Video: The commutative Law of Addition using aggregation

﻿Hello. My name is Mrs. Duerdoth. And I'm going to be taking your lesson today. Can you have a look at the picture, and say what you can see? You can pause the video if you like, and tell an adult, or you can just tell me. You might be able to see lots of things in this picture. I can see that there are two adult cats, and four kittens. Did you see that? So how many cats are there altogether? That's right. There are six cats altogether. Can I also say that there are four kittens and two adult cats? And how many cats are there altogether? That's right, there are six cats altogether. So I can say it both ways. I'd like you now to pause the video, and find six objects of the same thing. So you might have six pieces of Lego, or six pebbles. I've got six counters in this image. Can you find them and put two in one hand, and four in the other? Pause the video now. If we think back to our picture of the cats, what does the two represent? That's right. The two represents the two adult cats. And what does the four represent? Yes the four represents the four kittens. So I have two adult cats, and four kittens. How many cats do I have altogether? Six, that's right. Now, keeping the two objects in one hand, and four in the other, can you swap your hands over? So now I have four kittens, and two cats. What does the four represent? Yes, the four represents the four kittens. And what does the two represent? The two adult cats. Do I still have six altogether? Yes. I still have six cats altogether. So, altogether, I have six cats. Now you might have seen this part, part, whole model before. I have six cats altogether. Two of them are adult cats, four of them are kittens. What does the six represent? The six represents the six cats. What does the two represent? The two represents the two adult cats. And what does the four represent? That's right. The four represents the four kittens. So I can write an addition equation to go with this. I can write two adult cats, plus four kittens, is equal to six cats. What does the two represent? Yes, the addend two represents the two adult cats. What does the four represent? The addend four represents the four kittens. And what does the six represent? Yes, six is the sum. It represents how many cats we have altogether. So can I also write my equation like this: Six cats is equal to two adult cats plus four kittens? That's right. I can start with the sum, or end with the sum. So in my second equation, what does the two represent? The two adult cats. And what does the four represent? The four kittens. Excellent. But we also thought about our picture in a different way, didn't we? We still have six cats. But we've said that there were four kittens and two adults. So how would I write this addition equation? That's right. This time I need to start with the four, the addend four. So what does the four represent? The four kittens. So I've got four kittens plus that addend two. And what does that two represent? The two cats. And what's my sum? Yes, I have six cats altogether. And so, can I also write six cats is equal to four kittens plus two adults? Is it okay to say that? So, that must mean that two plus four is equal to four plus two. Do you think that that's true? It is. It means, because we have the equals symbol, this means that both sides have equal value. We know that two plus four is equal to six. And we know four plus two is equal to six. So two plus four is equal to four plus two. We can also represent the picture using a bar model. What does that two represent? Yes, the two adult cats. And the four? The four kittens. So there were six cats altogether. And we could also say there were four kittens and two adult cats. Can you help me complete this stem sentence? Mmm is an addend, mmm is an addend, mmm is the sum. Pause the video and have a go. Shall we do it together? Two is an addend, four is an addend, six is the sum. You might have said four is an addend, two is an addend, six is the sum, because we know that those are equal. Two plus four is equal to four plus two. What can you see in this picture? Pause the video and tell an adult, or you can tell me. I can see two red hats, and three blue hats. What would the addition equation be to go with this image? Did you say it would be two plus three is equal to five? What does the two represent? Yes, the two represents the two red hats. And what does the three represent? Yes. The three blue hats. And what does the five represent? Yes, the five is how many there are altogether. Could we also start out with the five, could be start with the sum? Yes, we could say five is equal to two plus three. The sum is five. Two is an addend. And three is an addend. So could we also start with the three? Is that okay? Could we say three plus two is equal to five? What does the three represent in this new equation? Yes, the three represents the three blue hats. What does the addend two represent? It still represents the two red hats. And what does the five represent? Yes, the five represents how many hats there are altogether. So, can we also start with the five in this equation? Can we start with the five, and say it is equal to three plus two? Yes we can. Can you help me with this sentence? Mmm is an addend, mmm is an addend, mmm is the sum. Which numbers would I put in there? Did you say two is an addend, three is an addend, five is the sum? I could also say three is an addend, two is an addend, five is the sum. So if that's true, if both of the equations represent the image, can I say that two plus three is equal to three plus two? I can say that, because two plus three is equal to five. And three plus two is equal to five, because both sides of the equation are equal. They have the same value. Can you have a look at this picture? How many have we got now? You can join in this activity if you like. You can get your objects again. In the first hand there are three, aren't there? So you can get your Lego pieces or your pebbles, and put three in that hand. How many are in the other hand? That's right, four. So you can do that. You can put three in one hand, and four in the other. Can we switch our hands around? Will we still have the same altogether? Will our sums still be the same? Absolutely. We have still got three and four. We've just switched them over. We have changed the position of the addends. So we can make a generalisation about what we've learned today. Can you practise saying it with me? If we change the order of the addends, the sum remains the same. Shall we have another go at that? Ready? One, two, three. If we change the order of the addends, the sum remains the same. I've got a practise activity for you now. So you can do this after you pause the video. Have a look at the picture, and what can you see? I can see two blue bags and five yellow bags. Did you see that? What addition equation could you write for this picture? How many different ways can you write your addition equation? Can you remember our generalisation? If we change the order of the addends, the sum remains the same. Absolutely. If you're ready for a bit of a challenge, yo might see more than one pair of addition equations in this picture. You can see how many different equations you can write. Don't forget our generalisation. If we change the order of the addends, the sum remains the same. Well done for all your hard work today everybody. Bye.

Completed: The commutative Law of Addition using aggregation

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

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The commutative Law of Addition using aggregation

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