Lesson video

Hello everyone, welcome back to another maths lesson with me, Mrs. Pochciol.

As always, I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

This lesson is called, "Explain What the Difference is Between Consecutive Numbers" and it comes from the unit "Calculating Within 20".

By the end of this lesson, you should be able to explain what the difference is between consecutive numbers.

Let's have a look at this lesson's keywords: consecutive, odd, even, and difference.

Let's practise them.

My turn, consecutive, your turn.

My turn, odd, your turn.

My turn, even, your turn.

My turn, difference, your turn.

Wonderful, now that we've said them, let's use them.

Here is this lesson's outline.

In the first part of our learning, we're going to be looking at the difference between consecutive numbers and in the second part of our learning, we're going to be looking at the difference between consecutive odd and even numbers.

So let's get started with the first part, looking at the difference between consecutive numbers.

Within this lesson, you're going to meet Laura and Andeep.

They're going to help us with our learning.

Are you ready guys? Let's go.

Andeep is playing with some cubes.

He has made a staircase.

Wow, look at that staircase.

It's a very tall staircase, Andeep.

Andeep has noticed that his towers have one more cube each time, so they do! A lovely thing to notice there, Andeep.

One cube add another cube gives the next step of two cubes.

Two cubes add another cube gives the next step of three cubes.

Three cubes add another cube give the next step of four cubes.

Four cubes add another cube gives the next step of five cubes.

What's the next one going to be? Five cubes add another cube gives the next step of six cubes, well done.

Six cubes add another cube gives the next step of seven cubes.

What number is in the next tower? Hmm, I wonder, let's have a look.

Seven cubes add another cube gives the next step of eight cubes.

Did you get that right? Eight cubes add another cube gives the next step of nine cubes.

Nine cubes add another cube gives the final step of 10 cubes.

Wow, a huge staircase! Well done, Andeep.

You're right, Andeep, we are adding one more each time, one, two, three, four, five, six, seven, eight, nine, 10.

Well done! Andeep notices something when he looks at the first two steps.

We can see that the difference between one and two is one.

We can see each of the consecutive numbers has a difference of one because remember, each time we've added one more cube as we've gone up our staircase.

So that shows that they have a difference of one.

There we go, look, consecutive numbers must have a difference of one.

Andeep now represents this difference as an equation.

We can show the difference as a subtraction.

So two subtract one shows the difference of one.

Three cubes and two cubes, let's have a look.

Three subtract two we can see is equal to one.

It has a difference of one.

Ooh, what's this equation going to be? Four subtract three is equal to one.

They are consecutive numbers.

Five subtract four is also equal to one.

Six subtract five is equal to one.

Seven subtract six is equal to one.

Eight subtract seven, what do we think that's going to be equal to? One, of course, because they're consecutive numbers.

Eight subtract nine is equal to one, and finally, 10 subtract nine is equal to one.

We can say that a number subtract the number before has a difference of one.

Can you see there? That's what all of Andeep's equations are showing.

Two subtract the number before, which is one, is equal to one.

Seven subtract six, which is the number before it, is equal to one.

A very interesting point to notice there, Andeep.

Let's have a look then.

So which of these equations will result in a difference of one? Could a: eight subtract five be equal to one? Could b: eight subtract seven be equal to one? Or could it be c: something is equal to eight subtract seven? Hmm, pause this video and have a think.

Which of those equations would result in a difference of one? Welcome back, I hope you had some good exploring time there.

Let's have a look then.

Which of these equations do you think would have a difference of one, Andeep? Ooh, b and c.

Can you explain it to us, Andeep? b and c are both correct because we can see that seven and eight are consecutive numbers.

They are, they follow on from each other if we count on in ones.

Eight subtract seven would be equal to one.

But then what about c, Andeep? Andeep nearly missed c because the equal symbol had been moved.

But doesn't change anything.

The difference is still one because if you look carefully, b and c are actually the same equation.

The equal sign has just been moved to the beginning of the equation.

Well done, Andeep, I'm glad you didn't miss c.

Did you get both of those too? Let's continue with our learning.

Numbers which follow each other in order without gaps from smallest to largest are known as consecutive numbers.

We can say that consecutive numbers always have a difference of one.

We could see this as each number is one more than the one before.

So one plus one is equal to two.

Two plus one is equal to three.

Or we could see it in a different way.

We could see that the number after can be seen as one less.

10 subtract one will be equal to nine.

This fact is really going to help us if we see any consecutive numbers when we're adding or subtracting.

Andeep explores this further with Laura.

If consecutive numbers always have a difference of one, this should work for any consecutive number.

Hmm, I know what's coming here, Andeep.

There we go, he's got his number line.

We could say that 14 and 15 have a difference of one.

Is he correct, Laura? Yes, 14 and 15 are consecutive, so that is correct.

They will have a difference of one.

Andeep thinks that 18 subtract 17 will be equal to one.

Is he correct, Laura? The difference is the result of a subtraction.

So 18 and 17 are consecutive numbers, so the difference will be one.

Yes, well done, Andeep.

What about 11 subtract 12? Hmm, does that equal one, Laura? 11 and 12 do have a difference of one because they're consecutive but we don't record the equation like that.

Remember, Andeep, subtraction isn't commutative so we can't just put the numbers in any order.

We have to put the larger number first.

Oh, Andeep, you do like tricking us, don't you? Of course, you knew that it was 12 subtract 11 would be equal to one, not the other way around.

Oh, dear.

Over to you then.

Can you now use that knowledge to fill in these missing numbers? Two subtract one is equal to what? Three subtract two is equal to what? Four subtract something is equal to one, and something subtract 12 is equal to one.

All of these equations are using our knowledge of consecutive numbers and differences of one.

So pause this video, have a go at all of those equations and come on back once you've filled in the missing numbers.

Welcome back.

Come on then, Andeep, you can answer these to make up for tricking me on that last slide.

Two and one are consecutive numbers, so the difference will be one.

Well done if you spotted that.

Three and two are also consecutive numbers.

So three subtract two will be equal to one because they have a difference of one.

Now let's look at this next one.

How is this one slightly different? Here we know that the difference is one, so we must have subtracted the number before four, which we know in our count it would be the number three.

Four subtract three would be equal to one.

And finally, we can see that the difference again is one.

We know that we are subtracting 12 from something.

We know that if the difference is one, it must be subtracted from a consecutive number.

The number after 12 in our count will be our missing number, which we know is 13.

Well done to you if you've got all of those correct, and thank you, Andeep, for your help.

You have redeemed yourself.

Andeep now asks Laura to help him with this problem.

He can see that in this equation, we have 18 and 17 that are consecutive numbers, but 17 is the answer now.

Hmm, what would be the missing number? We know that the difference between consecutive numbers is one.

So if we start with 18 and subtract something, it is equal to 17, the number before it.

Oh, so the missing number must be one because 18 subtract one will give the number before, which is 17.

Thank you for your help there, Laura.

We know the difference between 18 and 17 is one, but we can create many different equations using that fact.

We might also say that 18 subtract 17 is equal to one.

Remember, we can create lots of different equations from one bar model, both addition and subtraction.

So that's all we've done here.

Okay then, let's practise this learning within Task A.

Task A, part one is to fill in the missing numbers.

All of these missing number problems are linked to our learning of consecutive numbers and differences of one.

So remember that when you're solving these.

You might want to look out for any patterns you might notice.

This might also help you to solve a few more.

Part two is to then play a number card game.

You're going to select a card and write the equation that shows a difference of one using that number.

Hmm, can you show us, Laura, Andeep? I'm not 100% sure what we're doing.

Andeep turns over the number three.

Three, he could subtract the consecutive number before it.

So he could write the equation three subtract two is equal to one.

He has shown a difference of one with that equation.

Laura, how would you show a difference of one? Laura subtracted it from the consecutive number after.

She wrote the equation, four subtract three is equal to one.

So we need to turn over a card and write an equation that shows a difference of one.

You might want to subtract it from the consecutive number after, like Laura, or you might want to subtract the consecutive number before it, like Andeep.

Have a go at task A, part one and part two and come on back when you're ready to continue the lesson.

Welcome back, well done for completing task A.

Let's have a look at part one.

Here are the missing numbers.

Six subtract five is equal to one.

Seven subtract six is equal to one.

And eight subtract seven is equal to one.

You may have noticed when solving these first three that as the number we subtract from increases, so does the number we subtract, six, seven, eight, and the numbers that we subtract are five, six, seven.

Well done if you noticed that.

The next one, we were missing our starting number.

We know that when there's a difference of one, the number that we have subtracted from must be the consecutive number after.

So 11 subtract 10 is equal to one.

15 subtract one, so we're subtracting one which would give us the consecutive number before, which we know is 14.

13 subtract something was equal to 12.

12 is the consecutive number before 13.

So we must have subtracted one because we know they have a difference of one.

You may have noticed that the next three equations are all involving the same numbers.

These are the same equations, just with different parts missing.

So 13 subtract one is equal to 12.

13 subtract one is equal to 12.

And this time, we swapped our equal sign round.

So it's still 13 subtract one, but the missing number was 12.

Well done if you completed all of those questions.

Now let's have a look at part two.

How did Andeep and Laura get on with the next part of their game? Laura now turns over the number 17.

What equations could you record to show a difference of one, guys? Oh, Andeep decides to write 17 subtract 16 is equal to one.

He has subtracted the consecutive number before to find a difference of one.

Laura, on the other hand, has subtracted 17 from the consecutive number after to show that they have a difference of one.

I hope you enjoyed playing that game and finding lots of different ways to find a difference of one between consecutive numbers.

Let's move on to the second part of our learning.

We're now going to look at the difference between consecutive odd and even numbers.

Let's get going.

Laura now explores Andeep's staircase.

When I add two cubes, I notice it is the difference between every other tower.

Hmm, let's have a look then, Laura.

Two and zero has a difference of two.

One and three has a difference of two.

Can you see when she puts the cubes on top of one that it's the same as the three tower? Hmm, I wonder what she's going to do next.

Ooh, two and what have a difference of two? Which tower is that equal to? I can see that that's equal to four.

So two and four have a difference of two.

What about the next one? (gasps) Three and five have a difference of two.

Four and six have a difference of two.

Five and seven have a difference of two, what about six? Six and eight have a difference of two.

They do, and seven? Seven and, it's the same as nine.

Seven and nine have a difference of two.

And eight and 10 have a difference of two.

Did you notice anything there, Laura? When we add the two cubes, we notice that it's the difference between every other tower.

The difference between one and three was two.

The difference between two and four was two.

It was every other tower.

Laura now records these as equations just like Andeep did.

Two and zero has a difference of two.

So we can record this as two is equal to two subtract zero.

One and three has a difference of two.

So two is equal to three subtract one.

Two and four have a difference of two.

How would we record this as a subtraction? That's right, four subtract two.

But this time, Laura is recording her equations with the equals at the start.

So our equation would be two is equal to four subtract two.

Let's have a look at the next one then.

Two is equal to five subtract three.

Two is equal to six subtract four.

The difference of two is equal to seven subtract five.

Eight subtract six is equal to two.

Nine subtract seven is equal to two.

And 10 subtract eight is equal to two.

Laura explores something that she has noticed using a number line.

The difference between zero and two is two.

The difference between one and three is two.

The difference between two and four is two.

The difference between three and five is two.

The difference between four and six is two.

The difference between five and seven is two.

The difference between six and eight is two.

The difference between seven and nine is two.

And the difference between eight and 10 is two.

Laura now organises the statements in this way.

What has Laura noticed? So on the left, she has the difference between one and three, three and five, five and seven, seven and nine.

And on the right, she's got the statements of zero and two, two and four, four and six, six and eight, eight and 10.

Hmm, Laura, what have you noticed? Why have you sorted them in that way? Laura noticed that all the equations on the left include odd numbers.

Of course they do, one, three, five, seven, and nine.

And all the equations on the right include even numbers, zero, two, four, six, eight, and 10.

Oh, well done for that, Laura.

That's a really good thing to notice.

Let's explore this a little bit further then.

Two more than an even number gives the even number after.

So two more than two is equal to four.

Two more than four is equal to six.

Two more than six is equal to eight.

And two more than eight is equal to 10.

So we can say that the difference between consecutive even numbers is two.

When we subtract an even number from the even number before, it will have a difference of two.

So four subtract two will be equal to two.

Six subtract four will be equal to two.

Eight subtract six will be equal to two.

And 10 subtract eight will be equal to two.

So if you see any equations that are subtracting consecutive even numbers, you know that the difference will be two.

But we can also say that two less than an even number gives the even number before.

So 10 subtract two would be equal to eight.

Eight subtract two would be equal to six.

Six subtract two would be equal to four.

Four subtract two would be equal to two.

So we can now see that consecutive even numbers will always have a difference of two.

Let's have a practise of this then.

Pause this video, have a look at all the equations, and find the ones that you think will have a difference of two.

Welcome back.

Come on then, Andeep, what did you notice? Andeep noticed that in a and b, both of the numbers are even but they are not consecutive even numbers.

So 10 and six, they don't follow each other if I count in my even numbers.

Six and two, two, four, six, no, they're not consecutive.

So that must mean that c will have a difference of two.

Am I right, Andeep? Yes, eight and six, and six and eight are consecutive even numbers.

So this equation would have a difference of two.

Well done if you spotted that c was the correct answer.

Laura now explores the odd numbers.

Two more than an odd number gives the odd number after.

So two more than one would be equal to three.

Two more than three is equal to five.

Two more than five is equal to seven.

And two more than seven is equal to nine.

So we can now say that the difference between consecutive odd numbers is also two.

When we subtract an odd number from the odd number before, it will have a difference of two.

So three subtract one is equal to two.

Five subtract three is equal to two.

Seven subtract five is equal to two.

And you guessed it, nine subtract seven is equal to two.

Two less than an odd number gives the odd number before it.

So if we subtract two from an odd number, it will give us the odd number before.

So nine subtract two is equal to seven.

Seven subtract two is equal to five.

Five subtract two is equal to three.

And three subtract two is equal to one.

Consecutive odd numbers always have a difference of two.

So let's now have a practise of this.

Which of these equations would result in a difference of two? Pause this video and find the equations that would have a difference of two and then come on back to see how you get on.

Welcome back.

Come on then, Andeep, what did you notice this time? Andeep noticed that they are all odd numbers but you get a difference of two when the odd numbers are consecutive.

Okay, so which of my equations have consecutive odd numbers then? Well done, Andeep, seven and nine or nine and seven are consecutive odd numbers.

So this equation would have a difference of two because they follow each other if we count in our odd numbers: one, three, five, seven, nine.

Well done, Andeep.

And well done to you if you got that too.

Andeep explores this a little bit further with Laura.

If consecutive odd or even numbers always have a difference of two, we can say 14 and 16 have a difference of two.

Is he right, Laura? Yes, 14 and 16 are consecutive even numbers, so they will have a difference of two.

And 19 subtract 17 will be equal to two? The difference is a result of a subtraction and 19 and 17 are consecutive odd numbers.

So yes, 19 subtract 17 will be equal to two.

What about 10 subtract two is equal to 12? Hmm, 10 and 12 do have a difference of two because they are consecutive even numbers.

But Laura, is Andeep's equation, right? Not quite, you're subtracting two.

So it would be equal to the even number before it, which isn't 12.

12 is the even number after 10.

So what would be the new equation? Oh, Andeep is just testing us again.

He knows that it was 10 subtract two is equal to eight, not 12.

Okay then, let's finish off this learning cycle with task B.

Task B is to select a number card and write an equation that shows a difference of two using that number.

So Andeep turns over a number four card.

Four is an even number.

So we know if we subtract consecutive even numbers, they will have a difference of two.

Four subtract two is equal to two, well done.

We subtracted the consecutive even number before from it.

So four subtract two is equal to two.

Laura subtracted it from the consecutive even number after it.

So she recorded the equation, six subtract four.

She also recorded this with the equal sign at the front, just to test Andeep to get him back for testing her earlier.

And then part two is to fill in the missing numbers.

So just like we did with a difference of one, this time, all of our missing numbers are related to a difference of two or consecutive odd and even numbers.

Make sure in each problem that you check whether you're looking at odd or even numbers.

It's easy to get those mixed up.

Pause this video, have a go at the game in task one and have a go at the missing number problems and come on back when you're ready to complete the lesson.

Welcome back, let's have a look then at Laura and Andeep's next turn of their game.

It might have looked a little similar to your game.

Andeep now turns over the number 17.

He records the equation 17 subtract 15 is equal to two.

He subtracted the consecutive odd number from 17, which was 15.

Well done, Andeep.

Laura, what did you write? Laura wrote 19 subtract 17 equals two, is she correct? Yes, she subtracted 17 from the consecutive odd number after, which was 19.

And of course, that does have a difference of two.

Well done, guys, I hope you enjoyed playing that game.

Part two then, let's have a look at our missing numbers.

Six subtract four is equal to two.

Seven subtract five is equal to two.

And eight subtract six is equal to two.

We can see that we subtract the consecutive odd or even number before to equal the difference of two.

12 subtract 10 is equal to two.

18 subtract two is equal to 16, because that's the even number before it.

And the next three, you might have noticed that these are again the same equations.

They've just got different parts missing.

16 subtract two is equal to 14.

In the next equation, we're then missing the starting number.

So if we subtract two from something, it results in 14.

So of course, our missing number was 16.

You could have used the equation above to help you to recall that fact.

And finally, we swapped our equal sign over.

16 subtract two we know is equal to 14.

Well done for completing task B.

Let's have a look at what we've covered today.

Consecutive numbers have a difference of one.

Consecutive numbers have one more than the one before.

Consecutive numbers are one less than the one after.

Consecutive odd numbers have a difference of two.

And consecutive even numbers have a difference of two.

Thank you so much for all of your hard work today.

I can't wait to see you all again soon for some more maths learning, goodbye!.