Lesson video

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

This lesson comes from the unit on addition and subtraction of two-digit numbers.

Is this new for you? Have you done anything like this before? I'm sure you've got lots of skills about numbers and addition and subtraction that you are going to be able to bring to this lesson.

So if you're ready, let's make a stars.

In this lesson, we're going to be thinking about using efficient methods to solve subtraction equations.

There's lots of different ways we can solve a subtraction, but we are going to think about the way to solve each one that is the most efficient.

So it's one that you can do easily, and that gets you the right answer relatively quickly.

So let's have a look at what's in today's lesson.

We've got lots of keywords.

We've got consecutive, difference, whole, and part, so let's rehearse saying those before we get into the lesson.

Are you ready? My turn, consecutive.

Your turn.

My turn, difference.

Your turn.

My turn, whole.

Your turn.

My turn, part.

Your turn.

Well done, I'm sure those are words that you've used before, but you might have not used some of them for a little while, so look out for them as we go through our lesson.

In the first part of our lesson, we're going to be looking at the subtraction of consecutive numbers.

That's one of our keywords.

And in the second part, we're going to be looking at subtraction where one part is a multiple of 10.

So let's make a start on part one, and explore some consecutive numbers.

And we've got Andeep and Izzy helping us in our lesson today.

Andeep wants to solve this equation.

He spots something that can help him to solve it more efficiently.

I wonder what he's noticed.

Well, it's 25 subtract 24.

Now, you might be thinking, "Well, I can partition the number I'm taking away, and then I can work out what the difference is, and what the answer is, but I wonder if and Andeep spotted something that would make us more efficient." Let's see.

He says, "I've noticed something about the whole and the known parts." Have you noticed something? You might want to pause before Andeep tells us what he's noticed.

Did you have a think? I wonder if you've noticed what Andeep noticed.

He says, "They are next to each other when we count in ones." That's right, 24, 25, 20, yes, they are.

They're next to each other in the count, aren't they? There they are on a number line, 24 and 25.

They're next to each other.

Ah, there's our keyword.

They are consecutive numbers.

When we are counting in ones, they're next to each other.

They're consecutive.

25 is one more than 24, and 24 is one less than 25.

I'm sure you've used that language to describe numbers before, but have you used it to help you to calculate? So there we go, 25 is one more than 24, and 24 is one less than 25.

So we know that consecutive numbers, Andeep says, have a difference of one.

So the missing part must be one.

That's right, the whole is 25 and our part is 24.

So if the whole is 25 and one part is 24, the other part must be one.

Here's 25 on the bead string, and there's 24 of the beads.

So if we subtracted those 24, we'd be left with 1 bead, wouldn't we? The consecutive numbers have a difference of one, so the missing part must be one.

So Izzy thinks that this shows 25 subtract 1, and not 25 subtract 24.

What do you think, can she be right, as well? Andeep says, "Remember, we can subtract either of the parts from the whole.

If 25 is the whole, then 24 is a part, and 1 is a part." and if we subtract either of those parts, we'll be left with the other parts.

So Izzy's right, this could be representing 25 subtract 24, or 25 subtract 1.

There are our whole and parts.

25 is the whole, 24 is a part, and 1 is a part.

If we subtract 24, we're left with 1.

And if we subtract 1, we are left with 24.

When we subtract 24 by partitioning it from the whole, we can see that 1 is the other part.

So there's our 25 as a whole, and we're subtracting 24.

If we have removed all of those beads, we'd be left with one bead.

It's equal to 1.

25 subtract 24 is equal to 1.

Time to check your understanding.

Which of the following equations will have a difference of 1? Can you think about consecutive numbers here? So is it A, B, or C? Pause the video, have a think.

And when you're ready for the answer and some feedback, press play.

How did you get on, did you spot it? That's right, it was A, wasn't it? How did we know it was A? Ah, 67 and 66 are consecutive numbers, so they will have a difference of 1.

If we imagine them on a bead string, there'd be 1 more bead for 67 than for 66.

And if we picture them on a number line, they will be next door to each other.

Well done if you spotted that.

Izzy wonders if she can use the same strategy to solve this equation.

Let's see what we notice about the numbers here.

We've got 40 subtract 39 is equal to something, and we've got 40 beads on our bead string, 4 lots of 10.

Ah, Izzy spotted 40 and 39 are also consecutive numbers.

They'd be next to each other on the number line.

40 is one more than 39.

So if I subtract 39 from 40, the remaining part will be 1.

So if 40 is the whole, 39 is a part, and 1 is a part.

She says, "That means I don't need to calculate.

I know the difference will be 1." So there's 40, all our 40 beads, and there are 39 of the beads.

So we could imagine taking away those 39, subtracting them from the 40 and there'd be 1 bead left.

There it is.

So 40 subtract 39 will be equal to 1, if 40 as the whole and 39 is a part, the other part is 1.

And there's our bar model to show that.

Andeep wants to use the number 79 in an equation.

He says the difference in his equation is 1.

What could his equation be? So he wants to use 79, but he wants the difference, the answer to his subtraction to be 1.

So one of his parts must be one.

Andeep says 79 is 1 more than 78, so it could be 79, subtract 78 is equal to 1.

79 and 78 are consecutive numbers, so that would work.

They would have a difference of 1.

Can you picture where they'd be on the number line there? Is there another way he can do it though? What do you think? You might want to have a think before Andeep shares his ideas.

Ah, Andeep also says 79 is 1 less than 80.

So it could also be 80.

Subtract 79 is equal to 1.

So 79 could be our whole or 79 could be a part.

Time to check your understanding.

One of the missing numbers in this equation is 69.

Write all the possible equations that could be correct.

So something subtract something is equal to 1.

and one of those somethings is 69.

Pause the video, have a go.

And when you're ready for the answers and some feedback, press play.

What did you think? Well, 69 and 68 are consecutive numbers.

So it could be 69 subtract 68 is equal to 1.

That would be with 69, the number we had to use as our whole.

And there's the bar model to show 69 is the whole, 68 is a part, and 1 is a part.

But is there another way we could use 69 in an equation where the answer is 1? Ah yes, 69 and 70 are consecutive numbers.

So it could also be 70 subtract 69 is equal to 1.

What's the 69 this time, is it a whole or is it a part? That's right, it's a part this time.

70 is our whole, 69 is a part, and 1 is a part.

Well done if you've got both of those equations.

Izzy thinks she can solve this equation without calculating.

1 is equal to 99 subtract something.

Can you see we've got our difference of one first here? Can you think about consecutive numbers? What's going to be the missing number? Andeep says, "99 is the whole," a well done, Andeep.

You spotted that our whole is not the first number we've recorded.

The difference is the first number we've recorded, but our whole is still 99.

And he says, "99 is the whole, so 1 must be the known part." Ah, so 99 is the whole and 1 is the part we know.

So what's the missing part got to be? Andeep says, "If I subtract 1 from 99, the remaining part will be 98." Ah yes, he's remembered, to find the missing part, we subtract the known part from the whole.

99 subtract 1 is equal to 98.

And there's a bar model to show it, but Izzy says, "I didn't have to calculate.

99 and 98 are consecutive numbers, so they have a difference of 1." So she knew that the difference was 1, so that the number we were subtracting had to be 1 less than 99, had to be the consecutive number 1 less.

Well done if you spotted that, as well.

Great thinking, Izzy, but good reasoning, as well, Andeep.

Time to check your understanding.

Which of the following numbers will complete the equation? 1 is equal to 35 subtract something.

Which of those is the something? Pause the video, have a go.

And when you're ready for the answer and some feedback, press play.

So was it A, B, or C? 1 is equal to 35 subtract, 34, that's right.

I hope you weren't tempted by 36.

35 and 36 are consecutive numbers, but 36 is 1 more than 35.

So subtracting it wouldn't give us an answer of 1.

35 and 36 have a difference of 1, but we'd have to be careful when we're recording that difference as a subtraction equation.

In this case, 35 subtract 34.

34 and 35 are consecutive numbers.

So the difference will be 1.

1 is equal to 35 subtract 34.

Izzy sets Andeep a challenge.

Let's use the clues to find the missing numbers.

I wonder what Izzy's challenge is going to be.

You might want to have a think about these clues that she's giving as well before Andeep gives his ideas.

So Izzy says, "The ones digit of the whole is less than 3 and odd." So where's our whole? Oh, it's that number after the equal sign, 1 is equal to the whole subtract another part.

So the ones digit of the whole is less than 3 and odd.

So let's think, less than three.

That's two or one and it's odd.

Oh, it must be a one then, mustn't it? So that's our ones digit.

And she says, "The tens digit of the whole is double the ones digit of the whole." So our ones digit was one, double one is two, so it must be two.

Andeep says, "The whole is 21, so the known part must be 20." How does he know that? Oh, that's right, because we know that one part is one.

We know one of the parts is 1, so the other part must be 20.

They're consecutive numbers, they have a difference of 1.

And here's the bar model to show it.

We knew that one was our part.

We used the clues to work out that 21 was the whole.

So we knew that the other part had to be 20.

Well done if you followed all those clues through.

That was exciting, I enjoyed that.

And here is your task for the end of part one.

Use what you've learned to complete the equations.

So we're going to find some missing parts and some missing wholes.

Think carefully about how those subtractions have been recorded.

Make sure you know exactly where the whole is.

And in question two, you are going to solve a little puzzle, as well.

Use the numbers shown to complete as many equations with a difference of one.

You can use each number more than once.

You've got 52, 49, 53, 54, 51, and 50 to use to make an equation with something subtract something is equal to 1.

Pause the video, have a go at questions one and two.

And when you're ready for the answers and some feedback, press play.

How did you get on? So in question one, you were completing the missing numbers.

So we had 81 subtract something is equal to 1.

Well, we know that consecutive numbers have a difference of 1.

So we are looking for the number that is 1 less than 81.

That will be our part if 1 is the known part, so it must be 80.

And in the next one, we had 80 subtract something is equal to 1, so that must be 79.

And then 79 subtract something is equal to 1, and that must be 78.

The missing part always had to be 1 less than the whole.

What about B, are we missing a part or a whole this time? We are missing the whole, aren't we? Something subtract 75 is equal to 1.

Our parts are 75 and 1, so our whole must be 76.

In each example in B, the whole is missing.

So it must be 1 more than the known part to be subtracted.

So 76 subtract 75 is equal to 1, 77 subtract 76 is equal to 1, and 78 subtract 77 is equal to 1.

Can you see those consecutive numbers? Now, in C, we had to be careful, because our difference was recorded first.

So the known part of 1 was recorded at the beginning of the equation each time.

1 is equal to 78 subtract, oh, we're looking for those consecutive numbers, aren't we? There we go, in each example in C, the whole has eight ones.

So to have a difference of one, the missing part had to have a ones digit of seven.

So 1 is equal to 78 subtract 77, or 88 subtract 87, or 98 subtract 97.

I hope you spotted all of those, and used your knowledge of consecutive numbers.

Let's see what question two was all about.

So we had to use the digit cards to complete the equation in as many ways as possible.

So we are looking for those pairs of consecutive numbers.

Our whole needs to be one more than the part we're subtracting.

So we could have had 54 subtract 53 is equal to 1, or 53 subtract 52 is equal to 1, or 52 subtract 51, or 51 subtract 50, or 50 subtract 49.

Did you find all of those possibilities? Well done if you did.

Well done for spotting those consecutive numbers, and realising that your whole had to be one more than the number you were subtracting.

And let's get into the second part of our lesson.

This time, we're going to look at subtraction where one part is a multiple of 10.

Izzy thinks she also has an easier way to solve this equation.

So Andeep shared his way of thinking about consecutive numbers.

I wonder what Izzy's thinking about.

What can you spot here? We've got 67 subtract 37, anything you spot? Izzy says, "I have noticed something about the whole and the known part." Have you spotted something? Izzy says, "The ones digit is the same." That's right, we've got seven ones is our whole and our known part, 67 and 37.

She says, "I know when we subtract a multiple of 10, the ones digit does not change." So we've got a whole of 67 and a known part of 37.

So our other part isn't going to change our ones, so it must be a multiple of 10.

"And there it is.

The missing part must be a multiple of 10," she says.

We can show this on a number line.

Let's have a look.

"So it's easier to show if we subtract the ones first," says Izzy.

So we're doing 67 subtract 37.

So we're subtracting seven ones.

67 subtract 7 is equal to 60.

The ones digit is the same, so when we subtract the ones we're subtracting all the ones, there are only tens left to subtract.

67 subtract 7 is equal to 60.

And then we can subtract the 30 which is equal to 30.

So our missing part was 30, a multiple of 10 as Izzy said.

Time to check your understanding.

In which of the following equations will the missing part be a multiple of 10? So you've got a whole and a known part there.

What will it look like when you do the subtraction, and which one will give you a missing part of a multiple of 10? Is it A, B, or C? Pause the video, have a think.

And when you're ready for the answer and some feedback, press play.

Which one did you think? Did you spot that it was B? Our ones digits are the same, aren't they? So in a subtraction equation where both the whole and one part, the known part, have the same ones digit, the difference is a multiple of 10.

So what would our difference be here? 28 subtract 8 would be 20, subtract 10 would be 10.

So the difference would be 10.

Andeep sets Izzy a challenge this time.

70 something subtract something and 8 is equal to 20.

Ah, we've got difference, that's a multiple of 10.

I wonder if that's gonna help us.

You might wanna have a little think about this before Andeep and Izzy start to talk about this problem.

Andeep says, "Find the missing digits in the equation." Izzy says, "The difference is a multiple of 10, so I know that the ones digit in the whole and the part must be the same." So a whole must be 78.

And the difference between the whole and the missing part is 20.

So the tens digit in the part must be two less than seven.

If seven is the whole and two is a part, then the other part must be a five.

78 subtract 58 is equal to 20.

Well done, Izzy, great reasoning.

Time to check your understanding of that.

Can you find the missing digits in the equation here? 90 something subtract something 6 is equal to 50.

Pause the video, have a go.

And when you're ready for the answer and some feedback, press play.

How did you get on? Did you spot that multiple of 10 as our difference? So if the difference is a multiple of 10, I know that the ones digits in the whole and the part must be the same.

So that means my whole must be 96, it must have 6 ones, and then I've got 96 subtracts something and 6 is equal to 50.

Well, let's think about parts and wholes.

If nine is the whole and five is a part, the other part must be four.

So the difference between the whole and the missing part is 50.

So the tens digit in the part must be five less than nine.

So 96 subtract 46 is equal to 50.

Well done if you work that out.

The children are trying to find all the possible solutions to this problem.

Let's help them find the missing digits.

This time, we've got something 7 subtract something 7 is equal to 30.

Hmm.

You might want to have a little think before we hear what Izzy and Andeep have been talking about.

Izzy says, "The ones digit in the whole and the parts are the same, because the difference is a multiple of 10." She says, "The difference is 30, so the whole must be 30 more, and the missing part must be 30 less than the whole." Ah, so we've got a difference of 30.

So we need tens digits that have a difference of 30.

Andeep says, "The whole must have three more tens than the missing part." Great thinking, Andeep, I like that.

He says, "I will work systematically to find all the possible tens digits with a difference of three." So he's going to start either with the biggest or the smallest, and then work through systematically in an order.

He started by subtracting the smallest number of tens he could.

1 10 and 7 ones, 17.

The difference is 30.

So our whole must be 30 more, 3 tens more.

So 47 subtract 17 is to 30.

Now, he can gradually increase each one.

57 subtract 27 will be equal to 30.

67 subtract 37, 77 subtract 47, 87 subtract 57, and 97 subtract 67.

Can he go on? He can't, can he? 'Cause if he makes his 97, 10 more, it won't be a 2-digit number anymore.

So nine and six have a difference of three, as did eight and five, seven and four, six and three, five and two, and four and one.

And it's time for you to do some practise.

In question one, you are going to complete the equations using what you've learned to help you.

So we're thinking about those subtractions where 1 part is a multiple of 10.

And remember, you can always draw a bar model or a number line to help you if you need to.

And in question two, you are going to work systematically just like Andeep did to find all the possible solutions to this problem.

Something 3 subtract something 3 is equal to 40.

Pause the video, have a go at questions one and two.

And when you're ready for the answers and some feedback, press play.

How did you get on? Let's have a look at question one.

So 47 subtract 20.

Ah, we're subtracting 20 and all of these, aren't we? So we're going to subtract two tens from our whole.

Our ones digit won't change, because remember, when one of our parts is a multiple of 10, the other part must have the same number of ones as the whole.

So our ones digit is not going to change.

47 subtract 20 is equal to 27.

57 subtract 20 is equal to 37, and 67 subtract 20 is equal to 47.

So in set A, we knew the ones digit would stay the same, and the tens digit must be two less than the tens digit in the whole.

And did you also notice that our whole got 10 bigger each time, and so therefore, our missing part also had to be 10 bigger each time, because our known parts stayed the same.

And you may also have noticed for set A, that the whole increased by 10 each time.

So the missing part also increased by 10.

Let's have a look at set B.

Did you notice this time that the difference was recorded first in our equation? 30 is equal to 78 subtract something, 88 subtract something, and 98 subtract something.

So our whole is increasing by 10 again, but this time, our difference is a multiple of 10.

So that means our part must have a ones digit of eight.

So in B, we knew that the ones digit would stay the same, and the tens digit must be three less than the tens digit in the whole, because we've got three tens in our difference.

So 78 subtract 48, 88 subtract 58, and 98 subtract 68.

30 is equal to all of those, because there's a difference of three tens between seven tens and four tens, eight tens and five tens, nine tens and six tens.

You may also have noticed that the whole increased by 10 each time, so the missing part also increased by 10.

So let's look at C.

And this time, it's the whole that's missing.

We're subtracting 24 each time, and our answer is a multiple of 10, but it gets bigger each time.

So something subtract 24 is equal to 20.

Well, we know it must have a four in the ones, because we need to get rid of that four by subtracting the four to make our multiple of 10.

So we must have something with a four in the ones and a tens digit that's two more than two.

So it must be 44.

And there we go, we can work out the others now.

So the whole is missing.

We knew the ones digit would stay the same, and the tens digit must increase by the number of tens in the difference.

So 44 is 20 more than 24, 54 is 30 more than 24, and 64 is 40 more than 24.

And you may have noticed that the difference increased by 10 each time and the other part stayed the same.

So the missing whole also increased by 10 each time.

I hope you were able to reason your way through those, and not just to do all the calculations.

If you worked out all the calculations and used a bar model or a number line, have a look now at those patterns, and see if you can explain them to somebody near you.

And onto question two, you had to find as many different ways as possible to complete the equation.

So this time, our difference was 40.

And that's four tens.

So the tens digit of the whole must be four more than the tens digit of the missing part.

So we've got a difference of 40.

So let's think about what that would look like.

So we're going to find all the single digits with a difference of four, starting with five subtract one.

Aha, so five subtract one is equal to four.

So five tens subtract one 10 must be equal to four tens.

So we can start off with 53 subtract 13.

Now, we need to find another pair of digits with a difference of four.

Well, six and two have a difference of four.

So 63 subtract 23 is equal to 40 as is 73 subtract 33, 83 subtract 43, and 93 subtract 53.

All our tens digits had a difference of four.

Well done if you spotted all of that.

And we've come to the end of our lesson.

We've been using efficient methods to solve subtraction equations.

What have we been thinking about today? Well, we've reminded ourselves that consecutive numbers, those numbers next to each other when we're counting in ones always have a difference of one.

And we can use that in our subtraction.

If the whole and the known part in a subtraction equation are consecutive numbers, the missing part will always be one.

And if the known part in a subtraction equation is one, then the whole and the missing part will be consecutive numbers.

And we've also learned that when the ones digits in the whole and in the known part are the same, then the missing part will be a multiple of 10.

And we also know that if the known part is a multiple of 10, then the whole and the missing part will have the same ones digit, as well.

It's always worth looking carefully at equations before we leap in and try to solve them.

There are efficient methods we can use based on facts that we know well.

Thank you for all your hard work and your mathematical thinking in this lesson, and I hope I get to work with you again soon.

Bye-bye.