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're going to be able to bring to this lesson.

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

In this lesson, we're going to be solving equations involving the subtraction of two-digit numbers.

Hmm, have you been doing some subtraction recently? Have you been thinking about two-digit numbers, maybe? We're going to be using our knowledge of numbers and our number facts to help us today.

So I hope you've got those ready.

Let's get started then.

We've got two Keywords in our lesson today.

I'm sure they're words you've come across before.

They're partition and part, but let's just rehearse them.

I'll say them and then it'll be your turn.

So my turn, partition, your turn.

My turn, part, your turn.

Well done, I'm sure you've done lots of partitioning of two-digit numbers and I'm sure you've thought about parts and wholes as well, when you've been solving problems. So let's see if we can bring all that together today in our lesson.

There are two parts to our lesson today.

In the first part, we're going to subtract by partitioning one part, and in the second part of our lesson, we're going to find missing numbers when subtracting.

So let's make a start on part one of our lesson.

And we've got Andeep and Izzy helping us with our learning today.

First, Izzy has 87 pounds, but then she bought a rocket and then a car.

How much money does she have left now? I wonder, you might want to have a think about this before Izzy tells us how she's going to work it out.

Izzy says, "I will use Base 10 blocks to represent the numbers.

I subtract 50 and then I subtract 2." So she's got 87 there, eight tens, and seven ones.

She's going to subtract 50, and then she's going to subtract 2.

So she's removed 5 tens and 2 ones.

What's she got? And she says that means, "I have 35 pounds left." Andeep has 87 pounds as well, but then he bought a unicorn.

How much money does he have left now? His unicorn costs 52 pounds.

So he subtracted the 50 pounds and the 2 pounds part and he's got 35 pounds.

He says, "I have 35 pounds left." Let's look at the equations that Izzy and Andeep solved.

What's the same about them both? You might want to have a think before they share their thoughts.

What did you notice? Well, both equations start with the same amount and subtract the same amount and are left with the same amount.

So the whole in both cases is 87 pounds, and they both end up with 35 pounds, and they've subtracted the same amount, haven't they? But what's different? Well, although they both subtracted 52 pounds, Andeep subtracted one amount of 52 pounds, but Izzy subtracted two amounts, 50 pounds and 2 pounds, but in total, her rocket and her car cost the same as Andeep's unicorn.

Andeep partitioned the part being subtracted into tens and ones to make it easier to subtract.

So he was subtracting 52 pounds, but he partitioned it into 50 pounds and 2 pounds.

And that's exactly what Izzy spent, 50 pounds and 2 pounds.

Let's check your understanding.

Andeep bought the trainers and Izzy bought two different items. They each started with the same amount of money and had the same amount left.

So what did Izzy buy? Remember Andeep bought the trainers for 43 pounds.

They started and ended with the same amount of money.

So what did Izzy buy? Pause the video, have a think, and when you're ready for the answer and some feedback, press play.

What did you think? That's right, she must have bought the sunglasses for 3 pounds and the T-shirt for 40 pounds.

43 pounds can be partitioned into 40 pounds and 3 pounds.

So subtracting 43 pounds is the same as subtracting 40 pounds and then 3 pounds or 3 pounds and then 40 pounds.

Well done, if you spotted that C was the correct answer there.

So we're going to have a think about how we can partition the part being subtracted to solve this equation.

And we can use some stem sentences to help us.

We can think of it as a part, 'cause if we represented this as a bar model or a part-part whole model, our whole would be 87.

One part would be 62, and we'd have a missing part that we are calculating.

So the part being subtracted helps us to work out what the other part is.

So can we use the stem sentences to help us here? We've got 87 represented in base 10 blocks, and we're going to use the stem sentence.

To subtract, hmm, we can subtract, hmm, then subtract, hmm.

So we're going to think about partitioning.

So we're going to partition the part being subtracted into 60 and 2.

So to subtract 62, we can subtract 60, and we can see that in the base 10 blocks, then subtract 2, and we can see that in the base 10 blocks as well.

87 - 60 - 2 = 25.

87 - 60 = 27 and 27 - 2 = 25.

Izzy says, "I wonder if I could have subtracted the ones first?" Do you think she could? "Let's try," she says.

So to subtract 62, we can subtract 2, we can see it in the base 10 blocks, and then subtract 60.

87 - 2 = 85 - 60 = 25.

What do you notice? Yes, well done, Izzy.

We can subtract the tens and ones in any order and the remaining part will be the same.

Izzy thinks the known part of this equation can be written differently.

Oh, I wonder what she thinks about that.

So we've got 58 and we're subtracting 34.

So 58 is our whole, 34 is one part, and we're going to calculate the other part.

And we've represented our whole with base 10 blocks.

Andeep says, "Well I can partition the part being subtracted to show an equation that will have the same value." Go on then, Andeep, show us.

He says, "You can partition the parts into tens and ones." So this is the part we're subtracting the 34 and we can partition it into 30 and 4.

"This shows that you can subtract the tens and the ones separately." 58, subtract something, subtract something.

So we could do 58 - 30, and then subtract 4.

Or 58 - 4 and then subtract 30.

Now we can solve the equation.

58 - 30 - 4.

We're going to subtract the tens first.

So subtract the 30, which leaves us with 28, and subtract the 4, which is 24.

So we have 24 as our missing part.

And we can show this on a number line as well.

58 - 30 = 28 and 28 - 4 = 24.

So our missing part, the answer to our subtraction is 24.

Andeep wonders if he can use the same strategy when subtracting from a multiple of 10.

Ooh, let's try.

We've got 90 - 62.

He says, "I will partition the tens and ones, then subtract them separately." So 62 partition's into 60 and 2, 6 tens and 2 ones.

First, he's going to subtract the tens.

90 - 60 = 30 and then 30 - 2.

Well, he can use his known facts.

If we subtract 2 from 10, we have 8 left.

So if we subtract 2 from a multiple of 10, we will have a number with the 8 and the ones.

30 - 2 = 28.

"This strategy works when subtracting any pair of two-digit numbers," says Andeep.

We just need to know those number facts to help us to subtract the tens and then subtract the ones.

So time to check your understanding.

Can you partition the part being subtracted and then draw a number line to solve the equation? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

How did you get on? So you were partitioning the part being subtracted.

So 70 - 43, we were subtracting 43.

So we can partition that into 40 and 3.

Now we've got a number line to help us.

70 - 40, let's subtract the ten first.

7 tens subtract 4 tens is equal to 3 tens, so 30.

Now we've got 30 - 3.

So we know that when we subtract 3 from 10, we have 7.

So when we subtract 3 from 30, we will have 27.

So 70 - 43 = 27.

Izzy notices something about the numbers in this equation.

72 - 42.

Hmm, you might want to have a think before Izzy tells us what she's noticed.

Go on then, Izzy, what have you noticed? She says, "Only the tens digit is different." She says, "I predict that the difference will be a multiple of 10." Oh, that's interesting.

The ones aren't changing are they? 72 - 42, the tens are changing, but the ones are staying the same.

"7 tens - 4 tens = 3 tens and the ones digit is the same, so the other part must be 30.

I'll check I'm right by partitioning one part," she says.

So she's partitioned the 42 into 40 and 2.

72 - 40 = 32 and 32 - 2 = 30.

"I was right," she says.

Time to check your understanding.

Can you use Izzy's thinking? Which of the following will have a difference that is a multiple of 10? And can you check you are right by partitioning the part being subtracted? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

Which one did you think? Did you use Izzy's thinking, and look at the ones digits? Ah yes, so in B we have 52 - 32.

The ones digits are the same, only the tens digits are changing.

Let's just check on the number line.

So we can partition our 32 into 30 and 2.

52 - 30 = 22 and 22 - 2 = 20.

So the missing part or the difference in our subtraction is 20.

Well done, if you spotted that.

We know that 52 - 32 will have a difference that is a multiple of 10, because the ones digits are the same, so they have a difference of zero.

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

Can you solve these equations? Can you see that we're writing out equivalent expressions in A and B? We're not just finding an answer, we're finding a missing value in an equation.

And in C, we're working out the difference, the answer to our subtraction.

So pause the video, have a go, and when you're ready for the answers and some feedback, press play.

How did you get on? So let's have a look at A.

We have 84 - 12 = 84 - 10 - 2.

That's right, it's showing that partitioning, isn't it? 68 - 23 = 68 - something - 20.

Ah, this time we're subtracting the ones first, subtract 3, subtract 20.

And the third one.

47 - 25 = 47 - 20 - 5.

Or you might have had subtract 5, subtract 20.

Let's look at B.

80 - 13 is the same as 80 - 3 - 10.

74 - 34, oh, do you notice, we've got our one digits that are the same.

It's the same as 74 - 30 - 4.

And you can see that that four's going to disappear when we subtract.

And our answer will be a multiple of 10.

63 - 23 again, we've got that ones digit staying the same.

63 - 20 - 3.

Or we could have had 63 - 3 - 20 there.

And the final one, 50 - 24 = 50 - 20 - 4.

Or we could have had subtract 4 and subtract 20.

So let's look at C.

We were solving these ones, so 80 - 15.

Well, 80 - 10 = 70 and 70 - 5 = 65.

67 - 27, oh, can you see those ones digits? 67 - 20 = 47 and 47 - 7 = 40.

So our answer is a multiple of 10.

69 - 36.

69 - 30 = 39 and 39 - 6 = 33.

And in C, again, we're subtracting from a multiple of 10, aren't we? So 50 - 20 = 30 and 30 - 4 = 26.

Well done, if you've got all of those right.

And on into the second part of our lesson, we're going to find missing numbers when subtracting.

Izzy solves this equation by partitioning both the whole and the part.

So 76 is 70 and 6, 25 is 20 and 5.

She says, "70 - 20 = 50, and 6 - 5 = 1." But it is giving her the right answer.

But she says, "This is not a good strategy, because it does not work for all subtraction equations." Hmm, worth remembering.

It's always good just to partition the number we are subtracting, the known part.

So, "To subtract, you only need to partition the part being subtracted." And that's a good strategy to remember.

That will always work.

This strategy will not always work.

So Izzy's now, only partitioned her 25.

And, "We can show this on a number line," she says.

76 - 20 = 56 and 56 - 5 = 51.

So our answer, our missing part is 51.

Izzy had 47 p and she spent 24 p.

How much money does she have left? Write the equation to solve the problem.

And can you draw a number line to help you? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

So she had 47 p and she spent 24 p.

So 47 - 24 is our equation.

47 - 20 = 27 and 27 - 4 = 23.

So 47 - 24 = 23.

Izzy had 23 p left.

Andeep's looking at a bar model.

He thinks he can find the missing number in the bar model.

His whole is 58 and one of his parts is 32.

He says, "I'll draw a number line to help me.

The whole is 58 and one part is 32.

I will subtract 30 and then 2 to find the other part." So 58 - 30 = 28 and 28 - 2 = 26.

So our missing part must be 26.

Can you find the missing number in the bar model? Remember you can draw a number line to help you.

Our whole is 76 and the part we know is 24.

Pause the video, have a go, when you're ready for the answer and some feedback, press play.

How did you get on? So the whole is 76 and one part is 24.

So we must subtract the 20 and then the 4 to find the other part.

If we know the whole and one part, we can subtract the part we know to find the other part.

So 76 - 20 = 56 and 56 - 4 = 52.

So our missing part is 52.

Ooh, this is interesting.

Izzy thinks she can find the missing number on the number line by subtracting the tens and ones in her head.

Can you see what's happened here though? Our missing part is the part we are subtracting.

She says, "I will subtract the multiple of 10 until I can't subtract any more tens.

If I reach a number before 33 or less than 33," she says, "I will have subtracted too many." So 58 - 20 = 38 and 38 - 5 = 33.

So what's she subtracted in total? She subtracted 20 and 5.

Ah, so she subtracted 25.

So 58 - 25 = 33.

Can you subtract tens and ones in your head to complete the equation on the number line here? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

How did you get on? So you're going to subtract a multiple of 10 until you can't subtract any more tens.

So we're going to carry on subtracting tens until we get to a number that is close to 43, but not less than 43.

So 78 - 10 would be 68, subtract 20 would be 58, and subtract 30 would be 48.

So I can subtract 30.

It doesn't give me a number before or less than 43.

So that will be all right.

78 - 30 = 48.

So I've got to 48.

My target number is 43.

48 - 5 = 43, because I know that 8 - 5 = 3.

So I subtracted 30 and then 5, so I subtracted 35.

So 78 - 35 = 43.

Well done, if you've got that.

Andeep uses a different strategy to find the missing number.

He's got 58 subtract something is equal to 33.

He says, "I will think about the parts and the whole and draw a bar model to help me." He says, "58 is the whole and one part is 33." Does that remind you of something? What's the missing part? He says, "I know that a whole subtract part is equal to a part, so I can use 58 - 33 to find the missing part." We know one part and we are finding out the other.

And we know that if we know the whole, we can subtract one part and find the missing part.

So we can rewrite this equation.

58 - 33 = to something.

So he can then solve it by subtracting 30 and then subtracting 3.

So 58 - 30 = 28, then 28 - 3 = 25.

So the missing part is 25.

Time to check your understanding.

Can you draw a bar model and use what you know about parts and wholes to solve the equation? Can you write the equation in a different way, perhaps? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

How did you get on? So our bar model will have 78 as the whole and a part has been subtracted that we don't know about, and we're left with 43.

So how can we think about this? Ah, that's right, if we know one part, we can subtract it from the whole to find the other part.

Whole subtract part is equal to part.

So now we can solve this as 78 - 43.

So we can partition the number we're subtracting, the part we're taking away, 78 - 40 = 38 and 38 - 3 = 35.

So we subtracted 40 and then 3 to reach 35.

So the missing part is 35.

And we can put that back into the original equation, 78 - 35 = 43.

So the children want to find the missing numbers on the number line.

So can we help them here? We've got a number, subtract 40 and 2, and it gets us to a number in the thirties, and then a number with a 4 in the ones.

Oh, this is interesting.

You might want to have a think before Andeep shares his thinking.

Andeep says, "When I subtract 40, I reach a number in the thirties, so I must have started with a number in the seventies." Oh, good thinking, Andeep.

If we just move the arrow to go the other direction, we can see that we'd be adding on 40, wouldn't we? So we must have a number with a 7 in the tens place to represent 70.

What else do we know? He says, "When 2 ones are subtracted from this number, the one's digit is 4, so it must be a six.

It must be 36 - 2 = 34.

Aha, so now can we fill in the last digit that's missing? 70 something subtract 42 is equal to 34.

Well, it must be six, because when we subtracted a multiple of 10, we had a 6 in the ones.

So we must have 76 - 42 = 34.

Well done, Andeep, and well done, you, if you followed that, or maybe you'd thought of it already.

Really good thinking.

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

In question one, you're going to partition the known part into tens and ones and then draw a number line to solve each equation.

And for A and B, we're trying to find the missing part, that is the answer that we're looking for.

In C, our missing part is the part we're subtracting.

So can you remember what Andeep did and how he rewrote his equation, thinking about what he knew about wholes and parts? For D, we've got to find that missing number.

What is the number we've subtracted? And in E, we're finding the missing part in the bar model.

And in question two, just like that one we've just solved with Andeep, can you find the missing numbers on the number line? Can you fill in those digits? We've got three, two-digit numbers there.

The whole that we're starting with, the number that we get to after we've subtracted 30, and the number we get to after we've subtracted the final 5.

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 let's have a look at question one.

Let's look at A.

We've got 76 - 13, 76 - 23, and 76 - 33.

Do you notice something there? Hmm, let's have a look at 76 - 13.

Well that's 76 - 10, which is 66, subtract another 3, which is 63.

What about the next one? This time we were taking away, subtracting 10 more.

So our answer will be 10 less.

It'll be 53.

And then 76 - 33.

Again, we've taken away 10 more, so our answer will be 10 less, 43.

What about B? This time the missing part was written first.

So the answer to our subtraction came first.

Something is equal to 84 - 43.

So for the first one in B, we had to calculate 84 - 43.

84 - 40 is 44 and 44 - 3 = 41.

Now can we use that to help us to work out the other answers? In the next one, we had 84 - 33, so we subtracted 10 less.

So our answer must be 10 more, 51.

And for the final one, again, we're subtracting 10 less again, so our answer will be 10 more.

84 - 23 = 61.

And for C, remember our missing part now, was sort of in the middle of our equation, it was the number we were subtracting.

But do you remember Andeep told us, if we think of this as a bar model, then if we know the whole, then we can subtract one part to find the other part.

So we could rewrite this equation as 53 - 31.

So let's think about subtracting 31.

53 - 31, 53 -30 = 23 and 23 - 1 = 22.

So 53 - 22 = 31.

Now this time, we've got 63, so we've got 10 more, but our answer is 10 more as well.

So we must be subtracting the same thing, 22.

And for the last one, again, we're starting with 10 more, but we're ending up with 10 more.

So we must be subtracting the same thing again.

So the answer for all of those was 22.

So in D, we know that 48 is the whole and 27 is one part.

So we can use 48 - 27 to help us.

48 - 20 = 28, and then 28 - 7 = 21.

But we could also have thought about counting backwards and about taking away 20 to get to 28, and then taking away another one to get to 27.

And in E, we know that 48 is the whole and 21 is a part.

So we can use 48 - 21 to help us.

48 - 20 = 28, then 28 - 1 = 27.

So our missing part must be 27.

And question two, we were trying to fill in those missing digits in our two-digit numbers.

So how did you work? What did you think? Well, when I subtract 30, I reach a number in the fifties.

So I must have started with a number in the eighties.

So my missing tens digit of my whole must be an 8.

When 5 ones are subtracted from this number in the fifties, the ones digit is a 4, so it must be 59 - 5 = 54 So that means that the tens digit of our final number must also be a 5 for 54, because we haven't bridged through 10.

What about the missing ones digit of our whole? Well, 80 something subtract 30 is equal to 59.

We've only subtracted tens, so our ones digit is the same.

So it must be 89.

So this number line represents 89 - 30 - 5, or 89 - 35.

Well done, if you filled in all those numbers.

I hope you enjoyed thinking about that problem.

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

We've been solving equations involving the subtraction of two-digit numbers.

What have we learned about? Well, we've learned that we can partition the part being subtracted to help subtract two-digit numbers.

And it's actually better just to partition the part we're subtracting.

And we also know that we can use known facts and we can partition numbers to help solve missing number equations.

Thank you for all your hard work and your mathematical thinking.

I hope you've enjoyed the lesson, and I hope I get to work with you again soon.

Bye-bye.