Video: The commutative Law of Addition using augmentation

﻿Hi everyone, it's Mrs. Paula here again, at the end of the last session you were left with this independent practise activity, it says can you write some pairs to some pairs of addition equation to go with this image, okay? And we were asked to remember the generalisation from the last session should we just check that again? If we change the order of the addends the sum remains the same, let's see how you got on. So I've rearranged my backpacks to make it easier to see my addends. So I put my blue backpacks over here and my yellow backpacks here to help us write our equation. So the first equation I've written is we have two blue backpacks plus four yellow backpacks is equal to six backpacks altogether. But if we wanted to start with the yellow backpacks that would be fine and we would write our equation like this four backpacks plus two backpacks is equal to six backpacks. Now I wonder, did anybody arrange that in a different way? Did they not use colour? Maybe you looked at different thing to organise them by, there we go. Now I have a group of two big backpacks and a group of four little backpacks but actually they're exactly the same equations our two here and here represents our big backpacks and our four here and our four here represents our small backpacks. So today we're going to carry on looking at addition, looking at adding but we're going to do it slightly differently. We're going to think of it as a story instead of putting two groups together, we're going to start with a number and look at our story through the numbers, okay? So tell me what you see on the screen first. Good, we've got one child on the swings first there was one child on the swings then, three more children came along now they're all four children on the swings. So our story goes in that direction and let's have a look at the numbers. We've got one first, there was one then we added three, now we have four and here is our equation, one plus three is equal to four. So in the last session you learned that if we change the order of the addends, can you finish that sentence for me? The sum remains the same, well done. Okay, so let's give that a go, we're going to change the order of the addends here are my pictures and now we're going to add the story. So our first addends here is three then we add one and now we have four. So there is our equation to go with our pictures everybody happy with that. Have you spotted a problem? Have a look, here's our first addends three does it match up picture? No, it doesn't does it? I've changed round I changed the order of the addends which is fine it gives us the sum four our equation here makes sense, doesn't it? But it doesn't match the pictures what do I need to do? I need to change my story round as well. Okay, so now I've sorted out my pictures i've got a different picture to begin with what could you say about that picture? First, there were three children on the swings then one more came to join them. Now we have four children all together excellent, let's have a look at our number sentence and our story then, three is our first addend, isn't it? We have three children on the swings plus the one that comes along and now we have four altogether. So our equation is three add one is equal to four we have exactly the same sum as last time we've just swapped our addends around and that meant we had to change our story, didn't we? So here's off the equation again we can see that we have one child, three more children and now we have four and here we begin first of all, we have three children. Then one more comes so we have four all together, can you see that the sum is the same? In this equation here, up here what does the one represent? Good, it represents the first child, doesn't it? But down here, what does the one represent here? It represents the then bit, but then one more child came here our three represents the three children that came but down here our three represents the children that were there first, well done can you spot the bit that's the same? Well done, you know this now doesn't don't you it gives us the sum, both equations give us the same sum. So we know then that because both of them, sum to four, we can see here that one plus three is equal to three plus one. If we change the order of the addends the sum remains the same. So let's have a go with another example first what can you see on the bus? First we have six children, well done you might have spotted that there's four on the top and two underneath so altogether there first we have six then one more child wants to get on now we have seven, well done. So have a think, what are our addends and what is our sum? First we have six children then one more is added now we have seven, here is our equation down here. So let's try swapping those addends round in our story now can you think our addends before we're six add one. So what do you think they might be this time? There's a bit of a clue on the screen there for you, isn't there. Good our first we have one child on the bus and you think what's coming, then I bet you were right six children wanted to get on, now we have seven we have the sum. We started with one first we had one child and six more came now we have seven. So our addends have been swapped round but our sum remains the same. So let's have a look at our equations and our pictures side by side again so we can compare the number sentences, compare the equations. Okay, so here we got first we have six children on the bus good, so this addends here, what does it represent? The six children on the bus, well done and the one represents? The one child there. Okay, here,we've got a different equation down here because our addends sorry, have been swapped round, okay? So have a think, what does the six represent in the first picture? What does the six represent in the second set of pictures? Good, first of all, the six represents the first children there then the six represents the six children who want to get on. Now have a think about the addends one what does that represent in the first set? What does it represent in the second set? Good, there's the one child who's getting on in the then section, but here our one is our first addend. So we know that both equations give us the sum seven, okay? Whichever way the addends around gives us the sum seven so we also know that six add one is equal to one add six it doesn't matter we've just swapped the addends round. If we change the order of the addends the sum remains the same. So here we have some pictures and you're going to have a go at writing the equations to go with them. Before you do that, I just want you to have a look what is the same about these two picture stories? What is the same? Have a good luck, good, I bet lots of you have spotted that the now picture is the same. Do you remember what the now picture represents? It represents the sum, well done we're going to end up with the same number the same sum at the end of our equations but these bits are going to look a little bit different. What I'd like you to do now is to pause the video and have a go at writing the equation for these once you have told the story, tell the story first, okay? So tell the story of these pictures and then have a go at writing the equation and then tell the story of the pictures at the bottom and write the equation for that, off you go. Okay, let's have a go at doing this together then let's have a look at this one. First, there were three flowers growing in the pot then one more flower was planted now, there are four flowers. So let's write our number sentence for this let's write our equation. First, there were three flowers in the pot then one more was added, good. Now, there are four, so our three plus one is equal to four okay, let's have a look down here at the bottom. First, there was one flower growing in the pot then three more flowers were planted now, there are four flowers all together should we write this one as well? Okay, first there was one flower in the pot then three more were added, well done. Now there are four, excellent can you see children that you have just swapped around the addends. There's the three, there's the one and the sum has remained the same, well done everyone. So this is what I'd like you to do for your practise activity now that we've finished the lesson, you are going to draw out on a piece of paper or a whiteboard or whatever you've got with an adult with you. You're going to draw your three boxes first, then and now add another three boxes underneath first, then and now, okay? And you are going to draw your own pictures for your story and write your own equation, okay? So you're going to have your first picture in this box first, then you're going to need to draw whatever you had in your first box and then whatever's coming to join it, whatever your second addend is. Now, and we'll draw the picture of your sum, okay? Then you're going to swap them around the addends round first, we're going to have the other addend then what comes to join it now should be the same sum if we've got it right. If you're not sure you can always go back and check in our flowers picture to see how we did it there and maybe you could even do the same flowers for a practise go if you're not sure. Okay, see you soon, bye.

Completed: The commutative Law of Addition using augmentation

In this lesson, we learn about the commutative law of addition using augmentation. 

Maths

The commutative Law of Addition using augmentation

Video

Lesson Complete