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 the addition and subtraction of two-digit numbers.

So we're mixing up our addition and subtraction this time.

So you're going to have to make decisions.

Is it about addition or is it about subtraction? Let's have a look at what's in the lesson.

We've got some keywords here.

We've got addition, subtraction, and bridge 10.

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

Are you ready? My turn, addition, your turn.

My turn, subtraction, your turn.

My turn, bridge 10, your turn.

Well done, I'm sure they are words you are familiar with.

Bridging 10's interesting, isn't it? That's where we have to make sure that we've partitioned the ones digits in our addend or in the number we're subtracting in order to help us to get through to the next 10 or to the previous 10, so watch out for that as we go through.

Can you spot when we need to bridge 10? So in the first part of our lesson, we're going to be looking at solving problems involving two parts, and in the second part involving three parts.

And watch out for some bar models to help us to make sense of the problems that we're solving.

Let's make a start on part one.

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

The children are playing a computer game.

They can use points that they win to buy items for their avatar, for their character in the game.

So they can buy some sunglasses, they can buy some hats, and they can buy some T-shirts.

I wonder what you'd choose for your avatar? Izzy says, "I have 96 points.

I think I will buy the pink sunglasses." Ooh, good choice, Izzy.

I'm not sure they suit me, but they might suit my avatar.

I hope they suit yours.

So there are the pink sunglasses, but how many points do they cost? Ah, they cost 63 points.

She says, "I wonder how many points I will have left." Hmm, how could she work that out do you think? Do you think she'll add or subtract? You might want to have a think before Izzy shows us what she's going to do.

She's got 96 points, she wants to buy the sunglasses for 63 points, and she wonders how many points she'll have left.

Let's find out.

She says, "I have 96 points and I spend some.

I'm going to decrease the amount." Her amount's going to get smaller, isn't it? Ah, so she thinks this means she's going to subtract.

I think she's right.

She's going to spend part of her money, so she's going to take part of it away.

So she's going to calculate 96 subtract 63.

And here's a bar model.

Our whole is the 96 points and the part she's subtracting is the sunglasses, the 63 points, so she needs to work out the other part, the unknown part.

Andeep's been thinking about bridging through 10.

Did you have a think about that as well? He says, "When we subtract 3 from 96, we do not bridge 10." So if we look at our ones digits, we're going to subtract a 3 from the 63, and that won't bridge through 10.

He says, "I can draw a number line or just imagine it to help solve this problem," and he might be able to do it mentally.

Let's draw the number line just to help us.

So there's 96, that's the whole amount, and we are going to subtract 63.

So we can subtract our ones first.

You might subtract the tens first.

We can do that in any order, but let's subtract our ones.

96 subtract 3 or 6 subtract 3 is 3, so 96 subtract 3 will be 93.

And then we've partitioned our known part, the 63 into 60 and 3, so now we have to subtract the 60.

93 subtract 60, well that's 9 tens in 93, subtracting 6 tens, so 3 tens left.

So 93 subtract 60 is 33.

So 96 subtract 63 is equal to 33, so that's our missing part.

And Izzy will have 33 points left after she's bought the pink sunglasses.

Andeep wants to buy these glasses and this T-shirt, so he's gone for the white sunglasses and a T-shirt with, I think that's Saturn the planet on it, isn't it, with the rings.

So the sunglasses cost 35 points and the T-shirt costs 47 points.

How many points will he need all together? Hmm, what equation or what calculation is he going to do? He says, "Should I add or subtract to find out?" What do you think? He says, "I'm combining the two parts to find the whole, so I will add." Well done Andeep.

So he's drawn a bar model.

His parts are the sunglasses and the T-shirt, that's 35 points and 47 points, so he's got to combine his parts to find the whole, 35 add 47.

You had to think about that bridging through 10? Oh Andeep has, he says, "The ones digits sum to greater than 10, so we will bridge through 10." We've got 5 ones and 7 ones, 5 plus 7 is more than 10.

Izzy says, "You can draw a number line or imagine it and solve it mentally." I think let's draw a number line 'cause this is the first one we've done today like this.

So we're going to start with 35 and just partition the number we are adding.

So we're going to partition it into 40 and 7.

I wonder what we're going to add first.

Should we add the tens or the ones? We're going to add the tens first.

35 add 40.

3 tens add 4 tens is 7 tens, so that will be 75.

Now we've got to add our 7 ones and we're going to bridge through 10.

So we can partition our 7 into 5 and 2.

75 add 5 is equal to 80, 80 add 2 is equal to 82, and you can see we've added on 7 ones that partition them into 5 and 2.

So what's our sum? It's 82.

So the glasses and the T-shirt will cost 82 points together, as Izzy says.

Time to check your understanding now.

Can you use an efficient strategy to solve each problem? Remember, you can represent it as a bar model first.

Andeep has 58 points and he buys this skeleton hat for his avatar.

How many points does he have left? And then Izzy wonders what it would cost her to buy the skeleton hat and the cap.

So you can draw a bar model and then you can draw a number line to solve it, or you might be able to solve it mentally, but use a number line just to check that you are right or to explain your thinking to somebody else.

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 Andeep has 58 points and he buys this skeleton hat.

How many points does he have left? So what's his whole? Well his whole is the 58 points and the part he's subtracting is the 26 points that he's spending on the hat, and we need to work out the missing part, which is what he's got left.

So 58 subtract, he's going to subtract his ones first and we're not bridging 10 this time, are we? 58 subtract 6, well 8 subtract 6 is equal to 2, so 58 subtract 6 will be equal to 52.

Now he's got to subtract the other part of his known part, which is the 20.

52 subtract 20, so we're taking away 2 tens from our 52, so that will leave us with 3 tens and 2 ones, 32.

So he'll have 32 points left.

And Izzy was wondering what it would cost her to buy the skeleton hat and the cap, 26 add 56.

So those are her two parts and she's going to combine them to find the whole.

Did you think about the bridging 10? We've got 6 ones and 6 ones, 6 add 6 is greater than 10, so we are going to bridge through 10.

So we're starting with 26 and we're going to partition our 56.

We could have started with 56 and added on 26 as well.

So we're adding the 50 first, 26 add 50.

So we've got 2 tens in our 26 and we're adding on 5 more tens, so that's 76.

Now we've got to add on our 6 ones, so we need to partition them to bridge through 10.

6 is equal to 4 plus 2, so we can add 4 to get to 80, and the other 2 to get to 82.

So altogether the hat and the cap cost 82 points.

I hope you were using efficient strategies in spotting when you had to bridge through 10.

Here's another problem, 73 points are needed to buy a skeleton hat and a T-shirt.

The skeleton hat costs 26 points.

How many points does the T-shirt cost? So what do we know this time? So we know that we've got 73 points and we know that the hat costs 26 points, but we don't know how much the T-shirt costs.

How are we going to work this one out? Andeep says, "Should we add or subtract to find out?" What do you think? Well, Izzy says, "You know the whole and you know one part so you can subtract to find the remaining part." That's right, if we know the whole and we know one part, we can subtract our known part to work out the missing part.

So we know that our whole is 73, and we're going to subtract 26.

"How can we solve this efficiently?" says Andeep.

Is this something you can do in your head? Do we need to bridge through 10? Let's have a look.

Well, Izzy says, "If we subtract 6 from 73, so if we think about our ones, we will bridge through 10." She says, "I'm going to draw a number line.

I could imagine it in my head, but I think let's draw a number line so we can really see what's going on." So we're starting with a whole of 73 and we're going to subtract the 6 ones to start with.

We're going to partition the 6 into 3 and 3.

73 subtract 3 is equal to 70, subtract another 3 is equal to 67.

We've subtracted our 6 ones, now, we need to subtract the 20.

And 67 subtract 20 is equal to 47.

So the T-shirt must cost 47 points.

Here's another one.

First, Izzy spends 56 points on a cap, then she spends another 32 points on some sunglasses.

How many of her points has she spent now? Izzy says, "I wonder if I should add or subtract to solve this?" What do you think? She spent some of her points on a cap and some more on a pair of glasses.

Ah, she says, "I'm increasing an amount.

I'm trying to work out what I've spent altogether, so I will add," she says.

56 add 32, and we can put those parts into a bar model, 56 points and 32 points are our parts, and we want to know what they're worth altogether.

That's our whole and that's what's missing.

"How can we solve this efficiently?" says Andeep.

Have you thought about the bridging through 10 bit? Let's have a look.

Izzy says, "I will partition one part or draw or imagine a number line to help me solve it." So here's the number line.

So she's starting with 56, and she's going to partition the 32 to add on.

What about bridging through 10? Well let's add our tens first.

56 add 30 is equal to 86.

And then we've just got two more ones to add, so we're not going to bridge through 10.

86 add 2 is 88.

Andeep said, "You could also have partitioned both parts to solve this because we weren't bridging through 10." We could have said 50 plus 30 is equal to 80, and 6 plus 2 is equal to 8, and then we combine 80 plus 8 is equal to 88.

So there's another way we could have done it as well.

But we know that they cost 88 points altogether, so she'll have spent or used 88 of her points.

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

You're going to write the equation and draw a bar model to represent each problem, then solve it by drawing a number line.

If you can solve it mentally, that's great, but use a number line to check that you are right or maybe to explain how you worked it out to somebody else.

So in A, Izzy buys a hat and these glasses, how much does she spend altogether? In B, the items shown cost 82 points altogether.

How much do the glasses cost? In C, Izzy has 92 points and she buys the T-shirt.

How many points does she have left? And in D, Andeep spends 45 points and then he buys this T-shirt.

How many points has he spent now? So decide whether you are adding or subtracting, draw a bar model to help you, and then calculate and show how you worked it out on a number line.

Pause the video, have a go at A, B, C, and D, and when you're ready for the answers and some feedback, press play.

How did you get on? So for A, Izzy buys a hat and some glasses, how much did she spend altogether? So is she adding or subtracting? She's adding.

Those are our parts and we're going to combine our parts to find our whole.

So she's starting with the 63 and she's going to add on the 32.

63 add 30 is equal to 93 and 93 add 2 is equal to 95, so she spent 95 of her points all together, and that's one where we didn't have to bridge through 10.

So we could have thought about 60 add 30 and then 3 add 2 and recombined.

You may have done it like that as well.

Izzy spends 95 points altogether.

In B, the items shown cost 82 points altogether.

How much do the glasses cost? So what do we know this time and what is missing? We know the whole this time.

They cost 82 points altogether, so that's our whole.

We know that the hat costs 56 points, so we are working out the missing part, our glasses.

So to calculate the missing part, we subtract the known part from the whole.

So we're going to subtract 56 from 82.

Now are we going to bridge 10? I think we are here, aren't we? We've got 82 and we've got to subtract 6 ones, so we're going to need to partition our ones.

So 82 subtract 2 is equal to 80.

We've partitioned our 6 into 2 and 4, so we've got another 4 to subtract.

80 subtract 4 is equal to 76 and now we've got to subtract our 50 from our partitioned 56.

76 subtract 50 is equal to 26.

So what did the glasses cost? They must have cost 26 points.

And in C, Izzy has 92 points and she buys the T-shirt shown, it's 47 points.

How many points does she have left? So she's subtracting isn't she? She has 92 as her whole and 47 is her known part, so we're going to subtract the known part from the whole and work out the missing part.

92 subtract 40 is equal to 52.

Now we are going to bridge through 10, but we can subtract the tens first, that's fine.

So we've got 52 and we need to subtract 7, so let's partition our 7 into 2 and 5.

52 subtract 2 is equal to 50, subtract another 5 is equal to 45, so she'll have 45 points left.

And for D, Andeep spends 45 points and then he buys this T-shirt.

How many points has he spent now? Well those are our two parts aren't they? So we're going to combine our parts to find our missing whole.

Ooh, can you spot here? 5 plus 7 ones is going to bridge through 10.

So let's start with 45 and add on our 47.

45 plus 40 is equal to 85, and now we've got to add on 7, so we can partition our 7 again into 5 and 2 this time.

We're going to add the 5 on to reach 90 and then another 2 to reach 92.

So Andeep has spent 92 points altogether.

I hope you enjoyed working out what you had to do to solve the problems, and then showing your thinking and your calculating your efficient strategies using a number line.

Well done.

And on into part two of our lesson, we're going to solve problems involving three parts.

Andeep buys these items for his avatar.

How much does he spend on them? He's bought some glasses for 14 points, a rather nice looking top hat for 30 points, and a T-shirt for 21 points, so he's got three items to add together.

What's different about this problem? Ah yes, Izzy, this time you have three items to combine.

We can solve this in two steps.

So here's our bar model to show us that we've got three parts to our whole this time.

Andeep says, "I will add two parts and then the third part, 14 plus 30." Well he says he can do that very easily, so it's 14 plus 33 tens plus another one 10 plus our 4 ones is 44.

And there it is on the number line: 14 add 30 is 44.

What have we got left to add now? Ah, we've got the third part.

We've got the 21 points for the T-shirt.

So we're going to add that onto 44.

44 add 21 is equal to 65, 44 add 20 is equal to 64, add 1 is equal to 65.

So altogether the items cost 65 points, and we solved it by combining two items first and then adding on the third.

Izzy adds the items in a different order.

How much will they cost now? She's got the glasses and the T-shirt and then the hat.

She says, "I find it easier to combine 14 and 21 first." That's okay, Izzy.

14 add 20 is 34, add another 1 is 35, so 14 add 21 is equal to 35.

Now, she's got to add on the cost of the hat.

"Now," she says, "I'll add the third part." 35 plus 30 is equal to 65." So she's added on the final item, the hat, which was 30 points.

Did you notice that the items cost exactly the same? We can change the order of the addends and the sum remains the same.

So we can add our parts in any order because we know that addition is commutative.

I'm sure you've heard that word before.

Time to check your understanding.

Can you match the equations that will have the same total and then solve them in the way you find easiest? Pause the video, have a go, and when you're ready for the answers and some feedback, press play.

How did you get on? Did you match the equations with the same total? Let's have a look.

So let's start with 25 plus 30 plus 42.

What does that match with? That's right, 42 plus 30 plus 25, the same three add-ins but in a different order.

And then 14 plus 22 plus 30 will give the same total as 30 plus 22 plus 14.

So let's just check that our last two match.

30 plus 21 plus 32, yes, that matches with 32 plus 21 plus 30.

How did you solve them? You could have added the parts in any order.

I'm going to give you an example of one way.

So 25 plus 30 is equal to 55 and then plus 40 is equal to 95 and another 2 is equal to 97.

So that will be the same for both of those equations.

What about this next one? 14 plus 20 is 34 plus another 2 is 36.

36 plus 30 is equal to 66, so that will be the sum for both of those equations.

And for the last one, 21 plus 30 this time, ah, so we've changed it round and started with the 21.

21 plus 30 is equal to 51, 51 plus 2 is equal to 53, plus another 30 is equal to 83, so that will be the sum of those two matching equations as well, but you could have added the parts in any order.

Here's another problem.

First, Izzy has 95 points, then she buys a trilby hat, that's 40 points, then she buys a pair of glasses for 32 points, how many points will she have left? Hmm, this is an interesting one.

What you notice? This is a two step problem, it can be solved in two parts.

So we've got a whole which is 95 and we've got two known parts which are 40 and 32, and one unknown part.

I wonder how we can solve this.

Izzy says, "I will subtract one part, then subtract another part to find the part that's missing." That's a good idea, Izzy.

So starting with 95, we can subtract one of our parts, and then from that answer we can subtract another part.

So she's going to start by subtracting the 40 points.

95 subtract 40 is equal to 55, and she's shown that on the number line.

Now we've got 55, we need to subtract the 32.

55 subtract 32.

55 subtract 30 is equal to 25, subtract another 2 is equal to 23, so 55 subtract 32 is equal to 23.

So she says, "I will have 23 points left." The next day, Izzy also buys three different items. They cost 100 points altogether.

What is the cost of the hat? Hmm, do you wanna have a think? What will the bar model look like for this one? Izzy says, "I know the whole and I know two parts." They cost 100 points altogether, that's our whole, and we know two of the parts: a T-shirt for 20 points and some glasses for 63 points.

So we can draw our bar model in.

Our whole is 100, two of our parts are worth 20 points and 63 points, but we don't know the cost of the hat.

That's our missing part.

She says, "I must subtract the two known parts to find the missing part." 100 subtract 20 subtract 63.

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

100 subtract 20, well that might be a fact we know.

It's a bit like 10 subtract 2 isn't it? 10 tens subtract 2 tens is 8 tens, that's 80.

Now we've got to subtract the 63.

So Izzy's going to subtract 60 first.

80 subtract 60 is equal to 20, and then we've got to bridge through that multiple of 10 to subtract the 3.

20 subtract 3 is equal to 17, so 100 subtract 20 subtract 63 is equal to 17.

That's the cost of the hat.

Excellent, well calculated, Izzy.

Andeep wonders if he could subtract the parts in a different order to reach the same answer.

He says, "I'll try this on a number line.

100 subtract 63." He's going to subtract the 60 first.

100 subtract 60 is equal to 40, and then subtract the 3.

40 subtract 3 is equal to 37.

What's he got to subtract now? That's right, the cost of the T-shirt, 20 points.

So 37 subtract 20 is equal to 17.

Yes, he's reached the same answer.

He's still calculated that the hat costs 17 points.

He says, "We can subtract the parts in any order and the remaining part will be the same." Time to check your understanding.

Can you draw a bar model to represent this problem then solve it in the way that you find easiest using a number line? The children find the total cost of the items shown was 86 points.

How much did the shoes 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? So we knew the whole was 86 and we knew two of the parts.

The T-shirt costs 35 points and the bag costs 30 points, but we don't know the cost of the shoes.

How did you do your subtractions, I wonder? So you might have said 86 subtract 35 and then subtract 30, but you could have subtracted the 30 first.

So let's look 86 subtract 30 is equal to 56, subtract the 5 is equal to 51, subtract another 30 is equal to 21.

So 86 subtract 35 subtract 30 is equal to 21, so the shoes cost 21 points.

But I wonder if you subtracted in a different order.

Mind you looking at that number line, that sort of is a different order as well.

The 30 that we subtracted first could have been the cost of the bag or it could have been the 30 part of the cost of the T-shirt, couldn't it? Izzy notices that they subtracted 2 tens and then 6 tens when they were doing this calculation: 100 subtract 63 subtract 20.

"I wonder if we could have subtracted 8 tens altogether," she says.

"Let's try my idea.

Subtracting 20 and then subtracting 60 is the same as subtracting 80." It is, Izzy, well done.

So we've replaced our arrows for 60 and 20 with one big arrow for subtracting 80, and 100 subtract 80 is equal to 20.

She says, "I reached the same answer." We still have the 3 to subtract as well, didn't we? Time to check your understanding.

Which number line subtracts the same amount as the one shown? So we've got 74 subtract 20 subtract 30 and subtract 3.

So which one shows the same, A, B, or C? Pause the video, have a think, and when you're ready for some feedback, press play.

Which one did you think? So we were subtracting 30 and then 20.

So using Izzy's thinking she would say that we could replace that by subtracting 50 all in one go.

So C shows the same calculation as our number line at the top: 74 subtract 50 subtract 3 is the same as saying 74 subtract 20 subtract 30 subtract 3.

Well done if you spotted that and were able to explain why.

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

So you're going to write an equation and draw a bar model to represent each problem and then solve it by drawing a number line.

So in A, Izzy buys a t-shirt, then she buys some glasses, and then she buys a hat.

How many points has she spent all together? In B, Andeep has 99 points.

He buys a pair of glasses and a T-shirt.

How many points does he have left? In C, Izzy wants to buy these items for her avatar.

What is the total cost of the items shown below? And in D, Andeep has 99 points.

He buys a hat and a pair of headphones and a watch.

How many points does the watch cost? Pause the video, have a go at A, B, C, and D, and when you're ready for the answers and some feedback, press play.

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

First, Izzy buys a T-shirt, that's 30 points, then some glasses for 32 points, and then a hat for 17 points.

How many points has she spent altogether? So what sort of calculation is this? Ah, that's right, this time we were adding, we knew the value of our three parts and we had to add them all together to find the value of the whole, which was 79.

And remember, you can add the parts in the order that you find easiest.

So you might have added the 30 and the 32 and then added on 17.

That's what we did.

We started with the 32 added on 30 to get to 62 and then added on 17.

Added on 10 to get to 72 and then another 7 to get to 79.

So Izzy spent 79 points altogether.

In B, Andeep has 99 points.

He buys a pair of glasses and a T-shirt.

How many points does he have left? What sort of calculation are we doing here? That's right, we knew the whole was 99.

We know that one part is 53 points for the sunglasses and another part is 30 points for the T-shirt, and the final part is how many points he has left.

So remember, you can subtract the parts in the order that you find easiest.

So I wonder if you subtracted the 30 first or the 53 first? We started with the 30.

99 subtract 30 is 69.

Now we've got to subtract the 53.

69 subtract 50 is 19, 19 subtract 3 gives us 16, so Andeep had 16 points left.

In C, Izzy wants to buy these items for her avatar.

What is the total cost of the items shown? So she's got three parts to combine to create her whole, hasn't she? Again, we can add these in any order.

We've started with 32 points for the glasses and added on 40 points for the blue and yellow hat with stars on.

32 add 40 is equal to 72.

Then we're going to add the other 17 points.

72 add 10 is equal to 82, add another 7 is equal to 89, so the total cost of the items is 89 points.

And finally, in D, Andeep has 99 points.

He buys a hat, a pair of headphones, and a watch, but how many points does the watch cost? So we know that the total cost is 99 points, that's what he spent, we know that the hat is 17, and the headphones are 50 points.

How much does the watch cost? So we've got to subtract 50 and 17 from 99.

I wonder what you subtracted first? We went with the 50 first.

99 subtract 50 is equal to 49.

Now we've got to subtract the 17.

49 subtract 10 is 39, subtract another 7 is 32, so the watch costs 32 points.

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

We've been solving problems involving addition and subtraction.

When solving problems, we must decide whether we need to add or subtract in order to solve it, and drawing a bar model can help us to make sense of that and decide what calculation we need to do.

We can look to see if the ones digits cross the tens boundary to find out if we must use the bridge 10 strategy, and that's for addition or subtraction.

And we can draw or imagine a number line to help us solve problems efficiently.

Drawing the number line helps us to explain to somebody else how we've worked things out as well, doesn't it, and maybe help us to spot if we've made a mistake.

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.