﻿Welcome to math lesson. With me, Mrs. Harris. We're going to be looking at some addition and subtraction problems together. Here's what we're going to be doing. We're going to spend a little bit of time noticing relationships between numbers. Before we move on to multi-step problems, followed by using the inverse to solve problems. And then I have an independent task for you. You need a few things, a pencil and a rubber, maybe a ruler, paper, and a book or a book, something to write on. So if you don't have those things now, pause the video, go and find them and then come back to me. Okay, that's everything we need. Let's look at relationships between numbers. Now I have a problem for you to try and tackle. I need you to choose four different digits, and this gives us four two-digit numbers. And you need to find the sum, and remember the sum is the total of your addition. And then find me some other examples, use different digits. And what do you notice? Here's my example. So I chose the digits five, two, one, and 19. This gave me the numbers 52, 19, 51, and 29. Their sum is 151. And we still got a challenge, if you'd like the challenge. Use four digits to give four numbers that total 100. But I think to do that, you might need some subtraction as well, maybe. So, pause the video now and have a go. Welcome back. How did you get on with this challenge? I have done loads of combinations. I noticed that if in the top left-hand corner, I had a lower number, my total was lower because that was a tens digit always. I noticed that I needed a lower digit in my top right-hand corner if I wanted a lower number. So to get to a hundred, you need these numbers. You need one, four, two, and seven. And when you add all them up, you get 100. We're going to use column subtraction here to solve 10,000 subtract 4,737. So pause the video and just do that quickly for me now. Got it? Here is mine. The answer is 5,263. And I've got another subtraction for you to do. Solve, 9,999 subtract 4,736. That didn't take long. Did it? Did you notice that the answers are the same? Why did that happen? What we noticed, is the minuend and the subtrahend are one digit less. one, one less. Therefore the answer remains the same. The difference is the same because both our minuend and our subtrahend are just by one. Now let's move on to multi-step problems.

Hello everyone, my name is Ms. Jones and I'm going to be helping Mrs. Harris out with the lesson today by doing a couple of the problems, starting with your multi-step problem. Now, our multi-step problem today is going to be based around the data in this table. You might want to take a moment now to familiarise yourself with what this table is telling you. We can see that it's exploring different objects or in this case, animals and their weight on different planets compared to their weight on earth. Very interesting information. But let's have a look at the problem that goes alongside this table. Which weighs more, and by how much? A rhino and a zebra weighed together on Jupiter, or an elephant and a rhino weighed together on Venus. Okay, interesting. Before we solve this, I want you now to think about what steps are required in order to solve this problem. I don't need you to solve it just yet. But think about what we might need to do first, what we might need to do next, and how we're going to get to our answer. Pause the video now to either verbally talk about that or jot down some of your ideas. Okay. Hopefully you've had to think about what steps we might need. Now. First of all, there's a lot of information in this table. Not all of it is information that we need to solve this particular question. So you might want to identify which bits of information relate to this question. We know that we were looking at a rhino and a zebra on Jupiter and elephant and a rhino on Venus. So let's get rid of human. We don't need that at all. And some of the other information that we don't need, just to leave us with the information that we do need. we've got elephant, rhino, and zebra here. Okay, That's a little bit better. Now, We can concentrate on the information that we do need. So on Jupiter, we need to look at the rhino and the zebra, and I'm going to represent each of their weights using a bar model, so that I can compare what they look like. I know that the rhino weighs 7,800 Newtons on Jupiter, this information here. And I know that the zebra, which am going to mark with red, is 936 Newtons on Jupiter. Now on Venus, we were looking at the elephant and the rhino, just put the rhino again on the left so we can compare it to the one above. And we were looking at the elephant, which I know is 6,480, okay? So I can already see some information from those bar models. I can see clearly that the weight on Jupiter is different for the same animal as it is on Venus, which is very interesting. But I'm starting to get a sense of what those totals might look like as well. So what do we need to do next? We need to now think of a method to efficiently sum the totals up. And then we need to think about by how much, or in other words, the difference between the two. I have just summed in a little bit here, and we need to total them up. So what I've done is, I've added these up and you might use something like column methods or a number line to do that, or a mental strategy. I've done it already, and I know that combined, there are 8,736 Newtons. Now I need to add up my other two amounts, which is the weight on Venus, 2,700 added to the 6,490. Again, you might use a mental strategy or a written strategy for this. It's okay. But you get then 9,180. What do we need to do next? We need to find the difference. If you need to pause the video now and have a go at that yourself, if you haven't done so already. If not, let's have a look together. Now we can label the difference in this space here, the amount that this is compared to this. And we can use subtraction perhaps to help us solve that. And we can do that again mentally or using a written strategy. What is my difference? You may have already worked out that the difference here is 444 Newtons.Okay? So which weight is more? I know that the weights of the elephant and the rhino on Venus weighed more than the other two on Jupiter. And they weighed 444 Newtons more. Okay. Let me pass you back over to Ms. Harris, Who's going to explain a different kind of problem to you.

Now let's move on to using the inverse, to solve problems. I'm thinking of a number. I'm going to add 104 to it. Then I'm going to add 73 to it. My answer is 439. What was my number? is my number greater than, or less than 439? It's less than, isn't it? Because we had to do some adding to get that. So I think you might have to use the inverse to find my answer. Pause the video and use all this information to find my number. Welcome back, think you got my number? Well, let me show you how you could have worked it out. You could have used a number line. You could have added some mystery number 104 and 73 to get you to 439. But, that still doesn't really help you know my number. All we had to do was the inverse. Even though it was adding something to the mystery number, you had to take them away from my final answer, from the sum. And it would look on a number line like this. We would start with 439, take away the 73, then take away the 104. My mystery number was 262.

Hello, everyone, it's Ms. Jones again. And again, I've got a problem with some extra steps. This is very similar to the problem you've looked at already, but with perhaps an extra step further. Pause the video now to have a look at this and see if you can solve it. Remember to explain your answer. And if you need to represent your thinking on a number line. okay. Hopefully you've had a go at that. If you're not sure, we can go over it together, if you've completed that, we can check our answers here. So the number I was thinking of was 17.2. So let me explain my thinking and how I got there and show you my number line. So here's our number line and it shows the steps we need to get to from own unknown all the way to 42.5. However, we don't know where we're starting with. So what we can do is start with what we do know, the final number, and work our way backwards using the inverse case and look at this number line now. So I'm starting with 42.5. Instead of adding 9.1, I'm going to take away 9.1. And instead of subtracting 21.4, I'm going to add it on. And instead of adding 37.6, I'm going to then subtract it. Which will get me back to my original number 17.2. And what you might want to do then to double-check, is to take 17.2 and go through this process. And then, you're a hundred percent sure that your number is correct. If you've checked using both the inverse and the sort of forwards way as well. Okay. Back to you Mrs. Harris.

Now it's time for your independent learning. I'd like to pause the video. After you've navigated to the task, do the task, and then come back to me and we'll discuss the answers. See you in a few minutes. Okay. So you had this menu with these prices, and you had these problems. How did you get on with them? Did you have to do the inverse at all? Did you have to multi-steps? Here's my answers, but first let's just read the question together. Anne buys a cheeseburger, salad, a banana and a bottle of water. How much does she pay? So what we had to do, is just find the right data on the chart, listed on the table. And then add them together. Well, I found that she needed 5.55, 2.50, 45P and 69P. The easiest way to do that was in my head, to find numbers that I knew went together really well. So I added 45P to 5.55 giving me six pound. For my six pound, I added the 2.50 from the salad, giving me to 8.50, and what I needed to do then was add the 69P And I had 9.19. Our second problem is about Sally. And Sally buys a burger, chips, and a bottle of water. She pays with a 20 pound note, and we needed to find out how much change she got. So this was a multi-step problem. First, we have to do some addition to find out how much money she spent. And then we have to do subtraction, to find out what change she got. This is how I did it. So I knew that I needed 20 pounds, subtract the total will give me the change. Which is what our question is asking for. I knew I needed to add together 4.95, 1.99 and 69 P. But I decided to round them up. I rounded them up to five pound, two pound and 70 P, As you can see on the screen. I rounded them up in total by 7P. Then I subtracted the 7.70 from the 20 pound to give me 12.30. And all that was left for me to do was add on my 7P to find out that the change she got was 12.37. And finally, you had Fin. And Fin bought three things from the shop and he paid with a 10 pound note. Gets less than two pounds change. What could he have bought? There are a few combinations here. Let me read you a few of mine. I just had to make sure that he got less than two pound change each time and he had had three items. So 8.24, Fin could have bought a cheeseburger, chips, and a fruit bag. That would have given him less than two pound change. For 9.44, he could have bought, burger, chips, and salad. And that coming in at 9.44, he would have got less than two pound change, or maybe he bought burger, chips, and a milkshake, with 9.3 Pounds, definitely giving him less than two pound change. Well done for all your hard work today on using your addition and subtraction skills. If you're going to share any of your work with me or anybody at Oak National, you can ask your parents or carers to upload some of your work in Twitter, tagging @OakNational. I'll be looking out for it, especially if you found any other ways that Fin could have spent his money. We have just one thing left for you to do. And that's to navigate to the quiz and answer the multiple-choice questions. Bye.

I subtract 612, then take away a further 111. I add 904. My answer is 1187. What was my number?

I subtract 9314. I then add 72,097. I subtract 32,982. My answer is 168,373. What was my number?

I add 3.62, then subtract 9.4. I then add 12.45. My answer is 16.17. What was my number?

The sum of three consecutive numbers is odd.

Addition and Subtraction Problems Quiz

In this lesson, we will build on prior learning to develop a range of strategies to efficiently add and subtract within one problem.

Maths

Y6 Maths

Key Stage 2

Year 6

Addition and subtraction problems

Integers & Decimals

Number

THEME

UNIT

Understanding other powers of ten within one-million

Reading and writing 7-digit numbers

Understanding how the digits in a number indicate its structure

Compare and order numbers to ten million

Rounding to a required degree of accuracy

Estimating and rounding contexts

Strategies for addition

Strategies for subtraction

Applying addition and subtraction

There are 2271 satellites currently in space. What is this number rounded to the nearest 10?

The moon Ganymede takes 172 hours to orbit Jupiter. What is this number rounded to the nearest 100?

When rounded to the nearest 10, it takes Mars approximately 690 days to orbit the Sun. What is the greatest number of days it can take?

Solve this addition: 52,805 + 9695 =?

What is the value of the digit 4 in 5 672 543

Round the number 8,478,365 to the nearest 100,000

Sally buys three items. She pays more than £35 but less than £40. What could she have bought?

7 460 400 is one hundred thousand larger than 7 450 400

Work out 6,084,926 - 1,795,319

Lesson overview:Addition and subtraction problems

Core Content

Integers & Decimals: