've made a mistake there as well. The number should be 482, and well done If you saw that. I've made a mistake on my side so well done as well for getting that regrouping correct in your ones. Okay, your turn without being dishonest as you can have a go at this column addition question. Let's see how you did. Three add... Was quite nice for you here. If you look at the blue squares carefully, you can see that I've let you know which column needs to be grouping. It's not the ones because three add two is five, so that just goes in there like that. Four add eight is 12, so we need to put the two in the tens column and the one comes under the hundreds, and then adding those together properly we'll see five add two is not three, is it? Five add two is seven, add the one is eight. The correct answer is 825. Well done if you got that correct. Okay, let's check this out together then. Have a look and see if you think this answer is correct. Okay, let's have a look. Well six add seven is 13. So it doesn't matter if we've the right number in the ones column there because 13 has got three in the ones. Two add two is six, but it looks like maybe they forgotten to move their one from their 13 into that column. Add four add three is seven, so the hundreds column looks right. I think they've made a mistake in their tenth column here. They've forgotten to put that one in, because six add seven is 13. So they should have the one in there. The correct answer should be 773. Okay, time to pause the video, and have a go at your independent task. Take as long as you need, and then come back for the answers. Let's see how you got on. Here with the answer to the questions, I'm not going to go through them in too much detail. Really well done if you saw that the ones where the answer is needed at the beginning is exactly the same type of question. You really understand your equal sign, just means that each side of the equation needs to be equal. So well done, if you were able to answer those questions. They just required you to add the numbers together in the same way. Some of these required regrouping. They didn't all in every column, but well done if you got these answers right. I'll put them all up and leave them here for a moment, you need to see how you got on. If you did make some mistakes, just have a think about, maybe it was a regrouping after that? Especially ones and if you got that last question right where you needed to regroup three or hundreds and go into the thousands column. What about these questions then? So what could be our missing numbers? Well, as a part one, if you're looking for the missing number which is in that second part, so we've got the two parts, which we're trying to add together to find the whole. So 100 and something three, and we know that it's got to be bigger. It's got to be six or bigger. Why has that number got to be six or bigger? Well, because add four add six is 10, and we know we've got to regroup into the hundreds because two add one is three. So if we've got four in the hundreds, some of it must have been regrouped over from the tens. So as long as you put a number in there, which is six or bigger that's absolutely fine. So six, seven, eight or nine is perfect, and then it depends what you wrote in to get that added up, but really really well done if you saw that needed to be a number six or bigger. Checking this answer then, have they made a mistake here at all, or hopefully again you can see that they haven't quite got it right here, and they've done four add seven is 11, and so they put the one in the right place in the tens column, but forgotten to migrate that one into the hundreds, and the 100 should say 600. Really really good work, if you've got those right. It really shows that you've understood today's learning about regrouping. Time to complete the final knowledge quiz. Really really well done on today's learning everybody. Bye bye.

Adding two 3-digit numbers (regrouping in one column)

Adding two 3-digit numbers (regrouping in one column)

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UnitMaths / Addition and subtraction

Maths