Applying mental calculation strategies to adding and subtracting decimals

Key Stage 2

Maths

Calculating with whole numbers and decimals

﻿Hello, and welcome to today's Maths lesson with Oak National. My name is Miss Sew, and today we are using our mental strategies, for adding and subtracting using decimals. Make sure you have a comfortable space so you're ready to learn and let's get started. Welcome to today's math lesson. We're going to be applying our mental calculator strategies when adding and subtracting decimals. Make sure you put your brain ready, because this lesson is going to require you to be doing lots of mental work. So, to start with, we're going to warm-up with some mental calculations, with whole numbers, then we'll be looking at our addition strategies, and then we'll look at our subtraction strategies. At the end of the lesson, there'll be a time to show what you've learned, at during our independent task and quiz. For today's lesson, you will need a pencil and some paper to take some jottings but you're going to need your brain most of all, so turn that on, and let's get ready. To start with, we're going to do a warm up. Pause the video, and have a go at these mental calculations. See if you can do them without writing anything down, do them in your head, and write the answer. Off you go. Okay, how did you find that? I wonder if you managed to do that mostly in your head, or whether you took a few jottings, or if you used another strategy. We're trying to focus on using our mental calculations today in our learning. So, the answers are 102, 113, 355, and 452. Think about how you solved these equations, what strategy did you use? There is more than one way of solving these, but I'm going to show you, the strategies I would have used. Before I start a question, I try and think about what is the most efficient way to solve an equation. When I think of an efficient strategy, I think of one that is quick, and I think of one that has the least steps possible. What will make it easier for me? Rather than having to spend ages writing something out or subtracting, or adding lots of different parts. I try and think about what will make the equation easier to solve. So, for 50 add 52 I would use my near doubles, for 76 add 37, I would try make 100 first, for 230 add 125, I would partition these numbers into their ones tens and hundreds. And the 253 add 199, I would round and adjust. So, if you're not sure about these terms, we're going to cover them today. Let's start with our near doubles. So, welcome let's get our brains ready. Let me show you how I would solve 50 add 52. First of all, 50 and 52 have the same number of tens. They both have 50. I know that five add five is equal to 10. So I knew that 50 add 50 is equal to 100 double 50. Then I just add the two and the answer is 52. So, I want you, to join me for the next equation. When I show you the question, pause the video and have a go. But actually, if you want some help, just keep playing the video and I'll show you my strategy. You can listen and pause, as I explain it if you want me to slow down so that you can help yourself understand, think about what will help you the most. I'm going to show you the equation, and if you want help keep playing the video, if you will try it on your own using our near doubles, pause the video and have a go. 6.4 add 6.3. So, let me show you my first step. I can see that this number, both has the same number of ones they both have six. So I'm going to double, six double six is equal to 12. Following me so far? Now, I just have to add my tenths my 0.4, and my 0.3. 12 add 0.4, is 12.4 and 12.4 add 0.3, is 12.7, the answer is 12.7. We've just had a look at our near double strategy. Let's have a look at our next strategy which is, make 100. We're going to go through all the strategies in this list. Welcome to our next strategy, make 100. Now this strategy isn't always about making 100. It's sometimes we're making a 10, or a multiple of 10, or a whole, it's much easier to add a number, when there are empty placeholders when our number has digits that end in zero, rather than adding a number that has lots of different digits. Let me show you how. For 76 add 37, I'm going to try and make 100 first. I'm starting with my largest number which is 70, and adding 30, to make 100. I know that seven add three equals 10, so 70 add 30 is equal to 100. It's now much easier to add my ones. 100 add six is 106, and 106 add seven is 113. The answer is 113. So, get ready, you can join me with the next one, we're going to have a go via decimals. Remember, if you want some help keep the video playing, if you think you can do it on your own, with my strategy, pause it and have a go. You can also play my steps and pause, to work out each step with me. We're going to try and solve, getting my number line ready to help me, 4.2 add 6.51 pause the video, if you want to have a go yourself first. Try to make 10. So, I'm going to have a look at how I could make 10 and make a whole number with digits ending in zero first. I need to look at my ones. I have four and I have six. I know that six add four is equal to 10. I can make my number ones or ten. So now I want to add my tenths next, my 0.2 and my 0.5. 10 add 0.5, is 10.5, add 0.2 is 10.7, and now I just have to add my hundredths my 0.01 that I have left here. The answer is 10.71. We have now learnt two strategies. Our strategies were, near doubles and make a whole. Have a look at these three equations. Which strategy would you use and why? I want you to look at these equations and think about which strategy would be most efficient and easiest for you to do. Solve the equation once you've decided your strategy. Pause the video and have a go now. So, which strategy did you use? Let me show you what I would have done. So, for our first one, 2.4, 2.1, I would have used my near doubles because both of these numbers in our equation have the number two, so I can double them. For our second equation, I would have done make a whole, because I know 0.2 add 0.8, is equal to one. And for our last equation, I would have done near doubles because I know 11 add 11, is 22. What strategy did you use? Think, which is the most efficient way to solve these equations. This is not the only way solve these equations. You could use lots of other methods. You could use your formal written methods, you could use your place value counters, you could use deans, you could use your number line, or you could use the mental strategies that I showed you today. But what we need to remember is, which is the most efficient. which one is quickest, and which one has the least steps and which one has the least room for error. Remember, the strategy you use is personal to you. You might feel more confident with one strategy, than another. But it's really important that you are able to have a go at different strategies, and you can explain why you've chosen your strategy. Our mental strategies that we've looked at so far, have been on near doubles and make 100. Let's look at the next one, partitioning. My equation is 230 add 125. Let's see how I would partition this, I'm going to look at my hundreds, tens and ones separately. To start with, I have 200 add 100. This is equal to 300. Really easy. Next, I'm going to look at my tens, 30 add 20, is equal to 50. Easy once again, and now I just need to look at my ones. I have nothing in my ones column for 230, and I have five and my ones in 125, and now that I have partitioned these numbers, I am just going to add them all together. So, 350 and five, is equal to 355. Now it's your turn to get ready with our decimal numbers. Listen to me, and have a go with me, or pause the video, and try and do it yourself 6.2 add 1.6. So, I'm going to start by partitioning my ones. Six, add one is equal to seven. Next, I'm going to partition my tenths. 0.2 add 0.6 is equal to 0.8. And now I add my two different partitions together. Seven, add 0.8 is equal to 7.8. Our last strategy for addition is going to be, round and adjust. I really like this strategy because it's really useful in a real life context. When you go shopping, you see lots of things that cost 99P, or 199 or 299, and I use this strategy all the time when I go to the shops. Let's look at this number. 253 add 199. Let me show you how I do this first, I can see from the number 199, that it's really close to the number 200 and 200 is much easier to add on, so I'm just going to round up 199 to 200. When I round it up to 200, I added one. Now, that one didn't come from nowhere, I had to get one from somewhere. Now where can I get one from? Hmm, if I look at the other number in my equation, it's 253. I could take one away from 253 and make it into 252. And then this one that I subtracted, I added on to 199 to make 200. So now, I just have to add 200 and 252. This is much easier. I know what the answer is, 452. So, you're going to have a go with this same strategy with our decimals. Pause the video and have a go yourself or keep playing the video and pause and see if you can follow my steps. 5.98 add 1.26. So, let's think about which number we round first, would you round 1.26 or 5.98? I think 5.98 is closer to a whole number. If I add 0.02 or two tenths, then I would have six. So 5.98 add 0.02, is going to be six. So, where do I get those two tenths from? Hmm, I've got to subtract it from 1.26 1.26 subtract two hundredths 0.02, is going to be 1.24. Now I just have to add these two numbers together. Six plus 1.24 is 7.24. Good work. Thank you for following me so far, and that's the end of our addition strategies. We have looked at four different strategies for all our mental addition, near doubles, make 100, partitioning and round and adjust. Think about which would be the most efficient for you, when you solve different equations. With the two strategies we've just looked at closely, partitioning and round and adjust, which strategy will you use for these equations? Choose the strategy you'd use, and solve the equations. When you know the answers, start the video again, and listen to the answers. Pause the video now to have a go. Let's have a look at the answers. Which strategy did you use? For 1.9 add 0.2, I used round and adjust. I rounded up to two first of all. For 1.35 add 2.2, I partitioned, I added the tenths and I added the ones separately. And for 0.79 add 0.06 I rounded and adjusted again. I rounded 0.79 to 0.8. Now, there is always more than one way to solve a problem. And fantastic mathematicians, know which strategy they're using and why? And they can also prove their answer, by solving their equations with more than one method. So if you use a different method, but you got the correct answer, that's fine. Now it's time to look at our subtraction strategies. Here I've got four mental subtraction equations for you. I want you to have a go, at solving these equations, which is the most efficient way to solve these equations? Here are some of the strategies we discussed earlier, that we can use for subtraction as well as addition. Pause the video now, and have a go. Okay, let's look at the answers. Here are the answers to our subtraction equations. Check to see which ones you got right. These are the strategies, I would have used in each equation. For 135 subtract 42, I would try and make 100 first, I can partition 42 into 35 and seven 135, subtract 35 is 100, and then subtract seven is 93. For 476, subtract 250, I would have partitioned, I would have done 476, subtract the 200 first and then subtract the 50, I would have been left with 226. For 253, subtract 199, I would have rounded and adjusted. I know that 199 is really close to 200. So, if I subtract one more, and subtract 200, I would get 253. And then because I subtracted a greater number, I would add one more back to it, and get 54. For our last equation, I would have done a subtraction strategy called adding on. We're going to look at this more closely on the next slide. When I subtract numbers, I can use a strategy called adding on. Adding on is really useful, when I have two numbers that are close together. I'm going to represent this using a number line. When I add on, I find the difference between the two numbers. This is the same as subtracting them from each other. The difference between two numbers is the same as subtracting one from another. 500 and 489 are very close together. Let me show you using this number line. I'm going to add on. 489, plus one is equal to 490. I'm going to keep adding on until I get to 500 490 add 10, is equal to 500. So I found the difference between these two numbers. 10 add one is equal to 11, so 500 subtract 489 is equal to 11. The difference is 11, which means that 489 subtracted from 500, is equal to 11. Let's have a look at how this strategy could be used for some decimals. Pause the video and have a go, or listen to my explanation and pause as I go along. Remember, adding on is really useful for two numbers that are close together. 2.621 subtract 2.618 I'm going to start with a number line to represent my thinking. The smallest number goes at the beginning of the number line and I'm trying to get to the greater number at the end of the number line. So, my smaller number is 2.618. I want to try and add on to get to 2.621 2.618, add 0.02 add two thousandths is equal to 2.620. If I add on one more thousandth, I will get to 2.621. If I now add, these two numbers together, 0.02 add 0.001, it is equal to 0.003, three thousandths The answer is 0.003. Thank you so much for joining in with me for my mental calculations. It's now time for you to have a go with your independent task. Here's your first task with mental addition. I have put the different strategies we've used down the side, so you can try and think about which one is most efficient for you. For the second part of your independent task, you are doing mental subtraction. Think about which strategy is most efficient for you. I've got a help sheet to support you. This will give you some clues, as to which strategy to use. Pause the video and complete your task. Great work team on finishing your independent task. I hope your brain's hurting from all the mental strategies you've been using. It's now time to show you the answers so get ready to mark. Here are the answers for our addition equations. I've shown you some of my number lines and jottings, to help you understand what the answer is and why. Here are the answers to the subtraction equations. Thank you so much for joining on today's lesson. If you want to show your work with Oak National, please ask your parent or carer to share your work on Instagram, Facebook or Twitter, tagging @OakNational and #LearnwithOak. Thank you so much for joining in with your math lesson today. I hope you enjoyed it and I hope you feel really successful the end of this lesson. Now it's time to show what you know by going and completing the quiz. Have a fantastic day learning, and enjoy the rest of your lessons at Oak National Academy today. Bye.

Applying mental calculation strategies to adding and subtracting decimals

Applying mental calculation strategies to adding and subtracting decimals

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UnitMaths / Calculating with whole numbers and decimals

Maths