Measures Contexts to Show the Commutative Law of Addition

Key Stage 1

Maths

Addition and Subtraction

﻿Hi, everyone. Welcome to your math lesson with me, Mrs. Harris. Let's get started by looking at the practise activity that Mrs. Parr set as last time, because I had to go as well. Mrs. Parr asked us to write an addition story, a math story, where we had to have our addends come together. And then, we ended up with our sum, but then she wanted us to swap our addends over and convince us that the sum remained the same. Just pause the video, and tell your two stories with the same addends to somebody in your house. I bet whoever you told your story to you thought it was fabulous. I wish I could hear them, but I'm too far away. Now, I'm hoping that you used your pictures to help you tell a story, and that you remembered to swap your addends over for your second story. And maybe even the person listening, if they listened really really closely, could tell that the sum remained the same. Now I'm going to tell you my story, but you might notice I didn't draw pictures. Instead, I chose to take photographs. So here is my first, then, now addition math story. First, I had two girls in the book area. Then along came three boys. Now I have five children in the book area all together. I could write that as an equation. I could say, first, I had two children in the book area. That's my two girls. So first, I had two girls in the book area. Then along came three boys, and now I have five children in the book area all together. I'm going to tell you my story again, but I'll remember just what my addends over, and listen carefully to check that I remember to keep the some the same. Have you noticed how my story this time starts with the three boys in the book area? Last time it started with the two girls. So I've definitely swapped my addends over. So listen carefully to my second story. First, there were three boys in the book area. Then, along came two girls, and now I have five children all together in the book area. So that's my new story. And I write it differently as well, don't I? Last time I wrote the two first, because I had my two girls in the book area first. This time I'm going to write my three first to represent the three boys in the book area. My second addend, this time, represents my two girls waiting to go in the book area. And my sum remains the same with five children all together in the book area. Did you notice how my story swapped over, how my addends swapped? Did you? Well done! So, we need to remember our generalisation, and I've got that written up here. If we changed the order of the addends, the sum remains the same. Let me say it again. I would like you to try and join him with me. If we change the order of the addends, the sum remains the same. Your turn. Well done. And, let's do it one more time together. If we change the order of the addends, the sum remains the same. My story proved that. Did yours? Well done. This time, I'm going to show you my equations, but without the pictures. If you got time, you could draw your very own pictures to go with them. So first, I had my three. Hmm, actually that was my second story. It doesn't matter. So this was my three boys in the book area. Then along came two girls, and then we had five children altogether in the book area. Three plus two equals five. And now I need to do it the other way. I need to swap my addends around. Could you really really, really quickly just do that for me? Did you remember to put the two first? Well done. So the two has moved from here to here. So what's my next number going to be here? Of course, it's going to be the three. There we are. There's the three moved from here to here in my equation. So what is the total going to be? Yeah, it's going to remain five, because if we change the order of the addends, yep, we've done that, this sum remains the same. The five is our sum, so that's going to remain the same. Fantastic. If you didn't quite do some equations to match your story, why don't you pause the video now and do them now just to convince yourself that if we change the order of the addends, the sum remains the same. Well done. Oh, a fence? Fences aren't usually that interesting, are they? But this fence, this is a special fence. This fence is to keep the dinosaurs out, rah! And, well, we started off with a fence being this long, but the dinosaurs they grew and they grew and they grew, so we needed to make the fence this long. So my first addend is going to be one two, three, four, five, six. Oh, I've just noticed some more information. I don't need to count the fence panels at all. I've got this information here. And in this information here, it tells me this fence is two m, and the m stands for metres. This section of fence is two metres long. So I don't need to count the fence panels at all. That's good. That would've taken me quite a while, and it wouldn't have been right. This fence panel is two metres long. And the second bit of fence that we had to build to keep the dinosaurs out was three metres long. Just wondering how long is my fence altogether? I know my two addends, two metres and three metres. Think, I might use a bar model here. And my bar model is going to show me that I have two and three, two metres of fence plus three metres of fence that we added when the dinosaurs got too big. Can't have them escaping around the school, can we? So, two plus three will give us our sum and tell us how long the fence is all together, and it is five metres all together. This fence all together is five metres long. I could write that as an equation as well, couldn't I? I could write two plus three equals five. So that could be my first equation. But today we're really thinking about swapping addends over, changing the addends, and the sum remaining the same. I think I'm going to need another fence. So here is my second fence. And if I've got this right, it will also be five metres long, because we're really thinking about the sum remaining the same, but swapping the addends over. So this time my fence started off as three metres long. Here's my three m representing three metres. Didn't want to write the whole word metres. So, three metres plus two metres of fence. The two metres of fence is the extra fence we had to pop on the end to make the fence longer. So if this is right, three plus two is going to be five metres just like two plus three is going to be five metres. Can I use a bar model again? Do you like my bar models? Aha, I've got my three metres and my two metres. Yes, my sum has remained the same, and that's because I've used the same addends. I've just changed the order they were in. And my equation will look different as well, won't it? Because I'll put my three first, then my plus sign, then my two, my second addend, and then my equal sign and my five, the sum. And here it is, look, three plus two equals five. My sum has remained the same. Yeah! Thought you might just need a little bit, a little smidge more convincing that I've changed the order of the addends, but my sum has remained the same. So I'm going to put my fences one on top of the other, so you can see nice and clearly. So my first fence, this was my first fence, and we couldn't count it, could we? And, in fact, we didn't even need to, because we had the measurements provided for us. We had two metres and three metres. They were our two addends, and when we added them together, we said two plus three equals five, and five is our sum. And we need to check that that has remained the same in my next fence, even though I've swapped the addends over. So here is my second fence, and already just by looking at it, I can see, can you see, that it looks the same length? Let's just check by looking at the measurements, though, in case my drawing wasn't quite accurate. So I've got my three metres and my two metres. That's really helpful. So my two addends are three and two. And look how they've changed here. I've got my two metres, but that was my first section of fence in the first fence, two metres, two metres. Remember that m stands for metres, and here on my first fence, I had my three metres, but it's first in my second fence. So I'll change the order of them in the equation as well. But, hey hey, the sum has remained the same, but this time I have three plus two equals five. Do you know there's a really, really cool way we can write them where we don't even write the sum? We can write three plus two equals two plus three. Hey, that's saying that three plus two is actually the same as two plus three. Whoa, that's really cool. I think we should use it again in a minute. I come across two children, and they're having a little bit of an argument, and I think we can settle it for them. They're arguing over who's got the most money. This is Lola's purse. Here it is. Lola's got four pounds in her purse, and this many pound coins out of it. But Finn, he's got five pound in his purse, and this many coins out of it. Let's see if we can help them find out who's got the most money. I think we're going to need to look at the addends, so the money in the purse and the money outside the purse, and find out the sum for both of them, 'cause then we might find out who's got the most money. So can you just write the equations for me now? You knew I was going to ask that, didn't you? Okay, here's the equation to go with Lola's purse, four pound in the purse, five pound out of the purse, nine pounds all together. Here's the equation to go with Finn's money, five pounds in the purse, four pounds out the purse, nine pounds all together. They've the same amounts of money! Why is that? Just tell somebody you're near why have they got the same amount of money. Why is their sum the same? I really, really hope you told somebody, just because they've got the same addends, haven't they? The addends have just changed places, because, remember, we know that if we change the order of the addends, the sum remains the same. Great mathematical thinking if you use that reasoning. So, Lola started with four pounds in her purse, but Finn, he had four pounds outside of his purse. The four has changed places. Lola had five pounds out of the purse, but that's exactly what Finn had in the purse. Four plus five equals nine. Five plus four equals nine. Argument's settled. They've got the same amount of money. Phew, thanks for helping them out on that. But do you remember, we found a new way of writing our equations where we didn't write the sum? Wonder if you could have a really quick go at that now, and then I'll show you what I've done. Okay, so I've got Lola and Finn's purses, and I can pop a little plus sign in here. Lola has four pounds plus five pounds. Finn has five pounds plus four pounds. And we know that they are equal. Four plus five is equal to five plus four. Brilliant. I hope you did have a go at writing our new style of equation. And maybe you got it right? Maybe you didn't this time. That's okay. We're learning. And we'll learn together in the next slide too. Okay, I've got some more purses here, and this is your chance to practise our new way of writing equations where we don't write the sum. We just write it with the addends changed places, because we know if the addends change places, the sum remains the same. So I've got two purses. One purse has six pounds in it. The other purse has two pounds in it. I'd like you to take a second to write the new style of equation for me, but I'm not going to show you the purses swapped places yet. That's your job to imagine, or maybe even draw if you have time. So take a second now to do that for me. Okay, so this is what I wrote. I wrote, maybe you could say it with me, six plus two equals two plus six. Look, this addend just went there, and my addend of two just went there. The six here represents my pink purse, and the two here represents my green purse. They represent the same things in the second part of my equation, don't they? But they've just swapped places. To help me, I did draw it as well. So here is my addends swapped places as a pictorial representation. There's my picture. There's my two pound purse first, and here is my six pound purse. Before I wrote the equation, as well, I was a little sneaky. I popped myself a plus sign in there, an equal sign in there, and a plus sign in there. Six plus two equals two plus six. They're the same, aren't they? They would have the same sum. Good job for giving it a go. I'm really proud of you. You're working really hard today. Okay, I got a little problem for you, and to solve it, you're going to have to think about all the information we've had in this lesson. Okay, it says true or false. True means something is right, it's correct. And false means, unh-uh, it's not right, it's wrong. So, I've written an equation. Say it with me. Four plus three is the same as four plus four. Hey, don't shout at me. Is it true? Is this one right? Okay, maybe you can tell me really quickly if it is true or false, but you're going to have to tell me why. So, do take a second to think is it true, is it false, and why? Okay, so it is, in fact, it's false. This is wrong. I hope you told me it was wrong, because, well, my addends aren't the same, are they? My addends have not changed places, but different addends come in. Look, on this side, I've got a four and a three, and on this side, woohoo, I have got a four, but, unh-uh, I haven't got a three, have I? Got another four. Now we could go just that little step further to convince me, well, the sum over here, four plus three is seven, and four plus four, well, that's not seven, is it? Four and four more, ugh, not seven, eight. I can't draw an equal sign in the middle, can I? Because they're not equal. They're not the same. So well done if you said that this was false. Good job. I was trying to trick you. Very hungry caterpillar. He's been getting closer and closer all through this lesson. And now he's here to see your practise activity. The thing I'm going to leave you with ready for your next lesson. So, your job is to match the expressions and use an equal symbol to create an equation. So I've got a red column, and I need to match them with an equation from the blue column, but where the addends have changed places. Hmm. Think I'll do a little example for you first, because I don't just want you to draw lines to match them up. I'd like you to write it as our new style equation with the equal sign in the middle. Now my first one is two plus one. So I know from everything I've learned in this lesson, that I'm looking for an equation on this side where the addends have changed places. So definitely looking for one with a two. Yep, no two in that one. Oh, two in that one. Oh, it's in the same place, and the second addend is not the same. Yep, that's not the one I'm looking for. Okay, no. No. That one's got a six, has got a one, but it's in the same place, and it's not right, because six isn't an addend in my first one. So, two plus one is the same as one plus two. So the first thing I'll do, and you might have a ruler to make it a little neater if you're writing them out, is I'm going to join them up. But remember, I'd like you to create the equation. So, I'd like you to say two plus one is equal tom our nice equal symbol... It's equal to, ah yes, I matched it up to help me, one plus two. So, our addends have changed places, but the sum has remained the same. We just didn't write the sum, did we? We wrote our equation of two plus one is equal to one plus two. And when you've done that, you have done your math lesson today, and we are really proud of how well you've been working today, how much attention you paid. And I look forward to hearing about how you've got on with your practise activity. So, bye! Bye from me, Mrs. Harris.

Measures Contexts to Show the Commutative Law of Addition

Measures Contexts to Show the Commutative Law of Addition

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UnitMaths / Addition and Subtraction

Maths