Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this maths lesson.

So if you are ready to work hard, let's make a start and see what this learning is all about.

So welcome to this lesson on recognising and using consecutive numbers, those numbers next to each other when we count.

And this comes from our unit of addition and subtraction facts within 10.

So let's get on and see what we're gonna be learning about consecutive numbers today.

We've got some key words in our lesson.

Words you might well know, but they're useful to repeat and to look out for as we go through our lesson 'cause they're going to help us.

So I'll say them first and then you repeat them back.

So my turn, difference, your turn.

My turn, one less, your turn.

My turn, consecutive, your turn.

Well done.

I'm sure you've heard of difference and one less before.

Consecutive might be new though.

Consecutive means next to each other, and we'll learn more about that as we go through the lesson.

So in the first part, we're going to be identifying and using consecutive numbers, and in the second part of our lesson, we're going to be using consecutive numbers to solve problems. So let's identify and use some consecutive numbers.

And we've got Sam and Jacob helping us in our lesson today.

Sam and Jacob are at a party.

Lucky them.

Do you like going to parties? And they've got some cakes.

They're going to tell a story, a First, Then, Now story.

So let's think about the story.

First, there are five cakes on the plate.

Then four cakes were eaten.

I wonder if Sam and Jacob ate them all.

Now, how many cakes will be left on the plate? Hmm.

Let's have a think.

First, there were five, then four cakes were eaten, so we've subtracted four, now, there is one cake left on the plate.

We can represent this with an equation and a part-part-whole model.

So five cakes subtract four cakes is equal to one cake.

And we can think about that as our part-part-whole model.

So five is the whole, four is a part, and one is a part.

Five take away four is equal to one.

What do you notice about the minuend and the subtrahend? So the minuend is the number we start with, like the whole, and the subtrahend is the number we take away, so one of the parts.

So our minuend is five and our subtrahend is four.

First, there were five cakes, and then four were eaten.

So what do you notice about those two numbers? Jacob says, "The numbers are next to each other when we count.

The difference is one." So five and four are next to each other.

If we count up, 1, 2, 3, 4, 5, and if we count backwards, 5, 4, 3, 2, 1.

Five is one more than four, four is one less than five.

The difference between them is one.

Let's have a look at another problem.

Sam has eight candles on her cake.

She blows out all except one.

She blows out seven of them.

And there we are.

She's blown them out, and there's one candle left.

So how many candles are not blown out? Well, we can see there's one candle not blown out.

Eight subtract seven is equal to? The eight candles she started with take away the seven she blew out is equal to one.

Seven is one less than eight, so there must be one candle left.

She blew out all but one of them.

And we can represent this with an equation and a part-part-whole model.

Eight subtract seven is equal to one.

And there's eight is our whole, the number of candles we started with, that's the seven is the part that she blew out, and the part she didn't blow out is the one.

So eight is our whole, seven is a part, and one is a part.

Again, what you notice about the minuend and the subtrahend? Those are the words we give to the number we start with and the number we take away.

So in this case, the number of candles that were on the cake and the number that Sam blew out.

So our minuend is eight, the number we started with, and the subtrahend, the number she blew out, the number we're taking away is seven.

And we need to take away those ones that she blew out to work out how many were still alight at the end so our difference was one.

The numbers are next to each other when we count and the difference is one.

Eight is one more than seven, seven is one less than eight.

Here are those two problems represented as bar models.

So our five cakes and we ate four, eight candles and Sam blew out seven represented as bar models.

What do you notice about the minuend and the subtrahend? So let's think that minuend, the number we started with.

So the minuend is five in our cake story, and the minuend was eight in our candle story.

There were five cakes at the beginning of the story, there were eight candles on the cake in total.

So that's like the whole.

And the subtrahend was the number of cakes that were eaten.

So four cakes were eaten.

And it was the number of candles that Sam blew out.

So seven candles were blown out.

So it's one of our parts.

What do you notice about those numbers? So in each equation, those numbers are next to each other.

Five and four are next to each other when we count and eight and seven are next to each other when we count.

Four is one less than five and seven is one less than eight.

The difference is one for both of those problems. Five might subtract four is equal to one and eight subtract seven is equal to one.

The missing part on the bar model was one in both cases.

Time to check your understanding now.

Is Jacob correct? Jacob says, "The numbers are next to each other when we count.

The difference is one." So Jacob is saying that in these subtractions, the minuend, the number we start with, and the subtrahend, the number we take away, are next to each other when you count.

Is Jacob correct? Let's just remind ourselves what the minuend and the subtrahend are.

So the minuend is the number we start with.

So we've put a circle around the minuend in each of our equations.

And the subtrahend is the number that we take away.

And we've put a rectangle around those.

So is Jacob correct? Are the minuend and the subtrahend next to each other when you count? Pause the video, have a think about it, and then we'll talk about it together.

How did you get on? Is Jacob correct? Hmm, I wonder.

He says that the minuend and the subtrahend are next to each other when we count in all of these equations.

Is he right? Let's have a look at A.

So we've got six subtract five.

Well, six and five are next to each other when we count.

So if we have start with six and we take away five of them, then the answer will be one, the difference will be one.

So yes, he's correct for A, the difference is one.

What about B, six take away four? Are six and four next to each other when we count? Not when we count in ones, are they? No.

So six and four are not next to each other when we count in one so they won't have a difference of one.

What about two subtract one? Two minus one? Two and one, they are next to each other when we count in ones, aren't they? So they will have a difference of one.

And eight subtract one.

Well, eight and one aren't next to each other when we count in ones.

So Jacob wasn't correct for all of them.

Two of them were next to each other when we count, but two of them weren't so they would not have a difference of one.

So can you see five and four on the number line? I expect you can.

Let's have a look.

There we are, five and four.

Five and four are next to each other when we count.

Five and four are consecutive numbers.

When we count in ones, they're next to each other on the number line.

And we can say that four is one less than five and five is one more than four.

We can also say that five take away four is equal to one, five subtract four is equal to one.

If I start with five and I subtract four, I'm left with one.

Jacob says, "Consecutive numbers have a difference of one." We can see there's one jump there on the number line in between four and five.

So that was what we call the difference of one.

And there we can see it.

Can you see seven and eight on the number line? Seven and eight are next to each other when we count.

Seven and eight are consecutive numbers.

Seven is one less than eight and eight is one more than seven.

So if we say eight take away seven, then we are left with one.

We've taken away all but one of them.

And we can see that they're next to each other, there is a difference of one.

Consecutive numbers have a difference of one, and we can see that jump of one between them on the number line.

What are the consecutive numbers can you see, I wonder? Can you see some more consecutive numbers on this number line? I bet you can.

Let's see what Sam and Jacob have seen.

Jacob says, "I see three and four.

They are consecutive." They're next to each other on the number line.

They have a difference of one.

Sam says, "I can see five and seven.

Are they consecutive?" Jacob says, "No.

Five and seven are not consecutive.

They're not next to each other when you count in ones." Can you see there's a six in between them? Ah.

Sam says, "I can see that five and seven do not have a difference of one." When she puts her arrow, her jump of one from seven, she gets to six.

She doesn't get to five, does she? Okay, time to check your understanding.

Sam has circled three on the number line.

What could she circle to show a consecutive number to three? And is there more than one answer? Pause the video, have a go, and then we'll talk about it together.

What did you think? What consecutive numbers did you find for three? Sam says, "I can circle four.

Four is next to three on the number line.

And I can also circle two.

Two is next to three on the number line." So she circled three to begin with.

Four is one more than three and two is one less than three.

So there are two consecutive numbers we could give that are next to three on the number line when we count in ones.

So all these equations have six, five, and one in them, but which one shows that consecutive numbers have a difference of one? Ooh, right, that's an interesting one.

Have a look at them.

What do you think? We've got five add one is equal to six, one add five is equal to six, six subtract one is equal to five, and six subtract five is equal to one.

So which of these equations show us that consecutive numbers have a difference of one? Hmm, I wonder.

Jacob says, "Well, they all do in a way." Well, they all do, don't they? 'Cause we know that five and six are consecutive numbers.

So five plus one is equal to six, one plus five is equal to six, six subtract one is equal to five, and six subtract five is equal to one.

Hmm, that last one though is interesting.

Six subtract five equals one shows that one is the difference.

The difference is the name we give to the answer to a subtraction.

The number we are left with at the end, perhaps, in a First, Then, Now story.

So that one actually has a difference of one.

Six take away five is equal to one.

But all of them show us that six and five are consecutive.

We can add one to five to equal six and we can take one away from six to equal five.

Time for you to do some practise.

All of the following questions have a missing difference.

Sometimes it's part of a bar model, sometimes it's part of a part-part-whole model, sometimes it's the answer to a subtraction.

So all of them have a missing difference.

Can you tick the ones that have a difference of one? And then we've got a bit of a game for you to play.

You'll need a set of one to nine cards, and you're going to turn over a card, and you're going to write down two numbers that are consecutive.

So there's numbers that are next to that number when you count in ones.

You could use the number line to help you, and the sentences.

I think Sam's got an example to show you.

Yes, Sam says, "I turned over number four.

So I turned over number four.

I could say that three and four are consecutive numbers or four and five are consecutive numbers." So pause the video, have a go at your tasks, and then we'll talk them through together.

How did you get on? Did you find the ones that had a difference of one? Let's have a look.

So the first part-part-whole model, two is the whole, one is a part, so the other part is one.

Let's have a look for another one with a difference of one.

What about four subtract three? So four and three are consecutive numbers.

They're next to each other on the number line.

They have a difference of one.

Are there any others we can see in there? What about the bar model at the bottom with the whole is nine and eight is a part? Eight and nine are consecutive numbers, aren't they? So they will have a difference of one.

And there it is.

And then one subtract zero.

Well, one and zero are next to each other on the number line, so they will have a difference of one.

What about the other ones then? What's about eight is a whole and three is a part? Well, eight and three aren't consecutive numbers, so our other part isn't going to be one, is it? Our other part is five.

And three subtract one.

Well, three and one aren't consecutive numbers, so they won't have a difference of one, they have a difference of two.

And then if seven is the whole and five is a part, seven and five are not consecutive numbers.

If seven is the whole, five is a part, the other part is two.

And what about six subtract two? We can think about that as whole and part, can't we? But we can see that six and two are not consecutive numbers.

And if six is the whole and two is a part, the other part must be four.

So six subtract two is equal to four.

Now, there are lots and lots of possible answers for your game.

I wonder which cards you turned over.

But Sam turned over a nine, she says.

So her sentences said, "I turned over number nine.

Nine and 10 are consecutive numbers.

Eight and nine are consecutive numbers as well." So you might have had lots of fun turning over lots of different numbers and saying those sentences.

And there's Sam's nine.

Nine and one more is 10 and one less than nine is eight.

So the two consecutive numbers to nine are 10 and eight.

So in the second part of our lesson, we're going to be using consecutive numbers to solve problems. So, "My coat has 10 buttons," says Jacob.

That's a lot of buttons on your coat, Jacob.

"I have fastened nine buttons." So he's done up nine of his buttons.

"How many more buttons do I still need to fasten?" Hmm.

We can represent the problem as a bar model.

So there's the total number of buttons.

All the buttons is 10 buttons and the part that Jacob has fastened is nine buttons.

What do you notice about 10 and nine? They're next to each other on the number line when we count in ones, aren't they? Nine and 10 are consecutive numbers, and we know that consecutive numbers have a difference of one.

We could also think that we'd only have to fasten one more button than nine to fasten all 10 buttons.

And Jacob says, "You need to fasten one more button because 10 take away nine is equal to one." They are consecutive numbers.

Let's look at it on the number line as well.

My coat has 10 buttons and I've fastened nine.

How many more buttons do I need to fasten? What do you notice about the numbers nine and 10? There we go, nine and 10 are consecutive numbers.

They have a difference of one.

There's a jump of one between them on the number line.

Let's have a look at another problem.

Jacob says, "I had eight cakes, and now I have one cake left." Jacob, you've eaten a lot of cakes.

I hope you share them with your friends.

"How many cakes have been eaten?" Jacob had eight, and now he has one left.

We can represent the problem as a bar model.

What's our whole going to be? That's right, our whole is eight cakes, and we could imagine those eight cakes lined up in our bar, couldn't we? And lots of cakes have been eaten, and we've only got one cake left.

So one of our parts, so what is our missing part? Hmm.

Eight take away something is equal to one.

Jacob says, "But I know consecutive numbers have a difference of one." So what might our consecutive number be here? Ah, Jacob says, "Eight and seven are consecutive numbers.

The missing number is seven." So if they ate seven cakes, they ate all but one of the cakes, there's one cake left.

So eight take away seven is equal to one.

Here's that bar model again with the missing number.

Sam's got another idea.

Sam says, "Could the answer be nine? Because eight and nine are consecutive numbers." So could the answer be nine? What do you think? Hmm.

Wonder what Jacob thinks.

Jacob says, "But there were only eight cakes to eat.

Nine could not have been eaten." We know from the story that we're starting with eight cakes.

Nine is a consecutive number, we only had eight cakes to start with, so this time we were looking for the consecutive number that is smaller than eight.

So seven is one less than eight, seven plus one is equal to eight, so if we had eight cakes and we ate seven of them, we would have one left.

Sam has hidden the numbers in some equations.

Jacob says he knows how to find the missing numbers.

Should we help him? We know that consecutive numbers have a difference of one.

And in all of those equations, we've got an equals one.

That's our difference at the end of a subtraction.

So Jacob says, "The minuend and the subtrahend must be consecutive numbers." There's a lot of big words in there, aren't there? Let's have a think about those.

Let's remind ourselves.

The minuend is the number we start with and the subtrahend is the number that we take away.

So we can see the minuends there in our equations, but what we can't see are the subtrahends.

Now, Jacob says that the minuend and the subtrahend must be consecutive numbers, next to each other on the number line.

So let's have a think and see if we can use that to help us.

So he says, "In each equation, the subtrahend must be one less than the minuend." We're taking something away and we're going to have one left, so we must be taking away a number that is one less than the number we started with.

So Sam says, "One less than six is five," so six subtract five is equal to one.

One less than five is four, so five subtract four is equal to one.

And one less than four is three.

Four subtract three is equal to one.

Does that match with what Jacob said that our number that we were taking away is a consecutive number to the number we started with? Six and five are consecutive numbers, five and four are consecutive numbers, four and three are consecutive numbers, and we know that consecutive numbers have a difference of one.

Time to check your understanding.

Can you write the equation and solve the problem? So the problem is I have three pictures.

I have coloured two of them.

How many more pictures do I still need to colour in? And we can see we've got a bar model there.

So can you write the equation and solve the problem? Pause the video, and then we'll talk through it.

How did you get on? We were starting with three pictures and we'd coloured in two of them.

So we've done two, how many have we not coloured in yet? So our bar model has a three as a whole, two as a part, and we can see something special about that whole and that part, that minuend and subtrahend.

"Two and three are consecutive numbers," says Jacob.

"They have a difference of one." So there must be one picture left to colour in.

And that would make sense.

I could check that.

If I've coloured in two and I've got one more, two and one more is equal to three, so that would be the three pictures that I started with.

One more for you to have a go at.

So write the equation and solve the problem.

I had five stickers and I have one left.

How many stickers did I give away? You've got a bar model there to help you.

So pause the video while you write the equation and solve the problem, and then we'll talk it through.

How did you get on? This time, we didn't know the number of stickers that I'd given away.

So I started with five, I gave some away, and I was left with one.

Hmm, but that's a difference of one, isn't it? That answer to our subtraction, that's our difference of one.

Jacob's reminding us, "Consecutive numbers have a difference of one." So we must have given away all but one of the stickers.

So we started with five, so we must have given away four stickers.

Five and four are consecutive numbers, so they have a difference of one.

You can picture them on the number line and we can see it there in our bar model.

So we're going to look at this First, Then, Now story.

Oh, we've got some bits that we don't know about though.

First, there was something, then something happened, and now there's one.

What could the First and Then parts be? Sam says, "The equation could be five subtract six is equal to one." Hmm.

Well, we know there's an equal to one, and I think Sam spotted there that there's something important about consecutive numbers having a difference of one, but what's the mistake she's made? Jacob says, "Five counters is not enough to subtract six counters and have one left." So we can't start with five subtract six and have one left over, can we? The subtrahend, the number we're taking away, must be one less than the minuend.

So our first number needs to be one more than the number we're taking away.

"Oh yes!" says Sam.

"It could be six subtract five is equal to one." Would that work? Six subtract five is equal to one? It would work, wouldn't it? Six and five are consecutive numbers, six is one more than five, so if we take five away, we will have one left.

Time to check your understanding.

Which of the following numbers is the missing subtrahend in the equation? So what's the missing number that we've taken away? Seven subtract, hmm, is equal to one.

So is our missing number eight, one, or six? Pause the video, have a think, and then we'll talk about it.

How did you get on? Did you remember that there was something important about consecutive numbers having a difference of one? Ooh, but there's two different one numbers in there that we could have because we know that if we think about seven on the number line, it's got two numbers that we can say are consecutive.

But we are doing a subtraction here and we are left with one, so it must be six.

Seven and eight are consecutive numbers, but if we start with seven and we take away eight, we can't have one left.

So if we start with seven and take away six, we can have.

The subtrahend must be one less than the minuend.

So the part we're taking away must be one less than the whole.

Six and seven are consecutive numbers.

The difference between them is one.

Time for you to do some practise.

So in this first question, we want you to find as many possible solutions to this problem as you can and record them as equations.

So we've got a First, Then, Now story.

And Jacob's reminding us that this First, Then, Now story happens on a 10 frame.

So we've got some counters on a 10 frame first, then we take some away, and now we have one left.

So we can't start with more than 10 because our counters have got to fit on our 10 frame.

Find as many different possibilities for this problem as you can and record your answers as an equation.

Hmm, take away, hmm, is equal to one.

Now, for the second part, Jacob has had a go at that problem and he thinks he's found all the possible equations to solve question one.

Can you find a way to organise his equations and check that he's found them all? I wonder if you can.

So pause the video, have a go at both parts of your task, and then we'll look through them together.

How did you get on? Lots of different possibilities you might have found, but here are some you may have found.

And can you look at how we've organised our answers? So we might have started with 10 counters.

So first, there were 10 counters, then we took away nine, and now there is one left.

Or we could have started with nine counters.

First, there were nine counters, and we took eight away, and now there is one left.

First, we started with eight counters, then we took away seven, and now there is one left.

Can you see a pattern here, perhaps? Can you also see that we're realising that what we start with and the number we take away are consecutive numbers because they have a difference of one? So you might have had seven take away six is equal to one, six take away five is equal to one, five take away four is equal to one, four take away three is equal to one, three take away two is equal to one, two take away one is equal to one, or one take away zero is equal to one.

The minuend and the subtrahend decreased by one each time.

Ooh, let's have a look at that.

Hang on.

The minuend and the subtrahend, that's the number we start with and the number we're taking away.

So we had 10 take away nine, and then we had nine take away eight, and then we had eight take away seven, so, yes, it's one less each time for each of those numbers.

10, 9, 8 for our minuend, 9, 8, 7 for our subtrahend.

But the difference is always one because they were consecutive numbers.

So for part two, you had to help Jacob to organise his work.

So Jacob thought he'd found all the possibilities.

You might have organised Jacob's answers like this, a bit like we did for the answers to question one.

Can you see his mistake though? Can you follow that pattern? Can you see what happened? Jacob says, "Oh, I've got seven take away six twice and I've missed eight take away seven." He says, "I need to organise my answers systematically." So by putting his answers in order with a pattern, Jacob was able to see that he'd got one answer twice and he'd missed one out.

And that's called working systematically, organising our answers.

And we've come to the end of our lesson about finding the difference between consecutive numbers, those numbers next to each other on the number line when we count in ones.

So what have we learned about? We've learned that in a subtraction equation, when the subtrahend is one less than the minuend, all except one is subtracted and we get that difference of one.

So when we start with a number and we take away the number that is one less, we've taken away all but one of them so we're left with one.

Numbers that are one more or one less than each other are called consecutive numbers.

Consecutive numbers have a difference of one.

And we've also seen that spotting consecutive numbers in subtraction equations can help us to solve equations more quickly.

You've worked really hard and done lots of thinking.

I hope you've enjoyed it as much as I have, and I hope I'll see you again soon.

Bye-bye.