Quiz to be completed following the lesson on: 'Adding and subtracting using the 'round and adjust' strategy.

What is the 'round and adjust' strategy?

2. Use 'rounding and adjusting' to solve: 53 700 + 3998 =

3. Use 'rounding and adjusting' to solve: 6880 - 2990 =

4. Use 'rounding and adjusting' to solve: 17 456 + 1980 =

5. Use 'rounding and adjusting' to solve: 215 678 + 3800 =

Adding and subtracting using the 'round and adjust' strategy.

﻿Hi everyone, my name is Ms. Jeremy. Thank you for joining me. And today's math lesson is focused on partitioning in order to solve addition and subtraction equations. So find yourself a nice quiet spot ready for your learning, and then press play when you're ready to begin your lesson. So let's begin by looking at our lesson agenda. We're going to start with a recap of the round and adjust strategy. We'll then be looking at using partitioning to add partitioning to subtract, and finally applying partitioning. We'll finish with our independent task and quiz at the end of the lesson. For today's lesson, you'll need a pencil and some paper and a nice quiet space. So find your resources, press pause now, and then press play when you're ready to begin the lesson. So beginning with our warm up, we're going to recap the round and adjust strategy. Remembering that the round and adjust strategy is a great way to subtract or add values together if those values are really, really close to other numbers that are easier to manipulate, easier to use. Let's look at this example on the screen, I've got 14,789 minus 3,998. Now I could use the column method to solve this, but that's going to require a lot of regrouping. It's going to take me quite a while. What I can do instead is use round and adjust. I can see that 3,998 is very close the number 4,000. In fact, it's just two less than that. So what if I were to take away 4,000 and then adjust for it later, by adding on two. Let me show you what I mean. So I'm starting from this end here because I'm subtracting and I'm going to place 14,789 here. And I'm going to subtract 4,000 because that's my rounded value. So I'm going to take it all the way back to there. The only digit that's going to change is my digit in the thousands columns, because I'm just subtracting 4,000. So 14,789 minus 4,000. And I'm not going to have anything in the thousands column anymore because I subtracted those four thousands. So it's going to be... Yeah, let me write this out. 10,789, but because I have subtracted two too many, remember we rounded and I subtracted two too many. I need to add two back on because I didn't want to subtract that many, I wanted to add, I need to adjust for that subtraction. I'm going to add two back on. So 10,789 add on two is 10,791. 10,791, I've rounded and adjusted to calculate the answer to this question here. So moving on, let's look at the partitioning strategy. So reminding ourselves that partitioning means breaking up a number into its components to make it easier to add or subtract. So let's have a look at this example here. This is an example where regrouping is not required and you can use partitioning really effectively when there is no regrouping. In fact, you can partition numbers in your head and add them or subtract them if there's no regrouping, it's fairly simple, but let's explain how this works. I've got the equation 132,000 and I'm adding 46,000. What I'm going to do is partition out these numbers into their a hundred thousand, 10,000 thousands, and then add the relevant parts together to work out what my final answer is. So looking at the first number, this is going to partition into 100,000. What is the value of that three there? That the value of the three is 30,000 and the value of the two is 2000. Partitioning out my 46,000 now. The value of the four is 40,000 and the value of the six is 6,000. So now that I've partitioned the number, I'm going to put the parts, the component parts together, according to which columns they match up to. So I know I'm going to have 100,000 on its own because there's no digit in the hundred thousands column here. So I'm going to have 100,000 at the beginning, I'm going to add together my 10 thousands. I've got 30,000 plus 40,000. That's equal to 70,000. And then I've got my thousands, I've got 2000 plus 6,000, that's equal to 8,000. And I'm going to add in my place holders for the rest of the number. So my answer is 178,000. Now I could have done that in my head. I could have looked at those numbers and decided, Well, I can add in my thousands. I can add in my 10 thousands, I've got 100,000 at the beginning, but it's nice to see how you can break up the numbers, add them together when no regrouping is required. So let's look at this example. Now that regrouping is required because in this example on the screen, it is required. How could we use partitioning in this particular example? So, let's think about this and let's think about how partitioning might help us out here. I'm going to partition both numbers into their components. Here, I've got 100,000. I've then got 80,000 and 2000. And looking at this number here, the five is representative of 50,000 and the seven is representative of 7,000. So I'm adding together these numbers, but there is going to be some regrouping required. So let's look at what that might look like. Well, once again, I've got 100,000 on its own. So I'm just going to put that at the top there to remind myself to add it. Now I'm going to focus on the digits in my 10 thousands place. So I've got 80,000 plus 50,000. This is where my regrouping is needed. Now I'm going to use a known fact here. If I know that eight plus five is equal to 13, then 80,000 plus 50,000 must be equal to 130,000. I use my known facts there to help me derive that fact. Finally, I've got to add on my thousands. I've got 2000 here and I'm adding on 7,000, no regrouping for this. I should just see that it's equal to 9,000. And now I've got all of my component parts, 100,000 plus 130,000 plus 9,000. Add those together really quickly in your head. I'm going to give you five seconds. What is the final answer? So you should have seen the final answer was 239,000, 239,000. Let me just explain to you again what I've done there. So I've partitioned each number into its components. I've separated them out. So I've added together the 10 thousands together and the thousands together. And I didn't have a hundred thousands from my second number. So I just had my first number, a hundred thousands at the top there. And then once I've done that, I add them all together separately to get my final answer of 239,000. And now it's your turn to have a go. As you can see, you are going to use partitioning to add the following numbers together. For the first example, you do not need to use regrouping. You can probably do that in your head, for the second number you may have to regroup. So have a look how at you might use partitioning to help you calculate that. I'm going to give you a couple of minutes to do that. Pause the video to complete your task, and then resume it once a couple of minutes are up and once you're finished. So how did you get on with partitioning those numbers to add them together? Let's have a look at the answers. So your first answer was 726,000. And your second answer was 615,000. Hopefully you're able to partition that second number out and add together the different component parts in order to get those answers. So moving on, let's think about how we can use partitioning to subtract. So in exactly the same way with addition, sometimes we will need to use regrouping and sometimes we won't. Partitioning can be used for both of those examples. The first example on our screen here, we do not need to regroup for. You can see that our equation is 742,000 subtract 210,000. So let's have a look how we might use partitioning to subtract this. Well, I'm going to break up and partition my number into its component parts. So I've got 700,000 there, 40,000 there, the two stands for 2000. Can you help me with this one here? The two in 210,000 is representative of 200,000. And the one is representative of 10,000, has a value of 10,000. So what we can do here is we can subtract the relevant parts just by looking at our screen, just by looking at the partition numbers that we've got. I'm going to start with my hundred thousands. I've got 700,000 minus 200,000 and that's equal to 500,000. So five goes in my hundred thousands column, then I'm going to subtract my 10,000. So I've got 40,000 subtract 10,000, which is equal to 30,000. A three is going to go into my 10 thousands column. And then I've got 2000 subtract nothing. So that's 2000 and I've got my place holders there. Same answer 532,000. Now another example of how we can use partitioning is when we do have to regroup, but we can use a number line to help us with this. So my second equation, 610,000 minus 247,000. I'm only going to partition out the second number. This is a slightly different strategy. So I've got 200,000 here. I've got 40,000 and I've got 7,000. And what I'm going to do is start with my 610,000 and then take away each of those component parts until I find my answer. So I'm going to place my 610,000 at the end here because I'm subtracting, I'm working backwards. I'm going to start by taking a big jump off. I'm going to jump backwards 200,000. So that I've subtracted the first parts. So that's subtract 200,000 there. I've done that part there 610,000 minus 200,000. When I'm focusing on the digit, that's in my hundred thousands and I'm subtracting by 200,000. So that would give me 410,000. So I've done the first part. Now I've got to take away 40,000. So a smaller jump this time taking away 40,000. So, 410,000 minus 40,000. Well, to help you out here, let's use a known fact. Let's do 41 minus four. What does that give us? 41 minus four is equal to 37. So in this case, my number would be 370,000 once I've taken away my 40,000 and the only thing I have to do is now take away my 7,000, the very last bit. And I've got 370,000 minus 7,000. So using my known facts here, I'm going to do 70 in my head minus seven. That will be 63. So 370,000 minus 7,000 is 363,000. So here I've used partitioning in order to subtract different parts of the number from my whole in order to work out what the other part is. And this is another way you can use partitioning with a number line as well. So it's your turn to have a go. On the screen you've got two examples. The first one does not require any regrouping. The second one does require some regrouping. So you'll need to look at how to do that one. Use our number line method, partition the second number and take that away incrementally. Pause the video to complete these two questions and then resume it once you're finished. Okay, let's look at the answers. So for the first one, you should have got 344,000. And for the second one, you should have got 226,000. Did you use that number line method to subtract as you went with your partitioned second number? Hopefully that works well for you. And hopefully what you've seen is that partitioning is another way to solve addition and subtraction questions without the need to write a column method out. So let's apply some of this understanding. As you can see on the screen here, we've got a bar chart and this bar chart shows merchandise. That means kind of products that are sold at the Olympics. We've got t-shirts, flags, key chains and water bottles. The blue bar shows you how many were sold in week one. And the red bar shows you how many were sold in week two. The question asks us, "How many t-shirts were sold overall in week one and two?" Really quickly spend five seconds working out what our equation is to answer this question. Okay, so hopefully you've seen that we're going to have to add together the values for week one and week two in order to work out how many t-shirts are sold overall. So I'm going to just look at what the value is for week one first. Well, it's halfway between 200,000 and 250,000. And I know halfway between 200,000 and 250,000 is 225,000. And for week two, can you read what that is? That says 250,000. So I'm going to add on 250,000. We're focusing on our equation at the bottom of the screen there. Are you able to add these two numbers together without writing anything down? Use that partitioning in your head, see whether you can work out what the hundred thousands, 10 thousands, and thousands added together would be. Five seconds to see if you can do that without writing anything down. Okay, so I can see I'm adding together my hundred thousands. There's no regrouping needed for this. So I've got 400,000. Then I'm adding together my 10 thousands. That's 70,000, and my thousands, 475,000. Didn't need to partition out on the screen. Didn't need to write out the different partition components. I was able to do it just using the equation in front. And you can do that as well. So if you don't need to regroup, you can just add together those numbers using your mental arithmetic skills of partitioning. Now it's your turn to have a go. Have a look at this question and look at the table on the right alongside it. It says, "How many more key chains were sold in week one "compared to week two?" So we are looking specifically at key chains and we're doing a comparison with finding the difference. When we find the difference between two sets of numbers, are we adding or subtracting? Have a think. What I'd like you to do is see if you can work out what the equation might be, and then see if you can use partitioning strategies to calculate the answer to the question. Pause the video now to complete your task and resume it once you're finished. Okay, let's have a look together. So if you might have seen, we are finding the difference between the two values. So we are subtracting. Whenever you find a difference between two numbers, you are subtracting. So the equation would be 510,000 subtract 450,000. Now I can see straight away here that there is going to be an element of regrouping if we were to partition both those numbers. But if I were to use my number line strategy, and I were to partition the second number into 400,000 and 50,000, I can complete the subtraction using this partitioning. So I'm going to place 510,000 at the end here. I'll start by subtracting 400,000 and then I'll subtract the 50,000. And because I've partitioned it, I should be able to do that fairly simply. So, first of all, let me start by doing a big jump to subtract 400,000 here. So 510,000 subtract 400,000 is equal to 110,000. And then the final bit I need to subtract is 50,000. And I'm starting at 110,000 subtract 50,000 is equal to 60,000. So you can see that 60,000 more key chains were sold in week one compared to week two. And you could have used petitioning to complete that. Other strategies were available to you. You could have used the counting on strategy instead as well. You could have used the column method if you wanted to as well. This just demonstrates how partitioning is one of the methods that you could have used. So moving on to your independent task, you've got five questions on the board and I'd like you to use either partitioning or other athletic strategies, for example, rounding and adjusting to solve those five equations. I would like you to try and use mental arithmetic strategies where possible, some will require regrouping. And we've talked about how you might do that, but use mental arithmetic strategies where possible to solve these five equations. Pause the video now to complete your task and then resume it once you're finished. Okay, how did you get on with those? On the screen are the answers. You can see, these are the answers to the five questions. If you'd like to, pause the video now to mark your answers and then pop back to see us before you complete your quiz. So thank you for joining me today for your learning. If you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. Now it's time to complete the quiz. Thank you so much for joining me for your math lesson today. It's been great to have you. Do join me again soon for some more math.

Quiz to be completed following lesson on: 'Adding and subtracting using partitioning'.

Which equation demonstrates how the number 346 000 can be partitioned?

2. Use partitioning to solve the equation: 723 000 + 15 000 =

3. Use partitioning to solve the equation: 456 000 - 132 000 =

4. Use partitioning to solve the equation: 158 000 + 26 000 =

5. Use partitioning to solve the equation: 738 000 - 156 000 =

Adding and subtracting using partitioning

In this lesson, we will use partitioning to add and subtract large integers, both where regrouping is required and where it is not needed.

Maths

Y5 Maths

Key Stage 2

Year 5

Problem solving with integer addition and subtraction

Number

THEME

UNIT

Using and explaining addition strategies

Using and explaining addition and subtraction strategies

Adding and subtracting using multiples of 10, 100, 1000, 10 000 and 100 000

Adding and subtracting using the 'round and adjust' strategy

Rounding to estimate

Adding using the column method

Subtracting using the column method

Problem solving using the column method

Solving multi-step addition and subtraction problems

5. Which strategy would be most appropriate/efficient when solving: 33 + 21 =

150 365 people attend an event. 80 000 people leave early. How many people are left?

Which derived fact could help us solve: 14 000 - 9000?

Round '456 244' to the nearest multiple of 10 000.

4. Use rounding to the nearest multiple of 1000 to estimate the answer to: 187 221 + 243 891 =

4. Use the column method to solve: 632 781 + 10 385 =

4. Use the column method to calculate the answer to: 183 609 - 21 788 =

Select the equation below that matches this maths story: '87 315 cars were sold over the weekend. 12 872 of these cars were new and the rest were secondhand. How many cars were secondhand?'

3. Write out the following column method calculation and describe the error that has occurred: 562 088 - 134 199 = 432 111.

Lesson overview:Adding and subtracting using partitioning

Core Content

Problem solving with integer addition and subtraction: