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

﻿Hi there, thank you for joining me. My name is Ms. Jeremy, and today's Math lesson is focused on rounding to estimate. So find yourself a nice quiet space and get yourself sorted ready for the lesson. And then once you're ready, press play to begin. Looking at our agenda to begin, we're going to start with a warm up where we will look at partitioning. We'll then look at how to round, and recap how to round generally to the nearest 10,000, and to the nearest 1000. We'll then look at rounding in order to estimate the answer to equations before applying our knowledge of grounding to real problems. We'll finish with an independent task and quiz at the end of the lesson. For today's lesson, you will need a pencil and some paper and a nice quiet space. So feel free to pause the video now to find these resources. And once you're ready, press play to continue with your lesson. We'll get started with this warm up where we look at partitioning. The question says, how could I use partitioning to solve the following equation? 673,000 plus 24,000. So I'd like you to have a look at this equation and have a think, how could we use partitioning in order to solve this? Will we need to regroup? If so, how will we do it? I'm going to give you 10 seconds to have a think about how petitioning could be used to solve this. So you might have noticed that no regrouping is required for this equation. And so what we can do is we can partition out the numbers, add them on together, and we can do this in a fairly straightforward way. You can probably even do this in your head. I'm going to show you some workings out, just so you can see what I'm thinking. But generally, equations like this can be completed in our heads fairly easily. So I can see that we've got 673,000. I can partition this into 600,000, 70,000, and the three represents, 3000. Here, for this one I've got 24,000. The two represents 20,000. And the four represents 4,000. And I'm adding together these values. So I want to add like for like. So, I have a digit in 100,000 for my first digit, for my first number. And I can see that is a six. I've got 600,000 there. I'm not adding any other 100,000s to that number. Then looking at my 10,000s column, I've got 70,000 plus 20,000, and that is 90,000. So I put nine in the 10,000s column. And then looking at my thousands, I've got 3000 plus 4,000, which is equal to 7,000 and so I put a seven in my thousands column. The rest of my digits I'll just zero because I haven't got anything to add there. So my answer is 697,000. You could have done that without writing anything down and just seen that you would need to add your 10,000s first, and then your thousands together. And keep your 100,000s exactly the same. But just to write it down, just to show you how you can partition in order to add those numbers together. So moving on to a recap of rounding. What I'd like us to do is round this number to the nearest multiple of 10,000, and then to the nearest multiple of 1000. This is going to help us later on because we'll be using rounding in order to estimate the answer to equations. So our number is 47,351. And the first thing I want to do is round to the nearest multiple of 10,000. So I'm looking at that digit, it's in the 10,000's place, and identifying whether I'm going rounding that up or down. There are two ways you can do this. The first way is to use a number line method, and identify what the smaller multiple of 10,000 is. The large multiple of 10,000 is, the halfway point. And then see whether it is closer to the larger multiple, or closer to the smaller multiple. We'll use that method first, and then I'll show you the other one as well. So I know that if 47,351 is my number, my smaller multiple that comes before this number is 40,000. I'm going to jump 10,000 up to get to my larger multiple. What is my larger multiple? It is 50,000. My halfway point directly between 40,000 and 50,000 is 45,000. Now I'm going to place my number 47,351 onto my number line. So I can see that 47,000 would be around here. So 47,351 is probably there. And you can see straight away, it's much closer to 50,000 than it is to 40,000. So therefore this rounds up to 50,000. I'm going to write 50,000 just here to remind us. Okay, now rubbing out my markings because I'm going to look at whether I can round this number also, to the nearest multiple of 1000. So this time I'm focusing on that 1000 digit. And I'm looking at the smaller multiple and the larger multiple. What is the smaller multiple in this case? The smaller multiple is 47,000. And then counting on 1000 to get to my larger multiple, my larger multiple is 48,000. My halfway point is 47,500. And you can see in this case, 47,351 is probably around here. So in this case, I'm rounding down. In this case, it rounds down to 47,000. Now let me show you the other method. Cause I said there were two methods in order to round to the nearest 10,000 and the nearest 1000. The other method you can use is this. If I'm rounding to the nearest 1000 for example, underline the value that you're rounding to, the digit that you're rounding. And then, having a look at the number that comes next. The number that is right of this digit. If the number is four or below. Is less than four or is four itself, you are rounding that number down to the smaller multiple of 1000. If the number is five or above, you are rounding the number up to the next multiples, the larger multiple of 1000. So in this case, you can see here, I've underlined the seven in its 1000s column. And I've had a look at the 100s column and I can see, that that digit is less than five. Therefore, I'm rounding it down. I'm rounding that number down to 47,000. So you can use either method in order to round. The number line method, you do have to draw a number line outs. So the other method might be slightly simpler, if you want to round fairly quickly. I'd like you to have a go at this. You've got the number 183,627. Can you use either the number line method or the method I showed you which was slightly quicker where you look at the digits in order to round this number to the nearest 10,000 and to the nearest 1000. Pause the video to complete your task and resume once you're finished. Okay, let's have a look at the answers and see how you got on. So, whether you use the number line method or the digit method, these are the answers. So you should have seen that 193,625 is approximately 180,000 when rounded to the nearest 10,000. And if you're rounding to the nearest 1000, it is approximately 184,000. So there we have rounded down to find for the nearest 10,000. And we've rounded up when we are rounding to the nearest 1000. I always think about how rounding could help us with estimating an answer to a question. So let's imagine that we have this equation here, 64,038 plus 51,182. Now this question is going to require some calculation. I've got lots of digits that I need to consider. There's regrouping in that as well. One way of working out, whether my answer is correct when I have calculated it, is comparing it to an estimate. If we were to estimate, which means to have a really good, solid, educated guess at the answer, prior to calculating before calculating, we can look at our estimate and we can look at our calculation, and we can compare them to see how similar they are. If they're wildly different, I know there's somewhere I've made a mistake. The estimation can really help us improve the accuracy of our actual calculations. And in order to estimate the answer to a question like this, we can use rounding. And we can either round in this case to the nearest 10,000 or to the nearest 1000, because rounding helps us create numbers that are much easier to manipulate, much easier to calculate with. And so we can quickly calculate an estimation, whereas actually calculating the answer will take us a bit longer. So let me demonstrate how we would do this. I'm going to start by rounding both of these numbers to the nearest multiple of 10,000, and adding them together to provide my estimate. So starting with the first number there I can see that if I underline the digit that I'm focusing on and have a peak at the next door number, I can see this is going to round down to the smaller, the lower multiple of 10,000, which is 60,000. So my first digit is, or my first number is 60,000. Looking at the next number there, and we're rounding again to the nearest 10,000. Again, this is rounding down to that smaller multiple. So this is rounding to 50,000. And straight away you can see, that actually creating my estimate is going to be much simpler than my actual answer, because 60,000 plus 50,000 is really easy to calculate in our heads. Let's use our known facts. We know that six plus five is equal to 11. And so therefore 60,000 plus 50,000 must be equal to 110,000. So, that's an approximate answer. That is our estimate, when we rounded to the nearest multiple of 10,000. Now, let's have a go at rounding exactly the same thing, but making our estimate a little bit more accurate. Because we're going to round to the nearest multiple of 1000. So, looking at my first number again, but this time I'm focused on the digit in the 1000s column, and I'm going to take a peak next door. Again, this rounds down to the smaller multiple of 1000, which is 64,000. And the next number I'm going to have a look at the digit in the 1000s column and have a look next door. This again also rounds down to 51,000. So here we've got a slightly more accurate estimate because we've been slightly more accurate in our rounding. We've rounded to the nearest 1000 rather than to the nearest 10,000. So, I'm calculating 64,000 plus 51,000. Well I already know that 60,000 plus 50,000 is 110,000. So what I need to add on if my 4,000 and my 1,000. 4,000 plus 1,000 is equal to 5,000. So my answer must be 115,000. Really simple. Created my estimates. There were two different ways of doing it. A slightly less accurate version, which was around to the nearest 10,000. A slightly more accurate version, which was to round to the nearest 1000. It's your turn to have a go. You've got a calculation on the screen. 581,823 plus 233,872. I'd like you to have go at rounding both of those to the nearest 10,000 first and creating your estimate, and then to the nearest 1000 and creating your second estimates. Spend some time doing that. Now, pause the video to complete your task and resume it once you're finished. Okay, let's have a look how you got on. So when you around into your nearest 10,000, you should have found that your calculation was 580,000 plus 230,000 is equal to 810,000. Then looking at rounding to the nearest 1000 a slightly more accurate estimate. 582,000 plus 234,000 is equal to 816,000. And those were two estimates that you could have used. So when you calculate the real answer, you can compare to those estimates and say, oh, I'm actually... That I'm very, very close. I must be correct in my answer because my estimation and my real answer are really similar. So let's think about which of these equations is most appropriate for using when we're estimating. Here's our question. 58,943 minus 12,875. There are four options. We'll call them option A, B, C, and D. Have a look at those four options. What has happened in each of those options? What have we rounded to for each of those options? Which one would you choose to create your estimate and why? Spend some time having a think about that. I'll give you about 10 seconds. Okay, so let's have a look at what's happened for each one here. So for the first one, we can see that we have rounded, we've got 59,000 minus 13,000. We've rounded there to the nearest multiple of 1000 for each of those. And in terms of subtracting those values, that will be fairly straightforward because we don't have to regroup. We can do 50,000 minus 10,000. 9,000 minus 3,000. Be fairly straightforward to do. So that's an option for us. In option B, we've got a slightly broader estimation here because we rounded the first number to the nearest multiple of 10,000, whereas the second number is being rounded to the nearest multiple of 1000. You can mix and match a little bit like that as well. Again, fairly straightforward to subtract. We could partition the 13,000, Subtract 1000 first, subtract the 3,000 afterwards. But that will be slightly less accurate than the equation we put for A. For C, that's even less accurate because here we rounded to the nearest multiple of 10,000 for both of those numbers. And the last one is probably the most accurate one because we've rounded to the nearest multiple of 100 for both of those answers. Or for both of those parts of the equation. Which would you use and why? Well there's no right or wrong answer here. You can use any them, but actually what you want to do is get a balance between accuracy, but also ease of calculation. I would not use D personally. And that's because that calculation is harder for me to complete than for example, A, B or C. Ready to make it nice and quickly. I also wouldn't you C because I think it's not as accurate as the other two options. And the other two options can increase your accuracy. I think out of the two options and B personally, I would use A. And that's because A offers us accuracy, in that we rounded to the nearest 1000 rather than the nearest 10,000, but also it's fairly easy to calculate. There's no regrouping. I won't find it a challenge in order to kind of find my answer here. So, that's my option here, but actually all of those possibilities are absolutely fine to choose from. You could have selected D if you wanted to. You could have seen that actually even though you have to subtract more digits, there also isn't any regrouping there. So that would be fine to do as well. Or you might have gone for a slightly less accurate estimation, but thought about that when comparing your actual answer to it. So again, no real right or wrong answer here, but as long as you can provide a reason for why you would select a particular estimation strategy over another. So let's move on to an example for you to practise by yourself. As you can see on the screen here, we've got some information about two cities in the U.K. We've got Cambridge here and Cambridge's population, which is 123,945. And Edinburgh, which has a population of 495,360. And the question asks you, what is the total approximate population of Cambridge and Edinburgh? And that key word there is the word approximate, because we are going to be rounding to work this out. What you're going to have a go at doing, is rounding each of these numbers to the nearest 100,000, 10,000, 1000, and 100. And using that information to work out some approximates total populations. Let me just demonstrate one for you. So here, I'm going to firstly start off with rounding Cambridge's population to the nearest multiple of 100,000. So looking at my slightly shorter strategy, I'm looking at the digit that's in the 100,000s column. And taking a peak next door I can see I'm rounding down. So the approximate population of Cambridge is 100,000. Then looking Edinburgh, I can see this is going to be rounding up to 500,000. And so if I add those two values together, I can see that the total approximate population when rounded to the nearest 100,000 is 600,000. So I'd like you to do the same thing, but for the rest of the different types of rounding and for the rest of the table that you can see on your screen. Pause the video to complete your task and resume it once you're finished. How did you get on with activity? As you can see on the screen here we've got the answers for all of the different types of rounding that you might've done. Have a look at the answers and mark your own learning. You can pause the video now if you'd like to, and then resume once you're finished. So let's move on to your independent task. We have couple of activities here. I'd like you to use rounding to the nearest 10,000 and to the nearest 1000, in order to estimate the answers to the questions that are on the screen there. And then for question number five, I'd like you to tell me whether you'd be more likely to round to the nearest 10,000 or 1000 when you're estimating in the future and your reasons why. Why would you round to the nearest 10,000 to 1000? You might like to give me an example, if you would like to as well, if that helps you explain your reasoning. Pause the video now to complete this task, and then resume it once you're finished. Okay, how did you get on? Let's have a look at some of the answers on the screen. So you can see that the answers are written in pink. On the left hand side, that's rounding to the nearest 10,000, and then on the right hand side, that's rounding to the nearest 1000. And then you've got a kind of very brief answer to question five there. If you selected rounding to the nearest 10,000, you might have mentioned that rounding to nearest 10,000 is typically easier to calculate. Whereas rounding to the nearest 1000 increases your accuracy. So you might have chosen one of those two and provided those reasons to explain why. So thank you so much for joining me for our lesson today. It's been really nice to have you. 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 for joining me for another lesson of Maths. It's been great to have you. Do join me again soon. Bye bye.

Quiz to be completed following lesson on: 'Rounding to estimate'.

What does 'rounding to estimate' mean?

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

3. Using rounding to the nearest multiple of 10 000 to estimate the answer to: 341 782 + 456 913 =

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

What is one of the problems associated with rounding to estimate?

Rounding to estimate

In this lesson, we will apply our understanding of rounding to the nearest multiples of 10 000 and 1000 to estimate the answer to addition equations.

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

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?

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

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:Rounding to estimate

Core Content

Problem solving with integer addition and subtraction: