We estimate when answering questions to...

We always need to use column addition or subtraction when answering word problems?

Class B won 456 house-points before Christmas. Class D won 106 more. How many did Class D win? Does this question require addition or subtraction to answer it?

Edinburgh castle sold 345 tickets for tours on Monday. On Tuesday it sold 109 less. How many tickets were sold on Tuesday?

Solving addition and subtraction word problems

Key Stage 2

Maths

Addition and subtraction

Which of these calculations require regrouping?

Does this look like a reasonable answer?                       754 - 569 = 501

﻿Hello everyone, I'm Miss Brinkworth. I'm going to be going through this math lesson with you today, which is all about word problems. So, if we have a look at our learning objective, and what we're doing today, is we're dealing with addition and subtraction word problems. Now you probably come across word problems before, they've probably come at the end of a unit of learning. And you've maybe learnt about some multiplication and then you put it into word problems. I wonder if you've ever wondered why. Why do we make you do word problems at the end of your units? Well, it's because we're hoping that maths will enable you in whatever profession, job or career you choose, you are going to encounter maths every day. So, we want to give you some practise at how to apply what you've been learning all about addition and subtraction, into some real life contexts. So that it helps you throughout your life. So lets have a look at today's, what we're going to be doing on the agenda for today. So, what we 're going to look at first is some mental strategies, we will talk about written strategies later in the lesson as well, but we are going to concentrate on just the mental strategies at the beginning. Then we're going to look at how bar models can really help us when we look at a word problem and we think "I don't know what it's asking me to do." Bar models are your friend today, then it's time to think about the best method to answer that question. You've got lots of methods, you might not feel like you do but you do, I promise you. So we are going to talk about what is the best method to use for different types of questions. And then towards the end of the lesson there will be that independent work so a chance for you to practise what you have learnt, and then the exit quiz to see how many you can get right. Okay, so all you need for today's lesson is something to write with, a pen or pencil, and something to write on, and a positive attitude's going to get you really far. So pause the video and get what you need. Well done, let's get started. So, here are some really simple mental addition and subtraction questions. I want you to be able to do them in your head, they should be done really quickly, but while you're going through them please think about what facts you are using, where your mind goes when you look at these questions. Pause the video and get those answers. Lets see how you got on. Now, I'll put the answers up, but the point of this exercise is not the get the question right, although I expect that you would, because they are quite simple addition and subtraction questions. What I'm interested in is the strategies we've used when we're looking at mental, mental questions, ones that we can do in our heads. What do we actually think of when we're answering these questions? So if I think of 12 take away nine for example, that first question, I'm sure you all got the right answer of three. But I wonder how you knew that? I wonder if you're using the fact that nine add three is 12. I wonder if you used your three times table and you know that nine and 12 are in the three times table, you know the different between them is a jump of three. So it's all about these questions, just thinking about what strategies you're using to get them answered. Um, maybe with eight take away four, you know that four is, sorry double four is eight, so if we take one four away, we've got one four left. Maybe when you look at 34 take away 22, you partition it, you do the ones first and the 10's afterwards. So you do four take away two and three take away two to give you 12. So just about these different strategies that you might not be aware that you're using, but you are every time you do a bit of maths in your head. So we've got 14 take away eight, I would probably partition eight into four and four take away one four, and then take away another four, to give me six. I put the same question twice, but it's a good one, 12 take away nine again is three. Six add seven, maybe you know six add six, and you can just adapt that a little bit for six add seven is 13. Five add four, maybe you know that five add five is 10, so five add four is just one less, and that gives you nine. 11 take away eight, maybe you can count on eight, nine, 10, 11 well there's just a difference of three, between eight and 11. And again here are those answers for the rest of them. And you can see with that last question nine add three, and you can use the facts from before to answer that question. So these are going to come in really handy today as we move onto slightly more complicated questions. We are still going to have to utilise these mental strategies that you know really well. So, one more warm up for you. One of these questions has been answered incorrectly, one is good, one they've made a mistake. I wonder if you can identify which one is wrong, and as a little bit of a challenge, why or how do you think they've made that mistake? Okay, how did you get on? So, hopefully you can see that the question with a problem is this one here. And that's because on this subtraction question they've got it the wrong way round. They haven't taken the part, the second number away from the whole which is the top number. And they've done that because I imagine is because it requires some regrouping. So instead of doing eight take away nine and regrouping from their 10's, they've done nine take away eight and put the number one. I can see why people choose to do that, I can see that it's slightly easier, but it does get the wrong answer. So try and regroup when you need to when you see subtraction questions. Okay, so this is what today's lesson is going to look like, word problems. We're going to go through quite a few of them together, and I'm going to give you my ideas of how to answer them. Now these are just my ideas and they are some efficient strategies but you are welcome to answer these word problems however you wish. So lets have a look at this word problem together. A one hour traffic survey on the M8 motorway between Edinburgh and Glasgow counted 567 cars and 254 lorries. How many vehicles were counted altogether? Right I would probably read the question at least twice just to make sure I understand what it's asking me. Then I would get a picture in my head, okay Edinburgh and Glasgow big places, they've counted lots of cars and lorries, there must be lots of traffic, I can see this motorway it's going really quickly, people are nipping passed. I can see that in my head. And then going to imagine someone has got their clipboard maybe and they're writing down, they're doing a tally each time they see a car or a lorry. And the question says "How many vehicles "were counted altogether?" Well lets see if a bar model, I'm going to underline the numbers I use, and let me see if a bar model is going to help me. There you can see in green, my green bar are my cars, and my purple bar is my lorries, and then I've written the numbers above them. Right, does this help me work out what I need to do to answer this question? I've got what I know there, I know how many cars there were, and I know how many lorries. The question is saying "How many vehicles were counted altogether?" Right, well, this bar model makes it clear to me that what I'm looking for is the whole. I've got two parts, I need to find the whole. Finding the whole means that this is an addition question, I need to add together how many cars and how many lorries were found altogether. Now it's tempting to look at the altogether word in that word problem and always assume that it's addition, but be careful that's not always the case, it is in this case, this is an addition question because we've got two parts and we need to find the whole. But don't just focus in one word, really try and get the picture of what the whole question is telling you. Get that picture in your head before you decide what the operation is. To help you today the operation is only going to be addition or subtraction. So, here's my addition question and what I've done here is, so it's 567 add 254, and what I've done is I've had a go at a quick estimate. Now remember estimates are there to get you an idea of what the answer might be, they should be quick and simple, you should be able to do them in your head, and it should give you the kind of number that you're looking for. So that when I get my exact answer at the end I can just check it against my estimate just to check that it looks reasonable. So to get that estimate I rounded, I rounded to the nearest 10 and I rounded 567 to 570, and I rounded 254 to 250. I then added them together and got that number 820. So I would expect my answer to quite near to the answer 820. You don't have to do an estimate as you go through these but I find that they really help me, even if I just do them in my head and don't necessarily write them down. Okay there's my bar model again to help me. So I'm going to just choose column addition for this question. That's because there's some regrouping needed, I can see that I'm going to get to a number bigger than 10 when I add together my 10's and my ones, and I know that column addition is a nice clear way of setting that out and making sure I get an accurate answer. So remember with column addition that you start with your ones, seven add four. Oh what mental strategy can we use to help us with seven add four? I know the number bond seven add three, seven add three is 10, four is one more than three so I'm going to end up with a number one bigger than 10. I'm going to end up with 11. Remember that your one in 11 is in the 10's column so it comes under the 10's column. And we remember when we add together our 10's column. Five add six or six add five, it doesn't matter which order you do those in, well five add five is 10, so six add five must be 11 but don't forget the one that we've moved over from ones that's underneath there. So we write 12 and we've moved our ones this time into our 100's column. Five add two in my 100's is seven add one is eight. And there's my answer. Looking back at my estimate I can see that I was really close. Lets try another one. It's the same question but lets have a look at how's it's worded slightly different, we've got a lot of the same information, slightly different question. A one hour traffic survey on the M8 motorway between Edinburgh and Glasgow counted 567 cars and 254 lorries. How many more cars were there than lorries? So we haven't got the word "Altogether" this time we've got "How many more." Right let me have a think about a bar model then that can help me with this question. How many more? Well my whole is cars 567, my part is lorries and what I'm looking for is the other part. If I'm looking for a part it's a subtraction question. So there's my bar model which shows my known and my unknown. Okay so column subtraction then, got another estimate there, this time I'm subtracting, I rounded them again to get an idea of what my answer might be, and now I need to do some column subtraction. Now, this question doesn't actually require any regrouping, so you might be able to do it as a mental question which would be absolutely brilliant. If we did column subtraction though, we can lay it out it doesn't take too long and we can be really sure of getting the right answer. So seven take away four is three, six take away five is one, and five take away two is three. And I can check that against my estimate and see that 313 my accurate answer is really close to my estimate of 310. Okay we're going to go through one more word problem together before it's time for your independent work. This question is slightly different, and it's going to be really useful for us to get a picture of what's going on in our heads. Adbi's family used 137 litres of petrol to drive to Edinburgh and back. They used some more petrol to drive to France and back for a camping holiday. They used 229 litres altogether, so how much did they use on their camping holiday? Well I like to picture Abdi's family in their car, they're doing lots of driving around. They drove to Edinburgh and back, maybe they went on a day trip to see the castle. And then they drove to France and back. And what we've got there is how much petrol they used altogether. We've got altogether, we've got the whole, we know how much petrol they used in total, the whole amount of petrol they used. What we're looking for then is a part, which of these bar models do you think will be most useful to answer this question? It's actually this one here. We've got our part and now we need to look, sorry we've got our whole and we've got one part, we now need to look for the second part. So as we are looking for a part, we know that it's a subtraction question. And again it's quite a nice subtraction question, we do have a little bit of regrouping to do but I can see that's just in the one column. So, nine take away seven, oh I'm going to do an estimate first, there we are, I've rounded my numbers again and done a quick estimate, so I'm looking for a number around 90. So, nine take away seven is two, I then need to regroup in my 10's so I'm going to use one from my 100's which will change my 100 from a two to a one, and changes my 10's from two to 12, 12 take away three, that was back we did that quite a lot at the beginning of the lesson, so 12 take away three, three times table gives me nine, and then be careful here. With my 100's I haven't got two take away one, I've got one take away one. And sometimes people make a mistake when they do one take away one, if you've got one and you take it away, you've got zero. So there we are. My answer is 92 and I can see, I just check that against my estimate but that's really close to the figure that I thought I was going to get to. Okay, so, here is another question for you, I would like you to pause the video and have a go at answering this question please. I've given you a bar model there so hopefully you can see that this is a subtraction question, you've got the whole, you've got one part, you're looking for the other part. So, here's my estimate, 600, sorry 360 take away 30 is 330, that can be the estimate to work out there. And here's my question, my accurate question, it's quite simple because there's no regrouping needed. And there's my answer, 322. Well done if you got that. Okay so, this is a success criteria, that means it's a list of things like a menu that you, if you follow you should be able to answer word problems really accurately. So, it's useful I find to draw a bar model to show what you know and what is unknown. It can be useful to round and estimate to see what ballpark that you're looking for. Complete using the best method, it might not be that a written method is needed, you might decide that a mental method is fine and that's great. And then you can check your answer against your estimate or at least have a look at your answer and see whether it looks reasonable. If it's an addition question has it got bigger? If it's a subtraction question has it got smaller? Does it look like it's in the right, in the right kind of size? Okay pause the video here and have a go at some of those word problems on your own. Lets see how you got on. So I'm going to give you the answer questions and the answers. I'm not going to tell you what method you needed to have used, whatever method you used as long as you got the right answer is absolutely fine. So at a school fair the raffle raised £168. The cake stall raised £176. How much did both stalls raise together? Well we're looking for the whole aren't we? We've got two parts, we're looking for the whole, so that makes that an addition question, and well done if you got 344. Question two, we've got an number of children who visited a zoo on Saturday, it says that 277 more visited on Sunday, so how many children went to the zoo on Sunday? Well we know how many went on Saturday and we know how many more went, so again we need to add them together to find our whole. And well done if you got 645 for that. And the final question says there is a primary school with a number of children and a secondary school next door which has 648 more. Be careful because sometimes what happens with these questions is people don't necessarily read them really clearly. It doesn't say that the secondary school had 648 children, it's says that the secondary school has 648 children more than the primary school. So that's when it becomes really careful, really clear that you need to read the question carefully. Get the picture in your head of really what it's telling you. Again this is an addition question, we've got two parts we need to find the whole. Well done if you got 924 for that. Okay for part B any question that you come up with which is a subtraction question is absolutely fine. So you might want to say something like, "A school which has 465 children in total, "274 of them went on a school trip. "How many stayed at school?" That would be a perfect word problem. For the second part of that question, can you spot my mistake? Really well done if you could, because this is quite a tricky question. The question says that tiger class are counting their coloured pencils and they 374 pencils sharpened and ready to use, there are 86 fewer than this that need sharpening. How many pencils are there in total? Well the problem with this bar model is that it suggests that we've already found the whole, and we haven't. We are still looking for it, so what the questions really, what the questions really asking for is 374 add 374 take away 86. So we need to work out what 374 take away is 86 is and that would be a bit of a more useful bar model to show that a bit more clearly. Okay time for you to complete the final knowledge quiz. Well done on a lot of new learning today everybody, I'm really pleased with you. Enjoy the rest of your day, bye bye.

Solving addition and subtraction word problems

Solving addition and subtraction word problems

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UnitMaths / Addition and subtraction

Maths