Consolidating order of operations

Key Stage 2

Maths

Calculation problems

﻿Hello, welcome to today's math lesson with me, Miss Jones. Hope you're doing okay today. I am super excited to get started. Now just to warm up our brains, let's do one of our riddles together. Okay, are you ready? What has hands but cannot clap? What has hands but cannot clap? Have a little think. Okay, the answer is a clock. Ah, seems obvious now, doesn't it? Be sure to share that with your family and friends later on. Okay, let's get started with our math lesson. In this lesson, we're going to be consolidating what we know about the order of operations. We're going to start by applying what we know about the order of operations to some problems based on perimeter, then we're going to do a Let's Explore task around that, and then we've got a detective task looking at brackets when we're looking at order of operations. Finally, we've got challenge question and the multiple choice quiz for you to have a go at. Before we start today, make sure you've got something to write with and something to write on, pencil and piece of paper should do the trick. If you haven't got that at the moment, pause the video and go and get what you need. Okay, hopefully you've got what you need and you're ready to start. Let's have a look at our first question today. What calculations might you use to find the perimeter of this rectangle? I want you to just have a little think about that. What might your calculation look like? What do we know about this rectangle, and what do we know about how to find the perimeter? I'm going to show you four different calculations. Now, each of these calculations could be used to find the perimeter, and each of these calculations will get me the perimeter and the same answer. How is that true when they all look quite different? Well, let's go through each one. So looking at the first one, we've got 23, which is my width here, and I've got 87, add 23, add 87, it goes all the way around and should give us our perimeter. And when we get our answer, we do 23 add 87 it's 110, we add another 23, which gets us to 133, and then we add our other 87, which gets us to 220, okay? Now looking at our second calculation, it's a different way that we might solve our perimeter. We've got two lots of 23 added to two lots of 87. 46 added to 174 gets us 220. When we're using this one, we need to remember that multiplication has priority over addition, so we need to do our two multiplications first before we add them together. Let's look as our third one, two times 23 is 46, two times 87 is 174 added together gets 220. It's quite similar to the one we've just done, isn't it? Look at these two, what's the same and what's different? Well, they are very similar, but this one's got brackets. Now the brackets are around the multiplication, multiplication has priority anyway so we actually don't need the brackets there and we still get the same answer if we have them in. Just looking our final one, we've got two lots of 23 add 87. So they've added the length and the width and then doubled it. If we do that, we have 110, we do the brackets first 'cause brackets have priority, and then let's double it, two times 110 is 220. So there are lots of different ways we could use the calculate to perimeter, and if we understand our rules in terms of orders of operation, knowing that multiplication and division takes priority and brackets take the ultimate priority, then we can use any of these to help us work out the perimeter, choosing the most efficient one for us. For your Let's Explore task, we're going to focus on explaining how a particular calculation will help us to find the perimeter, and how we can work it out using our knowledge of order of operations. So let's take these two, and let's look at some example explanations from these two pupils. Looking at the first one first, two times 23 added to two times 87. How do we know that helps us find the perimeter, and how can we work it out? He says, "Because I know that multiplication has priority over addition, I know that I have to complete the two times 23, and two times 87 before I add the products together." Okay, and he's absolutely right. He is referring to order of operations. He knows to find the perimeter, he's going to have to do the multiplication first in each instance, before he adds them together. Okay, let's look at this next one, two times 23 plus 87. "Because I know that calculations in brackets need to be completed first, I can see that this calculation is adding the two side lengths together and then doubling the total. The lengths of the sides are 23 and 87, and the perimeter will be double that." I like the way that she's referred back to the lengths of the sides in her explanation, so it's really clear that this is linking to perimeter. And you can see that she's absolutely right, we do the brackets first, find the perimeter, and then we double it, and that's how we can write down our calculation nice and clearly. Okay, all right, let's have a look at your Let's Explore task. Here we have four other rectangles, and I want you to think about finding the calculation that will help us find the perimeter. Now you've got some options here. I want you to think about which ones will help us find the perimeter for each rectangle. Do they all match of a rectangle, or are there any that don't help us find the perimeter? Okay, make sure that when you're going through each one, you're using an explanation. Now you can either say your explanation out loud, or you can write it down, it's up to you, but try and use some of the sentence stems that the pupils before you used. How about, because I know, that might be a good way to start your sentence. Okay, pause the video now to have a go at your Let's Explore task. Okay, let's go through each of these together. So looking at our first one, two times 25, we can see that that matches with this one here. Now you might be wondering, well, where does the 25 come from? If you look closely, if we add our length and our width together, we get 25 then we can double that to find the perimeter. So this is a bit like saying 22 plus three, then doubled, okay? Let's have a look. This one matches with this rectangle so we've got our length and our width, 12 and nine, and again, they're being doubled. Now look at the use of brackets. And because I know that brackets have priority over any other operation, I know that I do everything in the brackets first, and then I multiply by two. So that calculation works to find the perimeter for this rectangle. Okay, four times nine will help to find the perimeter of this rectangle, which is also a square. We've got four equal sides, because I know this is a square with four equal sides, I know that I can multiply by four to find the perimeter. And finally, this one matches to this one, we've got our length and our width 12 times five, I'm sorry, 12 and five added together, and doubled. But here we've got 12 times two. So what they've done is they've doubled 12, the length, and then the length again, and then they've doubled five, five, and then this again, and looking at our operations, we know, because I know that multiplication takes priority over addition, I know that I do this and this first before I add them together, and that will get me my perimeter. And let's have a look at the two that we didn't use. Let's think about why these wouldn't help us find the perimeter. Now, this one has similar numbers to use for this rectangle here, but it's using multiplication, 12 lots of two plus five times two. Now I notify in the perimeter, that's thinking about our side lengths here, we've got two added to 10 to make 12 but then we multiply by 12. Now, 12 multiplied by 12 isn't going to find us our perimeter. I've got nine squared here, which is the same as nine times nine. You might think that this might relate to this one, but we know that the perimeter will be four lots of nine rather than nine times nine. This equation might be used to find the area of the square rather than the perimeter. So hopefully you notice that one. Okay, let's move on. Okay, it's time for your main task. Now today's task I'm quite excited about. We are going to become detectives. I'd like you to become Detective Bracket. Now Detective Bracket's boss has sent him a message. Should we read it out? I don't know what this boss is like, but I imagine they're quite posh so I'm going to do a posh voice. You have been assigned a special task. On your activity sheet, you will encounter a series of questions. Some have been answered correctly, some have not. Your mission, should you choose to accept it, is to go through the questions and sniff out the errors. Where there are errors, your job is to fix them by putting the brackets in to make the answer correct. Best of luck." Wasn't a very great voice really, was it? Okay, so what we need to do is look at each calculation and see if it's correct. If it's not correct, we need to add in brackets to make it correct. But the trick is thinking about where we add the brackets. Let's have a look at two examples before we start. Okay, so on my first one here, I can see that we've got some multiplication here and some division which need to take priority. So I'm going to start off by doing the multiplication and division. Now multiplication and division have equal priority so I can do those in any order, but I need to do those first before I look at 68. So we've got eight times seven is 56 divided by four is 16. Okay, 68 take away 16 is 54, great. This one is actually correct. Now let's have a think about our next one. 24 added to eight divided by four times two equals 52. So quite similar in the fact that we've got division and multiplication to do first, and then we think about the 24 afterwards. So we've got eight divided by four is two times by two is four 24 add four is 28. But our answer doesn't say 28, so this one is incorrect. But what we need to do now is add in brackets to make it correct. I'm not sure where to put the brackets, so I'm going to try it in a certain place and see if it works. I'm going to put them here first. So this time I've got 24 added to eight, which gets me 32, then I'm going to divide 32 by four, which gets me to eight then times by two, and I get 16. That's still not my right answer. So let's try the brackets in a different place. This time I'm going to try my brackets here. So this time I've got to do everything in the brackets first, but within my brackets, I've got some division so I do the division before I do the addition. So we've got eight divided by four here, which is two so 24 added to two is 26. Then I do the bit outside the brackets times by two 26 times two is 52, so now it's correct. Okay, so now you know what you need to do, I'd like you to pause the video and go and do your task. Okay, let's go over some of the answers for the task together. Okay, so looking at this first one, I know let's just try it without any brackets. So I know that division and multiplication have priority over the subtraction here, so I need to make sure that I do everything over here first. Division and multiplication have equal priority so it doesn't matter which order I do these three in as long as I leave that 14 for later. Okay, so six divided by two is three, three times three is nine, 14 takeaway nine is equal to five, great. So this one is correct. Let's have a look at one more. Let's see if this one needs any changes, let's try it as it is. So we've got eight times six, multiplication remember takes priority so we do this bit first is 48 take away two is 46 add three is 49, just a different answer. So this one isn't correct. So what you needed to do for this one is add in some brackets. Let's try it now. We've got eight times by six takeaway two, so that's eight times by four, so that will give you 32 added to the three is 35. Now it works, okay? So you get the idea. So I'll go through the others to make sure and to allow you a chance to check over your answers. So, for this one, you should have put the brackets here and then here in order to get the answer six. This one, the brackets go here. This one was correct just as it is, no need for any brackets. This next one, the brackets go between the three numbers of 34 takeaway six add seven and we multiply the whole thing by three, then this one was correct as it was, this one we needed some brackets to make it correct, 12 multiplied by seven and then take away one. And then finally this one was correct as it is. So make sure you check your answers against this to see if you were correct. Okay, to finish off, we've got a challenge question that was in your independent task. And for this problem, decide if the calculation, which we can see here in green, will provide a correct solution to the problem, or whether we need to add brackets to ensure the correct order of operations is going to get us the answer we need for this problem. Okay, so let's look at the problem. A recipe suggested to allow 250 grammes of meat per person. Roasting the meat takes 25 minutes per 500 grammes, and an additional 20 minutes. How long will it take to roast the meat for six people? Now there's a lots of information there so let's take it step by step. So we know that we need 250 grammes of meat for each person, we also know that there are six people. So this first part of the equation seems correct to find out the total amount of meat. Six times 250 grammes will tell us how much meat we need. But the question is asking us how long it takes to cook. So let's look at the next bit of information. We know that in order to work out our cooking time, we need to think how many lots of 500 grammes we need. So we need to divide our total amount of meat, which is here, by 500, okay? And then for every 500 grammes, we need to use 25 minutes. So we times that by 25. So, so far so good, this calculation is correct. Now the last bit of information is to add on an additional 20 minutes to cooking time. So we add 20. So hopefully after some investigating, you came to the conclusion that this will give us the correct answer. And if you managed to work it out, the answer was 95 minutes which we can say is the same as one hour 35 minutes. Hope you enjoyed today's lesson. Please ask your parent or carer to share your work if you want to. When you're done, please complete the multiple choice quiz. Thanks very much.

Consolidating order of operations

Consolidating order of operations

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UnitMaths / Calculation problems

Maths