Video: Consecutive numbers

﻿Hi, everyone. My name is Mrs. Santis. And I'm going to take you through today's lesson. But first, let's have a little look at the practise activity from last lesson. Let's have a little look at the practise activity. There were two questions. Let's look at the first one. I find one conker in the playground. I pick up six more on the way home. How many do I have now? Let's see what the equations . I wonder if you have any of these. You may have one add six equals seven, or seven equals one and six, because you found one conker in the playground, and then you picked up six more. But some of you may have realised that you can change the addend, and then put the six first, so six add one equals seven, to help you with the calculation. Remember, when you change the order of the addend, that the sum remains the same. Let's have a look at the second question. I challenge myself to swim four widths of the swimming pool. I have swum one width. How many more widths do I need to swim? I wonder if you got any of these equations. You may have that four subtract one equals three. Because you had to swim four widths of the swimming pool, and you'd only done one so far. And so, one less than four is three, and that links to our last lesson. And then some of you might have noticed that one adds three equals four, so you used your related facts. How clever. Well done. Let me tell you a math story. First, there were six children playing. Looks like they're playing football. Then five children went home. We're going to use the mathematical vocabulary of minuend today. So, the minuend story tells us the quantity there is before anything is subtracted. So, six is the minuend because there are six children playing football before any go away. First, there were six children playing football. Six is the minuend. Then five children went home. In the story, the subtrahend tells us how much is being subtracted from the minuend. Hmm, can you work out what the subtrahend is for this math story? You're right! The subtrahend is five because five children are going home. Oh, before we solve this, can we look very carefully at those two numbers? Because I don't want to have to count back. That would take too long. Is there something very special about those numbers that we could use to help us solve this? Hmm, have a think. Did I hear some of you say five is one less than six? If you did, well done. You're right. Five is one less than six, so there must be only one left over. Brilliant. That's really interesting. Did you know that six and five are consecutive numbers? And consecutive numbers are numbers that are next to each other when we count, and their next to each other on a number line. Can you see? There's six, and there's five. Five is one less than six, so these consecutive numbers have a difference of one. Hmm, I wonder if that's always true. Let's have a go at another problem to see whether consecutive numbers always have a difference of one. So, I have five counters on the tens frame, and then I'm going to take four of those counters away. So, five is the... Hmm, can anyone remember the mathematical word we used earlier on? Five is the minuend! Brilliant. And that means that four must be the, hmm, ah, subtrahend, because it's being taken away from the minuend. Excellent use of the mathematical vocabulary. So, I have five counters, and I subtract four. How many counters am I going to have left? Oh, stop! Don't count back. What do we notice about those numbers, five and four? Hmm, I can hear lots and lots of you say that they're consecutive numbers. Brilliant! You're right. Five and four are consecutive numbers because they sit next to each other on the number line. Hmm, how can I now use that knowledge to help me answer this question? Ah, did some of you say that four is one less than five? So, there must be one left over. Excellent work. Let's check it, though. So, I have five counters on my tens frame. Five is the minuend, and I'm going to subtract four, so four is my subtrahend. So, five subtract four is one because I have one left over. I think we found a new generalisation, that consecutive numbers have a difference of one, and that is always true. Well done. Let's have a look at a new math story. There are nine children here, and eight of them are reading. How many children are not reading? Before we start calculating, let's look at the numbers. What do you notice? What do you think that nine represents? Well done. The nine is the minuend, and it represents the nine children that are all there. What do you think the eight represents? That's it! The eight is the subtrahend, and it represents the eight children who are reading. How am I going to use that knowledge to help me work out this missing number? Look carefully at those numbers. What do you notice? Ah, well done, they're consecutive numbers. Eight and nine are consecutive numbers. They're next to each other on the number line. So, what do we know about consecutive numbers? Consecutive numbers have a difference of one. Well done. Brilliant working out. Can you also see that eight is one less than nine? That uses your knowledge from the previous lesson. Excellent work. Before we start calculating, let's have a little look at their numbers in this part part whole model. So, I've got a seven and I've got the six. What do you notice about those two numbers? Brilliant. Well done. They are consecutive numbers, and we know consecutive numbers have a difference of one. How are you going to use that knowledge to help you work out this missing number? What is that missing number, and can you explain why you found it, or how it works? Oh, well done. The missing number is one, and the reason it is one is because the six is one less than seven, and we know that consecutive numbers have a difference of one. Brilliant work. Let's have a go at solving these equations. Look at those numbers carefully, though. What do you notice about them? You're right, they're consecutive numbers. Can you use that to help you solve these equations really quickly? Pause the video, and then join us once you're ready. That was super quick. Well done. Let's have a little look. 10 subtract nine. Oh, I noticed that nine is one less than 10. And then nine subtract eight. Eight is one less than nine, so there's one left over. Eight subtract seven. Oh, seven is one less than eight, so there's one left over. And then this one, one subtract zero. Well one and zero are consecutive numbers, and zero is one less than one. Have a little look at your number line just to check that one. Can you see they're next to each other, and zero is one less than one? Something very interesting. They've all got ones here. Do you know what we have? Why are all the answers one? Oh, you guys are brilliant. You're right. They're all one because consecutive numbers have a difference of one. Well done for using that generalisation. Super work. Let's work together to solve these missing box problems. Have a little look at them. Can you spot any that could be calculated really quickly? Can you spot any consecutive numbers? Yeah, I spotted that one, too. Seven subtract six. Have a go at solving it. Seven subtract six equals one. Well done. Why does it equal one? Can you tell me? Brilliant. Seven subtract six equals one because six is one less than seven, and we know that consecutive numbers have a difference of one. Super work. Can you spot any more consecutive numbers? Yeah, I spotted this one, too. It's a little bit different because it's got the missing box at the start, but we've still got our consecutive numbers, so we can still use our generalisation. So, can you fill that missing box in? Brilliant. One equals four subtract three, because three is one less than four. Excellent work. Have a little look at these ones. Let's have a think about them. So, let's have a look at these two. You might want to use your previous lesson's knowledge. So, five subtract one equals what? Have a think. Five subtract one is four, because four is one less than five. Brilliant work. What about the next one? We've got our missing box here, haven't we? But we can still use nine subtract one. Ooh, nine subtract one is eight. So, eight equals nine subtract one. Excellent. Because eight is one less than nine. Can you work out the missing values in these three representations? Have a little look. What do you notice about those numbers? Yes, that's it. They're consecutive numbers again, aren't they? And what do we know about consecutive numbers? Consecutive numbers always have a difference of one. Well done. Now use that knowledge to help you solve these. Pause the video and then come join us once you're done. Wow, that was super quick. Brilliant work. Let's go through them. Here we go, we've got four and three. Hmm, what's the missing value there? Well, I know that four and three are consecutive numbers, so the missing value is one. Well done, because three is one less than four, and we know that consecutive numbers have a difference of one. Let's have a look at the number line. Again, we've got consecutive numbers, eight and seven. Seven is one less than eight, so one must be the missing number. Let's have a look at the bar model. We've got six and five. These are consecutive numbers again, and we know the consecutive numbers have a difference of one. Well done. Brilliant work. Let's take a look at this last story. My coat has eight buttons, and I've done up seven buttons. How many more buttons do I still need to do up? Have a little look at that. Can you write an equation that math story? Can you solve it? Think very carefully about the numbers that you've got. You have a coat with eight buttons, and I've done up seven buttons. Pause the video now, and then come back to us once you're ready. Did you do it? Did you write the equation? Wonder if your equation looks something like this? I've got eight subtract seven equals one. What does the eight represent? That's it, the eight represented the eight buttons. What did the seven represent, that subtrahend? That's it, it represented the seven buttons I had already done up. And I got the answer of one button left to do up. Did you? Can you tell me how? How is it that we've got the one? That's it! We got one because seven and eight are consecutive numbers, and seven is one less than eight. So, there's a difference of one. Brilliant work. Now it's time for the practise activity. Can you have a little look? Can you see that we've got lots of expressions here? What I'd like you to do is sort them in the table. Can you sort the expressions that have a difference of one, and can you sort the ones that don't have a difference of one? And to challenge yourself, you may want to come up with your own expressions and sort those in the table, too. I hope you enjoyed the activity. See you again soon.

Lesson summary: Consecutive numbers

In this lesson we learn that consecutive numbers have a difference of one.

Maths

Y1 Maths

Key Stage 1

Year 1

Consecutive numbers

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

Adding two

Subtracting two

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

Adding or subtracting Zero

Subtracting a number from itself

Consecutive numbers

Video

Lesson summary: Consecutive numbers

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