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 problems involving subtraction of two-digit numbers that cross the tens boundary.

So that's when we have to partition our ones digits and bridge through 10 when we're subtracting.

Let's have a look at what's in our lesson today.

We've got three key words.

We've got partition, parts, and bridge 10.

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

My turn, partition.

Your turn.

My turn, parts.

Your turn.

My turn, bridge 10.

Your turn.

Well done.

I'm sure they're words that you know very well, but it's useful to remind ourselves about them, and to look out for them because they're all going to be really useful to talk about our work in this lesson.

So there are two parts to our lesson.

In the first part, we're going to be looking at problems where we bridge 10, and in the second part, we're going to be deciding when to bridge 10.

So let's make a start on part one.

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

The children were playing in the garden.

They collected 83 millilitres of water to give to the minibeasts.

Andeep poured out 34 millilitres.

How much water was left in the jug? Our Andeep has drawn a bar model.

He says there was 83 millilitres of water altogether.

This is the whole.

Well done, Andeep.

So he's written that in the whole of his bar model.

What else do we know? Oh, we know that 34 millilitres was poured out.

That's what Andeep poured out.

This is one part.

He says to find the missing parts, I must subtract the known part from the whole, and that will give us how much water was left in the jug.

That's the part represented by our question mark.

83, subtract 34.

Andeep says, "When I look at the ones digits, I can see that I will have to bridge 10 to solve this." How does he know that? Well, if we imagine partitioning 80 and three, 30 and four, when we came to do the one subtraction, we'd have three ones subtract four ones.

That's three ones subtract four ones.

I haven't got four ones to subtract, so that's not going to help me this time.

So yes, he spotted that we will need to bridge 10.

So he's drawn a number line and he's going to remember that we only partition the number that we are subtracting.

So we're going to partition the 34 into 30 and four, 83, subtract 30, taking away three of the tens leaves us with 53.

Now we're going to bridge through 10.

So we're going to partition our four into three and one.

Taking away three takes us to 50, our multiple of 10, and taking away another one takes us to 49.

So 83, subtract 34 is equal to 49.

We've subtracted 30 and four.

So there was 49 millilitres of water left in the jug.

And there it is in our bar model.

Izzy thinks she could have solved it in a different way.

Go on, Izzy, tell us how.

She says, "34 partitions into 30 and four.

I can subtract the tens and ones in any order.

I find it easier to subtract the ones first." Okay, Izzy, let's have a look at it, subtracting the ones first.

She says, "I know I have to bridge 10 because when I subtract four ones from 83, I will go into the previous decade." That's right, she'll go into the seventies numbers.

So here's her number line and she's going to partition four into three and one to subtract it.

83, subtract three is equal to 80, subtract another one is equal to 79.

She subtracted the four.

Now she needs to subtract the 30.

79, subtract 30.

We are taking away three of the tens, so we've got four tens left, we've got 49.

So just as Andeep calculated, there was 49 millilitres of water left in the jug.

And there it is in our bar model, the missing part.

Time to check your understanding.

Solve the problem by subtracting the tens first and then the ones, and then check it by subtracting the ones first, and then the tens.

So here's the problem.

The next day the children collected 93 millilitres of water and poured out 15 millilitres.

How much water did they have left? Pause the video, calculate, and then check.

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

How did you get on? So this time our whole was 93 and the part we were pouring out was 15.

So we need to subtract the known part 15 to work out the missing part.

So 93, subtract 15.

When we subtracted the tens first, then the ones, we found that the missing part was 78.

Let's have a look.

So we're going to subtract the tens first, 15 partitions into 10 and five.

93, subtract 10 is equal to 83, and then we're going to partition our five into three and two.

83, subtract three is equal to 80, and 80, subtract two is equal to 78.

There were 78 millilitres left, but now we're going to check it by subtracting our ones first.

So again, we're going to partition our five ones into three and two to bridge through 10.

So 93, subtract three is equal to 90, and 90, subtract two is equal to 88.

And now we're going to subtract the 10.

And 88, subtract 10 is equal to 78.

So we have got the answer right.

And there it is, the missing part in our bar model.

This time, Izzy collected 34 pebbles from the garden.

26 were grey and the rest were black.

How many black pebbles did she collect? Hmm, can you picture what the bar model's going to look like for this? Andeep is gonna help her to solve the problem.

Andeep says, "There were 34 pebbles altogether.

This is the whole that all the pebbles that Izzy collected.

26 were grey.

This is one part.

And he says that if I know the whole and I have a known part, I can subtract my part to find the other part, one whole, subtract part equals the other part.

So 34, subtract 26 will tell us how many black pebbles were in the other part.

26 was the grey pebbles.

So let's subtract.

We're going to partition our 26 into 20 and six.

34, subtract 20.

Well, that's taking away two of the 10.

So we've only got one 10 and four ones, that's 14.

Now we can partition our six into four and two to bridge through 10.

14, subtract four is equal to 10.

Subtract another two is equal to eight.

So there were eight black pebbles.

And there it is in our bar model as well.

Izzy checks that Andeep is correct by subtracting the tens and ones in a different order.

Andeep subtracted the tens first.

Izzy's gonna subtract the ones first.

So 34, subtract 26.

This time we're subtracting the ones, we're still going to partition into four and two, so we can bridge through the multiple of 10.

34, subtract four is equal to 30, subtract another two is equal to 28.

We've subtracted our six.

Now we need to subtract our 20.

28, subtract 20.

We're taking away all the tens, aren't we? So we've just got eight.

So eight pebbles were black.

You were right, says Izzy.

The same answer.

We've subtracted the same amount.

We've just subtracted the tens and ones in a different order.

Izzy counted 43 minibeasts in the garden.

26 were woodlice and the rest were ants.

How many ants did she count? Andeep thinks he could solve this problem by partitioning the whole and the known part.

But what mistake has been made? You might want to have a look before Andeep looks for his mistake.

Go on that, Andeep, have a look.

He says, "I partitioned the whole as well as the part." So the whole is 43 and he partitioned that into 40 and three and then he subtracted his tens, 40, subtract 20 is equal to 20.

That's right, yes.

But three, subtract six is not equal to three.

No, it isn't, is it? He said, "I've spotted my mistake.

When subtracting, we only partition the known part." So he's going to partition just the known part now and subtract that.

And he's going to use a number line to keep track.

43, subtract three, oh, he's going to subtract the ones first.

So he's going to bridge through 10.

He's going to partition his six into three and three so he can bridge through the multiple of 10.

43, subtract three is equal to 40.

40, subtract three is equal to 37.

So he subtracted the six.

Now he's going to subtract the 20.

37, subtract 20 is equal to 17.

So the missing part is 17.

17 were ants.

Now time to check your understanding.

Have a look at A, B, and C.

Which of the equations is correct? Remember, draw a number line to help you.

Can you spot the correct equations? Are there any mistakes? Pause the video, have a go.

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

What did you find out? Well, C is correct, isn't it? 71, subtract 40 is equal to 31.

And then 31, subtract five where we can bridge through the 10, subtract one and then subtract four is equal to 26.

In A and B, the ones digits should have bridged 10.

But can you see what's happened? I think whoever's done this has tried to partition both the whole and the part.

And so they've wrongly said that four, subtract six is equal to two, and three, subtract five is equal to two.

We've got to think really carefully when we're subtracting.

At the moment, we want to avoid subtracting a bigger number.

You'll learn how to do it later on though.

So let's look at the number line.

71, subtract 40 is equal to 31.

And then we can partition our five into one and four.

31, subtract one is equal to 30, and subtract four is equal to 26.

So we've subtracted 45 and our missing part was 26.

Time for you to do some practise now.

You're going to draw a bar model and a number line to solve each problem by bridging 10.

And then you're going to check it by subtracting the tens and the ones in a different order.

So here are your problems. So in A, I had a piece of string that was 62 centimetres long and I cut off 25 centimetres.

How long is the piece of string I have left? In B, a toy car and a doll cost 53 pounds altogether.

The car costs 26 pounds, so how much does the doll cost? And in C, there were 41 people in the classroom.

25 were children.

How many were adults? So, have a go at drawing a bar model and using a number line to solve the problems in two ways, subtracting the tens first, and then subtracting the ones first.

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, this was the 62-centimeter piece of string and I cut off 25 centimetres.

So 62 is our whole, 25 is a part, and we need to work out the missing part.

So we need to do 62, subtract 25.

I can subtract the known part from the whole.

So 62, I'm going to subtract my tens first.

So I'm partitioning 25 into 20 and five.

62, subtract 20 is equal to 42.

Now I need to bridge through 10, so I'm going to partition my five into two and three.

42, subtract two is equal to 40, and 40, subtract three is equal to 37.

So the piece of string that was left was 37 centimetres long.

So you may have subtracted the ones first and then the tens and you can subtract the parts in any order because you're subtracting the same amount in total.

So in B, a toy car and a doll cost 53 pounds altogether.

So that's our total, our whole.

The car cost 26 pounds, that's one part.

So, how much did the doll cost? Well, here's our bar model.

53 is the whole and 26 was the cost of the car.

So what we don't know was the cost of the doll, the other part.

So we can subtract the known part from the whole, 53, subtract 26 is equal to something, and that's the cost of our doll.

So let's look on the number line.

53.

This time we're going to subtract our ones first.

We're subtracting six ones, so we need to partition our six into three and three.

53, subtract three is equal to 50, and 50, subtract three is equal to 47.

So we've subtracted our ones, six ones.

Now we need to subtract the 20.

47, subtract 20 is equal to 27.

So the doll costs 27 pounds, that was our missing part.

And you might have subtracted the tens first and then the ones.

You can subtract the parts in any order because you're subtracting the same amount in total and you should get the same answer.

And in C, there were 41 people in the classroom, and 25 people were children.

How many were adults? Gosh, what a lot of adults there in that classroom I think, haven't we? Let's have a look at the bar model.

So 41 represented all the people.

25 is one part and that's the children.

And the part we don't know are the adults.

So we need to take away the part we know from the whole.

41, subtract 25.

We're going to subtract the tens first.

41, subtract 20 is equal to 21.

Now we've got to subtract five, and we're going to bridge through 10, so we can partition our five into one and four.

21, subtract one is equal to 20, and 20, subtract four is equal to 16.

So there were 16 adults in the classroom.

And again, you may have subtracted the ones first and then the tens.

And we know we can do it in any order because we're subtracting the same amount in total and it will give us the same answer.

And on into the second part of our lesson, we are going to decide when to bridge 10.

Oh, Andeep and Izzy have visited their local arcade for a fun day out.

I wonder if you've ever been to an arcade and played on the games.

Izzy's won a ticket from playing on the games and she visits the ticket shop.

So her ticket is worth 54.

She says, "The crayons are 27 tickets.

I think I will buy them.

I wonder how many tickets I will have left." So she's got 54 tickets or 54 on her ticket and she's going to spend 27 of those points on her crayons.

Let's see how they work it out.

You might want to have a little think before Andeep and Izzy share their way of working.

Izzy says, "I wonder if we'll need to bridge 10 to work this out." What do you think? Let's write the equation, she says.

54 is the whole number of tickets she has, and she's going to spend part of them, 27 of them on her crayons.

So that's our known part.

She wants to know how many she'll have left.

That's our missing part.

Andeep says, "Let's look at the ones digits.

If we subtract the seven from four, we will cross a tens boundary." You're absolutely right, Andeep.

So we're just going to partition the 27 and we're going to look at how we can bridge through 10 as Izzy says.

So here's our number line, 54.

Izzy's going to subtract the ones first.

So we're going to partition our seven into four and three.

54, subtract four is equal to 50, and 50, subtract three is equal to 47.

So we've subtracted all seven ones.

Now we've got to subtract 20, and 47, subtract 20, taking away two of the tens is equal to 27.

You'll have 27 tickets left, says Andeep.

Oh, did you notice? She spent half of her tickets, hasn't she? 27, add 27 must be equal to 54.

27 is half of 54.

Oh, now they've got some more ticket calculations to do here.

58 tickets are needed to buy a car and a panda.

If the panda costs 35 tickets, how much does the car cost? So 58 is our whole and our parts are 35 tickets for the panda and some tickets for the car.

So we know that if we have a whole and a known part, we can subtract the known part from the whole and find out the missing part.

So 58 tickets, subtract 35 tickets will tell us how much the car costs in tickets.

Will we bridge 10 to solve this? What do you think? Izzy says, "If we subtract five from eight, we will not cross the tens boundary." We've got eight ones in 58 and we're subtracting five ones.

So no, we won't.

We don't need to bridge 10 this time.

So we can subtract our fives all in one go.

58, subtract five, well, eight, subtract five is equal to three.

So 58, subtract five is equal to 53.

And now we've got to subtract our 30, our three tens.

53, subtract 30, I've got five tens and I'm taking away three of them, so I'll have two tens left and my three.

So 53, subtract 30 is equal to 23.

So our car costs 23 tickets.

Time to check your understanding.

In which problem will you need to bridge 10? So you're going to look really carefully at the whole and the known part.

So in A, a plane and a robot cost 73 tickets altogether.

If the plane costs 41 tickets, how much does the robot cost? So you're just going to think about whether you need to bridge 10.

In B, Andeep had 57 tickets and he spent 34 on a football.

How many tickets does he have left? And in C, a teddy and a cap cost 42 tickets.

The teddy costs 26 tickets, so how much did the cap cost? Pause the video, have a go.

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

How did you get on? Which one did you need to bridge 10 for? It was C, wasn't it? 42 tickets and we're subtracting 26 tickets.

So the ones digit that we're subtracting is bigger than the ones digit in our whole.

So we will need to bridge 10.

The equation to solve C is 42, subtract 26.

If six is subtracted from 42, it will cross the tens boundary, so we will bridge 10.

Well done if you spotted that.

Izzy thinks she can also use the bridge 10 strategy to solve missing number problems. Let's see if she's right.

Andeep had 73 tickets and he bought a knight at the ticket shop.

Now, he has 46 tickets left.

How much did the knight cost? Hmm, can you visualise what the bar model might look like for this or the equation? Well, there's the equation.

73 is our whole, he spent some tickets on a knight and he's got 46 tickets left.

How much did the knight cost? What's our missing number? Ah, Izzy says, here's the bar model.

73 is the whole and 46 is a known part.

So to work out the missing part, we subtract the known part from our whole.

She says, "I must subtract 46 from 73." Oh, Andeep says, "If you subtract six from 73, it will cross the tens boundary, so you will need to bridge 10." So, let's have a look.

73, she's going to subtract the ones first, so she's going to partition the six from the 46 into three and three.

73, subtract three is equal to 70.

70, subtract three is equal to 67.

And now she's got to subtract the four tens, the 40.

67, subtract 40, six tens, subtract four tens is two tens is equal to 27.

So our missing number was 27.

And the knight costs 27 tickets.

Andeep solves another missing number problem.

Izzy had 46 tickets.

She bought a balloon and had 34 tickets left to buy a ball.

How many tickets did the balloon cost? So 46 was our whole.

She spent some money on a balloon and she had 34 tickets left to buy the ball.

So here is our bar model.

Andeep says, "46 is the whole and 34 is the known part.

So, I must subtract 34 from 46." 46, subtract 34.

Izzy says, "If you subtract four from 46, it will not cross the tens boundaries, so you will not need to bridge 10." Well spotted, Izzy.

So here's our number line, 46, subtract 34.

She's going to subtract the ones first.

46, subtract four is equal to 42.

We haven't bridged 10.

So that's the four dealt with.

Now we've got to subtract 30.

42, subtract 30.

So we're taking away three tens from four tens, we've got 12 left.

So the balloon must have cost 12 tokens.

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

You are going to decide whether to bridge 10 to solve each problem, and then solve it.

Remember, you can draw a bar model to help you understand the problem and a number line to help you solve it.

So in A, the total cost of a pack of pencils and a teddy was 67 tickets.

If the teddy cost 23 tickets, how much did the pencils cost? In B, Izzy had 72 tickets to spend and she spent 35 on a panda.

How many tickets did she have left? And in C, Andeep had 71 tickets.

After he bought a piggy bank from the shop, he had 25 tickets left.

How much did the piggy bank cost? So you might want to draw a bar model to represent those and then use a number line to help you.

Do you need to bridge 10 or not to solve the problems? 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 here's A, so the total cost of the pencils and the teddy was 67 tickets.

The teddy cost 23.

So we are working out how much the pencils cost.

So can you picture the bar model? You may have drawn something like this.

The whole was 67, the teddy costs 23, and we don't know how much the pencils cost.

So that's the missing part we're going to work out.

So we're going to subtract the known part from the whole, 67, subtract 23.

So there's our 67.

Do we have to bridge 10? Well, we're only subtracting three ones from our 67, aren't we? So no, we're not going to bridge 10 this time.

We're going to subtract the tens first as well.

67, subtract 20 is equal to 47.

And then we're subtracting our three ones.

47, subtract three is equal to 44.

The pencils cost 44 tickets and you did not need to bridge 10 to solve this one.

What about B? Izzy had 72 tickets and she spent 35 on a panda.

How many tickets did she have left? So the whole was 72 and the amount she spent was 35.

How much did she have left? That's our missing part.

So we can subtract our known part from the whole.

72, subtract 35.

What about this bridging 10? Do you think we're going to have to this time? I think we are, aren't we? We've got two ones in 72 and we're going to subtract five, so we're going to need to bridge through 10.

So here's our number line to help us.

We're going to take away the tens first.

72, subtract 30 is equal to 42.

Now we've got to subtract our five ones so we can partition into two and three.

42, subtract two is equal to 40, and 40, subtract three is equal to 37.

So Izzy had 37 tickets left and you did need to bridge through 10 to solve this one.

What about the last one? Andeep had 71 tickets, and after he bought a piggy bank from the ticket shop, he had 25 tickets left.

We need to work out the cost of the piggy bank.

Are we going to need to bridge through 10? If we think about taking our ones digit away from 71, we're taking away five.

So yes, we will bridge through 10.

So let's look at our bar model first.

71 tickets was our whole.

We spent some money.

We're not sure how much, and he had 25 tickets left.

So 25 is our known part and we can subtract that from our whole to find our missing part.

71, subtract 25.

This time we're going to subtract our ones first and we're going to partition our five into one and four to bridge through the 10.

71, subtract one is equal to 70, and 70, subtract four is equal to 66, so we have had to bridge through 10.

And then we need to subtract our two tens from the 25.

66, subtract 20 is equal to 46.

The piggy bank cost 46 tickets, and you did need to bridge 10 to solve this one.

I hope you spotted that before you started calculating.

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

We've been solving problems involving subtraction by bridging 10.

Some problems involving subtraction of two-digit numbers can be solved by bridging 10.

We can look to see if the ones digits cross the tens boundary to find out if we must use a bridge 10 strategy.

And we can use our knowledge of parts and whole to write an equation to solve a problem.

We know that part plus part is equal to whole, and so whole subtract one part is equal to the other part.

And a bar model can really help us to understand what the problem is all about.

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.