Lesson video

Hi there.

So our math lesson today is going to be all about consecutive numbers.

But before we get started, my name is Miss Darwish.

And if I could just ask you for a favour to take yourself to a nice quiet place somewhere where you can work.

Okay, so we're going to start off with a bit of mental maths and then talk about consecutive numbers, what they are and recognising them.

And then we'll be having a look at spotting some patterns.

At the end of the session, of course there will be a quiz for you to complete on today's learning on consecutive numbers.

So you will need a pencil, a sheets of paper or a notepad, either is fine and a ruler.

If you want to go and grab those things, then we can start the lesson.

Okay.

So one, two, three, four, five, six, seven, eight.

First, eight numbers.

Seven and eight we can say are consecutive.

We can also say 82 and 83 are consecutive numbers.

I'll give you one more example and then I want you to tell me what are consecutive numbers.

Are you ready? Four and five are consecutive numbers.

So seven and eight consecutive numbers, 82 and 83 consecutive numbers.

Four and five are consecutive numbers.

So what do you think consecutive numbers are? I'll give you some other examples.

4 and -5 are consecutive numbers.

97 and 99 are not consecutive numbers.

Has that confirmed what you think consecutive numbers were? So consecutive numbers are literally numbers that follow on from each other.

We can say zero and one are consecutive numbers.

Three, four, and five consecutive numbers.

Seven and eight are consecutive numbers.

1,293 and 1,294 are consecutive numbers, seven and six are consecutive numbers, okay? 51 and 55 and not consecutive numbers, okay? So that's it.

Consecutive numbers usually have a difference of one.

Okay.

So two consecutive numbers add up to make 11.

What are they? Of course they are five and six.

So we can check, are five and six consecutive numbers? Yes, they are consecutive numbers.

They follow on from each other and they have a difference of one.

And do five and six add, do they have a sum of 11? Do they have a total of 11 when we add them? Yes, six add five is 11.

So if this was a problem, a word problem, a big problem solving task.

And it said two consecutive numbers add up to make 11.

What are they? You can say five and six.

They are consecutive numbers.

And five add six is equal to 11.

Okay.

This time I want you to grab your pen or your pencil and your notepad and see if you can answer this question.

Two consecutive numbers, add up to make 17.

What are they? So two consecutive numbers add up to make 17.

What are they? I'll give a few seconds to have a think and then write down what you think those two numbers are.

Okay, I'll give you 10 more seconds.

Have you found them? If you think you have found them check that they are consecutive and then check that they add to make 17? Okay, should we have a look together? Let's have a look.

Eight and nine.

Are they consecutive numbers first of all? Yes, they are, tick.

And what's the total of eight and nine? 17, well done.

Eight and nine are 17, are the two consecutive numbers.

Well, I don't know if he said that.

Okay.

This time you got to think a bit different.

The product of two consecutive numbers is 132.

What does that mean? What does the word product mean? So what does that first sentence mean? The product of two consecutive numbers is 132.

So if we have two consecutive numbers, two different consecutive numbers.

If we multiply them this time, we're not looking for the sum.

If we multiply them, we get 132.

What are the two numbers? Can you think of two consecutive numbers? Yeah.

As soon as you say 132 and the times tables, I think aha, I think I've got it.

Of course 11 and 12.

11 and 12 are factors of 132.

11 times 12 is equal to 132 and 11 and 12 of course are consecutive numbers.

They have a difference of one, they're right next to each other.

Okay, well done if you said 11 and 12.

So, can I give you a statement, and I'd like you to tell me, is this always, sometimes or never true, okay? The sum, the total sum of two consecutive numbers is always odd.

I want you to keep writing the sum of at least five sets of two consecutive numbers.

And I want you to find out, is it odd or even, okay.

I'm going to have a go as well.

So I've got my notepad.

And I'm going to give you a few seconds.

We're both going to have a go let's write down five sets of two consecutive numbers, add them up and see, is this true? Is it always true? Is it sometimes true or is it never true? Are you ready? Go.

How did you get on? I finished my five.

Have you done yours? What did you notice? I noticed something in mine.

What did you notice? So always, sometimes, or never true, what do you think? So you've come up with five different examples to just test it.

I've come up with five different examples.

Well, hopefully they're different to yours and together we'll then have 10 examples, a bigger sample to see if this is always sometimes or never true.

But I have my ideas and maybe I think maybe you do too.

Let's see.

So the sum of two consecutive numbers is always odd.

Is that always sometimes or never true? Let's look at some examples.

Three add four, they are consecutive number seven is odd.

Okay? Five add six, two consecutive numbers, 11 is odd.

102 add 103, 205 odd.

I also had four add five, which is equal to nine, odd.

What did you have? What else did you have, read yours out for me.

Okay.

So you found something similar to me then.

45 add 44 is equal to 89, odd.

Maybe we're thinking the same thing now.

That means if we go back to it, does it always, sometimes or never true? It seems to be always true.

The sum of two consecutive numbers is always odd.

So it seems to be always true.

I'll recall our examples to prove that as well.

Okay.

Now we're going to have a look at spotting some patterns.

I would like you, I'm going to do the same as well.

My notepad and my pen.

I would like you to write down three consecutive numbers, any three consecutive numbers, okay? I'm going to give you six seconds, go.

Any three consecutive numbers, write them down.

Okay, finished? Right, keep that pad, pencil or pen down.

So, my three that I've chosen are eight, nine and 10.

It doesn't matter if you've got yours are the same or different, okay? So you've got yours, these are my three consecutive numbers.

Eight, nine, 10.

Let's check, are they consecutive? Did I do the right thing? Yeah, eight, nine, 10.

Okay.

Now, what is the total of your three consecutive numbers? So my three consecutive numbers are eight, nine, 10.

So I'm going to add them up.

I'm going to do eight add nine add 10.

And I want you to add your three consecutive numbers.

Find me the sum of them.

Can you do that for me? Okay, have you written that down, the total for your three consecutive numbers? Okay, well done.

I've written mine down as well.

So my three numbers, you don't have to share yours.

You can share yours later.

I'm sharing one with you.

So my three consecutive numbers are eight, nine and 10.

I've added them up and my score or my total is 27, okay? What's the total of your three consecutive numbers? Now you can share them with me, what's your sum? Okay, so when you added them up, that's what you found.

You had the total, okay.

Now, do you notice anything with the total? Let's have a look? So when I added my three consecutive numbers, eight add night add 10 is equal to 27 and I spotted something, but I'm not sure if this is always sometimes or never true, but because you've got your example and I've got my example, we've got more examples.

Maybe you can help me out here and by you sharing your example and us looking for more examples, we can see if this is always, sometimes or never true.

Should I tell you what I spotted? Did you spot anything first of all? I'm going to ask you first and then I'll tell you what I spotted.

Okay, so I noticed, on my example, anyway, I'm not sure about your example, but this is where we're going to see if maybe you got the same, that the total of three consecutive numbers is like saying, finding my middle number, multiplying it by three, nine times three is 27.

What about you? Can you find your middle number and multiply it by three? What do you get? Is it the same as the total? So is my theory always true? Sometimes true or never true? Well it can't be never true because it worked for this example.

For my example, it worked.

So is it always true or only sometimes true? So I found that eight add nine add 10 is 27.

And that's the same as finding that middle number and multiplying it by three.

Okay.

So nine times three equals 27.

That's the same as the total.

I'd love to know what you got.

Okay.

Let's have a look at another example and we can see if it's always or sometimes true.

So I picked a different three consecutive numbers.

If you want to choose a different three consecutive numbers, go for it.

Write down three consecutive numbers and we'll just keep repeating it, okay? So these are my three, don't choose the same as me.

You choose your own three consecutive numbers.

Okay, ready? So three, four, five.

I'm going to add them up.

It's 12.

I've got to find that middle number, four times three.

It's 12, it worked.

Did yours work as well? That's pretty cool.

So actually this is actually a really cool thing we've worked out here because if I was to give you three numbers, like 99, 100, 101, you wouldn't have to add it in your head.

You just go, right, the middle number is 100.

100 times three is 300 add all three numbers up is 300, simple.

And the other person will go to, "Oh, that was really quick, quick adding in your head." You'd be like, "Yeah, it was." That is a really cool way, a really cool trick to quickly add things.

Okay.

Now, three consecutive numbers have a sum of 42.

So we're looking at a different question now.

So three consecutive numbers, when they're added together they have a sum 42.

What could these three consecutive numbers be? What do we know about that middle number? When we multiply it by three, the answer will be 42.

So 42 divided by three basically.

Can you work out what that might be? 14.

14 times three is equal to 42.

So what would the other two numbers be? One less than 14 is 13, one more than 14 is 15.

So it's 13, 14 and 15.

If we add them together, we would get a total of 42.

And of course, just to check 13, 14, and 15, are three consecutive numbers and 14 times three is equal to 42.

That is a pretty cool trick, but don't tell anyone that trick that can just be our secret, okay? Okay, well done.

Now it's time for you to pause the video to complete your independent tasks.

Good luck with that.

Once you finish, come back and we'll check through the answers together.

Welcome back, hopefully you found that.

Okay, not too bad.

Okay, should we look for the answers together? If you got pens to mark with.

Okay, so the independent task, the first question said the sum of three consecutive numbers is 60.

What are the three numbers? And the second question said the sum of three consecutive numbers this time is 30.

What is their product? Okay, let's look at one question at a time.

So the first one, three consecutive numbers, the sum of them is 60, what are the three numbers? So let's first of all do our two checks.

The first check, are these three numbers consecutive? Do you want to check yours? Say I got 19, 20, 21.

Hopefully you did too.

So 19, 20, 21.

Yes, they are consecutive.

And then if I add them together, do I get 60? Yes.

And hopefully you found that in the way that I showed you, the little trick that we're not going to tell anyone else, our secret.

20 times three.

Find the middle number, 20 times three is equal to 60.

Well done.

So well done if you said 19, 20, 21.

Give it a tick.

Okay, question two now.

The sum of three consecutive numbers is 30.

What is their product? So you've got to find the three consecutive numbers, which when we add them, the total is equal to 30.

So that middle number would be 10 because 10 times three is 30, which means one less than 10 is nine, one more than 10 is 11.

So our three consecutive numbers would be nine, 10 and 11.

But the question isn't asking for what the consecutive numbers are, it's asking for their product.

Okay.

So I know that nine times 11 is 99 and 99 times 10 is equal to 990.

Well done if you said 990.

Okay, if you would like to share your work with us here at Oak National, then please ask your parent or carer to show your work on Twitter, tagging @OakNational, and to use the hashtag @LearnwithOak.

Now, I just want to say well done for all the brilliant learning that you have achieved in today's session.

Now it's time for you to go and complete the quiz.

Good luck.