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 missing number equations involving subtracting two-digit numbers.

Have you been doing some work on subtracting and thinking about two-digit numbers recently? I hope so.

Let's see if we can solve some missing number equations then, find out what's missing.

There are two keywords in our lesson today, part and whole.

I'll take my turn to say them, and then it'll be your turn.

So my turn, part.

Your turn.

My turn, whole.

Your turn.

I'm sure you've been talking about parts and wholes in your maths work for a very long time, but they're going to be really useful to think about today.

And there are two parts to our lesson today, one part and another part, and that will make our whole lesson.

In the first part, we're going to be finding the missing parts in a subtraction equation.

And in the second part of our lesson, we're going to be finding the missing whole in a subtraction equation.

So let's make a start on part one.

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

Izzy wants to find the missing number in this equation.

She's got 80 subtract something is equal to 21.

She says, "I will draw a bar model to show the parts and the whole." So here's her bar model.

Where do you think those numbers are going to fit in? What's our whole, and what are our parts? You might want to have a think before Izzy fills in her bar model.

So go on, Izzy, what do you know? Ah, she knows that 80 is the whole.

That's the number we're starting with.

And then we're subtracting a number, and we've got 21 left.

So 21 is one of our parts.

But what is the other part? She says, "80 is the whole, and 21 is the known part." When we subtract the number that we subtract, you might have called it the subtrahend, and the number that we're left with, you might call it the difference, they are the parts in our bar model or our part-part-whole model.

She says, "To find the missing part, I can use 80 subtract 21." If we know the whole and one part, we can work out the value of the other part by subtracting the known part from the whole.

So that's exactly what she's going to do.

So she's going to do 80 subtract 21.

So there's 80.

80 subtract 20.

Well, 80 is eight 10s, and we're subtracting two 10s, so we'll have six 10s, 60.

But then what have we got to subtract? That's right, we've got to subtract the 1.

So she's partitioned her 21 into 20 and 1, subtracted the 20, and then subtracted the 1.

So what must our missing part be? Well, it must be 59.

That's where she's landed on the number line.

Andeep says he found a different way to solve this.

I wonder if you can think what Andeep's different way would be.

Go on, Andeep, tell us.

He says, "I know that 80 partitions into 60 and 20." Yes, well, 8 is a whole, 6 is a part and 2 is a part.

So if 80 is a whole, then 60 is a part and 20 is a part.

Hmm, that 20's quite close to 21, isn't it? So he's used a part-part-whole model to show 80 as our whole, 60 as a part, and 20 as a part.

Can you see what he might be going to do here? He says, "If I increase one part by 1 to keep the whole the same, I must decrease the other part by 1." So he's sort of taken 1 from the 60 and given it to the 20.

And there it goes.

So our 20 has become 21, and the 1 we've taken away means that our 60 has become 59.

And he says, "Therefore, we can say that 80 will also partition into 59 and 21." Great thinking, Andeep, I really like that.

So time to check your understanding.

Can you draw a bar model and find the missing number in this equation? You might use Izzy's method, but I wonder if you could think about Andeep's method as well.

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 here's our bar model.

What's our whole, and what are our parts? That's right, 70 is the whole.

70 is the number we're starting with.

And we're subtracting one part, we don't what that value is.

And the part that we're left with is 32.

So 70 is our whole, and our parts are our missing number and 32.

Now, we know that to find a missing part, we subtract the known part from the whole, so we can subtract 32.

So 70 subtract 30.

Well seven 10s subtract three 10s is equal to four 10s, so that's 40.

And then we've got to subtract another two.

40 subtract two is equal to 38.

So our missing part must be 38.

Now, this equation does not subtract from a multiple of 10, hmm.

I wonder if we can still use the same strategy to solve it.

64 subtract something is equal to 21.

You might want to have a think before Andeep shares what he's been up to.

Go on, Andeep, what are you going to do? He says, "I still know the whole and one part, so I can draw a bar model again." That's right, Andeep.

64 subtract something subtract a part is equal to 21, the other part.

So there's our bar model.

So he says, "64 is the whole, and 21 is the known part." So he says, "To find the missing parts, I can use 64 subtract 21." And let's draw a number line.

He can partition the 21, the part he's subtracting, into 20 and 1.

64 subtract 20, so we're taking away two of the 10s.

Our 1s will stay the same.

Six 10s subtract two 10s is four 10s, so it must be 44.

And then we've still got 1 to subtract.

44 subtract 1 is equal to 43, the number before.

So our missing number must be 43.

"That's the missing part," says Andeep.

Well done, Andeep, I like your thinking there.

So yes, we can still use the same strategy even when we're not subtracting from a multiple of 10.

Izzy thinks about how she can check that she's right with this one.

So we had 64 subtract 43 is equal to 21.

Andeep showed us that our missing part was 43.

How can she check she's right? Ooh, good thinking, Izzy.

She says, "Addition is the inverse of subtraction." We know that a whole subtract a part is equal to a part, and we also know that a part plus a part is equal to a whole.

If we add the parts, we find the value of the whole.

So we could check this by doing an addition.

Part plus part is equal to whole.

So Izzy knows if she adds 21 and 43, our two parts, we should find a total or a sum of 64, our whole.

We're not going to bridge 10 here with our 1s, so we can partition both of our addends.

20 and 1 plus 40 and 3.

So we've partitioned.

First we add the 10s, 20 plus 40 is equal to 60.

Then we add the 1s.

1 plus 3 is equal to 4.

And then we recombine.

60 plus 4 is equal to 64.

So she was right.

Yes, that's a good check.

And our whole is 64, so we did get our subtraction right.

Well done, Izzy, great checking.

Time to check your understanding.

Can you write an equation to check that this equation is correct? 64 subtract 42 is equal to 22.

And there we've got the parts and the whole filled in in our bar model.

So can you write an equation to check that this is correct? 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 did you use Izzy's thinking? When we look at a bar model, we know that we can add our parts to find the value of our whole.

Part plus part is equal to whole.

So 64 is a whole, 22 is a part, and 42 is a part.

Part plus part is equal to whole.

So if the equation is correct, then 22 plus 42 will be equal to 64.

Let's check.

We know that our ones digits are not going to bridge 10, so we can partition both our addends, both our parts.

Now we're going to add the 10s.

20 plus 40 is equal to 60.

Now we can add the 1s.

2 plus 2 is equal to 4.

And then we recombine, 60 plus 4 is equal to 64.

Yes, that was our value of our whole.

So those parts are correct.

When we add them, the whole is 64.

Well done.

Ooh, this equation is arranged differently.

What's the missing number now? Is it a part? Is it a whole? Have a look and a think before Andeep shares what he's worked out.

Hmm, well we haven't started with our whole this time, have we? We've started with our difference with one of our parts.

We're subtracting from 64, so 64 is still the whole.

But our equation this time says 23 is equal to 64 subtract something.

So 64 is still the whole.

We're still subtracting a part that we don't know about, but the other part is 23.

23 is equal to 64 subtract one part, so 23 must be the other part.

And Andeep says he can solve this with 64 subtract 23.

We know that if we subtract the known part from our whole, we can work out the value of the missing part.

So 64 subtract 23.

Let's partition the 23 into 20 and 3.

64 subtract 20 is equal to 44, and 4 subtract 3 is equal to 1.

So our missing part is 41.

Time to check your understanding on that part too.

Can you draw a bar model to find the missing number in this equation? Think carefully about what's the whole and what are the parts.

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

How did you get on? Well, 24 is the same as 64 subtract one part.

24 is equal to 64 subtract something, so 24 must be the other part.

Again, our whole is sort of in the middle of our equation here, isn't it? So our bar model will look like this.

64 is our whole.

We're subtracting a part that we don't know.

And our other part is 24.

So we can solve this and find the missing part by subtracting our known part from the whole.

64 subtract 24.

So we can partition the 24 into 20 and 4.

64 subtract 20 is equal to 44.

And then we've got to subtract 4.

44 subtract 4 is equal to 40.

Did you notice that our ones digits were the same in our whole and in our known part? So our difference, our missing part, must be a multiple of 10.

64 subtract 24 is equal to 40.

There's our missing part.

Izzy wonders if this strategy still works when the equation has bridged 10, hmm.

So this time we've got 64 subtract something is equal to 25.

Hmm, so yes, we are going to bridge 10 here.

If we look at our 1s, we can see that our whole has four 1s and our part has five 1s, so we must be bridging through 10.

She says, "I still know the whole and one part, so I can still find the missing part." 64 is our whole.

We're subtracting a part that we don't know, and the part that's left is 25.

So she knows that she can subtract the known part from the whole.

64 subtract 25.

She says, "I'll bridge 10 to subtract 25." So we can partition our 25 into 20 and 5.

64 subtract 20 is equal to 44.

We've taken away two of the 10s.

Now we've got to subtract 5.

So we can partition our 5 into 4 and 1.

44 subtract 4 is equal to 40, subtract another 1 is equal to 39.

So 64 subtract 39 must be equal to 25.

39 is our missing part.

Time to check your understanding.

Can you find the missing number in this equation? 64 subtract something is equal to 26.

Pause the video, have a go, draw a bar model, and then use a number line to help you.

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

How did you get on? Well, our whole is 64, we're subtracting a number we don't know, and what we're left with is 26.

So our parts are our missing number and 26.

So to find the missing part, we subtract the known part from the whole, 64 subtract 26.

64 is the whole, 26 is one part, and I'll subtract by bridging 10 to find the missing part.

So let's partition our 26 into 20 and 6.

64 minus 20 is equal to 44.

And then we need to partition our 6 into 4 and 2.

44 subtract 4 is equal to 40, and 40 subtract 2 is equal to 38, so our missing part is 38.

Well done.

Izzy writes a missing number equation, and she sets Andeep a challenge.

So her equation is 58 subtract something is equal to something, and they're two two-digit numbers.

And she's given Andeep some number cards, 1, 2, 3, and 7.

Izzy's challenge is to complete the equation only using the digits shown.

Hmm.

Are you ready for this challenge, Andeep? I wonder if you want to have a think before Andeep shares his way of working this out.

Go for it, Andeep.

Andeep says the whole has five 10s and eight 1s.

That's 58.

He says, "If 5 is the whole, then 3 is a part and 2 is a part, so the missing 10s digits must be 2 and 3." Oh, that's great thinking, Andeep.

I don't think there's any other way we could make a total of 5 using those cards.

So he's going to put the 2 and the 3 in as the 10s digits.

So we'd have 58 subtract 20-something is equal to 30-something.

He says, "Then let's look at the 1s.

If 8 is the whole, then 1 is a part and 7 is a part, so the missing ones digits must be 1 and 7." Well done again, Andeep.

So he said that 58 subtract 21 is equal to 37.

Izzy says, "Are there any other possible equations that could be made?" What do you think? Are there any others that could be made? Hmm.

Ah yes.

58 subtract 27 could be equal to 31.

"Or," says Andeep, "We could say, ah, 58 subtract 37 is equal to 21.

If five 10s is the whole, three 10s is a part, and two 10s is a part, we can swap those around." Great thinking, Andeep, and well done, Izzy, for realising that there was more than one answer in asking that question.

I hope you enjoyed looking at that.

Maybe you'll get to have a go at one of those in your practise.

And here is your practise.

So in task one, you're going to draw a bar model or maybe even a part-part-whole model to show the parts and the whole in each equation.

Then draw a number line to find the missing number in each equation.

And just make sure that you check how is the equation written.

Where is the whole, and where are the parts? Think carefully, especially when you're looking at the set in B.

And then in part two, you're going to have a go at a challenge like Izzy set for Andeep.

Use the digit cards to complete the equation.

How many different ways can you find? 97 subtract something is equal to something.

And you've got 2, 3, 4, and 7 to use.

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 for A, you had 78 subtract something is equal to 52.

So we can draw our bar model, and we know that our known part is 52, so we can subtract that from 78.

78 subtract 50 is equal to 28, and 28 subtract 2 is equal to 26, so our missing number was 26.

Then we had 78 subtract something is equal to 53.

Ah.

So our part that we know about is one larger, but our whole is still the same.

So what do you think's gonna happen to our missing part? Well, if one part has got one bigger, the other part must be one smaller.

Let's check.

78 subtract 53 this time.

78 subtract 50 is equal to 28, subtract 3 is equal to 25.

So did you notice that the known part increased by one, so the missing part decreased by one.

And what about the last one? 88 subtract something is equal to 53.

Oh, this time our whole is 10 bigger.

So there's our bar model.

Now, our whole is 10 bigger, but our known part is still 53, so our missing part must be 10 bigger as well.

Let's check.

88 subtract 50 is equal to 38, and 38 subtract 3 is equal to 35.

Yes, that was right.

The whole increased by 10, and the known part stayed the same, so the missing part increased by 10.

Let's look at B.

This time, we had our known part as the first element of our equation, didn't we? 23 is equal to 65 subtract something.

We can still draw that bar model.

65 is our whole, 23 is our known part, so we can subtract that to find the missing part.

65 subtract 20 is equal to 45, and subtract another 3 is equal to 42.

So our missing part is 42.

What about our next equation? 33 is equal to 65 subtract something.

Ah, can you see our known part has got bigger by 10? So if our known part is 10 more, then our missing part must be 10 less.

Let's check with the number line.

65 subtract 30 is equal to 35, and 35 subtract 3 is equal to 32.

So yes, that's right.

We noticed that the known part had increased by 10, so the missing part must have decreased by 10.

And what about our last one? 33 is equal to 66 subtract something.

Ooh, what's happened to our whole this time? Our whole is one bigger, but our known part is the same.

So that surely means our missing part must be one bigger as well for our whole to be one bigger.

Let's check.

66 subtract 30 is equal to 36, and 36 subtract 3 is equal to 33.

Yes, we were right.

The whole increased by one, and the known part stayed the same, so the missing part increased by one.

And what about C? 54 subtract something is equal to 27.

So my known part is 27, I can subtract it, 54 subtract 20 is equal to 34, but I'm subtracting 7 this time, so I've got to bridge through 10.

So I'm going to partition 7 into 4 and 3, and I get my answer of 27.

Ah, half of 54.

This time, 54 subtract something is equal to 28.

So my known part is one bigger, so my missing part must be one smaller.

Let's check.

Subtract 20 is 34, subtract 4 is 30, and subtract another 4 this time because I'm partitioning my 8 into 4 and 4, is 26.

Yes, my missing part is one smaller.

The known part increased by one, so the missing part decreased by one.

And finally, 55 subtract something is equal to 28.

What's happened this time? My whole is one bigger, but my known part is the same, so my missing part must have increased by one.

55 subtract 20 is equal to 35, subtract 5 is equal to 30, and then subtract 3 because I've partitioned my 8 into 5 and 3, is equal to 27.

So yes, my missing part has increased by one.

The whole increased by one, the known part stayed the same, so the missing part increased by one.

And for two, lots of possibilities here.

So the whole has nine 10s, so the 10s digits must sum to 10, so 2 and 7 must be our 10s digits.

And we can write them in any order.

We could have subtracting the 20-something or we could subtract the 70-something.

The ones digit is 7, so the ones digits must sum to 7, so that's the 3 and the 4.

And again, we can write those in any order.

So the possible equations are here.

Four different possibilities.

Did you get them all? I hope you enjoyed playing around with that problem.

And on into the second part, we're going to find the missing whole in a subtraction equation.

Andeep wonders how he can find the missing number in this equation.

Hmm.

Do you spot something here? It's a bit like Izzy's checking strategy in part one.

"What is missing this time?" he says.

"Is it a part or a whole? Whole subtract part is equal to part, so it must be the whole that's missing." He's going to draw a bar model.

So this time, the whole is missing, but we know the parts.

How are we gonna work out the missing whole then? He says, "I know in addition, we combine the parts to make the whole, so I can add to find the whole." 42 add 21.

We're not bridging 10, so we can partition both our addends.

We can add the 10s, which is equal to 60, add the 1s, which is 3, so our whole is 60 plus 3, which is equal to 63.

So that's our missing whole.

Andeep draws this bar model to help him solve this equation.

Well, mistake has been made.

Have a little look before Andeep has a think.

Go on, Andeep, what have you done? He says, "42 is equal to something minus 22." He says, "We subtract one part from the whole to find the other part." Oh, he says, "It's the whole that's missing." 42 is equal to something subtract 22.

So it's our whole that's missing.

He'd written 42 is the whole, hadn't he? Because we're often used to seeing the whole first in our subtraction equation.

But we have to be really careful.

We don't have to write it like that.

Sometimes, the whole is not the first number that we record.

Now he can see that addition is the inverse of subtraction, so we can find the missing whole by adding the parts.

42 add 22.

First, he's going to partition.

We don't bridge 10, so we can partition both of them.

Combine the 10s.

40 plus 20 is 60.

Then the 1s.

2 plus 2 is equal to 4.

Recombine.

60 plus 4 is equal to 64.

So our missing whole is 64.

He says, "I must remember the parts are subtracted from the whole." That's right, Andeep.

Always look carefully at the equation to make sure you've identified where your whole and your parts are.

Time to check your understanding.

Can you draw a bar model to represent this problem? Then use what you know about the parts and the whole to solve it.

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

How did you get on? That's right, we knew the two parts.

Something subtract 43 is equal to 21.

So 43 and 21 were our parts.

So we could use our partition, add the 10s, add the 1s, and recombine to solve.

40 plus 20 is equal to 60.

3 plus 1 is equal to 4.

And we recombine, and our whole is 64.

Well done.

Izzy notices something about the parts that can help her in this equation.

Something subtract 42 is equal to 28.

So 42 and 28 are our parts.

She says, "I notice the ones digits sum to 10.

The whole must be a multiple of 10." Good thinking there, Izzy.

Let's check.

She's going to partition both her addends.

She's going to combine the 10s.

40 plus 20 is equal to 60.

2 plus 8 is equal to 10.

So 60 plus 10 is equal to 70.

Yes, Izzy, you were right.

The whole is a multiple of 10.

Time to check your understanding.

Look at A, B, and C.

In which of the following equations will the missing whole be a multiple of 10? Look carefully at the ones digits.

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

What did you think? It was C, wasn't it? Our parts were 35 and 25, and 5 plus 5 is equal to 10.

In the other equations, we didn't have ones digits that had a sum of 10, did we? And there's the answer, 30 plus 20 is equal to 50.

5 plus 5 is equal to 10.

50 plus 10 is equal to 60, so our whole was 60.

Andeep thinks he will have to bridge 10 to find the missing number in this equation.

Is he right? So we've got something subtract 42 is equal to 29.

Well, yes, if we think about the ones digits, something subtract 2 is equal to 9.

Well, that's 11, isn't it? And we can't have 11 in our ones column of a two-digit number, so there must be some bridging 10 going on here.

He says, "I will add the parts to find the whole." So our parts are 42 and 29, and we've got a missing whole.

He says, "I can see the ones digits in the parts sum to greater than 10.

So to find the whole, I must bridge 10." So this time, he's just going to partition his 29.

It helps us when we're bridging through 10.

So 42 add 20 is equal to 62.

And then we've got to add on nine 1s, so we can bridge through 10.

We can add on 8 to get to 70 and another 1 to get to 71.

We partitioned our 9 into 8 and 1.

So our whole this time was 71.

So yes, we did have to bridge through 10.

71 subtract 42 is equal to 29.

Time to check your understanding.

Draw a bar model to help you find the missing part in this equation.

Will you bridge through 10 to solve it? 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 whole is our unknown, and our parts are 43 and 29, so we need to add them to find the whole.

43 plus 29.

43 plus 20 is equal to 63, and we're going to partition our 9 into 7 and 2.

63 plus 7 is equal to 70, add another 2 is equal to 72.

So yes, we did bridge through 10.

Our whole was 72.

And time for you to do some practise.

In question one, you're going to draw a bar model or a part-part-whole model to show the parts and the whole in each equation.

Then draw a number line to find the missing number in each equation.

Again, think carefully about where the whole is in each equation.

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 in A, we had our missing whole as the first part of our equation.

Something subtract 56 each time.

Oh, and we were subtracting 56 each time, I wonder if that'll help us.

So something subtract 56 is equal to 23.

Those are our two known parts, so we can combine them.

50 add 20 is equal to 70.

6 plus 3 is equal to 9.

70 plus 9 is equal to 79.

So our missing whole was 79.

In the next one, our known parts were 56 and 24.

Ah, so we've got one more, haven't we? So, what does that tell us about our sum? And can you also see that our ones digits sum to 10? So this time, our whole will be one more, it'll be 80.

So you may have noticed that the ones digits summed to 10 this time.

I hope you did.

And in our last one, something subtract 56 is equal to 25.

So again, that part's got one bigger again, so our whole must have got one bigger as well.

And this time, our ones digits are 6 plus 5, aren't they, which again will give us an answer one bigger.

56 add 20 is 76, and then we're going to bridge through 10.

We're going to add the 4 to make 80 and the 1 to make 81.

So this time, we needed to bridge through 10 because the ones digits summed to more than 10.

What about set B? This time, one of our parts was recorded first.

34 is equal to something subtract 45.

So our whole was the number after the equal sign in these equations.

But that meant our parts were 34 and 45.

And if we add those, we get a total of 79, so our missing whole was 79.

In the second one, 34 is equal to something subtract 46.

Ah.

So, what's happened to our whole this time? We're subtracting one more.

One of our parts is one bigger, so our whole must be one bigger as well.

And did you spot also here that we had multiple of 10 because our ones digits summed to 10.

34 plus 46 is equal to 80.

And what about the last one? Again, we were subtracting one more, so our part had got one bigger.

So this time, our parts were 34 and 47, so our whole is going to be one more again.

But this time, we're gonna have to bridge through 10 because 4 plus 7 is equal to more than 10.

34 plus 40 is equal to 74.

And then we can partition our 7 into 6 and 1.

74 plus 6 is equal to 80, and another 1 is equal to 81.

So I hope you noticed that the ones digits of the parts summed to greater than 10, so we must bridge through 10 to find the whole.

And then in C, our missing whole was the first part of our equation.

So this time, we had to combine 22 and 37 to equal our whole.

No bridging through 10, so we can add our 10s, add our 1s, and recombine, and we get a whole of 59.

What about the next one? This time, one of our parts was 10 greater.

So our parts were 22 and 47, so our whole must be 10 greater as well.

And when we partition, add our 10s and our 1s, and recombine, we find our whole is 69.

So well done if you noticed that one part increased by 10 and the other part remained the same, so the whole must increase by 10.

And finally, something subtract 23 is equal to 47.

So this time, one of our parts is still 47, but the other part has increased by one as well.

And we've got 3 plus 7 equaling a multiple of 10, so I think our whole is going to be one greater than the last time.

So one of the parts has increased by one, the other part's the same, so the whole must increase by one.

So when we combine our parts this time, 20 plus 40 is equal to 60, 3 plus 7 is equal to 10, so 60 plus 10 is equal to 70.

So yes, our whole had increased by one.

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

We've been finding the missing part when subtracting two-digit numbers.

What have we learned? We've learned that we can rearrange the parts and the wholes to help us to solve equations.

We can use a bar model or a part-part-whole model to understand missing number equations.

We can use addition to check subtraction equations.

And we can use addition to solve missing number subtraction equations when the whole is unknown.

Thank you for all your hard work in this lesson, and I hope we get to work together again soon.

Bye-bye.