Solve the following equation. You may use any strategy you think is best.

Adding two digit numbers with regrouping

Key Stage 1

Maths

Addition and subtraction of 2-digit numbers (regrouping and adjusting)

Does the following calculation require regrouping?

﻿Hello everyone and welcome to maths with Ms. Dobrowolski. It's really nice to see some familiar faces. And for those of you who haven't met me before, welcome to class. So in today's lesson we will be adding two digit numbers involving regrouping. Let's have a look at today's lesson agenda. First, we'll be adding by partitioning the second number only. Then we'll have our talk task. Then we'll be adding by partitioning, both the numbers. And finally, you'll be off your independent task. For this lesson you will need a pencil, a notebook, and possibly some pasta shapes. If you can get them. If you can get some spaghetti and macaroni or penne, that would be fantastic. If you don't have pasta shapes, that's completely fine. And I know that's really weird. What does pasta have to do with maths? Just trust me on this one. So if you don't have these items, pause the video now and go get them. Resume when you're ready, great. So let's start by learning how we can partition the second number, when adding let's have a look here. What are my parts? Well, I can see that I'm adding 27 plus 14. So 27 and 14 must be my parts. In order to add these two numbers together, I'm going to use my part-whole model to help me. So let's have a look, great. So I want to add 27 plus 14. And in order to do that, I'll make a part-whole model to help me. And you can do this really easily at home. Just draw one big box to represent your whole and then we're going to have two smaller ones to represent our parts, just like this. And don't worry they don't have to be perfect. So let's have a look. What are our parts again? Oh, that's right, 27 and 14 are our parts. So we have to represent them in our parts. So 27 has two tens, one, two or 10 20, and it also has seven, ones. Count with me, one, two, three, four, five, six, seven, and 14 has one 10 and four ones, one, two, three, four. We're going to add these numbers by partitioning the 14. By partitioning, the second number or splitting it into tens and ones. So step one, is to move our 27, our first number into the whole So we're going to move these all into the whole, excellent. Okay, so we've moved 20 into the whole. So I'm going to put 27 on the other side of the equation. Every time I put something into the whole, I'll add it. Now, we're going to add our tens first. I know that I have one 10 in 14, so I put it in my whole, right? Because I know that, two plus one is equal to three. So 10, 20, 20 plus 10 is equal to 30. So 27 plus 10 is equal to 37. So remember I added a 10 so I'm going to write that up here, excellent. So now I need to look at my ones. Well let's use the make 10 strategy. I know that I have seven ones here already, right? From my 27, I have seven ones. How can I make a 10, if I have seven? What can I add to make a 10? Oh, that's right, seven plus three is equal to 10. So that must mean, 37 plus one, two, three is equal to 40, I have four tens now, but remember, whenever we make a 10, we have to exchange it. Whenever we make a 10 with 10 ones, we have to exchange it for one 10. Let me just write that we added three before I forget. Do you see how 10 ones, are exactly the same size of one 10? That must mean, 10 ones are equal to one 10. So now I need to regroup. I need to exchange my 10 ones for one 10, 10, 20, 30, 40, excellent. So now I can't forget about my leftover one. I added three to my ones to make a 10 and now I add 40 plus one, which is equal to 41, 10, 20, 30, 41, my whole is 41. I'd like to look at something very quickly here with you. Do you see that both sides of this equation are equal? 27 plus 14 is equal to 27 plus 10 plus three plus one because we partitioned the 14, 10 plus three is equal to 13 and 13 plus one is equal to 14. So all we did, was partition 14 into a 10, a three and a one and we still got a whole of 41. Great, let's try another one. Great, so now I'm going to add 27 plus 15. What are my parts? Tell the screen. That's right my parts are 27 and 15. So first let's make 27. How many tens do I need? Two, 10 20. How many ones do I need? Seven, count with me, one, two, three, four, five, six, seven. And now let's make 15, how many tens do I need? That's right, just one. And how many ones do I need? I need five, one, two, three, four, five, excellent. So remember, I'm going to partition the second number. I'm going to partition or split the 15 into tens and ones to add this, but first I'm going to move 27 into my whole. So let's move 27 into the whole, excellent. Now, because I've put 27 into the whole, I'm going to write it on the opposite side of the equation. Whenever I move anything into the whole. Now I need to add my 15. So I start with my tens because I've partitioned 15 into tens and ones. So I have one, 10 and 15, so I can add that to my two tens here, two tens plus one 10 is equal to three tens. So that must mean 27 plus 10, is equal to 37, 10, 20, 30, seven, 37. So let me just write that I added a 10. Now I need to look at my ones. Let's use the make 10 strategy. If I already have seven ones, what can I add to seven to make 10? Oh, that's right, I just need three more because seven plus three is equal to 10. So I can add three here. So now, 37 plus three that I've added is equal to 40. 10, 20, 30, 40. Remember I have 10 ones, so what do I need to do now? I need to? That's right, regroup. So I regrouped my 10 ones, for one 10 because they had equal value, 10 20, 30, 40. And I've added three. I can't forget about my two that I still have left. I need to add those in. 40 plus two is equal to 42. So my whole is 42. Let's just have a look at these equations at the top again. So I can see that 27 plus 15 is equal to 27 plus 10 plus three plus two, because all I did was partition the 15, 10 plus three is equal to 13, 13 plus two is equal to 15. I still added 15, I just did it in little bits, that made sense to me. Let's try one more example. So this time we'll be adding 27 plus 16, but instead of using my deans for my tens and ones, I'm going to use my pasta shapes. So I'm going to use spaghetti to represent my ones. And I'm going to use some macaroni Oh, sorry, I'm going to use spaghetti to represent my tens. That was a silly mistake for me to make. So the spaghetti represents my tens and now the macaroni is going to represent my ones. So if you have these pasta shapes, make sure you grab them now, pause the video and get them. And you can do what I'm doing and follow along. If you don't have the pasta shapes, don't worry. You could just watch what we're doing. So what are our parts? That's right, 27 and 16. So let's make 27 first. How many tens do I need? That's right, I need two tens. So I'll put two spaghetti's 10, 20. How many ones do I need? That's right, I need seven. And you can do this too, one, two, three, four, five, six, seven, great, that's 27. Now let's make 16. How many tens do I need? That's right just one 'cause I have one 10. And how many ones do I need? That's right, I need six one, two, three, four, five, six, excellent. So I'm going to move 27 into the whole and I'm going to partition 16. So let's move 27 into the whole. Just like that and remember, because we moved 27 into the whole. we're going to write it on the opposite side of my equation. Good, so first we need to add our tens. I know that 16 has one 10. So I add that to my two tens here. Two plus one is equal to three. So that must mean 20 plus 10 is equal to 30. So 27 plus 10 is equal to 37. So I'll just write that I added a 10 here and now I have 37. Now I need to add my ones. I know that in my whole, I have seven ones because of 27. If I have seven ones, let's use the make 10 strategy to make the 10, seven plus something is equal to 10. Oh, that's right, seven plus three is equal to 10 so I can move three ones into my whole. Now, if I know I have 10 ones, what do I need to do? I need to regroup. So I need to regroup my 10 ones for a 10 so we can get rid of these. Goodbye macaroni and hello spaghetti. So how many tens do I have still 10, 20, 30, 40, excellent. Now, I know that I've added three ones, but I can't forget about the other three that I have here. So I need to move those into my whole. 40 plus three 40 plus one, two, three is equal to 43, 43 is my whole. Now, let's have a look at our equations before we've gone to the next activity. As you can see, both sides of these equations are equal because 16 was partitioned into 10 plus three plus three, 10 plus three is equal to 13 and 13 plus three is equal to 16. So all I did was partitioned my 16 into tens and ones. It's already time for your talk task. So in this talk task you'll be using the whole, part-whole model and make 10 strategy to solve the following equations. Now in this box, it'll tell you say this. So make sure that when you're completing your top task, you are using this mathematical language. So let's see, I'll do the first one as an example, so that you're super clear on what you need to do. And of course we have our whole part model here and you are free to draw your own if you'd like to and use your pasta shapes of course, to help. So I'll do 39 plus 14. So I have the equation 39 plus 14. I know one part is, 39 and the other is 14. So I will partition 14 into tens and ones First let's put 39 into the whole, 39 and we're going to add our tens first. So 39 plus 10 is equal to 49. So I have no more tens left in my parts because I've added them to my whole. If I have nine in my ones, how can I use the make 10 strategy? Oh, I know nine plus one is equal to 10. So 49 plus one is equal to 50. I can partition the four into one and three. 49 plus one is equal to 50, 50 plus three is equal to 53. So your turn now, make sure you complete the talk task. And pause the video, when you're ready, resume the video and we'll go over the answers together. Great, so hopefully you've completed your talk task. Here are the answers. So we know 39 plus 14 was equal to 53. 39 plus 15 was equal to 54 and 39 plus 16 was equal to 55. On the other side, we had 48 plus 26 was equal to 74, 40 plus 25 was equal to 73 and 48 plus 24 is equal to 72. Now, since you're all such a clever bunch, can you think, what patterns do you notice? What's the same? What's different? Have a think Well, I can see that in this column, we always had nine in the ones, which meant that whenever we were adding our ones, all we had to do was add one more nine plus one is equal to 10. So 39 plus one was equal to 40 each time. Now on this side, over here, we always had an eight in the ones. So that meant every time we wanted to make a 10, we had to add two because eight plus two is equal to 10. So that must mean 48 plus two was equal to 50, great. So, now we're going to move on to partitioning both numbers. In this equation, what are our parts? That's right, it's 27 and 14, same numbers as we saw before. But this time we're going to look at how we can partition both numbers. So let's have a look at that. So let's have a look at what happens when we partition both numbers. So I want to add 27 and 14 those are my parts, but instead of partitioning only the 14, I'm going to partition both numbers. First, let's fill them in on our whole, on our parts I should say. So 27 has two tens, one, two or 10, 20 and seven ones. Count with me, one, two, three, four, five, six, seven and 14 has one 10 and four ones. One, two, three, four. First I'm going to add my tens. So how many tens are there altogether? Well, I know that two plus one is equal to three. So 20 plus 10 is equal to 30. So I have three tens or 30 altogether. Now I need to make sure that I add my ones, but I'm going to use the make 10 strategy. So I know that I have seven ones plus four ones. If I have seven, how much more do I need to make 10? Oh, that's right, seven plus three is equal to 10. So I'll move these seven over plus one, two, three. So now I've added a 10, so that's 10, 20, 30, 40. But remember whenever we make 10 ones, we have to regroup for one 10. so we can get rid of these and put in one 10. We still have 10, 20, 30, 40, good. So now I can't forget to add my one here, 40 plus one. 40 plus one is equal to 41. And both sides of this equation are correct. I've just partitioned, both numbers. Great, let's try this with 20 plus 14. I know that 28 has two tens and eight ones, so 10 20 and now we need eight ones, one, two, three, four, five, six, seven, eight, and 14 has one 10 and four ones. One, two, three, four excellent. So ,first I'm going to add my tens. I know that two plus one is equal to three. So 20 plus 10 is equal to 30, so I can put 30 up here, I've moved it to my whole. Now I need to add my ones, I have eight ones here and four ones down here. If I have eight, how much more do I need to make 10? Oh, I know, eight plus two is equal to 10. So, I'll put eight here plus two is equal to 10, 10, 20, 30, 40, I've added a 10. But remember, when we have 10 ones, what do we need to do? We need to regroup 10 ones, for one 10. So I still have 10, 20, 30, 40. And I can't forget about the rest of my ones. And I have 40 plus two. 40 plus two is equal to 42, so my whole is 42 and again, both sides of this equation are correct. Alright, let's try one more example. If you have your pasta shapes at hand, that's great. Make sure they're ready, if you don't, don't worry. So again, we're going to partition both numbers. First let's make our parts. So I know that 29 has two tens, one, two and nine ones, one, two, three, four, five, six, seven, eight, nine. And 14 has one 10 and four ones. One, two, three, four, good. Let's add our tens first. I know that two Plus one is equal to three. So 20 plus 10 is equal to 30. So that's in my whole now. Now I need to add my ones by using the make 10 strategy. I know that I have nine ones here and four ones here. If I have nine ones, how much more do I need to make 10? Oh, that's right, nine plus one is equal to 10. So I can move these nine into my whole. Plus one is equal to 10, excellent. So now I have 30 plus 10 is equal to 40. But remember whenever I have make 10 ones, I need to regroup, regroup for one 10, regroup. I still have four tens, I still have 40, I've just regrouped. And I can't forget to add the rest of my ones. 40 plus one, two, three 40 plus three is equal to 43. Wow everyone, it's already time for your independent task. Time really flies when you're having fun. So for this independent task, there's only two steps. Step one, is to solve by partitioning one number. So for example, in 36 plus 15, if I'd like to solve this by partitioning the 15, I would partition it by adding 36 plus 10 plus four plus one. Step two, is to solve the equation by partitioning both numbers. So in step two, you need to add the tens first and then the ones again for 36 plus 15, I partitioned the tens into 40 plus 10 plus one. And hopefully both times I get the same answer of 51. That's how I know I'm correct. Your turn, pause the video, complete the rest of the equations following step one and step two and when you're ready resume so we can go over the independent task good luck. Well done everyone. So, hopefully you finished your independent tasks. So for number one, we both got the answer 51. For number two, our answer was 52. For number three, our answer was 53. And for number four, our answer was 54. If you'd like to, you can share your work with Oak National by asking a parent or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and LearnwithOak. And as always, don't forget to complete the quiz. Well done everyone and I really hope to see you next time for future lessons. Bye bye.

Adding two digit numbers with regrouping

Adding two digit numbers with regrouping

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UnitMaths / Addition and subtraction of 2-digit numbers (regrouping and adjusting)

Maths