Video: Subtracting two

﻿Hi everyone. How did you get on with the practise activity? Good, we needed those generalisations, didn't we? Should we just go over them before we look at the answers? Okay, so adding two to an odd number gives the next odd number, good. Adding two to an even number gives the next even number, well done. And then this important one that we've used lots. When you change the order of the addends, the sum remains the same. So, we're going to use all three of those generalisations to help us with these equations. So, here we go. Here's our first set. Should we go down this list first? What do you notice about all of those ones there? What did you spot? Did you spot that all of these numbers here are odd? Well done, I hope so. So we can use our generalisation adding two to an odd number, gives the next odd number. Now, what's a bit different about these number sentences that we haven't come across before? Did you spot it? Good. They start with the two, but we know that when you change the order of the addends, the sum remains the same. So, we're going to start with the odd number and add the two to that because we know it gives us the next odd number. So, are you ready? Do you remember all of that? I bet you did, well done. So instead of to add one, I'm going to think one add two, gives me the next odd number one, three. Well done, I bet you've got that. Brilliant. So, two add three, I'm going to think three and two more will be five. Brilliant. The next one, two add five. So if I start on five, I can say it'll be the next odd number seven. Well done. And then we've got seven add two, or two add seven. Seven in my head, the next odd number will be, could you say it? I bet you did, nine, well done. And if we're on nine, the next odd number when we add two will be 11, good job. Well done everyone. Okay, so did you spot on this side that we had exactly the same pattern but here we've got even numbers. So, we need our other generalisation adding two to an even number, gives the next even number. They also begin with our two, don't they? Just like before. So again, we're going to think when you change the order of the addend, the sum remains the same. So, I'm going to think zero plus two is going to give me two, well done. And then two add two, it's going to take me to my next even numbe, four. Then we start on four and our next even number because we're adding two will be six. Then we'll start on six and we'll add two on six to our next even number is eight, brilliant! And last one, if we start on eight, we add two which takes us to our next even number, which is 10. Well done everyone. It was a lot there but if you remembered all these generalisations and you use those to help you, you should have had no problem at all. So, I bet that was brilliant. Well done everyone. So our friends the number blocks are back and we've got the new McConn shapes underneath as well to help us remember our odds are not evens. What was special about the odd numbers? They have a sticky up there, don't they? An odd bit, okay. And the even numbers, they're all even across the top. You could fit the piece number two in to all of them, couldn't you? Well done. Okay, so we're going to have a quick go at just counting in our even numbers. Skip counting in twos, starting on zero, ready? Zero, two, four, six, eight 10. And let's go back, 10 eight, six, four, two, zero. Little bit trickier backwards, isn't? We're going to need that today. Okay, let's start on one and skip counting two. So, we will be saying all our odd numbers, well done. We'll just go to nine, one, three, five, seven, nine. And let's go back the other way. We start on nine, nine, seven, five, three, one. Good job. So, here's our number line. And we just want to think about what happens when we skip count backwards in twos, shall we have a go? 10 goes to eight, six, you know the next one four, well done, two, zero. So, let's have a look at that pattern. What's happening each time we jumped? What are we doing? What operation are we doing? Well done everyone. We're subtracting two, aren't we? We're taking two away each time we jumped back. Should we just count backwards again cause it's a little bit trickier? 10 take away two is eight, six, four, two, zero. Okay so here, we've got our 10 sprain and it's full, isn't it? So, we know straight away that we have 10, well done. And we're going to, are you ready, subtract two. There are the two that we're going to take away in blue. I'm going to move them out and everything else slots down. So, now we have eight, well done. So, those two at the bottom we just slid out and now we've got eight. So, our 10 subtract two gave us eight. There it is in the frame. What are we going to do this time? Eight subtract two. So, there are two that are going to disappear. Can you see what's going to happen? There they go, and now we have six. So, we started with an even number. It was nice and flat at the top and all the way round, there were no gaps, there we go, and then we took away two from the bottom and we've still got a nice flat top. So we started with an even number, we subtracted two and we've still got an even number. It's the even number that came before eight, the previous even number. So, we had eight subtract two, which equals six. So, here's our six. And now we're going to subtract another two. What do you think is going to be, can you predict? We had even number, we subtract two, what's it going to give us? The previous even number, well done, which will be? Can you see it? Four, well done. So, you can see our equation that got us to four. So, now we're starting with four. We're going to subtract two. So, we've started with an even number, we're subtracting two. We're going to end up with an even number, aren't we? Do you know which even number is previous? There we go, it's two, well done. And our last one, look, we've only got two now and we're going to take away two. What's that going to do? There they go, what are we left with? Well done, zero, there's nothing left. So, from all that practise, we can see that subtracting two from an even number gives us the previous even number. It's a bit like our generalisation from the last session, isn't it? But this time we're subtracting two from an even number and it gives us that previous even number. Okay, so we've got our number line back but this time we're going to skip counting twos back from an odd number. Now, I bet some of you might've already worked out what's going to happen. So, we're going to whiz through this. You're doing brilliantly. So, we go from nine to seven, five, three, one. So what are we doing? What have we done? We're subtracting two again. We're just going from an odd number and it's taking us to another odd number. Have you spotted the pattern? I bet you have. So, here we can see that we've started with our odd number. Do you remember? Here's the gap, there's a sticky one up, an odd sticking up one so we can see that it's one less than 10, so it is nine. So, there's our odd number that we're starting with. And just like before, we're going to subtract two. I wonder if you can imagine what's going to happen. We're going to slide those two blue ones down and they're all going to slip into place. And are we going to have an odd number or an even number? Should we try it? There they go, and we've still got a sticky up one, haven't we? So, it must be an odd number. There we go, it is, it's seven. It's still an odd number. Should we see if it works here with the seven? Let's give it a try. Seven, subtract two, there they go. What have we got now? We've got five, haven't we? So, seven subtract two is equal to five. We had our odd number, we subtracted two, and now we've got five, which is the previous odd number. Well done. Let's keep going then we've got five and we're subtracting two, and it's going to leave us with, I bet you guessed, didn't you? Three, because it's the previous odd number. Okay, can you guess what's coming next? Can you guess what number we're going to start with? Let's go on and see. You knew it was going to be three, didn't you? So, we've got three and we're subtracting two, and it's going to leave us with just one. So, now we've also realised the generalisation that subtracting two from an odd number gives you the previous odd number. It's the same rule, isn't it? But we're just on odd numbers this time, but it doesn't matter. Whenever you subtract two, it's going to leave you on the previous odd number. Well done. So, here are our two generalisations from today and we can see that some things are the same and some things are different. Can you spot something that's the same? Can you see, or let me read them to you. Subtracting two from an odd number gives the previous odd number. Subtracting two from an even number gives the previous even number. In both of them were subtracting two, aren't we? And also the thing that's the same is that if you start with an odd number, you'll still get an odd number. And if you start with an even number, you'll still get an even number when you subtract two. So, we've got some problems for you to do. We've got some missing numbers. We need to make our equations whole, okay? So, we're going to start with this one here and we're going to do this one together and a few together and then you're going to have a go on your own. So what do you spot straight away about our first equation? It begins with a 10. Is 10 even or odd? Good, it's even. So, we have an even number subtract two is going to give us the previous even number. What's the previous even number? I can hear you all, well done. It is eight, lovely. Now this time we're going to start on eight. Is it an even number or an odd number? It's an even the number, and if we subtract two, we will get to our previous even number which is, think along your number line, six. Well done! Okay, we're going to do one more together. So now we're starting with six, an even number, well done. And we're subtracting two. It's going to give us our previous even number which is four. Okay, now what I would like you to do now is you're going to pause the video and you are going to have a go at these two here and then you're going to have a go at these four. Now, when you have a go at these four, there's something different about these that you're going to need to spot. I wonder if you can. Well done for coming back everyone. So, this next one down here, we were looking at four, subtract two. You might have spotted a pattern, is going to be our next even number, which is two. Have you sponsored a pattern down here? Eight, six, four, two. Let's look at this last one, two subtract two is going to be equal to zero. Well done everyone. Oops, it's outside the box, sorry. Now, what did you do about them on this side? What happened over here? What changed? We're still subtracting two, that's the same, but we're now starting on an odd number, well done. We are, we're starting on an odd number, so let's have a look. Nine is an odd number, subtract two is going to give us our previous odd number. Can you think back on your number line, what would the previous odd number be? Seven, well done. So if we start on seven, got the number line in my head. Seven subtract two is going to give me five, well done. Five subtract two on my number line, three, that's our previous odd number. And three subtract two, our previous odd number will be one. So, we've learnt a lot over our last two sessions, and we've got two generalisations here that are connected. Shall we have a look? Our first one says adding two to an even number gives the next even number. Then this one says subtracting two from an even number, gives the previous even number. So, when we add two, we jumped to the next even number. And when we subtract two, we jump back to the previous even number. Let's have a look at that on the number line. So, if we start on four and we add two, we get to six. And if we subtract two, we get to two. Okay, but we still staying on the even numbers. And it works exactly the same when we're looking at odd numbers. If we add two to an odd number, we get the next odd number. If we subtract two from an odd number, we get the previous odd number, just like before. Well done, everyone. So, here is your practise activity for today. I want you to look really carefully about odd or even numbers and whether we're adding two or subtracting two. You're also going to need that rule about the addends. What happens when we changed them around? When we changed the order of the addends, the sum remains the same. Well done. Okay, so I want you to have a go at these and your teacher in the next session will go through them with you. When you finished your practise activity, we've got a bit of a challenge for you, okay? So I'm not going to give you too many clues but we'll be using exactly the same generalisations as we've used before to help us. And your teacher for the next session, will run through this one with you. Well done everyone, bye.

Lesson summary: Subtracting two

In this lesson we subtract two from odd numbers and from even numbers.

Maths

Y1 Maths

Key Stage 1

Year 1

Subtracting two

Addition and subtraction

UNIT

The commutative Law of Addition using aggregation

The commutative Law of Addition using augmentation

Measures Contexts to Show the Commutative Law of Addition

Embedding Understanding of Equivalent Expressions

Ten can be partitioned into pairs of numbers that sum to ten

Reasoning with number bonds

Numbers that Sum to 10

Adding one

Subtracting one

Consecutive numbers

Adding two

Adding and subtracting with 5 and 3 and with 6 and 3

Adding or subtracting Zero

Subtracting a number from itself

Maths

Subtracting two

Video

Lesson summary: Subtracting two

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