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 start.

In this lesson, we're going to be subtracting two digit numbers crossing the tens boundary.

Well, I wonder if you've done crossing the tens boundaries before? You might have used partitioning strategies when you are adding and crossing the tens boundaries.

Well, in this lesson we're going to look at what that's like when we do it with subtraction.

There are two key words in our lesson, partition and part.

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

So my turn, partition.

Your turn? My turn, part.

Your turn? I think you probably know those words, don't you? I think you've been partitioning numbers for a long time.

So we're going to be doing that today.

Partitioning numbers into tens and ones, and then partitioning ones numbers as well.

And we're going to be thinking about subtracting a part from a whole when we solve a problem.

So let's make a start.

In part one of our lesson, we're going to be looking at patterns when subtracting two digit numbers.

And in the second part, we're going to be thinking about making decisions when subtracting.

Knowing which strategy to use and when is a really important part of our mathematical thinking.

So I'm looking forward to that in part two.

But let's make a start on the first part.

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

Izzy has 75 pounds and she buys a rocket.

How much money will she have left? So she's got 75 pounds and she's buying a rocket for 35 pounds.

Let's see how she's going to work it out.

Have you got any ideas? Well, what equation should be right to find out? Can you think? That's right, 75 - 35.

75 is the whole amount of money and she's going to spend part of that money, 35 pounds, and the part that's left will be the money she has left over.

She says, "I will partition the known part and subtract the ones first." So she's going to draw a number line to help her.

So her whole is 75.

She's partitioned the part she's taking away into 30 and 5, and she's going to take away the ones first.

So 75 - 5 will take her back to 70.

What else does she need to subtract? That's right, the 30.

So then she's going to subtract the tens part, which is 30, or 3 tens, and 70 - 30, 7 tens - 3 tens is equal to 4 tens, that's equal to 40.

She says, "I subtracted all the ones, and then a multiple of 10, so I will have 40 pounds left." Andeep solved it in a different way.

I wonder what he did.

He says, "I will subtract the tens first." So here's his number line with 75 on it.

He's going to subtract the 30 from our 35 first.

So 75 - 30.

7 tens - 3 tens is equal to 4 tens, and we've still got our five.

So subtracting 30 will give us 45.

Now what's he got to do? He's got to subtract that five, hasn't he? 45 - the 5 ones is equal to 40.

He says, "I subtracted a multiple of 10 and then all the ones, so I know Izzy will have 40 pounds left as well." Andy also has 75 pounds and wants to buy a spaceship.

His spaceship costs 36 pounds.

Hmm, do you spot something there? 75 - 36 is equal to something, the money he'll have left over.

How is this equation different from the previous equation? Can you remember how much Izzy spent? That's right, she spent 35 pounds.

So what's different? Hmm, Andeep spotted it, the parts to be subtracted increases by one.

So he says, "I'll need to bridge the multiple of 10." In the first example we were subtracting 35.

Now we're subtracting 36, which is one more.

So we can partition our 36 into 30 and 6.

We've subtracted the 30 and we can partition our six into five and one, so that we can subtract the five to get us to a multiple of 10 and then subtract the extra 1.

So we've already subtracted five.

We need to subtract one more.

and 40 - 1 = 39.

Andeep says, "I subtracted one more.

So the part remaining was 1 less, I'll have 39 left.

There's a bar model representing the first equation, 75, we take away a part of 35, and we have 40 left.

This time we're taking away one more, so let's watch the bar model change.

Hmm, so the 35 got 1 more to be 36.

So the 40 became 1 less to be 39.

Izzy thinks about what is the same and what is different in each equation, and she spots the beginnings of a pattern.

Hmm, I wonder if you can see the pattern as well, before Izzy tells us what she's seen? Izzy says, "The whole stays the same, but the known part increases by one each time." So our whole is 75, but the part we knew about was 35 in the first equation and 36 in the second.

Hmm.

She thinks, "I wonder what the next equation in the pattern will be." You might want to have a think before Izzy shares her ideas.

So our whole stays the same, but the known part increases by one.

So following on from 75 - 35, 75 - 36, we'd have 75 - 37, what do you think that's going to be equal to? Well, she says, "For the whole to stay the same, the missing part must decrease by one." She says, "I predict the missing part will be 38." Can you picture that bar model again, with the known part getting bigger by one, so the missing part will be getting smaller by one again? So I think Izzy might be right.

Let's use a number line to see if she is right.

So we're going to partition our 37 into 30 and 7.

75 is our whole, that's where we're starting.

So we can subtract 30.

We're taking away 3 tens, so we've got 4 tens and 5 ones now, 45.

Now we've got to subtract seven and we're going to bridge through the 10.

So we can partition our seven into five and two, subtracting the five will take us to 40, and then we need to subtract another two.

And 40 - 2 = 38.

"I was right", says Izzy.

That pattern she spotted has worked and we've been able to check it with the number line as well.

Time to check your understanding.

Can you write the next equation in the pattern? Predict the missing part and then use a number line to prove that you are right.

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

How did you get on? What did you think it was going to be? Well, our whole stays the same.

And the known part, the part we're subtracting, increases by one.

So our next equation would be 75 - 38.

So we can predict that the missing part will be 37, because for the whole to stay the same, if the known part is increased by one, the missing part must decrease by one.

So our known part has increased from 37 to 38.

So our missing part must be decreasing from 38 to 37.

Can you see the pattern there? And the pattern there, our next number will be 37, but we're going to check it using a number line.

So we'll partition 38 that we're subtracting into 30 and 8.

75 - 30, taking away 3 tens, so I'll have 4 tens left, so that'll be 45.

And then I've got to subtract eight, I'm going to bridge through the next multiple of 10.

So let's partition the eight into five and three.

5 will let us reach 40.

So 45 - 5 = 40.

And then I've got another three to subtract.

40 - 3 = 37.

So yes, we were right.

We can predict and check that the missing part in this case was going to be 37, one less than it had been before.

Andeep solves the next equation like this.

So what mistake has been made? So we've increased the known part by 1 again, 75 - 39.

Andeep has partitioned both the numbers, the whole and the known part.

70 - 30 = 40, well, that's true.

5 - 9 = 4, I'm not so sure about that.

Well, that would give us an answer of 44, wouldn't it? And he says, "That can't be right.

75 - 38 = 37.

So 75 - 39 cannot be equal to 44." It can't have a larger answer can it? So what's gone wrong? He says "I'll check to find the problem.

70 - 30 = 40, but 5 - 9 is not equal to 4.

If there are 5 ones, then to subtract nine, I must bridge the previous 10.

That's right, we can't use that 5 - 4 to help us in this equation at the moment.

Let's think about bridging.

So here's our number line.

Let's think about bridging through 10.

So this time we're only going to partition the known part, the part we're subtracting.

And we're going to partition it into 30 and 9.

Now we can use our number line to help us.

75 - 30 = 45.

But now we've got to subtract nine.

So we need to partition it so that we can bridge through the next multiple of 10.

45 - 9, well, we're going to partition our 9 into 5 and 4.

45 - 5 = 40, - 4 = 36.

That sounds more like it doesn't it? So 75 - 39 = 36.

The missing part is 36.

Izzy thinks she would've reached the same number if she'd subtracted the ones first.

Is she right? Let's have a look.

So she's partitioned the 39 into 30 and 9.

She's going to start by subtracting the 9.

75 - 9? Well, we can partition because we need to bridge through 10, partition the nine into five and four.

75 - 5 = 70, - 4 = 66.

And now we've got to subtract the 30.

66 - 30 = 36.

"I was right", she says, "We can subtract the ones first or the tens first and the part remaining will be the same." Because we've subtracted the same number in total.

Time for you to do some practise.

So in question one, you're going to use the pattern in the equations to predict the next answer.

You've got two sets there, A and B.

When you've done that prediction, solve the equations by partitioning the known part and drawing a number line.

Subtract the tens first to solve and then you could check your answers by subtracting the ones first.

Were your predictions right? Could you predict the answers? And were you right when you checked? Pause the video, have a go at A and B, and when you're ready for some feedback and answers, press play.

How did you get on? So the setting A had 35 - 15, 35 - 16, and 35 - 17.

So the known part increases by one each time, the whole stays the same, doesn't it? So I'm going to predict that if the whole is to stay the same, the missing part will decrease by one each time.

It will be one less than the previous answer.

Well, let's start with 35 - 15.

We can partition the 15 into 10 and 5.

35 - 10 = 25.

And 25 - 5 = 20.

So 35 - 15 = 20, and we can check it like this.

We can subtract the ones first.

35 - 5 = 30.

And 30 - 10 = 20.

So yes, we've got the same answer.

So we spotted that the known part was increasing by one, but the whole was staying the same.

So we're subtracting one more each time.

So that means that our answer should be one less each time.

Let's check.

35 - 16, we can partition into 10 and 6.

Subtract the 10 to get 25, then subtract 5 to get 20, and another 1 to get 19.

And we can check it by doing the ones first.

35 - 5 = 30, - 1 = 29, - 10 = 19.

So yes, our missing part is one less.

And we can predict that it would be one less again, because we're subtracting one more.

35 - 10 = 25.

And then we can partition our seven into five and two.

<v ->5 to get to 20 and then another 2 to get to 18.

</v> And we can check it by doing the ones subtraction first.

35 - 5 = 30, - 2 because we're subtracting 7 ones, 28.

And - 10 to get to 18.

So using the pattern and both ways of calculating, we've worked out that 35 - 17 = 18.

And what about B? This time our whole was 62 and our known part was 15, and then 25, and then 35.

It wasn't increasing by one this time was it? So the known part increases by 10 each time.

So I'm going to predict that if the whole is to stay the same, the missing part, the answer, will decrease by 10 each time, it will be 10 less than the previous answer.

If you imagine a bar model with the whole staying the same, if one part increases by 10, then the other part must decrease by 10.

So 62 - 15, we're going to partition our 15 into 10 and 5.

62 - 10 = 52, - 2 = 50, and then we need to - 3 = 47.

So 62 - 15 = 47.

And we can check it by subtracting the ones first, and we'll still get an answer of 47.

This time our known part has increased by 10, so our missing part should decrease by 10.

Let's have a look.

62 - 20 and 5, - 20 = 42, and to subtract five, we're going to partition into two and three, so we can bridge through the multiple of 10.

So our answer is 37, it is 10 less than before.

It's what we predicted.

And we can check it by subtracting the ones first.

And we still get an answer of 37 for our missing part.

What about 62 - 35 then? what do you think it's going to be? Well, I predict it's going to be 27, 10 less.

Let's look.

Partitioning the number we are taking away, our known part, 62 - 30 = 32.

Partition our five into two and three, so we can bridge through 30, and we get an answer of 27.

And we can check it by subtracting the ones first.

So whether we subtract the tens or the ones first, we get a missing part of 27, 10 less than it was before, because we've subtracted 10 more with our known part.

Well done if you spotted all those patterns and were able to check your calculations.

And we're going into the second part of our lesson, we're going to be making decisions when subtracting.

Andeep usually uses a pattern to help him subtract when he has to cross the tens boundary, but he's just got one equation here.

He says, "How can I solve this? There's no pattern to help me." "I remember", he says, "That I must partition the known part." Well done, Andeep.

And can you see that we know we're going to have to bridge through 10, because there are 6 ones in our known part and there are 3 ones in our whole.

So first we're going to partition, 56 is 50 and 6.

Now we can subtract the tens.

73 - 50, we're taking away five of those tens, so we're going to have 23 left.

73 - 50 = 23.

Now we've got to subtract the ones, and we're going to bridge through 10 here, aren't we? So we can partition our six into three and three, <v ->3 to get to 20, - 3 to get to 17.

</v> So subtracting the ones, 23 - 6 = 17.

So 73 - 56 = 17.

Izzy solves the equation in a different order and subtracts the ones first to check that Andeep is correct.

She says, "I know I can subtract the tens first or the ones first and the answer should be the same." So first she's going to partition 56 into 50 and 6.

This time, though, she's going to subtract the ones first, 73 - 6.

So we're going to partition our six into three and three so we can bridge through that multiple of 10, and we get to 67.

Now we've got to subtract 50.

67 - 50, we're taking away five of the tens, so we're left with one 10 and seven ones, 17, the same answer.

73 - 56 = 17.

She says, "I reached an answer of 17 as well, so we know we are right." Time to check your understanding.

Can you solve the equation by partitioning the known part and then subtracting the tens first, then check it by subtracting the ones first? 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 we're going to partition the known part, which is 28.

45 is our whole 28 is our known part, and we're going to calculate the missing part.

So we've partitioned.

Now we can subtract the tens.

45 - 20, we're taking away two of the tens, so we're going to have 25 left.

Now we're going to subtract the ones.

We're subtracting 8 ones, so we need to bridge through 10.

So we can partition our eight into five and three.

<v ->5 to get to 20 and - 3 to get to 17.

</v> So 45 - 28 = 17.

Now we're going to check that 17 is the right answer by subtracting the ones first.

So again, we're going to partition, but this time we're going to subtract the ones.

45 - 8, we're going to partition our eight into five and three.

45 - 5 = 40, - 3 = 37.

And then we're going to subtract our 20.

37 - 20, so we're taking away two of the tens.

So we've got 1 ten and 7 ones left, 17.

That was the answer we wanted, wasn't it? So yes, we've checked and we were correct.

We reached the same answer so we know we're right.

I hope you did too.

So let's use what we've learned to find the missing part in the bar model.

So our whole is 51 and our known part is 28.

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

51 - 28, we're going to have to bridge, aren't we? So first we're going to partition our known part into 20 and 8.

Then we're going to subtract the tens.

51 - 20, so we're taking away 2 tens.

So 51 - two of the tens = 31.

So 51 - 20 = 31.

Now we've got to subtract the ones, and we can partition our eight into one and seven, and we end up with an answer of 23.

So 51 - 28 = 23.

23 is our missing part.

Izzy draws this number line to solve the equation.

Has she used the most efficient strategy? Do you want to have a little look before Andeep makes a comment? What's Andeep spotted? He says, "The equation is correct, she's got the right answer, but it's not the most efficient way, because when you partitioned the nine when she was subtracting the 9 ones, you didn't reach the previous multiple of 10." So she partitioned nine into four and five, which is fine, but we were subtracting 9 from 87.

So it would've made more sense to partition into two numbers where she could bridge through the multiple of 10.

"When you bridge 10, you can use your number pairs to 10 to subtract from the multiple of 10, so it is more efficient." So there we go.

She could have partitioned her nine into seven and two.

87 - 7 = 80, - 2 = 78.

So she wasn't wrong in her calculation, but she maybe could have been more efficient.

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

You are going to write the equations represented by each number line, and you're going to circle the number lines that do not use the bridge 10 strategy.

And you're going to draw a number line to show how we could have used the bridging 10 strategy to solve the problem.

So write the equations and then have a look carefully at the number lines, which ones have used bridging 10 and which ones haven't? In question two, you're going to find the missing parts in each bar model and then write a subtraction equation that could represent it.

And for question three, you're going to draw a number line to subtract one part from the whole and find which bar model is incorrect, one of them is not right.

Circle the incorrect bar model and then correct it using a number line.

So pause the video, have a go at questions one, two, and three.

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

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

Here you were looking for the number lines that had or hadn't used a bridging 10 strategy.

So what did you spot? So in A, we have bridged through 10, haven't we? 68 - 29 = 39.

We subtracted the 20, and then we subtracted the nine by subtracting 8 to get to 40 and 1 to get to 39.

What about this one in B? Well, it was 73 - 45.

Yes, that's right, and it's the right answer, but have they bridged through 10? They haven't, have they? No.

Can you see that they partitioned their five into two and three and subtracted the two first? So this number line's going to show the same equation using a bridge 10 strategy.

So we subtract the 40, the 4 tens, to get to 33, and then we still partition the five into three and two, but this time we're going to subtract the three first, so we get to a multiple of 10, and then the two to get to 28.

The answer was right, but it perhaps wasn't the most efficient way to use the strategy.

And did you spot that they had used bridging through 10 in C? 44 - 17 = 27, and they bridged through that multiple of 10, they bridged through 30, partitioned the seven into four and three.

What about D? I can't see a multiple of 10 on the number line, so I don't think they did.

What have they subtracted though? Well, they started with 52 and they subtracted 39, but they didn't perhaps partition their 9 in the most efficient way.

Let's have a look at it bridging through 10.

So 52 - 30 = 22, but then we can partition our nine into two and seven.

We can subtract the two and then subtract the seven.

The answer is correct, but the bottom number line shows perhaps a more efficient strategy.

So for question two, you are finding the missing parts in these bar models.

So for A, we were calculating 43 - 24, which was our known part.

So we partitioned the 24 and bridged through 10, and we've got the answer 19, which was our missing part.

For B, our whole was 62 and our known part was 38.

So we can partition the 38 to subtract 30, and then subtract the eight by subtracting two and six, and our missing part was 24.

And in C, our whole was 54 and our known part was 39, so we could partition that into 30 and 9, subtract the 30, and then partition the 9 into four and five to bridge through 20.

And our missing part was 15.

And for question three we were spotting the bar model that was incorrect.

So which one was incorrect? It was A, wasn't it? 41 - 16 is not equal to 35, so this is incorrect.

So let's check 41 - 16, I wonder if you did it like this.

So we partitioned the 16 into 10 and 6, we subtracted the ten first, 41 - 10 = 31, and then we partition the six into one and five, subtracting 1 to get to 30 and subtracting 5 to get to 25.

So 41 - 16 = 25.

So if we were subtracting 16, then the other part would have to be 25.

I wonder if there was another way to correct it though as well? And you may also have drawn the number line to show that 41 - 35 = 6, and not 16.

So we could have corrected the bar model in two ways.

We could have kept the 35 and changed the 16 to 6 or we could have kept the 16 and changed the 35 to 25.

And what about B? Well, B was correct.

And you might have checked by drawing this number line to do 62 - 28 to check.

So you can partition the 28 into 20 and 8, subtract the 20, get to 42, and then we can partition our eight into two and six, so we can bridge through 40.

And we find out that the other part indeed is 34, so B was correct.

Well done if you sorted all of those out.

You may also, of course, have drawn a line to show that 62 - 34 = 28.

Well done for completing task B, and indeed, completing the lesson, because we've come to the end.

We've been subtracting two digit numbers crossing the tens boundary.

So what have we been thinking about? Well, when subtracting two digit numbers, it's important to partition the known part of the whole, and then partition it further to subtract the tens and the ones.

We do not partition the whole and the part into tens and ones, because this does not give the correct answer when the ones digits bridge 10.

We have to be really careful with that.

And we've learned that we can subtract the tens and ones in any order, and the remaining part will stay the same.

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

Bye-bye.